Ur/Web: doc/manual.tex annotate

annotate doc/manual.tex @ 1333:dab85a49e0ab

Warn about XHTML looseness

author	Adam Chlipala <adam@chlipala.net>
date	Sat, 11 Dec 2010 19:57:22 -0500
parents	4dd5d23bace2
children	79557535b843

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

Mercurial > urweb

annotate doc/manual.tex @ 1333:dab85a49e0ab