annotate doc/manual.tex @ 1472:18d18a70821e

Implicit argument insertion for local variables
author Adam Chlipala <adam@chlipala.net>
date Tue, 14 Jun 2011 08:54:45 -0400
parents a354b306f948
children a10d080123ec
rev   line source
adamc@524 1 \documentclass{article}
adamc@554 2 \usepackage{fullpage,amsmath,amssymb,proof,url}
adamc@524 3
adamc@524 4 \newcommand{\cd}[1]{\texttt{#1}}
adamc@524 5 \newcommand{\mt}[1]{\mathsf{#1}}
adamc@524 6
adamc@524 7 \newcommand{\rc}{+ \hspace{-.075in} + \;}
adamc@527 8 \newcommand{\rcut}{\; \texttt{--} \;}
adamc@527 9 \newcommand{\rcutM}{\; \texttt{---} \;}
adamc@524 10
adamc@524 11 \begin{document}
adamc@524 12
adamc@524 13 \title{The Ur/Web Manual}
adamc@524 14 \author{Adam Chlipala}
adamc@524 15
adamc@524 16 \maketitle
adamc@524 17
adamc@540 18 \tableofcontents
adamc@540 19
adamc@554 20
adamc@554 21 \section{Introduction}
adamc@554 22
adamc@1160 23 \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 24
adamc@554 25 \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 26
adamc@554 27 \begin{itemize}
adamc@554 28 \item Suffer from any kinds of code-injection attacks
adamc@554 29 \item Return invalid HTML
adamc@554 30 \item Contain dead intra-application links
adamc@554 31 \item Have mismatches between HTML forms and the fields expected by their handlers
adamc@652 32 \item Include client-side code that makes incorrect assumptions about the ``AJAX''-style services that the remote web server provides
adamc@554 33 \item Attempt invalid SQL queries
adamc@652 34 \item Use improper marshaling or unmarshaling in communication with SQL databases or between browsers and web servers
adamc@554 35 \end{itemize}
adamc@554 36
adamc@554 37 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 38
adamc@652 39 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 40
adamc@554 41 \medskip
adamc@554 42
adamc@554 43 The official web site for Ur is:
adamc@554 44 \begin{center}
adamc@554 45 \url{http://www.impredicative.com/ur/}
adamc@554 46 \end{center}
adamc@554 47
adamc@555 48
adamc@555 49 \section{Installation}
adamc@555 50
adamc@555 51 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 52
adamc@555 53 \begin{verbatim}
adamc@555 54 ./configure
adamc@555 55 make
adamc@555 56 sudo make install
adamc@555 57 \end{verbatim}
adamc@555 58
adam@1368 59 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 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 60 \begin{verbatim}
adam@1368 61 apt-get install mlton libssl-dev
adamc@896 62 \end{verbatim}
adamc@555 63
adamc@896 64 To build programs that access SQL databases, you also need one of these client libraries for supported backends.
adamc@555 65 \begin{verbatim}
adamc@896 66 apt-get install libpq-dev libmysqlclient15-dev libsqlite3-dev
adamc@555 67 \end{verbatim}
adamc@555 68
adamc@555 69 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 70 \begin{verbatim}
adamc@555 71 apt-get install smlnj libsmlnj-smlnj ml-yacc ml-lpt
adamc@555 72 \end{verbatim}
adamc@555 73
adamc@555 74 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 75
adamc@896 76 To run an SQL-backed application with a backend besides SQLite, you will probably want to install one of these servers.
adamc@555 77
adamc@555 78 \begin{verbatim}
adam@1400 79 apt-get install postgresql-8.4 mysql-server-5.1
adamc@555 80 \end{verbatim}
adamc@555 81
adamc@555 82 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 83
adamc@555 84 \begin{verbatim}
adamc@555 85 apt-get install emacs-goodies-el
adamc@555 86 \end{verbatim}
adamc@555 87
adam@1441 88 If you don't want to install the Emacs mode, run \texttt{./configure} with the argument \texttt{--without-emacs}.
adam@1441 89
adamc@555 90 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 GCC on every invocation.
adamc@555 91
adamc@555 92 \begin{verbatim}
adamc@555 93 GCCARGS=-fnested-functions ./configure
adamc@555 94 \end{verbatim}
adamc@555 95
adamc@1137 96 Some Mac OS X users have reported needing to use this particular GCCARGS value.
adamc@1137 97
adam@1464 98 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{GCCARGS="-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 99
adamc@555 100 The Emacs mode can be set to autoload by adding the following to your \texttt{.emacs} file.
adamc@555 101
adamc@555 102 \begin{verbatim}
adamc@555 103 (add-to-list 'load-path "/usr/local/share/emacs/site-lisp/urweb-mode")
adamc@555 104 (load "urweb-mode-startup")
adamc@555 105 \end{verbatim}
adamc@555 106
adamc@555 107 Change the path in the first line if you chose a different Emacs installation path during configuration.
adamc@555 108
adamc@555 109
adamc@556 110 \section{Command-Line Compiler}
adamc@556 111
adamc@556 112 \subsection{Project Files}
adamc@556 113
adamc@556 114 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@556 115
adamc@556 116 \begin{verbatim}
adamc@556 117 database dbname=test
adamc@556 118 sql crud1.sql
adamc@556 119
adamc@556 120 crud
adamc@556 121 crud1
adamc@556 122 \end{verbatim}
adamc@556 123
adamc@556 124 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@556 125
adamc@556 126 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@556 127
adamc@556 128 \begin{verbatim}
adamc@556 129 createdb test
adamc@556 130 psql -f crud1.sql test
adamc@556 131 \end{verbatim}
adamc@556 132
adam@1331 133 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@556 134
adamc@556 135 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@556 136
adamc@783 137 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@783 138 \begin{itemize}
adam@1465 139 \item \texttt{[allow|deny] [url|mime|requestHeader|responseHeader] PATTERN} registers a rule governing which URLs, MIME types, HTTP request headers, or HTTP response headers 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 140 \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 141 \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@783 142 \item \texttt{clientOnly Module.ident} registers an FFI function or transaction that may only be run in client browsers.
adamc@783 143 \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.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.
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.
adamc@783 146 \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. Every effectful FFI function must be registered, or the optimizer may make invalid transformations.
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}.
adamc@783 148 \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.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@1309 155 \item \texttt{database}: maximum size of database files (currently only used by SQLite)
adam@1309 156 \item \texttt{deltas}: maximum number of messages sendable in a single request handler with \texttt{Basis.send}
adam@1309 157 \item \texttt{globals}: maximum number of global variables that FFI libraries may set in a single request context
adam@1309 158 \item \texttt{headers}: maximum size (in bytes) of per-request buffer used to hold HTTP headers for generated pages
adam@1309 159 \item \texttt{heap}: maximum size (in bytes) of per-request heap for dynamically-allocated data
adam@1309 160 \item \texttt{inputs}: maximum number of top-level form fields per request
adam@1309 161 \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 162 \item \texttt{page}: maximum size (in bytes) of per-request buffer used to hold HTML content of generated pages
adam@1309 163 \item \texttt{script}: maximum size (in bytes) of per-request buffer used to hold JavaScript content of generated pages
adam@1309 164 \item \texttt{subinputs}: maximum number of form fields per request, excluding top-level fields
adam@1309 165 \item \texttt{time}: maximum running time of a single page request, in units of approximately 0.1 seconds
adam@1309 166 \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 167 \end{itemize}
adamc@783 168 \item \texttt{link FILENAME} adds \texttt{FILENAME} to the list of files to be passed to the GCC linker at the end of compilation. This is most useful for importing extra libraries needed by new FFI modules.
adam@1332 169 \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@1297 170 \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@852 171 \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@783 172 \item \texttt{prefix PREFIX} sets the prefix included before every URI within the generated application. The default is \texttt{/}.
adamc@783 173 \item \texttt{profile} generates an executable that may be used with gprof.
adam@1300 174 \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.
adamc@1183 175 \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@783 176 \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@783 177 \item \texttt{serverOnly Module.ident} registers an FFI function or transaction that may only be run on the server.
adamc@1164 178 \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@783 179 \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.
adamc@783 180 \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@783 181 \end{itemize}
adamc@701 182
adamc@701 183
adamc@557 184 \subsection{Building an Application}
adamc@557 185
adamc@557 186 To compile project \texttt{P.urp}, simply run
adamc@557 187 \begin{verbatim}
adamc@557 188 urweb P
adamc@557 189 \end{verbatim}
adamc@1198 190 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@557 191
adamc@557 192 To time how long the different compiler phases run, without generating an executable, run
adamc@557 193 \begin{verbatim}
adamc@557 194 urweb -timing P
adamc@557 195 \end{verbatim}
adamc@557 196
adamc@1086 197 To stop the compilation process after type-checking, run
adamc@1086 198 \begin{verbatim}
adamc@1086 199 urweb -tc P
adamc@1086 200 \end{verbatim}
adamc@1086 201
adamc@1170 202 To output information relevant to CSS stylesheets (and not finish regular compilation), run
adamc@1170 203 \begin{verbatim}
adamc@1170 204 urweb -css P
adamc@1170 205 \end{verbatim}
adamc@1170 206 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 207
adamc@896 208 Some other command-line parameters are accepted:
adamc@896 209 \begin{itemize}
adamc@896 210 \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@896 211
adamc@896 212 \item \texttt{-dbms [postgres|mysql|sqlite]}: Sets the database backend to use.
adamc@896 213 \begin{itemize}
adamc@896 214 \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@896 215
adamc@896 216 A command sequence like this can initialize a Postgres database, using a file \texttt{app.sql} generated by the compiler:
adamc@896 217 \begin{verbatim}
adamc@896 218 createdb app
adamc@896 219 psql -f app.sql app
adamc@896 220 \end{verbatim}
adamc@896 221
adamc@896 222 \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@896 223
adamc@896 224 A command sequence like this can initialize a MySQL database:
adamc@896 225 \begin{verbatim}
adamc@896 226 echo "CREATE DATABASE app" | mysql
adamc@896 227 mysql -D app <app.sql
adamc@896 228 \end{verbatim}
adamc@896 229
adamc@896 230 \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@896 231
adamc@896 232 A command like this can initialize an SQLite database:
adamc@896 233 \begin{verbatim}
adamc@896 234 sqlite3 path/to/database/file <app.sql
adamc@896 235 \end{verbatim}
adamc@896 236 \end{itemize}
adamc@896 237
adam@1309 238 \item \texttt{-limit class num}: Equivalent to the \texttt{limit} directive from \texttt{.urp} files
adam@1309 239
adamc@896 240 \item \texttt{-output FILENAME}: Set where the application executable is written.
adamc@896 241
adamc@1127 242 \item \texttt{-path NAME VALUE}: Set the value of path variable \texttt{\$NAME} to \texttt{VALUE}, for use in \texttt{.urp} files.
adamc@1127 243
adam@1335 244 \item \texttt{-prefix PREFIX}: Equivalent to the \texttt{prefix} directive from \texttt{.urp} files
adam@1335 245
adamc@896 246 \item \texttt{-protocol [http|cgi|fastcgi]}: Set the protocol that the generated application speaks.
adamc@896 247 \begin{itemize}
adamc@896 248 \item \texttt{http}: This is the default. It is for building standalone web servers that can be accessed by web browsers directly.
adamc@896 249
adamc@896 250 \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@896 251
adamc@896 252 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@896 253 \begin{verbatim}
adamc@896 254 ScriptAlias /Hello /path/to/hello.exe
adamc@896 255 \end{verbatim}
adamc@896 256
adamc@1163 257 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 258 \begin{verbatim}
adamc@1163 259 Options +ExecCGI
adamc@1163 260 AddHandler cgi-script .exe
adamc@1163 261 \end{verbatim}
adamc@1163 262
adamc@1163 263 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 264 \begin{verbatim}
adamc@1163 265 prefix /dir/script.exe/
adamc@1163 266 \end{verbatim}
adamc@1163 267
adamc@1163 268 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 269
adamc@1164 270 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 271
adamc@896 272 \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@896 273
adamc@896 274 To configure a FastCGI program with Apache, one could combine the above \texttt{ScriptAlias} line with a line like this:
adamc@896 275 \begin{verbatim}
adamc@896 276 FastCgiServer /path/to/hello.exe -idle-timeout 99999
adamc@896 277 \end{verbatim}
adamc@896 278 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@896 279
adamc@896 280 Here is some lighttpd configuration for the same application.
adamc@896 281 \begin{verbatim}
adamc@896 282 fastcgi.server = (
adamc@896 283 "/Hello/" =>
adamc@896 284 (( "bin-path" => "/path/to/hello.exe",
adamc@896 285 "socket" => "/tmp/hello",
adamc@896 286 "check-local" => "disable",
adamc@896 287 "docroot" => "/",
adamc@896 288 "max-procs" => "1"
adamc@896 289 ))
adamc@896 290 )
adamc@896 291 \end{verbatim}
adamc@896 292 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@896 293
adamc@896 294 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.
adamc@896 295 \end{itemize}
adamc@896 296
adamc@1127 297 \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 298
adamc@1164 299 \item \texttt{-sigfile PATH}: Same as the \texttt{sigfile} directive in \texttt{.urp} files
adamc@1164 300
adamc@896 301 \item \texttt{-sql FILENAME}: Set where a database set-up SQL script is written.
adamc@1095 302
adamc@1095 303 \item \texttt{-static}: Link the runtime system statically. The default is to link against dynamic libraries.
adamc@896 304 \end{itemize}
adamc@896 305
adam@1297 306 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@556 307
adamc@529 308 \section{Ur Syntax}
adamc@529 309
adamc@784 310 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@524 311
adamc@524 312 \subsection{Lexical Conventions}
adamc@524 313
adamc@524 314 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@524 315
adamc@524 316 \begin{center}
adamc@524 317 \begin{tabular}{rl}
adamc@524 318 \textbf{\LaTeX} & \textbf{ASCII} \\
adamc@524 319 $\to$ & \cd{->} \\
adamc@652 320 $\longrightarrow$ & \cd{-->} \\
adamc@524 321 $\times$ & \cd{*} \\
adamc@524 322 $\lambda$ & \cd{fn} \\
adamc@524 323 $\Rightarrow$ & \cd{=>} \\
adamc@652 324 $\Longrightarrow$ & \cd{==>} \\
adamc@529 325 $\neq$ & \cd{<>} \\
adamc@529 326 $\leq$ & \cd{<=} \\
adamc@529 327 $\geq$ & \cd{>=} \\
adamc@524 328 \\
adamc@524 329 $x$ & Normal textual identifier, not beginning with an uppercase letter \\
adamc@525 330 $X$ & Normal textual identifier, beginning with an uppercase letter \\
adamc@524 331 \end{tabular}
adamc@524 332 \end{center}
adamc@524 333
adamc@525 334 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@524 335
adamc@873 336 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@526 337
adamc@527 338 This version of the manual doesn't include operator precedences; see \texttt{src/urweb.grm} for that.
adamc@527 339
adam@1297 340 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 341
adamc@552 342 \subsection{\label{core}Core Syntax}
adamc@524 343
adamc@524 344 \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@524 345 $$\begin{array}{rrcll}
adamc@524 346 \textrm{Kinds} & \kappa &::=& \mt{Type} & \textrm{proper types} \\
adamc@525 347 &&& \mt{Unit} & \textrm{the trivial constructor} \\
adamc@525 348 &&& \mt{Name} & \textrm{field names} \\
adamc@525 349 &&& \kappa \to \kappa & \textrm{type-level functions} \\
adamc@525 350 &&& \{\kappa\} & \textrm{type-level records} \\
adamc@525 351 &&& (\kappa\times^+) & \textrm{type-level tuples} \\
adamc@652 352 &&& X & \textrm{variable} \\
adamc@652 353 &&& X \longrightarrow k & \textrm{kind-polymorphic type-level function} \\
adamc@529 354 &&& \_\_ & \textrm{wildcard} \\
adamc@525 355 &&& (\kappa) & \textrm{explicit precedence} \\
adamc@524 356 \end{array}$$
adamc@524 357
adamc@524 358 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@524 359 $$\begin{array}{rrcll}
adamc@524 360 \textrm{Explicitness} & ? &::=& :: & \textrm{explicit} \\
adamc@558 361 &&& ::: & \textrm{implicit}
adamc@524 362 \end{array}$$
adamc@524 363
adamc@524 364 \emph{Constructors} are the main class of compile-time-only data. They include proper types and are classified by kinds.
adamc@524 365 $$\begin{array}{rrcll}
adamc@524 366 \textrm{Constructors} & c, \tau &::=& (c) :: \kappa & \textrm{kind annotation} \\
adamc@530 367 &&& \hat{x} & \textrm{constructor variable} \\
adamc@524 368 \\
adamc@525 369 &&& \tau \to \tau & \textrm{function type} \\
adamc@525 370 &&& x \; ? \; \kappa \to \tau & \textrm{polymorphic function type} \\
adamc@652 371 &&& X \longrightarrow \tau & \textrm{kind-polymorphic function type} \\
adamc@525 372 &&& \$ c & \textrm{record type} \\
adamc@524 373 \\
adamc@525 374 &&& c \; c & \textrm{type-level function application} \\
adamc@530 375 &&& \lambda x \; :: \; \kappa \Rightarrow c & \textrm{type-level function abstraction} \\
adamc@524 376 \\
adamc@652 377 &&& X \Longrightarrow c & \textrm{type-level kind-polymorphic function abstraction} \\
adamc@655 378 &&& c [\kappa] & \textrm{type-level kind-polymorphic function application} \\
adamc@652 379 \\
adamc@525 380 &&& () & \textrm{type-level unit} \\
adamc@525 381 &&& \#X & \textrm{field name} \\
adamc@524 382 \\
adamc@525 383 &&& [(c = c)^*] & \textrm{known-length type-level record} \\
adamc@525 384 &&& c \rc c & \textrm{type-level record concatenation} \\
adamc@652 385 &&& \mt{map} & \textrm{type-level record map} \\
adamc@524 386 \\
adamc@558 387 &&& (c,^+) & \textrm{type-level tuple} \\
adamc@525 388 &&& c.n & \textrm{type-level tuple projection ($n \in \mathbb N^+$)} \\
adamc@524 389 \\
adamc@652 390 &&& [c \sim c] \Rightarrow \tau & \textrm{guarded type} \\
adamc@524 391 \\
adamc@529 392 &&& \_ :: \kappa & \textrm{wildcard} \\
adamc@525 393 &&& (c) & \textrm{explicit precedence} \\
adamc@530 394 \\
adamc@530 395 \textrm{Qualified uncapitalized variables} & \hat{x} &::=& x & \textrm{not from a module} \\
adamc@530 396 &&& M.x & \textrm{projection from a module} \\
adamc@525 397 \end{array}$$
adamc@525 398
adamc@655 399 We include both abstraction and application for kind polymorphism, but applications are only inferred internally; they may not be written explicitly in source programs.
adamc@655 400
adamc@525 401 Modules of the module system are described by \emph{signatures}.
adamc@525 402 $$\begin{array}{rrcll}
adamc@525 403 \textrm{Signatures} & S &::=& \mt{sig} \; s^* \; \mt{end} & \textrm{constant} \\
adamc@525 404 &&& X & \textrm{variable} \\
adamc@525 405 &&& \mt{functor}(X : S) : S & \textrm{functor} \\
adamc@529 406 &&& S \; \mt{where} \; \mt{con} \; x = c & \textrm{concretizing an abstract constructor} \\
adamc@525 407 &&& M.X & \textrm{projection from a module} \\
adamc@525 408 \\
adamc@525 409 \textrm{Signature items} & s &::=& \mt{con} \; x :: \kappa & \textrm{abstract constructor} \\
adamc@525 410 &&& \mt{con} \; x :: \kappa = c & \textrm{concrete constructor} \\
adamc@528 411 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529 412 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@525 413 &&& \mt{val} \; x : \tau & \textrm{value} \\
adamc@525 414 &&& \mt{structure} \; X : S & \textrm{sub-module} \\
adamc@525 415 &&& \mt{signature} \; X = S & \textrm{sub-signature} \\
adamc@525 416 &&& \mt{include} \; S & \textrm{signature inclusion} \\
adamc@525 417 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@654 418 &&& \mt{class} \; x :: \kappa & \textrm{abstract constructor class} \\
adamc@654 419 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@525 420 \\
adamc@525 421 \textrm{Datatype constructors} & dc &::=& X & \textrm{nullary constructor} \\
adamc@525 422 &&& X \; \mt{of} \; \tau & \textrm{unary constructor} \\
adamc@524 423 \end{array}$$
adamc@524 424
adamc@526 425 \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@526 426 $$\begin{array}{rrcll}
adamc@526 427 \textrm{Patterns} & p &::=& \_ & \textrm{wildcard} \\
adamc@526 428 &&& x & \textrm{variable} \\
adamc@526 429 &&& \ell & \textrm{constant} \\
adamc@526 430 &&& \hat{X} & \textrm{nullary constructor} \\
adamc@526 431 &&& \hat{X} \; p & \textrm{unary constructor} \\
adamc@526 432 &&& \{(x = p,)^*\} & \textrm{rigid record pattern} \\
adamc@526 433 &&& \{(x = p,)^+, \ldots\} & \textrm{flexible record pattern} \\
adamc@852 434 &&& p : \tau & \textrm{type annotation} \\
adamc@527 435 &&& (p) & \textrm{explicit precedence} \\
adamc@526 436 \\
adamc@529 437 \textrm{Qualified capitalized variables} & \hat{X} &::=& X & \textrm{not from a module} \\
adamc@526 438 &&& M.X & \textrm{projection from a module} \\
adamc@526 439 \end{array}$$
adamc@526 440
adamc@527 441 \emph{Expressions} are the main run-time entities, corresponding to both ``expressions'' and ``statements'' in mainstream imperative languages.
adamc@527 442 $$\begin{array}{rrcll}
adamc@527 443 \textrm{Expressions} & e &::=& e : \tau & \textrm{type annotation} \\
adamc@529 444 &&& \hat{x} & \textrm{variable} \\
adamc@529 445 &&& \hat{X} & \textrm{datatype constructor} \\
adamc@527 446 &&& \ell & \textrm{constant} \\
adamc@527 447 \\
adamc@527 448 &&& e \; e & \textrm{function application} \\
adamc@527 449 &&& \lambda x : \tau \Rightarrow e & \textrm{function abstraction} \\
adamc@527 450 &&& e [c] & \textrm{polymorphic function application} \\
adamc@852 451 &&& \lambda [x \; ? \; \kappa] \Rightarrow e & \textrm{polymorphic function abstraction} \\
adamc@655 452 &&& e [\kappa] & \textrm{kind-polymorphic function application} \\
adamc@652 453 &&& X \Longrightarrow e & \textrm{kind-polymorphic function abstraction} \\
adamc@527 454 \\
adamc@527 455 &&& \{(c = e,)^*\} & \textrm{known-length record} \\
adamc@527 456 &&& e.c & \textrm{record field projection} \\
adamc@527 457 &&& e \rc e & \textrm{record concatenation} \\
adamc@527 458 &&& e \rcut c & \textrm{removal of a single record field} \\
adamc@527 459 &&& e \rcutM c & \textrm{removal of multiple record fields} \\
adamc@527 460 \\
adamc@527 461 &&& \mt{let} \; ed^* \; \mt{in} \; e \; \mt{end} & \textrm{local definitions} \\
adamc@527 462 \\
adamc@527 463 &&& \mt{case} \; e \; \mt{of} \; (p \Rightarrow e|)^+ & \textrm{pattern matching} \\
adamc@527 464 \\
adamc@654 465 &&& \lambda [c \sim c] \Rightarrow e & \textrm{guarded expression abstraction} \\
adamc@654 466 &&& e \; ! & \textrm{guarded expression application} \\
adamc@527 467 \\
adamc@527 468 &&& \_ & \textrm{wildcard} \\
adamc@527 469 &&& (e) & \textrm{explicit precedence} \\
adamc@527 470 \\
adamc@527 471 \textrm{Local declarations} & ed &::=& \cd{val} \; x : \tau = e & \textrm{non-recursive value} \\
adamc@527 472 &&& \cd{val} \; \cd{rec} \; (x : \tau = e \; \cd{and})^+ & \textrm{mutually-recursive values} \\
adamc@527 473 \end{array}$$
adamc@527 474
adamc@655 475 As with constructors, we include both abstraction and application for kind polymorphism, but applications are only inferred internally.
adamc@655 476
adamc@528 477 \emph{Declarations} primarily bring new symbols into context.
adamc@528 478 $$\begin{array}{rrcll}
adamc@528 479 \textrm{Declarations} & d &::=& \mt{con} \; x :: \kappa = c & \textrm{constructor synonym} \\
adamc@528 480 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529 481 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@528 482 &&& \mt{val} \; x : \tau = e & \textrm{value} \\
adamc@528 483 &&& \mt{val} \; \cd{rec} \; (x : \tau = e \; \mt{and})^+ & \textrm{mutually-recursive values} \\
adamc@528 484 &&& \mt{structure} \; X : S = M & \textrm{module definition} \\
adamc@528 485 &&& \mt{signature} \; X = S & \textrm{signature definition} \\
adamc@528 486 &&& \mt{open} \; M & \textrm{module inclusion} \\
adamc@528 487 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@528 488 &&& \mt{open} \; \mt{constraints} \; M & \textrm{inclusion of just the constraints from a module} \\
adamc@528 489 &&& \mt{table} \; x : c & \textrm{SQL table} \\
adamc@784 490 &&& \mt{view} \; x : c & \textrm{SQL view} \\
adamc@528 491 &&& \mt{sequence} \; x & \textrm{SQL sequence} \\
adamc@535 492 &&& \mt{cookie} \; x : \tau & \textrm{HTTP cookie} \\
adamc@784 493 &&& \mt{style} \; x : \tau & \textrm{CSS class} \\
adamc@654 494 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@1085 495 &&& \mt{task} \; e = e & \textrm{recurring task} \\
adamc@528 496 \\
adamc@529 497 \textrm{Modules} & M &::=& \mt{struct} \; d^* \; \mt{end} & \textrm{constant} \\
adamc@529 498 &&& X & \textrm{variable} \\
adamc@529 499 &&& M.X & \textrm{projection} \\
adamc@529 500 &&& M(M) & \textrm{functor application} \\
adamc@529 501 &&& \mt{functor}(X : S) : S = M & \textrm{functor abstraction} \\
adamc@528 502 \end{array}$$
adamc@528 503
adamc@528 504 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@527 505
adamc@784 506 We omit some extra possibilities in $\mt{table}$ syntax, deferring them to Section \ref{tables}.
adamc@784 507
adamc@529 508 \subsection{Shorthands}
adamc@529 509
adamc@529 510 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@529 511
adamc@529 512 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@529 513
adamc@529 514 A record type may be written $\{(c = c,)^*\}$, which elaborates to $\$[(c = c,)^*]$.
adamc@529 515
adamc@533 516 The notation $[c_1, \ldots, c_n]$ is shorthand for $[c_1 = (), \ldots, c_n = ()]$.
adamc@533 517
adam@1350 518 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@529 519
adamc@852 520 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@529 521
adam@1306 522 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 523
adamc@529 524 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@529 525
adamc@529 526 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@529 527
adamc@654 528 A signature item or declaration $\mt{class} \; x = \lambda y \Rightarrow c$ may be abbreviated $\mt{class} \; x \; y = c$.
adamc@529 529
adam@1472 530 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. 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@529 531
adamc@852 532 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@529 533
adamc@852 534 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@852 535
adamc@852 536 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@529 537
adamc@529 538 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@529 539
adamc@852 540 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@852 541
adamc@853 542 A declaration $\mt{table} \; x : \{(c = c,)^*\}$ is elaborated into $\mt{table} \; x : [(c = c,)^*]$.
adamc@529 543
adamc@529 544 The syntax $\mt{where} \; \mt{type}$ is an alternate form of $\mt{where} \; \mt{con}$.
adamc@529 545
adamc@529 546 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@529 547
adamc@529 548 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@529 549
adamc@784 550 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@529 551
adamc@530 552
adamc@530 553 \section{Static Semantics}
adamc@530 554
adamc@530 555 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@530 556
adamc@530 557 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@530 558 \begin{itemize}
adamc@655 559 \item $\Gamma \vdash \kappa$ expresses kind well-formedness.
adamc@530 560 \item $\Gamma \vdash c :: \kappa$ assigns a kind to a constructor in a context.
adamc@530 561 \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@531 562 \item $\Gamma \vdash c \hookrightarrow C$ proves that record constructor $c$ decomposes into set $C$ of field names and record constructors.
adamc@530 563 \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@530 564 \item $\Gamma \vdash e : \tau$ is a standard typing judgment.
adamc@534 565 \item $\Gamma \vdash p \leadsto \Gamma; \tau$ combines typing of patterns with calculation of which new variables they bind.
adamc@537 566 \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@537 567 \item $\Gamma \vdash S \equiv S$ is the signature equivalence judgment.
adamc@536 568 \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@530 569 \item $\Gamma \vdash M : S$ is the module signature checking judgment.
adamc@537 570 \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@539 571 \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@530 572 \end{itemize}
adamc@530 573
adamc@655 574
adamc@655 575 \subsection{Kind Well-Formedness}
adamc@655 576
adamc@655 577 $$\infer{\Gamma \vdash \mt{Type}}{}
adamc@655 578 \quad \infer{\Gamma \vdash \mt{Unit}}{}
adamc@655 579 \quad \infer{\Gamma \vdash \mt{Name}}{}
adamc@655 580 \quad \infer{\Gamma \vdash \kappa_1 \to \kappa_2}{
adamc@655 581 \Gamma \vdash \kappa_1
adamc@655 582 & \Gamma \vdash \kappa_2
adamc@655 583 }
adamc@655 584 \quad \infer{\Gamma \vdash \{\kappa\}}{
adamc@655 585 \Gamma \vdash \kappa
adamc@655 586 }
adamc@655 587 \quad \infer{\Gamma \vdash (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@655 588 \forall i: \Gamma \vdash \kappa_i
adamc@655 589 }$$
adamc@655 590
adamc@655 591 $$\infer{\Gamma \vdash X}{
adamc@655 592 X \in \Gamma
adamc@655 593 }
adamc@655 594 \quad \infer{\Gamma \vdash X \longrightarrow \kappa}{
adamc@655 595 \Gamma, X \vdash \kappa
adamc@655 596 }$$
adamc@655 597
adamc@530 598 \subsection{Kinding}
adamc@530 599
adamc@655 600 We write $[X \mapsto \kappa_1]\kappa_2$ for capture-avoiding substitution of $\kappa_1$ for $X$ in $\kappa_2$.
adamc@655 601
adamc@530 602 $$\infer{\Gamma \vdash (c) :: \kappa :: \kappa}{
adamc@530 603 \Gamma \vdash c :: \kappa
adamc@530 604 }
adamc@530 605 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530 606 x :: \kappa \in \Gamma
adamc@530 607 }
adamc@530 608 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530 609 x :: \kappa = c \in \Gamma
adamc@530 610 }$$
adamc@530 611
adamc@530 612 $$\infer{\Gamma \vdash M.x :: \kappa}{
adamc@537 613 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 614 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = \kappa
adamc@530 615 }
adamc@530 616 \quad \infer{\Gamma \vdash M.x :: \kappa}{
adamc@537 617 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 618 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@530 619 }$$
adamc@530 620
adamc@530 621 $$\infer{\Gamma \vdash \tau_1 \to \tau_2 :: \mt{Type}}{
adamc@530 622 \Gamma \vdash \tau_1 :: \mt{Type}
adamc@530 623 & \Gamma \vdash \tau_2 :: \mt{Type}
adamc@530 624 }
adamc@530 625 \quad \infer{\Gamma \vdash x \; ? \: \kappa \to \tau :: \mt{Type}}{
adamc@530 626 \Gamma, x :: \kappa \vdash \tau :: \mt{Type}
adamc@530 627 }
adamc@655 628 \quad \infer{\Gamma \vdash X \longrightarrow \tau :: \mt{Type}}{
adamc@655 629 \Gamma, X \vdash \tau :: \mt{Type}
adamc@655 630 }
adamc@530 631 \quad \infer{\Gamma \vdash \$c :: \mt{Type}}{
adamc@530 632 \Gamma \vdash c :: \{\mt{Type}\}
adamc@530 633 }$$
adamc@530 634
adamc@530 635 $$\infer{\Gamma \vdash c_1 \; c_2 :: \kappa_2}{
adamc@530 636 \Gamma \vdash c_1 :: \kappa_1 \to \kappa_2
adamc@530 637 & \Gamma \vdash c_2 :: \kappa_1
adamc@530 638 }
adamc@530 639 \quad \infer{\Gamma \vdash \lambda x \; :: \; \kappa_1 \Rightarrow c :: \kappa_1 \to \kappa_2}{
adamc@530 640 \Gamma, x :: \kappa_1 \vdash c :: \kappa_2
adamc@530 641 }$$
adamc@530 642
adamc@655 643 $$\infer{\Gamma \vdash c[\kappa'] :: [X \mapsto \kappa']\kappa}{
adamc@655 644 \Gamma \vdash c :: X \to \kappa
adamc@655 645 & \Gamma \vdash \kappa'
adamc@655 646 }
adamc@655 647 \quad \infer{\Gamma \vdash X \Longrightarrow c :: X \to \kappa}{
adamc@655 648 \Gamma, X \vdash c :: \kappa
adamc@655 649 }$$
adamc@655 650
adamc@530 651 $$\infer{\Gamma \vdash () :: \mt{Unit}}{}
adamc@530 652 \quad \infer{\Gamma \vdash \#X :: \mt{Name}}{}$$
adamc@530 653
adamc@530 654 $$\infer{\Gamma \vdash [\overline{c_i = c'_i}] :: \{\kappa\}}{
adamc@530 655 \forall i: \Gamma \vdash c_i : \mt{Name}
adamc@530 656 & \Gamma \vdash c'_i :: \kappa
adamc@530 657 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@530 658 }
adamc@530 659 \quad \infer{\Gamma \vdash c_1 \rc c_2 :: \{\kappa\}}{
adamc@530 660 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530 661 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@530 662 & \Gamma \vdash c_1 \sim c_2
adamc@530 663 }$$
adamc@530 664
adamc@655 665 $$\infer{\Gamma \vdash \mt{map} :: (\kappa_1 \to \kappa_2) \to \{\kappa_1\} \to \{\kappa_2\}}{}$$
adamc@530 666
adamc@573 667 $$\infer{\Gamma \vdash (\overline c) :: (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@573 668 \forall i: \Gamma \vdash c_i :: \kappa_i
adamc@530 669 }
adamc@573 670 \quad \infer{\Gamma \vdash c.i :: \kappa_i}{
adamc@573 671 \Gamma \vdash c :: (\kappa_1 \times \ldots \times \kappa_n)
adamc@530 672 }$$
adamc@530 673
adamc@655 674 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow \tau :: \mt{Type}}{
adamc@655 675 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530 676 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@655 677 & \Gamma, c_1 \sim c_2 \vdash \tau :: \mt{Type}
adamc@530 678 }$$
adamc@530 679
adamc@531 680 \subsection{Record Disjointness}
adamc@531 681
adamc@531 682 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@558 683 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@558 684 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@558 685 & \forall c'_1 \in C_1, c'_2 \in C_2: \Gamma \vdash c'_1 \sim c'_2
adamc@531 686 }
adamc@531 687 \quad \infer{\Gamma \vdash X \sim X'}{
adamc@531 688 X \neq X'
adamc@531 689 }$$
adamc@531 690
adamc@531 691 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@531 692 c'_1 \sim c'_2 \in \Gamma
adamc@558 693 & \Gamma \vdash c'_1 \hookrightarrow C_1
adamc@558 694 & \Gamma \vdash c'_2 \hookrightarrow C_2
adamc@558 695 & c_1 \in C_1
adamc@558 696 & c_2 \in C_2
adamc@531 697 }$$
adamc@531 698
adamc@531 699 $$\infer{\Gamma \vdash c \hookrightarrow \{c\}}{}
adamc@531 700 \quad \infer{\Gamma \vdash [\overline{c = c'}] \hookrightarrow \{\overline{c}\}}{}
adamc@531 701 \quad \infer{\Gamma \vdash c_1 \rc c_2 \hookrightarrow C_1 \cup C_2}{
adamc@531 702 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@531 703 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@531 704 }
adamc@531 705 \quad \infer{\Gamma \vdash c \hookrightarrow C}{
adamc@531 706 \Gamma \vdash c \equiv c'
adamc@531 707 & \Gamma \vdash c' \hookrightarrow C
adamc@531 708 }
adamc@531 709 \quad \infer{\Gamma \vdash \mt{map} \; f \; c \hookrightarrow C}{
adamc@531 710 \Gamma \vdash c \hookrightarrow C
adamc@531 711 }$$
adamc@531 712
adamc@541 713 \subsection{\label{definitional}Definitional Equality}
adamc@532 714
adamc@655 715 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@532 716
adamc@532 717 $$\infer{\Gamma \vdash c \equiv c}{}
adamc@532 718 \quad \infer{\Gamma \vdash c_1 \equiv c_2}{
adamc@532 719 \Gamma \vdash c_2 \equiv c_1
adamc@532 720 }
adamc@532 721 \quad \infer{\Gamma \vdash c_1 \equiv c_3}{
adamc@532 722 \Gamma \vdash c_1 \equiv c_2
adamc@532 723 & \Gamma \vdash c_2 \equiv c_3
adamc@532 724 }
adamc@532 725 \quad \infer{\Gamma \vdash \mathcal C[c_1] \equiv \mathcal C[c_2]}{
adamc@532 726 \Gamma \vdash c_1 \equiv c_2
adamc@532 727 }$$
adamc@532 728
adamc@532 729 $$\infer{\Gamma \vdash x \equiv c}{
adamc@532 730 x :: \kappa = c \in \Gamma
adamc@532 731 }
adamc@532 732 \quad \infer{\Gamma \vdash M.x \equiv c}{
adamc@537 733 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 734 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@532 735 }
adamc@532 736 \quad \infer{\Gamma \vdash (\overline c).i \equiv c_i}{}$$
adamc@532 737
adamc@532 738 $$\infer{\Gamma \vdash (\lambda x :: \kappa \Rightarrow c) \; c' \equiv [x \mapsto c'] c}{}
adamc@655 739 \quad \infer{\Gamma \vdash (X \Longrightarrow c) [\kappa] \equiv [X \mapsto \kappa] c}{}$$
adamc@655 740
adamc@655 741 $$\infer{\Gamma \vdash c_1 \rc c_2 \equiv c_2 \rc c_1}{}
adamc@532 742 \quad \infer{\Gamma \vdash c_1 \rc (c_2 \rc c_3) \equiv (c_1 \rc c_2) \rc c_3}{}$$
adamc@532 743
adamc@532 744 $$\infer{\Gamma \vdash [] \rc c \equiv c}{}
adamc@532 745 \quad \infer{\Gamma \vdash [\overline{c_1 = c'_1}] \rc [\overline{c_2 = c'_2}] \equiv [\overline{c_1 = c'_1}, \overline{c_2 = c'_2}]}{}$$
adamc@532 746
adamc@655 747 $$\infer{\Gamma \vdash \mt{map} \; f \; [] \equiv []}{}
adamc@655 748 \quad \infer{\Gamma \vdash \mt{map} \; f \; ([c_1 = c_2] \rc c) \equiv [c_1 = f \; c_2] \rc \mt{map} \; f \; c}{}$$
adamc@532 749
adamc@532 750 $$\infer{\Gamma \vdash \mt{map} \; (\lambda x \Rightarrow x) \; c \equiv c}{}
adamc@655 751 \quad \infer{\Gamma \vdash \mt{map} \; f \; (\mt{map} \; f' \; c)
adamc@655 752 \equiv \mt{map} \; (\lambda x \Rightarrow f \; (f' \; x)) \; c}{}$$
adamc@532 753
adamc@532 754 $$\infer{\Gamma \vdash \mt{map} \; f \; (c_1 \rc c_2) \equiv \mt{map} \; f \; c_1 \rc \mt{map} \; f \; c_2}{}$$
adamc@531 755
adamc@534 756 \subsection{Expression Typing}
adamc@533 757
adamc@873 758 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@533 759
adamc@533 760 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@533 761
adamc@533 762 $$\infer{\Gamma \vdash e : \tau : \tau}{
adamc@533 763 \Gamma \vdash e : \tau
adamc@533 764 }
adamc@533 765 \quad \infer{\Gamma \vdash e : \tau}{
adamc@533 766 \Gamma \vdash e : \tau'
adamc@533 767 & \Gamma \vdash \tau' \equiv \tau
adamc@533 768 }
adamc@533 769 \quad \infer{\Gamma \vdash \ell : T(\ell)}{}$$
adamc@533 770
adamc@533 771 $$\infer{\Gamma \vdash x : \mathcal I(\tau)}{
adamc@533 772 x : \tau \in \Gamma
adamc@533 773 }
adamc@533 774 \quad \infer{\Gamma \vdash M.x : \mathcal I(\tau)}{
adamc@537 775 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 776 & \mt{proj}(M, \overline{s}, \mt{val} \; x) = \tau
adamc@533 777 }
adamc@533 778 \quad \infer{\Gamma \vdash X : \mathcal I(\tau)}{
adamc@533 779 X : \tau \in \Gamma
adamc@533 780 }
adamc@533 781 \quad \infer{\Gamma \vdash M.X : \mathcal I(\tau)}{
adamc@537 782 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 783 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \tau
adamc@533 784 }$$
adamc@533 785
adamc@533 786 $$\infer{\Gamma \vdash e_1 \; e_2 : \tau_2}{
adamc@533 787 \Gamma \vdash e_1 : \tau_1 \to \tau_2
adamc@533 788 & \Gamma \vdash e_2 : \tau_1
adamc@533 789 }
adamc@533 790 \quad \infer{\Gamma \vdash \lambda x : \tau_1 \Rightarrow e : \tau_1 \to \tau_2}{
adamc@533 791 \Gamma, x : \tau_1 \vdash e : \tau_2
adamc@533 792 }$$
adamc@533 793
adamc@533 794 $$\infer{\Gamma \vdash e [c] : [x \mapsto c]\tau}{
adamc@533 795 \Gamma \vdash e : x :: \kappa \to \tau
adamc@533 796 & \Gamma \vdash c :: \kappa
adamc@533 797 }
adamc@852 798 \quad \infer{\Gamma \vdash \lambda [x \; ? \; \kappa] \Rightarrow e : x \; ? \; \kappa \to \tau}{
adamc@533 799 \Gamma, x :: \kappa \vdash e : \tau
adamc@533 800 }$$
adamc@533 801
adamc@655 802 $$\infer{\Gamma \vdash e [\kappa] : [X \mapsto \kappa]\tau}{
adamc@655 803 \Gamma \vdash e : X \longrightarrow \tau
adamc@655 804 & \Gamma \vdash \kappa
adamc@655 805 }
adamc@655 806 \quad \infer{\Gamma \vdash X \Longrightarrow e : X \longrightarrow \tau}{
adamc@655 807 \Gamma, X \vdash e : \tau
adamc@655 808 }$$
adamc@655 809
adamc@533 810 $$\infer{\Gamma \vdash \{\overline{c = e}\} : \{\overline{c : \tau}\}}{
adamc@533 811 \forall i: \Gamma \vdash c_i :: \mt{Name}
adamc@533 812 & \Gamma \vdash e_i : \tau_i
adamc@533 813 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@533 814 }
adamc@533 815 \quad \infer{\Gamma \vdash e.c : \tau}{
adamc@533 816 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533 817 }
adamc@533 818 \quad \infer{\Gamma \vdash e_1 \rc e_2 : \$(c_1 \rc c_2)}{
adamc@533 819 \Gamma \vdash e_1 : \$c_1
adamc@533 820 & \Gamma \vdash e_2 : \$c_2
adamc@573 821 & \Gamma \vdash c_1 \sim c_2
adamc@533 822 }$$
adamc@533 823
adamc@533 824 $$\infer{\Gamma \vdash e \rcut c : \$c'}{
adamc@533 825 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533 826 }
adamc@533 827 \quad \infer{\Gamma \vdash e \rcutM c : \$c'}{
adamc@533 828 \Gamma \vdash e : \$(c \rc c')
adamc@533 829 }$$
adamc@533 830
adamc@533 831 $$\infer{\Gamma \vdash \mt{let} \; \overline{ed} \; \mt{in} \; e \; \mt{end} : \tau}{
adamc@533 832 \Gamma \vdash \overline{ed} \leadsto \Gamma'
adamc@533 833 & \Gamma' \vdash e : \tau
adamc@533 834 }
adamc@533 835 \quad \infer{\Gamma \vdash \mt{case} \; e \; \mt{of} \; \overline{p \Rightarrow e} : \tau}{
adamc@533 836 \forall i: \Gamma \vdash p_i \leadsto \Gamma_i, \tau'
adamc@533 837 & \Gamma_i \vdash e_i : \tau
adamc@533 838 }$$
adamc@533 839
adamc@573 840 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow e : \lambda [c_1 \sim c_2] \Rightarrow \tau}{
adamc@533 841 \Gamma \vdash c_1 :: \{\kappa\}
adamc@655 842 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@533 843 & \Gamma, c_1 \sim c_2 \vdash e : \tau
adamc@662 844 }
adamc@662 845 \quad \infer{\Gamma \vdash e \; ! : \tau}{
adamc@662 846 \Gamma \vdash e : [c_1 \sim c_2] \Rightarrow \tau
adamc@662 847 & \Gamma \vdash c_1 \sim c_2
adamc@533 848 }$$
adamc@533 849
adamc@534 850 \subsection{Pattern Typing}
adamc@534 851
adamc@534 852 $$\infer{\Gamma \vdash \_ \leadsto \Gamma; \tau}{}
adamc@534 853 \quad \infer{\Gamma \vdash x \leadsto \Gamma, x : \tau; \tau}{}
adamc@534 854 \quad \infer{\Gamma \vdash \ell \leadsto \Gamma; T(\ell)}{}$$
adamc@534 855
adamc@534 856 $$\infer{\Gamma \vdash X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534 857 X : \overline{x ::: \mt{Type}} \to \tau \in \Gamma
adamc@534 858 & \textrm{$\tau$ not a function type}
adamc@534 859 }
adamc@534 860 \quad \infer{\Gamma \vdash X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534 861 X : \overline{x ::: \mt{Type}} \to \tau'' \to \tau \in \Gamma
adamc@534 862 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534 863 }$$
adamc@534 864
adamc@534 865 $$\infer{\Gamma \vdash M.X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537 866 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 867 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau
adamc@534 868 & \textrm{$\tau$ not a function type}
adamc@534 869 }$$
adamc@534 870
adamc@534 871 $$\infer{\Gamma \vdash M.X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537 872 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 873 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau'' \to \tau
adamc@534 874 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534 875 }$$
adamc@534 876
adamc@534 877 $$\infer{\Gamma \vdash \{\overline{x = p}\} \leadsto \Gamma_n; \{\overline{x = \tau}\}}{
adamc@534 878 \Gamma_0 = \Gamma
adamc@534 879 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534 880 }
adamc@534 881 \quad \infer{\Gamma \vdash \{\overline{x = p}, \ldots\} \leadsto \Gamma_n; \$([\overline{x = \tau}] \rc c)}{
adamc@534 882 \Gamma_0 = \Gamma
adamc@534 883 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534 884 }$$
adamc@534 885
adamc@852 886 $$\infer{\Gamma \vdash p : \tau \leadsto \Gamma'; \tau}{
adamc@852 887 \Gamma \vdash p \leadsto \Gamma'; \tau'
adamc@852 888 & \Gamma \vdash \tau' \equiv \tau
adamc@852 889 }$$
adamc@852 890
adamc@535 891 \subsection{Declaration Typing}
adamc@535 892
adamc@535 893 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@535 894
adamc@655 895 This is the first judgment where we deal with constructor classes, for the $\mt{class}$ declaration form. We will omit their special handling in this formal specification. Section \ref{typeclasses} gives an informal description of how constructor classes influence type inference.
adamc@535 896
adamc@558 897 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@537 898 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@535 899
adamc@535 900 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535 901 \quad \infer{\Gamma \vdash d, \overline{d} \leadsto \Gamma''}{
adamc@535 902 \Gamma \vdash d \leadsto \Gamma'
adamc@535 903 & \Gamma' \vdash \overline{d} \leadsto \Gamma''
adamc@535 904 }$$
adamc@535 905
adamc@535 906 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@535 907 \Gamma \vdash c :: \kappa
adamc@535 908 }
adamc@535 909 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@535 910 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@535 911 }$$
adamc@535 912
adamc@535 913 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537 914 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 915 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@535 916 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@535 917 }$$
adamc@535 918
adamc@535 919 $$\infer{\Gamma \vdash \mt{val} \; x : \tau = e \leadsto \Gamma, x : \tau}{
adamc@535 920 \Gamma \vdash e : \tau
adamc@535 921 }$$
adamc@535 922
adamc@535 923 $$\infer{\Gamma \vdash \mt{val} \; \mt{rec} \; \overline{x : \tau = e} \leadsto \Gamma, \overline{x : \tau}}{
adamc@535 924 \forall i: \Gamma, \overline{x : \tau} \vdash e_i : \tau_i
adamc@535 925 & \textrm{$e_i$ starts with an expression $\lambda$, optionally preceded by constructor and disjointness $\lambda$s}
adamc@535 926 }$$
adamc@535 927
adamc@535 928 $$\infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : S}{
adamc@535 929 \Gamma \vdash M : S
adamc@558 930 & \textrm{ $M$ not a constant or application}
adamc@535 931 }
adamc@558 932 \quad \infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : \mt{selfify}(X, \overline{s})}{
adamc@558 933 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@539 934 }$$
adamc@539 935
adamc@539 936 $$\infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@535 937 \Gamma \vdash S
adamc@535 938 }$$
adamc@535 939
adamc@537 940 $$\infer{\Gamma \vdash \mt{open} \; M \leadsto \Gamma, \mathcal O(M, \overline{s})}{
adamc@537 941 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535 942 }$$
adamc@535 943
adamc@535 944 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma}{
adamc@535 945 \Gamma \vdash c_1 :: \{\kappa\}
adamc@535 946 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@535 947 & \Gamma \vdash c_1 \sim c_2
adamc@535 948 }
adamc@537 949 \quad \infer{\Gamma \vdash \mt{open} \; \mt{constraints} \; M \leadsto \Gamma, \mathcal O_c(M, \overline{s})}{
adamc@537 950 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535 951 }$$
adamc@535 952
adamc@784 953 $$\infer{\Gamma \vdash \mt{table} \; x : c \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_table} \; c \; []}{
adamc@535 954 \Gamma \vdash c :: \{\mt{Type}\}
adamc@535 955 }
adamc@784 956 \quad \infer{\Gamma \vdash \mt{view} \; x : c \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_view} \; c}{
adamc@784 957 \Gamma \vdash c :: \{\mt{Type}\}
adamc@784 958 }$$
adamc@784 959
adamc@784 960 $$\infer{\Gamma \vdash \mt{sequence} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_sequence}}{}$$
adamc@535 961
adamc@535 962 $$\infer{\Gamma \vdash \mt{cookie} \; x : \tau \leadsto \Gamma, x : \mt{Basis}.\mt{http\_cookie} \; \tau}{
adamc@535 963 \Gamma \vdash \tau :: \mt{Type}
adamc@784 964 }
adamc@784 965 \quad \infer{\Gamma \vdash \mt{style} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{css\_class}}{}$$
adamc@535 966
adamc@1085 967 $$\infer{\Gamma \vdash \mt{task} \; e_1 = e_2 \leadsto \Gamma}{
adam@1348 968 \Gamma \vdash e_1 :: \mt{Basis}.\mt{task\_kind} \; \tau
adam@1348 969 & \Gamma \vdash e_2 :: \tau \to \mt{Basis}.\mt{transaction} \; \{\}
adamc@1085 970 }$$
adamc@1085 971
adamc@784 972 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784 973 \Gamma \vdash c :: \kappa
adamc@535 974 }$$
adamc@535 975
adamc@535 976 $$\infer{\overline{y}; x; \Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535 977 \quad \infer{\overline{y}; x; \Gamma \vdash X \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to x \; \overline{y}}{
adamc@535 978 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535 979 }
adamc@535 980 \quad \infer{\overline{y}; x; \Gamma \vdash X \; \mt{of} \; \tau \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to \tau \to x \; \overline{y}}{
adamc@535 981 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535 982 }$$
adamc@535 983
adamc@537 984 \subsection{Signature Item Typing}
adamc@537 985
adamc@537 986 We appeal to a signature item analogue of the $\mathcal O$ function from the last subsection.
adamc@537 987
adamc@537 988 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@537 989 \quad \infer{\Gamma \vdash s, \overline{s} \leadsto \Gamma''}{
adamc@537 990 \Gamma \vdash s \leadsto \Gamma'
adamc@537 991 & \Gamma' \vdash \overline{s} \leadsto \Gamma''
adamc@537 992 }$$
adamc@537 993
adamc@537 994 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}
adamc@537 995 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@537 996 \Gamma \vdash c :: \kappa
adamc@537 997 }
adamc@537 998 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@537 999 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@537 1000 }$$
adamc@537 1001
adamc@537 1002 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537 1003 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1004 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1005 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@537 1006 }$$
adamc@537 1007
adamc@537 1008 $$\infer{\Gamma \vdash \mt{val} \; x : \tau \leadsto \Gamma, x : \tau}{
adamc@537 1009 \Gamma \vdash \tau :: \mt{Type}
adamc@537 1010 }$$
adamc@537 1011
adamc@537 1012 $$\infer{\Gamma \vdash \mt{structure} \; X : S \leadsto \Gamma, X : S}{
adamc@537 1013 \Gamma \vdash S
adamc@537 1014 }
adamc@537 1015 \quad \infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@537 1016 \Gamma \vdash S
adamc@537 1017 }$$
adamc@537 1018
adamc@537 1019 $$\infer{\Gamma \vdash \mt{include} \; S \leadsto \Gamma, \mathcal O(\overline{s})}{
adamc@537 1020 \Gamma \vdash S
adamc@537 1021 & \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1022 }$$
adamc@537 1023
adamc@537 1024 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma, c_1 \sim c_2}{
adamc@537 1025 \Gamma \vdash c_1 :: \{\kappa\}
adamc@537 1026 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@537 1027 }$$
adamc@537 1028
adamc@784 1029 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784 1030 \Gamma \vdash c :: \kappa
adamc@537 1031 }
adamc@784 1032 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}$$
adamc@537 1033
adamc@536 1034 \subsection{Signature Compatibility}
adamc@536 1035
adamc@558 1036 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 1037
adamc@537 1038 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 1039
adamc@536 1040 $$\infer{\Gamma \vdash S \equiv S}{}
adamc@536 1041 \quad \infer{\Gamma \vdash S_1 \equiv S_2}{
adamc@536 1042 \Gamma \vdash S_2 \equiv S_1
adamc@536 1043 }
adamc@536 1044 \quad \infer{\Gamma \vdash X \equiv S}{
adamc@536 1045 X = S \in \Gamma
adamc@536 1046 }
adamc@536 1047 \quad \infer{\Gamma \vdash M.X \equiv S}{
adamc@537 1048 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1049 & \mt{proj}(M, \overline{s}, \mt{signature} \; X) = S
adamc@536 1050 }$$
adamc@536 1051
adamc@536 1052 $$\infer{\Gamma \vdash S \; \mt{where} \; \mt{con} \; x = c \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa = c \; \overline{s_2} \; \mt{end}}{
adamc@536 1053 \Gamma \vdash S \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa \; \overline{s_2} \; \mt{end}
adamc@536 1054 & \Gamma \vdash c :: \kappa
adamc@537 1055 }
adamc@537 1056 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s^1} \; \mt{include} \; S \; \overline{s^2} \; \mt{end} \equiv \mt{sig} \; \overline{s^1} \; \overline{s} \; \overline{s^2} \; \mt{end}}{
adamc@537 1057 \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@536 1058 }$$
adamc@536 1059
adamc@536 1060 $$\infer{\Gamma \vdash S_1 \leq S_2}{
adamc@536 1061 \Gamma \vdash S_1 \equiv S_2
adamc@536 1062 }
adamc@536 1063 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \mt{end}}{}
adamc@537 1064 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; s' \; \overline{s'} \; \mt{end}}{
adamc@537 1065 \Gamma \vdash \overline{s} \leq s'
adamc@537 1066 & \Gamma \vdash s' \leadsto \Gamma'
adamc@537 1067 & \Gamma' \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \overline{s'} \; \mt{end}
adamc@537 1068 }$$
adamc@537 1069
adamc@537 1070 $$\infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537 1071 \Gamma \vdash s \leq s'
adamc@537 1072 }
adamc@537 1073 \quad \infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537 1074 \Gamma \vdash s \leadsto \Gamma'
adamc@537 1075 & \Gamma' \vdash \overline{s} \leq s'
adamc@536 1076 }$$
adamc@536 1077
adamc@536 1078 $$\infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 \leq \mt{functor} (X : S'_1) : S'_2}{
adamc@536 1079 \Gamma \vdash S'_1 \leq S_1
adamc@536 1080 & \Gamma, X : S'_1 \vdash S_2 \leq S'_2
adamc@536 1081 }$$
adamc@536 1082
adamc@537 1083 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@537 1084 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}
adamc@558 1085 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type}}{}$$
adamc@537 1086
adamc@537 1087 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(y)} \to \mt{Type}}{
adamc@537 1088 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1089 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1090 }$$
adamc@537 1091
adamc@784 1092 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@784 1093 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}$$
adamc@537 1094
adamc@537 1095 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \mt{\kappa} = c_2}{
adamc@537 1096 \Gamma \vdash c_1 \equiv c_2
adamc@537 1097 }
adamc@784 1098 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \kappa = c_2}{
adamc@537 1099 \Gamma \vdash c_1 \equiv c_2
adamc@537 1100 }$$
adamc@537 1101
adamc@537 1102 $$\infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537 1103 \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1104 }$$
adamc@537 1105
adamc@537 1106 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537 1107 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1108 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1109 & \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1110 }$$
adamc@537 1111
adamc@537 1112 $$\infer{\Gamma \vdash \cdot \leq \cdot}{}
adamc@537 1113 \quad \infer{\Gamma \vdash X; \overline{dc} \leq X; \overline{dc'}}{
adamc@537 1114 \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1115 }
adamc@537 1116 \quad \infer{\Gamma \vdash X \; \mt{of} \; \tau_1; \overline{dc} \leq X \; \mt{of} \; \tau_2; \overline{dc'}}{
adamc@537 1117 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537 1118 & \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1119 }$$
adamc@537 1120
adamc@537 1121 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x = \mt{datatype} \; M'.z'}{
adamc@537 1122 \Gamma \vdash M.z \equiv M'.z'
adamc@537 1123 }$$
adamc@537 1124
adamc@537 1125 $$\infer{\Gamma \vdash \mt{val} \; x : \tau_1 \leq \mt{val} \; x : \tau_2}{
adamc@537 1126 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537 1127 }
adamc@537 1128 \quad \infer{\Gamma \vdash \mt{structure} \; X : S_1 \leq \mt{structure} \; X : S_2}{
adamc@537 1129 \Gamma \vdash S_1 \leq S_2
adamc@537 1130 }
adamc@537 1131 \quad \infer{\Gamma \vdash \mt{signature} \; X = S_1 \leq \mt{signature} \; X = S_2}{
adamc@537 1132 \Gamma \vdash S_1 \leq S_2
adamc@537 1133 & \Gamma \vdash S_2 \leq S_1
adamc@537 1134 }$$
adamc@537 1135
adamc@537 1136 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leq \mt{constraint} \; c'_1 \sim c'_2}{
adamc@537 1137 \Gamma \vdash c_1 \equiv c'_1
adamc@537 1138 & \Gamma \vdash c_2 \equiv c'_2
adamc@537 1139 }$$
adamc@537 1140
adamc@655 1141 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{class} \; x :: \kappa}{}
adamc@655 1142 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{class} \; x :: \kappa}{}
adamc@655 1143 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{class} \; x :: \kappa = c_2}{
adamc@537 1144 \Gamma \vdash c_1 \equiv c_2
adamc@537 1145 }$$
adamc@537 1146
adamc@538 1147 \subsection{Module Typing}
adamc@538 1148
adamc@538 1149 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 1150
adamc@538 1151 $$\infer{\Gamma \vdash M : S}{
adamc@538 1152 \Gamma \vdash M : S'
adamc@538 1153 & \Gamma \vdash S' \leq S
adamc@538 1154 }
adamc@538 1155 \quad \infer{\Gamma \vdash \mt{struct} \; \overline{d} \; \mt{end} : \mt{sig} \; \mt{sigOf}(\overline{d}) \; \mt{end}}{
adamc@538 1156 \Gamma \vdash \overline{d} \leadsto \Gamma'
adamc@538 1157 }
adamc@538 1158 \quad \infer{\Gamma \vdash X : S}{
adamc@538 1159 X : S \in \Gamma
adamc@538 1160 }$$
adamc@538 1161
adamc@538 1162 $$\infer{\Gamma \vdash M.X : S}{
adamc@538 1163 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@538 1164 & \mt{proj}(M, \overline{s}, \mt{structure} \; X) = S
adamc@538 1165 }$$
adamc@538 1166
adamc@538 1167 $$\infer{\Gamma \vdash M_1(M_2) : [X \mapsto M_2]S_2}{
adamc@538 1168 \Gamma \vdash M_1 : \mt{functor}(X : S_1) : S_2
adamc@538 1169 & \Gamma \vdash M_2 : S_1
adamc@538 1170 }
adamc@538 1171 \quad \infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 = M : \mt{functor} (X : S_1) : S_2}{
adamc@538 1172 \Gamma \vdash S_1
adamc@538 1173 & \Gamma, X : S_1 \vdash S_2
adamc@538 1174 & \Gamma, X : S_1 \vdash M : S_2
adamc@538 1175 }$$
adamc@538 1176
adamc@538 1177 \begin{eqnarray*}
adamc@538 1178 \mt{sigOf}(\cdot) &=& \cdot \\
adamc@538 1179 \mt{sigOf}(s \; \overline{s'}) &=& \mt{sigOf}(s) \; \mt{sigOf}(\overline{s'}) \\
adamc@538 1180 \\
adamc@538 1181 \mt{sigOf}(\mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@538 1182 \mt{sigOf}(\mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \overline{dc} \\
adamc@538 1183 \mt{sigOf}(\mt{datatype} \; x = \mt{datatype} \; M.z) &=& \mt{datatype} \; x = \mt{datatype} \; M.z \\
adamc@538 1184 \mt{sigOf}(\mt{val} \; x : \tau = e) &=& \mt{val} \; x : \tau \\
adamc@538 1185 \mt{sigOf}(\mt{val} \; \mt{rec} \; \overline{x : \tau = e}) &=& \overline{\mt{val} \; x : \tau} \\
adamc@538 1186 \mt{sigOf}(\mt{structure} \; X : S = M) &=& \mt{structure} \; X : S \\
adamc@538 1187 \mt{sigOf}(\mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@538 1188 \mt{sigOf}(\mt{open} \; M) &=& \mt{include} \; S \textrm{ (where $\Gamma \vdash M : S$)} \\
adamc@538 1189 \mt{sigOf}(\mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@538 1190 \mt{sigOf}(\mt{open} \; \mt{constraints} \; M) &=& \cdot \\
adamc@538 1191 \mt{sigOf}(\mt{table} \; x : c) &=& \mt{table} \; x : c \\
adamc@784 1192 \mt{sigOf}(\mt{view} \; x : c) &=& \mt{view} \; x : c \\
adamc@538 1193 \mt{sigOf}(\mt{sequence} \; x) &=& \mt{sequence} \; x \\
adamc@538 1194 \mt{sigOf}(\mt{cookie} \; x : \tau) &=& \mt{cookie} \; x : \tau \\
adamc@784 1195 \mt{sigOf}(\mt{style} \; x) &=& \mt{style} \; x \\
adamc@655 1196 \mt{sigOf}(\mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@538 1197 \end{eqnarray*}
adamc@539 1198 \begin{eqnarray*}
adamc@539 1199 \mt{selfify}(M, \cdot) &=& \cdot \\
adamc@558 1200 \mt{selfify}(M, s \; \overline{s'}) &=& \mt{selfify}(M, s) \; \mt{selfify}(M, \overline{s'}) \\
adamc@539 1201 \\
adamc@539 1202 \mt{selfify}(M, \mt{con} \; x :: \kappa) &=& \mt{con} \; x :: \kappa = M.x \\
adamc@539 1203 \mt{selfify}(M, \mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@539 1204 \mt{selfify}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \mt{datatype} \; M.x \\
adamc@539 1205 \mt{selfify}(M, \mt{datatype} \; x = \mt{datatype} \; M'.z) &=& \mt{datatype} \; x = \mt{datatype} \; M'.z \\
adamc@539 1206 \mt{selfify}(M, \mt{val} \; x : \tau) &=& \mt{val} \; x : \tau \\
adamc@539 1207 \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 1208 \mt{selfify}(M, \mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@539 1209 \mt{selfify}(M, \mt{include} \; S) &=& \mt{include} \; S \\
adamc@539 1210 \mt{selfify}(M, \mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@655 1211 \mt{selfify}(M, \mt{class} \; x :: \kappa) &=& \mt{class} \; x :: \kappa = M.x \\
adamc@655 1212 \mt{selfify}(M, \mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@539 1213 \end{eqnarray*}
adamc@539 1214
adamc@540 1215 \subsection{Module Projection}
adamc@540 1216
adamc@540 1217 \begin{eqnarray*}
adamc@540 1218 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \\
adamc@540 1219 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa, c) \\
adamc@540 1220 \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 1221 \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 1222 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})$)} \\
adamc@655 1223 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \to \mt{Type} \\
adamc@655 1224 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa \to \mt{Type}, c) \\
adamc@540 1225 \\
adamc@540 1226 \mt{proj}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc} \; \overline{s}, \mt{datatype} \; x) &=& (\overline{y}, \overline{dc}) \\
adamc@540 1227 \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 1228 \\
adamc@540 1229 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, \mt{val} \; x) &=& \tau \\
adamc@540 1230 \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 1231 \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 1232 \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 1233 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \in \overline{dc}$)} \\
adamc@540 1234 \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 1235 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \; \mt{of} \; \tau \in \overline{dc}$)} \\
adamc@540 1236 \\
adamc@540 1237 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, \mt{structure} \; X) &=& S \\
adamc@540 1238 \\
adamc@540 1239 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, \mt{signature} \; X) &=& S \\
adamc@540 1240 \\
adamc@540 1241 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1242 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1243 \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 1244 \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 1245 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@540 1246 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1247 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1248 \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 1249 \mt{proj}(M, \mt{constraint} \; c_1 \sim c_2 \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@655 1250 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@655 1251 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1252 \end{eqnarray*}
adamc@540 1253
adamc@541 1254
adamc@541 1255 \section{Type Inference}
adamc@541 1256
adamc@541 1257 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 1258
adamc@541 1259 \subsection{Basic Unification}
adamc@541 1260
adamc@560 1261 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 1262
adamc@656 1263 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 1264
adamc@541 1265 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 1266
adamc@541 1267 \subsection{Unifying Record Types}
adamc@541 1268
adamc@570 1269 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 1270
adamc@656 1271 \subsection{\label{typeclasses}Constructor Classes}
adamc@541 1272
adamc@784 1273 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 1274
adamc@784 1275 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.
adamc@541 1276
adamc@656 1277 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.
adamc@541 1278
adamc@656 1279 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. Abstract constructor classes 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.
adamc@541 1280
adamc@541 1281 \subsection{Reverse-Engineering Record Types}
adamc@541 1282
adamc@656 1283 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 1284
adamc@541 1285 \subsection{Implicit Arguments in Functor Applications}
adamc@541 1286
adamc@656 1287 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 1288
adamc@541 1289
adamc@542 1290 \section{The Ur Standard Library}
adamc@542 1291
adamc@542 1292 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 1293
adamc@542 1294 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 1295
adamc@542 1296 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 1297 $$\begin{array}{l}
adamc@542 1298 \mt{type} \; \mt{int} \\
adamc@542 1299 \mt{type} \; \mt{float} \\
adamc@873 1300 \mt{type} \; \mt{char} \\
adamc@542 1301 \mt{type} \; \mt{string} \\
adamc@542 1302 \mt{type} \; \mt{time} \\
adamc@785 1303 \mt{type} \; \mt{blob} \\
adamc@542 1304 \\
adamc@542 1305 \mt{type} \; \mt{unit} = \{\} \\
adamc@542 1306 \\
adamc@542 1307 \mt{datatype} \; \mt{bool} = \mt{False} \mid \mt{True} \\
adamc@542 1308 \\
adamc@785 1309 \mt{datatype} \; \mt{option} \; \mt{t} = \mt{None} \mid \mt{Some} \; \mt{of} \; \mt{t} \\
adamc@785 1310 \\
adamc@785 1311 \mt{datatype} \; \mt{list} \; \mt{t} = \mt{Nil} \mid \mt{Cons} \; \mt{of} \; \mt{t} \times \mt{list} \; \mt{t}
adamc@542 1312 \end{array}$$
adamc@542 1313
adamc@1123 1314 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 1315
adam@1297 1316 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 1317 $$\begin{array}{l}
adam@1297 1318 \mt{con} \; \mt{variant} :: \{\mt{Type}\} \to \mt{Type} \\
adam@1297 1319 \mt{val} \; \mt{make} : \mt{nm} :: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{ts} ::: \{\mt{Type}\} \to [[\mt{nm}] \sim \mt{ts}] \Rightarrow \mt{t} \to \mt{variant} \; ([\mt{nm} = \mt{t}] \rc \mt{ts}) \\
adam@1297 1320 \mt{val} \; \mt{match} : \mt{ts} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{variant} \; \mt{ts} \to \$(\mt{map} \; (\lambda \mt{t'} \Rightarrow \mt{t'} \to \mt{t}) \; \mt{ts}) \to \mt{t}
adam@1297 1321 \end{array}$$
adam@1297 1322
adamc@657 1323 Another important generic Ur element comes at the beginning of \texttt{top.urs}.
adamc@657 1324
adamc@657 1325 $$\begin{array}{l}
adamc@657 1326 \mt{con} \; \mt{folder} :: \mt{K} \longrightarrow \{\mt{K}\} \to \mt{Type} \\
adamc@657 1327 \\
adamc@657 1328 \mt{val} \; \mt{fold} : \mt{K} \longrightarrow \mt{tf} :: (\{\mt{K}\} \to \mt{Type}) \\
adamc@657 1329 \hspace{.1in} \to (\mt{nm} :: \mt{Name} \to \mt{v} :: \mt{K} \to \mt{r} :: \{\mt{K}\} \to [[\mt{nm}] \sim \mt{r}] \Rightarrow \\
adamc@657 1330 \hspace{.2in} \mt{tf} \; \mt{r} \to \mt{tf} \; ([\mt{nm} = \mt{v}] \rc \mt{r})) \\
adamc@657 1331 \hspace{.1in} \to \mt{tf} \; [] \\
adamc@657 1332 \hspace{.1in} \to \mt{r} :: \{\mt{K}\} \to \mt{folder} \; \mt{r} \to \mt{tf} \; \mt{r}
adamc@657 1333 \end{array}$$
adamc@657 1334
adamc@657 1335 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 1336
adamc@664 1337 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 1338
adamc@542 1339
adamc@542 1340 \section{The Ur/Web Standard Library}
adamc@542 1341
adam@1400 1342 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 1343
adamc@658 1344 \subsection{Monads}
adamc@658 1345
adamc@658 1346 The Ur Basis defines the monad constructor class from Haskell.
adamc@658 1347
adamc@658 1348 $$\begin{array}{l}
adamc@658 1349 \mt{class} \; \mt{monad} :: \mt{Type} \to \mt{Type} \\
adamc@658 1350 \mt{val} \; \mt{return} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t} ::: \mt{Type} \\
adamc@658 1351 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658 1352 \hspace{.1in} \to \mt{t} \to \mt{m} \; \mt{t} \\
adamc@658 1353 \mt{val} \; \mt{bind} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t1} ::: \mt{Type} \to \mt{t2} ::: \mt{Type} \\
adamc@658 1354 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658 1355 \hspace{.1in} \to \mt{m} \; \mt{t1} \to (\mt{t1} \to \mt{m} \; \mt{t2}) \\
adamc@658 1356 \hspace{.1in} \to \mt{m} \; \mt{t2}
adamc@658 1357 \end{array}$$
adamc@658 1358
adamc@542 1359 \subsection{Transactions}
adamc@542 1360
adamc@542 1361 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 1362 $$\begin{array}{l}
adamc@542 1363 \mt{con} \; \mt{transaction} :: \mt{Type} \to \mt{Type} \\
adamc@658 1364 \mt{val} \; \mt{transaction\_monad} : \mt{monad} \; \mt{transaction}
adamc@542 1365 \end{array}$$
adamc@542 1366
adamc@1123 1367 For debugging purposes, a transactional function is provided for outputting a string on the server process' \texttt{stderr}.
adamc@1123 1368 $$\begin{array}{l}
adamc@1123 1369 \mt{val} \; \mt{debug} : \mt{string} \to \mt{transaction} \; \mt{unit}
adamc@1123 1370 \end{array}$$
adamc@1123 1371
adamc@542 1372 \subsection{HTTP}
adamc@542 1373
adam@1400 1374 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 1375 $$\begin{array}{l}
adamc@786 1376 \mt{con} \; \mt{http\_cookie} :: \mt{Type} \to \mt{Type} \\
adamc@786 1377 \mt{val} \; \mt{getCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; (\mt{option} \; \mt{t}) \\
adamc@1050 1378 \mt{val} \; \mt{setCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \{\mt{Value} : \mt{t}, \mt{Expires} : \mt{option} \; \mt{time}, \mt{Secure} : \mt{bool}\} \to \mt{transaction} \; \mt{unit} \\
adamc@1050 1379 \mt{val} \; \mt{clearCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; \mt{unit}
adamc@786 1380 \end{array}$$
adamc@786 1381
adamc@786 1382 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 1383 $$\begin{array}{l}
adamc@786 1384 \mt{type} \; \mt{url} \\
adamc@786 1385 \mt{val} \; \mt{bless} : \mt{string} \to \mt{url} \\
adamc@786 1386 \mt{val} \; \mt{checkUrl} : \mt{string} \to \mt{option} \; \mt{url}
adamc@786 1387 \end{array}$$
adamc@786 1388 $\mt{bless}$ raises a runtime error if the string passed to it fails the URL policy.
adamc@786 1389
adam@1400 1390 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 1391 $$\begin{array}{l}
adamc@1085 1392 \mt{val} \; \mt{currentUrl} : \mt{transaction} \; \mt{url} \\
adamc@1085 1393 \mt{val} \; \mt{url} : \mt{transaction} \; \mt{page} \to \mt{url}
adamc@1085 1394 \end{array}$$
adamc@1085 1395
adamc@1085 1396 Page generation may be interrupted at any time with a request to redirect to a particular URL instead.
adamc@1085 1397 $$\begin{array}{l}
adamc@1085 1398 \mt{val} \; \mt{redirect} : \mt{t} ::: \mt{Type} \to \mt{url} \to \mt{transaction} \; \mt{t}
adamc@1085 1399 \end{array}$$
adamc@1085 1400
adam@1400 1401 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 1402 $$\begin{array}{l}
adamc@786 1403 \mt{type} \; \mt{file} \\
adamc@786 1404 \mt{val} \; \mt{fileName} : \mt{file} \to \mt{option} \; \mt{string} \\
adamc@786 1405 \mt{val} \; \mt{fileMimeType} : \mt{file} \to \mt{string} \\
adamc@786 1406 \mt{val} \; \mt{fileData} : \mt{file} \to \mt{blob}
adamc@786 1407 \end{array}$$
adamc@786 1408
adam@1465 1409 It is also possible to get HTTP request headers and set HTTP response headers, using abstract types similar to the one for URLs.
adam@1465 1410
adam@1465 1411 $$\begin{array}{l}
adam@1465 1412 \mt{type} \; \mt{requestHeader} \\
adam@1465 1413 \mt{val} \; \mt{blessRequestHeader} : \mt{string} \to \mt{requestHeader} \\
adam@1465 1414 \mt{val} \; \mt{checkRequestHeader} : \mt{string} \to \mt{option} \; \mt{requestHeader} \\
adam@1465 1415 \mt{val} \; \mt{getHeader} : \mt{requestHeader} \to \mt{transaction} \; (\mt{option} \; \mt{string}) \\
adam@1465 1416 \\
adam@1465 1417 \mt{type} \; \mt{responseHeader} \\
adam@1465 1418 \mt{val} \; \mt{blessResponseHeader} : \mt{string} \to \mt{responseHeader} \\
adam@1465 1419 \mt{val} \; \mt{checkResponseHeader} : \mt{string} \to \mt{option} \; \mt{responseHeader} \\
adam@1465 1420 \mt{val} \; \mt{setHeader} : \mt{responseHeader} \to \mt{string} \to \mt{transaction} \; \mt{unit}
adam@1465 1421 \end{array}$$
adam@1465 1422
adamc@786 1423 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 1424 $$\begin{array}{l}
adamc@786 1425 \mt{type} \; \mt{mimeType} \\
adamc@786 1426 \mt{val} \; \mt{blessMime} : \mt{string} \to \mt{mimeType} \\
adamc@786 1427 \mt{val} \; \mt{checkMime} : \mt{string} \to \mt{option} \; \mt{mimeType} \\
adamc@786 1428 \mt{val} \; \mt{returnBlob} : \mt{t} ::: \mt{Type} \to \mt{blob} \to \mt{mimeType} \to \mt{transaction} \; \mt{t}
adamc@542 1429 \end{array}$$
adamc@542 1430
adamc@543 1431 \subsection{SQL}
adamc@543 1432
adam@1400 1433 Everything about SQL database access is restricted to server-side code.
adam@1400 1434
adamc@543 1435 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 1436 $$\begin{array}{l}
adamc@785 1437 \mt{con} \; \mt{sql\_table} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785 1438 \end{array}$$
adamc@785 1439 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 1440
adamc@785 1441 We also have the simpler type family of SQL views, which have no keys.
adamc@785 1442 $$\begin{array}{l}
adamc@785 1443 \mt{con} \; \mt{sql\_view} :: \{\mt{Type}\} \to \mt{Type}
adamc@543 1444 \end{array}$$
adamc@543 1445
adamc@785 1446 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 1447 $$\begin{array}{l}
adamc@785 1448 \mt{class} \; \mt{fieldsOf} :: \mt{Type} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1449 \mt{val} \; \mt{fieldsOf\_table} : \mt{fs} ::: \{\mt{Type}\} \to \mt{keys} ::: \{\{\mt{Unit}\}\} \to \mt{fieldsOf} \; (\mt{sql\_table} \; \mt{fs} \; \mt{keys}) \; \mt{fs} \\
adamc@785 1450 \mt{val} \; \mt{fieldsOf\_view} : \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; (\mt{sql\_view} \; \mt{fs}) \; \mt{fs}
adamc@785 1451 \end{array}$$
adamc@785 1452
adamc@785 1453 \subsubsection{Table Constraints}
adamc@785 1454
adamc@785 1455 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 1456
adamc@785 1457 $$\begin{array}{l}
adamc@785 1458 \mt{con} \; \mt{primary\_key} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type} \\
adamc@785 1459 \mt{val} \; \mt{no\_primary\_key} : \mt{fs} ::: \{\mt{Type}\} \to \mt{primary\_key} \; \mt{fs} \; [] \\
adamc@785 1460 \mt{val} \; \mt{primary\_key} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{key1} :: \mt{Name} \to \mt{keys} :: \{\mt{Type}\} \\
adamc@785 1461 \hspace{.1in} \to [[\mt{key1}] \sim \mt{keys}] \Rightarrow [[\mt{key1} = \mt{t}] \rc \mt{keys} \sim \mt{rest}] \\
adamc@785 1462 \hspace{.1in} \Rightarrow \$([\mt{key1} = \mt{sql\_injectable\_prim} \; \mt{t}] \rc \mt{map} \; \mt{sql\_injectable\_prim} \; \mt{keys}) \\
adamc@785 1463 \hspace{.1in} \to \mt{primary\_key} \; ([\mt{key1} = \mt{t}] \rc \mt{keys} \rc \mt{rest}) \; [\mt{Pkey} = [\mt{key1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{keys}]
adamc@785 1464 \end{array}$$
adamc@785 1465 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 1466
adamc@785 1467 A type family stands for sets of named constraints of the remaining varieties.
adamc@785 1468 $$\begin{array}{l}
adamc@785 1469 \mt{con} \; \mt{sql\_constraints} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785 1470 \end{array}$$
adamc@785 1471 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 1472
adamc@785 1473 There is a type family of individual, unnamed constraints.
adamc@785 1474 $$\begin{array}{l}
adamc@785 1475 \mt{con} \; \mt{sql\_constraint} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \mt{Type}
adamc@785 1476 \end{array}$$
adamc@785 1477 The first argument is the same as above, and the second argument gives the key columns for just this constraint.
adamc@785 1478
adamc@785 1479 We have operations for assembling constraints into constraint sets.
adamc@785 1480 $$\begin{array}{l}
adamc@785 1481 \mt{val} \; \mt{no\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_constraints} \; \mt{fs} \; [] \\
adamc@785 1482 \mt{val} \; \mt{one\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{unique} ::: \{\mt{Unit}\} \to \mt{name} :: \mt{Name} \\
adamc@785 1483 \hspace{.1in} \to \mt{sql\_constraint} \; \mt{fs} \; \mt{unique} \to \mt{sql\_constraints} \; \mt{fs} \; [\mt{name} = \mt{unique}] \\
adamc@785 1484 \mt{val} \; \mt{join\_constraints} : \mt{fs} ::: \{\mt{Type}\} \to \mt{uniques1} ::: \{\{\mt{Unit}\}\} \to \mt{uniques2} ::: \{\{\mt{Unit}\}\} \to [\mt{uniques1} \sim \mt{uniques2}] \\
adamc@785 1485 \hspace{.1in} \Rightarrow \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques1} \to \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques2} \to \mt{sql\_constraints} \; \mt{fs} \; (\mt{uniques1} \rc \mt{uniques2})
adamc@785 1486 \end{array}$$
adamc@785 1487
adamc@785 1488 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 1489 $$\begin{array}{l}
adamc@785 1490 \mt{val} \; \mt{unique} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{unique1} :: \mt{Name} \to \mt{unique} :: \{\mt{Type}\} \\
adamc@785 1491 \hspace{.1in} \to [[\mt{unique1}] \sim \mt{unique}] \Rightarrow [[\mt{unique1} = \mt{t}] \rc \mt{unique} \sim \mt{rest}] \\
adamc@785 1492 \hspace{.1in} \Rightarrow \mt{sql\_constraint} \; ([\mt{unique1} = \mt{t}] \rc \mt{unique} \rc \mt{rest}) \; ([\mt{unique1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{unique})
adamc@785 1493 \end{array}$$
adamc@785 1494
adamc@785 1495 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 1496 $$\begin{array}{l}
adamc@785 1497 \mt{class} \; \mt{linkable} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@785 1498 \mt{val} \; \mt{linkable\_same} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; \mt{t} \\
adamc@785 1499 \mt{val} \; \mt{linkable\_from\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; (\mt{option} \; \mt{t}) \; \mt{t} \\
adamc@785 1500 \mt{val} \; \mt{linkable\_to\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@785 1501 \end{array}$$
adamc@785 1502
adamc@785 1503 The $\mt{matching}$ type family uses $\mt{linkable}$ to define when two keys match up type-wise.
adamc@785 1504 $$\begin{array}{l}
adamc@785 1505 \mt{con} \; \mt{matching} :: \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1506 \mt{val} \; \mt{mat\_nil} : \mt{matching} \; [] \; [] \\
adamc@785 1507 \mt{val} \; \mt{mat\_cons} : \mt{t1} ::: \mt{Type} \to \mt{rest1} ::: \{\mt{Type}\} \to \mt{t2} ::: \mt{Type} \to \mt{rest2} ::: \{\mt{Type}\} \to \mt{nm1} :: \mt{Name} \to \mt{nm2} :: \mt{Name} \\
adamc@785 1508 \hspace{.1in} \to [[\mt{nm1}] \sim \mt{rest1}] \Rightarrow [[\mt{nm2}] \sim \mt{rest2}] \Rightarrow \mt{linkable} \; \mt{t1} \; \mt{t2} \to \mt{matching} \; \mt{rest1} \; \mt{rest2} \\
adamc@785 1509 \hspace{.1in} \to \mt{matching} \; ([\mt{nm1} = \mt{t1}] \rc \mt{rest1}) \; ([\mt{nm2} = \mt{t2}] \rc \mt{rest2})
adamc@785 1510 \end{array}$$
adamc@785 1511
adamc@785 1512 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 1513 $$\begin{array}{l}
adamc@785 1514 \mt{con} \; \mt{propagation\_mode} :: \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1515 \mt{val} \; \mt{restrict} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1516 \mt{val} \; \mt{cascade} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1517 \mt{val} \; \mt{no\_action} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1518 \mt{val} \; \mt{set\_null} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; (\mt{map} \; \mt{option} \; \mt{fs})
adamc@785 1519 \end{array}$$
adamc@785 1520
adamc@785 1521 Finally, we put these ingredient together to define the \texttt{FOREIGN KEY} constraint function.
adamc@785 1522 $$\begin{array}{l}
adamc@785 1523 \mt{val} \; \mt{foreign\_key} : \mt{mine1} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{mine} ::: \{\mt{Type}\} \to \mt{munused} ::: \{\mt{Type}\} \to \mt{foreign} ::: \{\mt{Type}\} \\
adamc@785 1524 \hspace{.1in} \to \mt{funused} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{uniques} ::: \{\{\mt{Unit}\}\} \\
adamc@785 1525 \hspace{.1in} \to [[\mt{mine1}] \sim \mt{mine}] \Rightarrow [[\mt{mine1} = \mt{t}] \rc \mt{mine} \sim \mt{munused}] \Rightarrow [\mt{foreign} \sim \mt{funused}] \Rightarrow [[\mt{nm}] \sim \mt{uniques}] \\
adamc@785 1526 \hspace{.1in} \Rightarrow \mt{matching} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}) \; \mt{foreign} \\
adamc@785 1527 \hspace{.1in} \to \mt{sql\_table} \; (\mt{foreign} \rc \mt{funused}) \; ([\mt{nm} = \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{foreign}] \rc \mt{uniques}) \\
adamc@785 1528 \hspace{.1in} \to \{\mt{OnDelete} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}), \\
adamc@785 1529 \hspace{.2in} \mt{OnUpdate} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine})\} \\
adamc@785 1530 \hspace{.1in} \to \mt{sql\_constraint} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine} \rc \mt{munused}) \; []
adamc@785 1531 \end{array}$$
adamc@785 1532
adamc@785 1533 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 1534 $$\begin{array}{l}
adamc@785 1535 \mt{val} \; \mt{check} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; [] \; [] \; \mt{fs} \; \mt{bool} \to \mt{sql\_constraint} \; \mt{fs} \; []
adamc@785 1536 \end{array}$$
adamc@785 1537
adamc@785 1538 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 1539
adamc@784 1540
adamc@543 1541 \subsubsection{Queries}
adamc@543 1542
adam@1400 1543 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 1544 $$\begin{array}{l}
adam@1400 1545 \mt{con} \; \mt{sql\_query} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@1193 1546 \mt{val} \; \mt{sql\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400 1547 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1548 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543 1549 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1550 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1193 1551 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adam@1400 1552 \hspace{.1in} \Rightarrow \{\mt{Rows} : \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}, \\
adamc@1193 1553 \hspace{.2in} \mt{OrderBy} : \mt{sql\_order\_by} \; (\mt{free} \rc \mt{tables}) \; \mt{selectedExps}, \\
adamc@543 1554 \hspace{.2in} \mt{Limit} : \mt{sql\_limit}, \\
adamc@543 1555 \hspace{.2in} \mt{Offset} : \mt{sql\_offset}\} \\
adam@1400 1556 \hspace{.1in} \to \mt{sql\_query} \; \mt{free} \; \mt{afree} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1557 \end{array}$$
adamc@543 1558
adamc@545 1559 Queries are used by folding over their results inside transactions.
adamc@545 1560 $$\begin{array}{l}
adam@1400 1561 \mt{val} \; \mt{query} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to [\mt{tables} \sim \mt{exps}] \Rightarrow \mt{state} ::: \mt{Type} \to \mt{sql\_query} \; [] \; [] \; \mt{tables} \; \mt{exps} \\
adamc@658 1562 \hspace{.1in} \to (\$(\mt{exps} \rc \mt{map} \; (\lambda \mt{fields} :: \{\mt{Type}\} \Rightarrow \$\mt{fields}) \; \mt{tables}) \\
adamc@545 1563 \hspace{.2in} \to \mt{state} \to \mt{transaction} \; \mt{state}) \\
adamc@545 1564 \hspace{.1in} \to \mt{state} \to \mt{transaction} \; \mt{state}
adamc@545 1565 \end{array}$$
adamc@545 1566
adam@1400 1567 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 1568 $$\begin{array}{l}
adam@1400 1569 \mt{con} \; \mt{sql\_query1} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@543 1570 \\
adamc@543 1571 \mt{type} \; \mt{sql\_relop} \\
adamc@543 1572 \mt{val} \; \mt{sql\_union} : \mt{sql\_relop} \\
adamc@543 1573 \mt{val} \; \mt{sql\_intersect} : \mt{sql\_relop} \\
adamc@543 1574 \mt{val} \; \mt{sql\_except} : \mt{sql\_relop} \\
adam@1400 1575 \mt{val} \; \mt{sql\_relop} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400 1576 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adam@1400 1577 \hspace{.1in} \to \mt{tables1} ::: \{\{\mt{Type}\}\} \\
adamc@543 1578 \hspace{.1in} \to \mt{tables2} ::: \{\{\mt{Type}\}\} \\
adamc@543 1579 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1580 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@543 1581 \hspace{.1in} \to \mt{sql\_relop} \\
adam@1458 1582 \hspace{.1in} \to \mt{bool} \; (* \; \mt{ALL} \; *) \\
adam@1400 1583 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables1} \; \mt{selectedFields} \; \mt{selectedExps} \\
adam@1400 1584 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables2} \; \mt{selectedFields} \; \mt{selectedExps} \\
adam@1400 1585 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{selectedFields} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1586 \end{array}$$
adamc@543 1587
adamc@543 1588 $$\begin{array}{l}
adamc@1193 1589 \mt{val} \; \mt{sql\_query1} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400 1590 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1591 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543 1592 \hspace{.1in} \to \mt{grouped} ::: \{\{\mt{Type}\}\} \\
adamc@543 1593 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1594 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1085 1595 \hspace{.1in} \to \mt{empties} :: \{\mt{Unit}\} \\
adamc@1193 1596 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adamc@1193 1597 \hspace{.1in} \Rightarrow [\mt{free} \sim \mt{grouped}] \\
adam@1400 1598 \hspace{.1in} \Rightarrow [\mt{afree} \sim \mt{tables}] \\
adamc@1193 1599 \hspace{.1in} \Rightarrow [\mt{empties} \sim \mt{selectedFields}] \\
adamc@1085 1600 \hspace{.1in} \Rightarrow \{\mt{Distinct} : \mt{bool}, \\
adamc@1193 1601 \hspace{.2in} \mt{From} : \mt{sql\_from\_items} \; \mt{free} \; \mt{tables}, \\
adam@1400 1602 \hspace{.2in} \mt{Where} : \mt{sql\_exp} \; (\mt{free} \rc \mt{tables}) \; \mt{afree} \; [] \; \mt{bool}, \\
adamc@543 1603 \hspace{.2in} \mt{GroupBy} : \mt{sql\_subset} \; \mt{tables} \; \mt{grouped}, \\
adam@1400 1604 \hspace{.2in} \mt{Having} : \mt{sql\_exp} \; (\mt{free} \rc \mt{grouped}) \; (\mt{afree} \rc \mt{tables}) \; [] \; \mt{bool}, \\
adamc@1085 1605 \hspace{.2in} \mt{SelectFields} : \mt{sql\_subset} \; \mt{grouped} \; (\mt{map} \; (\lambda \_ \Rightarrow []) \; \mt{empties} \rc \mt{selectedFields}), \\
adam@1400 1606 \hspace{.2in} \mt {SelectExps} : \$(\mt{map} \; (\mt{sql\_exp} \; (\mt{free} \rc \mt{grouped}) \; (\mt{afree} \rc \mt{tables}) \; []) \; \mt{selectedExps}) \} \\
adam@1400 1607 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1608 \end{array}$$
adamc@543 1609
adamc@543 1610 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 1611 $$\begin{array}{l}
adamc@543 1612 \mt{con} \; \mt{sql\_subset} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@543 1613 \mt{val} \; \mt{sql\_subset} : \mt{keep\_drop} :: \{(\{\mt{Type}\} \times \{\mt{Type}\})\} \\
adamc@543 1614 \hspace{.1in} \to \mt{sql\_subset} \\
adamc@658 1615 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1 \rc \mt{fields}.2)\; \mt{keep\_drop}) \\
adamc@658 1616 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1) \; \mt{keep\_drop}) \\
adamc@543 1617 \mt{val} \; \mt{sql\_subset\_all} : \mt{tables} :: \{\{\mt{Type}\}\} \to \mt{sql\_subset} \; \mt{tables} \; \mt{tables}
adamc@543 1618 \end{array}$$
adamc@543 1619
adamc@560 1620 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 1621 $$\begin{array}{l}
adamc@543 1622 \mt{con} \; \mt{sql\_exp} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}
adamc@543 1623 \end{array}$$
adamc@543 1624
adamc@543 1625 Any field in scope may be converted to an expression.
adamc@543 1626 $$\begin{array}{l}
adamc@543 1627 \mt{val} \; \mt{sql\_field} : \mt{otherTabs} ::: \{\{\mt{Type}\}\} \to \mt{otherFields} ::: \{\mt{Type}\} \\
adamc@543 1628 \hspace{.1in} \to \mt{fieldType} ::: \mt{Type} \to \mt{agg} ::: \{\{\mt{Type}\}\} \\
adamc@543 1629 \hspace{.1in} \to \mt{exps} ::: \{\mt{Type}\} \\
adamc@543 1630 \hspace{.1in} \to \mt{tab} :: \mt{Name} \to \mt{field} :: \mt{Name} \\
adamc@543 1631 \hspace{.1in} \to \mt{sql\_exp} \; ([\mt{tab} = [\mt{field} = \mt{fieldType}] \rc \mt{otherFields}] \rc \mt{otherTabs}) \; \mt{agg} \; \mt{exps} \; \mt{fieldType}
adamc@543 1632 \end{array}$$
adamc@543 1633
adamc@544 1634 There is an analogous function for referencing named expressions.
adamc@544 1635 $$\begin{array}{l}
adamc@544 1636 \mt{val} \; \mt{sql\_exp} : \mt{tabs} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{t} ::: \mt{Type} \to \mt{rest} ::: \{\mt{Type}\} \to \mt{nm} :: \mt{Name} \\
adamc@544 1637 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tabs} \; \mt{agg} \; ([\mt{nm} = \mt{t}] \rc \mt{rest}) \; \mt{t}
adamc@544 1638 \end{array}$$
adamc@544 1639
adamc@544 1640 Ur values of appropriate types may be injected into SQL expressions.
adamc@544 1641 $$\begin{array}{l}
adamc@786 1642 \mt{class} \; \mt{sql\_injectable\_prim} \\
adamc@786 1643 \mt{val} \; \mt{sql\_bool} : \mt{sql\_injectable\_prim} \; \mt{bool} \\
adamc@786 1644 \mt{val} \; \mt{sql\_int} : \mt{sql\_injectable\_prim} \; \mt{int} \\
adamc@786 1645 \mt{val} \; \mt{sql\_float} : \mt{sql\_injectable\_prim} \; \mt{float} \\
adamc@786 1646 \mt{val} \; \mt{sql\_string} : \mt{sql\_injectable\_prim} \; \mt{string} \\
adamc@786 1647 \mt{val} \; \mt{sql\_time} : \mt{sql\_injectable\_prim} \; \mt{time} \\
adamc@786 1648 \mt{val} \; \mt{sql\_blob} : \mt{sql\_injectable\_prim} \; \mt{blob} \\
adamc@786 1649 \mt{val} \; \mt{sql\_channel} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{channel} \; \mt{t}) \\
adamc@786 1650 \mt{val} \; \mt{sql\_client} : \mt{sql\_injectable\_prim} \; \mt{client} \\
adamc@786 1651 \\
adamc@544 1652 \mt{class} \; \mt{sql\_injectable} \\
adamc@786 1653 \mt{val} \; \mt{sql\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@786 1654 \mt{val} \; \mt{sql\_option\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; (\mt{option} \; \mt{t}) \\
adamc@786 1655 \\
adamc@544 1656 \mt{val} \; \mt{sql\_inject} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@544 1657 \hspace{.1in} \to \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adamc@544 1658 \end{array}$$
adamc@544 1659
adamc@1123 1660 Additionally, most function-free types may be injected safely, via the $\mt{serialized}$ type family.
adamc@1123 1661 $$\begin{array}{l}
adamc@1123 1662 \mt{con} \; \mt{serialized} :: \mt{Type} \to \mt{Type} \\
adamc@1123 1663 \mt{val} \; \mt{serialize} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{serialized} \; \mt{t} \\
adamc@1123 1664 \mt{val} \; \mt{deserialize} : \mt{t} ::: \mt{Type} \to \mt{serialized} \; \mt{t} \to \mt{t} \\
adamc@1123 1665 \mt{val} \; \mt{sql\_serialized} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{serialized} \; \mt{t})
adamc@1123 1666 \end{array}$$
adamc@1123 1667
adamc@544 1668 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 1669 $$\begin{array}{l}
adamc@544 1670 \mt{val} \; \mt{sql\_is\_null} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544 1671 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; (\mt{option} \; \mt{t}) \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{bool}
adamc@544 1672 \end{array}$$
adamc@544 1673
adamc@559 1674 We have generic nullary, unary, and binary operators.
adamc@544 1675 $$\begin{array}{l}
adamc@544 1676 \mt{con} \; \mt{sql\_nfunc} :: \mt{Type} \to \mt{Type} \\
adamc@544 1677 \mt{val} \; \mt{sql\_current\_timestamp} : \mt{sql\_nfunc} \; \mt{time} \\
adamc@544 1678 \mt{val} \; \mt{sql\_nfunc} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544 1679 \hspace{.1in} \to \mt{sql\_nfunc} \; \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\\end{array}$$
adamc@544 1680
adamc@544 1681 $$\begin{array}{l}
adamc@544 1682 \mt{con} \; \mt{sql\_unary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544 1683 \mt{val} \; \mt{sql\_not} : \mt{sql\_unary} \; \mt{bool} \; \mt{bool} \\
adamc@544 1684 \mt{val} \; \mt{sql\_unary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adamc@544 1685 \hspace{.1in} \to \mt{sql\_unary} \; \mt{arg} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res} \\
adamc@544 1686 \end{array}$$
adamc@544 1687
adamc@544 1688 $$\begin{array}{l}
adamc@544 1689 \mt{con} \; \mt{sql\_binary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544 1690 \mt{val} \; \mt{sql\_and} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544 1691 \mt{val} \; \mt{sql\_or} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544 1692 \mt{val} \; \mt{sql\_binary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg_1} ::: \mt{Type} \to \mt{arg_2} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adamc@544 1693 \hspace{.1in} \to \mt{sql\_binary} \; \mt{arg_1} \; \mt{arg_2} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_1} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_2} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res}
adamc@544 1694 \end{array}$$
adamc@544 1695
adamc@544 1696 $$\begin{array}{l}
adamc@559 1697 \mt{class} \; \mt{sql\_arith} \\
adamc@559 1698 \mt{val} \; \mt{sql\_int\_arith} : \mt{sql\_arith} \; \mt{int} \\
adamc@559 1699 \mt{val} \; \mt{sql\_float\_arith} : \mt{sql\_arith} \; \mt{float} \\
adamc@559 1700 \mt{val} \; \mt{sql\_neg} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_unary} \; \mt{t} \; \mt{t} \\
adamc@559 1701 \mt{val} \; \mt{sql\_plus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1702 \mt{val} \; \mt{sql\_minus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1703 \mt{val} \; \mt{sql\_times} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1704 \mt{val} \; \mt{sql\_div} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1705 \mt{val} \; \mt{sql\_mod} : \mt{sql\_binary} \; \mt{int} \; \mt{int} \; \mt{int}
adamc@559 1706 \end{array}$$
adamc@544 1707
adamc@656 1708 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 1709 $$\begin{array}{l}
adamc@544 1710 \mt{val} \; \mt{sql\_count} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int}
adamc@544 1711 \end{array}$$
adamc@544 1712
adamc@544 1713 $$\begin{array}{l}
adamc@1188 1714 \mt{con} \; \mt{sql\_aggregate} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@1188 1715 \mt{val} \; \mt{sql\_aggregate} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{dom} ::: \mt{Type} \to \mt{ran} ::: \mt{Type} \\
adamc@1188 1716 \hspace{.1in} \to \mt{sql\_aggregate} \; \mt{dom} \; \mt{ran} \to \mt{sql\_exp} \; \mt{agg} \; \mt{agg} \; \mt{exps} \; \mt{dom} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{ran}
adamc@1188 1717 \end{array}$$
adamc@1188 1718
adamc@1188 1719 $$\begin{array}{l}
adamc@1188 1720 \mt{val} \; \mt{sql\_count\_col} : \mt{t} ::: \mt{Type} \to \mt{sql\_aggregate} \; (\mt{option} \; \mt{t}) \; \mt{int}
adamc@544 1721 \end{array}$$
adam@1400 1722
adam@1400 1723 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 1724
adamc@544 1725 $$\begin{array}{l}
adamc@544 1726 \mt{class} \; \mt{sql\_summable} \\
adamc@544 1727 \mt{val} \; \mt{sql\_summable\_int} : \mt{sql\_summable} \; \mt{int} \\
adamc@544 1728 \mt{val} \; \mt{sql\_summable\_float} : \mt{sql\_summable} \; \mt{float} \\
adam@1400 1729 \mt{val} \; \mt{sql\_avg} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt} \\
adam@1400 1730 \mt{val} \; \mt{sql\_sum} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt}
adamc@544 1731 \end{array}$$
adamc@544 1732
adamc@544 1733 $$\begin{array}{l}
adamc@544 1734 \mt{class} \; \mt{sql\_maxable} \\
adamc@544 1735 \mt{val} \; \mt{sql\_maxable\_int} : \mt{sql\_maxable} \; \mt{int} \\
adamc@544 1736 \mt{val} \; \mt{sql\_maxable\_float} : \mt{sql\_maxable} \; \mt{float} \\
adamc@544 1737 \mt{val} \; \mt{sql\_maxable\_string} : \mt{sql\_maxable} \; \mt{string} \\
adamc@544 1738 \mt{val} \; \mt{sql\_maxable\_time} : \mt{sql\_maxable} \; \mt{time} \\
adam@1400 1739 \mt{val} \; \mt{sql\_max} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt} \\
adam@1400 1740 \mt{val} \; \mt{sql\_min} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt}
adamc@544 1741 \end{array}$$
adamc@544 1742
adamc@1193 1743 Any SQL query that returns single columns may be turned into a subquery expression.
adamc@1193 1744
adamc@786 1745 $$\begin{array}{l}
adam@1421 1746 \mt{val} \; \mt{sql\_subquery} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \\
adam@1421 1747 \hspace{.1in} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_query} \; \mt{tables} \; \mt{agg} \; [\mt{nm} = \mt{t}] \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{nt}
adamc@1193 1748 \end{array}$$
adamc@1193 1749
adamc@1193 1750 \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 1751 $$\begin{array}{l}
adamc@1193 1752 \mt{con} \; \mt{sql\_from\_items} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@1193 1753 \mt{val} \; \mt{sql\_from\_table} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1754 \hspace{.1in} \to \mt{t} ::: \mt{Type} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; \mt{t} \; \mt{fs} \to \mt{name} :: \mt{Name} \to \mt{t} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193 1755 \mt{val} \; \mt{sql\_from\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{name} :: \mt{Name} \to \mt{sql\_query} \; \mt{free} \; [] \; \mt{fs} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193 1756 \mt{val} \; \mt{sql\_from\_comma} : \mt{free} ::: \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \to [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193 1757 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adamc@1193 1758 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2}) \\
adamc@1193 1759 \mt{val} \; \mt{sql\_inner\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1760 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193 1761 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adamc@1193 1762 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193 1763 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2})
adamc@786 1764 \end{array}$$
adamc@786 1765
adamc@786 1766 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 1767 $$\begin{array}{l}
adamc@786 1768 \mt{class} \; \mt{nullify} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@786 1769 \mt{val} \; \mt{nullify\_option} : \mt{t} ::: \mt{Type} \to \mt{nullify} \; (\mt{option} \; \mt{t}) \; (\mt{option} \; \mt{t}) \\
adamc@786 1770 \mt{val} \; \mt{nullify\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{nullify} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@786 1771 \end{array}$$
adamc@786 1772
adamc@786 1773 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 1774
adamc@786 1775 $$\begin{array}{l}
adamc@1193 1776 \mt{val} \; \mt{sql\_left\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{(\mt{Type} \times \mt{Type})\}\} \\
adamc@1193 1777 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@786 1778 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\lambda \mt{r} \Rightarrow \$(\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{nullify} \; \mt{p}.1 \; \mt{p}.2) \; \mt{r})) \; \mt{tabs2}) \\
adamc@1193 1779 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \\
adamc@1193 1780 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193 1781 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.2)) \; \mt{tabs2})
adamc@786 1782 \end{array}$$
adamc@786 1783
adamc@544 1784 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 1785 $$\begin{array}{l}
adamc@544 1786 \mt{type} \; \mt{sql\_direction} \\
adamc@544 1787 \mt{val} \; \mt{sql\_asc} : \mt{sql\_direction} \\
adamc@544 1788 \mt{val} \; \mt{sql\_desc} : \mt{sql\_direction} \\
adamc@544 1789 \\
adamc@544 1790 \mt{con} \; \mt{sql\_order\_by} :: \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@544 1791 \mt{val} \; \mt{sql\_order\_by\_Nil} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} :: \{\mt{Type}\} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544 1792 \mt{val} \; \mt{sql\_order\_by\_Cons} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544 1793 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; [] \; \mt{exps} \; \mt{t} \to \mt{sql\_direction} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544 1794 \\
adamc@544 1795 \mt{type} \; \mt{sql\_limit} \\
adamc@544 1796 \mt{val} \; \mt{sql\_no\_limit} : \mt{sql\_limit} \\
adamc@544 1797 \mt{val} \; \mt{sql\_limit} : \mt{int} \to \mt{sql\_limit} \\
adamc@544 1798 \\
adamc@544 1799 \mt{type} \; \mt{sql\_offset} \\
adamc@544 1800 \mt{val} \; \mt{sql\_no\_offset} : \mt{sql\_offset} \\
adamc@544 1801 \mt{val} \; \mt{sql\_offset} : \mt{int} \to \mt{sql\_offset}
adamc@544 1802 \end{array}$$
adamc@544 1803
adamc@545 1804
adamc@545 1805 \subsubsection{DML}
adamc@545 1806
adamc@545 1807 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 1808
adamc@545 1809 $$\begin{array}{l}
adamc@545 1810 \mt{type} \; \mt{dml} \\
adamc@545 1811 \mt{val} \; \mt{dml} : \mt{dml} \to \mt{transaction} \; \mt{unit}
adamc@545 1812 \end{array}$$
adamc@545 1813
adam@1297 1814 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 1815
adam@1297 1816 $$\begin{array}{l}
adam@1297 1817 \mt{val} \; \mt{tryDml} : \mt{dml} \to \mt{transaction} \; (\mt{option} \; \mt{string})
adam@1297 1818 \end{array}$$
adam@1297 1819
adamc@545 1820 Properly-typed records may be used to form $\mt{INSERT}$ commands.
adamc@545 1821 $$\begin{array}{l}
adamc@545 1822 \mt{val} \; \mt{insert} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \\
adamc@658 1823 \hspace{.1in} \to \$(\mt{map} \; (\mt{sql\_exp} \; [] \; [] \; []) \; \mt{fields}) \to \mt{dml}
adamc@545 1824 \end{array}$$
adamc@545 1825
adamc@545 1826 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.
adamc@545 1827 $$\begin{array}{l}
adam@1380 1828 \mt{val} \; \mt{update} : \mt{unchanged} ::: \{\mt{Type}\} \to \mt{changed} :: \{\mt{Type}\} \to [\mt{changed} \sim \mt{unchanged}] \\
adamc@658 1829 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; []) \; \mt{changed}) \\
adamc@545 1830 \hspace{.1in} \to \mt{sql\_table} \; (\mt{changed} \rc \mt{unchanged}) \to \mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545 1831 \end{array}$$
adamc@545 1832
adamc@545 1833 A $\mt{DELETE}$ command is formed from a table and a $\mt{WHERE}$ clause.
adamc@545 1834 $$\begin{array}{l}
adamc@545 1835 \mt{val} \; \mt{delete} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \to \mt{sql\_exp} \; [\mt{T} = \mt{fields}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545 1836 \end{array}$$
adamc@545 1837
adamc@546 1838 \subsubsection{Sequences}
adamc@546 1839
adamc@546 1840 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 1841
adamc@546 1842 $$\begin{array}{l}
adamc@546 1843 \mt{type} \; \mt{sql\_sequence} \\
adamc@1085 1844 \mt{val} \; \mt{nextval} : \mt{sql\_sequence} \to \mt{transaction} \; \mt{int} \\
adamc@1085 1845 \mt{val} \; \mt{setval} : \mt{sql\_sequence} \to \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@546 1846 \end{array}$$
adamc@546 1847
adamc@546 1848
adamc@547 1849 \subsection{XML}
adamc@547 1850
adam@1333 1851 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 1852
adam@1345 1853 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 $[\mt{Body}, \mt{Tr}]$, to indicate a kind of nesting inside \texttt{<body>} and \texttt{<tr>}. 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 1854 $$\begin{array}{l}
adamc@547 1855 \mt{con} \; \mt{xml} :: \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547 1856 \end{array}$$
adamc@547 1857
adamc@547 1858 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 1859 $$\begin{array}{l}
adamc@547 1860 \mt{con} \; \mt{tag} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547 1861 \end{array}$$
adamc@547 1862
adamc@547 1863 Literal text may be injected into XML as ``CDATA.''
adamc@547 1864 $$\begin{array}{l}
adamc@547 1865 \mt{val} \; \mt{cdata} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{string} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adamc@547 1866 \end{array}$$
adamc@547 1867
adam@1358 1868 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 1869 $$\begin{array}{l}
adam@1358 1870 \mt{val} \; \mt{cdataChar} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{char} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adam@1358 1871 \end{array}$$
adam@1358 1872
adamc@547 1873 There is a function for producing an XML tree with a particular tag at its root.
adamc@547 1874 $$\begin{array}{l}
adamc@547 1875 \mt{val} \; \mt{tag} : \mt{attrsGiven} ::: \{\mt{Type}\} \to \mt{attrsAbsent} ::: \{\mt{Type}\} \to \mt{ctxOuter} ::: \{\mt{Unit}\} \to \mt{ctxInner} ::: \{\mt{Unit}\} \\
adamc@547 1876 \hspace{.1in} \to \mt{useOuter} ::: \{\mt{Type}\} \to \mt{useInner} ::: \{\mt{Type}\} \to \mt{bindOuter} ::: \{\mt{Type}\} \to \mt{bindInner} ::: \{\mt{Type}\} \\
adam@1380 1877 \hspace{.1in} \to [\mt{attrsGiven} \sim \mt{attrsAbsent}] \Rightarrow [\mt{useOuter} \sim \mt{useInner}] \Rightarrow [\mt{bindOuter} \sim \mt{bindInner}] \\
adamc@787 1878 \hspace{.1in} \Rightarrow \mt{option} \; \mt{css\_class} \\
adamc@787 1879 \hspace{.1in} \to \$\mt{attrsGiven} \\
adamc@547 1880 \hspace{.1in} \to \mt{tag} \; (\mt{attrsGiven} \rc \mt{attrsAbsent}) \; \mt{ctxOuter} \; \mt{ctxInner} \; \mt{useOuter} \; \mt{bindOuter} \\
adamc@547 1881 \hspace{.1in} \to \mt{xml} \; \mt{ctxInner} \; \mt{useInner} \; \mt{bindInner} \to \mt{xml} \; \mt{ctxOuter} \; (\mt{useOuter} \rc \mt{useInner}) \; (\mt{bindOuter} \rc \mt{bindInner})
adamc@547 1882 \end{array}$$
adam@1297 1883 Note that any tag may be assigned a CSS class. This is the sole way of making use of the values produced by $\mt{style}$ declarations. Ur/Web itself doesn't deal with the syntax or semantics of style sheets; they can be linked via URLs with \texttt{link} tags. However, Ur/Web does make it easy to calculate upper bounds on usage of CSS classes through program analysis. The function $\mt{Basis.classes}$ can be used to specify a list of CSS classes for a single tag.
adamc@547 1884
adamc@547 1885 Two XML fragments may be concatenated.
adamc@547 1886 $$\begin{array}{l}
adamc@547 1887 \mt{val} \; \mt{join} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{bind_1} ::: \{\mt{Type}\} \to \mt{bind_2} ::: \{\mt{Type}\} \\
adam@1380 1888 \hspace{.1in} \to [\mt{use_1} \sim \mt{bind_1}] \Rightarrow [\mt{bind_1} \sim \mt{bind_2}] \\
adamc@547 1889 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind_1} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{bind_1}) \; \mt{bind_2} \to \mt{xml} \; \mt{ctx} \; \mt{use_1} \; (\mt{bind_1} \rc \mt{bind_2})
adamc@547 1890 \end{array}$$
adamc@547 1891
adamc@547 1892 Finally, any XML fragment may be updated to ``claim'' to use more form fields than it does.
adamc@547 1893 $$\begin{array}{l}
adam@1380 1894 \mt{val} \; \mt{useMore} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{use_2} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to [\mt{use_1} \sim \mt{use_2}] \\
adamc@547 1895 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{use_2}) \; \mt{bind}
adamc@547 1896 \end{array}$$
adamc@547 1897
adam@1344 1898 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 1899
adamc@547 1900 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 1901 $$\begin{array}{l}
adamc@547 1902 \mt{val} \; \mt{error} : \mt{t} ::: \mt{Type} \to \mt{xml} \; [\mt{Body}] \; [] \; [] \to \mt{t}
adamc@547 1903 \end{array}$$
adamc@547 1904
adamc@549 1905
adamc@701 1906 \subsection{Client-Side Programming}
adamc@659 1907
adamc@701 1908 Ur/Web supports running code on web browsers, via automatic compilation to JavaScript.
adamc@701 1909
adamc@701 1910 \subsubsection{The Basics}
adamc@701 1911
adam@1400 1912 All of the functions in this subsection are client-side only.
adam@1400 1913
adam@1297 1914 Clients can open alert and confirm dialog boxes, in the usual annoying JavaScript way.
adamc@701 1915 $$\begin{array}{l}
adam@1297 1916 \mt{val} \; \mt{alert} : \mt{string} \to \mt{transaction} \; \mt{unit} \\
adam@1297 1917 \mt{val} \; \mt{confirm} : \mt{string} \to \mt{transaction} \; \mt{bool}
adamc@701 1918 \end{array}$$
adamc@701 1919
adamc@701 1920 Any transaction may be run in a new thread with the $\mt{spawn}$ function.
adamc@701 1921 $$\begin{array}{l}
adamc@701 1922 \mt{val} \; \mt{spawn} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit}
adamc@701 1923 \end{array}$$
adamc@701 1924
adamc@701 1925 The current thread can be paused for at least a specified number of milliseconds.
adamc@701 1926 $$\begin{array}{l}
adamc@701 1927 \mt{val} \; \mt{sleep} : \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@701 1928 \end{array}$$
adamc@701 1929
adamc@787 1930 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 occurrences of that error are ignored silently.
adamc@787 1931 $$\begin{array}{l}
adamc@787 1932 \mt{val} \; \mt{onError} : (\mt{xbody} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787 1933 \mt{val} \; \mt{onFail} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787 1934 \mt{val} \; \mt{onConnectFail} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787 1935 \mt{val} \; \mt{onDisconnect} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787 1936 \mt{val} \; \mt{onServerError} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit}
adamc@787 1937 \end{array}$$
adamc@787 1938
adamc@701 1939 \subsubsection{Functional-Reactive Page Generation}
adamc@701 1940
adamc@701 1941 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 1942
adam@1403 1943 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 1944
adamc@659 1945 $$\begin{array}{l}
adamc@659 1946 \mt{con} \; \mt{source} :: \mt{Type} \to \mt{Type} \\
adamc@659 1947 \mt{val} \; \mt{source} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{transaction} \; (\mt{source} \; \mt{t}) \\
adamc@659 1948 \mt{val} \; \mt{set} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@659 1949 \mt{val} \; \mt{get} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@659 1950 \end{array}$$
adamc@659 1951
adam@1400 1952 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 1953
adam@1403 1954 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.
adamc@659 1955
adamc@659 1956 $$\begin{array}{l}
adamc@659 1957 \mt{con} \; \mt{signal} :: \mt{Type} \to \mt{Type} \\
adamc@659 1958 \mt{val} \; \mt{signal\_monad} : \mt{monad} \; \mt{signal} \\
adamc@659 1959 \mt{val} \; \mt{signal} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{signal} \; \mt{t}
adamc@659 1960 \end{array}$$
adamc@659 1961
adamc@659 1962 A reactive portion of an HTML page is injected with a $\mt{dyn}$ tag, which has a signal-valued attribute $\mt{Signal}$.
adamc@659 1963
adamc@659 1964 $$\begin{array}{l}
adamc@701 1965 \mt{val} \; \mt{dyn} : \mt{use} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to \mt{unit} \\
adamc@701 1966 \hspace{.1in} \to \mt{tag} \; [\mt{Signal} = \mt{signal} \; (\mt{xml} \; \mt{body} \; \mt{use} \; \mt{bind})] \; \mt{body} \; [] \; \mt{use} \; \mt{bind}
adamc@659 1967 \end{array}$$
adamc@659 1968
adamc@701 1969 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.
adamc@701 1970
adamc@914 1971 \subsubsection{Remote Procedure Calls}
adamc@914 1972
adamc@914 1973 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 1974
adamc@914 1975 $$\begin{array}{l}
adamc@914 1976 \mt{val} \; \mt{rpc} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@914 1977 \end{array}$$
adamc@914 1978
adamc@701 1979 \subsubsection{Asynchronous Message-Passing}
adamc@701 1980
adamc@701 1981 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 1982
adamc@701 1983 $$\begin{array}{l}
adamc@701 1984 \mt{type} \; \mt{client} \\
adamc@701 1985 \mt{val} \; \mt{self} : \mt{transaction} \; \mt{client}
adamc@701 1986 \end{array}$$
adamc@701 1987
adamc@701 1988 \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 1989
adamc@701 1990 $$\begin{array}{l}
adamc@701 1991 \mt{con} \; \mt{channel} :: \mt{Type} \to \mt{Type} \\
adamc@701 1992 \mt{val} \; \mt{channel} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; (\mt{channel} \; \mt{t}) \\
adamc@701 1993 \mt{val} \; \mt{send} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@701 1994 \mt{val} \; \mt{recv} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@701 1995 \end{array}$$
adamc@701 1996
adamc@701 1997 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 1998
adamc@701 1999 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 2000
adamc@659 2001
adamc@549 2002 \section{Ur/Web Syntax Extensions}
adamc@549 2003
adamc@549 2004 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 2005
adamc@549 2006 \subsection{SQL}
adamc@549 2007
adamc@786 2008 \subsubsection{\label{tables}Table Declarations}
adamc@786 2009
adamc@788 2010 $\mt{table}$ declarations may include constraints, via these grammar rules.
adamc@788 2011 $$\begin{array}{rrcll}
adamc@788 2012 \textrm{Declarations} & d &::=& \mt{table} \; x : c \; [pk[,]] \; cts \\
adamc@788 2013 \textrm{Primary key constraints} & pk &::=& \mt{PRIMARY} \; \mt{KEY} \; K \\
adamc@788 2014 \textrm{Keys} & K &::=& f \mid (f, (f,)^+) \\
adamc@788 2015 \textrm{Constraint sets} & cts &::=& \mt{CONSTRAINT} f \; ct \mid cts, cts \mid \{\{e\}\} \\
adamc@788 2016 \textrm{Constraints} & ct &::=& \mt{UNIQUE} \; K \mid \mt{CHECK} \; E \\
adamc@788 2017 &&& \mid \mt{FOREIGN} \; \mt{KEY} \; K \; \mt{REFERENCES} \; F \; (K) \; [\mt{ON} \; \mt{DELETE} \; pr] \; [\mt{ON} \; \mt{UPDATE} \; pr] \\
adamc@788 2018 \textrm{Foreign tables} & F &::=& x \mid \{\{e\}\} \\
adamc@788 2019 \textrm{Propagation modes} & pr &::=& \mt{NO} \; \mt{ACTION} \mid \mt{RESTRICT} \mid \mt{CASCADE} \mid \mt{SET} \; \mt{NULL}
adamc@788 2020 \end{array}$$
adamc@788 2021
adamc@788 2022 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 2023
adamc@788 2024
adamc@549 2025 \subsubsection{Queries}
adamc@549 2026
adamc@550 2027 Queries $Q$ are added to the rules for expressions $e$.
adamc@550 2028
adamc@549 2029 $$\begin{array}{rrcll}
adamc@550 2030 \textrm{Queries} & Q &::=& (q \; [\mt{ORDER} \; \mt{BY} \; (E \; [o],)^+] \; [\mt{LIMIT} \; N] \; [\mt{OFFSET} \; N]) \\
adamc@1085 2031 \textrm{Pre-queries} & q &::=& \mt{SELECT} \; [\mt{DISTINCT}] \; P \; \mt{FROM} \; F,^+ \; [\mt{WHERE} \; E] \; [\mt{GROUP} \; \mt{BY} \; p,^+] \; [\mt{HAVING} \; E] \\
adamc@1085 2032 &&& \mid q \; R \; q \mid \{\{\{e\}\}\} \\
adamc@549 2033 \textrm{Relational operators} & R &::=& \mt{UNION} \mid \mt{INTERSECT} \mid \mt{EXCEPT}
adamc@549 2034 \end{array}$$
adamc@549 2035
adamc@549 2036 $$\begin{array}{rrcll}
adamc@549 2037 \textrm{Projections} & P &::=& \ast & \textrm{all columns} \\
adamc@549 2038 &&& p,^+ & \textrm{particular columns} \\
adamc@549 2039 \textrm{Pre-projections} & p &::=& t.f & \textrm{one column from a table} \\
adamc@558 2040 &&& t.\{\{c\}\} & \textrm{a record of columns from a table (of kind $\{\mt{Type}\}$)} \\
adamc@1194 2041 &&& E \; [\mt{AS} \; f] & \textrm{expression column} \\
adamc@549 2042 \textrm{Table names} & t &::=& x & \textrm{constant table name (automatically capitalized)} \\
adamc@549 2043 &&& X & \textrm{constant table name} \\
adamc@549 2044 &&& \{\{c\}\} & \textrm{computed table name (of kind $\mt{Name}$)} \\
adamc@549 2045 \textrm{Column names} & f &::=& X & \textrm{constant column name} \\
adamc@549 2046 &&& \{c\} & \textrm{computed column name (of kind $\mt{Name}$)} \\
adamc@549 2047 \textrm{Tables} & T &::=& x & \textrm{table variable, named locally by its own capitalization} \\
adamc@549 2048 &&& x \; \mt{AS} \; t & \textrm{table variable, with local name} \\
adamc@549 2049 &&& \{\{e\}\} \; \mt{AS} \; t & \textrm{computed table expression, with local name} \\
adamc@1085 2050 \textrm{$\mt{FROM}$ items} & F &::=& T \mid \{\{e\}\} \mid F \; J \; \mt{JOIN} \; F \; \mt{ON} \; E \\
adamc@1085 2051 &&& \mid F \; \mt{CROSS} \; \mt{JOIN} \ F \\
adamc@1193 2052 &&& \mid (Q) \; \mt{AS} \; t \\
adamc@1085 2053 \textrm{Joins} & J &::=& [\mt{INNER}] \\
adamc@1085 2054 &&& \mid [\mt{LEFT} \mid \mt{RIGHT} \mid \mt{FULL}] \; [\mt{OUTER}] \\
adamc@549 2055 \textrm{SQL expressions} & E &::=& p & \textrm{column references} \\
adamc@549 2056 &&& X & \textrm{named expression references} \\
adamc@549 2057 &&& \{\{e\}\} & \textrm{injected native Ur expressions} \\
adamc@549 2058 &&& \{e\} & \textrm{computed expressions, probably using $\mt{sql\_exp}$ directly} \\
adamc@549 2059 &&& \mt{TRUE} \mid \mt{FALSE} & \textrm{boolean constants} \\
adamc@549 2060 &&& \ell & \textrm{primitive type literals} \\
adamc@549 2061 &&& \mt{NULL} & \textrm{null value (injection of $\mt{None}$)} \\
adamc@549 2062 &&& E \; \mt{IS} \; \mt{NULL} & \textrm{nullness test} \\
adamc@549 2063 &&& n & \textrm{nullary operators} \\
adamc@549 2064 &&& u \; E & \textrm{unary operators} \\
adamc@549 2065 &&& E \; b \; E & \textrm{binary operators} \\
adamc@549 2066 &&& \mt{COUNT}(\ast) & \textrm{count number of rows} \\
adamc@549 2067 &&& a(E) & \textrm{other aggregate function} \\
adamc@1193 2068 &&& (Q) & \textrm{subquery (must return a single expression column)} \\
adamc@549 2069 &&& (E) & \textrm{explicit precedence} \\
adamc@549 2070 \textrm{Nullary operators} & n &::=& \mt{CURRENT\_TIMESTAMP} \\
adamc@549 2071 \textrm{Unary operators} & u &::=& \mt{NOT} \\
adamc@549 2072 \textrm{Binary operators} & b &::=& \mt{AND} \mid \mt{OR} \mid \neq \mid < \mid \leq \mid > \mid \geq \\
adamc@1188 2073 \textrm{Aggregate functions} & a &::=& \mt{COUNT} \mid \mt{AVG} \mid \mt{SUM} \mid \mt{MIN} \mid \mt{MAX} \\
adamc@550 2074 \textrm{Directions} & o &::=& \mt{ASC} \mid \mt{DESC} \\
adamc@549 2075 \textrm{SQL integer} & N &::=& n \mid \{e\} \\
adamc@549 2076 \end{array}$$
adamc@549 2077
adamc@1085 2078 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 2079
adamc@1194 2080 Unnamed expression columns in $\mt{SELECT}$ clauses are assigned consecutive natural numbers, starting with 1.
adamc@1194 2081
adamc@550 2082 \subsubsection{DML}
adamc@550 2083
adamc@550 2084 DML commands $D$ are added to the rules for expressions $e$.
adamc@550 2085
adamc@550 2086 $$\begin{array}{rrcll}
adamc@550 2087 \textrm{Commands} & D &::=& (\mt{INSERT} \; \mt{INTO} \; T^E \; (f,^+) \; \mt{VALUES} \; (E,^+)) \\
adamc@550 2088 &&& (\mt{UPDATE} \; T^E \; \mt{SET} \; (f = E,)^+ \; \mt{WHERE} \; E) \\
adamc@550 2089 &&& (\mt{DELETE} \; \mt{FROM} \; T^E \; \mt{WHERE} \; E) \\
adamc@550 2090 \textrm{Table expressions} & T^E &::=& x \mid \{\{e\}\}
adamc@550 2091 \end{array}$$
adamc@550 2092
adamc@550 2093 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 2094
adamc@551 2095 \subsection{XML}
adamc@551 2096
adamc@551 2097 XML fragments $L$ are added to the rules for expressions $e$.
adamc@551 2098
adamc@551 2099 $$\begin{array}{rrcll}
adamc@551 2100 \textrm{XML fragments} & L &::=& \texttt{<xml/>} \mid \texttt{<xml>}l^*\texttt{</xml>} \\
adamc@551 2101 \textrm{XML pieces} & l &::=& \textrm{text} & \textrm{cdata} \\
adamc@551 2102 &&& \texttt{<}g\texttt{/>} & \textrm{tag with no children} \\
adamc@551 2103 &&& \texttt{<}g\texttt{>}l^*\texttt{</}x\texttt{>} & \textrm{tag with children} \\
adamc@559 2104 &&& \{e\} & \textrm{computed XML fragment} \\
adamc@559 2105 &&& \{[e]\} & \textrm{injection of an Ur expression, via the $\mt{Top}.\mt{txt}$ function} \\
adamc@551 2106 \textrm{Tag} & g &::=& h \; (x = v)^* \\
adamc@551 2107 \textrm{Tag head} & h &::=& x & \textrm{tag name} \\
adamc@551 2108 &&& h\{c\} & \textrm{constructor parameter} \\
adamc@551 2109 \textrm{Attribute value} & v &::=& \ell & \textrm{literal value} \\
adamc@551 2110 &&& \{e\} & \textrm{computed value} \\
adamc@551 2111 \end{array}$$
adamc@551 2112
adamc@552 2113
adamc@1198 2114 \section{\label{structure}The Structure of Web Applications}
adamc@553 2115
adamc@1127 2116 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. Arguments to an entry-point function are deserialized from the part of the URI following \texttt{f}.
adamc@553 2117
adam@1347 2118 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 will only work with \texttt{POST} payloads of MIME types besides those associated with HTML forms; for these, use Ur/Web's built-in support, as described below.
adam@1347 2119
adam@1370 2120 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 2121
adamc@553 2122 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 2123
adamc@553 2124 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 2125
adamc@558 2126 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.
adamc@553 2127
adamc@660 2128 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 2129
adamc@789 2130 \medskip
adamc@789 2131
adam@1347 2132 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 2133
adamc@789 2134 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 2135
adam@1348 2136 \subsection{Tasks}
adam@1348 2137
adam@1348 2138 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 2139
adam@1348 2140 $$\begin{array}{l}
adam@1348 2141 \mt{con} \; \mt{task\_kind} :: \mt{Type} \to \mt{Type} \\
adam@1348 2142 \mt{val} \; \mt{initialize} : \mt{task\_kind} \; \mt{unit} \\
adam@1349 2143 \mt{val} \; \mt{clientLeaves} : \mt{task\_kind} \; \mt{client} \\
adam@1349 2144 \mt{val} \; \mt{periodic} : \mt{int} \to \mt{task\_kind} \; \mt{unit}
adam@1348 2145 \end{array}$$
adam@1348 2146
adam@1348 2147 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 2148
adam@1348 2149 The currently supported task kinds are:
adam@1348 2150 \begin{itemize}
adam@1349 2151 \item $\mt{initialize}$: Code that is run when the application starts up.
adam@1348 2152 \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 2153 \item $\mt{periodic} \; n$: Code that is run when the application starts up and then every $n$ seconds thereafter.
adam@1348 2154 \end{itemize}
adam@1348 2155
adamc@553 2156
adamc@897 2157 \section{The Foreign Function Interface}
adamc@897 2158
adamc@897 2159 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 2160
adamc@897 2161 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 2162
adamc@897 2163 \begin{itemize}
adamc@897 2164 \item \texttt{clientOnly Module.ident} registers a value as being allowed only in client-side code.
adamc@897 2165 \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.
adamc@897 2166 \item \texttt{effectful Module.ident} registers a function that can have side effects. It is important to remember to use this directive for each such function, or else the optimizer might change program semantics.
adamc@897 2167 \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 2168 \item \texttt{include FILE} requests inclusion of a C header file.
adamc@897 2169 \item \texttt{jsFunc Module.ident=name} gives a mapping from an Ur name for a value to a JavaScript name.
adamc@897 2170 \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 2171 \item \texttt{script URL} requests inclusion of a JavaScript source file within application HTML.
adamc@897 2172 \item \texttt{serverOnly Module.ident} registers a value as being allowed only in server-side code.
adamc@897 2173 \end{itemize}
adamc@897 2174
adamc@897 2175 \subsection{Writing C FFI Code}
adamc@897 2176
adamc@897 2177 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 2178
adamc@897 2179 \begin{itemize}
adamc@897 2180 \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/types.h} for their definitions.
adamc@897 2181 \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 2182 \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*}.
adamc@897 2183 \end{itemize}
adamc@897 2184
adamc@897 2185 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.h}. Most should only be used internally by the compiler. A few are useful in general FFI implementation:
adamc@897 2186 \begin{itemize}
adamc@897 2187 \item \begin{verbatim}
adamc@897 2188 void uw_error(uw_context, failure_kind, const char *fmt, ...);
adamc@897 2189 \end{verbatim}
adamc@897 2190 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 2191
adam@1329 2192 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 2193
adamc@897 2194 \item \begin{verbatim}
adam@1469 2195 void uw_set_error_message(uw_context, const char *fmt, ...);
adam@1469 2196 \end{verbatim}
adam@1469 2197 This simpler form of \texttt{uw\_error()} saves an error message without immediately aborting execution.
adam@1469 2198
adam@1469 2199 \item \begin{verbatim}
adamc@897 2200 void uw_push_cleanup(uw_context, void (*func)(void *), void *arg);
adamc@897 2201 void uw_pop_cleanup(uw_context);
adamc@897 2202 \end{verbatim}
adam@1329 2203 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 2204
adam@1329 2205 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 2206
adamc@897 2207 \item \begin{verbatim}
adamc@897 2208 void *uw_malloc(uw_context, size_t);
adamc@897 2209 \end{verbatim}
adam@1329 2210 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 2211
adam@1329 2212 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 2213
adamc@897 2214 \item \begin{verbatim}
adamc@897 2215 typedef void (*uw_callback)(void *);
adam@1328 2216 typedef void (*uw_callback_with_retry)(void *, int will_retry);
adamc@897 2217 void uw_register_transactional(uw_context, void *data, uw_callback commit,
adam@1328 2218 uw_callback rollback, uw_callback_with_retry free);
adamc@897 2219 \end{verbatim}
adam@1328 2220 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 2221
adamc@1085 2222 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 2223
adam@1329 2224 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 2225
adam@1329 2226 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 2227
adam@1469 2228 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 2229
adamc@1085 2230 \item \begin{verbatim}
adamc@1085 2231 void *uw_get_global(uw_context, char *name);
adamc@1085 2232 void uw_set_global(uw_context, char *name, void *data, uw_callback free);
adamc@1085 2233 \end{verbatim}
adam@1329 2234 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 2235
adamc@897 2236 \end{itemize}
adamc@897 2237
adamc@897 2238 \subsection{Writing JavaScript FFI Code}
adamc@897 2239
adamc@897 2240 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 2241
adamc@897 2242 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 2243
adamc@897 2244 \begin{itemize}
adamc@897 2245 \item Integers, floats, strings, characters, and booleans are represented in the usual JavaScript way.
adamc@985 2246 \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)}.
adamc@897 2247 \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 2248 \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 2249 \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.
adamc@897 2250 \end{itemize}
adamc@897 2251
adamc@897 2252 It is possible to write JavaScript FFI code that interacts with the functional-reactive structure of a document, but this version of the manual doesn't cover the details.
adamc@897 2253
adamc@897 2254
adamc@552 2255 \section{Compiler Phases}
adamc@552 2256
adamc@552 2257 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 2258
adamc@552 2259 In this section, we step through the main phases of compilation, noting what consequences each phase has for effective programming.
adamc@552 2260
adamc@552 2261 \subsection{Parse}
adamc@552 2262
adamc@552 2263 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 2264
adamc@552 2265 \subsection{Elaborate}
adamc@552 2266
adamc@552 2267 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 2268
adam@1378 2269 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 2270
adamc@552 2271 \subsection{Unnest}
adamc@552 2272
adamc@552 2273 Named local function definitions are moved to the top level, to avoid the need to generate closures.
adamc@552 2274
adamc@552 2275 \subsection{Corify}
adamc@552 2276
adamc@552 2277 Module system features are compiled away, through inlining of functor definitions at application sites. Afterward, most abstraction boundaries are broken, facilitating optimization.
adamc@552 2278
adamc@552 2279 \subsection{Especialize}
adamc@552 2280
adam@1356 2281 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 2282
adamc@552 2283 \subsection{Untangle}
adamc@552 2284
adamc@552 2285 Remove unnecessary mutual recursion, splitting recursive groups into strongly-connected components.
adamc@552 2286
adamc@552 2287 \subsection{Shake}
adamc@552 2288
adamc@552 2289 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 2290
adamc@661 2291 \subsection{Rpcify}
adamc@661 2292
adamc@661 2293 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 2294
adamc@661 2295 \subsection{Untangle, Shake}
adamc@661 2296
adamc@661 2297 Repeat these simplifications.
adamc@661 2298
adamc@553 2299 \subsection{\label{tag}Tag}
adamc@552 2300
adamc@552 2301 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 2302
adamc@552 2303 \subsection{Reduce}
adamc@552 2304
adamc@552 2305 Apply definitional equality rules to simplify the program as much as possible. This effectively includes inlining of every non-recursive definition.
adamc@552 2306
adamc@552 2307 \subsection{Unpoly}
adamc@552 2308
adamc@552 2309 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 2310
adamc@552 2311 \subsection{Specialize}
adamc@552 2312
adamc@558 2313 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 2314
adamc@552 2315 \subsection{Shake}
adamc@552 2316
adamc@558 2317 Here the compiler repeats the earlier Shake phase.
adamc@552 2318
adamc@552 2319 \subsection{Monoize}
adamc@552 2320
adamc@552 2321 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 2322
adamc@552 2323 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 2324
adamc@552 2325 \subsection{MonoOpt}
adamc@552 2326
adamc@552 2327 Simple algebraic laws are applied to simplify the program, focusing especially on efficient imperative generation of HTML pages.
adamc@552 2328
adamc@552 2329 \subsection{MonoUntangle}
adamc@552 2330
adamc@552 2331 Unnecessary mutual recursion is broken up again.
adamc@552 2332
adamc@552 2333 \subsection{MonoReduce}
adamc@552 2334
adamc@552 2335 Equivalents of the definitional equality rules are applied to simplify programs, with inlining again playing a major role.
adamc@552 2336
adamc@552 2337 \subsection{MonoShake, MonoOpt}
adamc@552 2338
adamc@552 2339 Unneeded declarations are removed, and basic optimizations are repeated.
adamc@552 2340
adamc@552 2341 \subsection{Fuse}
adamc@552 2342
adamc@552 2343 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 2344
adamc@552 2345 \subsection{MonoUntangle, MonoShake}
adamc@552 2346
adamc@552 2347 Fuse often creates more opportunities to remove spurious mutual recursion.
adamc@552 2348
adamc@552 2349 \subsection{Pathcheck}
adamc@552 2350
adamc@552 2351 The compiler checks that no link or action name has been used more than once.
adamc@552 2352
adamc@552 2353 \subsection{Cjrize}
adamc@552 2354
adamc@552 2355 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 2356
adamc@552 2357 \subsection{C Compilation and Linking}
adamc@552 2358
adamc@552 2359 The output of the last phase is pretty-printed as C source code and passed to GCC.
adamc@552 2360
adamc@552 2361
adamc@524 2362 \end{document}