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New lessSafeFfi
author Adam Chlipala <adam@chlipala.net>
date Fri, 02 May 2014 19:19:09 -0400
parents 799be3911ce3
children 3ed2ee0815d2
rev   line source
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} + \;}
adamc@527 9 \newcommand{\rcut}{\; \texttt{--} \;}
adamc@527 10 \newcommand{\rcutM}{\; \texttt{---} \;}
adamc@524 11
adamc@524 12 \begin{document}
adamc@524 13
adamc@524 14 \title{The Ur/Web Manual}
adamc@524 15 \author{Adam Chlipala}
adamc@524 16
adamc@524 17 \maketitle
adamc@524 18
adamc@540 19 \tableofcontents
adamc@540 20
adamc@554 21
adamc@554 22 \section{Introduction}
adamc@554 23
adam@1797 24 \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 25
adamc@554 26 \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 27
adamc@554 28 \begin{itemize}
adamc@554 29 \item Suffer from any kinds of code-injection attacks
adamc@554 30 \item Return invalid HTML
adamc@554 31 \item Contain dead intra-application links
adamc@554 32 \item Have mismatches between HTML forms and the fields expected by their handlers
adamc@652 33 \item Include client-side code that makes incorrect assumptions about the ``AJAX''-style services that the remote web server provides
adamc@554 34 \item Attempt invalid SQL queries
adamc@652 35 \item Use improper marshaling or unmarshaling in communication with SQL databases or between browsers and web servers
adamc@554 36 \end{itemize}
adamc@554 37
adamc@554 38 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 39
adamc@652 40 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 41
adamc@554 42 \medskip
adamc@554 43
adamc@554 44 The official web site for Ur is:
adamc@554 45 \begin{center}
adamc@554 46 \url{http://www.impredicative.com/ur/}
adamc@554 47 \end{center}
adamc@554 48
adamc@555 49
adamc@555 50 \section{Installation}
adamc@555 51
adamc@555 52 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 53
adamc@555 54 \begin{verbatim}
adamc@555 55 ./configure
adamc@555 56 make
adamc@555 57 sudo make install
adamc@555 58 \end{verbatim}
adamc@555 59
adam@1523 60 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 61 \begin{verbatim}
adam@1368 62 apt-get install mlton libssl-dev
adamc@896 63 \end{verbatim}
adamc@555 64
adamc@896 65 To build programs that access SQL databases, you also need one of these client libraries for supported backends.
adamc@555 66 \begin{verbatim}
adam@1960 67 apt-get install libpq-dev libmysqlclient-dev libsqlite3-dev
adamc@555 68 \end{verbatim}
adamc@555 69
adamc@555 70 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 71 \begin{verbatim}
adamc@555 72 apt-get install smlnj libsmlnj-smlnj ml-yacc ml-lpt
adamc@555 73 \end{verbatim}
adamc@555 74
adamc@555 75 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.
adamc@555 76
adamc@896 77 To run an SQL-backed application with a backend besides SQLite, you will probably want to install one of these servers.
adamc@555 78
adamc@555 79 \begin{verbatim}
adam@1960 80 apt-get install postgresql mysql-server
adamc@555 81 \end{verbatim}
adamc@555 82
adamc@555 83 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 84
adamc@555 85 \begin{verbatim}
adamc@555 86 apt-get install emacs-goodies-el
adamc@555 87 \end{verbatim}
adamc@555 88
adam@1441 89 If you don't want to install the Emacs mode, run \texttt{./configure} with the argument \texttt{--without-emacs}.
adam@1441 90
adam@1523 91 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 92
adamc@555 93 \begin{verbatim}
adam@1523 94 CCARGS=-fno-inline ./configure
adamc@555 95 \end{verbatim}
adamc@555 96
adam@1523 97 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 98
adamc@555 99 The Emacs mode can be set to autoload by adding the following to your \texttt{.emacs} file.
adamc@555 100
adamc@555 101 \begin{verbatim}
adamc@555 102 (add-to-list 'load-path "/usr/local/share/emacs/site-lisp/urweb-mode")
adamc@555 103 (load "urweb-mode-startup")
adamc@555 104 \end{verbatim}
adamc@555 105
adamc@555 106 Change the path in the first line if you chose a different Emacs installation path during configuration.
adamc@555 107
adamc@555 108
adamc@556 109 \section{Command-Line Compiler}
adamc@556 110
adam@1604 111 \subsection{\label{cl}Project Files}
adamc@556 112
adamc@556 113 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@556 114
adamc@556 115 \begin{verbatim}
adamc@556 116 database dbname=test
adamc@556 117 sql crud1.sql
adamc@556 118
adamc@556 119 crud
adamc@556 120 crud1
adamc@556 121 \end{verbatim}
adamc@556 122
adamc@556 123 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@556 124
adamc@556 125 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@556 126
adamc@556 127 \begin{verbatim}
adamc@556 128 createdb test
adamc@556 129 psql -f crud1.sql test
adamc@556 130 \end{verbatim}
adamc@556 131
adam@1331 132 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@556 133
adamc@556 134 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@556 135
adamc@783 136 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@783 137 \begin{itemize}
adam@1799 138 \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 139 \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 140 \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@783 141 \item \texttt{clientOnly Module.ident} registers an FFI function or transaction that may only be run in client browsers.
adam@1881 142 \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 143 \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@783 144 \item \texttt{database DBSTRING} sets the string to pass to libpq to open a database connection.
adamc@783 145 \item \texttt{debug} saves some intermediate C files, which is mostly useful to help in debugging the compiler itself.
adam@1878 146 \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.
adamc@783 147 \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@1881 148 \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 149 \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 150 \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.
adamc@783 151 \item \texttt{jsFunc Module.ident=name} gives the JavaScript name of an FFI value.
adamc@1089 152 \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 153 \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 154 \begin{itemize}
adam@1309 155 \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 156 \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 157 \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 158 \item \texttt{deltas}: maximum number of messages sendable in a single request handler with \texttt{Basis.send}
adam@1309 159 \item \texttt{globals}: maximum number of global variables that FFI libraries may set in a single request context
adam@1309 160 \item \texttt{headers}: maximum size (in bytes) of per-request buffer used to hold HTTP headers for generated pages
adam@1797 161 \item \texttt{heap}: maximum size (in bytes) of per-request heap for dynamically allocated data
adam@1309 162 \item \texttt{inputs}: maximum number of top-level form fields per request
adam@1309 163 \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 164 \item \texttt{page}: maximum size (in bytes) of per-request buffer used to hold HTML content of generated pages
adam@1309 165 \item \texttt{script}: maximum size (in bytes) of per-request buffer used to hold JavaScript content of generated pages
adam@1309 166 \item \texttt{subinputs}: maximum number of form fields per request, excluding top-level fields
adam@1309 167 \item \texttt{time}: maximum running time of a single page request, in units of approximately 0.1 seconds
adam@1309 168 \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 169 \end{itemize}
adam@1523 170 \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 171 \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 172 \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 173 \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 174 \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 175 \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 176 \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 177 \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@852 178 \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@783 179 \item \texttt{prefix PREFIX} sets the prefix included before every URI within the generated application. The default is \texttt{/}.
adamc@783 180 \item \texttt{profile} generates an executable that may be used with gprof.
adam@1752 181 \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 182 \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@783 183 \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@783 184 \item \texttt{serverOnly Module.ident} registers an FFI function or transaction that may only be run on the server.
adamc@1164 185 \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@783 186 \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 187 \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@783 188 \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@783 189 \end{itemize}
adamc@701 190
adamc@701 191
adamc@557 192 \subsection{Building an Application}
adamc@557 193
adamc@557 194 To compile project \texttt{P.urp}, simply run
adamc@557 195 \begin{verbatim}
adamc@557 196 urweb P
adamc@557 197 \end{verbatim}
adamc@1198 198 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@557 199
adamc@557 200 To time how long the different compiler phases run, without generating an executable, run
adamc@557 201 \begin{verbatim}
adamc@557 202 urweb -timing P
adamc@557 203 \end{verbatim}
adamc@557 204
adamc@1086 205 To stop the compilation process after type-checking, run
adamc@1086 206 \begin{verbatim}
adamc@1086 207 urweb -tc P
adamc@1086 208 \end{verbatim}
adam@1530 209 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 210
adam@1745 211 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 212
adam@1723 213 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 214
adamc@1170 215 To output information relevant to CSS stylesheets (and not finish regular compilation), run
adamc@1170 216 \begin{verbatim}
adamc@1170 217 urweb -css P
adamc@1170 218 \end{verbatim}
adamc@1170 219 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 220
adam@1733 221 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 222 \begin{verbatim}
adam@1733 223 urweb daemon start
adam@1733 224 \end{verbatim}
adam@1733 225 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 226 \begin{verbatim}
adam@1733 227 urweb daemon stop
adam@1733 228 \end{verbatim}
adam@1733 229 Communication happens via a UNIX domain socket in file \cd{.urweb\_daemon} in the working directory.
adam@1733 230
adam@1733 231 \medskip
adam@1733 232
adamc@896 233 Some other command-line parameters are accepted:
adamc@896 234 \begin{itemize}
ezyang@1739 235 \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 236
adam@1875 237 \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 238
adamc@896 239 \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@896 240
adamc@896 241 \item \texttt{-dbms [postgres|mysql|sqlite]}: Sets the database backend to use.
adamc@896 242 \begin{itemize}
adamc@896 243 \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@896 244
adamc@896 245 A command sequence like this can initialize a Postgres database, using a file \texttt{app.sql} generated by the compiler:
adamc@896 246 \begin{verbatim}
adamc@896 247 createdb app
adamc@896 248 psql -f app.sql app
adamc@896 249 \end{verbatim}
adamc@896 250
adamc@896 251 \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@896 252
adamc@896 253 A command sequence like this can initialize a MySQL database:
adamc@896 254 \begin{verbatim}
adamc@896 255 echo "CREATE DATABASE app" | mysql
adamc@896 256 mysql -D app <app.sql
adamc@896 257 \end{verbatim}
adamc@896 258
adamc@896 259 \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@896 260
adamc@896 261 A command like this can initialize an SQLite database:
adamc@896 262 \begin{verbatim}
adamc@896 263 sqlite3 path/to/database/file <app.sql
adamc@896 264 \end{verbatim}
adamc@896 265 \end{itemize}
adamc@896 266
adam@1693 267 \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 268
adam@1995 269 \item \texttt{-explainEmbed}: Trigger more verbose error messages about inability to embed server-side values in client-side code.
adam@1995 270
adam@1309 271 \item \texttt{-limit class num}: Equivalent to the \texttt{limit} directive from \texttt{.urp} files
adam@1309 272
adam@1850 273 \item \texttt{-moduleOf FILENAME}: Prints the Ur/Web module name corresponding to source file \texttt{FILENAME}, exiting immediately afterward.
adam@1850 274
adamc@896 275 \item \texttt{-output FILENAME}: Set where the application executable is written.
adamc@896 276
adamc@1127 277 \item \texttt{-path NAME VALUE}: Set the value of path variable \texttt{\$NAME} to \texttt{VALUE}, for use in \texttt{.urp} files.
adamc@1127 278
adam@1335 279 \item \texttt{-prefix PREFIX}: Equivalent to the \texttt{prefix} directive from \texttt{.urp} files
adam@1335 280
adam@1875 281 \item \texttt{-print-ccompiler}: Print the C compiler being used.
adam@1875 282
adam@1923 283 \item \texttt{-print-cinclude}: Print the name of the directory where C/C++ header files are installed.
adam@1923 284
adam@1753 285 \item \texttt{-protocol [http|cgi|fastcgi|static]}: Set the protocol that the generated application speaks.
adamc@896 286 \begin{itemize}
adamc@896 287 \item \texttt{http}: This is the default. It is for building standalone web servers that can be accessed by web browsers directly.
adamc@896 288
adamc@896 289 \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@896 290
adamc@896 291 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@896 292 \begin{verbatim}
adamc@896 293 ScriptAlias /Hello /path/to/hello.exe
adamc@896 294 \end{verbatim}
adamc@896 295
adamc@1163 296 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 297 \begin{verbatim}
adamc@1163 298 Options +ExecCGI
adamc@1163 299 AddHandler cgi-script .exe
adamc@1163 300 \end{verbatim}
adamc@1163 301
adamc@1163 302 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 303 \begin{verbatim}
adamc@1163 304 prefix /dir/script.exe/
adamc@1163 305 \end{verbatim}
adamc@1163 306
adamc@1163 307 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 308
adamc@1164 309 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 310
adamc@896 311 \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@896 312
adamc@896 313 To configure a FastCGI program with Apache, one could combine the above \texttt{ScriptAlias} line with a line like this:
adamc@896 314 \begin{verbatim}
adamc@896 315 FastCgiServer /path/to/hello.exe -idle-timeout 99999
adamc@896 316 \end{verbatim}
adamc@896 317 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@896 318
adam@1753 319 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 320
adamc@896 321 Here is some lighttpd configuration for the same application.
adamc@896 322 \begin{verbatim}
adamc@896 323 fastcgi.server = (
adamc@896 324 "/Hello/" =>
adamc@896 325 (( "bin-path" => "/path/to/hello.exe",
adamc@896 326 "socket" => "/tmp/hello",
adamc@896 327 "check-local" => "disable",
adamc@896 328 "docroot" => "/",
adamc@896 329 "max-procs" => "1"
adamc@896 330 ))
adamc@896 331 )
adamc@896 332 \end{verbatim}
adamc@896 333 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@896 334
adamc@896 335 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 336
adam@1509 337 \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@896 338 \end{itemize}
adamc@896 339
adamc@1127 340 \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 341
adamc@1164 342 \item \texttt{-sigfile PATH}: Same as the \texttt{sigfile} directive in \texttt{.urp} files
adamc@1164 343
adamc@896 344 \item \texttt{-sql FILENAME}: Set where a database set-up SQL script is written.
adamc@1095 345
adamc@1095 346 \item \texttt{-static}: Link the runtime system statically. The default is to link against dynamic libraries.
adam@1961 347
adam@1961 348 \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@896 349 \end{itemize}
adamc@896 350
adam@1297 351 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@556 352
adam@1509 353 \subsection{Tutorial Formatting}
adam@1509 354
adam@1509 355 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 356
adam@1509 357 These input files follow normal Ur syntax, with a few exceptions:
adam@1509 358 \begin{itemize}
adam@1509 359 \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 360 \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 361 \item A comment like \cd{(* * HEADING *)} introduces a section heading, with text \cd{HEADING} of your choice.
adam@1509 362 \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 363 \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 364 \end{itemize}
adam@1509 365
adam@1509 366 A word of warning: as for demo generation, tutorial generation calls Emacs to syntax-highlight Ur code.
adam@1509 367
adam@1522 368 \subsection{Run-Time Options}
adam@1522 369
adam@1522 370 Compiled applications consult a few environment variables to modify their behavior:
adam@1522 371
adam@1522 372 \begin{itemize}
adam@1522 373 \item \cd{URWEB\_NUM\_THREADS}: alternative to the \cd{-t} command-line argument (currently used only by FastCGI)
adam@1522 374 \item \cd{URWEB\_STACK\_SIZE}: size of per-thread stacks, in bytes
as@1564 375 \item \cd{URWEB\_PQ\_CON}: when using PostgreSQL, overrides the compiled-in connection string
adam@1522 376 \end{itemize}
adam@1522 377
adam@1509 378
adamc@529 379 \section{Ur Syntax}
adamc@529 380
adamc@784 381 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@524 382
adamc@524 383 \subsection{Lexical Conventions}
adamc@524 384
adamc@524 385 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@524 386
adamc@524 387 \begin{center}
adamc@524 388 \begin{tabular}{rl}
adamc@524 389 \textbf{\LaTeX} & \textbf{ASCII} \\
adamc@524 390 $\to$ & \cd{->} \\
adam@1687 391 $\longrightarrow$ & \cd{-{}->} \\
adamc@524 392 $\times$ & \cd{*} \\
adamc@524 393 $\lambda$ & \cd{fn} \\
adamc@524 394 $\Rightarrow$ & \cd{=>} \\
adamc@652 395 $\Longrightarrow$ & \cd{==>} \\
adamc@529 396 $\neq$ & \cd{<>} \\
adamc@529 397 $\leq$ & \cd{<=} \\
adamc@529 398 $\geq$ & \cd{>=} \\
adamc@524 399 \\
adamc@524 400 $x$ & Normal textual identifier, not beginning with an uppercase letter \\
adamc@525 401 $X$ & Normal textual identifier, beginning with an uppercase letter \\
adamc@524 402 \end{tabular}
adamc@524 403 \end{center}
adamc@524 404
adamc@525 405 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@524 406
adamc@873 407 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@526 408
adamc@527 409 This version of the manual doesn't include operator precedences; see \texttt{src/urweb.grm} for that.
adamc@527 410
adam@1297 411 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 412
adamc@552 413 \subsection{\label{core}Core Syntax}
adamc@524 414
adamc@524 415 \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@524 416 $$\begin{array}{rrcll}
adamc@524 417 \textrm{Kinds} & \kappa &::=& \mt{Type} & \textrm{proper types} \\
adamc@525 418 &&& \mt{Unit} & \textrm{the trivial constructor} \\
adamc@525 419 &&& \mt{Name} & \textrm{field names} \\
adamc@525 420 &&& \kappa \to \kappa & \textrm{type-level functions} \\
adamc@525 421 &&& \{\kappa\} & \textrm{type-level records} \\
adamc@525 422 &&& (\kappa\times^+) & \textrm{type-level tuples} \\
adamc@652 423 &&& X & \textrm{variable} \\
adam@1574 424 &&& X \longrightarrow \kappa & \textrm{kind-polymorphic type-level function} \\
adamc@529 425 &&& \_\_ & \textrm{wildcard} \\
adamc@525 426 &&& (\kappa) & \textrm{explicit precedence} \\
adamc@524 427 \end{array}$$
adamc@524 428
adamc@524 429 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@524 430 $$\begin{array}{rrcll}
adamc@524 431 \textrm{Explicitness} & ? &::=& :: & \textrm{explicit} \\
adamc@558 432 &&& ::: & \textrm{implicit}
adamc@524 433 \end{array}$$
adamc@524 434
adamc@524 435 \emph{Constructors} are the main class of compile-time-only data. They include proper types and are classified by kinds.
adamc@524 436 $$\begin{array}{rrcll}
adamc@524 437 \textrm{Constructors} & c, \tau &::=& (c) :: \kappa & \textrm{kind annotation} \\
adamc@530 438 &&& \hat{x} & \textrm{constructor variable} \\
adamc@524 439 \\
adamc@525 440 &&& \tau \to \tau & \textrm{function type} \\
adamc@525 441 &&& x \; ? \; \kappa \to \tau & \textrm{polymorphic function type} \\
adamc@652 442 &&& X \longrightarrow \tau & \textrm{kind-polymorphic function type} \\
adamc@525 443 &&& \$ c & \textrm{record type} \\
adamc@524 444 \\
adamc@525 445 &&& c \; c & \textrm{type-level function application} \\
adamc@530 446 &&& \lambda x \; :: \; \kappa \Rightarrow c & \textrm{type-level function abstraction} \\
adamc@524 447 \\
adamc@652 448 &&& X \Longrightarrow c & \textrm{type-level kind-polymorphic function abstraction} \\
adamc@655 449 &&& c [\kappa] & \textrm{type-level kind-polymorphic function application} \\
adamc@652 450 \\
adamc@525 451 &&& () & \textrm{type-level unit} \\
adamc@525 452 &&& \#X & \textrm{field name} \\
adamc@524 453 \\
adamc@525 454 &&& [(c = c)^*] & \textrm{known-length type-level record} \\
adamc@525 455 &&& c \rc c & \textrm{type-level record concatenation} \\
adamc@652 456 &&& \mt{map} & \textrm{type-level record map} \\
adamc@524 457 \\
adamc@558 458 &&& (c,^+) & \textrm{type-level tuple} \\
adamc@525 459 &&& c.n & \textrm{type-level tuple projection ($n \in \mathbb N^+$)} \\
adamc@524 460 \\
adamc@652 461 &&& [c \sim c] \Rightarrow \tau & \textrm{guarded type} \\
adamc@524 462 \\
adamc@529 463 &&& \_ :: \kappa & \textrm{wildcard} \\
adamc@525 464 &&& (c) & \textrm{explicit precedence} \\
adamc@530 465 \\
adamc@530 466 \textrm{Qualified uncapitalized variables} & \hat{x} &::=& x & \textrm{not from a module} \\
adamc@530 467 &&& M.x & \textrm{projection from a module} \\
adamc@525 468 \end{array}$$
adamc@525 469
adam@1579 470 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@655 471
adamc@525 472 Modules of the module system are described by \emph{signatures}.
adamc@525 473 $$\begin{array}{rrcll}
adamc@525 474 \textrm{Signatures} & S &::=& \mt{sig} \; s^* \; \mt{end} & \textrm{constant} \\
adamc@525 475 &&& X & \textrm{variable} \\
adamc@525 476 &&& \mt{functor}(X : S) : S & \textrm{functor} \\
adamc@529 477 &&& S \; \mt{where} \; \mt{con} \; x = c & \textrm{concretizing an abstract constructor} \\
adamc@525 478 &&& M.X & \textrm{projection from a module} \\
adamc@525 479 \\
adamc@525 480 \textrm{Signature items} & s &::=& \mt{con} \; x :: \kappa & \textrm{abstract constructor} \\
adamc@525 481 &&& \mt{con} \; x :: \kappa = c & \textrm{concrete constructor} \\
adamc@528 482 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529 483 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@525 484 &&& \mt{val} \; x : \tau & \textrm{value} \\
adamc@525 485 &&& \mt{structure} \; X : S & \textrm{sub-module} \\
adamc@525 486 &&& \mt{signature} \; X = S & \textrm{sub-signature} \\
adamc@525 487 &&& \mt{include} \; S & \textrm{signature inclusion} \\
adamc@525 488 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@654 489 &&& \mt{class} \; x :: \kappa & \textrm{abstract constructor class} \\
adamc@654 490 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@525 491 \\
adamc@525 492 \textrm{Datatype constructors} & dc &::=& X & \textrm{nullary constructor} \\
adamc@525 493 &&& X \; \mt{of} \; \tau & \textrm{unary constructor} \\
adamc@524 494 \end{array}$$
adamc@524 495
adamc@526 496 \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@526 497 $$\begin{array}{rrcll}
adamc@526 498 \textrm{Patterns} & p &::=& \_ & \textrm{wildcard} \\
adamc@526 499 &&& x & \textrm{variable} \\
adamc@526 500 &&& \ell & \textrm{constant} \\
adamc@526 501 &&& \hat{X} & \textrm{nullary constructor} \\
adamc@526 502 &&& \hat{X} \; p & \textrm{unary constructor} \\
adamc@526 503 &&& \{(x = p,)^*\} & \textrm{rigid record pattern} \\
adamc@526 504 &&& \{(x = p,)^+, \ldots\} & \textrm{flexible record pattern} \\
adamc@852 505 &&& p : \tau & \textrm{type annotation} \\
adamc@527 506 &&& (p) & \textrm{explicit precedence} \\
adamc@526 507 \\
adamc@529 508 \textrm{Qualified capitalized variables} & \hat{X} &::=& X & \textrm{not from a module} \\
adamc@526 509 &&& M.X & \textrm{projection from a module} \\
adamc@526 510 \end{array}$$
adamc@526 511
adamc@527 512 \emph{Expressions} are the main run-time entities, corresponding to both ``expressions'' and ``statements'' in mainstream imperative languages.
adamc@527 513 $$\begin{array}{rrcll}
adamc@527 514 \textrm{Expressions} & e &::=& e : \tau & \textrm{type annotation} \\
adamc@529 515 &&& \hat{x} & \textrm{variable} \\
adamc@529 516 &&& \hat{X} & \textrm{datatype constructor} \\
adamc@527 517 &&& \ell & \textrm{constant} \\
adamc@527 518 \\
adamc@527 519 &&& e \; e & \textrm{function application} \\
adamc@527 520 &&& \lambda x : \tau \Rightarrow e & \textrm{function abstraction} \\
adamc@527 521 &&& e [c] & \textrm{polymorphic function application} \\
adamc@852 522 &&& \lambda [x \; ? \; \kappa] \Rightarrow e & \textrm{polymorphic function abstraction} \\
adamc@655 523 &&& e [\kappa] & \textrm{kind-polymorphic function application} \\
adamc@652 524 &&& X \Longrightarrow e & \textrm{kind-polymorphic function abstraction} \\
adamc@527 525 \\
adamc@527 526 &&& \{(c = e,)^*\} & \textrm{known-length record} \\
adamc@527 527 &&& e.c & \textrm{record field projection} \\
adamc@527 528 &&& e \rc e & \textrm{record concatenation} \\
adamc@527 529 &&& e \rcut c & \textrm{removal of a single record field} \\
adamc@527 530 &&& e \rcutM c & \textrm{removal of multiple record fields} \\
adamc@527 531 \\
adamc@527 532 &&& \mt{let} \; ed^* \; \mt{in} \; e \; \mt{end} & \textrm{local definitions} \\
adamc@527 533 \\
adamc@527 534 &&& \mt{case} \; e \; \mt{of} \; (p \Rightarrow e|)^+ & \textrm{pattern matching} \\
adamc@527 535 \\
adamc@654 536 &&& \lambda [c \sim c] \Rightarrow e & \textrm{guarded expression abstraction} \\
adamc@654 537 &&& e \; ! & \textrm{guarded expression application} \\
adamc@527 538 \\
adamc@527 539 &&& \_ & \textrm{wildcard} \\
adamc@527 540 &&& (e) & \textrm{explicit precedence} \\
adamc@527 541 \\
adamc@527 542 \textrm{Local declarations} & ed &::=& \cd{val} \; x : \tau = e & \textrm{non-recursive value} \\
adam@1797 543 &&& \cd{val} \; \cd{rec} \; (x : \tau = e \; \cd{and})^+ & \textrm{mutually recursive values} \\
adamc@527 544 \end{array}$$
adamc@527 545
adamc@655 546 As with constructors, we include both abstraction and application for kind polymorphism, but applications are only inferred internally.
adamc@655 547
adamc@528 548 \emph{Declarations} primarily bring new symbols into context.
adamc@528 549 $$\begin{array}{rrcll}
adamc@528 550 \textrm{Declarations} & d &::=& \mt{con} \; x :: \kappa = c & \textrm{constructor synonym} \\
adamc@528 551 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529 552 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@528 553 &&& \mt{val} \; x : \tau = e & \textrm{value} \\
adam@1797 554 &&& \mt{val} \; \cd{rec} \; (x : \tau = e \; \mt{and})^+ & \textrm{mutually recursive values} \\
adamc@528 555 &&& \mt{structure} \; X : S = M & \textrm{module definition} \\
adamc@528 556 &&& \mt{signature} \; X = S & \textrm{signature definition} \\
adamc@528 557 &&& \mt{open} \; M & \textrm{module inclusion} \\
adamc@528 558 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@528 559 &&& \mt{open} \; \mt{constraints} \; M & \textrm{inclusion of just the constraints from a module} \\
adamc@528 560 &&& \mt{table} \; x : c & \textrm{SQL table} \\
adam@1594 561 &&& \mt{view} \; x = e & \textrm{SQL view} \\
adamc@528 562 &&& \mt{sequence} \; x & \textrm{SQL sequence} \\
adamc@535 563 &&& \mt{cookie} \; x : \tau & \textrm{HTTP cookie} \\
adamc@784 564 &&& \mt{style} \; x : \tau & \textrm{CSS class} \\
adamc@1085 565 &&& \mt{task} \; e = e & \textrm{recurring task} \\
adamc@528 566 \\
adamc@529 567 \textrm{Modules} & M &::=& \mt{struct} \; d^* \; \mt{end} & \textrm{constant} \\
adamc@529 568 &&& X & \textrm{variable} \\
adamc@529 569 &&& M.X & \textrm{projection} \\
adamc@529 570 &&& M(M) & \textrm{functor application} \\
adamc@529 571 &&& \mt{functor}(X : S) : S = M & \textrm{functor abstraction} \\
adamc@528 572 \end{array}$$
adamc@528 573
adamc@528 574 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@527 575
adam@1594 576 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@784 577
adamc@529 578 \subsection{Shorthands}
adamc@529 579
adamc@529 580 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@529 581
adamc@529 582 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@529 583
adamc@529 584 A record type may be written $\{(c = c,)^*\}$, which elaborates to $\$[(c = c,)^*]$.
adamc@529 585
adamc@533 586 The notation $[c_1, \ldots, c_n]$ is shorthand for $[c_1 = (), \ldots, c_n = ()]$.
adamc@533 587
adam@1350 588 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@529 589
adam@1687 590 The syntax $()$ expands to $\{\}$ as a pattern or expression.
adam@1687 591
adamc@852 592 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@529 593
adam@1574 594 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 595
adam@1306 596 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 597
adamc@529 598 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@529 599
adamc@529 600 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@529 601
adamc@654 602 A signature item or declaration $\mt{class} \; x = \lambda y \Rightarrow c$ may be abbreviated $\mt{class} \; x \; y = c$.
adamc@529 603
adam@1738 604 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@529 605
adamc@852 606 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@529 607
adamc@852 608 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@852 609
adam@1797 610 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@529 611
adamc@529 612 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@529 613
adamc@852 614 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@852 615
adamc@853 616 A declaration $\mt{table} \; x : \{(c = c,)^*\}$ is elaborated into $\mt{table} \; x : [(c = c,)^*]$.
adamc@529 617
adamc@529 618 The syntax $\mt{where} \; \mt{type}$ is an alternate form of $\mt{where} \; \mt{con}$.
adamc@529 619
adamc@529 620 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@529 621
adamc@529 622 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@529 623
adamc@784 624 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@529 625
adamc@530 626
adamc@530 627 \section{Static Semantics}
adamc@530 628
adamc@530 629 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@530 630
adam@1891 631 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 632 \begin{quote}
adam@1891 633 Benjamin C. Pierce, \emph{Types and Programming Languages}, MIT Press, 2002.
adam@1891 634 \end{quote}
adam@1891 635
adamc@530 636 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@530 637 \begin{itemize}
adamc@655 638 \item $\Gamma \vdash \kappa$ expresses kind well-formedness.
adamc@530 639 \item $\Gamma \vdash c :: \kappa$ assigns a kind to a constructor in a context.
adamc@530 640 \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@531 641 \item $\Gamma \vdash c \hookrightarrow C$ proves that record constructor $c$ decomposes into set $C$ of field names and record constructors.
adamc@530 642 \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@530 643 \item $\Gamma \vdash e : \tau$ is a standard typing judgment.
adamc@534 644 \item $\Gamma \vdash p \leadsto \Gamma; \tau$ combines typing of patterns with calculation of which new variables they bind.
adamc@537 645 \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@537 646 \item $\Gamma \vdash S \equiv S$ is the signature equivalence judgment.
adamc@536 647 \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@530 648 \item $\Gamma \vdash M : S$ is the module signature checking judgment.
adamc@537 649 \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@539 650 \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@530 651 \end{itemize}
adamc@530 652
adamc@655 653
adamc@655 654 \subsection{Kind Well-Formedness}
adamc@655 655
adamc@655 656 $$\infer{\Gamma \vdash \mt{Type}}{}
adamc@655 657 \quad \infer{\Gamma \vdash \mt{Unit}}{}
adamc@655 658 \quad \infer{\Gamma \vdash \mt{Name}}{}
adamc@655 659 \quad \infer{\Gamma \vdash \kappa_1 \to \kappa_2}{
adamc@655 660 \Gamma \vdash \kappa_1
adamc@655 661 & \Gamma \vdash \kappa_2
adamc@655 662 }
adamc@655 663 \quad \infer{\Gamma \vdash \{\kappa\}}{
adamc@655 664 \Gamma \vdash \kappa
adamc@655 665 }
adamc@655 666 \quad \infer{\Gamma \vdash (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@655 667 \forall i: \Gamma \vdash \kappa_i
adamc@655 668 }$$
adamc@655 669
adamc@655 670 $$\infer{\Gamma \vdash X}{
adamc@655 671 X \in \Gamma
adamc@655 672 }
adamc@655 673 \quad \infer{\Gamma \vdash X \longrightarrow \kappa}{
adamc@655 674 \Gamma, X \vdash \kappa
adamc@655 675 }$$
adamc@655 676
adamc@530 677 \subsection{Kinding}
adamc@530 678
adamc@655 679 We write $[X \mapsto \kappa_1]\kappa_2$ for capture-avoiding substitution of $\kappa_1$ for $X$ in $\kappa_2$.
adamc@655 680
adamc@530 681 $$\infer{\Gamma \vdash (c) :: \kappa :: \kappa}{
adamc@530 682 \Gamma \vdash c :: \kappa
adamc@530 683 }
adamc@530 684 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530 685 x :: \kappa \in \Gamma
adamc@530 686 }
adamc@530 687 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530 688 x :: \kappa = c \in \Gamma
adamc@530 689 }$$
adamc@530 690
adamc@530 691 $$\infer{\Gamma \vdash M.x :: \kappa}{
adamc@537 692 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 693 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = \kappa
adamc@530 694 }
adamc@530 695 \quad \infer{\Gamma \vdash M.x :: \kappa}{
adamc@537 696 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 697 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@530 698 }$$
adamc@530 699
adamc@530 700 $$\infer{\Gamma \vdash \tau_1 \to \tau_2 :: \mt{Type}}{
adamc@530 701 \Gamma \vdash \tau_1 :: \mt{Type}
adamc@530 702 & \Gamma \vdash \tau_2 :: \mt{Type}
adamc@530 703 }
adamc@530 704 \quad \infer{\Gamma \vdash x \; ? \: \kappa \to \tau :: \mt{Type}}{
adamc@530 705 \Gamma, x :: \kappa \vdash \tau :: \mt{Type}
adamc@530 706 }
adamc@655 707 \quad \infer{\Gamma \vdash X \longrightarrow \tau :: \mt{Type}}{
adamc@655 708 \Gamma, X \vdash \tau :: \mt{Type}
adamc@655 709 }
adamc@530 710 \quad \infer{\Gamma \vdash \$c :: \mt{Type}}{
adamc@530 711 \Gamma \vdash c :: \{\mt{Type}\}
adamc@530 712 }$$
adamc@530 713
adamc@530 714 $$\infer{\Gamma \vdash c_1 \; c_2 :: \kappa_2}{
adamc@530 715 \Gamma \vdash c_1 :: \kappa_1 \to \kappa_2
adamc@530 716 & \Gamma \vdash c_2 :: \kappa_1
adamc@530 717 }
adamc@530 718 \quad \infer{\Gamma \vdash \lambda x \; :: \; \kappa_1 \Rightarrow c :: \kappa_1 \to \kappa_2}{
adamc@530 719 \Gamma, x :: \kappa_1 \vdash c :: \kappa_2
adamc@530 720 }$$
adamc@530 721
adamc@655 722 $$\infer{\Gamma \vdash c[\kappa'] :: [X \mapsto \kappa']\kappa}{
adamc@655 723 \Gamma \vdash c :: X \to \kappa
adamc@655 724 & \Gamma \vdash \kappa'
adamc@655 725 }
adamc@655 726 \quad \infer{\Gamma \vdash X \Longrightarrow c :: X \to \kappa}{
adamc@655 727 \Gamma, X \vdash c :: \kappa
adamc@655 728 }$$
adamc@655 729
adamc@530 730 $$\infer{\Gamma \vdash () :: \mt{Unit}}{}
adamc@530 731 \quad \infer{\Gamma \vdash \#X :: \mt{Name}}{}$$
adamc@530 732
adamc@530 733 $$\infer{\Gamma \vdash [\overline{c_i = c'_i}] :: \{\kappa\}}{
adamc@530 734 \forall i: \Gamma \vdash c_i : \mt{Name}
adamc@530 735 & \Gamma \vdash c'_i :: \kappa
adamc@530 736 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@530 737 }
adamc@530 738 \quad \infer{\Gamma \vdash c_1 \rc c_2 :: \{\kappa\}}{
adamc@530 739 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530 740 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@530 741 & \Gamma \vdash c_1 \sim c_2
adamc@530 742 }$$
adamc@530 743
adamc@655 744 $$\infer{\Gamma \vdash \mt{map} :: (\kappa_1 \to \kappa_2) \to \{\kappa_1\} \to \{\kappa_2\}}{}$$
adamc@530 745
adamc@573 746 $$\infer{\Gamma \vdash (\overline c) :: (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@573 747 \forall i: \Gamma \vdash c_i :: \kappa_i
adamc@530 748 }
adamc@573 749 \quad \infer{\Gamma \vdash c.i :: \kappa_i}{
adamc@573 750 \Gamma \vdash c :: (\kappa_1 \times \ldots \times \kappa_n)
adamc@530 751 }$$
adamc@530 752
adamc@655 753 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow \tau :: \mt{Type}}{
adamc@655 754 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530 755 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@655 756 & \Gamma, c_1 \sim c_2 \vdash \tau :: \mt{Type}
adamc@530 757 }$$
adamc@530 758
adamc@531 759 \subsection{Record Disjointness}
adamc@531 760
adamc@531 761 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@558 762 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@558 763 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@558 764 & \forall c'_1 \in C_1, c'_2 \in C_2: \Gamma \vdash c'_1 \sim c'_2
adamc@531 765 }
adamc@531 766 \quad \infer{\Gamma \vdash X \sim X'}{
adamc@531 767 X \neq X'
adamc@531 768 }$$
adamc@531 769
adamc@531 770 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@531 771 c'_1 \sim c'_2 \in \Gamma
adamc@558 772 & \Gamma \vdash c'_1 \hookrightarrow C_1
adamc@558 773 & \Gamma \vdash c'_2 \hookrightarrow C_2
adamc@558 774 & c_1 \in C_1
adamc@558 775 & c_2 \in C_2
adamc@531 776 }$$
adamc@531 777
adamc@531 778 $$\infer{\Gamma \vdash c \hookrightarrow \{c\}}{}
adamc@531 779 \quad \infer{\Gamma \vdash [\overline{c = c'}] \hookrightarrow \{\overline{c}\}}{}
adamc@531 780 \quad \infer{\Gamma \vdash c_1 \rc c_2 \hookrightarrow C_1 \cup C_2}{
adamc@531 781 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@531 782 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@531 783 }
adamc@531 784 \quad \infer{\Gamma \vdash c \hookrightarrow C}{
adamc@531 785 \Gamma \vdash c \equiv c'
adamc@531 786 & \Gamma \vdash c' \hookrightarrow C
adamc@531 787 }
adamc@531 788 \quad \infer{\Gamma \vdash \mt{map} \; f \; c \hookrightarrow C}{
adamc@531 789 \Gamma \vdash c \hookrightarrow C
adamc@531 790 }$$
adamc@531 791
adamc@541 792 \subsection{\label{definitional}Definitional Equality}
adamc@532 793
adamc@655 794 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@532 795
adamc@532 796 $$\infer{\Gamma \vdash c \equiv c}{}
adamc@532 797 \quad \infer{\Gamma \vdash c_1 \equiv c_2}{
adamc@532 798 \Gamma \vdash c_2 \equiv c_1
adamc@532 799 }
adamc@532 800 \quad \infer{\Gamma \vdash c_1 \equiv c_3}{
adamc@532 801 \Gamma \vdash c_1 \equiv c_2
adamc@532 802 & \Gamma \vdash c_2 \equiv c_3
adamc@532 803 }
adamc@532 804 \quad \infer{\Gamma \vdash \mathcal C[c_1] \equiv \mathcal C[c_2]}{
adamc@532 805 \Gamma \vdash c_1 \equiv c_2
adamc@532 806 }$$
adamc@532 807
adamc@532 808 $$\infer{\Gamma \vdash x \equiv c}{
adamc@532 809 x :: \kappa = c \in \Gamma
adamc@532 810 }
adamc@532 811 \quad \infer{\Gamma \vdash M.x \equiv c}{
adamc@537 812 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 813 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@532 814 }
adamc@532 815 \quad \infer{\Gamma \vdash (\overline c).i \equiv c_i}{}$$
adamc@532 816
adamc@532 817 $$\infer{\Gamma \vdash (\lambda x :: \kappa \Rightarrow c) \; c' \equiv [x \mapsto c'] c}{}
adamc@655 818 \quad \infer{\Gamma \vdash (X \Longrightarrow c) [\kappa] \equiv [X \mapsto \kappa] c}{}$$
adamc@655 819
adamc@655 820 $$\infer{\Gamma \vdash c_1 \rc c_2 \equiv c_2 \rc c_1}{}
adamc@532 821 \quad \infer{\Gamma \vdash c_1 \rc (c_2 \rc c_3) \equiv (c_1 \rc c_2) \rc c_3}{}$$
adamc@532 822
adamc@532 823 $$\infer{\Gamma \vdash [] \rc c \equiv c}{}
adamc@532 824 \quad \infer{\Gamma \vdash [\overline{c_1 = c'_1}] \rc [\overline{c_2 = c'_2}] \equiv [\overline{c_1 = c'_1}, \overline{c_2 = c'_2}]}{}$$
adamc@532 825
adamc@655 826 $$\infer{\Gamma \vdash \mt{map} \; f \; [] \equiv []}{}
adamc@655 827 \quad \infer{\Gamma \vdash \mt{map} \; f \; ([c_1 = c_2] \rc c) \equiv [c_1 = f \; c_2] \rc \mt{map} \; f \; c}{}$$
adamc@532 828
adamc@532 829 $$\infer{\Gamma \vdash \mt{map} \; (\lambda x \Rightarrow x) \; c \equiv c}{}
adamc@655 830 \quad \infer{\Gamma \vdash \mt{map} \; f \; (\mt{map} \; f' \; c)
adamc@655 831 \equiv \mt{map} \; (\lambda x \Rightarrow f \; (f' \; x)) \; c}{}$$
adamc@532 832
adamc@532 833 $$\infer{\Gamma \vdash \mt{map} \; f \; (c_1 \rc c_2) \equiv \mt{map} \; f \; c_1 \rc \mt{map} \; f \; c_2}{}$$
adamc@531 834
adamc@534 835 \subsection{Expression Typing}
adamc@533 836
adamc@873 837 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@533 838
adamc@533 839 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@533 840
adamc@533 841 $$\infer{\Gamma \vdash e : \tau : \tau}{
adamc@533 842 \Gamma \vdash e : \tau
adamc@533 843 }
adamc@533 844 \quad \infer{\Gamma \vdash e : \tau}{
adamc@533 845 \Gamma \vdash e : \tau'
adamc@533 846 & \Gamma \vdash \tau' \equiv \tau
adamc@533 847 }
adamc@533 848 \quad \infer{\Gamma \vdash \ell : T(\ell)}{}$$
adamc@533 849
adamc@533 850 $$\infer{\Gamma \vdash x : \mathcal I(\tau)}{
adamc@533 851 x : \tau \in \Gamma
adamc@533 852 }
adamc@533 853 \quad \infer{\Gamma \vdash M.x : \mathcal I(\tau)}{
adamc@537 854 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 855 & \mt{proj}(M, \overline{s}, \mt{val} \; x) = \tau
adamc@533 856 }
adamc@533 857 \quad \infer{\Gamma \vdash X : \mathcal I(\tau)}{
adamc@533 858 X : \tau \in \Gamma
adamc@533 859 }
adamc@533 860 \quad \infer{\Gamma \vdash M.X : \mathcal I(\tau)}{
adamc@537 861 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 862 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \tau
adamc@533 863 }$$
adamc@533 864
adamc@533 865 $$\infer{\Gamma \vdash e_1 \; e_2 : \tau_2}{
adamc@533 866 \Gamma \vdash e_1 : \tau_1 \to \tau_2
adamc@533 867 & \Gamma \vdash e_2 : \tau_1
adamc@533 868 }
adamc@533 869 \quad \infer{\Gamma \vdash \lambda x : \tau_1 \Rightarrow e : \tau_1 \to \tau_2}{
adamc@533 870 \Gamma, x : \tau_1 \vdash e : \tau_2
adamc@533 871 }$$
adamc@533 872
adamc@533 873 $$\infer{\Gamma \vdash e [c] : [x \mapsto c]\tau}{
adamc@533 874 \Gamma \vdash e : x :: \kappa \to \tau
adamc@533 875 & \Gamma \vdash c :: \kappa
adamc@533 876 }
adamc@852 877 \quad \infer{\Gamma \vdash \lambda [x \; ? \; \kappa] \Rightarrow e : x \; ? \; \kappa \to \tau}{
adamc@533 878 \Gamma, x :: \kappa \vdash e : \tau
adamc@533 879 }$$
adamc@533 880
adamc@655 881 $$\infer{\Gamma \vdash e [\kappa] : [X \mapsto \kappa]\tau}{
adamc@655 882 \Gamma \vdash e : X \longrightarrow \tau
adamc@655 883 & \Gamma \vdash \kappa
adamc@655 884 }
adamc@655 885 \quad \infer{\Gamma \vdash X \Longrightarrow e : X \longrightarrow \tau}{
adamc@655 886 \Gamma, X \vdash e : \tau
adamc@655 887 }$$
adamc@655 888
adamc@533 889 $$\infer{\Gamma \vdash \{\overline{c = e}\} : \{\overline{c : \tau}\}}{
adamc@533 890 \forall i: \Gamma \vdash c_i :: \mt{Name}
adamc@533 891 & \Gamma \vdash e_i : \tau_i
adamc@533 892 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@533 893 }
adamc@533 894 \quad \infer{\Gamma \vdash e.c : \tau}{
adamc@533 895 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533 896 }
adamc@533 897 \quad \infer{\Gamma \vdash e_1 \rc e_2 : \$(c_1 \rc c_2)}{
adamc@533 898 \Gamma \vdash e_1 : \$c_1
adamc@533 899 & \Gamma \vdash e_2 : \$c_2
adamc@573 900 & \Gamma \vdash c_1 \sim c_2
adamc@533 901 }$$
adamc@533 902
adamc@533 903 $$\infer{\Gamma \vdash e \rcut c : \$c'}{
adamc@533 904 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533 905 }
adamc@533 906 \quad \infer{\Gamma \vdash e \rcutM c : \$c'}{
adamc@533 907 \Gamma \vdash e : \$(c \rc c')
adamc@533 908 }$$
adamc@533 909
adamc@533 910 $$\infer{\Gamma \vdash \mt{let} \; \overline{ed} \; \mt{in} \; e \; \mt{end} : \tau}{
adamc@533 911 \Gamma \vdash \overline{ed} \leadsto \Gamma'
adamc@533 912 & \Gamma' \vdash e : \tau
adamc@533 913 }
adamc@533 914 \quad \infer{\Gamma \vdash \mt{case} \; e \; \mt{of} \; \overline{p \Rightarrow e} : \tau}{
adamc@533 915 \forall i: \Gamma \vdash p_i \leadsto \Gamma_i, \tau'
adamc@533 916 & \Gamma_i \vdash e_i : \tau
adamc@533 917 }$$
adamc@533 918
adamc@573 919 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow e : \lambda [c_1 \sim c_2] \Rightarrow \tau}{
adamc@533 920 \Gamma \vdash c_1 :: \{\kappa\}
adamc@655 921 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@533 922 & \Gamma, c_1 \sim c_2 \vdash e : \tau
adamc@662 923 }
adamc@662 924 \quad \infer{\Gamma \vdash e \; ! : \tau}{
adamc@662 925 \Gamma \vdash e : [c_1 \sim c_2] \Rightarrow \tau
adamc@662 926 & \Gamma \vdash c_1 \sim c_2
adamc@533 927 }$$
adamc@533 928
adamc@534 929 \subsection{Pattern Typing}
adamc@534 930
adamc@534 931 $$\infer{\Gamma \vdash \_ \leadsto \Gamma; \tau}{}
adamc@534 932 \quad \infer{\Gamma \vdash x \leadsto \Gamma, x : \tau; \tau}{}
adamc@534 933 \quad \infer{\Gamma \vdash \ell \leadsto \Gamma; T(\ell)}{}$$
adamc@534 934
adamc@534 935 $$\infer{\Gamma \vdash X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534 936 X : \overline{x ::: \mt{Type}} \to \tau \in \Gamma
adamc@534 937 & \textrm{$\tau$ not a function type}
adamc@534 938 }
adamc@534 939 \quad \infer{\Gamma \vdash X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534 940 X : \overline{x ::: \mt{Type}} \to \tau'' \to \tau \in \Gamma
adamc@534 941 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534 942 }$$
adamc@534 943
adamc@534 944 $$\infer{\Gamma \vdash M.X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537 945 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 946 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau
adamc@534 947 & \textrm{$\tau$ not a function type}
adamc@534 948 }$$
adamc@534 949
adamc@534 950 $$\infer{\Gamma \vdash M.X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537 951 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 952 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau'' \to \tau
adamc@534 953 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534 954 }$$
adamc@534 955
adamc@534 956 $$\infer{\Gamma \vdash \{\overline{x = p}\} \leadsto \Gamma_n; \{\overline{x = \tau}\}}{
adamc@534 957 \Gamma_0 = \Gamma
adamc@534 958 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534 959 }
adamc@534 960 \quad \infer{\Gamma \vdash \{\overline{x = p}, \ldots\} \leadsto \Gamma_n; \$([\overline{x = \tau}] \rc c)}{
adamc@534 961 \Gamma_0 = \Gamma
adamc@534 962 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534 963 }$$
adamc@534 964
adamc@852 965 $$\infer{\Gamma \vdash p : \tau \leadsto \Gamma'; \tau}{
adamc@852 966 \Gamma \vdash p \leadsto \Gamma'; \tau'
adamc@852 967 & \Gamma \vdash \tau' \equiv \tau
adamc@852 968 }$$
adamc@852 969
adamc@535 970 \subsection{Declaration Typing}
adamc@535 971
adamc@535 972 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@535 973
adamc@558 974 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@537 975 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@535 976
adamc@535 977 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535 978 \quad \infer{\Gamma \vdash d, \overline{d} \leadsto \Gamma''}{
adamc@535 979 \Gamma \vdash d \leadsto \Gamma'
adamc@535 980 & \Gamma' \vdash \overline{d} \leadsto \Gamma''
adamc@535 981 }$$
adamc@535 982
adamc@535 983 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@535 984 \Gamma \vdash c :: \kappa
adamc@535 985 }
adamc@535 986 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@535 987 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@535 988 }$$
adamc@535 989
adamc@535 990 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537 991 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 992 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@535 993 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@535 994 }$$
adamc@535 995
adamc@535 996 $$\infer{\Gamma \vdash \mt{val} \; x : \tau = e \leadsto \Gamma, x : \tau}{
adamc@535 997 \Gamma \vdash e : \tau
adamc@535 998 }$$
adamc@535 999
adamc@535 1000 $$\infer{\Gamma \vdash \mt{val} \; \mt{rec} \; \overline{x : \tau = e} \leadsto \Gamma, \overline{x : \tau}}{
adamc@535 1001 \forall i: \Gamma, \overline{x : \tau} \vdash e_i : \tau_i
adamc@535 1002 & \textrm{$e_i$ starts with an expression $\lambda$, optionally preceded by constructor and disjointness $\lambda$s}
adamc@535 1003 }$$
adamc@535 1004
adamc@535 1005 $$\infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : S}{
adamc@535 1006 \Gamma \vdash M : S
adamc@558 1007 & \textrm{ $M$ not a constant or application}
adamc@535 1008 }
adamc@558 1009 \quad \infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : \mt{selfify}(X, \overline{s})}{
adamc@558 1010 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@539 1011 }$$
adamc@539 1012
adamc@539 1013 $$\infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@535 1014 \Gamma \vdash S
adamc@535 1015 }$$
adamc@535 1016
adamc@537 1017 $$\infer{\Gamma \vdash \mt{open} \; M \leadsto \Gamma, \mathcal O(M, \overline{s})}{
adamc@537 1018 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535 1019 }$$
adamc@535 1020
adamc@535 1021 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma}{
adamc@535 1022 \Gamma \vdash c_1 :: \{\kappa\}
adamc@535 1023 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@535 1024 & \Gamma \vdash c_1 \sim c_2
adamc@535 1025 }
adamc@537 1026 \quad \infer{\Gamma \vdash \mt{open} \; \mt{constraints} \; M \leadsto \Gamma, \mathcal O_c(M, \overline{s})}{
adamc@537 1027 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535 1028 }$$
adamc@535 1029
adamc@784 1030 $$\infer{\Gamma \vdash \mt{table} \; x : c \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_table} \; c \; []}{
adamc@535 1031 \Gamma \vdash c :: \{\mt{Type}\}
adamc@535 1032 }
adam@1594 1033 \quad \infer{\Gamma \vdash \mt{view} \; x = e \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_view} \; c}{
adam@1594 1034 \Gamma \vdash e :: \mt{Basis}.\mt{sql\_query} \; [] \; [] \; (\mt{map} \; (\lambda \_ \Rightarrow []) \; c') \; c
adamc@784 1035 }$$
adamc@784 1036
adamc@784 1037 $$\infer{\Gamma \vdash \mt{sequence} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_sequence}}{}$$
adamc@535 1038
adamc@535 1039 $$\infer{\Gamma \vdash \mt{cookie} \; x : \tau \leadsto \Gamma, x : \mt{Basis}.\mt{http\_cookie} \; \tau}{
adamc@535 1040 \Gamma \vdash \tau :: \mt{Type}
adamc@784 1041 }
adamc@784 1042 \quad \infer{\Gamma \vdash \mt{style} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{css\_class}}{}$$
adamc@535 1043
adamc@1085 1044 $$\infer{\Gamma \vdash \mt{task} \; e_1 = e_2 \leadsto \Gamma}{
adam@1348 1045 \Gamma \vdash e_1 :: \mt{Basis}.\mt{task\_kind} \; \tau
adam@1348 1046 & \Gamma \vdash e_2 :: \tau \to \mt{Basis}.\mt{transaction} \; \{\}
adamc@1085 1047 }$$
adamc@1085 1048
adamc@535 1049 $$\infer{\overline{y}; x; \Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535 1050 \quad \infer{\overline{y}; x; \Gamma \vdash X \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to x \; \overline{y}}{
adamc@535 1051 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535 1052 }
adamc@535 1053 \quad \infer{\overline{y}; x; \Gamma \vdash X \; \mt{of} \; \tau \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to \tau \to x \; \overline{y}}{
adamc@535 1054 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535 1055 }$$
adamc@535 1056
adamc@537 1057 \subsection{Signature Item Typing}
adamc@537 1058
adamc@537 1059 We appeal to a signature item analogue of the $\mathcal O$ function from the last subsection.
adamc@537 1060
adam@1797 1061 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 1062
adamc@537 1063 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@537 1064 \quad \infer{\Gamma \vdash s, \overline{s} \leadsto \Gamma''}{
adamc@537 1065 \Gamma \vdash s \leadsto \Gamma'
adamc@537 1066 & \Gamma' \vdash \overline{s} \leadsto \Gamma''
adamc@537 1067 }$$
adamc@537 1068
adamc@537 1069 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}
adamc@537 1070 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@537 1071 \Gamma \vdash c :: \kappa
adamc@537 1072 }
adamc@537 1073 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@537 1074 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@537 1075 }$$
adamc@537 1076
adamc@537 1077 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537 1078 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1079 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1080 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@537 1081 }$$
adamc@537 1082
adamc@537 1083 $$\infer{\Gamma \vdash \mt{val} \; x : \tau \leadsto \Gamma, x : \tau}{
adamc@537 1084 \Gamma \vdash \tau :: \mt{Type}
adamc@537 1085 }$$
adamc@537 1086
adamc@537 1087 $$\infer{\Gamma \vdash \mt{structure} \; X : S \leadsto \Gamma, X : S}{
adamc@537 1088 \Gamma \vdash S
adamc@537 1089 }
adamc@537 1090 \quad \infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@537 1091 \Gamma \vdash S
adamc@537 1092 }$$
adamc@537 1093
adamc@537 1094 $$\infer{\Gamma \vdash \mt{include} \; S \leadsto \Gamma, \mathcal O(\overline{s})}{
adamc@537 1095 \Gamma \vdash S
adamc@537 1096 & \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1097 }$$
adamc@537 1098
adamc@537 1099 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma, c_1 \sim c_2}{
adamc@537 1100 \Gamma \vdash c_1 :: \{\kappa\}
adamc@537 1101 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@537 1102 }$$
adamc@537 1103
adamc@784 1104 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784 1105 \Gamma \vdash c :: \kappa
adamc@537 1106 }
adamc@784 1107 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}$$
adamc@537 1108
adamc@536 1109 \subsection{Signature Compatibility}
adamc@536 1110
adam@1797 1111 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 1112
adamc@537 1113 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 1114
adamc@536 1115 $$\infer{\Gamma \vdash S \equiv S}{}
adamc@536 1116 \quad \infer{\Gamma \vdash S_1 \equiv S_2}{
adamc@536 1117 \Gamma \vdash S_2 \equiv S_1
adamc@536 1118 }
adamc@536 1119 \quad \infer{\Gamma \vdash X \equiv S}{
adamc@536 1120 X = S \in \Gamma
adamc@536 1121 }
adamc@536 1122 \quad \infer{\Gamma \vdash M.X \equiv S}{
adamc@537 1123 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1124 & \mt{proj}(M, \overline{s}, \mt{signature} \; X) = S
adamc@536 1125 }$$
adamc@536 1126
adamc@536 1127 $$\infer{\Gamma \vdash S \; \mt{where} \; \mt{con} \; x = c \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa = c \; \overline{s_2} \; \mt{end}}{
adamc@536 1128 \Gamma \vdash S \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa \; \overline{s_2} \; \mt{end}
adamc@536 1129 & \Gamma \vdash c :: \kappa
adamc@537 1130 }
adamc@537 1131 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s^1} \; \mt{include} \; S \; \overline{s^2} \; \mt{end} \equiv \mt{sig} \; \overline{s^1} \; \overline{s} \; \overline{s^2} \; \mt{end}}{
adamc@537 1132 \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@536 1133 }$$
adamc@536 1134
adamc@536 1135 $$\infer{\Gamma \vdash S_1 \leq S_2}{
adamc@536 1136 \Gamma \vdash S_1 \equiv S_2
adamc@536 1137 }
adamc@536 1138 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \mt{end}}{}
adamc@537 1139 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; s' \; \overline{s'} \; \mt{end}}{
adamc@537 1140 \Gamma \vdash \overline{s} \leq s'
adamc@537 1141 & \Gamma \vdash s' \leadsto \Gamma'
adamc@537 1142 & \Gamma' \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \overline{s'} \; \mt{end}
adamc@537 1143 }$$
adamc@537 1144
adamc@537 1145 $$\infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537 1146 \Gamma \vdash s \leq s'
adamc@537 1147 }
adamc@537 1148 \quad \infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537 1149 \Gamma \vdash s \leadsto \Gamma'
adamc@537 1150 & \Gamma' \vdash \overline{s} \leq s'
adamc@536 1151 }$$
adamc@536 1152
adamc@536 1153 $$\infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 \leq \mt{functor} (X : S'_1) : S'_2}{
adamc@536 1154 \Gamma \vdash S'_1 \leq S_1
adamc@536 1155 & \Gamma, X : S'_1 \vdash S_2 \leq S'_2
adamc@536 1156 }$$
adamc@536 1157
adamc@537 1158 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@537 1159 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}
adamc@558 1160 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type}}{}$$
adamc@537 1161
adamc@537 1162 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(y)} \to \mt{Type}}{
adamc@537 1163 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1164 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1165 }$$
adamc@537 1166
adamc@784 1167 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@784 1168 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}$$
adamc@537 1169
adamc@537 1170 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \mt{\kappa} = c_2}{
adamc@537 1171 \Gamma \vdash c_1 \equiv c_2
adamc@537 1172 }
adamc@784 1173 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \kappa = c_2}{
adamc@537 1174 \Gamma \vdash c_1 \equiv c_2
adamc@537 1175 }$$
adamc@537 1176
adamc@537 1177 $$\infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537 1178 \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1179 }$$
adamc@537 1180
adamc@537 1181 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537 1182 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1183 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1184 & \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1185 }$$
adamc@537 1186
adamc@537 1187 $$\infer{\Gamma \vdash \cdot \leq \cdot}{}
adamc@537 1188 \quad \infer{\Gamma \vdash X; \overline{dc} \leq X; \overline{dc'}}{
adamc@537 1189 \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1190 }
adamc@537 1191 \quad \infer{\Gamma \vdash X \; \mt{of} \; \tau_1; \overline{dc} \leq X \; \mt{of} \; \tau_2; \overline{dc'}}{
adamc@537 1192 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537 1193 & \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1194 }$$
adamc@537 1195
adamc@537 1196 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x = \mt{datatype} \; M'.z'}{
adamc@537 1197 \Gamma \vdash M.z \equiv M'.z'
adamc@537 1198 }$$
adamc@537 1199
adamc@537 1200 $$\infer{\Gamma \vdash \mt{val} \; x : \tau_1 \leq \mt{val} \; x : \tau_2}{
adamc@537 1201 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537 1202 }
adamc@537 1203 \quad \infer{\Gamma \vdash \mt{structure} \; X : S_1 \leq \mt{structure} \; X : S_2}{
adamc@537 1204 \Gamma \vdash S_1 \leq S_2
adamc@537 1205 }
adamc@537 1206 \quad \infer{\Gamma \vdash \mt{signature} \; X = S_1 \leq \mt{signature} \; X = S_2}{
adamc@537 1207 \Gamma \vdash S_1 \leq S_2
adamc@537 1208 & \Gamma \vdash S_2 \leq S_1
adamc@537 1209 }$$
adamc@537 1210
adamc@537 1211 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leq \mt{constraint} \; c'_1 \sim c'_2}{
adamc@537 1212 \Gamma \vdash c_1 \equiv c'_1
adamc@537 1213 & \Gamma \vdash c_2 \equiv c'_2
adamc@537 1214 }$$
adamc@537 1215
adamc@655 1216 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{class} \; x :: \kappa}{}
adamc@655 1217 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{class} \; x :: \kappa}{}
adamc@655 1218 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{class} \; x :: \kappa = c_2}{
adamc@537 1219 \Gamma \vdash c_1 \equiv c_2
adamc@537 1220 }$$
adamc@537 1221
adam@1797 1222 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leq \mt{class} \; x :: \kappa}{}
adam@1797 1223 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leq \mt{class} \; x :: \kappa}{}
adam@1797 1224 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c_1 \leq \mt{class} \; x :: \kappa = c_2}{
adam@1797 1225 \Gamma \vdash c_1 \equiv c_2
adam@1797 1226 }$$
adam@1797 1227
adamc@538 1228 \subsection{Module Typing}
adamc@538 1229
adamc@538 1230 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 1231
adamc@538 1232 $$\infer{\Gamma \vdash M : S}{
adamc@538 1233 \Gamma \vdash M : S'
adamc@538 1234 & \Gamma \vdash S' \leq S
adamc@538 1235 }
adamc@538 1236 \quad \infer{\Gamma \vdash \mt{struct} \; \overline{d} \; \mt{end} : \mt{sig} \; \mt{sigOf}(\overline{d}) \; \mt{end}}{
adamc@538 1237 \Gamma \vdash \overline{d} \leadsto \Gamma'
adamc@538 1238 }
adamc@538 1239 \quad \infer{\Gamma \vdash X : S}{
adamc@538 1240 X : S \in \Gamma
adamc@538 1241 }$$
adamc@538 1242
adamc@538 1243 $$\infer{\Gamma \vdash M.X : S}{
adamc@538 1244 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@538 1245 & \mt{proj}(M, \overline{s}, \mt{structure} \; X) = S
adamc@538 1246 }$$
adamc@538 1247
adamc@538 1248 $$\infer{\Gamma \vdash M_1(M_2) : [X \mapsto M_2]S_2}{
adamc@538 1249 \Gamma \vdash M_1 : \mt{functor}(X : S_1) : S_2
adamc@538 1250 & \Gamma \vdash M_2 : S_1
adamc@538 1251 }
adamc@538 1252 \quad \infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 = M : \mt{functor} (X : S_1) : S_2}{
adamc@538 1253 \Gamma \vdash S_1
adamc@538 1254 & \Gamma, X : S_1 \vdash S_2
adamc@538 1255 & \Gamma, X : S_1 \vdash M : S_2
adamc@538 1256 }$$
adamc@538 1257
adamc@538 1258 \begin{eqnarray*}
adamc@538 1259 \mt{sigOf}(\cdot) &=& \cdot \\
adamc@538 1260 \mt{sigOf}(s \; \overline{s'}) &=& \mt{sigOf}(s) \; \mt{sigOf}(\overline{s'}) \\
adamc@538 1261 \\
adamc@538 1262 \mt{sigOf}(\mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@538 1263 \mt{sigOf}(\mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \overline{dc} \\
adamc@538 1264 \mt{sigOf}(\mt{datatype} \; x = \mt{datatype} \; M.z) &=& \mt{datatype} \; x = \mt{datatype} \; M.z \\
adamc@538 1265 \mt{sigOf}(\mt{val} \; x : \tau = e) &=& \mt{val} \; x : \tau \\
adamc@538 1266 \mt{sigOf}(\mt{val} \; \mt{rec} \; \overline{x : \tau = e}) &=& \overline{\mt{val} \; x : \tau} \\
adamc@538 1267 \mt{sigOf}(\mt{structure} \; X : S = M) &=& \mt{structure} \; X : S \\
adamc@538 1268 \mt{sigOf}(\mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@538 1269 \mt{sigOf}(\mt{open} \; M) &=& \mt{include} \; S \textrm{ (where $\Gamma \vdash M : S$)} \\
adamc@538 1270 \mt{sigOf}(\mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@538 1271 \mt{sigOf}(\mt{open} \; \mt{constraints} \; M) &=& \cdot \\
adamc@538 1272 \mt{sigOf}(\mt{table} \; x : c) &=& \mt{table} \; x : c \\
adam@1594 1273 \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 1274 \mt{sigOf}(\mt{sequence} \; x) &=& \mt{sequence} \; x \\
adamc@538 1275 \mt{sigOf}(\mt{cookie} \; x : \tau) &=& \mt{cookie} \; x : \tau \\
adam@1797 1276 \mt{sigOf}(\mt{style} \; x) &=& \mt{style} \; x
adamc@538 1277 \end{eqnarray*}
adamc@539 1278 \begin{eqnarray*}
adamc@539 1279 \mt{selfify}(M, \cdot) &=& \cdot \\
adamc@558 1280 \mt{selfify}(M, s \; \overline{s'}) &=& \mt{selfify}(M, s) \; \mt{selfify}(M, \overline{s'}) \\
adamc@539 1281 \\
adamc@539 1282 \mt{selfify}(M, \mt{con} \; x :: \kappa) &=& \mt{con} \; x :: \kappa = M.x \\
adamc@539 1283 \mt{selfify}(M, \mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@539 1284 \mt{selfify}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \mt{datatype} \; M.x \\
adamc@539 1285 \mt{selfify}(M, \mt{datatype} \; x = \mt{datatype} \; M'.z) &=& \mt{datatype} \; x = \mt{datatype} \; M'.z \\
adamc@539 1286 \mt{selfify}(M, \mt{val} \; x : \tau) &=& \mt{val} \; x : \tau \\
adamc@539 1287 \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 1288 \mt{selfify}(M, \mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@539 1289 \mt{selfify}(M, \mt{include} \; S) &=& \mt{include} \; S \\
adamc@539 1290 \mt{selfify}(M, \mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@655 1291 \mt{selfify}(M, \mt{class} \; x :: \kappa) &=& \mt{class} \; x :: \kappa = M.x \\
adamc@655 1292 \mt{selfify}(M, \mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@539 1293 \end{eqnarray*}
adamc@539 1294
adamc@540 1295 \subsection{Module Projection}
adamc@540 1296
adamc@540 1297 \begin{eqnarray*}
adamc@540 1298 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \\
adamc@540 1299 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa, c) \\
adamc@540 1300 \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 1301 \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 1302 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})$)} \\
adamc@655 1303 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \to \mt{Type} \\
adamc@655 1304 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa \to \mt{Type}, c) \\
adamc@540 1305 \\
adamc@540 1306 \mt{proj}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc} \; \overline{s}, \mt{datatype} \; x) &=& (\overline{y}, \overline{dc}) \\
adamc@540 1307 \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 1308 \\
adamc@540 1309 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, \mt{val} \; x) &=& \tau \\
adamc@540 1310 \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 1311 \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 1312 \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 1313 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \in \overline{dc}$)} \\
adamc@540 1314 \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 1315 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \; \mt{of} \; \tau \in \overline{dc}$)} \\
adamc@540 1316 \\
adamc@540 1317 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, \mt{structure} \; X) &=& S \\
adamc@540 1318 \\
adamc@540 1319 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, \mt{signature} \; X) &=& S \\
adamc@540 1320 \\
adamc@540 1321 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1322 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1323 \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 1324 \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 1325 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@540 1326 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1327 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1328 \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 1329 \mt{proj}(M, \mt{constraint} \; c_1 \sim c_2 \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@655 1330 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@655 1331 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1332 \end{eqnarray*}
adamc@540 1333
adamc@541 1334
adamc@541 1335 \section{Type Inference}
adamc@541 1336
adamc@541 1337 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 1338
adamc@541 1339 \subsection{Basic Unification}
adamc@541 1340
adamc@560 1341 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 1342
adamc@656 1343 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 1344
adamc@541 1345 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 1346
adamc@541 1347 \subsection{Unifying Record Types}
adamc@541 1348
adamc@570 1349 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 1350
adamc@656 1351 \subsection{\label{typeclasses}Constructor Classes}
adamc@541 1352
adamc@784 1353 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 1354
adam@1797 1355 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 1356
adam@1797 1357 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 1358
adam@1797 1359 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 1360
adamc@541 1361 \subsection{Reverse-Engineering Record Types}
adamc@541 1362
adamc@656 1363 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 1364
adamc@541 1365 \subsection{Implicit Arguments in Functor Applications}
adamc@541 1366
adamc@656 1367 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 1368
adamc@541 1369
adamc@542 1370 \section{The Ur Standard Library}
adamc@542 1371
adamc@542 1372 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 1373
adamc@542 1374 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 1375
adamc@542 1376 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 1377 $$\begin{array}{l}
adamc@542 1378 \mt{type} \; \mt{int} \\
adamc@542 1379 \mt{type} \; \mt{float} \\
adamc@873 1380 \mt{type} \; \mt{char} \\
adamc@542 1381 \mt{type} \; \mt{string} \\
adamc@542 1382 \mt{type} \; \mt{time} \\
adamc@785 1383 \mt{type} \; \mt{blob} \\
adamc@542 1384 \\
adamc@542 1385 \mt{type} \; \mt{unit} = \{\} \\
adamc@542 1386 \\
adamc@542 1387 \mt{datatype} \; \mt{bool} = \mt{False} \mid \mt{True} \\
adamc@542 1388 \\
adamc@785 1389 \mt{datatype} \; \mt{option} \; \mt{t} = \mt{None} \mid \mt{Some} \; \mt{of} \; \mt{t} \\
adamc@785 1390 \\
adamc@785 1391 \mt{datatype} \; \mt{list} \; \mt{t} = \mt{Nil} \mid \mt{Cons} \; \mt{of} \; \mt{t} \times \mt{list} \; \mt{t}
adamc@542 1392 \end{array}$$
adamc@542 1393
adamc@1123 1394 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 1395
adam@1297 1396 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 1397 $$\begin{array}{l}
adam@1297 1398 \mt{con} \; \mt{variant} :: \{\mt{Type}\} \to \mt{Type} \\
adam@1297 1399 \mt{val} \; \mt{make} : \mt{nm} :: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{ts} ::: \{\mt{Type}\} \to [[\mt{nm}] \sim \mt{ts}] \Rightarrow \mt{t} \to \mt{variant} \; ([\mt{nm} = \mt{t}] \rc \mt{ts}) \\
adam@1297 1400 \mt{val} \; \mt{match} : \mt{ts} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{variant} \; \mt{ts} \to \$(\mt{map} \; (\lambda \mt{t'} \Rightarrow \mt{t'} \to \mt{t}) \; \mt{ts}) \to \mt{t}
adam@1297 1401 \end{array}$$
adam@1297 1402
adamc@657 1403 Another important generic Ur element comes at the beginning of \texttt{top.urs}.
adamc@657 1404
adamc@657 1405 $$\begin{array}{l}
adamc@657 1406 \mt{con} \; \mt{folder} :: \mt{K} \longrightarrow \{\mt{K}\} \to \mt{Type} \\
adamc@657 1407 \\
adamc@657 1408 \mt{val} \; \mt{fold} : \mt{K} \longrightarrow \mt{tf} :: (\{\mt{K}\} \to \mt{Type}) \\
adamc@657 1409 \hspace{.1in} \to (\mt{nm} :: \mt{Name} \to \mt{v} :: \mt{K} \to \mt{r} :: \{\mt{K}\} \to [[\mt{nm}] \sim \mt{r}] \Rightarrow \\
adamc@657 1410 \hspace{.2in} \mt{tf} \; \mt{r} \to \mt{tf} \; ([\mt{nm} = \mt{v}] \rc \mt{r})) \\
adamc@657 1411 \hspace{.1in} \to \mt{tf} \; [] \\
adamc@657 1412 \hspace{.1in} \to \mt{r} :: \{\mt{K}\} \to \mt{folder} \; \mt{r} \to \mt{tf} \; \mt{r}
adamc@657 1413 \end{array}$$
adamc@657 1414
adamc@657 1415 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 1416
adamc@664 1417 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 1418
adamc@542 1419
adamc@542 1420 \section{The Ur/Web Standard Library}
adamc@542 1421
adam@1400 1422 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 1423
adamc@658 1424 \subsection{Monads}
adamc@658 1425
adamc@658 1426 The Ur Basis defines the monad constructor class from Haskell.
adamc@658 1427
adamc@658 1428 $$\begin{array}{l}
adamc@658 1429 \mt{class} \; \mt{monad} :: \mt{Type} \to \mt{Type} \\
adamc@658 1430 \mt{val} \; \mt{return} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t} ::: \mt{Type} \\
adamc@658 1431 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658 1432 \hspace{.1in} \to \mt{t} \to \mt{m} \; \mt{t} \\
adamc@658 1433 \mt{val} \; \mt{bind} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t1} ::: \mt{Type} \to \mt{t2} ::: \mt{Type} \\
adamc@658 1434 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658 1435 \hspace{.1in} \to \mt{m} \; \mt{t1} \to (\mt{t1} \to \mt{m} \; \mt{t2}) \\
adam@1544 1436 \hspace{.1in} \to \mt{m} \; \mt{t2} \\
adam@1544 1437 \mt{val} \; \mt{mkMonad} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \\
adam@1544 1438 \hspace{.1in} \to \{\mt{Return} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{m} \; \mt{t}, \\
adam@1544 1439 \hspace{.3in} \mt{Bind} : \mt{t1} ::: \mt{Type} \to \mt{t2} ::: \mt{Type} \to \mt{m} \; \mt{t1} \to (\mt{t1} \to \mt{m} \; \mt{t2}) \to \mt{m} \; \mt{t2}\} \\
adam@1544 1440 \hspace{.1in} \to \mt{monad} \; \mt{m}
adamc@658 1441 \end{array}$$
adamc@658 1442
adam@1687 1443 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 1444
adam@2009 1445 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 1446
adamc@542 1447 \subsection{Transactions}
adamc@542 1448
adamc@542 1449 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 1450 $$\begin{array}{l}
adamc@542 1451 \mt{con} \; \mt{transaction} :: \mt{Type} \to \mt{Type} \\
adamc@658 1452 \mt{val} \; \mt{transaction\_monad} : \mt{monad} \; \mt{transaction}
adamc@542 1453 \end{array}$$
adamc@542 1454
adamc@1123 1455 For debugging purposes, a transactional function is provided for outputting a string on the server process' \texttt{stderr}.
adamc@1123 1456 $$\begin{array}{l}
adamc@1123 1457 \mt{val} \; \mt{debug} : \mt{string} \to \mt{transaction} \; \mt{unit}
adamc@1123 1458 \end{array}$$
adamc@1123 1459
adamc@542 1460 \subsection{HTTP}
adamc@542 1461
adam@1797 1462 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 1463 $$\begin{array}{l}
adamc@786 1464 \mt{con} \; \mt{http\_cookie} :: \mt{Type} \to \mt{Type} \\
adamc@786 1465 \mt{val} \; \mt{getCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; (\mt{option} \; \mt{t}) \\
adamc@1050 1466 \mt{val} \; \mt{setCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \{\mt{Value} : \mt{t}, \mt{Expires} : \mt{option} \; \mt{time}, \mt{Secure} : \mt{bool}\} \to \mt{transaction} \; \mt{unit} \\
adamc@1050 1467 \mt{val} \; \mt{clearCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; \mt{unit}
adamc@786 1468 \end{array}$$
adamc@786 1469
adamc@786 1470 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 1471 $$\begin{array}{l}
adamc@786 1472 \mt{type} \; \mt{url} \\
adamc@786 1473 \mt{val} \; \mt{bless} : \mt{string} \to \mt{url} \\
adamc@786 1474 \mt{val} \; \mt{checkUrl} : \mt{string} \to \mt{option} \; \mt{url}
adamc@786 1475 \end{array}$$
adamc@786 1476 $\mt{bless}$ raises a runtime error if the string passed to it fails the URL policy.
adamc@786 1477
adam@1400 1478 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 1479 $$\begin{array}{l}
adamc@1085 1480 \mt{val} \; \mt{currentUrl} : \mt{transaction} \; \mt{url} \\
adamc@1085 1481 \mt{val} \; \mt{url} : \mt{transaction} \; \mt{page} \to \mt{url}
adamc@1085 1482 \end{array}$$
adamc@1085 1483
adamc@1085 1484 Page generation may be interrupted at any time with a request to redirect to a particular URL instead.
adamc@1085 1485 $$\begin{array}{l}
adamc@1085 1486 \mt{val} \; \mt{redirect} : \mt{t} ::: \mt{Type} \to \mt{url} \to \mt{transaction} \; \mt{t}
adamc@1085 1487 \end{array}$$
adamc@1085 1488
adam@1400 1489 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 1490 $$\begin{array}{l}
adamc@786 1491 \mt{type} \; \mt{file} \\
adamc@786 1492 \mt{val} \; \mt{fileName} : \mt{file} \to \mt{option} \; \mt{string} \\
adamc@786 1493 \mt{val} \; \mt{fileMimeType} : \mt{file} \to \mt{string} \\
adamc@786 1494 \mt{val} \; \mt{fileData} : \mt{file} \to \mt{blob}
adamc@786 1495 \end{array}$$
adamc@786 1496
adam@1799 1497 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 1498
adam@1465 1499 $$\begin{array}{l}
adam@1465 1500 \mt{type} \; \mt{requestHeader} \\
adam@1465 1501 \mt{val} \; \mt{blessRequestHeader} : \mt{string} \to \mt{requestHeader} \\
adam@1465 1502 \mt{val} \; \mt{checkRequestHeader} : \mt{string} \to \mt{option} \; \mt{requestHeader} \\
adam@1465 1503 \mt{val} \; \mt{getHeader} : \mt{requestHeader} \to \mt{transaction} \; (\mt{option} \; \mt{string}) \\
adam@1465 1504 \\
adam@1799 1505 \mt{type} \; \mt{envVar} \\
adam@1799 1506 \mt{val} \; \mt{blessEnvVar} : \mt{string} \to \mt{envVar} \\
adam@1799 1507 \mt{val} \; \mt{checkEnvVar} : \mt{string} \to \mt{option} \; \mt{envVar} \\
adam@1799 1508 \mt{val} \; \mt{getenv} : \mt{envVar} \to \mt{transaction} \; (\mt{option} \; \mt{string}) \\
adam@1799 1509 \\
adam@1465 1510 \mt{type} \; \mt{responseHeader} \\
adam@1465 1511 \mt{val} \; \mt{blessResponseHeader} : \mt{string} \to \mt{responseHeader} \\
adam@1465 1512 \mt{val} \; \mt{checkResponseHeader} : \mt{string} \to \mt{option} \; \mt{responseHeader} \\
adam@1465 1513 \mt{val} \; \mt{setHeader} : \mt{responseHeader} \to \mt{string} \to \mt{transaction} \; \mt{unit}
adam@1465 1514 \end{array}$$
adam@1465 1515
adamc@786 1516 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 1517 $$\begin{array}{l}
adamc@786 1518 \mt{type} \; \mt{mimeType} \\
adamc@786 1519 \mt{val} \; \mt{blessMime} : \mt{string} \to \mt{mimeType} \\
adamc@786 1520 \mt{val} \; \mt{checkMime} : \mt{string} \to \mt{option} \; \mt{mimeType} \\
adamc@786 1521 \mt{val} \; \mt{returnBlob} : \mt{t} ::: \mt{Type} \to \mt{blob} \to \mt{mimeType} \to \mt{transaction} \; \mt{t}
adamc@542 1522 \end{array}$$
adamc@542 1523
adamc@543 1524 \subsection{SQL}
adamc@543 1525
adam@1400 1526 Everything about SQL database access is restricted to server-side code.
adam@1400 1527
adamc@543 1528 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 1529 $$\begin{array}{l}
adamc@785 1530 \mt{con} \; \mt{sql\_table} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785 1531 \end{array}$$
adamc@785 1532 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 1533
adamc@785 1534 We also have the simpler type family of SQL views, which have no keys.
adamc@785 1535 $$\begin{array}{l}
adamc@785 1536 \mt{con} \; \mt{sql\_view} :: \{\mt{Type}\} \to \mt{Type}
adamc@543 1537 \end{array}$$
adamc@543 1538
adamc@785 1539 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 1540 $$\begin{array}{l}
adamc@785 1541 \mt{class} \; \mt{fieldsOf} :: \mt{Type} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1542 \mt{val} \; \mt{fieldsOf\_table} : \mt{fs} ::: \{\mt{Type}\} \to \mt{keys} ::: \{\{\mt{Unit}\}\} \to \mt{fieldsOf} \; (\mt{sql\_table} \; \mt{fs} \; \mt{keys}) \; \mt{fs} \\
adamc@785 1543 \mt{val} \; \mt{fieldsOf\_view} : \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; (\mt{sql\_view} \; \mt{fs}) \; \mt{fs}
adamc@785 1544 \end{array}$$
adamc@785 1545
adamc@785 1546 \subsubsection{Table Constraints}
adamc@785 1547
adamc@785 1548 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 1549
adamc@785 1550 $$\begin{array}{l}
adamc@785 1551 \mt{con} \; \mt{primary\_key} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type} \\
adamc@785 1552 \mt{val} \; \mt{no\_primary\_key} : \mt{fs} ::: \{\mt{Type}\} \to \mt{primary\_key} \; \mt{fs} \; [] \\
adamc@785 1553 \mt{val} \; \mt{primary\_key} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{key1} :: \mt{Name} \to \mt{keys} :: \{\mt{Type}\} \\
adamc@785 1554 \hspace{.1in} \to [[\mt{key1}] \sim \mt{keys}] \Rightarrow [[\mt{key1} = \mt{t}] \rc \mt{keys} \sim \mt{rest}] \\
adamc@785 1555 \hspace{.1in} \Rightarrow \$([\mt{key1} = \mt{sql\_injectable\_prim} \; \mt{t}] \rc \mt{map} \; \mt{sql\_injectable\_prim} \; \mt{keys}) \\
adamc@785 1556 \hspace{.1in} \to \mt{primary\_key} \; ([\mt{key1} = \mt{t}] \rc \mt{keys} \rc \mt{rest}) \; [\mt{Pkey} = [\mt{key1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{keys}]
adamc@785 1557 \end{array}$$
adamc@785 1558 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 1559
adamc@785 1560 A type family stands for sets of named constraints of the remaining varieties.
adamc@785 1561 $$\begin{array}{l}
adamc@785 1562 \mt{con} \; \mt{sql\_constraints} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785 1563 \end{array}$$
adamc@785 1564 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 1565
adamc@785 1566 There is a type family of individual, unnamed constraints.
adamc@785 1567 $$\begin{array}{l}
adamc@785 1568 \mt{con} \; \mt{sql\_constraint} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \mt{Type}
adamc@785 1569 \end{array}$$
adamc@785 1570 The first argument is the same as above, and the second argument gives the key columns for just this constraint.
adamc@785 1571
adamc@785 1572 We have operations for assembling constraints into constraint sets.
adamc@785 1573 $$\begin{array}{l}
adamc@785 1574 \mt{val} \; \mt{no\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_constraints} \; \mt{fs} \; [] \\
adamc@785 1575 \mt{val} \; \mt{one\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{unique} ::: \{\mt{Unit}\} \to \mt{name} :: \mt{Name} \\
adamc@785 1576 \hspace{.1in} \to \mt{sql\_constraint} \; \mt{fs} \; \mt{unique} \to \mt{sql\_constraints} \; \mt{fs} \; [\mt{name} = \mt{unique}] \\
adamc@785 1577 \mt{val} \; \mt{join\_constraints} : \mt{fs} ::: \{\mt{Type}\} \to \mt{uniques1} ::: \{\{\mt{Unit}\}\} \to \mt{uniques2} ::: \{\{\mt{Unit}\}\} \to [\mt{uniques1} \sim \mt{uniques2}] \\
adamc@785 1578 \hspace{.1in} \Rightarrow \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques1} \to \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques2} \to \mt{sql\_constraints} \; \mt{fs} \; (\mt{uniques1} \rc \mt{uniques2})
adamc@785 1579 \end{array}$$
adamc@785 1580
adamc@785 1581 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 1582 $$\begin{array}{l}
adamc@785 1583 \mt{val} \; \mt{unique} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{unique1} :: \mt{Name} \to \mt{unique} :: \{\mt{Type}\} \\
adamc@785 1584 \hspace{.1in} \to [[\mt{unique1}] \sim \mt{unique}] \Rightarrow [[\mt{unique1} = \mt{t}] \rc \mt{unique} \sim \mt{rest}] \\
adamc@785 1585 \hspace{.1in} \Rightarrow \mt{sql\_constraint} \; ([\mt{unique1} = \mt{t}] \rc \mt{unique} \rc \mt{rest}) \; ([\mt{unique1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{unique})
adamc@785 1586 \end{array}$$
adamc@785 1587
adamc@785 1588 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 1589 $$\begin{array}{l}
adamc@785 1590 \mt{class} \; \mt{linkable} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@785 1591 \mt{val} \; \mt{linkable\_same} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; \mt{t} \\
adamc@785 1592 \mt{val} \; \mt{linkable\_from\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; (\mt{option} \; \mt{t}) \; \mt{t} \\
adamc@785 1593 \mt{val} \; \mt{linkable\_to\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@785 1594 \end{array}$$
adamc@785 1595
adamc@785 1596 The $\mt{matching}$ type family uses $\mt{linkable}$ to define when two keys match up type-wise.
adamc@785 1597 $$\begin{array}{l}
adamc@785 1598 \mt{con} \; \mt{matching} :: \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1599 \mt{val} \; \mt{mat\_nil} : \mt{matching} \; [] \; [] \\
adamc@785 1600 \mt{val} \; \mt{mat\_cons} : \mt{t1} ::: \mt{Type} \to \mt{rest1} ::: \{\mt{Type}\} \to \mt{t2} ::: \mt{Type} \to \mt{rest2} ::: \{\mt{Type}\} \to \mt{nm1} :: \mt{Name} \to \mt{nm2} :: \mt{Name} \\
adamc@785 1601 \hspace{.1in} \to [[\mt{nm1}] \sim \mt{rest1}] \Rightarrow [[\mt{nm2}] \sim \mt{rest2}] \Rightarrow \mt{linkable} \; \mt{t1} \; \mt{t2} \to \mt{matching} \; \mt{rest1} \; \mt{rest2} \\
adamc@785 1602 \hspace{.1in} \to \mt{matching} \; ([\mt{nm1} = \mt{t1}] \rc \mt{rest1}) \; ([\mt{nm2} = \mt{t2}] \rc \mt{rest2})
adamc@785 1603 \end{array}$$
adamc@785 1604
adamc@785 1605 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 1606 $$\begin{array}{l}
adamc@785 1607 \mt{con} \; \mt{propagation\_mode} :: \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1608 \mt{val} \; \mt{restrict} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1609 \mt{val} \; \mt{cascade} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1610 \mt{val} \; \mt{no\_action} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1611 \mt{val} \; \mt{set\_null} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; (\mt{map} \; \mt{option} \; \mt{fs})
adamc@785 1612 \end{array}$$
adamc@785 1613
adamc@785 1614 Finally, we put these ingredient together to define the \texttt{FOREIGN KEY} constraint function.
adamc@785 1615 $$\begin{array}{l}
adamc@785 1616 \mt{val} \; \mt{foreign\_key} : \mt{mine1} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{mine} ::: \{\mt{Type}\} \to \mt{munused} ::: \{\mt{Type}\} \to \mt{foreign} ::: \{\mt{Type}\} \\
adamc@785 1617 \hspace{.1in} \to \mt{funused} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{uniques} ::: \{\{\mt{Unit}\}\} \\
adamc@785 1618 \hspace{.1in} \to [[\mt{mine1}] \sim \mt{mine}] \Rightarrow [[\mt{mine1} = \mt{t}] \rc \mt{mine} \sim \mt{munused}] \Rightarrow [\mt{foreign} \sim \mt{funused}] \Rightarrow [[\mt{nm}] \sim \mt{uniques}] \\
adamc@785 1619 \hspace{.1in} \Rightarrow \mt{matching} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}) \; \mt{foreign} \\
adamc@785 1620 \hspace{.1in} \to \mt{sql\_table} \; (\mt{foreign} \rc \mt{funused}) \; ([\mt{nm} = \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{foreign}] \rc \mt{uniques}) \\
adamc@785 1621 \hspace{.1in} \to \{\mt{OnDelete} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}), \\
adamc@785 1622 \hspace{.2in} \mt{OnUpdate} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine})\} \\
adamc@785 1623 \hspace{.1in} \to \mt{sql\_constraint} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine} \rc \mt{munused}) \; []
adamc@785 1624 \end{array}$$
adamc@785 1625
adamc@785 1626 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 1627 $$\begin{array}{l}
adam@1778 1628 \mt{val} \; \mt{check} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; [] \; [] \; \mt{fs} \; \mt{bool} \to \mt{sql\_constraint} \; \mt{fs} \; []
adamc@785 1629 \end{array}$$
adamc@785 1630
adamc@785 1631 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 1632
adamc@784 1633
adamc@543 1634 \subsubsection{Queries}
adamc@543 1635
adam@1400 1636 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 1637 $$\begin{array}{l}
adam@1400 1638 \mt{con} \; \mt{sql\_query} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@1193 1639 \mt{val} \; \mt{sql\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400 1640 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1641 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543 1642 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1643 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1193 1644 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adam@1400 1645 \hspace{.1in} \Rightarrow \{\mt{Rows} : \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}, \\
adamc@1193 1646 \hspace{.2in} \mt{OrderBy} : \mt{sql\_order\_by} \; (\mt{free} \rc \mt{tables}) \; \mt{selectedExps}, \\
adamc@543 1647 \hspace{.2in} \mt{Limit} : \mt{sql\_limit}, \\
adamc@543 1648 \hspace{.2in} \mt{Offset} : \mt{sql\_offset}\} \\
adam@1400 1649 \hspace{.1in} \to \mt{sql\_query} \; \mt{free} \; \mt{afree} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1650 \end{array}$$
adamc@543 1651
adamc@545 1652 Queries are used by folding over their results inside transactions.
adamc@545 1653 $$\begin{array}{l}
adam@1400 1654 \mt{val} \; \mt{query} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to [\mt{tables} \sim \mt{exps}] \Rightarrow \mt{state} ::: \mt{Type} \to \mt{sql\_query} \; [] \; [] \; \mt{tables} \; \mt{exps} \\
adamc@658 1655 \hspace{.1in} \to (\$(\mt{exps} \rc \mt{map} \; (\lambda \mt{fields} :: \{\mt{Type}\} \Rightarrow \$\mt{fields}) \; \mt{tables}) \\
adamc@545 1656 \hspace{.2in} \to \mt{state} \to \mt{transaction} \; \mt{state}) \\
adamc@545 1657 \hspace{.1in} \to \mt{state} \to \mt{transaction} \; \mt{state}
adamc@545 1658 \end{array}$$
adamc@545 1659
adam@1400 1660 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 1661 $$\begin{array}{l}
adam@1400 1662 \mt{con} \; \mt{sql\_query1} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@543 1663 \\
adamc@543 1664 \mt{type} \; \mt{sql\_relop} \\
adamc@543 1665 \mt{val} \; \mt{sql\_union} : \mt{sql\_relop} \\
adamc@543 1666 \mt{val} \; \mt{sql\_intersect} : \mt{sql\_relop} \\
adamc@543 1667 \mt{val} \; \mt{sql\_except} : \mt{sql\_relop} \\
adam@1400 1668 \mt{val} \; \mt{sql\_relop} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400 1669 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adam@1400 1670 \hspace{.1in} \to \mt{tables1} ::: \{\{\mt{Type}\}\} \\
adamc@543 1671 \hspace{.1in} \to \mt{tables2} ::: \{\{\mt{Type}\}\} \\
adamc@543 1672 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1673 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@543 1674 \hspace{.1in} \to \mt{sql\_relop} \\
adam@1458 1675 \hspace{.1in} \to \mt{bool} \; (* \; \mt{ALL} \; *) \\
adam@1400 1676 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables1} \; \mt{selectedFields} \; \mt{selectedExps} \\
adam@1400 1677 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables2} \; \mt{selectedFields} \; \mt{selectedExps} \\
adam@1400 1678 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{selectedFields} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1679 \end{array}$$
adamc@543 1680
adamc@543 1681 $$\begin{array}{l}
adamc@1193 1682 \mt{val} \; \mt{sql\_query1} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400 1683 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1684 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543 1685 \hspace{.1in} \to \mt{grouped} ::: \{\{\mt{Type}\}\} \\
adamc@543 1686 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1687 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1085 1688 \hspace{.1in} \to \mt{empties} :: \{\mt{Unit}\} \\
adamc@1193 1689 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adamc@1193 1690 \hspace{.1in} \Rightarrow [\mt{free} \sim \mt{grouped}] \\
adam@1400 1691 \hspace{.1in} \Rightarrow [\mt{afree} \sim \mt{tables}] \\
adamc@1193 1692 \hspace{.1in} \Rightarrow [\mt{empties} \sim \mt{selectedFields}] \\
adamc@1085 1693 \hspace{.1in} \Rightarrow \{\mt{Distinct} : \mt{bool}, \\
adamc@1193 1694 \hspace{.2in} \mt{From} : \mt{sql\_from\_items} \; \mt{free} \; \mt{tables}, \\
adam@1778 1695 \hspace{.2in} \mt{Where} : \mt{sql\_exp} \; (\mt{free} \rc \mt{tables}) \; \mt{afree} \; [] \; \mt{bool}, \\
adamc@543 1696 \hspace{.2in} \mt{GroupBy} : \mt{sql\_subset} \; \mt{tables} \; \mt{grouped}, \\
adam@1778 1697 \hspace{.2in} \mt{Having} : \mt{sql\_exp} \; (\mt{free} \rc \mt{grouped}) \; (\mt{afree} \rc \mt{tables}) \; [] \; \mt{bool}, \\
adamc@1085 1698 \hspace{.2in} \mt{SelectFields} : \mt{sql\_subset} \; \mt{grouped} \; (\mt{map} \; (\lambda \_ \Rightarrow []) \; \mt{empties} \rc \mt{selectedFields}), \\
adam@1778 1699 \hspace{.2in} \mt {SelectExps} : \$(\mt{map} \; (\mt{sql\_expw} \; (\mt{free} \rc \mt{grouped}) \; (\mt{afree} \rc \mt{tables}) \; []) \; \mt{selectedExps}) \} \\
adam@1400 1700 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1701 \end{array}$$
adamc@543 1702
adamc@543 1703 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 1704 $$\begin{array}{l}
adamc@543 1705 \mt{con} \; \mt{sql\_subset} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@543 1706 \mt{val} \; \mt{sql\_subset} : \mt{keep\_drop} :: \{(\{\mt{Type}\} \times \{\mt{Type}\})\} \\
adamc@543 1707 \hspace{.1in} \to \mt{sql\_subset} \\
adamc@658 1708 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1 \rc \mt{fields}.2)\; \mt{keep\_drop}) \\
adamc@658 1709 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1) \; \mt{keep\_drop}) \\
adamc@543 1710 \mt{val} \; \mt{sql\_subset\_all} : \mt{tables} :: \{\{\mt{Type}\}\} \to \mt{sql\_subset} \; \mt{tables} \; \mt{tables}
adamc@543 1711 \end{array}$$
adamc@543 1712
adam@1778 1713 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 1714 $$\begin{array}{l}
adam@1778 1715 \mt{con} \; \mt{sql\_exp} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}
adamc@543 1716 \end{array}$$
adamc@543 1717
adamc@543 1718 Any field in scope may be converted to an expression.
adamc@543 1719 $$\begin{array}{l}
adamc@543 1720 \mt{val} \; \mt{sql\_field} : \mt{otherTabs} ::: \{\{\mt{Type}\}\} \to \mt{otherFields} ::: \{\mt{Type}\} \\
adam@1778 1721 \hspace{.1in} \to \mt{fieldType} ::: \mt{Type} \to \mt{agg} ::: \{\{\mt{Type}\}\} \\
adamc@543 1722 \hspace{.1in} \to \mt{exps} ::: \{\mt{Type}\} \\
adamc@543 1723 \hspace{.1in} \to \mt{tab} :: \mt{Name} \to \mt{field} :: \mt{Name} \\
adam@1778 1724 \hspace{.1in} \to \mt{sql\_exp} \; ([\mt{tab} = [\mt{field} = \mt{fieldType}] \rc \mt{otherFields}] \rc \mt{otherTabs}) \; \mt{agg} \; \mt{exps} \; \mt{fieldType}
adamc@543 1725 \end{array}$$
adamc@543 1726
adamc@544 1727 There is an analogous function for referencing named expressions.
adamc@544 1728 $$\begin{array}{l}
adam@1778 1729 \mt{val} \; \mt{sql\_exp} : \mt{tabs} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{t} ::: \mt{Type} \to \mt{rest} ::: \{\mt{Type}\} \to \mt{nm} :: \mt{Name} \\
adam@1778 1730 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tabs} \; \mt{agg} \; ([\mt{nm} = \mt{t}] \rc \mt{rest}) \; \mt{t}
adamc@544 1731 \end{array}$$
adamc@544 1732
adamc@544 1733 Ur values of appropriate types may be injected into SQL expressions.
adamc@544 1734 $$\begin{array}{l}
adamc@786 1735 \mt{class} \; \mt{sql\_injectable\_prim} \\
adamc@786 1736 \mt{val} \; \mt{sql\_bool} : \mt{sql\_injectable\_prim} \; \mt{bool} \\
adamc@786 1737 \mt{val} \; \mt{sql\_int} : \mt{sql\_injectable\_prim} \; \mt{int} \\
adamc@786 1738 \mt{val} \; \mt{sql\_float} : \mt{sql\_injectable\_prim} \; \mt{float} \\
adamc@786 1739 \mt{val} \; \mt{sql\_string} : \mt{sql\_injectable\_prim} \; \mt{string} \\
adamc@786 1740 \mt{val} \; \mt{sql\_time} : \mt{sql\_injectable\_prim} \; \mt{time} \\
adamc@786 1741 \mt{val} \; \mt{sql\_blob} : \mt{sql\_injectable\_prim} \; \mt{blob} \\
adamc@786 1742 \mt{val} \; \mt{sql\_channel} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{channel} \; \mt{t}) \\
adamc@786 1743 \mt{val} \; \mt{sql\_client} : \mt{sql\_injectable\_prim} \; \mt{client} \\
adamc@786 1744 \\
adamc@544 1745 \mt{class} \; \mt{sql\_injectable} \\
adamc@786 1746 \mt{val} \; \mt{sql\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@786 1747 \mt{val} \; \mt{sql\_option\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; (\mt{option} \; \mt{t}) \\
adamc@786 1748 \\
adam@1778 1749 \mt{val} \; \mt{sql\_inject} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{sql\_injectable} \; \mt{t} \\
adam@1778 1750 \hspace{.1in} \to \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adamc@544 1751 \end{array}$$
adamc@544 1752
adamc@1123 1753 Additionally, most function-free types may be injected safely, via the $\mt{serialized}$ type family.
adamc@1123 1754 $$\begin{array}{l}
adamc@1123 1755 \mt{con} \; \mt{serialized} :: \mt{Type} \to \mt{Type} \\
adamc@1123 1756 \mt{val} \; \mt{serialize} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{serialized} \; \mt{t} \\
adamc@1123 1757 \mt{val} \; \mt{deserialize} : \mt{t} ::: \mt{Type} \to \mt{serialized} \; \mt{t} \to \mt{t} \\
adamc@1123 1758 \mt{val} \; \mt{sql\_serialized} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{serialized} \; \mt{t})
adamc@1123 1759 \end{array}$$
adamc@1123 1760
adamc@544 1761 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 1762 $$\begin{array}{l}
adam@1778 1763 \mt{val} \; \mt{sql\_is\_null} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778 1764 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; (\mt{option} \; \mt{t}) \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{bool}
adamc@544 1765 \end{array}$$
adamc@544 1766
adam@1602 1767 As another way of dealing with null values, there is also a restricted form of the standard \cd{COALESCE} function.
adam@1602 1768 $$\begin{array}{l}
adam@1602 1769 \mt{val} \; \mt{sql\_coalesce} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778 1770 \hspace{.1in} \to \mt{t} ::: \mt{Type} \\
adam@1778 1771 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; (\mt{option} \; \mt{t}) \\
adam@1778 1772 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1773 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adam@1602 1774 \end{array}$$
adam@1602 1775
adamc@559 1776 We have generic nullary, unary, and binary operators.
adamc@544 1777 $$\begin{array}{l}
adamc@544 1778 \mt{con} \; \mt{sql\_nfunc} :: \mt{Type} \to \mt{Type} \\
adamc@544 1779 \mt{val} \; \mt{sql\_current\_timestamp} : \mt{sql\_nfunc} \; \mt{time} \\
adam@1778 1780 \mt{val} \; \mt{sql\_nfunc} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778 1781 \hspace{.1in} \to \mt{sql\_nfunc} \; \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\\end{array}$$
adamc@544 1782
adamc@544 1783 $$\begin{array}{l}
adamc@544 1784 \mt{con} \; \mt{sql\_unary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544 1785 \mt{val} \; \mt{sql\_not} : \mt{sql\_unary} \; \mt{bool} \; \mt{bool} \\
adam@1778 1786 \mt{val} \; \mt{sql\_unary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adam@1778 1787 \hspace{.1in} \to \mt{sql\_unary} \; \mt{arg} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res} \\
adamc@544 1788 \end{array}$$
adamc@544 1789
adamc@544 1790 $$\begin{array}{l}
adamc@544 1791 \mt{con} \; \mt{sql\_binary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544 1792 \mt{val} \; \mt{sql\_and} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544 1793 \mt{val} \; \mt{sql\_or} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adam@1778 1794 \mt{val} \; \mt{sql\_binary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg_1} ::: \mt{Type} \to \mt{arg_2} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adam@1778 1795 \hspace{.1in} \to \mt{sql\_binary} \; \mt{arg_1} \; \mt{arg_2} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_1} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_2} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res}
adamc@544 1796 \end{array}$$
adamc@544 1797
adamc@544 1798 $$\begin{array}{l}
adamc@559 1799 \mt{class} \; \mt{sql\_arith} \\
adamc@559 1800 \mt{val} \; \mt{sql\_int\_arith} : \mt{sql\_arith} \; \mt{int} \\
adamc@559 1801 \mt{val} \; \mt{sql\_float\_arith} : \mt{sql\_arith} \; \mt{float} \\
adamc@559 1802 \mt{val} \; \mt{sql\_neg} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_unary} \; \mt{t} \; \mt{t} \\
adamc@559 1803 \mt{val} \; \mt{sql\_plus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1804 \mt{val} \; \mt{sql\_minus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1805 \mt{val} \; \mt{sql\_times} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1806 \mt{val} \; \mt{sql\_div} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1807 \mt{val} \; \mt{sql\_mod} : \mt{sql\_binary} \; \mt{int} \; \mt{int} \; \mt{int}
adamc@559 1808 \end{array}$$
adamc@544 1809
adam@1797 1810 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 1811 $$\begin{array}{l}
adam@1778 1812 \mt{val} \; \mt{sql\_count} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int}
adamc@544 1813 \end{array}$$
adamc@544 1814
adamc@544 1815 $$\begin{array}{l}
adamc@1188 1816 \mt{con} \; \mt{sql\_aggregate} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adam@1778 1817 \mt{val} \; \mt{sql\_aggregate} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{dom} ::: \mt{Type} \to \mt{ran} ::: \mt{Type} \\
adam@1778 1818 \hspace{.1in} \to \mt{sql\_aggregate} \; \mt{dom} \; \mt{ran} \to \mt{sql\_exp} \; \mt{agg} \; \mt{agg} \; \mt{exps} \; \mt{dom} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{ran}
adamc@1188 1819 \end{array}$$
adamc@1188 1820
adamc@1188 1821 $$\begin{array}{l}
adamc@1188 1822 \mt{val} \; \mt{sql\_count\_col} : \mt{t} ::: \mt{Type} \to \mt{sql\_aggregate} \; (\mt{option} \; \mt{t}) \; \mt{int}
adamc@544 1823 \end{array}$$
adam@1400 1824
adam@1400 1825 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 1826
adamc@544 1827 $$\begin{array}{l}
adamc@544 1828 \mt{class} \; \mt{sql\_summable} \\
adamc@544 1829 \mt{val} \; \mt{sql\_summable\_int} : \mt{sql\_summable} \; \mt{int} \\
adamc@544 1830 \mt{val} \; \mt{sql\_summable\_float} : \mt{sql\_summable} \; \mt{float} \\
adam@1777 1831 \mt{val} \; \mt{sql\_avg} : \mt{t} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{sql\_aggregate} \; \mt{t} \; (\mt{option} \; \mt{float}) \\
adam@1400 1832 \mt{val} \; \mt{sql\_sum} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt}
adamc@544 1833 \end{array}$$
adamc@544 1834
adamc@544 1835 $$\begin{array}{l}
adamc@544 1836 \mt{class} \; \mt{sql\_maxable} \\
adamc@544 1837 \mt{val} \; \mt{sql\_maxable\_int} : \mt{sql\_maxable} \; \mt{int} \\
adamc@544 1838 \mt{val} \; \mt{sql\_maxable\_float} : \mt{sql\_maxable} \; \mt{float} \\
adamc@544 1839 \mt{val} \; \mt{sql\_maxable\_string} : \mt{sql\_maxable} \; \mt{string} \\
adamc@544 1840 \mt{val} \; \mt{sql\_maxable\_time} : \mt{sql\_maxable} \; \mt{time} \\
adam@1400 1841 \mt{val} \; \mt{sql\_max} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt} \\
adam@1400 1842 \mt{val} \; \mt{sql\_min} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt}
adamc@544 1843 \end{array}$$
adamc@544 1844
adam@1778 1845 Any SQL query that returns single columns may be turned into a subquery expression.
adam@1777 1846
adam@1777 1847 $$\begin{array}{l}
adam@1778 1848 \mt{val} \; \mt{sql\_subquery} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \\
adam@1778 1849 \hspace{.1in} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_query} \; \mt{tables} \; \mt{agg} \; [\mt{nm} = \mt{t}] \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{nt}
adamc@1193 1850 \end{array}$$
adamc@1193 1851
adam@1573 1852 There is also an \cd{IF..THEN..ELSE..} construct that is compiled into standard SQL \cd{CASE} expressions.
adam@1573 1853 $$\begin{array}{l}
adam@1778 1854 \mt{val} \; \mt{sql\_if\_then\_else} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778 1855 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{bool} \\
adam@1778 1856 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1857 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1858 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adam@1573 1859 \end{array}$$
adam@1573 1860
adamc@1193 1861 \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 1862 $$\begin{array}{l}
adamc@1193 1863 \mt{con} \; \mt{sql\_from\_items} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@1193 1864 \mt{val} \; \mt{sql\_from\_table} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1865 \hspace{.1in} \to \mt{t} ::: \mt{Type} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; \mt{t} \; \mt{fs} \to \mt{name} :: \mt{Name} \to \mt{t} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193 1866 \mt{val} \; \mt{sql\_from\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{name} :: \mt{Name} \to \mt{sql\_query} \; \mt{free} \; [] \; \mt{fs} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193 1867 \mt{val} \; \mt{sql\_from\_comma} : \mt{free} ::: \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \to [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193 1868 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adamc@1193 1869 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2}) \\
adamc@1193 1870 \mt{val} \; \mt{sql\_inner\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1871 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193 1872 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adam@1778 1873 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193 1874 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2})
adamc@786 1875 \end{array}$$
adamc@786 1876
adamc@786 1877 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 1878 $$\begin{array}{l}
adamc@786 1879 \mt{class} \; \mt{nullify} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@786 1880 \mt{val} \; \mt{nullify\_option} : \mt{t} ::: \mt{Type} \to \mt{nullify} \; (\mt{option} \; \mt{t}) \; (\mt{option} \; \mt{t}) \\
adamc@786 1881 \mt{val} \; \mt{nullify\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{nullify} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@786 1882 \end{array}$$
adamc@786 1883
adamc@786 1884 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 1885
adamc@786 1886 $$\begin{array}{l}
adamc@1193 1887 \mt{val} \; \mt{sql\_left\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{(\mt{Type} \times \mt{Type})\}\} \\
adamc@1193 1888 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@786 1889 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\lambda \mt{r} \Rightarrow \$(\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{nullify} \; \mt{p}.1 \; \mt{p}.2) \; \mt{r})) \; \mt{tabs2}) \\
adamc@1193 1890 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \\
adam@1778 1891 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193 1892 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.2)) \; \mt{tabs2})
adamc@786 1893 \end{array}$$
adamc@786 1894
adamc@544 1895 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 1896 $$\begin{array}{l}
adamc@544 1897 \mt{type} \; \mt{sql\_direction} \\
adamc@544 1898 \mt{val} \; \mt{sql\_asc} : \mt{sql\_direction} \\
adamc@544 1899 \mt{val} \; \mt{sql\_desc} : \mt{sql\_direction} \\
adamc@544 1900 \\
adamc@544 1901 \mt{con} \; \mt{sql\_order\_by} :: \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@544 1902 \mt{val} \; \mt{sql\_order\_by\_Nil} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} :: \{\mt{Type}\} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adam@1778 1903 \mt{val} \; \mt{sql\_order\_by\_Cons} : \mt{tf} ::: (\{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}) \\
adam@1778 1904 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778 1905 \hspace{.1in} \to \mt{sql\_window} \; \mt{tf} \to \mt{tf} \; \mt{tables} \; [] \; \mt{exps} \; \mt{t} \to \mt{sql\_direction} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adam@1684 1906 \mt{val} \; \mt{sql\_order\_by\_random} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544 1907 \\
adamc@544 1908 \mt{type} \; \mt{sql\_limit} \\
adamc@544 1909 \mt{val} \; \mt{sql\_no\_limit} : \mt{sql\_limit} \\
adamc@544 1910 \mt{val} \; \mt{sql\_limit} : \mt{int} \to \mt{sql\_limit} \\
adamc@544 1911 \\
adamc@544 1912 \mt{type} \; \mt{sql\_offset} \\
adamc@544 1913 \mt{val} \; \mt{sql\_no\_offset} : \mt{sql\_offset} \\
adamc@544 1914 \mt{val} \; \mt{sql\_offset} : \mt{int} \to \mt{sql\_offset}
adamc@544 1915 \end{array}$$
adamc@544 1916
adam@1778 1917 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 1918 $$\begin{array}{l}
adam@1778 1919 \mt{con} \; \mt{sql\_expw} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type} \\
adam@1778 1920 \\
adam@1778 1921 \mt{class} \; \mt{sql\_window} :: (\{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}) \to \mt{Type} \\
adam@1778 1922 \mt{val} \; \mt{sql\_window\_normal} : \mt{sql\_window} \; \mt{sql\_exp} \\
adam@1778 1923 \mt{val} \; \mt{sql\_window\_fancy} : \mt{sql\_window} \; \mt{sql\_expw} \\
adam@1778 1924 \mt{val} \; \mt{sql\_window} : \mt{tf} ::: (\{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}) \\
adam@1778 1925 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778 1926 \hspace{.1in} \to \mt{sql\_window} \; \mt{tf} \\
adam@1778 1927 \hspace{.1in} \to \mt{tf} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1928 \hspace{.1in} \to \mt{sql\_expw} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1929 \\
adam@1778 1930 \mt{con} \; \mt{sql\_partition} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adam@1778 1931 \mt{val} \; \mt{sql\_no\_partition} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778 1932 \hspace{.1in} \to \mt{sql\_partition} \; \mt{tables} \; \mt{agg} \; \mt{exps} \\
adam@1778 1933 \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 1934 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1935 \hspace{.1in} \to \mt{sql\_partition} \; \mt{tables} \; \mt{agg} \; \mt{exps} \\
adam@1778 1936 \\
adam@1778 1937 \mt{con} \; \mt{sql\_window\_function} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type} \\
adam@1778 1938 \mt{val} \; \mt{sql\_window\_function} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778 1939 \hspace{.1in} \to \mt{t} ::: \mt{Type} \\
adam@1778 1940 \hspace{.1in} \to \mt{sql\_window\_function} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1941 \hspace{.1in} \to \mt{sql\_partition} \; \mt{tables} \; \mt{agg} \; \mt{exps} \\
adam@1778 1942 \hspace{.1in} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adam@1778 1943 \hspace{.1in} \to \mt{sql\_expw} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1944 \\
adam@1778 1945 \mt{val} \; \mt{sql\_window\_aggregate} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778 1946 \hspace{.1in} \to \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \\
adam@1778 1947 \hspace{.1in} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt} \\
adam@1778 1948 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1949 \hspace{.1in} \to \mt{sql\_window\_function} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{nt} \\
adam@1778 1950 \mt{val} \; \mt{sql\_window\_count} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778 1951 \hspace{.1in} \to \mt{sql\_window\_function} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int} \\
adam@1778 1952 \mt{val} \; \mt{sql\_rank} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778 1953 \hspace{.1in} \to \mt{sql\_window\_function} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int}
adam@1778 1954 \end{array}$$
adam@1778 1955
adamc@545 1956
adamc@545 1957 \subsubsection{DML}
adamc@545 1958
adamc@545 1959 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 1960
adamc@545 1961 $$\begin{array}{l}
adamc@545 1962 \mt{type} \; \mt{dml} \\
adamc@545 1963 \mt{val} \; \mt{dml} : \mt{dml} \to \mt{transaction} \; \mt{unit}
adamc@545 1964 \end{array}$$
adamc@545 1965
adam@1297 1966 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 1967
adam@1297 1968 $$\begin{array}{l}
adam@1297 1969 \mt{val} \; \mt{tryDml} : \mt{dml} \to \mt{transaction} \; (\mt{option} \; \mt{string})
adam@1297 1970 \end{array}$$
adam@1297 1971
adam@1797 1972 Properly typed records may be used to form $\mt{INSERT}$ commands.
adamc@545 1973 $$\begin{array}{l}
adamc@545 1974 \mt{val} \; \mt{insert} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \\
adam@1778 1975 \hspace{.1in} \to \$(\mt{map} \; (\mt{sql\_exp} \; [] \; [] \; []) \; \mt{fields}) \to \mt{dml}
adamc@545 1976 \end{array}$$
adamc@545 1977
adam@1578 1978 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 table variable $\mt{T}$.
adamc@545 1979 $$\begin{array}{l}
adam@1380 1980 \mt{val} \; \mt{update} : \mt{unchanged} ::: \{\mt{Type}\} \to \mt{changed} :: \{\mt{Type}\} \to [\mt{changed} \sim \mt{unchanged}] \\
adam@1778 1981 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; []) \; \mt{changed}) \\
adam@1778 1982 \hspace{.1in} \to \mt{sql\_table} \; (\mt{changed} \rc \mt{unchanged}) \to \mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545 1983 \end{array}$$
adamc@545 1984
adam@1578 1985 A $\mt{DELETE}$ command is formed from a table and a $\mt{WHERE}$ clause. The above use of $\mt{T}$ is repeated.
adamc@545 1986 $$\begin{array}{l}
adam@1778 1987 \mt{val} \; \mt{delete} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \to \mt{sql\_exp} \; [\mt{T} = \mt{fields}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545 1988 \end{array}$$
adamc@545 1989
adamc@546 1990 \subsubsection{Sequences}
adamc@546 1991
adamc@546 1992 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 1993
adamc@546 1994 $$\begin{array}{l}
adamc@546 1995 \mt{type} \; \mt{sql\_sequence} \\
adamc@1085 1996 \mt{val} \; \mt{nextval} : \mt{sql\_sequence} \to \mt{transaction} \; \mt{int} \\
adamc@1085 1997 \mt{val} \; \mt{setval} : \mt{sql\_sequence} \to \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@546 1998 \end{array}$$
adamc@546 1999
adamc@546 2000
adam@1648 2001 \subsection{\label{xml}XML}
adamc@547 2002
adam@1333 2003 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 2004
adam@1642 2005 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 2006 $$\begin{array}{l}
adamc@547 2007 \mt{con} \; \mt{xml} :: \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547 2008 \end{array}$$
adamc@547 2009
adamc@547 2010 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 2011 $$\begin{array}{l}
adamc@547 2012 \mt{con} \; \mt{tag} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547 2013 \end{array}$$
adamc@547 2014
adamc@547 2015 Literal text may be injected into XML as ``CDATA.''
adamc@547 2016 $$\begin{array}{l}
adamc@547 2017 \mt{val} \; \mt{cdata} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{string} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adamc@547 2018 \end{array}$$
adamc@547 2019
adam@1358 2020 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 2021 $$\begin{array}{l}
adam@1358 2022 \mt{val} \; \mt{cdataChar} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{char} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adam@1358 2023 \end{array}$$
adam@1358 2024
adamc@547 2025 There is a function for producing an XML tree with a particular tag at its root.
adamc@547 2026 $$\begin{array}{l}
adamc@547 2027 \mt{val} \; \mt{tag} : \mt{attrsGiven} ::: \{\mt{Type}\} \to \mt{attrsAbsent} ::: \{\mt{Type}\} \to \mt{ctxOuter} ::: \{\mt{Unit}\} \to \mt{ctxInner} ::: \{\mt{Unit}\} \\
adamc@547 2028 \hspace{.1in} \to \mt{useOuter} ::: \{\mt{Type}\} \to \mt{useInner} ::: \{\mt{Type}\} \to \mt{bindOuter} ::: \{\mt{Type}\} \to \mt{bindInner} ::: \{\mt{Type}\} \\
adam@1380 2029 \hspace{.1in} \to [\mt{attrsGiven} \sim \mt{attrsAbsent}] \Rightarrow [\mt{useOuter} \sim \mt{useInner}] \Rightarrow [\mt{bindOuter} \sim \mt{bindInner}] \\
adam@1749 2030 \hspace{.1in} \Rightarrow \mt{css\_class} \\
adam@1643 2031 \hspace{.1in} \to \mt{option} \; (\mt{signal} \; \mt{css\_class}) \\
adam@1750 2032 \hspace{.1in} \to \mt{css\_style} \\
adam@1751 2033 \hspace{.1in} \to \mt{option} \; (\mt{signal} \; \mt{css\_style}) \\
adamc@787 2034 \hspace{.1in} \to \$\mt{attrsGiven} \\
adamc@547 2035 \hspace{.1in} \to \mt{tag} \; (\mt{attrsGiven} \rc \mt{attrsAbsent}) \; \mt{ctxOuter} \; \mt{ctxInner} \; \mt{useOuter} \; \mt{bindOuter} \\
adamc@547 2036 \hspace{.1in} \to \mt{xml} \; \mt{ctxInner} \; \mt{useInner} \; \mt{bindInner} \to \mt{xml} \; \mt{ctxOuter} \; (\mt{useOuter} \rc \mt{useInner}) \; (\mt{bindOuter} \rc \mt{bindInner})
adamc@547 2037 \end{array}$$
adam@1750 2038 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 2039
adam@1643 2040 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 2041
adam@1751 2042 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 2043
adamc@547 2044 Two XML fragments may be concatenated.
adamc@547 2045 $$\begin{array}{l}
adamc@547 2046 \mt{val} \; \mt{join} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{bind_1} ::: \{\mt{Type}\} \to \mt{bind_2} ::: \{\mt{Type}\} \\
adam@1380 2047 \hspace{.1in} \to [\mt{use_1} \sim \mt{bind_1}] \Rightarrow [\mt{bind_1} \sim \mt{bind_2}] \\
adamc@547 2048 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind_1} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{bind_1}) \; \mt{bind_2} \to \mt{xml} \; \mt{ctx} \; \mt{use_1} \; (\mt{bind_1} \rc \mt{bind_2})
adamc@547 2049 \end{array}$$
adamc@547 2050
adamc@547 2051 Finally, any XML fragment may be updated to ``claim'' to use more form fields than it does.
adamc@547 2052 $$\begin{array}{l}
adam@1380 2053 \mt{val} \; \mt{useMore} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{use_2} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to [\mt{use_1} \sim \mt{use_2}] \\
adamc@547 2054 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{use_2}) \; \mt{bind}
adamc@547 2055 \end{array}$$
adamc@547 2056
adam@2008 2057 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 2058
adam@2008 2059 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.
adamc@547 2060
adamc@547 2061 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 2062 $$\begin{array}{l}
adam@1641 2063 \mt{val} \; \mt{error} : \mt{t} ::: \mt{Type} \to \mt{xbody} \to \mt{t}
adamc@547 2064 \end{array}$$
adamc@547 2065
adamc@549 2066
adamc@701 2067 \subsection{Client-Side Programming}
adamc@659 2068
adamc@701 2069 Ur/Web supports running code on web browsers, via automatic compilation to JavaScript.
adamc@701 2070
adamc@701 2071 \subsubsection{The Basics}
adamc@701 2072
adam@1400 2073 All of the functions in this subsection are client-side only.
adam@1400 2074
adam@1297 2075 Clients can open alert and confirm dialog boxes, in the usual annoying JavaScript way.
adamc@701 2076 $$\begin{array}{l}
adam@1297 2077 \mt{val} \; \mt{alert} : \mt{string} \to \mt{transaction} \; \mt{unit} \\
adam@1297 2078 \mt{val} \; \mt{confirm} : \mt{string} \to \mt{transaction} \; \mt{bool}
adamc@701 2079 \end{array}$$
adamc@701 2080
adamc@701 2081 Any transaction may be run in a new thread with the $\mt{spawn}$ function.
adamc@701 2082 $$\begin{array}{l}
adamc@701 2083 \mt{val} \; \mt{spawn} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit}
adamc@701 2084 \end{array}$$
adamc@701 2085
adamc@701 2086 The current thread can be paused for at least a specified number of milliseconds.
adamc@701 2087 $$\begin{array}{l}
adamc@701 2088 \mt{val} \; \mt{sleep} : \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@701 2089 \end{array}$$
adamc@701 2090
adam@1770 2091 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 2092 $$\begin{array}{l}
adamc@787 2093 \mt{val} \; \mt{onError} : (\mt{xbody} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787 2094 \mt{val} \; \mt{onFail} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787 2095 \mt{val} \; \mt{onConnectFail} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787 2096 \mt{val} \; \mt{onDisconnect} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787 2097 \mt{val} \; \mt{onServerError} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit}
adamc@787 2098 \end{array}$$
adamc@787 2099
adam@1555 2100 There are also functions to register standard document-level event handlers.
adam@1555 2101
adam@1555 2102 $$\begin{array}{l}
adam@1783 2103 \mt{val} \; \mt{onClick} : (\mt{mouseEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783 2104 \mt{val} \; \mt{onDblclick} : (\mt{mouseEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783 2105 \mt{val} \; \mt{onKeydown} : (\mt{keyEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783 2106 \mt{val} \; \mt{onKeypress} : (\mt{keyEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783 2107 \mt{val} \; \mt{onKeyup} : (\mt{keyEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783 2108 \mt{val} \; \mt{onMousedown} : (\mt{mouseEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783 2109 \mt{val} \; \mt{onMouseup} : (\mt{mouseEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit}
adam@1555 2110 \end{array}$$
adam@1555 2111
adam@1559 2112 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 2113
adam@1559 2114 $$\begin{array}{l}
adam@1559 2115 \mt{val} \; \mt{preventDefault} : \mt{transaction} \; \mt{unit} \\
adam@1559 2116 \mt{val} \; \mt{stopPropagation} : \mt{transaction} \; \mt{unit}
adam@1559 2117 \end{array}$$
adam@1559 2118
adam@1926 2119 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 2120
adam@1926 2121 $$\begin{array}{l}
adam@1926 2122 \mt{val} \; \mt{script} : \mt{unit} \to \mt{tag} \; [\mt{Code} = \mt{transaction} \; \mt{unit}] \; \mt{head} \; [] \; [] \; []
adam@1926 2123 \end{array}$$
adam@1926 2124
adam@1926 2125 Note that the Ur/Web version of \cd{<script>} is used like \cd{<script code=\{...\}/>}, rather than \cd{<script>...</script>}.
adam@1926 2126
adam@1556 2127 \subsubsection{Node IDs}
adam@1556 2128
adam@1556 2129 There is an abstract type of node IDs that may be assigned to \cd{id} attributes of most HTML tags.
adam@1556 2130
adam@1556 2131 $$\begin{array}{l}
adam@1556 2132 \mt{type} \; \mt{id} \\
adam@1556 2133 \mt{val} \; \mt{fresh} : \mt{transaction} \; \mt{id}
adam@1556 2134 \end{array}$$
adam@1556 2135
adam@1785 2136 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 2137
adam@1785 2138 One further use of IDs is as handles for requesting that \emph{focus} be given to specific tags.
adam@1785 2139
adam@1785 2140 $$\begin{array}{l}
adam@1785 2141 \mt{val} \; \mt{giveFocus} : \mt{id} \to \mt{transaction} \; \mt{unit}
adam@1785 2142 \end{array}$$
adam@1556 2143
adam@1643 2144 \subsubsection{\label{signals}Functional-Reactive Page Generation}
adamc@701 2145
adamc@701 2146 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 2147
adam@1403 2148 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 2149
adamc@659 2150 $$\begin{array}{l}
adamc@659 2151 \mt{con} \; \mt{source} :: \mt{Type} \to \mt{Type} \\
adamc@659 2152 \mt{val} \; \mt{source} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{transaction} \; (\mt{source} \; \mt{t}) \\
adamc@659 2153 \mt{val} \; \mt{set} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@659 2154 \mt{val} \; \mt{get} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@659 2155 \end{array}$$
adamc@659 2156
adam@1400 2157 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 2158
adam@1608 2159 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 2160
adamc@659 2161 $$\begin{array}{l}
adamc@659 2162 \mt{con} \; \mt{signal} :: \mt{Type} \to \mt{Type} \\
adamc@659 2163 \mt{val} \; \mt{signal\_monad} : \mt{monad} \; \mt{signal} \\
adam@1608 2164 \mt{val} \; \mt{signal} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{signal} \; \mt{t} \\
adam@1608 2165 \mt{val} \; \mt{current} : \mt{t} ::: \mt{Type} \to \mt{signal} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@659 2166 \end{array}$$
adamc@659 2167
adamc@659 2168 A reactive portion of an HTML page is injected with a $\mt{dyn}$ tag, which has a signal-valued attribute $\mt{Signal}$.
adamc@659 2169
adamc@659 2170 $$\begin{array}{l}
adam@1641 2171 \mt{val} \; \mt{dyn} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to [\mt{ctx} \sim [\mt{Dyn}]] \Rightarrow \mt{unit} \\
adam@1641 2172 \hspace{.1in} \to \mt{tag} \; [\mt{Signal} = \mt{signal} \; (\mt{xml} \; ([\mt{Dyn}] \rc \mt{ctx}) \; \mt{use} \; \mt{bind})] \; ([\mt{Dyn}] \rc \mt{ctx}) \; [] \; \mt{use} \; \mt{bind}
adamc@659 2173 \end{array}$$
adamc@659 2174
adam@1648 2175 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 2176
adam@1648 2177 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 2178
adam@1786 2179 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 2180
adam@1786 2181 $$\begin{array}{l}
adam@1786 2182 \mt{val} \; \mt{active} : \mt{unit} \to \mt{tag} \; [\mt{Code} = \mt{transaction} \; \mt{xbody}] \; \mt{body} \; [] \; [] \; []
adam@1786 2183 \end{array}$$
adamc@701 2184
adamc@914 2185 \subsubsection{Remote Procedure Calls}
adamc@914 2186
adamc@914 2187 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 2188
adamc@914 2189 $$\begin{array}{l}
adamc@914 2190 \mt{val} \; \mt{rpc} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@914 2191 \end{array}$$
adamc@914 2192
adam@1848 2193 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 2194
adam@1848 2195 $$\begin{array}{l}
adam@1848 2196 \mt{val} \; \mt{tryRpc} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; \mt{t} \to \mt{transaction} \; (\mt{option} \; \mt{t})
adam@1848 2197 \end{array}$$
adam@1848 2198
adamc@701 2199 \subsubsection{Asynchronous Message-Passing}
adamc@701 2200
adamc@701 2201 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 2202
adamc@701 2203 $$\begin{array}{l}
adamc@701 2204 \mt{type} \; \mt{client} \\
adamc@701 2205 \mt{val} \; \mt{self} : \mt{transaction} \; \mt{client}
adamc@701 2206 \end{array}$$
adamc@701 2207
adam@1940 2208 \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 2209
adamc@701 2210 $$\begin{array}{l}
adamc@701 2211 \mt{con} \; \mt{channel} :: \mt{Type} \to \mt{Type} \\
adamc@701 2212 \mt{val} \; \mt{channel} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; (\mt{channel} \; \mt{t}) \\
adamc@701 2213 \mt{val} \; \mt{send} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@701 2214 \mt{val} \; \mt{recv} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@701 2215 \end{array}$$
adamc@701 2216
adamc@701 2217 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 2218
adamc@701 2219 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 2220
adam@1551 2221 \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 2222
adamc@659 2223
adamc@549 2224 \section{Ur/Web Syntax Extensions}
adamc@549 2225
adamc@549 2226 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 2227
adamc@549 2228 \subsection{SQL}
adamc@549 2229
adamc@786 2230 \subsubsection{\label{tables}Table Declarations}
adamc@786 2231
adamc@788 2232 $\mt{table}$ declarations may include constraints, via these grammar rules.
adamc@788 2233 $$\begin{array}{rrcll}
adam@1594 2234 \textrm{Declarations} & d &::=& \mt{table} \; x : c \; [pk[,]] \; cts \mid \mt{view} \; x = V \\
adamc@788 2235 \textrm{Primary key constraints} & pk &::=& \mt{PRIMARY} \; \mt{KEY} \; K \\
adam@1722 2236 \textrm{Keys} & K &::=& f \mid (f, (f,)^+) \mid \{\{e\}\} \\
adamc@788 2237 \textrm{Constraint sets} & cts &::=& \mt{CONSTRAINT} f \; ct \mid cts, cts \mid \{\{e\}\} \\
adamc@788 2238 \textrm{Constraints} & ct &::=& \mt{UNIQUE} \; K \mid \mt{CHECK} \; E \\
adamc@788 2239 &&& \mid \mt{FOREIGN} \; \mt{KEY} \; K \; \mt{REFERENCES} \; F \; (K) \; [\mt{ON} \; \mt{DELETE} \; pr] \; [\mt{ON} \; \mt{UPDATE} \; pr] \\
adamc@788 2240 \textrm{Foreign tables} & F &::=& x \mid \{\{e\}\} \\
adam@1594 2241 \textrm{Propagation modes} & pr &::=& \mt{NO} \; \mt{ACTION} \mid \mt{RESTRICT} \mid \mt{CASCADE} \mid \mt{SET} \; \mt{NULL} \\
adam@1594 2242 \textrm{View expressions} & V &::=& Q \mid \{e\}
adamc@788 2243 \end{array}$$
adamc@788 2244
adamc@788 2245 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 2246
adamc@788 2247
adamc@549 2248 \subsubsection{Queries}
adamc@549 2249
adamc@550 2250 Queries $Q$ are added to the rules for expressions $e$.
adamc@550 2251
adamc@549 2252 $$\begin{array}{rrcll}
adam@1684 2253 \textrm{Queries} & Q &::=& (q \; [\mt{ORDER} \; \mt{BY} \; O] \; [\mt{LIMIT} \; N] \; [\mt{OFFSET} \; N]) \\
adamc@1085 2254 \textrm{Pre-queries} & q &::=& \mt{SELECT} \; [\mt{DISTINCT}] \; P \; \mt{FROM} \; F,^+ \; [\mt{WHERE} \; E] \; [\mt{GROUP} \; \mt{BY} \; p,^+] \; [\mt{HAVING} \; E] \\
adamc@1085 2255 &&& \mid q \; R \; q \mid \{\{\{e\}\}\} \\
adam@1684 2256 \textrm{Relational operators} & R &::=& \mt{UNION} \mid \mt{INTERSECT} \mid \mt{EXCEPT} \\
adam@1778 2257 \textrm{$\mt{ORDER \; BY}$ items} & O &::=& \mt{RANDOM} [()] \mid \hat{E} \; [o] \mid \hat{E} \; [o], O
adamc@549 2258 \end{array}$$
adamc@549 2259
adamc@549 2260 $$\begin{array}{rrcll}
adamc@549 2261 \textrm{Projections} & P &::=& \ast & \textrm{all columns} \\
adamc@549 2262 &&& p,^+ & \textrm{particular columns} \\
adamc@549 2263 \textrm{Pre-projections} & p &::=& t.f & \textrm{one column from a table} \\
adamc@558 2264 &&& t.\{\{c\}\} & \textrm{a record of columns from a table (of kind $\{\mt{Type}\}$)} \\
adam@1627 2265 &&& t.* & \textrm{all columns from a table} \\
adam@1778 2266 &&& \hat{E} \; [\mt{AS} \; f] & \textrm{expression column} \\
adamc@549 2267 \textrm{Table names} & t &::=& x & \textrm{constant table name (automatically capitalized)} \\
adamc@549 2268 &&& X & \textrm{constant table name} \\
adamc@549 2269 &&& \{\{c\}\} & \textrm{computed table name (of kind $\mt{Name}$)} \\
adamc@549 2270 \textrm{Column names} & f &::=& X & \textrm{constant column name} \\
adamc@549 2271 &&& \{c\} & \textrm{computed column name (of kind $\mt{Name}$)} \\
adamc@549 2272 \textrm{Tables} & T &::=& x & \textrm{table variable, named locally by its own capitalization} \\
adam@1756 2273 &&& x \; \mt{AS} \; X & \textrm{table variable, with local name} \\
adam@1756 2274 &&& x \; \mt{AS} \; \{c\} & \textrm{table variable, with computed local name} \\
adamc@549 2275 &&& \{\{e\}\} \; \mt{AS} \; t & \textrm{computed table expression, with local name} \\
adam@1756 2276 &&& \{\{e\}\} \; \mt{AS} \; \{c\} & \textrm{computed table expression, with computed local name} \\
adamc@1085 2277 \textrm{$\mt{FROM}$ items} & F &::=& T \mid \{\{e\}\} \mid F \; J \; \mt{JOIN} \; F \; \mt{ON} \; E \\
adamc@1085 2278 &&& \mid F \; \mt{CROSS} \; \mt{JOIN} \ F \\
adamc@1193 2279 &&& \mid (Q) \; \mt{AS} \; t \\
adamc@1085 2280 \textrm{Joins} & J &::=& [\mt{INNER}] \\
adamc@1085 2281 &&& \mid [\mt{LEFT} \mid \mt{RIGHT} \mid \mt{FULL}] \; [\mt{OUTER}] \\
adam@1587 2282 \textrm{SQL expressions} & E &::=& t.f & \textrm{column references} \\
adamc@549 2283 &&& X & \textrm{named expression references} \\
adam@1490 2284 &&& \{[e]\} & \textrm{injected native Ur expressions} \\
adam@1778 2285 &&& \{e\} & \textrm{computed expressions, probably using $\mt{sql\_exp}$ directly} \\
adamc@549 2286 &&& \mt{TRUE} \mid \mt{FALSE} & \textrm{boolean constants} \\
adamc@549 2287 &&& \ell & \textrm{primitive type literals} \\
adamc@549 2288 &&& \mt{NULL} & \textrm{null value (injection of $\mt{None}$)} \\
adamc@549 2289 &&& E \; \mt{IS} \; \mt{NULL} & \textrm{nullness test} \\
adam@1602 2290 &&& \mt{COALESCE}(E, E) & \textrm{take first non-null value} \\
adamc@549 2291 &&& n & \textrm{nullary operators} \\
adamc@549 2292 &&& u \; E & \textrm{unary operators} \\
adamc@549 2293 &&& E \; b \; E & \textrm{binary operators} \\
adam@1778 2294 &&& \mt{COUNT}(\ast) & \textrm{count number of rows} \\
adam@1778 2295 &&& a(E) & \textrm{other aggregate function} \\
adam@1573 2296 &&& \mt{IF} \; E \; \mt{THEN} \; E \; \mt{ELSE} \; E & \textrm{conditional} \\
adam@1778 2297 &&& (Q) & \textrm{subquery (must return a single expression column)} \\
adamc@549 2298 &&& (E) & \textrm{explicit precedence} \\
adamc@549 2299 \textrm{Nullary operators} & n &::=& \mt{CURRENT\_TIMESTAMP} \\
adamc@549 2300 \textrm{Unary operators} & u &::=& \mt{NOT} \\
adam@1688 2301 \textrm{Binary operators} & b &::=& \mt{AND} \mid \mt{OR} \mid = \mid \neq \mid < \mid \leq \mid > \mid \geq \\
adamc@1188 2302 \textrm{Aggregate functions} & a &::=& \mt{COUNT} \mid \mt{AVG} \mid \mt{SUM} \mid \mt{MIN} \mid \mt{MAX} \\
adam@1543 2303 \textrm{Directions} & o &::=& \mt{ASC} \mid \mt{DESC} \mid \{e\} \\
adamc@549 2304 \textrm{SQL integer} & N &::=& n \mid \{e\} \\
adam@1778 2305 \textrm{Windowable expressions} & \hat{E} &::=& E \\
adam@1778 2306 &&& w \; [\mt{OVER} \; ( & \textrm{(Postgres only)} \\
adam@1778 2307 &&& \hspace{.1in} [\mt{PARTITION} \; \mt{BY} \; E] \\
adam@1778 2308 &&& \hspace{.1in} [\mt{ORDER} \; \mt{BY} \; O])] \\
adam@1778 2309 \textrm{Window function} & w &::=& \mt{RANK}() \\
adam@1778 2310 &&& \mt{COUNT}(*) \\
adam@1778 2311 &&& a(E)
adamc@549 2312 \end{array}$$
adamc@549 2313
adamc@1085 2314 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 2315
adam@1683 2316 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 2317
adamc@550 2318 \subsubsection{DML}
adamc@550 2319
adamc@550 2320 DML commands $D$ are added to the rules for expressions $e$.
adamc@550 2321
adamc@550 2322 $$\begin{array}{rrcll}
adamc@550 2323 \textrm{Commands} & D &::=& (\mt{INSERT} \; \mt{INTO} \; T^E \; (f,^+) \; \mt{VALUES} \; (E,^+)) \\
adamc@550 2324 &&& (\mt{UPDATE} \; T^E \; \mt{SET} \; (f = E,)^+ \; \mt{WHERE} \; E) \\
adamc@550 2325 &&& (\mt{DELETE} \; \mt{FROM} \; T^E \; \mt{WHERE} \; E) \\
adamc@550 2326 \textrm{Table expressions} & T^E &::=& x \mid \{\{e\}\}
adamc@550 2327 \end{array}$$
adamc@550 2328
adamc@550 2329 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 2330
adamc@551 2331 \subsection{XML}
adamc@551 2332
adamc@551 2333 XML fragments $L$ are added to the rules for expressions $e$.
adamc@551 2334
adamc@551 2335 $$\begin{array}{rrcll}
adamc@551 2336 \textrm{XML fragments} & L &::=& \texttt{<xml/>} \mid \texttt{<xml>}l^*\texttt{</xml>} \\
adamc@551 2337 \textrm{XML pieces} & l &::=& \textrm{text} & \textrm{cdata} \\
adamc@551 2338 &&& \texttt{<}g\texttt{/>} & \textrm{tag with no children} \\
adamc@551 2339 &&& \texttt{<}g\texttt{>}l^*\texttt{</}x\texttt{>} & \textrm{tag with children} \\
adamc@559 2340 &&& \{e\} & \textrm{computed XML fragment} \\
adamc@559 2341 &&& \{[e]\} & \textrm{injection of an Ur expression, via the $\mt{Top}.\mt{txt}$ function} \\
adamc@551 2342 \textrm{Tag} & g &::=& h \; (x = v)^* \\
adamc@551 2343 \textrm{Tag head} & h &::=& x & \textrm{tag name} \\
adamc@551 2344 &&& h\{c\} & \textrm{constructor parameter} \\
adamc@551 2345 \textrm{Attribute value} & v &::=& \ell & \textrm{literal value} \\
adamc@551 2346 &&& \{e\} & \textrm{computed value} \\
adamc@551 2347 \end{array}$$
adamc@551 2348
adam@1751 2349 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 2350
adam@1751 2351 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 2352
adamc@1198 2353 \section{\label{structure}The Structure of Web Applications}
adamc@553 2354
adam@1797 2355 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 2356
adam@1532 2357 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 2358
adam@1787 2359 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 2360
adam@1370 2361 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 2362
adamc@553 2363 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 2364
adamc@553 2365 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 2366
adam@1653 2367 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 2368 \begin{itemize}
adam@1653 2369 \item Functions are disallowed, since there is no obvious way to serialize them safely.
adam@1653 2370 \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 2371 \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 2372 \end{itemize}
adamc@553 2373
adamc@660 2374 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 2375
adamc@789 2376 \medskip
adamc@789 2377
adam@1347 2378 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 2379
adamc@789 2380 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 2381
adam@1348 2382 \subsection{Tasks}
adam@1348 2383
adam@1348 2384 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 2385
adam@1348 2386 $$\begin{array}{l}
adam@1348 2387 \mt{con} \; \mt{task\_kind} :: \mt{Type} \to \mt{Type} \\
adam@1348 2388 \mt{val} \; \mt{initialize} : \mt{task\_kind} \; \mt{unit} \\
adam@1349 2389 \mt{val} \; \mt{clientLeaves} : \mt{task\_kind} \; \mt{client} \\
adam@1349 2390 \mt{val} \; \mt{periodic} : \mt{int} \to \mt{task\_kind} \; \mt{unit}
adam@1348 2391 \end{array}$$
adam@1348 2392
adam@1348 2393 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 2394
adam@1348 2395 The currently supported task kinds are:
adam@1348 2396 \begin{itemize}
adam@1349 2397 \item $\mt{initialize}$: Code that is run when the application starts up.
adam@1348 2398 \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 2399 \item $\mt{periodic} \; n$: Code that is run when the application starts up and then every $n$ seconds thereafter.
adam@1348 2400 \end{itemize}
adam@1348 2401
adamc@553 2402
adam@2008 2403 \section{\label{ffi}The Foreign Function Interface}
adamc@897 2404
adamc@897 2405 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 2406
adamc@897 2407 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 2408
adamc@897 2409 \begin{itemize}
adamc@897 2410 \item \texttt{clientOnly Module.ident} registers a value as being allowed only in client-side code.
adamc@897 2411 \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 2412 \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 2413 \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 2414 \item \texttt{include FILE} requests inclusion of a C header file.
adamc@897 2415 \item \texttt{jsFunc Module.ident=name} gives a mapping from an Ur name for a value to a JavaScript name.
adamc@897 2416 \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 2417 \item \texttt{script URL} requests inclusion of a JavaScript source file within application HTML.
adamc@897 2418 \item \texttt{serverOnly Module.ident} registers a value as being allowed only in server-side code.
adamc@897 2419 \end{itemize}
adamc@897 2420
adamc@897 2421 \subsection{Writing C FFI Code}
adamc@897 2422
adam@1881 2423 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 2424
adamc@897 2425 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 2426
adamc@897 2427 \begin{itemize}
adam@1881 2428 \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 2429 \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 2430 \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 2431 \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 2432 \end{itemize}
adamc@897 2433
adam@1881 2434 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 2435 \begin{itemize}
adamc@897 2436 \item \begin{verbatim}
adamc@897 2437 void uw_error(uw_context, failure_kind, const char *fmt, ...);
adamc@897 2438 \end{verbatim}
adamc@897 2439 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 2440
adam@1329 2441 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 2442
adamc@897 2443 \item \begin{verbatim}
adam@1469 2444 void uw_set_error_message(uw_context, const char *fmt, ...);
adam@1469 2445 \end{verbatim}
adam@1469 2446 This simpler form of \texttt{uw\_error()} saves an error message without immediately aborting execution.
adam@1469 2447
adam@1469 2448 \item \begin{verbatim}
adamc@897 2449 void uw_push_cleanup(uw_context, void (*func)(void *), void *arg);
adamc@897 2450 void uw_pop_cleanup(uw_context);
adamc@897 2451 \end{verbatim}
adam@1329 2452 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 2453
adam@1329 2454 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 2455
adamc@897 2456 \item \begin{verbatim}
adamc@897 2457 void *uw_malloc(uw_context, size_t);
adamc@897 2458 \end{verbatim}
adam@1329 2459 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 2460
adam@1329 2461 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 2462
adamc@897 2463 \item \begin{verbatim}
adamc@897 2464 typedef void (*uw_callback)(void *);
adam@1328 2465 typedef void (*uw_callback_with_retry)(void *, int will_retry);
adam@2001 2466 int uw_register_transactional(uw_context, void *data, uw_callback commit,
adam@2001 2467 uw_callback rollback, uw_callback_with_retry free);
adamc@897 2468 \end{verbatim}
adam@2001 2469 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 2470
adam@2000 2471 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 2472
adam@1329 2473 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 2474
adam@1329 2475 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 2476
adam@1469 2477 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 2478
adamc@1085 2479 \item \begin{verbatim}
adamc@1085 2480 void *uw_get_global(uw_context, char *name);
adamc@1085 2481 void uw_set_global(uw_context, char *name, void *data, uw_callback free);
adamc@1085 2482 \end{verbatim}
adam@1329 2483 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 2484
adamc@897 2485 \end{itemize}
adamc@897 2486
adamc@897 2487 \subsection{Writing JavaScript FFI Code}
adamc@897 2488
adamc@897 2489 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.
adamc@897 2490
adamc@897 2491 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 2492
adamc@897 2493 \begin{itemize}
adamc@897 2494 \item Integers, floats, strings, characters, and booleans are represented in the usual JavaScript way.
adam@1996 2495 \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 2496 \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 2497 \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 2498 \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 2499 \item As in the C FFI, all abstract types of program syntax are implemented with strings in JavaScript.
adam@1996 2500 \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 2501 \end{itemize}
adamc@897 2502
adam@1644 2503 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 2504
adam@1644 2505 \begin{itemize}
adam@1644 2506 \item Sources should be treated as an abstract type, manipulated via:
adam@1644 2507 \begin{itemize}
adam@1644 2508 \item \cd{sc(v)}, to create a source initialized to \cd{v}
adam@1644 2509 \item \cd{sg(s)}, to retrieve the current value of source \cd{s}
adam@1644 2510 \item \cd{sv(s, v)}, to set source \cd{s} to value \cd{v}
adam@1644 2511 \end{itemize}
adam@1644 2512
adam@1644 2513 \item Signals should be treated as an abstract type, manipulated via:
adam@1644 2514 \begin{itemize}
adam@1644 2515 \item \cd{sr(v)} and \cd{sb(s, f)}, the ``return'' and ``bind'' monad operators, respectively
adam@1644 2516 \item \cd{ss(s)}, to produce the signal corresponding to source \cd{s}
adam@1644 2517 \item \cd{scur(s)}, to get the current value of signal \cd{s}
adam@1644 2518 \end{itemize}
adam@1644 2519
adam@1644 2520 \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 2521
adam@1702 2522 \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 2523
adam@1644 2524 \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 2525 \end{itemize}
adamc@897 2526
adam@1833 2527 \subsection{Introducing New HTML Tags}
adam@1833 2528
adam@1833 2529 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 2530
adam@1833 2531 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 2532
adam@2010 2533 \subsection{The Less Safe FFI}
adam@2010 2534
adam@2010 2535 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 2536
adam@2010 2537 When the less safe mode is enabled, declarations like this one are accepted, at the top level of a \texttt{.ur} file:
adam@2010 2538 \begin{verbatim}
adam@2010 2539 ffi foo : int -> int
adam@2010 2540 \end{verbatim}
adam@2010 2541
adam@2010 2542 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 2543 \begin{itemize}
adam@2010 2544 \item \texttt{effectful}
adam@2010 2545 \item \texttt{benignEffectful}
adam@2010 2546 \item \texttt{clientOnly}
adam@2010 2547 \item \texttt{serverOnly}
adam@2010 2548 \item \texttt{jsFunc "putJsFuncNameHere"}
adam@2010 2549 \end{itemize}
adam@2010 2550
adamc@897 2551
adamc@552 2552 \section{Compiler Phases}
adamc@552 2553
adamc@552 2554 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.
adamc@552 2555
adamc@552 2556 In this section, we step through the main phases of compilation, noting what consequences each phase has for effective programming.
adamc@552 2557
adamc@552 2558 \subsection{Parse}
adamc@552 2559
adamc@552 2560 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 2561
adamc@552 2562 \subsection{Elaborate}
adamc@552 2563
adamc@552 2564 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 2565
adam@1378 2566 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 2567
adamc@552 2568 \subsection{Unnest}
adamc@552 2569
adamc@552 2570 Named local function definitions are moved to the top level, to avoid the need to generate closures.
adamc@552 2571
adamc@552 2572 \subsection{Corify}
adamc@552 2573
adamc@552 2574 Module system features are compiled away, through inlining of functor definitions at application sites. Afterward, most abstraction boundaries are broken, facilitating optimization.
adamc@552 2575
adamc@552 2576 \subsection{Especialize}
adamc@552 2577
adam@1356 2578 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 2579
adamc@552 2580 \subsection{Untangle}
adamc@552 2581
adam@1797 2582 Remove unnecessary mutual recursion, splitting recursive groups into strongly connected components.
adamc@552 2583
adamc@552 2584 \subsection{Shake}
adamc@552 2585
adamc@552 2586 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 2587
adamc@661 2588 \subsection{Rpcify}
adamc@661 2589
adamc@661 2590 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 2591
adamc@661 2592 \subsection{Untangle, Shake}
adamc@661 2593
adamc@661 2594 Repeat these simplifications.
adamc@661 2595
adamc@553 2596 \subsection{\label{tag}Tag}
adamc@552 2597
adamc@552 2598 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 2599
adamc@552 2600 \subsection{Reduce}
adamc@552 2601
adamc@552 2602 Apply definitional equality rules to simplify the program as much as possible. This effectively includes inlining of every non-recursive definition.
adamc@552 2603
adamc@552 2604 \subsection{Unpoly}
adamc@552 2605
adamc@552 2606 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 2607
adamc@552 2608 \subsection{Specialize}
adamc@552 2609
adamc@558 2610 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 2611
adamc@552 2612 \subsection{Shake}
adamc@552 2613
adamc@558 2614 Here the compiler repeats the earlier Shake phase.
adamc@552 2615
adamc@552 2616 \subsection{Monoize}
adamc@552 2617
adamc@552 2618 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 2619
adamc@552 2620 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 2621
adamc@552 2622 \subsection{MonoOpt}
adamc@552 2623
adamc@552 2624 Simple algebraic laws are applied to simplify the program, focusing especially on efficient imperative generation of HTML pages.
adamc@552 2625
adamc@552 2626 \subsection{MonoUntangle}
adamc@552 2627
adamc@552 2628 Unnecessary mutual recursion is broken up again.
adamc@552 2629
adamc@552 2630 \subsection{MonoReduce}
adamc@552 2631
adamc@552 2632 Equivalents of the definitional equality rules are applied to simplify programs, with inlining again playing a major role.
adamc@552 2633
adamc@552 2634 \subsection{MonoShake, MonoOpt}
adamc@552 2635
adamc@552 2636 Unneeded declarations are removed, and basic optimizations are repeated.
adamc@552 2637
adamc@552 2638 \subsection{Fuse}
adamc@552 2639
adamc@552 2640 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 2641
adamc@552 2642 \subsection{MonoUntangle, MonoShake}
adamc@552 2643
adamc@552 2644 Fuse often creates more opportunities to remove spurious mutual recursion.
adamc@552 2645
adamc@552 2646 \subsection{Pathcheck}
adamc@552 2647
adamc@552 2648 The compiler checks that no link or action name has been used more than once.
adamc@552 2649
adamc@552 2650 \subsection{Cjrize}
adamc@552 2651
adamc@552 2652 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 2653
adamc@552 2654 \subsection{C Compilation and Linking}
adamc@552 2655
adam@1523 2656 The output of the last phase is pretty-printed as C source code and passed to the C compiler.
adamc@552 2657
adamc@552 2658
as@1564 2659 \end{document}