annotate doc/manual.tex @ 1499:92c929793d0f

Preserve tutorial indentation
author Adam Chlipala <adam@chlipala.net>
date Fri, 15 Jul 2011 19:00:59 -0400
parents a77fa7e7bb7b
children dbb461e55eda
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@1478 170 \item \texttt{noXsrfProtection URIPREFIX} turns off automatic cross-site request forgery protection for the page handler identified by the given URI prefix. This will avoid checking cryptographic signatures on cookies, which is generally a reasonable idea for some pages, such as login pages that are going to discard all old cookie values, anyway.
adam@1297 171 \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@852 172 \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@783 173 \item \texttt{prefix PREFIX} sets the prefix included before every URI within the generated application. The default is \texttt{/}.
adamc@783 174 \item \texttt{profile} generates an executable that may be used with gprof.
adam@1300 175 \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 176 \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@783 177 \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@783 178 \item \texttt{serverOnly Module.ident} registers an FFI function or transaction that may only be run on the server.
adamc@1164 179 \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@783 180 \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@783 181 \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@783 182 \end{itemize}
adamc@701 183
adamc@701 184
adamc@557 185 \subsection{Building an Application}
adamc@557 186
adamc@557 187 To compile project \texttt{P.urp}, simply run
adamc@557 188 \begin{verbatim}
adamc@557 189 urweb P
adamc@557 190 \end{verbatim}
adamc@1198 191 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@557 192
adamc@557 193 To time how long the different compiler phases run, without generating an executable, run
adamc@557 194 \begin{verbatim}
adamc@557 195 urweb -timing P
adamc@557 196 \end{verbatim}
adamc@557 197
adamc@1086 198 To stop the compilation process after type-checking, run
adamc@1086 199 \begin{verbatim}
adamc@1086 200 urweb -tc P
adamc@1086 201 \end{verbatim}
adamc@1086 202
adamc@1170 203 To output information relevant to CSS stylesheets (and not finish regular compilation), run
adamc@1170 204 \begin{verbatim}
adamc@1170 205 urweb -css P
adamc@1170 206 \end{verbatim}
adamc@1170 207 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 208
adamc@896 209 Some other command-line parameters are accepted:
adamc@896 210 \begin{itemize}
adamc@896 211 \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@896 212
adamc@896 213 \item \texttt{-dbms [postgres|mysql|sqlite]}: Sets the database backend to use.
adamc@896 214 \begin{itemize}
adamc@896 215 \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@896 216
adamc@896 217 A command sequence like this can initialize a Postgres database, using a file \texttt{app.sql} generated by the compiler:
adamc@896 218 \begin{verbatim}
adamc@896 219 createdb app
adamc@896 220 psql -f app.sql app
adamc@896 221 \end{verbatim}
adamc@896 222
adamc@896 223 \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@896 224
adamc@896 225 A command sequence like this can initialize a MySQL database:
adamc@896 226 \begin{verbatim}
adamc@896 227 echo "CREATE DATABASE app" | mysql
adamc@896 228 mysql -D app <app.sql
adamc@896 229 \end{verbatim}
adamc@896 230
adamc@896 231 \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@896 232
adamc@896 233 A command like this can initialize an SQLite database:
adamc@896 234 \begin{verbatim}
adamc@896 235 sqlite3 path/to/database/file <app.sql
adamc@896 236 \end{verbatim}
adamc@896 237 \end{itemize}
adamc@896 238
adam@1309 239 \item \texttt{-limit class num}: Equivalent to the \texttt{limit} directive from \texttt{.urp} files
adam@1309 240
adamc@896 241 \item \texttt{-output FILENAME}: Set where the application executable is written.
adamc@896 242
adamc@1127 243 \item \texttt{-path NAME VALUE}: Set the value of path variable \texttt{\$NAME} to \texttt{VALUE}, for use in \texttt{.urp} files.
adamc@1127 244
adam@1335 245 \item \texttt{-prefix PREFIX}: Equivalent to the \texttt{prefix} directive from \texttt{.urp} files
adam@1335 246
adamc@896 247 \item \texttt{-protocol [http|cgi|fastcgi]}: Set the protocol that the generated application speaks.
adamc@896 248 \begin{itemize}
adamc@896 249 \item \texttt{http}: This is the default. It is for building standalone web servers that can be accessed by web browsers directly.
adamc@896 250
adamc@896 251 \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@896 252
adamc@896 253 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@896 254 \begin{verbatim}
adamc@896 255 ScriptAlias /Hello /path/to/hello.exe
adamc@896 256 \end{verbatim}
adamc@896 257
adamc@1163 258 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 259 \begin{verbatim}
adamc@1163 260 Options +ExecCGI
adamc@1163 261 AddHandler cgi-script .exe
adamc@1163 262 \end{verbatim}
adamc@1163 263
adamc@1163 264 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 265 \begin{verbatim}
adamc@1163 266 prefix /dir/script.exe/
adamc@1163 267 \end{verbatim}
adamc@1163 268
adamc@1163 269 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 270
adamc@1164 271 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 272
adamc@896 273 \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@896 274
adamc@896 275 To configure a FastCGI program with Apache, one could combine the above \texttt{ScriptAlias} line with a line like this:
adamc@896 276 \begin{verbatim}
adamc@896 277 FastCgiServer /path/to/hello.exe -idle-timeout 99999
adamc@896 278 \end{verbatim}
adamc@896 279 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@896 280
adamc@896 281 Here is some lighttpd configuration for the same application.
adamc@896 282 \begin{verbatim}
adamc@896 283 fastcgi.server = (
adamc@896 284 "/Hello/" =>
adamc@896 285 (( "bin-path" => "/path/to/hello.exe",
adamc@896 286 "socket" => "/tmp/hello",
adamc@896 287 "check-local" => "disable",
adamc@896 288 "docroot" => "/",
adamc@896 289 "max-procs" => "1"
adamc@896 290 ))
adamc@896 291 )
adamc@896 292 \end{verbatim}
adamc@896 293 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@896 294
adamc@896 295 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@896 296 \end{itemize}
adamc@896 297
adamc@1127 298 \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 299
adamc@1164 300 \item \texttt{-sigfile PATH}: Same as the \texttt{sigfile} directive in \texttt{.urp} files
adamc@1164 301
adamc@896 302 \item \texttt{-sql FILENAME}: Set where a database set-up SQL script is written.
adamc@1095 303
adamc@1095 304 \item \texttt{-static}: Link the runtime system statically. The default is to link against dynamic libraries.
adamc@896 305 \end{itemize}
adamc@896 306
adam@1297 307 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@556 308
adamc@529 309 \section{Ur Syntax}
adamc@529 310
adamc@784 311 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@524 312
adamc@524 313 \subsection{Lexical Conventions}
adamc@524 314
adamc@524 315 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@524 316
adamc@524 317 \begin{center}
adamc@524 318 \begin{tabular}{rl}
adamc@524 319 \textbf{\LaTeX} & \textbf{ASCII} \\
adamc@524 320 $\to$ & \cd{->} \\
adamc@652 321 $\longrightarrow$ & \cd{-->} \\
adamc@524 322 $\times$ & \cd{*} \\
adamc@524 323 $\lambda$ & \cd{fn} \\
adamc@524 324 $\Rightarrow$ & \cd{=>} \\
adamc@652 325 $\Longrightarrow$ & \cd{==>} \\
adamc@529 326 $\neq$ & \cd{<>} \\
adamc@529 327 $\leq$ & \cd{<=} \\
adamc@529 328 $\geq$ & \cd{>=} \\
adamc@524 329 \\
adamc@524 330 $x$ & Normal textual identifier, not beginning with an uppercase letter \\
adamc@525 331 $X$ & Normal textual identifier, beginning with an uppercase letter \\
adamc@524 332 \end{tabular}
adamc@524 333 \end{center}
adamc@524 334
adamc@525 335 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@524 336
adamc@873 337 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@526 338
adamc@527 339 This version of the manual doesn't include operator precedences; see \texttt{src/urweb.grm} for that.
adamc@527 340
adam@1297 341 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 342
adamc@552 343 \subsection{\label{core}Core Syntax}
adamc@524 344
adamc@524 345 \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@524 346 $$\begin{array}{rrcll}
adamc@524 347 \textrm{Kinds} & \kappa &::=& \mt{Type} & \textrm{proper types} \\
adamc@525 348 &&& \mt{Unit} & \textrm{the trivial constructor} \\
adamc@525 349 &&& \mt{Name} & \textrm{field names} \\
adamc@525 350 &&& \kappa \to \kappa & \textrm{type-level functions} \\
adamc@525 351 &&& \{\kappa\} & \textrm{type-level records} \\
adamc@525 352 &&& (\kappa\times^+) & \textrm{type-level tuples} \\
adamc@652 353 &&& X & \textrm{variable} \\
adamc@652 354 &&& X \longrightarrow k & \textrm{kind-polymorphic type-level function} \\
adamc@529 355 &&& \_\_ & \textrm{wildcard} \\
adamc@525 356 &&& (\kappa) & \textrm{explicit precedence} \\
adamc@524 357 \end{array}$$
adamc@524 358
adamc@524 359 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@524 360 $$\begin{array}{rrcll}
adamc@524 361 \textrm{Explicitness} & ? &::=& :: & \textrm{explicit} \\
adamc@558 362 &&& ::: & \textrm{implicit}
adamc@524 363 \end{array}$$
adamc@524 364
adamc@524 365 \emph{Constructors} are the main class of compile-time-only data. They include proper types and are classified by kinds.
adamc@524 366 $$\begin{array}{rrcll}
adamc@524 367 \textrm{Constructors} & c, \tau &::=& (c) :: \kappa & \textrm{kind annotation} \\
adamc@530 368 &&& \hat{x} & \textrm{constructor variable} \\
adamc@524 369 \\
adamc@525 370 &&& \tau \to \tau & \textrm{function type} \\
adamc@525 371 &&& x \; ? \; \kappa \to \tau & \textrm{polymorphic function type} \\
adamc@652 372 &&& X \longrightarrow \tau & \textrm{kind-polymorphic function type} \\
adamc@525 373 &&& \$ c & \textrm{record type} \\
adamc@524 374 \\
adamc@525 375 &&& c \; c & \textrm{type-level function application} \\
adamc@530 376 &&& \lambda x \; :: \; \kappa \Rightarrow c & \textrm{type-level function abstraction} \\
adamc@524 377 \\
adamc@652 378 &&& X \Longrightarrow c & \textrm{type-level kind-polymorphic function abstraction} \\
adamc@655 379 &&& c [\kappa] & \textrm{type-level kind-polymorphic function application} \\
adamc@652 380 \\
adamc@525 381 &&& () & \textrm{type-level unit} \\
adamc@525 382 &&& \#X & \textrm{field name} \\
adamc@524 383 \\
adamc@525 384 &&& [(c = c)^*] & \textrm{known-length type-level record} \\
adamc@525 385 &&& c \rc c & \textrm{type-level record concatenation} \\
adamc@652 386 &&& \mt{map} & \textrm{type-level record map} \\
adamc@524 387 \\
adamc@558 388 &&& (c,^+) & \textrm{type-level tuple} \\
adamc@525 389 &&& c.n & \textrm{type-level tuple projection ($n \in \mathbb N^+$)} \\
adamc@524 390 \\
adamc@652 391 &&& [c \sim c] \Rightarrow \tau & \textrm{guarded type} \\
adamc@524 392 \\
adamc@529 393 &&& \_ :: \kappa & \textrm{wildcard} \\
adamc@525 394 &&& (c) & \textrm{explicit precedence} \\
adamc@530 395 \\
adamc@530 396 \textrm{Qualified uncapitalized variables} & \hat{x} &::=& x & \textrm{not from a module} \\
adamc@530 397 &&& M.x & \textrm{projection from a module} \\
adamc@525 398 \end{array}$$
adamc@525 399
adamc@655 400 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@655 401
adamc@525 402 Modules of the module system are described by \emph{signatures}.
adamc@525 403 $$\begin{array}{rrcll}
adamc@525 404 \textrm{Signatures} & S &::=& \mt{sig} \; s^* \; \mt{end} & \textrm{constant} \\
adamc@525 405 &&& X & \textrm{variable} \\
adamc@525 406 &&& \mt{functor}(X : S) : S & \textrm{functor} \\
adamc@529 407 &&& S \; \mt{where} \; \mt{con} \; x = c & \textrm{concretizing an abstract constructor} \\
adamc@525 408 &&& M.X & \textrm{projection from a module} \\
adamc@525 409 \\
adamc@525 410 \textrm{Signature items} & s &::=& \mt{con} \; x :: \kappa & \textrm{abstract constructor} \\
adamc@525 411 &&& \mt{con} \; x :: \kappa = c & \textrm{concrete constructor} \\
adamc@528 412 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529 413 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@525 414 &&& \mt{val} \; x : \tau & \textrm{value} \\
adamc@525 415 &&& \mt{structure} \; X : S & \textrm{sub-module} \\
adamc@525 416 &&& \mt{signature} \; X = S & \textrm{sub-signature} \\
adamc@525 417 &&& \mt{include} \; S & \textrm{signature inclusion} \\
adamc@525 418 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@654 419 &&& \mt{class} \; x :: \kappa & \textrm{abstract constructor class} \\
adamc@654 420 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@525 421 \\
adamc@525 422 \textrm{Datatype constructors} & dc &::=& X & \textrm{nullary constructor} \\
adamc@525 423 &&& X \; \mt{of} \; \tau & \textrm{unary constructor} \\
adamc@524 424 \end{array}$$
adamc@524 425
adamc@526 426 \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@526 427 $$\begin{array}{rrcll}
adamc@526 428 \textrm{Patterns} & p &::=& \_ & \textrm{wildcard} \\
adamc@526 429 &&& x & \textrm{variable} \\
adamc@526 430 &&& \ell & \textrm{constant} \\
adamc@526 431 &&& \hat{X} & \textrm{nullary constructor} \\
adamc@526 432 &&& \hat{X} \; p & \textrm{unary constructor} \\
adamc@526 433 &&& \{(x = p,)^*\} & \textrm{rigid record pattern} \\
adamc@526 434 &&& \{(x = p,)^+, \ldots\} & \textrm{flexible record pattern} \\
adamc@852 435 &&& p : \tau & \textrm{type annotation} \\
adamc@527 436 &&& (p) & \textrm{explicit precedence} \\
adamc@526 437 \\
adamc@529 438 \textrm{Qualified capitalized variables} & \hat{X} &::=& X & \textrm{not from a module} \\
adamc@526 439 &&& M.X & \textrm{projection from a module} \\
adamc@526 440 \end{array}$$
adamc@526 441
adamc@527 442 \emph{Expressions} are the main run-time entities, corresponding to both ``expressions'' and ``statements'' in mainstream imperative languages.
adamc@527 443 $$\begin{array}{rrcll}
adamc@527 444 \textrm{Expressions} & e &::=& e : \tau & \textrm{type annotation} \\
adamc@529 445 &&& \hat{x} & \textrm{variable} \\
adamc@529 446 &&& \hat{X} & \textrm{datatype constructor} \\
adamc@527 447 &&& \ell & \textrm{constant} \\
adamc@527 448 \\
adamc@527 449 &&& e \; e & \textrm{function application} \\
adamc@527 450 &&& \lambda x : \tau \Rightarrow e & \textrm{function abstraction} \\
adamc@527 451 &&& e [c] & \textrm{polymorphic function application} \\
adamc@852 452 &&& \lambda [x \; ? \; \kappa] \Rightarrow e & \textrm{polymorphic function abstraction} \\
adamc@655 453 &&& e [\kappa] & \textrm{kind-polymorphic function application} \\
adamc@652 454 &&& X \Longrightarrow e & \textrm{kind-polymorphic function abstraction} \\
adamc@527 455 \\
adamc@527 456 &&& \{(c = e,)^*\} & \textrm{known-length record} \\
adamc@527 457 &&& e.c & \textrm{record field projection} \\
adamc@527 458 &&& e \rc e & \textrm{record concatenation} \\
adamc@527 459 &&& e \rcut c & \textrm{removal of a single record field} \\
adamc@527 460 &&& e \rcutM c & \textrm{removal of multiple record fields} \\
adamc@527 461 \\
adamc@527 462 &&& \mt{let} \; ed^* \; \mt{in} \; e \; \mt{end} & \textrm{local definitions} \\
adamc@527 463 \\
adamc@527 464 &&& \mt{case} \; e \; \mt{of} \; (p \Rightarrow e|)^+ & \textrm{pattern matching} \\
adamc@527 465 \\
adamc@654 466 &&& \lambda [c \sim c] \Rightarrow e & \textrm{guarded expression abstraction} \\
adamc@654 467 &&& e \; ! & \textrm{guarded expression application} \\
adamc@527 468 \\
adamc@527 469 &&& \_ & \textrm{wildcard} \\
adamc@527 470 &&& (e) & \textrm{explicit precedence} \\
adamc@527 471 \\
adamc@527 472 \textrm{Local declarations} & ed &::=& \cd{val} \; x : \tau = e & \textrm{non-recursive value} \\
adamc@527 473 &&& \cd{val} \; \cd{rec} \; (x : \tau = e \; \cd{and})^+ & \textrm{mutually-recursive values} \\
adamc@527 474 \end{array}$$
adamc@527 475
adamc@655 476 As with constructors, we include both abstraction and application for kind polymorphism, but applications are only inferred internally.
adamc@655 477
adamc@528 478 \emph{Declarations} primarily bring new symbols into context.
adamc@528 479 $$\begin{array}{rrcll}
adamc@528 480 \textrm{Declarations} & d &::=& \mt{con} \; x :: \kappa = c & \textrm{constructor synonym} \\
adamc@528 481 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529 482 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@528 483 &&& \mt{val} \; x : \tau = e & \textrm{value} \\
adamc@528 484 &&& \mt{val} \; \cd{rec} \; (x : \tau = e \; \mt{and})^+ & \textrm{mutually-recursive values} \\
adamc@528 485 &&& \mt{structure} \; X : S = M & \textrm{module definition} \\
adamc@528 486 &&& \mt{signature} \; X = S & \textrm{signature definition} \\
adamc@528 487 &&& \mt{open} \; M & \textrm{module inclusion} \\
adamc@528 488 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@528 489 &&& \mt{open} \; \mt{constraints} \; M & \textrm{inclusion of just the constraints from a module} \\
adamc@528 490 &&& \mt{table} \; x : c & \textrm{SQL table} \\
adamc@784 491 &&& \mt{view} \; x : c & \textrm{SQL view} \\
adamc@528 492 &&& \mt{sequence} \; x & \textrm{SQL sequence} \\
adamc@535 493 &&& \mt{cookie} \; x : \tau & \textrm{HTTP cookie} \\
adamc@784 494 &&& \mt{style} \; x : \tau & \textrm{CSS class} \\
adamc@654 495 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@1085 496 &&& \mt{task} \; e = e & \textrm{recurring task} \\
adamc@528 497 \\
adamc@529 498 \textrm{Modules} & M &::=& \mt{struct} \; d^* \; \mt{end} & \textrm{constant} \\
adamc@529 499 &&& X & \textrm{variable} \\
adamc@529 500 &&& M.X & \textrm{projection} \\
adamc@529 501 &&& M(M) & \textrm{functor application} \\
adamc@529 502 &&& \mt{functor}(X : S) : S = M & \textrm{functor abstraction} \\
adamc@528 503 \end{array}$$
adamc@528 504
adamc@528 505 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@527 506
adamc@784 507 We omit some extra possibilities in $\mt{table}$ syntax, deferring them to Section \ref{tables}.
adamc@784 508
adamc@529 509 \subsection{Shorthands}
adamc@529 510
adamc@529 511 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@529 512
adamc@529 513 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@529 514
adamc@529 515 A record type may be written $\{(c = c,)^*\}$, which elaborates to $\$[(c = c,)^*]$.
adamc@529 516
adamc@533 517 The notation $[c_1, \ldots, c_n]$ is shorthand for $[c_1 = (), \ldots, c_n = ()]$.
adamc@533 518
adam@1350 519 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@529 520
adamc@852 521 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@529 522
adam@1306 523 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 524
adamc@529 525 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@529 526
adamc@529 527 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@529 528
adamc@654 529 A signature item or declaration $\mt{class} \; x = \lambda y \Rightarrow c$ may be abbreviated $\mt{class} \; x \; y = c$.
adamc@529 530
adam@1482 531 Handling of implicit and explicit constructor arguments may be tweaked with some prefixes to variable references. An expression $@x$ is a version of $x$ where all type class instance and disjointness arguments have been made explicit. (For the purposes of this paragraph, the type family $\mt{Top.folder}$ is a type class, though it isn't marked as one by the usual means.) 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@529 532
adamc@852 533 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@529 534
adamc@852 535 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@852 536
adamc@852 537 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@529 538
adamc@529 539 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@529 540
adamc@852 541 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@852 542
adamc@853 543 A declaration $\mt{table} \; x : \{(c = c,)^*\}$ is elaborated into $\mt{table} \; x : [(c = c,)^*]$.
adamc@529 544
adamc@529 545 The syntax $\mt{where} \; \mt{type}$ is an alternate form of $\mt{where} \; \mt{con}$.
adamc@529 546
adamc@529 547 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@529 548
adamc@529 549 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@529 550
adamc@784 551 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@529 552
adamc@530 553
adamc@530 554 \section{Static Semantics}
adamc@530 555
adamc@530 556 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@530 557
adamc@530 558 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@530 559 \begin{itemize}
adamc@655 560 \item $\Gamma \vdash \kappa$ expresses kind well-formedness.
adamc@530 561 \item $\Gamma \vdash c :: \kappa$ assigns a kind to a constructor in a context.
adamc@530 562 \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@531 563 \item $\Gamma \vdash c \hookrightarrow C$ proves that record constructor $c$ decomposes into set $C$ of field names and record constructors.
adamc@530 564 \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@530 565 \item $\Gamma \vdash e : \tau$ is a standard typing judgment.
adamc@534 566 \item $\Gamma \vdash p \leadsto \Gamma; \tau$ combines typing of patterns with calculation of which new variables they bind.
adamc@537 567 \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@537 568 \item $\Gamma \vdash S \equiv S$ is the signature equivalence judgment.
adamc@536 569 \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@530 570 \item $\Gamma \vdash M : S$ is the module signature checking judgment.
adamc@537 571 \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@539 572 \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@530 573 \end{itemize}
adamc@530 574
adamc@655 575
adamc@655 576 \subsection{Kind Well-Formedness}
adamc@655 577
adamc@655 578 $$\infer{\Gamma \vdash \mt{Type}}{}
adamc@655 579 \quad \infer{\Gamma \vdash \mt{Unit}}{}
adamc@655 580 \quad \infer{\Gamma \vdash \mt{Name}}{}
adamc@655 581 \quad \infer{\Gamma \vdash \kappa_1 \to \kappa_2}{
adamc@655 582 \Gamma \vdash \kappa_1
adamc@655 583 & \Gamma \vdash \kappa_2
adamc@655 584 }
adamc@655 585 \quad \infer{\Gamma \vdash \{\kappa\}}{
adamc@655 586 \Gamma \vdash \kappa
adamc@655 587 }
adamc@655 588 \quad \infer{\Gamma \vdash (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@655 589 \forall i: \Gamma \vdash \kappa_i
adamc@655 590 }$$
adamc@655 591
adamc@655 592 $$\infer{\Gamma \vdash X}{
adamc@655 593 X \in \Gamma
adamc@655 594 }
adamc@655 595 \quad \infer{\Gamma \vdash X \longrightarrow \kappa}{
adamc@655 596 \Gamma, X \vdash \kappa
adamc@655 597 }$$
adamc@655 598
adamc@530 599 \subsection{Kinding}
adamc@530 600
adamc@655 601 We write $[X \mapsto \kappa_1]\kappa_2$ for capture-avoiding substitution of $\kappa_1$ for $X$ in $\kappa_2$.
adamc@655 602
adamc@530 603 $$\infer{\Gamma \vdash (c) :: \kappa :: \kappa}{
adamc@530 604 \Gamma \vdash c :: \kappa
adamc@530 605 }
adamc@530 606 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530 607 x :: \kappa \in \Gamma
adamc@530 608 }
adamc@530 609 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530 610 x :: \kappa = c \in \Gamma
adamc@530 611 }$$
adamc@530 612
adamc@530 613 $$\infer{\Gamma \vdash M.x :: \kappa}{
adamc@537 614 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 615 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = \kappa
adamc@530 616 }
adamc@530 617 \quad \infer{\Gamma \vdash M.x :: \kappa}{
adamc@537 618 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 619 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@530 620 }$$
adamc@530 621
adamc@530 622 $$\infer{\Gamma \vdash \tau_1 \to \tau_2 :: \mt{Type}}{
adamc@530 623 \Gamma \vdash \tau_1 :: \mt{Type}
adamc@530 624 & \Gamma \vdash \tau_2 :: \mt{Type}
adamc@530 625 }
adamc@530 626 \quad \infer{\Gamma \vdash x \; ? \: \kappa \to \tau :: \mt{Type}}{
adamc@530 627 \Gamma, x :: \kappa \vdash \tau :: \mt{Type}
adamc@530 628 }
adamc@655 629 \quad \infer{\Gamma \vdash X \longrightarrow \tau :: \mt{Type}}{
adamc@655 630 \Gamma, X \vdash \tau :: \mt{Type}
adamc@655 631 }
adamc@530 632 \quad \infer{\Gamma \vdash \$c :: \mt{Type}}{
adamc@530 633 \Gamma \vdash c :: \{\mt{Type}\}
adamc@530 634 }$$
adamc@530 635
adamc@530 636 $$\infer{\Gamma \vdash c_1 \; c_2 :: \kappa_2}{
adamc@530 637 \Gamma \vdash c_1 :: \kappa_1 \to \kappa_2
adamc@530 638 & \Gamma \vdash c_2 :: \kappa_1
adamc@530 639 }
adamc@530 640 \quad \infer{\Gamma \vdash \lambda x \; :: \; \kappa_1 \Rightarrow c :: \kappa_1 \to \kappa_2}{
adamc@530 641 \Gamma, x :: \kappa_1 \vdash c :: \kappa_2
adamc@530 642 }$$
adamc@530 643
adamc@655 644 $$\infer{\Gamma \vdash c[\kappa'] :: [X \mapsto \kappa']\kappa}{
adamc@655 645 \Gamma \vdash c :: X \to \kappa
adamc@655 646 & \Gamma \vdash \kappa'
adamc@655 647 }
adamc@655 648 \quad \infer{\Gamma \vdash X \Longrightarrow c :: X \to \kappa}{
adamc@655 649 \Gamma, X \vdash c :: \kappa
adamc@655 650 }$$
adamc@655 651
adamc@530 652 $$\infer{\Gamma \vdash () :: \mt{Unit}}{}
adamc@530 653 \quad \infer{\Gamma \vdash \#X :: \mt{Name}}{}$$
adamc@530 654
adamc@530 655 $$\infer{\Gamma \vdash [\overline{c_i = c'_i}] :: \{\kappa\}}{
adamc@530 656 \forall i: \Gamma \vdash c_i : \mt{Name}
adamc@530 657 & \Gamma \vdash c'_i :: \kappa
adamc@530 658 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@530 659 }
adamc@530 660 \quad \infer{\Gamma \vdash c_1 \rc c_2 :: \{\kappa\}}{
adamc@530 661 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530 662 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@530 663 & \Gamma \vdash c_1 \sim c_2
adamc@530 664 }$$
adamc@530 665
adamc@655 666 $$\infer{\Gamma \vdash \mt{map} :: (\kappa_1 \to \kappa_2) \to \{\kappa_1\} \to \{\kappa_2\}}{}$$
adamc@530 667
adamc@573 668 $$\infer{\Gamma \vdash (\overline c) :: (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@573 669 \forall i: \Gamma \vdash c_i :: \kappa_i
adamc@530 670 }
adamc@573 671 \quad \infer{\Gamma \vdash c.i :: \kappa_i}{
adamc@573 672 \Gamma \vdash c :: (\kappa_1 \times \ldots \times \kappa_n)
adamc@530 673 }$$
adamc@530 674
adamc@655 675 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow \tau :: \mt{Type}}{
adamc@655 676 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530 677 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@655 678 & \Gamma, c_1 \sim c_2 \vdash \tau :: \mt{Type}
adamc@530 679 }$$
adamc@530 680
adamc@531 681 \subsection{Record Disjointness}
adamc@531 682
adamc@531 683 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@558 684 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@558 685 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@558 686 & \forall c'_1 \in C_1, c'_2 \in C_2: \Gamma \vdash c'_1 \sim c'_2
adamc@531 687 }
adamc@531 688 \quad \infer{\Gamma \vdash X \sim X'}{
adamc@531 689 X \neq X'
adamc@531 690 }$$
adamc@531 691
adamc@531 692 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@531 693 c'_1 \sim c'_2 \in \Gamma
adamc@558 694 & \Gamma \vdash c'_1 \hookrightarrow C_1
adamc@558 695 & \Gamma \vdash c'_2 \hookrightarrow C_2
adamc@558 696 & c_1 \in C_1
adamc@558 697 & c_2 \in C_2
adamc@531 698 }$$
adamc@531 699
adamc@531 700 $$\infer{\Gamma \vdash c \hookrightarrow \{c\}}{}
adamc@531 701 \quad \infer{\Gamma \vdash [\overline{c = c'}] \hookrightarrow \{\overline{c}\}}{}
adamc@531 702 \quad \infer{\Gamma \vdash c_1 \rc c_2 \hookrightarrow C_1 \cup C_2}{
adamc@531 703 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@531 704 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@531 705 }
adamc@531 706 \quad \infer{\Gamma \vdash c \hookrightarrow C}{
adamc@531 707 \Gamma \vdash c \equiv c'
adamc@531 708 & \Gamma \vdash c' \hookrightarrow C
adamc@531 709 }
adamc@531 710 \quad \infer{\Gamma \vdash \mt{map} \; f \; c \hookrightarrow C}{
adamc@531 711 \Gamma \vdash c \hookrightarrow C
adamc@531 712 }$$
adamc@531 713
adamc@541 714 \subsection{\label{definitional}Definitional Equality}
adamc@532 715
adamc@655 716 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@532 717
adamc@532 718 $$\infer{\Gamma \vdash c \equiv c}{}
adamc@532 719 \quad \infer{\Gamma \vdash c_1 \equiv c_2}{
adamc@532 720 \Gamma \vdash c_2 \equiv c_1
adamc@532 721 }
adamc@532 722 \quad \infer{\Gamma \vdash c_1 \equiv c_3}{
adamc@532 723 \Gamma \vdash c_1 \equiv c_2
adamc@532 724 & \Gamma \vdash c_2 \equiv c_3
adamc@532 725 }
adamc@532 726 \quad \infer{\Gamma \vdash \mathcal C[c_1] \equiv \mathcal C[c_2]}{
adamc@532 727 \Gamma \vdash c_1 \equiv c_2
adamc@532 728 }$$
adamc@532 729
adamc@532 730 $$\infer{\Gamma \vdash x \equiv c}{
adamc@532 731 x :: \kappa = c \in \Gamma
adamc@532 732 }
adamc@532 733 \quad \infer{\Gamma \vdash M.x \equiv c}{
adamc@537 734 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 735 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@532 736 }
adamc@532 737 \quad \infer{\Gamma \vdash (\overline c).i \equiv c_i}{}$$
adamc@532 738
adamc@532 739 $$\infer{\Gamma \vdash (\lambda x :: \kappa \Rightarrow c) \; c' \equiv [x \mapsto c'] c}{}
adamc@655 740 \quad \infer{\Gamma \vdash (X \Longrightarrow c) [\kappa] \equiv [X \mapsto \kappa] c}{}$$
adamc@655 741
adamc@655 742 $$\infer{\Gamma \vdash c_1 \rc c_2 \equiv c_2 \rc c_1}{}
adamc@532 743 \quad \infer{\Gamma \vdash c_1 \rc (c_2 \rc c_3) \equiv (c_1 \rc c_2) \rc c_3}{}$$
adamc@532 744
adamc@532 745 $$\infer{\Gamma \vdash [] \rc c \equiv c}{}
adamc@532 746 \quad \infer{\Gamma \vdash [\overline{c_1 = c'_1}] \rc [\overline{c_2 = c'_2}] \equiv [\overline{c_1 = c'_1}, \overline{c_2 = c'_2}]}{}$$
adamc@532 747
adamc@655 748 $$\infer{\Gamma \vdash \mt{map} \; f \; [] \equiv []}{}
adamc@655 749 \quad \infer{\Gamma \vdash \mt{map} \; f \; ([c_1 = c_2] \rc c) \equiv [c_1 = f \; c_2] \rc \mt{map} \; f \; c}{}$$
adamc@532 750
adamc@532 751 $$\infer{\Gamma \vdash \mt{map} \; (\lambda x \Rightarrow x) \; c \equiv c}{}
adamc@655 752 \quad \infer{\Gamma \vdash \mt{map} \; f \; (\mt{map} \; f' \; c)
adamc@655 753 \equiv \mt{map} \; (\lambda x \Rightarrow f \; (f' \; x)) \; c}{}$$
adamc@532 754
adamc@532 755 $$\infer{\Gamma \vdash \mt{map} \; f \; (c_1 \rc c_2) \equiv \mt{map} \; f \; c_1 \rc \mt{map} \; f \; c_2}{}$$
adamc@531 756
adamc@534 757 \subsection{Expression Typing}
adamc@533 758
adamc@873 759 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@533 760
adamc@533 761 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@533 762
adamc@533 763 $$\infer{\Gamma \vdash e : \tau : \tau}{
adamc@533 764 \Gamma \vdash e : \tau
adamc@533 765 }
adamc@533 766 \quad \infer{\Gamma \vdash e : \tau}{
adamc@533 767 \Gamma \vdash e : \tau'
adamc@533 768 & \Gamma \vdash \tau' \equiv \tau
adamc@533 769 }
adamc@533 770 \quad \infer{\Gamma \vdash \ell : T(\ell)}{}$$
adamc@533 771
adamc@533 772 $$\infer{\Gamma \vdash x : \mathcal I(\tau)}{
adamc@533 773 x : \tau \in \Gamma
adamc@533 774 }
adamc@533 775 \quad \infer{\Gamma \vdash M.x : \mathcal I(\tau)}{
adamc@537 776 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 777 & \mt{proj}(M, \overline{s}, \mt{val} \; x) = \tau
adamc@533 778 }
adamc@533 779 \quad \infer{\Gamma \vdash X : \mathcal I(\tau)}{
adamc@533 780 X : \tau \in \Gamma
adamc@533 781 }
adamc@533 782 \quad \infer{\Gamma \vdash M.X : \mathcal I(\tau)}{
adamc@537 783 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 784 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \tau
adamc@533 785 }$$
adamc@533 786
adamc@533 787 $$\infer{\Gamma \vdash e_1 \; e_2 : \tau_2}{
adamc@533 788 \Gamma \vdash e_1 : \tau_1 \to \tau_2
adamc@533 789 & \Gamma \vdash e_2 : \tau_1
adamc@533 790 }
adamc@533 791 \quad \infer{\Gamma \vdash \lambda x : \tau_1 \Rightarrow e : \tau_1 \to \tau_2}{
adamc@533 792 \Gamma, x : \tau_1 \vdash e : \tau_2
adamc@533 793 }$$
adamc@533 794
adamc@533 795 $$\infer{\Gamma \vdash e [c] : [x \mapsto c]\tau}{
adamc@533 796 \Gamma \vdash e : x :: \kappa \to \tau
adamc@533 797 & \Gamma \vdash c :: \kappa
adamc@533 798 }
adamc@852 799 \quad \infer{\Gamma \vdash \lambda [x \; ? \; \kappa] \Rightarrow e : x \; ? \; \kappa \to \tau}{
adamc@533 800 \Gamma, x :: \kappa \vdash e : \tau
adamc@533 801 }$$
adamc@533 802
adamc@655 803 $$\infer{\Gamma \vdash e [\kappa] : [X \mapsto \kappa]\tau}{
adamc@655 804 \Gamma \vdash e : X \longrightarrow \tau
adamc@655 805 & \Gamma \vdash \kappa
adamc@655 806 }
adamc@655 807 \quad \infer{\Gamma \vdash X \Longrightarrow e : X \longrightarrow \tau}{
adamc@655 808 \Gamma, X \vdash e : \tau
adamc@655 809 }$$
adamc@655 810
adamc@533 811 $$\infer{\Gamma \vdash \{\overline{c = e}\} : \{\overline{c : \tau}\}}{
adamc@533 812 \forall i: \Gamma \vdash c_i :: \mt{Name}
adamc@533 813 & \Gamma \vdash e_i : \tau_i
adamc@533 814 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@533 815 }
adamc@533 816 \quad \infer{\Gamma \vdash e.c : \tau}{
adamc@533 817 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533 818 }
adamc@533 819 \quad \infer{\Gamma \vdash e_1 \rc e_2 : \$(c_1 \rc c_2)}{
adamc@533 820 \Gamma \vdash e_1 : \$c_1
adamc@533 821 & \Gamma \vdash e_2 : \$c_2
adamc@573 822 & \Gamma \vdash c_1 \sim c_2
adamc@533 823 }$$
adamc@533 824
adamc@533 825 $$\infer{\Gamma \vdash e \rcut c : \$c'}{
adamc@533 826 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533 827 }
adamc@533 828 \quad \infer{\Gamma \vdash e \rcutM c : \$c'}{
adamc@533 829 \Gamma \vdash e : \$(c \rc c')
adamc@533 830 }$$
adamc@533 831
adamc@533 832 $$\infer{\Gamma \vdash \mt{let} \; \overline{ed} \; \mt{in} \; e \; \mt{end} : \tau}{
adamc@533 833 \Gamma \vdash \overline{ed} \leadsto \Gamma'
adamc@533 834 & \Gamma' \vdash e : \tau
adamc@533 835 }
adamc@533 836 \quad \infer{\Gamma \vdash \mt{case} \; e \; \mt{of} \; \overline{p \Rightarrow e} : \tau}{
adamc@533 837 \forall i: \Gamma \vdash p_i \leadsto \Gamma_i, \tau'
adamc@533 838 & \Gamma_i \vdash e_i : \tau
adamc@533 839 }$$
adamc@533 840
adamc@573 841 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow e : \lambda [c_1 \sim c_2] \Rightarrow \tau}{
adamc@533 842 \Gamma \vdash c_1 :: \{\kappa\}
adamc@655 843 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@533 844 & \Gamma, c_1 \sim c_2 \vdash e : \tau
adamc@662 845 }
adamc@662 846 \quad \infer{\Gamma \vdash e \; ! : \tau}{
adamc@662 847 \Gamma \vdash e : [c_1 \sim c_2] \Rightarrow \tau
adamc@662 848 & \Gamma \vdash c_1 \sim c_2
adamc@533 849 }$$
adamc@533 850
adamc@534 851 \subsection{Pattern Typing}
adamc@534 852
adamc@534 853 $$\infer{\Gamma \vdash \_ \leadsto \Gamma; \tau}{}
adamc@534 854 \quad \infer{\Gamma \vdash x \leadsto \Gamma, x : \tau; \tau}{}
adamc@534 855 \quad \infer{\Gamma \vdash \ell \leadsto \Gamma; T(\ell)}{}$$
adamc@534 856
adamc@534 857 $$\infer{\Gamma \vdash X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534 858 X : \overline{x ::: \mt{Type}} \to \tau \in \Gamma
adamc@534 859 & \textrm{$\tau$ not a function type}
adamc@534 860 }
adamc@534 861 \quad \infer{\Gamma \vdash X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534 862 X : \overline{x ::: \mt{Type}} \to \tau'' \to \tau \in \Gamma
adamc@534 863 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534 864 }$$
adamc@534 865
adamc@534 866 $$\infer{\Gamma \vdash M.X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537 867 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 868 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau
adamc@534 869 & \textrm{$\tau$ not a function type}
adamc@534 870 }$$
adamc@534 871
adamc@534 872 $$\infer{\Gamma \vdash M.X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537 873 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 874 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau'' \to \tau
adamc@534 875 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534 876 }$$
adamc@534 877
adamc@534 878 $$\infer{\Gamma \vdash \{\overline{x = p}\} \leadsto \Gamma_n; \{\overline{x = \tau}\}}{
adamc@534 879 \Gamma_0 = \Gamma
adamc@534 880 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534 881 }
adamc@534 882 \quad \infer{\Gamma \vdash \{\overline{x = p}, \ldots\} \leadsto \Gamma_n; \$([\overline{x = \tau}] \rc c)}{
adamc@534 883 \Gamma_0 = \Gamma
adamc@534 884 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534 885 }$$
adamc@534 886
adamc@852 887 $$\infer{\Gamma \vdash p : \tau \leadsto \Gamma'; \tau}{
adamc@852 888 \Gamma \vdash p \leadsto \Gamma'; \tau'
adamc@852 889 & \Gamma \vdash \tau' \equiv \tau
adamc@852 890 }$$
adamc@852 891
adamc@535 892 \subsection{Declaration Typing}
adamc@535 893
adamc@535 894 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@535 895
adamc@655 896 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@535 897
adamc@558 898 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@537 899 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@535 900
adamc@535 901 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535 902 \quad \infer{\Gamma \vdash d, \overline{d} \leadsto \Gamma''}{
adamc@535 903 \Gamma \vdash d \leadsto \Gamma'
adamc@535 904 & \Gamma' \vdash \overline{d} \leadsto \Gamma''
adamc@535 905 }$$
adamc@535 906
adamc@535 907 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@535 908 \Gamma \vdash c :: \kappa
adamc@535 909 }
adamc@535 910 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@535 911 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@535 912 }$$
adamc@535 913
adamc@535 914 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537 915 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 916 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@535 917 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@535 918 }$$
adamc@535 919
adamc@535 920 $$\infer{\Gamma \vdash \mt{val} \; x : \tau = e \leadsto \Gamma, x : \tau}{
adamc@535 921 \Gamma \vdash e : \tau
adamc@535 922 }$$
adamc@535 923
adamc@535 924 $$\infer{\Gamma \vdash \mt{val} \; \mt{rec} \; \overline{x : \tau = e} \leadsto \Gamma, \overline{x : \tau}}{
adamc@535 925 \forall i: \Gamma, \overline{x : \tau} \vdash e_i : \tau_i
adamc@535 926 & \textrm{$e_i$ starts with an expression $\lambda$, optionally preceded by constructor and disjointness $\lambda$s}
adamc@535 927 }$$
adamc@535 928
adamc@535 929 $$\infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : S}{
adamc@535 930 \Gamma \vdash M : S
adamc@558 931 & \textrm{ $M$ not a constant or application}
adamc@535 932 }
adamc@558 933 \quad \infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : \mt{selfify}(X, \overline{s})}{
adamc@558 934 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@539 935 }$$
adamc@539 936
adamc@539 937 $$\infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@535 938 \Gamma \vdash S
adamc@535 939 }$$
adamc@535 940
adamc@537 941 $$\infer{\Gamma \vdash \mt{open} \; M \leadsto \Gamma, \mathcal O(M, \overline{s})}{
adamc@537 942 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535 943 }$$
adamc@535 944
adamc@535 945 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma}{
adamc@535 946 \Gamma \vdash c_1 :: \{\kappa\}
adamc@535 947 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@535 948 & \Gamma \vdash c_1 \sim c_2
adamc@535 949 }
adamc@537 950 \quad \infer{\Gamma \vdash \mt{open} \; \mt{constraints} \; M \leadsto \Gamma, \mathcal O_c(M, \overline{s})}{
adamc@537 951 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535 952 }$$
adamc@535 953
adamc@784 954 $$\infer{\Gamma \vdash \mt{table} \; x : c \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_table} \; c \; []}{
adamc@535 955 \Gamma \vdash c :: \{\mt{Type}\}
adamc@535 956 }
adamc@784 957 \quad \infer{\Gamma \vdash \mt{view} \; x : c \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_view} \; c}{
adamc@784 958 \Gamma \vdash c :: \{\mt{Type}\}
adamc@784 959 }$$
adamc@784 960
adamc@784 961 $$\infer{\Gamma \vdash \mt{sequence} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_sequence}}{}$$
adamc@535 962
adamc@535 963 $$\infer{\Gamma \vdash \mt{cookie} \; x : \tau \leadsto \Gamma, x : \mt{Basis}.\mt{http\_cookie} \; \tau}{
adamc@535 964 \Gamma \vdash \tau :: \mt{Type}
adamc@784 965 }
adamc@784 966 \quad \infer{\Gamma \vdash \mt{style} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{css\_class}}{}$$
adamc@535 967
adamc@1085 968 $$\infer{\Gamma \vdash \mt{task} \; e_1 = e_2 \leadsto \Gamma}{
adam@1348 969 \Gamma \vdash e_1 :: \mt{Basis}.\mt{task\_kind} \; \tau
adam@1348 970 & \Gamma \vdash e_2 :: \tau \to \mt{Basis}.\mt{transaction} \; \{\}
adamc@1085 971 }$$
adamc@1085 972
adamc@784 973 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784 974 \Gamma \vdash c :: \kappa
adamc@535 975 }$$
adamc@535 976
adamc@535 977 $$\infer{\overline{y}; x; \Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535 978 \quad \infer{\overline{y}; x; \Gamma \vdash X \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to x \; \overline{y}}{
adamc@535 979 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535 980 }
adamc@535 981 \quad \infer{\overline{y}; x; \Gamma \vdash X \; \mt{of} \; \tau \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to \tau \to x \; \overline{y}}{
adamc@535 982 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535 983 }$$
adamc@535 984
adamc@537 985 \subsection{Signature Item Typing}
adamc@537 986
adamc@537 987 We appeal to a signature item analogue of the $\mathcal O$ function from the last subsection.
adamc@537 988
adamc@537 989 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@537 990 \quad \infer{\Gamma \vdash s, \overline{s} \leadsto \Gamma''}{
adamc@537 991 \Gamma \vdash s \leadsto \Gamma'
adamc@537 992 & \Gamma' \vdash \overline{s} \leadsto \Gamma''
adamc@537 993 }$$
adamc@537 994
adamc@537 995 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}
adamc@537 996 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@537 997 \Gamma \vdash c :: \kappa
adamc@537 998 }
adamc@537 999 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@537 1000 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@537 1001 }$$
adamc@537 1002
adamc@537 1003 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537 1004 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1005 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1006 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@537 1007 }$$
adamc@537 1008
adamc@537 1009 $$\infer{\Gamma \vdash \mt{val} \; x : \tau \leadsto \Gamma, x : \tau}{
adamc@537 1010 \Gamma \vdash \tau :: \mt{Type}
adamc@537 1011 }$$
adamc@537 1012
adamc@537 1013 $$\infer{\Gamma \vdash \mt{structure} \; X : S \leadsto \Gamma, X : S}{
adamc@537 1014 \Gamma \vdash S
adamc@537 1015 }
adamc@537 1016 \quad \infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@537 1017 \Gamma \vdash S
adamc@537 1018 }$$
adamc@537 1019
adamc@537 1020 $$\infer{\Gamma \vdash \mt{include} \; S \leadsto \Gamma, \mathcal O(\overline{s})}{
adamc@537 1021 \Gamma \vdash S
adamc@537 1022 & \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1023 }$$
adamc@537 1024
adamc@537 1025 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma, c_1 \sim c_2}{
adamc@537 1026 \Gamma \vdash c_1 :: \{\kappa\}
adamc@537 1027 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@537 1028 }$$
adamc@537 1029
adamc@784 1030 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784 1031 \Gamma \vdash c :: \kappa
adamc@537 1032 }
adamc@784 1033 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}$$
adamc@537 1034
adamc@536 1035 \subsection{Signature Compatibility}
adamc@536 1036
adamc@558 1037 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 1038
adamc@537 1039 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 1040
adamc@536 1041 $$\infer{\Gamma \vdash S \equiv S}{}
adamc@536 1042 \quad \infer{\Gamma \vdash S_1 \equiv S_2}{
adamc@536 1043 \Gamma \vdash S_2 \equiv S_1
adamc@536 1044 }
adamc@536 1045 \quad \infer{\Gamma \vdash X \equiv S}{
adamc@536 1046 X = S \in \Gamma
adamc@536 1047 }
adamc@536 1048 \quad \infer{\Gamma \vdash M.X \equiv S}{
adamc@537 1049 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1050 & \mt{proj}(M, \overline{s}, \mt{signature} \; X) = S
adamc@536 1051 }$$
adamc@536 1052
adamc@536 1053 $$\infer{\Gamma \vdash S \; \mt{where} \; \mt{con} \; x = c \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa = c \; \overline{s_2} \; \mt{end}}{
adamc@536 1054 \Gamma \vdash S \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa \; \overline{s_2} \; \mt{end}
adamc@536 1055 & \Gamma \vdash c :: \kappa
adamc@537 1056 }
adamc@537 1057 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s^1} \; \mt{include} \; S \; \overline{s^2} \; \mt{end} \equiv \mt{sig} \; \overline{s^1} \; \overline{s} \; \overline{s^2} \; \mt{end}}{
adamc@537 1058 \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@536 1059 }$$
adamc@536 1060
adamc@536 1061 $$\infer{\Gamma \vdash S_1 \leq S_2}{
adamc@536 1062 \Gamma \vdash S_1 \equiv S_2
adamc@536 1063 }
adamc@536 1064 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \mt{end}}{}
adamc@537 1065 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; s' \; \overline{s'} \; \mt{end}}{
adamc@537 1066 \Gamma \vdash \overline{s} \leq s'
adamc@537 1067 & \Gamma \vdash s' \leadsto \Gamma'
adamc@537 1068 & \Gamma' \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \overline{s'} \; \mt{end}
adamc@537 1069 }$$
adamc@537 1070
adamc@537 1071 $$\infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537 1072 \Gamma \vdash s \leq s'
adamc@537 1073 }
adamc@537 1074 \quad \infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537 1075 \Gamma \vdash s \leadsto \Gamma'
adamc@537 1076 & \Gamma' \vdash \overline{s} \leq s'
adamc@536 1077 }$$
adamc@536 1078
adamc@536 1079 $$\infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 \leq \mt{functor} (X : S'_1) : S'_2}{
adamc@536 1080 \Gamma \vdash S'_1 \leq S_1
adamc@536 1081 & \Gamma, X : S'_1 \vdash S_2 \leq S'_2
adamc@536 1082 }$$
adamc@536 1083
adamc@537 1084 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@537 1085 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}
adamc@558 1086 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type}}{}$$
adamc@537 1087
adamc@537 1088 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(y)} \to \mt{Type}}{
adamc@537 1089 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1090 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1091 }$$
adamc@537 1092
adamc@784 1093 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@784 1094 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}$$
adamc@537 1095
adamc@537 1096 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \mt{\kappa} = c_2}{
adamc@537 1097 \Gamma \vdash c_1 \equiv c_2
adamc@537 1098 }
adamc@784 1099 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \kappa = c_2}{
adamc@537 1100 \Gamma \vdash c_1 \equiv c_2
adamc@537 1101 }$$
adamc@537 1102
adamc@537 1103 $$\infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537 1104 \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1105 }$$
adamc@537 1106
adamc@537 1107 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537 1108 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1109 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1110 & \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1111 }$$
adamc@537 1112
adamc@537 1113 $$\infer{\Gamma \vdash \cdot \leq \cdot}{}
adamc@537 1114 \quad \infer{\Gamma \vdash X; \overline{dc} \leq X; \overline{dc'}}{
adamc@537 1115 \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1116 }
adamc@537 1117 \quad \infer{\Gamma \vdash X \; \mt{of} \; \tau_1; \overline{dc} \leq X \; \mt{of} \; \tau_2; \overline{dc'}}{
adamc@537 1118 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537 1119 & \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1120 }$$
adamc@537 1121
adamc@537 1122 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x = \mt{datatype} \; M'.z'}{
adamc@537 1123 \Gamma \vdash M.z \equiv M'.z'
adamc@537 1124 }$$
adamc@537 1125
adamc@537 1126 $$\infer{\Gamma \vdash \mt{val} \; x : \tau_1 \leq \mt{val} \; x : \tau_2}{
adamc@537 1127 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537 1128 }
adamc@537 1129 \quad \infer{\Gamma \vdash \mt{structure} \; X : S_1 \leq \mt{structure} \; X : S_2}{
adamc@537 1130 \Gamma \vdash S_1 \leq S_2
adamc@537 1131 }
adamc@537 1132 \quad \infer{\Gamma \vdash \mt{signature} \; X = S_1 \leq \mt{signature} \; X = S_2}{
adamc@537 1133 \Gamma \vdash S_1 \leq S_2
adamc@537 1134 & \Gamma \vdash S_2 \leq S_1
adamc@537 1135 }$$
adamc@537 1136
adamc@537 1137 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leq \mt{constraint} \; c'_1 \sim c'_2}{
adamc@537 1138 \Gamma \vdash c_1 \equiv c'_1
adamc@537 1139 & \Gamma \vdash c_2 \equiv c'_2
adamc@537 1140 }$$
adamc@537 1141
adamc@655 1142 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{class} \; x :: \kappa}{}
adamc@655 1143 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{class} \; x :: \kappa}{}
adamc@655 1144 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{class} \; x :: \kappa = c_2}{
adamc@537 1145 \Gamma \vdash c_1 \equiv c_2
adamc@537 1146 }$$
adamc@537 1147
adamc@538 1148 \subsection{Module Typing}
adamc@538 1149
adamc@538 1150 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 1151
adamc@538 1152 $$\infer{\Gamma \vdash M : S}{
adamc@538 1153 \Gamma \vdash M : S'
adamc@538 1154 & \Gamma \vdash S' \leq S
adamc@538 1155 }
adamc@538 1156 \quad \infer{\Gamma \vdash \mt{struct} \; \overline{d} \; \mt{end} : \mt{sig} \; \mt{sigOf}(\overline{d}) \; \mt{end}}{
adamc@538 1157 \Gamma \vdash \overline{d} \leadsto \Gamma'
adamc@538 1158 }
adamc@538 1159 \quad \infer{\Gamma \vdash X : S}{
adamc@538 1160 X : S \in \Gamma
adamc@538 1161 }$$
adamc@538 1162
adamc@538 1163 $$\infer{\Gamma \vdash M.X : S}{
adamc@538 1164 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@538 1165 & \mt{proj}(M, \overline{s}, \mt{structure} \; X) = S
adamc@538 1166 }$$
adamc@538 1167
adamc@538 1168 $$\infer{\Gamma \vdash M_1(M_2) : [X \mapsto M_2]S_2}{
adamc@538 1169 \Gamma \vdash M_1 : \mt{functor}(X : S_1) : S_2
adamc@538 1170 & \Gamma \vdash M_2 : S_1
adamc@538 1171 }
adamc@538 1172 \quad \infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 = M : \mt{functor} (X : S_1) : S_2}{
adamc@538 1173 \Gamma \vdash S_1
adamc@538 1174 & \Gamma, X : S_1 \vdash S_2
adamc@538 1175 & \Gamma, X : S_1 \vdash M : S_2
adamc@538 1176 }$$
adamc@538 1177
adamc@538 1178 \begin{eqnarray*}
adamc@538 1179 \mt{sigOf}(\cdot) &=& \cdot \\
adamc@538 1180 \mt{sigOf}(s \; \overline{s'}) &=& \mt{sigOf}(s) \; \mt{sigOf}(\overline{s'}) \\
adamc@538 1181 \\
adamc@538 1182 \mt{sigOf}(\mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@538 1183 \mt{sigOf}(\mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \overline{dc} \\
adamc@538 1184 \mt{sigOf}(\mt{datatype} \; x = \mt{datatype} \; M.z) &=& \mt{datatype} \; x = \mt{datatype} \; M.z \\
adamc@538 1185 \mt{sigOf}(\mt{val} \; x : \tau = e) &=& \mt{val} \; x : \tau \\
adamc@538 1186 \mt{sigOf}(\mt{val} \; \mt{rec} \; \overline{x : \tau = e}) &=& \overline{\mt{val} \; x : \tau} \\
adamc@538 1187 \mt{sigOf}(\mt{structure} \; X : S = M) &=& \mt{structure} \; X : S \\
adamc@538 1188 \mt{sigOf}(\mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@538 1189 \mt{sigOf}(\mt{open} \; M) &=& \mt{include} \; S \textrm{ (where $\Gamma \vdash M : S$)} \\
adamc@538 1190 \mt{sigOf}(\mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@538 1191 \mt{sigOf}(\mt{open} \; \mt{constraints} \; M) &=& \cdot \\
adamc@538 1192 \mt{sigOf}(\mt{table} \; x : c) &=& \mt{table} \; x : c \\
adamc@784 1193 \mt{sigOf}(\mt{view} \; x : c) &=& \mt{view} \; x : c \\
adamc@538 1194 \mt{sigOf}(\mt{sequence} \; x) &=& \mt{sequence} \; x \\
adamc@538 1195 \mt{sigOf}(\mt{cookie} \; x : \tau) &=& \mt{cookie} \; x : \tau \\
adamc@784 1196 \mt{sigOf}(\mt{style} \; x) &=& \mt{style} \; x \\
adamc@655 1197 \mt{sigOf}(\mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@538 1198 \end{eqnarray*}
adamc@539 1199 \begin{eqnarray*}
adamc@539 1200 \mt{selfify}(M, \cdot) &=& \cdot \\
adamc@558 1201 \mt{selfify}(M, s \; \overline{s'}) &=& \mt{selfify}(M, s) \; \mt{selfify}(M, \overline{s'}) \\
adamc@539 1202 \\
adamc@539 1203 \mt{selfify}(M, \mt{con} \; x :: \kappa) &=& \mt{con} \; x :: \kappa = M.x \\
adamc@539 1204 \mt{selfify}(M, \mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@539 1205 \mt{selfify}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \mt{datatype} \; M.x \\
adamc@539 1206 \mt{selfify}(M, \mt{datatype} \; x = \mt{datatype} \; M'.z) &=& \mt{datatype} \; x = \mt{datatype} \; M'.z \\
adamc@539 1207 \mt{selfify}(M, \mt{val} \; x : \tau) &=& \mt{val} \; x : \tau \\
adamc@539 1208 \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 1209 \mt{selfify}(M, \mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@539 1210 \mt{selfify}(M, \mt{include} \; S) &=& \mt{include} \; S \\
adamc@539 1211 \mt{selfify}(M, \mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@655 1212 \mt{selfify}(M, \mt{class} \; x :: \kappa) &=& \mt{class} \; x :: \kappa = M.x \\
adamc@655 1213 \mt{selfify}(M, \mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@539 1214 \end{eqnarray*}
adamc@539 1215
adamc@540 1216 \subsection{Module Projection}
adamc@540 1217
adamc@540 1218 \begin{eqnarray*}
adamc@540 1219 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \\
adamc@540 1220 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa, c) \\
adamc@540 1221 \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 1222 \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 1223 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})$)} \\
adamc@655 1224 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \to \mt{Type} \\
adamc@655 1225 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa \to \mt{Type}, c) \\
adamc@540 1226 \\
adamc@540 1227 \mt{proj}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc} \; \overline{s}, \mt{datatype} \; x) &=& (\overline{y}, \overline{dc}) \\
adamc@540 1228 \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 1229 \\
adamc@540 1230 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, \mt{val} \; x) &=& \tau \\
adamc@540 1231 \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 1232 \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 1233 \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 1234 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \in \overline{dc}$)} \\
adamc@540 1235 \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 1236 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \; \mt{of} \; \tau \in \overline{dc}$)} \\
adamc@540 1237 \\
adamc@540 1238 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, \mt{structure} \; X) &=& S \\
adamc@540 1239 \\
adamc@540 1240 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, \mt{signature} \; X) &=& S \\
adamc@540 1241 \\
adamc@540 1242 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1243 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1244 \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 1245 \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 1246 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@540 1247 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1248 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1249 \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 1250 \mt{proj}(M, \mt{constraint} \; c_1 \sim c_2 \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@655 1251 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@655 1252 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1253 \end{eqnarray*}
adamc@540 1254
adamc@541 1255
adamc@541 1256 \section{Type Inference}
adamc@541 1257
adamc@541 1258 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 1259
adamc@541 1260 \subsection{Basic Unification}
adamc@541 1261
adamc@560 1262 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 1263
adamc@656 1264 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 1265
adamc@541 1266 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 1267
adamc@541 1268 \subsection{Unifying Record Types}
adamc@541 1269
adamc@570 1270 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 1271
adamc@656 1272 \subsection{\label{typeclasses}Constructor Classes}
adamc@541 1273
adamc@784 1274 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 1275
adamc@784 1276 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 1277
adamc@656 1278 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 1279
adamc@656 1280 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 1281
adamc@541 1282 \subsection{Reverse-Engineering Record Types}
adamc@541 1283
adamc@656 1284 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 1285
adamc@541 1286 \subsection{Implicit Arguments in Functor Applications}
adamc@541 1287
adamc@656 1288 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 1289
adamc@541 1290
adamc@542 1291 \section{The Ur Standard Library}
adamc@542 1292
adamc@542 1293 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 1294
adamc@542 1295 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 1296
adamc@542 1297 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 1298 $$\begin{array}{l}
adamc@542 1299 \mt{type} \; \mt{int} \\
adamc@542 1300 \mt{type} \; \mt{float} \\
adamc@873 1301 \mt{type} \; \mt{char} \\
adamc@542 1302 \mt{type} \; \mt{string} \\
adamc@542 1303 \mt{type} \; \mt{time} \\
adamc@785 1304 \mt{type} \; \mt{blob} \\
adamc@542 1305 \\
adamc@542 1306 \mt{type} \; \mt{unit} = \{\} \\
adamc@542 1307 \\
adamc@542 1308 \mt{datatype} \; \mt{bool} = \mt{False} \mid \mt{True} \\
adamc@542 1309 \\
adamc@785 1310 \mt{datatype} \; \mt{option} \; \mt{t} = \mt{None} \mid \mt{Some} \; \mt{of} \; \mt{t} \\
adamc@785 1311 \\
adamc@785 1312 \mt{datatype} \; \mt{list} \; \mt{t} = \mt{Nil} \mid \mt{Cons} \; \mt{of} \; \mt{t} \times \mt{list} \; \mt{t}
adamc@542 1313 \end{array}$$
adamc@542 1314
adamc@1123 1315 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 1316
adam@1297 1317 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 1318 $$\begin{array}{l}
adam@1297 1319 \mt{con} \; \mt{variant} :: \{\mt{Type}\} \to \mt{Type} \\
adam@1297 1320 \mt{val} \; \mt{make} : \mt{nm} :: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{ts} ::: \{\mt{Type}\} \to [[\mt{nm}] \sim \mt{ts}] \Rightarrow \mt{t} \to \mt{variant} \; ([\mt{nm} = \mt{t}] \rc \mt{ts}) \\
adam@1297 1321 \mt{val} \; \mt{match} : \mt{ts} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{variant} \; \mt{ts} \to \$(\mt{map} \; (\lambda \mt{t'} \Rightarrow \mt{t'} \to \mt{t}) \; \mt{ts}) \to \mt{t}
adam@1297 1322 \end{array}$$
adam@1297 1323
adamc@657 1324 Another important generic Ur element comes at the beginning of \texttt{top.urs}.
adamc@657 1325
adamc@657 1326 $$\begin{array}{l}
adamc@657 1327 \mt{con} \; \mt{folder} :: \mt{K} \longrightarrow \{\mt{K}\} \to \mt{Type} \\
adamc@657 1328 \\
adamc@657 1329 \mt{val} \; \mt{fold} : \mt{K} \longrightarrow \mt{tf} :: (\{\mt{K}\} \to \mt{Type}) \\
adamc@657 1330 \hspace{.1in} \to (\mt{nm} :: \mt{Name} \to \mt{v} :: \mt{K} \to \mt{r} :: \{\mt{K}\} \to [[\mt{nm}] \sim \mt{r}] \Rightarrow \\
adamc@657 1331 \hspace{.2in} \mt{tf} \; \mt{r} \to \mt{tf} \; ([\mt{nm} = \mt{v}] \rc \mt{r})) \\
adamc@657 1332 \hspace{.1in} \to \mt{tf} \; [] \\
adamc@657 1333 \hspace{.1in} \to \mt{r} :: \{\mt{K}\} \to \mt{folder} \; \mt{r} \to \mt{tf} \; \mt{r}
adamc@657 1334 \end{array}$$
adamc@657 1335
adamc@657 1336 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 1337
adamc@664 1338 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 1339
adamc@542 1340
adamc@542 1341 \section{The Ur/Web Standard Library}
adamc@542 1342
adam@1400 1343 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 1344
adamc@658 1345 \subsection{Monads}
adamc@658 1346
adamc@658 1347 The Ur Basis defines the monad constructor class from Haskell.
adamc@658 1348
adamc@658 1349 $$\begin{array}{l}
adamc@658 1350 \mt{class} \; \mt{monad} :: \mt{Type} \to \mt{Type} \\
adamc@658 1351 \mt{val} \; \mt{return} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t} ::: \mt{Type} \\
adamc@658 1352 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658 1353 \hspace{.1in} \to \mt{t} \to \mt{m} \; \mt{t} \\
adamc@658 1354 \mt{val} \; \mt{bind} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t1} ::: \mt{Type} \to \mt{t2} ::: \mt{Type} \\
adamc@658 1355 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658 1356 \hspace{.1in} \to \mt{m} \; \mt{t1} \to (\mt{t1} \to \mt{m} \; \mt{t2}) \\
adamc@658 1357 \hspace{.1in} \to \mt{m} \; \mt{t2}
adamc@658 1358 \end{array}$$
adamc@658 1359
adamc@542 1360 \subsection{Transactions}
adamc@542 1361
adamc@542 1362 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 1363 $$\begin{array}{l}
adamc@542 1364 \mt{con} \; \mt{transaction} :: \mt{Type} \to \mt{Type} \\
adamc@658 1365 \mt{val} \; \mt{transaction\_monad} : \mt{monad} \; \mt{transaction}
adamc@542 1366 \end{array}$$
adamc@542 1367
adamc@1123 1368 For debugging purposes, a transactional function is provided for outputting a string on the server process' \texttt{stderr}.
adamc@1123 1369 $$\begin{array}{l}
adamc@1123 1370 \mt{val} \; \mt{debug} : \mt{string} \to \mt{transaction} \; \mt{unit}
adamc@1123 1371 \end{array}$$
adamc@1123 1372
adamc@542 1373 \subsection{HTTP}
adamc@542 1374
adam@1400 1375 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 1376 $$\begin{array}{l}
adamc@786 1377 \mt{con} \; \mt{http\_cookie} :: \mt{Type} \to \mt{Type} \\
adamc@786 1378 \mt{val} \; \mt{getCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; (\mt{option} \; \mt{t}) \\
adamc@1050 1379 \mt{val} \; \mt{setCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \{\mt{Value} : \mt{t}, \mt{Expires} : \mt{option} \; \mt{time}, \mt{Secure} : \mt{bool}\} \to \mt{transaction} \; \mt{unit} \\
adamc@1050 1380 \mt{val} \; \mt{clearCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; \mt{unit}
adamc@786 1381 \end{array}$$
adamc@786 1382
adamc@786 1383 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 1384 $$\begin{array}{l}
adamc@786 1385 \mt{type} \; \mt{url} \\
adamc@786 1386 \mt{val} \; \mt{bless} : \mt{string} \to \mt{url} \\
adamc@786 1387 \mt{val} \; \mt{checkUrl} : \mt{string} \to \mt{option} \; \mt{url}
adamc@786 1388 \end{array}$$
adamc@786 1389 $\mt{bless}$ raises a runtime error if the string passed to it fails the URL policy.
adamc@786 1390
adam@1400 1391 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 1392 $$\begin{array}{l}
adamc@1085 1393 \mt{val} \; \mt{currentUrl} : \mt{transaction} \; \mt{url} \\
adamc@1085 1394 \mt{val} \; \mt{url} : \mt{transaction} \; \mt{page} \to \mt{url}
adamc@1085 1395 \end{array}$$
adamc@1085 1396
adamc@1085 1397 Page generation may be interrupted at any time with a request to redirect to a particular URL instead.
adamc@1085 1398 $$\begin{array}{l}
adamc@1085 1399 \mt{val} \; \mt{redirect} : \mt{t} ::: \mt{Type} \to \mt{url} \to \mt{transaction} \; \mt{t}
adamc@1085 1400 \end{array}$$
adamc@1085 1401
adam@1400 1402 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 1403 $$\begin{array}{l}
adamc@786 1404 \mt{type} \; \mt{file} \\
adamc@786 1405 \mt{val} \; \mt{fileName} : \mt{file} \to \mt{option} \; \mt{string} \\
adamc@786 1406 \mt{val} \; \mt{fileMimeType} : \mt{file} \to \mt{string} \\
adamc@786 1407 \mt{val} \; \mt{fileData} : \mt{file} \to \mt{blob}
adamc@786 1408 \end{array}$$
adamc@786 1409
adam@1465 1410 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 1411
adam@1465 1412 $$\begin{array}{l}
adam@1465 1413 \mt{type} \; \mt{requestHeader} \\
adam@1465 1414 \mt{val} \; \mt{blessRequestHeader} : \mt{string} \to \mt{requestHeader} \\
adam@1465 1415 \mt{val} \; \mt{checkRequestHeader} : \mt{string} \to \mt{option} \; \mt{requestHeader} \\
adam@1465 1416 \mt{val} \; \mt{getHeader} : \mt{requestHeader} \to \mt{transaction} \; (\mt{option} \; \mt{string}) \\
adam@1465 1417 \\
adam@1465 1418 \mt{type} \; \mt{responseHeader} \\
adam@1465 1419 \mt{val} \; \mt{blessResponseHeader} : \mt{string} \to \mt{responseHeader} \\
adam@1465 1420 \mt{val} \; \mt{checkResponseHeader} : \mt{string} \to \mt{option} \; \mt{responseHeader} \\
adam@1465 1421 \mt{val} \; \mt{setHeader} : \mt{responseHeader} \to \mt{string} \to \mt{transaction} \; \mt{unit}
adam@1465 1422 \end{array}$$
adam@1465 1423
adamc@786 1424 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 1425 $$\begin{array}{l}
adamc@786 1426 \mt{type} \; \mt{mimeType} \\
adamc@786 1427 \mt{val} \; \mt{blessMime} : \mt{string} \to \mt{mimeType} \\
adamc@786 1428 \mt{val} \; \mt{checkMime} : \mt{string} \to \mt{option} \; \mt{mimeType} \\
adamc@786 1429 \mt{val} \; \mt{returnBlob} : \mt{t} ::: \mt{Type} \to \mt{blob} \to \mt{mimeType} \to \mt{transaction} \; \mt{t}
adamc@542 1430 \end{array}$$
adamc@542 1431
adamc@543 1432 \subsection{SQL}
adamc@543 1433
adam@1400 1434 Everything about SQL database access is restricted to server-side code.
adam@1400 1435
adamc@543 1436 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 1437 $$\begin{array}{l}
adamc@785 1438 \mt{con} \; \mt{sql\_table} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785 1439 \end{array}$$
adamc@785 1440 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 1441
adamc@785 1442 We also have the simpler type family of SQL views, which have no keys.
adamc@785 1443 $$\begin{array}{l}
adamc@785 1444 \mt{con} \; \mt{sql\_view} :: \{\mt{Type}\} \to \mt{Type}
adamc@543 1445 \end{array}$$
adamc@543 1446
adamc@785 1447 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 1448 $$\begin{array}{l}
adamc@785 1449 \mt{class} \; \mt{fieldsOf} :: \mt{Type} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1450 \mt{val} \; \mt{fieldsOf\_table} : \mt{fs} ::: \{\mt{Type}\} \to \mt{keys} ::: \{\{\mt{Unit}\}\} \to \mt{fieldsOf} \; (\mt{sql\_table} \; \mt{fs} \; \mt{keys}) \; \mt{fs} \\
adamc@785 1451 \mt{val} \; \mt{fieldsOf\_view} : \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; (\mt{sql\_view} \; \mt{fs}) \; \mt{fs}
adamc@785 1452 \end{array}$$
adamc@785 1453
adamc@785 1454 \subsubsection{Table Constraints}
adamc@785 1455
adamc@785 1456 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 1457
adamc@785 1458 $$\begin{array}{l}
adamc@785 1459 \mt{con} \; \mt{primary\_key} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type} \\
adamc@785 1460 \mt{val} \; \mt{no\_primary\_key} : \mt{fs} ::: \{\mt{Type}\} \to \mt{primary\_key} \; \mt{fs} \; [] \\
adamc@785 1461 \mt{val} \; \mt{primary\_key} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{key1} :: \mt{Name} \to \mt{keys} :: \{\mt{Type}\} \\
adamc@785 1462 \hspace{.1in} \to [[\mt{key1}] \sim \mt{keys}] \Rightarrow [[\mt{key1} = \mt{t}] \rc \mt{keys} \sim \mt{rest}] \\
adamc@785 1463 \hspace{.1in} \Rightarrow \$([\mt{key1} = \mt{sql\_injectable\_prim} \; \mt{t}] \rc \mt{map} \; \mt{sql\_injectable\_prim} \; \mt{keys}) \\
adamc@785 1464 \hspace{.1in} \to \mt{primary\_key} \; ([\mt{key1} = \mt{t}] \rc \mt{keys} \rc \mt{rest}) \; [\mt{Pkey} = [\mt{key1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{keys}]
adamc@785 1465 \end{array}$$
adamc@785 1466 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 1467
adamc@785 1468 A type family stands for sets of named constraints of the remaining varieties.
adamc@785 1469 $$\begin{array}{l}
adamc@785 1470 \mt{con} \; \mt{sql\_constraints} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785 1471 \end{array}$$
adamc@785 1472 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 1473
adamc@785 1474 There is a type family of individual, unnamed constraints.
adamc@785 1475 $$\begin{array}{l}
adamc@785 1476 \mt{con} \; \mt{sql\_constraint} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \mt{Type}
adamc@785 1477 \end{array}$$
adamc@785 1478 The first argument is the same as above, and the second argument gives the key columns for just this constraint.
adamc@785 1479
adamc@785 1480 We have operations for assembling constraints into constraint sets.
adamc@785 1481 $$\begin{array}{l}
adamc@785 1482 \mt{val} \; \mt{no\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_constraints} \; \mt{fs} \; [] \\
adamc@785 1483 \mt{val} \; \mt{one\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{unique} ::: \{\mt{Unit}\} \to \mt{name} :: \mt{Name} \\
adamc@785 1484 \hspace{.1in} \to \mt{sql\_constraint} \; \mt{fs} \; \mt{unique} \to \mt{sql\_constraints} \; \mt{fs} \; [\mt{name} = \mt{unique}] \\
adamc@785 1485 \mt{val} \; \mt{join\_constraints} : \mt{fs} ::: \{\mt{Type}\} \to \mt{uniques1} ::: \{\{\mt{Unit}\}\} \to \mt{uniques2} ::: \{\{\mt{Unit}\}\} \to [\mt{uniques1} \sim \mt{uniques2}] \\
adamc@785 1486 \hspace{.1in} \Rightarrow \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques1} \to \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques2} \to \mt{sql\_constraints} \; \mt{fs} \; (\mt{uniques1} \rc \mt{uniques2})
adamc@785 1487 \end{array}$$
adamc@785 1488
adamc@785 1489 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 1490 $$\begin{array}{l}
adamc@785 1491 \mt{val} \; \mt{unique} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{unique1} :: \mt{Name} \to \mt{unique} :: \{\mt{Type}\} \\
adamc@785 1492 \hspace{.1in} \to [[\mt{unique1}] \sim \mt{unique}] \Rightarrow [[\mt{unique1} = \mt{t}] \rc \mt{unique} \sim \mt{rest}] \\
adamc@785 1493 \hspace{.1in} \Rightarrow \mt{sql\_constraint} \; ([\mt{unique1} = \mt{t}] \rc \mt{unique} \rc \mt{rest}) \; ([\mt{unique1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{unique})
adamc@785 1494 \end{array}$$
adamc@785 1495
adamc@785 1496 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 1497 $$\begin{array}{l}
adamc@785 1498 \mt{class} \; \mt{linkable} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@785 1499 \mt{val} \; \mt{linkable\_same} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; \mt{t} \\
adamc@785 1500 \mt{val} \; \mt{linkable\_from\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; (\mt{option} \; \mt{t}) \; \mt{t} \\
adamc@785 1501 \mt{val} \; \mt{linkable\_to\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@785 1502 \end{array}$$
adamc@785 1503
adamc@785 1504 The $\mt{matching}$ type family uses $\mt{linkable}$ to define when two keys match up type-wise.
adamc@785 1505 $$\begin{array}{l}
adamc@785 1506 \mt{con} \; \mt{matching} :: \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1507 \mt{val} \; \mt{mat\_nil} : \mt{matching} \; [] \; [] \\
adamc@785 1508 \mt{val} \; \mt{mat\_cons} : \mt{t1} ::: \mt{Type} \to \mt{rest1} ::: \{\mt{Type}\} \to \mt{t2} ::: \mt{Type} \to \mt{rest2} ::: \{\mt{Type}\} \to \mt{nm1} :: \mt{Name} \to \mt{nm2} :: \mt{Name} \\
adamc@785 1509 \hspace{.1in} \to [[\mt{nm1}] \sim \mt{rest1}] \Rightarrow [[\mt{nm2}] \sim \mt{rest2}] \Rightarrow \mt{linkable} \; \mt{t1} \; \mt{t2} \to \mt{matching} \; \mt{rest1} \; \mt{rest2} \\
adamc@785 1510 \hspace{.1in} \to \mt{matching} \; ([\mt{nm1} = \mt{t1}] \rc \mt{rest1}) \; ([\mt{nm2} = \mt{t2}] \rc \mt{rest2})
adamc@785 1511 \end{array}$$
adamc@785 1512
adamc@785 1513 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 1514 $$\begin{array}{l}
adamc@785 1515 \mt{con} \; \mt{propagation\_mode} :: \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1516 \mt{val} \; \mt{restrict} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1517 \mt{val} \; \mt{cascade} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1518 \mt{val} \; \mt{no\_action} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1519 \mt{val} \; \mt{set\_null} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; (\mt{map} \; \mt{option} \; \mt{fs})
adamc@785 1520 \end{array}$$
adamc@785 1521
adamc@785 1522 Finally, we put these ingredient together to define the \texttt{FOREIGN KEY} constraint function.
adamc@785 1523 $$\begin{array}{l}
adamc@785 1524 \mt{val} \; \mt{foreign\_key} : \mt{mine1} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{mine} ::: \{\mt{Type}\} \to \mt{munused} ::: \{\mt{Type}\} \to \mt{foreign} ::: \{\mt{Type}\} \\
adamc@785 1525 \hspace{.1in} \to \mt{funused} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{uniques} ::: \{\{\mt{Unit}\}\} \\
adamc@785 1526 \hspace{.1in} \to [[\mt{mine1}] \sim \mt{mine}] \Rightarrow [[\mt{mine1} = \mt{t}] \rc \mt{mine} \sim \mt{munused}] \Rightarrow [\mt{foreign} \sim \mt{funused}] \Rightarrow [[\mt{nm}] \sim \mt{uniques}] \\
adamc@785 1527 \hspace{.1in} \Rightarrow \mt{matching} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}) \; \mt{foreign} \\
adamc@785 1528 \hspace{.1in} \to \mt{sql\_table} \; (\mt{foreign} \rc \mt{funused}) \; ([\mt{nm} = \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{foreign}] \rc \mt{uniques}) \\
adamc@785 1529 \hspace{.1in} \to \{\mt{OnDelete} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}), \\
adamc@785 1530 \hspace{.2in} \mt{OnUpdate} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine})\} \\
adamc@785 1531 \hspace{.1in} \to \mt{sql\_constraint} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine} \rc \mt{munused}) \; []
adamc@785 1532 \end{array}$$
adamc@785 1533
adamc@785 1534 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 1535 $$\begin{array}{l}
adamc@785 1536 \mt{val} \; \mt{check} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; [] \; [] \; \mt{fs} \; \mt{bool} \to \mt{sql\_constraint} \; \mt{fs} \; []
adamc@785 1537 \end{array}$$
adamc@785 1538
adamc@785 1539 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 1540
adamc@784 1541
adamc@543 1542 \subsubsection{Queries}
adamc@543 1543
adam@1400 1544 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 1545 $$\begin{array}{l}
adam@1400 1546 \mt{con} \; \mt{sql\_query} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@1193 1547 \mt{val} \; \mt{sql\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400 1548 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1549 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543 1550 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1551 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1193 1552 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adam@1400 1553 \hspace{.1in} \Rightarrow \{\mt{Rows} : \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}, \\
adamc@1193 1554 \hspace{.2in} \mt{OrderBy} : \mt{sql\_order\_by} \; (\mt{free} \rc \mt{tables}) \; \mt{selectedExps}, \\
adamc@543 1555 \hspace{.2in} \mt{Limit} : \mt{sql\_limit}, \\
adamc@543 1556 \hspace{.2in} \mt{Offset} : \mt{sql\_offset}\} \\
adam@1400 1557 \hspace{.1in} \to \mt{sql\_query} \; \mt{free} \; \mt{afree} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1558 \end{array}$$
adamc@543 1559
adamc@545 1560 Queries are used by folding over their results inside transactions.
adamc@545 1561 $$\begin{array}{l}
adam@1400 1562 \mt{val} \; \mt{query} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to [\mt{tables} \sim \mt{exps}] \Rightarrow \mt{state} ::: \mt{Type} \to \mt{sql\_query} \; [] \; [] \; \mt{tables} \; \mt{exps} \\
adamc@658 1563 \hspace{.1in} \to (\$(\mt{exps} \rc \mt{map} \; (\lambda \mt{fields} :: \{\mt{Type}\} \Rightarrow \$\mt{fields}) \; \mt{tables}) \\
adamc@545 1564 \hspace{.2in} \to \mt{state} \to \mt{transaction} \; \mt{state}) \\
adamc@545 1565 \hspace{.1in} \to \mt{state} \to \mt{transaction} \; \mt{state}
adamc@545 1566 \end{array}$$
adamc@545 1567
adam@1400 1568 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 1569 $$\begin{array}{l}
adam@1400 1570 \mt{con} \; \mt{sql\_query1} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@543 1571 \\
adamc@543 1572 \mt{type} \; \mt{sql\_relop} \\
adamc@543 1573 \mt{val} \; \mt{sql\_union} : \mt{sql\_relop} \\
adamc@543 1574 \mt{val} \; \mt{sql\_intersect} : \mt{sql\_relop} \\
adamc@543 1575 \mt{val} \; \mt{sql\_except} : \mt{sql\_relop} \\
adam@1400 1576 \mt{val} \; \mt{sql\_relop} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400 1577 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adam@1400 1578 \hspace{.1in} \to \mt{tables1} ::: \{\{\mt{Type}\}\} \\
adamc@543 1579 \hspace{.1in} \to \mt{tables2} ::: \{\{\mt{Type}\}\} \\
adamc@543 1580 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1581 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@543 1582 \hspace{.1in} \to \mt{sql\_relop} \\
adam@1458 1583 \hspace{.1in} \to \mt{bool} \; (* \; \mt{ALL} \; *) \\
adam@1400 1584 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables1} \; \mt{selectedFields} \; \mt{selectedExps} \\
adam@1400 1585 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables2} \; \mt{selectedFields} \; \mt{selectedExps} \\
adam@1400 1586 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{selectedFields} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1587 \end{array}$$
adamc@543 1588
adamc@543 1589 $$\begin{array}{l}
adamc@1193 1590 \mt{val} \; \mt{sql\_query1} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400 1591 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1592 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543 1593 \hspace{.1in} \to \mt{grouped} ::: \{\{\mt{Type}\}\} \\
adamc@543 1594 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1595 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1085 1596 \hspace{.1in} \to \mt{empties} :: \{\mt{Unit}\} \\
adamc@1193 1597 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adamc@1193 1598 \hspace{.1in} \Rightarrow [\mt{free} \sim \mt{grouped}] \\
adam@1400 1599 \hspace{.1in} \Rightarrow [\mt{afree} \sim \mt{tables}] \\
adamc@1193 1600 \hspace{.1in} \Rightarrow [\mt{empties} \sim \mt{selectedFields}] \\
adamc@1085 1601 \hspace{.1in} \Rightarrow \{\mt{Distinct} : \mt{bool}, \\
adamc@1193 1602 \hspace{.2in} \mt{From} : \mt{sql\_from\_items} \; \mt{free} \; \mt{tables}, \\
adam@1400 1603 \hspace{.2in} \mt{Where} : \mt{sql\_exp} \; (\mt{free} \rc \mt{tables}) \; \mt{afree} \; [] \; \mt{bool}, \\
adamc@543 1604 \hspace{.2in} \mt{GroupBy} : \mt{sql\_subset} \; \mt{tables} \; \mt{grouped}, \\
adam@1400 1605 \hspace{.2in} \mt{Having} : \mt{sql\_exp} \; (\mt{free} \rc \mt{grouped}) \; (\mt{afree} \rc \mt{tables}) \; [] \; \mt{bool}, \\
adamc@1085 1606 \hspace{.2in} \mt{SelectFields} : \mt{sql\_subset} \; \mt{grouped} \; (\mt{map} \; (\lambda \_ \Rightarrow []) \; \mt{empties} \rc \mt{selectedFields}), \\
adam@1400 1607 \hspace{.2in} \mt {SelectExps} : \$(\mt{map} \; (\mt{sql\_exp} \; (\mt{free} \rc \mt{grouped}) \; (\mt{afree} \rc \mt{tables}) \; []) \; \mt{selectedExps}) \} \\
adam@1400 1608 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1609 \end{array}$$
adamc@543 1610
adamc@543 1611 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 1612 $$\begin{array}{l}
adamc@543 1613 \mt{con} \; \mt{sql\_subset} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@543 1614 \mt{val} \; \mt{sql\_subset} : \mt{keep\_drop} :: \{(\{\mt{Type}\} \times \{\mt{Type}\})\} \\
adamc@543 1615 \hspace{.1in} \to \mt{sql\_subset} \\
adamc@658 1616 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1 \rc \mt{fields}.2)\; \mt{keep\_drop}) \\
adamc@658 1617 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1) \; \mt{keep\_drop}) \\
adamc@543 1618 \mt{val} \; \mt{sql\_subset\_all} : \mt{tables} :: \{\{\mt{Type}\}\} \to \mt{sql\_subset} \; \mt{tables} \; \mt{tables}
adamc@543 1619 \end{array}$$
adamc@543 1620
adamc@560 1621 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 1622 $$\begin{array}{l}
adamc@543 1623 \mt{con} \; \mt{sql\_exp} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}
adamc@543 1624 \end{array}$$
adamc@543 1625
adamc@543 1626 Any field in scope may be converted to an expression.
adamc@543 1627 $$\begin{array}{l}
adamc@543 1628 \mt{val} \; \mt{sql\_field} : \mt{otherTabs} ::: \{\{\mt{Type}\}\} \to \mt{otherFields} ::: \{\mt{Type}\} \\
adamc@543 1629 \hspace{.1in} \to \mt{fieldType} ::: \mt{Type} \to \mt{agg} ::: \{\{\mt{Type}\}\} \\
adamc@543 1630 \hspace{.1in} \to \mt{exps} ::: \{\mt{Type}\} \\
adamc@543 1631 \hspace{.1in} \to \mt{tab} :: \mt{Name} \to \mt{field} :: \mt{Name} \\
adamc@543 1632 \hspace{.1in} \to \mt{sql\_exp} \; ([\mt{tab} = [\mt{field} = \mt{fieldType}] \rc \mt{otherFields}] \rc \mt{otherTabs}) \; \mt{agg} \; \mt{exps} \; \mt{fieldType}
adamc@543 1633 \end{array}$$
adamc@543 1634
adamc@544 1635 There is an analogous function for referencing named expressions.
adamc@544 1636 $$\begin{array}{l}
adamc@544 1637 \mt{val} \; \mt{sql\_exp} : \mt{tabs} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{t} ::: \mt{Type} \to \mt{rest} ::: \{\mt{Type}\} \to \mt{nm} :: \mt{Name} \\
adamc@544 1638 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tabs} \; \mt{agg} \; ([\mt{nm} = \mt{t}] \rc \mt{rest}) \; \mt{t}
adamc@544 1639 \end{array}$$
adamc@544 1640
adamc@544 1641 Ur values of appropriate types may be injected into SQL expressions.
adamc@544 1642 $$\begin{array}{l}
adamc@786 1643 \mt{class} \; \mt{sql\_injectable\_prim} \\
adamc@786 1644 \mt{val} \; \mt{sql\_bool} : \mt{sql\_injectable\_prim} \; \mt{bool} \\
adamc@786 1645 \mt{val} \; \mt{sql\_int} : \mt{sql\_injectable\_prim} \; \mt{int} \\
adamc@786 1646 \mt{val} \; \mt{sql\_float} : \mt{sql\_injectable\_prim} \; \mt{float} \\
adamc@786 1647 \mt{val} \; \mt{sql\_string} : \mt{sql\_injectable\_prim} \; \mt{string} \\
adamc@786 1648 \mt{val} \; \mt{sql\_time} : \mt{sql\_injectable\_prim} \; \mt{time} \\
adamc@786 1649 \mt{val} \; \mt{sql\_blob} : \mt{sql\_injectable\_prim} \; \mt{blob} \\
adamc@786 1650 \mt{val} \; \mt{sql\_channel} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{channel} \; \mt{t}) \\
adamc@786 1651 \mt{val} \; \mt{sql\_client} : \mt{sql\_injectable\_prim} \; \mt{client} \\
adamc@786 1652 \\
adamc@544 1653 \mt{class} \; \mt{sql\_injectable} \\
adamc@786 1654 \mt{val} \; \mt{sql\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@786 1655 \mt{val} \; \mt{sql\_option\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; (\mt{option} \; \mt{t}) \\
adamc@786 1656 \\
adamc@544 1657 \mt{val} \; \mt{sql\_inject} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@544 1658 \hspace{.1in} \to \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adamc@544 1659 \end{array}$$
adamc@544 1660
adamc@1123 1661 Additionally, most function-free types may be injected safely, via the $\mt{serialized}$ type family.
adamc@1123 1662 $$\begin{array}{l}
adamc@1123 1663 \mt{con} \; \mt{serialized} :: \mt{Type} \to \mt{Type} \\
adamc@1123 1664 \mt{val} \; \mt{serialize} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{serialized} \; \mt{t} \\
adamc@1123 1665 \mt{val} \; \mt{deserialize} : \mt{t} ::: \mt{Type} \to \mt{serialized} \; \mt{t} \to \mt{t} \\
adamc@1123 1666 \mt{val} \; \mt{sql\_serialized} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{serialized} \; \mt{t})
adamc@1123 1667 \end{array}$$
adamc@1123 1668
adamc@544 1669 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 1670 $$\begin{array}{l}
adamc@544 1671 \mt{val} \; \mt{sql\_is\_null} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544 1672 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; (\mt{option} \; \mt{t}) \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{bool}
adamc@544 1673 \end{array}$$
adamc@544 1674
adamc@559 1675 We have generic nullary, unary, and binary operators.
adamc@544 1676 $$\begin{array}{l}
adamc@544 1677 \mt{con} \; \mt{sql\_nfunc} :: \mt{Type} \to \mt{Type} \\
adamc@544 1678 \mt{val} \; \mt{sql\_current\_timestamp} : \mt{sql\_nfunc} \; \mt{time} \\
adamc@544 1679 \mt{val} \; \mt{sql\_nfunc} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544 1680 \hspace{.1in} \to \mt{sql\_nfunc} \; \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\\end{array}$$
adamc@544 1681
adamc@544 1682 $$\begin{array}{l}
adamc@544 1683 \mt{con} \; \mt{sql\_unary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544 1684 \mt{val} \; \mt{sql\_not} : \mt{sql\_unary} \; \mt{bool} \; \mt{bool} \\
adamc@544 1685 \mt{val} \; \mt{sql\_unary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adamc@544 1686 \hspace{.1in} \to \mt{sql\_unary} \; \mt{arg} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res} \\
adamc@544 1687 \end{array}$$
adamc@544 1688
adamc@544 1689 $$\begin{array}{l}
adamc@544 1690 \mt{con} \; \mt{sql\_binary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544 1691 \mt{val} \; \mt{sql\_and} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544 1692 \mt{val} \; \mt{sql\_or} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544 1693 \mt{val} \; \mt{sql\_binary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg_1} ::: \mt{Type} \to \mt{arg_2} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adamc@544 1694 \hspace{.1in} \to \mt{sql\_binary} \; \mt{arg_1} \; \mt{arg_2} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_1} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_2} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res}
adamc@544 1695 \end{array}$$
adamc@544 1696
adamc@544 1697 $$\begin{array}{l}
adamc@559 1698 \mt{class} \; \mt{sql\_arith} \\
adamc@559 1699 \mt{val} \; \mt{sql\_int\_arith} : \mt{sql\_arith} \; \mt{int} \\
adamc@559 1700 \mt{val} \; \mt{sql\_float\_arith} : \mt{sql\_arith} \; \mt{float} \\
adamc@559 1701 \mt{val} \; \mt{sql\_neg} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_unary} \; \mt{t} \; \mt{t} \\
adamc@559 1702 \mt{val} \; \mt{sql\_plus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1703 \mt{val} \; \mt{sql\_minus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1704 \mt{val} \; \mt{sql\_times} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1705 \mt{val} \; \mt{sql\_div} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1706 \mt{val} \; \mt{sql\_mod} : \mt{sql\_binary} \; \mt{int} \; \mt{int} \; \mt{int}
adamc@559 1707 \end{array}$$
adamc@544 1708
adamc@656 1709 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 1710 $$\begin{array}{l}
adamc@544 1711 \mt{val} \; \mt{sql\_count} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int}
adamc@544 1712 \end{array}$$
adamc@544 1713
adamc@544 1714 $$\begin{array}{l}
adamc@1188 1715 \mt{con} \; \mt{sql\_aggregate} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@1188 1716 \mt{val} \; \mt{sql\_aggregate} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{dom} ::: \mt{Type} \to \mt{ran} ::: \mt{Type} \\
adamc@1188 1717 \hspace{.1in} \to \mt{sql\_aggregate} \; \mt{dom} \; \mt{ran} \to \mt{sql\_exp} \; \mt{agg} \; \mt{agg} \; \mt{exps} \; \mt{dom} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{ran}
adamc@1188 1718 \end{array}$$
adamc@1188 1719
adamc@1188 1720 $$\begin{array}{l}
adamc@1188 1721 \mt{val} \; \mt{sql\_count\_col} : \mt{t} ::: \mt{Type} \to \mt{sql\_aggregate} \; (\mt{option} \; \mt{t}) \; \mt{int}
adamc@544 1722 \end{array}$$
adam@1400 1723
adam@1400 1724 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 1725
adamc@544 1726 $$\begin{array}{l}
adamc@544 1727 \mt{class} \; \mt{sql\_summable} \\
adamc@544 1728 \mt{val} \; \mt{sql\_summable\_int} : \mt{sql\_summable} \; \mt{int} \\
adamc@544 1729 \mt{val} \; \mt{sql\_summable\_float} : \mt{sql\_summable} \; \mt{float} \\
adam@1400 1730 \mt{val} \; \mt{sql\_avg} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt} \\
adam@1400 1731 \mt{val} \; \mt{sql\_sum} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt}
adamc@544 1732 \end{array}$$
adamc@544 1733
adamc@544 1734 $$\begin{array}{l}
adamc@544 1735 \mt{class} \; \mt{sql\_maxable} \\
adamc@544 1736 \mt{val} \; \mt{sql\_maxable\_int} : \mt{sql\_maxable} \; \mt{int} \\
adamc@544 1737 \mt{val} \; \mt{sql\_maxable\_float} : \mt{sql\_maxable} \; \mt{float} \\
adamc@544 1738 \mt{val} \; \mt{sql\_maxable\_string} : \mt{sql\_maxable} \; \mt{string} \\
adamc@544 1739 \mt{val} \; \mt{sql\_maxable\_time} : \mt{sql\_maxable} \; \mt{time} \\
adam@1400 1740 \mt{val} \; \mt{sql\_max} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt} \\
adam@1400 1741 \mt{val} \; \mt{sql\_min} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt}
adamc@544 1742 \end{array}$$
adamc@544 1743
adamc@1193 1744 Any SQL query that returns single columns may be turned into a subquery expression.
adamc@1193 1745
adamc@786 1746 $$\begin{array}{l}
adam@1421 1747 \mt{val} \; \mt{sql\_subquery} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \\
adam@1421 1748 \hspace{.1in} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_query} \; \mt{tables} \; \mt{agg} \; [\mt{nm} = \mt{t}] \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{nt}
adamc@1193 1749 \end{array}$$
adamc@1193 1750
adamc@1193 1751 \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 1752 $$\begin{array}{l}
adamc@1193 1753 \mt{con} \; \mt{sql\_from\_items} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@1193 1754 \mt{val} \; \mt{sql\_from\_table} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1755 \hspace{.1in} \to \mt{t} ::: \mt{Type} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; \mt{t} \; \mt{fs} \to \mt{name} :: \mt{Name} \to \mt{t} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193 1756 \mt{val} \; \mt{sql\_from\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{name} :: \mt{Name} \to \mt{sql\_query} \; \mt{free} \; [] \; \mt{fs} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193 1757 \mt{val} \; \mt{sql\_from\_comma} : \mt{free} ::: \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \to [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193 1758 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adamc@1193 1759 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2}) \\
adamc@1193 1760 \mt{val} \; \mt{sql\_inner\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1761 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193 1762 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adamc@1193 1763 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193 1764 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2})
adamc@786 1765 \end{array}$$
adamc@786 1766
adamc@786 1767 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 1768 $$\begin{array}{l}
adamc@786 1769 \mt{class} \; \mt{nullify} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@786 1770 \mt{val} \; \mt{nullify\_option} : \mt{t} ::: \mt{Type} \to \mt{nullify} \; (\mt{option} \; \mt{t}) \; (\mt{option} \; \mt{t}) \\
adamc@786 1771 \mt{val} \; \mt{nullify\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{nullify} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@786 1772 \end{array}$$
adamc@786 1773
adamc@786 1774 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 1775
adamc@786 1776 $$\begin{array}{l}
adamc@1193 1777 \mt{val} \; \mt{sql\_left\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{(\mt{Type} \times \mt{Type})\}\} \\
adamc@1193 1778 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@786 1779 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\lambda \mt{r} \Rightarrow \$(\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{nullify} \; \mt{p}.1 \; \mt{p}.2) \; \mt{r})) \; \mt{tabs2}) \\
adamc@1193 1780 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \\
adamc@1193 1781 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193 1782 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.2)) \; \mt{tabs2})
adamc@786 1783 \end{array}$$
adamc@786 1784
adamc@544 1785 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 1786 $$\begin{array}{l}
adamc@544 1787 \mt{type} \; \mt{sql\_direction} \\
adamc@544 1788 \mt{val} \; \mt{sql\_asc} : \mt{sql\_direction} \\
adamc@544 1789 \mt{val} \; \mt{sql\_desc} : \mt{sql\_direction} \\
adamc@544 1790 \\
adamc@544 1791 \mt{con} \; \mt{sql\_order\_by} :: \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@544 1792 \mt{val} \; \mt{sql\_order\_by\_Nil} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} :: \{\mt{Type}\} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544 1793 \mt{val} \; \mt{sql\_order\_by\_Cons} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544 1794 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; [] \; \mt{exps} \; \mt{t} \to \mt{sql\_direction} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544 1795 \\
adamc@544 1796 \mt{type} \; \mt{sql\_limit} \\
adamc@544 1797 \mt{val} \; \mt{sql\_no\_limit} : \mt{sql\_limit} \\
adamc@544 1798 \mt{val} \; \mt{sql\_limit} : \mt{int} \to \mt{sql\_limit} \\
adamc@544 1799 \\
adamc@544 1800 \mt{type} \; \mt{sql\_offset} \\
adamc@544 1801 \mt{val} \; \mt{sql\_no\_offset} : \mt{sql\_offset} \\
adamc@544 1802 \mt{val} \; \mt{sql\_offset} : \mt{int} \to \mt{sql\_offset}
adamc@544 1803 \end{array}$$
adamc@544 1804
adamc@545 1805
adamc@545 1806 \subsubsection{DML}
adamc@545 1807
adamc@545 1808 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 1809
adamc@545 1810 $$\begin{array}{l}
adamc@545 1811 \mt{type} \; \mt{dml} \\
adamc@545 1812 \mt{val} \; \mt{dml} : \mt{dml} \to \mt{transaction} \; \mt{unit}
adamc@545 1813 \end{array}$$
adamc@545 1814
adam@1297 1815 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 1816
adam@1297 1817 $$\begin{array}{l}
adam@1297 1818 \mt{val} \; \mt{tryDml} : \mt{dml} \to \mt{transaction} \; (\mt{option} \; \mt{string})
adam@1297 1819 \end{array}$$
adam@1297 1820
adamc@545 1821 Properly-typed records may be used to form $\mt{INSERT}$ commands.
adamc@545 1822 $$\begin{array}{l}
adamc@545 1823 \mt{val} \; \mt{insert} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \\
adamc@658 1824 \hspace{.1in} \to \$(\mt{map} \; (\mt{sql\_exp} \; [] \; [] \; []) \; \mt{fields}) \to \mt{dml}
adamc@545 1825 \end{array}$$
adamc@545 1826
adamc@545 1827 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 1828 $$\begin{array}{l}
adam@1380 1829 \mt{val} \; \mt{update} : \mt{unchanged} ::: \{\mt{Type}\} \to \mt{changed} :: \{\mt{Type}\} \to [\mt{changed} \sim \mt{unchanged}] \\
adamc@658 1830 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; []) \; \mt{changed}) \\
adamc@545 1831 \hspace{.1in} \to \mt{sql\_table} \; (\mt{changed} \rc \mt{unchanged}) \to \mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545 1832 \end{array}$$
adamc@545 1833
adamc@545 1834 A $\mt{DELETE}$ command is formed from a table and a $\mt{WHERE}$ clause.
adamc@545 1835 $$\begin{array}{l}
adamc@545 1836 \mt{val} \; \mt{delete} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \to \mt{sql\_exp} \; [\mt{T} = \mt{fields}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545 1837 \end{array}$$
adamc@545 1838
adamc@546 1839 \subsubsection{Sequences}
adamc@546 1840
adamc@546 1841 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 1842
adamc@546 1843 $$\begin{array}{l}
adamc@546 1844 \mt{type} \; \mt{sql\_sequence} \\
adamc@1085 1845 \mt{val} \; \mt{nextval} : \mt{sql\_sequence} \to \mt{transaction} \; \mt{int} \\
adamc@1085 1846 \mt{val} \; \mt{setval} : \mt{sql\_sequence} \to \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@546 1847 \end{array}$$
adamc@546 1848
adamc@546 1849
adamc@547 1850 \subsection{XML}
adamc@547 1851
adam@1333 1852 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 1853
adam@1345 1854 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 1855 $$\begin{array}{l}
adamc@547 1856 \mt{con} \; \mt{xml} :: \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547 1857 \end{array}$$
adamc@547 1858
adamc@547 1859 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 1860 $$\begin{array}{l}
adamc@547 1861 \mt{con} \; \mt{tag} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547 1862 \end{array}$$
adamc@547 1863
adamc@547 1864 Literal text may be injected into XML as ``CDATA.''
adamc@547 1865 $$\begin{array}{l}
adamc@547 1866 \mt{val} \; \mt{cdata} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{string} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adamc@547 1867 \end{array}$$
adamc@547 1868
adam@1358 1869 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 1870 $$\begin{array}{l}
adam@1358 1871 \mt{val} \; \mt{cdataChar} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{char} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adam@1358 1872 \end{array}$$
adam@1358 1873
adamc@547 1874 There is a function for producing an XML tree with a particular tag at its root.
adamc@547 1875 $$\begin{array}{l}
adamc@547 1876 \mt{val} \; \mt{tag} : \mt{attrsGiven} ::: \{\mt{Type}\} \to \mt{attrsAbsent} ::: \{\mt{Type}\} \to \mt{ctxOuter} ::: \{\mt{Unit}\} \to \mt{ctxInner} ::: \{\mt{Unit}\} \\
adamc@547 1877 \hspace{.1in} \to \mt{useOuter} ::: \{\mt{Type}\} \to \mt{useInner} ::: \{\mt{Type}\} \to \mt{bindOuter} ::: \{\mt{Type}\} \to \mt{bindInner} ::: \{\mt{Type}\} \\
adam@1380 1878 \hspace{.1in} \to [\mt{attrsGiven} \sim \mt{attrsAbsent}] \Rightarrow [\mt{useOuter} \sim \mt{useInner}] \Rightarrow [\mt{bindOuter} \sim \mt{bindInner}] \\
adamc@787 1879 \hspace{.1in} \Rightarrow \mt{option} \; \mt{css\_class} \\
adamc@787 1880 \hspace{.1in} \to \$\mt{attrsGiven} \\
adamc@547 1881 \hspace{.1in} \to \mt{tag} \; (\mt{attrsGiven} \rc \mt{attrsAbsent}) \; \mt{ctxOuter} \; \mt{ctxInner} \; \mt{useOuter} \; \mt{bindOuter} \\
adamc@547 1882 \hspace{.1in} \to \mt{xml} \; \mt{ctxInner} \; \mt{useInner} \; \mt{bindInner} \to \mt{xml} \; \mt{ctxOuter} \; (\mt{useOuter} \rc \mt{useInner}) \; (\mt{bindOuter} \rc \mt{bindInner})
adamc@547 1883 \end{array}$$
adam@1297 1884 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 1885
adamc@547 1886 Two XML fragments may be concatenated.
adamc@547 1887 $$\begin{array}{l}
adamc@547 1888 \mt{val} \; \mt{join} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{bind_1} ::: \{\mt{Type}\} \to \mt{bind_2} ::: \{\mt{Type}\} \\
adam@1380 1889 \hspace{.1in} \to [\mt{use_1} \sim \mt{bind_1}] \Rightarrow [\mt{bind_1} \sim \mt{bind_2}] \\
adamc@547 1890 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind_1} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{bind_1}) \; \mt{bind_2} \to \mt{xml} \; \mt{ctx} \; \mt{use_1} \; (\mt{bind_1} \rc \mt{bind_2})
adamc@547 1891 \end{array}$$
adamc@547 1892
adamc@547 1893 Finally, any XML fragment may be updated to ``claim'' to use more form fields than it does.
adamc@547 1894 $$\begin{array}{l}
adam@1380 1895 \mt{val} \; \mt{useMore} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{use_2} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to [\mt{use_1} \sim \mt{use_2}] \\
adamc@547 1896 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{use_2}) \; \mt{bind}
adamc@547 1897 \end{array}$$
adamc@547 1898
adam@1344 1899 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 1900
adamc@547 1901 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 1902 $$\begin{array}{l}
adamc@547 1903 \mt{val} \; \mt{error} : \mt{t} ::: \mt{Type} \to \mt{xml} \; [\mt{Body}] \; [] \; [] \to \mt{t}
adamc@547 1904 \end{array}$$
adamc@547 1905
adamc@549 1906
adamc@701 1907 \subsection{Client-Side Programming}
adamc@659 1908
adamc@701 1909 Ur/Web supports running code on web browsers, via automatic compilation to JavaScript.
adamc@701 1910
adamc@701 1911 \subsubsection{The Basics}
adamc@701 1912
adam@1400 1913 All of the functions in this subsection are client-side only.
adam@1400 1914
adam@1297 1915 Clients can open alert and confirm dialog boxes, in the usual annoying JavaScript way.
adamc@701 1916 $$\begin{array}{l}
adam@1297 1917 \mt{val} \; \mt{alert} : \mt{string} \to \mt{transaction} \; \mt{unit} \\
adam@1297 1918 \mt{val} \; \mt{confirm} : \mt{string} \to \mt{transaction} \; \mt{bool}
adamc@701 1919 \end{array}$$
adamc@701 1920
adamc@701 1921 Any transaction may be run in a new thread with the $\mt{spawn}$ function.
adamc@701 1922 $$\begin{array}{l}
adamc@701 1923 \mt{val} \; \mt{spawn} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit}
adamc@701 1924 \end{array}$$
adamc@701 1925
adamc@701 1926 The current thread can be paused for at least a specified number of milliseconds.
adamc@701 1927 $$\begin{array}{l}
adamc@701 1928 \mt{val} \; \mt{sleep} : \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@701 1929 \end{array}$$
adamc@701 1930
adamc@787 1931 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 1932 $$\begin{array}{l}
adamc@787 1933 \mt{val} \; \mt{onError} : (\mt{xbody} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787 1934 \mt{val} \; \mt{onFail} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787 1935 \mt{val} \; \mt{onConnectFail} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787 1936 \mt{val} \; \mt{onDisconnect} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787 1937 \mt{val} \; \mt{onServerError} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit}
adamc@787 1938 \end{array}$$
adamc@787 1939
adamc@701 1940 \subsubsection{Functional-Reactive Page Generation}
adamc@701 1941
adamc@701 1942 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 1943
adam@1403 1944 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 1945
adamc@659 1946 $$\begin{array}{l}
adamc@659 1947 \mt{con} \; \mt{source} :: \mt{Type} \to \mt{Type} \\
adamc@659 1948 \mt{val} \; \mt{source} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{transaction} \; (\mt{source} \; \mt{t}) \\
adamc@659 1949 \mt{val} \; \mt{set} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@659 1950 \mt{val} \; \mt{get} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@659 1951 \end{array}$$
adamc@659 1952
adam@1400 1953 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 1954
adam@1403 1955 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 1956
adamc@659 1957 $$\begin{array}{l}
adamc@659 1958 \mt{con} \; \mt{signal} :: \mt{Type} \to \mt{Type} \\
adamc@659 1959 \mt{val} \; \mt{signal\_monad} : \mt{monad} \; \mt{signal} \\
adamc@659 1960 \mt{val} \; \mt{signal} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{signal} \; \mt{t}
adamc@659 1961 \end{array}$$
adamc@659 1962
adamc@659 1963 A reactive portion of an HTML page is injected with a $\mt{dyn}$ tag, which has a signal-valued attribute $\mt{Signal}$.
adamc@659 1964
adamc@659 1965 $$\begin{array}{l}
adamc@701 1966 \mt{val} \; \mt{dyn} : \mt{use} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to \mt{unit} \\
adamc@701 1967 \hspace{.1in} \to \mt{tag} \; [\mt{Signal} = \mt{signal} \; (\mt{xml} \; \mt{body} \; \mt{use} \; \mt{bind})] \; \mt{body} \; [] \; \mt{use} \; \mt{bind}
adamc@659 1968 \end{array}$$
adamc@659 1969
adamc@701 1970 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 1971
adamc@914 1972 \subsubsection{Remote Procedure Calls}
adamc@914 1973
adamc@914 1974 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 1975
adamc@914 1976 $$\begin{array}{l}
adamc@914 1977 \mt{val} \; \mt{rpc} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@914 1978 \end{array}$$
adamc@914 1979
adamc@701 1980 \subsubsection{Asynchronous Message-Passing}
adamc@701 1981
adamc@701 1982 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 1983
adamc@701 1984 $$\begin{array}{l}
adamc@701 1985 \mt{type} \; \mt{client} \\
adamc@701 1986 \mt{val} \; \mt{self} : \mt{transaction} \; \mt{client}
adamc@701 1987 \end{array}$$
adamc@701 1988
adamc@701 1989 \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 1990
adamc@701 1991 $$\begin{array}{l}
adamc@701 1992 \mt{con} \; \mt{channel} :: \mt{Type} \to \mt{Type} \\
adamc@701 1993 \mt{val} \; \mt{channel} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; (\mt{channel} \; \mt{t}) \\
adamc@701 1994 \mt{val} \; \mt{send} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@701 1995 \mt{val} \; \mt{recv} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@701 1996 \end{array}$$
adamc@701 1997
adamc@701 1998 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 1999
adamc@701 2000 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 2001
adamc@659 2002
adamc@549 2003 \section{Ur/Web Syntax Extensions}
adamc@549 2004
adamc@549 2005 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 2006
adamc@549 2007 \subsection{SQL}
adamc@549 2008
adamc@786 2009 \subsubsection{\label{tables}Table Declarations}
adamc@786 2010
adamc@788 2011 $\mt{table}$ declarations may include constraints, via these grammar rules.
adamc@788 2012 $$\begin{array}{rrcll}
adamc@788 2013 \textrm{Declarations} & d &::=& \mt{table} \; x : c \; [pk[,]] \; cts \\
adamc@788 2014 \textrm{Primary key constraints} & pk &::=& \mt{PRIMARY} \; \mt{KEY} \; K \\
adamc@788 2015 \textrm{Keys} & K &::=& f \mid (f, (f,)^+) \\
adamc@788 2016 \textrm{Constraint sets} & cts &::=& \mt{CONSTRAINT} f \; ct \mid cts, cts \mid \{\{e\}\} \\
adamc@788 2017 \textrm{Constraints} & ct &::=& \mt{UNIQUE} \; K \mid \mt{CHECK} \; E \\
adamc@788 2018 &&& \mid \mt{FOREIGN} \; \mt{KEY} \; K \; \mt{REFERENCES} \; F \; (K) \; [\mt{ON} \; \mt{DELETE} \; pr] \; [\mt{ON} \; \mt{UPDATE} \; pr] \\
adamc@788 2019 \textrm{Foreign tables} & F &::=& x \mid \{\{e\}\} \\
adamc@788 2020 \textrm{Propagation modes} & pr &::=& \mt{NO} \; \mt{ACTION} \mid \mt{RESTRICT} \mid \mt{CASCADE} \mid \mt{SET} \; \mt{NULL}
adamc@788 2021 \end{array}$$
adamc@788 2022
adamc@788 2023 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 2024
adamc@788 2025
adamc@549 2026 \subsubsection{Queries}
adamc@549 2027
adamc@550 2028 Queries $Q$ are added to the rules for expressions $e$.
adamc@550 2029
adamc@549 2030 $$\begin{array}{rrcll}
adamc@550 2031 \textrm{Queries} & Q &::=& (q \; [\mt{ORDER} \; \mt{BY} \; (E \; [o],)^+] \; [\mt{LIMIT} \; N] \; [\mt{OFFSET} \; N]) \\
adamc@1085 2032 \textrm{Pre-queries} & q &::=& \mt{SELECT} \; [\mt{DISTINCT}] \; P \; \mt{FROM} \; F,^+ \; [\mt{WHERE} \; E] \; [\mt{GROUP} \; \mt{BY} \; p,^+] \; [\mt{HAVING} \; E] \\
adamc@1085 2033 &&& \mid q \; R \; q \mid \{\{\{e\}\}\} \\
adamc@549 2034 \textrm{Relational operators} & R &::=& \mt{UNION} \mid \mt{INTERSECT} \mid \mt{EXCEPT}
adamc@549 2035 \end{array}$$
adamc@549 2036
adamc@549 2037 $$\begin{array}{rrcll}
adamc@549 2038 \textrm{Projections} & P &::=& \ast & \textrm{all columns} \\
adamc@549 2039 &&& p,^+ & \textrm{particular columns} \\
adamc@549 2040 \textrm{Pre-projections} & p &::=& t.f & \textrm{one column from a table} \\
adamc@558 2041 &&& t.\{\{c\}\} & \textrm{a record of columns from a table (of kind $\{\mt{Type}\}$)} \\
adamc@1194 2042 &&& E \; [\mt{AS} \; f] & \textrm{expression column} \\
adamc@549 2043 \textrm{Table names} & t &::=& x & \textrm{constant table name (automatically capitalized)} \\
adamc@549 2044 &&& X & \textrm{constant table name} \\
adamc@549 2045 &&& \{\{c\}\} & \textrm{computed table name (of kind $\mt{Name}$)} \\
adamc@549 2046 \textrm{Column names} & f &::=& X & \textrm{constant column name} \\
adamc@549 2047 &&& \{c\} & \textrm{computed column name (of kind $\mt{Name}$)} \\
adamc@549 2048 \textrm{Tables} & T &::=& x & \textrm{table variable, named locally by its own capitalization} \\
adamc@549 2049 &&& x \; \mt{AS} \; t & \textrm{table variable, with local name} \\
adamc@549 2050 &&& \{\{e\}\} \; \mt{AS} \; t & \textrm{computed table expression, with local name} \\
adamc@1085 2051 \textrm{$\mt{FROM}$ items} & F &::=& T \mid \{\{e\}\} \mid F \; J \; \mt{JOIN} \; F \; \mt{ON} \; E \\
adamc@1085 2052 &&& \mid F \; \mt{CROSS} \; \mt{JOIN} \ F \\
adamc@1193 2053 &&& \mid (Q) \; \mt{AS} \; t \\
adamc@1085 2054 \textrm{Joins} & J &::=& [\mt{INNER}] \\
adamc@1085 2055 &&& \mid [\mt{LEFT} \mid \mt{RIGHT} \mid \mt{FULL}] \; [\mt{OUTER}] \\
adamc@549 2056 \textrm{SQL expressions} & E &::=& p & \textrm{column references} \\
adamc@549 2057 &&& X & \textrm{named expression references} \\
adam@1490 2058 &&& \{[e]\} & \textrm{injected native Ur expressions} \\
adamc@549 2059 &&& \{e\} & \textrm{computed expressions, probably using $\mt{sql\_exp}$ directly} \\
adamc@549 2060 &&& \mt{TRUE} \mid \mt{FALSE} & \textrm{boolean constants} \\
adamc@549 2061 &&& \ell & \textrm{primitive type literals} \\
adamc@549 2062 &&& \mt{NULL} & \textrm{null value (injection of $\mt{None}$)} \\
adamc@549 2063 &&& E \; \mt{IS} \; \mt{NULL} & \textrm{nullness test} \\
adamc@549 2064 &&& n & \textrm{nullary operators} \\
adamc@549 2065 &&& u \; E & \textrm{unary operators} \\
adamc@549 2066 &&& E \; b \; E & \textrm{binary operators} \\
adamc@549 2067 &&& \mt{COUNT}(\ast) & \textrm{count number of rows} \\
adamc@549 2068 &&& a(E) & \textrm{other aggregate function} \\
adamc@1193 2069 &&& (Q) & \textrm{subquery (must return a single expression column)} \\
adamc@549 2070 &&& (E) & \textrm{explicit precedence} \\
adamc@549 2071 \textrm{Nullary operators} & n &::=& \mt{CURRENT\_TIMESTAMP} \\
adamc@549 2072 \textrm{Unary operators} & u &::=& \mt{NOT} \\
adamc@549 2073 \textrm{Binary operators} & b &::=& \mt{AND} \mid \mt{OR} \mid \neq \mid < \mid \leq \mid > \mid \geq \\
adamc@1188 2074 \textrm{Aggregate functions} & a &::=& \mt{COUNT} \mid \mt{AVG} \mid \mt{SUM} \mid \mt{MIN} \mid \mt{MAX} \\
adamc@550 2075 \textrm{Directions} & o &::=& \mt{ASC} \mid \mt{DESC} \\
adamc@549 2076 \textrm{SQL integer} & N &::=& n \mid \{e\} \\
adamc@549 2077 \end{array}$$
adamc@549 2078
adamc@1085 2079 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 2080
adamc@1194 2081 Unnamed expression columns in $\mt{SELECT}$ clauses are assigned consecutive natural numbers, starting with 1.
adamc@1194 2082
adamc@550 2083 \subsubsection{DML}
adamc@550 2084
adamc@550 2085 DML commands $D$ are added to the rules for expressions $e$.
adamc@550 2086
adamc@550 2087 $$\begin{array}{rrcll}
adamc@550 2088 \textrm{Commands} & D &::=& (\mt{INSERT} \; \mt{INTO} \; T^E \; (f,^+) \; \mt{VALUES} \; (E,^+)) \\
adamc@550 2089 &&& (\mt{UPDATE} \; T^E \; \mt{SET} \; (f = E,)^+ \; \mt{WHERE} \; E) \\
adamc@550 2090 &&& (\mt{DELETE} \; \mt{FROM} \; T^E \; \mt{WHERE} \; E) \\
adamc@550 2091 \textrm{Table expressions} & T^E &::=& x \mid \{\{e\}\}
adamc@550 2092 \end{array}$$
adamc@550 2093
adamc@550 2094 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 2095
adamc@551 2096 \subsection{XML}
adamc@551 2097
adamc@551 2098 XML fragments $L$ are added to the rules for expressions $e$.
adamc@551 2099
adamc@551 2100 $$\begin{array}{rrcll}
adamc@551 2101 \textrm{XML fragments} & L &::=& \texttt{<xml/>} \mid \texttt{<xml>}l^*\texttt{</xml>} \\
adamc@551 2102 \textrm{XML pieces} & l &::=& \textrm{text} & \textrm{cdata} \\
adamc@551 2103 &&& \texttt{<}g\texttt{/>} & \textrm{tag with no children} \\
adamc@551 2104 &&& \texttt{<}g\texttt{>}l^*\texttt{</}x\texttt{>} & \textrm{tag with children} \\
adamc@559 2105 &&& \{e\} & \textrm{computed XML fragment} \\
adamc@559 2106 &&& \{[e]\} & \textrm{injection of an Ur expression, via the $\mt{Top}.\mt{txt}$ function} \\
adamc@551 2107 \textrm{Tag} & g &::=& h \; (x = v)^* \\
adamc@551 2108 \textrm{Tag head} & h &::=& x & \textrm{tag name} \\
adamc@551 2109 &&& h\{c\} & \textrm{constructor parameter} \\
adamc@551 2110 \textrm{Attribute value} & v &::=& \ell & \textrm{literal value} \\
adamc@551 2111 &&& \{e\} & \textrm{computed value} \\
adamc@551 2112 \end{array}$$
adamc@551 2113
adamc@552 2114
adamc@1198 2115 \section{\label{structure}The Structure of Web Applications}
adamc@553 2116
adamc@1127 2117 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 2118
adam@1347 2119 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 2120
adam@1370 2121 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 2122
adamc@553 2123 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 2124
adamc@553 2125 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 2126
adamc@558 2127 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 2128
adamc@660 2129 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 2130
adamc@789 2131 \medskip
adamc@789 2132
adam@1347 2133 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 2134
adamc@789 2135 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 2136
adam@1348 2137 \subsection{Tasks}
adam@1348 2138
adam@1348 2139 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 2140
adam@1348 2141 $$\begin{array}{l}
adam@1348 2142 \mt{con} \; \mt{task\_kind} :: \mt{Type} \to \mt{Type} \\
adam@1348 2143 \mt{val} \; \mt{initialize} : \mt{task\_kind} \; \mt{unit} \\
adam@1349 2144 \mt{val} \; \mt{clientLeaves} : \mt{task\_kind} \; \mt{client} \\
adam@1349 2145 \mt{val} \; \mt{periodic} : \mt{int} \to \mt{task\_kind} \; \mt{unit}
adam@1348 2146 \end{array}$$
adam@1348 2147
adam@1348 2148 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 2149
adam@1348 2150 The currently supported task kinds are:
adam@1348 2151 \begin{itemize}
adam@1349 2152 \item $\mt{initialize}$: Code that is run when the application starts up.
adam@1348 2153 \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 2154 \item $\mt{periodic} \; n$: Code that is run when the application starts up and then every $n$ seconds thereafter.
adam@1348 2155 \end{itemize}
adam@1348 2156
adamc@553 2157
adamc@897 2158 \section{The Foreign Function Interface}
adamc@897 2159
adamc@897 2160 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 2161
adamc@897 2162 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 2163
adamc@897 2164 \begin{itemize}
adamc@897 2165 \item \texttt{clientOnly Module.ident} registers a value as being allowed only in client-side code.
adamc@897 2166 \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 2167 \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 2168 \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 2169 \item \texttt{include FILE} requests inclusion of a C header file.
adamc@897 2170 \item \texttt{jsFunc Module.ident=name} gives a mapping from an Ur name for a value to a JavaScript name.
adamc@897 2171 \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 2172 \item \texttt{script URL} requests inclusion of a JavaScript source file within application HTML.
adamc@897 2173 \item \texttt{serverOnly Module.ident} registers a value as being allowed only in server-side code.
adamc@897 2174 \end{itemize}
adamc@897 2175
adamc@897 2176 \subsection{Writing C FFI Code}
adamc@897 2177
adamc@897 2178 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 2179
adamc@897 2180 \begin{itemize}
adamc@897 2181 \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 2182 \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 2183 \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 2184 \end{itemize}
adamc@897 2185
adamc@897 2186 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 2187 \begin{itemize}
adamc@897 2188 \item \begin{verbatim}
adamc@897 2189 void uw_error(uw_context, failure_kind, const char *fmt, ...);
adamc@897 2190 \end{verbatim}
adamc@897 2191 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 2192
adam@1329 2193 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 2194
adamc@897 2195 \item \begin{verbatim}
adam@1469 2196 void uw_set_error_message(uw_context, const char *fmt, ...);
adam@1469 2197 \end{verbatim}
adam@1469 2198 This simpler form of \texttt{uw\_error()} saves an error message without immediately aborting execution.
adam@1469 2199
adam@1469 2200 \item \begin{verbatim}
adamc@897 2201 void uw_push_cleanup(uw_context, void (*func)(void *), void *arg);
adamc@897 2202 void uw_pop_cleanup(uw_context);
adamc@897 2203 \end{verbatim}
adam@1329 2204 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 2205
adam@1329 2206 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 2207
adamc@897 2208 \item \begin{verbatim}
adamc@897 2209 void *uw_malloc(uw_context, size_t);
adamc@897 2210 \end{verbatim}
adam@1329 2211 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 2212
adam@1329 2213 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 2214
adamc@897 2215 \item \begin{verbatim}
adamc@897 2216 typedef void (*uw_callback)(void *);
adam@1328 2217 typedef void (*uw_callback_with_retry)(void *, int will_retry);
adamc@897 2218 void uw_register_transactional(uw_context, void *data, uw_callback commit,
adam@1328 2219 uw_callback rollback, uw_callback_with_retry free);
adamc@897 2220 \end{verbatim}
adam@1328 2221 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 2222
adamc@1085 2223 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 2224
adam@1329 2225 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 2226
adam@1329 2227 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 2228
adam@1469 2229 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 2230
adamc@1085 2231 \item \begin{verbatim}
adamc@1085 2232 void *uw_get_global(uw_context, char *name);
adamc@1085 2233 void uw_set_global(uw_context, char *name, void *data, uw_callback free);
adamc@1085 2234 \end{verbatim}
adam@1329 2235 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 2236
adamc@897 2237 \end{itemize}
adamc@897 2238
adamc@897 2239 \subsection{Writing JavaScript FFI Code}
adamc@897 2240
adamc@897 2241 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 2242
adamc@897 2243 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 2244
adamc@897 2245 \begin{itemize}
adamc@897 2246 \item Integers, floats, strings, characters, and booleans are represented in the usual JavaScript way.
adamc@985 2247 \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 2248 \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 2249 \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 2250 \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 2251 \end{itemize}
adamc@897 2252
adamc@897 2253 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 2254
adamc@897 2255
adamc@552 2256 \section{Compiler Phases}
adamc@552 2257
adamc@552 2258 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 2259
adamc@552 2260 In this section, we step through the main phases of compilation, noting what consequences each phase has for effective programming.
adamc@552 2261
adamc@552 2262 \subsection{Parse}
adamc@552 2263
adamc@552 2264 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 2265
adamc@552 2266 \subsection{Elaborate}
adamc@552 2267
adamc@552 2268 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 2269
adam@1378 2270 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 2271
adamc@552 2272 \subsection{Unnest}
adamc@552 2273
adamc@552 2274 Named local function definitions are moved to the top level, to avoid the need to generate closures.
adamc@552 2275
adamc@552 2276 \subsection{Corify}
adamc@552 2277
adamc@552 2278 Module system features are compiled away, through inlining of functor definitions at application sites. Afterward, most abstraction boundaries are broken, facilitating optimization.
adamc@552 2279
adamc@552 2280 \subsection{Especialize}
adamc@552 2281
adam@1356 2282 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 2283
adamc@552 2284 \subsection{Untangle}
adamc@552 2285
adamc@552 2286 Remove unnecessary mutual recursion, splitting recursive groups into strongly-connected components.
adamc@552 2287
adamc@552 2288 \subsection{Shake}
adamc@552 2289
adamc@552 2290 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 2291
adamc@661 2292 \subsection{Rpcify}
adamc@661 2293
adamc@661 2294 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 2295
adamc@661 2296 \subsection{Untangle, Shake}
adamc@661 2297
adamc@661 2298 Repeat these simplifications.
adamc@661 2299
adamc@553 2300 \subsection{\label{tag}Tag}
adamc@552 2301
adamc@552 2302 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 2303
adamc@552 2304 \subsection{Reduce}
adamc@552 2305
adamc@552 2306 Apply definitional equality rules to simplify the program as much as possible. This effectively includes inlining of every non-recursive definition.
adamc@552 2307
adamc@552 2308 \subsection{Unpoly}
adamc@552 2309
adamc@552 2310 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 2311
adamc@552 2312 \subsection{Specialize}
adamc@552 2313
adamc@558 2314 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 2315
adamc@552 2316 \subsection{Shake}
adamc@552 2317
adamc@558 2318 Here the compiler repeats the earlier Shake phase.
adamc@552 2319
adamc@552 2320 \subsection{Monoize}
adamc@552 2321
adamc@552 2322 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 2323
adamc@552 2324 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 2325
adamc@552 2326 \subsection{MonoOpt}
adamc@552 2327
adamc@552 2328 Simple algebraic laws are applied to simplify the program, focusing especially on efficient imperative generation of HTML pages.
adamc@552 2329
adamc@552 2330 \subsection{MonoUntangle}
adamc@552 2331
adamc@552 2332 Unnecessary mutual recursion is broken up again.
adamc@552 2333
adamc@552 2334 \subsection{MonoReduce}
adamc@552 2335
adamc@552 2336 Equivalents of the definitional equality rules are applied to simplify programs, with inlining again playing a major role.
adamc@552 2337
adamc@552 2338 \subsection{MonoShake, MonoOpt}
adamc@552 2339
adamc@552 2340 Unneeded declarations are removed, and basic optimizations are repeated.
adamc@552 2341
adamc@552 2342 \subsection{Fuse}
adamc@552 2343
adamc@552 2344 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 2345
adamc@552 2346 \subsection{MonoUntangle, MonoShake}
adamc@552 2347
adamc@552 2348 Fuse often creates more opportunities to remove spurious mutual recursion.
adamc@552 2349
adamc@552 2350 \subsection{Pathcheck}
adamc@552 2351
adamc@552 2352 The compiler checks that no link or action name has been used more than once.
adamc@552 2353
adamc@552 2354 \subsection{Cjrize}
adamc@552 2355
adamc@552 2356 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 2357
adamc@552 2358 \subsection{C Compilation and Linking}
adamc@552 2359
adamc@552 2360 The output of the last phase is pretty-printed as C source code and passed to GCC.
adamc@552 2361
adamc@552 2362
adamc@524 2363 \end{document}