Ur/Web: doc/manual.tex annotate

annotate doc/manual.tex @ 1472:18d18a70821e

Implicit argument insertion for local variables

author	Adam Chlipala <adam@chlipala.net>
date	Tue, 14 Jun 2011 08:54:45 -0400
parents	a354b306f948
children	a10d080123ec

rev	line source
adamc@524	1 \documentclass{article}
adamc@554	2 \usepackage{fullpage,amsmath,amssymb,proof,url}
adamc@524	3
adamc@524	4 \newcommand{\cd}[1]{\texttt{#1}}
adamc@524	5 \newcommand{\mt}[1]{\mathsf{#1}}
adamc@524	6
adamc@524	7 \newcommand{\rc}{+ \hspace{-.075in} + \;}
adamc@527	8 \newcommand{\rcut}{\; \texttt{--} \;}
adamc@527	9 \newcommand{\rcutM}{\; \texttt{---} \;}
adamc@524	10
adamc@524	11 \begin{document}
adamc@524	12
adamc@524	13 \title{The Ur/Web Manual}
adamc@524	14 \author{Adam Chlipala}
adamc@524	15
adamc@524	16 \maketitle
adamc@524	17
adamc@540	18 \tableofcontents
adamc@540	19
adamc@554	20
adamc@554	21 \section{Introduction}
adamc@554	22
adamc@1160	23 \emph{Ur} is a programming language designed to introduce richer type system features into functional programming in the tradition of ML and Haskell. Ur is functional, pure, statically-typed, and strict. Ur supports a powerful kind of \emph{metaprogramming} based on \emph{type-level computation with type-level records}.
adamc@554	24
adamc@554	25 \emph{Ur/Web} is Ur plus a special standard library and associated rules for parsing and optimization. Ur/Web supports construction of dynamic web applications backed by SQL databases. The signature of the standard library is such that well-typed Ur/Web programs ``don't go wrong'' in a very broad sense. Not only do they not crash during particular page generations, but they also may not:
adamc@554	26
adamc@554	27 \begin{itemize}
adamc@554	28 \item Suffer from any kinds of code-injection attacks
adamc@554	29 \item Return invalid HTML
adamc@554	30 \item Contain dead intra-application links
adamc@554	31 \item Have mismatches between HTML forms and the fields expected by their handlers
adamc@652	32 \item Include client-side code that makes incorrect assumptions about the ``AJAX''-style services that the remote web server provides
adamc@554	33 \item Attempt invalid SQL queries
adamc@652	34 \item Use improper marshaling or unmarshaling in communication with SQL databases or between browsers and web servers
adamc@554	35 \end{itemize}
adamc@554	36
adamc@554	37 This type safety is just the foundation of the Ur/Web methodology. It is also possible to use metaprogramming to build significant application pieces by analysis of type structure. For instance, the demo includes an ML-style functor for building an admin interface for an arbitrary SQL table. The type system guarantees that the admin interface sub-application that comes out will always be free of the above-listed bugs, no matter which well-typed table description is given as input.
adamc@554	38
adamc@652	39 The Ur/Web compiler also produces very efficient object code that does not use garbage collection. These compiled programs will often be even more efficient than what most programmers would bother to write in C. The compiler also generates JavaScript versions of client-side code, with no need to write those parts of applications in a different language.
adamc@554	40
adamc@554	41 \medskip
adamc@554	42
adamc@554	43 The official web site for Ur is:
adamc@554	44 \begin{center}
adamc@554	45 \url{http://www.impredicative.com/ur/}
adamc@554	46 \end{center}
adamc@554	47
adamc@555	48
adamc@555	49 \section{Installation}
adamc@555	50
adamc@555	51 If you are lucky, then the following standard command sequence will suffice for installation, in a directory to which you have unpacked the latest distribution tarball.
adamc@555	52
adamc@555	53 \begin{verbatim}
adamc@555	54 ./configure
adamc@555	55 make
adamc@555	56 sudo make install
adamc@555	57 \end{verbatim}
adamc@555	58
adam@1368	59 Some other packages must be installed for the above to work. At a minimum, you need a standard UNIX shell, with standard UNIX tools like sed and GCC in your execution path; MLton, the whole-program optimizing compiler for Standard ML; and the development files for the OpenSSL C library. As of this writing, in the ``testing'' version of Debian Linux, this command will install the more uncommon of these dependencies:
adamc@896	60 \begin{verbatim}
adam@1368	61 apt-get install mlton libssl-dev
adamc@896	62 \end{verbatim}
adamc@555	63
adamc@896	64 To build programs that access SQL databases, you also need one of these client libraries for supported backends.
adamc@555	65 \begin{verbatim}
adamc@896	66 apt-get install libpq-dev libmysqlclient15-dev libsqlite3-dev
adamc@555	67 \end{verbatim}
adamc@555	68
adamc@555	69 It is also possible to access the modules of the Ur/Web compiler interactively, within Standard ML of New Jersey. To install the prerequisites in Debian testing:
adamc@555	70 \begin{verbatim}
adamc@555	71 apt-get install smlnj libsmlnj-smlnj ml-yacc ml-lpt
adamc@555	72 \end{verbatim}
adamc@555	73
adamc@555	74 To begin an interactive session with the Ur compiler modules, run \texttt{make smlnj}, and then, from within an \texttt{sml} session, run \texttt{CM.make "src/urweb.cm";}. The \texttt{Compiler} module is the main entry point.
adamc@555	75
adamc@896	76 To run an SQL-backed application with a backend besides SQLite, you will probably want to install one of these servers.
adamc@555	77
adamc@555	78 \begin{verbatim}
adam@1400	79 apt-get install postgresql-8.4 mysql-server-5.1
adamc@555	80 \end{verbatim}
adamc@555	81
adamc@555	82 To use the Emacs mode, you must have a modern Emacs installed. We assume that you already know how to do this, if you're in the business of looking for an Emacs mode. The demo generation facility of the compiler will also call out to Emacs to syntax-highlight code, and that process depends on the \texttt{htmlize} module, which can be installed in Debian testing via:
adamc@555	83
adamc@555	84 \begin{verbatim}
adamc@555	85 apt-get install emacs-goodies-el
adamc@555	86 \end{verbatim}
adamc@555	87
adam@1441	88 If you don't want to install the Emacs mode, run \texttt{./configure} with the argument \texttt{--without-emacs}.
adam@1441	89
adamc@555	90 Even with the right packages installed, configuration and building might fail to work. After you run \texttt{./configure}, you will see the values of some named environment variables printed. You may need to adjust these values to get proper installation for your system. To change a value, store your preferred alternative in the corresponding UNIX environment variable, before running \texttt{./configure}. For instance, here is how to change the list of extra arguments that the Ur/Web compiler will pass to GCC on every invocation.
adamc@555	91
adamc@555	92 \begin{verbatim}
adamc@555	93 GCCARGS=-fnested-functions ./configure
adamc@555	94 \end{verbatim}
adamc@555	95
adamc@1137	96 Some Mac OS X users have reported needing to use this particular GCCARGS value.
adamc@1137	97
adam@1464	98 Since the author is still getting a handle on the GNU Autotools that provide the build system, you may need to do some further work to get started, especially in environments with significant differences from Linux (where most testing is done). The variables \texttt{PGHEADER}, \texttt{MSHEADER}, and \texttt{SQHEADER} may be used to set the proper C header files to include for the development libraries of PostgreSQL, MySQL, and SQLite, respectively. To get libpq to link, one OS X user reported setting \texttt{GCCARGS="-I/opt/local/include -L/opt/local/lib/postgresql84"}, after creating a symbolic link with \texttt{ln -s /opt/local/include/postgresql84 /opt/local/include/postgresql}.
adamc@555	99
adamc@555	100 The Emacs mode can be set to autoload by adding the following to your \texttt{.emacs} file.
adamc@555	101
adamc@555	102 \begin{verbatim}
adamc@555	103 (add-to-list 'load-path "/usr/local/share/emacs/site-lisp/urweb-mode")
adamc@555	104 (load "urweb-mode-startup")
adamc@555	105 \end{verbatim}
adamc@555	106
adamc@555	107 Change the path in the first line if you chose a different Emacs installation path during configuration.
adamc@555	108
adamc@555	109
adamc@556	110 \section{Command-Line Compiler}
adamc@556	111
adamc@556	112 \subsection{Project Files}
adamc@556	113
adamc@556	114 The basic inputs to the \texttt{urweb} compiler are project files, which have the extension \texttt{.urp}. Here is a sample \texttt{.urp} file.
adamc@556	115
adamc@556	116 \begin{verbatim}
adamc@556	117 database dbname=test
adamc@556	118 sql crud1.sql
adamc@556	119
adamc@556	120 crud
adamc@556	121 crud1
adamc@556	122 \end{verbatim}
adamc@556	123
adamc@556	124 The \texttt{database} line gives the database information string to pass to libpq. In this case, the string only says to connect to a local database named \texttt{test}.
adamc@556	125
adamc@556	126 The \texttt{sql} line asks for an SQL source file to be generated, giving the commands to run to create the tables and sequences that this application expects to find. After building this \texttt{.urp} file, the following commands could be used to initialize the database, assuming that the current UNIX user exists as a Postgres user with database creation privileges:
adamc@556	127
adamc@556	128 \begin{verbatim}
adamc@556	129 createdb test
adamc@556	130 psql -f crud1.sql test
adamc@556	131 \end{verbatim}
adamc@556	132
adam@1331	133 A blank line separates the named directives from a list of modules to include in the project. Any line may contain a shell-script-style comment, where any suffix of a line starting at a hash character \texttt{\#} is ignored.
adamc@556	134
adamc@556	135 For each entry \texttt{M} in the module list, the file \texttt{M.urs} is included in the project if it exists, and the file \texttt{M.ur} must exist and is always included.
adamc@556	136
adamc@783	137 Here is the complete list of directive forms. ``FFI'' stands for ``foreign function interface,'' Ur's facility for interaction between Ur programs and C and JavaScript libraries.
adamc@783	138 \begin{itemize}
adam@1465	139 \item \texttt{[allow\|deny] [url\|mime\|requestHeader\|responseHeader] PATTERN} registers a rule governing which URLs, MIME types, HTTP request headers, or HTTP response headers are allowed to appear explicitly in this application. The first such rule to match a name determines the verdict. If \texttt{PATTERN} ends in \texttt{*}, it is interpreted as a prefix rule. Otherwise, a string must match it exactly.
adam@1400	140 \item \texttt{alwaysInline PATH} requests that every call to the referenced function be inlined. Section \ref{structure} explains how functions are assigned path strings.
adam@1462	141 \item \texttt{benignEffectful Module.ident} registers an FFI function or transaction as having side effects. The optimizer avoids removing, moving, or duplicating calls to such functions. Every effectful FFI function must be registered, or the optimizer may make invalid transformations. This version of the \texttt{effectful} directive registers that this function only has side effects that remain local to a single page generation.
adamc@783	142 \item \texttt{clientOnly Module.ident} registers an FFI function or transaction that may only be run in client browsers.
adamc@783	143 \item \texttt{clientToServer Module.ident} adds FFI type \texttt{Module.ident} to the list of types that are OK to marshal from clients to servers. Values like XML trees and SQL queries are hard to marshal without introducing expensive validity checks, so it's easier to ensure that the server never trusts clients to send such values. The file \texttt{include/urweb.h} shows examples of the C support functions that are required of any type that may be marshalled. These include \texttt{attrify}, \texttt{urlify}, and \texttt{unurlify} functions.
adamc@783	144 \item \texttt{database DBSTRING} sets the string to pass to libpq to open a database connection.
adamc@783	145 \item \texttt{debug} saves some intermediate C files, which is mostly useful to help in debugging the compiler itself.
adamc@783	146 \item \texttt{effectful Module.ident} registers an FFI function or transaction as having side effects. The optimizer avoids removing, moving, or duplicating calls to such functions. Every effectful FFI function must be registered, or the optimizer may make invalid transformations.
adamc@783	147 \item \texttt{exe FILENAME} sets the filename to which to write the output executable. The default for file \texttt{P.urp} is \texttt{P.exe}.
adamc@783	148 \item \texttt{ffi FILENAME} reads the file \texttt{FILENAME.urs} to determine the interface to a new FFI module. The name of the module is calculated from \texttt{FILENAME} in the same way as for normal source files. See the files \texttt{include/urweb.h} and \texttt{src/c/urweb.c} for examples of C headers and implementations for FFI modules. In general, every type or value \texttt{Module.ident} becomes \texttt{uw\_Module\_ident} in C.
adamc@1099	149 \item \texttt{include FILENAME} adds \texttt{FILENAME} to the list of files to be \texttt{\#include}d in C sources. This is most useful for interfacing with new FFI modules.
adamc@783	150 \item \texttt{jsFunc Module.ident=name} gives the JavaScript name of an FFI value.
adamc@1089	151 \item \texttt{library FILENAME} parses \texttt{FILENAME.urp} and merges its contents with the rest of the current file's contents. If \texttt{FILENAME.urp} doesn't exist, the compiler also tries \texttt{FILENAME/lib.urp}.
adam@1309	152 \item \texttt{limit class num} sets a resource usage limit for generated applications. The limit \texttt{class} will be set to the non-negative integer \texttt{num}. The classes are:
adam@1309	153 \begin{itemize}
adam@1309	154 \item \texttt{cleanup}: maximum number of cleanup operations (e.g., entries recording the need to deallocate certain temporary objects) that may be active at once per request
adam@1309	155 \item \texttt{database}: maximum size of database files (currently only used by SQLite)
adam@1309	156 \item \texttt{deltas}: maximum number of messages sendable in a single request handler with \texttt{Basis.send}
adam@1309	157 \item \texttt{globals}: maximum number of global variables that FFI libraries may set in a single request context
adam@1309	158 \item \texttt{headers}: maximum size (in bytes) of per-request buffer used to hold HTTP headers for generated pages
adam@1309	159 \item \texttt{heap}: maximum size (in bytes) of per-request heap for dynamically-allocated data
adam@1309	160 \item \texttt{inputs}: maximum number of top-level form fields per request
adam@1309	161 \item \texttt{messages}: maximum size (in bytes) of per-request buffer used to hold a single outgoing message sent with \texttt{Basis.send}
adam@1309	162 \item \texttt{page}: maximum size (in bytes) of per-request buffer used to hold HTML content of generated pages
adam@1309	163 \item \texttt{script}: maximum size (in bytes) of per-request buffer used to hold JavaScript content of generated pages
adam@1309	164 \item \texttt{subinputs}: maximum number of form fields per request, excluding top-level fields
adam@1309	165 \item \texttt{time}: maximum running time of a single page request, in units of approximately 0.1 seconds
adam@1309	166 \item \texttt{transactionals}: maximum number of custom transactional actions (e.g., sending an e-mail) that may be run in a single page generation
adam@1309	167 \end{itemize}
adamc@783	168 \item \texttt{link FILENAME} adds \texttt{FILENAME} to the list of files to be passed to the GCC linker at the end of compilation. This is most useful for importing extra libraries needed by new FFI modules.
adam@1332	169 \item \texttt{minHeap NUMBYTES} sets the initial size for thread-local heaps used in handling requests. These heaps grow automatically as needed (up to any maximum set with \texttt{limit}), but each regrow requires restarting the request handling process.
adam@1297	170 \item \texttt{onError Module.var} changes the handling of fatal application errors. Instead of displaying a default, ugly error 500 page, the error page will be generated by calling function \texttt{Module.var} on a piece of XML representing the error message. The error handler should have type $\mt{xbody} \to \mt{transaction} \; \mt{page}$. Note that the error handler \emph{cannot} be in the application's main module, since that would register it as explicitly callable via URLs.
adamc@852	171 \item \texttt{path NAME=VALUE} creates a mapping from \texttt{NAME} to \texttt{VALUE}. This mapping may be used at the beginnings of filesystem paths given to various other configuration directives. A path like \texttt{\$NAME/rest} is expanded to \texttt{VALUE/rest}. There is an initial mapping from the empty name (for paths like \texttt{\$/list}) to the directory where the Ur/Web standard library is installed. If you accept the default \texttt{configure} options, this directory is \texttt{/usr/local/lib/urweb/ur}.
adamc@783	172 \item \texttt{prefix PREFIX} sets the prefix included before every URI within the generated application. The default is \texttt{/}.
adamc@783	173 \item \texttt{profile} generates an executable that may be used with gprof.
adam@1300	174 \item \texttt{rewrite KIND FROM TO} gives a rule for rewriting canonical module paths. For instance, the canonical path of a page may be \texttt{Mod1.Mod2.mypage}, while you would rather the page were accessed via a URL containing only \texttt{page}. The directive \texttt{rewrite url Mod1/Mod2/mypage page} would accomplish that. The possible values of \texttt{KIND} determine which kinds of objects are affected. The kind \texttt{all} matches any object, and \texttt{url} matches page URLs. The kinds \texttt{table}, \texttt{sequence}, and \texttt{view} match those sorts of SQL entities, and \texttt{relation} matches any of those three. \texttt{cookie} matches HTTP cookies, and \texttt{style} matches CSS class names. If \texttt{FROM} ends in \texttt{/}, it is interpreted as a prefix matching rule, and rewriting occurs by replacing only the appropriate prefix of a path with \texttt{TO}. The \texttt{TO} field may be left empty to express the idea of deleting a prefix. For instance, \texttt{rewrite url Main/} will strip all \texttt{Main/} prefixes from URLs. While the actual external names of relations and styles have parts separated by underscores instead of slashes, all rewrite rules must be written in terms of slashes.
adamc@1183	175 \item \texttt{safeGet URI} asks to allow the page handler assigned this canonical URI prefix to cause persistent side effects, even if accessed via an HTTP \cd{GET} request.
adamc@783	176 \item \texttt{script URL} adds \texttt{URL} to the list of extra JavaScript files to be included at the beginning of any page that uses JavaScript. This is most useful for importing JavaScript versions of functions found in new FFI modules.
adamc@783	177 \item \texttt{serverOnly Module.ident} registers an FFI function or transaction that may only be run on the server.
adamc@1164	178 \item \texttt{sigfile PATH} sets a path where your application should look for a key to use in cryptographic signing. This is used to prevent cross-site request forgery attacks for any form handler that both reads a cookie and creates side effects. If the referenced file doesn't exist, an application will create it and read its saved data on future invocations. You can also initialize the file manually with any contents at least 16 bytes long; the first 16 bytes will be treated as the key.
adamc@783	179 \item \texttt{sql FILENAME} sets where to write an SQL file with the commands to create the expected database schema. The default is not to create such a file.
adamc@783	180 \item \texttt{timeout N} sets to \texttt{N} seconds the amount of time that the generated server will wait after the last contact from a client before determining that that client has exited the application. Clients that remain active will take the timeout setting into account in determining how often to ping the server, so it only makes sense to set a high timeout to cope with browser and network delays and failures. Higher timeouts can lead to more unnecessary client information taking up memory on the server. The timeout goes unused by any page that doesn't involve the \texttt{recv} function, since the server only needs to store per-client information for clients that receive asynchronous messages.
adamc@783	181 \end{itemize}
adamc@701	182
adamc@701	183
adamc@557	184 \subsection{Building an Application}
adamc@557	185
adamc@557	186 To compile project \texttt{P.urp}, simply run
adamc@557	187 \begin{verbatim}
adamc@557	188 urweb P
adamc@557	189 \end{verbatim}
adamc@1198	190 The output executable is a standalone web server. Run it with the command-line argument \texttt{-h} to see which options it takes. If the project file lists a database, the web server will attempt to connect to that database on startup. See Section \ref{structure} for an explanation of the URI mapping convention, which determines how each page of your application may be accessed via URLs.
adamc@557	191
adamc@557	192 To time how long the different compiler phases run, without generating an executable, run
adamc@557	193 \begin{verbatim}
adamc@557	194 urweb -timing P
adamc@557	195 \end{verbatim}
adamc@557	196
adamc@1086	197 To stop the compilation process after type-checking, run
adamc@1086	198 \begin{verbatim}
adamc@1086	199 urweb -tc P
adamc@1086	200 \end{verbatim}
adamc@1086	201
adamc@1170	202 To output information relevant to CSS stylesheets (and not finish regular compilation), run
adamc@1170	203 \begin{verbatim}
adamc@1170	204 urweb -css P
adamc@1170	205 \end{verbatim}
adamc@1170	206 The first output line is a list of categories of CSS properties that would be worth setting on the document body. The remaining lines are space-separated pairs of CSS class names and categories of properties that would be worth setting for that class. The category codes are divided into two varieties. Codes that reveal properties of a tag or its (recursive) children are \cd{B} for block-level elements, \cd{C} for table captions, \cd{D} for table cells, \cd{L} for lists, and \cd{T} for tables. Codes that reveal properties of the precise tag that uses a class are \cd{b} for block-level elements, \cd{t} for tables, \cd{d} for table cells, \cd{-} for table rows, \cd{H} for the possibility to set a height, \cd{N} for non-replaced inline-level elements, \cd{R} for replaced inline elements, and \cd{W} for the possibility to set a width.
adamc@1170	207
adamc@896	208 Some other command-line parameters are accepted:
adamc@896	209 \begin{itemize}
adamc@896	210 \item \texttt{-db <DBSTRING>}: Set database connection information, using the format expected by Postgres's \texttt{PQconnectdb()}, which is \texttt{name1=value1 ... nameN=valueN}. The same format is also parsed and used to discover connection parameters for MySQL and SQLite. The only significant settings for MySQL are \texttt{host}, \texttt{hostaddr}, \texttt{port}, \texttt{dbname}, \texttt{user}, and \texttt{password}. The only significant setting for SQLite is \texttt{dbname}, which is interpreted as the filesystem path to the database. Additionally, when using SQLite, a database string may be just a file path.
adamc@896	211
adamc@896	212 \item \texttt{-dbms [postgres\|mysql\|sqlite]}: Sets the database backend to use.
adamc@896	213 \begin{itemize}
adamc@896	214 \item \texttt{postgres}: This is PostgreSQL, the default. Among the supported engines, Postgres best matches the design philosophy behind Ur, with a focus on consistent views of data, even in the face of much concurrency. Different database engines have different quirks of SQL syntax. Ur/Web tends to use Postgres idioms where there are choices to be made, though the compiler translates SQL as needed to support other backends.
adamc@896	215
adamc@896	216 A command sequence like this can initialize a Postgres database, using a file \texttt{app.sql} generated by the compiler:
adamc@896	217 \begin{verbatim}
adamc@896	218 createdb app
adamc@896	219 psql -f app.sql app
adamc@896	220 \end{verbatim}
adamc@896	221
adamc@896	222 \item \texttt{mysql}: This is MySQL, another popular relational database engine that uses persistent server processes. Ur/Web needs transactions to function properly. Many installations of MySQL use non-transactional storage engines by default. Ur/Web generates table definitions that try to use MySQL's InnoDB engine, which supports transactions. You can edit the first line of a generated \texttt{.sql} file to change this behavior, but it really is true that Ur/Web applications will exhibit bizarre behavior if you choose an engine that ignores transaction commands.
adamc@896	223
adamc@896	224 A command sequence like this can initialize a MySQL database:
adamc@896	225 \begin{verbatim}
adamc@896	226 echo "CREATE DATABASE app" \| mysql
adamc@896	227 mysql -D app <app.sql
adamc@896	228 \end{verbatim}
adamc@896	229
adamc@896	230 \item \texttt{sqlite}: This is SQLite, a simple filesystem-based transactional database engine. With this backend, Ur/Web applications can run without any additional server processes. The other engines are generally preferred for large-workload performance and full admin feature sets, while SQLite is popular for its low resource footprint and ease of set-up.
adamc@896	231
adamc@896	232 A command like this can initialize an SQLite database:
adamc@896	233 \begin{verbatim}
adamc@896	234 sqlite3 path/to/database/file <app.sql
adamc@896	235 \end{verbatim}
adamc@896	236 \end{itemize}
adamc@896	237
adam@1309	238 \item \texttt{-limit class num}: Equivalent to the \texttt{limit} directive from \texttt{.urp} files
adam@1309	239
adamc@896	240 \item \texttt{-output FILENAME}: Set where the application executable is written.
adamc@896	241
adamc@1127	242 \item \texttt{-path NAME VALUE}: Set the value of path variable \texttt{\$NAME} to \texttt{VALUE}, for use in \texttt{.urp} files.
adamc@1127	243
adam@1335	244 \item \texttt{-prefix PREFIX}: Equivalent to the \texttt{prefix} directive from \texttt{.urp} files
adam@1335	245
adamc@896	246 \item \texttt{-protocol [http\|cgi\|fastcgi]}: Set the protocol that the generated application speaks.
adamc@896	247 \begin{itemize}
adamc@896	248 \item \texttt{http}: This is the default. It is for building standalone web servers that can be accessed by web browsers directly.
adamc@896	249
adamc@896	250 \item \texttt{cgi}: This is the classic protocol that web servers use to generate dynamic content by spawning new processes. While Ur/Web programs may in general use message-passing with the \texttt{send} and \texttt{recv} functions, that functionality is not yet supported in CGI, since CGI needs a fresh process for each request, and message-passing needs to use persistent sockets to deliver messages.
adamc@896	251
adamc@896	252 Since Ur/Web treats paths in an unusual way, a configuration line like this one can be used to configure an application that was built with URL prefix \texttt{/Hello}:
adamc@896	253 \begin{verbatim}
adamc@896	254 ScriptAlias /Hello /path/to/hello.exe
adamc@896	255 \end{verbatim}
adamc@896	256
adamc@1163	257 A different method can be used for, e.g., a shared host, where you can only configure Apache via \texttt{.htaccess} files. Drop the generated executable into your web space and mark it as CGI somehow. For instance, if the script ends in \texttt{.exe}, you might put this in \texttt{.htaccess} in the directory containing the script:
adamc@1163	258 \begin{verbatim}
adamc@1163	259 Options +ExecCGI
adamc@1163	260 AddHandler cgi-script .exe
adamc@1163	261 \end{verbatim}
adamc@1163	262
adamc@1163	263 Additionally, make sure that Ur/Web knows the proper URI prefix for your script. For instance, if the script is accessed via \texttt{http://somewhere/dir/script.exe}, then include this line in your \texttt{.urp} file:
adamc@1163	264 \begin{verbatim}
adamc@1163	265 prefix /dir/script.exe/
adamc@1163	266 \end{verbatim}
adamc@1163	267
adamc@1163	268 To access the \texttt{foo} function in the \texttt{Bar} module, you would then hit \texttt{http://somewhere/dir/script.exe/Bar/foo}.
adamc@1163	269
adamc@1164	270 If your application contains form handlers that read cookies before causing side effects, then you will need to use the \texttt{sigfile} \texttt{.urp} directive, too.
adamc@1164	271
adamc@896	272 \item \texttt{fastcgi}: This is a newer protocol inspired by CGI, wherein web servers can start and reuse persistent external processes to generate dynamic content. Ur/Web doesn't implement the whole protocol, but Ur/Web's support has been tested to work with the \texttt{mod\_fastcgi}s of Apache and lighttpd.
adamc@896	273
adamc@896	274 To configure a FastCGI program with Apache, one could combine the above \texttt{ScriptAlias} line with a line like this:
adamc@896	275 \begin{verbatim}
adamc@896	276 FastCgiServer /path/to/hello.exe -idle-timeout 99999
adamc@896	277 \end{verbatim}
adamc@896	278 The idle timeout is only important for applications that use message-passing. Client connections may go long periods without receiving messages, and Apache tries to be helpful and garbage collect them in such cases. To prevent that behavior, we specify how long a connection must be idle to be collected.
adamc@896	279
adamc@896	280 Here is some lighttpd configuration for the same application.
adamc@896	281 \begin{verbatim}
adamc@896	282 fastcgi.server = (
adamc@896	283 "/Hello/" =>
adamc@896	284 (( "bin-path" => "/path/to/hello.exe",
adamc@896	285 "socket" => "/tmp/hello",
adamc@896	286 "check-local" => "disable",
adamc@896	287 "docroot" => "/",
adamc@896	288 "max-procs" => "1"
adamc@896	289 ))
adamc@896	290 )
adamc@896	291 \end{verbatim}
adamc@896	292 The least obvious requirement is setting \texttt{max-procs} to 1, so that lighttpd doesn't try to multiplex requests across multiple external processes. This is required for message-passing applications, where a single database of client connections is maintained within a multi-threaded server process. Multiple processes may, however, be used safely with applications that don't use message-passing.
adamc@896	293
adamc@896	294 A FastCGI process reads the environment variable \texttt{URWEB\_NUM\_THREADS} to determine how many threads to spawn for handling client requests. The default is 1.
adamc@896	295 \end{itemize}
adamc@896	296
adamc@1127	297 \item \texttt{-root Name PATH}: Trigger an alternate module convention for all source files found in directory \texttt{PATH} or any of its subdirectories. Any file \texttt{PATH/foo.ur} defines a module \texttt{Name.Foo} instead of the usual \texttt{Foo}. Any file \texttt{PATH/subdir/foo.ur} defines a module \texttt{Name.Subdir.Foo}, and so on for arbitrary nesting of subdirectories.
adamc@1127	298
adamc@1164	299 \item \texttt{-sigfile PATH}: Same as the \texttt{sigfile} directive in \texttt{.urp} files
adamc@1164	300
adamc@896	301 \item \texttt{-sql FILENAME}: Set where a database set-up SQL script is written.
adamc@1095	302
adamc@1095	303 \item \texttt{-static}: Link the runtime system statically. The default is to link against dynamic libraries.
adamc@896	304 \end{itemize}
adamc@896	305
adam@1297	306 There is an additional convenience method for invoking \texttt{urweb}. If the main argument is \texttt{FOO}, and \texttt{FOO.ur} exists but \texttt{FOO.urp} doesn't, then the invocation is interpreted as if called on a \texttt{.urp} file containing \texttt{FOO} as its only main entry, with an additional \texttt{rewrite all FOO/*} directive.
adamc@556	307
adamc@529	308 \section{Ur Syntax}
adamc@529	309
adamc@784	310 In this section, we describe the syntax of Ur, deferring to a later section discussion of most of the syntax specific to SQL and XML. The sole exceptions are the declaration forms for relations, cookies, and styles.
adamc@524	311
adamc@524	312 \subsection{Lexical Conventions}
adamc@524	313
adamc@524	314 We give the Ur language definition in \LaTeX $\;$ math mode, since that is prettier than monospaced ASCII. The corresponding ASCII syntax can be read off directly. Here is the key for mapping math symbols to ASCII character sequences.
adamc@524	315
adamc@524	316 \begin{center}
adamc@524	317 \begin{tabular}{rl}
adamc@524	318 \textbf{\LaTeX} & \textbf{ASCII} \\
adamc@524	319 $\to$ & \cd{->} \\
adamc@652	320 $\longrightarrow$ & \cd{-->} \\
adamc@524	321 $\times$ & \cd{*} \\
adamc@524	322 $\lambda$ & \cd{fn} \\
adamc@524	323 $\Rightarrow$ & \cd{=>} \\
adamc@652	324 $\Longrightarrow$ & \cd{==>} \\
adamc@529	325 $\neq$ & \cd{<>} \\
adamc@529	326 $\leq$ & \cd{<=} \\
adamc@529	327 $\geq$ & \cd{>=} \\
adamc@524	328 \\
adamc@524	329 $x$ & Normal textual identifier, not beginning with an uppercase letter \\
adamc@525	330 $X$ & Normal textual identifier, beginning with an uppercase letter \\
adamc@524	331 \end{tabular}
adamc@524	332 \end{center}
adamc@524	333
adamc@525	334 We often write syntax like $e^$ to indicate zero or more copies of $e$, $e^+$ to indicate one or more copies, and $e,^$ and $e,^+$ to indicate multiple copies separated by commas. Another separator may be used in place of a comma. The $e$ term may be surrounded by parentheses to indicate grouping; those parentheses should not be included in the actual ASCII.
adamc@524	335
adamc@873	336 We write $\ell$ for literals of the primitive types, for the most part following C conventions. There are $\mt{int}$, $\mt{float}$, $\mt{char}$, and $\mt{string}$ literals. Character literals follow the SML convention instead of the C convention, written like \texttt{\#"a"} instead of \texttt{'a'}.
adamc@526	337
adamc@527	338 This version of the manual doesn't include operator precedences; see \texttt{src/urweb.grm} for that.
adamc@527	339
adam@1297	340 As in the ML language family, the syntax \texttt{(* ... *)} is used for (nestable) comments. Within XML literals, Ur/Web also supports the usual \texttt{<!-- ... -->} XML comments.
adam@1297	341
adamc@552	342 \subsection{\label{core}Core Syntax}
adamc@524	343
adamc@524	344 \emph{Kinds} classify types and other compile-time-only entities. Each kind in the grammar is listed with a description of the sort of data it classifies.
adamc@524	345 $$\begin{array}{rrcll}
adamc@524	346 \textrm{Kinds} & \kappa &::=& \mt{Type} & \textrm{proper types} \\
adamc@525	347 &&& \mt{Unit} & \textrm{the trivial constructor} \\
adamc@525	348 &&& \mt{Name} & \textrm{field names} \\
adamc@525	349 &&& \kappa \to \kappa & \textrm{type-level functions} \\
adamc@525	350 &&& \{\kappa\} & \textrm{type-level records} \\
adamc@525	351 &&& (\kappa\times^+) & \textrm{type-level tuples} \\
adamc@652	352 &&& X & \textrm{variable} \\
adamc@652	353 &&& X \longrightarrow k & \textrm{kind-polymorphic type-level function} \\
adamc@529	354 &&& \_\_ & \textrm{wildcard} \\
adamc@525	355 &&& (\kappa) & \textrm{explicit precedence} \\
adamc@524	356 \end{array}$$
adamc@524	357
adamc@524	358 Ur supports several different notions of functions that take types as arguments. These arguments can be either implicit, causing them to be inferred at use sites; or explicit, forcing them to be specified manually at use sites. There is a common explicitness annotation convention applied at the definitions of and in the types of such functions.
adamc@524	359 $$\begin{array}{rrcll}
adamc@524	360 \textrm{Explicitness} & ? &::=& :: & \textrm{explicit} \\
adamc@558	361 &&& ::: & \textrm{implicit}
adamc@524	362 \end{array}$$
adamc@524	363
adamc@524	364 \emph{Constructors} are the main class of compile-time-only data. They include proper types and are classified by kinds.
adamc@524	365 $$\begin{array}{rrcll}
adamc@524	366 \textrm{Constructors} & c, \tau &::=& (c) :: \kappa & \textrm{kind annotation} \\
adamc@530	367 &&& \hat{x} & \textrm{constructor variable} \\
adamc@524	368 \\
adamc@525	369 &&& \tau \to \tau & \textrm{function type} \\
adamc@525	370 &&& x \; ? \; \kappa \to \tau & \textrm{polymorphic function type} \\
adamc@652	371 &&& X \longrightarrow \tau & \textrm{kind-polymorphic function type} \\
adamc@525	372 &&& \$ c & \textrm{record type} \\
adamc@524	373 \\
adamc@525	374 &&& c \; c & \textrm{type-level function application} \\
adamc@530	375 &&& \lambda x \; :: \; \kappa \Rightarrow c & \textrm{type-level function abstraction} \\
adamc@524	376 \\
adamc@652	377 &&& X \Longrightarrow c & \textrm{type-level kind-polymorphic function abstraction} \\
adamc@655	378 &&& c [\kappa] & \textrm{type-level kind-polymorphic function application} \\
adamc@652	379 \\
adamc@525	380 &&& () & \textrm{type-level unit} \\
adamc@525	381 &&& \#X & \textrm{field name} \\
adamc@524	382 \\
adamc@525	383 &&& [(c = c)^*] & \textrm{known-length type-level record} \\
adamc@525	384 &&& c \rc c & \textrm{type-level record concatenation} \\
adamc@652	385 &&& \mt{map} & \textrm{type-level record map} \\
adamc@524	386 \\
adamc@558	387 &&& (c,^+) & \textrm{type-level tuple} \\
adamc@525	388 &&& c.n & \textrm{type-level tuple projection ($n \in \mathbb N^+$)} \\
adamc@524	389 \\
adamc@652	390 &&& [c \sim c] \Rightarrow \tau & \textrm{guarded type} \\
adamc@524	391 \\
adamc@529	392 &&& \_ :: \kappa & \textrm{wildcard} \\
adamc@525	393 &&& (c) & \textrm{explicit precedence} \\
adamc@530	394 \\
adamc@530	395 \textrm{Qualified uncapitalized variables} & \hat{x} &::=& x & \textrm{not from a module} \\
adamc@530	396 &&& M.x & \textrm{projection from a module} \\
adamc@525	397 \end{array}$$
adamc@525	398
adamc@655	399 We include both abstraction and application for kind polymorphism, but applications are only inferred internally; they may not be written explicitly in source programs.
adamc@655	400
adamc@525	401 Modules of the module system are described by \emph{signatures}.
adamc@525	402 $$\begin{array}{rrcll}
adamc@525	403 \textrm{Signatures} & S &::=& \mt{sig} \; s^* \; \mt{end} & \textrm{constant} \\
adamc@525	404 &&& X & \textrm{variable} \\
adamc@525	405 &&& \mt{functor}(X : S) : S & \textrm{functor} \\
adamc@529	406 &&& S \; \mt{where} \; \mt{con} \; x = c & \textrm{concretizing an abstract constructor} \\
adamc@525	407 &&& M.X & \textrm{projection from a module} \\
adamc@525	408 \\
adamc@525	409 \textrm{Signature items} & s &::=& \mt{con} \; x :: \kappa & \textrm{abstract constructor} \\
adamc@525	410 &&& \mt{con} \; x :: \kappa = c & \textrm{concrete constructor} \\
adamc@528	411 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529	412 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@525	413 &&& \mt{val} \; x : \tau & \textrm{value} \\
adamc@525	414 &&& \mt{structure} \; X : S & \textrm{sub-module} \\
adamc@525	415 &&& \mt{signature} \; X = S & \textrm{sub-signature} \\
adamc@525	416 &&& \mt{include} \; S & \textrm{signature inclusion} \\
adamc@525	417 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@654	418 &&& \mt{class} \; x :: \kappa & \textrm{abstract constructor class} \\
adamc@654	419 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@525	420 \\
adamc@525	421 \textrm{Datatype constructors} & dc &::=& X & \textrm{nullary constructor} \\
adamc@525	422 &&& X \; \mt{of} \; \tau & \textrm{unary constructor} \\
adamc@524	423 \end{array}$$
adamc@524	424
adamc@526	425 \emph{Patterns} are used to describe structural conditions on expressions, such that expressions may be tested against patterns, generating assignments to pattern variables if successful.
adamc@526	426 $$\begin{array}{rrcll}
adamc@526	427 \textrm{Patterns} & p &::=& \_ & \textrm{wildcard} \\
adamc@526	428 &&& x & \textrm{variable} \\
adamc@526	429 &&& \ell & \textrm{constant} \\
adamc@526	430 &&& \hat{X} & \textrm{nullary constructor} \\
adamc@526	431 &&& \hat{X} \; p & \textrm{unary constructor} \\
adamc@526	432 &&& \{(x = p,)^*\} & \textrm{rigid record pattern} \\
adamc@526	433 &&& \{(x = p,)^+, \ldots\} & \textrm{flexible record pattern} \\
adamc@852	434 &&& p : \tau & \textrm{type annotation} \\
adamc@527	435 &&& (p) & \textrm{explicit precedence} \\
adamc@526	436 \\
adamc@529	437 \textrm{Qualified capitalized variables} & \hat{X} &::=& X & \textrm{not from a module} \\
adamc@526	438 &&& M.X & \textrm{projection from a module} \\
adamc@526	439 \end{array}$$
adamc@526	440
adamc@527	441 \emph{Expressions} are the main run-time entities, corresponding to both ``expressions'' and ``statements'' in mainstream imperative languages.
adamc@527	442 $$\begin{array}{rrcll}
adamc@527	443 \textrm{Expressions} & e &::=& e : \tau & \textrm{type annotation} \\
adamc@529	444 &&& \hat{x} & \textrm{variable} \\
adamc@529	445 &&& \hat{X} & \textrm{datatype constructor} \\
adamc@527	446 &&& \ell & \textrm{constant} \\
adamc@527	447 \\
adamc@527	448 &&& e \; e & \textrm{function application} \\
adamc@527	449 &&& \lambda x : \tau \Rightarrow e & \textrm{function abstraction} \\
adamc@527	450 &&& e [c] & \textrm{polymorphic function application} \\
adamc@852	451 &&& \lambda [x \; ? \; \kappa] \Rightarrow e & \textrm{polymorphic function abstraction} \\
adamc@655	452 &&& e [\kappa] & \textrm{kind-polymorphic function application} \\
adamc@652	453 &&& X \Longrightarrow e & \textrm{kind-polymorphic function abstraction} \\
adamc@527	454 \\
adamc@527	455 &&& \{(c = e,)^*\} & \textrm{known-length record} \\
adamc@527	456 &&& e.c & \textrm{record field projection} \\
adamc@527	457 &&& e \rc e & \textrm{record concatenation} \\
adamc@527	458 &&& e \rcut c & \textrm{removal of a single record field} \\
adamc@527	459 &&& e \rcutM c & \textrm{removal of multiple record fields} \\
adamc@527	460 \\
adamc@527	461 &&& \mt{let} \; ed^* \; \mt{in} \; e \; \mt{end} & \textrm{local definitions} \\
adamc@527	462 \\
adamc@527	463 &&& \mt{case} \; e \; \mt{of} \; (p \Rightarrow e\|)^+ & \textrm{pattern matching} \\
adamc@527	464 \\
adamc@654	465 &&& \lambda [c \sim c] \Rightarrow e & \textrm{guarded expression abstraction} \\
adamc@654	466 &&& e \; ! & \textrm{guarded expression application} \\
adamc@527	467 \\
adamc@527	468 &&& \_ & \textrm{wildcard} \\
adamc@527	469 &&& (e) & \textrm{explicit precedence} \\
adamc@527	470 \\
adamc@527	471 \textrm{Local declarations} & ed &::=& \cd{val} \; x : \tau = e & \textrm{non-recursive value} \\
adamc@527	472 &&& \cd{val} \; \cd{rec} \; (x : \tau = e \; \cd{and})^+ & \textrm{mutually-recursive values} \\
adamc@527	473 \end{array}$$
adamc@527	474
adamc@655	475 As with constructors, we include both abstraction and application for kind polymorphism, but applications are only inferred internally.
adamc@655	476
adamc@528	477 \emph{Declarations} primarily bring new symbols into context.
adamc@528	478 $$\begin{array}{rrcll}
adamc@528	479 \textrm{Declarations} & d &::=& \mt{con} \; x :: \kappa = c & \textrm{constructor synonym} \\
adamc@528	480 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529	481 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@528	482 &&& \mt{val} \; x : \tau = e & \textrm{value} \\
adamc@528	483 &&& \mt{val} \; \cd{rec} \; (x : \tau = e \; \mt{and})^+ & \textrm{mutually-recursive values} \\
adamc@528	484 &&& \mt{structure} \; X : S = M & \textrm{module definition} \\
adamc@528	485 &&& \mt{signature} \; X = S & \textrm{signature definition} \\
adamc@528	486 &&& \mt{open} \; M & \textrm{module inclusion} \\
adamc@528	487 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@528	488 &&& \mt{open} \; \mt{constraints} \; M & \textrm{inclusion of just the constraints from a module} \\
adamc@528	489 &&& \mt{table} \; x : c & \textrm{SQL table} \\
adamc@784	490 &&& \mt{view} \; x : c & \textrm{SQL view} \\
adamc@528	491 &&& \mt{sequence} \; x & \textrm{SQL sequence} \\
adamc@535	492 &&& \mt{cookie} \; x : \tau & \textrm{HTTP cookie} \\
adamc@784	493 &&& \mt{style} \; x : \tau & \textrm{CSS class} \\
adamc@654	494 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@1085	495 &&& \mt{task} \; e = e & \textrm{recurring task} \\
adamc@528	496 \\
adamc@529	497 \textrm{Modules} & M &::=& \mt{struct} \; d^* \; \mt{end} & \textrm{constant} \\
adamc@529	498 &&& X & \textrm{variable} \\
adamc@529	499 &&& M.X & \textrm{projection} \\
adamc@529	500 &&& M(M) & \textrm{functor application} \\
adamc@529	501 &&& \mt{functor}(X : S) : S = M & \textrm{functor abstraction} \\
adamc@528	502 \end{array}$$
adamc@528	503
adamc@528	504 There are two kinds of Ur files. A file named $M\texttt{.ur}$ is an \emph{implementation file}, and it should contain a sequence of declarations $d^$. A file named $M\texttt{.urs}$ is an \emph{interface file}; it must always have a matching $M\texttt{.ur}$ and should contain a sequence of signature items $s^$. When both files are present, the overall effect is the same as a monolithic declaration $\mt{structure} \; M : \mt{sig} \; s^* \; \mt{end} = \mt{struct} \; d^* \; \mt{end}$. When no interface file is included, the overall effect is similar, with a signature for module $M$ being inferred rather than just checked against an interface.
adamc@527	505
adamc@784	506 We omit some extra possibilities in $\mt{table}$ syntax, deferring them to Section \ref{tables}.
adamc@784	507
adamc@529	508 \subsection{Shorthands}
adamc@529	509
adamc@529	510 There are a variety of derived syntactic forms that elaborate into the core syntax from the last subsection. We will present the additional forms roughly following the order in which we presented the constructs that they elaborate into.
adamc@529	511
adamc@529	512 In many contexts where record fields are expected, like in a projection $e.c$, a constant field may be written as simply $X$, rather than $\#X$.
adamc@529	513
adamc@529	514 A record type may be written $\{(c = c,)^\}$, which elaborates to $\$[(c = c,)^]$.
adamc@529	515
adamc@533	516 The notation $[c_1, \ldots, c_n]$ is shorthand for $[c_1 = (), \ldots, c_n = ()]$.
adamc@533	517
adam@1350	518 A tuple type $\tau_1 \times \ldots \times \tau_n$ expands to a record type $\{1 : \tau_1, \ldots, n : \tau_n\}$, with natural numbers as field names. A tuple expression $(e_1, \ldots, e_n)$ expands to a record expression $\{1 = e_1, \ldots, n = e_n\}$. A tuple pattern $(p_1, \ldots, p_n)$ expands to a rigid record pattern $\{1 = p_1, \ldots, n = p_n\}$. Positive natural numbers may be used in most places where field names would be allowed.
adamc@529	519
adamc@852	520 In general, several adjacent $\lambda$ forms may be combined into one, and kind and type annotations may be omitted, in which case they are implicitly included as wildcards. More formally, for constructor-level abstractions, we can define a new non-terminal $b ::= x \mid (x :: \kappa) \mid X$ and allow composite abstractions of the form $\lambda b^+ \Rightarrow c$, elaborating into the obvious sequence of one core $\lambda$ per element of $b^+$.
adamc@529	521
adam@1306	522 In some contexts, the parser isn't happy with token sequences like $x :: \_$, to indicate a constructor variable of wildcard kind. In such cases, write the second two tokens as $::\hspace{-.05in}\_$, with no intervening spaces. Analogous syntax $:::\hspace{-.05in}\_$ is available for implicit constructor arguments.
adam@1302	523
adamc@529	524 For any signature item or declaration that defines some entity to be equal to $A$ with classification annotation $B$ (e.g., $\mt{val} \; x : B = A$), $B$ and the preceding colon (or similar punctuation) may be omitted, in which case it is filled in as a wildcard.
adamc@529	525
adamc@529	526 A signature item or declaration $\mt{type} \; x$ or $\mt{type} \; x = \tau$ is elaborated into $\mt{con} \; x :: \mt{Type}$ or $\mt{con} \; x :: \mt{Type} = \tau$, respectively.
adamc@529	527
adamc@654	528 A signature item or declaration $\mt{class} \; x = \lambda y \Rightarrow c$ may be abbreviated $\mt{class} \; x \; y = c$.
adamc@529	529
adam@1472	530 Handling of implicit and explicit constructor arguments may be tweaked with some prefixes to variable references. An expression $@x$ is a version of $x$ where all type class instance and disjointness arguments have been made explicit. An expression $@@x$ achieves the same effect, additionally making explicit all implicit constructor arguments. The default is that implicit arguments are inserted automatically after any reference to a variable, or after any application of a variable to one or more arguments. For such an expression, implicit wildcard arguments are added for the longest prefix of the expression's type consisting only of implicit polymorphism, type class instances, and disjointness obligations. The same syntax works for variables projected out of modules and for capitalized variables (datatype constructors).
adamc@529	531
adamc@852	532 At the expression level, an analogue is available of the composite $\lambda$ form for constructors. We define the language of binders as $b ::= p \mid [x] \mid [x \; ? \; \kappa] \mid X \mid [c \sim c]$. A lone variable $[x]$ stands for an implicit constructor variable of unspecified kind. The standard value-level function binder is recovered as the type-annotated pattern form $x : \tau$. It is a compile-time error to include a pattern $p$ that does not match every value of the appropriate type.
adamc@529	533
adamc@852	534 A local $\mt{val}$ declaration may bind a pattern instead of just a plain variable. As for function arguments, only irrefutable patterns are legal.
adamc@852	535
adamc@852	536 The keyword $\mt{fun}$ is a shorthand for $\mt{val} \; \mt{rec}$ that allows arguments to be specified before the equal sign in the definition of each mutually-recursive function, as in SML. Each curried argument must follow the grammar of the $b$ non-terminal introduced two paragraphs ago. A $\mt{fun}$ declaration is elaborated into a version that adds additional $\lambda$s to the fronts of the righthand sides, as appropriate.
adamc@529	537
adamc@529	538 A signature item $\mt{functor} \; X_1 \; (X_2 : S_1) : S_2$ is elaborated into $\mt{structure} \; X_1 : \mt{functor}(X_2 : S_1) : S_2$. A declaration $\mt{functor} \; X_1 \; (X_2 : S_1) : S_2 = M$ is elaborated into $\mt{structure} \; X_1 : \mt{functor}(X_2 : S_1) : S_2 = \mt{functor}(X_2 : S_1) : S_2 = M$.
adamc@529	539
adamc@852	540 An $\mt{open} \; \mt{constraints}$ declaration is implicitly inserted for the argument of every functor at the beginning of the functor body. For every declaration of the form $\mt{structure} \; X : S = \mt{struct} \ldots \mt{end}$, an $\mt{open} \; \mt{constraints} \; X$ declaration is implicitly inserted immediately afterward.
adamc@852	541
adamc@853	542 A declaration $\mt{table} \; x : \{(c = c,)^\}$ is elaborated into $\mt{table} \; x : [(c = c,)^]$.
adamc@529	543
adamc@529	544 The syntax $\mt{where} \; \mt{type}$ is an alternate form of $\mt{where} \; \mt{con}$.
adamc@529	545
adamc@529	546 The syntax $\mt{if} \; e \; \mt{then} \; e_1 \; \mt{else} \; e_2$ expands to $\mt{case} \; e \; \mt{of} \; \mt{Basis}.\mt{True} \Rightarrow e_1 \mid \mt{Basis}.\mt{False} \Rightarrow e_2$.
adamc@529	547
adamc@529	548 There are infix operator syntaxes for a number of functions defined in the $\mt{Basis}$ module. There is $=$ for $\mt{eq}$, $\neq$ for $\mt{neq}$, $-$ for $\mt{neg}$ (as a prefix operator) and $\mt{minus}$, $+$ for $\mt{plus}$, $\times$ for $\mt{times}$, $/$ for $\mt{div}$, $\%$ for $\mt{mod}$, $<$ for $\mt{lt}$, $\leq$ for $\mt{le}$, $>$ for $\mt{gt}$, and $\geq$ for $\mt{ge}$.
adamc@529	549
adamc@784	550 A signature item $\mt{table} \; x : c$ is shorthand for $\mt{val} \; x : \mt{Basis}.\mt{sql\_table} \; c \; []$. $\mt{view} \; x : c$ is shorthand for $\mt{val} \; x : \mt{Basis}.\mt{sql\_view} \; c$, $\mt{sequence} \; x$ is short for $\mt{val} \; x : \mt{Basis}.\mt{sql\_sequence}$. $\mt{cookie} \; x : \tau$ is shorthand for $\mt{val} \; x : \mt{Basis}.\mt{http\_cookie} \; \tau$, and $\mt{style} \; x$ is shorthand for $\mt{val} \; x : \mt{Basis}.\mt{css\_class}$.
adamc@529	551
adamc@530	552
adamc@530	553 \section{Static Semantics}
adamc@530	554
adamc@530	555 In this section, we give a declarative presentation of Ur's typing rules and related judgments. Inference is the subject of the next section; here, we assume that an oracle has filled in all wildcards with concrete values.
adamc@530	556
adamc@530	557 Since there is significant mutual recursion among the judgments, we introduce them all before beginning to give rules. We use the same variety of contexts throughout this section, implicitly introducing new sorts of context entries as needed.
adamc@530	558 \begin{itemize}
adamc@655	559 \item $\Gamma \vdash \kappa$ expresses kind well-formedness.
adamc@530	560 \item $\Gamma \vdash c :: \kappa$ assigns a kind to a constructor in a context.
adamc@530	561 \item $\Gamma \vdash c \sim c$ proves the disjointness of two record constructors; that is, that they share no field names. We overload the judgment to apply to pairs of field names as well.
adamc@531	562 \item $\Gamma \vdash c \hookrightarrow C$ proves that record constructor $c$ decomposes into set $C$ of field names and record constructors.
adamc@530	563 \item $\Gamma \vdash c \equiv c$ proves the computational equivalence of two constructors. This is often called a \emph{definitional equality} in the world of type theory.
adamc@530	564 \item $\Gamma \vdash e : \tau$ is a standard typing judgment.
adamc@534	565 \item $\Gamma \vdash p \leadsto \Gamma; \tau$ combines typing of patterns with calculation of which new variables they bind.
adamc@537	566 \item $\Gamma \vdash d \leadsto \Gamma$ expresses how a declaration modifies a context. We overload this judgment to apply to sequences of declarations, as well as to signature items and sequences of signature items.
adamc@537	567 \item $\Gamma \vdash S \equiv S$ is the signature equivalence judgment.
adamc@536	568 \item $\Gamma \vdash S \leq S$ is the signature compatibility judgment. We write $\Gamma \vdash S$ as shorthand for $\Gamma \vdash S \leq S$.
adamc@530	569 \item $\Gamma \vdash M : S$ is the module signature checking judgment.
adamc@537	570 \item $\mt{proj}(M, \overline{s}, V)$ is a partial function for projecting a signature item from $\overline{s}$, given the module $M$ that we project from. $V$ may be $\mt{con} \; x$, $\mt{datatype} \; x$, $\mt{val} \; x$, $\mt{signature} \; X$, or $\mt{structure} \; X$. The parameter $M$ is needed because the projected signature item may refer to other items from $\overline{s}$.
adamc@539	571 \item $\mt{selfify}(M, \overline{s})$ adds information to signature items $\overline{s}$ to reflect the fact that we are concerned with the particular module $M$. This function is overloaded to work over individual signature items as well.
adamc@530	572 \end{itemize}
adamc@530	573
adamc@655	574
adamc@655	575 \subsection{Kind Well-Formedness}
adamc@655	576
adamc@655	577 $$\infer{\Gamma \vdash \mt{Type}}{}
adamc@655	578 \quad \infer{\Gamma \vdash \mt{Unit}}{}
adamc@655	579 \quad \infer{\Gamma \vdash \mt{Name}}{}
adamc@655	580 \quad \infer{\Gamma \vdash \kappa_1 \to \kappa_2}{
adamc@655	581 \Gamma \vdash \kappa_1
adamc@655	582 & \Gamma \vdash \kappa_2
adamc@655	583 }
adamc@655	584 \quad \infer{\Gamma \vdash \{\kappa\}}{
adamc@655	585 \Gamma \vdash \kappa
adamc@655	586 }
adamc@655	587 \quad \infer{\Gamma \vdash (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@655	588 \forall i: \Gamma \vdash \kappa_i
adamc@655	589 }$$
adamc@655	590
adamc@655	591 $$\infer{\Gamma \vdash X}{
adamc@655	592 X \in \Gamma
adamc@655	593 }
adamc@655	594 \quad \infer{\Gamma \vdash X \longrightarrow \kappa}{
adamc@655	595 \Gamma, X \vdash \kappa
adamc@655	596 }$$
adamc@655	597
adamc@530	598 \subsection{Kinding}
adamc@530	599
adamc@655	600 We write $[X \mapsto \kappa_1]\kappa_2$ for capture-avoiding substitution of $\kappa_1$ for $X$ in $\kappa_2$.
adamc@655	601
adamc@530	602 $$\infer{\Gamma \vdash (c) :: \kappa :: \kappa}{
adamc@530	603 \Gamma \vdash c :: \kappa
adamc@530	604 }
adamc@530	605 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530	606 x :: \kappa \in \Gamma
adamc@530	607 }
adamc@530	608 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530	609 x :: \kappa = c \in \Gamma
adamc@530	610 }$$
adamc@530	611
adamc@530	612 $$\infer{\Gamma \vdash M.x :: \kappa}{
adamc@537	613 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	614 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = \kappa
adamc@530	615 }
adamc@530	616 \quad \infer{\Gamma \vdash M.x :: \kappa}{
adamc@537	617 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	618 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@530	619 }$$
adamc@530	620
adamc@530	621 $$\infer{\Gamma \vdash \tau_1 \to \tau_2 :: \mt{Type}}{
adamc@530	622 \Gamma \vdash \tau_1 :: \mt{Type}
adamc@530	623 & \Gamma \vdash \tau_2 :: \mt{Type}
adamc@530	624 }
adamc@530	625 \quad \infer{\Gamma \vdash x \; ? \: \kappa \to \tau :: \mt{Type}}{
adamc@530	626 \Gamma, x :: \kappa \vdash \tau :: \mt{Type}
adamc@530	627 }
adamc@655	628 \quad \infer{\Gamma \vdash X \longrightarrow \tau :: \mt{Type}}{
adamc@655	629 \Gamma, X \vdash \tau :: \mt{Type}
adamc@655	630 }
adamc@530	631 \quad \infer{\Gamma \vdash \$c :: \mt{Type}}{
adamc@530	632 \Gamma \vdash c :: \{\mt{Type}\}
adamc@530	633 }$$
adamc@530	634
adamc@530	635 $$\infer{\Gamma \vdash c_1 \; c_2 :: \kappa_2}{
adamc@530	636 \Gamma \vdash c_1 :: \kappa_1 \to \kappa_2
adamc@530	637 & \Gamma \vdash c_2 :: \kappa_1
adamc@530	638 }
adamc@530	639 \quad \infer{\Gamma \vdash \lambda x \; :: \; \kappa_1 \Rightarrow c :: \kappa_1 \to \kappa_2}{
adamc@530	640 \Gamma, x :: \kappa_1 \vdash c :: \kappa_2
adamc@530	641 }$$
adamc@530	642
adamc@655	643 $$\infer{\Gamma \vdash c[\kappa'] :: [X \mapsto \kappa']\kappa}{
adamc@655	644 \Gamma \vdash c :: X \to \kappa
adamc@655	645 & \Gamma \vdash \kappa'
adamc@655	646 }
adamc@655	647 \quad \infer{\Gamma \vdash X \Longrightarrow c :: X \to \kappa}{
adamc@655	648 \Gamma, X \vdash c :: \kappa
adamc@655	649 }$$
adamc@655	650
adamc@530	651 $$\infer{\Gamma \vdash () :: \mt{Unit}}{}
adamc@530	652 \quad \infer{\Gamma \vdash \#X :: \mt{Name}}{}$$
adamc@530	653
adamc@530	654 $$\infer{\Gamma \vdash [\overline{c_i = c'_i}] :: \{\kappa\}}{
adamc@530	655 \forall i: \Gamma \vdash c_i : \mt{Name}
adamc@530	656 & \Gamma \vdash c'_i :: \kappa
adamc@530	657 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@530	658 }
adamc@530	659 \quad \infer{\Gamma \vdash c_1 \rc c_2 :: \{\kappa\}}{
adamc@530	660 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530	661 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@530	662 & \Gamma \vdash c_1 \sim c_2
adamc@530	663 }$$
adamc@530	664
adamc@655	665 $$\infer{\Gamma \vdash \mt{map} :: (\kappa_1 \to \kappa_2) \to \{\kappa_1\} \to \{\kappa_2\}}{}$$
adamc@530	666
adamc@573	667 $$\infer{\Gamma \vdash (\overline c) :: (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@573	668 \forall i: \Gamma \vdash c_i :: \kappa_i
adamc@530	669 }
adamc@573	670 \quad \infer{\Gamma \vdash c.i :: \kappa_i}{
adamc@573	671 \Gamma \vdash c :: (\kappa_1 \times \ldots \times \kappa_n)
adamc@530	672 }$$
adamc@530	673
adamc@655	674 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow \tau :: \mt{Type}}{
adamc@655	675 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530	676 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@655	677 & \Gamma, c_1 \sim c_2 \vdash \tau :: \mt{Type}
adamc@530	678 }$$
adamc@530	679
adamc@531	680 \subsection{Record Disjointness}
adamc@531	681
adamc@531	682 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@558	683 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@558	684 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@558	685 & \forall c'_1 \in C_1, c'_2 \in C_2: \Gamma \vdash c'_1 \sim c'_2
adamc@531	686 }
adamc@531	687 \quad \infer{\Gamma \vdash X \sim X'}{
adamc@531	688 X \neq X'
adamc@531	689 }$$
adamc@531	690
adamc@531	691 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@531	692 c'_1 \sim c'_2 \in \Gamma
adamc@558	693 & \Gamma \vdash c'_1 \hookrightarrow C_1
adamc@558	694 & \Gamma \vdash c'_2 \hookrightarrow C_2
adamc@558	695 & c_1 \in C_1
adamc@558	696 & c_2 \in C_2
adamc@531	697 }$$
adamc@531	698
adamc@531	699 $$\infer{\Gamma \vdash c \hookrightarrow \{c\}}{}
adamc@531	700 \quad \infer{\Gamma \vdash [\overline{c = c'}] \hookrightarrow \{\overline{c}\}}{}
adamc@531	701 \quad \infer{\Gamma \vdash c_1 \rc c_2 \hookrightarrow C_1 \cup C_2}{
adamc@531	702 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@531	703 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@531	704 }
adamc@531	705 \quad \infer{\Gamma \vdash c \hookrightarrow C}{
adamc@531	706 \Gamma \vdash c \equiv c'
adamc@531	707 & \Gamma \vdash c' \hookrightarrow C
adamc@531	708 }
adamc@531	709 \quad \infer{\Gamma \vdash \mt{map} \; f \; c \hookrightarrow C}{
adamc@531	710 \Gamma \vdash c \hookrightarrow C
adamc@531	711 }$$
adamc@531	712
adamc@541	713 \subsection{\label{definitional}Definitional Equality}
adamc@532	714
adamc@655	715 We use $\mathcal C$ to stand for a one-hole context that, when filled, yields a constructor. The notation $\mathcal C[c]$ plugs $c$ into $\mathcal C$. We omit the standard definition of one-hole contexts. We write $[x \mapsto c_1]c_2$ for capture-avoiding substitution of $c_1$ for $x$ in $c_2$, with analogous notation for substituting a kind in a constructor.
adamc@532	716
adamc@532	717 $$\infer{\Gamma \vdash c \equiv c}{}
adamc@532	718 \quad \infer{\Gamma \vdash c_1 \equiv c_2}{
adamc@532	719 \Gamma \vdash c_2 \equiv c_1
adamc@532	720 }
adamc@532	721 \quad \infer{\Gamma \vdash c_1 \equiv c_3}{
adamc@532	722 \Gamma \vdash c_1 \equiv c_2
adamc@532	723 & \Gamma \vdash c_2 \equiv c_3
adamc@532	724 }
adamc@532	725 \quad \infer{\Gamma \vdash \mathcal C[c_1] \equiv \mathcal C[c_2]}{
adamc@532	726 \Gamma \vdash c_1 \equiv c_2
adamc@532	727 }$$
adamc@532	728
adamc@532	729 $$\infer{\Gamma \vdash x \equiv c}{
adamc@532	730 x :: \kappa = c \in \Gamma
adamc@532	731 }
adamc@532	732 \quad \infer{\Gamma \vdash M.x \equiv c}{
adamc@537	733 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	734 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@532	735 }
adamc@532	736 \quad \infer{\Gamma \vdash (\overline c).i \equiv c_i}{}$$
adamc@532	737
adamc@532	738 $$\infer{\Gamma \vdash (\lambda x :: \kappa \Rightarrow c) \; c' \equiv [x \mapsto c'] c}{}
adamc@655	739 \quad \infer{\Gamma \vdash (X \Longrightarrow c) [\kappa] \equiv [X \mapsto \kappa] c}{}$$
adamc@655	740
adamc@655	741 $$\infer{\Gamma \vdash c_1 \rc c_2 \equiv c_2 \rc c_1}{}
adamc@532	742 \quad \infer{\Gamma \vdash c_1 \rc (c_2 \rc c_3) \equiv (c_1 \rc c_2) \rc c_3}{}$$
adamc@532	743
adamc@532	744 $$\infer{\Gamma \vdash [] \rc c \equiv c}{}
adamc@532	745 \quad \infer{\Gamma \vdash [\overline{c_1 = c'_1}] \rc [\overline{c_2 = c'_2}] \equiv [\overline{c_1 = c'_1}, \overline{c_2 = c'_2}]}{}$$
adamc@532	746
adamc@655	747 $$\infer{\Gamma \vdash \mt{map} \; f \; [] \equiv []}{}
adamc@655	748 \quad \infer{\Gamma \vdash \mt{map} \; f \; ([c_1 = c_2] \rc c) \equiv [c_1 = f \; c_2] \rc \mt{map} \; f \; c}{}$$
adamc@532	749
adamc@532	750 $$\infer{\Gamma \vdash \mt{map} \; (\lambda x \Rightarrow x) \; c \equiv c}{}
adamc@655	751 \quad \infer{\Gamma \vdash \mt{map} \; f \; (\mt{map} \; f' \; c)
adamc@655	752 \equiv \mt{map} \; (\lambda x \Rightarrow f \; (f' \; x)) \; c}{}$$
adamc@532	753
adamc@532	754 $$\infer{\Gamma \vdash \mt{map} \; f \; (c_1 \rc c_2) \equiv \mt{map} \; f \; c_1 \rc \mt{map} \; f \; c_2}{}$$
adamc@531	755
adamc@534	756 \subsection{Expression Typing}
adamc@533	757
adamc@873	758 We assume the existence of a function $T$ assigning types to literal constants. It maps integer constants to $\mt{Basis}.\mt{int}$, float constants to $\mt{Basis}.\mt{float}$, character constants to $\mt{Basis}.\mt{char}$, and string constants to $\mt{Basis}.\mt{string}$.
adamc@533	759
adamc@533	760 We also refer to a function $\mathcal I$, such that $\mathcal I(\tau)$ ``uses an oracle'' to instantiate all constructor function arguments at the beginning of $\tau$ that are marked implicit; i.e., replace $x_1 ::: \kappa_1 \to \ldots \to x_n ::: \kappa_n \to \tau$ with $[x_1 \mapsto c_1]\ldots[x_n \mapsto c_n]\tau$, where the $c_i$s are inferred and $\tau$ does not start like $x ::: \kappa \to \tau'$.
adamc@533	761
adamc@533	762 $$\infer{\Gamma \vdash e : \tau : \tau}{
adamc@533	763 \Gamma \vdash e : \tau
adamc@533	764 }
adamc@533	765 \quad \infer{\Gamma \vdash e : \tau}{
adamc@533	766 \Gamma \vdash e : \tau'
adamc@533	767 & \Gamma \vdash \tau' \equiv \tau
adamc@533	768 }
adamc@533	769 \quad \infer{\Gamma \vdash \ell : T(\ell)}{}$$
adamc@533	770
adamc@533	771 $$\infer{\Gamma \vdash x : \mathcal I(\tau)}{
adamc@533	772 x : \tau \in \Gamma
adamc@533	773 }
adamc@533	774 \quad \infer{\Gamma \vdash M.x : \mathcal I(\tau)}{
adamc@537	775 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	776 & \mt{proj}(M, \overline{s}, \mt{val} \; x) = \tau
adamc@533	777 }
adamc@533	778 \quad \infer{\Gamma \vdash X : \mathcal I(\tau)}{
adamc@533	779 X : \tau \in \Gamma
adamc@533	780 }
adamc@533	781 \quad \infer{\Gamma \vdash M.X : \mathcal I(\tau)}{
adamc@537	782 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	783 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \tau
adamc@533	784 }$$
adamc@533	785
adamc@533	786 $$\infer{\Gamma \vdash e_1 \; e_2 : \tau_2}{
adamc@533	787 \Gamma \vdash e_1 : \tau_1 \to \tau_2
adamc@533	788 & \Gamma \vdash e_2 : \tau_1
adamc@533	789 }
adamc@533	790 \quad \infer{\Gamma \vdash \lambda x : \tau_1 \Rightarrow e : \tau_1 \to \tau_2}{
adamc@533	791 \Gamma, x : \tau_1 \vdash e : \tau_2
adamc@533	792 }$$
adamc@533	793
adamc@533	794 $$\infer{\Gamma \vdash e [c] : [x \mapsto c]\tau}{
adamc@533	795 \Gamma \vdash e : x :: \kappa \to \tau
adamc@533	796 & \Gamma \vdash c :: \kappa
adamc@533	797 }
adamc@852	798 \quad \infer{\Gamma \vdash \lambda [x \; ? \; \kappa] \Rightarrow e : x \; ? \; \kappa \to \tau}{
adamc@533	799 \Gamma, x :: \kappa \vdash e : \tau
adamc@533	800 }$$
adamc@533	801
adamc@655	802 $$\infer{\Gamma \vdash e [\kappa] : [X \mapsto \kappa]\tau}{
adamc@655	803 \Gamma \vdash e : X \longrightarrow \tau
adamc@655	804 & \Gamma \vdash \kappa
adamc@655	805 }
adamc@655	806 \quad \infer{\Gamma \vdash X \Longrightarrow e : X \longrightarrow \tau}{
adamc@655	807 \Gamma, X \vdash e : \tau
adamc@655	808 }$$
adamc@655	809
adamc@533	810 $$\infer{\Gamma \vdash \{\overline{c = e}\} : \{\overline{c : \tau}\}}{
adamc@533	811 \forall i: \Gamma \vdash c_i :: \mt{Name}
adamc@533	812 & \Gamma \vdash e_i : \tau_i
adamc@533	813 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@533	814 }
adamc@533	815 \quad \infer{\Gamma \vdash e.c : \tau}{
adamc@533	816 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533	817 }
adamc@533	818 \quad \infer{\Gamma \vdash e_1 \rc e_2 : \$(c_1 \rc c_2)}{
adamc@533	819 \Gamma \vdash e_1 : \$c_1
adamc@533	820 & \Gamma \vdash e_2 : \$c_2
adamc@573	821 & \Gamma \vdash c_1 \sim c_2
adamc@533	822 }$$
adamc@533	823
adamc@533	824 $$\infer{\Gamma \vdash e \rcut c : \$c'}{
adamc@533	825 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533	826 }
adamc@533	827 \quad \infer{\Gamma \vdash e \rcutM c : \$c'}{
adamc@533	828 \Gamma \vdash e : \$(c \rc c')
adamc@533	829 }$$
adamc@533	830
adamc@533	831 $$\infer{\Gamma \vdash \mt{let} \; \overline{ed} \; \mt{in} \; e \; \mt{end} : \tau}{
adamc@533	832 \Gamma \vdash \overline{ed} \leadsto \Gamma'
adamc@533	833 & \Gamma' \vdash e : \tau
adamc@533	834 }
adamc@533	835 \quad \infer{\Gamma \vdash \mt{case} \; e \; \mt{of} \; \overline{p \Rightarrow e} : \tau}{
adamc@533	836 \forall i: \Gamma \vdash p_i \leadsto \Gamma_i, \tau'
adamc@533	837 & \Gamma_i \vdash e_i : \tau
adamc@533	838 }$$
adamc@533	839
adamc@573	840 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow e : \lambda [c_1 \sim c_2] \Rightarrow \tau}{
adamc@533	841 \Gamma \vdash c_1 :: \{\kappa\}
adamc@655	842 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@533	843 & \Gamma, c_1 \sim c_2 \vdash e : \tau
adamc@662	844 }
adamc@662	845 \quad \infer{\Gamma \vdash e \; ! : \tau}{
adamc@662	846 \Gamma \vdash e : [c_1 \sim c_2] \Rightarrow \tau
adamc@662	847 & \Gamma \vdash c_1 \sim c_2
adamc@533	848 }$$
adamc@533	849
adamc@534	850 \subsection{Pattern Typing}
adamc@534	851
adamc@534	852 $$\infer{\Gamma \vdash \_ \leadsto \Gamma; \tau}{}
adamc@534	853 \quad \infer{\Gamma \vdash x \leadsto \Gamma, x : \tau; \tau}{}
adamc@534	854 \quad \infer{\Gamma \vdash \ell \leadsto \Gamma; T(\ell)}{}$$
adamc@534	855
adamc@534	856 $$\infer{\Gamma \vdash X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534	857 X : \overline{x ::: \mt{Type}} \to \tau \in \Gamma
adamc@534	858 & \textrm{$\tau$ not a function type}
adamc@534	859 }
adamc@534	860 \quad \infer{\Gamma \vdash X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534	861 X : \overline{x ::: \mt{Type}} \to \tau'' \to \tau \in \Gamma
adamc@534	862 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534	863 }$$
adamc@534	864
adamc@534	865 $$\infer{\Gamma \vdash M.X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537	866 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	867 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau
adamc@534	868 & \textrm{$\tau$ not a function type}
adamc@534	869 }$$
adamc@534	870
adamc@534	871 $$\infer{\Gamma \vdash M.X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537	872 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	873 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau'' \to \tau
adamc@534	874 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534	875 }$$
adamc@534	876
adamc@534	877 $$\infer{\Gamma \vdash \{\overline{x = p}\} \leadsto \Gamma_n; \{\overline{x = \tau}\}}{
adamc@534	878 \Gamma_0 = \Gamma
adamc@534	879 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534	880 }
adamc@534	881 \quad \infer{\Gamma \vdash \{\overline{x = p}, \ldots\} \leadsto \Gamma_n; \$([\overline{x = \tau}] \rc c)}{
adamc@534	882 \Gamma_0 = \Gamma
adamc@534	883 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534	884 }$$
adamc@534	885
adamc@852	886 $$\infer{\Gamma \vdash p : \tau \leadsto \Gamma'; \tau}{
adamc@852	887 \Gamma \vdash p \leadsto \Gamma'; \tau'
adamc@852	888 & \Gamma \vdash \tau' \equiv \tau
adamc@852	889 }$$
adamc@852	890
adamc@535	891 \subsection{Declaration Typing}
adamc@535	892
adamc@535	893 We use an auxiliary judgment $\overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'$, expressing the enrichment of $\Gamma$ with the types of the datatype constructors $\overline{dc}$, when they are known to belong to datatype $x$ with type parameters $\overline{y}$.
adamc@535	894
adamc@655	895 This is the first judgment where we deal with constructor classes, for the $\mt{class}$ declaration form. We will omit their special handling in this formal specification. Section \ref{typeclasses} gives an informal description of how constructor classes influence type inference.
adamc@535	896
adamc@558	897 We presuppose the existence of a function $\mathcal O$, where $\mathcal O(M, \overline{s})$ implements the $\mt{open}$ declaration by producing a context with the appropriate entry for each available component of module $M$ with signature items $\overline{s}$. Where possible, $\mathcal O$ uses ``transparent'' entries (e.g., an abstract type $M.x$ is mapped to $x :: \mt{Type} = M.x$), so that the relationship with $M$ is maintained. A related function $\mathcal O_c$ builds a context containing the disjointness constraints found in $\overline s$.
adamc@537	898 We write $\kappa_1^n \to \kappa$ as a shorthand, where $\kappa_1^0 \to \kappa = \kappa$ and $\kappa_1^{n+1} \to \kappa_2 = \kappa_1 \to (\kappa_1^n \to \kappa_2)$. We write $\mt{len}(\overline{y})$ for the length of vector $\overline{y}$ of variables.
adamc@535	899
adamc@535	900 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535	901 \quad \infer{\Gamma \vdash d, \overline{d} \leadsto \Gamma''}{
adamc@535	902 \Gamma \vdash d \leadsto \Gamma'
adamc@535	903 & \Gamma' \vdash \overline{d} \leadsto \Gamma''
adamc@535	904 }$$
adamc@535	905
adamc@535	906 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@535	907 \Gamma \vdash c :: \kappa
adamc@535	908 }
adamc@535	909 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@535	910 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@535	911 }$$
adamc@535	912
adamc@535	913 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537	914 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	915 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@535	916 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@535	917 }$$
adamc@535	918
adamc@535	919 $$\infer{\Gamma \vdash \mt{val} \; x : \tau = e \leadsto \Gamma, x : \tau}{
adamc@535	920 \Gamma \vdash e : \tau
adamc@535	921 }$$
adamc@535	922
adamc@535	923 $$\infer{\Gamma \vdash \mt{val} \; \mt{rec} \; \overline{x : \tau = e} \leadsto \Gamma, \overline{x : \tau}}{
adamc@535	924 \forall i: \Gamma, \overline{x : \tau} \vdash e_i : \tau_i
adamc@535	925 & \textrm{$e_i$ starts with an expression $\lambda$, optionally preceded by constructor and disjointness $\lambda$s}
adamc@535	926 }$$
adamc@535	927
adamc@535	928 $$\infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : S}{
adamc@535	929 \Gamma \vdash M : S
adamc@558	930 & \textrm{ $M$ not a constant or application}
adamc@535	931 }
adamc@558	932 \quad \infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : \mt{selfify}(X, \overline{s})}{
adamc@558	933 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@539	934 }$$
adamc@539	935
adamc@539	936 $$\infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@535	937 \Gamma \vdash S
adamc@535	938 }$$
adamc@535	939
adamc@537	940 $$\infer{\Gamma \vdash \mt{open} \; M \leadsto \Gamma, \mathcal O(M, \overline{s})}{
adamc@537	941 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535	942 }$$
adamc@535	943
adamc@535	944 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma}{
adamc@535	945 \Gamma \vdash c_1 :: \{\kappa\}
adamc@535	946 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@535	947 & \Gamma \vdash c_1 \sim c_2
adamc@535	948 }
adamc@537	949 \quad \infer{\Gamma \vdash \mt{open} \; \mt{constraints} \; M \leadsto \Gamma, \mathcal O_c(M, \overline{s})}{
adamc@537	950 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535	951 }$$
adamc@535	952
adamc@784	953 $$\infer{\Gamma \vdash \mt{table} \; x : c \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_table} \; c \; []}{
adamc@535	954 \Gamma \vdash c :: \{\mt{Type}\}
adamc@535	955 }
adamc@784	956 \quad \infer{\Gamma \vdash \mt{view} \; x : c \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_view} \; c}{
adamc@784	957 \Gamma \vdash c :: \{\mt{Type}\}
adamc@784	958 }$$
adamc@784	959
adamc@784	960 $$\infer{\Gamma \vdash \mt{sequence} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_sequence}}{}$$
adamc@535	961
adamc@535	962 $$\infer{\Gamma \vdash \mt{cookie} \; x : \tau \leadsto \Gamma, x : \mt{Basis}.\mt{http\_cookie} \; \tau}{
adamc@535	963 \Gamma \vdash \tau :: \mt{Type}
adamc@784	964 }
adamc@784	965 \quad \infer{\Gamma \vdash \mt{style} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{css\_class}}{}$$
adamc@535	966
adamc@1085	967 $$\infer{\Gamma \vdash \mt{task} \; e_1 = e_2 \leadsto \Gamma}{
adam@1348	968 \Gamma \vdash e_1 :: \mt{Basis}.\mt{task\_kind} \; \tau
adam@1348	969 & \Gamma \vdash e_2 :: \tau \to \mt{Basis}.\mt{transaction} \; \{\}
adamc@1085	970 }$$
adamc@1085	971
adamc@784	972 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784	973 \Gamma \vdash c :: \kappa
adamc@535	974 }$$
adamc@535	975
adamc@535	976 $$\infer{\overline{y}; x; \Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535	977 \quad \infer{\overline{y}; x; \Gamma \vdash X \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to x \; \overline{y}}{
adamc@535	978 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535	979 }
adamc@535	980 \quad \infer{\overline{y}; x; \Gamma \vdash X \; \mt{of} \; \tau \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to \tau \to x \; \overline{y}}{
adamc@535	981 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535	982 }$$
adamc@535	983
adamc@537	984 \subsection{Signature Item Typing}
adamc@537	985
adamc@537	986 We appeal to a signature item analogue of the $\mathcal O$ function from the last subsection.
adamc@537	987
adamc@537	988 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@537	989 \quad \infer{\Gamma \vdash s, \overline{s} \leadsto \Gamma''}{
adamc@537	990 \Gamma \vdash s \leadsto \Gamma'
adamc@537	991 & \Gamma' \vdash \overline{s} \leadsto \Gamma''
adamc@537	992 }$$
adamc@537	993
adamc@537	994 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}
adamc@537	995 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@537	996 \Gamma \vdash c :: \kappa
adamc@537	997 }
adamc@537	998 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@537	999 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@537	1000 }$$
adamc@537	1001
adamc@537	1002 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537	1003 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1004 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537	1005 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@537	1006 }$$
adamc@537	1007
adamc@537	1008 $$\infer{\Gamma \vdash \mt{val} \; x : \tau \leadsto \Gamma, x : \tau}{
adamc@537	1009 \Gamma \vdash \tau :: \mt{Type}
adamc@537	1010 }$$
adamc@537	1011
adamc@537	1012 $$\infer{\Gamma \vdash \mt{structure} \; X : S \leadsto \Gamma, X : S}{
adamc@537	1013 \Gamma \vdash S
adamc@537	1014 }
adamc@537	1015 \quad \infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@537	1016 \Gamma \vdash S
adamc@537	1017 }$$
adamc@537	1018
adamc@537	1019 $$\infer{\Gamma \vdash \mt{include} \; S \leadsto \Gamma, \mathcal O(\overline{s})}{
adamc@537	1020 \Gamma \vdash S
adamc@537	1021 & \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1022 }$$
adamc@537	1023
adamc@537	1024 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma, c_1 \sim c_2}{
adamc@537	1025 \Gamma \vdash c_1 :: \{\kappa\}
adamc@537	1026 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@537	1027 }$$
adamc@537	1028
adamc@784	1029 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784	1030 \Gamma \vdash c :: \kappa
adamc@537	1031 }
adamc@784	1032 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}$$
adamc@537	1033
adamc@536	1034 \subsection{Signature Compatibility}
adamc@536	1035
adamc@558	1036 To simplify the judgments in this section, we assume that all signatures are alpha-varied as necessary to avoid including multiple bindings for the same identifier. This is in addition to the usual alpha-variation of locally-bound variables.
adamc@537	1037
adamc@537	1038 We rely on a judgment $\Gamma \vdash \overline{s} \leq s'$, which expresses the occurrence in signature items $\overline{s}$ of an item compatible with $s'$. We also use a judgment $\Gamma \vdash \overline{dc} \leq \overline{dc}$, which expresses compatibility of datatype definitions.
adamc@537	1039
adamc@536	1040 $$\infer{\Gamma \vdash S \equiv S}{}
adamc@536	1041 \quad \infer{\Gamma \vdash S_1 \equiv S_2}{
adamc@536	1042 \Gamma \vdash S_2 \equiv S_1
adamc@536	1043 }
adamc@536	1044 \quad \infer{\Gamma \vdash X \equiv S}{
adamc@536	1045 X = S \in \Gamma
adamc@536	1046 }
adamc@536	1047 \quad \infer{\Gamma \vdash M.X \equiv S}{
adamc@537	1048 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1049 & \mt{proj}(M, \overline{s}, \mt{signature} \; X) = S
adamc@536	1050 }$$
adamc@536	1051
adamc@536	1052 $$\infer{\Gamma \vdash S \; \mt{where} \; \mt{con} \; x = c \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa = c \; \overline{s_2} \; \mt{end}}{
adamc@536	1053 \Gamma \vdash S \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa \; \overline{s_2} \; \mt{end}
adamc@536	1054 & \Gamma \vdash c :: \kappa
adamc@537	1055 }
adamc@537	1056 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s^1} \; \mt{include} \; S \; \overline{s^2} \; \mt{end} \equiv \mt{sig} \; \overline{s^1} \; \overline{s} \; \overline{s^2} \; \mt{end}}{
adamc@537	1057 \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@536	1058 }$$
adamc@536	1059
adamc@536	1060 $$\infer{\Gamma \vdash S_1 \leq S_2}{
adamc@536	1061 \Gamma \vdash S_1 \equiv S_2
adamc@536	1062 }
adamc@536	1063 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \mt{end}}{}
adamc@537	1064 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; s' \; \overline{s'} \; \mt{end}}{
adamc@537	1065 \Gamma \vdash \overline{s} \leq s'
adamc@537	1066 & \Gamma \vdash s' \leadsto \Gamma'
adamc@537	1067 & \Gamma' \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \overline{s'} \; \mt{end}
adamc@537	1068 }$$
adamc@537	1069
adamc@537	1070 $$\infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537	1071 \Gamma \vdash s \leq s'
adamc@537	1072 }
adamc@537	1073 \quad \infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537	1074 \Gamma \vdash s \leadsto \Gamma'
adamc@537	1075 & \Gamma' \vdash \overline{s} \leq s'
adamc@536	1076 }$$
adamc@536	1077
adamc@536	1078 $$\infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 \leq \mt{functor} (X : S'_1) : S'_2}{
adamc@536	1079 \Gamma \vdash S'_1 \leq S_1
adamc@536	1080 & \Gamma, X : S'_1 \vdash S_2 \leq S'_2
adamc@536	1081 }$$
adamc@536	1082
adamc@537	1083 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@537	1084 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}
adamc@558	1085 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type}}{}$$
adamc@537	1086
adamc@537	1087 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(y)} \to \mt{Type}}{
adamc@537	1088 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1089 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537	1090 }$$
adamc@537	1091
adamc@784	1092 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@784	1093 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}$$
adamc@537	1094
adamc@537	1095 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \mt{\kappa} = c_2}{
adamc@537	1096 \Gamma \vdash c_1 \equiv c_2
adamc@537	1097 }
adamc@784	1098 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \kappa = c_2}{
adamc@537	1099 \Gamma \vdash c_1 \equiv c_2
adamc@537	1100 }$$
adamc@537	1101
adamc@537	1102 $$\infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537	1103 \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537	1104 }$$
adamc@537	1105
adamc@537	1106 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537	1107 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1108 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537	1109 & \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537	1110 }$$
adamc@537	1111
adamc@537	1112 $$\infer{\Gamma \vdash \cdot \leq \cdot}{}
adamc@537	1113 \quad \infer{\Gamma \vdash X; \overline{dc} \leq X; \overline{dc'}}{
adamc@537	1114 \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537	1115 }
adamc@537	1116 \quad \infer{\Gamma \vdash X \; \mt{of} \; \tau_1; \overline{dc} \leq X \; \mt{of} \; \tau_2; \overline{dc'}}{
adamc@537	1117 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537	1118 & \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537	1119 }$$
adamc@537	1120
adamc@537	1121 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x = \mt{datatype} \; M'.z'}{
adamc@537	1122 \Gamma \vdash M.z \equiv M'.z'
adamc@537	1123 }$$
adamc@537	1124
adamc@537	1125 $$\infer{\Gamma \vdash \mt{val} \; x : \tau_1 \leq \mt{val} \; x : \tau_2}{
adamc@537	1126 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537	1127 }
adamc@537	1128 \quad \infer{\Gamma \vdash \mt{structure} \; X : S_1 \leq \mt{structure} \; X : S_2}{
adamc@537	1129 \Gamma \vdash S_1 \leq S_2
adamc@537	1130 }
adamc@537	1131 \quad \infer{\Gamma \vdash \mt{signature} \; X = S_1 \leq \mt{signature} \; X = S_2}{
adamc@537	1132 \Gamma \vdash S_1 \leq S_2
adamc@537	1133 & \Gamma \vdash S_2 \leq S_1
adamc@537	1134 }$$
adamc@537	1135
adamc@537	1136 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leq \mt{constraint} \; c'_1 \sim c'_2}{
adamc@537	1137 \Gamma \vdash c_1 \equiv c'_1
adamc@537	1138 & \Gamma \vdash c_2 \equiv c'_2
adamc@537	1139 }$$
adamc@537	1140
adamc@655	1141 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{class} \; x :: \kappa}{}
adamc@655	1142 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{class} \; x :: \kappa}{}
adamc@655	1143 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{class} \; x :: \kappa = c_2}{
adamc@537	1144 \Gamma \vdash c_1 \equiv c_2
adamc@537	1145 }$$
adamc@537	1146
adamc@538	1147 \subsection{Module Typing}
adamc@538	1148
adamc@538	1149 We use a helper function $\mt{sigOf}$, which converts declarations and sequences of declarations into their principal signature items and sequences of signature items, respectively.
adamc@538	1150
adamc@538	1151 $$\infer{\Gamma \vdash M : S}{
adamc@538	1152 \Gamma \vdash M : S'
adamc@538	1153 & \Gamma \vdash S' \leq S
adamc@538	1154 }
adamc@538	1155 \quad \infer{\Gamma \vdash \mt{struct} \; \overline{d} \; \mt{end} : \mt{sig} \; \mt{sigOf}(\overline{d}) \; \mt{end}}{
adamc@538	1156 \Gamma \vdash \overline{d} \leadsto \Gamma'
adamc@538	1157 }
adamc@538	1158 \quad \infer{\Gamma \vdash X : S}{
adamc@538	1159 X : S \in \Gamma
adamc@538	1160 }$$
adamc@538	1161
adamc@538	1162 $$\infer{\Gamma \vdash M.X : S}{
adamc@538	1163 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@538	1164 & \mt{proj}(M, \overline{s}, \mt{structure} \; X) = S
adamc@538	1165 }$$
adamc@538	1166
adamc@538	1167 $$\infer{\Gamma \vdash M_1(M_2) : [X \mapsto M_2]S_2}{
adamc@538	1168 \Gamma \vdash M_1 : \mt{functor}(X : S_1) : S_2
adamc@538	1169 & \Gamma \vdash M_2 : S_1
adamc@538	1170 }
adamc@538	1171 \quad \infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 = M : \mt{functor} (X : S_1) : S_2}{
adamc@538	1172 \Gamma \vdash S_1
adamc@538	1173 & \Gamma, X : S_1 \vdash S_2
adamc@538	1174 & \Gamma, X : S_1 \vdash M : S_2
adamc@538	1175 }$$
adamc@538	1176
adamc@538	1177 \begin{eqnarray*}
adamc@538	1178 \mt{sigOf}(\cdot) &=& \cdot \\
adamc@538	1179 \mt{sigOf}(s \; \overline{s'}) &=& \mt{sigOf}(s) \; \mt{sigOf}(\overline{s'}) \\
adamc@538	1180 \\
adamc@538	1181 \mt{sigOf}(\mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@538	1182 \mt{sigOf}(\mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \overline{dc} \\
adamc@538	1183 \mt{sigOf}(\mt{datatype} \; x = \mt{datatype} \; M.z) &=& \mt{datatype} \; x = \mt{datatype} \; M.z \\
adamc@538	1184 \mt{sigOf}(\mt{val} \; x : \tau = e) &=& \mt{val} \; x : \tau \\
adamc@538	1185 \mt{sigOf}(\mt{val} \; \mt{rec} \; \overline{x : \tau = e}) &=& \overline{\mt{val} \; x : \tau} \\
adamc@538	1186 \mt{sigOf}(\mt{structure} \; X : S = M) &=& \mt{structure} \; X : S \\
adamc@538	1187 \mt{sigOf}(\mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@538	1188 \mt{sigOf}(\mt{open} \; M) &=& \mt{include} \; S \textrm{ (where $\Gamma \vdash M : S$)} \\
adamc@538	1189 \mt{sigOf}(\mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@538	1190 \mt{sigOf}(\mt{open} \; \mt{constraints} \; M) &=& \cdot \\
adamc@538	1191 \mt{sigOf}(\mt{table} \; x : c) &=& \mt{table} \; x : c \\
adamc@784	1192 \mt{sigOf}(\mt{view} \; x : c) &=& \mt{view} \; x : c \\
adamc@538	1193 \mt{sigOf}(\mt{sequence} \; x) &=& \mt{sequence} \; x \\
adamc@538	1194 \mt{sigOf}(\mt{cookie} \; x : \tau) &=& \mt{cookie} \; x : \tau \\
adamc@784	1195 \mt{sigOf}(\mt{style} \; x) &=& \mt{style} \; x \\
adamc@655	1196 \mt{sigOf}(\mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@538	1197 \end{eqnarray*}
adamc@539	1198 \begin{eqnarray*}
adamc@539	1199 \mt{selfify}(M, \cdot) &=& \cdot \\
adamc@558	1200 \mt{selfify}(M, s \; \overline{s'}) &=& \mt{selfify}(M, s) \; \mt{selfify}(M, \overline{s'}) \\
adamc@539	1201 \\
adamc@539	1202 \mt{selfify}(M, \mt{con} \; x :: \kappa) &=& \mt{con} \; x :: \kappa = M.x \\
adamc@539	1203 \mt{selfify}(M, \mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@539	1204 \mt{selfify}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \mt{datatype} \; M.x \\
adamc@539	1205 \mt{selfify}(M, \mt{datatype} \; x = \mt{datatype} \; M'.z) &=& \mt{datatype} \; x = \mt{datatype} \; M'.z \\
adamc@539	1206 \mt{selfify}(M, \mt{val} \; x : \tau) &=& \mt{val} \; x : \tau \\
adamc@539	1207 \mt{selfify}(M, \mt{structure} \; X : S) &=& \mt{structure} \; X : \mt{selfify}(M.X, \overline{s}) \textrm{ (where $\Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}$)} \\
adamc@539	1208 \mt{selfify}(M, \mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@539	1209 \mt{selfify}(M, \mt{include} \; S) &=& \mt{include} \; S \\
adamc@539	1210 \mt{selfify}(M, \mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@655	1211 \mt{selfify}(M, \mt{class} \; x :: \kappa) &=& \mt{class} \; x :: \kappa = M.x \\
adamc@655	1212 \mt{selfify}(M, \mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@539	1213 \end{eqnarray*}
adamc@539	1214
adamc@540	1215 \subsection{Module Projection}
adamc@540	1216
adamc@540	1217 \begin{eqnarray*}
adamc@540	1218 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \\
adamc@540	1219 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa, c) \\
adamc@540	1220 \mt{proj}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc} \; \overline{s}, \mt{con} \; x) &=& \mt{Type}^{\mt{len}(\overline{y})} \to \mt{Type} \\
adamc@540	1221 \mt{proj}(M, \mt{datatype} \; x = \mt{datatype} \; M'.z \; \overline{s}, \mt{con} \; x) &=& (\mt{Type}^{\mt{len}(\overline{y})} \to \mt{Type}, M'.z) \textrm{ (where $\Gamma \vdash M' : \mt{sig} \; \overline{s'} \; \mt{end}$} \\
adamc@540	1222 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})$)} \\
adamc@655	1223 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \to \mt{Type} \\
adamc@655	1224 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa \to \mt{Type}, c) \\
adamc@540	1225 \\
adamc@540	1226 \mt{proj}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc} \; \overline{s}, \mt{datatype} \; x) &=& (\overline{y}, \overline{dc}) \\
adamc@540	1227 \mt{proj}(M, \mt{datatype} \; x = \mt{datatype} \; M'.z \; \overline{s}, \mt{con} \; x) &=& \mt{proj}(M', \overline{s'}, \mt{datatype} \; z) \textrm{ (where $\Gamma \vdash M' : \mt{sig} \; \overline{s'} \; \mt{end}$)} \\
adamc@540	1228 \\
adamc@540	1229 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, \mt{val} \; x) &=& \tau \\
adamc@540	1230 \mt{proj}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc} \; \overline{s}, \mt{val} \; X) &=& \overline{y ::: \mt{Type}} \to M.x \; \overline y \textrm{ (where $X \in \overline{dc}$)} \\
adamc@540	1231 \mt{proj}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc} \; \overline{s}, \mt{val} \; X) &=& \overline{y ::: \mt{Type}} \to \tau \to M.x \; \overline y \textrm{ (where $X \; \mt{of} \; \tau \in \overline{dc}$)} \\
adamc@540	1232 \mt{proj}(M, \mt{datatype} \; x = \mt{datatype} \; M'.z, \mt{val} \; X) &=& \overline{y ::: \mt{Type}} \to M.x \; \overline y \textrm{ (where $\Gamma \vdash M' : \mt{sig} \; \overline{s'} \; \mt{end}$} \\
adamc@540	1233 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \in \overline{dc}$)} \\
adamc@540	1234 \mt{proj}(M, \mt{datatype} \; x = \mt{datatype} \; M'.z, \mt{val} \; X) &=& \overline{y ::: \mt{Type}} \to \tau \to M.x \; \overline y \textrm{ (where $\Gamma \vdash M' : \mt{sig} \; \overline{s'} \; \mt{end}$} \\
adamc@558	1235 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \; \mt{of} \; \tau \in \overline{dc}$)} \\
adamc@540	1236 \\
adamc@540	1237 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, \mt{structure} \; X) &=& S \\
adamc@540	1238 \\
adamc@540	1239 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, \mt{signature} \; X) &=& S \\
adamc@540	1240 \\
adamc@540	1241 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1242 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1243 \mt{proj}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc} \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1244 \mt{proj}(M, \mt{datatype} \; x = \mt{datatype} \; M'.z \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1245 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@540	1246 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1247 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1248 \mt{proj}(M, \mt{include} \; S \; \overline{s}, V) &=& \mt{proj}(M, \overline{s'} \; \overline{s}, V) \textrm{ (where $\Gamma \vdash S \equiv \mt{sig} \; \overline{s'} \; \mt{end}$)} \\
adamc@540	1249 \mt{proj}(M, \mt{constraint} \; c_1 \sim c_2 \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@655	1250 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@655	1251 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1252 \end{eqnarray*}
adamc@540	1253
adamc@541	1254
adamc@541	1255 \section{Type Inference}
adamc@541	1256
adamc@541	1257 The Ur/Web compiler uses \emph{heuristic type inference}, with no claims of completeness with respect to the declarative specification of the last section. The rules in use seem to work well in practice. This section summarizes those rules, to help Ur programmers predict what will work and what won't.
adamc@541	1258
adamc@541	1259 \subsection{Basic Unification}
adamc@541	1260
adamc@560	1261 Type-checkers for languages based on the Hindley-Milner type discipline, like ML and Haskell, take advantage of \emph{principal typing} properties, making complete type inference relatively straightforward. Inference algorithms are traditionally implemented using type unification variables, at various points asserting equalities between types, in the process discovering the values of type variables. The Ur/Web compiler uses the same basic strategy, but the complexity of the type system rules out easy completeness.
adamc@541	1262
adamc@656	1263 Type-checking can require evaluating recursive functional programs, thanks to the type-level $\mt{map}$ operator. When a unification variable appears in such a type, the next step of computation can be undetermined. The value of that variable might be determined later, but this would be ``too late'' for the unification problems generated at the first occurrence. This is the essential source of incompleteness.
adamc@541	1264
adamc@541	1265 Nonetheless, the unification engine tends to do reasonably well. Unlike in ML, polymorphism is never inferred in definitions; it must be indicated explicitly by writing out constructor-level parameters. By writing these and other annotations, the programmer can generally get the type inference engine to do most of the type reconstruction work.
adamc@541	1266
adamc@541	1267 \subsection{Unifying Record Types}
adamc@541	1268
adamc@570	1269 The type inference engine tries to take advantage of the algebraic rules governing type-level records, as shown in Section \ref{definitional}. When two constructors of record kind are unified, they are reduced to normal forms, with like terms crossed off from each normal form until, hopefully, nothing remains. This cannot be complete, with the inclusion of unification variables. The type-checker can help you understand what goes wrong when the process fails, as it outputs the unmatched remainders of the two normal forms.
adamc@541	1270
adamc@656	1271 \subsection{\label{typeclasses}Constructor Classes}
adamc@541	1272
adamc@784	1273 Ur includes a constructor class facility inspired by Haskell's. The current version is experimental, with very general Prolog-like facilities that can lead to compile-time non-termination.
adamc@541	1274
adamc@784	1275 Constructor classes are integrated with the module system. A constructor class of kind $\kappa$ is just a constructor of kind $\kappa$. By marking such a constructor $c$ as a constructor class, the programmer instructs the type inference engine to, in each scope, record all values of types $c \; c_1 \; \ldots \; c_n$ as \emph{instances}. Any function argument whose type is of such a form is treated as implicit, to be determined by examining the current instance database.
adamc@541	1276
adamc@656	1277 The ``dictionary encoding'' often used in Haskell implementations is made explicit in Ur. Constructor class instances are just properly-typed values, and they can also be considered as ``proofs'' of membership in the class. In some cases, it is useful to pass these proofs around explicitly. An underscore written where a proof is expected will also be inferred, if possible, from the current instance database.
adamc@541	1278
adamc@656	1279 Just as for constructors, constructors classes may be exported from modules, and they may be exported as concrete or abstract. Concrete constructor classes have their ``real'' definitions exposed, so that client code may add new instances freely. Abstract constructor classes are useful as ``predicates'' that can be used to enforce invariants, as we will see in some definitions of SQL syntax in the Ur/Web standard library.
adamc@541	1280
adamc@541	1281 \subsection{Reverse-Engineering Record Types}
adamc@541	1282
adamc@656	1283 It's useful to write Ur functions and functors that take record constructors as inputs, but these constructors can grow quite long, even though their values are often implied by other arguments. The compiler uses a simple heuristic to infer the values of unification variables that are mapped over, yielding known results. If the result is empty, we're done; if it's not empty, we replace a single unification variable with a new constructor formed from three new unification variables, as in $[\alpha = \beta] \rc \gamma$. This process can often be repeated to determine a unification variable fully.
adamc@541	1284
adamc@541	1285 \subsection{Implicit Arguments in Functor Applications}
adamc@541	1286
adamc@656	1287 Constructor, constraint, and constructor class witness members of structures may be omitted, when those structures are used in contexts where their assigned signatures imply how to fill in those missing members. This feature combines well with reverse-engineering to allow for uses of complicated meta-programming functors with little more code than would be necessary to invoke an untyped, ad-hoc code generator.
adamc@541	1288
adamc@541	1289
adamc@542	1290 \section{The Ur Standard Library}
adamc@542	1291
adamc@542	1292 The built-in parts of the Ur/Web standard library are described by the signature in \texttt{lib/basis.urs} in the distribution. A module $\mt{Basis}$ ascribing to that signature is available in the initial environment, and every program is implicitly prefixed by $\mt{open} \; \mt{Basis}$.
adamc@542	1293
adamc@542	1294 Additionally, other common functions that are definable within Ur are included in \texttt{lib/top.urs} and \texttt{lib/top.ur}. This $\mt{Top}$ module is also opened implicitly.
adamc@542	1295
adamc@542	1296 The idea behind Ur is to serve as the ideal host for embedded domain-specific languages. For now, however, the ``generic'' functionality is intermixed with Ur/Web-specific functionality, including in these two library modules. We hope that these generic library components have types that speak for themselves. The next section introduces the Ur/Web-specific elements. Here, we only give the type declarations from the beginning of $\mt{Basis}$.
adamc@542	1297 $$\begin{array}{l}
adamc@542	1298 \mt{type} \; \mt{int} \\
adamc@542	1299 \mt{type} \; \mt{float} \\
adamc@873	1300 \mt{type} \; \mt{char} \\
adamc@542	1301 \mt{type} \; \mt{string} \\
adamc@542	1302 \mt{type} \; \mt{time} \\
adamc@785	1303 \mt{type} \; \mt{blob} \\
adamc@542	1304 \\
adamc@542	1305 \mt{type} \; \mt{unit} = \{\} \\
adamc@542	1306 \\
adamc@542	1307 \mt{datatype} \; \mt{bool} = \mt{False} \mid \mt{True} \\
adamc@542	1308 \\
adamc@785	1309 \mt{datatype} \; \mt{option} \; \mt{t} = \mt{None} \mid \mt{Some} \; \mt{of} \; \mt{t} \\
adamc@785	1310 \\
adamc@785	1311 \mt{datatype} \; \mt{list} \; \mt{t} = \mt{Nil} \mid \mt{Cons} \; \mt{of} \; \mt{t} \times \mt{list} \; \mt{t}
adamc@542	1312 \end{array}$$
adamc@542	1313
adamc@1123	1314 The only unusual element of this list is the $\mt{blob}$ type, which stands for binary sequences. Simple blobs can be created from strings via $\mt{Basis.textBlob}$. Blobs will also be generated from HTTP file uploads.
adamc@785	1315
adam@1297	1316 Ur also supports \emph{polymorphic variants}, a dual to extensible records that has been popularized by OCaml. A type $\mt{variant} \; r$ represents an $n$-ary sum type, with one constructor for each field of record $r$. Each constructor $c$ takes an argument of type $r.c$; the type $\{\}$ can be used to ``simulate'' a nullary constructor. The \cd{make} function builds a variant value, while \cd{match} implements pattern-matching, with match cases represented as records of functions.
adam@1297	1317 $$\begin{array}{l}
adam@1297	1318 \mt{con} \; \mt{variant} :: \{\mt{Type}\} \to \mt{Type} \\
adam@1297	1319 \mt{val} \; \mt{make} : \mt{nm} :: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{ts} ::: \{\mt{Type}\} \to [[\mt{nm}] \sim \mt{ts}] \Rightarrow \mt{t} \to \mt{variant} \; ([\mt{nm} = \mt{t}] \rc \mt{ts}) \\
adam@1297	1320 \mt{val} \; \mt{match} : \mt{ts} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{variant} \; \mt{ts} \to \$(\mt{map} \; (\lambda \mt{t'} \Rightarrow \mt{t'} \to \mt{t}) \; \mt{ts}) \to \mt{t}
adam@1297	1321 \end{array}$$
adam@1297	1322
adamc@657	1323 Another important generic Ur element comes at the beginning of \texttt{top.urs}.
adamc@657	1324
adamc@657	1325 $$\begin{array}{l}
adamc@657	1326 \mt{con} \; \mt{folder} :: \mt{K} \longrightarrow \{\mt{K}\} \to \mt{Type} \\
adamc@657	1327 \\
adamc@657	1328 \mt{val} \; \mt{fold} : \mt{K} \longrightarrow \mt{tf} :: (\{\mt{K}\} \to \mt{Type}) \\
adamc@657	1329 \hspace{.1in} \to (\mt{nm} :: \mt{Name} \to \mt{v} :: \mt{K} \to \mt{r} :: \{\mt{K}\} \to [[\mt{nm}] \sim \mt{r}] \Rightarrow \\
adamc@657	1330 \hspace{.2in} \mt{tf} \; \mt{r} \to \mt{tf} \; ([\mt{nm} = \mt{v}] \rc \mt{r})) \\
adamc@657	1331 \hspace{.1in} \to \mt{tf} \; [] \\
adamc@657	1332 \hspace{.1in} \to \mt{r} :: \{\mt{K}\} \to \mt{folder} \; \mt{r} \to \mt{tf} \; \mt{r}
adamc@657	1333 \end{array}$$
adamc@657	1334
adamc@657	1335 For a type-level record $\mt{r}$, a $\mt{folder} \; \mt{r}$ encodes a permutation of $\mt{r}$'s elements. The $\mt{fold}$ function can be called on a $\mt{folder}$ to iterate over the elements of $\mt{r}$ in that order. $\mt{fold}$ is parameterized on a type-level function to be used to calculate the type of each intermediate result of folding. After processing a subset $\mt{r'}$ of $\mt{r}$'s entries, the type of the accumulator should be $\mt{tf} \; \mt{r'}$. The next two expression arguments to $\mt{fold}$ are the usual step function and initial accumulator, familiar from fold functions over lists. The final two arguments are the record to fold over and a $\mt{folder}$ for it.
adamc@657	1336
adamc@664	1337 The Ur compiler treats $\mt{folder}$ like a constructor class, using built-in rules to infer $\mt{folder}$s for records with known structure. The order in which field names are mentioned in source code is used as a hint about the permutation that the programmer would like.
adamc@657	1338
adamc@542	1339
adamc@542	1340 \section{The Ur/Web Standard Library}
adamc@542	1341
adam@1400	1342 Some operations are only allowed in server-side code or only in client-side code. The type system does not enforce such restrictions, but the compiler enforces them in the process of whole-program compilation. In the discussion below, we note when a set of operations has a location restriction.
adam@1400	1343
adamc@658	1344 \subsection{Monads}
adamc@658	1345
adamc@658	1346 The Ur Basis defines the monad constructor class from Haskell.
adamc@658	1347
adamc@658	1348 $$\begin{array}{l}
adamc@658	1349 \mt{class} \; \mt{monad} :: \mt{Type} \to \mt{Type} \\
adamc@658	1350 \mt{val} \; \mt{return} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t} ::: \mt{Type} \\
adamc@658	1351 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658	1352 \hspace{.1in} \to \mt{t} \to \mt{m} \; \mt{t} \\
adamc@658	1353 \mt{val} \; \mt{bind} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t1} ::: \mt{Type} \to \mt{t2} ::: \mt{Type} \\
adamc@658	1354 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658	1355 \hspace{.1in} \to \mt{m} \; \mt{t1} \to (\mt{t1} \to \mt{m} \; \mt{t2}) \\
adamc@658	1356 \hspace{.1in} \to \mt{m} \; \mt{t2}
adamc@658	1357 \end{array}$$
adamc@658	1358
adamc@542	1359 \subsection{Transactions}
adamc@542	1360
adamc@542	1361 Ur is a pure language; we use Haskell's trick to support controlled side effects. The standard library defines a monad $\mt{transaction}$, meant to stand for actions that may be undone cleanly. By design, no other kinds of actions are supported.
adamc@542	1362 $$\begin{array}{l}
adamc@542	1363 \mt{con} \; \mt{transaction} :: \mt{Type} \to \mt{Type} \\
adamc@658	1364 \mt{val} \; \mt{transaction\_monad} : \mt{monad} \; \mt{transaction}
adamc@542	1365 \end{array}$$
adamc@542	1366
adamc@1123	1367 For debugging purposes, a transactional function is provided for outputting a string on the server process' \texttt{stderr}.
adamc@1123	1368 $$\begin{array}{l}
adamc@1123	1369 \mt{val} \; \mt{debug} : \mt{string} \to \mt{transaction} \; \mt{unit}
adamc@1123	1370 \end{array}$$
adamc@1123	1371
adamc@542	1372 \subsection{HTTP}
adamc@542	1373
adam@1400	1374 There are transactions for reading an HTTP header by name and for getting and setting strongly-typed cookies. Cookies may only be created by the $\mt{cookie}$ declaration form, ensuring that they be named consistently based on module structure. For now, cookie operations are server-side only.
adamc@542	1375 $$\begin{array}{l}
adamc@786	1376 \mt{con} \; \mt{http\_cookie} :: \mt{Type} \to \mt{Type} \\
adamc@786	1377 \mt{val} \; \mt{getCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; (\mt{option} \; \mt{t}) \\
adamc@1050	1378 \mt{val} \; \mt{setCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \{\mt{Value} : \mt{t}, \mt{Expires} : \mt{option} \; \mt{time}, \mt{Secure} : \mt{bool}\} \to \mt{transaction} \; \mt{unit} \\
adamc@1050	1379 \mt{val} \; \mt{clearCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; \mt{unit}
adamc@786	1380 \end{array}$$
adamc@786	1381
adamc@786	1382 There are also an abstract $\mt{url}$ type and functions for converting to it, based on the policy defined by \texttt{[allow\|deny] url} directives in the project file.
adamc@786	1383 $$\begin{array}{l}
adamc@786	1384 \mt{type} \; \mt{url} \\
adamc@786	1385 \mt{val} \; \mt{bless} : \mt{string} \to \mt{url} \\
adamc@786	1386 \mt{val} \; \mt{checkUrl} : \mt{string} \to \mt{option} \; \mt{url}
adamc@786	1387 \end{array}$$
adamc@786	1388 $\mt{bless}$ raises a runtime error if the string passed to it fails the URL policy.
adamc@786	1389
adam@1400	1390 It is possible to grab the current page's URL or to build a URL for an arbitrary transaction that would also be an acceptable value of a \texttt{link} attribute of the \texttt{a} tag. These are server-side operations.
adamc@1085	1391 $$\begin{array}{l}
adamc@1085	1392 \mt{val} \; \mt{currentUrl} : \mt{transaction} \; \mt{url} \\
adamc@1085	1393 \mt{val} \; \mt{url} : \mt{transaction} \; \mt{page} \to \mt{url}
adamc@1085	1394 \end{array}$$
adamc@1085	1395
adamc@1085	1396 Page generation may be interrupted at any time with a request to redirect to a particular URL instead.
adamc@1085	1397 $$\begin{array}{l}
adamc@1085	1398 \mt{val} \; \mt{redirect} : \mt{t} ::: \mt{Type} \to \mt{url} \to \mt{transaction} \; \mt{t}
adamc@1085	1399 \end{array}$$
adamc@1085	1400
adam@1400	1401 It's possible for pages to return files of arbitrary MIME types. A file can be input from the user using this data type, along with the $\mt{upload}$ form tag. These functions and those described in the following paragraph are server-side.
adamc@786	1402 $$\begin{array}{l}
adamc@786	1403 \mt{type} \; \mt{file} \\
adamc@786	1404 \mt{val} \; \mt{fileName} : \mt{file} \to \mt{option} \; \mt{string} \\
adamc@786	1405 \mt{val} \; \mt{fileMimeType} : \mt{file} \to \mt{string} \\
adamc@786	1406 \mt{val} \; \mt{fileData} : \mt{file} \to \mt{blob}
adamc@786	1407 \end{array}$$
adamc@786	1408
adam@1465	1409 It is also possible to get HTTP request headers and set HTTP response headers, using abstract types similar to the one for URLs.
adam@1465	1410
adam@1465	1411 $$\begin{array}{l}
adam@1465	1412 \mt{type} \; \mt{requestHeader} \\
adam@1465	1413 \mt{val} \; \mt{blessRequestHeader} : \mt{string} \to \mt{requestHeader} \\
adam@1465	1414 \mt{val} \; \mt{checkRequestHeader} : \mt{string} \to \mt{option} \; \mt{requestHeader} \\
adam@1465	1415 \mt{val} \; \mt{getHeader} : \mt{requestHeader} \to \mt{transaction} \; (\mt{option} \; \mt{string}) \\
adam@1465	1416 \\
adam@1465	1417 \mt{type} \; \mt{responseHeader} \\
adam@1465	1418 \mt{val} \; \mt{blessResponseHeader} : \mt{string} \to \mt{responseHeader} \\
adam@1465	1419 \mt{val} \; \mt{checkResponseHeader} : \mt{string} \to \mt{option} \; \mt{responseHeader} \\
adam@1465	1420 \mt{val} \; \mt{setHeader} : \mt{responseHeader} \to \mt{string} \to \mt{transaction} \; \mt{unit}
adam@1465	1421 \end{array}$$
adam@1465	1422
adamc@786	1423 A blob can be extracted from a file and returned as the page result. There are bless and check functions for MIME types analogous to those for URLs.
adamc@786	1424 $$\begin{array}{l}
adamc@786	1425 \mt{type} \; \mt{mimeType} \\
adamc@786	1426 \mt{val} \; \mt{blessMime} : \mt{string} \to \mt{mimeType} \\
adamc@786	1427 \mt{val} \; \mt{checkMime} : \mt{string} \to \mt{option} \; \mt{mimeType} \\
adamc@786	1428 \mt{val} \; \mt{returnBlob} : \mt{t} ::: \mt{Type} \to \mt{blob} \to \mt{mimeType} \to \mt{transaction} \; \mt{t}
adamc@542	1429 \end{array}$$
adamc@542	1430
adamc@543	1431 \subsection{SQL}
adamc@543	1432
adam@1400	1433 Everything about SQL database access is restricted to server-side code.
adam@1400	1434
adamc@543	1435 The fundamental unit of interest in the embedding of SQL is tables, described by a type family and creatable only via the $\mt{table}$ declaration form.
adamc@543	1436 $$\begin{array}{l}
adamc@785	1437 \mt{con} \; \mt{sql\_table} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785	1438 \end{array}$$
adamc@785	1439 The first argument to this constructor gives the names and types of a table's columns, and the second argument gives the set of valid keys. Keys are the only subsets of the columns that may be referenced as foreign keys. Each key has a name.
adamc@785	1440
adamc@785	1441 We also have the simpler type family of SQL views, which have no keys.
adamc@785	1442 $$\begin{array}{l}
adamc@785	1443 \mt{con} \; \mt{sql\_view} :: \{\mt{Type}\} \to \mt{Type}
adamc@543	1444 \end{array}$$
adamc@543	1445
adamc@785	1446 A multi-parameter type class is used to allow tables and views to be used interchangeably, with a way of extracting the set of columns from each.
adamc@785	1447 $$\begin{array}{l}
adamc@785	1448 \mt{class} \; \mt{fieldsOf} :: \mt{Type} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785	1449 \mt{val} \; \mt{fieldsOf\_table} : \mt{fs} ::: \{\mt{Type}\} \to \mt{keys} ::: \{\{\mt{Unit}\}\} \to \mt{fieldsOf} \; (\mt{sql\_table} \; \mt{fs} \; \mt{keys}) \; \mt{fs} \\
adamc@785	1450 \mt{val} \; \mt{fieldsOf\_view} : \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; (\mt{sql\_view} \; \mt{fs}) \; \mt{fs}
adamc@785	1451 \end{array}$$
adamc@785	1452
adamc@785	1453 \subsubsection{Table Constraints}
adamc@785	1454
adamc@785	1455 Tables may be declared with constraints, such that database modifications that violate the constraints are blocked. A table may have at most one \texttt{PRIMARY KEY} constraint, which gives the subset of columns that will most often be used to look up individual rows in the table.
adamc@785	1456
adamc@785	1457 $$\begin{array}{l}
adamc@785	1458 \mt{con} \; \mt{primary\_key} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type} \\
adamc@785	1459 \mt{val} \; \mt{no\_primary\_key} : \mt{fs} ::: \{\mt{Type}\} \to \mt{primary\_key} \; \mt{fs} \; [] \\
adamc@785	1460 \mt{val} \; \mt{primary\_key} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{key1} :: \mt{Name} \to \mt{keys} :: \{\mt{Type}\} \\
adamc@785	1461 \hspace{.1in} \to [[\mt{key1}] \sim \mt{keys}] \Rightarrow [[\mt{key1} = \mt{t}] \rc \mt{keys} \sim \mt{rest}] \\
adamc@785	1462 \hspace{.1in} \Rightarrow \$([\mt{key1} = \mt{sql\_injectable\_prim} \; \mt{t}] \rc \mt{map} \; \mt{sql\_injectable\_prim} \; \mt{keys}) \\
adamc@785	1463 \hspace{.1in} \to \mt{primary\_key} \; ([\mt{key1} = \mt{t}] \rc \mt{keys} \rc \mt{rest}) \; [\mt{Pkey} = [\mt{key1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{keys}]
adamc@785	1464 \end{array}$$
adamc@785	1465 The type class $\mt{sql\_injectable\_prim}$ characterizes which types are allowed in SQL and are not $\mt{option}$ types. In SQL, a \texttt{PRIMARY KEY} constraint enforces after-the-fact that a column may not contain \texttt{NULL}s, but Ur/Web forces that information to be included in table types from the beginning. Thus, the only effect of this kind of constraint in Ur/Web is to enforce uniqueness of the given key within the table.
adamc@785	1466
adamc@785	1467 A type family stands for sets of named constraints of the remaining varieties.
adamc@785	1468 $$\begin{array}{l}
adamc@785	1469 \mt{con} \; \mt{sql\_constraints} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785	1470 \end{array}$$
adamc@785	1471 The first argument gives the column types of the table being constrained, and the second argument maps constraint names to the keys that they define. Constraints that don't define keys are mapped to ``empty keys.''
adamc@785	1472
adamc@785	1473 There is a type family of individual, unnamed constraints.
adamc@785	1474 $$\begin{array}{l}
adamc@785	1475 \mt{con} \; \mt{sql\_constraint} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \mt{Type}
adamc@785	1476 \end{array}$$
adamc@785	1477 The first argument is the same as above, and the second argument gives the key columns for just this constraint.
adamc@785	1478
adamc@785	1479 We have operations for assembling constraints into constraint sets.
adamc@785	1480 $$\begin{array}{l}
adamc@785	1481 \mt{val} \; \mt{no\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_constraints} \; \mt{fs} \; [] \\
adamc@785	1482 \mt{val} \; \mt{one\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{unique} ::: \{\mt{Unit}\} \to \mt{name} :: \mt{Name} \\
adamc@785	1483 \hspace{.1in} \to \mt{sql\_constraint} \; \mt{fs} \; \mt{unique} \to \mt{sql\_constraints} \; \mt{fs} \; [\mt{name} = \mt{unique}] \\
adamc@785	1484 \mt{val} \; \mt{join\_constraints} : \mt{fs} ::: \{\mt{Type}\} \to \mt{uniques1} ::: \{\{\mt{Unit}\}\} \to \mt{uniques2} ::: \{\{\mt{Unit}\}\} \to [\mt{uniques1} \sim \mt{uniques2}] \\
adamc@785	1485 \hspace{.1in} \Rightarrow \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques1} \to \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques2} \to \mt{sql\_constraints} \; \mt{fs} \; (\mt{uniques1} \rc \mt{uniques2})
adamc@785	1486 \end{array}$$
adamc@785	1487
adamc@785	1488 A \texttt{UNIQUE} constraint forces a set of columns to be a key, which means that no combination of column values may occur more than once in the table. The $\mt{unique1}$ and $\mt{unique}$ arguments are separated out only to ensure that empty \texttt{UNIQUE} constraints are rejected.
adamc@785	1489 $$\begin{array}{l}
adamc@785	1490 \mt{val} \; \mt{unique} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{unique1} :: \mt{Name} \to \mt{unique} :: \{\mt{Type}\} \\
adamc@785	1491 \hspace{.1in} \to [[\mt{unique1}] \sim \mt{unique}] \Rightarrow [[\mt{unique1} = \mt{t}] \rc \mt{unique} \sim \mt{rest}] \\
adamc@785	1492 \hspace{.1in} \Rightarrow \mt{sql\_constraint} \; ([\mt{unique1} = \mt{t}] \rc \mt{unique} \rc \mt{rest}) \; ([\mt{unique1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{unique})
adamc@785	1493 \end{array}$$
adamc@785	1494
adamc@785	1495 A \texttt{FOREIGN KEY} constraint connects a set of local columns to a local or remote key, enforcing that the local columns always reference an existent row of the foreign key's table. A local column of type $\mt{t}$ may be linked to a foreign column of type $\mt{option} \; \mt{t}$, and vice versa. We formalize that notion with a type class.
adamc@785	1496 $$\begin{array}{l}
adamc@785	1497 \mt{class} \; \mt{linkable} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@785	1498 \mt{val} \; \mt{linkable\_same} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; \mt{t} \\
adamc@785	1499 \mt{val} \; \mt{linkable\_from\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; (\mt{option} \; \mt{t}) \; \mt{t} \\
adamc@785	1500 \mt{val} \; \mt{linkable\_to\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@785	1501 \end{array}$$
adamc@785	1502
adamc@785	1503 The $\mt{matching}$ type family uses $\mt{linkable}$ to define when two keys match up type-wise.
adamc@785	1504 $$\begin{array}{l}
adamc@785	1505 \mt{con} \; \mt{matching} :: \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785	1506 \mt{val} \; \mt{mat\_nil} : \mt{matching} \; [] \; [] \\
adamc@785	1507 \mt{val} \; \mt{mat\_cons} : \mt{t1} ::: \mt{Type} \to \mt{rest1} ::: \{\mt{Type}\} \to \mt{t2} ::: \mt{Type} \to \mt{rest2} ::: \{\mt{Type}\} \to \mt{nm1} :: \mt{Name} \to \mt{nm2} :: \mt{Name} \\
adamc@785	1508 \hspace{.1in} \to [[\mt{nm1}] \sim \mt{rest1}] \Rightarrow [[\mt{nm2}] \sim \mt{rest2}] \Rightarrow \mt{linkable} \; \mt{t1} \; \mt{t2} \to \mt{matching} \; \mt{rest1} \; \mt{rest2} \\
adamc@785	1509 \hspace{.1in} \to \mt{matching} \; ([\mt{nm1} = \mt{t1}] \rc \mt{rest1}) \; ([\mt{nm2} = \mt{t2}] \rc \mt{rest2})
adamc@785	1510 \end{array}$$
adamc@785	1511
adamc@785	1512 SQL provides a number of different propagation modes for \texttt{FOREIGN KEY} constraints, governing what happens when a row containing a still-referenced foreign key value is deleted or modified to have a different key value. The argument of a propagation mode's type gives the local key type.
adamc@785	1513 $$\begin{array}{l}
adamc@785	1514 \mt{con} \; \mt{propagation\_mode} :: \{\mt{Type}\} \to \mt{Type} \\
adamc@785	1515 \mt{val} \; \mt{restrict} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785	1516 \mt{val} \; \mt{cascade} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785	1517 \mt{val} \; \mt{no\_action} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785	1518 \mt{val} \; \mt{set\_null} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; (\mt{map} \; \mt{option} \; \mt{fs})
adamc@785	1519 \end{array}$$
adamc@785	1520
adamc@785	1521 Finally, we put these ingredient together to define the \texttt{FOREIGN KEY} constraint function.
adamc@785	1522 $$\begin{array}{l}
adamc@785	1523 \mt{val} \; \mt{foreign\_key} : \mt{mine1} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{mine} ::: \{\mt{Type}\} \to \mt{munused} ::: \{\mt{Type}\} \to \mt{foreign} ::: \{\mt{Type}\} \\
adamc@785	1524 \hspace{.1in} \to \mt{funused} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{uniques} ::: \{\{\mt{Unit}\}\} \\
adamc@785	1525 \hspace{.1in} \to [[\mt{mine1}] \sim \mt{mine}] \Rightarrow [[\mt{mine1} = \mt{t}] \rc \mt{mine} \sim \mt{munused}] \Rightarrow [\mt{foreign} \sim \mt{funused}] \Rightarrow [[\mt{nm}] \sim \mt{uniques}] \\
adamc@785	1526 \hspace{.1in} \Rightarrow \mt{matching} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}) \; \mt{foreign} \\
adamc@785	1527 \hspace{.1in} \to \mt{sql\_table} \; (\mt{foreign} \rc \mt{funused}) \; ([\mt{nm} = \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{foreign}] \rc \mt{uniques}) \\
adamc@785	1528 \hspace{.1in} \to \{\mt{OnDelete} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}), \\
adamc@785	1529 \hspace{.2in} \mt{OnUpdate} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine})\} \\
adamc@785	1530 \hspace{.1in} \to \mt{sql\_constraint} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine} \rc \mt{munused}) \; []
adamc@785	1531 \end{array}$$
adamc@785	1532
adamc@785	1533 The last kind of constraint is a \texttt{CHECK} constraint, which attaches a boolean invariant over a row's contents. It is defined using the $\mt{sql\_exp}$ type family, which we discuss in more detail below.
adamc@785	1534 $$\begin{array}{l}
adamc@785	1535 \mt{val} \; \mt{check} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; [] \; [] \; \mt{fs} \; \mt{bool} \to \mt{sql\_constraint} \; \mt{fs} \; []
adamc@785	1536 \end{array}$$
adamc@785	1537
adamc@785	1538 Section \ref{tables} shows the expanded syntax of the $\mt{table}$ declaration and signature item that includes constraints. There is no other way to use constraints with SQL in Ur/Web.
adamc@785	1539
adamc@784	1540
adamc@543	1541 \subsubsection{Queries}
adamc@543	1542
adam@1400	1543 A final query is constructed via the $\mt{sql\_query}$ function. Constructor arguments respectively specify the unrestricted free table variables (which will only be available in subqueries), the free table variables that may only be mentioned within arguments to aggregate functions, table fields we select (as records mapping tables to the subsets of their fields that we choose), and the (always named) extra expressions that we select.
adamc@543	1544 $$\begin{array}{l}
adam@1400	1545 \mt{con} \; \mt{sql\_query} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@1193	1546 \mt{val} \; \mt{sql\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400	1547 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adamc@1193	1548 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543	1549 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543	1550 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1193	1551 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adam@1400	1552 \hspace{.1in} \Rightarrow \{\mt{Rows} : \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}, \\
adamc@1193	1553 \hspace{.2in} \mt{OrderBy} : \mt{sql\_order\_by} \; (\mt{free} \rc \mt{tables}) \; \mt{selectedExps}, \\
adamc@543	1554 \hspace{.2in} \mt{Limit} : \mt{sql\_limit}, \\
adamc@543	1555 \hspace{.2in} \mt{Offset} : \mt{sql\_offset}\} \\
adam@1400	1556 \hspace{.1in} \to \mt{sql\_query} \; \mt{free} \; \mt{afree} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543	1557 \end{array}$$
adamc@543	1558
adamc@545	1559 Queries are used by folding over their results inside transactions.
adamc@545	1560 $$\begin{array}{l}
adam@1400	1561 \mt{val} \; \mt{query} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to [\mt{tables} \sim \mt{exps}] \Rightarrow \mt{state} ::: \mt{Type} \to \mt{sql\_query} \; [] \; [] \; \mt{tables} \; \mt{exps} \\
adamc@658	1562 \hspace{.1in} \to (\$(\mt{exps} \rc \mt{map} \; (\lambda \mt{fields} :: \{\mt{Type}\} \Rightarrow \$\mt{fields}) \; \mt{tables}) \\
adamc@545	1563 \hspace{.2in} \to \mt{state} \to \mt{transaction} \; \mt{state}) \\
adamc@545	1564 \hspace{.1in} \to \mt{state} \to \mt{transaction} \; \mt{state}
adamc@545	1565 \end{array}$$
adamc@545	1566
adam@1400	1567 Most of the complexity of the query encoding is in the type $\mt{sql\_query1}$, which includes simple queries and derived queries based on relational operators. Constructor arguments respectively specify the unrestricted free table veriables, the aggregate-only free table variables, the tables we select from, the subset of fields that we keep from each table for the result rows, and the extra expressions that we select.
adamc@543	1568 $$\begin{array}{l}
adam@1400	1569 \mt{con} \; \mt{sql\_query1} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@543	1570 \\
adamc@543	1571 \mt{type} \; \mt{sql\_relop} \\
adamc@543	1572 \mt{val} \; \mt{sql\_union} : \mt{sql\_relop} \\
adamc@543	1573 \mt{val} \; \mt{sql\_intersect} : \mt{sql\_relop} \\
adamc@543	1574 \mt{val} \; \mt{sql\_except} : \mt{sql\_relop} \\
adam@1400	1575 \mt{val} \; \mt{sql\_relop} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400	1576 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adam@1400	1577 \hspace{.1in} \to \mt{tables1} ::: \{\{\mt{Type}\}\} \\
adamc@543	1578 \hspace{.1in} \to \mt{tables2} ::: \{\{\mt{Type}\}\} \\
adamc@543	1579 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543	1580 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@543	1581 \hspace{.1in} \to \mt{sql\_relop} \\
adam@1458	1582 \hspace{.1in} \to \mt{bool} \; (* \; \mt{ALL} \; *) \\
adam@1400	1583 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables1} \; \mt{selectedFields} \; \mt{selectedExps} \\
adam@1400	1584 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables2} \; \mt{selectedFields} \; \mt{selectedExps} \\
adam@1400	1585 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{selectedFields} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543	1586 \end{array}$$
adamc@543	1587
adamc@543	1588 $$\begin{array}{l}
adamc@1193	1589 \mt{val} \; \mt{sql\_query1} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400	1590 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adamc@1193	1591 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543	1592 \hspace{.1in} \to \mt{grouped} ::: \{\{\mt{Type}\}\} \\
adamc@543	1593 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543	1594 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1085	1595 \hspace{.1in} \to \mt{empties} :: \{\mt{Unit}\} \\
adamc@1193	1596 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adamc@1193	1597 \hspace{.1in} \Rightarrow [\mt{free} \sim \mt{grouped}] \\
adam@1400	1598 \hspace{.1in} \Rightarrow [\mt{afree} \sim \mt{tables}] \\
adamc@1193	1599 \hspace{.1in} \Rightarrow [\mt{empties} \sim \mt{selectedFields}] \\
adamc@1085	1600 \hspace{.1in} \Rightarrow \{\mt{Distinct} : \mt{bool}, \\
adamc@1193	1601 \hspace{.2in} \mt{From} : \mt{sql\_from\_items} \; \mt{free} \; \mt{tables}, \\
adam@1400	1602 \hspace{.2in} \mt{Where} : \mt{sql\_exp} \; (\mt{free} \rc \mt{tables}) \; \mt{afree} \; [] \; \mt{bool}, \\
adamc@543	1603 \hspace{.2in} \mt{GroupBy} : \mt{sql\_subset} \; \mt{tables} \; \mt{grouped}, \\
adam@1400	1604 \hspace{.2in} \mt{Having} : \mt{sql\_exp} \; (\mt{free} \rc \mt{grouped}) \; (\mt{afree} \rc \mt{tables}) \; [] \; \mt{bool}, \\
adamc@1085	1605 \hspace{.2in} \mt{SelectFields} : \mt{sql\_subset} \; \mt{grouped} \; (\mt{map} \; (\lambda \_ \Rightarrow []) \; \mt{empties} \rc \mt{selectedFields}), \\
adam@1400	1606 \hspace{.2in} \mt {SelectExps} : \$(\mt{map} \; (\mt{sql\_exp} \; (\mt{free} \rc \mt{grouped}) \; (\mt{afree} \rc \mt{tables}) \; []) \; \mt{selectedExps}) \} \\
adam@1400	1607 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543	1608 \end{array}$$
adamc@543	1609
adamc@543	1610 To encode projection of subsets of fields in $\mt{SELECT}$ clauses, and to encode $\mt{GROUP} \; \mt{BY}$ clauses, we rely on a type family $\mt{sql\_subset}$, capturing what it means for one record of table fields to be a subset of another. The main constructor $\mt{sql\_subset}$ ``proves subset facts'' by requiring a split of a record into kept and dropped parts. The extra constructor $\mt{sql\_subset\_all}$ is a convenience for keeping all fields of a record.
adamc@543	1611 $$\begin{array}{l}
adamc@543	1612 \mt{con} \; \mt{sql\_subset} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@543	1613 \mt{val} \; \mt{sql\_subset} : \mt{keep\_drop} :: \{(\{\mt{Type}\} \times \{\mt{Type}\})\} \\
adamc@543	1614 \hspace{.1in} \to \mt{sql\_subset} \\
adamc@658	1615 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1 \rc \mt{fields}.2)\; \mt{keep\_drop}) \\
adamc@658	1616 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1) \; \mt{keep\_drop}) \\
adamc@543	1617 \mt{val} \; \mt{sql\_subset\_all} : \mt{tables} :: \{\{\mt{Type}\}\} \to \mt{sql\_subset} \; \mt{tables} \; \mt{tables}
adamc@543	1618 \end{array}$$
adamc@543	1619
adamc@560	1620 SQL expressions are used in several places, including $\mt{SELECT}$, $\mt{WHERE}$, $\mt{HAVING}$, and $\mt{ORDER} \; \mt{BY}$ clauses. They reify a fragment of the standard SQL expression language, while making it possible to inject ``native'' Ur values in some places. The arguments to the $\mt{sql\_exp}$ type family respectively give the unrestricted-availability table fields, the table fields that may only be used in arguments to aggregate functions, the available selected expressions, and the type of the expression.
adamc@543	1621 $$\begin{array}{l}
adamc@543	1622 \mt{con} \; \mt{sql\_exp} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}
adamc@543	1623 \end{array}$$
adamc@543	1624
adamc@543	1625 Any field in scope may be converted to an expression.
adamc@543	1626 $$\begin{array}{l}
adamc@543	1627 \mt{val} \; \mt{sql\_field} : \mt{otherTabs} ::: \{\{\mt{Type}\}\} \to \mt{otherFields} ::: \{\mt{Type}\} \\
adamc@543	1628 \hspace{.1in} \to \mt{fieldType} ::: \mt{Type} \to \mt{agg} ::: \{\{\mt{Type}\}\} \\
adamc@543	1629 \hspace{.1in} \to \mt{exps} ::: \{\mt{Type}\} \\
adamc@543	1630 \hspace{.1in} \to \mt{tab} :: \mt{Name} \to \mt{field} :: \mt{Name} \\
adamc@543	1631 \hspace{.1in} \to \mt{sql\_exp} \; ([\mt{tab} = [\mt{field} = \mt{fieldType}] \rc \mt{otherFields}] \rc \mt{otherTabs}) \; \mt{agg} \; \mt{exps} \; \mt{fieldType}
adamc@543	1632 \end{array}$$
adamc@543	1633
adamc@544	1634 There is an analogous function for referencing named expressions.
adamc@544	1635 $$\begin{array}{l}
adamc@544	1636 \mt{val} \; \mt{sql\_exp} : \mt{tabs} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{t} ::: \mt{Type} \to \mt{rest} ::: \{\mt{Type}\} \to \mt{nm} :: \mt{Name} \\
adamc@544	1637 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tabs} \; \mt{agg} \; ([\mt{nm} = \mt{t}] \rc \mt{rest}) \; \mt{t}
adamc@544	1638 \end{array}$$
adamc@544	1639
adamc@544	1640 Ur values of appropriate types may be injected into SQL expressions.
adamc@544	1641 $$\begin{array}{l}
adamc@786	1642 \mt{class} \; \mt{sql\_injectable\_prim} \\
adamc@786	1643 \mt{val} \; \mt{sql\_bool} : \mt{sql\_injectable\_prim} \; \mt{bool} \\
adamc@786	1644 \mt{val} \; \mt{sql\_int} : \mt{sql\_injectable\_prim} \; \mt{int} \\
adamc@786	1645 \mt{val} \; \mt{sql\_float} : \mt{sql\_injectable\_prim} \; \mt{float} \\
adamc@786	1646 \mt{val} \; \mt{sql\_string} : \mt{sql\_injectable\_prim} \; \mt{string} \\
adamc@786	1647 \mt{val} \; \mt{sql\_time} : \mt{sql\_injectable\_prim} \; \mt{time} \\
adamc@786	1648 \mt{val} \; \mt{sql\_blob} : \mt{sql\_injectable\_prim} \; \mt{blob} \\
adamc@786	1649 \mt{val} \; \mt{sql\_channel} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{channel} \; \mt{t}) \\
adamc@786	1650 \mt{val} \; \mt{sql\_client} : \mt{sql\_injectable\_prim} \; \mt{client} \\
adamc@786	1651 \\
adamc@544	1652 \mt{class} \; \mt{sql\_injectable} \\
adamc@786	1653 \mt{val} \; \mt{sql\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@786	1654 \mt{val} \; \mt{sql\_option\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; (\mt{option} \; \mt{t}) \\
adamc@786	1655 \\
adamc@544	1656 \mt{val} \; \mt{sql\_inject} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@544	1657 \hspace{.1in} \to \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adamc@544	1658 \end{array}$$
adamc@544	1659
adamc@1123	1660 Additionally, most function-free types may be injected safely, via the $\mt{serialized}$ type family.
adamc@1123	1661 $$\begin{array}{l}
adamc@1123	1662 \mt{con} \; \mt{serialized} :: \mt{Type} \to \mt{Type} \\
adamc@1123	1663 \mt{val} \; \mt{serialize} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{serialized} \; \mt{t} \\
adamc@1123	1664 \mt{val} \; \mt{deserialize} : \mt{t} ::: \mt{Type} \to \mt{serialized} \; \mt{t} \to \mt{t} \\
adamc@1123	1665 \mt{val} \; \mt{sql\_serialized} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{serialized} \; \mt{t})
adamc@1123	1666 \end{array}$$
adamc@1123	1667
adamc@544	1668 We have the SQL nullness test, which is necessary because of the strange SQL semantics of equality in the presence of null values.
adamc@544	1669 $$\begin{array}{l}
adamc@544	1670 \mt{val} \; \mt{sql\_is\_null} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544	1671 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; (\mt{option} \; \mt{t}) \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{bool}
adamc@544	1672 \end{array}$$
adamc@544	1673
adamc@559	1674 We have generic nullary, unary, and binary operators.
adamc@544	1675 $$\begin{array}{l}
adamc@544	1676 \mt{con} \; \mt{sql\_nfunc} :: \mt{Type} \to \mt{Type} \\
adamc@544	1677 \mt{val} \; \mt{sql\_current\_timestamp} : \mt{sql\_nfunc} \; \mt{time} \\
adamc@544	1678 \mt{val} \; \mt{sql\_nfunc} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544	1679 \hspace{.1in} \to \mt{sql\_nfunc} \; \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\\end{array}$$
adamc@544	1680
adamc@544	1681 $$\begin{array}{l}
adamc@544	1682 \mt{con} \; \mt{sql\_unary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544	1683 \mt{val} \; \mt{sql\_not} : \mt{sql\_unary} \; \mt{bool} \; \mt{bool} \\
adamc@544	1684 \mt{val} \; \mt{sql\_unary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adamc@544	1685 \hspace{.1in} \to \mt{sql\_unary} \; \mt{arg} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res} \\
adamc@544	1686 \end{array}$$
adamc@544	1687
adamc@544	1688 $$\begin{array}{l}
adamc@544	1689 \mt{con} \; \mt{sql\_binary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544	1690 \mt{val} \; \mt{sql\_and} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544	1691 \mt{val} \; \mt{sql\_or} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544	1692 \mt{val} \; \mt{sql\_binary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg_1} ::: \mt{Type} \to \mt{arg_2} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adamc@544	1693 \hspace{.1in} \to \mt{sql\_binary} \; \mt{arg_1} \; \mt{arg_2} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_1} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_2} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res}
adamc@544	1694 \end{array}$$
adamc@544	1695
adamc@544	1696 $$\begin{array}{l}
adamc@559	1697 \mt{class} \; \mt{sql\_arith} \\
adamc@559	1698 \mt{val} \; \mt{sql\_int\_arith} : \mt{sql\_arith} \; \mt{int} \\
adamc@559	1699 \mt{val} \; \mt{sql\_float\_arith} : \mt{sql\_arith} \; \mt{float} \\
adamc@559	1700 \mt{val} \; \mt{sql\_neg} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_unary} \; \mt{t} \; \mt{t} \\
adamc@559	1701 \mt{val} \; \mt{sql\_plus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559	1702 \mt{val} \; \mt{sql\_minus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559	1703 \mt{val} \; \mt{sql\_times} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559	1704 \mt{val} \; \mt{sql\_div} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559	1705 \mt{val} \; \mt{sql\_mod} : \mt{sql\_binary} \; \mt{int} \; \mt{int} \; \mt{int}
adamc@559	1706 \end{array}$$
adamc@544	1707
adamc@656	1708 Finally, we have aggregate functions. The $\mt{COUNT(\ast)}$ syntax is handled specially, since it takes no real argument. The other aggregate functions are placed into a general type family, using constructor classes to restrict usage to properly-typed arguments. The key aspect of the $\mt{sql\_aggregate}$ function's type is the shift of aggregate-function-only fields into unrestricted fields.
adamc@544	1709 $$\begin{array}{l}
adamc@544	1710 \mt{val} \; \mt{sql\_count} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int}
adamc@544	1711 \end{array}$$
adamc@544	1712
adamc@544	1713 $$\begin{array}{l}
adamc@1188	1714 \mt{con} \; \mt{sql\_aggregate} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@1188	1715 \mt{val} \; \mt{sql\_aggregate} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{dom} ::: \mt{Type} \to \mt{ran} ::: \mt{Type} \\
adamc@1188	1716 \hspace{.1in} \to \mt{sql\_aggregate} \; \mt{dom} \; \mt{ran} \to \mt{sql\_exp} \; \mt{agg} \; \mt{agg} \; \mt{exps} \; \mt{dom} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{ran}
adamc@1188	1717 \end{array}$$
adamc@1188	1718
adamc@1188	1719 $$\begin{array}{l}
adamc@1188	1720 \mt{val} \; \mt{sql\_count\_col} : \mt{t} ::: \mt{Type} \to \mt{sql\_aggregate} \; (\mt{option} \; \mt{t}) \; \mt{int}
adamc@544	1721 \end{array}$$
adam@1400	1722
adam@1400	1723 Most aggregate functions are typed using a two-parameter constructor class $\mt{nullify}$ which maps $\mt{option}$ types to themselves and adds $\mt{option}$ to others. That is, this constructor class represents the process of making an SQL type ``nullable.''
adamc@544	1724
adamc@544	1725 $$\begin{array}{l}
adamc@544	1726 \mt{class} \; \mt{sql\_summable} \\
adamc@544	1727 \mt{val} \; \mt{sql\_summable\_int} : \mt{sql\_summable} \; \mt{int} \\
adamc@544	1728 \mt{val} \; \mt{sql\_summable\_float} : \mt{sql\_summable} \; \mt{float} \\
adam@1400	1729 \mt{val} \; \mt{sql\_avg} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt} \\
adam@1400	1730 \mt{val} \; \mt{sql\_sum} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt}
adamc@544	1731 \end{array}$$
adamc@544	1732
adamc@544	1733 $$\begin{array}{l}
adamc@544	1734 \mt{class} \; \mt{sql\_maxable} \\
adamc@544	1735 \mt{val} \; \mt{sql\_maxable\_int} : \mt{sql\_maxable} \; \mt{int} \\
adamc@544	1736 \mt{val} \; \mt{sql\_maxable\_float} : \mt{sql\_maxable} \; \mt{float} \\
adamc@544	1737 \mt{val} \; \mt{sql\_maxable\_string} : \mt{sql\_maxable} \; \mt{string} \\
adamc@544	1738 \mt{val} \; \mt{sql\_maxable\_time} : \mt{sql\_maxable} \; \mt{time} \\
adam@1400	1739 \mt{val} \; \mt{sql\_max} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt} \\
adam@1400	1740 \mt{val} \; \mt{sql\_min} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt}
adamc@544	1741 \end{array}$$
adamc@544	1742
adamc@1193	1743 Any SQL query that returns single columns may be turned into a subquery expression.
adamc@1193	1744
adamc@786	1745 $$\begin{array}{l}
adam@1421	1746 \mt{val} \; \mt{sql\_subquery} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \\
adam@1421	1747 \hspace{.1in} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_query} \; \mt{tables} \; \mt{agg} \; [\mt{nm} = \mt{t}] \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{nt}
adamc@1193	1748 \end{array}$$
adamc@1193	1749
adamc@1193	1750 \texttt{FROM} clauses are specified using a type family, whose arguments are the free table variables and the table variables bound by this clause.
adamc@1193	1751 $$\begin{array}{l}
adamc@1193	1752 \mt{con} \; \mt{sql\_from\_items} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@1193	1753 \mt{val} \; \mt{sql\_from\_table} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adamc@1193	1754 \hspace{.1in} \to \mt{t} ::: \mt{Type} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; \mt{t} \; \mt{fs} \to \mt{name} :: \mt{Name} \to \mt{t} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193	1755 \mt{val} \; \mt{sql\_from\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{name} :: \mt{Name} \to \mt{sql\_query} \; \mt{free} \; [] \; \mt{fs} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193	1756 \mt{val} \; \mt{sql\_from\_comma} : \mt{free} ::: \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \to [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193	1757 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adamc@1193	1758 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2}) \\
adamc@1193	1759 \mt{val} \; \mt{sql\_inner\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \\
adamc@1193	1760 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193	1761 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adamc@1193	1762 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193	1763 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2})
adamc@786	1764 \end{array}$$
adamc@786	1765
adamc@786	1766 Besides these basic cases, outer joins are supported, which requires a type class for turning non-$\mt{option}$ columns into $\mt{option}$ columns.
adamc@786	1767 $$\begin{array}{l}
adamc@786	1768 \mt{class} \; \mt{nullify} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@786	1769 \mt{val} \; \mt{nullify\_option} : \mt{t} ::: \mt{Type} \to \mt{nullify} \; (\mt{option} \; \mt{t}) \; (\mt{option} \; \mt{t}) \\
adamc@786	1770 \mt{val} \; \mt{nullify\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{nullify} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@786	1771 \end{array}$$
adamc@786	1772
adamc@786	1773 Left, right, and full outer joins can now be expressed using functions that accept records of $\mt{nullify}$ instances. Here, we give only the type for a left join as an example.
adamc@786	1774
adamc@786	1775 $$\begin{array}{l}
adamc@1193	1776 \mt{val} \; \mt{sql\_left\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{(\mt{Type} \times \mt{Type})\}\} \\
adamc@1193	1777 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@786	1778 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\lambda \mt{r} \Rightarrow \$(\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{nullify} \; \mt{p}.1 \; \mt{p}.2) \; \mt{r})) \; \mt{tabs2}) \\
adamc@1193	1779 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \\
adamc@1193	1780 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193	1781 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.2)) \; \mt{tabs2})
adamc@786	1782 \end{array}$$
adamc@786	1783
adamc@544	1784 We wrap up the definition of query syntax with the types used in representing $\mt{ORDER} \; \mt{BY}$, $\mt{LIMIT}$, and $\mt{OFFSET}$ clauses.
adamc@544	1785 $$\begin{array}{l}
adamc@544	1786 \mt{type} \; \mt{sql\_direction} \\
adamc@544	1787 \mt{val} \; \mt{sql\_asc} : \mt{sql\_direction} \\
adamc@544	1788 \mt{val} \; \mt{sql\_desc} : \mt{sql\_direction} \\
adamc@544	1789 \\
adamc@544	1790 \mt{con} \; \mt{sql\_order\_by} :: \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@544	1791 \mt{val} \; \mt{sql\_order\_by\_Nil} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} :: \{\mt{Type}\} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544	1792 \mt{val} \; \mt{sql\_order\_by\_Cons} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544	1793 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; [] \; \mt{exps} \; \mt{t} \to \mt{sql\_direction} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544	1794 \\
adamc@544	1795 \mt{type} \; \mt{sql\_limit} \\
adamc@544	1796 \mt{val} \; \mt{sql\_no\_limit} : \mt{sql\_limit} \\
adamc@544	1797 \mt{val} \; \mt{sql\_limit} : \mt{int} \to \mt{sql\_limit} \\
adamc@544	1798 \\
adamc@544	1799 \mt{type} \; \mt{sql\_offset} \\
adamc@544	1800 \mt{val} \; \mt{sql\_no\_offset} : \mt{sql\_offset} \\
adamc@544	1801 \mt{val} \; \mt{sql\_offset} : \mt{int} \to \mt{sql\_offset}
adamc@544	1802 \end{array}$$
adamc@544	1803
adamc@545	1804
adamc@545	1805 \subsubsection{DML}
adamc@545	1806
adamc@545	1807 The Ur/Web library also includes an embedding of a fragment of SQL's DML, the Data Manipulation Language, for modifying database tables. Any piece of DML may be executed in a transaction.
adamc@545	1808
adamc@545	1809 $$\begin{array}{l}
adamc@545	1810 \mt{type} \; \mt{dml} \\
adamc@545	1811 \mt{val} \; \mt{dml} : \mt{dml} \to \mt{transaction} \; \mt{unit}
adamc@545	1812 \end{array}$$
adamc@545	1813
adam@1297	1814 The function $\mt{Basis.dml}$ will trigger a fatal application error if the command fails, for instance, because a data integrity constraint is violated. An alternate function returns an error message as a string instead.
adam@1297	1815
adam@1297	1816 $$\begin{array}{l}
adam@1297	1817 \mt{val} \; \mt{tryDml} : \mt{dml} \to \mt{transaction} \; (\mt{option} \; \mt{string})
adam@1297	1818 \end{array}$$
adam@1297	1819
adamc@545	1820 Properly-typed records may be used to form $\mt{INSERT}$ commands.
adamc@545	1821 $$\begin{array}{l}
adamc@545	1822 \mt{val} \; \mt{insert} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \\
adamc@658	1823 \hspace{.1in} \to \$(\mt{map} \; (\mt{sql\_exp} \; [] \; [] \; []) \; \mt{fields}) \to \mt{dml}
adamc@545	1824 \end{array}$$
adamc@545	1825
adamc@545	1826 An $\mt{UPDATE}$ command is formed from a choice of which table fields to leave alone and which to change, along with an expression to use to compute the new value of each changed field and a $\mt{WHERE}$ clause.
adamc@545	1827 $$\begin{array}{l}
adam@1380	1828 \mt{val} \; \mt{update} : \mt{unchanged} ::: \{\mt{Type}\} \to \mt{changed} :: \{\mt{Type}\} \to [\mt{changed} \sim \mt{unchanged}] \\
adamc@658	1829 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; []) \; \mt{changed}) \\
adamc@545	1830 \hspace{.1in} \to \mt{sql\_table} \; (\mt{changed} \rc \mt{unchanged}) \to \mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545	1831 \end{array}$$
adamc@545	1832
adamc@545	1833 A $\mt{DELETE}$ command is formed from a table and a $\mt{WHERE}$ clause.
adamc@545	1834 $$\begin{array}{l}
adamc@545	1835 \mt{val} \; \mt{delete} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \to \mt{sql\_exp} \; [\mt{T} = \mt{fields}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545	1836 \end{array}$$
adamc@545	1837
adamc@546	1838 \subsubsection{Sequences}
adamc@546	1839
adamc@546	1840 SQL sequences are counters with concurrency control, often used to assign unique IDs. Ur/Web supports them via a simple interface. The only way to create a sequence is with the $\mt{sequence}$ declaration form.
adamc@546	1841
adamc@546	1842 $$\begin{array}{l}
adamc@546	1843 \mt{type} \; \mt{sql\_sequence} \\
adamc@1085	1844 \mt{val} \; \mt{nextval} : \mt{sql\_sequence} \to \mt{transaction} \; \mt{int} \\
adamc@1085	1845 \mt{val} \; \mt{setval} : \mt{sql\_sequence} \to \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@546	1846 \end{array}$$
adamc@546	1847
adamc@546	1848
adamc@547	1849 \subsection{XML}
adamc@547	1850
adam@1333	1851 Ur/Web's library contains an encoding of XML syntax and semantic constraints. We make no effort to follow the standards governing XML schemas. Rather, XML fragments are viewed more as values of ML datatypes, and we only track which tags are allowed inside which other tags. The Ur/Web standard library encodes a very loose version of XHTML, where it is very easy to produce documents which are invalid XHTML, but which still display properly in all major browsers. The main purposes of the invariants that are enforced are first, to provide some documentation about the places where it would make sense to insert XML fragments; and second, to rule out code injection attacks and other abstraction violations related to HTML syntax.
adamc@547	1852
adam@1345	1853 The basic XML type family has arguments respectively indicating the \emph{context} of a fragment, the fields that the fragment expects to be bound on entry (and their types), and the fields that the fragment will bind (and their types). Contexts are a record-based ``poor man's subtyping'' encoding, with each possible set of valid tags corresponding to a different context record. For instance, the context for the \texttt{<td>} tag is $[\mt{Body}, \mt{Tr}]$, to indicate a kind of nesting inside \texttt{<body>} and \texttt{<tr>}. Contexts are maintained in a somewhat ad-hoc way; the only definitive reference for their meanings is the types of the tag values in \texttt{basis.urs}. The arguments dealing with field binding are only relevant to HTML forms.
adamc@547	1854 $$\begin{array}{l}
adamc@547	1855 \mt{con} \; \mt{xml} :: \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547	1856 \end{array}$$
adamc@547	1857
adamc@547	1858 We also have a type family of XML tags, indexed respectively by the record of optional attributes accepted by the tag, the context in which the tag may be placed, the context required of children of the tag, which form fields the tag uses, and which fields the tag defines.
adamc@547	1859 $$\begin{array}{l}
adamc@547	1860 \mt{con} \; \mt{tag} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547	1861 \end{array}$$
adamc@547	1862
adamc@547	1863 Literal text may be injected into XML as ``CDATA.''
adamc@547	1864 $$\begin{array}{l}
adamc@547	1865 \mt{val} \; \mt{cdata} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{string} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adamc@547	1866 \end{array}$$
adamc@547	1867
adam@1358	1868 There is also a function to insert the literal value of a character. Since Ur/Web uses the UTF-8 text encoding, the $\mt{cdata}$ function is only sufficient to encode characters with ASCII codes below 128. Higher codes have alternate meanings in UTF-8 than in usual ASCII, so this alternate function should be used with them.
adam@1358	1869 $$\begin{array}{l}
adam@1358	1870 \mt{val} \; \mt{cdataChar} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{char} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adam@1358	1871 \end{array}$$
adam@1358	1872
adamc@547	1873 There is a function for producing an XML tree with a particular tag at its root.
adamc@547	1874 $$\begin{array}{l}
adamc@547	1875 \mt{val} \; \mt{tag} : \mt{attrsGiven} ::: \{\mt{Type}\} \to \mt{attrsAbsent} ::: \{\mt{Type}\} \to \mt{ctxOuter} ::: \{\mt{Unit}\} \to \mt{ctxInner} ::: \{\mt{Unit}\} \\
adamc@547	1876 \hspace{.1in} \to \mt{useOuter} ::: \{\mt{Type}\} \to \mt{useInner} ::: \{\mt{Type}\} \to \mt{bindOuter} ::: \{\mt{Type}\} \to \mt{bindInner} ::: \{\mt{Type}\} \\
adam@1380	1877 \hspace{.1in} \to [\mt{attrsGiven} \sim \mt{attrsAbsent}] \Rightarrow [\mt{useOuter} \sim \mt{useInner}] \Rightarrow [\mt{bindOuter} \sim \mt{bindInner}] \\
adamc@787	1878 \hspace{.1in} \Rightarrow \mt{option} \; \mt{css\_class} \\
adamc@787	1879 \hspace{.1in} \to \$\mt{attrsGiven} \\
adamc@547	1880 \hspace{.1in} \to \mt{tag} \; (\mt{attrsGiven} \rc \mt{attrsAbsent}) \; \mt{ctxOuter} \; \mt{ctxInner} \; \mt{useOuter} \; \mt{bindOuter} \\
adamc@547	1881 \hspace{.1in} \to \mt{xml} \; \mt{ctxInner} \; \mt{useInner} \; \mt{bindInner} \to \mt{xml} \; \mt{ctxOuter} \; (\mt{useOuter} \rc \mt{useInner}) \; (\mt{bindOuter} \rc \mt{bindInner})
adamc@547	1882 \end{array}$$
adam@1297	1883 Note that any tag may be assigned a CSS class. This is the sole way of making use of the values produced by $\mt{style}$ declarations. Ur/Web itself doesn't deal with the syntax or semantics of style sheets; they can be linked via URLs with \texttt{link} tags. However, Ur/Web does make it easy to calculate upper bounds on usage of CSS classes through program analysis. The function $\mt{Basis.classes}$ can be used to specify a list of CSS classes for a single tag.
adamc@547	1884
adamc@547	1885 Two XML fragments may be concatenated.
adamc@547	1886 $$\begin{array}{l}
adamc@547	1887 \mt{val} \; \mt{join} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{bind_1} ::: \{\mt{Type}\} \to \mt{bind_2} ::: \{\mt{Type}\} \\
adam@1380	1888 \hspace{.1in} \to [\mt{use_1} \sim \mt{bind_1}] \Rightarrow [\mt{bind_1} \sim \mt{bind_2}] \\
adamc@547	1889 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind_1} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{bind_1}) \; \mt{bind_2} \to \mt{xml} \; \mt{ctx} \; \mt{use_1} \; (\mt{bind_1} \rc \mt{bind_2})
adamc@547	1890 \end{array}$$
adamc@547	1891
adamc@547	1892 Finally, any XML fragment may be updated to ``claim'' to use more form fields than it does.
adamc@547	1893 $$\begin{array}{l}
adam@1380	1894 \mt{val} \; \mt{useMore} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{use_2} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to [\mt{use_1} \sim \mt{use_2}] \\
adamc@547	1895 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{use_2}) \; \mt{bind}
adamc@547	1896 \end{array}$$
adamc@547	1897
adam@1344	1898 We will not list here the different HTML tags and related functions from the standard library. They should be easy enough to understand from the code in \texttt{basis.urs}. The set of tags in the library is not yet claimed to be complete for HTML standards. Also note that there is currently no way for the programmer to add his own tags. It \emph{is} possible to add new tags directly to \texttt{basis.urs}, but this should only be done as a prelude to suggesting a patch to the main distribution.
adamc@547	1899
adamc@547	1900 One last useful function is for aborting any page generation, returning some XML as an error message. This function takes the place of some uses of a general exception mechanism.
adamc@547	1901 $$\begin{array}{l}
adamc@547	1902 \mt{val} \; \mt{error} : \mt{t} ::: \mt{Type} \to \mt{xml} \; [\mt{Body}] \; [] \; [] \to \mt{t}
adamc@547	1903 \end{array}$$
adamc@547	1904
adamc@549	1905
adamc@701	1906 \subsection{Client-Side Programming}
adamc@659	1907
adamc@701	1908 Ur/Web supports running code on web browsers, via automatic compilation to JavaScript.
adamc@701	1909
adamc@701	1910 \subsubsection{The Basics}
adamc@701	1911
adam@1400	1912 All of the functions in this subsection are client-side only.
adam@1400	1913
adam@1297	1914 Clients can open alert and confirm dialog boxes, in the usual annoying JavaScript way.
adamc@701	1915 $$\begin{array}{l}
adam@1297	1916 \mt{val} \; \mt{alert} : \mt{string} \to \mt{transaction} \; \mt{unit} \\
adam@1297	1917 \mt{val} \; \mt{confirm} : \mt{string} \to \mt{transaction} \; \mt{bool}
adamc@701	1918 \end{array}$$
adamc@701	1919
adamc@701	1920 Any transaction may be run in a new thread with the $\mt{spawn}$ function.
adamc@701	1921 $$\begin{array}{l}
adamc@701	1922 \mt{val} \; \mt{spawn} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit}
adamc@701	1923 \end{array}$$
adamc@701	1924
adamc@701	1925 The current thread can be paused for at least a specified number of milliseconds.
adamc@701	1926 $$\begin{array}{l}
adamc@701	1927 \mt{val} \; \mt{sleep} : \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@701	1928 \end{array}$$
adamc@701	1929
adamc@787	1930 A few functions are available to registers callbacks for particular error events. Respectively, they are triggered on calls to $\mt{error}$, uncaught JavaScript exceptions, failure of remote procedure calls, the severance of the connection serving asynchronous messages, or the occurrence of some other error with that connection. If no handlers are registered for a kind of error, then occurrences of that error are ignored silently.
adamc@787	1931 $$\begin{array}{l}
adamc@787	1932 \mt{val} \; \mt{onError} : (\mt{xbody} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787	1933 \mt{val} \; \mt{onFail} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787	1934 \mt{val} \; \mt{onConnectFail} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787	1935 \mt{val} \; \mt{onDisconnect} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787	1936 \mt{val} \; \mt{onServerError} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit}
adamc@787	1937 \end{array}$$
adamc@787	1938
adamc@701	1939 \subsubsection{Functional-Reactive Page Generation}
adamc@701	1940
adamc@701	1941 Most approaches to ``AJAX''-style coding involve imperative manipulation of the DOM tree representing an HTML document's structure. Ur/Web follows the \emph{functional-reactive} approach instead. Programs may allocate mutable \emph{sources} of arbitrary types, and an HTML page is effectively a pure function over the latest values of the sources. The page is not mutated directly, but rather it changes automatically as the sources are mutated.
adamc@659	1942
adam@1403	1943 More operationally, you can think of a source as a mutable cell with facilities for subscription to change notifications. That level of detail is hidden behind a monadic facility to be described below. First, there are three primitive operations for working with sources just as if they were ML \cd{ref} cells, corresponding to ML's \cd{ref}, \cd{:=}, and \cd{!} operations.
adam@1403	1944
adamc@659	1945 $$\begin{array}{l}
adamc@659	1946 \mt{con} \; \mt{source} :: \mt{Type} \to \mt{Type} \\
adamc@659	1947 \mt{val} \; \mt{source} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{transaction} \; (\mt{source} \; \mt{t}) \\
adamc@659	1948 \mt{val} \; \mt{set} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@659	1949 \mt{val} \; \mt{get} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@659	1950 \end{array}$$
adamc@659	1951
adam@1400	1952 Only source creation and setting are supported server-side, as a convenience to help in setting up a page, where you may wish to allocate many sources that will be referenced through the page. All server-side storage of values inside sources uses string serializations of values, while client-side storage uses normal JavaScript values.
adam@1400	1953
adam@1403	1954 Pure functions over arbitrary numbers of sources are represented in a monad of \emph{signals}, which may only be used in client-side code. This is presented to the programmer in the form of a monad $\mt{signal}$, each of whose values represents (conceptually) some pure function over all sources that may be allocated in the course of program execution. A monad operation $\mt{signal}$ denotes the identity function over a particular source. By using $\mt{signal}$ on a source, you implicitly subscribe to change notifications for that source. That is, your signal will automatically be recomputed as that source changes. The usual monad operators make it possible to build up complex signals that depend on multiple sources; automatic updating upon source-value changes still happens automatically.
adamc@659	1955
adamc@659	1956 $$\begin{array}{l}
adamc@659	1957 \mt{con} \; \mt{signal} :: \mt{Type} \to \mt{Type} \\
adamc@659	1958 \mt{val} \; \mt{signal\_monad} : \mt{monad} \; \mt{signal} \\
adamc@659	1959 \mt{val} \; \mt{signal} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{signal} \; \mt{t}
adamc@659	1960 \end{array}$$
adamc@659	1961
adamc@659	1962 A reactive portion of an HTML page is injected with a $\mt{dyn}$ tag, which has a signal-valued attribute $\mt{Signal}$.
adamc@659	1963
adamc@659	1964 $$\begin{array}{l}
adamc@701	1965 \mt{val} \; \mt{dyn} : \mt{use} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to \mt{unit} \\
adamc@701	1966 \hspace{.1in} \to \mt{tag} \; [\mt{Signal} = \mt{signal} \; (\mt{xml} \; \mt{body} \; \mt{use} \; \mt{bind})] \; \mt{body} \; [] \; \mt{use} \; \mt{bind}
adamc@659	1967 \end{array}$$
adamc@659	1968
adamc@701	1969 Transactions can be run on the client by including them in attributes like the $\mt{Onclick}$ attribute of $\mt{button}$, and GUI widgets like $\mt{ctextbox}$ have $\mt{Source}$ attributes that can be used to connect them to sources, so that their values can be read by code running because of, e.g., an $\mt{Onclick}$ event.
adamc@701	1970
adamc@914	1971 \subsubsection{Remote Procedure Calls}
adamc@914	1972
adamc@914	1973 Any function call may be made a client-to-server ``remote procedure call'' if the function being called needs no features that are only available to client code. To make a function call an RPC, pass that function call as the argument to $\mt{Basis.rpc}$:
adamc@914	1974
adamc@914	1975 $$\begin{array}{l}
adamc@914	1976 \mt{val} \; \mt{rpc} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@914	1977 \end{array}$$
adamc@914	1978
adamc@701	1979 \subsubsection{Asynchronous Message-Passing}
adamc@701	1980
adamc@701	1981 To support asynchronous, ``server push'' delivery of messages to clients, any client that might need to receive an asynchronous message is assigned a unique ID. These IDs may be retrieved both on the client and on the server, during execution of code related to a client.
adamc@701	1982
adamc@701	1983 $$\begin{array}{l}
adamc@701	1984 \mt{type} \; \mt{client} \\
adamc@701	1985 \mt{val} \; \mt{self} : \mt{transaction} \; \mt{client}
adamc@701	1986 \end{array}$$
adamc@701	1987
adamc@701	1988 \emph{Channels} are the means of message-passing. Each channel is created in the context of a client and belongs to that client; no other client may receive the channel's messages. Each channel type includes the type of values that may be sent over the channel. Sending and receiving are asynchronous, in the sense that a client need not be ready to receive a message right away. Rather, sent messages may queue up, waiting to be processed.
adamc@701	1989
adamc@701	1990 $$\begin{array}{l}
adamc@701	1991 \mt{con} \; \mt{channel} :: \mt{Type} \to \mt{Type} \\
adamc@701	1992 \mt{val} \; \mt{channel} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; (\mt{channel} \; \mt{t}) \\
adamc@701	1993 \mt{val} \; \mt{send} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@701	1994 \mt{val} \; \mt{recv} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@701	1995 \end{array}$$
adamc@701	1996
adamc@701	1997 The $\mt{channel}$ and $\mt{send}$ operations may only be executed on the server, and $\mt{recv}$ may only be executed on a client. Neither clients nor channels may be passed as arguments from clients to server-side functions, so persistent channels can only be maintained by storing them in the database and looking them up using the current client ID or some application-specific value as a key.
adamc@701	1998
adamc@701	1999 Clients and channels live only as long as the web browser page views that they are associated with. When a user surfs away, his client and its channels will be garbage-collected, after that user is not heard from for the timeout period. Garbage collection deletes any database row that contains a client or channel directly. Any reference to one of these types inside an $\mt{option}$ is set to $\mt{None}$ instead. Both kinds of handling have the flavor of weak pointers, and that is a useful way to think about clients and channels in the database.
adamc@701	2000
adamc@659	2001
adamc@549	2002 \section{Ur/Web Syntax Extensions}
adamc@549	2003
adamc@549	2004 Ur/Web features some syntactic shorthands for building values using the functions from the last section. This section sketches the grammar of those extensions. We write spans of syntax inside brackets to indicate that they are optional.
adamc@549	2005
adamc@549	2006 \subsection{SQL}
adamc@549	2007
adamc@786	2008 \subsubsection{\label{tables}Table Declarations}
adamc@786	2009
adamc@788	2010 $\mt{table}$ declarations may include constraints, via these grammar rules.
adamc@788	2011 $$\begin{array}{rrcll}
adamc@788	2012 \textrm{Declarations} & d &::=& \mt{table} \; x : c \; [pk[,]] \; cts \\
adamc@788	2013 \textrm{Primary key constraints} & pk &::=& \mt{PRIMARY} \; \mt{KEY} \; K \\
adamc@788	2014 \textrm{Keys} & K &::=& f \mid (f, (f,)^+) \\
adamc@788	2015 \textrm{Constraint sets} & cts &::=& \mt{CONSTRAINT} f \; ct \mid cts, cts \mid \{\{e\}\} \\
adamc@788	2016 \textrm{Constraints} & ct &::=& \mt{UNIQUE} \; K \mid \mt{CHECK} \; E \\
adamc@788	2017 &&& \mid \mt{FOREIGN} \; \mt{KEY} \; K \; \mt{REFERENCES} \; F \; (K) \; [\mt{ON} \; \mt{DELETE} \; pr] \; [\mt{ON} \; \mt{UPDATE} \; pr] \\
adamc@788	2018 \textrm{Foreign tables} & F &::=& x \mid \{\{e\}\} \\
adamc@788	2019 \textrm{Propagation modes} & pr &::=& \mt{NO} \; \mt{ACTION} \mid \mt{RESTRICT} \mid \mt{CASCADE} \mid \mt{SET} \; \mt{NULL}
adamc@788	2020 \end{array}$$
adamc@788	2021
adamc@788	2022 A signature item $\mt{table} \; \mt{x} : \mt{c}$ is actually elaborated into two signature items: $\mt{con} \; \mt{x\_hidden\_constraints} :: \{\{\mt{Unit}\}\}$ and $\mt{val} \; \mt{x} : \mt{sql\_table} \; \mt{c} \; \mt{x\_hidden\_constraints}$. This is appropriate for common cases where client code doesn't care which keys a table has. It's also possible to include constraints after a $\mt{table}$ signature item, with the same syntax as for $\mt{table}$ declarations. This may look like dependent typing, but it's just a convenience. The constraints are type-checked to determine a constructor $u$ to include in $\mt{val} \; \mt{x} : \mt{sql\_table} \; \mt{c} \; (u \rc \mt{x\_hidden\_constraints})$, and then the expressions are thrown away. Nonetheless, it can be useful for documentation purposes to include table constraint details in signatures. Note that the automatic generation of $\mt{x\_hidden\_constraints}$ leads to a kind of free subtyping with respect to which constraints are defined.
adamc@788	2023
adamc@788	2024
adamc@549	2025 \subsubsection{Queries}
adamc@549	2026
adamc@550	2027 Queries $Q$ are added to the rules for expressions $e$.
adamc@550	2028
adamc@549	2029 $$\begin{array}{rrcll}
adamc@550	2030 \textrm{Queries} & Q &::=& (q \; [\mt{ORDER} \; \mt{BY} \; (E \; [o],)^+] \; [\mt{LIMIT} \; N] \; [\mt{OFFSET} \; N]) \\
adamc@1085	2031 \textrm{Pre-queries} & q &::=& \mt{SELECT} \; [\mt{DISTINCT}] \; P \; \mt{FROM} \; F,^+ \; [\mt{WHERE} \; E] \; [\mt{GROUP} \; \mt{BY} \; p,^+] \; [\mt{HAVING} \; E] \\
adamc@1085	2032 &&& \mid q \; R \; q \mid \{\{\{e\}\}\} \\
adamc@549	2033 \textrm{Relational operators} & R &::=& \mt{UNION} \mid \mt{INTERSECT} \mid \mt{EXCEPT}
adamc@549	2034 \end{array}$$
adamc@549	2035
adamc@549	2036 $$\begin{array}{rrcll}
adamc@549	2037 \textrm{Projections} & P &::=& \ast & \textrm{all columns} \\
adamc@549	2038 &&& p,^+ & \textrm{particular columns} \\
adamc@549	2039 \textrm{Pre-projections} & p &::=& t.f & \textrm{one column from a table} \\
adamc@558	2040 &&& t.\{\{c\}\} & \textrm{a record of columns from a table (of kind $\{\mt{Type}\}$)} \\
adamc@1194	2041 &&& E \; [\mt{AS} \; f] & \textrm{expression column} \\
adamc@549	2042 \textrm{Table names} & t &::=& x & \textrm{constant table name (automatically capitalized)} \\
adamc@549	2043 &&& X & \textrm{constant table name} \\
adamc@549	2044 &&& \{\{c\}\} & \textrm{computed table name (of kind $\mt{Name}$)} \\
adamc@549	2045 \textrm{Column names} & f &::=& X & \textrm{constant column name} \\
adamc@549	2046 &&& \{c\} & \textrm{computed column name (of kind $\mt{Name}$)} \\
adamc@549	2047 \textrm{Tables} & T &::=& x & \textrm{table variable, named locally by its own capitalization} \\
adamc@549	2048 &&& x \; \mt{AS} \; t & \textrm{table variable, with local name} \\
adamc@549	2049 &&& \{\{e\}\} \; \mt{AS} \; t & \textrm{computed table expression, with local name} \\
adamc@1085	2050 \textrm{$\mt{FROM}$ items} & F &::=& T \mid \{\{e\}\} \mid F \; J \; \mt{JOIN} \; F \; \mt{ON} \; E \\
adamc@1085	2051 &&& \mid F \; \mt{CROSS} \; \mt{JOIN} \ F \\
adamc@1193	2052 &&& \mid (Q) \; \mt{AS} \; t \\
adamc@1085	2053 \textrm{Joins} & J &::=& [\mt{INNER}] \\
adamc@1085	2054 &&& \mid [\mt{LEFT} \mid \mt{RIGHT} \mid \mt{FULL}] \; [\mt{OUTER}] \\
adamc@549	2055 \textrm{SQL expressions} & E &::=& p & \textrm{column references} \\
adamc@549	2056 &&& X & \textrm{named expression references} \\
adamc@549	2057 &&& \{\{e\}\} & \textrm{injected native Ur expressions} \\
adamc@549	2058 &&& \{e\} & \textrm{computed expressions, probably using $\mt{sql\_exp}$ directly} \\
adamc@549	2059 &&& \mt{TRUE} \mid \mt{FALSE} & \textrm{boolean constants} \\
adamc@549	2060 &&& \ell & \textrm{primitive type literals} \\
adamc@549	2061 &&& \mt{NULL} & \textrm{null value (injection of $\mt{None}$)} \\
adamc@549	2062 &&& E \; \mt{IS} \; \mt{NULL} & \textrm{nullness test} \\
adamc@549	2063 &&& n & \textrm{nullary operators} \\
adamc@549	2064 &&& u \; E & \textrm{unary operators} \\
adamc@549	2065 &&& E \; b \; E & \textrm{binary operators} \\
adamc@549	2066 &&& \mt{COUNT}(\ast) & \textrm{count number of rows} \\
adamc@549	2067 &&& a(E) & \textrm{other aggregate function} \\
adamc@1193	2068 &&& (Q) & \textrm{subquery (must return a single expression column)} \\
adamc@549	2069 &&& (E) & \textrm{explicit precedence} \\
adamc@549	2070 \textrm{Nullary operators} & n &::=& \mt{CURRENT\_TIMESTAMP} \\
adamc@549	2071 \textrm{Unary operators} & u &::=& \mt{NOT} \\
adamc@549	2072 \textrm{Binary operators} & b &::=& \mt{AND} \mid \mt{OR} \mid \neq \mid < \mid \leq \mid > \mid \geq \\
adamc@1188	2073 \textrm{Aggregate functions} & a &::=& \mt{COUNT} \mid \mt{AVG} \mid \mt{SUM} \mid \mt{MIN} \mid \mt{MAX} \\
adamc@550	2074 \textrm{Directions} & o &::=& \mt{ASC} \mid \mt{DESC} \\
adamc@549	2075 \textrm{SQL integer} & N &::=& n \mid \{e\} \\
adamc@549	2076 \end{array}$$
adamc@549	2077
adamc@1085	2078 Additionally, an SQL expression may be inserted into normal Ur code with the syntax $(\mt{SQL} \; E)$ or $(\mt{WHERE} \; E)$. Similar shorthands exist for other nonterminals, with the prefix $\mt{FROM}$ for $\mt{FROM}$ items and $\mt{SELECT1}$ for pre-queries.
adamc@549	2079
adamc@1194	2080 Unnamed expression columns in $\mt{SELECT}$ clauses are assigned consecutive natural numbers, starting with 1.
adamc@1194	2081
adamc@550	2082 \subsubsection{DML}
adamc@550	2083
adamc@550	2084 DML commands $D$ are added to the rules for expressions $e$.
adamc@550	2085
adamc@550	2086 $$\begin{array}{rrcll}
adamc@550	2087 \textrm{Commands} & D &::=& (\mt{INSERT} \; \mt{INTO} \; T^E \; (f,^+) \; \mt{VALUES} \; (E,^+)) \\
adamc@550	2088 &&& (\mt{UPDATE} \; T^E \; \mt{SET} \; (f = E,)^+ \; \mt{WHERE} \; E) \\
adamc@550	2089 &&& (\mt{DELETE} \; \mt{FROM} \; T^E \; \mt{WHERE} \; E) \\
adamc@550	2090 \textrm{Table expressions} & T^E &::=& x \mid \{\{e\}\}
adamc@550	2091 \end{array}$$
adamc@550	2092
adamc@550	2093 Inside $\mt{UPDATE}$ and $\mt{DELETE}$ commands, lone variables $X$ are interpreted as references to columns of the implicit table $\mt{T}$, rather than to named expressions.
adamc@549	2094
adamc@551	2095 \subsection{XML}
adamc@551	2096
adamc@551	2097 XML fragments $L$ are added to the rules for expressions $e$.
adamc@551	2098
adamc@551	2099 $$\begin{array}{rrcll}
adamc@551	2100 \textrm{XML fragments} & L &::=& \texttt{<xml/>} \mid \texttt{<xml>}l^*\texttt{</xml>} \\
adamc@551	2101 \textrm{XML pieces} & l &::=& \textrm{text} & \textrm{cdata} \\
adamc@551	2102 &&& \texttt{<}g\texttt{/>} & \textrm{tag with no children} \\
adamc@551	2103 &&& \texttt{<}g\texttt{>}l^*\texttt{</}x\texttt{>} & \textrm{tag with children} \\
adamc@559	2104 &&& \{e\} & \textrm{computed XML fragment} \\
adamc@559	2105 &&& \{[e]\} & \textrm{injection of an Ur expression, via the $\mt{Top}.\mt{txt}$ function} \\
adamc@551	2106 \textrm{Tag} & g &::=& h \; (x = v)^* \\
adamc@551	2107 \textrm{Tag head} & h &::=& x & \textrm{tag name} \\
adamc@551	2108 &&& h\{c\} & \textrm{constructor parameter} \\
adamc@551	2109 \textrm{Attribute value} & v &::=& \ell & \textrm{literal value} \\
adamc@551	2110 &&& \{e\} & \textrm{computed value} \\
adamc@551	2111 \end{array}$$
adamc@551	2112
adamc@552	2113
adamc@1198	2114 \section{\label{structure}The Structure of Web Applications}
adamc@553	2115
adamc@1127	2116 A web application is built from a series of modules, with one module, the last one appearing in the \texttt{.urp} file, designated as the main module. The signature of the main module determines the URL entry points to the application. Such an entry point should have type $\mt{t1} \to \ldots \to \mt{tn} \to \mt{transaction} \; \mt{page}$, for any integer $n \geq 0$, where $\mt{page}$ is a type synonym for top-level HTML pages, defined in $\mt{Basis}$. If such a function is at the top level of main module $M$, with $n = 0$, it will be accessible at URI \texttt{/M/f}, and so on for more deeply-nested functions, as described in Section \ref{tag} below. Arguments to an entry-point function are deserialized from the part of the URI following \texttt{f}.
adamc@553	2117
adam@1347	2118 Normal links are accessible via HTTP \texttt{GET}, which the relevant standard says should never cause side effects. To export a page which may cause side effects, accessible only via HTTP \texttt{POST}, include one argument of the page handler of type $\mt{Basis.postBody}$. When the handler is called, this argument will receive a value that can be deconstructed into a MIME type (with $\mt{Basis.postType}$) and payload (with $\mt{Basis.postData}$). This kind of handler will only work with \texttt{POST} payloads of MIME types besides those associated with HTML forms; for these, use Ur/Web's built-in support, as described below.
adam@1347	2119
adam@1370	2120 Any normal page handler may also include arguments of type $\mt{option \; Basis.queryString}$, which will be handled specially. Rather than being deserialized from the current URI, such an argument is passed the whole query string that the handler received. The string may be analyzed by calling $\mt{Basis.show}$ on it. A handler of this kind may be passed as an argument to $\mt{Basis.effectfulUrl}$ to generate a URL to a page that may be used as a ``callback'' by an external service, such that the handler is allowed to cause side effects.
adam@1370	2121
adamc@553	2122 When the standalone web server receives a request for a known page, it calls the function for that page, ``running'' the resulting transaction to produce the page to return to the client. Pages link to other pages with the \texttt{link} attribute of the \texttt{a} HTML tag. A link has type $\mt{transaction} \; \mt{page}$, and the semantics of a link are that this transaction should be run to compute the result page, when the link is followed. Link targets are assigned URL names in the same way as top-level entry points.
adamc@553	2123
adamc@553	2124 HTML forms are handled in a similar way. The $\mt{action}$ attribute of a $\mt{submit}$ form tag takes a value of type $\$\mt{use} \to \mt{transaction} \; \mt{page}$, where $\mt{use}$ is a kind-$\{\mt{Type}\}$ record of the form fields used by this action handler. Action handlers are assigned URL patterns in the same way as above.
adamc@553	2125
adamc@558	2126 For both links and actions, direct arguments and local variables mentioned implicitly via closures are automatically included in serialized form in URLs, in the order in which they appear in the source code.
adamc@553	2127
adamc@660	2128 Ur/Web programs generally mix server- and client-side code in a fairly transparent way. The one important restriction is that mixed client-server code must encapsulate all server-side pieces within named functions. This is because execution of such pieces will be implemented by explicit calls to the remote web server, and it is useful to get the programmer's help in designing the interface to be used. For example, this makes it easier to allow a client running an old version of an application to continue interacting with a server that has been upgraded to a new version, if the programmer took care to keep the interfaces of all of the old remote calls the same. The functions implementing these services are assigned names in the same way as normal web entry points, by using module structure.
adamc@660	2129
adamc@789	2130 \medskip
adamc@789	2131
adam@1347	2132 The HTTP standard suggests that GET requests only be used in ways that generate no side effects. Side effecting operations should use POST requests instead. The Ur/Web compiler enforces this rule strictly, via a simple conservative program analysis. Any page that may have a side effect must be accessed through a form, all of which use POST requests, or via a direct call to a page handler with some argument of type $\mt{Basis.postBody}$. A page is judged to have a side effect if its code depends syntactically on any of the side-effecting, server-side FFI functions. Links, forms, and most client-side event handlers are not followed during this syntactic traversal, but \texttt{<body onload=\{...\}>} handlers \emph{are} examined, since they run right away and could just as well be considered parts of main page handlers.
adamc@789	2133
adamc@789	2134 Ur/Web includes a kind of automatic protection against cross site request forgery attacks. Whenever any page execution can have side effects and can also read at least one cookie value, all cookie values must be signed cryptographically, to ensure that the user has come to the current page by submitting a form on a real page generated by the proper server. Signing and signature checking are inserted automatically by the compiler. This prevents attacks like phishing schemes where users are directed to counterfeit pages with forms that submit to your application, where a user's cookies might be submitted without his knowledge, causing some undesired side effect.
adamc@789	2135
adam@1348	2136 \subsection{Tasks}
adam@1348	2137
adam@1348	2138 In many web applications, it's useful to run code at points other than requests from browsers. Ur/Web's \emph{task} mechanism facilitates this. A type family of \emph{task kinds} is in the standard library:
adam@1348	2139
adam@1348	2140 $$\begin{array}{l}
adam@1348	2141 \mt{con} \; \mt{task\_kind} :: \mt{Type} \to \mt{Type} \\
adam@1348	2142 \mt{val} \; \mt{initialize} : \mt{task\_kind} \; \mt{unit} \\
adam@1349	2143 \mt{val} \; \mt{clientLeaves} : \mt{task\_kind} \; \mt{client} \\
adam@1349	2144 \mt{val} \; \mt{periodic} : \mt{int} \to \mt{task\_kind} \; \mt{unit}
adam@1348	2145 \end{array}$$
adam@1348	2146
adam@1348	2147 A task kind names a particular extension point of generated applications, where the type parameter of a task kind describes which extra input data is available at that extension point. Add task code with the special declaration form $\mt{task} \; e_1 = e_2$, where $e_1$ is a task kind with data $\tau$, and $e_2$ is a function from $\tau$ to $\mt{transaction} \; \mt{unit}$.
adam@1348	2148
adam@1348	2149 The currently supported task kinds are:
adam@1348	2150 \begin{itemize}
adam@1349	2151 \item $\mt{initialize}$: Code that is run when the application starts up.
adam@1348	2152 \item $\mt{clientLeaves}$: Code that is run for each client that the runtime system decides has surfed away. When a request that generates a new client handle is aborted, that handle will still eventually be passed to $\mt{clientLeaves}$ task code, even though the corresponding browser was never informed of the client handle's existence. In other words, in general, $\mt{clientLeaves}$ handlers will be called more times than there are actual clients.
adam@1349	2153 \item $\mt{periodic} \; n$: Code that is run when the application starts up and then every $n$ seconds thereafter.
adam@1348	2154 \end{itemize}
adam@1348	2155
adamc@553	2156
adamc@897	2157 \section{The Foreign Function Interface}
adamc@897	2158
adamc@897	2159 It is possible to call your own C and JavaScript code from Ur/Web applications, via the foreign function interface (FFI). The starting point for a new binding is a \texttt{.urs} signature file that presents your external library as a single Ur/Web module (with no nested modules). Compilation conventions map the types and values that you use into C and/or JavaScript types and values.
adamc@897	2160
adamc@897	2161 It is most convenient to encapsulate an FFI binding with a new \texttt{.urp} file, which applications can include with the \texttt{library} directive in their own \texttt{.urp} files. A number of directives are likely to show up in the library's project file.
adamc@897	2162
adamc@897	2163 \begin{itemize}
adamc@897	2164 \item \texttt{clientOnly Module.ident} registers a value as being allowed only in client-side code.
adamc@897	2165 \item \texttt{clientToServer Module.ident} declares a type as OK to marshal between clients and servers. By default, abstract FFI types are not allowed to be marshalled, since your library might be maintaining invariants that the simple serialization code doesn't check.
adamc@897	2166 \item \texttt{effectful Module.ident} registers a function that can have side effects. It is important to remember to use this directive for each such function, or else the optimizer might change program semantics.
adamc@897	2167 \item \texttt{ffi FILE.urs} names the file giving your library's signature. You can include multiple such files in a single \texttt{.urp} file, and each file \texttt{mod.urp} defines an FFI module \texttt{Mod}.
adamc@1099	2168 \item \texttt{include FILE} requests inclusion of a C header file.
adamc@897	2169 \item \texttt{jsFunc Module.ident=name} gives a mapping from an Ur name for a value to a JavaScript name.
adamc@897	2170 \item \texttt{link FILE} requests that \texttt{FILE} be linked into applications. It should be a C object or library archive file, and you are responsible for generating it with your own build process.
adamc@897	2171 \item \texttt{script URL} requests inclusion of a JavaScript source file within application HTML.
adamc@897	2172 \item \texttt{serverOnly Module.ident} registers a value as being allowed only in server-side code.
adamc@897	2173 \end{itemize}
adamc@897	2174
adamc@897	2175 \subsection{Writing C FFI Code}
adamc@897	2176
adamc@897	2177 A server-side FFI type or value \texttt{Module.ident} must have a corresponding type or value definition \texttt{uw\_Module\_ident} in C code. With the current Ur/Web version, it's not generally possible to work with Ur records or complex datatypes in C code, but most other kinds of types are fair game.
adamc@897	2178
adamc@897	2179 \begin{itemize}
adamc@897	2180 \item Primitive types defined in \texttt{Basis} are themselves using the standard FFI interface, so you may refer to them like \texttt{uw\_Basis\_t}. See \texttt{include/types.h} for their definitions.
adamc@897	2181 \item Enumeration datatypes, which have only constructors that take no arguments, should be defined using C \texttt{enum}s. The type is named as for any other type identifier, and each constructor \texttt{c} gets an enumeration constant named \texttt{uw\_Module\_c}.
adamc@897	2182 \item A datatype \texttt{dt} (such as \texttt{Basis.option}) that has one non-value-carrying constructor \texttt{NC} and one value-carrying constructor \texttt{C} gets special treatment. Where \texttt{T} is the type of \texttt{C}'s argument, and where we represent \texttt{T} as \texttt{t} in C, we represent \texttt{NC} with \texttt{NULL}. The representation of \texttt{C} depends on whether we're sure that we don't need to use \texttt{NULL} to represent \texttt{t} values; this condition holds only for strings and complex datatypes. For such types, \texttt{C v} is represented with the C encoding of \texttt{v}, such that the translation of \texttt{dt} is \texttt{t}. For other types, \texttt{C v} is represented with a pointer to the C encoding of v, such that the translation of \texttt{dt} is \texttt{t*}.
adamc@897	2183 \end{itemize}
adamc@897	2184
adamc@897	2185 The C FFI version of a Ur function with type \texttt{T1 -> ... -> TN -> R} or \texttt{T1 -> ... -> TN -> transaction R} has a C prototype like \texttt{R uw\_Module\_ident(uw\_context, T1, ..., TN)}. Only functions with types of the second form may have side effects. \texttt{uw\_context} is the type of state that persists across handling a client request. Many functions that operate on contexts are prototyped in \texttt{include/urweb.h}. Most should only be used internally by the compiler. A few are useful in general FFI implementation:
adamc@897	2186 \begin{itemize}
adamc@897	2187 \item \begin{verbatim}
adamc@897	2188 void uw_error(uw_context, failure_kind, const char *fmt, ...);
adamc@897	2189 \end{verbatim}
adamc@897	2190 Abort the current request processing, giving a \texttt{printf}-style format string and arguments for generating an error message. The \texttt{failure\_kind} argument can be \texttt{FATAL}, to abort the whole execution; \texttt{BOUNDED\_RETRY}, to try processing the request again from the beginning, but failing if this happens too many times; or \texttt{UNLIMITED\_RETRY}, to repeat processing, with no cap on how many times this can recur.
adamc@897	2191
adam@1329	2192 All pointers to the context-local heap (see description below of \texttt{uw\_malloc()}) become invalid at the start and end of any execution of a main entry point function of an application. For example, if the request handler is restarted because of a \texttt{uw\_error()} call with \texttt{BOUNDED\_RETRY} or for any other reason, it is unsafe to access any local heap pointers that may have been stashed somewhere beforehand.
adam@1329	2193
adamc@897	2194 \item \begin{verbatim}
adam@1469	2195 void uw_set_error_message(uw_context, const char *fmt, ...);
adam@1469	2196 \end{verbatim}
adam@1469	2197 This simpler form of \texttt{uw\_error()} saves an error message without immediately aborting execution.
adam@1469	2198
adam@1469	2199 \item \begin{verbatim}
adamc@897	2200 void uw_push_cleanup(uw_context, void (func)(void ), void *arg);
adamc@897	2201 void uw_pop_cleanup(uw_context);
adamc@897	2202 \end{verbatim}
adam@1329	2203 Manipulate a stack of actions that should be taken if any kind of error condition arises. Calling the ``pop'' function both removes an action from the stack and executes it. It is a bug to let a page request handler finish successfully with unpopped cleanup actions.
adam@1329	2204
adam@1329	2205 Pending cleanup actions aren't intended to have any complex relationship amongst themselves, so, upon request handler abort, pending actions are executed in first-in-first-out order.
adamc@897	2206
adamc@897	2207 \item \begin{verbatim}
adamc@897	2208 void *uw_malloc(uw_context, size_t);
adamc@897	2209 \end{verbatim}
adam@1329	2210 A version of \texttt{malloc()} that allocates memory inside a context's heap, which is managed with region allocation. Thus, there is no \texttt{uw\_free()}, but you need to be careful not to keep ad-hoc C pointers to this area of memory. In general, \texttt{uw\_malloc()}ed memory should only be used in ways compatible with the computation model of pure Ur. This means it is fine to allocate and return a value that could just as well have been built with core Ur code. In contrast, it is almost never safe to store \texttt{uw\_malloc()}ed pointers in global variables, including when the storage happens implicitly by registering a callback that would take the pointer as an argument.
adam@1329	2211
adam@1329	2212 For performance and correctness reasons, it is usually preferable to use \texttt{uw\_malloc()} instead of \texttt{malloc()}. The former manipulates a local heap that can be kept allocated across page requests, while the latter uses global data structures that may face contention during concurrent execution. However, we emphasize again that \texttt{uw\_malloc()} should never be used to implement some logic that couldn't be implemented trivially by a constant-valued expression in Ur.
adamc@897	2213
adamc@897	2214 \item \begin{verbatim}
adamc@897	2215 typedef void (uw_callback)(void );
adam@1328	2216 typedef void (uw_callback_with_retry)(void , int will_retry);
adamc@897	2217 void uw_register_transactional(uw_context, void *data, uw_callback commit,
adam@1328	2218 uw_callback rollback, uw_callback_with_retry free);
adamc@897	2219 \end{verbatim}
adam@1328	2220 All side effects in Ur/Web programs need to be compatible with transactions, such that any set of actions can be undone at any time. Thus, you should not perform actions with non-local side effects directly; instead, register handlers to be called when the current transaction is committed or rolled back. The arguments here give an arbitary piece of data to be passed to callbacks, a function to call on commit, a function to call on rollback, and a function to call afterward in either case to clean up any allocated resources. A rollback handler may be called after the associated commit handler has already been called, if some later part of the commit process fails. A free handler is told whether the runtime system expects to retry the current page request after rollback finishes.
adamc@897	2221
adamc@1085	2222 Any of the callbacks may be \texttt{NULL}. To accommodate some stubbornly non-transactional real-world actions like sending an e-mail message, Ur/Web treats \texttt{NULL} \texttt{rollback} callbacks specially. When a transaction commits, all \texttt{commit} actions that have non-\texttt{NULL} rollback actions are tried before any \texttt{commit} actions that have \texttt{NULL} rollback actions. Thus, if a single execution uses only one non-transactional action, and if that action never fails partway through its execution while still causing an observable side effect, then Ur/Web can maintain the transactional abstraction.
adamc@1085	2223
adam@1329	2224 When a request handler ends with multiple pending transactional actions, their handlers are run in a first-in-last-out stack-like order, wherever the order would otherwise be ambiguous.
adam@1329	2225
adam@1329	2226 It is not safe for any of these handlers to access a context-local heap through a pointer returned previously by \texttt{uw\_malloc()}, nor should any new calls to that function be made. Think of the context-local heap as meant for use by the Ur/Web code itself, while transactional handlers execute after the Ur/Web code has finished.
adam@1329	2227
adam@1469	2228 A handler may signal an error by calling \texttt{uw\_set\_error\_message()}, but it is not safe to call \texttt{uw\_error()} from a handler. Signaling an error in a commit handler will cause the runtime system to switch to aborting the transaction, immediately after the current commit handler returns.
adam@1469	2229
adamc@1085	2230 \item \begin{verbatim}
adamc@1085	2231 void uw_get_global(uw_context, char name);
adamc@1085	2232 void uw_set_global(uw_context, char name, void data, uw_callback free);
adamc@1085	2233 \end{verbatim}
adam@1329	2234 Different FFI-based extensions may want to associate their own pieces of data with contexts. The global interface provides a way of doing that, where each extension must come up with its own unique key. The \texttt{free} argument to \texttt{uw\_set\_global()} explains how to deallocate the saved data. It is never safe to store \texttt{uw\_malloc()}ed pointers in global variable slots.
adamc@1085	2235
adamc@897	2236 \end{itemize}
adamc@897	2237
adamc@897	2238 \subsection{Writing JavaScript FFI Code}
adamc@897	2239
adamc@897	2240 JavaScript is dynamically typed, so Ur/Web type definitions imply no JavaScript code. The JavaScript identifier for each FFI function is set with the \texttt{jsFunc} directive. Each identifier can be defined in any JavaScript file that you ask to include with the \texttt{script} directive.
adamc@897	2241
adamc@897	2242 In contrast to C FFI code, JavaScript FFI functions take no extra context argument. Their argument lists are as you would expect from their Ur types. Only functions whose ranges take the form \texttt{transaction T} should have side effects; the JavaScript ``return type'' of such a function is \texttt{T}. Here are the conventions for representing Ur values in JavaScript.
adamc@897	2243
adamc@897	2244 \begin{itemize}
adamc@897	2245 \item Integers, floats, strings, characters, and booleans are represented in the usual JavaScript way.
adamc@985	2246 \item Ur functions are represented in an unspecified way. This means that you should not rely on any details of function representation. Named FFI functions are represented as JavaScript functions with as many arguments as their Ur types specify. To call a non-FFI function \texttt{f} on argument \texttt{x}, run \texttt{execF(f, x)}.
adamc@897	2247 \item An Ur record is represented with a JavaScript record, where Ur field name \texttt{N} translates to JavaScript field name \texttt{\_N}. An exception to this rule is that the empty record is encoded as \texttt{null}.
adamc@897	2248 \item \texttt{option}-like types receive special handling similar to their handling in C. The ``\texttt{None}'' constructor is \texttt{null}, and a use of the ``\texttt{Some}'' constructor on a value \texttt{v} is either \texttt{v}, if the underlying type doesn't need to use \texttt{null}; or \texttt{\{v:v\}} otherwise.
adamc@985	2249 \item Any other datatypes represent a non-value-carrying constructor \texttt{C} as \texttt{"C"} and an application of a constructor \texttt{C} to value \texttt{v} as \texttt{\{n:"C", v:v\}}. This rule only applies to datatypes defined in FFI module signatures; the compiler is free to optimize the representations of other, non-\texttt{option}-like datatypes in arbitrary ways.
adamc@897	2250 \end{itemize}
adamc@897	2251
adamc@897	2252 It is possible to write JavaScript FFI code that interacts with the functional-reactive structure of a document, but this version of the manual doesn't cover the details.
adamc@897	2253
adamc@897	2254
adamc@552	2255 \section{Compiler Phases}
adamc@552	2256
adamc@552	2257 The Ur/Web compiler is unconventional in that it relies on a kind of \emph{heuristic compilation}. Not all valid programs will compile successfully. Informally, programs fail to compile when they are ``too higher order.'' Compiler phases do their best to eliminate different kinds of higher order-ness, but some programs just won't compile. This is a trade-off for producing very efficient executables. Compiled Ur/Web programs use native C representations and require no garbage collection.
adamc@552	2258
adamc@552	2259 In this section, we step through the main phases of compilation, noting what consequences each phase has for effective programming.
adamc@552	2260
adamc@552	2261 \subsection{Parse}
adamc@552	2262
adamc@552	2263 The compiler reads a \texttt{.urp} file, figures out which \texttt{.urs} and \texttt{.ur} files it references, and combines them all into what is conceptually a single sequence of declarations in the core language of Section \ref{core}.
adamc@552	2264
adamc@552	2265 \subsection{Elaborate}
adamc@552	2266
adamc@552	2267 This is where type inference takes place, translating programs into an explicit form with no more wildcards. This phase is the most likely source of compiler error messages.
adamc@552	2268
adam@1378	2269 Those crawling through the compiler source will also want to be aware of another compiler phase, Explify, that occurs immediately afterward. This phase just translates from an AST language that includes unification variables to a very similar language that doesn't; all variables should have been determined by the end of Elaborate, anyway. The new AST language also drops some features that are used only for static checking and that have no influence on runtime behavior, like disjointness constraints.
adam@1378	2270
adamc@552	2271 \subsection{Unnest}
adamc@552	2272
adamc@552	2273 Named local function definitions are moved to the top level, to avoid the need to generate closures.
adamc@552	2274
adamc@552	2275 \subsection{Corify}
adamc@552	2276
adamc@552	2277 Module system features are compiled away, through inlining of functor definitions at application sites. Afterward, most abstraction boundaries are broken, facilitating optimization.
adamc@552	2278
adamc@552	2279 \subsection{Especialize}
adamc@552	2280
adam@1356	2281 Functions are specialized to particular argument patterns. This is an important trick for avoiding the need to maintain any closures at runtime. Currently, specialization only happens for prefixes of a function's full list of parameters, so you may need to take care to put arguments of function types before other arguments. The optimizer will not be effective enough if you use arguments that mix functions and values that must be calculated at run-time. For instance, a tuple of a function and an integer counter would not lead to successful code generation; these should be split into separate arguments via currying.
adamc@552	2282
adamc@552	2283 \subsection{Untangle}
adamc@552	2284
adamc@552	2285 Remove unnecessary mutual recursion, splitting recursive groups into strongly-connected components.
adamc@552	2286
adamc@552	2287 \subsection{Shake}
adamc@552	2288
adamc@552	2289 Remove all definitions not needed to run the page handlers that are visible in the signature of the last module listed in the \texttt{.urp} file.
adamc@552	2290
adamc@661	2291 \subsection{Rpcify}
adamc@661	2292
adamc@661	2293 Pieces of code are determined to be client-side, server-side, neither, or both, by figuring out which standard library functions might be needed to execute them. Calls to server-side functions (e.g., $\mt{query}$) within mixed client-server code are identified and replaced with explicit remote calls. Some mixed functions may be converted to continuation-passing style to facilitate this transformation.
adamc@661	2294
adamc@661	2295 \subsection{Untangle, Shake}
adamc@661	2296
adamc@661	2297 Repeat these simplifications.
adamc@661	2298
adamc@553	2299 \subsection{\label{tag}Tag}
adamc@552	2300
adamc@552	2301 Assign a URL name to each link and form action. It is important that these links and actions are written as applications of named functions, because such names are used to generate URL patterns. A URL pattern has a name built from the full module path of the named function, followed by the function name, with all pieces separated by slashes. The path of a functor application is based on the name given to the result, rather than the path of the functor itself.
adamc@552	2302
adamc@552	2303 \subsection{Reduce}
adamc@552	2304
adamc@552	2305 Apply definitional equality rules to simplify the program as much as possible. This effectively includes inlining of every non-recursive definition.
adamc@552	2306
adamc@552	2307 \subsection{Unpoly}
adamc@552	2308
adamc@552	2309 This phase specializes polymorphic functions to the specific arguments passed to them in the program. If the program contains real polymorphic recursion, Unpoly will be insufficient to avoid later error messages about too much polymorphism.
adamc@552	2310
adamc@552	2311 \subsection{Specialize}
adamc@552	2312
adamc@558	2313 Replace uses of parameterized datatypes with versions specialized to specific parameters. As for Unpoly, this phase will not be effective enough in the presence of polymorphic recursion or other fancy uses of impredicative polymorphism.
adamc@552	2314
adamc@552	2315 \subsection{Shake}
adamc@552	2316
adamc@558	2317 Here the compiler repeats the earlier Shake phase.
adamc@552	2318
adamc@552	2319 \subsection{Monoize}
adamc@552	2320
adamc@552	2321 Programs are translated to a new intermediate language without polymorphism or non-$\mt{Type}$ constructors. Error messages may pop up here if earlier phases failed to remove such features.
adamc@552	2322
adamc@552	2323 This is the stage at which concrete names are generated for cookies, tables, and sequences. They are named following the same convention as for links and actions, based on module path information saved from earlier stages. Table and sequence names separate path elements with underscores instead of slashes, and they are prefixed by \texttt{uw\_}.
adamc@664	2324
adamc@552	2325 \subsection{MonoOpt}
adamc@552	2326
adamc@552	2327 Simple algebraic laws are applied to simplify the program, focusing especially on efficient imperative generation of HTML pages.
adamc@552	2328
adamc@552	2329 \subsection{MonoUntangle}
adamc@552	2330
adamc@552	2331 Unnecessary mutual recursion is broken up again.
adamc@552	2332
adamc@552	2333 \subsection{MonoReduce}
adamc@552	2334
adamc@552	2335 Equivalents of the definitional equality rules are applied to simplify programs, with inlining again playing a major role.
adamc@552	2336
adamc@552	2337 \subsection{MonoShake, MonoOpt}
adamc@552	2338
adamc@552	2339 Unneeded declarations are removed, and basic optimizations are repeated.
adamc@552	2340
adamc@552	2341 \subsection{Fuse}
adamc@552	2342
adamc@552	2343 The compiler tries to simplify calls to recursive functions whose results are immediately written as page output. The write action is pushed inside the function definitions to avoid allocation of intermediate results.
adamc@552	2344
adamc@552	2345 \subsection{MonoUntangle, MonoShake}
adamc@552	2346
adamc@552	2347 Fuse often creates more opportunities to remove spurious mutual recursion.
adamc@552	2348
adamc@552	2349 \subsection{Pathcheck}
adamc@552	2350
adamc@552	2351 The compiler checks that no link or action name has been used more than once.
adamc@552	2352
adamc@552	2353 \subsection{Cjrize}
adamc@552	2354
adamc@552	2355 The program is translated to what is more or less a subset of C. If any use of functions as data remains at this point, the compiler will complain.
adamc@552	2356
adamc@552	2357 \subsection{C Compilation and Linking}
adamc@552	2358
adamc@552	2359 The output of the last phase is pretty-printed as C source code and passed to GCC.
adamc@552	2360
adamc@552	2361
adamc@524	2362 \end{document}

Mercurial > urweb

annotate doc/manual.tex @ 1472:18d18a70821e