annotate doc/manual.tex @ 1913:d67e043d3f0d

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author Adam Chlipala <adam@chlipala.net>
date Sun, 24 Nov 2013 10:06:37 -0500
parents 779c390382b9
children afdc823563de 44f607a7f4cd
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adamc@524 1 \documentclass{article}
adamc@554 2 \usepackage{fullpage,amsmath,amssymb,proof,url}
rmbruijn@1568 3 \usepackage[T1]{fontenc}
vshabanoff@1765 4 \usepackage{ae,aecompl}
adamc@524 5 \newcommand{\cd}[1]{\texttt{#1}}
adamc@524 6 \newcommand{\mt}[1]{\mathsf{#1}}
adamc@524 7
adamc@524 8 \newcommand{\rc}{+ \hspace{-.075in} + \;}
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}
adamc@896 67 apt-get install libpq-dev libmysqlclient15-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@1400 80 apt-get install postgresql-8.4 mysql-server-5.1
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.
adamc@1099 149 \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@783 150 \item \texttt{jsFunc Module.ident=name} gives the JavaScript name of an FFI value.
adamc@1089 151 \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 152 \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 153 \begin{itemize}
adam@1309 154 \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 155 \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 156 \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 157 \item \texttt{deltas}: maximum number of messages sendable in a single request handler with \texttt{Basis.send}
adam@1309 158 \item \texttt{globals}: maximum number of global variables that FFI libraries may set in a single request context
adam@1309 159 \item \texttt{headers}: maximum size (in bytes) of per-request buffer used to hold HTTP headers for generated pages
adam@1797 160 \item \texttt{heap}: maximum size (in bytes) of per-request heap for dynamically allocated data
adam@1309 161 \item \texttt{inputs}: maximum number of top-level form fields per request
adam@1309 162 \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 163 \item \texttt{page}: maximum size (in bytes) of per-request buffer used to hold HTML content of generated pages
adam@1309 164 \item \texttt{script}: maximum size (in bytes) of per-request buffer used to hold JavaScript content of generated pages
adam@1309 165 \item \texttt{subinputs}: maximum number of form fields per request, excluding top-level fields
adam@1309 166 \item \texttt{time}: maximum running time of a single page request, in units of approximately 0.1 seconds
adam@1309 167 \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 168 \end{itemize}
adam@1523 169 \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 170 \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 171 \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 172 \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@1478 173 \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 174 \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@852 175 \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@783 176 \item \texttt{prefix PREFIX} sets the prefix included before every URI within the generated application. The default is \texttt{/}.
adamc@783 177 \item \texttt{profile} generates an executable that may be used with gprof.
adam@1752 178 \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 179 \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@783 180 \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@783 181 \item \texttt{serverOnly Module.ident} registers an FFI function or transaction that may only be run on the server.
adamc@1164 182 \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@783 183 \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 184 \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@783 185 \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@783 186 \end{itemize}
adamc@701 187
adamc@701 188
adamc@557 189 \subsection{Building an Application}
adamc@557 190
adamc@557 191 To compile project \texttt{P.urp}, simply run
adamc@557 192 \begin{verbatim}
adamc@557 193 urweb P
adamc@557 194 \end{verbatim}
adamc@1198 195 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@557 196
adamc@557 197 To time how long the different compiler phases run, without generating an executable, run
adamc@557 198 \begin{verbatim}
adamc@557 199 urweb -timing P
adamc@557 200 \end{verbatim}
adamc@557 201
adamc@1086 202 To stop the compilation process after type-checking, run
adamc@1086 203 \begin{verbatim}
adamc@1086 204 urweb -tc P
adamc@1086 205 \end{verbatim}
adam@1530 206 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 207
adam@1745 208 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 209
adam@1723 210 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 211
adamc@1170 212 To output information relevant to CSS stylesheets (and not finish regular compilation), run
adamc@1170 213 \begin{verbatim}
adamc@1170 214 urweb -css P
adamc@1170 215 \end{verbatim}
adamc@1170 216 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 217
adam@1733 218 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 219 \begin{verbatim}
adam@1733 220 urweb daemon start
adam@1733 221 \end{verbatim}
adam@1733 222 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 223 \begin{verbatim}
adam@1733 224 urweb daemon stop
adam@1733 225 \end{verbatim}
adam@1733 226 Communication happens via a UNIX domain socket in file \cd{.urweb\_daemon} in the working directory.
adam@1733 227
adam@1733 228 \medskip
adam@1733 229
adamc@896 230 Some other command-line parameters are accepted:
adamc@896 231 \begin{itemize}
ezyang@1739 232 \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 233
adam@1875 234 \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 235
adamc@896 236 \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@896 237
adamc@896 238 \item \texttt{-dbms [postgres|mysql|sqlite]}: Sets the database backend to use.
adamc@896 239 \begin{itemize}
adamc@896 240 \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@896 241
adamc@896 242 A command sequence like this can initialize a Postgres database, using a file \texttt{app.sql} generated by the compiler:
adamc@896 243 \begin{verbatim}
adamc@896 244 createdb app
adamc@896 245 psql -f app.sql app
adamc@896 246 \end{verbatim}
adamc@896 247
adamc@896 248 \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@896 249
adamc@896 250 A command sequence like this can initialize a MySQL database:
adamc@896 251 \begin{verbatim}
adamc@896 252 echo "CREATE DATABASE app" | mysql
adamc@896 253 mysql -D app <app.sql
adamc@896 254 \end{verbatim}
adamc@896 255
adamc@896 256 \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@896 257
adamc@896 258 A command like this can initialize an SQLite database:
adamc@896 259 \begin{verbatim}
adamc@896 260 sqlite3 path/to/database/file <app.sql
adamc@896 261 \end{verbatim}
adamc@896 262 \end{itemize}
adamc@896 263
adam@1693 264 \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 265
adam@1309 266 \item \texttt{-limit class num}: Equivalent to the \texttt{limit} directive from \texttt{.urp} files
adam@1309 267
adam@1850 268 \item \texttt{-moduleOf FILENAME}: Prints the Ur/Web module name corresponding to source file \texttt{FILENAME}, exiting immediately afterward.
adam@1850 269
adamc@896 270 \item \texttt{-output FILENAME}: Set where the application executable is written.
adamc@896 271
adamc@1127 272 \item \texttt{-path NAME VALUE}: Set the value of path variable \texttt{\$NAME} to \texttt{VALUE}, for use in \texttt{.urp} files.
adamc@1127 273
adam@1335 274 \item \texttt{-prefix PREFIX}: Equivalent to the \texttt{prefix} directive from \texttt{.urp} files
adam@1335 275
adam@1875 276 \item \texttt{-print-ccompiler}: Print the C compiler being used.
adam@1875 277
adam@1753 278 \item \texttt{-protocol [http|cgi|fastcgi|static]}: Set the protocol that the generated application speaks.
adamc@896 279 \begin{itemize}
adamc@896 280 \item \texttt{http}: This is the default. It is for building standalone web servers that can be accessed by web browsers directly.
adamc@896 281
adamc@896 282 \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@896 283
adamc@896 284 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@896 285 \begin{verbatim}
adamc@896 286 ScriptAlias /Hello /path/to/hello.exe
adamc@896 287 \end{verbatim}
adamc@896 288
adamc@1163 289 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 290 \begin{verbatim}
adamc@1163 291 Options +ExecCGI
adamc@1163 292 AddHandler cgi-script .exe
adamc@1163 293 \end{verbatim}
adamc@1163 294
adamc@1163 295 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 296 \begin{verbatim}
adamc@1163 297 prefix /dir/script.exe/
adamc@1163 298 \end{verbatim}
adamc@1163 299
adamc@1163 300 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 301
adamc@1164 302 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 303
adamc@896 304 \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@896 305
adamc@896 306 To configure a FastCGI program with Apache, one could combine the above \texttt{ScriptAlias} line with a line like this:
adamc@896 307 \begin{verbatim}
adamc@896 308 FastCgiServer /path/to/hello.exe -idle-timeout 99999
adamc@896 309 \end{verbatim}
adamc@896 310 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@896 311
adam@1753 312 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 313
adamc@896 314 Here is some lighttpd configuration for the same application.
adamc@896 315 \begin{verbatim}
adamc@896 316 fastcgi.server = (
adamc@896 317 "/Hello/" =>
adamc@896 318 (( "bin-path" => "/path/to/hello.exe",
adamc@896 319 "socket" => "/tmp/hello",
adamc@896 320 "check-local" => "disable",
adamc@896 321 "docroot" => "/",
adamc@896 322 "max-procs" => "1"
adamc@896 323 ))
adamc@896 324 )
adamc@896 325 \end{verbatim}
adamc@896 326 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@896 327
adamc@896 328 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 329
adam@1509 330 \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@896 331 \end{itemize}
adamc@896 332
adamc@1127 333 \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 334
adamc@1164 335 \item \texttt{-sigfile PATH}: Same as the \texttt{sigfile} directive in \texttt{.urp} files
adamc@1164 336
adamc@896 337 \item \texttt{-sql FILENAME}: Set where a database set-up SQL script is written.
adamc@1095 338
adamc@1095 339 \item \texttt{-static}: Link the runtime system statically. The default is to link against dynamic libraries.
adamc@896 340 \end{itemize}
adamc@896 341
adam@1297 342 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@556 343
adam@1509 344 \subsection{Tutorial Formatting}
adam@1509 345
adam@1509 346 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 347
adam@1509 348 These input files follow normal Ur syntax, with a few exceptions:
adam@1509 349 \begin{itemize}
adam@1509 350 \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 351 \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 352 \item A comment like \cd{(* * HEADING *)} introduces a section heading, with text \cd{HEADING} of your choice.
adam@1509 353 \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 354 \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 355 \end{itemize}
adam@1509 356
adam@1509 357 A word of warning: as for demo generation, tutorial generation calls Emacs to syntax-highlight Ur code.
adam@1509 358
adam@1522 359 \subsection{Run-Time Options}
adam@1522 360
adam@1522 361 Compiled applications consult a few environment variables to modify their behavior:
adam@1522 362
adam@1522 363 \begin{itemize}
adam@1522 364 \item \cd{URWEB\_NUM\_THREADS}: alternative to the \cd{-t} command-line argument (currently used only by FastCGI)
adam@1522 365 \item \cd{URWEB\_STACK\_SIZE}: size of per-thread stacks, in bytes
as@1564 366 \item \cd{URWEB\_PQ\_CON}: when using PostgreSQL, overrides the compiled-in connection string
adam@1522 367 \end{itemize}
adam@1522 368
adam@1509 369
adamc@529 370 \section{Ur Syntax}
adamc@529 371
adamc@784 372 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@524 373
adamc@524 374 \subsection{Lexical Conventions}
adamc@524 375
adamc@524 376 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@524 377
adamc@524 378 \begin{center}
adamc@524 379 \begin{tabular}{rl}
adamc@524 380 \textbf{\LaTeX} & \textbf{ASCII} \\
adamc@524 381 $\to$ & \cd{->} \\
adam@1687 382 $\longrightarrow$ & \cd{-{}->} \\
adamc@524 383 $\times$ & \cd{*} \\
adamc@524 384 $\lambda$ & \cd{fn} \\
adamc@524 385 $\Rightarrow$ & \cd{=>} \\
adamc@652 386 $\Longrightarrow$ & \cd{==>} \\
adamc@529 387 $\neq$ & \cd{<>} \\
adamc@529 388 $\leq$ & \cd{<=} \\
adamc@529 389 $\geq$ & \cd{>=} \\
adamc@524 390 \\
adamc@524 391 $x$ & Normal textual identifier, not beginning with an uppercase letter \\
adamc@525 392 $X$ & Normal textual identifier, beginning with an uppercase letter \\
adamc@524 393 \end{tabular}
adamc@524 394 \end{center}
adamc@524 395
adamc@525 396 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@524 397
adamc@873 398 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@526 399
adamc@527 400 This version of the manual doesn't include operator precedences; see \texttt{src/urweb.grm} for that.
adamc@527 401
adam@1297 402 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 403
adamc@552 404 \subsection{\label{core}Core Syntax}
adamc@524 405
adamc@524 406 \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@524 407 $$\begin{array}{rrcll}
adamc@524 408 \textrm{Kinds} & \kappa &::=& \mt{Type} & \textrm{proper types} \\
adamc@525 409 &&& \mt{Unit} & \textrm{the trivial constructor} \\
adamc@525 410 &&& \mt{Name} & \textrm{field names} \\
adamc@525 411 &&& \kappa \to \kappa & \textrm{type-level functions} \\
adamc@525 412 &&& \{\kappa\} & \textrm{type-level records} \\
adamc@525 413 &&& (\kappa\times^+) & \textrm{type-level tuples} \\
adamc@652 414 &&& X & \textrm{variable} \\
adam@1574 415 &&& X \longrightarrow \kappa & \textrm{kind-polymorphic type-level function} \\
adamc@529 416 &&& \_\_ & \textrm{wildcard} \\
adamc@525 417 &&& (\kappa) & \textrm{explicit precedence} \\
adamc@524 418 \end{array}$$
adamc@524 419
adamc@524 420 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@524 421 $$\begin{array}{rrcll}
adamc@524 422 \textrm{Explicitness} & ? &::=& :: & \textrm{explicit} \\
adamc@558 423 &&& ::: & \textrm{implicit}
adamc@524 424 \end{array}$$
adamc@524 425
adamc@524 426 \emph{Constructors} are the main class of compile-time-only data. They include proper types and are classified by kinds.
adamc@524 427 $$\begin{array}{rrcll}
adamc@524 428 \textrm{Constructors} & c, \tau &::=& (c) :: \kappa & \textrm{kind annotation} \\
adamc@530 429 &&& \hat{x} & \textrm{constructor variable} \\
adamc@524 430 \\
adamc@525 431 &&& \tau \to \tau & \textrm{function type} \\
adamc@525 432 &&& x \; ? \; \kappa \to \tau & \textrm{polymorphic function type} \\
adamc@652 433 &&& X \longrightarrow \tau & \textrm{kind-polymorphic function type} \\
adamc@525 434 &&& \$ c & \textrm{record type} \\
adamc@524 435 \\
adamc@525 436 &&& c \; c & \textrm{type-level function application} \\
adamc@530 437 &&& \lambda x \; :: \; \kappa \Rightarrow c & \textrm{type-level function abstraction} \\
adamc@524 438 \\
adamc@652 439 &&& X \Longrightarrow c & \textrm{type-level kind-polymorphic function abstraction} \\
adamc@655 440 &&& c [\kappa] & \textrm{type-level kind-polymorphic function application} \\
adamc@652 441 \\
adamc@525 442 &&& () & \textrm{type-level unit} \\
adamc@525 443 &&& \#X & \textrm{field name} \\
adamc@524 444 \\
adamc@525 445 &&& [(c = c)^*] & \textrm{known-length type-level record} \\
adamc@525 446 &&& c \rc c & \textrm{type-level record concatenation} \\
adamc@652 447 &&& \mt{map} & \textrm{type-level record map} \\
adamc@524 448 \\
adamc@558 449 &&& (c,^+) & \textrm{type-level tuple} \\
adamc@525 450 &&& c.n & \textrm{type-level tuple projection ($n \in \mathbb N^+$)} \\
adamc@524 451 \\
adamc@652 452 &&& [c \sim c] \Rightarrow \tau & \textrm{guarded type} \\
adamc@524 453 \\
adamc@529 454 &&& \_ :: \kappa & \textrm{wildcard} \\
adamc@525 455 &&& (c) & \textrm{explicit precedence} \\
adamc@530 456 \\
adamc@530 457 \textrm{Qualified uncapitalized variables} & \hat{x} &::=& x & \textrm{not from a module} \\
adamc@530 458 &&& M.x & \textrm{projection from a module} \\
adamc@525 459 \end{array}$$
adamc@525 460
adam@1579 461 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@655 462
adamc@525 463 Modules of the module system are described by \emph{signatures}.
adamc@525 464 $$\begin{array}{rrcll}
adamc@525 465 \textrm{Signatures} & S &::=& \mt{sig} \; s^* \; \mt{end} & \textrm{constant} \\
adamc@525 466 &&& X & \textrm{variable} \\
adamc@525 467 &&& \mt{functor}(X : S) : S & \textrm{functor} \\
adamc@529 468 &&& S \; \mt{where} \; \mt{con} \; x = c & \textrm{concretizing an abstract constructor} \\
adamc@525 469 &&& M.X & \textrm{projection from a module} \\
adamc@525 470 \\
adamc@525 471 \textrm{Signature items} & s &::=& \mt{con} \; x :: \kappa & \textrm{abstract constructor} \\
adamc@525 472 &&& \mt{con} \; x :: \kappa = c & \textrm{concrete constructor} \\
adamc@528 473 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529 474 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@525 475 &&& \mt{val} \; x : \tau & \textrm{value} \\
adamc@525 476 &&& \mt{structure} \; X : S & \textrm{sub-module} \\
adamc@525 477 &&& \mt{signature} \; X = S & \textrm{sub-signature} \\
adamc@525 478 &&& \mt{include} \; S & \textrm{signature inclusion} \\
adamc@525 479 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@654 480 &&& \mt{class} \; x :: \kappa & \textrm{abstract constructor class} \\
adamc@654 481 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@525 482 \\
adamc@525 483 \textrm{Datatype constructors} & dc &::=& X & \textrm{nullary constructor} \\
adamc@525 484 &&& X \; \mt{of} \; \tau & \textrm{unary constructor} \\
adamc@524 485 \end{array}$$
adamc@524 486
adamc@526 487 \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@526 488 $$\begin{array}{rrcll}
adamc@526 489 \textrm{Patterns} & p &::=& \_ & \textrm{wildcard} \\
adamc@526 490 &&& x & \textrm{variable} \\
adamc@526 491 &&& \ell & \textrm{constant} \\
adamc@526 492 &&& \hat{X} & \textrm{nullary constructor} \\
adamc@526 493 &&& \hat{X} \; p & \textrm{unary constructor} \\
adamc@526 494 &&& \{(x = p,)^*\} & \textrm{rigid record pattern} \\
adamc@526 495 &&& \{(x = p,)^+, \ldots\} & \textrm{flexible record pattern} \\
adamc@852 496 &&& p : \tau & \textrm{type annotation} \\
adamc@527 497 &&& (p) & \textrm{explicit precedence} \\
adamc@526 498 \\
adamc@529 499 \textrm{Qualified capitalized variables} & \hat{X} &::=& X & \textrm{not from a module} \\
adamc@526 500 &&& M.X & \textrm{projection from a module} \\
adamc@526 501 \end{array}$$
adamc@526 502
adamc@527 503 \emph{Expressions} are the main run-time entities, corresponding to both ``expressions'' and ``statements'' in mainstream imperative languages.
adamc@527 504 $$\begin{array}{rrcll}
adamc@527 505 \textrm{Expressions} & e &::=& e : \tau & \textrm{type annotation} \\
adamc@529 506 &&& \hat{x} & \textrm{variable} \\
adamc@529 507 &&& \hat{X} & \textrm{datatype constructor} \\
adamc@527 508 &&& \ell & \textrm{constant} \\
adamc@527 509 \\
adamc@527 510 &&& e \; e & \textrm{function application} \\
adamc@527 511 &&& \lambda x : \tau \Rightarrow e & \textrm{function abstraction} \\
adamc@527 512 &&& e [c] & \textrm{polymorphic function application} \\
adamc@852 513 &&& \lambda [x \; ? \; \kappa] \Rightarrow e & \textrm{polymorphic function abstraction} \\
adamc@655 514 &&& e [\kappa] & \textrm{kind-polymorphic function application} \\
adamc@652 515 &&& X \Longrightarrow e & \textrm{kind-polymorphic function abstraction} \\
adamc@527 516 \\
adamc@527 517 &&& \{(c = e,)^*\} & \textrm{known-length record} \\
adamc@527 518 &&& e.c & \textrm{record field projection} \\
adamc@527 519 &&& e \rc e & \textrm{record concatenation} \\
adamc@527 520 &&& e \rcut c & \textrm{removal of a single record field} \\
adamc@527 521 &&& e \rcutM c & \textrm{removal of multiple record fields} \\
adamc@527 522 \\
adamc@527 523 &&& \mt{let} \; ed^* \; \mt{in} \; e \; \mt{end} & \textrm{local definitions} \\
adamc@527 524 \\
adamc@527 525 &&& \mt{case} \; e \; \mt{of} \; (p \Rightarrow e|)^+ & \textrm{pattern matching} \\
adamc@527 526 \\
adamc@654 527 &&& \lambda [c \sim c] \Rightarrow e & \textrm{guarded expression abstraction} \\
adamc@654 528 &&& e \; ! & \textrm{guarded expression application} \\
adamc@527 529 \\
adamc@527 530 &&& \_ & \textrm{wildcard} \\
adamc@527 531 &&& (e) & \textrm{explicit precedence} \\
adamc@527 532 \\
adamc@527 533 \textrm{Local declarations} & ed &::=& \cd{val} \; x : \tau = e & \textrm{non-recursive value} \\
adam@1797 534 &&& \cd{val} \; \cd{rec} \; (x : \tau = e \; \cd{and})^+ & \textrm{mutually recursive values} \\
adamc@527 535 \end{array}$$
adamc@527 536
adamc@655 537 As with constructors, we include both abstraction and application for kind polymorphism, but applications are only inferred internally.
adamc@655 538
adamc@528 539 \emph{Declarations} primarily bring new symbols into context.
adamc@528 540 $$\begin{array}{rrcll}
adamc@528 541 \textrm{Declarations} & d &::=& \mt{con} \; x :: \kappa = c & \textrm{constructor synonym} \\
adamc@528 542 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529 543 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@528 544 &&& \mt{val} \; x : \tau = e & \textrm{value} \\
adam@1797 545 &&& \mt{val} \; \cd{rec} \; (x : \tau = e \; \mt{and})^+ & \textrm{mutually recursive values} \\
adamc@528 546 &&& \mt{structure} \; X : S = M & \textrm{module definition} \\
adamc@528 547 &&& \mt{signature} \; X = S & \textrm{signature definition} \\
adamc@528 548 &&& \mt{open} \; M & \textrm{module inclusion} \\
adamc@528 549 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@528 550 &&& \mt{open} \; \mt{constraints} \; M & \textrm{inclusion of just the constraints from a module} \\
adamc@528 551 &&& \mt{table} \; x : c & \textrm{SQL table} \\
adam@1594 552 &&& \mt{view} \; x = e & \textrm{SQL view} \\
adamc@528 553 &&& \mt{sequence} \; x & \textrm{SQL sequence} \\
adamc@535 554 &&& \mt{cookie} \; x : \tau & \textrm{HTTP cookie} \\
adamc@784 555 &&& \mt{style} \; x : \tau & \textrm{CSS class} \\
adamc@1085 556 &&& \mt{task} \; e = e & \textrm{recurring task} \\
adamc@528 557 \\
adamc@529 558 \textrm{Modules} & M &::=& \mt{struct} \; d^* \; \mt{end} & \textrm{constant} \\
adamc@529 559 &&& X & \textrm{variable} \\
adamc@529 560 &&& M.X & \textrm{projection} \\
adamc@529 561 &&& M(M) & \textrm{functor application} \\
adamc@529 562 &&& \mt{functor}(X : S) : S = M & \textrm{functor abstraction} \\
adamc@528 563 \end{array}$$
adamc@528 564
adamc@528 565 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@527 566
adam@1594 567 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@784 568
adamc@529 569 \subsection{Shorthands}
adamc@529 570
adamc@529 571 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@529 572
adamc@529 573 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@529 574
adamc@529 575 A record type may be written $\{(c = c,)^*\}$, which elaborates to $\$[(c = c,)^*]$.
adamc@529 576
adamc@533 577 The notation $[c_1, \ldots, c_n]$ is shorthand for $[c_1 = (), \ldots, c_n = ()]$.
adamc@533 578
adam@1350 579 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@529 580
adam@1687 581 The syntax $()$ expands to $\{\}$ as a pattern or expression.
adam@1687 582
adamc@852 583 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@529 584
adam@1574 585 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 586
adam@1306 587 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 588
adamc@529 589 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@529 590
adamc@529 591 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@529 592
adamc@654 593 A signature item or declaration $\mt{class} \; x = \lambda y \Rightarrow c$ may be abbreviated $\mt{class} \; x \; y = c$.
adamc@529 594
adam@1738 595 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@529 596
adamc@852 597 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@529 598
adamc@852 599 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@852 600
adam@1797 601 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@529 602
adamc@529 603 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@529 604
adamc@852 605 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@852 606
adamc@853 607 A declaration $\mt{table} \; x : \{(c = c,)^*\}$ is elaborated into $\mt{table} \; x : [(c = c,)^*]$.
adamc@529 608
adamc@529 609 The syntax $\mt{where} \; \mt{type}$ is an alternate form of $\mt{where} \; \mt{con}$.
adamc@529 610
adamc@529 611 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@529 612
adamc@529 613 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@529 614
adamc@784 615 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@529 616
adamc@530 617
adamc@530 618 \section{Static Semantics}
adamc@530 619
adamc@530 620 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@530 621
adam@1891 622 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 623 \begin{quote}
adam@1891 624 Benjamin C. Pierce, \emph{Types and Programming Languages}, MIT Press, 2002.
adam@1891 625 \end{quote}
adam@1891 626
adamc@530 627 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@530 628 \begin{itemize}
adamc@655 629 \item $\Gamma \vdash \kappa$ expresses kind well-formedness.
adamc@530 630 \item $\Gamma \vdash c :: \kappa$ assigns a kind to a constructor in a context.
adamc@530 631 \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@531 632 \item $\Gamma \vdash c \hookrightarrow C$ proves that record constructor $c$ decomposes into set $C$ of field names and record constructors.
adamc@530 633 \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@530 634 \item $\Gamma \vdash e : \tau$ is a standard typing judgment.
adamc@534 635 \item $\Gamma \vdash p \leadsto \Gamma; \tau$ combines typing of patterns with calculation of which new variables they bind.
adamc@537 636 \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@537 637 \item $\Gamma \vdash S \equiv S$ is the signature equivalence judgment.
adamc@536 638 \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@530 639 \item $\Gamma \vdash M : S$ is the module signature checking judgment.
adamc@537 640 \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@539 641 \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@530 642 \end{itemize}
adamc@530 643
adamc@655 644
adamc@655 645 \subsection{Kind Well-Formedness}
adamc@655 646
adamc@655 647 $$\infer{\Gamma \vdash \mt{Type}}{}
adamc@655 648 \quad \infer{\Gamma \vdash \mt{Unit}}{}
adamc@655 649 \quad \infer{\Gamma \vdash \mt{Name}}{}
adamc@655 650 \quad \infer{\Gamma \vdash \kappa_1 \to \kappa_2}{
adamc@655 651 \Gamma \vdash \kappa_1
adamc@655 652 & \Gamma \vdash \kappa_2
adamc@655 653 }
adamc@655 654 \quad \infer{\Gamma \vdash \{\kappa\}}{
adamc@655 655 \Gamma \vdash \kappa
adamc@655 656 }
adamc@655 657 \quad \infer{\Gamma \vdash (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@655 658 \forall i: \Gamma \vdash \kappa_i
adamc@655 659 }$$
adamc@655 660
adamc@655 661 $$\infer{\Gamma \vdash X}{
adamc@655 662 X \in \Gamma
adamc@655 663 }
adamc@655 664 \quad \infer{\Gamma \vdash X \longrightarrow \kappa}{
adamc@655 665 \Gamma, X \vdash \kappa
adamc@655 666 }$$
adamc@655 667
adamc@530 668 \subsection{Kinding}
adamc@530 669
adamc@655 670 We write $[X \mapsto \kappa_1]\kappa_2$ for capture-avoiding substitution of $\kappa_1$ for $X$ in $\kappa_2$.
adamc@655 671
adamc@530 672 $$\infer{\Gamma \vdash (c) :: \kappa :: \kappa}{
adamc@530 673 \Gamma \vdash c :: \kappa
adamc@530 674 }
adamc@530 675 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530 676 x :: \kappa \in \Gamma
adamc@530 677 }
adamc@530 678 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530 679 x :: \kappa = c \in \Gamma
adamc@530 680 }$$
adamc@530 681
adamc@530 682 $$\infer{\Gamma \vdash M.x :: \kappa}{
adamc@537 683 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 684 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = \kappa
adamc@530 685 }
adamc@530 686 \quad \infer{\Gamma \vdash M.x :: \kappa}{
adamc@537 687 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 688 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@530 689 }$$
adamc@530 690
adamc@530 691 $$\infer{\Gamma \vdash \tau_1 \to \tau_2 :: \mt{Type}}{
adamc@530 692 \Gamma \vdash \tau_1 :: \mt{Type}
adamc@530 693 & \Gamma \vdash \tau_2 :: \mt{Type}
adamc@530 694 }
adamc@530 695 \quad \infer{\Gamma \vdash x \; ? \: \kappa \to \tau :: \mt{Type}}{
adamc@530 696 \Gamma, x :: \kappa \vdash \tau :: \mt{Type}
adamc@530 697 }
adamc@655 698 \quad \infer{\Gamma \vdash X \longrightarrow \tau :: \mt{Type}}{
adamc@655 699 \Gamma, X \vdash \tau :: \mt{Type}
adamc@655 700 }
adamc@530 701 \quad \infer{\Gamma \vdash \$c :: \mt{Type}}{
adamc@530 702 \Gamma \vdash c :: \{\mt{Type}\}
adamc@530 703 }$$
adamc@530 704
adamc@530 705 $$\infer{\Gamma \vdash c_1 \; c_2 :: \kappa_2}{
adamc@530 706 \Gamma \vdash c_1 :: \kappa_1 \to \kappa_2
adamc@530 707 & \Gamma \vdash c_2 :: \kappa_1
adamc@530 708 }
adamc@530 709 \quad \infer{\Gamma \vdash \lambda x \; :: \; \kappa_1 \Rightarrow c :: \kappa_1 \to \kappa_2}{
adamc@530 710 \Gamma, x :: \kappa_1 \vdash c :: \kappa_2
adamc@530 711 }$$
adamc@530 712
adamc@655 713 $$\infer{\Gamma \vdash c[\kappa'] :: [X \mapsto \kappa']\kappa}{
adamc@655 714 \Gamma \vdash c :: X \to \kappa
adamc@655 715 & \Gamma \vdash \kappa'
adamc@655 716 }
adamc@655 717 \quad \infer{\Gamma \vdash X \Longrightarrow c :: X \to \kappa}{
adamc@655 718 \Gamma, X \vdash c :: \kappa
adamc@655 719 }$$
adamc@655 720
adamc@530 721 $$\infer{\Gamma \vdash () :: \mt{Unit}}{}
adamc@530 722 \quad \infer{\Gamma \vdash \#X :: \mt{Name}}{}$$
adamc@530 723
adamc@530 724 $$\infer{\Gamma \vdash [\overline{c_i = c'_i}] :: \{\kappa\}}{
adamc@530 725 \forall i: \Gamma \vdash c_i : \mt{Name}
adamc@530 726 & \Gamma \vdash c'_i :: \kappa
adamc@530 727 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@530 728 }
adamc@530 729 \quad \infer{\Gamma \vdash c_1 \rc c_2 :: \{\kappa\}}{
adamc@530 730 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530 731 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@530 732 & \Gamma \vdash c_1 \sim c_2
adamc@530 733 }$$
adamc@530 734
adamc@655 735 $$\infer{\Gamma \vdash \mt{map} :: (\kappa_1 \to \kappa_2) \to \{\kappa_1\} \to \{\kappa_2\}}{}$$
adamc@530 736
adamc@573 737 $$\infer{\Gamma \vdash (\overline c) :: (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@573 738 \forall i: \Gamma \vdash c_i :: \kappa_i
adamc@530 739 }
adamc@573 740 \quad \infer{\Gamma \vdash c.i :: \kappa_i}{
adamc@573 741 \Gamma \vdash c :: (\kappa_1 \times \ldots \times \kappa_n)
adamc@530 742 }$$
adamc@530 743
adamc@655 744 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow \tau :: \mt{Type}}{
adamc@655 745 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530 746 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@655 747 & \Gamma, c_1 \sim c_2 \vdash \tau :: \mt{Type}
adamc@530 748 }$$
adamc@530 749
adamc@531 750 \subsection{Record Disjointness}
adamc@531 751
adamc@531 752 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@558 753 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@558 754 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@558 755 & \forall c'_1 \in C_1, c'_2 \in C_2: \Gamma \vdash c'_1 \sim c'_2
adamc@531 756 }
adamc@531 757 \quad \infer{\Gamma \vdash X \sim X'}{
adamc@531 758 X \neq X'
adamc@531 759 }$$
adamc@531 760
adamc@531 761 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@531 762 c'_1 \sim c'_2 \in \Gamma
adamc@558 763 & \Gamma \vdash c'_1 \hookrightarrow C_1
adamc@558 764 & \Gamma \vdash c'_2 \hookrightarrow C_2
adamc@558 765 & c_1 \in C_1
adamc@558 766 & c_2 \in C_2
adamc@531 767 }$$
adamc@531 768
adamc@531 769 $$\infer{\Gamma \vdash c \hookrightarrow \{c\}}{}
adamc@531 770 \quad \infer{\Gamma \vdash [\overline{c = c'}] \hookrightarrow \{\overline{c}\}}{}
adamc@531 771 \quad \infer{\Gamma \vdash c_1 \rc c_2 \hookrightarrow C_1 \cup C_2}{
adamc@531 772 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@531 773 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@531 774 }
adamc@531 775 \quad \infer{\Gamma \vdash c \hookrightarrow C}{
adamc@531 776 \Gamma \vdash c \equiv c'
adamc@531 777 & \Gamma \vdash c' \hookrightarrow C
adamc@531 778 }
adamc@531 779 \quad \infer{\Gamma \vdash \mt{map} \; f \; c \hookrightarrow C}{
adamc@531 780 \Gamma \vdash c \hookrightarrow C
adamc@531 781 }$$
adamc@531 782
adamc@541 783 \subsection{\label{definitional}Definitional Equality}
adamc@532 784
adamc@655 785 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@532 786
adamc@532 787 $$\infer{\Gamma \vdash c \equiv c}{}
adamc@532 788 \quad \infer{\Gamma \vdash c_1 \equiv c_2}{
adamc@532 789 \Gamma \vdash c_2 \equiv c_1
adamc@532 790 }
adamc@532 791 \quad \infer{\Gamma \vdash c_1 \equiv c_3}{
adamc@532 792 \Gamma \vdash c_1 \equiv c_2
adamc@532 793 & \Gamma \vdash c_2 \equiv c_3
adamc@532 794 }
adamc@532 795 \quad \infer{\Gamma \vdash \mathcal C[c_1] \equiv \mathcal C[c_2]}{
adamc@532 796 \Gamma \vdash c_1 \equiv c_2
adamc@532 797 }$$
adamc@532 798
adamc@532 799 $$\infer{\Gamma \vdash x \equiv c}{
adamc@532 800 x :: \kappa = c \in \Gamma
adamc@532 801 }
adamc@532 802 \quad \infer{\Gamma \vdash M.x \equiv c}{
adamc@537 803 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 804 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@532 805 }
adamc@532 806 \quad \infer{\Gamma \vdash (\overline c).i \equiv c_i}{}$$
adamc@532 807
adamc@532 808 $$\infer{\Gamma \vdash (\lambda x :: \kappa \Rightarrow c) \; c' \equiv [x \mapsto c'] c}{}
adamc@655 809 \quad \infer{\Gamma \vdash (X \Longrightarrow c) [\kappa] \equiv [X \mapsto \kappa] c}{}$$
adamc@655 810
adamc@655 811 $$\infer{\Gamma \vdash c_1 \rc c_2 \equiv c_2 \rc c_1}{}
adamc@532 812 \quad \infer{\Gamma \vdash c_1 \rc (c_2 \rc c_3) \equiv (c_1 \rc c_2) \rc c_3}{}$$
adamc@532 813
adamc@532 814 $$\infer{\Gamma \vdash [] \rc c \equiv c}{}
adamc@532 815 \quad \infer{\Gamma \vdash [\overline{c_1 = c'_1}] \rc [\overline{c_2 = c'_2}] \equiv [\overline{c_1 = c'_1}, \overline{c_2 = c'_2}]}{}$$
adamc@532 816
adamc@655 817 $$\infer{\Gamma \vdash \mt{map} \; f \; [] \equiv []}{}
adamc@655 818 \quad \infer{\Gamma \vdash \mt{map} \; f \; ([c_1 = c_2] \rc c) \equiv [c_1 = f \; c_2] \rc \mt{map} \; f \; c}{}$$
adamc@532 819
adamc@532 820 $$\infer{\Gamma \vdash \mt{map} \; (\lambda x \Rightarrow x) \; c \equiv c}{}
adamc@655 821 \quad \infer{\Gamma \vdash \mt{map} \; f \; (\mt{map} \; f' \; c)
adamc@655 822 \equiv \mt{map} \; (\lambda x \Rightarrow f \; (f' \; x)) \; c}{}$$
adamc@532 823
adamc@532 824 $$\infer{\Gamma \vdash \mt{map} \; f \; (c_1 \rc c_2) \equiv \mt{map} \; f \; c_1 \rc \mt{map} \; f \; c_2}{}$$
adamc@531 825
adamc@534 826 \subsection{Expression Typing}
adamc@533 827
adamc@873 828 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@533 829
adamc@533 830 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@533 831
adamc@533 832 $$\infer{\Gamma \vdash e : \tau : \tau}{
adamc@533 833 \Gamma \vdash e : \tau
adamc@533 834 }
adamc@533 835 \quad \infer{\Gamma \vdash e : \tau}{
adamc@533 836 \Gamma \vdash e : \tau'
adamc@533 837 & \Gamma \vdash \tau' \equiv \tau
adamc@533 838 }
adamc@533 839 \quad \infer{\Gamma \vdash \ell : T(\ell)}{}$$
adamc@533 840
adamc@533 841 $$\infer{\Gamma \vdash x : \mathcal I(\tau)}{
adamc@533 842 x : \tau \in \Gamma
adamc@533 843 }
adamc@533 844 \quad \infer{\Gamma \vdash M.x : \mathcal I(\tau)}{
adamc@537 845 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 846 & \mt{proj}(M, \overline{s}, \mt{val} \; x) = \tau
adamc@533 847 }
adamc@533 848 \quad \infer{\Gamma \vdash X : \mathcal I(\tau)}{
adamc@533 849 X : \tau \in \Gamma
adamc@533 850 }
adamc@533 851 \quad \infer{\Gamma \vdash M.X : \mathcal I(\tau)}{
adamc@537 852 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 853 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \tau
adamc@533 854 }$$
adamc@533 855
adamc@533 856 $$\infer{\Gamma \vdash e_1 \; e_2 : \tau_2}{
adamc@533 857 \Gamma \vdash e_1 : \tau_1 \to \tau_2
adamc@533 858 & \Gamma \vdash e_2 : \tau_1
adamc@533 859 }
adamc@533 860 \quad \infer{\Gamma \vdash \lambda x : \tau_1 \Rightarrow e : \tau_1 \to \tau_2}{
adamc@533 861 \Gamma, x : \tau_1 \vdash e : \tau_2
adamc@533 862 }$$
adamc@533 863
adamc@533 864 $$\infer{\Gamma \vdash e [c] : [x \mapsto c]\tau}{
adamc@533 865 \Gamma \vdash e : x :: \kappa \to \tau
adamc@533 866 & \Gamma \vdash c :: \kappa
adamc@533 867 }
adamc@852 868 \quad \infer{\Gamma \vdash \lambda [x \; ? \; \kappa] \Rightarrow e : x \; ? \; \kappa \to \tau}{
adamc@533 869 \Gamma, x :: \kappa \vdash e : \tau
adamc@533 870 }$$
adamc@533 871
adamc@655 872 $$\infer{\Gamma \vdash e [\kappa] : [X \mapsto \kappa]\tau}{
adamc@655 873 \Gamma \vdash e : X \longrightarrow \tau
adamc@655 874 & \Gamma \vdash \kappa
adamc@655 875 }
adamc@655 876 \quad \infer{\Gamma \vdash X \Longrightarrow e : X \longrightarrow \tau}{
adamc@655 877 \Gamma, X \vdash e : \tau
adamc@655 878 }$$
adamc@655 879
adamc@533 880 $$\infer{\Gamma \vdash \{\overline{c = e}\} : \{\overline{c : \tau}\}}{
adamc@533 881 \forall i: \Gamma \vdash c_i :: \mt{Name}
adamc@533 882 & \Gamma \vdash e_i : \tau_i
adamc@533 883 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@533 884 }
adamc@533 885 \quad \infer{\Gamma \vdash e.c : \tau}{
adamc@533 886 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533 887 }
adamc@533 888 \quad \infer{\Gamma \vdash e_1 \rc e_2 : \$(c_1 \rc c_2)}{
adamc@533 889 \Gamma \vdash e_1 : \$c_1
adamc@533 890 & \Gamma \vdash e_2 : \$c_2
adamc@573 891 & \Gamma \vdash c_1 \sim c_2
adamc@533 892 }$$
adamc@533 893
adamc@533 894 $$\infer{\Gamma \vdash e \rcut c : \$c'}{
adamc@533 895 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533 896 }
adamc@533 897 \quad \infer{\Gamma \vdash e \rcutM c : \$c'}{
adamc@533 898 \Gamma \vdash e : \$(c \rc c')
adamc@533 899 }$$
adamc@533 900
adamc@533 901 $$\infer{\Gamma \vdash \mt{let} \; \overline{ed} \; \mt{in} \; e \; \mt{end} : \tau}{
adamc@533 902 \Gamma \vdash \overline{ed} \leadsto \Gamma'
adamc@533 903 & \Gamma' \vdash e : \tau
adamc@533 904 }
adamc@533 905 \quad \infer{\Gamma \vdash \mt{case} \; e \; \mt{of} \; \overline{p \Rightarrow e} : \tau}{
adamc@533 906 \forall i: \Gamma \vdash p_i \leadsto \Gamma_i, \tau'
adamc@533 907 & \Gamma_i \vdash e_i : \tau
adamc@533 908 }$$
adamc@533 909
adamc@573 910 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow e : \lambda [c_1 \sim c_2] \Rightarrow \tau}{
adamc@533 911 \Gamma \vdash c_1 :: \{\kappa\}
adamc@655 912 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@533 913 & \Gamma, c_1 \sim c_2 \vdash e : \tau
adamc@662 914 }
adamc@662 915 \quad \infer{\Gamma \vdash e \; ! : \tau}{
adamc@662 916 \Gamma \vdash e : [c_1 \sim c_2] \Rightarrow \tau
adamc@662 917 & \Gamma \vdash c_1 \sim c_2
adamc@533 918 }$$
adamc@533 919
adamc@534 920 \subsection{Pattern Typing}
adamc@534 921
adamc@534 922 $$\infer{\Gamma \vdash \_ \leadsto \Gamma; \tau}{}
adamc@534 923 \quad \infer{\Gamma \vdash x \leadsto \Gamma, x : \tau; \tau}{}
adamc@534 924 \quad \infer{\Gamma \vdash \ell \leadsto \Gamma; T(\ell)}{}$$
adamc@534 925
adamc@534 926 $$\infer{\Gamma \vdash X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534 927 X : \overline{x ::: \mt{Type}} \to \tau \in \Gamma
adamc@534 928 & \textrm{$\tau$ not a function type}
adamc@534 929 }
adamc@534 930 \quad \infer{\Gamma \vdash X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534 931 X : \overline{x ::: \mt{Type}} \to \tau'' \to \tau \in \Gamma
adamc@534 932 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534 933 }$$
adamc@534 934
adamc@534 935 $$\infer{\Gamma \vdash M.X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537 936 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 937 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau
adamc@534 938 & \textrm{$\tau$ not a function type}
adamc@534 939 }$$
adamc@534 940
adamc@534 941 $$\infer{\Gamma \vdash M.X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537 942 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 943 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau'' \to \tau
adamc@534 944 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534 945 }$$
adamc@534 946
adamc@534 947 $$\infer{\Gamma \vdash \{\overline{x = p}\} \leadsto \Gamma_n; \{\overline{x = \tau}\}}{
adamc@534 948 \Gamma_0 = \Gamma
adamc@534 949 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534 950 }
adamc@534 951 \quad \infer{\Gamma \vdash \{\overline{x = p}, \ldots\} \leadsto \Gamma_n; \$([\overline{x = \tau}] \rc c)}{
adamc@534 952 \Gamma_0 = \Gamma
adamc@534 953 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534 954 }$$
adamc@534 955
adamc@852 956 $$\infer{\Gamma \vdash p : \tau \leadsto \Gamma'; \tau}{
adamc@852 957 \Gamma \vdash p \leadsto \Gamma'; \tau'
adamc@852 958 & \Gamma \vdash \tau' \equiv \tau
adamc@852 959 }$$
adamc@852 960
adamc@535 961 \subsection{Declaration Typing}
adamc@535 962
adamc@535 963 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@535 964
adamc@558 965 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@537 966 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@535 967
adamc@535 968 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535 969 \quad \infer{\Gamma \vdash d, \overline{d} \leadsto \Gamma''}{
adamc@535 970 \Gamma \vdash d \leadsto \Gamma'
adamc@535 971 & \Gamma' \vdash \overline{d} \leadsto \Gamma''
adamc@535 972 }$$
adamc@535 973
adamc@535 974 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@535 975 \Gamma \vdash c :: \kappa
adamc@535 976 }
adamc@535 977 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@535 978 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@535 979 }$$
adamc@535 980
adamc@535 981 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537 982 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 983 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@535 984 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@535 985 }$$
adamc@535 986
adamc@535 987 $$\infer{\Gamma \vdash \mt{val} \; x : \tau = e \leadsto \Gamma, x : \tau}{
adamc@535 988 \Gamma \vdash e : \tau
adamc@535 989 }$$
adamc@535 990
adamc@535 991 $$\infer{\Gamma \vdash \mt{val} \; \mt{rec} \; \overline{x : \tau = e} \leadsto \Gamma, \overline{x : \tau}}{
adamc@535 992 \forall i: \Gamma, \overline{x : \tau} \vdash e_i : \tau_i
adamc@535 993 & \textrm{$e_i$ starts with an expression $\lambda$, optionally preceded by constructor and disjointness $\lambda$s}
adamc@535 994 }$$
adamc@535 995
adamc@535 996 $$\infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : S}{
adamc@535 997 \Gamma \vdash M : S
adamc@558 998 & \textrm{ $M$ not a constant or application}
adamc@535 999 }
adamc@558 1000 \quad \infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : \mt{selfify}(X, \overline{s})}{
adamc@558 1001 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@539 1002 }$$
adamc@539 1003
adamc@539 1004 $$\infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@535 1005 \Gamma \vdash S
adamc@535 1006 }$$
adamc@535 1007
adamc@537 1008 $$\infer{\Gamma \vdash \mt{open} \; M \leadsto \Gamma, \mathcal O(M, \overline{s})}{
adamc@537 1009 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535 1010 }$$
adamc@535 1011
adamc@535 1012 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma}{
adamc@535 1013 \Gamma \vdash c_1 :: \{\kappa\}
adamc@535 1014 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@535 1015 & \Gamma \vdash c_1 \sim c_2
adamc@535 1016 }
adamc@537 1017 \quad \infer{\Gamma \vdash \mt{open} \; \mt{constraints} \; M \leadsto \Gamma, \mathcal O_c(M, \overline{s})}{
adamc@537 1018 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535 1019 }$$
adamc@535 1020
adamc@784 1021 $$\infer{\Gamma \vdash \mt{table} \; x : c \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_table} \; c \; []}{
adamc@535 1022 \Gamma \vdash c :: \{\mt{Type}\}
adamc@535 1023 }
adam@1594 1024 \quad \infer{\Gamma \vdash \mt{view} \; x = e \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_view} \; c}{
adam@1594 1025 \Gamma \vdash e :: \mt{Basis}.\mt{sql\_query} \; [] \; [] \; (\mt{map} \; (\lambda \_ \Rightarrow []) \; c') \; c
adamc@784 1026 }$$
adamc@784 1027
adamc@784 1028 $$\infer{\Gamma \vdash \mt{sequence} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_sequence}}{}$$
adamc@535 1029
adamc@535 1030 $$\infer{\Gamma \vdash \mt{cookie} \; x : \tau \leadsto \Gamma, x : \mt{Basis}.\mt{http\_cookie} \; \tau}{
adamc@535 1031 \Gamma \vdash \tau :: \mt{Type}
adamc@784 1032 }
adamc@784 1033 \quad \infer{\Gamma \vdash \mt{style} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{css\_class}}{}$$
adamc@535 1034
adamc@1085 1035 $$\infer{\Gamma \vdash \mt{task} \; e_1 = e_2 \leadsto \Gamma}{
adam@1348 1036 \Gamma \vdash e_1 :: \mt{Basis}.\mt{task\_kind} \; \tau
adam@1348 1037 & \Gamma \vdash e_2 :: \tau \to \mt{Basis}.\mt{transaction} \; \{\}
adamc@1085 1038 }$$
adamc@1085 1039
adamc@535 1040 $$\infer{\overline{y}; x; \Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535 1041 \quad \infer{\overline{y}; x; \Gamma \vdash X \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to x \; \overline{y}}{
adamc@535 1042 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535 1043 }
adamc@535 1044 \quad \infer{\overline{y}; x; \Gamma \vdash X \; \mt{of} \; \tau \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to \tau \to x \; \overline{y}}{
adamc@535 1045 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535 1046 }$$
adamc@535 1047
adamc@537 1048 \subsection{Signature Item Typing}
adamc@537 1049
adamc@537 1050 We appeal to a signature item analogue of the $\mathcal O$ function from the last subsection.
adamc@537 1051
adam@1797 1052 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 1053
adamc@537 1054 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@537 1055 \quad \infer{\Gamma \vdash s, \overline{s} \leadsto \Gamma''}{
adamc@537 1056 \Gamma \vdash s \leadsto \Gamma'
adamc@537 1057 & \Gamma' \vdash \overline{s} \leadsto \Gamma''
adamc@537 1058 }$$
adamc@537 1059
adamc@537 1060 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}
adamc@537 1061 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@537 1062 \Gamma \vdash c :: \kappa
adamc@537 1063 }
adamc@537 1064 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@537 1065 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@537 1066 }$$
adamc@537 1067
adamc@537 1068 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537 1069 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1070 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1071 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@537 1072 }$$
adamc@537 1073
adamc@537 1074 $$\infer{\Gamma \vdash \mt{val} \; x : \tau \leadsto \Gamma, x : \tau}{
adamc@537 1075 \Gamma \vdash \tau :: \mt{Type}
adamc@537 1076 }$$
adamc@537 1077
adamc@537 1078 $$\infer{\Gamma \vdash \mt{structure} \; X : S \leadsto \Gamma, X : S}{
adamc@537 1079 \Gamma \vdash S
adamc@537 1080 }
adamc@537 1081 \quad \infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@537 1082 \Gamma \vdash S
adamc@537 1083 }$$
adamc@537 1084
adamc@537 1085 $$\infer{\Gamma \vdash \mt{include} \; S \leadsto \Gamma, \mathcal O(\overline{s})}{
adamc@537 1086 \Gamma \vdash S
adamc@537 1087 & \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1088 }$$
adamc@537 1089
adamc@537 1090 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma, c_1 \sim c_2}{
adamc@537 1091 \Gamma \vdash c_1 :: \{\kappa\}
adamc@537 1092 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@537 1093 }$$
adamc@537 1094
adamc@784 1095 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784 1096 \Gamma \vdash c :: \kappa
adamc@537 1097 }
adamc@784 1098 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}$$
adamc@537 1099
adamc@536 1100 \subsection{Signature Compatibility}
adamc@536 1101
adam@1797 1102 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 1103
adamc@537 1104 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 1105
adamc@536 1106 $$\infer{\Gamma \vdash S \equiv S}{}
adamc@536 1107 \quad \infer{\Gamma \vdash S_1 \equiv S_2}{
adamc@536 1108 \Gamma \vdash S_2 \equiv S_1
adamc@536 1109 }
adamc@536 1110 \quad \infer{\Gamma \vdash X \equiv S}{
adamc@536 1111 X = S \in \Gamma
adamc@536 1112 }
adamc@536 1113 \quad \infer{\Gamma \vdash M.X \equiv S}{
adamc@537 1114 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1115 & \mt{proj}(M, \overline{s}, \mt{signature} \; X) = S
adamc@536 1116 }$$
adamc@536 1117
adamc@536 1118 $$\infer{\Gamma \vdash S \; \mt{where} \; \mt{con} \; x = c \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa = c \; \overline{s_2} \; \mt{end}}{
adamc@536 1119 \Gamma \vdash S \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa \; \overline{s_2} \; \mt{end}
adamc@536 1120 & \Gamma \vdash c :: \kappa
adamc@537 1121 }
adamc@537 1122 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s^1} \; \mt{include} \; S \; \overline{s^2} \; \mt{end} \equiv \mt{sig} \; \overline{s^1} \; \overline{s} \; \overline{s^2} \; \mt{end}}{
adamc@537 1123 \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@536 1124 }$$
adamc@536 1125
adamc@536 1126 $$\infer{\Gamma \vdash S_1 \leq S_2}{
adamc@536 1127 \Gamma \vdash S_1 \equiv S_2
adamc@536 1128 }
adamc@536 1129 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \mt{end}}{}
adamc@537 1130 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; s' \; \overline{s'} \; \mt{end}}{
adamc@537 1131 \Gamma \vdash \overline{s} \leq s'
adamc@537 1132 & \Gamma \vdash s' \leadsto \Gamma'
adamc@537 1133 & \Gamma' \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \overline{s'} \; \mt{end}
adamc@537 1134 }$$
adamc@537 1135
adamc@537 1136 $$\infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537 1137 \Gamma \vdash s \leq s'
adamc@537 1138 }
adamc@537 1139 \quad \infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537 1140 \Gamma \vdash s \leadsto \Gamma'
adamc@537 1141 & \Gamma' \vdash \overline{s} \leq s'
adamc@536 1142 }$$
adamc@536 1143
adamc@536 1144 $$\infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 \leq \mt{functor} (X : S'_1) : S'_2}{
adamc@536 1145 \Gamma \vdash S'_1 \leq S_1
adamc@536 1146 & \Gamma, X : S'_1 \vdash S_2 \leq S'_2
adamc@536 1147 }$$
adamc@536 1148
adamc@537 1149 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@537 1150 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}
adamc@558 1151 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type}}{}$$
adamc@537 1152
adamc@537 1153 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(y)} \to \mt{Type}}{
adamc@537 1154 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1155 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1156 }$$
adamc@537 1157
adamc@784 1158 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@784 1159 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}$$
adamc@537 1160
adamc@537 1161 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \mt{\kappa} = c_2}{
adamc@537 1162 \Gamma \vdash c_1 \equiv c_2
adamc@537 1163 }
adamc@784 1164 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \kappa = c_2}{
adamc@537 1165 \Gamma \vdash c_1 \equiv c_2
adamc@537 1166 }$$
adamc@537 1167
adamc@537 1168 $$\infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537 1169 \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1170 }$$
adamc@537 1171
adamc@537 1172 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537 1173 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1174 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1175 & \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1176 }$$
adamc@537 1177
adamc@537 1178 $$\infer{\Gamma \vdash \cdot \leq \cdot}{}
adamc@537 1179 \quad \infer{\Gamma \vdash X; \overline{dc} \leq X; \overline{dc'}}{
adamc@537 1180 \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1181 }
adamc@537 1182 \quad \infer{\Gamma \vdash X \; \mt{of} \; \tau_1; \overline{dc} \leq X \; \mt{of} \; \tau_2; \overline{dc'}}{
adamc@537 1183 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537 1184 & \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1185 }$$
adamc@537 1186
adamc@537 1187 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x = \mt{datatype} \; M'.z'}{
adamc@537 1188 \Gamma \vdash M.z \equiv M'.z'
adamc@537 1189 }$$
adamc@537 1190
adamc@537 1191 $$\infer{\Gamma \vdash \mt{val} \; x : \tau_1 \leq \mt{val} \; x : \tau_2}{
adamc@537 1192 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537 1193 }
adamc@537 1194 \quad \infer{\Gamma \vdash \mt{structure} \; X : S_1 \leq \mt{structure} \; X : S_2}{
adamc@537 1195 \Gamma \vdash S_1 \leq S_2
adamc@537 1196 }
adamc@537 1197 \quad \infer{\Gamma \vdash \mt{signature} \; X = S_1 \leq \mt{signature} \; X = S_2}{
adamc@537 1198 \Gamma \vdash S_1 \leq S_2
adamc@537 1199 & \Gamma \vdash S_2 \leq S_1
adamc@537 1200 }$$
adamc@537 1201
adamc@537 1202 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leq \mt{constraint} \; c'_1 \sim c'_2}{
adamc@537 1203 \Gamma \vdash c_1 \equiv c'_1
adamc@537 1204 & \Gamma \vdash c_2 \equiv c'_2
adamc@537 1205 }$$
adamc@537 1206
adamc@655 1207 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{class} \; x :: \kappa}{}
adamc@655 1208 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{class} \; x :: \kappa}{}
adamc@655 1209 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{class} \; x :: \kappa = c_2}{
adamc@537 1210 \Gamma \vdash c_1 \equiv c_2
adamc@537 1211 }$$
adamc@537 1212
adam@1797 1213 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leq \mt{class} \; x :: \kappa}{}
adam@1797 1214 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leq \mt{class} \; x :: \kappa}{}
adam@1797 1215 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c_1 \leq \mt{class} \; x :: \kappa = c_2}{
adam@1797 1216 \Gamma \vdash c_1 \equiv c_2
adam@1797 1217 }$$
adam@1797 1218
adamc@538 1219 \subsection{Module Typing}
adamc@538 1220
adamc@538 1221 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 1222
adamc@538 1223 $$\infer{\Gamma \vdash M : S}{
adamc@538 1224 \Gamma \vdash M : S'
adamc@538 1225 & \Gamma \vdash S' \leq S
adamc@538 1226 }
adamc@538 1227 \quad \infer{\Gamma \vdash \mt{struct} \; \overline{d} \; \mt{end} : \mt{sig} \; \mt{sigOf}(\overline{d}) \; \mt{end}}{
adamc@538 1228 \Gamma \vdash \overline{d} \leadsto \Gamma'
adamc@538 1229 }
adamc@538 1230 \quad \infer{\Gamma \vdash X : S}{
adamc@538 1231 X : S \in \Gamma
adamc@538 1232 }$$
adamc@538 1233
adamc@538 1234 $$\infer{\Gamma \vdash M.X : S}{
adamc@538 1235 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@538 1236 & \mt{proj}(M, \overline{s}, \mt{structure} \; X) = S
adamc@538 1237 }$$
adamc@538 1238
adamc@538 1239 $$\infer{\Gamma \vdash M_1(M_2) : [X \mapsto M_2]S_2}{
adamc@538 1240 \Gamma \vdash M_1 : \mt{functor}(X : S_1) : S_2
adamc@538 1241 & \Gamma \vdash M_2 : S_1
adamc@538 1242 }
adamc@538 1243 \quad \infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 = M : \mt{functor} (X : S_1) : S_2}{
adamc@538 1244 \Gamma \vdash S_1
adamc@538 1245 & \Gamma, X : S_1 \vdash S_2
adamc@538 1246 & \Gamma, X : S_1 \vdash M : S_2
adamc@538 1247 }$$
adamc@538 1248
adamc@538 1249 \begin{eqnarray*}
adamc@538 1250 \mt{sigOf}(\cdot) &=& \cdot \\
adamc@538 1251 \mt{sigOf}(s \; \overline{s'}) &=& \mt{sigOf}(s) \; \mt{sigOf}(\overline{s'}) \\
adamc@538 1252 \\
adamc@538 1253 \mt{sigOf}(\mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@538 1254 \mt{sigOf}(\mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \overline{dc} \\
adamc@538 1255 \mt{sigOf}(\mt{datatype} \; x = \mt{datatype} \; M.z) &=& \mt{datatype} \; x = \mt{datatype} \; M.z \\
adamc@538 1256 \mt{sigOf}(\mt{val} \; x : \tau = e) &=& \mt{val} \; x : \tau \\
adamc@538 1257 \mt{sigOf}(\mt{val} \; \mt{rec} \; \overline{x : \tau = e}) &=& \overline{\mt{val} \; x : \tau} \\
adamc@538 1258 \mt{sigOf}(\mt{structure} \; X : S = M) &=& \mt{structure} \; X : S \\
adamc@538 1259 \mt{sigOf}(\mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@538 1260 \mt{sigOf}(\mt{open} \; M) &=& \mt{include} \; S \textrm{ (where $\Gamma \vdash M : S$)} \\
adamc@538 1261 \mt{sigOf}(\mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@538 1262 \mt{sigOf}(\mt{open} \; \mt{constraints} \; M) &=& \cdot \\
adamc@538 1263 \mt{sigOf}(\mt{table} \; x : c) &=& \mt{table} \; x : c \\
adam@1594 1264 \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 1265 \mt{sigOf}(\mt{sequence} \; x) &=& \mt{sequence} \; x \\
adamc@538 1266 \mt{sigOf}(\mt{cookie} \; x : \tau) &=& \mt{cookie} \; x : \tau \\
adam@1797 1267 \mt{sigOf}(\mt{style} \; x) &=& \mt{style} \; x
adamc@538 1268 \end{eqnarray*}
adamc@539 1269 \begin{eqnarray*}
adamc@539 1270 \mt{selfify}(M, \cdot) &=& \cdot \\
adamc@558 1271 \mt{selfify}(M, s \; \overline{s'}) &=& \mt{selfify}(M, s) \; \mt{selfify}(M, \overline{s'}) \\
adamc@539 1272 \\
adamc@539 1273 \mt{selfify}(M, \mt{con} \; x :: \kappa) &=& \mt{con} \; x :: \kappa = M.x \\
adamc@539 1274 \mt{selfify}(M, \mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@539 1275 \mt{selfify}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \mt{datatype} \; M.x \\
adamc@539 1276 \mt{selfify}(M, \mt{datatype} \; x = \mt{datatype} \; M'.z) &=& \mt{datatype} \; x = \mt{datatype} \; M'.z \\
adamc@539 1277 \mt{selfify}(M, \mt{val} \; x : \tau) &=& \mt{val} \; x : \tau \\
adamc@539 1278 \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 1279 \mt{selfify}(M, \mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@539 1280 \mt{selfify}(M, \mt{include} \; S) &=& \mt{include} \; S \\
adamc@539 1281 \mt{selfify}(M, \mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@655 1282 \mt{selfify}(M, \mt{class} \; x :: \kappa) &=& \mt{class} \; x :: \kappa = M.x \\
adamc@655 1283 \mt{selfify}(M, \mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@539 1284 \end{eqnarray*}
adamc@539 1285
adamc@540 1286 \subsection{Module Projection}
adamc@540 1287
adamc@540 1288 \begin{eqnarray*}
adamc@540 1289 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \\
adamc@540 1290 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa, c) \\
adamc@540 1291 \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 1292 \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 1293 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})$)} \\
adamc@655 1294 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \to \mt{Type} \\
adamc@655 1295 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa \to \mt{Type}, c) \\
adamc@540 1296 \\
adamc@540 1297 \mt{proj}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc} \; \overline{s}, \mt{datatype} \; x) &=& (\overline{y}, \overline{dc}) \\
adamc@540 1298 \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 1299 \\
adamc@540 1300 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, \mt{val} \; x) &=& \tau \\
adamc@540 1301 \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 1302 \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 1303 \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 1304 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \in \overline{dc}$)} \\
adamc@540 1305 \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 1306 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \; \mt{of} \; \tau \in \overline{dc}$)} \\
adamc@540 1307 \\
adamc@540 1308 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, \mt{structure} \; X) &=& S \\
adamc@540 1309 \\
adamc@540 1310 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, \mt{signature} \; X) &=& S \\
adamc@540 1311 \\
adamc@540 1312 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1313 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1314 \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 1315 \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 1316 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@540 1317 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1318 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1319 \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 1320 \mt{proj}(M, \mt{constraint} \; c_1 \sim c_2 \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@655 1321 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@655 1322 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1323 \end{eqnarray*}
adamc@540 1324
adamc@541 1325
adamc@541 1326 \section{Type Inference}
adamc@541 1327
adamc@541 1328 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 1329
adamc@541 1330 \subsection{Basic Unification}
adamc@541 1331
adamc@560 1332 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 1333
adamc@656 1334 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 1335
adamc@541 1336 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 1337
adamc@541 1338 \subsection{Unifying Record Types}
adamc@541 1339
adamc@570 1340 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 1341
adamc@656 1342 \subsection{\label{typeclasses}Constructor Classes}
adamc@541 1343
adamc@784 1344 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 1345
adam@1797 1346 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 1347
adam@1797 1348 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 1349
adam@1797 1350 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 1351
adamc@541 1352 \subsection{Reverse-Engineering Record Types}
adamc@541 1353
adamc@656 1354 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 1355
adamc@541 1356 \subsection{Implicit Arguments in Functor Applications}
adamc@541 1357
adamc@656 1358 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 1359
adamc@541 1360
adamc@542 1361 \section{The Ur Standard Library}
adamc@542 1362
adamc@542 1363 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 1364
adamc@542 1365 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 1366
adamc@542 1367 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 1368 $$\begin{array}{l}
adamc@542 1369 \mt{type} \; \mt{int} \\
adamc@542 1370 \mt{type} \; \mt{float} \\
adamc@873 1371 \mt{type} \; \mt{char} \\
adamc@542 1372 \mt{type} \; \mt{string} \\
adamc@542 1373 \mt{type} \; \mt{time} \\
adamc@785 1374 \mt{type} \; \mt{blob} \\
adamc@542 1375 \\
adamc@542 1376 \mt{type} \; \mt{unit} = \{\} \\
adamc@542 1377 \\
adamc@542 1378 \mt{datatype} \; \mt{bool} = \mt{False} \mid \mt{True} \\
adamc@542 1379 \\
adamc@785 1380 \mt{datatype} \; \mt{option} \; \mt{t} = \mt{None} \mid \mt{Some} \; \mt{of} \; \mt{t} \\
adamc@785 1381 \\
adamc@785 1382 \mt{datatype} \; \mt{list} \; \mt{t} = \mt{Nil} \mid \mt{Cons} \; \mt{of} \; \mt{t} \times \mt{list} \; \mt{t}
adamc@542 1383 \end{array}$$
adamc@542 1384
adamc@1123 1385 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 1386
adam@1297 1387 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 1388 $$\begin{array}{l}
adam@1297 1389 \mt{con} \; \mt{variant} :: \{\mt{Type}\} \to \mt{Type} \\
adam@1297 1390 \mt{val} \; \mt{make} : \mt{nm} :: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{ts} ::: \{\mt{Type}\} \to [[\mt{nm}] \sim \mt{ts}] \Rightarrow \mt{t} \to \mt{variant} \; ([\mt{nm} = \mt{t}] \rc \mt{ts}) \\
adam@1297 1391 \mt{val} \; \mt{match} : \mt{ts} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{variant} \; \mt{ts} \to \$(\mt{map} \; (\lambda \mt{t'} \Rightarrow \mt{t'} \to \mt{t}) \; \mt{ts}) \to \mt{t}
adam@1297 1392 \end{array}$$
adam@1297 1393
adamc@657 1394 Another important generic Ur element comes at the beginning of \texttt{top.urs}.
adamc@657 1395
adamc@657 1396 $$\begin{array}{l}
adamc@657 1397 \mt{con} \; \mt{folder} :: \mt{K} \longrightarrow \{\mt{K}\} \to \mt{Type} \\
adamc@657 1398 \\
adamc@657 1399 \mt{val} \; \mt{fold} : \mt{K} \longrightarrow \mt{tf} :: (\{\mt{K}\} \to \mt{Type}) \\
adamc@657 1400 \hspace{.1in} \to (\mt{nm} :: \mt{Name} \to \mt{v} :: \mt{K} \to \mt{r} :: \{\mt{K}\} \to [[\mt{nm}] \sim \mt{r}] \Rightarrow \\
adamc@657 1401 \hspace{.2in} \mt{tf} \; \mt{r} \to \mt{tf} \; ([\mt{nm} = \mt{v}] \rc \mt{r})) \\
adamc@657 1402 \hspace{.1in} \to \mt{tf} \; [] \\
adamc@657 1403 \hspace{.1in} \to \mt{r} :: \{\mt{K}\} \to \mt{folder} \; \mt{r} \to \mt{tf} \; \mt{r}
adamc@657 1404 \end{array}$$
adamc@657 1405
adamc@657 1406 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 1407
adamc@664 1408 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 1409
adamc@542 1410
adamc@542 1411 \section{The Ur/Web Standard Library}
adamc@542 1412
adam@1400 1413 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 1414
adamc@658 1415 \subsection{Monads}
adamc@658 1416
adamc@658 1417 The Ur Basis defines the monad constructor class from Haskell.
adamc@658 1418
adamc@658 1419 $$\begin{array}{l}
adamc@658 1420 \mt{class} \; \mt{monad} :: \mt{Type} \to \mt{Type} \\
adamc@658 1421 \mt{val} \; \mt{return} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t} ::: \mt{Type} \\
adamc@658 1422 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658 1423 \hspace{.1in} \to \mt{t} \to \mt{m} \; \mt{t} \\
adamc@658 1424 \mt{val} \; \mt{bind} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t1} ::: \mt{Type} \to \mt{t2} ::: \mt{Type} \\
adamc@658 1425 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658 1426 \hspace{.1in} \to \mt{m} \; \mt{t1} \to (\mt{t1} \to \mt{m} \; \mt{t2}) \\
adam@1544 1427 \hspace{.1in} \to \mt{m} \; \mt{t2} \\
adam@1544 1428 \mt{val} \; \mt{mkMonad} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \\
adam@1544 1429 \hspace{.1in} \to \{\mt{Return} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{m} \; \mt{t}, \\
adam@1544 1430 \hspace{.3in} \mt{Bind} : \mt{t1} ::: \mt{Type} \to \mt{t2} ::: \mt{Type} \to \mt{m} \; \mt{t1} \to (\mt{t1} \to \mt{m} \; \mt{t2}) \to \mt{m} \; \mt{t2}\} \\
adam@1544 1431 \hspace{.1in} \to \mt{monad} \; \mt{m}
adamc@658 1432 \end{array}$$
adamc@658 1433
adam@1687 1434 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 1435
adamc@542 1436 \subsection{Transactions}
adamc@542 1437
adamc@542 1438 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 1439 $$\begin{array}{l}
adamc@542 1440 \mt{con} \; \mt{transaction} :: \mt{Type} \to \mt{Type} \\
adamc@658 1441 \mt{val} \; \mt{transaction\_monad} : \mt{monad} \; \mt{transaction}
adamc@542 1442 \end{array}$$
adamc@542 1443
adamc@1123 1444 For debugging purposes, a transactional function is provided for outputting a string on the server process' \texttt{stderr}.
adamc@1123 1445 $$\begin{array}{l}
adamc@1123 1446 \mt{val} \; \mt{debug} : \mt{string} \to \mt{transaction} \; \mt{unit}
adamc@1123 1447 \end{array}$$
adamc@1123 1448
adamc@542 1449 \subsection{HTTP}
adamc@542 1450
adam@1797 1451 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 1452 $$\begin{array}{l}
adamc@786 1453 \mt{con} \; \mt{http\_cookie} :: \mt{Type} \to \mt{Type} \\
adamc@786 1454 \mt{val} \; \mt{getCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; (\mt{option} \; \mt{t}) \\
adamc@1050 1455 \mt{val} \; \mt{setCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \{\mt{Value} : \mt{t}, \mt{Expires} : \mt{option} \; \mt{time}, \mt{Secure} : \mt{bool}\} \to \mt{transaction} \; \mt{unit} \\
adamc@1050 1456 \mt{val} \; \mt{clearCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; \mt{unit}
adamc@786 1457 \end{array}$$
adamc@786 1458
adamc@786 1459 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 1460 $$\begin{array}{l}
adamc@786 1461 \mt{type} \; \mt{url} \\
adamc@786 1462 \mt{val} \; \mt{bless} : \mt{string} \to \mt{url} \\
adamc@786 1463 \mt{val} \; \mt{checkUrl} : \mt{string} \to \mt{option} \; \mt{url}
adamc@786 1464 \end{array}$$
adamc@786 1465 $\mt{bless}$ raises a runtime error if the string passed to it fails the URL policy.
adamc@786 1466
adam@1400 1467 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 1468 $$\begin{array}{l}
adamc@1085 1469 \mt{val} \; \mt{currentUrl} : \mt{transaction} \; \mt{url} \\
adamc@1085 1470 \mt{val} \; \mt{url} : \mt{transaction} \; \mt{page} \to \mt{url}
adamc@1085 1471 \end{array}$$
adamc@1085 1472
adamc@1085 1473 Page generation may be interrupted at any time with a request to redirect to a particular URL instead.
adamc@1085 1474 $$\begin{array}{l}
adamc@1085 1475 \mt{val} \; \mt{redirect} : \mt{t} ::: \mt{Type} \to \mt{url} \to \mt{transaction} \; \mt{t}
adamc@1085 1476 \end{array}$$
adamc@1085 1477
adam@1400 1478 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 1479 $$\begin{array}{l}
adamc@786 1480 \mt{type} \; \mt{file} \\
adamc@786 1481 \mt{val} \; \mt{fileName} : \mt{file} \to \mt{option} \; \mt{string} \\
adamc@786 1482 \mt{val} \; \mt{fileMimeType} : \mt{file} \to \mt{string} \\
adamc@786 1483 \mt{val} \; \mt{fileData} : \mt{file} \to \mt{blob}
adamc@786 1484 \end{array}$$
adamc@786 1485
adam@1799 1486 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 1487
adam@1465 1488 $$\begin{array}{l}
adam@1465 1489 \mt{type} \; \mt{requestHeader} \\
adam@1465 1490 \mt{val} \; \mt{blessRequestHeader} : \mt{string} \to \mt{requestHeader} \\
adam@1465 1491 \mt{val} \; \mt{checkRequestHeader} : \mt{string} \to \mt{option} \; \mt{requestHeader} \\
adam@1465 1492 \mt{val} \; \mt{getHeader} : \mt{requestHeader} \to \mt{transaction} \; (\mt{option} \; \mt{string}) \\
adam@1465 1493 \\
adam@1799 1494 \mt{type} \; \mt{envVar} \\
adam@1799 1495 \mt{val} \; \mt{blessEnvVar} : \mt{string} \to \mt{envVar} \\
adam@1799 1496 \mt{val} \; \mt{checkEnvVar} : \mt{string} \to \mt{option} \; \mt{envVar} \\
adam@1799 1497 \mt{val} \; \mt{getenv} : \mt{envVar} \to \mt{transaction} \; (\mt{option} \; \mt{string}) \\
adam@1799 1498 \\
adam@1465 1499 \mt{type} \; \mt{responseHeader} \\
adam@1465 1500 \mt{val} \; \mt{blessResponseHeader} : \mt{string} \to \mt{responseHeader} \\
adam@1465 1501 \mt{val} \; \mt{checkResponseHeader} : \mt{string} \to \mt{option} \; \mt{responseHeader} \\
adam@1465 1502 \mt{val} \; \mt{setHeader} : \mt{responseHeader} \to \mt{string} \to \mt{transaction} \; \mt{unit}
adam@1465 1503 \end{array}$$
adam@1465 1504
adamc@786 1505 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 1506 $$\begin{array}{l}
adamc@786 1507 \mt{type} \; \mt{mimeType} \\
adamc@786 1508 \mt{val} \; \mt{blessMime} : \mt{string} \to \mt{mimeType} \\
adamc@786 1509 \mt{val} \; \mt{checkMime} : \mt{string} \to \mt{option} \; \mt{mimeType} \\
adamc@786 1510 \mt{val} \; \mt{returnBlob} : \mt{t} ::: \mt{Type} \to \mt{blob} \to \mt{mimeType} \to \mt{transaction} \; \mt{t}
adamc@542 1511 \end{array}$$
adamc@542 1512
adamc@543 1513 \subsection{SQL}
adamc@543 1514
adam@1400 1515 Everything about SQL database access is restricted to server-side code.
adam@1400 1516
adamc@543 1517 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 1518 $$\begin{array}{l}
adamc@785 1519 \mt{con} \; \mt{sql\_table} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785 1520 \end{array}$$
adamc@785 1521 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 1522
adamc@785 1523 We also have the simpler type family of SQL views, which have no keys.
adamc@785 1524 $$\begin{array}{l}
adamc@785 1525 \mt{con} \; \mt{sql\_view} :: \{\mt{Type}\} \to \mt{Type}
adamc@543 1526 \end{array}$$
adamc@543 1527
adamc@785 1528 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 1529 $$\begin{array}{l}
adamc@785 1530 \mt{class} \; \mt{fieldsOf} :: \mt{Type} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1531 \mt{val} \; \mt{fieldsOf\_table} : \mt{fs} ::: \{\mt{Type}\} \to \mt{keys} ::: \{\{\mt{Unit}\}\} \to \mt{fieldsOf} \; (\mt{sql\_table} \; \mt{fs} \; \mt{keys}) \; \mt{fs} \\
adamc@785 1532 \mt{val} \; \mt{fieldsOf\_view} : \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; (\mt{sql\_view} \; \mt{fs}) \; \mt{fs}
adamc@785 1533 \end{array}$$
adamc@785 1534
adamc@785 1535 \subsubsection{Table Constraints}
adamc@785 1536
adamc@785 1537 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 1538
adamc@785 1539 $$\begin{array}{l}
adamc@785 1540 \mt{con} \; \mt{primary\_key} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type} \\
adamc@785 1541 \mt{val} \; \mt{no\_primary\_key} : \mt{fs} ::: \{\mt{Type}\} \to \mt{primary\_key} \; \mt{fs} \; [] \\
adamc@785 1542 \mt{val} \; \mt{primary\_key} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{key1} :: \mt{Name} \to \mt{keys} :: \{\mt{Type}\} \\
adamc@785 1543 \hspace{.1in} \to [[\mt{key1}] \sim \mt{keys}] \Rightarrow [[\mt{key1} = \mt{t}] \rc \mt{keys} \sim \mt{rest}] \\
adamc@785 1544 \hspace{.1in} \Rightarrow \$([\mt{key1} = \mt{sql\_injectable\_prim} \; \mt{t}] \rc \mt{map} \; \mt{sql\_injectable\_prim} \; \mt{keys}) \\
adamc@785 1545 \hspace{.1in} \to \mt{primary\_key} \; ([\mt{key1} = \mt{t}] \rc \mt{keys} \rc \mt{rest}) \; [\mt{Pkey} = [\mt{key1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{keys}]
adamc@785 1546 \end{array}$$
adamc@785 1547 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 1548
adamc@785 1549 A type family stands for sets of named constraints of the remaining varieties.
adamc@785 1550 $$\begin{array}{l}
adamc@785 1551 \mt{con} \; \mt{sql\_constraints} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785 1552 \end{array}$$
adamc@785 1553 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 1554
adamc@785 1555 There is a type family of individual, unnamed constraints.
adamc@785 1556 $$\begin{array}{l}
adamc@785 1557 \mt{con} \; \mt{sql\_constraint} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \mt{Type}
adamc@785 1558 \end{array}$$
adamc@785 1559 The first argument is the same as above, and the second argument gives the key columns for just this constraint.
adamc@785 1560
adamc@785 1561 We have operations for assembling constraints into constraint sets.
adamc@785 1562 $$\begin{array}{l}
adamc@785 1563 \mt{val} \; \mt{no\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_constraints} \; \mt{fs} \; [] \\
adamc@785 1564 \mt{val} \; \mt{one\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{unique} ::: \{\mt{Unit}\} \to \mt{name} :: \mt{Name} \\
adamc@785 1565 \hspace{.1in} \to \mt{sql\_constraint} \; \mt{fs} \; \mt{unique} \to \mt{sql\_constraints} \; \mt{fs} \; [\mt{name} = \mt{unique}] \\
adamc@785 1566 \mt{val} \; \mt{join\_constraints} : \mt{fs} ::: \{\mt{Type}\} \to \mt{uniques1} ::: \{\{\mt{Unit}\}\} \to \mt{uniques2} ::: \{\{\mt{Unit}\}\} \to [\mt{uniques1} \sim \mt{uniques2}] \\
adamc@785 1567 \hspace{.1in} \Rightarrow \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques1} \to \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques2} \to \mt{sql\_constraints} \; \mt{fs} \; (\mt{uniques1} \rc \mt{uniques2})
adamc@785 1568 \end{array}$$
adamc@785 1569
adamc@785 1570 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 1571 $$\begin{array}{l}
adamc@785 1572 \mt{val} \; \mt{unique} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{unique1} :: \mt{Name} \to \mt{unique} :: \{\mt{Type}\} \\
adamc@785 1573 \hspace{.1in} \to [[\mt{unique1}] \sim \mt{unique}] \Rightarrow [[\mt{unique1} = \mt{t}] \rc \mt{unique} \sim \mt{rest}] \\
adamc@785 1574 \hspace{.1in} \Rightarrow \mt{sql\_constraint} \; ([\mt{unique1} = \mt{t}] \rc \mt{unique} \rc \mt{rest}) \; ([\mt{unique1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{unique})
adamc@785 1575 \end{array}$$
adamc@785 1576
adamc@785 1577 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 1578 $$\begin{array}{l}
adamc@785 1579 \mt{class} \; \mt{linkable} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@785 1580 \mt{val} \; \mt{linkable\_same} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; \mt{t} \\
adamc@785 1581 \mt{val} \; \mt{linkable\_from\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; (\mt{option} \; \mt{t}) \; \mt{t} \\
adamc@785 1582 \mt{val} \; \mt{linkable\_to\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@785 1583 \end{array}$$
adamc@785 1584
adamc@785 1585 The $\mt{matching}$ type family uses $\mt{linkable}$ to define when two keys match up type-wise.
adamc@785 1586 $$\begin{array}{l}
adamc@785 1587 \mt{con} \; \mt{matching} :: \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1588 \mt{val} \; \mt{mat\_nil} : \mt{matching} \; [] \; [] \\
adamc@785 1589 \mt{val} \; \mt{mat\_cons} : \mt{t1} ::: \mt{Type} \to \mt{rest1} ::: \{\mt{Type}\} \to \mt{t2} ::: \mt{Type} \to \mt{rest2} ::: \{\mt{Type}\} \to \mt{nm1} :: \mt{Name} \to \mt{nm2} :: \mt{Name} \\
adamc@785 1590 \hspace{.1in} \to [[\mt{nm1}] \sim \mt{rest1}] \Rightarrow [[\mt{nm2}] \sim \mt{rest2}] \Rightarrow \mt{linkable} \; \mt{t1} \; \mt{t2} \to \mt{matching} \; \mt{rest1} \; \mt{rest2} \\
adamc@785 1591 \hspace{.1in} \to \mt{matching} \; ([\mt{nm1} = \mt{t1}] \rc \mt{rest1}) \; ([\mt{nm2} = \mt{t2}] \rc \mt{rest2})
adamc@785 1592 \end{array}$$
adamc@785 1593
adamc@785 1594 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 1595 $$\begin{array}{l}
adamc@785 1596 \mt{con} \; \mt{propagation\_mode} :: \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1597 \mt{val} \; \mt{restrict} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1598 \mt{val} \; \mt{cascade} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1599 \mt{val} \; \mt{no\_action} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1600 \mt{val} \; \mt{set\_null} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; (\mt{map} \; \mt{option} \; \mt{fs})
adamc@785 1601 \end{array}$$
adamc@785 1602
adamc@785 1603 Finally, we put these ingredient together to define the \texttt{FOREIGN KEY} constraint function.
adamc@785 1604 $$\begin{array}{l}
adamc@785 1605 \mt{val} \; \mt{foreign\_key} : \mt{mine1} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{mine} ::: \{\mt{Type}\} \to \mt{munused} ::: \{\mt{Type}\} \to \mt{foreign} ::: \{\mt{Type}\} \\
adamc@785 1606 \hspace{.1in} \to \mt{funused} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{uniques} ::: \{\{\mt{Unit}\}\} \\
adamc@785 1607 \hspace{.1in} \to [[\mt{mine1}] \sim \mt{mine}] \Rightarrow [[\mt{mine1} = \mt{t}] \rc \mt{mine} \sim \mt{munused}] \Rightarrow [\mt{foreign} \sim \mt{funused}] \Rightarrow [[\mt{nm}] \sim \mt{uniques}] \\
adamc@785 1608 \hspace{.1in} \Rightarrow \mt{matching} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}) \; \mt{foreign} \\
adamc@785 1609 \hspace{.1in} \to \mt{sql\_table} \; (\mt{foreign} \rc \mt{funused}) \; ([\mt{nm} = \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{foreign}] \rc \mt{uniques}) \\
adamc@785 1610 \hspace{.1in} \to \{\mt{OnDelete} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}), \\
adamc@785 1611 \hspace{.2in} \mt{OnUpdate} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine})\} \\
adamc@785 1612 \hspace{.1in} \to \mt{sql\_constraint} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine} \rc \mt{munused}) \; []
adamc@785 1613 \end{array}$$
adamc@785 1614
adamc@785 1615 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 1616 $$\begin{array}{l}
adam@1778 1617 \mt{val} \; \mt{check} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; [] \; [] \; \mt{fs} \; \mt{bool} \to \mt{sql\_constraint} \; \mt{fs} \; []
adamc@785 1618 \end{array}$$
adamc@785 1619
adamc@785 1620 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 1621
adamc@784 1622
adamc@543 1623 \subsubsection{Queries}
adamc@543 1624
adam@1400 1625 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 1626 $$\begin{array}{l}
adam@1400 1627 \mt{con} \; \mt{sql\_query} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@1193 1628 \mt{val} \; \mt{sql\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400 1629 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1630 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543 1631 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1632 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1193 1633 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adam@1400 1634 \hspace{.1in} \Rightarrow \{\mt{Rows} : \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}, \\
adamc@1193 1635 \hspace{.2in} \mt{OrderBy} : \mt{sql\_order\_by} \; (\mt{free} \rc \mt{tables}) \; \mt{selectedExps}, \\
adamc@543 1636 \hspace{.2in} \mt{Limit} : \mt{sql\_limit}, \\
adamc@543 1637 \hspace{.2in} \mt{Offset} : \mt{sql\_offset}\} \\
adam@1400 1638 \hspace{.1in} \to \mt{sql\_query} \; \mt{free} \; \mt{afree} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1639 \end{array}$$
adamc@543 1640
adamc@545 1641 Queries are used by folding over their results inside transactions.
adamc@545 1642 $$\begin{array}{l}
adam@1400 1643 \mt{val} \; \mt{query} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to [\mt{tables} \sim \mt{exps}] \Rightarrow \mt{state} ::: \mt{Type} \to \mt{sql\_query} \; [] \; [] \; \mt{tables} \; \mt{exps} \\
adamc@658 1644 \hspace{.1in} \to (\$(\mt{exps} \rc \mt{map} \; (\lambda \mt{fields} :: \{\mt{Type}\} \Rightarrow \$\mt{fields}) \; \mt{tables}) \\
adamc@545 1645 \hspace{.2in} \to \mt{state} \to \mt{transaction} \; \mt{state}) \\
adamc@545 1646 \hspace{.1in} \to \mt{state} \to \mt{transaction} \; \mt{state}
adamc@545 1647 \end{array}$$
adamc@545 1648
adam@1400 1649 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 1650 $$\begin{array}{l}
adam@1400 1651 \mt{con} \; \mt{sql\_query1} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@543 1652 \\
adamc@543 1653 \mt{type} \; \mt{sql\_relop} \\
adamc@543 1654 \mt{val} \; \mt{sql\_union} : \mt{sql\_relop} \\
adamc@543 1655 \mt{val} \; \mt{sql\_intersect} : \mt{sql\_relop} \\
adamc@543 1656 \mt{val} \; \mt{sql\_except} : \mt{sql\_relop} \\
adam@1400 1657 \mt{val} \; \mt{sql\_relop} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400 1658 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adam@1400 1659 \hspace{.1in} \to \mt{tables1} ::: \{\{\mt{Type}\}\} \\
adamc@543 1660 \hspace{.1in} \to \mt{tables2} ::: \{\{\mt{Type}\}\} \\
adamc@543 1661 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1662 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@543 1663 \hspace{.1in} \to \mt{sql\_relop} \\
adam@1458 1664 \hspace{.1in} \to \mt{bool} \; (* \; \mt{ALL} \; *) \\
adam@1400 1665 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables1} \; \mt{selectedFields} \; \mt{selectedExps} \\
adam@1400 1666 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables2} \; \mt{selectedFields} \; \mt{selectedExps} \\
adam@1400 1667 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{selectedFields} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1668 \end{array}$$
adamc@543 1669
adamc@543 1670 $$\begin{array}{l}
adamc@1193 1671 \mt{val} \; \mt{sql\_query1} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400 1672 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1673 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543 1674 \hspace{.1in} \to \mt{grouped} ::: \{\{\mt{Type}\}\} \\
adamc@543 1675 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1676 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1085 1677 \hspace{.1in} \to \mt{empties} :: \{\mt{Unit}\} \\
adamc@1193 1678 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adamc@1193 1679 \hspace{.1in} \Rightarrow [\mt{free} \sim \mt{grouped}] \\
adam@1400 1680 \hspace{.1in} \Rightarrow [\mt{afree} \sim \mt{tables}] \\
adamc@1193 1681 \hspace{.1in} \Rightarrow [\mt{empties} \sim \mt{selectedFields}] \\
adamc@1085 1682 \hspace{.1in} \Rightarrow \{\mt{Distinct} : \mt{bool}, \\
adamc@1193 1683 \hspace{.2in} \mt{From} : \mt{sql\_from\_items} \; \mt{free} \; \mt{tables}, \\
adam@1778 1684 \hspace{.2in} \mt{Where} : \mt{sql\_exp} \; (\mt{free} \rc \mt{tables}) \; \mt{afree} \; [] \; \mt{bool}, \\
adamc@543 1685 \hspace{.2in} \mt{GroupBy} : \mt{sql\_subset} \; \mt{tables} \; \mt{grouped}, \\
adam@1778 1686 \hspace{.2in} \mt{Having} : \mt{sql\_exp} \; (\mt{free} \rc \mt{grouped}) \; (\mt{afree} \rc \mt{tables}) \; [] \; \mt{bool}, \\
adamc@1085 1687 \hspace{.2in} \mt{SelectFields} : \mt{sql\_subset} \; \mt{grouped} \; (\mt{map} \; (\lambda \_ \Rightarrow []) \; \mt{empties} \rc \mt{selectedFields}), \\
adam@1778 1688 \hspace{.2in} \mt {SelectExps} : \$(\mt{map} \; (\mt{sql\_expw} \; (\mt{free} \rc \mt{grouped}) \; (\mt{afree} \rc \mt{tables}) \; []) \; \mt{selectedExps}) \} \\
adam@1400 1689 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1690 \end{array}$$
adamc@543 1691
adamc@543 1692 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 1693 $$\begin{array}{l}
adamc@543 1694 \mt{con} \; \mt{sql\_subset} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@543 1695 \mt{val} \; \mt{sql\_subset} : \mt{keep\_drop} :: \{(\{\mt{Type}\} \times \{\mt{Type}\})\} \\
adamc@543 1696 \hspace{.1in} \to \mt{sql\_subset} \\
adamc@658 1697 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1 \rc \mt{fields}.2)\; \mt{keep\_drop}) \\
adamc@658 1698 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1) \; \mt{keep\_drop}) \\
adamc@543 1699 \mt{val} \; \mt{sql\_subset\_all} : \mt{tables} :: \{\{\mt{Type}\}\} \to \mt{sql\_subset} \; \mt{tables} \; \mt{tables}
adamc@543 1700 \end{array}$$
adamc@543 1701
adam@1778 1702 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 1703 $$\begin{array}{l}
adam@1778 1704 \mt{con} \; \mt{sql\_exp} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}
adamc@543 1705 \end{array}$$
adamc@543 1706
adamc@543 1707 Any field in scope may be converted to an expression.
adamc@543 1708 $$\begin{array}{l}
adamc@543 1709 \mt{val} \; \mt{sql\_field} : \mt{otherTabs} ::: \{\{\mt{Type}\}\} \to \mt{otherFields} ::: \{\mt{Type}\} \\
adam@1778 1710 \hspace{.1in} \to \mt{fieldType} ::: \mt{Type} \to \mt{agg} ::: \{\{\mt{Type}\}\} \\
adamc@543 1711 \hspace{.1in} \to \mt{exps} ::: \{\mt{Type}\} \\
adamc@543 1712 \hspace{.1in} \to \mt{tab} :: \mt{Name} \to \mt{field} :: \mt{Name} \\
adam@1778 1713 \hspace{.1in} \to \mt{sql\_exp} \; ([\mt{tab} = [\mt{field} = \mt{fieldType}] \rc \mt{otherFields}] \rc \mt{otherTabs}) \; \mt{agg} \; \mt{exps} \; \mt{fieldType}
adamc@543 1714 \end{array}$$
adamc@543 1715
adamc@544 1716 There is an analogous function for referencing named expressions.
adamc@544 1717 $$\begin{array}{l}
adam@1778 1718 \mt{val} \; \mt{sql\_exp} : \mt{tabs} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{t} ::: \mt{Type} \to \mt{rest} ::: \{\mt{Type}\} \to \mt{nm} :: \mt{Name} \\
adam@1778 1719 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tabs} \; \mt{agg} \; ([\mt{nm} = \mt{t}] \rc \mt{rest}) \; \mt{t}
adamc@544 1720 \end{array}$$
adamc@544 1721
adamc@544 1722 Ur values of appropriate types may be injected into SQL expressions.
adamc@544 1723 $$\begin{array}{l}
adamc@786 1724 \mt{class} \; \mt{sql\_injectable\_prim} \\
adamc@786 1725 \mt{val} \; \mt{sql\_bool} : \mt{sql\_injectable\_prim} \; \mt{bool} \\
adamc@786 1726 \mt{val} \; \mt{sql\_int} : \mt{sql\_injectable\_prim} \; \mt{int} \\
adamc@786 1727 \mt{val} \; \mt{sql\_float} : \mt{sql\_injectable\_prim} \; \mt{float} \\
adamc@786 1728 \mt{val} \; \mt{sql\_string} : \mt{sql\_injectable\_prim} \; \mt{string} \\
adamc@786 1729 \mt{val} \; \mt{sql\_time} : \mt{sql\_injectable\_prim} \; \mt{time} \\
adamc@786 1730 \mt{val} \; \mt{sql\_blob} : \mt{sql\_injectable\_prim} \; \mt{blob} \\
adamc@786 1731 \mt{val} \; \mt{sql\_channel} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{channel} \; \mt{t}) \\
adamc@786 1732 \mt{val} \; \mt{sql\_client} : \mt{sql\_injectable\_prim} \; \mt{client} \\
adamc@786 1733 \\
adamc@544 1734 \mt{class} \; \mt{sql\_injectable} \\
adamc@786 1735 \mt{val} \; \mt{sql\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@786 1736 \mt{val} \; \mt{sql\_option\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; (\mt{option} \; \mt{t}) \\
adamc@786 1737 \\
adam@1778 1738 \mt{val} \; \mt{sql\_inject} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{sql\_injectable} \; \mt{t} \\
adam@1778 1739 \hspace{.1in} \to \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adamc@544 1740 \end{array}$$
adamc@544 1741
adamc@1123 1742 Additionally, most function-free types may be injected safely, via the $\mt{serialized}$ type family.
adamc@1123 1743 $$\begin{array}{l}
adamc@1123 1744 \mt{con} \; \mt{serialized} :: \mt{Type} \to \mt{Type} \\
adamc@1123 1745 \mt{val} \; \mt{serialize} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{serialized} \; \mt{t} \\
adamc@1123 1746 \mt{val} \; \mt{deserialize} : \mt{t} ::: \mt{Type} \to \mt{serialized} \; \mt{t} \to \mt{t} \\
adamc@1123 1747 \mt{val} \; \mt{sql\_serialized} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{serialized} \; \mt{t})
adamc@1123 1748 \end{array}$$
adamc@1123 1749
adamc@544 1750 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 1751 $$\begin{array}{l}
adam@1778 1752 \mt{val} \; \mt{sql\_is\_null} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778 1753 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; (\mt{option} \; \mt{t}) \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{bool}
adamc@544 1754 \end{array}$$
adamc@544 1755
adam@1602 1756 As another way of dealing with null values, there is also a restricted form of the standard \cd{COALESCE} function.
adam@1602 1757 $$\begin{array}{l}
adam@1602 1758 \mt{val} \; \mt{sql\_coalesce} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778 1759 \hspace{.1in} \to \mt{t} ::: \mt{Type} \\
adam@1778 1760 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; (\mt{option} \; \mt{t}) \\
adam@1778 1761 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1762 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adam@1602 1763 \end{array}$$
adam@1602 1764
adamc@559 1765 We have generic nullary, unary, and binary operators.
adamc@544 1766 $$\begin{array}{l}
adamc@544 1767 \mt{con} \; \mt{sql\_nfunc} :: \mt{Type} \to \mt{Type} \\
adamc@544 1768 \mt{val} \; \mt{sql\_current\_timestamp} : \mt{sql\_nfunc} \; \mt{time} \\
adam@1778 1769 \mt{val} \; \mt{sql\_nfunc} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778 1770 \hspace{.1in} \to \mt{sql\_nfunc} \; \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\\end{array}$$
adamc@544 1771
adamc@544 1772 $$\begin{array}{l}
adamc@544 1773 \mt{con} \; \mt{sql\_unary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544 1774 \mt{val} \; \mt{sql\_not} : \mt{sql\_unary} \; \mt{bool} \; \mt{bool} \\
adam@1778 1775 \mt{val} \; \mt{sql\_unary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adam@1778 1776 \hspace{.1in} \to \mt{sql\_unary} \; \mt{arg} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res} \\
adamc@544 1777 \end{array}$$
adamc@544 1778
adamc@544 1779 $$\begin{array}{l}
adamc@544 1780 \mt{con} \; \mt{sql\_binary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544 1781 \mt{val} \; \mt{sql\_and} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544 1782 \mt{val} \; \mt{sql\_or} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adam@1778 1783 \mt{val} \; \mt{sql\_binary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg_1} ::: \mt{Type} \to \mt{arg_2} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adam@1778 1784 \hspace{.1in} \to \mt{sql\_binary} \; \mt{arg_1} \; \mt{arg_2} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_1} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_2} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res}
adamc@544 1785 \end{array}$$
adamc@544 1786
adamc@544 1787 $$\begin{array}{l}
adamc@559 1788 \mt{class} \; \mt{sql\_arith} \\
adamc@559 1789 \mt{val} \; \mt{sql\_int\_arith} : \mt{sql\_arith} \; \mt{int} \\
adamc@559 1790 \mt{val} \; \mt{sql\_float\_arith} : \mt{sql\_arith} \; \mt{float} \\
adamc@559 1791 \mt{val} \; \mt{sql\_neg} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_unary} \; \mt{t} \; \mt{t} \\
adamc@559 1792 \mt{val} \; \mt{sql\_plus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1793 \mt{val} \; \mt{sql\_minus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1794 \mt{val} \; \mt{sql\_times} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1795 \mt{val} \; \mt{sql\_div} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1796 \mt{val} \; \mt{sql\_mod} : \mt{sql\_binary} \; \mt{int} \; \mt{int} \; \mt{int}
adamc@559 1797 \end{array}$$
adamc@544 1798
adam@1797 1799 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 1800 $$\begin{array}{l}
adam@1778 1801 \mt{val} \; \mt{sql\_count} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int}
adamc@544 1802 \end{array}$$
adamc@544 1803
adamc@544 1804 $$\begin{array}{l}
adamc@1188 1805 \mt{con} \; \mt{sql\_aggregate} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adam@1778 1806 \mt{val} \; \mt{sql\_aggregate} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{dom} ::: \mt{Type} \to \mt{ran} ::: \mt{Type} \\
adam@1778 1807 \hspace{.1in} \to \mt{sql\_aggregate} \; \mt{dom} \; \mt{ran} \to \mt{sql\_exp} \; \mt{agg} \; \mt{agg} \; \mt{exps} \; \mt{dom} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{ran}
adamc@1188 1808 \end{array}$$
adamc@1188 1809
adamc@1188 1810 $$\begin{array}{l}
adamc@1188 1811 \mt{val} \; \mt{sql\_count\_col} : \mt{t} ::: \mt{Type} \to \mt{sql\_aggregate} \; (\mt{option} \; \mt{t}) \; \mt{int}
adamc@544 1812 \end{array}$$
adam@1400 1813
adam@1400 1814 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 1815
adamc@544 1816 $$\begin{array}{l}
adamc@544 1817 \mt{class} \; \mt{sql\_summable} \\
adamc@544 1818 \mt{val} \; \mt{sql\_summable\_int} : \mt{sql\_summable} \; \mt{int} \\
adamc@544 1819 \mt{val} \; \mt{sql\_summable\_float} : \mt{sql\_summable} \; \mt{float} \\
adam@1777 1820 \mt{val} \; \mt{sql\_avg} : \mt{t} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{sql\_aggregate} \; \mt{t} \; (\mt{option} \; \mt{float}) \\
adam@1400 1821 \mt{val} \; \mt{sql\_sum} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt}
adamc@544 1822 \end{array}$$
adamc@544 1823
adamc@544 1824 $$\begin{array}{l}
adamc@544 1825 \mt{class} \; \mt{sql\_maxable} \\
adamc@544 1826 \mt{val} \; \mt{sql\_maxable\_int} : \mt{sql\_maxable} \; \mt{int} \\
adamc@544 1827 \mt{val} \; \mt{sql\_maxable\_float} : \mt{sql\_maxable} \; \mt{float} \\
adamc@544 1828 \mt{val} \; \mt{sql\_maxable\_string} : \mt{sql\_maxable} \; \mt{string} \\
adamc@544 1829 \mt{val} \; \mt{sql\_maxable\_time} : \mt{sql\_maxable} \; \mt{time} \\
adam@1400 1830 \mt{val} \; \mt{sql\_max} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt} \\
adam@1400 1831 \mt{val} \; \mt{sql\_min} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt}
adamc@544 1832 \end{array}$$
adamc@544 1833
adam@1778 1834 Any SQL query that returns single columns may be turned into a subquery expression.
adam@1777 1835
adam@1777 1836 $$\begin{array}{l}
adam@1778 1837 \mt{val} \; \mt{sql\_subquery} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \\
adam@1778 1838 \hspace{.1in} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_query} \; \mt{tables} \; \mt{agg} \; [\mt{nm} = \mt{t}] \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{nt}
adamc@1193 1839 \end{array}$$
adamc@1193 1840
adam@1573 1841 There is also an \cd{IF..THEN..ELSE..} construct that is compiled into standard SQL \cd{CASE} expressions.
adam@1573 1842 $$\begin{array}{l}
adam@1778 1843 \mt{val} \; \mt{sql\_if\_then\_else} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778 1844 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{bool} \\
adam@1778 1845 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1846 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1847 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adam@1573 1848 \end{array}$$
adam@1573 1849
adamc@1193 1850 \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 1851 $$\begin{array}{l}
adamc@1193 1852 \mt{con} \; \mt{sql\_from\_items} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@1193 1853 \mt{val} \; \mt{sql\_from\_table} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1854 \hspace{.1in} \to \mt{t} ::: \mt{Type} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; \mt{t} \; \mt{fs} \to \mt{name} :: \mt{Name} \to \mt{t} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193 1855 \mt{val} \; \mt{sql\_from\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{name} :: \mt{Name} \to \mt{sql\_query} \; \mt{free} \; [] \; \mt{fs} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193 1856 \mt{val} \; \mt{sql\_from\_comma} : \mt{free} ::: \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \to [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193 1857 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adamc@1193 1858 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2}) \\
adamc@1193 1859 \mt{val} \; \mt{sql\_inner\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1860 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193 1861 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adam@1778 1862 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193 1863 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2})
adamc@786 1864 \end{array}$$
adamc@786 1865
adamc@786 1866 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 1867 $$\begin{array}{l}
adamc@786 1868 \mt{class} \; \mt{nullify} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@786 1869 \mt{val} \; \mt{nullify\_option} : \mt{t} ::: \mt{Type} \to \mt{nullify} \; (\mt{option} \; \mt{t}) \; (\mt{option} \; \mt{t}) \\
adamc@786 1870 \mt{val} \; \mt{nullify\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{nullify} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@786 1871 \end{array}$$
adamc@786 1872
adamc@786 1873 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 1874
adamc@786 1875 $$\begin{array}{l}
adamc@1193 1876 \mt{val} \; \mt{sql\_left\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{(\mt{Type} \times \mt{Type})\}\} \\
adamc@1193 1877 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@786 1878 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\lambda \mt{r} \Rightarrow \$(\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{nullify} \; \mt{p}.1 \; \mt{p}.2) \; \mt{r})) \; \mt{tabs2}) \\
adamc@1193 1879 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \\
adam@1778 1880 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193 1881 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.2)) \; \mt{tabs2})
adamc@786 1882 \end{array}$$
adamc@786 1883
adamc@544 1884 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 1885 $$\begin{array}{l}
adamc@544 1886 \mt{type} \; \mt{sql\_direction} \\
adamc@544 1887 \mt{val} \; \mt{sql\_asc} : \mt{sql\_direction} \\
adamc@544 1888 \mt{val} \; \mt{sql\_desc} : \mt{sql\_direction} \\
adamc@544 1889 \\
adamc@544 1890 \mt{con} \; \mt{sql\_order\_by} :: \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@544 1891 \mt{val} \; \mt{sql\_order\_by\_Nil} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} :: \{\mt{Type}\} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adam@1778 1892 \mt{val} \; \mt{sql\_order\_by\_Cons} : \mt{tf} ::: (\{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}) \\
adam@1778 1893 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778 1894 \hspace{.1in} \to \mt{sql\_window} \; \mt{tf} \to \mt{tf} \; \mt{tables} \; [] \; \mt{exps} \; \mt{t} \to \mt{sql\_direction} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adam@1684 1895 \mt{val} \; \mt{sql\_order\_by\_random} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544 1896 \\
adamc@544 1897 \mt{type} \; \mt{sql\_limit} \\
adamc@544 1898 \mt{val} \; \mt{sql\_no\_limit} : \mt{sql\_limit} \\
adamc@544 1899 \mt{val} \; \mt{sql\_limit} : \mt{int} \to \mt{sql\_limit} \\
adamc@544 1900 \\
adamc@544 1901 \mt{type} \; \mt{sql\_offset} \\
adamc@544 1902 \mt{val} \; \mt{sql\_no\_offset} : \mt{sql\_offset} \\
adamc@544 1903 \mt{val} \; \mt{sql\_offset} : \mt{int} \to \mt{sql\_offset}
adamc@544 1904 \end{array}$$
adamc@544 1905
adam@1778 1906 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 1907 $$\begin{array}{l}
adam@1778 1908 \mt{con} \; \mt{sql\_expw} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type} \\
adam@1778 1909 \\
adam@1778 1910 \mt{class} \; \mt{sql\_window} :: (\{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}) \to \mt{Type} \\
adam@1778 1911 \mt{val} \; \mt{sql\_window\_normal} : \mt{sql\_window} \; \mt{sql\_exp} \\
adam@1778 1912 \mt{val} \; \mt{sql\_window\_fancy} : \mt{sql\_window} \; \mt{sql\_expw} \\
adam@1778 1913 \mt{val} \; \mt{sql\_window} : \mt{tf} ::: (\{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}) \\
adam@1778 1914 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778 1915 \hspace{.1in} \to \mt{sql\_window} \; \mt{tf} \\
adam@1778 1916 \hspace{.1in} \to \mt{tf} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1917 \hspace{.1in} \to \mt{sql\_expw} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1918 \\
adam@1778 1919 \mt{con} \; \mt{sql\_partition} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adam@1778 1920 \mt{val} \; \mt{sql\_no\_partition} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778 1921 \hspace{.1in} \to \mt{sql\_partition} \; \mt{tables} \; \mt{agg} \; \mt{exps} \\
adam@1778 1922 \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 1923 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1924 \hspace{.1in} \to \mt{sql\_partition} \; \mt{tables} \; \mt{agg} \; \mt{exps} \\
adam@1778 1925 \\
adam@1778 1926 \mt{con} \; \mt{sql\_window\_function} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type} \\
adam@1778 1927 \mt{val} \; \mt{sql\_window\_function} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778 1928 \hspace{.1in} \to \mt{t} ::: \mt{Type} \\
adam@1778 1929 \hspace{.1in} \to \mt{sql\_window\_function} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1930 \hspace{.1in} \to \mt{sql\_partition} \; \mt{tables} \; \mt{agg} \; \mt{exps} \\
adam@1778 1931 \hspace{.1in} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adam@1778 1932 \hspace{.1in} \to \mt{sql\_expw} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1933 \\
adam@1778 1934 \mt{val} \; \mt{sql\_window\_aggregate} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778 1935 \hspace{.1in} \to \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \\
adam@1778 1936 \hspace{.1in} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt} \\
adam@1778 1937 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1938 \hspace{.1in} \to \mt{sql\_window\_function} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{nt} \\
adam@1778 1939 \mt{val} \; \mt{sql\_window\_count} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778 1940 \hspace{.1in} \to \mt{sql\_window\_function} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int} \\
adam@1778 1941 \mt{val} \; \mt{sql\_rank} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778 1942 \hspace{.1in} \to \mt{sql\_window\_function} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int}
adam@1778 1943 \end{array}$$
adam@1778 1944
adamc@545 1945
adamc@545 1946 \subsubsection{DML}
adamc@545 1947
adamc@545 1948 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 1949
adamc@545 1950 $$\begin{array}{l}
adamc@545 1951 \mt{type} \; \mt{dml} \\
adamc@545 1952 \mt{val} \; \mt{dml} : \mt{dml} \to \mt{transaction} \; \mt{unit}
adamc@545 1953 \end{array}$$
adamc@545 1954
adam@1297 1955 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 1956
adam@1297 1957 $$\begin{array}{l}
adam@1297 1958 \mt{val} \; \mt{tryDml} : \mt{dml} \to \mt{transaction} \; (\mt{option} \; \mt{string})
adam@1297 1959 \end{array}$$
adam@1297 1960
adam@1797 1961 Properly typed records may be used to form $\mt{INSERT}$ commands.
adamc@545 1962 $$\begin{array}{l}
adamc@545 1963 \mt{val} \; \mt{insert} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \\
adam@1778 1964 \hspace{.1in} \to \$(\mt{map} \; (\mt{sql\_exp} \; [] \; [] \; []) \; \mt{fields}) \to \mt{dml}
adamc@545 1965 \end{array}$$
adamc@545 1966
adam@1578 1967 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 1968 $$\begin{array}{l}
adam@1380 1969 \mt{val} \; \mt{update} : \mt{unchanged} ::: \{\mt{Type}\} \to \mt{changed} :: \{\mt{Type}\} \to [\mt{changed} \sim \mt{unchanged}] \\
adam@1778 1970 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; []) \; \mt{changed}) \\
adam@1778 1971 \hspace{.1in} \to \mt{sql\_table} \; (\mt{changed} \rc \mt{unchanged}) \to \mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545 1972 \end{array}$$
adamc@545 1973
adam@1578 1974 A $\mt{DELETE}$ command is formed from a table and a $\mt{WHERE}$ clause. The above use of $\mt{T}$ is repeated.
adamc@545 1975 $$\begin{array}{l}
adam@1778 1976 \mt{val} \; \mt{delete} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \to \mt{sql\_exp} \; [\mt{T} = \mt{fields}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545 1977 \end{array}$$
adamc@545 1978
adamc@546 1979 \subsubsection{Sequences}
adamc@546 1980
adamc@546 1981 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 1982
adamc@546 1983 $$\begin{array}{l}
adamc@546 1984 \mt{type} \; \mt{sql\_sequence} \\
adamc@1085 1985 \mt{val} \; \mt{nextval} : \mt{sql\_sequence} \to \mt{transaction} \; \mt{int} \\
adamc@1085 1986 \mt{val} \; \mt{setval} : \mt{sql\_sequence} \to \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@546 1987 \end{array}$$
adamc@546 1988
adamc@546 1989
adam@1648 1990 \subsection{\label{xml}XML}
adamc@547 1991
adam@1333 1992 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 1993
adam@1642 1994 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 1995 $$\begin{array}{l}
adamc@547 1996 \mt{con} \; \mt{xml} :: \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547 1997 \end{array}$$
adamc@547 1998
adamc@547 1999 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 2000 $$\begin{array}{l}
adamc@547 2001 \mt{con} \; \mt{tag} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547 2002 \end{array}$$
adamc@547 2003
adamc@547 2004 Literal text may be injected into XML as ``CDATA.''
adamc@547 2005 $$\begin{array}{l}
adamc@547 2006 \mt{val} \; \mt{cdata} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{string} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adamc@547 2007 \end{array}$$
adamc@547 2008
adam@1358 2009 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 2010 $$\begin{array}{l}
adam@1358 2011 \mt{val} \; \mt{cdataChar} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{char} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adam@1358 2012 \end{array}$$
adam@1358 2013
adamc@547 2014 There is a function for producing an XML tree with a particular tag at its root.
adamc@547 2015 $$\begin{array}{l}
adamc@547 2016 \mt{val} \; \mt{tag} : \mt{attrsGiven} ::: \{\mt{Type}\} \to \mt{attrsAbsent} ::: \{\mt{Type}\} \to \mt{ctxOuter} ::: \{\mt{Unit}\} \to \mt{ctxInner} ::: \{\mt{Unit}\} \\
adamc@547 2017 \hspace{.1in} \to \mt{useOuter} ::: \{\mt{Type}\} \to \mt{useInner} ::: \{\mt{Type}\} \to \mt{bindOuter} ::: \{\mt{Type}\} \to \mt{bindInner} ::: \{\mt{Type}\} \\
adam@1380 2018 \hspace{.1in} \to [\mt{attrsGiven} \sim \mt{attrsAbsent}] \Rightarrow [\mt{useOuter} \sim \mt{useInner}] \Rightarrow [\mt{bindOuter} \sim \mt{bindInner}] \\
adam@1749 2019 \hspace{.1in} \Rightarrow \mt{css\_class} \\
adam@1643 2020 \hspace{.1in} \to \mt{option} \; (\mt{signal} \; \mt{css\_class}) \\
adam@1750 2021 \hspace{.1in} \to \mt{css\_style} \\
adam@1751 2022 \hspace{.1in} \to \mt{option} \; (\mt{signal} \; \mt{css\_style}) \\
adamc@787 2023 \hspace{.1in} \to \$\mt{attrsGiven} \\
adamc@547 2024 \hspace{.1in} \to \mt{tag} \; (\mt{attrsGiven} \rc \mt{attrsAbsent}) \; \mt{ctxOuter} \; \mt{ctxInner} \; \mt{useOuter} \; \mt{bindOuter} \\
adamc@547 2025 \hspace{.1in} \to \mt{xml} \; \mt{ctxInner} \; \mt{useInner} \; \mt{bindInner} \to \mt{xml} \; \mt{ctxOuter} \; (\mt{useOuter} \rc \mt{useInner}) \; (\mt{bindOuter} \rc \mt{bindInner})
adamc@547 2026 \end{array}$$
adam@1750 2027 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 2028
adam@1643 2029 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 2030
adam@1751 2031 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 2032
adamc@547 2033 Two XML fragments may be concatenated.
adamc@547 2034 $$\begin{array}{l}
adamc@547 2035 \mt{val} \; \mt{join} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{bind_1} ::: \{\mt{Type}\} \to \mt{bind_2} ::: \{\mt{Type}\} \\
adam@1380 2036 \hspace{.1in} \to [\mt{use_1} \sim \mt{bind_1}] \Rightarrow [\mt{bind_1} \sim \mt{bind_2}] \\
adamc@547 2037 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind_1} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{bind_1}) \; \mt{bind_2} \to \mt{xml} \; \mt{ctx} \; \mt{use_1} \; (\mt{bind_1} \rc \mt{bind_2})
adamc@547 2038 \end{array}$$
adamc@547 2039
adamc@547 2040 Finally, any XML fragment may be updated to ``claim'' to use more form fields than it does.
adamc@547 2041 $$\begin{array}{l}
adam@1380 2042 \mt{val} \; \mt{useMore} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{use_2} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to [\mt{use_1} \sim \mt{use_2}] \\
adamc@547 2043 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{use_2}) \; \mt{bind}
adamc@547 2044 \end{array}$$
adamc@547 2045
adam@1344 2046 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. It \emph{is} possible to add new tags directly to \texttt{basis.urs}, but this should only be done as a prelude to suggesting a patch to the main distribution.
adamc@547 2047
adamc@547 2048 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 2049 $$\begin{array}{l}
adam@1641 2050 \mt{val} \; \mt{error} : \mt{t} ::: \mt{Type} \to \mt{xbody} \to \mt{t}
adamc@547 2051 \end{array}$$
adamc@547 2052
adamc@549 2053
adamc@701 2054 \subsection{Client-Side Programming}
adamc@659 2055
adamc@701 2056 Ur/Web supports running code on web browsers, via automatic compilation to JavaScript.
adamc@701 2057
adamc@701 2058 \subsubsection{The Basics}
adamc@701 2059
adam@1400 2060 All of the functions in this subsection are client-side only.
adam@1400 2061
adam@1297 2062 Clients can open alert and confirm dialog boxes, in the usual annoying JavaScript way.
adamc@701 2063 $$\begin{array}{l}
adam@1297 2064 \mt{val} \; \mt{alert} : \mt{string} \to \mt{transaction} \; \mt{unit} \\
adam@1297 2065 \mt{val} \; \mt{confirm} : \mt{string} \to \mt{transaction} \; \mt{bool}
adamc@701 2066 \end{array}$$
adamc@701 2067
adamc@701 2068 Any transaction may be run in a new thread with the $\mt{spawn}$ function.
adamc@701 2069 $$\begin{array}{l}
adamc@701 2070 \mt{val} \; \mt{spawn} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit}
adamc@701 2071 \end{array}$$
adamc@701 2072
adamc@701 2073 The current thread can be paused for at least a specified number of milliseconds.
adamc@701 2074 $$\begin{array}{l}
adamc@701 2075 \mt{val} \; \mt{sleep} : \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@701 2076 \end{array}$$
adamc@701 2077
adam@1770 2078 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 2079 $$\begin{array}{l}
adamc@787 2080 \mt{val} \; \mt{onError} : (\mt{xbody} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787 2081 \mt{val} \; \mt{onFail} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787 2082 \mt{val} \; \mt{onConnectFail} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787 2083 \mt{val} \; \mt{onDisconnect} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787 2084 \mt{val} \; \mt{onServerError} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit}
adamc@787 2085 \end{array}$$
adamc@787 2086
adam@1555 2087 There are also functions to register standard document-level event handlers.
adam@1555 2088
adam@1555 2089 $$\begin{array}{l}
adam@1783 2090 \mt{val} \; \mt{onClick} : (\mt{mouseEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783 2091 \mt{val} \; \mt{onDblclick} : (\mt{mouseEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783 2092 \mt{val} \; \mt{onKeydown} : (\mt{keyEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783 2093 \mt{val} \; \mt{onKeypress} : (\mt{keyEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783 2094 \mt{val} \; \mt{onKeyup} : (\mt{keyEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783 2095 \mt{val} \; \mt{onMousedown} : (\mt{mouseEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783 2096 \mt{val} \; \mt{onMouseup} : (\mt{mouseEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit}
adam@1555 2097 \end{array}$$
adam@1555 2098
adam@1559 2099 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 2100
adam@1559 2101 $$\begin{array}{l}
adam@1559 2102 \mt{val} \; \mt{preventDefault} : \mt{transaction} \; \mt{unit} \\
adam@1559 2103 \mt{val} \; \mt{stopPropagation} : \mt{transaction} \; \mt{unit}
adam@1559 2104 \end{array}$$
adam@1559 2105
adam@1556 2106 \subsubsection{Node IDs}
adam@1556 2107
adam@1556 2108 There is an abstract type of node IDs that may be assigned to \cd{id} attributes of most HTML tags.
adam@1556 2109
adam@1556 2110 $$\begin{array}{l}
adam@1556 2111 \mt{type} \; \mt{id} \\
adam@1556 2112 \mt{val} \; \mt{fresh} : \mt{transaction} \; \mt{id}
adam@1556 2113 \end{array}$$
adam@1556 2114
adam@1785 2115 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 2116
adam@1785 2117 One further use of IDs is as handles for requesting that \emph{focus} be given to specific tags.
adam@1785 2118
adam@1785 2119 $$\begin{array}{l}
adam@1785 2120 \mt{val} \; \mt{giveFocus} : \mt{id} \to \mt{transaction} \; \mt{unit}
adam@1785 2121 \end{array}$$
adam@1556 2122
adam@1643 2123 \subsubsection{\label{signals}Functional-Reactive Page Generation}
adamc@701 2124
adamc@701 2125 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 2126
adam@1403 2127 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 2128
adamc@659 2129 $$\begin{array}{l}
adamc@659 2130 \mt{con} \; \mt{source} :: \mt{Type} \to \mt{Type} \\
adamc@659 2131 \mt{val} \; \mt{source} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{transaction} \; (\mt{source} \; \mt{t}) \\
adamc@659 2132 \mt{val} \; \mt{set} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@659 2133 \mt{val} \; \mt{get} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@659 2134 \end{array}$$
adamc@659 2135
adam@1400 2136 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 2137
adam@1608 2138 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 2139
adamc@659 2140 $$\begin{array}{l}
adamc@659 2141 \mt{con} \; \mt{signal} :: \mt{Type} \to \mt{Type} \\
adamc@659 2142 \mt{val} \; \mt{signal\_monad} : \mt{monad} \; \mt{signal} \\
adam@1608 2143 \mt{val} \; \mt{signal} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{signal} \; \mt{t} \\
adam@1608 2144 \mt{val} \; \mt{current} : \mt{t} ::: \mt{Type} \to \mt{signal} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@659 2145 \end{array}$$
adamc@659 2146
adamc@659 2147 A reactive portion of an HTML page is injected with a $\mt{dyn}$ tag, which has a signal-valued attribute $\mt{Signal}$.
adamc@659 2148
adamc@659 2149 $$\begin{array}{l}
adam@1641 2150 \mt{val} \; \mt{dyn} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to [\mt{ctx} \sim [\mt{Dyn}]] \Rightarrow \mt{unit} \\
adam@1641 2151 \hspace{.1in} \to \mt{tag} \; [\mt{Signal} = \mt{signal} \; (\mt{xml} \; ([\mt{Dyn}] \rc \mt{ctx}) \; \mt{use} \; \mt{bind})] \; ([\mt{Dyn}] \rc \mt{ctx}) \; [] \; \mt{use} \; \mt{bind}
adamc@659 2152 \end{array}$$
adamc@659 2153
adam@1648 2154 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 2155
adam@1648 2156 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 2157
adam@1786 2158 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 2159
adam@1786 2160 $$\begin{array}{l}
adam@1786 2161 \mt{val} \; \mt{active} : \mt{unit} \to \mt{tag} \; [\mt{Code} = \mt{transaction} \; \mt{xbody}] \; \mt{body} \; [] \; [] \; []
adam@1786 2162 \end{array}$$
adamc@701 2163
adamc@914 2164 \subsubsection{Remote Procedure Calls}
adamc@914 2165
adamc@914 2166 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 2167
adamc@914 2168 $$\begin{array}{l}
adamc@914 2169 \mt{val} \; \mt{rpc} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@914 2170 \end{array}$$
adamc@914 2171
adam@1848 2172 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 2173
adam@1848 2174 $$\begin{array}{l}
adam@1848 2175 \mt{val} \; \mt{tryRpc} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; \mt{t} \to \mt{transaction} \; (\mt{option} \; \mt{t})
adam@1848 2176 \end{array}$$
adam@1848 2177
adamc@701 2178 \subsubsection{Asynchronous Message-Passing}
adamc@701 2179
adamc@701 2180 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 2181
adamc@701 2182 $$\begin{array}{l}
adamc@701 2183 \mt{type} \; \mt{client} \\
adamc@701 2184 \mt{val} \; \mt{self} : \mt{transaction} \; \mt{client}
adamc@701 2185 \end{array}$$
adamc@701 2186
adamc@701 2187 \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. 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 2188
adamc@701 2189 $$\begin{array}{l}
adamc@701 2190 \mt{con} \; \mt{channel} :: \mt{Type} \to \mt{Type} \\
adamc@701 2191 \mt{val} \; \mt{channel} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; (\mt{channel} \; \mt{t}) \\
adamc@701 2192 \mt{val} \; \mt{send} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@701 2193 \mt{val} \; \mt{recv} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@701 2194 \end{array}$$
adamc@701 2195
adamc@701 2196 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 2197
adamc@701 2198 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 2199
adam@1551 2200 \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 2201
adamc@659 2202
adamc@549 2203 \section{Ur/Web Syntax Extensions}
adamc@549 2204
adamc@549 2205 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 2206
adamc@549 2207 \subsection{SQL}
adamc@549 2208
adamc@786 2209 \subsubsection{\label{tables}Table Declarations}
adamc@786 2210
adamc@788 2211 $\mt{table}$ declarations may include constraints, via these grammar rules.
adamc@788 2212 $$\begin{array}{rrcll}
adam@1594 2213 \textrm{Declarations} & d &::=& \mt{table} \; x : c \; [pk[,]] \; cts \mid \mt{view} \; x = V \\
adamc@788 2214 \textrm{Primary key constraints} & pk &::=& \mt{PRIMARY} \; \mt{KEY} \; K \\
adam@1722 2215 \textrm{Keys} & K &::=& f \mid (f, (f,)^+) \mid \{\{e\}\} \\
adamc@788 2216 \textrm{Constraint sets} & cts &::=& \mt{CONSTRAINT} f \; ct \mid cts, cts \mid \{\{e\}\} \\
adamc@788 2217 \textrm{Constraints} & ct &::=& \mt{UNIQUE} \; K \mid \mt{CHECK} \; E \\
adamc@788 2218 &&& \mid \mt{FOREIGN} \; \mt{KEY} \; K \; \mt{REFERENCES} \; F \; (K) \; [\mt{ON} \; \mt{DELETE} \; pr] \; [\mt{ON} \; \mt{UPDATE} \; pr] \\
adamc@788 2219 \textrm{Foreign tables} & F &::=& x \mid \{\{e\}\} \\
adam@1594 2220 \textrm{Propagation modes} & pr &::=& \mt{NO} \; \mt{ACTION} \mid \mt{RESTRICT} \mid \mt{CASCADE} \mid \mt{SET} \; \mt{NULL} \\
adam@1594 2221 \textrm{View expressions} & V &::=& Q \mid \{e\}
adamc@788 2222 \end{array}$$
adamc@788 2223
adamc@788 2224 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 2225
adamc@788 2226
adamc@549 2227 \subsubsection{Queries}
adamc@549 2228
adamc@550 2229 Queries $Q$ are added to the rules for expressions $e$.
adamc@550 2230
adamc@549 2231 $$\begin{array}{rrcll}
adam@1684 2232 \textrm{Queries} & Q &::=& (q \; [\mt{ORDER} \; \mt{BY} \; O] \; [\mt{LIMIT} \; N] \; [\mt{OFFSET} \; N]) \\
adamc@1085 2233 \textrm{Pre-queries} & q &::=& \mt{SELECT} \; [\mt{DISTINCT}] \; P \; \mt{FROM} \; F,^+ \; [\mt{WHERE} \; E] \; [\mt{GROUP} \; \mt{BY} \; p,^+] \; [\mt{HAVING} \; E] \\
adamc@1085 2234 &&& \mid q \; R \; q \mid \{\{\{e\}\}\} \\
adam@1684 2235 \textrm{Relational operators} & R &::=& \mt{UNION} \mid \mt{INTERSECT} \mid \mt{EXCEPT} \\
adam@1778 2236 \textrm{$\mt{ORDER \; BY}$ items} & O &::=& \mt{RANDOM} [()] \mid \hat{E} \; [o] \mid \hat{E} \; [o], O
adamc@549 2237 \end{array}$$
adamc@549 2238
adamc@549 2239 $$\begin{array}{rrcll}
adamc@549 2240 \textrm{Projections} & P &::=& \ast & \textrm{all columns} \\
adamc@549 2241 &&& p,^+ & \textrm{particular columns} \\
adamc@549 2242 \textrm{Pre-projections} & p &::=& t.f & \textrm{one column from a table} \\
adamc@558 2243 &&& t.\{\{c\}\} & \textrm{a record of columns from a table (of kind $\{\mt{Type}\}$)} \\
adam@1627 2244 &&& t.* & \textrm{all columns from a table} \\
adam@1778 2245 &&& \hat{E} \; [\mt{AS} \; f] & \textrm{expression column} \\
adamc@549 2246 \textrm{Table names} & t &::=& x & \textrm{constant table name (automatically capitalized)} \\
adamc@549 2247 &&& X & \textrm{constant table name} \\
adamc@549 2248 &&& \{\{c\}\} & \textrm{computed table name (of kind $\mt{Name}$)} \\
adamc@549 2249 \textrm{Column names} & f &::=& X & \textrm{constant column name} \\
adamc@549 2250 &&& \{c\} & \textrm{computed column name (of kind $\mt{Name}$)} \\
adamc@549 2251 \textrm{Tables} & T &::=& x & \textrm{table variable, named locally by its own capitalization} \\
adam@1756 2252 &&& x \; \mt{AS} \; X & \textrm{table variable, with local name} \\
adam@1756 2253 &&& x \; \mt{AS} \; \{c\} & \textrm{table variable, with computed local name} \\
adamc@549 2254 &&& \{\{e\}\} \; \mt{AS} \; t & \textrm{computed table expression, with local name} \\
adam@1756 2255 &&& \{\{e\}\} \; \mt{AS} \; \{c\} & \textrm{computed table expression, with computed local name} \\
adamc@1085 2256 \textrm{$\mt{FROM}$ items} & F &::=& T \mid \{\{e\}\} \mid F \; J \; \mt{JOIN} \; F \; \mt{ON} \; E \\
adamc@1085 2257 &&& \mid F \; \mt{CROSS} \; \mt{JOIN} \ F \\
adamc@1193 2258 &&& \mid (Q) \; \mt{AS} \; t \\
adamc@1085 2259 \textrm{Joins} & J &::=& [\mt{INNER}] \\
adamc@1085 2260 &&& \mid [\mt{LEFT} \mid \mt{RIGHT} \mid \mt{FULL}] \; [\mt{OUTER}] \\
adam@1587 2261 \textrm{SQL expressions} & E &::=& t.f & \textrm{column references} \\
adamc@549 2262 &&& X & \textrm{named expression references} \\
adam@1490 2263 &&& \{[e]\} & \textrm{injected native Ur expressions} \\
adam@1778 2264 &&& \{e\} & \textrm{computed expressions, probably using $\mt{sql\_exp}$ directly} \\
adamc@549 2265 &&& \mt{TRUE} \mid \mt{FALSE} & \textrm{boolean constants} \\
adamc@549 2266 &&& \ell & \textrm{primitive type literals} \\
adamc@549 2267 &&& \mt{NULL} & \textrm{null value (injection of $\mt{None}$)} \\
adamc@549 2268 &&& E \; \mt{IS} \; \mt{NULL} & \textrm{nullness test} \\
adam@1602 2269 &&& \mt{COALESCE}(E, E) & \textrm{take first non-null value} \\
adamc@549 2270 &&& n & \textrm{nullary operators} \\
adamc@549 2271 &&& u \; E & \textrm{unary operators} \\
adamc@549 2272 &&& E \; b \; E & \textrm{binary operators} \\
adam@1778 2273 &&& \mt{COUNT}(\ast) & \textrm{count number of rows} \\
adam@1778 2274 &&& a(E) & \textrm{other aggregate function} \\
adam@1573 2275 &&& \mt{IF} \; E \; \mt{THEN} \; E \; \mt{ELSE} \; E & \textrm{conditional} \\
adam@1778 2276 &&& (Q) & \textrm{subquery (must return a single expression column)} \\
adamc@549 2277 &&& (E) & \textrm{explicit precedence} \\
adamc@549 2278 \textrm{Nullary operators} & n &::=& \mt{CURRENT\_TIMESTAMP} \\
adamc@549 2279 \textrm{Unary operators} & u &::=& \mt{NOT} \\
adam@1688 2280 \textrm{Binary operators} & b &::=& \mt{AND} \mid \mt{OR} \mid = \mid \neq \mid < \mid \leq \mid > \mid \geq \\
adamc@1188 2281 \textrm{Aggregate functions} & a &::=& \mt{COUNT} \mid \mt{AVG} \mid \mt{SUM} \mid \mt{MIN} \mid \mt{MAX} \\
adam@1543 2282 \textrm{Directions} & o &::=& \mt{ASC} \mid \mt{DESC} \mid \{e\} \\
adamc@549 2283 \textrm{SQL integer} & N &::=& n \mid \{e\} \\
adam@1778 2284 \textrm{Windowable expressions} & \hat{E} &::=& E \\
adam@1778 2285 &&& w \; [\mt{OVER} \; ( & \textrm{(Postgres only)} \\
adam@1778 2286 &&& \hspace{.1in} [\mt{PARTITION} \; \mt{BY} \; E] \\
adam@1778 2287 &&& \hspace{.1in} [\mt{ORDER} \; \mt{BY} \; O])] \\
adam@1778 2288 \textrm{Window function} & w &::=& \mt{RANK}() \\
adam@1778 2289 &&& \mt{COUNT}(*) \\
adam@1778 2290 &&& a(E)
adamc@549 2291 \end{array}$$
adamc@549 2292
adamc@1085 2293 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 2294
adam@1683 2295 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 2296
adamc@550 2297 \subsubsection{DML}
adamc@550 2298
adamc@550 2299 DML commands $D$ are added to the rules for expressions $e$.
adamc@550 2300
adamc@550 2301 $$\begin{array}{rrcll}
adamc@550 2302 \textrm{Commands} & D &::=& (\mt{INSERT} \; \mt{INTO} \; T^E \; (f,^+) \; \mt{VALUES} \; (E,^+)) \\
adamc@550 2303 &&& (\mt{UPDATE} \; T^E \; \mt{SET} \; (f = E,)^+ \; \mt{WHERE} \; E) \\
adamc@550 2304 &&& (\mt{DELETE} \; \mt{FROM} \; T^E \; \mt{WHERE} \; E) \\
adamc@550 2305 \textrm{Table expressions} & T^E &::=& x \mid \{\{e\}\}
adamc@550 2306 \end{array}$$
adamc@550 2307
adamc@550 2308 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 2309
adamc@551 2310 \subsection{XML}
adamc@551 2311
adamc@551 2312 XML fragments $L$ are added to the rules for expressions $e$.
adamc@551 2313
adamc@551 2314 $$\begin{array}{rrcll}
adamc@551 2315 \textrm{XML fragments} & L &::=& \texttt{<xml/>} \mid \texttt{<xml>}l^*\texttt{</xml>} \\
adamc@551 2316 \textrm{XML pieces} & l &::=& \textrm{text} & \textrm{cdata} \\
adamc@551 2317 &&& \texttt{<}g\texttt{/>} & \textrm{tag with no children} \\
adamc@551 2318 &&& \texttt{<}g\texttt{>}l^*\texttt{</}x\texttt{>} & \textrm{tag with children} \\
adamc@559 2319 &&& \{e\} & \textrm{computed XML fragment} \\
adamc@559 2320 &&& \{[e]\} & \textrm{injection of an Ur expression, via the $\mt{Top}.\mt{txt}$ function} \\
adamc@551 2321 \textrm{Tag} & g &::=& h \; (x = v)^* \\
adamc@551 2322 \textrm{Tag head} & h &::=& x & \textrm{tag name} \\
adamc@551 2323 &&& h\{c\} & \textrm{constructor parameter} \\
adamc@551 2324 \textrm{Attribute value} & v &::=& \ell & \textrm{literal value} \\
adamc@551 2325 &&& \{e\} & \textrm{computed value} \\
adamc@551 2326 \end{array}$$
adamc@551 2327
adam@1751 2328 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 2329
adam@1751 2330 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 2331
adamc@1198 2332 \section{\label{structure}The Structure of Web Applications}
adamc@553 2333
adam@1797 2334 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 2335
adam@1532 2336 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 2337
adam@1787 2338 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 2339
adam@1370 2340 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 2341
adamc@553 2342 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 2343
adamc@553 2344 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 2345
adam@1653 2346 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 2347 \begin{itemize}
adam@1653 2348 \item Functions are disallowed, since there is no obvious way to serialize them safely.
adam@1653 2349 \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 2350 \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 2351 \end{itemize}
adamc@553 2352
adamc@660 2353 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 2354
adamc@789 2355 \medskip
adamc@789 2356
adam@1347 2357 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 2358
adamc@789 2359 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 2360
adam@1348 2361 \subsection{Tasks}
adam@1348 2362
adam@1348 2363 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 2364
adam@1348 2365 $$\begin{array}{l}
adam@1348 2366 \mt{con} \; \mt{task\_kind} :: \mt{Type} \to \mt{Type} \\
adam@1348 2367 \mt{val} \; \mt{initialize} : \mt{task\_kind} \; \mt{unit} \\
adam@1349 2368 \mt{val} \; \mt{clientLeaves} : \mt{task\_kind} \; \mt{client} \\
adam@1349 2369 \mt{val} \; \mt{periodic} : \mt{int} \to \mt{task\_kind} \; \mt{unit}
adam@1348 2370 \end{array}$$
adam@1348 2371
adam@1348 2372 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 2373
adam@1348 2374 The currently supported task kinds are:
adam@1348 2375 \begin{itemize}
adam@1349 2376 \item $\mt{initialize}$: Code that is run when the application starts up.
adam@1348 2377 \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 2378 \item $\mt{periodic} \; n$: Code that is run when the application starts up and then every $n$ seconds thereafter.
adam@1348 2379 \end{itemize}
adam@1348 2380
adamc@553 2381
adamc@897 2382 \section{The Foreign Function Interface}
adamc@897 2383
adamc@897 2384 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 2385
adamc@897 2386 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 2387
adamc@897 2388 \begin{itemize}
adamc@897 2389 \item \texttt{clientOnly Module.ident} registers a value as being allowed only in client-side code.
adamc@897 2390 \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 2391 \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 2392 \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 2393 \item \texttt{include FILE} requests inclusion of a C header file.
adamc@897 2394 \item \texttt{jsFunc Module.ident=name} gives a mapping from an Ur name for a value to a JavaScript name.
adamc@897 2395 \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 2396 \item \texttt{script URL} requests inclusion of a JavaScript source file within application HTML.
adamc@897 2397 \item \texttt{serverOnly Module.ident} registers a value as being allowed only in server-side code.
adamc@897 2398 \end{itemize}
adamc@897 2399
adamc@897 2400 \subsection{Writing C FFI Code}
adamc@897 2401
adam@1881 2402 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 2403
adamc@897 2404 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 2405
adamc@897 2406 \begin{itemize}
adam@1881 2407 \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 2408 \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 2409 \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 2410 \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 2411 \end{itemize}
adamc@897 2412
adam@1881 2413 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 2414 \begin{itemize}
adamc@897 2415 \item \begin{verbatim}
adamc@897 2416 void uw_error(uw_context, failure_kind, const char *fmt, ...);
adamc@897 2417 \end{verbatim}
adamc@897 2418 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 2419
adam@1329 2420 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 2421
adamc@897 2422 \item \begin{verbatim}
adam@1469 2423 void uw_set_error_message(uw_context, const char *fmt, ...);
adam@1469 2424 \end{verbatim}
adam@1469 2425 This simpler form of \texttt{uw\_error()} saves an error message without immediately aborting execution.
adam@1469 2426
adam@1469 2427 \item \begin{verbatim}
adamc@897 2428 void uw_push_cleanup(uw_context, void (*func)(void *), void *arg);
adamc@897 2429 void uw_pop_cleanup(uw_context);
adamc@897 2430 \end{verbatim}
adam@1329 2431 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 2432
adam@1329 2433 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 2434
adamc@897 2435 \item \begin{verbatim}
adamc@897 2436 void *uw_malloc(uw_context, size_t);
adamc@897 2437 \end{verbatim}
adam@1329 2438 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 2439
adam@1329 2440 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 2441
adamc@897 2442 \item \begin{verbatim}
adamc@897 2443 typedef void (*uw_callback)(void *);
adam@1328 2444 typedef void (*uw_callback_with_retry)(void *, int will_retry);
adamc@897 2445 void uw_register_transactional(uw_context, void *data, uw_callback commit,
adam@1328 2446 uw_callback rollback, uw_callback_with_retry free);
adamc@897 2447 \end{verbatim}
adam@1328 2448 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.
adamc@897 2449
adamc@1085 2450 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. Thus, if a single execution uses only one non-transactional action, and if that action never fails partway through its execution while still causing an observable side effect, then Ur/Web can maintain the transactional abstraction.
adamc@1085 2451
adam@1329 2452 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 2453
adam@1329 2454 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 2455
adam@1469 2456 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 2457
adamc@1085 2458 \item \begin{verbatim}
adamc@1085 2459 void *uw_get_global(uw_context, char *name);
adamc@1085 2460 void uw_set_global(uw_context, char *name, void *data, uw_callback free);
adamc@1085 2461 \end{verbatim}
adam@1329 2462 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 2463
adamc@897 2464 \end{itemize}
adamc@897 2465
adamc@897 2466 \subsection{Writing JavaScript FFI Code}
adamc@897 2467
adamc@897 2468 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 2469
adamc@897 2470 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 2471
adamc@897 2472 \begin{itemize}
adamc@897 2473 \item Integers, floats, strings, characters, and booleans are represented in the usual JavaScript way.
adam@1644 2474 \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)}. To lift a normal JavaScript function \cd{f} into an Ur/Web JavaScript function, run \cd{flift(f)}.
adamc@897 2475 \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 2476 \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 2477 \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 2478 \item As in the C FFI, all abstract types of program syntax are implemented with strings in JavaScript.
adam@1844 2479 \item A value of Ur type \texttt{transaction t} is represented in the same way as for \texttt{unit -> t}.
adamc@897 2480 \end{itemize}
adamc@897 2481
adam@1644 2482 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 2483
adam@1644 2484 \begin{itemize}
adam@1644 2485 \item Sources should be treated as an abstract type, manipulated via:
adam@1644 2486 \begin{itemize}
adam@1644 2487 \item \cd{sc(v)}, to create a source initialized to \cd{v}
adam@1644 2488 \item \cd{sg(s)}, to retrieve the current value of source \cd{s}
adam@1644 2489 \item \cd{sv(s, v)}, to set source \cd{s} to value \cd{v}
adam@1644 2490 \end{itemize}
adam@1644 2491
adam@1644 2492 \item Signals should be treated as an abstract type, manipulated via:
adam@1644 2493 \begin{itemize}
adam@1644 2494 \item \cd{sr(v)} and \cd{sb(s, f)}, the ``return'' and ``bind'' monad operators, respectively
adam@1644 2495 \item \cd{ss(s)}, to produce the signal corresponding to source \cd{s}
adam@1644 2496 \item \cd{scur(s)}, to get the current value of signal \cd{s}
adam@1644 2497 \end{itemize}
adam@1644 2498
adam@1644 2499 \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 2500
adam@1702 2501 \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 2502
adam@1644 2503 \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 2504 \end{itemize}
adamc@897 2505
adam@1833 2506 \subsection{Introducing New HTML Tags}
adam@1833 2507
adam@1833 2508 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 2509
adam@1833 2510 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 2511
adamc@897 2512
adamc@552 2513 \section{Compiler Phases}
adamc@552 2514
adamc@552 2515 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 2516
adamc@552 2517 In this section, we step through the main phases of compilation, noting what consequences each phase has for effective programming.
adamc@552 2518
adamc@552 2519 \subsection{Parse}
adamc@552 2520
adamc@552 2521 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 2522
adamc@552 2523 \subsection{Elaborate}
adamc@552 2524
adamc@552 2525 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 2526
adam@1378 2527 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 2528
adamc@552 2529 \subsection{Unnest}
adamc@552 2530
adamc@552 2531 Named local function definitions are moved to the top level, to avoid the need to generate closures.
adamc@552 2532
adamc@552 2533 \subsection{Corify}
adamc@552 2534
adamc@552 2535 Module system features are compiled away, through inlining of functor definitions at application sites. Afterward, most abstraction boundaries are broken, facilitating optimization.
adamc@552 2536
adamc@552 2537 \subsection{Especialize}
adamc@552 2538
adam@1356 2539 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 2540
adamc@552 2541 \subsection{Untangle}
adamc@552 2542
adam@1797 2543 Remove unnecessary mutual recursion, splitting recursive groups into strongly connected components.
adamc@552 2544
adamc@552 2545 \subsection{Shake}
adamc@552 2546
adamc@552 2547 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 2548
adamc@661 2549 \subsection{Rpcify}
adamc@661 2550
adamc@661 2551 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 2552
adamc@661 2553 \subsection{Untangle, Shake}
adamc@661 2554
adamc@661 2555 Repeat these simplifications.
adamc@661 2556
adamc@553 2557 \subsection{\label{tag}Tag}
adamc@552 2558
adamc@552 2559 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 2560
adamc@552 2561 \subsection{Reduce}
adamc@552 2562
adamc@552 2563 Apply definitional equality rules to simplify the program as much as possible. This effectively includes inlining of every non-recursive definition.
adamc@552 2564
adamc@552 2565 \subsection{Unpoly}
adamc@552 2566
adamc@552 2567 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 2568
adamc@552 2569 \subsection{Specialize}
adamc@552 2570
adamc@558 2571 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 2572
adamc@552 2573 \subsection{Shake}
adamc@552 2574
adamc@558 2575 Here the compiler repeats the earlier Shake phase.
adamc@552 2576
adamc@552 2577 \subsection{Monoize}
adamc@552 2578
adamc@552 2579 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 2580
adamc@552 2581 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 2582
adamc@552 2583 \subsection{MonoOpt}
adamc@552 2584
adamc@552 2585 Simple algebraic laws are applied to simplify the program, focusing especially on efficient imperative generation of HTML pages.
adamc@552 2586
adamc@552 2587 \subsection{MonoUntangle}
adamc@552 2588
adamc@552 2589 Unnecessary mutual recursion is broken up again.
adamc@552 2590
adamc@552 2591 \subsection{MonoReduce}
adamc@552 2592
adamc@552 2593 Equivalents of the definitional equality rules are applied to simplify programs, with inlining again playing a major role.
adamc@552 2594
adamc@552 2595 \subsection{MonoShake, MonoOpt}
adamc@552 2596
adamc@552 2597 Unneeded declarations are removed, and basic optimizations are repeated.
adamc@552 2598
adamc@552 2599 \subsection{Fuse}
adamc@552 2600
adamc@552 2601 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 2602
adamc@552 2603 \subsection{MonoUntangle, MonoShake}
adamc@552 2604
adamc@552 2605 Fuse often creates more opportunities to remove spurious mutual recursion.
adamc@552 2606
adamc@552 2607 \subsection{Pathcheck}
adamc@552 2608
adamc@552 2609 The compiler checks that no link or action name has been used more than once.
adamc@552 2610
adamc@552 2611 \subsection{Cjrize}
adamc@552 2612
adamc@552 2613 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 2614
adamc@552 2615 \subsection{C Compilation and Linking}
adamc@552 2616
adam@1523 2617 The output of the last phase is pretty-printed as C source code and passed to the C compiler.
adamc@552 2618
adamc@552 2619
as@1564 2620 \end{document}