Ur/Web: doc/manual.tex annotate

annotate doc/manual.tex @ 1362:fd34210bc3e5

Add an extra Especialize pass before Rpcify

author	Adam Chlipala <adam@chlipala.net>
date	Fri, 24 Dec 2010 12:51:46 -0500
parents	32c8a3509369
children	b2bc8bcd546f

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
adamc@896	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 mhash 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}
adamc@896	61 apt-get install mlton libmhash-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}
adamc@896	79 apt-get install postgresql-8.3 mysql-server-5.0
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
adamc@555	88 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	89
adamc@555	90 \begin{verbatim}
adamc@555	91 GCCARGS=-fnested-functions ./configure
adamc@555	92 \end{verbatim}
adamc@555	93
adamc@1137	94 Some Mac OS X users have reported needing to use this particular GCCARGS value.
adamc@1137	95
adamc@1161	96 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). One OS X user reported needing to run \texttt{./configure} with \texttt{CFLAGS=-I/opt/local/include}, since this directory wound up holding a header file associated with a \texttt{libmhash} package installed via DarwinPorts. Further, to get libpq to link, another 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	97
adamc@555	98 The Emacs mode can be set to autoload by adding the following to your \texttt{.emacs} file.
adamc@555	99
adamc@555	100 \begin{verbatim}
adamc@555	101 (add-to-list 'load-path "/usr/local/share/emacs/site-lisp/urweb-mode")
adamc@555	102 (load "urweb-mode-startup")
adamc@555	103 \end{verbatim}
adamc@555	104
adamc@555	105 Change the path in the first line if you chose a different Emacs installation path during configuration.
adamc@555	106
adamc@555	107
adamc@556	108 \section{Command-Line Compiler}
adamc@556	109
adamc@556	110 \subsection{Project Files}
adamc@556	111
adamc@556	112 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	113
adamc@556	114 \begin{verbatim}
adamc@556	115 database dbname=test
adamc@556	116 sql crud1.sql
adamc@556	117
adamc@556	118 crud
adamc@556	119 crud1
adamc@556	120 \end{verbatim}
adamc@556	121
adamc@556	122 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	123
adamc@556	124 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	125
adamc@556	126 \begin{verbatim}
adamc@556	127 createdb test
adamc@556	128 psql -f crud1.sql test
adamc@556	129 \end{verbatim}
adamc@556	130
adam@1331	131 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	132
adamc@556	133 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	134
adamc@783	135 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	136 \begin{itemize}
adamc@783	137 \item \texttt{[allow\|deny] [url\|mime] PATTERN} registers a rule governing which URLs or MIME types are allowed in this application. The first such rule to match a URL or MIME type determines the verdict. If \texttt{PATTERN} ends in \texttt{*}, it is interpreted as a prefix rule. Otherwise, a string must match it exactly.
adamc@1171	138 \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 has only session-local side effects.
adamc@783	139 \item \texttt{clientOnly Module.ident} registers an FFI function or transaction that may only be run in client browsers.
adamc@783	140 \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	141 \item \texttt{database DBSTRING} sets the string to pass to libpq to open a database connection.
adamc@783	142 \item \texttt{debug} saves some intermediate C files, which is mostly useful to help in debugging the compiler itself.
adamc@783	143 \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	144 \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	145 \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	146 \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	147 \item \texttt{jsFunc Module.ident=name} gives the JavaScript name of an FFI value.
adamc@1089	148 \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	149 \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	150 \begin{itemize}
adam@1309	151 \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	152 \item \texttt{database}: maximum size of database files (currently only used by SQLite)
adam@1309	153 \item \texttt{deltas}: maximum number of messages sendable in a single request handler with \texttt{Basis.send}
adam@1309	154 \item \texttt{globals}: maximum number of global variables that FFI libraries may set in a single request context
adam@1309	155 \item \texttt{headers}: maximum size (in bytes) of per-request buffer used to hold HTTP headers for generated pages
adam@1309	156 \item \texttt{heap}: maximum size (in bytes) of per-request heap for dynamically-allocated data
adam@1309	157 \item \texttt{inputs}: maximum number of top-level form fields per request
adam@1309	158 \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	159 \item \texttt{page}: maximum size (in bytes) of per-request buffer used to hold HTML content of generated pages
adam@1309	160 \item \texttt{script}: maximum size (in bytes) of per-request buffer used to hold JavaScript content of generated pages
adam@1309	161 \item \texttt{subinputs}: maximum number of form fields per request, excluding top-level fields
adam@1309	162 \item \texttt{time}: maximum running time of a single page request, in units of approximately 0.1 seconds
adam@1309	163 \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	164 \end{itemize}
adamc@783	165 \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	166 \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	167 \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	168 \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	169 \item \texttt{prefix PREFIX} sets the prefix included before every URI within the generated application. The default is \texttt{/}.
adamc@783	170 \item \texttt{profile} generates an executable that may be used with gprof.
adam@1300	171 \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	172 \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	173 \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	174 \item \texttt{serverOnly Module.ident} registers an FFI function or transaction that may only be run on the server.
adamc@1164	175 \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	176 \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	177 \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	178 \end{itemize}
adamc@701	179
adamc@701	180
adamc@557	181 \subsection{Building an Application}
adamc@557	182
adamc@557	183 To compile project \texttt{P.urp}, simply run
adamc@557	184 \begin{verbatim}
adamc@557	185 urweb P
adamc@557	186 \end{verbatim}
adamc@1198	187 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	188
adamc@557	189 To time how long the different compiler phases run, without generating an executable, run
adamc@557	190 \begin{verbatim}
adamc@557	191 urweb -timing P
adamc@557	192 \end{verbatim}
adamc@557	193
adamc@1086	194 To stop the compilation process after type-checking, run
adamc@1086	195 \begin{verbatim}
adamc@1086	196 urweb -tc P
adamc@1086	197 \end{verbatim}
adamc@1086	198
adamc@1170	199 To output information relevant to CSS stylesheets (and not finish regular compilation), run
adamc@1170	200 \begin{verbatim}
adamc@1170	201 urweb -css P
adamc@1170	202 \end{verbatim}
adamc@1170	203 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	204
adamc@896	205 Some other command-line parameters are accepted:
adamc@896	206 \begin{itemize}
adamc@896	207 \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	208
adamc@896	209 \item \texttt{-dbms [postgres\|mysql\|sqlite]}: Sets the database backend to use.
adamc@896	210 \begin{itemize}
adamc@896	211 \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	212
adamc@896	213 A command sequence like this can initialize a Postgres database, using a file \texttt{app.sql} generated by the compiler:
adamc@896	214 \begin{verbatim}
adamc@896	215 createdb app
adamc@896	216 psql -f app.sql app
adamc@896	217 \end{verbatim}
adamc@896	218
adamc@896	219 \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	220
adamc@896	221 A command sequence like this can initialize a MySQL database:
adamc@896	222 \begin{verbatim}
adamc@896	223 echo "CREATE DATABASE app" \| mysql
adamc@896	224 mysql -D app <app.sql
adamc@896	225 \end{verbatim}
adamc@896	226
adamc@896	227 \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	228
adamc@896	229 A command like this can initialize an SQLite database:
adamc@896	230 \begin{verbatim}
adamc@896	231 sqlite3 path/to/database/file <app.sql
adamc@896	232 \end{verbatim}
adamc@896	233 \end{itemize}
adamc@896	234
adam@1309	235 \item \texttt{-limit class num}: Equivalent to the \texttt{limit} directive from \texttt{.urp} files
adam@1309	236
adamc@896	237 \item \texttt{-output FILENAME}: Set where the application executable is written.
adamc@896	238
adamc@1127	239 \item \texttt{-path NAME VALUE}: Set the value of path variable \texttt{\$NAME} to \texttt{VALUE}, for use in \texttt{.urp} files.
adamc@1127	240
adam@1335	241 \item \texttt{-prefix PREFIX}: Equivalent to the \texttt{prefix} directive from \texttt{.urp} files
adam@1335	242
adamc@896	243 \item \texttt{-protocol [http\|cgi\|fastcgi]}: Set the protocol that the generated application speaks.
adamc@896	244 \begin{itemize}
adamc@896	245 \item \texttt{http}: This is the default. It is for building standalone web servers that can be accessed by web browsers directly.
adamc@896	246
adamc@896	247 \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	248
adamc@896	249 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	250 \begin{verbatim}
adamc@896	251 ScriptAlias /Hello /path/to/hello.exe
adamc@896	252 \end{verbatim}
adamc@896	253
adamc@1163	254 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	255 \begin{verbatim}
adamc@1163	256 Options +ExecCGI
adamc@1163	257 AddHandler cgi-script .exe
adamc@1163	258 \end{verbatim}
adamc@1163	259
adamc@1163	260 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	261 \begin{verbatim}
adamc@1163	262 prefix /dir/script.exe/
adamc@1163	263 \end{verbatim}
adamc@1163	264
adamc@1163	265 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	266
adamc@1164	267 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	268
adamc@896	269 \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	270
adamc@896	271 To configure a FastCGI program with Apache, one could combine the above \texttt{ScriptAlias} line with a line like this:
adamc@896	272 \begin{verbatim}
adamc@896	273 FastCgiServer /path/to/hello.exe -idle-timeout 99999
adamc@896	274 \end{verbatim}
adamc@896	275 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	276
adamc@896	277 Here is some lighttpd configuration for the same application.
adamc@896	278 \begin{verbatim}
adamc@896	279 fastcgi.server = (
adamc@896	280 "/Hello/" =>
adamc@896	281 (( "bin-path" => "/path/to/hello.exe",
adamc@896	282 "socket" => "/tmp/hello",
adamc@896	283 "check-local" => "disable",
adamc@896	284 "docroot" => "/",
adamc@896	285 "max-procs" => "1"
adamc@896	286 ))
adamc@896	287 )
adamc@896	288 \end{verbatim}
adamc@896	289 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	290
adamc@896	291 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	292 \end{itemize}
adamc@896	293
adamc@1127	294 \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	295
adamc@1164	296 \item \texttt{-sigfile PATH}: Same as the \texttt{sigfile} directive in \texttt{.urp} files
adamc@1164	297
adamc@896	298 \item \texttt{-sql FILENAME}: Set where a database set-up SQL script is written.
adamc@1095	299
adamc@1095	300 \item \texttt{-static}: Link the runtime system statically. The default is to link against dynamic libraries.
adamc@896	301 \end{itemize}
adamc@896	302
adam@1297	303 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	304
adamc@529	305 \section{Ur Syntax}
adamc@529	306
adamc@784	307 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	308
adamc@524	309 \subsection{Lexical Conventions}
adamc@524	310
adamc@524	311 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	312
adamc@524	313 \begin{center}
adamc@524	314 \begin{tabular}{rl}
adamc@524	315 \textbf{\LaTeX} & \textbf{ASCII} \\
adamc@524	316 $\to$ & \cd{->} \\
adamc@652	317 $\longrightarrow$ & \cd{-->} \\
adamc@524	318 $\times$ & \cd{*} \\
adamc@524	319 $\lambda$ & \cd{fn} \\
adamc@524	320 $\Rightarrow$ & \cd{=>} \\
adamc@652	321 $\Longrightarrow$ & \cd{==>} \\
adamc@529	322 $\neq$ & \cd{<>} \\
adamc@529	323 $\leq$ & \cd{<=} \\
adamc@529	324 $\geq$ & \cd{>=} \\
adamc@524	325 \\
adamc@524	326 $x$ & Normal textual identifier, not beginning with an uppercase letter \\
adamc@525	327 $X$ & Normal textual identifier, beginning with an uppercase letter \\
adamc@524	328 \end{tabular}
adamc@524	329 \end{center}
adamc@524	330
adamc@525	331 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	332
adamc@873	333 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	334
adamc@527	335 This version of the manual doesn't include operator precedences; see \texttt{src/urweb.grm} for that.
adamc@527	336
adam@1297	337 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	338
adamc@552	339 \subsection{\label{core}Core Syntax}
adamc@524	340
adamc@524	341 \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	342 $$\begin{array}{rrcll}
adamc@524	343 \textrm{Kinds} & \kappa &::=& \mt{Type} & \textrm{proper types} \\
adamc@525	344 &&& \mt{Unit} & \textrm{the trivial constructor} \\
adamc@525	345 &&& \mt{Name} & \textrm{field names} \\
adamc@525	346 &&& \kappa \to \kappa & \textrm{type-level functions} \\
adamc@525	347 &&& \{\kappa\} & \textrm{type-level records} \\
adamc@525	348 &&& (\kappa\times^+) & \textrm{type-level tuples} \\
adamc@652	349 &&& X & \textrm{variable} \\
adamc@652	350 &&& X \longrightarrow k & \textrm{kind-polymorphic type-level function} \\
adamc@529	351 &&& \_\_ & \textrm{wildcard} \\
adamc@525	352 &&& (\kappa) & \textrm{explicit precedence} \\
adamc@524	353 \end{array}$$
adamc@524	354
adamc@524	355 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	356 $$\begin{array}{rrcll}
adamc@524	357 \textrm{Explicitness} & ? &::=& :: & \textrm{explicit} \\
adamc@558	358 &&& ::: & \textrm{implicit}
adamc@524	359 \end{array}$$
adamc@524	360
adamc@524	361 \emph{Constructors} are the main class of compile-time-only data. They include proper types and are classified by kinds.
adamc@524	362 $$\begin{array}{rrcll}
adamc@524	363 \textrm{Constructors} & c, \tau &::=& (c) :: \kappa & \textrm{kind annotation} \\
adamc@530	364 &&& \hat{x} & \textrm{constructor variable} \\
adamc@524	365 \\
adamc@525	366 &&& \tau \to \tau & \textrm{function type} \\
adamc@525	367 &&& x \; ? \; \kappa \to \tau & \textrm{polymorphic function type} \\
adamc@652	368 &&& X \longrightarrow \tau & \textrm{kind-polymorphic function type} \\
adamc@525	369 &&& \$ c & \textrm{record type} \\
adamc@524	370 \\
adamc@525	371 &&& c \; c & \textrm{type-level function application} \\
adamc@530	372 &&& \lambda x \; :: \; \kappa \Rightarrow c & \textrm{type-level function abstraction} \\
adamc@524	373 \\
adamc@652	374 &&& X \Longrightarrow c & \textrm{type-level kind-polymorphic function abstraction} \\
adamc@655	375 &&& c [\kappa] & \textrm{type-level kind-polymorphic function application} \\
adamc@652	376 \\
adamc@525	377 &&& () & \textrm{type-level unit} \\
adamc@525	378 &&& \#X & \textrm{field name} \\
adamc@524	379 \\
adamc@525	380 &&& [(c = c)^*] & \textrm{known-length type-level record} \\
adamc@525	381 &&& c \rc c & \textrm{type-level record concatenation} \\
adamc@652	382 &&& \mt{map} & \textrm{type-level record map} \\
adamc@524	383 \\
adamc@558	384 &&& (c,^+) & \textrm{type-level tuple} \\
adamc@525	385 &&& c.n & \textrm{type-level tuple projection ($n \in \mathbb N^+$)} \\
adamc@524	386 \\
adamc@652	387 &&& [c \sim c] \Rightarrow \tau & \textrm{guarded type} \\
adamc@524	388 \\
adamc@529	389 &&& \_ :: \kappa & \textrm{wildcard} \\
adamc@525	390 &&& (c) & \textrm{explicit precedence} \\
adamc@530	391 \\
adamc@530	392 \textrm{Qualified uncapitalized variables} & \hat{x} &::=& x & \textrm{not from a module} \\
adamc@530	393 &&& M.x & \textrm{projection from a module} \\
adamc@525	394 \end{array}$$
adamc@525	395
adamc@655	396 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	397
adamc@525	398 Modules of the module system are described by \emph{signatures}.
adamc@525	399 $$\begin{array}{rrcll}
adamc@525	400 \textrm{Signatures} & S &::=& \mt{sig} \; s^* \; \mt{end} & \textrm{constant} \\
adamc@525	401 &&& X & \textrm{variable} \\
adamc@525	402 &&& \mt{functor}(X : S) : S & \textrm{functor} \\
adamc@529	403 &&& S \; \mt{where} \; \mt{con} \; x = c & \textrm{concretizing an abstract constructor} \\
adamc@525	404 &&& M.X & \textrm{projection from a module} \\
adamc@525	405 \\
adamc@525	406 \textrm{Signature items} & s &::=& \mt{con} \; x :: \kappa & \textrm{abstract constructor} \\
adamc@525	407 &&& \mt{con} \; x :: \kappa = c & \textrm{concrete constructor} \\
adamc@528	408 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529	409 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@525	410 &&& \mt{val} \; x : \tau & \textrm{value} \\
adamc@525	411 &&& \mt{structure} \; X : S & \textrm{sub-module} \\
adamc@525	412 &&& \mt{signature} \; X = S & \textrm{sub-signature} \\
adamc@525	413 &&& \mt{include} \; S & \textrm{signature inclusion} \\
adamc@525	414 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@654	415 &&& \mt{class} \; x :: \kappa & \textrm{abstract constructor class} \\
adamc@654	416 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@525	417 \\
adamc@525	418 \textrm{Datatype constructors} & dc &::=& X & \textrm{nullary constructor} \\
adamc@525	419 &&& X \; \mt{of} \; \tau & \textrm{unary constructor} \\
adamc@524	420 \end{array}$$
adamc@524	421
adamc@526	422 \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	423 $$\begin{array}{rrcll}
adamc@526	424 \textrm{Patterns} & p &::=& \_ & \textrm{wildcard} \\
adamc@526	425 &&& x & \textrm{variable} \\
adamc@526	426 &&& \ell & \textrm{constant} \\
adamc@526	427 &&& \hat{X} & \textrm{nullary constructor} \\
adamc@526	428 &&& \hat{X} \; p & \textrm{unary constructor} \\
adamc@526	429 &&& \{(x = p,)^*\} & \textrm{rigid record pattern} \\
adamc@526	430 &&& \{(x = p,)^+, \ldots\} & \textrm{flexible record pattern} \\
adamc@852	431 &&& p : \tau & \textrm{type annotation} \\
adamc@527	432 &&& (p) & \textrm{explicit precedence} \\
adamc@526	433 \\
adamc@529	434 \textrm{Qualified capitalized variables} & \hat{X} &::=& X & \textrm{not from a module} \\
adamc@526	435 &&& M.X & \textrm{projection from a module} \\
adamc@526	436 \end{array}$$
adamc@526	437
adamc@527	438 \emph{Expressions} are the main run-time entities, corresponding to both ``expressions'' and ``statements'' in mainstream imperative languages.
adamc@527	439 $$\begin{array}{rrcll}
adamc@527	440 \textrm{Expressions} & e &::=& e : \tau & \textrm{type annotation} \\
adamc@529	441 &&& \hat{x} & \textrm{variable} \\
adamc@529	442 &&& \hat{X} & \textrm{datatype constructor} \\
adamc@527	443 &&& \ell & \textrm{constant} \\
adamc@527	444 \\
adamc@527	445 &&& e \; e & \textrm{function application} \\
adamc@527	446 &&& \lambda x : \tau \Rightarrow e & \textrm{function abstraction} \\
adamc@527	447 &&& e [c] & \textrm{polymorphic function application} \\
adamc@852	448 &&& \lambda [x \; ? \; \kappa] \Rightarrow e & \textrm{polymorphic function abstraction} \\
adamc@655	449 &&& e [\kappa] & \textrm{kind-polymorphic function application} \\
adamc@652	450 &&& X \Longrightarrow e & \textrm{kind-polymorphic function abstraction} \\
adamc@527	451 \\
adamc@527	452 &&& \{(c = e,)^*\} & \textrm{known-length record} \\
adamc@527	453 &&& e.c & \textrm{record field projection} \\
adamc@527	454 &&& e \rc e & \textrm{record concatenation} \\
adamc@527	455 &&& e \rcut c & \textrm{removal of a single record field} \\
adamc@527	456 &&& e \rcutM c & \textrm{removal of multiple record fields} \\
adamc@527	457 \\
adamc@527	458 &&& \mt{let} \; ed^* \; \mt{in} \; e \; \mt{end} & \textrm{local definitions} \\
adamc@527	459 \\
adamc@527	460 &&& \mt{case} \; e \; \mt{of} \; (p \Rightarrow e\|)^+ & \textrm{pattern matching} \\
adamc@527	461 \\
adamc@654	462 &&& \lambda [c \sim c] \Rightarrow e & \textrm{guarded expression abstraction} \\
adamc@654	463 &&& e \; ! & \textrm{guarded expression application} \\
adamc@527	464 \\
adamc@527	465 &&& \_ & \textrm{wildcard} \\
adamc@527	466 &&& (e) & \textrm{explicit precedence} \\
adamc@527	467 \\
adamc@527	468 \textrm{Local declarations} & ed &::=& \cd{val} \; x : \tau = e & \textrm{non-recursive value} \\
adamc@527	469 &&& \cd{val} \; \cd{rec} \; (x : \tau = e \; \cd{and})^+ & \textrm{mutually-recursive values} \\
adamc@527	470 \end{array}$$
adamc@527	471
adamc@655	472 As with constructors, we include both abstraction and application for kind polymorphism, but applications are only inferred internally.
adamc@655	473
adamc@528	474 \emph{Declarations} primarily bring new symbols into context.
adamc@528	475 $$\begin{array}{rrcll}
adamc@528	476 \textrm{Declarations} & d &::=& \mt{con} \; x :: \kappa = c & \textrm{constructor synonym} \\
adamc@528	477 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529	478 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@528	479 &&& \mt{val} \; x : \tau = e & \textrm{value} \\
adamc@528	480 &&& \mt{val} \; \cd{rec} \; (x : \tau = e \; \mt{and})^+ & \textrm{mutually-recursive values} \\
adamc@528	481 &&& \mt{structure} \; X : S = M & \textrm{module definition} \\
adamc@528	482 &&& \mt{signature} \; X = S & \textrm{signature definition} \\
adamc@528	483 &&& \mt{open} \; M & \textrm{module inclusion} \\
adamc@528	484 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@528	485 &&& \mt{open} \; \mt{constraints} \; M & \textrm{inclusion of just the constraints from a module} \\
adamc@528	486 &&& \mt{table} \; x : c & \textrm{SQL table} \\
adamc@784	487 &&& \mt{view} \; x : c & \textrm{SQL view} \\
adamc@528	488 &&& \mt{sequence} \; x & \textrm{SQL sequence} \\
adamc@535	489 &&& \mt{cookie} \; x : \tau & \textrm{HTTP cookie} \\
adamc@784	490 &&& \mt{style} \; x : \tau & \textrm{CSS class} \\
adamc@654	491 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@1085	492 &&& \mt{task} \; e = e & \textrm{recurring task} \\
adamc@528	493 \\
adamc@529	494 \textrm{Modules} & M &::=& \mt{struct} \; d^* \; \mt{end} & \textrm{constant} \\
adamc@529	495 &&& X & \textrm{variable} \\
adamc@529	496 &&& M.X & \textrm{projection} \\
adamc@529	497 &&& M(M) & \textrm{functor application} \\
adamc@529	498 &&& \mt{functor}(X : S) : S = M & \textrm{functor abstraction} \\
adamc@528	499 \end{array}$$
adamc@528	500
adamc@528	501 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	502
adamc@784	503 We omit some extra possibilities in $\mt{table}$ syntax, deferring them to Section \ref{tables}.
adamc@784	504
adamc@529	505 \subsection{Shorthands}
adamc@529	506
adamc@529	507 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	508
adamc@529	509 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	510
adamc@529	511 A record type may be written $\{(c = c,)^\}$, which elaborates to $\$[(c = c,)^]$.
adamc@529	512
adamc@533	513 The notation $[c_1, \ldots, c_n]$ is shorthand for $[c_1 = (), \ldots, c_n = ()]$.
adamc@533	514
adam@1350	515 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	516
adamc@852	517 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	518
adam@1306	519 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	520
adamc@529	521 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	522
adamc@529	523 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	524
adamc@654	525 A signature item or declaration $\mt{class} \; x = \lambda y \Rightarrow c$ may be abbreviated $\mt{class} \; x \; y = c$.
adamc@529	526
adam@1354	527 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 non-local variable, or after any application of a non-local 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	528
adamc@852	529 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	530
adamc@852	531 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	532
adamc@852	533 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	534
adamc@529	535 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	536
adamc@852	537 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	538
adamc@853	539 A declaration $\mt{table} \; x : \{(c = c,)^\}$ is elaborated into $\mt{table} \; x : [(c = c,)^]$.
adamc@529	540
adamc@529	541 The syntax $\mt{where} \; \mt{type}$ is an alternate form of $\mt{where} \; \mt{con}$.
adamc@529	542
adamc@529	543 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	544
adamc@529	545 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	546
adamc@784	547 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	548
adamc@530	549
adamc@530	550 \section{Static Semantics}
adamc@530	551
adamc@530	552 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	553
adamc@530	554 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	555 \begin{itemize}
adamc@655	556 \item $\Gamma \vdash \kappa$ expresses kind well-formedness.
adamc@530	557 \item $\Gamma \vdash c :: \kappa$ assigns a kind to a constructor in a context.
adamc@530	558 \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	559 \item $\Gamma \vdash c \hookrightarrow C$ proves that record constructor $c$ decomposes into set $C$ of field names and record constructors.
adamc@530	560 \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	561 \item $\Gamma \vdash e : \tau$ is a standard typing judgment.
adamc@534	562 \item $\Gamma \vdash p \leadsto \Gamma; \tau$ combines typing of patterns with calculation of which new variables they bind.
adamc@537	563 \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	564 \item $\Gamma \vdash S \equiv S$ is the signature equivalence judgment.
adamc@536	565 \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	566 \item $\Gamma \vdash M : S$ is the module signature checking judgment.
adamc@537	567 \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	568 \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	569 \end{itemize}
adamc@530	570
adamc@655	571
adamc@655	572 \subsection{Kind Well-Formedness}
adamc@655	573
adamc@655	574 $$\infer{\Gamma \vdash \mt{Type}}{}
adamc@655	575 \quad \infer{\Gamma \vdash \mt{Unit}}{}
adamc@655	576 \quad \infer{\Gamma \vdash \mt{Name}}{}
adamc@655	577 \quad \infer{\Gamma \vdash \kappa_1 \to \kappa_2}{
adamc@655	578 \Gamma \vdash \kappa_1
adamc@655	579 & \Gamma \vdash \kappa_2
adamc@655	580 }
adamc@655	581 \quad \infer{\Gamma \vdash \{\kappa\}}{
adamc@655	582 \Gamma \vdash \kappa
adamc@655	583 }
adamc@655	584 \quad \infer{\Gamma \vdash (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@655	585 \forall i: \Gamma \vdash \kappa_i
adamc@655	586 }$$
adamc@655	587
adamc@655	588 $$\infer{\Gamma \vdash X}{
adamc@655	589 X \in \Gamma
adamc@655	590 }
adamc@655	591 \quad \infer{\Gamma \vdash X \longrightarrow \kappa}{
adamc@655	592 \Gamma, X \vdash \kappa
adamc@655	593 }$$
adamc@655	594
adamc@530	595 \subsection{Kinding}
adamc@530	596
adamc@655	597 We write $[X \mapsto \kappa_1]\kappa_2$ for capture-avoiding substitution of $\kappa_1$ for $X$ in $\kappa_2$.
adamc@655	598
adamc@530	599 $$\infer{\Gamma \vdash (c) :: \kappa :: \kappa}{
adamc@530	600 \Gamma \vdash c :: \kappa
adamc@530	601 }
adamc@530	602 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530	603 x :: \kappa \in \Gamma
adamc@530	604 }
adamc@530	605 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530	606 x :: \kappa = c \in \Gamma
adamc@530	607 }$$
adamc@530	608
adamc@530	609 $$\infer{\Gamma \vdash M.x :: \kappa}{
adamc@537	610 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	611 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = \kappa
adamc@530	612 }
adamc@530	613 \quad \infer{\Gamma \vdash M.x :: \kappa}{
adamc@537	614 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	615 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@530	616 }$$
adamc@530	617
adamc@530	618 $$\infer{\Gamma \vdash \tau_1 \to \tau_2 :: \mt{Type}}{
adamc@530	619 \Gamma \vdash \tau_1 :: \mt{Type}
adamc@530	620 & \Gamma \vdash \tau_2 :: \mt{Type}
adamc@530	621 }
adamc@530	622 \quad \infer{\Gamma \vdash x \; ? \: \kappa \to \tau :: \mt{Type}}{
adamc@530	623 \Gamma, x :: \kappa \vdash \tau :: \mt{Type}
adamc@530	624 }
adamc@655	625 \quad \infer{\Gamma \vdash X \longrightarrow \tau :: \mt{Type}}{
adamc@655	626 \Gamma, X \vdash \tau :: \mt{Type}
adamc@655	627 }
adamc@530	628 \quad \infer{\Gamma \vdash \$c :: \mt{Type}}{
adamc@530	629 \Gamma \vdash c :: \{\mt{Type}\}
adamc@530	630 }$$
adamc@530	631
adamc@530	632 $$\infer{\Gamma \vdash c_1 \; c_2 :: \kappa_2}{
adamc@530	633 \Gamma \vdash c_1 :: \kappa_1 \to \kappa_2
adamc@530	634 & \Gamma \vdash c_2 :: \kappa_1
adamc@530	635 }
adamc@530	636 \quad \infer{\Gamma \vdash \lambda x \; :: \; \kappa_1 \Rightarrow c :: \kappa_1 \to \kappa_2}{
adamc@530	637 \Gamma, x :: \kappa_1 \vdash c :: \kappa_2
adamc@530	638 }$$
adamc@530	639
adamc@655	640 $$\infer{\Gamma \vdash c[\kappa'] :: [X \mapsto \kappa']\kappa}{
adamc@655	641 \Gamma \vdash c :: X \to \kappa
adamc@655	642 & \Gamma \vdash \kappa'
adamc@655	643 }
adamc@655	644 \quad \infer{\Gamma \vdash X \Longrightarrow c :: X \to \kappa}{
adamc@655	645 \Gamma, X \vdash c :: \kappa
adamc@655	646 }$$
adamc@655	647
adamc@530	648 $$\infer{\Gamma \vdash () :: \mt{Unit}}{}
adamc@530	649 \quad \infer{\Gamma \vdash \#X :: \mt{Name}}{}$$
adamc@530	650
adamc@530	651 $$\infer{\Gamma \vdash [\overline{c_i = c'_i}] :: \{\kappa\}}{
adamc@530	652 \forall i: \Gamma \vdash c_i : \mt{Name}
adamc@530	653 & \Gamma \vdash c'_i :: \kappa
adamc@530	654 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@530	655 }
adamc@530	656 \quad \infer{\Gamma \vdash c_1 \rc c_2 :: \{\kappa\}}{
adamc@530	657 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530	658 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@530	659 & \Gamma \vdash c_1 \sim c_2
adamc@530	660 }$$
adamc@530	661
adamc@655	662 $$\infer{\Gamma \vdash \mt{map} :: (\kappa_1 \to \kappa_2) \to \{\kappa_1\} \to \{\kappa_2\}}{}$$
adamc@530	663
adamc@573	664 $$\infer{\Gamma \vdash (\overline c) :: (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@573	665 \forall i: \Gamma \vdash c_i :: \kappa_i
adamc@530	666 }
adamc@573	667 \quad \infer{\Gamma \vdash c.i :: \kappa_i}{
adamc@573	668 \Gamma \vdash c :: (\kappa_1 \times \ldots \times \kappa_n)
adamc@530	669 }$$
adamc@530	670
adamc@655	671 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow \tau :: \mt{Type}}{
adamc@655	672 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530	673 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@655	674 & \Gamma, c_1 \sim c_2 \vdash \tau :: \mt{Type}
adamc@530	675 }$$
adamc@530	676
adamc@531	677 \subsection{Record Disjointness}
adamc@531	678
adamc@531	679 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@558	680 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@558	681 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@558	682 & \forall c'_1 \in C_1, c'_2 \in C_2: \Gamma \vdash c'_1 \sim c'_2
adamc@531	683 }
adamc@531	684 \quad \infer{\Gamma \vdash X \sim X'}{
adamc@531	685 X \neq X'
adamc@531	686 }$$
adamc@531	687
adamc@531	688 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@531	689 c'_1 \sim c'_2 \in \Gamma
adamc@558	690 & \Gamma \vdash c'_1 \hookrightarrow C_1
adamc@558	691 & \Gamma \vdash c'_2 \hookrightarrow C_2
adamc@558	692 & c_1 \in C_1
adamc@558	693 & c_2 \in C_2
adamc@531	694 }$$
adamc@531	695
adamc@531	696 $$\infer{\Gamma \vdash c \hookrightarrow \{c\}}{}
adamc@531	697 \quad \infer{\Gamma \vdash [\overline{c = c'}] \hookrightarrow \{\overline{c}\}}{}
adamc@531	698 \quad \infer{\Gamma \vdash c_1 \rc c_2 \hookrightarrow C_1 \cup C_2}{
adamc@531	699 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@531	700 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@531	701 }
adamc@531	702 \quad \infer{\Gamma \vdash c \hookrightarrow C}{
adamc@531	703 \Gamma \vdash c \equiv c'
adamc@531	704 & \Gamma \vdash c' \hookrightarrow C
adamc@531	705 }
adamc@531	706 \quad \infer{\Gamma \vdash \mt{map} \; f \; c \hookrightarrow C}{
adamc@531	707 \Gamma \vdash c \hookrightarrow C
adamc@531	708 }$$
adamc@531	709
adamc@541	710 \subsection{\label{definitional}Definitional Equality}
adamc@532	711
adamc@655	712 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	713
adamc@532	714 $$\infer{\Gamma \vdash c \equiv c}{}
adamc@532	715 \quad \infer{\Gamma \vdash c_1 \equiv c_2}{
adamc@532	716 \Gamma \vdash c_2 \equiv c_1
adamc@532	717 }
adamc@532	718 \quad \infer{\Gamma \vdash c_1 \equiv c_3}{
adamc@532	719 \Gamma \vdash c_1 \equiv c_2
adamc@532	720 & \Gamma \vdash c_2 \equiv c_3
adamc@532	721 }
adamc@532	722 \quad \infer{\Gamma \vdash \mathcal C[c_1] \equiv \mathcal C[c_2]}{
adamc@532	723 \Gamma \vdash c_1 \equiv c_2
adamc@532	724 }$$
adamc@532	725
adamc@532	726 $$\infer{\Gamma \vdash x \equiv c}{
adamc@532	727 x :: \kappa = c \in \Gamma
adamc@532	728 }
adamc@532	729 \quad \infer{\Gamma \vdash M.x \equiv c}{
adamc@537	730 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	731 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@532	732 }
adamc@532	733 \quad \infer{\Gamma \vdash (\overline c).i \equiv c_i}{}$$
adamc@532	734
adamc@532	735 $$\infer{\Gamma \vdash (\lambda x :: \kappa \Rightarrow c) \; c' \equiv [x \mapsto c'] c}{}
adamc@655	736 \quad \infer{\Gamma \vdash (X \Longrightarrow c) [\kappa] \equiv [X \mapsto \kappa] c}{}$$
adamc@655	737
adamc@655	738 $$\infer{\Gamma \vdash c_1 \rc c_2 \equiv c_2 \rc c_1}{}
adamc@532	739 \quad \infer{\Gamma \vdash c_1 \rc (c_2 \rc c_3) \equiv (c_1 \rc c_2) \rc c_3}{}$$
adamc@532	740
adamc@532	741 $$\infer{\Gamma \vdash [] \rc c \equiv c}{}
adamc@532	742 \quad \infer{\Gamma \vdash [\overline{c_1 = c'_1}] \rc [\overline{c_2 = c'_2}] \equiv [\overline{c_1 = c'_1}, \overline{c_2 = c'_2}]}{}$$
adamc@532	743
adamc@655	744 $$\infer{\Gamma \vdash \mt{map} \; f \; [] \equiv []}{}
adamc@655	745 \quad \infer{\Gamma \vdash \mt{map} \; f \; ([c_1 = c_2] \rc c) \equiv [c_1 = f \; c_2] \rc \mt{map} \; f \; c}{}$$
adamc@532	746
adamc@532	747 $$\infer{\Gamma \vdash \mt{map} \; (\lambda x \Rightarrow x) \; c \equiv c}{}
adamc@655	748 \quad \infer{\Gamma \vdash \mt{map} \; f \; (\mt{map} \; f' \; c)
adamc@655	749 \equiv \mt{map} \; (\lambda x \Rightarrow f \; (f' \; x)) \; c}{}$$
adamc@532	750
adamc@532	751 $$\infer{\Gamma \vdash \mt{map} \; f \; (c_1 \rc c_2) \equiv \mt{map} \; f \; c_1 \rc \mt{map} \; f \; c_2}{}$$
adamc@531	752
adamc@534	753 \subsection{Expression Typing}
adamc@533	754
adamc@873	755 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	756
adamc@533	757 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	758
adamc@533	759 $$\infer{\Gamma \vdash e : \tau : \tau}{
adamc@533	760 \Gamma \vdash e : \tau
adamc@533	761 }
adamc@533	762 \quad \infer{\Gamma \vdash e : \tau}{
adamc@533	763 \Gamma \vdash e : \tau'
adamc@533	764 & \Gamma \vdash \tau' \equiv \tau
adamc@533	765 }
adamc@533	766 \quad \infer{\Gamma \vdash \ell : T(\ell)}{}$$
adamc@533	767
adamc@533	768 $$\infer{\Gamma \vdash x : \mathcal I(\tau)}{
adamc@533	769 x : \tau \in \Gamma
adamc@533	770 }
adamc@533	771 \quad \infer{\Gamma \vdash M.x : \mathcal I(\tau)}{
adamc@537	772 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	773 & \mt{proj}(M, \overline{s}, \mt{val} \; x) = \tau
adamc@533	774 }
adamc@533	775 \quad \infer{\Gamma \vdash X : \mathcal I(\tau)}{
adamc@533	776 X : \tau \in \Gamma
adamc@533	777 }
adamc@533	778 \quad \infer{\Gamma \vdash M.X : \mathcal I(\tau)}{
adamc@537	779 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	780 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \tau
adamc@533	781 }$$
adamc@533	782
adamc@533	783 $$\infer{\Gamma \vdash e_1 \; e_2 : \tau_2}{
adamc@533	784 \Gamma \vdash e_1 : \tau_1 \to \tau_2
adamc@533	785 & \Gamma \vdash e_2 : \tau_1
adamc@533	786 }
adamc@533	787 \quad \infer{\Gamma \vdash \lambda x : \tau_1 \Rightarrow e : \tau_1 \to \tau_2}{
adamc@533	788 \Gamma, x : \tau_1 \vdash e : \tau_2
adamc@533	789 }$$
adamc@533	790
adamc@533	791 $$\infer{\Gamma \vdash e [c] : [x \mapsto c]\tau}{
adamc@533	792 \Gamma \vdash e : x :: \kappa \to \tau
adamc@533	793 & \Gamma \vdash c :: \kappa
adamc@533	794 }
adamc@852	795 \quad \infer{\Gamma \vdash \lambda [x \; ? \; \kappa] \Rightarrow e : x \; ? \; \kappa \to \tau}{
adamc@533	796 \Gamma, x :: \kappa \vdash e : \tau
adamc@533	797 }$$
adamc@533	798
adamc@655	799 $$\infer{\Gamma \vdash e [\kappa] : [X \mapsto \kappa]\tau}{
adamc@655	800 \Gamma \vdash e : X \longrightarrow \tau
adamc@655	801 & \Gamma \vdash \kappa
adamc@655	802 }
adamc@655	803 \quad \infer{\Gamma \vdash X \Longrightarrow e : X \longrightarrow \tau}{
adamc@655	804 \Gamma, X \vdash e : \tau
adamc@655	805 }$$
adamc@655	806
adamc@533	807 $$\infer{\Gamma \vdash \{\overline{c = e}\} : \{\overline{c : \tau}\}}{
adamc@533	808 \forall i: \Gamma \vdash c_i :: \mt{Name}
adamc@533	809 & \Gamma \vdash e_i : \tau_i
adamc@533	810 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@533	811 }
adamc@533	812 \quad \infer{\Gamma \vdash e.c : \tau}{
adamc@533	813 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533	814 }
adamc@533	815 \quad \infer{\Gamma \vdash e_1 \rc e_2 : \$(c_1 \rc c_2)}{
adamc@533	816 \Gamma \vdash e_1 : \$c_1
adamc@533	817 & \Gamma \vdash e_2 : \$c_2
adamc@573	818 & \Gamma \vdash c_1 \sim c_2
adamc@533	819 }$$
adamc@533	820
adamc@533	821 $$\infer{\Gamma \vdash e \rcut c : \$c'}{
adamc@533	822 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533	823 }
adamc@533	824 \quad \infer{\Gamma \vdash e \rcutM c : \$c'}{
adamc@533	825 \Gamma \vdash e : \$(c \rc c')
adamc@533	826 }$$
adamc@533	827
adamc@533	828 $$\infer{\Gamma \vdash \mt{let} \; \overline{ed} \; \mt{in} \; e \; \mt{end} : \tau}{
adamc@533	829 \Gamma \vdash \overline{ed} \leadsto \Gamma'
adamc@533	830 & \Gamma' \vdash e : \tau
adamc@533	831 }
adamc@533	832 \quad \infer{\Gamma \vdash \mt{case} \; e \; \mt{of} \; \overline{p \Rightarrow e} : \tau}{
adamc@533	833 \forall i: \Gamma \vdash p_i \leadsto \Gamma_i, \tau'
adamc@533	834 & \Gamma_i \vdash e_i : \tau
adamc@533	835 }$$
adamc@533	836
adamc@573	837 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow e : \lambda [c_1 \sim c_2] \Rightarrow \tau}{
adamc@533	838 \Gamma \vdash c_1 :: \{\kappa\}
adamc@655	839 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@533	840 & \Gamma, c_1 \sim c_2 \vdash e : \tau
adamc@662	841 }
adamc@662	842 \quad \infer{\Gamma \vdash e \; ! : \tau}{
adamc@662	843 \Gamma \vdash e : [c_1 \sim c_2] \Rightarrow \tau
adamc@662	844 & \Gamma \vdash c_1 \sim c_2
adamc@533	845 }$$
adamc@533	846
adamc@534	847 \subsection{Pattern Typing}
adamc@534	848
adamc@534	849 $$\infer{\Gamma \vdash \_ \leadsto \Gamma; \tau}{}
adamc@534	850 \quad \infer{\Gamma \vdash x \leadsto \Gamma, x : \tau; \tau}{}
adamc@534	851 \quad \infer{\Gamma \vdash \ell \leadsto \Gamma; T(\ell)}{}$$
adamc@534	852
adamc@534	853 $$\infer{\Gamma \vdash X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534	854 X : \overline{x ::: \mt{Type}} \to \tau \in \Gamma
adamc@534	855 & \textrm{$\tau$ not a function type}
adamc@534	856 }
adamc@534	857 \quad \infer{\Gamma \vdash X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534	858 X : \overline{x ::: \mt{Type}} \to \tau'' \to \tau \in \Gamma
adamc@534	859 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534	860 }$$
adamc@534	861
adamc@534	862 $$\infer{\Gamma \vdash M.X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537	863 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	864 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau
adamc@534	865 & \textrm{$\tau$ not a function type}
adamc@534	866 }$$
adamc@534	867
adamc@534	868 $$\infer{\Gamma \vdash M.X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537	869 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	870 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau'' \to \tau
adamc@534	871 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534	872 }$$
adamc@534	873
adamc@534	874 $$\infer{\Gamma \vdash \{\overline{x = p}\} \leadsto \Gamma_n; \{\overline{x = \tau}\}}{
adamc@534	875 \Gamma_0 = \Gamma
adamc@534	876 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534	877 }
adamc@534	878 \quad \infer{\Gamma \vdash \{\overline{x = p}, \ldots\} \leadsto \Gamma_n; \$([\overline{x = \tau}] \rc c)}{
adamc@534	879 \Gamma_0 = \Gamma
adamc@534	880 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534	881 }$$
adamc@534	882
adamc@852	883 $$\infer{\Gamma \vdash p : \tau \leadsto \Gamma'; \tau}{
adamc@852	884 \Gamma \vdash p \leadsto \Gamma'; \tau'
adamc@852	885 & \Gamma \vdash \tau' \equiv \tau
adamc@852	886 }$$
adamc@852	887
adamc@535	888 \subsection{Declaration Typing}
adamc@535	889
adamc@535	890 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	891
adamc@655	892 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	893
adamc@558	894 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	895 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	896
adamc@535	897 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535	898 \quad \infer{\Gamma \vdash d, \overline{d} \leadsto \Gamma''}{
adamc@535	899 \Gamma \vdash d \leadsto \Gamma'
adamc@535	900 & \Gamma' \vdash \overline{d} \leadsto \Gamma''
adamc@535	901 }$$
adamc@535	902
adamc@535	903 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@535	904 \Gamma \vdash c :: \kappa
adamc@535	905 }
adamc@535	906 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@535	907 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@535	908 }$$
adamc@535	909
adamc@535	910 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537	911 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	912 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@535	913 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@535	914 }$$
adamc@535	915
adamc@535	916 $$\infer{\Gamma \vdash \mt{val} \; x : \tau = e \leadsto \Gamma, x : \tau}{
adamc@535	917 \Gamma \vdash e : \tau
adamc@535	918 }$$
adamc@535	919
adamc@535	920 $$\infer{\Gamma \vdash \mt{val} \; \mt{rec} \; \overline{x : \tau = e} \leadsto \Gamma, \overline{x : \tau}}{
adamc@535	921 \forall i: \Gamma, \overline{x : \tau} \vdash e_i : \tau_i
adamc@535	922 & \textrm{$e_i$ starts with an expression $\lambda$, optionally preceded by constructor and disjointness $\lambda$s}
adamc@535	923 }$$
adamc@535	924
adamc@535	925 $$\infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : S}{
adamc@535	926 \Gamma \vdash M : S
adamc@558	927 & \textrm{ $M$ not a constant or application}
adamc@535	928 }
adamc@558	929 \quad \infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : \mt{selfify}(X, \overline{s})}{
adamc@558	930 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@539	931 }$$
adamc@539	932
adamc@539	933 $$\infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@535	934 \Gamma \vdash S
adamc@535	935 }$$
adamc@535	936
adamc@537	937 $$\infer{\Gamma \vdash \mt{open} \; M \leadsto \Gamma, \mathcal O(M, \overline{s})}{
adamc@537	938 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535	939 }$$
adamc@535	940
adamc@535	941 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma}{
adamc@535	942 \Gamma \vdash c_1 :: \{\kappa\}
adamc@535	943 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@535	944 & \Gamma \vdash c_1 \sim c_2
adamc@535	945 }
adamc@537	946 \quad \infer{\Gamma \vdash \mt{open} \; \mt{constraints} \; M \leadsto \Gamma, \mathcal O_c(M, \overline{s})}{
adamc@537	947 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535	948 }$$
adamc@535	949
adamc@784	950 $$\infer{\Gamma \vdash \mt{table} \; x : c \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_table} \; c \; []}{
adamc@535	951 \Gamma \vdash c :: \{\mt{Type}\}
adamc@535	952 }
adamc@784	953 \quad \infer{\Gamma \vdash \mt{view} \; x : c \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_view} \; c}{
adamc@784	954 \Gamma \vdash c :: \{\mt{Type}\}
adamc@784	955 }$$
adamc@784	956
adamc@784	957 $$\infer{\Gamma \vdash \mt{sequence} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_sequence}}{}$$
adamc@535	958
adamc@535	959 $$\infer{\Gamma \vdash \mt{cookie} \; x : \tau \leadsto \Gamma, x : \mt{Basis}.\mt{http\_cookie} \; \tau}{
adamc@535	960 \Gamma \vdash \tau :: \mt{Type}
adamc@784	961 }
adamc@784	962 \quad \infer{\Gamma \vdash \mt{style} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{css\_class}}{}$$
adamc@535	963
adamc@1085	964 $$\infer{\Gamma \vdash \mt{task} \; e_1 = e_2 \leadsto \Gamma}{
adam@1348	965 \Gamma \vdash e_1 :: \mt{Basis}.\mt{task\_kind} \; \tau
adam@1348	966 & \Gamma \vdash e_2 :: \tau \to \mt{Basis}.\mt{transaction} \; \{\}
adamc@1085	967 }$$
adamc@1085	968
adamc@784	969 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784	970 \Gamma \vdash c :: \kappa
adamc@535	971 }$$
adamc@535	972
adamc@535	973 $$\infer{\overline{y}; x; \Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535	974 \quad \infer{\overline{y}; x; \Gamma \vdash X \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to x \; \overline{y}}{
adamc@535	975 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535	976 }
adamc@535	977 \quad \infer{\overline{y}; x; \Gamma \vdash X \; \mt{of} \; \tau \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to \tau \to x \; \overline{y}}{
adamc@535	978 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535	979 }$$
adamc@535	980
adamc@537	981 \subsection{Signature Item Typing}
adamc@537	982
adamc@537	983 We appeal to a signature item analogue of the $\mathcal O$ function from the last subsection.
adamc@537	984
adamc@537	985 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@537	986 \quad \infer{\Gamma \vdash s, \overline{s} \leadsto \Gamma''}{
adamc@537	987 \Gamma \vdash s \leadsto \Gamma'
adamc@537	988 & \Gamma' \vdash \overline{s} \leadsto \Gamma''
adamc@537	989 }$$
adamc@537	990
adamc@537	991 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}
adamc@537	992 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@537	993 \Gamma \vdash c :: \kappa
adamc@537	994 }
adamc@537	995 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@537	996 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@537	997 }$$
adamc@537	998
adamc@537	999 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537	1000 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1001 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537	1002 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@537	1003 }$$
adamc@537	1004
adamc@537	1005 $$\infer{\Gamma \vdash \mt{val} \; x : \tau \leadsto \Gamma, x : \tau}{
adamc@537	1006 \Gamma \vdash \tau :: \mt{Type}
adamc@537	1007 }$$
adamc@537	1008
adamc@537	1009 $$\infer{\Gamma \vdash \mt{structure} \; X : S \leadsto \Gamma, X : S}{
adamc@537	1010 \Gamma \vdash S
adamc@537	1011 }
adamc@537	1012 \quad \infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@537	1013 \Gamma \vdash S
adamc@537	1014 }$$
adamc@537	1015
adamc@537	1016 $$\infer{\Gamma \vdash \mt{include} \; S \leadsto \Gamma, \mathcal O(\overline{s})}{
adamc@537	1017 \Gamma \vdash S
adamc@537	1018 & \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1019 }$$
adamc@537	1020
adamc@537	1021 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma, c_1 \sim c_2}{
adamc@537	1022 \Gamma \vdash c_1 :: \{\kappa\}
adamc@537	1023 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@537	1024 }$$
adamc@537	1025
adamc@784	1026 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784	1027 \Gamma \vdash c :: \kappa
adamc@537	1028 }
adamc@784	1029 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}$$
adamc@537	1030
adamc@536	1031 \subsection{Signature Compatibility}
adamc@536	1032
adamc@558	1033 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	1034
adamc@537	1035 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	1036
adamc@536	1037 $$\infer{\Gamma \vdash S \equiv S}{}
adamc@536	1038 \quad \infer{\Gamma \vdash S_1 \equiv S_2}{
adamc@536	1039 \Gamma \vdash S_2 \equiv S_1
adamc@536	1040 }
adamc@536	1041 \quad \infer{\Gamma \vdash X \equiv S}{
adamc@536	1042 X = S \in \Gamma
adamc@536	1043 }
adamc@536	1044 \quad \infer{\Gamma \vdash M.X \equiv S}{
adamc@537	1045 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1046 & \mt{proj}(M, \overline{s}, \mt{signature} \; X) = S
adamc@536	1047 }$$
adamc@536	1048
adamc@536	1049 $$\infer{\Gamma \vdash S \; \mt{where} \; \mt{con} \; x = c \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa = c \; \overline{s_2} \; \mt{end}}{
adamc@536	1050 \Gamma \vdash S \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa \; \overline{s_2} \; \mt{end}
adamc@536	1051 & \Gamma \vdash c :: \kappa
adamc@537	1052 }
adamc@537	1053 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s^1} \; \mt{include} \; S \; \overline{s^2} \; \mt{end} \equiv \mt{sig} \; \overline{s^1} \; \overline{s} \; \overline{s^2} \; \mt{end}}{
adamc@537	1054 \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@536	1055 }$$
adamc@536	1056
adamc@536	1057 $$\infer{\Gamma \vdash S_1 \leq S_2}{
adamc@536	1058 \Gamma \vdash S_1 \equiv S_2
adamc@536	1059 }
adamc@536	1060 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \mt{end}}{}
adamc@537	1061 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; s' \; \overline{s'} \; \mt{end}}{
adamc@537	1062 \Gamma \vdash \overline{s} \leq s'
adamc@537	1063 & \Gamma \vdash s' \leadsto \Gamma'
adamc@537	1064 & \Gamma' \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \overline{s'} \; \mt{end}
adamc@537	1065 }$$
adamc@537	1066
adamc@537	1067 $$\infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537	1068 \Gamma \vdash s \leq s'
adamc@537	1069 }
adamc@537	1070 \quad \infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537	1071 \Gamma \vdash s \leadsto \Gamma'
adamc@537	1072 & \Gamma' \vdash \overline{s} \leq s'
adamc@536	1073 }$$
adamc@536	1074
adamc@536	1075 $$\infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 \leq \mt{functor} (X : S'_1) : S'_2}{
adamc@536	1076 \Gamma \vdash S'_1 \leq S_1
adamc@536	1077 & \Gamma, X : S'_1 \vdash S_2 \leq S'_2
adamc@536	1078 }$$
adamc@536	1079
adamc@537	1080 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@537	1081 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}
adamc@558	1082 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type}}{}$$
adamc@537	1083
adamc@537	1084 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(y)} \to \mt{Type}}{
adamc@537	1085 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1086 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537	1087 }$$
adamc@537	1088
adamc@784	1089 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@784	1090 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}$$
adamc@537	1091
adamc@537	1092 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \mt{\kappa} = c_2}{
adamc@537	1093 \Gamma \vdash c_1 \equiv c_2
adamc@537	1094 }
adamc@784	1095 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \kappa = c_2}{
adamc@537	1096 \Gamma \vdash c_1 \equiv c_2
adamc@537	1097 }$$
adamc@537	1098
adamc@537	1099 $$\infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537	1100 \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537	1101 }$$
adamc@537	1102
adamc@537	1103 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537	1104 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1105 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537	1106 & \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537	1107 }$$
adamc@537	1108
adamc@537	1109 $$\infer{\Gamma \vdash \cdot \leq \cdot}{}
adamc@537	1110 \quad \infer{\Gamma \vdash X; \overline{dc} \leq X; \overline{dc'}}{
adamc@537	1111 \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537	1112 }
adamc@537	1113 \quad \infer{\Gamma \vdash X \; \mt{of} \; \tau_1; \overline{dc} \leq X \; \mt{of} \; \tau_2; \overline{dc'}}{
adamc@537	1114 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537	1115 & \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537	1116 }$$
adamc@537	1117
adamc@537	1118 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x = \mt{datatype} \; M'.z'}{
adamc@537	1119 \Gamma \vdash M.z \equiv M'.z'
adamc@537	1120 }$$
adamc@537	1121
adamc@537	1122 $$\infer{\Gamma \vdash \mt{val} \; x : \tau_1 \leq \mt{val} \; x : \tau_2}{
adamc@537	1123 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537	1124 }
adamc@537	1125 \quad \infer{\Gamma \vdash \mt{structure} \; X : S_1 \leq \mt{structure} \; X : S_2}{
adamc@537	1126 \Gamma \vdash S_1 \leq S_2
adamc@537	1127 }
adamc@537	1128 \quad \infer{\Gamma \vdash \mt{signature} \; X = S_1 \leq \mt{signature} \; X = S_2}{
adamc@537	1129 \Gamma \vdash S_1 \leq S_2
adamc@537	1130 & \Gamma \vdash S_2 \leq S_1
adamc@537	1131 }$$
adamc@537	1132
adamc@537	1133 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leq \mt{constraint} \; c'_1 \sim c'_2}{
adamc@537	1134 \Gamma \vdash c_1 \equiv c'_1
adamc@537	1135 & \Gamma \vdash c_2 \equiv c'_2
adamc@537	1136 }$$
adamc@537	1137
adamc@655	1138 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{class} \; x :: \kappa}{}
adamc@655	1139 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{class} \; x :: \kappa}{}
adamc@655	1140 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{class} \; x :: \kappa = c_2}{
adamc@537	1141 \Gamma \vdash c_1 \equiv c_2
adamc@537	1142 }$$
adamc@537	1143
adamc@538	1144 \subsection{Module Typing}
adamc@538	1145
adamc@538	1146 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	1147
adamc@538	1148 $$\infer{\Gamma \vdash M : S}{
adamc@538	1149 \Gamma \vdash M : S'
adamc@538	1150 & \Gamma \vdash S' \leq S
adamc@538	1151 }
adamc@538	1152 \quad \infer{\Gamma \vdash \mt{struct} \; \overline{d} \; \mt{end} : \mt{sig} \; \mt{sigOf}(\overline{d}) \; \mt{end}}{
adamc@538	1153 \Gamma \vdash \overline{d} \leadsto \Gamma'
adamc@538	1154 }
adamc@538	1155 \quad \infer{\Gamma \vdash X : S}{
adamc@538	1156 X : S \in \Gamma
adamc@538	1157 }$$
adamc@538	1158
adamc@538	1159 $$\infer{\Gamma \vdash M.X : S}{
adamc@538	1160 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@538	1161 & \mt{proj}(M, \overline{s}, \mt{structure} \; X) = S
adamc@538	1162 }$$
adamc@538	1163
adamc@538	1164 $$\infer{\Gamma \vdash M_1(M_2) : [X \mapsto M_2]S_2}{
adamc@538	1165 \Gamma \vdash M_1 : \mt{functor}(X : S_1) : S_2
adamc@538	1166 & \Gamma \vdash M_2 : S_1
adamc@538	1167 }
adamc@538	1168 \quad \infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 = M : \mt{functor} (X : S_1) : S_2}{
adamc@538	1169 \Gamma \vdash S_1
adamc@538	1170 & \Gamma, X : S_1 \vdash S_2
adamc@538	1171 & \Gamma, X : S_1 \vdash M : S_2
adamc@538	1172 }$$
adamc@538	1173
adamc@538	1174 \begin{eqnarray*}
adamc@538	1175 \mt{sigOf}(\cdot) &=& \cdot \\
adamc@538	1176 \mt{sigOf}(s \; \overline{s'}) &=& \mt{sigOf}(s) \; \mt{sigOf}(\overline{s'}) \\
adamc@538	1177 \\
adamc@538	1178 \mt{sigOf}(\mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@538	1179 \mt{sigOf}(\mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \overline{dc} \\
adamc@538	1180 \mt{sigOf}(\mt{datatype} \; x = \mt{datatype} \; M.z) &=& \mt{datatype} \; x = \mt{datatype} \; M.z \\
adamc@538	1181 \mt{sigOf}(\mt{val} \; x : \tau = e) &=& \mt{val} \; x : \tau \\
adamc@538	1182 \mt{sigOf}(\mt{val} \; \mt{rec} \; \overline{x : \tau = e}) &=& \overline{\mt{val} \; x : \tau} \\
adamc@538	1183 \mt{sigOf}(\mt{structure} \; X : S = M) &=& \mt{structure} \; X : S \\
adamc@538	1184 \mt{sigOf}(\mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@538	1185 \mt{sigOf}(\mt{open} \; M) &=& \mt{include} \; S \textrm{ (where $\Gamma \vdash M : S$)} \\
adamc@538	1186 \mt{sigOf}(\mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@538	1187 \mt{sigOf}(\mt{open} \; \mt{constraints} \; M) &=& \cdot \\
adamc@538	1188 \mt{sigOf}(\mt{table} \; x : c) &=& \mt{table} \; x : c \\
adamc@784	1189 \mt{sigOf}(\mt{view} \; x : c) &=& \mt{view} \; x : c \\
adamc@538	1190 \mt{sigOf}(\mt{sequence} \; x) &=& \mt{sequence} \; x \\
adamc@538	1191 \mt{sigOf}(\mt{cookie} \; x : \tau) &=& \mt{cookie} \; x : \tau \\
adamc@784	1192 \mt{sigOf}(\mt{style} \; x) &=& \mt{style} \; x \\
adamc@655	1193 \mt{sigOf}(\mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@538	1194 \end{eqnarray*}
adamc@539	1195 \begin{eqnarray*}
adamc@539	1196 \mt{selfify}(M, \cdot) &=& \cdot \\
adamc@558	1197 \mt{selfify}(M, s \; \overline{s'}) &=& \mt{selfify}(M, s) \; \mt{selfify}(M, \overline{s'}) \\
adamc@539	1198 \\
adamc@539	1199 \mt{selfify}(M, \mt{con} \; x :: \kappa) &=& \mt{con} \; x :: \kappa = M.x \\
adamc@539	1200 \mt{selfify}(M, \mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@539	1201 \mt{selfify}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \mt{datatype} \; M.x \\
adamc@539	1202 \mt{selfify}(M, \mt{datatype} \; x = \mt{datatype} \; M'.z) &=& \mt{datatype} \; x = \mt{datatype} \; M'.z \\
adamc@539	1203 \mt{selfify}(M, \mt{val} \; x : \tau) &=& \mt{val} \; x : \tau \\
adamc@539	1204 \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	1205 \mt{selfify}(M, \mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@539	1206 \mt{selfify}(M, \mt{include} \; S) &=& \mt{include} \; S \\
adamc@539	1207 \mt{selfify}(M, \mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@655	1208 \mt{selfify}(M, \mt{class} \; x :: \kappa) &=& \mt{class} \; x :: \kappa = M.x \\
adamc@655	1209 \mt{selfify}(M, \mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@539	1210 \end{eqnarray*}
adamc@539	1211
adamc@540	1212 \subsection{Module Projection}
adamc@540	1213
adamc@540	1214 \begin{eqnarray*}
adamc@540	1215 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \\
adamc@540	1216 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa, c) \\
adamc@540	1217 \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	1218 \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	1219 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})$)} \\
adamc@655	1220 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \to \mt{Type} \\
adamc@655	1221 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa \to \mt{Type}, c) \\
adamc@540	1222 \\
adamc@540	1223 \mt{proj}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc} \; \overline{s}, \mt{datatype} \; x) &=& (\overline{y}, \overline{dc}) \\
adamc@540	1224 \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	1225 \\
adamc@540	1226 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, \mt{val} \; x) &=& \tau \\
adamc@540	1227 \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	1228 \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	1229 \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	1230 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \in \overline{dc}$)} \\
adamc@540	1231 \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	1232 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \; \mt{of} \; \tau \in \overline{dc}$)} \\
adamc@540	1233 \\
adamc@540	1234 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, \mt{structure} \; X) &=& S \\
adamc@540	1235 \\
adamc@540	1236 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, \mt{signature} \; X) &=& S \\
adamc@540	1237 \\
adamc@540	1238 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1239 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1240 \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	1241 \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	1242 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@540	1243 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1244 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1245 \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	1246 \mt{proj}(M, \mt{constraint} \; c_1 \sim c_2 \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@655	1247 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@655	1248 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1249 \end{eqnarray*}
adamc@540	1250
adamc@541	1251
adamc@541	1252 \section{Type Inference}
adamc@541	1253
adamc@541	1254 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	1255
adamc@541	1256 \subsection{Basic Unification}
adamc@541	1257
adamc@560	1258 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	1259
adamc@656	1260 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	1261
adamc@541	1262 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	1263
adamc@541	1264 \subsection{Unifying Record Types}
adamc@541	1265
adamc@570	1266 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	1267
adamc@656	1268 \subsection{\label{typeclasses}Constructor Classes}
adamc@541	1269
adamc@784	1270 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	1271
adamc@784	1272 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	1273
adamc@656	1274 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	1275
adamc@656	1276 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	1277
adamc@541	1278 \subsection{Reverse-Engineering Record Types}
adamc@541	1279
adamc@656	1280 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	1281
adamc@541	1282 \subsection{Implicit Arguments in Functor Applications}
adamc@541	1283
adamc@656	1284 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	1285
adamc@541	1286
adamc@542	1287 \section{The Ur Standard Library}
adamc@542	1288
adamc@542	1289 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	1290
adamc@542	1291 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	1292
adamc@542	1293 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	1294 $$\begin{array}{l}
adamc@542	1295 \mt{type} \; \mt{int} \\
adamc@542	1296 \mt{type} \; \mt{float} \\
adamc@873	1297 \mt{type} \; \mt{char} \\
adamc@542	1298 \mt{type} \; \mt{string} \\
adamc@542	1299 \mt{type} \; \mt{time} \\
adamc@785	1300 \mt{type} \; \mt{blob} \\
adamc@542	1301 \\
adamc@542	1302 \mt{type} \; \mt{unit} = \{\} \\
adamc@542	1303 \\
adamc@542	1304 \mt{datatype} \; \mt{bool} = \mt{False} \mid \mt{True} \\
adamc@542	1305 \\
adamc@785	1306 \mt{datatype} \; \mt{option} \; \mt{t} = \mt{None} \mid \mt{Some} \; \mt{of} \; \mt{t} \\
adamc@785	1307 \\
adamc@785	1308 \mt{datatype} \; \mt{list} \; \mt{t} = \mt{Nil} \mid \mt{Cons} \; \mt{of} \; \mt{t} \times \mt{list} \; \mt{t}
adamc@542	1309 \end{array}$$
adamc@542	1310
adamc@1123	1311 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	1312
adam@1297	1313 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	1314 $$\begin{array}{l}
adam@1297	1315 \mt{con} \; \mt{variant} :: \{\mt{Type}\} \to \mt{Type} \\
adam@1297	1316 \mt{val} \; \mt{make} : \mt{nm} :: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{ts} ::: \{\mt{Type}\} \to [[\mt{nm}] \sim \mt{ts}] \Rightarrow \mt{t} \to \mt{variant} \; ([\mt{nm} = \mt{t}] \rc \mt{ts}) \\
adam@1297	1317 \mt{val} \; \mt{match} : \mt{ts} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{variant} \; \mt{ts} \to \$(\mt{map} \; (\lambda \mt{t'} \Rightarrow \mt{t'} \to \mt{t}) \; \mt{ts}) \to \mt{t}
adam@1297	1318 \end{array}$$
adam@1297	1319
adamc@657	1320 Another important generic Ur element comes at the beginning of \texttt{top.urs}.
adamc@657	1321
adamc@657	1322 $$\begin{array}{l}
adamc@657	1323 \mt{con} \; \mt{folder} :: \mt{K} \longrightarrow \{\mt{K}\} \to \mt{Type} \\
adamc@657	1324 \\
adamc@657	1325 \mt{val} \; \mt{fold} : \mt{K} \longrightarrow \mt{tf} :: (\{\mt{K}\} \to \mt{Type}) \\
adamc@657	1326 \hspace{.1in} \to (\mt{nm} :: \mt{Name} \to \mt{v} :: \mt{K} \to \mt{r} :: \{\mt{K}\} \to [[\mt{nm}] \sim \mt{r}] \Rightarrow \\
adamc@657	1327 \hspace{.2in} \mt{tf} \; \mt{r} \to \mt{tf} \; ([\mt{nm} = \mt{v}] \rc \mt{r})) \\
adamc@657	1328 \hspace{.1in} \to \mt{tf} \; [] \\
adamc@657	1329 \hspace{.1in} \to \mt{r} :: \{\mt{K}\} \to \mt{folder} \; \mt{r} \to \mt{tf} \; \mt{r}
adamc@657	1330 \end{array}$$
adamc@657	1331
adamc@657	1332 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	1333
adamc@664	1334 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	1335
adamc@542	1336
adamc@542	1337 \section{The Ur/Web Standard Library}
adamc@542	1338
adamc@658	1339 \subsection{Monads}
adamc@658	1340
adamc@658	1341 The Ur Basis defines the monad constructor class from Haskell.
adamc@658	1342
adamc@658	1343 $$\begin{array}{l}
adamc@658	1344 \mt{class} \; \mt{monad} :: \mt{Type} \to \mt{Type} \\
adamc@658	1345 \mt{val} \; \mt{return} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t} ::: \mt{Type} \\
adamc@658	1346 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658	1347 \hspace{.1in} \to \mt{t} \to \mt{m} \; \mt{t} \\
adamc@658	1348 \mt{val} \; \mt{bind} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t1} ::: \mt{Type} \to \mt{t2} ::: \mt{Type} \\
adamc@658	1349 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658	1350 \hspace{.1in} \to \mt{m} \; \mt{t1} \to (\mt{t1} \to \mt{m} \; \mt{t2}) \\
adamc@658	1351 \hspace{.1in} \to \mt{m} \; \mt{t2}
adamc@658	1352 \end{array}$$
adamc@658	1353
adamc@542	1354 \subsection{Transactions}
adamc@542	1355
adamc@542	1356 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	1357 $$\begin{array}{l}
adamc@542	1358 \mt{con} \; \mt{transaction} :: \mt{Type} \to \mt{Type} \\
adamc@658	1359 \mt{val} \; \mt{transaction\_monad} : \mt{monad} \; \mt{transaction}
adamc@542	1360 \end{array}$$
adamc@542	1361
adamc@1123	1362 For debugging purposes, a transactional function is provided for outputting a string on the server process' \texttt{stderr}.
adamc@1123	1363 $$\begin{array}{l}
adamc@1123	1364 \mt{val} \; \mt{debug} : \mt{string} \to \mt{transaction} \; \mt{unit}
adamc@1123	1365 \end{array}$$
adamc@1123	1366
adamc@542	1367 \subsection{HTTP}
adamc@542	1368
adamc@542	1369 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.
adamc@542	1370 $$\begin{array}{l}
adamc@786	1371 \mt{val} \; \mt{requestHeader} : \mt{string} \to \mt{transaction} \; (\mt{option} \; \mt{string}) \\
adamc@786	1372 \\
adamc@786	1373 \mt{con} \; \mt{http\_cookie} :: \mt{Type} \to \mt{Type} \\
adamc@786	1374 \mt{val} \; \mt{getCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; (\mt{option} \; \mt{t}) \\
adamc@1050	1375 \mt{val} \; \mt{setCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \{\mt{Value} : \mt{t}, \mt{Expires} : \mt{option} \; \mt{time}, \mt{Secure} : \mt{bool}\} \to \mt{transaction} \; \mt{unit} \\
adamc@1050	1376 \mt{val} \; \mt{clearCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; \mt{unit}
adamc@786	1377 \end{array}$$
adamc@786	1378
adamc@786	1379 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	1380 $$\begin{array}{l}
adamc@786	1381 \mt{type} \; \mt{url} \\
adamc@786	1382 \mt{val} \; \mt{bless} : \mt{string} \to \mt{url} \\
adamc@786	1383 \mt{val} \; \mt{checkUrl} : \mt{string} \to \mt{option} \; \mt{url}
adamc@786	1384 \end{array}$$
adamc@786	1385 $\mt{bless}$ raises a runtime error if the string passed to it fails the URL policy.
adamc@786	1386
adamc@1085	1387 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.
adamc@1085	1388 $$\begin{array}{l}
adamc@1085	1389 \mt{val} \; \mt{currentUrl} : \mt{transaction} \; \mt{url} \\
adamc@1085	1390 \mt{val} \; \mt{url} : \mt{transaction} \; \mt{page} \to \mt{url}
adamc@1085	1391 \end{array}$$
adamc@1085	1392
adamc@1085	1393 Page generation may be interrupted at any time with a request to redirect to a particular URL instead.
adamc@1085	1394 $$\begin{array}{l}
adamc@1085	1395 \mt{val} \; \mt{redirect} : \mt{t} ::: \mt{Type} \to \mt{url} \to \mt{transaction} \; \mt{t}
adamc@1085	1396 \end{array}$$
adamc@1085	1397
adamc@786	1398 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.
adamc@786	1399 $$\begin{array}{l}
adamc@786	1400 \mt{type} \; \mt{file} \\
adamc@786	1401 \mt{val} \; \mt{fileName} : \mt{file} \to \mt{option} \; \mt{string} \\
adamc@786	1402 \mt{val} \; \mt{fileMimeType} : \mt{file} \to \mt{string} \\
adamc@786	1403 \mt{val} \; \mt{fileData} : \mt{file} \to \mt{blob}
adamc@786	1404 \end{array}$$
adamc@786	1405
adamc@786	1406 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	1407 $$\begin{array}{l}
adamc@786	1408 \mt{type} \; \mt{mimeType} \\
adamc@786	1409 \mt{val} \; \mt{blessMime} : \mt{string} \to \mt{mimeType} \\
adamc@786	1410 \mt{val} \; \mt{checkMime} : \mt{string} \to \mt{option} \; \mt{mimeType} \\
adamc@786	1411 \mt{val} \; \mt{returnBlob} : \mt{t} ::: \mt{Type} \to \mt{blob} \to \mt{mimeType} \to \mt{transaction} \; \mt{t}
adamc@542	1412 \end{array}$$
adamc@542	1413
adamc@543	1414 \subsection{SQL}
adamc@543	1415
adamc@543	1416 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	1417 $$\begin{array}{l}
adamc@785	1418 \mt{con} \; \mt{sql\_table} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785	1419 \end{array}$$
adamc@785	1420 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	1421
adamc@785	1422 We also have the simpler type family of SQL views, which have no keys.
adamc@785	1423 $$\begin{array}{l}
adamc@785	1424 \mt{con} \; \mt{sql\_view} :: \{\mt{Type}\} \to \mt{Type}
adamc@543	1425 \end{array}$$
adamc@543	1426
adamc@785	1427 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	1428 $$\begin{array}{l}
adamc@785	1429 \mt{class} \; \mt{fieldsOf} :: \mt{Type} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785	1430 \mt{val} \; \mt{fieldsOf\_table} : \mt{fs} ::: \{\mt{Type}\} \to \mt{keys} ::: \{\{\mt{Unit}\}\} \to \mt{fieldsOf} \; (\mt{sql\_table} \; \mt{fs} \; \mt{keys}) \; \mt{fs} \\
adamc@785	1431 \mt{val} \; \mt{fieldsOf\_view} : \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; (\mt{sql\_view} \; \mt{fs}) \; \mt{fs}
adamc@785	1432 \end{array}$$
adamc@785	1433
adamc@785	1434 \subsubsection{Table Constraints}
adamc@785	1435
adamc@785	1436 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	1437
adamc@785	1438 $$\begin{array}{l}
adamc@785	1439 \mt{con} \; \mt{primary\_key} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type} \\
adamc@785	1440 \mt{val} \; \mt{no\_primary\_key} : \mt{fs} ::: \{\mt{Type}\} \to \mt{primary\_key} \; \mt{fs} \; [] \\
adamc@785	1441 \mt{val} \; \mt{primary\_key} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{key1} :: \mt{Name} \to \mt{keys} :: \{\mt{Type}\} \\
adamc@785	1442 \hspace{.1in} \to [[\mt{key1}] \sim \mt{keys}] \Rightarrow [[\mt{key1} = \mt{t}] \rc \mt{keys} \sim \mt{rest}] \\
adamc@785	1443 \hspace{.1in} \Rightarrow \$([\mt{key1} = \mt{sql\_injectable\_prim} \; \mt{t}] \rc \mt{map} \; \mt{sql\_injectable\_prim} \; \mt{keys}) \\
adamc@785	1444 \hspace{.1in} \to \mt{primary\_key} \; ([\mt{key1} = \mt{t}] \rc \mt{keys} \rc \mt{rest}) \; [\mt{Pkey} = [\mt{key1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{keys}]
adamc@785	1445 \end{array}$$
adamc@785	1446 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	1447
adamc@785	1448 A type family stands for sets of named constraints of the remaining varieties.
adamc@785	1449 $$\begin{array}{l}
adamc@785	1450 \mt{con} \; \mt{sql\_constraints} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785	1451 \end{array}$$
adamc@785	1452 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	1453
adamc@785	1454 There is a type family of individual, unnamed constraints.
adamc@785	1455 $$\begin{array}{l}
adamc@785	1456 \mt{con} \; \mt{sql\_constraint} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \mt{Type}
adamc@785	1457 \end{array}$$
adamc@785	1458 The first argument is the same as above, and the second argument gives the key columns for just this constraint.
adamc@785	1459
adamc@785	1460 We have operations for assembling constraints into constraint sets.
adamc@785	1461 $$\begin{array}{l}
adamc@785	1462 \mt{val} \; \mt{no\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_constraints} \; \mt{fs} \; [] \\
adamc@785	1463 \mt{val} \; \mt{one\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{unique} ::: \{\mt{Unit}\} \to \mt{name} :: \mt{Name} \\
adamc@785	1464 \hspace{.1in} \to \mt{sql\_constraint} \; \mt{fs} \; \mt{unique} \to \mt{sql\_constraints} \; \mt{fs} \; [\mt{name} = \mt{unique}] \\
adamc@785	1465 \mt{val} \; \mt{join\_constraints} : \mt{fs} ::: \{\mt{Type}\} \to \mt{uniques1} ::: \{\{\mt{Unit}\}\} \to \mt{uniques2} ::: \{\{\mt{Unit}\}\} \to [\mt{uniques1} \sim \mt{uniques2}] \\
adamc@785	1466 \hspace{.1in} \Rightarrow \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques1} \to \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques2} \to \mt{sql\_constraints} \; \mt{fs} \; (\mt{uniques1} \rc \mt{uniques2})
adamc@785	1467 \end{array}$$
adamc@785	1468
adamc@785	1469 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	1470 $$\begin{array}{l}
adamc@785	1471 \mt{val} \; \mt{unique} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{unique1} :: \mt{Name} \to \mt{unique} :: \{\mt{Type}\} \\
adamc@785	1472 \hspace{.1in} \to [[\mt{unique1}] \sim \mt{unique}] \Rightarrow [[\mt{unique1} = \mt{t}] \rc \mt{unique} \sim \mt{rest}] \\
adamc@785	1473 \hspace{.1in} \Rightarrow \mt{sql\_constraint} \; ([\mt{unique1} = \mt{t}] \rc \mt{unique} \rc \mt{rest}) \; ([\mt{unique1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{unique})
adamc@785	1474 \end{array}$$
adamc@785	1475
adamc@785	1476 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	1477 $$\begin{array}{l}
adamc@785	1478 \mt{class} \; \mt{linkable} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@785	1479 \mt{val} \; \mt{linkable\_same} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; \mt{t} \\
adamc@785	1480 \mt{val} \; \mt{linkable\_from\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; (\mt{option} \; \mt{t}) \; \mt{t} \\
adamc@785	1481 \mt{val} \; \mt{linkable\_to\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@785	1482 \end{array}$$
adamc@785	1483
adamc@785	1484 The $\mt{matching}$ type family uses $\mt{linkable}$ to define when two keys match up type-wise.
adamc@785	1485 $$\begin{array}{l}
adamc@785	1486 \mt{con} \; \mt{matching} :: \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785	1487 \mt{val} \; \mt{mat\_nil} : \mt{matching} \; [] \; [] \\
adamc@785	1488 \mt{val} \; \mt{mat\_cons} : \mt{t1} ::: \mt{Type} \to \mt{rest1} ::: \{\mt{Type}\} \to \mt{t2} ::: \mt{Type} \to \mt{rest2} ::: \{\mt{Type}\} \to \mt{nm1} :: \mt{Name} \to \mt{nm2} :: \mt{Name} \\
adamc@785	1489 \hspace{.1in} \to [[\mt{nm1}] \sim \mt{rest1}] \Rightarrow [[\mt{nm2}] \sim \mt{rest2}] \Rightarrow \mt{linkable} \; \mt{t1} \; \mt{t2} \to \mt{matching} \; \mt{rest1} \; \mt{rest2} \\
adamc@785	1490 \hspace{.1in} \to \mt{matching} \; ([\mt{nm1} = \mt{t1}] \rc \mt{rest1}) \; ([\mt{nm2} = \mt{t2}] \rc \mt{rest2})
adamc@785	1491 \end{array}$$
adamc@785	1492
adamc@785	1493 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	1494 $$\begin{array}{l}
adamc@785	1495 \mt{con} \; \mt{propagation\_mode} :: \{\mt{Type}\} \to \mt{Type} \\
adamc@785	1496 \mt{val} \; \mt{restrict} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785	1497 \mt{val} \; \mt{cascade} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785	1498 \mt{val} \; \mt{no\_action} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785	1499 \mt{val} \; \mt{set\_null} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; (\mt{map} \; \mt{option} \; \mt{fs})
adamc@785	1500 \end{array}$$
adamc@785	1501
adamc@785	1502 Finally, we put these ingredient together to define the \texttt{FOREIGN KEY} constraint function.
adamc@785	1503 $$\begin{array}{l}
adamc@785	1504 \mt{val} \; \mt{foreign\_key} : \mt{mine1} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{mine} ::: \{\mt{Type}\} \to \mt{munused} ::: \{\mt{Type}\} \to \mt{foreign} ::: \{\mt{Type}\} \\
adamc@785	1505 \hspace{.1in} \to \mt{funused} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{uniques} ::: \{\{\mt{Unit}\}\} \\
adamc@785	1506 \hspace{.1in} \to [[\mt{mine1}] \sim \mt{mine}] \Rightarrow [[\mt{mine1} = \mt{t}] \rc \mt{mine} \sim \mt{munused}] \Rightarrow [\mt{foreign} \sim \mt{funused}] \Rightarrow [[\mt{nm}] \sim \mt{uniques}] \\
adamc@785	1507 \hspace{.1in} \Rightarrow \mt{matching} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}) \; \mt{foreign} \\
adamc@785	1508 \hspace{.1in} \to \mt{sql\_table} \; (\mt{foreign} \rc \mt{funused}) \; ([\mt{nm} = \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{foreign}] \rc \mt{uniques}) \\
adamc@785	1509 \hspace{.1in} \to \{\mt{OnDelete} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}), \\
adamc@785	1510 \hspace{.2in} \mt{OnUpdate} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine})\} \\
adamc@785	1511 \hspace{.1in} \to \mt{sql\_constraint} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine} \rc \mt{munused}) \; []
adamc@785	1512 \end{array}$$
adamc@785	1513
adamc@785	1514 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	1515 $$\begin{array}{l}
adamc@785	1516 \mt{val} \; \mt{check} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; [] \; [] \; \mt{fs} \; \mt{bool} \to \mt{sql\_constraint} \; \mt{fs} \; []
adamc@785	1517 \end{array}$$
adamc@785	1518
adamc@785	1519 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	1520
adamc@784	1521
adamc@543	1522 \subsubsection{Queries}
adamc@543	1523
adamc@1193	1524 A final query is constructed via the $\mt{sql\_query}$ function. Constructor arguments respectively specify the free table variables (which will only be available in subqueries), 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	1525 $$\begin{array}{l}
adamc@1193	1526 \mt{con} \; \mt{sql\_query} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@1193	1527 \mt{val} \; \mt{sql\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adamc@1193	1528 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543	1529 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543	1530 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1193	1531 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adamc@1193	1532 \hspace{.1in} \Rightarrow \{\mt{Rows} : \mt{sql\_query1} \; \mt{free} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}, \\
adamc@1193	1533 \hspace{.2in} \mt{OrderBy} : \mt{sql\_order\_by} \; (\mt{free} \rc \mt{tables}) \; \mt{selectedExps}, \\
adamc@543	1534 \hspace{.2in} \mt{Limit} : \mt{sql\_limit}, \\
adamc@543	1535 \hspace{.2in} \mt{Offset} : \mt{sql\_offset}\} \\
adamc@1193	1536 \hspace{.1in} \to \mt{sql\_query} \; \mt{free} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543	1537 \end{array}$$
adamc@543	1538
adamc@545	1539 Queries are used by folding over their results inside transactions.
adamc@545	1540 $$\begin{array}{l}
adamc@1193	1541 \mt{val} \; \mt{query} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \lambda [\mt{tables} \sim \mt{exps}] \Rightarrow \mt{state} ::: \mt{Type} \to \mt{sql\_query} \; [] \; \mt{tables} \; \mt{exps} \\
adamc@658	1542 \hspace{.1in} \to (\$(\mt{exps} \rc \mt{map} \; (\lambda \mt{fields} :: \{\mt{Type}\} \Rightarrow \$\mt{fields}) \; \mt{tables}) \\
adamc@545	1543 \hspace{.2in} \to \mt{state} \to \mt{transaction} \; \mt{state}) \\
adamc@545	1544 \hspace{.1in} \to \mt{state} \to \mt{transaction} \; \mt{state}
adamc@545	1545 \end{array}$$
adamc@545	1546
adamc@1193	1547 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 free table veriables, 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	1548 $$\begin{array}{l}
adamc@1193	1549 \mt{con} \; \mt{sql\_query1} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@543	1550 \\
adamc@543	1551 \mt{type} \; \mt{sql\_relop} \\
adamc@543	1552 \mt{val} \; \mt{sql\_union} : \mt{sql\_relop} \\
adamc@543	1553 \mt{val} \; \mt{sql\_intersect} : \mt{sql\_relop} \\
adamc@543	1554 \mt{val} \; \mt{sql\_except} : \mt{sql\_relop} \\
adamc@543	1555 \mt{val} \; \mt{sql\_relop} : \mt{tables1} ::: \{\{\mt{Type}\}\} \\
adamc@543	1556 \hspace{.1in} \to \mt{tables2} ::: \{\{\mt{Type}\}\} \\
adamc@543	1557 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543	1558 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@543	1559 \hspace{.1in} \to \mt{sql\_relop} \\
adamc@543	1560 \hspace{.1in} \to \mt{sql\_query1} \; \mt{tables1} \; \mt{selectedFields} \; \mt{selectedExps} \\
adamc@543	1561 \hspace{.1in} \to \mt{sql\_query1} \; \mt{tables2} \; \mt{selectedFields} \; \mt{selectedExps} \\
adamc@543	1562 \hspace{.1in} \to \mt{sql\_query1} \; \mt{selectedFields} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543	1563 \end{array}$$
adamc@543	1564
adamc@543	1565 $$\begin{array}{l}
adamc@1193	1566 \mt{val} \; \mt{sql\_query1} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adamc@1193	1567 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543	1568 \hspace{.1in} \to \mt{grouped} ::: \{\{\mt{Type}\}\} \\
adamc@543	1569 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543	1570 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1085	1571 \hspace{.1in} \to \mt{empties} :: \{\mt{Unit}\} \\
adamc@1193	1572 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adamc@1193	1573 \hspace{.1in} \Rightarrow [\mt{free} \sim \mt{grouped}] \\
adamc@1193	1574 \hspace{.1in} \Rightarrow [\mt{empties} \sim \mt{selectedFields}] \\
adamc@1085	1575 \hspace{.1in} \Rightarrow \{\mt{Distinct} : \mt{bool}, \\
adamc@1193	1576 \hspace{.2in} \mt{From} : \mt{sql\_from\_items} \; \mt{free} \; \mt{tables}, \\
adamc@1193	1577 \hspace{.2in} \mt{Where} : \mt{sql\_exp} \; (\mt{free} \rc \mt{tables}) \; [] \; [] \; \mt{bool}, \\
adamc@543	1578 \hspace{.2in} \mt{GroupBy} : \mt{sql\_subset} \; \mt{tables} \; \mt{grouped}, \\
adamc@1193	1579 \hspace{.2in} \mt{Having} : \mt{sql\_exp} \; (\mt{free} \rc \mt{grouped}) \; \mt{tables} \; [] \; \mt{bool}, \\
adamc@1085	1580 \hspace{.2in} \mt{SelectFields} : \mt{sql\_subset} \; \mt{grouped} \; (\mt{map} \; (\lambda \_ \Rightarrow []) \; \mt{empties} \rc \mt{selectedFields}), \\
adamc@1193	1581 \hspace{.2in} \mt {SelectExps} : \$(\mt{map} \; (\mt{sql\_exp} \; (\mt{free} \rc \mt{grouped}) \; \mt{tables} \; []) \; \mt{selectedExps}) \} \\
adamc@1193	1582 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543	1583 \end{array}$$
adamc@543	1584
adamc@543	1585 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	1586 $$\begin{array}{l}
adamc@543	1587 \mt{con} \; \mt{sql\_subset} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@543	1588 \mt{val} \; \mt{sql\_subset} : \mt{keep\_drop} :: \{(\{\mt{Type}\} \times \{\mt{Type}\})\} \\
adamc@543	1589 \hspace{.1in} \to \mt{sql\_subset} \\
adamc@658	1590 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1 \rc \mt{fields}.2)\; \mt{keep\_drop}) \\
adamc@658	1591 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1) \; \mt{keep\_drop}) \\
adamc@543	1592 \mt{val} \; \mt{sql\_subset\_all} : \mt{tables} :: \{\{\mt{Type}\}\} \to \mt{sql\_subset} \; \mt{tables} \; \mt{tables}
adamc@543	1593 \end{array}$$
adamc@543	1594
adamc@560	1595 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	1596 $$\begin{array}{l}
adamc@543	1597 \mt{con} \; \mt{sql\_exp} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}
adamc@543	1598 \end{array}$$
adamc@543	1599
adamc@543	1600 Any field in scope may be converted to an expression.
adamc@543	1601 $$\begin{array}{l}
adamc@543	1602 \mt{val} \; \mt{sql\_field} : \mt{otherTabs} ::: \{\{\mt{Type}\}\} \to \mt{otherFields} ::: \{\mt{Type}\} \\
adamc@543	1603 \hspace{.1in} \to \mt{fieldType} ::: \mt{Type} \to \mt{agg} ::: \{\{\mt{Type}\}\} \\
adamc@543	1604 \hspace{.1in} \to \mt{exps} ::: \{\mt{Type}\} \\
adamc@543	1605 \hspace{.1in} \to \mt{tab} :: \mt{Name} \to \mt{field} :: \mt{Name} \\
adamc@543	1606 \hspace{.1in} \to \mt{sql\_exp} \; ([\mt{tab} = [\mt{field} = \mt{fieldType}] \rc \mt{otherFields}] \rc \mt{otherTabs}) \; \mt{agg} \; \mt{exps} \; \mt{fieldType}
adamc@543	1607 \end{array}$$
adamc@543	1608
adamc@544	1609 There is an analogous function for referencing named expressions.
adamc@544	1610 $$\begin{array}{l}
adamc@544	1611 \mt{val} \; \mt{sql\_exp} : \mt{tabs} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{t} ::: \mt{Type} \to \mt{rest} ::: \{\mt{Type}\} \to \mt{nm} :: \mt{Name} \\
adamc@544	1612 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tabs} \; \mt{agg} \; ([\mt{nm} = \mt{t}] \rc \mt{rest}) \; \mt{t}
adamc@544	1613 \end{array}$$
adamc@544	1614
adamc@544	1615 Ur values of appropriate types may be injected into SQL expressions.
adamc@544	1616 $$\begin{array}{l}
adamc@786	1617 \mt{class} \; \mt{sql\_injectable\_prim} \\
adamc@786	1618 \mt{val} \; \mt{sql\_bool} : \mt{sql\_injectable\_prim} \; \mt{bool} \\
adamc@786	1619 \mt{val} \; \mt{sql\_int} : \mt{sql\_injectable\_prim} \; \mt{int} \\
adamc@786	1620 \mt{val} \; \mt{sql\_float} : \mt{sql\_injectable\_prim} \; \mt{float} \\
adamc@786	1621 \mt{val} \; \mt{sql\_string} : \mt{sql\_injectable\_prim} \; \mt{string} \\
adamc@786	1622 \mt{val} \; \mt{sql\_time} : \mt{sql\_injectable\_prim} \; \mt{time} \\
adamc@786	1623 \mt{val} \; \mt{sql\_blob} : \mt{sql\_injectable\_prim} \; \mt{blob} \\
adamc@786	1624 \mt{val} \; \mt{sql\_channel} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{channel} \; \mt{t}) \\
adamc@786	1625 \mt{val} \; \mt{sql\_client} : \mt{sql\_injectable\_prim} \; \mt{client} \\
adamc@786	1626 \\
adamc@544	1627 \mt{class} \; \mt{sql\_injectable} \\
adamc@786	1628 \mt{val} \; \mt{sql\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@786	1629 \mt{val} \; \mt{sql\_option\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; (\mt{option} \; \mt{t}) \\
adamc@786	1630 \\
adamc@544	1631 \mt{val} \; \mt{sql\_inject} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@544	1632 \hspace{.1in} \to \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adamc@544	1633 \end{array}$$
adamc@544	1634
adamc@1123	1635 Additionally, most function-free types may be injected safely, via the $\mt{serialized}$ type family.
adamc@1123	1636 $$\begin{array}{l}
adamc@1123	1637 \mt{con} \; \mt{serialized} :: \mt{Type} \to \mt{Type} \\
adamc@1123	1638 \mt{val} \; \mt{serialize} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{serialized} \; \mt{t} \\
adamc@1123	1639 \mt{val} \; \mt{deserialize} : \mt{t} ::: \mt{Type} \to \mt{serialized} \; \mt{t} \to \mt{t} \\
adamc@1123	1640 \mt{val} \; \mt{sql\_serialized} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{serialized} \; \mt{t})
adamc@1123	1641 \end{array}$$
adamc@1123	1642
adamc@544	1643 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	1644 $$\begin{array}{l}
adamc@544	1645 \mt{val} \; \mt{sql\_is\_null} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544	1646 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; (\mt{option} \; \mt{t}) \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{bool}
adamc@544	1647 \end{array}$$
adamc@544	1648
adamc@559	1649 We have generic nullary, unary, and binary operators.
adamc@544	1650 $$\begin{array}{l}
adamc@544	1651 \mt{con} \; \mt{sql\_nfunc} :: \mt{Type} \to \mt{Type} \\
adamc@544	1652 \mt{val} \; \mt{sql\_current\_timestamp} : \mt{sql\_nfunc} \; \mt{time} \\
adamc@544	1653 \mt{val} \; \mt{sql\_nfunc} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544	1654 \hspace{.1in} \to \mt{sql\_nfunc} \; \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\\end{array}$$
adamc@544	1655
adamc@544	1656 $$\begin{array}{l}
adamc@544	1657 \mt{con} \; \mt{sql\_unary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544	1658 \mt{val} \; \mt{sql\_not} : \mt{sql\_unary} \; \mt{bool} \; \mt{bool} \\
adamc@544	1659 \mt{val} \; \mt{sql\_unary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adamc@544	1660 \hspace{.1in} \to \mt{sql\_unary} \; \mt{arg} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res} \\
adamc@544	1661 \end{array}$$
adamc@544	1662
adamc@544	1663 $$\begin{array}{l}
adamc@544	1664 \mt{con} \; \mt{sql\_binary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544	1665 \mt{val} \; \mt{sql\_and} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544	1666 \mt{val} \; \mt{sql\_or} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544	1667 \mt{val} \; \mt{sql\_binary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg_1} ::: \mt{Type} \to \mt{arg_2} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adamc@544	1668 \hspace{.1in} \to \mt{sql\_binary} \; \mt{arg_1} \; \mt{arg_2} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_1} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_2} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res}
adamc@544	1669 \end{array}$$
adamc@544	1670
adamc@544	1671 $$\begin{array}{l}
adamc@559	1672 \mt{class} \; \mt{sql\_arith} \\
adamc@559	1673 \mt{val} \; \mt{sql\_int\_arith} : \mt{sql\_arith} \; \mt{int} \\
adamc@559	1674 \mt{val} \; \mt{sql\_float\_arith} : \mt{sql\_arith} \; \mt{float} \\
adamc@559	1675 \mt{val} \; \mt{sql\_neg} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_unary} \; \mt{t} \; \mt{t} \\
adamc@559	1676 \mt{val} \; \mt{sql\_plus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559	1677 \mt{val} \; \mt{sql\_minus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559	1678 \mt{val} \; \mt{sql\_times} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559	1679 \mt{val} \; \mt{sql\_div} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559	1680 \mt{val} \; \mt{sql\_mod} : \mt{sql\_binary} \; \mt{int} \; \mt{int} \; \mt{int}
adamc@559	1681 \end{array}$$
adamc@544	1682
adamc@656	1683 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	1684 $$\begin{array}{l}
adamc@544	1685 \mt{val} \; \mt{sql\_count} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int}
adamc@544	1686 \end{array}$$
adamc@544	1687
adamc@544	1688 $$\begin{array}{l}
adamc@1188	1689 \mt{con} \; \mt{sql\_aggregate} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@1188	1690 \mt{val} \; \mt{sql\_aggregate} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{dom} ::: \mt{Type} \to \mt{ran} ::: \mt{Type} \\
adamc@1188	1691 \hspace{.1in} \to \mt{sql\_aggregate} \; \mt{dom} \; \mt{ran} \to \mt{sql\_exp} \; \mt{agg} \; \mt{agg} \; \mt{exps} \; \mt{dom} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{ran}
adamc@1188	1692 \end{array}$$
adamc@1188	1693
adamc@1188	1694 $$\begin{array}{l}
adamc@1188	1695 \mt{val} \; \mt{sql\_count\_col} : \mt{t} ::: \mt{Type} \to \mt{sql\_aggregate} \; (\mt{option} \; \mt{t}) \; \mt{int}
adamc@544	1696 \end{array}$$
adamc@544	1697
adamc@544	1698 $$\begin{array}{l}
adamc@544	1699 \mt{class} \; \mt{sql\_summable} \\
adamc@544	1700 \mt{val} \; \mt{sql\_summable\_int} : \mt{sql\_summable} \; \mt{int} \\
adamc@544	1701 \mt{val} \; \mt{sql\_summable\_float} : \mt{sql\_summable} \; \mt{float} \\
adamc@1188	1702 \mt{val} \; \mt{sql\_avg} : \mt{t} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{t} \\
adamc@1188	1703 \mt{val} \; \mt{sql\_sum} : \mt{t} ::: \mt{Type} \to \mt{sql\_summable} \mt{t} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{t}
adamc@544	1704 \end{array}$$
adamc@544	1705
adamc@544	1706 $$\begin{array}{l}
adamc@544	1707 \mt{class} \; \mt{sql\_maxable} \\
adamc@544	1708 \mt{val} \; \mt{sql\_maxable\_int} : \mt{sql\_maxable} \; \mt{int} \\
adamc@544	1709 \mt{val} \; \mt{sql\_maxable\_float} : \mt{sql\_maxable} \; \mt{float} \\
adamc@544	1710 \mt{val} \; \mt{sql\_maxable\_string} : \mt{sql\_maxable} \; \mt{string} \\
adamc@544	1711 \mt{val} \; \mt{sql\_maxable\_time} : \mt{sql\_maxable} \; \mt{time} \\
adamc@1188	1712 \mt{val} \; \mt{sql\_max} : \mt{t} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{t} \\
adamc@1188	1713 \mt{val} \; \mt{sql\_min} : \mt{t} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{t}
adamc@544	1714 \end{array}$$
adamc@544	1715
adamc@1193	1716 Any SQL query that returns single columns may be turned into a subquery expression.
adamc@1193	1717
adamc@786	1718 $$\begin{array}{l}
adamc@1193	1719 \mt{val} \; \mt{sql\_subquery} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \\
adamc@1193	1720 \hspace{.1in} \to \mt{sql\_query} \; \mt{tables} \; [] \; [\mt{nm} = \mt{t}] \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adamc@1193	1721 \end{array}$$
adamc@1193	1722
adamc@1193	1723 \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	1724 $$\begin{array}{l}
adamc@1193	1725 \mt{con} \; \mt{sql\_from\_items} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@1193	1726 \mt{val} \; \mt{sql\_from\_table} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adamc@1193	1727 \hspace{.1in} \to \mt{t} ::: \mt{Type} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; \mt{t} \; \mt{fs} \to \mt{name} :: \mt{Name} \to \mt{t} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193	1728 \mt{val} \; \mt{sql\_from\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{name} :: \mt{Name} \to \mt{sql\_query} \; \mt{free} \; [] \; \mt{fs} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193	1729 \mt{val} \; \mt{sql\_from\_comma} : \mt{free} ::: \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \to [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193	1730 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adamc@1193	1731 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2}) \\
adamc@1193	1732 \mt{val} \; \mt{sql\_inner\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \\
adamc@1193	1733 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193	1734 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adamc@1193	1735 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193	1736 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2})
adamc@786	1737 \end{array}$$
adamc@786	1738
adamc@786	1739 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	1740 $$\begin{array}{l}
adamc@786	1741 \mt{class} \; \mt{nullify} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@786	1742 \mt{val} \; \mt{nullify\_option} : \mt{t} ::: \mt{Type} \to \mt{nullify} \; (\mt{option} \; \mt{t}) \; (\mt{option} \; \mt{t}) \\
adamc@786	1743 \mt{val} \; \mt{nullify\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{nullify} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@786	1744 \end{array}$$
adamc@786	1745
adamc@786	1746 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	1747
adamc@786	1748 $$\begin{array}{l}
adamc@1193	1749 \mt{val} \; \mt{sql\_left\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{(\mt{Type} \times \mt{Type})\}\} \\
adamc@1193	1750 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@786	1751 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\lambda \mt{r} \Rightarrow \$(\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{nullify} \; \mt{p}.1 \; \mt{p}.2) \; \mt{r})) \; \mt{tabs2}) \\
adamc@1193	1752 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \\
adamc@1193	1753 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193	1754 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.2)) \; \mt{tabs2})
adamc@786	1755 \end{array}$$
adamc@786	1756
adamc@544	1757 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	1758 $$\begin{array}{l}
adamc@544	1759 \mt{type} \; \mt{sql\_direction} \\
adamc@544	1760 \mt{val} \; \mt{sql\_asc} : \mt{sql\_direction} \\
adamc@544	1761 \mt{val} \; \mt{sql\_desc} : \mt{sql\_direction} \\
adamc@544	1762 \\
adamc@544	1763 \mt{con} \; \mt{sql\_order\_by} :: \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@544	1764 \mt{val} \; \mt{sql\_order\_by\_Nil} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} :: \{\mt{Type}\} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544	1765 \mt{val} \; \mt{sql\_order\_by\_Cons} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544	1766 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; [] \; \mt{exps} \; \mt{t} \to \mt{sql\_direction} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544	1767 \\
adamc@544	1768 \mt{type} \; \mt{sql\_limit} \\
adamc@544	1769 \mt{val} \; \mt{sql\_no\_limit} : \mt{sql\_limit} \\
adamc@544	1770 \mt{val} \; \mt{sql\_limit} : \mt{int} \to \mt{sql\_limit} \\
adamc@544	1771 \\
adamc@544	1772 \mt{type} \; \mt{sql\_offset} \\
adamc@544	1773 \mt{val} \; \mt{sql\_no\_offset} : \mt{sql\_offset} \\
adamc@544	1774 \mt{val} \; \mt{sql\_offset} : \mt{int} \to \mt{sql\_offset}
adamc@544	1775 \end{array}$$
adamc@544	1776
adamc@545	1777
adamc@545	1778 \subsubsection{DML}
adamc@545	1779
adamc@545	1780 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	1781
adamc@545	1782 $$\begin{array}{l}
adamc@545	1783 \mt{type} \; \mt{dml} \\
adamc@545	1784 \mt{val} \; \mt{dml} : \mt{dml} \to \mt{transaction} \; \mt{unit}
adamc@545	1785 \end{array}$$
adamc@545	1786
adam@1297	1787 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	1788
adam@1297	1789 $$\begin{array}{l}
adam@1297	1790 \mt{val} \; \mt{tryDml} : \mt{dml} \to \mt{transaction} \; (\mt{option} \; \mt{string})
adam@1297	1791 \end{array}$$
adam@1297	1792
adamc@545	1793 Properly-typed records may be used to form $\mt{INSERT}$ commands.
adamc@545	1794 $$\begin{array}{l}
adamc@545	1795 \mt{val} \; \mt{insert} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \\
adamc@658	1796 \hspace{.1in} \to \$(\mt{map} \; (\mt{sql\_exp} \; [] \; [] \; []) \; \mt{fields}) \to \mt{dml}
adamc@545	1797 \end{array}$$
adamc@545	1798
adamc@545	1799 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	1800 $$\begin{array}{l}
adamc@545	1801 \mt{val} \; \mt{update} : \mt{unchanged} ::: \{\mt{Type}\} \to \mt{changed} :: \{\mt{Type}\} \to \lambda [\mt{changed} \sim \mt{unchanged}] \\
adamc@658	1802 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; []) \; \mt{changed}) \\
adamc@545	1803 \hspace{.1in} \to \mt{sql\_table} \; (\mt{changed} \rc \mt{unchanged}) \to \mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545	1804 \end{array}$$
adamc@545	1805
adamc@545	1806 A $\mt{DELETE}$ command is formed from a table and a $\mt{WHERE}$ clause.
adamc@545	1807 $$\begin{array}{l}
adamc@545	1808 \mt{val} \; \mt{delete} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \to \mt{sql\_exp} \; [\mt{T} = \mt{fields}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545	1809 \end{array}$$
adamc@545	1810
adamc@546	1811 \subsubsection{Sequences}
adamc@546	1812
adamc@546	1813 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	1814
adamc@546	1815 $$\begin{array}{l}
adamc@546	1816 \mt{type} \; \mt{sql\_sequence} \\
adamc@1085	1817 \mt{val} \; \mt{nextval} : \mt{sql\_sequence} \to \mt{transaction} \; \mt{int} \\
adamc@1085	1818 \mt{val} \; \mt{setval} : \mt{sql\_sequence} \to \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@546	1819 \end{array}$$
adamc@546	1820
adamc@546	1821
adamc@547	1822 \subsection{XML}
adamc@547	1823
adam@1333	1824 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	1825
adam@1345	1826 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	1827 $$\begin{array}{l}
adamc@547	1828 \mt{con} \; \mt{xml} :: \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547	1829 \end{array}$$
adamc@547	1830
adamc@547	1831 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	1832 $$\begin{array}{l}
adamc@547	1833 \mt{con} \; \mt{tag} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547	1834 \end{array}$$
adamc@547	1835
adamc@547	1836 Literal text may be injected into XML as ``CDATA.''
adamc@547	1837 $$\begin{array}{l}
adamc@547	1838 \mt{val} \; \mt{cdata} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{string} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adamc@547	1839 \end{array}$$
adamc@547	1840
adam@1358	1841 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	1842 $$\begin{array}{l}
adam@1358	1843 \mt{val} \; \mt{cdataChar} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{char} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adam@1358	1844 \end{array}$$
adam@1358	1845
adamc@547	1846 There is a function for producing an XML tree with a particular tag at its root.
adamc@547	1847 $$\begin{array}{l}
adamc@547	1848 \mt{val} \; \mt{tag} : \mt{attrsGiven} ::: \{\mt{Type}\} \to \mt{attrsAbsent} ::: \{\mt{Type}\} \to \mt{ctxOuter} ::: \{\mt{Unit}\} \to \mt{ctxInner} ::: \{\mt{Unit}\} \\
adamc@547	1849 \hspace{.1in} \to \mt{useOuter} ::: \{\mt{Type}\} \to \mt{useInner} ::: \{\mt{Type}\} \to \mt{bindOuter} ::: \{\mt{Type}\} \to \mt{bindInner} ::: \{\mt{Type}\} \\
adamc@787	1850 \hspace{.1in} \to \lambda [\mt{attrsGiven} \sim \mt{attrsAbsent}] \; [\mt{useOuter} \sim \mt{useInner}] \; [\mt{bindOuter} \sim \mt{bindInner}] \\
adamc@787	1851 \hspace{.1in} \Rightarrow \mt{option} \; \mt{css\_class} \\
adamc@787	1852 \hspace{.1in} \to \$\mt{attrsGiven} \\
adamc@547	1853 \hspace{.1in} \to \mt{tag} \; (\mt{attrsGiven} \rc \mt{attrsAbsent}) \; \mt{ctxOuter} \; \mt{ctxInner} \; \mt{useOuter} \; \mt{bindOuter} \\
adamc@547	1854 \hspace{.1in} \to \mt{xml} \; \mt{ctxInner} \; \mt{useInner} \; \mt{bindInner} \to \mt{xml} \; \mt{ctxOuter} \; (\mt{useOuter} \rc \mt{useInner}) \; (\mt{bindOuter} \rc \mt{bindInner})
adamc@547	1855 \end{array}$$
adam@1297	1856 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	1857
adamc@547	1858 Two XML fragments may be concatenated.
adamc@547	1859 $$\begin{array}{l}
adamc@547	1860 \mt{val} \; \mt{join} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{bind_1} ::: \{\mt{Type}\} \to \mt{bind_2} ::: \{\mt{Type}\} \\
adamc@547	1861 \hspace{.1in} \to \lambda [\mt{use_1} \sim \mt{bind_1}] \; [\mt{bind_1} \sim \mt{bind_2}] \\
adamc@547	1862 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind_1} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{bind_1}) \; \mt{bind_2} \to \mt{xml} \; \mt{ctx} \; \mt{use_1} \; (\mt{bind_1} \rc \mt{bind_2})
adamc@547	1863 \end{array}$$
adamc@547	1864
adamc@547	1865 Finally, any XML fragment may be updated to ``claim'' to use more form fields than it does.
adamc@547	1866 $$\begin{array}{l}
adamc@547	1867 \mt{val} \; \mt{useMore} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{use_2} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to \lambda [\mt{use_1} \sim \mt{use_2}] \\
adamc@547	1868 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{use_2}) \; \mt{bind}
adamc@547	1869 \end{array}$$
adamc@547	1870
adam@1344	1871 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	1872
adamc@547	1873 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	1874 $$\begin{array}{l}
adamc@547	1875 \mt{val} \; \mt{error} : \mt{t} ::: \mt{Type} \to \mt{xml} \; [\mt{Body}] \; [] \; [] \to \mt{t}
adamc@547	1876 \end{array}$$
adamc@547	1877
adamc@549	1878
adamc@701	1879 \subsection{Client-Side Programming}
adamc@659	1880
adamc@701	1881 Ur/Web supports running code on web browsers, via automatic compilation to JavaScript.
adamc@701	1882
adamc@701	1883 \subsubsection{The Basics}
adamc@701	1884
adam@1297	1885 Clients can open alert and confirm dialog boxes, in the usual annoying JavaScript way.
adamc@701	1886 $$\begin{array}{l}
adam@1297	1887 \mt{val} \; \mt{alert} : \mt{string} \to \mt{transaction} \; \mt{unit} \\
adam@1297	1888 \mt{val} \; \mt{confirm} : \mt{string} \to \mt{transaction} \; \mt{bool}
adamc@701	1889 \end{array}$$
adamc@701	1890
adamc@701	1891 Any transaction may be run in a new thread with the $\mt{spawn}$ function.
adamc@701	1892 $$\begin{array}{l}
adamc@701	1893 \mt{val} \; \mt{spawn} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit}
adamc@701	1894 \end{array}$$
adamc@701	1895
adamc@701	1896 The current thread can be paused for at least a specified number of milliseconds.
adamc@701	1897 $$\begin{array}{l}
adamc@701	1898 \mt{val} \; \mt{sleep} : \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@701	1899 \end{array}$$
adamc@701	1900
adamc@787	1901 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	1902 $$\begin{array}{l}
adamc@787	1903 \mt{val} \; \mt{onError} : (\mt{xbody} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787	1904 \mt{val} \; \mt{onFail} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787	1905 \mt{val} \; \mt{onConnectFail} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787	1906 \mt{val} \; \mt{onDisconnect} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787	1907 \mt{val} \; \mt{onServerError} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit}
adamc@787	1908 \end{array}$$
adamc@787	1909
adamc@701	1910 \subsubsection{Functional-Reactive Page Generation}
adamc@701	1911
adamc@701	1912 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	1913
adamc@659	1914 $$\begin{array}{l}
adamc@659	1915 \mt{con} \; \mt{source} :: \mt{Type} \to \mt{Type} \\
adamc@659	1916 \mt{val} \; \mt{source} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{transaction} \; (\mt{source} \; \mt{t}) \\
adamc@659	1917 \mt{val} \; \mt{set} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@659	1918 \mt{val} \; \mt{get} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@659	1919 \end{array}$$
adamc@659	1920
adamc@659	1921 Pure functions over sources are represented in a monad of \emph{signals}.
adamc@659	1922
adamc@659	1923 $$\begin{array}{l}
adamc@659	1924 \mt{con} \; \mt{signal} :: \mt{Type} \to \mt{Type} \\
adamc@659	1925 \mt{val} \; \mt{signal\_monad} : \mt{monad} \; \mt{signal} \\
adamc@659	1926 \mt{val} \; \mt{signal} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{signal} \; \mt{t}
adamc@659	1927 \end{array}$$
adamc@659	1928
adamc@659	1929 A reactive portion of an HTML page is injected with a $\mt{dyn}$ tag, which has a signal-valued attribute $\mt{Signal}$.
adamc@659	1930
adamc@659	1931 $$\begin{array}{l}
adamc@701	1932 \mt{val} \; \mt{dyn} : \mt{use} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to \mt{unit} \\
adamc@701	1933 \hspace{.1in} \to \mt{tag} \; [\mt{Signal} = \mt{signal} \; (\mt{xml} \; \mt{body} \; \mt{use} \; \mt{bind})] \; \mt{body} \; [] \; \mt{use} \; \mt{bind}
adamc@659	1934 \end{array}$$
adamc@659	1935
adamc@701	1936 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	1937
adamc@914	1938 \subsubsection{Remote Procedure Calls}
adamc@914	1939
adamc@914	1940 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	1941
adamc@914	1942 $$\begin{array}{l}
adamc@914	1943 \mt{val} \; \mt{rpc} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@914	1944 \end{array}$$
adamc@914	1945
adamc@701	1946 \subsubsection{Asynchronous Message-Passing}
adamc@701	1947
adamc@701	1948 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	1949
adamc@701	1950 $$\begin{array}{l}
adamc@701	1951 \mt{type} \; \mt{client} \\
adamc@701	1952 \mt{val} \; \mt{self} : \mt{transaction} \; \mt{client}
adamc@701	1953 \end{array}$$
adamc@701	1954
adamc@701	1955 \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	1956
adamc@701	1957 $$\begin{array}{l}
adamc@701	1958 \mt{con} \; \mt{channel} :: \mt{Type} \to \mt{Type} \\
adamc@701	1959 \mt{val} \; \mt{channel} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; (\mt{channel} \; \mt{t}) \\
adamc@701	1960 \mt{val} \; \mt{send} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@701	1961 \mt{val} \; \mt{recv} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@701	1962 \end{array}$$
adamc@701	1963
adamc@701	1964 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	1965
adamc@701	1966 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	1967
adamc@659	1968
adamc@549	1969 \section{Ur/Web Syntax Extensions}
adamc@549	1970
adamc@549	1971 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	1972
adamc@549	1973 \subsection{SQL}
adamc@549	1974
adamc@786	1975 \subsubsection{\label{tables}Table Declarations}
adamc@786	1976
adamc@788	1977 $\mt{table}$ declarations may include constraints, via these grammar rules.
adamc@788	1978 $$\begin{array}{rrcll}
adamc@788	1979 \textrm{Declarations} & d &::=& \mt{table} \; x : c \; [pk[,]] \; cts \\
adamc@788	1980 \textrm{Primary key constraints} & pk &::=& \mt{PRIMARY} \; \mt{KEY} \; K \\
adamc@788	1981 \textrm{Keys} & K &::=& f \mid (f, (f,)^+) \\
adamc@788	1982 \textrm{Constraint sets} & cts &::=& \mt{CONSTRAINT} f \; ct \mid cts, cts \mid \{\{e\}\} \\
adamc@788	1983 \textrm{Constraints} & ct &::=& \mt{UNIQUE} \; K \mid \mt{CHECK} \; E \\
adamc@788	1984 &&& \mid \mt{FOREIGN} \; \mt{KEY} \; K \; \mt{REFERENCES} \; F \; (K) \; [\mt{ON} \; \mt{DELETE} \; pr] \; [\mt{ON} \; \mt{UPDATE} \; pr] \\
adamc@788	1985 \textrm{Foreign tables} & F &::=& x \mid \{\{e\}\} \\
adamc@788	1986 \textrm{Propagation modes} & pr &::=& \mt{NO} \; \mt{ACTION} \mid \mt{RESTRICT} \mid \mt{CASCADE} \mid \mt{SET} \; \mt{NULL}
adamc@788	1987 \end{array}$$
adamc@788	1988
adamc@788	1989 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	1990
adamc@788	1991
adamc@549	1992 \subsubsection{Queries}
adamc@549	1993
adamc@550	1994 Queries $Q$ are added to the rules for expressions $e$.
adamc@550	1995
adamc@549	1996 $$\begin{array}{rrcll}
adamc@550	1997 \textrm{Queries} & Q &::=& (q \; [\mt{ORDER} \; \mt{BY} \; (E \; [o],)^+] \; [\mt{LIMIT} \; N] \; [\mt{OFFSET} \; N]) \\
adamc@1085	1998 \textrm{Pre-queries} & q &::=& \mt{SELECT} \; [\mt{DISTINCT}] \; P \; \mt{FROM} \; F,^+ \; [\mt{WHERE} \; E] \; [\mt{GROUP} \; \mt{BY} \; p,^+] \; [\mt{HAVING} \; E] \\
adamc@1085	1999 &&& \mid q \; R \; q \mid \{\{\{e\}\}\} \\
adamc@549	2000 \textrm{Relational operators} & R &::=& \mt{UNION} \mid \mt{INTERSECT} \mid \mt{EXCEPT}
adamc@549	2001 \end{array}$$
adamc@549	2002
adamc@549	2003 $$\begin{array}{rrcll}
adamc@549	2004 \textrm{Projections} & P &::=& \ast & \textrm{all columns} \\
adamc@549	2005 &&& p,^+ & \textrm{particular columns} \\
adamc@549	2006 \textrm{Pre-projections} & p &::=& t.f & \textrm{one column from a table} \\
adamc@558	2007 &&& t.\{\{c\}\} & \textrm{a record of columns from a table (of kind $\{\mt{Type}\}$)} \\
adamc@1194	2008 &&& E \; [\mt{AS} \; f] & \textrm{expression column} \\
adamc@549	2009 \textrm{Table names} & t &::=& x & \textrm{constant table name (automatically capitalized)} \\
adamc@549	2010 &&& X & \textrm{constant table name} \\
adamc@549	2011 &&& \{\{c\}\} & \textrm{computed table name (of kind $\mt{Name}$)} \\
adamc@549	2012 \textrm{Column names} & f &::=& X & \textrm{constant column name} \\
adamc@549	2013 &&& \{c\} & \textrm{computed column name (of kind $\mt{Name}$)} \\
adamc@549	2014 \textrm{Tables} & T &::=& x & \textrm{table variable, named locally by its own capitalization} \\
adamc@549	2015 &&& x \; \mt{AS} \; t & \textrm{table variable, with local name} \\
adamc@549	2016 &&& \{\{e\}\} \; \mt{AS} \; t & \textrm{computed table expression, with local name} \\
adamc@1085	2017 \textrm{$\mt{FROM}$ items} & F &::=& T \mid \{\{e\}\} \mid F \; J \; \mt{JOIN} \; F \; \mt{ON} \; E \\
adamc@1085	2018 &&& \mid F \; \mt{CROSS} \; \mt{JOIN} \ F \\
adamc@1193	2019 &&& \mid (Q) \; \mt{AS} \; t \\
adamc@1085	2020 \textrm{Joins} & J &::=& [\mt{INNER}] \\
adamc@1085	2021 &&& \mid [\mt{LEFT} \mid \mt{RIGHT} \mid \mt{FULL}] \; [\mt{OUTER}] \\
adamc@549	2022 \textrm{SQL expressions} & E &::=& p & \textrm{column references} \\
adamc@549	2023 &&& X & \textrm{named expression references} \\
adamc@549	2024 &&& \{\{e\}\} & \textrm{injected native Ur expressions} \\
adamc@549	2025 &&& \{e\} & \textrm{computed expressions, probably using $\mt{sql\_exp}$ directly} \\
adamc@549	2026 &&& \mt{TRUE} \mid \mt{FALSE} & \textrm{boolean constants} \\
adamc@549	2027 &&& \ell & \textrm{primitive type literals} \\
adamc@549	2028 &&& \mt{NULL} & \textrm{null value (injection of $\mt{None}$)} \\
adamc@549	2029 &&& E \; \mt{IS} \; \mt{NULL} & \textrm{nullness test} \\
adamc@549	2030 &&& n & \textrm{nullary operators} \\
adamc@549	2031 &&& u \; E & \textrm{unary operators} \\
adamc@549	2032 &&& E \; b \; E & \textrm{binary operators} \\
adamc@549	2033 &&& \mt{COUNT}(\ast) & \textrm{count number of rows} \\
adamc@549	2034 &&& a(E) & \textrm{other aggregate function} \\
adamc@1193	2035 &&& (Q) & \textrm{subquery (must return a single expression column)} \\
adamc@549	2036 &&& (E) & \textrm{explicit precedence} \\
adamc@549	2037 \textrm{Nullary operators} & n &::=& \mt{CURRENT\_TIMESTAMP} \\
adamc@549	2038 \textrm{Unary operators} & u &::=& \mt{NOT} \\
adamc@549	2039 \textrm{Binary operators} & b &::=& \mt{AND} \mid \mt{OR} \mid \neq \mid < \mid \leq \mid > \mid \geq \\
adamc@1188	2040 \textrm{Aggregate functions} & a &::=& \mt{COUNT} \mid \mt{AVG} \mid \mt{SUM} \mid \mt{MIN} \mid \mt{MAX} \\
adamc@550	2041 \textrm{Directions} & o &::=& \mt{ASC} \mid \mt{DESC} \\
adamc@549	2042 \textrm{SQL integer} & N &::=& n \mid \{e\} \\
adamc@549	2043 \end{array}$$
adamc@549	2044
adamc@1085	2045 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	2046
adamc@1194	2047 Unnamed expression columns in $\mt{SELECT}$ clauses are assigned consecutive natural numbers, starting with 1.
adamc@1194	2048
adamc@550	2049 \subsubsection{DML}
adamc@550	2050
adamc@550	2051 DML commands $D$ are added to the rules for expressions $e$.
adamc@550	2052
adamc@550	2053 $$\begin{array}{rrcll}
adamc@550	2054 \textrm{Commands} & D &::=& (\mt{INSERT} \; \mt{INTO} \; T^E \; (f,^+) \; \mt{VALUES} \; (E,^+)) \\
adamc@550	2055 &&& (\mt{UPDATE} \; T^E \; \mt{SET} \; (f = E,)^+ \; \mt{WHERE} \; E) \\
adamc@550	2056 &&& (\mt{DELETE} \; \mt{FROM} \; T^E \; \mt{WHERE} \; E) \\
adamc@550	2057 \textrm{Table expressions} & T^E &::=& x \mid \{\{e\}\}
adamc@550	2058 \end{array}$$
adamc@550	2059
adamc@550	2060 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	2061
adamc@551	2062 \subsection{XML}
adamc@551	2063
adamc@551	2064 XML fragments $L$ are added to the rules for expressions $e$.
adamc@551	2065
adamc@551	2066 $$\begin{array}{rrcll}
adamc@551	2067 \textrm{XML fragments} & L &::=& \texttt{<xml/>} \mid \texttt{<xml>}l^*\texttt{</xml>} \\
adamc@551	2068 \textrm{XML pieces} & l &::=& \textrm{text} & \textrm{cdata} \\
adamc@551	2069 &&& \texttt{<}g\texttt{/>} & \textrm{tag with no children} \\
adamc@551	2070 &&& \texttt{<}g\texttt{>}l^*\texttt{</}x\texttt{>} & \textrm{tag with children} \\
adamc@559	2071 &&& \{e\} & \textrm{computed XML fragment} \\
adamc@559	2072 &&& \{[e]\} & \textrm{injection of an Ur expression, via the $\mt{Top}.\mt{txt}$ function} \\
adamc@551	2073 \textrm{Tag} & g &::=& h \; (x = v)^* \\
adamc@551	2074 \textrm{Tag head} & h &::=& x & \textrm{tag name} \\
adamc@551	2075 &&& h\{c\} & \textrm{constructor parameter} \\
adamc@551	2076 \textrm{Attribute value} & v &::=& \ell & \textrm{literal value} \\
adamc@551	2077 &&& \{e\} & \textrm{computed value} \\
adamc@551	2078 \end{array}$$
adamc@551	2079
adamc@552	2080
adamc@1198	2081 \section{\label{structure}The Structure of Web Applications}
adamc@553	2082
adamc@1127	2083 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	2084
adam@1347	2085 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	2086
adamc@553	2087 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	2088
adamc@553	2089 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	2090
adamc@558	2091 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	2092
adamc@660	2093 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	2094
adamc@789	2095 \medskip
adamc@789	2096
adam@1347	2097 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	2098
adamc@789	2099 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	2100
adam@1348	2101 \subsection{Tasks}
adam@1348	2102
adam@1348	2103 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	2104
adam@1348	2105 $$\begin{array}{l}
adam@1348	2106 \mt{con} \; \mt{task\_kind} :: \mt{Type} \to \mt{Type} \\
adam@1348	2107 \mt{val} \; \mt{initialize} : \mt{task\_kind} \; \mt{unit} \\
adam@1349	2108 \mt{val} \; \mt{clientLeaves} : \mt{task\_kind} \; \mt{client} \\
adam@1349	2109 \mt{val} \; \mt{periodic} : \mt{int} \to \mt{task\_kind} \; \mt{unit}
adam@1348	2110 \end{array}$$
adam@1348	2111
adam@1348	2112 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	2113
adam@1348	2114 The currently supported task kinds are:
adam@1348	2115 \begin{itemize}
adam@1349	2116 \item $\mt{initialize}$: Code that is run when the application starts up.
adam@1348	2117 \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	2118 \item $\mt{periodic} \; n$: Code that is run when the application starts up and then every $n$ seconds thereafter.
adam@1348	2119 \end{itemize}
adam@1348	2120
adamc@553	2121
adamc@897	2122 \section{The Foreign Function Interface}
adamc@897	2123
adamc@897	2124 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	2125
adamc@897	2126 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	2127
adamc@897	2128 \begin{itemize}
adamc@897	2129 \item \texttt{clientOnly Module.ident} registers a value as being allowed only in client-side code.
adamc@897	2130 \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	2131 \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	2132 \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	2133 \item \texttt{include FILE} requests inclusion of a C header file.
adamc@897	2134 \item \texttt{jsFunc Module.ident=name} gives a mapping from an Ur name for a value to a JavaScript name.
adamc@897	2135 \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	2136 \item \texttt{script URL} requests inclusion of a JavaScript source file within application HTML.
adamc@897	2137 \item \texttt{serverOnly Module.ident} registers a value as being allowed only in server-side code.
adamc@897	2138 \end{itemize}
adamc@897	2139
adamc@897	2140 \subsection{Writing C FFI Code}
adamc@897	2141
adamc@897	2142 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	2143
adamc@897	2144 \begin{itemize}
adamc@897	2145 \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	2146 \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	2147 \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	2148 \end{itemize}
adamc@897	2149
adamc@897	2150 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	2151 \begin{itemize}
adamc@897	2152 \item \begin{verbatim}
adamc@897	2153 void uw_error(uw_context, failure_kind, const char *fmt, ...);
adamc@897	2154 \end{verbatim}
adamc@897	2155 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	2156
adam@1329	2157 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	2158
adamc@897	2159 \item \begin{verbatim}
adamc@897	2160 void uw_push_cleanup(uw_context, void (func)(void ), void *arg);
adamc@897	2161 void uw_pop_cleanup(uw_context);
adamc@897	2162 \end{verbatim}
adam@1329	2163 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	2164
adam@1329	2165 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	2166
adamc@897	2167 \item \begin{verbatim}
adamc@897	2168 void *uw_malloc(uw_context, size_t);
adamc@897	2169 \end{verbatim}
adam@1329	2170 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	2171
adam@1329	2172 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	2173
adamc@897	2174 \item \begin{verbatim}
adamc@897	2175 typedef void (uw_callback)(void );
adam@1328	2176 typedef void (uw_callback_with_retry)(void , int will_retry);
adamc@897	2177 void uw_register_transactional(uw_context, void *data, uw_callback commit,
adam@1328	2178 uw_callback rollback, uw_callback_with_retry free);
adamc@897	2179 \end{verbatim}
adam@1328	2180 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	2181
adamc@1085	2182 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	2183
adam@1329	2184 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	2185
adam@1329	2186 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	2187
adamc@1085	2188 \item \begin{verbatim}
adamc@1085	2189 void uw_get_global(uw_context, char name);
adamc@1085	2190 void uw_set_global(uw_context, char name, void data, uw_callback free);
adamc@1085	2191 \end{verbatim}
adam@1329	2192 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	2193
adamc@897	2194 \end{itemize}
adamc@897	2195
adamc@897	2196 \subsection{Writing JavaScript FFI Code}
adamc@897	2197
adamc@897	2198 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	2199
adamc@897	2200 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	2201
adamc@897	2202 \begin{itemize}
adamc@897	2203 \item Integers, floats, strings, characters, and booleans are represented in the usual JavaScript way.
adamc@985	2204 \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	2205 \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	2206 \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	2207 \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	2208 \end{itemize}
adamc@897	2209
adamc@897	2210 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	2211
adamc@897	2212
adamc@552	2213 \section{Compiler Phases}
adamc@552	2214
adamc@552	2215 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	2216
adamc@552	2217 In this section, we step through the main phases of compilation, noting what consequences each phase has for effective programming.
adamc@552	2218
adamc@552	2219 \subsection{Parse}
adamc@552	2220
adamc@552	2221 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	2222
adamc@552	2223 \subsection{Elaborate}
adamc@552	2224
adamc@552	2225 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	2226
adamc@552	2227 \subsection{Unnest}
adamc@552	2228
adamc@552	2229 Named local function definitions are moved to the top level, to avoid the need to generate closures.
adamc@552	2230
adamc@552	2231 \subsection{Corify}
adamc@552	2232
adamc@552	2233 Module system features are compiled away, through inlining of functor definitions at application sites. Afterward, most abstraction boundaries are broken, facilitating optimization.
adamc@552	2234
adamc@552	2235 \subsection{Especialize}
adamc@552	2236
adam@1356	2237 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	2238
adamc@552	2239 \subsection{Untangle}
adamc@552	2240
adamc@552	2241 Remove unnecessary mutual recursion, splitting recursive groups into strongly-connected components.
adamc@552	2242
adamc@552	2243 \subsection{Shake}
adamc@552	2244
adamc@552	2245 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	2246
adamc@661	2247 \subsection{Rpcify}
adamc@661	2248
adamc@661	2249 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	2250
adamc@661	2251 \subsection{Untangle, Shake}
adamc@661	2252
adamc@661	2253 Repeat these simplifications.
adamc@661	2254
adamc@553	2255 \subsection{\label{tag}Tag}
adamc@552	2256
adamc@552	2257 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	2258
adamc@552	2259 \subsection{Reduce}
adamc@552	2260
adamc@552	2261 Apply definitional equality rules to simplify the program as much as possible. This effectively includes inlining of every non-recursive definition.
adamc@552	2262
adamc@552	2263 \subsection{Unpoly}
adamc@552	2264
adamc@552	2265 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	2266
adamc@552	2267 \subsection{Specialize}
adamc@552	2268
adamc@558	2269 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	2270
adamc@552	2271 \subsection{Shake}
adamc@552	2272
adamc@558	2273 Here the compiler repeats the earlier Shake phase.
adamc@552	2274
adamc@552	2275 \subsection{Monoize}
adamc@552	2276
adamc@552	2277 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	2278
adamc@552	2279 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	2280
adamc@552	2281 \subsection{MonoOpt}
adamc@552	2282
adamc@552	2283 Simple algebraic laws are applied to simplify the program, focusing especially on efficient imperative generation of HTML pages.
adamc@552	2284
adamc@552	2285 \subsection{MonoUntangle}
adamc@552	2286
adamc@552	2287 Unnecessary mutual recursion is broken up again.
adamc@552	2288
adamc@552	2289 \subsection{MonoReduce}
adamc@552	2290
adamc@552	2291 Equivalents of the definitional equality rules are applied to simplify programs, with inlining again playing a major role.
adamc@552	2292
adamc@552	2293 \subsection{MonoShake, MonoOpt}
adamc@552	2294
adamc@552	2295 Unneeded declarations are removed, and basic optimizations are repeated.
adamc@552	2296
adamc@552	2297 \subsection{Fuse}
adamc@552	2298
adamc@552	2299 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	2300
adamc@552	2301 \subsection{MonoUntangle, MonoShake}
adamc@552	2302
adamc@552	2303 Fuse often creates more opportunities to remove spurious mutual recursion.
adamc@552	2304
adamc@552	2305 \subsection{Pathcheck}
adamc@552	2306
adamc@552	2307 The compiler checks that no link or action name has been used more than once.
adamc@552	2308
adamc@552	2309 \subsection{Cjrize}
adamc@552	2310
adamc@552	2311 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	2312
adamc@552	2313 \subsection{C Compilation and Linking}
adamc@552	2314
adamc@552	2315 The output of the last phase is pretty-printed as C source code and passed to GCC.
adamc@552	2316
adamc@552	2317
adamc@524	2318 \end{document}

Mercurial > urweb

annotate doc/manual.tex @ 1362:fd34210bc3e5