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author Adam Chlipala <adam@chlipala.net>
date Sun, 20 Dec 2015 14:39:50 -0500
parents 9083b44bad0a
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adamc@524 1 \documentclass{article}
adamc@554 2 \usepackage{fullpage,amsmath,amssymb,proof,url}
rmbruijn@1568 3 \usepackage[T1]{fontenc}
vshabanoff@1765 4 \usepackage{ae,aecompl}
adamc@524 5 \newcommand{\cd}[1]{\texttt{#1}}
adamc@524 6 \newcommand{\mt}[1]{\mathsf{#1}}
adamc@524 7
adamc@524 8 \newcommand{\rc}{+ \hspace{-.075in} + \;}
adam@2107 9 \newcommand{\rcut}{\; \texttt{-{}-} \;}
adam@2107 10 \newcommand{\rcutM}{\; \texttt{-{}-{}-} \;}
adamc@524 11
julian@2134 12 \usepackage{hyperref}
julian@2134 13
adamc@524 14 \begin{document}
adamc@524 15
adamc@524 16 \title{The Ur/Web Manual}
adamc@524 17 \author{Adam Chlipala}
adamc@524 18
adamc@524 19 \maketitle
adamc@524 20
adamc@540 21 \tableofcontents
adamc@540 22
adamc@554 23
adamc@554 24 \section{Introduction}
adamc@554 25
adam@1797 26 \emph{Ur} is a programming language designed to introduce richer type system features into functional programming in the tradition of ML and Haskell. Ur is functional, pure, statically typed, and strict. Ur supports a powerful kind of \emph{metaprogramming} based on \emph{type-level computation with type-level records}.
adamc@554 27
adamc@554 28 \emph{Ur/Web} is Ur plus a special standard library and associated rules for parsing and optimization. Ur/Web supports construction of dynamic web applications backed by SQL databases. The signature of the standard library is such that well-typed Ur/Web programs ``don't go wrong'' in a very broad sense. Not only do they not crash during particular page generations, but they also may not:
adamc@554 29
adamc@554 30 \begin{itemize}
adamc@554 31 \item Suffer from any kinds of code-injection attacks
adamc@554 32 \item Return invalid HTML
adamc@554 33 \item Contain dead intra-application links
adamc@554 34 \item Have mismatches between HTML forms and the fields expected by their handlers
adamc@652 35 \item Include client-side code that makes incorrect assumptions about the ``AJAX''-style services that the remote web server provides
adamc@554 36 \item Attempt invalid SQL queries
adamc@652 37 \item Use improper marshaling or unmarshaling in communication with SQL databases or between browsers and web servers
adamc@554 38 \end{itemize}
adamc@554 39
adamc@554 40 This type safety is just the foundation of the Ur/Web methodology. It is also possible to use metaprogramming to build significant application pieces by analysis of type structure. For instance, the demo includes an ML-style functor for building an admin interface for an arbitrary SQL table. The type system guarantees that the admin interface sub-application that comes out will always be free of the above-listed bugs, no matter which well-typed table description is given as input.
adamc@554 41
adamc@652 42 The Ur/Web compiler also produces very efficient object code that does not use garbage collection. These compiled programs will often be even more efficient than what most programmers would bother to write in C. The compiler also generates JavaScript versions of client-side code, with no need to write those parts of applications in a different language.
adamc@554 43
adamc@554 44 \medskip
adamc@554 45
adamc@554 46 The official web site for Ur is:
adamc@554 47 \begin{center}
adamc@554 48 \url{http://www.impredicative.com/ur/}
adamc@554 49 \end{center}
adamc@554 50
adamc@555 51
adamc@555 52 \section{Installation}
adamc@555 53
adamc@555 54 If you are lucky, then the following standard command sequence will suffice for installation, in a directory to which you have unpacked the latest distribution tarball.
adamc@555 55
adamc@555 56 \begin{verbatim}
adamc@555 57 ./configure
adamc@555 58 make
adamc@555 59 sudo make install
adamc@555 60 \end{verbatim}
adamc@555 61
adam@1523 62 Some other packages must be installed for the above to work. At a minimum, you need a standard UNIX shell, with standard UNIX tools like sed and GCC (or an alternate C compiler) in your execution path; MLton, the whole-program optimizing compiler for Standard ML; and the development files for the OpenSSL C library. As of this writing, in the ``testing'' version of Debian Linux, this command will install the more uncommon of these dependencies:
adamc@896 63 \begin{verbatim}
adam@1368 64 apt-get install mlton libssl-dev
adamc@896 65 \end{verbatim}
adamc@555 66
adam@2016 67 Note that, like the Ur/Web compiler, MLton is a whole-program optimizing compiler, so it frequently requires much more memory than old-fashioned compilers do. Expect building Ur/Web with MLton to require not much less than a gigabyte of RAM. If a \texttt{mlton} invocation ends suspiciously, the most likely explanation is that it has exhausted available memory.
adam@2016 68
adamc@896 69 To build programs that access SQL databases, you also need one of these client libraries for supported backends.
adamc@555 70 \begin{verbatim}
adam@1960 71 apt-get install libpq-dev libmysqlclient-dev libsqlite3-dev
adamc@555 72 \end{verbatim}
adamc@555 73
adamc@555 74 It is also possible to access the modules of the Ur/Web compiler interactively, within Standard ML of New Jersey. To install the prerequisites in Debian testing:
adamc@555 75 \begin{verbatim}
adamc@555 76 apt-get install smlnj libsmlnj-smlnj ml-yacc ml-lpt
adamc@555 77 \end{verbatim}
adamc@555 78
adam@2016 79 To begin an interactive session with the Ur compiler modules, run \texttt{make smlnj}, and then, from within an \texttt{sml} session, run \texttt{CM.make "src/urweb.cm";}. The \texttt{Compiler} module is the main entry point, and you can find its signature in \texttt{src/compiler.sig}.
adamc@555 80
adamc@896 81 To run an SQL-backed application with a backend besides SQLite, you will probably want to install one of these servers.
adamc@555 82
adamc@555 83 \begin{verbatim}
adam@1960 84 apt-get install postgresql mysql-server
adamc@555 85 \end{verbatim}
adamc@555 86
adamc@555 87 To use the Emacs mode, you must have a modern Emacs installed. We assume that you already know how to do this, if you're in the business of looking for an Emacs mode. The demo generation facility of the compiler will also call out to Emacs to syntax-highlight code, and that process depends on the \texttt{htmlize} module, which can be installed in Debian testing via:
adamc@555 88
adamc@555 89 \begin{verbatim}
adamc@555 90 apt-get install emacs-goodies-el
adamc@555 91 \end{verbatim}
adamc@555 92
adam@1441 93 If you don't want to install the Emacs mode, run \texttt{./configure} with the argument \texttt{--without-emacs}.
adam@1441 94
adam@1523 95 Even with the right packages installed, configuration and building might fail to work. After you run \texttt{./configure}, you will see the values of some named environment variables printed. You may need to adjust these values to get proper installation for your system. To change a value, store your preferred alternative in the corresponding UNIX environment variable, before running \texttt{./configure}. For instance, here is how to change the list of extra arguments that the Ur/Web compiler will pass to the C compiler and linker on every invocation. Some older GCC versions need this setting to mask a bug in function inlining.
adamc@555 96
adamc@555 97 \begin{verbatim}
adam@1523 98 CCARGS=-fno-inline ./configure
adamc@555 99 \end{verbatim}
adamc@555 100
adam@1523 101 Since the author is still getting a handle on the GNU Autotools that provide the build system, you may need to do some further work to get started, especially in environments with significant differences from Linux (where most testing is done). The variables \texttt{PGHEADER}, \texttt{MSHEADER}, and \texttt{SQHEADER} may be used to set the proper C header files to include for the development libraries of PostgreSQL, MySQL, and SQLite, respectively. To get libpq to link, one OS X user reported setting \texttt{CCARGS="-I/opt/local/include -L/opt/local/lib/postgresql84"}, after creating a symbolic link with \texttt{ln -s /opt/local/include/postgresql84 /opt/local/include/postgresql}.
adamc@555 102
adamc@555 103 The Emacs mode can be set to autoload by adding the following to your \texttt{.emacs} file.
adamc@555 104
adamc@555 105 \begin{verbatim}
adamc@555 106 (add-to-list 'load-path "/usr/local/share/emacs/site-lisp/urweb-mode")
adamc@555 107 (load "urweb-mode-startup")
adamc@555 108 \end{verbatim}
adamc@555 109
adamc@555 110 Change the path in the first line if you chose a different Emacs installation path during configuration.
adamc@555 111
adamc@555 112
adamc@556 113 \section{Command-Line Compiler}
adamc@556 114
adam@1604 115 \subsection{\label{cl}Project Files}
adamc@556 116
adamc@556 117 The basic inputs to the \texttt{urweb} compiler are project files, which have the extension \texttt{.urp}. Here is a sample \texttt{.urp} file.
adamc@556 118
adamc@556 119 \begin{verbatim}
adamc@556 120 database dbname=test
adamc@556 121 sql crud1.sql
adamc@556 122
adamc@556 123 crud
adamc@556 124 crud1
adamc@556 125 \end{verbatim}
adamc@556 126
adamc@556 127 The \texttt{database} line gives the database information string to pass to libpq. In this case, the string only says to connect to a local database named \texttt{test}.
adamc@556 128
adamc@556 129 The \texttt{sql} line asks for an SQL source file to be generated, giving the commands to run to create the tables and sequences that this application expects to find. After building this \texttt{.urp} file, the following commands could be used to initialize the database, assuming that the current UNIX user exists as a Postgres user with database creation privileges:
adamc@556 130
adamc@556 131 \begin{verbatim}
adamc@556 132 createdb test
adamc@556 133 psql -f crud1.sql test
adamc@556 134 \end{verbatim}
adamc@556 135
adam@1331 136 A blank line separates the named directives from a list of modules to include in the project. Any line may contain a shell-script-style comment, where any suffix of a line starting at a hash character \texttt{\#} is ignored.
adamc@556 137
adamc@556 138 For each entry \texttt{M} in the module list, the file \texttt{M.urs} is included in the project if it exists, and the file \texttt{M.ur} must exist and is always included.
adamc@556 139
adamc@783 140 Here is the complete list of directive forms. ``FFI'' stands for ``foreign function interface,'' Ur's facility for interaction between Ur programs and C and JavaScript libraries.
adamc@783 141 \begin{itemize}
adam@1799 142 \item \texttt{[allow|deny] [url|mime|requestHeader|responseHeader|env] PATTERN} registers a rule governing which URLs, MIME types, HTTP request headers, HTTP response headers, or environment variable names are allowed to appear explicitly in this application. The first such rule to match a name determines the verdict. If \texttt{PATTERN} ends in \texttt{*}, it is interpreted as a prefix rule. Otherwise, a string must match it exactly.
adam@1400 143 \item \texttt{alwaysInline PATH} requests that every call to the referenced function be inlined. Section \ref{structure} explains how functions are assigned path strings.
adam@1462 144 \item \texttt{benignEffectful Module.ident} registers an FFI function or transaction as having side effects. The optimizer avoids removing, moving, or duplicating calls to such functions. Every effectful FFI function must be registered, or the optimizer may make invalid transformations. This version of the \texttt{effectful} directive registers that this function only has side effects that remain local to a single page generation.
adamc@783 145 \item \texttt{clientOnly Module.ident} registers an FFI function or transaction that may only be run in client browsers.
adam@1881 146 \item \texttt{clientToServer Module.ident} adds FFI type \texttt{Module.ident} to the list of types that are OK to marshal from clients to servers. Values like XML trees and SQL queries are hard to marshal without introducing expensive validity checks, so it's easier to ensure that the server never trusts clients to send such values. The file \texttt{include/urweb/urweb\_cpp.h} shows examples of the C support functions that are required of any type that may be marshalled. These include \texttt{attrify}, \texttt{urlify}, and \texttt{unurlify} functions.
adam@1816 147 \item \texttt{coreInline TREESIZE} sets how many nodes the AST of a function definition may have before the optimizer stops trying hard to inline calls to that function. (This is one of two options for one of two intermediate languages within the compiler.)
adamc@783 148 \item \texttt{database DBSTRING} sets the string to pass to libpq to open a database connection.
adamc@783 149 \item \texttt{debug} saves some intermediate C files, which is mostly useful to help in debugging the compiler itself.
adam@1878 150 \item \texttt{effectful Module.ident} registers an FFI function or transaction as having side effects. The optimizer avoids removing, moving, or duplicating calls to such functions. This is the default behavior for \texttt{transaction}-based types.
adam@2046 151 \item \texttt{exe FILENAME} sets the filename to which to write the output executable. The default for file \texttt{P.urp} is \texttt{P.exe}.
adam@2046 152 \item \texttt{file URI FILENAME} asks for the application executable to respond to requests for \texttt{URI} by serving a snapshot of the contents of \texttt{FILENAME} as of compile time. That is, the file contents are baked into the executable. System file \texttt{/etc/mime.types} is consulted (again, at compile time) to figure out the right MIME type to suggest in the HTTP response.
adam@1881 153 \item \texttt{ffi FILENAME} reads the file \texttt{FILENAME.urs} to determine the interface to a new FFI module. The name of the module is calculated from \texttt{FILENAME} in the same way as for normal source files. See the files \texttt{include/urweb/urweb\_cpp.h} and \texttt{src/c/urweb.c} for examples of C headers and implementations for FFI modules. In general, every type or value \texttt{Module.ident} becomes \texttt{uw\_Module\_ident} in C.
adam@1956 154 \item \texttt{html5} activates work-in-progress support for generating HTML5 instead of XHTML. For now, this option only affects the first few tokens on any page, which are always the same.
adamc@1099 155 \item \texttt{include FILENAME} adds \texttt{FILENAME} to the list of files to be \texttt{\#include}d in C sources. This is most useful for interfacing with new FFI modules.
adam@2198 156 \item \texttt{jsFile FILENAME} asks to serve the contents of a file as JavaScript. All such content is concatenated into a single file, included via a \texttt{<script>} tag on every page that needs client-side scripting.
adamc@783 157 \item \texttt{jsFunc Module.ident=name} gives the JavaScript name of an FFI value.
adamc@1089 158 \item \texttt{library FILENAME} parses \texttt{FILENAME.urp} and merges its contents with the rest of the current file's contents. If \texttt{FILENAME.urp} doesn't exist, the compiler also tries \texttt{FILENAME/lib.urp}.
adam@1309 159 \item \texttt{limit class num} sets a resource usage limit for generated applications. The limit \texttt{class} will be set to the non-negative integer \texttt{num}. The classes are:
adam@1309 160 \begin{itemize}
adam@1309 161 \item \texttt{cleanup}: maximum number of cleanup operations (e.g., entries recording the need to deallocate certain temporary objects) that may be active at once per request
adam@1850 162 \item \texttt{clients}: maximum number of simultaneous connections to one application by web clients waiting for new asynchronous messages sent with \texttt{Basis.send}
adam@1850 163 \item \texttt{database}: maximum size of a database file (currently only used by SQLite, which interprets the parameter as a number of pages, where page size is itself a quantity configurable in SQLite)
adam@1309 164 \item \texttt{deltas}: maximum number of messages sendable in a single request handler with \texttt{Basis.send}
adam@1309 165 \item \texttt{globals}: maximum number of global variables that FFI libraries may set in a single request context
adam@1309 166 \item \texttt{headers}: maximum size (in bytes) of per-request buffer used to hold HTTP headers for generated pages
adam@1797 167 \item \texttt{heap}: maximum size (in bytes) of per-request heap for dynamically allocated data
adam@1309 168 \item \texttt{inputs}: maximum number of top-level form fields per request
adam@1309 169 \item \texttt{messages}: maximum size (in bytes) of per-request buffer used to hold a single outgoing message sent with \texttt{Basis.send}
adam@1309 170 \item \texttt{page}: maximum size (in bytes) of per-request buffer used to hold HTML content of generated pages
adam@1309 171 \item \texttt{script}: maximum size (in bytes) of per-request buffer used to hold JavaScript content of generated pages
adam@1309 172 \item \texttt{subinputs}: maximum number of form fields per request, excluding top-level fields
adam@1309 173 \item \texttt{time}: maximum running time of a single page request, in units of approximately 0.1 seconds
adam@1309 174 \item \texttt{transactionals}: maximum number of custom transactional actions (e.g., sending an e-mail) that may be run in a single page generation
adam@1309 175 \end{itemize}
adam@1523 176 \item \texttt{link FILENAME} adds \texttt{FILENAME} to the list of files to be passed to the linker at the end of compilation. This is most useful for importing extra libraries needed by new FFI modules.
adam@1725 177 \item \texttt{linker CMD} sets \texttt{CMD} as the command line prefix to use for linking C object files. The command line will be completed with a space-separated list of \texttt{.o} and \texttt{.a} files, \texttt{-L} and \texttt{-l} flags, and finally with a \texttt{-o} flag to set the location where the executable should be written.
adam@1332 178 \item \texttt{minHeap NUMBYTES} sets the initial size for thread-local heaps used in handling requests. These heaps grow automatically as needed (up to any maximum set with \texttt{limit}), but each regrow requires restarting the request handling process.
adam@1816 179 \item \texttt{monoInline TREESIZE} sets how many nodes the AST of a function definition may have before the optimizer stops trying hard to inline calls to that function. (This is one of two options for one of two intermediate languages within the compiler.)
adam@1966 180 \item \texttt{neverInline PATH} requests that no call to the referenced function be inlined. Section \ref{structure} explains how functions are assigned path strings.
adam@1953 181 \item \texttt{noMangleSql} avoids adding a \texttt{uw\_} prefix in front of each identifier in SQL. With this experimental feature, the burden is on the programmer to avoid naming tables or columns after SQL keywords!
adam@1478 182 \item \texttt{noXsrfProtection URIPREFIX} turns off automatic cross-site request forgery protection for the page handler identified by the given URI prefix. This will avoid checking cryptographic signatures on cookies, which is generally a reasonable idea for some pages, such as login pages that are going to discard all old cookie values, anyway.
adam@1297 183 \item \texttt{onError Module.var} changes the handling of fatal application errors. Instead of displaying a default, ugly error 500 page, the error page will be generated by calling function \texttt{Module.var} on a piece of XML representing the error message. The error handler should have type $\mt{xbody} \to \mt{transaction} \; \mt{page}$. Note that the error handler \emph{cannot} be in the application's main module, since that would register it as explicitly callable via URLs.
adamc@852 184 \item \texttt{path NAME=VALUE} creates a mapping from \texttt{NAME} to \texttt{VALUE}. This mapping may be used at the beginnings of filesystem paths given to various other configuration directives. A path like \texttt{\$NAME/rest} is expanded to \texttt{VALUE/rest}. There is an initial mapping from the empty name (for paths like \texttt{\$/list}) to the directory where the Ur/Web standard library is installed. If you accept the default \texttt{configure} options, this directory is \texttt{/usr/local/lib/urweb/ur}.
adamc@783 185 \item \texttt{prefix PREFIX} sets the prefix included before every URI within the generated application. The default is \texttt{/}.
adamc@783 186 \item \texttt{profile} generates an executable that may be used with gprof.
adam@1752 187 \item \texttt{rewrite KIND FROM TO} gives a rule for rewriting canonical module paths. For instance, the canonical path of a page may be \texttt{Mod1.Mod2.mypage}, while you would rather the page were accessed via a URL containing only \texttt{page}. The directive \texttt{rewrite url Mod1/Mod2/mypage page} would accomplish that. The possible values of \texttt{KIND} determine which kinds of objects are affected. The kind \texttt{all} matches any object, and \texttt{url} matches page URLs. The kinds \texttt{table}, \texttt{sequence}, and \texttt{view} match those sorts of SQL entities, and \texttt{relation} matches any of those three. \texttt{cookie} matches HTTP cookies, and \texttt{style} matches CSS class names. If \texttt{FROM} ends in \texttt{/*}, it is interpreted as a prefix matching rule, and rewriting occurs by replacing only the appropriate prefix of a path with \texttt{TO}. The \texttt{TO} field may be left empty to express the idea of deleting a prefix. For instance, \texttt{rewrite url Main/*} will strip all \texttt{Main/} prefixes from URLs. While the actual external names of relations and styles have parts separated by underscores instead of slashes, all rewrite rules must be written in terms of slashes. An optional suffix of \cd{[-]} for a \cd{rewrite} directive asks to additionally replace all \cd{\_} characters with \cd{-} characters, which can be handy for, e.g., interfacing with an off-the-shelf CSS library that prefers hyphens over underscores.
adamc@1183 188 \item \texttt{safeGet URI} asks to allow the page handler assigned this canonical URI prefix to cause persistent side effects, even if accessed via an HTTP \cd{GET} request.
adamc@783 189 \item \texttt{script URL} adds \texttt{URL} to the list of extra JavaScript files to be included at the beginning of any page that uses JavaScript. This is most useful for importing JavaScript versions of functions found in new FFI modules.
adamc@783 190 \item \texttt{serverOnly Module.ident} registers an FFI function or transaction that may only be run on the server.
adamc@1164 191 \item \texttt{sigfile PATH} sets a path where your application should look for a key to use in cryptographic signing. This is used to prevent cross-site request forgery attacks for any form handler that both reads a cookie and creates side effects. If the referenced file doesn't exist, an application will create it and read its saved data on future invocations. You can also initialize the file manually with any contents at least 16 bytes long; the first 16 bytes will be treated as the key.
adamc@783 192 \item \texttt{sql FILENAME} sets where to write an SQL file with the commands to create the expected database schema. The default is not to create such a file.
adam@1629 193 \item \texttt{timeFormat FMT} accepts a time format string, as processed by the POSIX C function \texttt{strftime()}. This controls the default rendering of $\mt{time}$ values, via the $\mt{show}$ instance for $\mt{time}$.
adamc@783 194 \item \texttt{timeout N} sets to \texttt{N} seconds the amount of time that the generated server will wait after the last contact from a client before determining that that client has exited the application. Clients that remain active will take the timeout setting into account in determining how often to ping the server, so it only makes sense to set a high timeout to cope with browser and network delays and failures. Higher timeouts can lead to more unnecessary client information taking up memory on the server. The timeout goes unused by any page that doesn't involve the \texttt{recv} function, since the server only needs to store per-client information for clients that receive asynchronous messages.
adamc@783 195 \end{itemize}
adamc@701 196
adamc@701 197
adamc@557 198 \subsection{Building an Application}
adamc@557 199
adamc@557 200 To compile project \texttt{P.urp}, simply run
adamc@557 201 \begin{verbatim}
adamc@557 202 urweb P
adamc@557 203 \end{verbatim}
adamc@1198 204 The output executable is a standalone web server. Run it with the command-line argument \texttt{-h} to see which options it takes. If the project file lists a database, the web server will attempt to connect to that database on startup. See Section \ref{structure} for an explanation of the URI mapping convention, which determines how each page of your application may be accessed via URLs.
adamc@557 205
adamc@557 206 To time how long the different compiler phases run, without generating an executable, run
adamc@557 207 \begin{verbatim}
adamc@557 208 urweb -timing P
adamc@557 209 \end{verbatim}
adamc@557 210
adamc@1086 211 To stop the compilation process after type-checking, run
adamc@1086 212 \begin{verbatim}
adamc@1086 213 urweb -tc P
adamc@1086 214 \end{verbatim}
adam@1530 215 It is often worthwhile to run \cd{urweb} in this mode, because later phases of compilation can take significantly longer than type-checking alone, and the type checker catches many errors that would traditionally be found through debugging a running application.
adamc@1086 216
adam@1745 217 A related option is \cd{-dumpTypes}, which, as long as parsing succeeds, outputs to stdout a summary of the kinds of all identifiers declared with \cd{con} and the types of all identifiers declared with \cd{val} or \cd{val rec}. This information is dumped even if there are errors during type inference. Compiler error messages go to stderr, not stdout, so it is easy to distinguish the two kinds of output programmatically. A refined version of this option is \cd{-dumpTypesOnError}, which only has an effect when there are compilation errors.
adam@1531 218
adam@1723 219 It may be useful to combine another option \cd{-unifyMore} with \cd{-dumpTypes}. Ur/Web type inference proceeds in a series of stages, where the first is standard Hindley-Milner type inference as in ML, and the later phases add more complex aspects. By default, an error detected in one phase cuts off the execution of later phases. However, the later phases might still determine more values of unification variables. These value choices might be ``misguided,'' since earlier phases have not come up with reasonable types at a coarser detail level; but the unification decisions may still be useful for debugging and program understanding. So, if a run with \cd{-dumpTypes} leaves unification variables undetermined in positions where you would like to see best-effort guesses instead, consider \cd{-unifyMore}. Note that \cd{-unifyMore} has no effect when type inference succeeds fully, but it may lead to many more error messages when inference fails.
adam@1723 220
adamc@1170 221 To output information relevant to CSS stylesheets (and not finish regular compilation), run
adamc@1170 222 \begin{verbatim}
adamc@1170 223 urweb -css P
adamc@1170 224 \end{verbatim}
adamc@1170 225 The first output line is a list of categories of CSS properties that would be worth setting on the document body. The remaining lines are space-separated pairs of CSS class names and categories of properties that would be worth setting for that class. The category codes are divided into two varieties. Codes that reveal properties of a tag or its (recursive) children are \cd{B} for block-level elements, \cd{C} for table captions, \cd{D} for table cells, \cd{L} for lists, and \cd{T} for tables. Codes that reveal properties of the precise tag that uses a class are \cd{b} for block-level elements, \cd{t} for tables, \cd{d} for table cells, \cd{-} for table rows, \cd{H} for the possibility to set a height, \cd{N} for non-replaced inline-level elements, \cd{R} for replaced inline elements, and \cd{W} for the possibility to set a width.
adamc@1170 226
adam@1733 227 Ur/Web type inference can take a significant amount of time, so it can be helpful to cache type-inferred versions of source files. This mode can be activated by running
adam@1733 228 \begin{verbatim}
adam@1733 229 urweb daemon start
adam@1733 230 \end{verbatim}
adam@1733 231 Further \cd{urweb} invocations in the same working directory will send requests to a background daemon process that reuses type inference results whenever possible, tracking source file dependencies and modification times. To stop the background daemon, run
adam@1733 232 \begin{verbatim}
adam@1733 233 urweb daemon stop
adam@1733 234 \end{verbatim}
adam@1733 235 Communication happens via a UNIX domain socket in file \cd{.urweb\_daemon} in the working directory.
adam@1733 236
adam@1733 237 \medskip
adam@1733 238
adamc@896 239 Some other command-line parameters are accepted:
adamc@896 240 \begin{itemize}
ezyang@1739 241 \item \texttt{-boot}: Run Ur/Web from a build tree (and not from a system install). This is useful if you're testing the compiler and don't want to install it. It forces generation of statically linked executables.
ezyang@1739 242
adam@1875 243 \item \texttt{-ccompiler <PROGRAM>}: Select an alternative C compiler to call with command lines in compiling Ur/Web applications. (It's possible to set the default compiler as part of the \texttt{configure} process, but it may sometimes be useful to override the default.)
adam@1875 244
adamc@896 245 \item \texttt{-db <DBSTRING>}: Set database connection information, using the format expected by Postgres's \texttt{PQconnectdb()}, which is \texttt{name1=value1 ... nameN=valueN}. The same format is also parsed and used to discover connection parameters for MySQL and SQLite. The only significant settings for MySQL are \texttt{host}, \texttt{hostaddr}, \texttt{port}, \texttt{dbname}, \texttt{user}, and \texttt{password}. The only significant setting for SQLite is \texttt{dbname}, which is interpreted as the filesystem path to the database. Additionally, when using SQLite, a database string may be just a file path.
adamc@896 246
adamc@896 247 \item \texttt{-dbms [postgres|mysql|sqlite]}: Sets the database backend to use.
adamc@896 248 \begin{itemize}
adamc@896 249 \item \texttt{postgres}: This is PostgreSQL, the default. Among the supported engines, Postgres best matches the design philosophy behind Ur, with a focus on consistent views of data, even in the face of much concurrency. Different database engines have different quirks of SQL syntax. Ur/Web tends to use Postgres idioms where there are choices to be made, though the compiler translates SQL as needed to support other backends.
adamc@896 250
adamc@896 251 A command sequence like this can initialize a Postgres database, using a file \texttt{app.sql} generated by the compiler:
adamc@896 252 \begin{verbatim}
adamc@896 253 createdb app
adamc@896 254 psql -f app.sql app
adamc@896 255 \end{verbatim}
adamc@896 256
adamc@896 257 \item \texttt{mysql}: This is MySQL, another popular relational database engine that uses persistent server processes. Ur/Web needs transactions to function properly. Many installations of MySQL use non-transactional storage engines by default. Ur/Web generates table definitions that try to use MySQL's InnoDB engine, which supports transactions. You can edit the first line of a generated \texttt{.sql} file to change this behavior, but it really is true that Ur/Web applications will exhibit bizarre behavior if you choose an engine that ignores transaction commands.
adamc@896 258
adamc@896 259 A command sequence like this can initialize a MySQL database:
adamc@896 260 \begin{verbatim}
adamc@896 261 echo "CREATE DATABASE app" | mysql
adamc@896 262 mysql -D app <app.sql
adamc@896 263 \end{verbatim}
adamc@896 264
adamc@896 265 \item \texttt{sqlite}: This is SQLite, a simple filesystem-based transactional database engine. With this backend, Ur/Web applications can run without any additional server processes. The other engines are generally preferred for large-workload performance and full admin feature sets, while SQLite is popular for its low resource footprint and ease of set-up.
adamc@896 266
adamc@896 267 A command like this can initialize an SQLite database:
adamc@896 268 \begin{verbatim}
adamc@896 269 sqlite3 path/to/database/file <app.sql
adamc@896 270 \end{verbatim}
adamc@896 271 \end{itemize}
adamc@896 272
adam@1693 273 \item \texttt{-dumpSource}: When compilation fails, output to stderr the complete source code of the last intermediate program before the compilation phase that signaled the error. (Warning: these outputs can be very long and aren't especially optimized for readability!)
adam@1693 274
adam@1995 275 \item \texttt{-explainEmbed}: Trigger more verbose error messages about inability to embed server-side values in client-side code.
adam@1995 276
adam@1309 277 \item \texttt{-limit class num}: Equivalent to the \texttt{limit} directive from \texttt{.urp} files
adam@1309 278
adam@1850 279 \item \texttt{-moduleOf FILENAME}: Prints the Ur/Web module name corresponding to source file \texttt{FILENAME}, exiting immediately afterward.
adam@1850 280
adamc@896 281 \item \texttt{-output FILENAME}: Set where the application executable is written.
adamc@896 282
adamc@1127 283 \item \texttt{-path NAME VALUE}: Set the value of path variable \texttt{\$NAME} to \texttt{VALUE}, for use in \texttt{.urp} files.
adamc@1127 284
adam@1335 285 \item \texttt{-prefix PREFIX}: Equivalent to the \texttt{prefix} directive from \texttt{.urp} files
adam@1335 286
adam@1875 287 \item \texttt{-print-ccompiler}: Print the C compiler being used.
adam@1875 288
adam@1923 289 \item \texttt{-print-cinclude}: Print the name of the directory where C/C++ header files are installed.
adam@1923 290
adam@1753 291 \item \texttt{-protocol [http|cgi|fastcgi|static]}: Set the protocol that the generated application speaks.
adamc@896 292 \begin{itemize}
adamc@896 293 \item \texttt{http}: This is the default. It is for building standalone web servers that can be accessed by web browsers directly.
adamc@896 294
adamc@896 295 \item \texttt{cgi}: This is the classic protocol that web servers use to generate dynamic content by spawning new processes. While Ur/Web programs may in general use message-passing with the \texttt{send} and \texttt{recv} functions, that functionality is not yet supported in CGI, since CGI needs a fresh process for each request, and message-passing needs to use persistent sockets to deliver messages.
adamc@896 296
adamc@896 297 Since Ur/Web treats paths in an unusual way, a configuration line like this one can be used to configure an application that was built with URL prefix \texttt{/Hello}:
adamc@896 298 \begin{verbatim}
adamc@896 299 ScriptAlias /Hello /path/to/hello.exe
adamc@896 300 \end{verbatim}
adamc@896 301
adamc@1163 302 A different method can be used for, e.g., a shared host, where you can only configure Apache via \texttt{.htaccess} files. Drop the generated executable into your web space and mark it as CGI somehow. For instance, if the script ends in \texttt{.exe}, you might put this in \texttt{.htaccess} in the directory containing the script:
adamc@1163 303 \begin{verbatim}
adamc@1163 304 Options +ExecCGI
adamc@1163 305 AddHandler cgi-script .exe
adamc@1163 306 \end{verbatim}
adamc@1163 307
adamc@1163 308 Additionally, make sure that Ur/Web knows the proper URI prefix for your script. For instance, if the script is accessed via \texttt{http://somewhere/dir/script.exe}, then include this line in your \texttt{.urp} file:
adamc@1163 309 \begin{verbatim}
adamc@1163 310 prefix /dir/script.exe/
adamc@1163 311 \end{verbatim}
adamc@1163 312
adamc@1163 313 To access the \texttt{foo} function in the \texttt{Bar} module, you would then hit \texttt{http://somewhere/dir/script.exe/Bar/foo}.
adamc@1163 314
adamc@1164 315 If your application contains form handlers that read cookies before causing side effects, then you will need to use the \texttt{sigfile} \texttt{.urp} directive, too.
adamc@1164 316
adamc@896 317 \item \texttt{fastcgi}: This is a newer protocol inspired by CGI, wherein web servers can start and reuse persistent external processes to generate dynamic content. Ur/Web doesn't implement the whole protocol, but Ur/Web's support has been tested to work with the \texttt{mod\_fastcgi}s of Apache and lighttpd.
adamc@896 318
adamc@896 319 To configure a FastCGI program with Apache, one could combine the above \texttt{ScriptAlias} line with a line like this:
adamc@896 320 \begin{verbatim}
adamc@896 321 FastCgiServer /path/to/hello.exe -idle-timeout 99999
adamc@896 322 \end{verbatim}
adamc@896 323 The idle timeout is only important for applications that use message-passing. Client connections may go long periods without receiving messages, and Apache tries to be helpful and garbage collect them in such cases. To prevent that behavior, we specify how long a connection must be idle to be collected.
adamc@896 324
adam@1753 325 Also see the discussion of the \cd{prefix} directive for CGI above; similar configuration is likely to be necessary for FastCGI. An Ur/Web application won't generally run correctly if it doesn't have a unique URI prefix assigned to it and configured with \cd{prefix}.
adam@1753 326
adamc@896 327 Here is some lighttpd configuration for the same application.
adamc@896 328 \begin{verbatim}
adamc@896 329 fastcgi.server = (
adamc@896 330 "/Hello/" =>
adamc@896 331 (( "bin-path" => "/path/to/hello.exe",
adamc@896 332 "socket" => "/tmp/hello",
adamc@896 333 "check-local" => "disable",
adamc@896 334 "docroot" => "/",
adamc@896 335 "max-procs" => "1"
adamc@896 336 ))
adamc@896 337 )
adamc@896 338 \end{verbatim}
adamc@896 339 The least obvious requirement is setting \texttt{max-procs} to 1, so that lighttpd doesn't try to multiplex requests across multiple external processes. This is required for message-passing applications, where a single database of client connections is maintained within a multi-threaded server process. Multiple processes may, however, be used safely with applications that don't use message-passing.
adamc@896 340
adamc@896 341 A FastCGI process reads the environment variable \texttt{URWEB\_NUM\_THREADS} to determine how many threads to spawn for handling client requests. The default is 1.
adam@1509 342
adam@1509 343 \item \texttt{static}: This protocol may be used to generate static web pages from Ur/Web code. The output executable expects a single command-line argument, giving the URI of a page to generate. For instance, this argument might be \cd{/main}, in which case a static HTTP response for that page will be written to stdout.
adamc@896 344 \end{itemize}
adamc@896 345
adamc@1127 346 \item \texttt{-root Name PATH}: Trigger an alternate module convention for all source files found in directory \texttt{PATH} or any of its subdirectories. Any file \texttt{PATH/foo.ur} defines a module \texttt{Name.Foo} instead of the usual \texttt{Foo}. Any file \texttt{PATH/subdir/foo.ur} defines a module \texttt{Name.Subdir.Foo}, and so on for arbitrary nesting of subdirectories.
adamc@1127 347
adamc@1164 348 \item \texttt{-sigfile PATH}: Same as the \texttt{sigfile} directive in \texttt{.urp} files
adamc@1164 349
adamc@896 350 \item \texttt{-sql FILENAME}: Set where a database set-up SQL script is written.
adamc@1095 351
adamc@1095 352 \item \texttt{-static}: Link the runtime system statically. The default is to link against dynamic libraries.
adam@1961 353
adam@1961 354 \item \texttt{-stop PHASE}: Stop compilation after the named phase, printing the intermediate program to stderr. This flag is mainly useful for debugging the Ur/Web compiler itself.
adamc@896 355 \end{itemize}
adamc@896 356
adam@1297 357 There is an additional convenience method for invoking \texttt{urweb}. If the main argument is \texttt{FOO}, and \texttt{FOO.ur} exists but \texttt{FOO.urp} doesn't, then the invocation is interpreted as if called on a \texttt{.urp} file containing \texttt{FOO} as its only main entry, with an additional \texttt{rewrite all FOO/*} directive.
adamc@556 358
adam@2305 359 There are also two experimental compiler extensions enabled with flags \texttt{-iflow} and \texttt{-sqlcache}. They are intentionally not documented further here, to indicate just how very experimental they are!
adam@2305 360
adam@1509 361 \subsection{Tutorial Formatting}
adam@1509 362
adam@1509 363 The Ur/Web compiler also supports rendering of nice HTML tutorials from Ur source files, when invoked like \cd{urweb -tutorial DIR}. The directory \cd{DIR} is examined for files whose names end in \cd{.ur}. Every such file is translated into a \cd{.html} version.
adam@1509 364
adam@1509 365 These input files follow normal Ur syntax, with a few exceptions:
adam@1509 366 \begin{itemize}
adam@1509 367 \item The first line must be a comment like \cd{(* TITLE *)}, where \cd{TITLE} is a string of your choice that will be used as the title of the output page.
adam@1509 368 \item While most code in the output HTML will be formatted as a monospaced code listing, text in regular Ur comments is formatted as normal English text.
adam@1509 369 \item A comment like \cd{(* * HEADING *)} introduces a section heading, with text \cd{HEADING} of your choice.
adam@1509 370 \item To include both a rendering of an Ur expression and a pretty-printed version of its value, bracket the expression with \cd{(* begin eval *)} and \cd{(* end *)}. The result of expression evaluation is pretty-printed with \cd{show}, so the expression type must belong to that type class.
adam@1509 371 \item To include code that should not be shown in the tutorial (e.g., to add a \cd{show} instance to use with \cd{eval}), bracket the code with \cd{(* begin hide *)} and \cd{(* end *)}.
adam@1509 372 \end{itemize}
adam@1509 373
adam@1509 374 A word of warning: as for demo generation, tutorial generation calls Emacs to syntax-highlight Ur code.
adam@1509 375
adam@1522 376 \subsection{Run-Time Options}
adam@1522 377
adam@1522 378 Compiled applications consult a few environment variables to modify their behavior:
adam@1522 379
adam@1522 380 \begin{itemize}
adam@1522 381 \item \cd{URWEB\_NUM\_THREADS}: alternative to the \cd{-t} command-line argument (currently used only by FastCGI)
adam@1522 382 \item \cd{URWEB\_STACK\_SIZE}: size of per-thread stacks, in bytes
as@1564 383 \item \cd{URWEB\_PQ\_CON}: when using PostgreSQL, overrides the compiled-in connection string
adam@1522 384 \end{itemize}
adam@1522 385
adam@2042 386 \subsection{A Word of Warning on Heuristic Compilation}
adam@2042 387
adam@2042 388 For server-side code, Ur/Web follows an unusual compilation model, where not all type-correct programs can be compiled successfully, especially when using functions as data not known until runtime. See Section \ref{phases} for more detail.
adam@2042 389
adam@1509 390
adamc@529 391 \section{Ur Syntax}
adamc@529 392
adamc@784 393 In this section, we describe the syntax of Ur, deferring to a later section discussion of most of the syntax specific to SQL and XML. The sole exceptions are the declaration forms for relations, cookies, and styles.
adamc@524 394
adamc@524 395 \subsection{Lexical Conventions}
adamc@524 396
adamc@524 397 We give the Ur language definition in \LaTeX $\;$ math mode, since that is prettier than monospaced ASCII. The corresponding ASCII syntax can be read off directly. Here is the key for mapping math symbols to ASCII character sequences.
adamc@524 398
adamc@524 399 \begin{center}
adamc@524 400 \begin{tabular}{rl}
adamc@524 401 \textbf{\LaTeX} & \textbf{ASCII} \\
adamc@524 402 $\to$ & \cd{->} \\
adam@1687 403 $\longrightarrow$ & \cd{-{}->} \\
adamc@524 404 $\times$ & \cd{*} \\
adamc@524 405 $\lambda$ & \cd{fn} \\
adamc@524 406 $\Rightarrow$ & \cd{=>} \\
adamc@652 407 $\Longrightarrow$ & \cd{==>} \\
adamc@529 408 $\neq$ & \cd{<>} \\
adamc@529 409 $\leq$ & \cd{<=} \\
adamc@529 410 $\geq$ & \cd{>=} \\
adamc@524 411 \\
adamc@524 412 $x$ & Normal textual identifier, not beginning with an uppercase letter \\
adamc@525 413 $X$ & Normal textual identifier, beginning with an uppercase letter \\
adamc@524 414 \end{tabular}
adamc@524 415 \end{center}
adamc@524 416
adamc@525 417 We often write syntax like $e^*$ to indicate zero or more copies of $e$, $e^+$ to indicate one or more copies, and $e,^*$ and $e,^+$ to indicate multiple copies separated by commas. Another separator may be used in place of a comma. The $e$ term may be surrounded by parentheses to indicate grouping; those parentheses should not be included in the actual ASCII.
adamc@524 418
adamc@873 419 We write $\ell$ for literals of the primitive types, for the most part following C conventions. There are $\mt{int}$, $\mt{float}$, $\mt{char}$, and $\mt{string}$ literals. Character literals follow the SML convention instead of the C convention, written like \texttt{\#"a"} instead of \texttt{'a'}.
adamc@526 420
adamc@527 421 This version of the manual doesn't include operator precedences; see \texttt{src/urweb.grm} for that.
adamc@527 422
adam@1297 423 As in the ML language family, the syntax \texttt{(* ... *)} is used for (nestable) comments. Within XML literals, Ur/Web also supports the usual \texttt{<!-- ... -->} XML comments.
adam@1297 424
adamc@552 425 \subsection{\label{core}Core Syntax}
adamc@524 426
adamc@524 427 \emph{Kinds} classify types and other compile-time-only entities. Each kind in the grammar is listed with a description of the sort of data it classifies.
adamc@524 428 $$\begin{array}{rrcll}
adamc@524 429 \textrm{Kinds} & \kappa &::=& \mt{Type} & \textrm{proper types} \\
adamc@525 430 &&& \mt{Unit} & \textrm{the trivial constructor} \\
adamc@525 431 &&& \mt{Name} & \textrm{field names} \\
adamc@525 432 &&& \kappa \to \kappa & \textrm{type-level functions} \\
adamc@525 433 &&& \{\kappa\} & \textrm{type-level records} \\
adamc@525 434 &&& (\kappa\times^+) & \textrm{type-level tuples} \\
adamc@652 435 &&& X & \textrm{variable} \\
adam@1574 436 &&& X \longrightarrow \kappa & \textrm{kind-polymorphic type-level function} \\
adamc@529 437 &&& \_\_ & \textrm{wildcard} \\
adamc@525 438 &&& (\kappa) & \textrm{explicit precedence} \\
adamc@524 439 \end{array}$$
adamc@524 440
adamc@524 441 Ur supports several different notions of functions that take types as arguments. These arguments can be either implicit, causing them to be inferred at use sites; or explicit, forcing them to be specified manually at use sites. There is a common explicitness annotation convention applied at the definitions of and in the types of such functions.
adamc@524 442 $$\begin{array}{rrcll}
adamc@524 443 \textrm{Explicitness} & ? &::=& :: & \textrm{explicit} \\
adamc@558 444 &&& ::: & \textrm{implicit}
adamc@524 445 \end{array}$$
adamc@524 446
adamc@524 447 \emph{Constructors} are the main class of compile-time-only data. They include proper types and are classified by kinds.
adamc@524 448 $$\begin{array}{rrcll}
adamc@524 449 \textrm{Constructors} & c, \tau &::=& (c) :: \kappa & \textrm{kind annotation} \\
adamc@530 450 &&& \hat{x} & \textrm{constructor variable} \\
adamc@524 451 \\
adamc@525 452 &&& \tau \to \tau & \textrm{function type} \\
adamc@525 453 &&& x \; ? \; \kappa \to \tau & \textrm{polymorphic function type} \\
adamc@652 454 &&& X \longrightarrow \tau & \textrm{kind-polymorphic function type} \\
adamc@525 455 &&& \$ c & \textrm{record type} \\
adamc@524 456 \\
adamc@525 457 &&& c \; c & \textrm{type-level function application} \\
adamc@530 458 &&& \lambda x \; :: \; \kappa \Rightarrow c & \textrm{type-level function abstraction} \\
adamc@524 459 \\
adamc@652 460 &&& X \Longrightarrow c & \textrm{type-level kind-polymorphic function abstraction} \\
adamc@655 461 &&& c [\kappa] & \textrm{type-level kind-polymorphic function application} \\
adamc@652 462 \\
adamc@525 463 &&& () & \textrm{type-level unit} \\
adamc@525 464 &&& \#X & \textrm{field name} \\
adamc@524 465 \\
adamc@525 466 &&& [(c = c)^*] & \textrm{known-length type-level record} \\
adamc@525 467 &&& c \rc c & \textrm{type-level record concatenation} \\
adamc@652 468 &&& \mt{map} & \textrm{type-level record map} \\
adamc@524 469 \\
adamc@558 470 &&& (c,^+) & \textrm{type-level tuple} \\
adamc@525 471 &&& c.n & \textrm{type-level tuple projection ($n \in \mathbb N^+$)} \\
adamc@524 472 \\
adamc@652 473 &&& [c \sim c] \Rightarrow \tau & \textrm{guarded type} \\
adamc@524 474 \\
adamc@529 475 &&& \_ :: \kappa & \textrm{wildcard} \\
adamc@525 476 &&& (c) & \textrm{explicit precedence} \\
adamc@530 477 \\
adamc@530 478 \textrm{Qualified uncapitalized variables} & \hat{x} &::=& x & \textrm{not from a module} \\
adamc@530 479 &&& M.x & \textrm{projection from a module} \\
adamc@525 480 \end{array}$$
adamc@525 481
adam@1579 482 We include both abstraction and application for kind polymorphism, but applications are only inferred internally; they may not be written explicitly in source programs. Also, in the ``known-length type-level record'' form, in $c_1 = c_2$ terms, the parser currently only allows $c_1$ to be of the forms $X$ (as a shorthand for $\#X$) or $x$, or a natural number to stand for the corresponding field name (e.g., for tuples).
adamc@655 483
adamc@525 484 Modules of the module system are described by \emph{signatures}.
adamc@525 485 $$\begin{array}{rrcll}
adamc@525 486 \textrm{Signatures} & S &::=& \mt{sig} \; s^* \; \mt{end} & \textrm{constant} \\
adamc@525 487 &&& X & \textrm{variable} \\
adamc@525 488 &&& \mt{functor}(X : S) : S & \textrm{functor} \\
adamc@529 489 &&& S \; \mt{where} \; \mt{con} \; x = c & \textrm{concretizing an abstract constructor} \\
adamc@525 490 &&& M.X & \textrm{projection from a module} \\
adamc@525 491 \\
adamc@525 492 \textrm{Signature items} & s &::=& \mt{con} \; x :: \kappa & \textrm{abstract constructor} \\
adamc@525 493 &&& \mt{con} \; x :: \kappa = c & \textrm{concrete constructor} \\
adamc@528 494 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529 495 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@525 496 &&& \mt{val} \; x : \tau & \textrm{value} \\
adamc@525 497 &&& \mt{structure} \; X : S & \textrm{sub-module} \\
adamc@525 498 &&& \mt{signature} \; X = S & \textrm{sub-signature} \\
adamc@525 499 &&& \mt{include} \; S & \textrm{signature inclusion} \\
adamc@525 500 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@654 501 &&& \mt{class} \; x :: \kappa & \textrm{abstract constructor class} \\
adamc@654 502 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@525 503 \\
adamc@525 504 \textrm{Datatype constructors} & dc &::=& X & \textrm{nullary constructor} \\
adamc@525 505 &&& X \; \mt{of} \; \tau & \textrm{unary constructor} \\
adamc@524 506 \end{array}$$
adamc@524 507
adamc@526 508 \emph{Patterns} are used to describe structural conditions on expressions, such that expressions may be tested against patterns, generating assignments to pattern variables if successful.
adamc@526 509 $$\begin{array}{rrcll}
adamc@526 510 \textrm{Patterns} & p &::=& \_ & \textrm{wildcard} \\
adamc@526 511 &&& x & \textrm{variable} \\
adamc@526 512 &&& \ell & \textrm{constant} \\
adamc@526 513 &&& \hat{X} & \textrm{nullary constructor} \\
adamc@526 514 &&& \hat{X} \; p & \textrm{unary constructor} \\
adam@2155 515 &&& \{(X = p,)^*\} & \textrm{rigid record pattern} \\
adam@2155 516 &&& \{(X = p,)^+, \ldots\} & \textrm{flexible record pattern} \\
adamc@852 517 &&& p : \tau & \textrm{type annotation} \\
adamc@527 518 &&& (p) & \textrm{explicit precedence} \\
adamc@526 519 \\
adamc@529 520 \textrm{Qualified capitalized variables} & \hat{X} &::=& X & \textrm{not from a module} \\
adamc@526 521 &&& M.X & \textrm{projection from a module} \\
adamc@526 522 \end{array}$$
adamc@526 523
adamc@527 524 \emph{Expressions} are the main run-time entities, corresponding to both ``expressions'' and ``statements'' in mainstream imperative languages.
adamc@527 525 $$\begin{array}{rrcll}
adamc@527 526 \textrm{Expressions} & e &::=& e : \tau & \textrm{type annotation} \\
adamc@529 527 &&& \hat{x} & \textrm{variable} \\
adamc@529 528 &&& \hat{X} & \textrm{datatype constructor} \\
adamc@527 529 &&& \ell & \textrm{constant} \\
adamc@527 530 \\
adamc@527 531 &&& e \; e & \textrm{function application} \\
adamc@527 532 &&& \lambda x : \tau \Rightarrow e & \textrm{function abstraction} \\
adamc@527 533 &&& e [c] & \textrm{polymorphic function application} \\
adamc@852 534 &&& \lambda [x \; ? \; \kappa] \Rightarrow e & \textrm{polymorphic function abstraction} \\
adamc@655 535 &&& e [\kappa] & \textrm{kind-polymorphic function application} \\
adamc@652 536 &&& X \Longrightarrow e & \textrm{kind-polymorphic function abstraction} \\
adamc@527 537 \\
adamc@527 538 &&& \{(c = e,)^*\} & \textrm{known-length record} \\
adamc@527 539 &&& e.c & \textrm{record field projection} \\
adamc@527 540 &&& e \rc e & \textrm{record concatenation} \\
adamc@527 541 &&& e \rcut c & \textrm{removal of a single record field} \\
adamc@527 542 &&& e \rcutM c & \textrm{removal of multiple record fields} \\
adamc@527 543 \\
adamc@527 544 &&& \mt{let} \; ed^* \; \mt{in} \; e \; \mt{end} & \textrm{local definitions} \\
adamc@527 545 \\
adamc@527 546 &&& \mt{case} \; e \; \mt{of} \; (p \Rightarrow e|)^+ & \textrm{pattern matching} \\
adamc@527 547 \\
adamc@654 548 &&& \lambda [c \sim c] \Rightarrow e & \textrm{guarded expression abstraction} \\
adamc@654 549 &&& e \; ! & \textrm{guarded expression application} \\
adamc@527 550 \\
adamc@527 551 &&& \_ & \textrm{wildcard} \\
adamc@527 552 &&& (e) & \textrm{explicit precedence} \\
adamc@527 553 \\
adamc@527 554 \textrm{Local declarations} & ed &::=& \cd{val} \; x : \tau = e & \textrm{non-recursive value} \\
adam@1797 555 &&& \cd{val} \; \cd{rec} \; (x : \tau = e \; \cd{and})^+ & \textrm{mutually recursive values} \\
adamc@527 556 \end{array}$$
adamc@527 557
adamc@655 558 As with constructors, we include both abstraction and application for kind polymorphism, but applications are only inferred internally.
adamc@655 559
adamc@528 560 \emph{Declarations} primarily bring new symbols into context.
adamc@528 561 $$\begin{array}{rrcll}
adamc@528 562 \textrm{Declarations} & d &::=& \mt{con} \; x :: \kappa = c & \textrm{constructor synonym} \\
adamc@528 563 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529 564 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@528 565 &&& \mt{val} \; x : \tau = e & \textrm{value} \\
adam@1797 566 &&& \mt{val} \; \cd{rec} \; (x : \tau = e \; \mt{and})^+ & \textrm{mutually recursive values} \\
adamc@528 567 &&& \mt{structure} \; X : S = M & \textrm{module definition} \\
adamc@528 568 &&& \mt{signature} \; X = S & \textrm{signature definition} \\
adamc@528 569 &&& \mt{open} \; M & \textrm{module inclusion} \\
adamc@528 570 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@528 571 &&& \mt{open} \; \mt{constraints} \; M & \textrm{inclusion of just the constraints from a module} \\
adamc@528 572 &&& \mt{table} \; x : c & \textrm{SQL table} \\
adam@1594 573 &&& \mt{view} \; x = e & \textrm{SQL view} \\
adamc@528 574 &&& \mt{sequence} \; x & \textrm{SQL sequence} \\
adamc@535 575 &&& \mt{cookie} \; x : \tau & \textrm{HTTP cookie} \\
adamc@784 576 &&& \mt{style} \; x : \tau & \textrm{CSS class} \\
adamc@1085 577 &&& \mt{task} \; e = e & \textrm{recurring task} \\
adamc@528 578 \\
adamc@529 579 \textrm{Modules} & M &::=& \mt{struct} \; d^* \; \mt{end} & \textrm{constant} \\
adamc@529 580 &&& X & \textrm{variable} \\
adamc@529 581 &&& M.X & \textrm{projection} \\
adamc@529 582 &&& M(M) & \textrm{functor application} \\
adamc@529 583 &&& \mt{functor}(X : S) : S = M & \textrm{functor abstraction} \\
adamc@528 584 \end{array}$$
adamc@528 585
adamc@528 586 There are two kinds of Ur files. A file named $M\texttt{.ur}$ is an \emph{implementation file}, and it should contain a sequence of declarations $d^*$. A file named $M\texttt{.urs}$ is an \emph{interface file}; it must always have a matching $M\texttt{.ur}$ and should contain a sequence of signature items $s^*$. When both files are present, the overall effect is the same as a monolithic declaration $\mt{structure} \; M : \mt{sig} \; s^* \; \mt{end} = \mt{struct} \; d^* \; \mt{end}$. When no interface file is included, the overall effect is similar, with a signature for module $M$ being inferred rather than just checked against an interface.
adamc@527 587
adam@1594 588 We omit some extra possibilities in $\mt{table}$ syntax, deferring them to Section \ref{tables}. The concrete syntax of $\mt{view}$ declarations is also more complex than shown in the table above, with details deferred to Section \ref{tables}.
adamc@784 589
adamc@529 590 \subsection{Shorthands}
adamc@529 591
adamc@529 592 There are a variety of derived syntactic forms that elaborate into the core syntax from the last subsection. We will present the additional forms roughly following the order in which we presented the constructs that they elaborate into.
adamc@529 593
adamc@529 594 In many contexts where record fields are expected, like in a projection $e.c$, a constant field may be written as simply $X$, rather than $\#X$.
adamc@529 595
adamc@529 596 A record type may be written $\{(c = c,)^*\}$, which elaborates to $\$[(c = c,)^*]$.
adamc@529 597
adamc@533 598 The notation $[c_1, \ldots, c_n]$ is shorthand for $[c_1 = (), \ldots, c_n = ()]$.
adamc@533 599
adam@1350 600 A tuple type $\tau_1 \times \ldots \times \tau_n$ expands to a record type $\{1 : \tau_1, \ldots, n : \tau_n\}$, with natural numbers as field names. A tuple expression $(e_1, \ldots, e_n)$ expands to a record expression $\{1 = e_1, \ldots, n = e_n\}$. A tuple pattern $(p_1, \ldots, p_n)$ expands to a rigid record pattern $\{1 = p_1, \ldots, n = p_n\}$. Positive natural numbers may be used in most places where field names would be allowed.
adamc@529 601
adam@1687 602 The syntax $()$ expands to $\{\}$ as a pattern or expression.
adam@1687 603
adamc@852 604 In general, several adjacent $\lambda$ forms may be combined into one, and kind and type annotations may be omitted, in which case they are implicitly included as wildcards. More formally, for constructor-level abstractions, we can define a new non-terminal $b ::= x \mid (x :: \kappa) \mid X$ and allow composite abstractions of the form $\lambda b^+ \Rightarrow c$, elaborating into the obvious sequence of one core $\lambda$ per element of $b^+$.
adamc@529 605
adam@1574 606 Further, the signature item or declaration syntax $\mt{con} \; x \; b^+ = c$ is shorthand for wrapping of the appropriate $\lambda$s around the righthand side $c$. The $b$ elements may not include $X$, and there may also be an optional $:: \kappa$ before the $=$.
adam@1574 607
adam@1306 608 In some contexts, the parser isn't happy with token sequences like $x :: \_$, to indicate a constructor variable of wildcard kind. In such cases, write the second two tokens as $::\hspace{-.05in}\_$, with no intervening spaces. Analogous syntax $:::\hspace{-.05in}\_$ is available for implicit constructor arguments.
adam@1302 609
adamc@529 610 For any signature item or declaration that defines some entity to be equal to $A$ with classification annotation $B$ (e.g., $\mt{val} \; x : B = A$), $B$ and the preceding colon (or similar punctuation) may be omitted, in which case it is filled in as a wildcard.
adamc@529 611
adamc@529 612 A signature item or declaration $\mt{type} \; x$ or $\mt{type} \; x = \tau$ is elaborated into $\mt{con} \; x :: \mt{Type}$ or $\mt{con} \; x :: \mt{Type} = \tau$, respectively.
adamc@529 613
adamc@654 614 A signature item or declaration $\mt{class} \; x = \lambda y \Rightarrow c$ may be abbreviated $\mt{class} \; x \; y = c$.
adamc@529 615
adam@1738 616 Handling of implicit and explicit constructor arguments may be tweaked with some prefixes to variable references. An expression $@x$ is a version of $x$ where all type class instance and disjointness arguments have been made explicit. (For the purposes of this paragraph, the type family $\mt{Top.folder}$ is a type class, though it isn't marked as one by the usual means; and any record type is considered to be a type class instance type when every field's type is a type class instance type.) An expression $@@x$ achieves the same effect, additionally making explicit all implicit constructor arguments. The default is that implicit arguments are inserted automatically after any reference to a variable, or after any application of a variable to one or more arguments. For such an expression, implicit wildcard arguments are added for the longest prefix of the expression's type consisting only of implicit polymorphism, type class instances, and disjointness obligations. The same syntax works for variables projected out of modules and for capitalized variables (datatype constructors).
adamc@529 617
adamc@852 618 At the expression level, an analogue is available of the composite $\lambda$ form for constructors. We define the language of binders as $b ::= p \mid [x] \mid [x \; ? \; \kappa] \mid X \mid [c \sim c]$. A lone variable $[x]$ stands for an implicit constructor variable of unspecified kind. The standard value-level function binder is recovered as the type-annotated pattern form $x : \tau$. It is a compile-time error to include a pattern $p$ that does not match every value of the appropriate type.
adamc@529 619
adamc@852 620 A local $\mt{val}$ declaration may bind a pattern instead of just a plain variable. As for function arguments, only irrefutable patterns are legal.
adamc@852 621
adam@1797 622 The keyword $\mt{fun}$ is a shorthand for $\mt{val} \; \mt{rec}$ that allows arguments to be specified before the equal sign in the definition of each mutually recursive function, as in SML. Each curried argument must follow the grammar of the $b$ non-terminal introduced two paragraphs ago. A $\mt{fun}$ declaration is elaborated into a version that adds additional $\lambda$s to the fronts of the righthand sides, as appropriate.
adamc@529 623
adamc@529 624 A signature item $\mt{functor} \; X_1 \; (X_2 : S_1) : S_2$ is elaborated into $\mt{structure} \; X_1 : \mt{functor}(X_2 : S_1) : S_2$. A declaration $\mt{functor} \; X_1 \; (X_2 : S_1) : S_2 = M$ is elaborated into $\mt{structure} \; X_1 : \mt{functor}(X_2 : S_1) : S_2 = \mt{functor}(X_2 : S_1) : S_2 = M$.
adamc@529 625
adamc@852 626 An $\mt{open} \; \mt{constraints}$ declaration is implicitly inserted for the argument of every functor at the beginning of the functor body. For every declaration of the form $\mt{structure} \; X : S = \mt{struct} \ldots \mt{end}$, an $\mt{open} \; \mt{constraints} \; X$ declaration is implicitly inserted immediately afterward.
adamc@852 627
adamc@853 628 A declaration $\mt{table} \; x : \{(c = c,)^*\}$ is elaborated into $\mt{table} \; x : [(c = c,)^*]$.
adamc@529 629
adamc@529 630 The syntax $\mt{where} \; \mt{type}$ is an alternate form of $\mt{where} \; \mt{con}$.
adamc@529 631
adamc@529 632 The syntax $\mt{if} \; e \; \mt{then} \; e_1 \; \mt{else} \; e_2$ expands to $\mt{case} \; e \; \mt{of} \; \mt{Basis}.\mt{True} \Rightarrow e_1 \mid \mt{Basis}.\mt{False} \Rightarrow e_2$.
adamc@529 633
adamc@529 634 There are infix operator syntaxes for a number of functions defined in the $\mt{Basis}$ module. There is $=$ for $\mt{eq}$, $\neq$ for $\mt{neq}$, $-$ for $\mt{neg}$ (as a prefix operator) and $\mt{minus}$, $+$ for $\mt{plus}$, $\times$ for $\mt{times}$, $/$ for $\mt{div}$, $\%$ for $\mt{mod}$, $<$ for $\mt{lt}$, $\leq$ for $\mt{le}$, $>$ for $\mt{gt}$, and $\geq$ for $\mt{ge}$.
adamc@529 635
adamc@784 636 A signature item $\mt{table} \; x : c$ is shorthand for $\mt{val} \; x : \mt{Basis}.\mt{sql\_table} \; c \; []$. $\mt{view} \; x : c$ is shorthand for $\mt{val} \; x : \mt{Basis}.\mt{sql\_view} \; c$, $\mt{sequence} \; x$ is short for $\mt{val} \; x : \mt{Basis}.\mt{sql\_sequence}$. $\mt{cookie} \; x : \tau$ is shorthand for $\mt{val} \; x : \mt{Basis}.\mt{http\_cookie} \; \tau$, and $\mt{style} \; x$ is shorthand for $\mt{val} \; x : \mt{Basis}.\mt{css\_class}$.
adamc@529 637
adam@2025 638 It is possible to write a $\mt{let}$ expression with its constituents in reverse order, along the lines of Haskell's \cd{where}. An expression $\mt{let} \; e \; \mt{where} \; ed^* \; \mt{end}$ desugars to $\mt{let} \; ed^* \; \mt{in} \; e \; \mt{end}$.
adam@2025 639
adam@2123 640 Ur/Web also includes a few more infix operators: $f \; \texttt{<|} \; x$ desugars to $f \; x$, $x \; \texttt{|>} \; f$ to $f \; x$, $f \; \texttt{<{}<{}<} \; g$ to $\mt{Top}.\mt{compose} \; f \; g$, and $g \; \texttt{>{}>{}>} \; f$ to $\mt{Top}.\mt{compose} \; f \; g$. (The latter two are doing function composition in the usual way.) Furthermore, any identifier may be changed into an infix operator by placing it between backticks, e.g. a silly way to do addition is $x \; \texttt{`}\mt{plus}\texttt{`} \; y$ instead of $x + y$.
adam@2123 641
adam@2125 642 Hexadecimal integer literals are supported like \texttt{0xDEADBEEF}. Only capital letters are allowed.
adam@2125 643
adamc@530 644
adamc@530 645 \section{Static Semantics}
adamc@530 646
adamc@530 647 In this section, we give a declarative presentation of Ur's typing rules and related judgments. Inference is the subject of the next section; here, we assume that an oracle has filled in all wildcards with concrete values.
adamc@530 648
adam@1891 649 The notations used here are the standard ones of programming language semantics. They are probably the most effective way to convey this information. At the same time, most Ur/Web users can probably get by \emph{without} knowing the contents of this section! If you're interested in diving into the details of Ur typing but are unfamiliar with ``inference rule notation,'' I recommend the following book:
adam@1891 650 \begin{quote}
adam@1891 651 Benjamin C. Pierce, \emph{Types and Programming Languages}, MIT Press, 2002.
adam@1891 652 \end{quote}
adam@1891 653
adamc@530 654 Since there is significant mutual recursion among the judgments, we introduce them all before beginning to give rules. We use the same variety of contexts throughout this section, implicitly introducing new sorts of context entries as needed.
adamc@530 655 \begin{itemize}
adamc@655 656 \item $\Gamma \vdash \kappa$ expresses kind well-formedness.
adamc@530 657 \item $\Gamma \vdash c :: \kappa$ assigns a kind to a constructor in a context.
adamc@530 658 \item $\Gamma \vdash c \sim c$ proves the disjointness of two record constructors; that is, that they share no field names. We overload the judgment to apply to pairs of field names as well.
adamc@531 659 \item $\Gamma \vdash c \hookrightarrow C$ proves that record constructor $c$ decomposes into set $C$ of field names and record constructors.
adamc@530 660 \item $\Gamma \vdash c \equiv c$ proves the computational equivalence of two constructors. This is often called a \emph{definitional equality} in the world of type theory.
adamc@530 661 \item $\Gamma \vdash e : \tau$ is a standard typing judgment.
adamc@534 662 \item $\Gamma \vdash p \leadsto \Gamma; \tau$ combines typing of patterns with calculation of which new variables they bind.
adamc@537 663 \item $\Gamma \vdash d \leadsto \Gamma$ expresses how a declaration modifies a context. We overload this judgment to apply to sequences of declarations, as well as to signature items and sequences of signature items.
adamc@537 664 \item $\Gamma \vdash S \equiv S$ is the signature equivalence judgment.
adamc@536 665 \item $\Gamma \vdash S \leq S$ is the signature compatibility judgment. We write $\Gamma \vdash S$ as shorthand for $\Gamma \vdash S \leq S$.
adamc@530 666 \item $\Gamma \vdash M : S$ is the module signature checking judgment.
adamc@537 667 \item $\mt{proj}(M, \overline{s}, V)$ is a partial function for projecting a signature item from $\overline{s}$, given the module $M$ that we project from. $V$ may be $\mt{con} \; x$, $\mt{datatype} \; x$, $\mt{val} \; x$, $\mt{signature} \; X$, or $\mt{structure} \; X$. The parameter $M$ is needed because the projected signature item may refer to other items from $\overline{s}$.
adamc@539 668 \item $\mt{selfify}(M, \overline{s})$ adds information to signature items $\overline{s}$ to reflect the fact that we are concerned with the particular module $M$. This function is overloaded to work over individual signature items as well.
adamc@530 669 \end{itemize}
adamc@530 670
adamc@655 671
adamc@655 672 \subsection{Kind Well-Formedness}
adamc@655 673
adamc@655 674 $$\infer{\Gamma \vdash \mt{Type}}{}
adamc@655 675 \quad \infer{\Gamma \vdash \mt{Unit}}{}
adamc@655 676 \quad \infer{\Gamma \vdash \mt{Name}}{}
adamc@655 677 \quad \infer{\Gamma \vdash \kappa_1 \to \kappa_2}{
adamc@655 678 \Gamma \vdash \kappa_1
adamc@655 679 & \Gamma \vdash \kappa_2
adamc@655 680 }
adamc@655 681 \quad \infer{\Gamma \vdash \{\kappa\}}{
adamc@655 682 \Gamma \vdash \kappa
adamc@655 683 }
adamc@655 684 \quad \infer{\Gamma \vdash (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@655 685 \forall i: \Gamma \vdash \kappa_i
adamc@655 686 }$$
adamc@655 687
adamc@655 688 $$\infer{\Gamma \vdash X}{
adamc@655 689 X \in \Gamma
adamc@655 690 }
adamc@655 691 \quad \infer{\Gamma \vdash X \longrightarrow \kappa}{
adamc@655 692 \Gamma, X \vdash \kappa
adamc@655 693 }$$
adamc@655 694
adamc@530 695 \subsection{Kinding}
adamc@530 696
adamc@655 697 We write $[X \mapsto \kappa_1]\kappa_2$ for capture-avoiding substitution of $\kappa_1$ for $X$ in $\kappa_2$.
adamc@655 698
adamc@530 699 $$\infer{\Gamma \vdash (c) :: \kappa :: \kappa}{
adamc@530 700 \Gamma \vdash c :: \kappa
adamc@530 701 }
adamc@530 702 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530 703 x :: \kappa \in \Gamma
adamc@530 704 }
adamc@530 705 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530 706 x :: \kappa = c \in \Gamma
adamc@530 707 }$$
adamc@530 708
adamc@530 709 $$\infer{\Gamma \vdash M.x :: \kappa}{
adamc@537 710 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 711 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = \kappa
adamc@530 712 }
adamc@530 713 \quad \infer{\Gamma \vdash M.x :: \kappa}{
adamc@537 714 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 715 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@530 716 }$$
adamc@530 717
adamc@530 718 $$\infer{\Gamma \vdash \tau_1 \to \tau_2 :: \mt{Type}}{
adamc@530 719 \Gamma \vdash \tau_1 :: \mt{Type}
adamc@530 720 & \Gamma \vdash \tau_2 :: \mt{Type}
adamc@530 721 }
adamc@530 722 \quad \infer{\Gamma \vdash x \; ? \: \kappa \to \tau :: \mt{Type}}{
adamc@530 723 \Gamma, x :: \kappa \vdash \tau :: \mt{Type}
adamc@530 724 }
adamc@655 725 \quad \infer{\Gamma \vdash X \longrightarrow \tau :: \mt{Type}}{
adamc@655 726 \Gamma, X \vdash \tau :: \mt{Type}
adamc@655 727 }
adamc@530 728 \quad \infer{\Gamma \vdash \$c :: \mt{Type}}{
adamc@530 729 \Gamma \vdash c :: \{\mt{Type}\}
adamc@530 730 }$$
adamc@530 731
adamc@530 732 $$\infer{\Gamma \vdash c_1 \; c_2 :: \kappa_2}{
adamc@530 733 \Gamma \vdash c_1 :: \kappa_1 \to \kappa_2
adamc@530 734 & \Gamma \vdash c_2 :: \kappa_1
adamc@530 735 }
adamc@530 736 \quad \infer{\Gamma \vdash \lambda x \; :: \; \kappa_1 \Rightarrow c :: \kappa_1 \to \kappa_2}{
adamc@530 737 \Gamma, x :: \kappa_1 \vdash c :: \kappa_2
adamc@530 738 }$$
adamc@530 739
adamc@655 740 $$\infer{\Gamma \vdash c[\kappa'] :: [X \mapsto \kappa']\kappa}{
adamc@655 741 \Gamma \vdash c :: X \to \kappa
adamc@655 742 & \Gamma \vdash \kappa'
adamc@655 743 }
adamc@655 744 \quad \infer{\Gamma \vdash X \Longrightarrow c :: X \to \kappa}{
adamc@655 745 \Gamma, X \vdash c :: \kappa
adamc@655 746 }$$
adamc@655 747
adamc@530 748 $$\infer{\Gamma \vdash () :: \mt{Unit}}{}
adamc@530 749 \quad \infer{\Gamma \vdash \#X :: \mt{Name}}{}$$
adamc@530 750
adamc@530 751 $$\infer{\Gamma \vdash [\overline{c_i = c'_i}] :: \{\kappa\}}{
adamc@530 752 \forall i: \Gamma \vdash c_i : \mt{Name}
adamc@530 753 & \Gamma \vdash c'_i :: \kappa
adamc@530 754 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@530 755 }
adamc@530 756 \quad \infer{\Gamma \vdash c_1 \rc c_2 :: \{\kappa\}}{
adamc@530 757 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530 758 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@530 759 & \Gamma \vdash c_1 \sim c_2
adamc@530 760 }$$
adamc@530 761
adamc@655 762 $$\infer{\Gamma \vdash \mt{map} :: (\kappa_1 \to \kappa_2) \to \{\kappa_1\} \to \{\kappa_2\}}{}$$
adamc@530 763
adamc@573 764 $$\infer{\Gamma \vdash (\overline c) :: (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@573 765 \forall i: \Gamma \vdash c_i :: \kappa_i
adamc@530 766 }
adamc@573 767 \quad \infer{\Gamma \vdash c.i :: \kappa_i}{
adamc@573 768 \Gamma \vdash c :: (\kappa_1 \times \ldots \times \kappa_n)
adamc@530 769 }$$
adamc@530 770
adamc@655 771 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow \tau :: \mt{Type}}{
adamc@655 772 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530 773 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@655 774 & \Gamma, c_1 \sim c_2 \vdash \tau :: \mt{Type}
adamc@530 775 }$$
adamc@530 776
adamc@531 777 \subsection{Record Disjointness}
adamc@531 778
adamc@531 779 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@558 780 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@558 781 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@558 782 & \forall c'_1 \in C_1, c'_2 \in C_2: \Gamma \vdash c'_1 \sim c'_2
adamc@531 783 }
adamc@531 784 \quad \infer{\Gamma \vdash X \sim X'}{
adamc@531 785 X \neq X'
adamc@531 786 }$$
adamc@531 787
adamc@531 788 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@531 789 c'_1 \sim c'_2 \in \Gamma
adamc@558 790 & \Gamma \vdash c'_1 \hookrightarrow C_1
adamc@558 791 & \Gamma \vdash c'_2 \hookrightarrow C_2
adamc@558 792 & c_1 \in C_1
adamc@558 793 & c_2 \in C_2
adamc@531 794 }$$
adamc@531 795
adamc@531 796 $$\infer{\Gamma \vdash c \hookrightarrow \{c\}}{}
adamc@531 797 \quad \infer{\Gamma \vdash [\overline{c = c'}] \hookrightarrow \{\overline{c}\}}{}
adamc@531 798 \quad \infer{\Gamma \vdash c_1 \rc c_2 \hookrightarrow C_1 \cup C_2}{
adamc@531 799 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@531 800 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@531 801 }
adamc@531 802 \quad \infer{\Gamma \vdash c \hookrightarrow C}{
adamc@531 803 \Gamma \vdash c \equiv c'
adamc@531 804 & \Gamma \vdash c' \hookrightarrow C
adamc@531 805 }
adamc@531 806 \quad \infer{\Gamma \vdash \mt{map} \; f \; c \hookrightarrow C}{
adamc@531 807 \Gamma \vdash c \hookrightarrow C
adamc@531 808 }$$
adamc@531 809
adamc@541 810 \subsection{\label{definitional}Definitional Equality}
adamc@532 811
adamc@655 812 We use $\mathcal C$ to stand for a one-hole context that, when filled, yields a constructor. The notation $\mathcal C[c]$ plugs $c$ into $\mathcal C$. We omit the standard definition of one-hole contexts. We write $[x \mapsto c_1]c_2$ for capture-avoiding substitution of $c_1$ for $x$ in $c_2$, with analogous notation for substituting a kind in a constructor.
adamc@532 813
adamc@532 814 $$\infer{\Gamma \vdash c \equiv c}{}
adamc@532 815 \quad \infer{\Gamma \vdash c_1 \equiv c_2}{
adamc@532 816 \Gamma \vdash c_2 \equiv c_1
adamc@532 817 }
adamc@532 818 \quad \infer{\Gamma \vdash c_1 \equiv c_3}{
adamc@532 819 \Gamma \vdash c_1 \equiv c_2
adamc@532 820 & \Gamma \vdash c_2 \equiv c_3
adamc@532 821 }
adamc@532 822 \quad \infer{\Gamma \vdash \mathcal C[c_1] \equiv \mathcal C[c_2]}{
adamc@532 823 \Gamma \vdash c_1 \equiv c_2
adamc@532 824 }$$
adamc@532 825
adamc@532 826 $$\infer{\Gamma \vdash x \equiv c}{
adamc@532 827 x :: \kappa = c \in \Gamma
adamc@532 828 }
adamc@532 829 \quad \infer{\Gamma \vdash M.x \equiv c}{
adamc@537 830 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 831 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@532 832 }
adamc@532 833 \quad \infer{\Gamma \vdash (\overline c).i \equiv c_i}{}$$
adamc@532 834
adamc@532 835 $$\infer{\Gamma \vdash (\lambda x :: \kappa \Rightarrow c) \; c' \equiv [x \mapsto c'] c}{}
adamc@655 836 \quad \infer{\Gamma \vdash (X \Longrightarrow c) [\kappa] \equiv [X \mapsto \kappa] c}{}$$
adamc@655 837
adamc@655 838 $$\infer{\Gamma \vdash c_1 \rc c_2 \equiv c_2 \rc c_1}{}
adamc@532 839 \quad \infer{\Gamma \vdash c_1 \rc (c_2 \rc c_3) \equiv (c_1 \rc c_2) \rc c_3}{}$$
adamc@532 840
adamc@532 841 $$\infer{\Gamma \vdash [] \rc c \equiv c}{}
adamc@532 842 \quad \infer{\Gamma \vdash [\overline{c_1 = c'_1}] \rc [\overline{c_2 = c'_2}] \equiv [\overline{c_1 = c'_1}, \overline{c_2 = c'_2}]}{}$$
adamc@532 843
adamc@655 844 $$\infer{\Gamma \vdash \mt{map} \; f \; [] \equiv []}{}
adamc@655 845 \quad \infer{\Gamma \vdash \mt{map} \; f \; ([c_1 = c_2] \rc c) \equiv [c_1 = f \; c_2] \rc \mt{map} \; f \; c}{}$$
adamc@532 846
adamc@532 847 $$\infer{\Gamma \vdash \mt{map} \; (\lambda x \Rightarrow x) \; c \equiv c}{}
adamc@655 848 \quad \infer{\Gamma \vdash \mt{map} \; f \; (\mt{map} \; f' \; c)
adamc@655 849 \equiv \mt{map} \; (\lambda x \Rightarrow f \; (f' \; x)) \; c}{}$$
adamc@532 850
adamc@532 851 $$\infer{\Gamma \vdash \mt{map} \; f \; (c_1 \rc c_2) \equiv \mt{map} \; f \; c_1 \rc \mt{map} \; f \; c_2}{}$$
adamc@531 852
adamc@534 853 \subsection{Expression Typing}
adamc@533 854
adamc@873 855 We assume the existence of a function $T$ assigning types to literal constants. It maps integer constants to $\mt{Basis}.\mt{int}$, float constants to $\mt{Basis}.\mt{float}$, character constants to $\mt{Basis}.\mt{char}$, and string constants to $\mt{Basis}.\mt{string}$.
adamc@533 856
adamc@533 857 We also refer to a function $\mathcal I$, such that $\mathcal I(\tau)$ ``uses an oracle'' to instantiate all constructor function arguments at the beginning of $\tau$ that are marked implicit; i.e., replace $x_1 ::: \kappa_1 \to \ldots \to x_n ::: \kappa_n \to \tau$ with $[x_1 \mapsto c_1]\ldots[x_n \mapsto c_n]\tau$, where the $c_i$s are inferred and $\tau$ does not start like $x ::: \kappa \to \tau'$.
adamc@533 858
adamc@533 859 $$\infer{\Gamma \vdash e : \tau : \tau}{
adamc@533 860 \Gamma \vdash e : \tau
adamc@533 861 }
adamc@533 862 \quad \infer{\Gamma \vdash e : \tau}{
adamc@533 863 \Gamma \vdash e : \tau'
adamc@533 864 & \Gamma \vdash \tau' \equiv \tau
adamc@533 865 }
adamc@533 866 \quad \infer{\Gamma \vdash \ell : T(\ell)}{}$$
adamc@533 867
adamc@533 868 $$\infer{\Gamma \vdash x : \mathcal I(\tau)}{
adamc@533 869 x : \tau \in \Gamma
adamc@533 870 }
adamc@533 871 \quad \infer{\Gamma \vdash M.x : \mathcal I(\tau)}{
adamc@537 872 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 873 & \mt{proj}(M, \overline{s}, \mt{val} \; x) = \tau
adamc@533 874 }
adamc@533 875 \quad \infer{\Gamma \vdash X : \mathcal I(\tau)}{
adamc@533 876 X : \tau \in \Gamma
adamc@533 877 }
adamc@533 878 \quad \infer{\Gamma \vdash M.X : \mathcal I(\tau)}{
adamc@537 879 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 880 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \tau
adamc@533 881 }$$
adamc@533 882
adamc@533 883 $$\infer{\Gamma \vdash e_1 \; e_2 : \tau_2}{
adamc@533 884 \Gamma \vdash e_1 : \tau_1 \to \tau_2
adamc@533 885 & \Gamma \vdash e_2 : \tau_1
adamc@533 886 }
adamc@533 887 \quad \infer{\Gamma \vdash \lambda x : \tau_1 \Rightarrow e : \tau_1 \to \tau_2}{
adamc@533 888 \Gamma, x : \tau_1 \vdash e : \tau_2
adamc@533 889 }$$
adamc@533 890
adamc@533 891 $$\infer{\Gamma \vdash e [c] : [x \mapsto c]\tau}{
adamc@533 892 \Gamma \vdash e : x :: \kappa \to \tau
adamc@533 893 & \Gamma \vdash c :: \kappa
adamc@533 894 }
adamc@852 895 \quad \infer{\Gamma \vdash \lambda [x \; ? \; \kappa] \Rightarrow e : x \; ? \; \kappa \to \tau}{
adamc@533 896 \Gamma, x :: \kappa \vdash e : \tau
adamc@533 897 }$$
adamc@533 898
adamc@655 899 $$\infer{\Gamma \vdash e [\kappa] : [X \mapsto \kappa]\tau}{
adamc@655 900 \Gamma \vdash e : X \longrightarrow \tau
adamc@655 901 & \Gamma \vdash \kappa
adamc@655 902 }
adamc@655 903 \quad \infer{\Gamma \vdash X \Longrightarrow e : X \longrightarrow \tau}{
adamc@655 904 \Gamma, X \vdash e : \tau
adamc@655 905 }$$
adamc@655 906
adamc@533 907 $$\infer{\Gamma \vdash \{\overline{c = e}\} : \{\overline{c : \tau}\}}{
adamc@533 908 \forall i: \Gamma \vdash c_i :: \mt{Name}
adamc@533 909 & \Gamma \vdash e_i : \tau_i
adamc@533 910 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@533 911 }
adamc@533 912 \quad \infer{\Gamma \vdash e.c : \tau}{
adamc@533 913 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533 914 }
adamc@533 915 \quad \infer{\Gamma \vdash e_1 \rc e_2 : \$(c_1 \rc c_2)}{
adamc@533 916 \Gamma \vdash e_1 : \$c_1
adamc@533 917 & \Gamma \vdash e_2 : \$c_2
adamc@573 918 & \Gamma \vdash c_1 \sim c_2
adamc@533 919 }$$
adamc@533 920
adamc@533 921 $$\infer{\Gamma \vdash e \rcut c : \$c'}{
adamc@533 922 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533 923 }
adamc@533 924 \quad \infer{\Gamma \vdash e \rcutM c : \$c'}{
adamc@533 925 \Gamma \vdash e : \$(c \rc c')
adamc@533 926 }$$
adamc@533 927
adamc@533 928 $$\infer{\Gamma \vdash \mt{let} \; \overline{ed} \; \mt{in} \; e \; \mt{end} : \tau}{
adamc@533 929 \Gamma \vdash \overline{ed} \leadsto \Gamma'
adamc@533 930 & \Gamma' \vdash e : \tau
adamc@533 931 }
adamc@533 932 \quad \infer{\Gamma \vdash \mt{case} \; e \; \mt{of} \; \overline{p \Rightarrow e} : \tau}{
adamc@533 933 \forall i: \Gamma \vdash p_i \leadsto \Gamma_i, \tau'
adamc@533 934 & \Gamma_i \vdash e_i : \tau
adamc@533 935 }$$
adamc@533 936
adamc@573 937 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow e : \lambda [c_1 \sim c_2] \Rightarrow \tau}{
adamc@533 938 \Gamma \vdash c_1 :: \{\kappa\}
adamc@655 939 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@533 940 & \Gamma, c_1 \sim c_2 \vdash e : \tau
adamc@662 941 }
adamc@662 942 \quad \infer{\Gamma \vdash e \; ! : \tau}{
adamc@662 943 \Gamma \vdash e : [c_1 \sim c_2] \Rightarrow \tau
adamc@662 944 & \Gamma \vdash c_1 \sim c_2
adamc@533 945 }$$
adamc@533 946
adamc@534 947 \subsection{Pattern Typing}
adamc@534 948
adamc@534 949 $$\infer{\Gamma \vdash \_ \leadsto \Gamma; \tau}{}
adamc@534 950 \quad \infer{\Gamma \vdash x \leadsto \Gamma, x : \tau; \tau}{}
adamc@534 951 \quad \infer{\Gamma \vdash \ell \leadsto \Gamma; T(\ell)}{}$$
adamc@534 952
adamc@534 953 $$\infer{\Gamma \vdash X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534 954 X : \overline{x ::: \mt{Type}} \to \tau \in \Gamma
adamc@534 955 & \textrm{$\tau$ not a function type}
adamc@534 956 }
adamc@534 957 \quad \infer{\Gamma \vdash X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534 958 X : \overline{x ::: \mt{Type}} \to \tau'' \to \tau \in \Gamma
adamc@534 959 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534 960 }$$
adamc@534 961
adamc@534 962 $$\infer{\Gamma \vdash M.X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537 963 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 964 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau
adamc@534 965 & \textrm{$\tau$ not a function type}
adamc@534 966 }$$
adamc@534 967
adamc@534 968 $$\infer{\Gamma \vdash M.X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537 969 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 970 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau'' \to \tau
adamc@534 971 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534 972 }$$
adamc@534 973
adam@2155 974 $$\infer{\Gamma \vdash \{\overline{X = p}\} \leadsto \Gamma_n; \{\overline{X = \tau}\}}{
adamc@534 975 \Gamma_0 = \Gamma
adamc@534 976 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534 977 }
adam@2155 978 \quad \infer{\Gamma \vdash \{\overline{X = p}, \ldots\} \leadsto \Gamma_n; \$([\overline{X = \tau}] \rc c)}{
adamc@534 979 \Gamma_0 = \Gamma
adamc@534 980 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534 981 }$$
adamc@534 982
adamc@852 983 $$\infer{\Gamma \vdash p : \tau \leadsto \Gamma'; \tau}{
adamc@852 984 \Gamma \vdash p \leadsto \Gamma'; \tau'
adamc@852 985 & \Gamma \vdash \tau' \equiv \tau
adamc@852 986 }$$
adamc@852 987
adamc@535 988 \subsection{Declaration Typing}
adamc@535 989
adamc@535 990 We use an auxiliary judgment $\overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'$, expressing the enrichment of $\Gamma$ with the types of the datatype constructors $\overline{dc}$, when they are known to belong to datatype $x$ with type parameters $\overline{y}$.
adamc@535 991
adamc@558 992 We presuppose the existence of a function $\mathcal O$, where $\mathcal O(M, \overline{s})$ implements the $\mt{open}$ declaration by producing a context with the appropriate entry for each available component of module $M$ with signature items $\overline{s}$. Where possible, $\mathcal O$ uses ``transparent'' entries (e.g., an abstract type $M.x$ is mapped to $x :: \mt{Type} = M.x$), so that the relationship with $M$ is maintained. A related function $\mathcal O_c$ builds a context containing the disjointness constraints found in $\overline s$.
adamc@537 993 We write $\kappa_1^n \to \kappa$ as a shorthand, where $\kappa_1^0 \to \kappa = \kappa$ and $\kappa_1^{n+1} \to \kappa_2 = \kappa_1 \to (\kappa_1^n \to \kappa_2)$. We write $\mt{len}(\overline{y})$ for the length of vector $\overline{y}$ of variables.
adamc@535 994
adamc@535 995 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535 996 \quad \infer{\Gamma \vdash d, \overline{d} \leadsto \Gamma''}{
adamc@535 997 \Gamma \vdash d \leadsto \Gamma'
adamc@535 998 & \Gamma' \vdash \overline{d} \leadsto \Gamma''
adamc@535 999 }$$
adamc@535 1000
adamc@535 1001 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@535 1002 \Gamma \vdash c :: \kappa
adamc@535 1003 }
adamc@535 1004 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@535 1005 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@535 1006 }$$
adamc@535 1007
adamc@535 1008 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537 1009 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1010 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@535 1011 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@535 1012 }$$
adamc@535 1013
adamc@535 1014 $$\infer{\Gamma \vdash \mt{val} \; x : \tau = e \leadsto \Gamma, x : \tau}{
adamc@535 1015 \Gamma \vdash e : \tau
adamc@535 1016 }$$
adamc@535 1017
adamc@535 1018 $$\infer{\Gamma \vdash \mt{val} \; \mt{rec} \; \overline{x : \tau = e} \leadsto \Gamma, \overline{x : \tau}}{
adamc@535 1019 \forall i: \Gamma, \overline{x : \tau} \vdash e_i : \tau_i
adamc@535 1020 & \textrm{$e_i$ starts with an expression $\lambda$, optionally preceded by constructor and disjointness $\lambda$s}
adamc@535 1021 }$$
adamc@535 1022
adamc@535 1023 $$\infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : S}{
adamc@535 1024 \Gamma \vdash M : S
adamc@558 1025 & \textrm{ $M$ not a constant or application}
adamc@535 1026 }
adamc@558 1027 \quad \infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : \mt{selfify}(X, \overline{s})}{
adamc@558 1028 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@539 1029 }$$
adamc@539 1030
adamc@539 1031 $$\infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@535 1032 \Gamma \vdash S
adamc@535 1033 }$$
adamc@535 1034
adamc@537 1035 $$\infer{\Gamma \vdash \mt{open} \; M \leadsto \Gamma, \mathcal O(M, \overline{s})}{
adamc@537 1036 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535 1037 }$$
adamc@535 1038
adamc@535 1039 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma}{
adamc@535 1040 \Gamma \vdash c_1 :: \{\kappa\}
adamc@535 1041 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@535 1042 & \Gamma \vdash c_1 \sim c_2
adamc@535 1043 }
adamc@537 1044 \quad \infer{\Gamma \vdash \mt{open} \; \mt{constraints} \; M \leadsto \Gamma, \mathcal O_c(M, \overline{s})}{
adamc@537 1045 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535 1046 }$$
adamc@535 1047
adamc@784 1048 $$\infer{\Gamma \vdash \mt{table} \; x : c \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_table} \; c \; []}{
adamc@535 1049 \Gamma \vdash c :: \{\mt{Type}\}
adamc@535 1050 }
adam@1594 1051 \quad \infer{\Gamma \vdash \mt{view} \; x = e \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_view} \; c}{
adam@1594 1052 \Gamma \vdash e :: \mt{Basis}.\mt{sql\_query} \; [] \; [] \; (\mt{map} \; (\lambda \_ \Rightarrow []) \; c') \; c
adamc@784 1053 }$$
adamc@784 1054
adamc@784 1055 $$\infer{\Gamma \vdash \mt{sequence} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_sequence}}{}$$
adamc@535 1056
adamc@535 1057 $$\infer{\Gamma \vdash \mt{cookie} \; x : \tau \leadsto \Gamma, x : \mt{Basis}.\mt{http\_cookie} \; \tau}{
adamc@535 1058 \Gamma \vdash \tau :: \mt{Type}
adamc@784 1059 }
adamc@784 1060 \quad \infer{\Gamma \vdash \mt{style} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{css\_class}}{}$$
adamc@535 1061
adamc@1085 1062 $$\infer{\Gamma \vdash \mt{task} \; e_1 = e_2 \leadsto \Gamma}{
adam@1348 1063 \Gamma \vdash e_1 :: \mt{Basis}.\mt{task\_kind} \; \tau
adam@1348 1064 & \Gamma \vdash e_2 :: \tau \to \mt{Basis}.\mt{transaction} \; \{\}
adamc@1085 1065 }$$
adamc@1085 1066
adamc@535 1067 $$\infer{\overline{y}; x; \Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535 1068 \quad \infer{\overline{y}; x; \Gamma \vdash X \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to x \; \overline{y}}{
adamc@535 1069 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535 1070 }
adamc@535 1071 \quad \infer{\overline{y}; x; \Gamma \vdash X \; \mt{of} \; \tau \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to \tau \to x \; \overline{y}}{
adamc@535 1072 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535 1073 }$$
adamc@535 1074
adamc@537 1075 \subsection{Signature Item Typing}
adamc@537 1076
adamc@537 1077 We appeal to a signature item analogue of the $\mathcal O$ function from the last subsection.
adamc@537 1078
adam@1797 1079 This is the first judgment where we deal with constructor classes, for the $\mt{class}$ forms. We will omit their special handling in this formal specification. Section \ref{typeclasses} gives an informal description of how constructor classes influence type inference.
adam@1797 1080
adamc@537 1081 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@537 1082 \quad \infer{\Gamma \vdash s, \overline{s} \leadsto \Gamma''}{
adamc@537 1083 \Gamma \vdash s \leadsto \Gamma'
adamc@537 1084 & \Gamma' \vdash \overline{s} \leadsto \Gamma''
adamc@537 1085 }$$
adamc@537 1086
adamc@537 1087 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}
adamc@537 1088 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@537 1089 \Gamma \vdash c :: \kappa
adamc@537 1090 }
adamc@537 1091 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@537 1092 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@537 1093 }$$
adamc@537 1094
adamc@537 1095 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537 1096 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1097 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1098 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@537 1099 }$$
adamc@537 1100
adamc@537 1101 $$\infer{\Gamma \vdash \mt{val} \; x : \tau \leadsto \Gamma, x : \tau}{
adamc@537 1102 \Gamma \vdash \tau :: \mt{Type}
adamc@537 1103 }$$
adamc@537 1104
adamc@537 1105 $$\infer{\Gamma \vdash \mt{structure} \; X : S \leadsto \Gamma, X : S}{
adamc@537 1106 \Gamma \vdash S
adamc@537 1107 }
adamc@537 1108 \quad \infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@537 1109 \Gamma \vdash S
adamc@537 1110 }$$
adamc@537 1111
adamc@537 1112 $$\infer{\Gamma \vdash \mt{include} \; S \leadsto \Gamma, \mathcal O(\overline{s})}{
adamc@537 1113 \Gamma \vdash S
adamc@537 1114 & \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1115 }$$
adamc@537 1116
adamc@537 1117 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma, c_1 \sim c_2}{
adamc@537 1118 \Gamma \vdash c_1 :: \{\kappa\}
adamc@537 1119 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@537 1120 }$$
adamc@537 1121
adamc@784 1122 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784 1123 \Gamma \vdash c :: \kappa
adamc@537 1124 }
adamc@784 1125 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}$$
adamc@537 1126
adamc@536 1127 \subsection{Signature Compatibility}
adamc@536 1128
adam@1797 1129 To simplify the judgments in this section, we assume that all signatures are alpha-varied as necessary to avoid including multiple bindings for the same identifier. This is in addition to the usual alpha-variation of locally bound variables.
adamc@537 1130
adamc@537 1131 We rely on a judgment $\Gamma \vdash \overline{s} \leq s'$, which expresses the occurrence in signature items $\overline{s}$ of an item compatible with $s'$. We also use a judgment $\Gamma \vdash \overline{dc} \leq \overline{dc}$, which expresses compatibility of datatype definitions.
adamc@537 1132
adamc@536 1133 $$\infer{\Gamma \vdash S \equiv S}{}
adamc@536 1134 \quad \infer{\Gamma \vdash S_1 \equiv S_2}{
adamc@536 1135 \Gamma \vdash S_2 \equiv S_1
adamc@536 1136 }
adamc@536 1137 \quad \infer{\Gamma \vdash X \equiv S}{
adamc@536 1138 X = S \in \Gamma
adamc@536 1139 }
adamc@536 1140 \quad \infer{\Gamma \vdash M.X \equiv S}{
adamc@537 1141 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1142 & \mt{proj}(M, \overline{s}, \mt{signature} \; X) = S
adamc@536 1143 }$$
adamc@536 1144
adamc@536 1145 $$\infer{\Gamma \vdash S \; \mt{where} \; \mt{con} \; x = c \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa = c \; \overline{s_2} \; \mt{end}}{
adamc@536 1146 \Gamma \vdash S \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa \; \overline{s_2} \; \mt{end}
adamc@536 1147 & \Gamma \vdash c :: \kappa
adamc@537 1148 }
adamc@537 1149 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s^1} \; \mt{include} \; S \; \overline{s^2} \; \mt{end} \equiv \mt{sig} \; \overline{s^1} \; \overline{s} \; \overline{s^2} \; \mt{end}}{
adamc@537 1150 \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@536 1151 }$$
adamc@536 1152
adamc@536 1153 $$\infer{\Gamma \vdash S_1 \leq S_2}{
adamc@536 1154 \Gamma \vdash S_1 \equiv S_2
adamc@536 1155 }
adamc@536 1156 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \mt{end}}{}
adamc@537 1157 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; s' \; \overline{s'} \; \mt{end}}{
adamc@537 1158 \Gamma \vdash \overline{s} \leq s'
adamc@537 1159 & \Gamma \vdash s' \leadsto \Gamma'
adamc@537 1160 & \Gamma' \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \overline{s'} \; \mt{end}
adamc@537 1161 }$$
adamc@537 1162
adamc@537 1163 $$\infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537 1164 \Gamma \vdash s \leq s'
adamc@537 1165 }
adamc@537 1166 \quad \infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537 1167 \Gamma \vdash s \leadsto \Gamma'
adamc@537 1168 & \Gamma' \vdash \overline{s} \leq s'
adamc@536 1169 }$$
adamc@536 1170
adamc@536 1171 $$\infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 \leq \mt{functor} (X : S'_1) : S'_2}{
adamc@536 1172 \Gamma \vdash S'_1 \leq S_1
adamc@536 1173 & \Gamma, X : S'_1 \vdash S_2 \leq S'_2
adamc@536 1174 }$$
adamc@536 1175
adamc@537 1176 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@537 1177 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}
adamc@558 1178 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type}}{}$$
adamc@537 1179
adamc@537 1180 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(y)} \to \mt{Type}}{
adamc@537 1181 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1182 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1183 }$$
adamc@537 1184
adamc@784 1185 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@784 1186 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}$$
adamc@537 1187
adamc@537 1188 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \mt{\kappa} = c_2}{
adamc@537 1189 \Gamma \vdash c_1 \equiv c_2
adamc@537 1190 }
adamc@784 1191 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \kappa = c_2}{
adamc@537 1192 \Gamma \vdash c_1 \equiv c_2
adamc@537 1193 }$$
adamc@537 1194
adamc@537 1195 $$\infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537 1196 \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1197 }$$
adamc@537 1198
adamc@537 1199 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537 1200 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1201 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1202 & \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1203 }$$
adamc@537 1204
adamc@537 1205 $$\infer{\Gamma \vdash \cdot \leq \cdot}{}
adamc@537 1206 \quad \infer{\Gamma \vdash X; \overline{dc} \leq X; \overline{dc'}}{
adamc@537 1207 \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1208 }
adamc@537 1209 \quad \infer{\Gamma \vdash X \; \mt{of} \; \tau_1; \overline{dc} \leq X \; \mt{of} \; \tau_2; \overline{dc'}}{
adamc@537 1210 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537 1211 & \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1212 }$$
adamc@537 1213
adamc@537 1214 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x = \mt{datatype} \; M'.z'}{
adamc@537 1215 \Gamma \vdash M.z \equiv M'.z'
adamc@537 1216 }$$
adamc@537 1217
adamc@537 1218 $$\infer{\Gamma \vdash \mt{val} \; x : \tau_1 \leq \mt{val} \; x : \tau_2}{
adamc@537 1219 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537 1220 }
adamc@537 1221 \quad \infer{\Gamma \vdash \mt{structure} \; X : S_1 \leq \mt{structure} \; X : S_2}{
adamc@537 1222 \Gamma \vdash S_1 \leq S_2
adamc@537 1223 }
adamc@537 1224 \quad \infer{\Gamma \vdash \mt{signature} \; X = S_1 \leq \mt{signature} \; X = S_2}{
adamc@537 1225 \Gamma \vdash S_1 \leq S_2
adamc@537 1226 & \Gamma \vdash S_2 \leq S_1
adamc@537 1227 }$$
adamc@537 1228
adamc@537 1229 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leq \mt{constraint} \; c'_1 \sim c'_2}{
adamc@537 1230 \Gamma \vdash c_1 \equiv c'_1
adamc@537 1231 & \Gamma \vdash c_2 \equiv c'_2
adamc@537 1232 }$$
adamc@537 1233
adamc@655 1234 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{class} \; x :: \kappa}{}
adamc@655 1235 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{class} \; x :: \kappa}{}
adamc@655 1236 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{class} \; x :: \kappa = c_2}{
adamc@537 1237 \Gamma \vdash c_1 \equiv c_2
adamc@537 1238 }$$
adamc@537 1239
adam@1797 1240 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leq \mt{class} \; x :: \kappa}{}
adam@1797 1241 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leq \mt{class} \; x :: \kappa}{}
adam@1797 1242 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c_1 \leq \mt{class} \; x :: \kappa = c_2}{
adam@1797 1243 \Gamma \vdash c_1 \equiv c_2
adam@1797 1244 }$$
adam@1797 1245
adamc@538 1246 \subsection{Module Typing}
adamc@538 1247
adamc@538 1248 We use a helper function $\mt{sigOf}$, which converts declarations and sequences of declarations into their principal signature items and sequences of signature items, respectively.
adamc@538 1249
adamc@538 1250 $$\infer{\Gamma \vdash M : S}{
adamc@538 1251 \Gamma \vdash M : S'
adamc@538 1252 & \Gamma \vdash S' \leq S
adamc@538 1253 }
adamc@538 1254 \quad \infer{\Gamma \vdash \mt{struct} \; \overline{d} \; \mt{end} : \mt{sig} \; \mt{sigOf}(\overline{d}) \; \mt{end}}{
adamc@538 1255 \Gamma \vdash \overline{d} \leadsto \Gamma'
adamc@538 1256 }
adamc@538 1257 \quad \infer{\Gamma \vdash X : S}{
adamc@538 1258 X : S \in \Gamma
adamc@538 1259 }$$
adamc@538 1260
adamc@538 1261 $$\infer{\Gamma \vdash M.X : S}{
adamc@538 1262 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@538 1263 & \mt{proj}(M, \overline{s}, \mt{structure} \; X) = S
adamc@538 1264 }$$
adamc@538 1265
adamc@538 1266 $$\infer{\Gamma \vdash M_1(M_2) : [X \mapsto M_2]S_2}{
adamc@538 1267 \Gamma \vdash M_1 : \mt{functor}(X : S_1) : S_2
adamc@538 1268 & \Gamma \vdash M_2 : S_1
adamc@538 1269 }
adamc@538 1270 \quad \infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 = M : \mt{functor} (X : S_1) : S_2}{
adamc@538 1271 \Gamma \vdash S_1
adamc@538 1272 & \Gamma, X : S_1 \vdash S_2
adamc@538 1273 & \Gamma, X : S_1 \vdash M : S_2
adamc@538 1274 }$$
adamc@538 1275
adamc@538 1276 \begin{eqnarray*}
adamc@538 1277 \mt{sigOf}(\cdot) &=& \cdot \\
adamc@538 1278 \mt{sigOf}(s \; \overline{s'}) &=& \mt{sigOf}(s) \; \mt{sigOf}(\overline{s'}) \\
adamc@538 1279 \\
adamc@538 1280 \mt{sigOf}(\mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@538 1281 \mt{sigOf}(\mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \overline{dc} \\
adamc@538 1282 \mt{sigOf}(\mt{datatype} \; x = \mt{datatype} \; M.z) &=& \mt{datatype} \; x = \mt{datatype} \; M.z \\
adamc@538 1283 \mt{sigOf}(\mt{val} \; x : \tau = e) &=& \mt{val} \; x : \tau \\
adamc@538 1284 \mt{sigOf}(\mt{val} \; \mt{rec} \; \overline{x : \tau = e}) &=& \overline{\mt{val} \; x : \tau} \\
adamc@538 1285 \mt{sigOf}(\mt{structure} \; X : S = M) &=& \mt{structure} \; X : S \\
adamc@538 1286 \mt{sigOf}(\mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@538 1287 \mt{sigOf}(\mt{open} \; M) &=& \mt{include} \; S \textrm{ (where $\Gamma \vdash M : S$)} \\
adamc@538 1288 \mt{sigOf}(\mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@538 1289 \mt{sigOf}(\mt{open} \; \mt{constraints} \; M) &=& \cdot \\
adamc@538 1290 \mt{sigOf}(\mt{table} \; x : c) &=& \mt{table} \; x : c \\
adam@1594 1291 \mt{sigOf}(\mt{view} \; x = e) &=& \mt{view} \; x : c \textrm{ (where $\Gamma \vdash e : \mt{Basis}.\mt{sql\_query} \; [] \; [] \; (\mt{map} \; (\lambda \_ \Rightarrow []) \; c') \; c$)} \\
adamc@538 1292 \mt{sigOf}(\mt{sequence} \; x) &=& \mt{sequence} \; x \\
adamc@538 1293 \mt{sigOf}(\mt{cookie} \; x : \tau) &=& \mt{cookie} \; x : \tau \\
adam@1797 1294 \mt{sigOf}(\mt{style} \; x) &=& \mt{style} \; x
adamc@538 1295 \end{eqnarray*}
adamc@539 1296 \begin{eqnarray*}
adamc@539 1297 \mt{selfify}(M, \cdot) &=& \cdot \\
adamc@558 1298 \mt{selfify}(M, s \; \overline{s'}) &=& \mt{selfify}(M, s) \; \mt{selfify}(M, \overline{s'}) \\
adamc@539 1299 \\
adamc@539 1300 \mt{selfify}(M, \mt{con} \; x :: \kappa) &=& \mt{con} \; x :: \kappa = M.x \\
adamc@539 1301 \mt{selfify}(M, \mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@539 1302 \mt{selfify}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \mt{datatype} \; M.x \\
adamc@539 1303 \mt{selfify}(M, \mt{datatype} \; x = \mt{datatype} \; M'.z) &=& \mt{datatype} \; x = \mt{datatype} \; M'.z \\
adamc@539 1304 \mt{selfify}(M, \mt{val} \; x : \tau) &=& \mt{val} \; x : \tau \\
adamc@539 1305 \mt{selfify}(M, \mt{structure} \; X : S) &=& \mt{structure} \; X : \mt{selfify}(M.X, \overline{s}) \textrm{ (where $\Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}$)} \\
adamc@539 1306 \mt{selfify}(M, \mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@539 1307 \mt{selfify}(M, \mt{include} \; S) &=& \mt{include} \; S \\
adamc@539 1308 \mt{selfify}(M, \mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@655 1309 \mt{selfify}(M, \mt{class} \; x :: \kappa) &=& \mt{class} \; x :: \kappa = M.x \\
adamc@655 1310 \mt{selfify}(M, \mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@539 1311 \end{eqnarray*}
adamc@539 1312
adamc@540 1313 \subsection{Module Projection}
adamc@540 1314
adamc@540 1315 \begin{eqnarray*}
adamc@540 1316 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \\
adamc@540 1317 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa, c) \\
adamc@540 1318 \mt{proj}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc} \; \overline{s}, \mt{con} \; x) &=& \mt{Type}^{\mt{len}(\overline{y})} \to \mt{Type} \\
adamc@540 1319 \mt{proj}(M, \mt{datatype} \; x = \mt{datatype} \; M'.z \; \overline{s}, \mt{con} \; x) &=& (\mt{Type}^{\mt{len}(\overline{y})} \to \mt{Type}, M'.z) \textrm{ (where $\Gamma \vdash M' : \mt{sig} \; \overline{s'} \; \mt{end}$} \\
adamc@540 1320 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})$)} \\
adamc@655 1321 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \to \mt{Type} \\
adamc@655 1322 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa \to \mt{Type}, c) \\
adamc@540 1323 \\
adamc@540 1324 \mt{proj}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc} \; \overline{s}, \mt{datatype} \; x) &=& (\overline{y}, \overline{dc}) \\
adamc@540 1325 \mt{proj}(M, \mt{datatype} \; x = \mt{datatype} \; M'.z \; \overline{s}, \mt{con} \; x) &=& \mt{proj}(M', \overline{s'}, \mt{datatype} \; z) \textrm{ (where $\Gamma \vdash M' : \mt{sig} \; \overline{s'} \; \mt{end}$)} \\
adamc@540 1326 \\
adamc@540 1327 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, \mt{val} \; x) &=& \tau \\
adamc@540 1328 \mt{proj}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc} \; \overline{s}, \mt{val} \; X) &=& \overline{y ::: \mt{Type}} \to M.x \; \overline y \textrm{ (where $X \in \overline{dc}$)} \\
adamc@540 1329 \mt{proj}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc} \; \overline{s}, \mt{val} \; X) &=& \overline{y ::: \mt{Type}} \to \tau \to M.x \; \overline y \textrm{ (where $X \; \mt{of} \; \tau \in \overline{dc}$)} \\
adamc@540 1330 \mt{proj}(M, \mt{datatype} \; x = \mt{datatype} \; M'.z, \mt{val} \; X) &=& \overline{y ::: \mt{Type}} \to M.x \; \overline y \textrm{ (where $\Gamma \vdash M' : \mt{sig} \; \overline{s'} \; \mt{end}$} \\
adamc@540 1331 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \in \overline{dc}$)} \\
adamc@540 1332 \mt{proj}(M, \mt{datatype} \; x = \mt{datatype} \; M'.z, \mt{val} \; X) &=& \overline{y ::: \mt{Type}} \to \tau \to M.x \; \overline y \textrm{ (where $\Gamma \vdash M' : \mt{sig} \; \overline{s'} \; \mt{end}$} \\
adamc@558 1333 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \; \mt{of} \; \tau \in \overline{dc}$)} \\
adamc@540 1334 \\
adamc@540 1335 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, \mt{structure} \; X) &=& S \\
adamc@540 1336 \\
adamc@540 1337 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, \mt{signature} \; X) &=& S \\
adamc@540 1338 \\
adamc@540 1339 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1340 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1341 \mt{proj}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc} \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1342 \mt{proj}(M, \mt{datatype} \; x = \mt{datatype} \; M'.z \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1343 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@540 1344 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1345 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1346 \mt{proj}(M, \mt{include} \; S \; \overline{s}, V) &=& \mt{proj}(M, \overline{s'} \; \overline{s}, V) \textrm{ (where $\Gamma \vdash S \equiv \mt{sig} \; \overline{s'} \; \mt{end}$)} \\
adamc@540 1347 \mt{proj}(M, \mt{constraint} \; c_1 \sim c_2 \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@655 1348 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@655 1349 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1350 \end{eqnarray*}
adamc@540 1351
adamc@541 1352
adamc@541 1353 \section{Type Inference}
adamc@541 1354
adamc@541 1355 The Ur/Web compiler uses \emph{heuristic type inference}, with no claims of completeness with respect to the declarative specification of the last section. The rules in use seem to work well in practice. This section summarizes those rules, to help Ur programmers predict what will work and what won't.
adamc@541 1356
adamc@541 1357 \subsection{Basic Unification}
adamc@541 1358
adamc@560 1359 Type-checkers for languages based on the Hindley-Milner type discipline, like ML and Haskell, take advantage of \emph{principal typing} properties, making complete type inference relatively straightforward. Inference algorithms are traditionally implemented using type unification variables, at various points asserting equalities between types, in the process discovering the values of type variables. The Ur/Web compiler uses the same basic strategy, but the complexity of the type system rules out easy completeness.
adamc@541 1360
adamc@656 1361 Type-checking can require evaluating recursive functional programs, thanks to the type-level $\mt{map}$ operator. When a unification variable appears in such a type, the next step of computation can be undetermined. The value of that variable might be determined later, but this would be ``too late'' for the unification problems generated at the first occurrence. This is the essential source of incompleteness.
adamc@541 1362
adamc@541 1363 Nonetheless, the unification engine tends to do reasonably well. Unlike in ML, polymorphism is never inferred in definitions; it must be indicated explicitly by writing out constructor-level parameters. By writing these and other annotations, the programmer can generally get the type inference engine to do most of the type reconstruction work.
adamc@541 1364
adamc@541 1365 \subsection{Unifying Record Types}
adamc@541 1366
adamc@570 1367 The type inference engine tries to take advantage of the algebraic rules governing type-level records, as shown in Section \ref{definitional}. When two constructors of record kind are unified, they are reduced to normal forms, with like terms crossed off from each normal form until, hopefully, nothing remains. This cannot be complete, with the inclusion of unification variables. The type-checker can help you understand what goes wrong when the process fails, as it outputs the unmatched remainders of the two normal forms.
adamc@541 1368
adamc@656 1369 \subsection{\label{typeclasses}Constructor Classes}
adamc@541 1370
adamc@784 1371 Ur includes a constructor class facility inspired by Haskell's. The current version is experimental, with very general Prolog-like facilities that can lead to compile-time non-termination.
adamc@541 1372
adam@1797 1373 Constructor classes are integrated with the module system. A constructor class of kind $\kappa$ is just a constructor of kind $\kappa$. By marking such a constructor $c$ as a constructor class, the programmer instructs the type inference engine to, in each scope, record all values of types $c \; c_1 \; \ldots \; c_n$ as \emph{instances}. Any function argument whose type is of such a form is treated as implicit, to be determined by examining the current instance database. Any suitably kinded constructor within a module may be exposed as a constructor class from outside the module, simply by using a $\mt{class}$ signature item instead of a $\mt{con}$ signature item in the module's signature.
adam@1797 1374
adam@1797 1375 The ``dictionary encoding'' often used in Haskell implementations is made explicit in Ur. Constructor class instances are just properly typed values, and they can also be considered as ``proofs'' of membership in the class. In some cases, it is useful to pass these proofs around explicitly. An underscore written where a proof is expected will also be inferred, if possible, from the current instance database.
adam@1797 1376
adam@1797 1377 Just as for constructors, constructors classes may be exported from modules, and they may be exported as concrete or abstract. Concrete constructor classes have their ``real'' definitions exposed, so that client code may add new instances freely. Automatic inference of concrete class instances will not generally work, so abstract classes are almost always the right choice. They are useful as ``predicates'' that can be used to enforce invariants, as we will see in some definitions of SQL syntax in the Ur/Web standard library. Free extension of a concrete class is easily supported by exporting a constructor function from a module, since the class implementation will be concrete within the module.
adamc@541 1378
adamc@541 1379 \subsection{Reverse-Engineering Record Types}
adamc@541 1380
adamc@656 1381 It's useful to write Ur functions and functors that take record constructors as inputs, but these constructors can grow quite long, even though their values are often implied by other arguments. The compiler uses a simple heuristic to infer the values of unification variables that are mapped over, yielding known results. If the result is empty, we're done; if it's not empty, we replace a single unification variable with a new constructor formed from three new unification variables, as in $[\alpha = \beta] \rc \gamma$. This process can often be repeated to determine a unification variable fully.
adamc@541 1382
adamc@541 1383 \subsection{Implicit Arguments in Functor Applications}
adamc@541 1384
adamc@656 1385 Constructor, constraint, and constructor class witness members of structures may be omitted, when those structures are used in contexts where their assigned signatures imply how to fill in those missing members. This feature combines well with reverse-engineering to allow for uses of complicated meta-programming functors with little more code than would be necessary to invoke an untyped, ad-hoc code generator.
adamc@541 1386
adamc@541 1387
adamc@542 1388 \section{The Ur Standard Library}
adamc@542 1389
adamc@542 1390 The built-in parts of the Ur/Web standard library are described by the signature in \texttt{lib/basis.urs} in the distribution. A module $\mt{Basis}$ ascribing to that signature is available in the initial environment, and every program is implicitly prefixed by $\mt{open} \; \mt{Basis}$.
adamc@542 1391
adamc@542 1392 Additionally, other common functions that are definable within Ur are included in \texttt{lib/top.urs} and \texttt{lib/top.ur}. This $\mt{Top}$ module is also opened implicitly.
adamc@542 1393
adamc@542 1394 The idea behind Ur is to serve as the ideal host for embedded domain-specific languages. For now, however, the ``generic'' functionality is intermixed with Ur/Web-specific functionality, including in these two library modules. We hope that these generic library components have types that speak for themselves. The next section introduces the Ur/Web-specific elements. Here, we only give the type declarations from the beginning of $\mt{Basis}$.
adamc@542 1395 $$\begin{array}{l}
adamc@542 1396 \mt{type} \; \mt{int} \\
adamc@542 1397 \mt{type} \; \mt{float} \\
adamc@873 1398 \mt{type} \; \mt{char} \\
adamc@542 1399 \mt{type} \; \mt{string} \\
adamc@542 1400 \mt{type} \; \mt{time} \\
adamc@785 1401 \mt{type} \; \mt{blob} \\
adamc@542 1402 \\
adamc@542 1403 \mt{type} \; \mt{unit} = \{\} \\
adamc@542 1404 \\
adamc@542 1405 \mt{datatype} \; \mt{bool} = \mt{False} \mid \mt{True} \\
adamc@542 1406 \\
adamc@785 1407 \mt{datatype} \; \mt{option} \; \mt{t} = \mt{None} \mid \mt{Some} \; \mt{of} \; \mt{t} \\
adamc@785 1408 \\
adamc@785 1409 \mt{datatype} \; \mt{list} \; \mt{t} = \mt{Nil} \mid \mt{Cons} \; \mt{of} \; \mt{t} \times \mt{list} \; \mt{t}
adamc@542 1410 \end{array}$$
adamc@542 1411
adamc@1123 1412 The only unusual element of this list is the $\mt{blob}$ type, which stands for binary sequences. Simple blobs can be created from strings via $\mt{Basis.textBlob}$. Blobs will also be generated from HTTP file uploads.
adamc@785 1413
adam@1297 1414 Ur also supports \emph{polymorphic variants}, a dual to extensible records that has been popularized by OCaml. A type $\mt{variant} \; r$ represents an $n$-ary sum type, with one constructor for each field of record $r$. Each constructor $c$ takes an argument of type $r.c$; the type $\{\}$ can be used to ``simulate'' a nullary constructor. The \cd{make} function builds a variant value, while \cd{match} implements pattern-matching, with match cases represented as records of functions.
adam@1297 1415 $$\begin{array}{l}
adam@1297 1416 \mt{con} \; \mt{variant} :: \{\mt{Type}\} \to \mt{Type} \\
adam@1297 1417 \mt{val} \; \mt{make} : \mt{nm} :: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{ts} ::: \{\mt{Type}\} \to [[\mt{nm}] \sim \mt{ts}] \Rightarrow \mt{t} \to \mt{variant} \; ([\mt{nm} = \mt{t}] \rc \mt{ts}) \\
adam@1297 1418 \mt{val} \; \mt{match} : \mt{ts} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{variant} \; \mt{ts} \to \$(\mt{map} \; (\lambda \mt{t'} \Rightarrow \mt{t'} \to \mt{t}) \; \mt{ts}) \to \mt{t}
adam@1297 1419 \end{array}$$
adam@1297 1420
adamc@657 1421 Another important generic Ur element comes at the beginning of \texttt{top.urs}.
adamc@657 1422
adamc@657 1423 $$\begin{array}{l}
adamc@657 1424 \mt{con} \; \mt{folder} :: \mt{K} \longrightarrow \{\mt{K}\} \to \mt{Type} \\
adamc@657 1425 \\
adamc@657 1426 \mt{val} \; \mt{fold} : \mt{K} \longrightarrow \mt{tf} :: (\{\mt{K}\} \to \mt{Type}) \\
adamc@657 1427 \hspace{.1in} \to (\mt{nm} :: \mt{Name} \to \mt{v} :: \mt{K} \to \mt{r} :: \{\mt{K}\} \to [[\mt{nm}] \sim \mt{r}] \Rightarrow \\
adamc@657 1428 \hspace{.2in} \mt{tf} \; \mt{r} \to \mt{tf} \; ([\mt{nm} = \mt{v}] \rc \mt{r})) \\
adamc@657 1429 \hspace{.1in} \to \mt{tf} \; [] \\
adam@2155 1430 \hspace{.1in} \to \mt{r} ::: \{\mt{K}\} \to \mt{folder} \; \mt{r} \to \mt{tf} \; \mt{r}
adamc@657 1431 \end{array}$$
adamc@657 1432
adamc@657 1433 For a type-level record $\mt{r}$, a $\mt{folder} \; \mt{r}$ encodes a permutation of $\mt{r}$'s elements. The $\mt{fold}$ function can be called on a $\mt{folder}$ to iterate over the elements of $\mt{r}$ in that order. $\mt{fold}$ is parameterized on a type-level function to be used to calculate the type of each intermediate result of folding. After processing a subset $\mt{r'}$ of $\mt{r}$'s entries, the type of the accumulator should be $\mt{tf} \; \mt{r'}$. The next two expression arguments to $\mt{fold}$ are the usual step function and initial accumulator, familiar from fold functions over lists. The final two arguments are the record to fold over and a $\mt{folder}$ for it.
adamc@657 1434
adamc@664 1435 The Ur compiler treats $\mt{folder}$ like a constructor class, using built-in rules to infer $\mt{folder}$s for records with known structure. The order in which field names are mentioned in source code is used as a hint about the permutation that the programmer would like.
adamc@657 1436
adamc@542 1437
adamc@542 1438 \section{The Ur/Web Standard Library}
adamc@542 1439
adam@1400 1440 Some operations are only allowed in server-side code or only in client-side code. The type system does not enforce such restrictions, but the compiler enforces them in the process of whole-program compilation. In the discussion below, we note when a set of operations has a location restriction.
adam@1400 1441
adamc@658 1442 \subsection{Monads}
adamc@658 1443
adamc@658 1444 The Ur Basis defines the monad constructor class from Haskell.
adamc@658 1445
adamc@658 1446 $$\begin{array}{l}
adamc@658 1447 \mt{class} \; \mt{monad} :: \mt{Type} \to \mt{Type} \\
adamc@658 1448 \mt{val} \; \mt{return} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t} ::: \mt{Type} \\
adamc@658 1449 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658 1450 \hspace{.1in} \to \mt{t} \to \mt{m} \; \mt{t} \\
adamc@658 1451 \mt{val} \; \mt{bind} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t1} ::: \mt{Type} \to \mt{t2} ::: \mt{Type} \\
adamc@658 1452 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658 1453 \hspace{.1in} \to \mt{m} \; \mt{t1} \to (\mt{t1} \to \mt{m} \; \mt{t2}) \\
adam@1544 1454 \hspace{.1in} \to \mt{m} \; \mt{t2} \\
adam@1544 1455 \mt{val} \; \mt{mkMonad} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \\
adam@1544 1456 \hspace{.1in} \to \{\mt{Return} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{m} \; \mt{t}, \\
adam@1544 1457 \hspace{.3in} \mt{Bind} : \mt{t1} ::: \mt{Type} \to \mt{t2} ::: \mt{Type} \to \mt{m} \; \mt{t1} \to (\mt{t1} \to \mt{m} \; \mt{t2}) \to \mt{m} \; \mt{t2}\} \\
adam@1544 1458 \hspace{.1in} \to \mt{monad} \; \mt{m}
adamc@658 1459 \end{array}$$
adamc@658 1460
adam@1687 1461 The Ur/Web compiler provides syntactic sugar for monads, similar to Haskell's \cd{do} notation. An expression $x \leftarrow e_1; e_2$ is desugared to $\mt{bind} \; e_1 \; (\lambda x \Rightarrow e_2)$, and an expression $e_1; e_2$ is desugared to $\mt{bind} \; e_1 \; (\lambda () \Rightarrow e_2)$. Note a difference from Haskell: as the $e_1; e_2$ case desugaring involves a function with $()$ as its formal argument, the type of $e_1$ must be of the form $m \; \{\}$, rather than some arbitrary $m \; t$.
adam@1548 1462
adam@2009 1463 The syntactic sugar also allows $p \leftarrow e_1; e_2$ for $p$ a pattern. The pattern should be guaranteed to match any value of the corresponding type, or there will be a compile-time error.
adam@2009 1464
adamc@542 1465 \subsection{Transactions}
adamc@542 1466
adamc@542 1467 Ur is a pure language; we use Haskell's trick to support controlled side effects. The standard library defines a monad $\mt{transaction}$, meant to stand for actions that may be undone cleanly. By design, no other kinds of actions are supported.
adamc@542 1468 $$\begin{array}{l}
adamc@542 1469 \mt{con} \; \mt{transaction} :: \mt{Type} \to \mt{Type} \\
adamc@658 1470 \mt{val} \; \mt{transaction\_monad} : \mt{monad} \; \mt{transaction}
adamc@542 1471 \end{array}$$
adamc@542 1472
adamc@1123 1473 For debugging purposes, a transactional function is provided for outputting a string on the server process' \texttt{stderr}.
adamc@1123 1474 $$\begin{array}{l}
adamc@1123 1475 \mt{val} \; \mt{debug} : \mt{string} \to \mt{transaction} \; \mt{unit}
adamc@1123 1476 \end{array}$$
adamc@1123 1477
adamc@542 1478 \subsection{HTTP}
adamc@542 1479
adam@1797 1480 There are transactions for reading an HTTP header by name and for getting and setting strongly typed cookies. Cookies may only be created by the $\mt{cookie}$ declaration form, ensuring that they be named consistently based on module structure. For now, cookie operations are server-side only.
adamc@542 1481 $$\begin{array}{l}
adamc@786 1482 \mt{con} \; \mt{http\_cookie} :: \mt{Type} \to \mt{Type} \\
adamc@786 1483 \mt{val} \; \mt{getCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; (\mt{option} \; \mt{t}) \\
adamc@1050 1484 \mt{val} \; \mt{setCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \{\mt{Value} : \mt{t}, \mt{Expires} : \mt{option} \; \mt{time}, \mt{Secure} : \mt{bool}\} \to \mt{transaction} \; \mt{unit} \\
adamc@1050 1485 \mt{val} \; \mt{clearCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; \mt{unit}
adamc@786 1486 \end{array}$$
adamc@786 1487
adamc@786 1488 There are also an abstract $\mt{url}$ type and functions for converting to it, based on the policy defined by \texttt{[allow|deny] url} directives in the project file.
adamc@786 1489 $$\begin{array}{l}
adamc@786 1490 \mt{type} \; \mt{url} \\
adamc@786 1491 \mt{val} \; \mt{bless} : \mt{string} \to \mt{url} \\
adamc@786 1492 \mt{val} \; \mt{checkUrl} : \mt{string} \to \mt{option} \; \mt{url}
adamc@786 1493 \end{array}$$
adamc@786 1494 $\mt{bless}$ raises a runtime error if the string passed to it fails the URL policy.
adamc@786 1495
adam@1400 1496 It is possible to grab the current page's URL or to build a URL for an arbitrary transaction that would also be an acceptable value of a \texttt{link} attribute of the \texttt{a} tag. These are server-side operations.
adamc@1085 1497 $$\begin{array}{l}
adamc@1085 1498 \mt{val} \; \mt{currentUrl} : \mt{transaction} \; \mt{url} \\
adamc@1085 1499 \mt{val} \; \mt{url} : \mt{transaction} \; \mt{page} \to \mt{url}
adamc@1085 1500 \end{array}$$
adamc@1085 1501
adamc@1085 1502 Page generation may be interrupted at any time with a request to redirect to a particular URL instead.
adamc@1085 1503 $$\begin{array}{l}
adamc@1085 1504 \mt{val} \; \mt{redirect} : \mt{t} ::: \mt{Type} \to \mt{url} \to \mt{transaction} \; \mt{t}
adamc@1085 1505 \end{array}$$
adamc@1085 1506
adam@1400 1507 It's possible for pages to return files of arbitrary MIME types. A file can be input from the user using this data type, along with the $\mt{upload}$ form tag. These functions and those described in the following paragraph are server-side.
adamc@786 1508 $$\begin{array}{l}
adamc@786 1509 \mt{type} \; \mt{file} \\
adamc@786 1510 \mt{val} \; \mt{fileName} : \mt{file} \to \mt{option} \; \mt{string} \\
adamc@786 1511 \mt{val} \; \mt{fileMimeType} : \mt{file} \to \mt{string} \\
adamc@786 1512 \mt{val} \; \mt{fileData} : \mt{file} \to \mt{blob}
adamc@786 1513 \end{array}$$
adamc@786 1514
adam@1799 1515 It is also possible to get HTTP request headers and environment variables, and set HTTP response headers, using abstract types similar to the one for URLs.
adam@1465 1516
adam@1465 1517 $$\begin{array}{l}
adam@1465 1518 \mt{type} \; \mt{requestHeader} \\
adam@1465 1519 \mt{val} \; \mt{blessRequestHeader} : \mt{string} \to \mt{requestHeader} \\
adam@1465 1520 \mt{val} \; \mt{checkRequestHeader} : \mt{string} \to \mt{option} \; \mt{requestHeader} \\
adam@1465 1521 \mt{val} \; \mt{getHeader} : \mt{requestHeader} \to \mt{transaction} \; (\mt{option} \; \mt{string}) \\
adam@1465 1522 \\
adam@1799 1523 \mt{type} \; \mt{envVar} \\
adam@1799 1524 \mt{val} \; \mt{blessEnvVar} : \mt{string} \to \mt{envVar} \\
adam@1799 1525 \mt{val} \; \mt{checkEnvVar} : \mt{string} \to \mt{option} \; \mt{envVar} \\
adam@1799 1526 \mt{val} \; \mt{getenv} : \mt{envVar} \to \mt{transaction} \; (\mt{option} \; \mt{string}) \\
adam@1799 1527 \\
adam@1465 1528 \mt{type} \; \mt{responseHeader} \\
adam@1465 1529 \mt{val} \; \mt{blessResponseHeader} : \mt{string} \to \mt{responseHeader} \\
adam@1465 1530 \mt{val} \; \mt{checkResponseHeader} : \mt{string} \to \mt{option} \; \mt{responseHeader} \\
adam@1465 1531 \mt{val} \; \mt{setHeader} : \mt{responseHeader} \to \mt{string} \to \mt{transaction} \; \mt{unit}
adam@1465 1532 \end{array}$$
adam@1465 1533
adamc@786 1534 A blob can be extracted from a file and returned as the page result. There are bless and check functions for MIME types analogous to those for URLs.
adamc@786 1535 $$\begin{array}{l}
adamc@786 1536 \mt{type} \; \mt{mimeType} \\
adamc@786 1537 \mt{val} \; \mt{blessMime} : \mt{string} \to \mt{mimeType} \\
adamc@786 1538 \mt{val} \; \mt{checkMime} : \mt{string} \to \mt{option} \; \mt{mimeType} \\
adamc@786 1539 \mt{val} \; \mt{returnBlob} : \mt{t} ::: \mt{Type} \to \mt{blob} \to \mt{mimeType} \to \mt{transaction} \; \mt{t}
adamc@542 1540 \end{array}$$
adamc@542 1541
adamc@543 1542 \subsection{SQL}
adamc@543 1543
adam@1400 1544 Everything about SQL database access is restricted to server-side code.
adam@1400 1545
adamc@543 1546 The fundamental unit of interest in the embedding of SQL is tables, described by a type family and creatable only via the $\mt{table}$ declaration form.
adamc@543 1547 $$\begin{array}{l}
adamc@785 1548 \mt{con} \; \mt{sql\_table} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785 1549 \end{array}$$
adamc@785 1550 The first argument to this constructor gives the names and types of a table's columns, and the second argument gives the set of valid keys. Keys are the only subsets of the columns that may be referenced as foreign keys. Each key has a name.
adamc@785 1551
adamc@785 1552 We also have the simpler type family of SQL views, which have no keys.
adamc@785 1553 $$\begin{array}{l}
adamc@785 1554 \mt{con} \; \mt{sql\_view} :: \{\mt{Type}\} \to \mt{Type}
adamc@543 1555 \end{array}$$
adamc@543 1556
adamc@785 1557 A multi-parameter type class is used to allow tables and views to be used interchangeably, with a way of extracting the set of columns from each.
adamc@785 1558 $$\begin{array}{l}
adamc@785 1559 \mt{class} \; \mt{fieldsOf} :: \mt{Type} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1560 \mt{val} \; \mt{fieldsOf\_table} : \mt{fs} ::: \{\mt{Type}\} \to \mt{keys} ::: \{\{\mt{Unit}\}\} \to \mt{fieldsOf} \; (\mt{sql\_table} \; \mt{fs} \; \mt{keys}) \; \mt{fs} \\
adamc@785 1561 \mt{val} \; \mt{fieldsOf\_view} : \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; (\mt{sql\_view} \; \mt{fs}) \; \mt{fs}
adamc@785 1562 \end{array}$$
adamc@785 1563
adamc@785 1564 \subsubsection{Table Constraints}
adamc@785 1565
adamc@785 1566 Tables may be declared with constraints, such that database modifications that violate the constraints are blocked. A table may have at most one \texttt{PRIMARY KEY} constraint, which gives the subset of columns that will most often be used to look up individual rows in the table.
adamc@785 1567
adamc@785 1568 $$\begin{array}{l}
adamc@785 1569 \mt{con} \; \mt{primary\_key} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type} \\
adamc@785 1570 \mt{val} \; \mt{no\_primary\_key} : \mt{fs} ::: \{\mt{Type}\} \to \mt{primary\_key} \; \mt{fs} \; [] \\
adamc@785 1571 \mt{val} \; \mt{primary\_key} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{key1} :: \mt{Name} \to \mt{keys} :: \{\mt{Type}\} \\
adamc@785 1572 \hspace{.1in} \to [[\mt{key1}] \sim \mt{keys}] \Rightarrow [[\mt{key1} = \mt{t}] \rc \mt{keys} \sim \mt{rest}] \\
adamc@785 1573 \hspace{.1in} \Rightarrow \$([\mt{key1} = \mt{sql\_injectable\_prim} \; \mt{t}] \rc \mt{map} \; \mt{sql\_injectable\_prim} \; \mt{keys}) \\
adamc@785 1574 \hspace{.1in} \to \mt{primary\_key} \; ([\mt{key1} = \mt{t}] \rc \mt{keys} \rc \mt{rest}) \; [\mt{Pkey} = [\mt{key1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{keys}]
adamc@785 1575 \end{array}$$
adamc@785 1576 The type class $\mt{sql\_injectable\_prim}$ characterizes which types are allowed in SQL and are not $\mt{option}$ types. In SQL, a \texttt{PRIMARY KEY} constraint enforces after-the-fact that a column may not contain \texttt{NULL}s, but Ur/Web forces that information to be included in table types from the beginning. Thus, the only effect of this kind of constraint in Ur/Web is to enforce uniqueness of the given key within the table.
adamc@785 1577
adamc@785 1578 A type family stands for sets of named constraints of the remaining varieties.
adamc@785 1579 $$\begin{array}{l}
adamc@785 1580 \mt{con} \; \mt{sql\_constraints} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785 1581 \end{array}$$
adamc@785 1582 The first argument gives the column types of the table being constrained, and the second argument maps constraint names to the keys that they define. Constraints that don't define keys are mapped to ``empty keys.''
adamc@785 1583
adamc@785 1584 There is a type family of individual, unnamed constraints.
adamc@785 1585 $$\begin{array}{l}
adamc@785 1586 \mt{con} \; \mt{sql\_constraint} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \mt{Type}
adamc@785 1587 \end{array}$$
adamc@785 1588 The first argument is the same as above, and the second argument gives the key columns for just this constraint.
adamc@785 1589
adamc@785 1590 We have operations for assembling constraints into constraint sets.
adamc@785 1591 $$\begin{array}{l}
adamc@785 1592 \mt{val} \; \mt{no\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_constraints} \; \mt{fs} \; [] \\
adamc@785 1593 \mt{val} \; \mt{one\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{unique} ::: \{\mt{Unit}\} \to \mt{name} :: \mt{Name} \\
adamc@785 1594 \hspace{.1in} \to \mt{sql\_constraint} \; \mt{fs} \; \mt{unique} \to \mt{sql\_constraints} \; \mt{fs} \; [\mt{name} = \mt{unique}] \\
adamc@785 1595 \mt{val} \; \mt{join\_constraints} : \mt{fs} ::: \{\mt{Type}\} \to \mt{uniques1} ::: \{\{\mt{Unit}\}\} \to \mt{uniques2} ::: \{\{\mt{Unit}\}\} \to [\mt{uniques1} \sim \mt{uniques2}] \\
adamc@785 1596 \hspace{.1in} \Rightarrow \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques1} \to \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques2} \to \mt{sql\_constraints} \; \mt{fs} \; (\mt{uniques1} \rc \mt{uniques2})
adamc@785 1597 \end{array}$$
adamc@785 1598
adamc@785 1599 A \texttt{UNIQUE} constraint forces a set of columns to be a key, which means that no combination of column values may occur more than once in the table. The $\mt{unique1}$ and $\mt{unique}$ arguments are separated out only to ensure that empty \texttt{UNIQUE} constraints are rejected.
adamc@785 1600 $$\begin{array}{l}
adamc@785 1601 \mt{val} \; \mt{unique} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{unique1} :: \mt{Name} \to \mt{unique} :: \{\mt{Type}\} \\
adamc@785 1602 \hspace{.1in} \to [[\mt{unique1}] \sim \mt{unique}] \Rightarrow [[\mt{unique1} = \mt{t}] \rc \mt{unique} \sim \mt{rest}] \\
adamc@785 1603 \hspace{.1in} \Rightarrow \mt{sql\_constraint} \; ([\mt{unique1} = \mt{t}] \rc \mt{unique} \rc \mt{rest}) \; ([\mt{unique1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{unique})
adamc@785 1604 \end{array}$$
adamc@785 1605
adamc@785 1606 A \texttt{FOREIGN KEY} constraint connects a set of local columns to a local or remote key, enforcing that the local columns always reference an existent row of the foreign key's table. A local column of type $\mt{t}$ may be linked to a foreign column of type $\mt{option} \; \mt{t}$, and vice versa. We formalize that notion with a type class.
adamc@785 1607 $$\begin{array}{l}
adamc@785 1608 \mt{class} \; \mt{linkable} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@785 1609 \mt{val} \; \mt{linkable\_same} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; \mt{t} \\
adamc@785 1610 \mt{val} \; \mt{linkable\_from\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; (\mt{option} \; \mt{t}) \; \mt{t} \\
adamc@785 1611 \mt{val} \; \mt{linkable\_to\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@785 1612 \end{array}$$
adamc@785 1613
adamc@785 1614 The $\mt{matching}$ type family uses $\mt{linkable}$ to define when two keys match up type-wise.
adamc@785 1615 $$\begin{array}{l}
adamc@785 1616 \mt{con} \; \mt{matching} :: \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1617 \mt{val} \; \mt{mat\_nil} : \mt{matching} \; [] \; [] \\
adamc@785 1618 \mt{val} \; \mt{mat\_cons} : \mt{t1} ::: \mt{Type} \to \mt{rest1} ::: \{\mt{Type}\} \to \mt{t2} ::: \mt{Type} \to \mt{rest2} ::: \{\mt{Type}\} \to \mt{nm1} :: \mt{Name} \to \mt{nm2} :: \mt{Name} \\
adamc@785 1619 \hspace{.1in} \to [[\mt{nm1}] \sim \mt{rest1}] \Rightarrow [[\mt{nm2}] \sim \mt{rest2}] \Rightarrow \mt{linkable} \; \mt{t1} \; \mt{t2} \to \mt{matching} \; \mt{rest1} \; \mt{rest2} \\
adamc@785 1620 \hspace{.1in} \to \mt{matching} \; ([\mt{nm1} = \mt{t1}] \rc \mt{rest1}) \; ([\mt{nm2} = \mt{t2}] \rc \mt{rest2})
adamc@785 1621 \end{array}$$
adamc@785 1622
adamc@785 1623 SQL provides a number of different propagation modes for \texttt{FOREIGN KEY} constraints, governing what happens when a row containing a still-referenced foreign key value is deleted or modified to have a different key value. The argument of a propagation mode's type gives the local key type.
adamc@785 1624 $$\begin{array}{l}
adamc@785 1625 \mt{con} \; \mt{propagation\_mode} :: \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1626 \mt{val} \; \mt{restrict} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1627 \mt{val} \; \mt{cascade} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1628 \mt{val} \; \mt{no\_action} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1629 \mt{val} \; \mt{set\_null} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; (\mt{map} \; \mt{option} \; \mt{fs})
adamc@785 1630 \end{array}$$
adamc@785 1631
adamc@785 1632 Finally, we put these ingredient together to define the \texttt{FOREIGN KEY} constraint function.
adamc@785 1633 $$\begin{array}{l}
adamc@785 1634 \mt{val} \; \mt{foreign\_key} : \mt{mine1} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{mine} ::: \{\mt{Type}\} \to \mt{munused} ::: \{\mt{Type}\} \to \mt{foreign} ::: \{\mt{Type}\} \\
adamc@785 1635 \hspace{.1in} \to \mt{funused} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{uniques} ::: \{\{\mt{Unit}\}\} \\
adamc@785 1636 \hspace{.1in} \to [[\mt{mine1}] \sim \mt{mine}] \Rightarrow [[\mt{mine1} = \mt{t}] \rc \mt{mine} \sim \mt{munused}] \Rightarrow [\mt{foreign} \sim \mt{funused}] \Rightarrow [[\mt{nm}] \sim \mt{uniques}] \\
adamc@785 1637 \hspace{.1in} \Rightarrow \mt{matching} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}) \; \mt{foreign} \\
adamc@785 1638 \hspace{.1in} \to \mt{sql\_table} \; (\mt{foreign} \rc \mt{funused}) \; ([\mt{nm} = \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{foreign}] \rc \mt{uniques}) \\
adamc@785 1639 \hspace{.1in} \to \{\mt{OnDelete} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}), \\
adamc@785 1640 \hspace{.2in} \mt{OnUpdate} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine})\} \\
adamc@785 1641 \hspace{.1in} \to \mt{sql\_constraint} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine} \rc \mt{munused}) \; []
adamc@785 1642 \end{array}$$
adamc@785 1643
adamc@785 1644 The last kind of constraint is a \texttt{CHECK} constraint, which attaches a boolean invariant over a row's contents. It is defined using the $\mt{sql\_exp}$ type family, which we discuss in more detail below.
adamc@785 1645 $$\begin{array}{l}
adam@1778 1646 \mt{val} \; \mt{check} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; [] \; [] \; \mt{fs} \; \mt{bool} \to \mt{sql\_constraint} \; \mt{fs} \; []
adamc@785 1647 \end{array}$$
adamc@785 1648
adamc@785 1649 Section \ref{tables} shows the expanded syntax of the $\mt{table}$ declaration and signature item that includes constraints. There is no other way to use constraints with SQL in Ur/Web.
adamc@785 1650
adamc@784 1651
adamc@543 1652 \subsubsection{Queries}
adamc@543 1653
adam@1400 1654 A final query is constructed via the $\mt{sql\_query}$ function. Constructor arguments respectively specify the unrestricted free table variables (which will only be available in subqueries), the free table variables that may only be mentioned within arguments to aggregate functions, table fields we select (as records mapping tables to the subsets of their fields that we choose), and the (always named) extra expressions that we select.
adamc@543 1655 $$\begin{array}{l}
adam@1400 1656 \mt{con} \; \mt{sql\_query} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@1193 1657 \mt{val} \; \mt{sql\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400 1658 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1659 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543 1660 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1661 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1193 1662 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adam@1400 1663 \hspace{.1in} \Rightarrow \{\mt{Rows} : \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}, \\
adamc@1193 1664 \hspace{.2in} \mt{OrderBy} : \mt{sql\_order\_by} \; (\mt{free} \rc \mt{tables}) \; \mt{selectedExps}, \\
adamc@543 1665 \hspace{.2in} \mt{Limit} : \mt{sql\_limit}, \\
adamc@543 1666 \hspace{.2in} \mt{Offset} : \mt{sql\_offset}\} \\
adam@1400 1667 \hspace{.1in} \to \mt{sql\_query} \; \mt{free} \; \mt{afree} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1668 \end{array}$$
adamc@543 1669
adamc@545 1670 Queries are used by folding over their results inside transactions.
adamc@545 1671 $$\begin{array}{l}
adam@1400 1672 \mt{val} \; \mt{query} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to [\mt{tables} \sim \mt{exps}] \Rightarrow \mt{state} ::: \mt{Type} \to \mt{sql\_query} \; [] \; [] \; \mt{tables} \; \mt{exps} \\
adamc@658 1673 \hspace{.1in} \to (\$(\mt{exps} \rc \mt{map} \; (\lambda \mt{fields} :: \{\mt{Type}\} \Rightarrow \$\mt{fields}) \; \mt{tables}) \\
adamc@545 1674 \hspace{.2in} \to \mt{state} \to \mt{transaction} \; \mt{state}) \\
adamc@545 1675 \hspace{.1in} \to \mt{state} \to \mt{transaction} \; \mt{state}
adamc@545 1676 \end{array}$$
adamc@545 1677
adam@1400 1678 Most of the complexity of the query encoding is in the type $\mt{sql\_query1}$, which includes simple queries and derived queries based on relational operators. Constructor arguments respectively specify the unrestricted free table veriables, the aggregate-only free table variables, the tables we select from, the subset of fields that we keep from each table for the result rows, and the extra expressions that we select.
adamc@543 1679 $$\begin{array}{l}
adam@1400 1680 \mt{con} \; \mt{sql\_query1} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@543 1681 \\
adamc@543 1682 \mt{type} \; \mt{sql\_relop} \\
adamc@543 1683 \mt{val} \; \mt{sql\_union} : \mt{sql\_relop} \\
adamc@543 1684 \mt{val} \; \mt{sql\_intersect} : \mt{sql\_relop} \\
adamc@543 1685 \mt{val} \; \mt{sql\_except} : \mt{sql\_relop} \\
adam@1400 1686 \mt{val} \; \mt{sql\_relop} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400 1687 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adam@1400 1688 \hspace{.1in} \to \mt{tables1} ::: \{\{\mt{Type}\}\} \\
adamc@543 1689 \hspace{.1in} \to \mt{tables2} ::: \{\{\mt{Type}\}\} \\
adamc@543 1690 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1691 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@543 1692 \hspace{.1in} \to \mt{sql\_relop} \\
adam@1458 1693 \hspace{.1in} \to \mt{bool} \; (* \; \mt{ALL} \; *) \\
adam@1400 1694 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables1} \; \mt{selectedFields} \; \mt{selectedExps} \\
adam@1400 1695 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables2} \; \mt{selectedFields} \; \mt{selectedExps} \\
adam@1400 1696 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{selectedFields} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1697 \end{array}$$
adamc@543 1698
adamc@543 1699 $$\begin{array}{l}
adamc@1193 1700 \mt{val} \; \mt{sql\_query1} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400 1701 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1702 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543 1703 \hspace{.1in} \to \mt{grouped} ::: \{\{\mt{Type}\}\} \\
adamc@543 1704 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1705 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1085 1706 \hspace{.1in} \to \mt{empties} :: \{\mt{Unit}\} \\
adamc@1193 1707 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adamc@1193 1708 \hspace{.1in} \Rightarrow [\mt{free} \sim \mt{grouped}] \\
adam@1400 1709 \hspace{.1in} \Rightarrow [\mt{afree} \sim \mt{tables}] \\
adamc@1193 1710 \hspace{.1in} \Rightarrow [\mt{empties} \sim \mt{selectedFields}] \\
adamc@1085 1711 \hspace{.1in} \Rightarrow \{\mt{Distinct} : \mt{bool}, \\
adamc@1193 1712 \hspace{.2in} \mt{From} : \mt{sql\_from\_items} \; \mt{free} \; \mt{tables}, \\
adam@1778 1713 \hspace{.2in} \mt{Where} : \mt{sql\_exp} \; (\mt{free} \rc \mt{tables}) \; \mt{afree} \; [] \; \mt{bool}, \\
adamc@543 1714 \hspace{.2in} \mt{GroupBy} : \mt{sql\_subset} \; \mt{tables} \; \mt{grouped}, \\
adam@1778 1715 \hspace{.2in} \mt{Having} : \mt{sql\_exp} \; (\mt{free} \rc \mt{grouped}) \; (\mt{afree} \rc \mt{tables}) \; [] \; \mt{bool}, \\
adamc@1085 1716 \hspace{.2in} \mt{SelectFields} : \mt{sql\_subset} \; \mt{grouped} \; (\mt{map} \; (\lambda \_ \Rightarrow []) \; \mt{empties} \rc \mt{selectedFields}), \\
adam@1778 1717 \hspace{.2in} \mt {SelectExps} : \$(\mt{map} \; (\mt{sql\_expw} \; (\mt{free} \rc \mt{grouped}) \; (\mt{afree} \rc \mt{tables}) \; []) \; \mt{selectedExps}) \} \\
adam@1400 1718 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1719 \end{array}$$
adamc@543 1720
adamc@543 1721 To encode projection of subsets of fields in $\mt{SELECT}$ clauses, and to encode $\mt{GROUP} \; \mt{BY}$ clauses, we rely on a type family $\mt{sql\_subset}$, capturing what it means for one record of table fields to be a subset of another. The main constructor $\mt{sql\_subset}$ ``proves subset facts'' by requiring a split of a record into kept and dropped parts. The extra constructor $\mt{sql\_subset\_all}$ is a convenience for keeping all fields of a record.
adamc@543 1722 $$\begin{array}{l}
adamc@543 1723 \mt{con} \; \mt{sql\_subset} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@543 1724 \mt{val} \; \mt{sql\_subset} : \mt{keep\_drop} :: \{(\{\mt{Type}\} \times \{\mt{Type}\})\} \\
adamc@543 1725 \hspace{.1in} \to \mt{sql\_subset} \\
adamc@658 1726 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1 \rc \mt{fields}.2)\; \mt{keep\_drop}) \\
adamc@658 1727 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1) \; \mt{keep\_drop}) \\
adamc@543 1728 \mt{val} \; \mt{sql\_subset\_all} : \mt{tables} :: \{\{\mt{Type}\}\} \to \mt{sql\_subset} \; \mt{tables} \; \mt{tables}
adamc@543 1729 \end{array}$$
adamc@543 1730
adam@1778 1731 SQL expressions are used in several places, including $\mt{SELECT}$, $\mt{WHERE}$, $\mt{HAVING}$, and $\mt{ORDER} \; \mt{BY}$ clauses. They reify a fragment of the standard SQL expression language, while making it possible to inject ``native'' Ur values in some places. The arguments to the $\mt{sql\_exp}$ type family respectively give the unrestricted-availability table fields, the table fields that may only be used in arguments to aggregate functions, the available selected expressions, and the type of the expression.
adamc@543 1732 $$\begin{array}{l}
adam@1778 1733 \mt{con} \; \mt{sql\_exp} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}
adamc@543 1734 \end{array}$$
adamc@543 1735
adamc@543 1736 Any field in scope may be converted to an expression.
adamc@543 1737 $$\begin{array}{l}
adamc@543 1738 \mt{val} \; \mt{sql\_field} : \mt{otherTabs} ::: \{\{\mt{Type}\}\} \to \mt{otherFields} ::: \{\mt{Type}\} \\
adam@1778 1739 \hspace{.1in} \to \mt{fieldType} ::: \mt{Type} \to \mt{agg} ::: \{\{\mt{Type}\}\} \\
adamc@543 1740 \hspace{.1in} \to \mt{exps} ::: \{\mt{Type}\} \\
adamc@543 1741 \hspace{.1in} \to \mt{tab} :: \mt{Name} \to \mt{field} :: \mt{Name} \\
adam@1778 1742 \hspace{.1in} \to \mt{sql\_exp} \; ([\mt{tab} = [\mt{field} = \mt{fieldType}] \rc \mt{otherFields}] \rc \mt{otherTabs}) \; \mt{agg} \; \mt{exps} \; \mt{fieldType}
adamc@543 1743 \end{array}$$
adamc@543 1744
adamc@544 1745 There is an analogous function for referencing named expressions.
adamc@544 1746 $$\begin{array}{l}
adam@1778 1747 \mt{val} \; \mt{sql\_exp} : \mt{tabs} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{t} ::: \mt{Type} \to \mt{rest} ::: \{\mt{Type}\} \to \mt{nm} :: \mt{Name} \\
adam@1778 1748 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tabs} \; \mt{agg} \; ([\mt{nm} = \mt{t}] \rc \mt{rest}) \; \mt{t}
adamc@544 1749 \end{array}$$
adamc@544 1750
adamc@544 1751 Ur values of appropriate types may be injected into SQL expressions.
adamc@544 1752 $$\begin{array}{l}
adamc@786 1753 \mt{class} \; \mt{sql\_injectable\_prim} \\
adamc@786 1754 \mt{val} \; \mt{sql\_bool} : \mt{sql\_injectable\_prim} \; \mt{bool} \\
adamc@786 1755 \mt{val} \; \mt{sql\_int} : \mt{sql\_injectable\_prim} \; \mt{int} \\
adamc@786 1756 \mt{val} \; \mt{sql\_float} : \mt{sql\_injectable\_prim} \; \mt{float} \\
adamc@786 1757 \mt{val} \; \mt{sql\_string} : \mt{sql\_injectable\_prim} \; \mt{string} \\
adamc@786 1758 \mt{val} \; \mt{sql\_time} : \mt{sql\_injectable\_prim} \; \mt{time} \\
adamc@786 1759 \mt{val} \; \mt{sql\_blob} : \mt{sql\_injectable\_prim} \; \mt{blob} \\
adamc@786 1760 \mt{val} \; \mt{sql\_channel} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{channel} \; \mt{t}) \\
adamc@786 1761 \mt{val} \; \mt{sql\_client} : \mt{sql\_injectable\_prim} \; \mt{client} \\
adamc@786 1762 \\
adamc@544 1763 \mt{class} \; \mt{sql\_injectable} \\
adamc@786 1764 \mt{val} \; \mt{sql\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@786 1765 \mt{val} \; \mt{sql\_option\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; (\mt{option} \; \mt{t}) \\
adamc@786 1766 \\
adam@1778 1767 \mt{val} \; \mt{sql\_inject} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{sql\_injectable} \; \mt{t} \\
adam@1778 1768 \hspace{.1in} \to \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adamc@544 1769 \end{array}$$
adamc@544 1770
adamc@1123 1771 Additionally, most function-free types may be injected safely, via the $\mt{serialized}$ type family.
adamc@1123 1772 $$\begin{array}{l}
adamc@1123 1773 \mt{con} \; \mt{serialized} :: \mt{Type} \to \mt{Type} \\
adamc@1123 1774 \mt{val} \; \mt{serialize} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{serialized} \; \mt{t} \\
adamc@1123 1775 \mt{val} \; \mt{deserialize} : \mt{t} ::: \mt{Type} \to \mt{serialized} \; \mt{t} \to \mt{t} \\
adamc@1123 1776 \mt{val} \; \mt{sql\_serialized} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{serialized} \; \mt{t})
adamc@1123 1777 \end{array}$$
adamc@1123 1778
adamc@544 1779 We have the SQL nullness test, which is necessary because of the strange SQL semantics of equality in the presence of null values.
adamc@544 1780 $$\begin{array}{l}
adam@1778 1781 \mt{val} \; \mt{sql\_is\_null} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778 1782 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; (\mt{option} \; \mt{t}) \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{bool}
adamc@544 1783 \end{array}$$
adamc@544 1784
adam@1602 1785 As another way of dealing with null values, there is also a restricted form of the standard \cd{COALESCE} function.
adam@1602 1786 $$\begin{array}{l}
adam@1602 1787 \mt{val} \; \mt{sql\_coalesce} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778 1788 \hspace{.1in} \to \mt{t} ::: \mt{Type} \\
adam@1778 1789 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; (\mt{option} \; \mt{t}) \\
adam@1778 1790 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1791 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adam@1602 1792 \end{array}$$
adam@1602 1793
adamc@559 1794 We have generic nullary, unary, and binary operators.
adamc@544 1795 $$\begin{array}{l}
adamc@544 1796 \mt{con} \; \mt{sql\_nfunc} :: \mt{Type} \to \mt{Type} \\
adamc@544 1797 \mt{val} \; \mt{sql\_current\_timestamp} : \mt{sql\_nfunc} \; \mt{time} \\
adam@1778 1798 \mt{val} \; \mt{sql\_nfunc} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778 1799 \hspace{.1in} \to \mt{sql\_nfunc} \; \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\\end{array}$$
adamc@544 1800
adamc@544 1801 $$\begin{array}{l}
adamc@544 1802 \mt{con} \; \mt{sql\_unary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544 1803 \mt{val} \; \mt{sql\_not} : \mt{sql\_unary} \; \mt{bool} \; \mt{bool} \\
adam@1778 1804 \mt{val} \; \mt{sql\_unary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adam@1778 1805 \hspace{.1in} \to \mt{sql\_unary} \; \mt{arg} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res} \\
adamc@544 1806 \end{array}$$
adamc@544 1807
adamc@544 1808 $$\begin{array}{l}
adamc@544 1809 \mt{con} \; \mt{sql\_binary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544 1810 \mt{val} \; \mt{sql\_and} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544 1811 \mt{val} \; \mt{sql\_or} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adam@1778 1812 \mt{val} \; \mt{sql\_binary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg_1} ::: \mt{Type} \to \mt{arg_2} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adam@1778 1813 \hspace{.1in} \to \mt{sql\_binary} \; \mt{arg_1} \; \mt{arg_2} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_1} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_2} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res}
adamc@544 1814 \end{array}$$
adamc@544 1815
adamc@544 1816 $$\begin{array}{l}
adamc@559 1817 \mt{class} \; \mt{sql\_arith} \\
adamc@559 1818 \mt{val} \; \mt{sql\_int\_arith} : \mt{sql\_arith} \; \mt{int} \\
adamc@559 1819 \mt{val} \; \mt{sql\_float\_arith} : \mt{sql\_arith} \; \mt{float} \\
adamc@559 1820 \mt{val} \; \mt{sql\_neg} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_unary} \; \mt{t} \; \mt{t} \\
adamc@559 1821 \mt{val} \; \mt{sql\_plus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1822 \mt{val} \; \mt{sql\_minus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1823 \mt{val} \; \mt{sql\_times} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1824 \mt{val} \; \mt{sql\_div} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1825 \mt{val} \; \mt{sql\_mod} : \mt{sql\_binary} \; \mt{int} \; \mt{int} \; \mt{int}
adamc@559 1826 \end{array}$$
adamc@544 1827
adam@1797 1828 Finally, we have aggregate functions. The $\mt{COUNT(\ast)}$ syntax is handled specially, since it takes no real argument. The other aggregate functions are placed into a general type family, using constructor classes to restrict usage to properly typed arguments. The key aspect of the $\mt{sql\_aggregate}$ function's type is the shift of aggregate-function-only fields into unrestricted fields.
adamc@544 1829 $$\begin{array}{l}
adam@1778 1830 \mt{val} \; \mt{sql\_count} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int}
adamc@544 1831 \end{array}$$
adamc@544 1832
adamc@544 1833 $$\begin{array}{l}
adamc@1188 1834 \mt{con} \; \mt{sql\_aggregate} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adam@1778 1835 \mt{val} \; \mt{sql\_aggregate} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{dom} ::: \mt{Type} \to \mt{ran} ::: \mt{Type} \\
adam@1778 1836 \hspace{.1in} \to \mt{sql\_aggregate} \; \mt{dom} \; \mt{ran} \to \mt{sql\_exp} \; \mt{agg} \; \mt{agg} \; \mt{exps} \; \mt{dom} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{ran}
adamc@1188 1837 \end{array}$$
adamc@1188 1838
adamc@1188 1839 $$\begin{array}{l}
adamc@1188 1840 \mt{val} \; \mt{sql\_count\_col} : \mt{t} ::: \mt{Type} \to \mt{sql\_aggregate} \; (\mt{option} \; \mt{t}) \; \mt{int}
adamc@544 1841 \end{array}$$
adam@1400 1842
adam@1400 1843 Most aggregate functions are typed using a two-parameter constructor class $\mt{nullify}$ which maps $\mt{option}$ types to themselves and adds $\mt{option}$ to others. That is, this constructor class represents the process of making an SQL type ``nullable.''
adamc@544 1844
adamc@544 1845 $$\begin{array}{l}
adamc@544 1846 \mt{class} \; \mt{sql\_summable} \\
adamc@544 1847 \mt{val} \; \mt{sql\_summable\_int} : \mt{sql\_summable} \; \mt{int} \\
adamc@544 1848 \mt{val} \; \mt{sql\_summable\_float} : \mt{sql\_summable} \; \mt{float} \\
adam@1777 1849 \mt{val} \; \mt{sql\_avg} : \mt{t} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{sql\_aggregate} \; \mt{t} \; (\mt{option} \; \mt{float}) \\
adam@1400 1850 \mt{val} \; \mt{sql\_sum} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt}
adamc@544 1851 \end{array}$$
adamc@544 1852
adamc@544 1853 $$\begin{array}{l}
adamc@544 1854 \mt{class} \; \mt{sql\_maxable} \\
adamc@544 1855 \mt{val} \; \mt{sql\_maxable\_int} : \mt{sql\_maxable} \; \mt{int} \\
adamc@544 1856 \mt{val} \; \mt{sql\_maxable\_float} : \mt{sql\_maxable} \; \mt{float} \\
adamc@544 1857 \mt{val} \; \mt{sql\_maxable\_string} : \mt{sql\_maxable} \; \mt{string} \\
adamc@544 1858 \mt{val} \; \mt{sql\_maxable\_time} : \mt{sql\_maxable} \; \mt{time} \\
adam@1400 1859 \mt{val} \; \mt{sql\_max} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt} \\
adam@1400 1860 \mt{val} \; \mt{sql\_min} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt}
adamc@544 1861 \end{array}$$
adamc@544 1862
adam@1778 1863 Any SQL query that returns single columns may be turned into a subquery expression.
adam@1777 1864
adam@1777 1865 $$\begin{array}{l}
adam@1778 1866 \mt{val} \; \mt{sql\_subquery} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \\
adam@2155 1867 \hspace{.1in} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_query} \; \mt{tables} \; \mt{agg} \; [] \; [\mt{nm} = \mt{t}] \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{nt}
adamc@1193 1868 \end{array}$$
adamc@1193 1869
adam@1573 1870 There is also an \cd{IF..THEN..ELSE..} construct that is compiled into standard SQL \cd{CASE} expressions.
adam@1573 1871 $$\begin{array}{l}
adam@1778 1872 \mt{val} \; \mt{sql\_if\_then\_else} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778 1873 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{bool} \\
adam@1778 1874 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1875 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1876 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adam@1573 1877 \end{array}$$
adam@1573 1878
adamc@1193 1879 \texttt{FROM} clauses are specified using a type family, whose arguments are the free table variables and the table variables bound by this clause.
adamc@1193 1880 $$\begin{array}{l}
adamc@1193 1881 \mt{con} \; \mt{sql\_from\_items} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@1193 1882 \mt{val} \; \mt{sql\_from\_table} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1883 \hspace{.1in} \to \mt{t} ::: \mt{Type} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; \mt{t} \; \mt{fs} \to \mt{name} :: \mt{Name} \to \mt{t} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193 1884 \mt{val} \; \mt{sql\_from\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{name} :: \mt{Name} \to \mt{sql\_query} \; \mt{free} \; [] \; \mt{fs} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193 1885 \mt{val} \; \mt{sql\_from\_comma} : \mt{free} ::: \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \to [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193 1886 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adamc@1193 1887 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2}) \\
adamc@1193 1888 \mt{val} \; \mt{sql\_inner\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1889 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193 1890 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adam@1778 1891 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193 1892 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2})
adamc@786 1893 \end{array}$$
adamc@786 1894
adamc@786 1895 Besides these basic cases, outer joins are supported, which requires a type class for turning non-$\mt{option}$ columns into $\mt{option}$ columns.
adamc@786 1896 $$\begin{array}{l}
adamc@786 1897 \mt{class} \; \mt{nullify} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@786 1898 \mt{val} \; \mt{nullify\_option} : \mt{t} ::: \mt{Type} \to \mt{nullify} \; (\mt{option} \; \mt{t}) \; (\mt{option} \; \mt{t}) \\
adamc@786 1899 \mt{val} \; \mt{nullify\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{nullify} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@786 1900 \end{array}$$
adamc@786 1901
adamc@786 1902 Left, right, and full outer joins can now be expressed using functions that accept records of $\mt{nullify}$ instances. Here, we give only the type for a left join as an example.
adamc@786 1903
adamc@786 1904 $$\begin{array}{l}
adamc@1193 1905 \mt{val} \; \mt{sql\_left\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{(\mt{Type} \times \mt{Type})\}\} \\
adamc@1193 1906 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@786 1907 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\lambda \mt{r} \Rightarrow \$(\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{nullify} \; \mt{p}.1 \; \mt{p}.2) \; \mt{r})) \; \mt{tabs2}) \\
adamc@1193 1908 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \\
adam@1778 1909 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193 1910 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.2)) \; \mt{tabs2})
adamc@786 1911 \end{array}$$
adamc@786 1912
adamc@544 1913 We wrap up the definition of query syntax with the types used in representing $\mt{ORDER} \; \mt{BY}$, $\mt{LIMIT}$, and $\mt{OFFSET}$ clauses.
adamc@544 1914 $$\begin{array}{l}
adamc@544 1915 \mt{type} \; \mt{sql\_direction} \\
adamc@544 1916 \mt{val} \; \mt{sql\_asc} : \mt{sql\_direction} \\
adamc@544 1917 \mt{val} \; \mt{sql\_desc} : \mt{sql\_direction} \\
adamc@544 1918 \\
adamc@544 1919 \mt{con} \; \mt{sql\_order\_by} :: \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@544 1920 \mt{val} \; \mt{sql\_order\_by\_Nil} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} :: \{\mt{Type}\} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adam@1778 1921 \mt{val} \; \mt{sql\_order\_by\_Cons} : \mt{tf} ::: (\{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}) \\
adam@1778 1922 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778 1923 \hspace{.1in} \to \mt{sql\_window} \; \mt{tf} \to \mt{tf} \; \mt{tables} \; [] \; \mt{exps} \; \mt{t} \to \mt{sql\_direction} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adam@1684 1924 \mt{val} \; \mt{sql\_order\_by\_random} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544 1925 \\
adamc@544 1926 \mt{type} \; \mt{sql\_limit} \\
adamc@544 1927 \mt{val} \; \mt{sql\_no\_limit} : \mt{sql\_limit} \\
adamc@544 1928 \mt{val} \; \mt{sql\_limit} : \mt{int} \to \mt{sql\_limit} \\
adamc@544 1929 \\
adamc@544 1930 \mt{type} \; \mt{sql\_offset} \\
adamc@544 1931 \mt{val} \; \mt{sql\_no\_offset} : \mt{sql\_offset} \\
adamc@544 1932 \mt{val} \; \mt{sql\_offset} : \mt{int} \to \mt{sql\_offset}
adamc@544 1933 \end{array}$$
adamc@544 1934
adam@1778 1935 When using Postgres, \cd{SELECT} and \cd{ORDER BY} are allowed to contain top-level uses of \emph{window functions}. A separate type family \cd{sql\_expw} is provided for such cases, with some type class convenience for overloading between normal and window expressions.
adam@1778 1936 $$\begin{array}{l}
adam@1778 1937 \mt{con} \; \mt{sql\_expw} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type} \\
adam@1778 1938 \\
adam@1778 1939 \mt{class} \; \mt{sql\_window} :: (\{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}) \to \mt{Type} \\
adam@1778 1940 \mt{val} \; \mt{sql\_window\_normal} : \mt{sql\_window} \; \mt{sql\_exp} \\
adam@1778 1941 \mt{val} \; \mt{sql\_window\_fancy} : \mt{sql\_window} \; \mt{sql\_expw} \\
adam@1778 1942 \mt{val} \; \mt{sql\_window} : \mt{tf} ::: (\{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}) \\
adam@1778 1943 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778 1944 \hspace{.1in} \to \mt{sql\_window} \; \mt{tf} \\
adam@1778 1945 \hspace{.1in} \to \mt{tf} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1946 \hspace{.1in} \to \mt{sql\_expw} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1947 \\
adam@1778 1948 \mt{con} \; \mt{sql\_partition} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adam@1778 1949 \mt{val} \; \mt{sql\_no\_partition} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778 1950 \hspace{.1in} \to \mt{sql\_partition} \; \mt{tables} \; \mt{agg} \; \mt{exps} \\
adam@1778 1951 \mt{val} \; \mt{sql\_partition} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778 1952 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1953 \hspace{.1in} \to \mt{sql\_partition} \; \mt{tables} \; \mt{agg} \; \mt{exps} \\
adam@1778 1954 \\
adam@1778 1955 \mt{con} \; \mt{sql\_window\_function} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type} \\
adam@1778 1956 \mt{val} \; \mt{sql\_window\_function} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778 1957 \hspace{.1in} \to \mt{t} ::: \mt{Type} \\
adam@1778 1958 \hspace{.1in} \to \mt{sql\_window\_function} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1959 \hspace{.1in} \to \mt{sql\_partition} \; \mt{tables} \; \mt{agg} \; \mt{exps} \\
adam@1778 1960 \hspace{.1in} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adam@1778 1961 \hspace{.1in} \to \mt{sql\_expw} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1962 \\
adam@1778 1963 \mt{val} \; \mt{sql\_window\_aggregate} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778 1964 \hspace{.1in} \to \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \\
adam@1778 1965 \hspace{.1in} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt} \\
adam@1778 1966 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1967 \hspace{.1in} \to \mt{sql\_window\_function} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{nt} \\
adam@1778 1968 \mt{val} \; \mt{sql\_window\_count} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778 1969 \hspace{.1in} \to \mt{sql\_window\_function} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int} \\
adam@1778 1970 \mt{val} \; \mt{sql\_rank} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778 1971 \hspace{.1in} \to \mt{sql\_window\_function} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int}
adam@1778 1972 \end{array}$$
adam@1778 1973
adamc@545 1974
adamc@545 1975 \subsubsection{DML}
adamc@545 1976
adamc@545 1977 The Ur/Web library also includes an embedding of a fragment of SQL's DML, the Data Manipulation Language, for modifying database tables. Any piece of DML may be executed in a transaction.
adamc@545 1978
adamc@545 1979 $$\begin{array}{l}
adamc@545 1980 \mt{type} \; \mt{dml} \\
adamc@545 1981 \mt{val} \; \mt{dml} : \mt{dml} \to \mt{transaction} \; \mt{unit}
adamc@545 1982 \end{array}$$
adamc@545 1983
adam@1297 1984 The function $\mt{Basis.dml}$ will trigger a fatal application error if the command fails, for instance, because a data integrity constraint is violated. An alternate function returns an error message as a string instead.
adam@1297 1985
adam@1297 1986 $$\begin{array}{l}
adam@1297 1987 \mt{val} \; \mt{tryDml} : \mt{dml} \to \mt{transaction} \; (\mt{option} \; \mt{string})
adam@1297 1988 \end{array}$$
adam@1297 1989
adam@1797 1990 Properly typed records may be used to form $\mt{INSERT}$ commands.
adamc@545 1991 $$\begin{array}{l}
adamc@545 1992 \mt{val} \; \mt{insert} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \\
adam@1778 1993 \hspace{.1in} \to \$(\mt{map} \; (\mt{sql\_exp} \; [] \; [] \; []) \; \mt{fields}) \to \mt{dml}
adamc@545 1994 \end{array}$$
adamc@545 1995
adam@2155 1996 An $\mt{UPDATE}$ command is formed from a choice of which table fields to leave alone and which to change, along with an expression to use to compute the new value of each changed field and a $\mt{WHERE}$ clause. Note that, in the table environment applied to expressions, the table being updated is hardcoded at the name $\mt{T}$. The parsing extension for $\mt{UPDATE}$ will elaborate all table-free field references to use constant table name $\mt{T}$.
adamc@545 1997 $$\begin{array}{l}
adam@1380 1998 \mt{val} \; \mt{update} : \mt{unchanged} ::: \{\mt{Type}\} \to \mt{changed} :: \{\mt{Type}\} \to [\mt{changed} \sim \mt{unchanged}] \\
adam@1778 1999 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; []) \; \mt{changed}) \\
adam@1778 2000 \hspace{.1in} \to \mt{sql\_table} \; (\mt{changed} \rc \mt{unchanged}) \to \mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545 2001 \end{array}$$
adamc@545 2002
adam@1578 2003 A $\mt{DELETE}$ command is formed from a table and a $\mt{WHERE}$ clause. The above use of $\mt{T}$ is repeated.
adamc@545 2004 $$\begin{array}{l}
adam@1778 2005 \mt{val} \; \mt{delete} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \to \mt{sql\_exp} \; [\mt{T} = \mt{fields}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545 2006 \end{array}$$
adamc@545 2007
adamc@546 2008 \subsubsection{Sequences}
adamc@546 2009
adamc@546 2010 SQL sequences are counters with concurrency control, often used to assign unique IDs. Ur/Web supports them via a simple interface. The only way to create a sequence is with the $\mt{sequence}$ declaration form.
adamc@546 2011
adamc@546 2012 $$\begin{array}{l}
adamc@546 2013 \mt{type} \; \mt{sql\_sequence} \\
adamc@1085 2014 \mt{val} \; \mt{nextval} : \mt{sql\_sequence} \to \mt{transaction} \; \mt{int} \\
adamc@1085 2015 \mt{val} \; \mt{setval} : \mt{sql\_sequence} \to \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@546 2016 \end{array}$$
adamc@546 2017
adamc@546 2018
adam@1648 2019 \subsection{\label{xml}XML}
adamc@547 2020
adam@1333 2021 Ur/Web's library contains an encoding of XML syntax and semantic constraints. We make no effort to follow the standards governing XML schemas. Rather, XML fragments are viewed more as values of ML datatypes, and we only track which tags are allowed inside which other tags. The Ur/Web standard library encodes a very loose version of XHTML, where it is very easy to produce documents which are invalid XHTML, but which still display properly in all major browsers. The main purposes of the invariants that are enforced are first, to provide some documentation about the places where it would make sense to insert XML fragments; and second, to rule out code injection attacks and other abstraction violations related to HTML syntax.
adamc@547 2022
adam@1642 2023 The basic XML type family has arguments respectively indicating the \emph{context} of a fragment, the fields that the fragment expects to be bound on entry (and their types), and the fields that the fragment will bind (and their types). Contexts are a record-based ``poor man's subtyping'' encoding, with each possible set of valid tags corresponding to a different context record. For instance, the context for the \texttt{<td>} tag is $[\mt{Dyn}, \mt{MakeForm}, \mt{Tr}]$, to indicate nesting inside a \texttt{<tr>} tag with the ability to nest \texttt{<form>} and \texttt{<dyn>} tags (see below). Contexts are maintained in a somewhat ad-hoc way; the only definitive reference for their meanings is the types of the tag values in \texttt{basis.urs}. The arguments dealing with field binding are only relevant to HTML forms.
adamc@547 2024 $$\begin{array}{l}
adamc@547 2025 \mt{con} \; \mt{xml} :: \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547 2026 \end{array}$$
adamc@547 2027
adamc@547 2028 We also have a type family of XML tags, indexed respectively by the record of optional attributes accepted by the tag, the context in which the tag may be placed, the context required of children of the tag, which form fields the tag uses, and which fields the tag defines.
adamc@547 2029 $$\begin{array}{l}
adamc@547 2030 \mt{con} \; \mt{tag} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547 2031 \end{array}$$
adamc@547 2032
adamc@547 2033 Literal text may be injected into XML as ``CDATA.''
adamc@547 2034 $$\begin{array}{l}
adamc@547 2035 \mt{val} \; \mt{cdata} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{string} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adamc@547 2036 \end{array}$$
adamc@547 2037
adam@1358 2038 There is also a function to insert the literal value of a character. Since Ur/Web uses the UTF-8 text encoding, the $\mt{cdata}$ function is only sufficient to encode characters with ASCII codes below 128. Higher codes have alternate meanings in UTF-8 than in usual ASCII, so this alternate function should be used with them.
adam@1358 2039 $$\begin{array}{l}
adam@1358 2040 \mt{val} \; \mt{cdataChar} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{char} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adam@1358 2041 \end{array}$$
adam@1358 2042
adamc@547 2043 There is a function for producing an XML tree with a particular tag at its root.
adamc@547 2044 $$\begin{array}{l}
adamc@547 2045 \mt{val} \; \mt{tag} : \mt{attrsGiven} ::: \{\mt{Type}\} \to \mt{attrsAbsent} ::: \{\mt{Type}\} \to \mt{ctxOuter} ::: \{\mt{Unit}\} \to \mt{ctxInner} ::: \{\mt{Unit}\} \\
adamc@547 2046 \hspace{.1in} \to \mt{useOuter} ::: \{\mt{Type}\} \to \mt{useInner} ::: \{\mt{Type}\} \to \mt{bindOuter} ::: \{\mt{Type}\} \to \mt{bindInner} ::: \{\mt{Type}\} \\
adam@1380 2047 \hspace{.1in} \to [\mt{attrsGiven} \sim \mt{attrsAbsent}] \Rightarrow [\mt{useOuter} \sim \mt{useInner}] \Rightarrow [\mt{bindOuter} \sim \mt{bindInner}] \\
adam@1749 2048 \hspace{.1in} \Rightarrow \mt{css\_class} \\
adam@1643 2049 \hspace{.1in} \to \mt{option} \; (\mt{signal} \; \mt{css\_class}) \\
adam@1750 2050 \hspace{.1in} \to \mt{css\_style} \\
adam@1751 2051 \hspace{.1in} \to \mt{option} \; (\mt{signal} \; \mt{css\_style}) \\
adamc@787 2052 \hspace{.1in} \to \$\mt{attrsGiven} \\
adamc@547 2053 \hspace{.1in} \to \mt{tag} \; (\mt{attrsGiven} \rc \mt{attrsAbsent}) \; \mt{ctxOuter} \; \mt{ctxInner} \; \mt{useOuter} \; \mt{bindOuter} \\
adamc@547 2054 \hspace{.1in} \to \mt{xml} \; \mt{ctxInner} \; \mt{useInner} \; \mt{bindInner} \to \mt{xml} \; \mt{ctxOuter} \; (\mt{useOuter} \rc \mt{useInner}) \; (\mt{bindOuter} \rc \mt{bindInner})
adamc@547 2055 \end{array}$$
adam@1750 2056 Note that any tag may be assigned a CSS class, or left without a class by passing $\mt{Basis.null}$ as the first value-level argument. This is the sole way of making use of the values produced by $\mt{style}$ declarations. The function $\mt{Basis.classes}$ can be used to specify a list of CSS classes for a single tag. Stylesheets to assign properties to the classes can be linked via URL's with \texttt{link} tags. Ur/Web makes it easy to calculate upper bounds on usage of CSS classes through program analysis, with the \cd{-css} command-line flag.
adamc@547 2057
adam@1643 2058 Also note that two different arguments are available for setting CSS classes: the first, associated with the \texttt{class} pseudo-attribute syntactic sugar, fixes the class of a tag for the duration of the tag's life; while the second, associated with the \texttt{dynClass} pseudo-attribute, allows the class to vary over the tag's life. See Section \ref{signals} for an introduction to the $\mt{signal}$ type family.
adam@1643 2059
adam@1751 2060 The third and fourth value-level arguments makes it possible to generate HTML \cd{style} attributes, either with fixed content (\cd{style} attribute) or dynamic content (\cd{dynStyle} pseudo-attribute).
adam@1750 2061
adamc@547 2062 Two XML fragments may be concatenated.
adamc@547 2063 $$\begin{array}{l}
adamc@547 2064 \mt{val} \; \mt{join} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{bind_1} ::: \{\mt{Type}\} \to \mt{bind_2} ::: \{\mt{Type}\} \\
adam@1380 2065 \hspace{.1in} \to [\mt{use_1} \sim \mt{bind_1}] \Rightarrow [\mt{bind_1} \sim \mt{bind_2}] \\
adamc@547 2066 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind_1} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{bind_1}) \; \mt{bind_2} \to \mt{xml} \; \mt{ctx} \; \mt{use_1} \; (\mt{bind_1} \rc \mt{bind_2})
adamc@547 2067 \end{array}$$
adamc@547 2068
adamc@547 2069 Finally, any XML fragment may be updated to ``claim'' to use more form fields than it does.
adamc@547 2070 $$\begin{array}{l}
adam@1380 2071 \mt{val} \; \mt{useMore} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{use_2} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to [\mt{use_1} \sim \mt{use_2}] \\
adamc@547 2072 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{use_2}) \; \mt{bind}
adamc@547 2073 \end{array}$$
adamc@547 2074
adam@2008 2075 We will not list here the different HTML tags and related functions from the standard library. They should be easy enough to understand from the code in \texttt{basis.urs}. The set of tags in the library is not yet claimed to be complete for HTML standards. Also note that there is currently no way for the programmer to add his own tags, without using the foreign function interface (Section \ref{ffi}).
adam@2008 2076
adam@2047 2077 Some tags support HTML5 \texttt{data-*} attributes, which in Ur/Web are encoded as a single attribute $\mt{Data}$ with type $\mt{data\_attrs}$ encoding one or more attributes of this kind. See \texttt{basis.urs} for details. The usual HTML5 syntax for these attributes is supported by the Ur/Web parser as syntactic sugar, and the same mechanism is reused to support \texttt{aria-*} attributes.
adamc@547 2078
adamc@547 2079 One last useful function is for aborting any page generation, returning some XML as an error message. This function takes the place of some uses of a general exception mechanism.
adamc@547 2080 $$\begin{array}{l}
adam@1641 2081 \mt{val} \; \mt{error} : \mt{t} ::: \mt{Type} \to \mt{xbody} \to \mt{t}
adamc@547 2082 \end{array}$$
adamc@547 2083
adamc@549 2084
adamc@701 2085 \subsection{Client-Side Programming}
adamc@659 2086
adamc@701 2087 Ur/Web supports running code on web browsers, via automatic compilation to JavaScript.
adamc@701 2088
adamc@701 2089 \subsubsection{The Basics}
adamc@701 2090
adam@1400 2091 All of the functions in this subsection are client-side only.
adam@1400 2092
adam@1297 2093 Clients can open alert and confirm dialog boxes, in the usual annoying JavaScript way.
adamc@701 2094 $$\begin{array}{l}
adam@1297 2095 \mt{val} \; \mt{alert} : \mt{string} \to \mt{transaction} \; \mt{unit} \\
adam@1297 2096 \mt{val} \; \mt{confirm} : \mt{string} \to \mt{transaction} \; \mt{bool}
adamc@701 2097 \end{array}$$
adamc@701 2098
adamc@701 2099 Any transaction may be run in a new thread with the $\mt{spawn}$ function.
adamc@701 2100 $$\begin{array}{l}
adamc@701 2101 \mt{val} \; \mt{spawn} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit}
adamc@701 2102 \end{array}$$
adamc@701 2103
adamc@701 2104 The current thread can be paused for at least a specified number of milliseconds.
adamc@701 2105 $$\begin{array}{l}
adamc@701 2106 \mt{val} \; \mt{sleep} : \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@701 2107 \end{array}$$
adamc@701 2108
adam@1770 2109 A few functions are available to registers callbacks for particular error events. Respectively, they are triggered on calls to $\mt{error}$, uncaught JavaScript exceptions, failure of remote procedure calls, the severance of the connection serving asynchronous messages, or the occurrence of some other error with that connection. If no handlers are registered for a kind of error, then a JavaScript \cd{alert()} is used to announce its occurrence. When one of these functions is called multiple times within a single page, all registered handlers are run when appropriate events occur, with handlers run in the reverse of their registration order.
adamc@787 2110 $$\begin{array}{l}
adamc@787 2111 \mt{val} \; \mt{onError} : (\mt{xbody} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787 2112 \mt{val} \; \mt{onFail} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787 2113 \mt{val} \; \mt{onConnectFail} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787 2114 \mt{val} \; \mt{onDisconnect} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787 2115 \mt{val} \; \mt{onServerError} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit}
adamc@787 2116 \end{array}$$
adamc@787 2117
adam@1555 2118 There are also functions to register standard document-level event handlers.
adam@1555 2119
adam@1555 2120 $$\begin{array}{l}
adam@1783 2121 \mt{val} \; \mt{onClick} : (\mt{mouseEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783 2122 \mt{val} \; \mt{onDblclick} : (\mt{mouseEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783 2123 \mt{val} \; \mt{onKeydown} : (\mt{keyEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783 2124 \mt{val} \; \mt{onKeypress} : (\mt{keyEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783 2125 \mt{val} \; \mt{onKeyup} : (\mt{keyEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783 2126 \mt{val} \; \mt{onMousedown} : (\mt{mouseEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783 2127 \mt{val} \; \mt{onMouseup} : (\mt{mouseEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit}
adam@1555 2128 \end{array}$$
adam@1555 2129
adam@1559 2130 Versions of standard JavaScript functions are provided that event handlers may call to mask default handling or prevent bubbling of events up to parent DOM nodes, respectively.
adam@1559 2131
adam@1559 2132 $$\begin{array}{l}
adam@1559 2133 \mt{val} \; \mt{preventDefault} : \mt{transaction} \; \mt{unit} \\
adam@1559 2134 \mt{val} \; \mt{stopPropagation} : \mt{transaction} \; \mt{unit}
adam@1559 2135 \end{array}$$
adam@1559 2136
adam@1926 2137 Finally, here is an HTML tag to leave a marker in the \cd{<head>} of a document asking for some side-effecting code to be run. This pattern is \emph{much} less common in Ur/Web applications than in normal HTML/JavaScript applications; see Section \ref{signals} for the more idiomatic, functional way of manipulating the visible page.
adam@1926 2138
adam@1926 2139 $$\begin{array}{l}
adam@1926 2140 \mt{val} \; \mt{script} : \mt{unit} \to \mt{tag} \; [\mt{Code} = \mt{transaction} \; \mt{unit}] \; \mt{head} \; [] \; [] \; []
adam@1926 2141 \end{array}$$
adam@1926 2142
adam@1926 2143 Note that the Ur/Web version of \cd{<script>} is used like \cd{<script code=\{...\}/>}, rather than \cd{<script>...</script>}.
adam@1926 2144
adam@1556 2145 \subsubsection{Node IDs}
adam@1556 2146
adam@1556 2147 There is an abstract type of node IDs that may be assigned to \cd{id} attributes of most HTML tags.
adam@1556 2148
adam@1556 2149 $$\begin{array}{l}
adam@1556 2150 \mt{type} \; \mt{id} \\
adam@1556 2151 \mt{val} \; \mt{fresh} : \mt{transaction} \; \mt{id}
adam@1556 2152 \end{array}$$
adam@1556 2153
adam@1785 2154 The \cd{fresh} function is allowed on both server and client, but there is no other way to create IDs, which includes lack of a way to force an ID to match a particular string. The main semantic importance of IDs within Ur/Web is in uses of the HTML \cd{<label>} tag. IDs play a much more central role in mainstream JavaScript programming, but Ur/Web uses a very different model to enable changes to particular nodes of a page tree, as the next manual subsection explains. IDs may still be useful in interfacing with JavaScript code (for instance, through Ur/Web's FFI).
adam@1785 2155
adam@1785 2156 One further use of IDs is as handles for requesting that \emph{focus} be given to specific tags.
adam@1785 2157
adam@1785 2158 $$\begin{array}{l}
adam@1785 2159 \mt{val} \; \mt{giveFocus} : \mt{id} \to \mt{transaction} \; \mt{unit}
adam@1785 2160 \end{array}$$
adam@1556 2161
adam@1643 2162 \subsubsection{\label{signals}Functional-Reactive Page Generation}
adamc@701 2163
adamc@701 2164 Most approaches to ``AJAX''-style coding involve imperative manipulation of the DOM tree representing an HTML document's structure. Ur/Web follows the \emph{functional-reactive} approach instead. Programs may allocate mutable \emph{sources} of arbitrary types, and an HTML page is effectively a pure function over the latest values of the sources. The page is not mutated directly, but rather it changes automatically as the sources are mutated.
adamc@659 2165
adam@1403 2166 More operationally, you can think of a source as a mutable cell with facilities for subscription to change notifications. That level of detail is hidden behind a monadic facility to be described below. First, there are three primitive operations for working with sources just as if they were ML \cd{ref} cells, corresponding to ML's \cd{ref}, \cd{:=}, and \cd{!} operations.
adam@1403 2167
adamc@659 2168 $$\begin{array}{l}
adamc@659 2169 \mt{con} \; \mt{source} :: \mt{Type} \to \mt{Type} \\
adamc@659 2170 \mt{val} \; \mt{source} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{transaction} \; (\mt{source} \; \mt{t}) \\
adamc@659 2171 \mt{val} \; \mt{set} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@659 2172 \mt{val} \; \mt{get} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@659 2173 \end{array}$$
adamc@659 2174
adam@1400 2175 Only source creation and setting are supported server-side, as a convenience to help in setting up a page, where you may wish to allocate many sources that will be referenced through the page. All server-side storage of values inside sources uses string serializations of values, while client-side storage uses normal JavaScript values.
adam@1400 2176
adam@1608 2177 Pure functions over arbitrary numbers of sources are represented in a monad of \emph{signals}, which may only be used in client-side code. This is presented to the programmer in the form of a monad $\mt{signal}$, each of whose values represents (conceptually) some pure function over all sources that may be allocated in the course of program execution. A monad operation $\mt{signal}$ denotes the identity function over a particular source. By using $\mt{signal}$ on a source, you implicitly subscribe to change notifications for that source. That is, your signal will automatically be recomputed as that source changes. The usual monad operators make it possible to build up complex signals that depend on multiple sources; automatic updating upon source-value changes still happens automatically. There is also an operator for computing a signal's current value within a transaction.
adamc@659 2178
adamc@659 2179 $$\begin{array}{l}
adamc@659 2180 \mt{con} \; \mt{signal} :: \mt{Type} \to \mt{Type} \\
adamc@659 2181 \mt{val} \; \mt{signal\_monad} : \mt{monad} \; \mt{signal} \\
adam@1608 2182 \mt{val} \; \mt{signal} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{signal} \; \mt{t} \\
adam@1608 2183 \mt{val} \; \mt{current} : \mt{t} ::: \mt{Type} \to \mt{signal} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@659 2184 \end{array}$$
adamc@659 2185
adamc@659 2186 A reactive portion of an HTML page is injected with a $\mt{dyn}$ tag, which has a signal-valued attribute $\mt{Signal}$.
adamc@659 2187
adamc@659 2188 $$\begin{array}{l}
adam@1641 2189 \mt{val} \; \mt{dyn} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to [\mt{ctx} \sim [\mt{Dyn}]] \Rightarrow \mt{unit} \\
adam@1641 2190 \hspace{.1in} \to \mt{tag} \; [\mt{Signal} = \mt{signal} \; (\mt{xml} \; ([\mt{Dyn}] \rc \mt{ctx}) \; \mt{use} \; \mt{bind})] \; ([\mt{Dyn}] \rc \mt{ctx}) \; [] \; \mt{use} \; \mt{bind}
adamc@659 2191 \end{array}$$
adamc@659 2192
adam@1648 2193 The semantics of \cd{<dyn>} tags is somewhat subtle. When the signal associated with such a tag changes value, the associated subtree of the HTML page is recreated. Some properties of the subtree, such as attributes and client-side widget values, are specified explicitly in the signal value, so these may be counted on to remain the same after recreation. Other properties, like focus and cursor position within textboxes, are \emph{not} specified by signal values, and these properties will be \emph{reset} upon subtree regeneration. Furthermore, user interaction with widgets may not work properly during regeneration. For instance, clicking a button while it is being regenerated may not trigger its \cd{onclick} event code.
adam@1648 2194
adam@1648 2195 Currently, the only way to avoid undesired resets is to avoid regeneration of containing subtrees. There are two main strategies for achieving that goal. First, when changes to a subtree can be confined to CSS classes of tags, the \texttt{dynClass} pseudo-attribute may be used instead (see Section \ref{xml}), as it does not regenerate subtrees. Second, a single \cd{<dyn>} tag may be broken into multiple tags, in a way that makes finer-grained dependency structure explicit. This latter strategy can avoid ``spurious'' regenerations that are not actually required to achieve the intended semantics.
adam@1648 2196
adam@1786 2197 Transactions can be run on the client by including them in attributes like the $\mt{Onclick}$ attribute of $\mt{button}$, and GUI widgets like $\mt{ctextbox}$ have $\mt{Source}$ attributes that can be used to connect them to sources, so that their values can be read by code running because of, e.g., an $\mt{Onclick}$ event. It is also possible to create an ``active'' HTML fragment that runs a $\mt{transaction}$ to determine its content, possibly allocating some sources in the process:
adam@1786 2198
adam@1786 2199 $$\begin{array}{l}
adam@1786 2200 \mt{val} \; \mt{active} : \mt{unit} \to \mt{tag} \; [\mt{Code} = \mt{transaction} \; \mt{xbody}] \; \mt{body} \; [] \; [] \; []
adam@1786 2201 \end{array}$$
adamc@701 2202
adamc@914 2203 \subsubsection{Remote Procedure Calls}
adamc@914 2204
adamc@914 2205 Any function call may be made a client-to-server ``remote procedure call'' if the function being called needs no features that are only available to client code. To make a function call an RPC, pass that function call as the argument to $\mt{Basis.rpc}$:
adamc@914 2206
adamc@914 2207 $$\begin{array}{l}
adamc@914 2208 \mt{val} \; \mt{rpc} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@914 2209 \end{array}$$
adamc@914 2210
adam@1848 2211 There is an alternate form that uses $\mt{None}$ to indicate that an error occurred during RPC processing, rather than raising an exception to abort this branch of control flow.
adam@1848 2212
adam@1848 2213 $$\begin{array}{l}
adam@1848 2214 \mt{val} \; \mt{tryRpc} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; \mt{t} \to \mt{transaction} \; (\mt{option} \; \mt{t})
adam@1848 2215 \end{array}$$
adam@1848 2216
adamc@701 2217 \subsubsection{Asynchronous Message-Passing}
adamc@701 2218
adamc@701 2219 To support asynchronous, ``server push'' delivery of messages to clients, any client that might need to receive an asynchronous message is assigned a unique ID. These IDs may be retrieved both on the client and on the server, during execution of code related to a client.
adamc@701 2220
adamc@701 2221 $$\begin{array}{l}
adamc@701 2222 \mt{type} \; \mt{client} \\
adamc@701 2223 \mt{val} \; \mt{self} : \mt{transaction} \; \mt{client}
adamc@701 2224 \end{array}$$
adamc@701 2225
adam@1940 2226 \emph{Channels} are the means of message-passing. Each channel is created in the context of a client and belongs to that client; no other client may receive the channel's messages. Note that here \emph{client} has a technical Ur/Web meaning so that it describes only \emph{single page views}, so a user following a traditional link within an application will remove the ability for \emph{any} code to receive messages on the channels associated with the previous client. Each channel type includes the type of values that may be sent over the channel. Sending and receiving are asynchronous, in the sense that a client need not be ready to receive a message right away. Rather, sent messages may queue up, waiting to be processed.
adamc@701 2227
adamc@701 2228 $$\begin{array}{l}
adamc@701 2229 \mt{con} \; \mt{channel} :: \mt{Type} \to \mt{Type} \\
adamc@701 2230 \mt{val} \; \mt{channel} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; (\mt{channel} \; \mt{t}) \\
adamc@701 2231 \mt{val} \; \mt{send} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@701 2232 \mt{val} \; \mt{recv} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@701 2233 \end{array}$$
adamc@701 2234
adamc@701 2235 The $\mt{channel}$ and $\mt{send}$ operations may only be executed on the server, and $\mt{recv}$ may only be executed on a client. Neither clients nor channels may be passed as arguments from clients to server-side functions, so persistent channels can only be maintained by storing them in the database and looking them up using the current client ID or some application-specific value as a key.
adamc@701 2236
adamc@701 2237 Clients and channels live only as long as the web browser page views that they are associated with. When a user surfs away, his client and its channels will be garbage-collected, after that user is not heard from for the timeout period. Garbage collection deletes any database row that contains a client or channel directly. Any reference to one of these types inside an $\mt{option}$ is set to $\mt{None}$ instead. Both kinds of handling have the flavor of weak pointers, and that is a useful way to think about clients and channels in the database.
adamc@701 2238
adam@1551 2239 \emph{Note}: Currently, there are known concurrency issues with multi-threaded applications that employ message-passing on top of database engines that don't support true serializable transactions. Postgres 9.1 is the only supported engine that does this properly.
adam@1551 2240
adamc@659 2241
adamc@549 2242 \section{Ur/Web Syntax Extensions}
adamc@549 2243
adamc@549 2244 Ur/Web features some syntactic shorthands for building values using the functions from the last section. This section sketches the grammar of those extensions. We write spans of syntax inside brackets to indicate that they are optional.
adamc@549 2245
adamc@549 2246 \subsection{SQL}
adamc@549 2247
adamc@786 2248 \subsubsection{\label{tables}Table Declarations}
adamc@786 2249
adamc@788 2250 $\mt{table}$ declarations may include constraints, via these grammar rules.
adamc@788 2251 $$\begin{array}{rrcll}
adam@1594 2252 \textrm{Declarations} & d &::=& \mt{table} \; x : c \; [pk[,]] \; cts \mid \mt{view} \; x = V \\
adamc@788 2253 \textrm{Primary key constraints} & pk &::=& \mt{PRIMARY} \; \mt{KEY} \; K \\
adam@1722 2254 \textrm{Keys} & K &::=& f \mid (f, (f,)^+) \mid \{\{e\}\} \\
adamc@788 2255 \textrm{Constraint sets} & cts &::=& \mt{CONSTRAINT} f \; ct \mid cts, cts \mid \{\{e\}\} \\
adamc@788 2256 \textrm{Constraints} & ct &::=& \mt{UNIQUE} \; K \mid \mt{CHECK} \; E \\
adamc@788 2257 &&& \mid \mt{FOREIGN} \; \mt{KEY} \; K \; \mt{REFERENCES} \; F \; (K) \; [\mt{ON} \; \mt{DELETE} \; pr] \; [\mt{ON} \; \mt{UPDATE} \; pr] \\
adamc@788 2258 \textrm{Foreign tables} & F &::=& x \mid \{\{e\}\} \\
adam@1594 2259 \textrm{Propagation modes} & pr &::=& \mt{NO} \; \mt{ACTION} \mid \mt{RESTRICT} \mid \mt{CASCADE} \mid \mt{SET} \; \mt{NULL} \\
adam@1594 2260 \textrm{View expressions} & V &::=& Q \mid \{e\}
adamc@788 2261 \end{array}$$
adamc@788 2262
adamc@788 2263 A signature item $\mt{table} \; \mt{x} : \mt{c}$ is actually elaborated into two signature items: $\mt{con} \; \mt{x\_hidden\_constraints} :: \{\{\mt{Unit}\}\}$ and $\mt{val} \; \mt{x} : \mt{sql\_table} \; \mt{c} \; \mt{x\_hidden\_constraints}$. This is appropriate for common cases where client code doesn't care which keys a table has. It's also possible to include constraints after a $\mt{table}$ signature item, with the same syntax as for $\mt{table}$ declarations. This may look like dependent typing, but it's just a convenience. The constraints are type-checked to determine a constructor $u$ to include in $\mt{val} \; \mt{x} : \mt{sql\_table} \; \mt{c} \; (u \rc \mt{x\_hidden\_constraints})$, and then the expressions are thrown away. Nonetheless, it can be useful for documentation purposes to include table constraint details in signatures. Note that the automatic generation of $\mt{x\_hidden\_constraints}$ leads to a kind of free subtyping with respect to which constraints are defined.
adamc@788 2264
adamc@788 2265
adamc@549 2266 \subsubsection{Queries}
adamc@549 2267
adamc@550 2268 Queries $Q$ are added to the rules for expressions $e$.
adamc@550 2269
adamc@549 2270 $$\begin{array}{rrcll}
adam@1684 2271 \textrm{Queries} & Q &::=& (q \; [\mt{ORDER} \; \mt{BY} \; O] \; [\mt{LIMIT} \; N] \; [\mt{OFFSET} \; N]) \\
adamc@1085 2272 \textrm{Pre-queries} & q &::=& \mt{SELECT} \; [\mt{DISTINCT}] \; P \; \mt{FROM} \; F,^+ \; [\mt{WHERE} \; E] \; [\mt{GROUP} \; \mt{BY} \; p,^+] \; [\mt{HAVING} \; E] \\
adamc@1085 2273 &&& \mid q \; R \; q \mid \{\{\{e\}\}\} \\
adam@1684 2274 \textrm{Relational operators} & R &::=& \mt{UNION} \mid \mt{INTERSECT} \mid \mt{EXCEPT} \\
adam@2093 2275 \textrm{$\mt{ORDER \; BY}$ items} & O &::=& \mt{RANDOM} [()] \mid \hat{E} \; [o] \mid \hat{E} \; [o], O \mid \{\{\{e\}\}\}
adamc@549 2276 \end{array}$$
adamc@549 2277
adamc@549 2278 $$\begin{array}{rrcll}
adamc@549 2279 \textrm{Projections} & P &::=& \ast & \textrm{all columns} \\
adamc@549 2280 &&& p,^+ & \textrm{particular columns} \\
adamc@549 2281 \textrm{Pre-projections} & p &::=& t.f & \textrm{one column from a table} \\
adamc@558 2282 &&& t.\{\{c\}\} & \textrm{a record of columns from a table (of kind $\{\mt{Type}\}$)} \\
adam@1627 2283 &&& t.* & \textrm{all columns from a table} \\
adam@1778 2284 &&& \hat{E} \; [\mt{AS} \; f] & \textrm{expression column} \\
adamc@549 2285 \textrm{Table names} & t &::=& x & \textrm{constant table name (automatically capitalized)} \\
adamc@549 2286 &&& X & \textrm{constant table name} \\
adamc@549 2287 &&& \{\{c\}\} & \textrm{computed table name (of kind $\mt{Name}$)} \\
adamc@549 2288 \textrm{Column names} & f &::=& X & \textrm{constant column name} \\
adamc@549 2289 &&& \{c\} & \textrm{computed column name (of kind $\mt{Name}$)} \\
adamc@549 2290 \textrm{Tables} & T &::=& x & \textrm{table variable, named locally by its own capitalization} \\
adam@1756 2291 &&& x \; \mt{AS} \; X & \textrm{table variable, with local name} \\
adam@1756 2292 &&& x \; \mt{AS} \; \{c\} & \textrm{table variable, with computed local name} \\
adam@2155 2293 &&& \{\{e\}\} \; \mt{AS} \; X & \textrm{computed table expression, with local name} \\
adam@1756 2294 &&& \{\{e\}\} \; \mt{AS} \; \{c\} & \textrm{computed table expression, with computed local name} \\
adamc@1085 2295 \textrm{$\mt{FROM}$ items} & F &::=& T \mid \{\{e\}\} \mid F \; J \; \mt{JOIN} \; F \; \mt{ON} \; E \\
adamc@1085 2296 &&& \mid F \; \mt{CROSS} \; \mt{JOIN} \ F \\
adam@2155 2297 &&& \mid (Q) \; \mt{AS} \; X \mid (Q) \; \mt{AS} \; \{c\} \\
adam@2155 2298 &&& \mid (\{\{e\}\}) \; \mt{AS} \; t \\
adamc@1085 2299 \textrm{Joins} & J &::=& [\mt{INNER}] \\
adamc@1085 2300 &&& \mid [\mt{LEFT} \mid \mt{RIGHT} \mid \mt{FULL}] \; [\mt{OUTER}] \\
adam@1587 2301 \textrm{SQL expressions} & E &::=& t.f & \textrm{column references} \\
adamc@549 2302 &&& X & \textrm{named expression references} \\
adam@1490 2303 &&& \{[e]\} & \textrm{injected native Ur expressions} \\
adam@1778 2304 &&& \{e\} & \textrm{computed expressions, probably using $\mt{sql\_exp}$ directly} \\
adamc@549 2305 &&& \mt{TRUE} \mid \mt{FALSE} & \textrm{boolean constants} \\
adamc@549 2306 &&& \ell & \textrm{primitive type literals} \\
adamc@549 2307 &&& \mt{NULL} & \textrm{null value (injection of $\mt{None}$)} \\
adamc@549 2308 &&& E \; \mt{IS} \; \mt{NULL} & \textrm{nullness test} \\
adam@1602 2309 &&& \mt{COALESCE}(E, E) & \textrm{take first non-null value} \\
adamc@549 2310 &&& n & \textrm{nullary operators} \\
adamc@549 2311 &&& u \; E & \textrm{unary operators} \\
adamc@549 2312 &&& E \; b \; E & \textrm{binary operators} \\
adam@1778 2313 &&& \mt{COUNT}(\ast) & \textrm{count number of rows} \\
adam@1778 2314 &&& a(E) & \textrm{other aggregate function} \\
adam@1573 2315 &&& \mt{IF} \; E \; \mt{THEN} \; E \; \mt{ELSE} \; E & \textrm{conditional} \\
adam@1778 2316 &&& (Q) & \textrm{subquery (must return a single expression column)} \\
adamc@549 2317 &&& (E) & \textrm{explicit precedence} \\
adamc@549 2318 \textrm{Nullary operators} & n &::=& \mt{CURRENT\_TIMESTAMP} \\
adamc@549 2319 \textrm{Unary operators} & u &::=& \mt{NOT} \\
adam@2169 2320 \textrm{Binary operators} & b &::=& \mt{AND} \mid \mt{OR} \mid = \mid \neq \mid < \mid \leq \mid > \mid \geq \mid \mt{LIKE} \\
adamc@1188 2321 \textrm{Aggregate functions} & a &::=& \mt{COUNT} \mid \mt{AVG} \mid \mt{SUM} \mid \mt{MIN} \mid \mt{MAX} \\
adam@1543 2322 \textrm{Directions} & o &::=& \mt{ASC} \mid \mt{DESC} \mid \{e\} \\
adamc@549 2323 \textrm{SQL integer} & N &::=& n \mid \{e\} \\
adam@1778 2324 \textrm{Windowable expressions} & \hat{E} &::=& E \\
adam@1778 2325 &&& w \; [\mt{OVER} \; ( & \textrm{(Postgres only)} \\
adam@1778 2326 &&& \hspace{.1in} [\mt{PARTITION} \; \mt{BY} \; E] \\
adam@1778 2327 &&& \hspace{.1in} [\mt{ORDER} \; \mt{BY} \; O])] \\
adam@1778 2328 \textrm{Window function} & w &::=& \mt{RANK}() \\
adam@1778 2329 &&& \mt{COUNT}(*) \\
adam@1778 2330 &&& a(E)
adamc@549 2331 \end{array}$$
adamc@549 2332
adamc@1085 2333 Additionally, an SQL expression may be inserted into normal Ur code with the syntax $(\mt{SQL} \; E)$ or $(\mt{WHERE} \; E)$. Similar shorthands exist for other nonterminals, with the prefix $\mt{FROM}$ for $\mt{FROM}$ items and $\mt{SELECT1}$ for pre-queries.
adamc@549 2334
adam@1683 2335 Unnamed expression columns in $\mt{SELECT}$ clauses are assigned consecutive natural numbers, starting with 1. Any expression in a $p$ position that is enclosed in parentheses is treated as an expression column, rather than a column pulled directly out of a table, even if it is only a field projection. (This distinction affects the record type used to describe query results.)
adamc@1194 2336
adamc@550 2337 \subsubsection{DML}
adamc@550 2338
adamc@550 2339 DML commands $D$ are added to the rules for expressions $e$.
adamc@550 2340
adamc@550 2341 $$\begin{array}{rrcll}
adamc@550 2342 \textrm{Commands} & D &::=& (\mt{INSERT} \; \mt{INTO} \; T^E \; (f,^+) \; \mt{VALUES} \; (E,^+)) \\
adamc@550 2343 &&& (\mt{UPDATE} \; T^E \; \mt{SET} \; (f = E,)^+ \; \mt{WHERE} \; E) \\
adamc@550 2344 &&& (\mt{DELETE} \; \mt{FROM} \; T^E \; \mt{WHERE} \; E) \\
adamc@550 2345 \textrm{Table expressions} & T^E &::=& x \mid \{\{e\}\}
adamc@550 2346 \end{array}$$
adamc@550 2347
adamc@550 2348 Inside $\mt{UPDATE}$ and $\mt{DELETE}$ commands, lone variables $X$ are interpreted as references to columns of the implicit table $\mt{T}$, rather than to named expressions.
adamc@549 2349
adamc@551 2350 \subsection{XML}
adamc@551 2351
adamc@551 2352 XML fragments $L$ are added to the rules for expressions $e$.
adamc@551 2353
adamc@551 2354 $$\begin{array}{rrcll}
adamc@551 2355 \textrm{XML fragments} & L &::=& \texttt{<xml/>} \mid \texttt{<xml>}l^*\texttt{</xml>} \\
adamc@551 2356 \textrm{XML pieces} & l &::=& \textrm{text} & \textrm{cdata} \\
adamc@551 2357 &&& \texttt{<}g\texttt{/>} & \textrm{tag with no children} \\
adamc@551 2358 &&& \texttt{<}g\texttt{>}l^*\texttt{</}x\texttt{>} & \textrm{tag with children} \\
adamc@559 2359 &&& \{e\} & \textrm{computed XML fragment} \\
adamc@559 2360 &&& \{[e]\} & \textrm{injection of an Ur expression, via the $\mt{Top}.\mt{txt}$ function} \\
adam@2075 2361 \textrm{Tag} & g &::=& h \; (x [= v])^* \\
adamc@551 2362 \textrm{Tag head} & h &::=& x & \textrm{tag name} \\
adamc@551 2363 &&& h\{c\} & \textrm{constructor parameter} \\
adamc@551 2364 \textrm{Attribute value} & v &::=& \ell & \textrm{literal value} \\
adamc@551 2365 &&& \{e\} & \textrm{computed value} \\
adamc@551 2366 \end{array}$$
adamc@551 2367
adam@2075 2368 When the optional $= v$ is omitted in an XML attribute, the attribute is assigned value $\mt{True}$ in Ur/Web, and it is rendered to HTML merely as including the attribute name without a value. If such a Boolean attribute is manually set to value $\mt{False}$, then it is omitted altogether in generating HTML.
adam@2075 2369
adam@1751 2370 Further, there is a special convenience and compatibility form for setting CSS classes of tags. If a \cd{class} attribute has a value that is a string literal, the literal is parsed in the usual HTML way and replaced with calls to appropriate Ur/Web combinators. Any dashes in the text are replaced with underscores to determine Ur identifiers. The same desugaring can be accessed in a normal expression context by calling the pseudo-function \cd{CLASS} on a string literal.
adam@1751 2371
adam@1751 2372 Similar support is provided for \cd{style} attributes. Normal CSS syntax may be used in string literals that are \cd{style} attribute values, and the desugaring may be accessed elsewhere with the pseudo-function \cd{STYLE}.
adamc@552 2373
adamc@1198 2374 \section{\label{structure}The Structure of Web Applications}
adamc@553 2375
adam@1797 2376 A web application is built from a series of modules, with one module, the last one appearing in the \texttt{.urp} file, designated as the main module. The signature of the main module determines the URL entry points to the application. Such an entry point should have type $\mt{t1} \to \ldots \to \mt{tn} \to \mt{transaction} \; \mt{page}$, for any integer $n \geq 0$, where $\mt{page}$ is a type synonym for top-level HTML pages, defined in $\mt{Basis}$. If such a function is at the top level of main module $M$, with $n = 0$, it will be accessible at URI \texttt{/M/f}, and so on for more deeply nested functions, as described in Section \ref{tag} below. See Section \ref{cl} for information on the \texttt{prefix} and \texttt{rewrite url} directives, which can be used to rewrite the default URIs of different entry point functions. The final URL of a function is its default module-based URI, with \texttt{rewrite url} rules applied, and with the \texttt{prefix} prepended. Arguments to an entry-point function are deserialized from the part of the URI following \texttt{f}.
adamc@553 2377
adam@1532 2378 Elements of modules beside the main module, including page handlers, will only be included in the final application if they are transitive dependencies of the handlers in the main module.
adam@1532 2379
adam@1787 2380 Normal links are accessible via HTTP \texttt{GET}, which the relevant standard says should never cause side effects. To export a page which may cause side effects, accessible only via HTTP \texttt{POST}, include one argument of the page handler of type $\mt{Basis.postBody}$. When the handler is called, this argument will receive a value that can be deconstructed into a MIME type (with $\mt{Basis.postType}$) and payload (with $\mt{Basis.postData}$). This kind of handler should not be used with forms that exist solely within Ur/Web apps; for these, use Ur/Web's built-in support, as described below. It may still be useful to use $\mt{Basis.postBody}$ with form requests submitted by code outside an Ur/Web app. For such cases, the function $\mt{Top.postFields} : \mt{postBody} \to \mt{list} \; (\mt{string} \times \mt{string})$ may be useful, breaking a \texttt{POST} body of type \texttt{application/x-www-form-urlencoded} into its name-value pairs.
adam@1347 2381
adam@1370 2382 Any normal page handler may also include arguments of type $\mt{option \; Basis.queryString}$, which will be handled specially. Rather than being deserialized from the current URI, such an argument is passed the whole query string that the handler received. The string may be analyzed by calling $\mt{Basis.show}$ on it. A handler of this kind may be passed as an argument to $\mt{Basis.effectfulUrl}$ to generate a URL to a page that may be used as a ``callback'' by an external service, such that the handler is allowed to cause side effects.
adam@1370 2383
adamc@553 2384 When the standalone web server receives a request for a known page, it calls the function for that page, ``running'' the resulting transaction to produce the page to return to the client. Pages link to other pages with the \texttt{link} attribute of the \texttt{a} HTML tag. A link has type $\mt{transaction} \; \mt{page}$, and the semantics of a link are that this transaction should be run to compute the result page, when the link is followed. Link targets are assigned URL names in the same way as top-level entry points.
adamc@553 2385
adamc@553 2386 HTML forms are handled in a similar way. The $\mt{action}$ attribute of a $\mt{submit}$ form tag takes a value of type $\$\mt{use} \to \mt{transaction} \; \mt{page}$, where $\mt{use}$ is a kind-$\{\mt{Type}\}$ record of the form fields used by this action handler. Action handlers are assigned URL patterns in the same way as above.
adamc@553 2387
adam@1653 2388 For both links and actions, direct arguments and local variables mentioned implicitly via closures are automatically included in serialized form in URLs, in the order in which they appear in the source code. Such serialized values may only be drawn from a limited set of types, and programs will fail to compile when the (implicit or explicit) arguments of page handler functions involve disallowed types. (Keep in mind that every free variable of a function is an implicit argument if it was not defined at the top level of a module.) For instance:
adam@1653 2389 \begin{itemize}
adam@1653 2390 \item Functions are disallowed, since there is no obvious way to serialize them safely.
adam@1653 2391 \item XML fragments are disallowed, since it is unclear how to check client-provided XML to be sure it doesn't break the HTML invariants of the application (for instance, by mutating the DOM in the conventional way, interfering with Ur/Web's functional-reactive regime).
adam@1653 2392 \item Blobs (``files'') are disallowed, since they can easily have very large serializations that could not fit within most web servers' URL size limits. (And you probably don't want to be serializing, e.g., image files in URLs, anyway.)
adam@1653 2393 \end{itemize}
adamc@553 2394
adamc@660 2395 Ur/Web programs generally mix server- and client-side code in a fairly transparent way. The one important restriction is that mixed client-server code must encapsulate all server-side pieces within named functions. This is because execution of such pieces will be implemented by explicit calls to the remote web server, and it is useful to get the programmer's help in designing the interface to be used. For example, this makes it easier to allow a client running an old version of an application to continue interacting with a server that has been upgraded to a new version, if the programmer took care to keep the interfaces of all of the old remote calls the same. The functions implementing these services are assigned names in the same way as normal web entry points, by using module structure.
adamc@660 2396
adamc@789 2397 \medskip
adamc@789 2398
adam@1347 2399 The HTTP standard suggests that GET requests only be used in ways that generate no side effects. Side effecting operations should use POST requests instead. The Ur/Web compiler enforces this rule strictly, via a simple conservative program analysis. Any page that may have a side effect must be accessed through a form, all of which use POST requests, or via a direct call to a page handler with some argument of type $\mt{Basis.postBody}$. A page is judged to have a side effect if its code depends syntactically on any of the side-effecting, server-side FFI functions. Links, forms, and most client-side event handlers are not followed during this syntactic traversal, but \texttt{<body onload=\{...\}>} handlers \emph{are} examined, since they run right away and could just as well be considered parts of main page handlers.
adamc@789 2400
adamc@789 2401 Ur/Web includes a kind of automatic protection against cross site request forgery attacks. Whenever any page execution can have side effects and can also read at least one cookie value, all cookie values must be signed cryptographically, to ensure that the user has come to the current page by submitting a form on a real page generated by the proper server. Signing and signature checking are inserted automatically by the compiler. This prevents attacks like phishing schemes where users are directed to counterfeit pages with forms that submit to your application, where a user's cookies might be submitted without his knowledge, causing some undesired side effect.
adamc@789 2402
adam@1348 2403 \subsection{Tasks}
adam@1348 2404
adam@1348 2405 In many web applications, it's useful to run code at points other than requests from browsers. Ur/Web's \emph{task} mechanism facilitates this. A type family of \emph{task kinds} is in the standard library:
adam@1348 2406
adam@1348 2407 $$\begin{array}{l}
adam@1348 2408 \mt{con} \; \mt{task\_kind} :: \mt{Type} \to \mt{Type} \\
adam@1348 2409 \mt{val} \; \mt{initialize} : \mt{task\_kind} \; \mt{unit} \\
adam@1349 2410 \mt{val} \; \mt{clientLeaves} : \mt{task\_kind} \; \mt{client} \\
adam@1349 2411 \mt{val} \; \mt{periodic} : \mt{int} \to \mt{task\_kind} \; \mt{unit}
adam@1348 2412 \end{array}$$
adam@1348 2413
adam@1348 2414 A task kind names a particular extension point of generated applications, where the type parameter of a task kind describes which extra input data is available at that extension point. Add task code with the special declaration form $\mt{task} \; e_1 = e_2$, where $e_1$ is a task kind with data $\tau$, and $e_2$ is a function from $\tau$ to $\mt{transaction} \; \mt{unit}$.
adam@1348 2415
adam@1348 2416 The currently supported task kinds are:
adam@1348 2417 \begin{itemize}
adam@1349 2418 \item $\mt{initialize}$: Code that is run when the application starts up.
adam@1348 2419 \item $\mt{clientLeaves}$: Code that is run for each client that the runtime system decides has surfed away. When a request that generates a new client handle is aborted, that handle will still eventually be passed to $\mt{clientLeaves}$ task code, even though the corresponding browser was never informed of the client handle's existence. In other words, in general, $\mt{clientLeaves}$ handlers will be called more times than there are actual clients.
adam@1349 2420 \item $\mt{periodic} \; n$: Code that is run when the application starts up and then every $n$ seconds thereafter.
adam@1348 2421 \end{itemize}
adam@1348 2422
adamc@553 2423
adam@2008 2424 \section{\label{ffi}The Foreign Function Interface}
adamc@897 2425
adamc@897 2426 It is possible to call your own C and JavaScript code from Ur/Web applications, via the foreign function interface (FFI). The starting point for a new binding is a \texttt{.urs} signature file that presents your external library as a single Ur/Web module (with no nested modules). Compilation conventions map the types and values that you use into C and/or JavaScript types and values.
adamc@897 2427
adamc@897 2428 It is most convenient to encapsulate an FFI binding with a new \texttt{.urp} file, which applications can include with the \texttt{library} directive in their own \texttt{.urp} files. A number of directives are likely to show up in the library's project file.
adamc@897 2429
adamc@897 2430 \begin{itemize}
adamc@897 2431 \item \texttt{clientOnly Module.ident} registers a value as being allowed only in client-side code.
adamc@897 2432 \item \texttt{clientToServer Module.ident} declares a type as OK to marshal between clients and servers. By default, abstract FFI types are not allowed to be marshalled, since your library might be maintaining invariants that the simple serialization code doesn't check.
adam@1878 2433 \item \texttt{effectful Module.ident} registers a function that can have side effects. This is the default for \texttt{transaction}-based types, and, actually, this directive is mostly present for legacy compatibility reasons, since it used to be required explicitly for each \texttt{transaction}al function.
adamc@897 2434 \item \texttt{ffi FILE.urs} names the file giving your library's signature. You can include multiple such files in a single \texttt{.urp} file, and each file \texttt{mod.urp} defines an FFI module \texttt{Mod}.
adamc@1099 2435 \item \texttt{include FILE} requests inclusion of a C header file.
adam@2198 2436 \item \texttt{jsFile FILE} requests inclusion of a JavaScript source file.
adamc@897 2437 \item \texttt{jsFunc Module.ident=name} gives a mapping from an Ur name for a value to a JavaScript name.
adamc@897 2438 \item \texttt{link FILE} requests that \texttt{FILE} be linked into applications. It should be a C object or library archive file, and you are responsible for generating it with your own build process.
adamc@897 2439 \item \texttt{script URL} requests inclusion of a JavaScript source file within application HTML.
adamc@897 2440 \item \texttt{serverOnly Module.ident} registers a value as being allowed only in server-side code.
adamc@897 2441 \end{itemize}
adamc@897 2442
adamc@897 2443 \subsection{Writing C FFI Code}
adamc@897 2444
adam@1881 2445 C source files connecting to the Ur/Web FFI should include \texttt{urweb.h}, and C++ source files should include \texttt{urweb\_cpp.h}.
adam@1881 2446
adamc@897 2447 A server-side FFI type or value \texttt{Module.ident} must have a corresponding type or value definition \texttt{uw\_Module\_ident} in C code. With the current Ur/Web version, it's not generally possible to work with Ur records or complex datatypes in C code, but most other kinds of types are fair game.
adamc@897 2448
adamc@897 2449 \begin{itemize}
adam@1881 2450 \item Primitive types defined in \texttt{Basis} are themselves using the standard FFI interface, so you may refer to them like \texttt{uw\_Basis\_t}. See \texttt{include/urweb/types.h} for their definitions.
adamc@897 2451 \item Enumeration datatypes, which have only constructors that take no arguments, should be defined using C \texttt{enum}s. The type is named as for any other type identifier, and each constructor \texttt{c} gets an enumeration constant named \texttt{uw\_Module\_c}.
adamc@897 2452 \item A datatype \texttt{dt} (such as \texttt{Basis.option}) that has one non-value-carrying constructor \texttt{NC} and one value-carrying constructor \texttt{C} gets special treatment. Where \texttt{T} is the type of \texttt{C}'s argument, and where we represent \texttt{T} as \texttt{t} in C, we represent \texttt{NC} with \texttt{NULL}. The representation of \texttt{C} depends on whether we're sure that we don't need to use \texttt{NULL} to represent \texttt{t} values; this condition holds only for strings and complex datatypes. For such types, \texttt{C v} is represented with the C encoding of \texttt{v}, such that the translation of \texttt{dt} is \texttt{t}. For other types, \texttt{C v} is represented with a pointer to the C encoding of v, such that the translation of \texttt{dt} is \texttt{t*}.
adam@1686 2453 \item Ur/Web involves many types of program syntax, such as for HTML and SQL code. All of these types are implemented with normal C strings, and you may take advantage of that encoding to manipulate code as strings in C FFI code. Be mindful that, in writing such code, it is your responsibility to maintain the appropriate code invariants, or you may reintroduce the code injection vulnerabilities that Ur/Web rules out. The most convenient way to extend Ur/Web with functions that, e.g., use natively unsupported HTML tags is to generate the HTML code with the FFI.
adamc@897 2454 \end{itemize}
adamc@897 2455
adam@1881 2456 The C FFI version of a Ur function with type \texttt{T1 -> ... -> TN -> R} or \texttt{T1 -> ... -> TN -> transaction R} has a C prototype like \texttt{R uw\_Module\_ident(uw\_context, T1, ..., TN)}. Only functions with types of the second form may have side effects. \texttt{uw\_context} is the type of state that persists across handling a client request. Many functions that operate on contexts are prototyped in \texttt{include/urweb/urweb\_cpp.h}. Most should only be used internally by the compiler. A few are useful in general FFI implementation:
adamc@897 2457 \begin{itemize}
adamc@897 2458 \item \begin{verbatim}
adamc@897 2459 void uw_error(uw_context, failure_kind, const char *fmt, ...);
adamc@897 2460 \end{verbatim}
adamc@897 2461 Abort the current request processing, giving a \texttt{printf}-style format string and arguments for generating an error message. The \texttt{failure\_kind} argument can be \texttt{FATAL}, to abort the whole execution; \texttt{BOUNDED\_RETRY}, to try processing the request again from the beginning, but failing if this happens too many times; or \texttt{UNLIMITED\_RETRY}, to repeat processing, with no cap on how many times this can recur.
adamc@897 2462
adam@1329 2463 All pointers to the context-local heap (see description below of \texttt{uw\_malloc()}) become invalid at the start and end of any execution of a main entry point function of an application. For example, if the request handler is restarted because of a \texttt{uw\_error()} call with \texttt{BOUNDED\_RETRY} or for any other reason, it is unsafe to access any local heap pointers that may have been stashed somewhere beforehand.
adam@1329 2464
adamc@897 2465 \item \begin{verbatim}
adam@1469 2466 void uw_set_error_message(uw_context, const char *fmt, ...);
adam@1469 2467 \end{verbatim}
adam@1469 2468 This simpler form of \texttt{uw\_error()} saves an error message without immediately aborting execution.
adam@1469 2469
adam@1469 2470 \item \begin{verbatim}
adamc@897 2471 void uw_push_cleanup(uw_context, void (*func)(void *), void *arg);
adamc@897 2472 void uw_pop_cleanup(uw_context);
adamc@897 2473 \end{verbatim}
adam@1329 2474 Manipulate a stack of actions that should be taken if any kind of error condition arises. Calling the ``pop'' function both removes an action from the stack and executes it. It is a bug to let a page request handler finish successfully with unpopped cleanup actions.
adam@1329 2475
adam@1329 2476 Pending cleanup actions aren't intended to have any complex relationship amongst themselves, so, upon request handler abort, pending actions are executed in first-in-first-out order.
adamc@897 2477
adamc@897 2478 \item \begin{verbatim}
adamc@897 2479 void *uw_malloc(uw_context, size_t);
adamc@897 2480 \end{verbatim}
adam@1329 2481 A version of \texttt{malloc()} that allocates memory inside a context's heap, which is managed with region allocation. Thus, there is no \texttt{uw\_free()}, but you need to be careful not to keep ad-hoc C pointers to this area of memory. In general, \texttt{uw\_malloc()}ed memory should only be used in ways compatible with the computation model of pure Ur. This means it is fine to allocate and return a value that could just as well have been built with core Ur code. In contrast, it is almost never safe to store \texttt{uw\_malloc()}ed pointers in global variables, including when the storage happens implicitly by registering a callback that would take the pointer as an argument.
adam@1329 2482
adam@1329 2483 For performance and correctness reasons, it is usually preferable to use \texttt{uw\_malloc()} instead of \texttt{malloc()}. The former manipulates a local heap that can be kept allocated across page requests, while the latter uses global data structures that may face contention during concurrent execution. However, we emphasize again that \texttt{uw\_malloc()} should never be used to implement some logic that couldn't be implemented trivially by a constant-valued expression in Ur.
adamc@897 2484
adamc@897 2485 \item \begin{verbatim}
adamc@897 2486 typedef void (*uw_callback)(void *);
adam@1328 2487 typedef void (*uw_callback_with_retry)(void *, int will_retry);
adam@2001 2488 int uw_register_transactional(uw_context, void *data, uw_callback commit,
adam@2001 2489 uw_callback rollback, uw_callback_with_retry free);
adamc@897 2490 \end{verbatim}
adam@2001 2491 All side effects in Ur/Web programs need to be compatible with transactions, such that any set of actions can be undone at any time. Thus, you should not perform actions with non-local side effects directly; instead, register handlers to be called when the current transaction is committed or rolled back. The arguments here give an arbitary piece of data to be passed to callbacks, a function to call on commit, a function to call on rollback, and a function to call afterward in either case to clean up any allocated resources. A rollback handler may be called after the associated commit handler has already been called, if some later part of the commit process fails. A free handler is told whether the runtime system expects to retry the current page request after rollback finishes. The return value of \texttt{uw\_register\_transactional()} is 0 on success and nonzero on failure (where failure currently only happens when exceeding configured limits on number of transactionals).
adamc@897 2492
adam@2000 2493 Any of the callbacks may be \texttt{NULL}. To accommodate some stubbornly non-transactional real-world actions like sending an e-mail message, Ur/Web treats \texttt{NULL} \texttt{rollback} callbacks specially. When a transaction commits, all \texttt{commit} actions that have non-\texttt{NULL} rollback actions are tried before any \texttt{commit} actions that have \texttt{NULL} rollback actions. Furthermore, an SQL \texttt{COMMIT} is also attempted in between the two phases, so the nicely transactional actions have a chance to influence whether data are committed to the database, while \texttt{NULL}-rollback actions only get run in the first place after committing data. The reason for all this is that it is \emph{expected} that concurrency interactions will cause database commits to fail in benign ways that call for transaction restart. A truly non-undoable action should only be run after we are sure the database transaction will commit.
adamc@1085 2494
adam@1329 2495 When a request handler ends with multiple pending transactional actions, their handlers are run in a first-in-last-out stack-like order, wherever the order would otherwise be ambiguous.
adam@1329 2496
adam@1329 2497 It is not safe for any of these handlers to access a context-local heap through a pointer returned previously by \texttt{uw\_malloc()}, nor should any new calls to that function be made. Think of the context-local heap as meant for use by the Ur/Web code itself, while transactional handlers execute after the Ur/Web code has finished.
adam@1329 2498
adam@1469 2499 A handler may signal an error by calling \texttt{uw\_set\_error\_message()}, but it is not safe to call \texttt{uw\_error()} from a handler. Signaling an error in a commit handler will cause the runtime system to switch to aborting the transaction, immediately after the current commit handler returns.
adam@1469 2500
adamc@1085 2501 \item \begin{verbatim}
adamc@1085 2502 void *uw_get_global(uw_context, char *name);
adamc@1085 2503 void uw_set_global(uw_context, char *name, void *data, uw_callback free);
adamc@1085 2504 \end{verbatim}
adam@1329 2505 Different FFI-based extensions may want to associate their own pieces of data with contexts. The global interface provides a way of doing that, where each extension must come up with its own unique key. The \texttt{free} argument to \texttt{uw\_set\_global()} explains how to deallocate the saved data. It is never safe to store \texttt{uw\_malloc()}ed pointers in global variable slots.
adamc@1085 2506
adamc@897 2507 \end{itemize}
adamc@897 2508
adamc@897 2509 \subsection{Writing JavaScript FFI Code}
adamc@897 2510
adam@2198 2511 JavaScript is dynamically typed, so Ur/Web type definitions imply no JavaScript code. The JavaScript identifier for each FFI function is set with the \texttt{jsFunc} directive. Each identifier can be defined in any JavaScript file that you ask to include with the \texttt{script} directive, and one easy way to get code included is with the \texttt{jsFile} directive.
adamc@897 2512
adamc@897 2513 In contrast to C FFI code, JavaScript FFI functions take no extra context argument. Their argument lists are as you would expect from their Ur types. Only functions whose ranges take the form \texttt{transaction T} should have side effects; the JavaScript ``return type'' of such a function is \texttt{T}. Here are the conventions for representing Ur values in JavaScript.
adamc@897 2514
adamc@897 2515 \begin{itemize}
adamc@897 2516 \item Integers, floats, strings, characters, and booleans are represented in the usual JavaScript way.
adam@1996 2517 \item Ur functions are represented in an unspecified way. This means that you should not rely on any details of function representation. Named FFI functions are represented as JavaScript functions with as many arguments as their Ur types specify. To call a non-FFI function \texttt{f} on argument \texttt{x}, run \texttt{execF(f, x)}. A normal JavaScript function may also be used in a position where the Ur/Web runtime system expects an Ur/Web function.
adamc@897 2518 \item An Ur record is represented with a JavaScript record, where Ur field name \texttt{N} translates to JavaScript field name \texttt{\_N}. An exception to this rule is that the empty record is encoded as \texttt{null}.
adamc@897 2519 \item \texttt{option}-like types receive special handling similar to their handling in C. The ``\texttt{None}'' constructor is \texttt{null}, and a use of the ``\texttt{Some}'' constructor on a value \texttt{v} is either \texttt{v}, if the underlying type doesn't need to use \texttt{null}; or \texttt{\{v:v\}} otherwise.
adamc@985 2520 \item Any other datatypes represent a non-value-carrying constructor \texttt{C} as \texttt{"C"} and an application of a constructor \texttt{C} to value \texttt{v} as \texttt{\{n:"C", v:v\}}. This rule only applies to datatypes defined in FFI module signatures; the compiler is free to optimize the representations of other, non-\texttt{option}-like datatypes in arbitrary ways.
adam@1686 2521 \item As in the C FFI, all abstract types of program syntax are implemented with strings in JavaScript.
adam@1996 2522 \item A value of Ur type \texttt{transaction t} is represented in the same way as for \texttt{unit -> t}. (Note that FFI functions skip this extra level of function encoding, which only applies to functions defined in Ur/Web.)
adamc@897 2523 \end{itemize}
adamc@897 2524
adam@1644 2525 It is possible to write JavaScript FFI code that interacts with the functional-reactive structure of a document. Here is a quick summary of some of the simpler functions to use; descriptions of fancier stuff may be added later on request (and such stuff should be considered ``undocumented features'' until then).
adam@1644 2526
adam@1644 2527 \begin{itemize}
adam@1644 2528 \item Sources should be treated as an abstract type, manipulated via:
adam@1644 2529 \begin{itemize}
adam@1644 2530 \item \cd{sc(v)}, to create a source initialized to \cd{v}
adam@1644 2531 \item \cd{sg(s)}, to retrieve the current value of source \cd{s}
adam@1644 2532 \item \cd{sv(s, v)}, to set source \cd{s} to value \cd{v}
adam@1644 2533 \end{itemize}
adam@1644 2534
adam@1644 2535 \item Signals should be treated as an abstract type, manipulated via:
adam@1644 2536 \begin{itemize}
adam@1644 2537 \item \cd{sr(v)} and \cd{sb(s, f)}, the ``return'' and ``bind'' monad operators, respectively
adam@1644 2538 \item \cd{ss(s)}, to produce the signal corresponding to source \cd{s}
adam@1644 2539 \item \cd{scur(s)}, to get the current value of signal \cd{s}
adam@1644 2540 \end{itemize}
adam@1644 2541
adam@1644 2542 \item The behavior of the \cd{<dyn>} pseudo-tag may be mimicked by following the right convention in a piece of HTML source code with a type like $\mt{xbody}$. Such a piece of source code may be encoded with a JavaScript string. To insert a dynamic section, include a \cd{<script>} tag whose content is just a call \cd{dyn(pnode, s)}. The argument \cd{pnode} specifies what the relevant enclosing parent tag is. Use value \cd{"tr"} when the immediate parent is \cd{<tr>}, use \cd{"table"} when the immediate parent is \cd{<table>}, and use \cd{"span"} otherwise. The argument \cd{s} is a string-valued signal giving the HTML code to be inserted at this point. As with the usual \cd{<dyn>} tag, that HTML subtree is automatically updated as the value of \cd{s} changes.
adam@1644 2543
adam@1702 2544 \item There is only one supported method of taking HTML values generated in Ur/Web code and adding them to the DOM in FFI JavaScript code: call \cd{setInnerHTML(node, html)} to add HTML content \cd{html} within DOM node \cd{node}. Merely running \cd{node.innerHTML = html} is not guaranteed to get the job done, though programmers familiar with JavaScript will probably find it useful to think of \cd{setInnerHTML} as having this effect. The unusual idiom is required because Ur/Web uses a nonstandard representation of HTML, to support infinite nesting of code that may generate code that may generate code that.... The \cd{node} value must already be in the DOM tree at the point when \cd{setInnerHTML} is called, because some plumbing must be set up to interact sensibly with \cd{<dyn>} tags.
adam@1702 2545
adam@1644 2546 \item It is possible to use the more standard ``IDs and mutation'' style of JavaScript coding, though that style is unidiomatic for Ur/Web and should be avoided wherever possible. Recall the abstract type $\mt{id}$ and its constructor $\mt{fresh}$, which can be used to generate new unique IDs in Ur/Web code. Values of this type are represented as strings in JavaScript, and a function \cd{fresh()} is available to generate new unique IDs. Application-specific ID generation schemes may cause bad interactions with Ur/Web code that also generates IDs, so the recommended approach is to produce IDs only via calls to \cd{fresh()}. FFI code shouldn't depend on the ID generation scheme (on either server side or client side), but it is safe to include these IDs in tag attributes (in either server-side or client-side code) and manipulate the associated DOM nodes in the standard way (in client-side code). Be forewarned that this kind of imperative DOM manipulation may confuse the Ur/Web runtime system and interfere with proper behavior of tags like \cd{<dyn>}!
adam@1644 2547 \end{itemize}
adamc@897 2548
adam@1833 2549 \subsection{Introducing New HTML Tags}
adam@1833 2550
adam@1833 2551 FFI modules may introduce new tags as values with $\mt{Basis.tag}$ types. See \texttt{basis.urs} for examples of how tags are declared. The identifier of a tag value is used as its rendering in HTML. The Ur/Web syntax sugar for XML literals desugars each use of a tag into a reference to an identifier with the same name. There is no need to provide implementations (i.e., in C or JavaScript code) for such identifiers.
adam@1833 2552
adam@1833 2553 The onus is on the coder of a new tag's interface to think about consequences for code injection attacks, messing with the DOM in ways that may break Ur/Web reactive programming, etc.
adam@1833 2554
adam@2010 2555 \subsection{The Less Safe FFI}
adam@2010 2556
adam@2010 2557 An alternative interface is provided for declaring FFI functions inline within normal Ur/Web modules. This facility must be opted into with the \texttt{lessSafeFfi} \texttt{.urp} directive, since it breaks a crucial property, allowing code in a \texttt{.ur} file to break basic invariants of the Ur/Web type system. Without this option, one only needs to audit \texttt{.urp} files to be sure an application obeys the type-system rules. The alternative interface may be more convenient for such purposes as declaring an FFI function typed in terms of some type local to a module.
adam@2010 2558
adam@2010 2559 When the less safe mode is enabled, declarations like this one are accepted, at the top level of a \texttt{.ur} file:
adam@2010 2560 \begin{verbatim}
adam@2010 2561 ffi foo : int -> int
adam@2010 2562 \end{verbatim}
adam@2010 2563
adam@2010 2564 Now \texttt{foo} is available as a normal function. If called in server-side code, and if the above declaration appeared in \texttt{bar.ur}, the C function will be linked as \texttt{uw\_Bar\_foo()}. It is also possible to declare an FFI function to be implemented in JavaScript, using a general facility for including modifiers in an FFI declaration. The modifiers appear before the colon, separated by spaces. Here are the available ones, which have the same semantics as corresponding \texttt{.urp} directives.
adam@2010 2565 \begin{itemize}
adam@2010 2566 \item \texttt{effectful}
adam@2010 2567 \item \texttt{benignEffectful}
adam@2010 2568 \item \texttt{clientOnly}
adam@2010 2569 \item \texttt{serverOnly}
adam@2010 2570 \item \texttt{jsFunc "putJsFuncNameHere"}
adam@2010 2571 \end{itemize}
adam@2010 2572
adam@2039 2573 When no \texttt{jsFunc} directive is present, the function is assumed to map to a JavaScript function of the same name, if used in a client-side context.
adam@2039 2574
adamc@897 2575
adam@2042 2576 \section{\label{phases}Compiler Phases}
adam@2042 2577
adam@2042 2578 The Ur/Web compiler is unconventional in that it relies on a kind of \emph{heuristic compilation}. Not all valid programs will compile successfully. Informally, programs fail to compile when they are ``too higher order.'' Compiler phases do their best to eliminate different kinds of higher order-ness, but some programs just won't compile. This is a trade-off for producing very efficient executables. Compiled Ur/Web programs use native C representations and require no garbage collection. Also, this warning only applies to server-side code, as client-side code runs in a normal JavaScript environment with garbage collection.
adamc@552 2579
adamc@552 2580 In this section, we step through the main phases of compilation, noting what consequences each phase has for effective programming.
adamc@552 2581
adamc@552 2582 \subsection{Parse}
adamc@552 2583
adamc@552 2584 The compiler reads a \texttt{.urp} file, figures out which \texttt{.urs} and \texttt{.ur} files it references, and combines them all into what is conceptually a single sequence of declarations in the core language of Section \ref{core}.
adamc@552 2585
adamc@552 2586 \subsection{Elaborate}
adamc@552 2587
adamc@552 2588 This is where type inference takes place, translating programs into an explicit form with no more wildcards. This phase is the most likely source of compiler error messages.
adamc@552 2589
adam@1378 2590 Those crawling through the compiler source will also want to be aware of another compiler phase, Explify, that occurs immediately afterward. This phase just translates from an AST language that includes unification variables to a very similar language that doesn't; all variables should have been determined by the end of Elaborate, anyway. The new AST language also drops some features that are used only for static checking and that have no influence on runtime behavior, like disjointness constraints.
adam@1378 2591
adamc@552 2592 \subsection{Unnest}
adamc@552 2593
adamc@552 2594 Named local function definitions are moved to the top level, to avoid the need to generate closures.
adamc@552 2595
adamc@552 2596 \subsection{Corify}
adamc@552 2597
adamc@552 2598 Module system features are compiled away, through inlining of functor definitions at application sites. Afterward, most abstraction boundaries are broken, facilitating optimization.
adamc@552 2599
adamc@552 2600 \subsection{Especialize}
adamc@552 2601
adam@1356 2602 Functions are specialized to particular argument patterns. This is an important trick for avoiding the need to maintain any closures at runtime. Currently, specialization only happens for prefixes of a function's full list of parameters, so you may need to take care to put arguments of function types before other arguments. The optimizer will not be effective enough if you use arguments that mix functions and values that must be calculated at run-time. For instance, a tuple of a function and an integer counter would not lead to successful code generation; these should be split into separate arguments via currying.
adamc@552 2603
adamc@552 2604 \subsection{Untangle}
adamc@552 2605
adam@1797 2606 Remove unnecessary mutual recursion, splitting recursive groups into strongly connected components.
adamc@552 2607
adamc@552 2608 \subsection{Shake}
adamc@552 2609
adamc@552 2610 Remove all definitions not needed to run the page handlers that are visible in the signature of the last module listed in the \texttt{.urp} file.
adamc@552 2611
adamc@661 2612 \subsection{Rpcify}
adamc@661 2613
adamc@661 2614 Pieces of code are determined to be client-side, server-side, neither, or both, by figuring out which standard library functions might be needed to execute them. Calls to server-side functions (e.g., $\mt{query}$) within mixed client-server code are identified and replaced with explicit remote calls. Some mixed functions may be converted to continuation-passing style to facilitate this transformation.
adamc@661 2615
adamc@661 2616 \subsection{Untangle, Shake}
adamc@661 2617
adamc@661 2618 Repeat these simplifications.
adamc@661 2619
adamc@553 2620 \subsection{\label{tag}Tag}
adamc@552 2621
adamc@552 2622 Assign a URL name to each link and form action. It is important that these links and actions are written as applications of named functions, because such names are used to generate URL patterns. A URL pattern has a name built from the full module path of the named function, followed by the function name, with all pieces separated by slashes. The path of a functor application is based on the name given to the result, rather than the path of the functor itself.
adamc@552 2623
adamc@552 2624 \subsection{Reduce}
adamc@552 2625
adamc@552 2626 Apply definitional equality rules to simplify the program as much as possible. This effectively includes inlining of every non-recursive definition.
adamc@552 2627
adamc@552 2628 \subsection{Unpoly}
adamc@552 2629
adamc@552 2630 This phase specializes polymorphic functions to the specific arguments passed to them in the program. If the program contains real polymorphic recursion, Unpoly will be insufficient to avoid later error messages about too much polymorphism.
adamc@552 2631
adamc@552 2632 \subsection{Specialize}
adamc@552 2633
adamc@558 2634 Replace uses of parameterized datatypes with versions specialized to specific parameters. As for Unpoly, this phase will not be effective enough in the presence of polymorphic recursion or other fancy uses of impredicative polymorphism.
adamc@552 2635
adamc@552 2636 \subsection{Shake}
adamc@552 2637
adamc@558 2638 Here the compiler repeats the earlier Shake phase.
adamc@552 2639
adamc@552 2640 \subsection{Monoize}
adamc@552 2641
adamc@552 2642 Programs are translated to a new intermediate language without polymorphism or non-$\mt{Type}$ constructors. Error messages may pop up here if earlier phases failed to remove such features.
adamc@552 2643
adamc@552 2644 This is the stage at which concrete names are generated for cookies, tables, and sequences. They are named following the same convention as for links and actions, based on module path information saved from earlier stages. Table and sequence names separate path elements with underscores instead of slashes, and they are prefixed by \texttt{uw\_}.
adamc@664 2645
adamc@552 2646 \subsection{MonoOpt}
adamc@552 2647
adamc@552 2648 Simple algebraic laws are applied to simplify the program, focusing especially on efficient imperative generation of HTML pages.
adamc@552 2649
adamc@552 2650 \subsection{MonoUntangle}
adamc@552 2651
adamc@552 2652 Unnecessary mutual recursion is broken up again.
adamc@552 2653
adamc@552 2654 \subsection{MonoReduce}
adamc@552 2655
adamc@552 2656 Equivalents of the definitional equality rules are applied to simplify programs, with inlining again playing a major role.
adamc@552 2657
adamc@552 2658 \subsection{MonoShake, MonoOpt}
adamc@552 2659
adamc@552 2660 Unneeded declarations are removed, and basic optimizations are repeated.
adamc@552 2661
adamc@552 2662 \subsection{Fuse}
adamc@552 2663
adamc@552 2664 The compiler tries to simplify calls to recursive functions whose results are immediately written as page output. The write action is pushed inside the function definitions to avoid allocation of intermediate results.
adamc@552 2665
adamc@552 2666 \subsection{MonoUntangle, MonoShake}
adamc@552 2667
adamc@552 2668 Fuse often creates more opportunities to remove spurious mutual recursion.
adamc@552 2669
adamc@552 2670 \subsection{Pathcheck}
adamc@552 2671
adamc@552 2672 The compiler checks that no link or action name has been used more than once.
adamc@552 2673
adamc@552 2674 \subsection{Cjrize}
adamc@552 2675
adamc@552 2676 The program is translated to what is more or less a subset of C. If any use of functions as data remains at this point, the compiler will complain.
adamc@552 2677
adamc@552 2678 \subsection{C Compilation and Linking}
adamc@552 2679
adam@1523 2680 The output of the last phase is pretty-printed as C source code and passed to the C compiler.
adamc@552 2681
adamc@552 2682
as@1564 2683 \end{document}