Ur/Web: doc/manual.tex annotate

annotate doc/manual.tex @ 1415:e65082d76d26

Only announce URI serving in standalone HTTP server (grandfathered into release!)

author	Adam Chlipala <adam@chlipala.net>
date	Sun, 23 Jan 2011 15:34:06 -0500
parents	860c245a7c4d
children	3dab4696d116

rev	line source
adamc@524	1 \documentclass{article}
adamc@554	2 \usepackage{fullpage,amsmath,amssymb,proof,url}
adamc@524	3
adamc@524	4 \newcommand{\cd}[1]{\texttt{#1}}
adamc@524	5 \newcommand{\mt}[1]{\mathsf{#1}}
adamc@524	6
adamc@524	7 \newcommand{\rc}{+ \hspace{-.075in} + \;}
adamc@527	8 \newcommand{\rcut}{\; \texttt{--} \;}
adamc@527	9 \newcommand{\rcutM}{\; \texttt{---} \;}
adamc@524	10
adamc@524	11 \begin{document}
adamc@524	12
adamc@524	13 \title{The Ur/Web Manual}
adamc@524	14 \author{Adam Chlipala}
adamc@524	15
adamc@524	16 \maketitle
adamc@524	17
adamc@540	18 \tableofcontents
adamc@540	19
adamc@554	20
adamc@554	21 \section{Introduction}
adamc@554	22
adamc@1160	23 \emph{Ur} is a programming language designed to introduce richer type system features into functional programming in the tradition of ML and Haskell. Ur is functional, pure, statically-typed, and strict. Ur supports a powerful kind of \emph{metaprogramming} based on \emph{type-level computation with type-level records}.
adamc@554	24
adamc@554	25 \emph{Ur/Web} is Ur plus a special standard library and associated rules for parsing and optimization. Ur/Web supports construction of dynamic web applications backed by SQL databases. The signature of the standard library is such that well-typed Ur/Web programs ``don't go wrong'' in a very broad sense. Not only do they not crash during particular page generations, but they also may not:
adamc@554	26
adamc@554	27 \begin{itemize}
adamc@554	28 \item Suffer from any kinds of code-injection attacks
adamc@554	29 \item Return invalid HTML
adamc@554	30 \item Contain dead intra-application links
adamc@554	31 \item Have mismatches between HTML forms and the fields expected by their handlers
adamc@652	32 \item Include client-side code that makes incorrect assumptions about the ``AJAX''-style services that the remote web server provides
adamc@554	33 \item Attempt invalid SQL queries
adamc@652	34 \item Use improper marshaling or unmarshaling in communication with SQL databases or between browsers and web servers
adamc@554	35 \end{itemize}
adamc@554	36
adamc@554	37 This type safety is just the foundation of the Ur/Web methodology. It is also possible to use metaprogramming to build significant application pieces by analysis of type structure. For instance, the demo includes an ML-style functor for building an admin interface for an arbitrary SQL table. The type system guarantees that the admin interface sub-application that comes out will always be free of the above-listed bugs, no matter which well-typed table description is given as input.
adamc@554	38
adamc@652	39 The Ur/Web compiler also produces very efficient object code that does not use garbage collection. These compiled programs will often be even more efficient than what most programmers would bother to write in C. The compiler also generates JavaScript versions of client-side code, with no need to write those parts of applications in a different language.
adamc@554	40
adamc@554	41 \medskip
adamc@554	42
adamc@554	43 The official web site for Ur is:
adamc@554	44 \begin{center}
adamc@554	45 \url{http://www.impredicative.com/ur/}
adamc@554	46 \end{center}
adamc@554	47
adamc@555	48
adamc@555	49 \section{Installation}
adamc@555	50
adamc@555	51 If you are lucky, then the following standard command sequence will suffice for installation, in a directory to which you have unpacked the latest distribution tarball.
adamc@555	52
adamc@555	53 \begin{verbatim}
adamc@555	54 ./configure
adamc@555	55 make
adamc@555	56 sudo make install
adamc@555	57 \end{verbatim}
adamc@555	58
adam@1368	59 Some other packages must be installed for the above to work. At a minimum, you need a standard UNIX shell, with standard UNIX tools like sed and GCC in your execution path; MLton, the whole-program optimizing compiler for Standard ML; and the development files for the OpenSSL C library. As of this writing, in the ``testing'' version of Debian Linux, this command will install the more uncommon of these dependencies:
adamc@896	60 \begin{verbatim}
adam@1368	61 apt-get install mlton libssl-dev
adamc@896	62 \end{verbatim}
adamc@555	63
adamc@896	64 To build programs that access SQL databases, you also need one of these client libraries for supported backends.
adamc@555	65 \begin{verbatim}
adamc@896	66 apt-get install libpq-dev libmysqlclient15-dev libsqlite3-dev
adamc@555	67 \end{verbatim}
adamc@555	68
adamc@555	69 It is also possible to access the modules of the Ur/Web compiler interactively, within Standard ML of New Jersey. To install the prerequisites in Debian testing:
adamc@555	70 \begin{verbatim}
adamc@555	71 apt-get install smlnj libsmlnj-smlnj ml-yacc ml-lpt
adamc@555	72 \end{verbatim}
adamc@555	73
adamc@555	74 To begin an interactive session with the Ur compiler modules, run \texttt{make smlnj}, and then, from within an \texttt{sml} session, run \texttt{CM.make "src/urweb.cm";}. The \texttt{Compiler} module is the main entry point.
adamc@555	75
adamc@896	76 To run an SQL-backed application with a backend besides SQLite, you will probably want to install one of these servers.
adamc@555	77
adamc@555	78 \begin{verbatim}
adam@1400	79 apt-get install postgresql-8.4 mysql-server-5.1
adamc@555	80 \end{verbatim}
adamc@555	81
adamc@555	82 To use the Emacs mode, you must have a modern Emacs installed. We assume that you already know how to do this, if you're in the business of looking for an Emacs mode. The demo generation facility of the compiler will also call out to Emacs to syntax-highlight code, and that process depends on the \texttt{htmlize} module, which can be installed in Debian testing via:
adamc@555	83
adamc@555	84 \begin{verbatim}
adamc@555	85 apt-get install emacs-goodies-el
adamc@555	86 \end{verbatim}
adamc@555	87
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.
adam@1400	138 \item \texttt{alwaysInline PATH} requests that every call to the referenced function be inlined. Section \ref{structure} explains how functions are assigned path strings.
adamc@1171	139 \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	140 \item \texttt{clientOnly Module.ident} registers an FFI function or transaction that may only be run in client browsers.
adamc@783	141 \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	142 \item \texttt{database DBSTRING} sets the string to pass to libpq to open a database connection.
adamc@783	143 \item \texttt{debug} saves some intermediate C files, which is mostly useful to help in debugging the compiler itself.
adamc@783	144 \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	145 \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	146 \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	147 \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	148 \item \texttt{jsFunc Module.ident=name} gives the JavaScript name of an FFI value.
adamc@1089	149 \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	150 \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	151 \begin{itemize}
adam@1309	152 \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	153 \item \texttt{database}: maximum size of database files (currently only used by SQLite)
adam@1309	154 \item \texttt{deltas}: maximum number of messages sendable in a single request handler with \texttt{Basis.send}
adam@1309	155 \item \texttt{globals}: maximum number of global variables that FFI libraries may set in a single request context
adam@1309	156 \item \texttt{headers}: maximum size (in bytes) of per-request buffer used to hold HTTP headers for generated pages
adam@1309	157 \item \texttt{heap}: maximum size (in bytes) of per-request heap for dynamically-allocated data
adam@1309	158 \item \texttt{inputs}: maximum number of top-level form fields per request
adam@1309	159 \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	160 \item \texttt{page}: maximum size (in bytes) of per-request buffer used to hold HTML content of generated pages
adam@1309	161 \item \texttt{script}: maximum size (in bytes) of per-request buffer used to hold JavaScript content of generated pages
adam@1309	162 \item \texttt{subinputs}: maximum number of form fields per request, excluding top-level fields
adam@1309	163 \item \texttt{time}: maximum running time of a single page request, in units of approximately 0.1 seconds
adam@1309	164 \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	165 \end{itemize}
adamc@783	166 \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	167 \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	168 \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	169 \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	170 \item \texttt{prefix PREFIX} sets the prefix included before every URI within the generated application. The default is \texttt{/}.
adamc@783	171 \item \texttt{profile} generates an executable that may be used with gprof.
adam@1300	172 \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	173 \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	174 \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	175 \item \texttt{serverOnly Module.ident} registers an FFI function or transaction that may only be run on the server.
adamc@1164	176 \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	177 \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	178 \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	179 \end{itemize}
adamc@701	180
adamc@701	181
adamc@557	182 \subsection{Building an Application}
adamc@557	183
adamc@557	184 To compile project \texttt{P.urp}, simply run
adamc@557	185 \begin{verbatim}
adamc@557	186 urweb P
adamc@557	187 \end{verbatim}
adamc@1198	188 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	189
adamc@557	190 To time how long the different compiler phases run, without generating an executable, run
adamc@557	191 \begin{verbatim}
adamc@557	192 urweb -timing P
adamc@557	193 \end{verbatim}
adamc@557	194
adamc@1086	195 To stop the compilation process after type-checking, run
adamc@1086	196 \begin{verbatim}
adamc@1086	197 urweb -tc P
adamc@1086	198 \end{verbatim}
adamc@1086	199
adamc@1170	200 To output information relevant to CSS stylesheets (and not finish regular compilation), run
adamc@1170	201 \begin{verbatim}
adamc@1170	202 urweb -css P
adamc@1170	203 \end{verbatim}
adamc@1170	204 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	205
adamc@896	206 Some other command-line parameters are accepted:
adamc@896	207 \begin{itemize}
adamc@896	208 \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	209
adamc@896	210 \item \texttt{-dbms [postgres\|mysql\|sqlite]}: Sets the database backend to use.
adamc@896	211 \begin{itemize}
adamc@896	212 \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	213
adamc@896	214 A command sequence like this can initialize a Postgres database, using a file \texttt{app.sql} generated by the compiler:
adamc@896	215 \begin{verbatim}
adamc@896	216 createdb app
adamc@896	217 psql -f app.sql app
adamc@896	218 \end{verbatim}
adamc@896	219
adamc@896	220 \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	221
adamc@896	222 A command sequence like this can initialize a MySQL database:
adamc@896	223 \begin{verbatim}
adamc@896	224 echo "CREATE DATABASE app" \| mysql
adamc@896	225 mysql -D app <app.sql
adamc@896	226 \end{verbatim}
adamc@896	227
adamc@896	228 \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	229
adamc@896	230 A command like this can initialize an SQLite database:
adamc@896	231 \begin{verbatim}
adamc@896	232 sqlite3 path/to/database/file <app.sql
adamc@896	233 \end{verbatim}
adamc@896	234 \end{itemize}
adamc@896	235
adam@1309	236 \item \texttt{-limit class num}: Equivalent to the \texttt{limit} directive from \texttt{.urp} files
adam@1309	237
adamc@896	238 \item \texttt{-output FILENAME}: Set where the application executable is written.
adamc@896	239
adamc@1127	240 \item \texttt{-path NAME VALUE}: Set the value of path variable \texttt{\$NAME} to \texttt{VALUE}, for use in \texttt{.urp} files.
adamc@1127	241
adam@1335	242 \item \texttt{-prefix PREFIX}: Equivalent to the \texttt{prefix} directive from \texttt{.urp} files
adam@1335	243
adamc@896	244 \item \texttt{-protocol [http\|cgi\|fastcgi]}: Set the protocol that the generated application speaks.
adamc@896	245 \begin{itemize}
adamc@896	246 \item \texttt{http}: This is the default. It is for building standalone web servers that can be accessed by web browsers directly.
adamc@896	247
adamc@896	248 \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	249
adamc@896	250 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	251 \begin{verbatim}
adamc@896	252 ScriptAlias /Hello /path/to/hello.exe
adamc@896	253 \end{verbatim}
adamc@896	254
adamc@1163	255 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	256 \begin{verbatim}
adamc@1163	257 Options +ExecCGI
adamc@1163	258 AddHandler cgi-script .exe
adamc@1163	259 \end{verbatim}
adamc@1163	260
adamc@1163	261 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	262 \begin{verbatim}
adamc@1163	263 prefix /dir/script.exe/
adamc@1163	264 \end{verbatim}
adamc@1163	265
adamc@1163	266 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	267
adamc@1164	268 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	269
adamc@896	270 \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	271
adamc@896	272 To configure a FastCGI program with Apache, one could combine the above \texttt{ScriptAlias} line with a line like this:
adamc@896	273 \begin{verbatim}
adamc@896	274 FastCgiServer /path/to/hello.exe -idle-timeout 99999
adamc@896	275 \end{verbatim}
adamc@896	276 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	277
adamc@896	278 Here is some lighttpd configuration for the same application.
adamc@896	279 \begin{verbatim}
adamc@896	280 fastcgi.server = (
adamc@896	281 "/Hello/" =>
adamc@896	282 (( "bin-path" => "/path/to/hello.exe",
adamc@896	283 "socket" => "/tmp/hello",
adamc@896	284 "check-local" => "disable",
adamc@896	285 "docroot" => "/",
adamc@896	286 "max-procs" => "1"
adamc@896	287 ))
adamc@896	288 )
adamc@896	289 \end{verbatim}
adamc@896	290 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	291
adamc@896	292 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	293 \end{itemize}
adamc@896	294
adamc@1127	295 \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	296
adamc@1164	297 \item \texttt{-sigfile PATH}: Same as the \texttt{sigfile} directive in \texttt{.urp} files
adamc@1164	298
adamc@896	299 \item \texttt{-sql FILENAME}: Set where a database set-up SQL script is written.
adamc@1095	300
adamc@1095	301 \item \texttt{-static}: Link the runtime system statically. The default is to link against dynamic libraries.
adamc@896	302 \end{itemize}
adamc@896	303
adam@1297	304 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	305
adamc@529	306 \section{Ur Syntax}
adamc@529	307
adamc@784	308 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	309
adamc@524	310 \subsection{Lexical Conventions}
adamc@524	311
adamc@524	312 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	313
adamc@524	314 \begin{center}
adamc@524	315 \begin{tabular}{rl}
adamc@524	316 \textbf{\LaTeX} & \textbf{ASCII} \\
adamc@524	317 $\to$ & \cd{->} \\
adamc@652	318 $\longrightarrow$ & \cd{-->} \\
adamc@524	319 $\times$ & \cd{*} \\
adamc@524	320 $\lambda$ & \cd{fn} \\
adamc@524	321 $\Rightarrow$ & \cd{=>} \\
adamc@652	322 $\Longrightarrow$ & \cd{==>} \\
adamc@529	323 $\neq$ & \cd{<>} \\
adamc@529	324 $\leq$ & \cd{<=} \\
adamc@529	325 $\geq$ & \cd{>=} \\
adamc@524	326 \\
adamc@524	327 $x$ & Normal textual identifier, not beginning with an uppercase letter \\
adamc@525	328 $X$ & Normal textual identifier, beginning with an uppercase letter \\
adamc@524	329 \end{tabular}
adamc@524	330 \end{center}
adamc@524	331
adamc@525	332 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	333
adamc@873	334 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	335
adamc@527	336 This version of the manual doesn't include operator precedences; see \texttt{src/urweb.grm} for that.
adamc@527	337
adam@1297	338 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	339
adamc@552	340 \subsection{\label{core}Core Syntax}
adamc@524	341
adamc@524	342 \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	343 $$\begin{array}{rrcll}
adamc@524	344 \textrm{Kinds} & \kappa &::=& \mt{Type} & \textrm{proper types} \\
adamc@525	345 &&& \mt{Unit} & \textrm{the trivial constructor} \\
adamc@525	346 &&& \mt{Name} & \textrm{field names} \\
adamc@525	347 &&& \kappa \to \kappa & \textrm{type-level functions} \\
adamc@525	348 &&& \{\kappa\} & \textrm{type-level records} \\
adamc@525	349 &&& (\kappa\times^+) & \textrm{type-level tuples} \\
adamc@652	350 &&& X & \textrm{variable} \\
adamc@652	351 &&& X \longrightarrow k & \textrm{kind-polymorphic type-level function} \\
adamc@529	352 &&& \_\_ & \textrm{wildcard} \\
adamc@525	353 &&& (\kappa) & \textrm{explicit precedence} \\
adamc@524	354 \end{array}$$
adamc@524	355
adamc@524	356 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	357 $$\begin{array}{rrcll}
adamc@524	358 \textrm{Explicitness} & ? &::=& :: & \textrm{explicit} \\
adamc@558	359 &&& ::: & \textrm{implicit}
adamc@524	360 \end{array}$$
adamc@524	361
adamc@524	362 \emph{Constructors} are the main class of compile-time-only data. They include proper types and are classified by kinds.
adamc@524	363 $$\begin{array}{rrcll}
adamc@524	364 \textrm{Constructors} & c, \tau &::=& (c) :: \kappa & \textrm{kind annotation} \\
adamc@530	365 &&& \hat{x} & \textrm{constructor variable} \\
adamc@524	366 \\
adamc@525	367 &&& \tau \to \tau & \textrm{function type} \\
adamc@525	368 &&& x \; ? \; \kappa \to \tau & \textrm{polymorphic function type} \\
adamc@652	369 &&& X \longrightarrow \tau & \textrm{kind-polymorphic function type} \\
adamc@525	370 &&& \$ c & \textrm{record type} \\
adamc@524	371 \\
adamc@525	372 &&& c \; c & \textrm{type-level function application} \\
adamc@530	373 &&& \lambda x \; :: \; \kappa \Rightarrow c & \textrm{type-level function abstraction} \\
adamc@524	374 \\
adamc@652	375 &&& X \Longrightarrow c & \textrm{type-level kind-polymorphic function abstraction} \\
adamc@655	376 &&& c [\kappa] & \textrm{type-level kind-polymorphic function application} \\
adamc@652	377 \\
adamc@525	378 &&& () & \textrm{type-level unit} \\
adamc@525	379 &&& \#X & \textrm{field name} \\
adamc@524	380 \\
adamc@525	381 &&& [(c = c)^*] & \textrm{known-length type-level record} \\
adamc@525	382 &&& c \rc c & \textrm{type-level record concatenation} \\
adamc@652	383 &&& \mt{map} & \textrm{type-level record map} \\
adamc@524	384 \\
adamc@558	385 &&& (c,^+) & \textrm{type-level tuple} \\
adamc@525	386 &&& c.n & \textrm{type-level tuple projection ($n \in \mathbb N^+$)} \\
adamc@524	387 \\
adamc@652	388 &&& [c \sim c] \Rightarrow \tau & \textrm{guarded type} \\
adamc@524	389 \\
adamc@529	390 &&& \_ :: \kappa & \textrm{wildcard} \\
adamc@525	391 &&& (c) & \textrm{explicit precedence} \\
adamc@530	392 \\
adamc@530	393 \textrm{Qualified uncapitalized variables} & \hat{x} &::=& x & \textrm{not from a module} \\
adamc@530	394 &&& M.x & \textrm{projection from a module} \\
adamc@525	395 \end{array}$$
adamc@525	396
adamc@655	397 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	398
adamc@525	399 Modules of the module system are described by \emph{signatures}.
adamc@525	400 $$\begin{array}{rrcll}
adamc@525	401 \textrm{Signatures} & S &::=& \mt{sig} \; s^* \; \mt{end} & \textrm{constant} \\
adamc@525	402 &&& X & \textrm{variable} \\
adamc@525	403 &&& \mt{functor}(X : S) : S & \textrm{functor} \\
adamc@529	404 &&& S \; \mt{where} \; \mt{con} \; x = c & \textrm{concretizing an abstract constructor} \\
adamc@525	405 &&& M.X & \textrm{projection from a module} \\
adamc@525	406 \\
adamc@525	407 \textrm{Signature items} & s &::=& \mt{con} \; x :: \kappa & \textrm{abstract constructor} \\
adamc@525	408 &&& \mt{con} \; x :: \kappa = c & \textrm{concrete constructor} \\
adamc@528	409 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529	410 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@525	411 &&& \mt{val} \; x : \tau & \textrm{value} \\
adamc@525	412 &&& \mt{structure} \; X : S & \textrm{sub-module} \\
adamc@525	413 &&& \mt{signature} \; X = S & \textrm{sub-signature} \\
adamc@525	414 &&& \mt{include} \; S & \textrm{signature inclusion} \\
adamc@525	415 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@654	416 &&& \mt{class} \; x :: \kappa & \textrm{abstract constructor class} \\
adamc@654	417 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@525	418 \\
adamc@525	419 \textrm{Datatype constructors} & dc &::=& X & \textrm{nullary constructor} \\
adamc@525	420 &&& X \; \mt{of} \; \tau & \textrm{unary constructor} \\
adamc@524	421 \end{array}$$
adamc@524	422
adamc@526	423 \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	424 $$\begin{array}{rrcll}
adamc@526	425 \textrm{Patterns} & p &::=& \_ & \textrm{wildcard} \\
adamc@526	426 &&& x & \textrm{variable} \\
adamc@526	427 &&& \ell & \textrm{constant} \\
adamc@526	428 &&& \hat{X} & \textrm{nullary constructor} \\
adamc@526	429 &&& \hat{X} \; p & \textrm{unary constructor} \\
adamc@526	430 &&& \{(x = p,)^*\} & \textrm{rigid record pattern} \\
adamc@526	431 &&& \{(x = p,)^+, \ldots\} & \textrm{flexible record pattern} \\
adamc@852	432 &&& p : \tau & \textrm{type annotation} \\
adamc@527	433 &&& (p) & \textrm{explicit precedence} \\
adamc@526	434 \\
adamc@529	435 \textrm{Qualified capitalized variables} & \hat{X} &::=& X & \textrm{not from a module} \\
adamc@526	436 &&& M.X & \textrm{projection from a module} \\
adamc@526	437 \end{array}$$
adamc@526	438
adamc@527	439 \emph{Expressions} are the main run-time entities, corresponding to both ``expressions'' and ``statements'' in mainstream imperative languages.
adamc@527	440 $$\begin{array}{rrcll}
adamc@527	441 \textrm{Expressions} & e &::=& e : \tau & \textrm{type annotation} \\
adamc@529	442 &&& \hat{x} & \textrm{variable} \\
adamc@529	443 &&& \hat{X} & \textrm{datatype constructor} \\
adamc@527	444 &&& \ell & \textrm{constant} \\
adamc@527	445 \\
adamc@527	446 &&& e \; e & \textrm{function application} \\
adamc@527	447 &&& \lambda x : \tau \Rightarrow e & \textrm{function abstraction} \\
adamc@527	448 &&& e [c] & \textrm{polymorphic function application} \\
adamc@852	449 &&& \lambda [x \; ? \; \kappa] \Rightarrow e & \textrm{polymorphic function abstraction} \\
adamc@655	450 &&& e [\kappa] & \textrm{kind-polymorphic function application} \\
adamc@652	451 &&& X \Longrightarrow e & \textrm{kind-polymorphic function abstraction} \\
adamc@527	452 \\
adamc@527	453 &&& \{(c = e,)^*\} & \textrm{known-length record} \\
adamc@527	454 &&& e.c & \textrm{record field projection} \\
adamc@527	455 &&& e \rc e & \textrm{record concatenation} \\
adamc@527	456 &&& e \rcut c & \textrm{removal of a single record field} \\
adamc@527	457 &&& e \rcutM c & \textrm{removal of multiple record fields} \\
adamc@527	458 \\
adamc@527	459 &&& \mt{let} \; ed^* \; \mt{in} \; e \; \mt{end} & \textrm{local definitions} \\
adamc@527	460 \\
adamc@527	461 &&& \mt{case} \; e \; \mt{of} \; (p \Rightarrow e\|)^+ & \textrm{pattern matching} \\
adamc@527	462 \\
adamc@654	463 &&& \lambda [c \sim c] \Rightarrow e & \textrm{guarded expression abstraction} \\
adamc@654	464 &&& e \; ! & \textrm{guarded expression application} \\
adamc@527	465 \\
adamc@527	466 &&& \_ & \textrm{wildcard} \\
adamc@527	467 &&& (e) & \textrm{explicit precedence} \\
adamc@527	468 \\
adamc@527	469 \textrm{Local declarations} & ed &::=& \cd{val} \; x : \tau = e & \textrm{non-recursive value} \\
adamc@527	470 &&& \cd{val} \; \cd{rec} \; (x : \tau = e \; \cd{and})^+ & \textrm{mutually-recursive values} \\
adamc@527	471 \end{array}$$
adamc@527	472
adamc@655	473 As with constructors, we include both abstraction and application for kind polymorphism, but applications are only inferred internally.
adamc@655	474
adamc@528	475 \emph{Declarations} primarily bring new symbols into context.
adamc@528	476 $$\begin{array}{rrcll}
adamc@528	477 \textrm{Declarations} & d &::=& \mt{con} \; x :: \kappa = c & \textrm{constructor synonym} \\
adamc@528	478 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529	479 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@528	480 &&& \mt{val} \; x : \tau = e & \textrm{value} \\
adamc@528	481 &&& \mt{val} \; \cd{rec} \; (x : \tau = e \; \mt{and})^+ & \textrm{mutually-recursive values} \\
adamc@528	482 &&& \mt{structure} \; X : S = M & \textrm{module definition} \\
adamc@528	483 &&& \mt{signature} \; X = S & \textrm{signature definition} \\
adamc@528	484 &&& \mt{open} \; M & \textrm{module inclusion} \\
adamc@528	485 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@528	486 &&& \mt{open} \; \mt{constraints} \; M & \textrm{inclusion of just the constraints from a module} \\
adamc@528	487 &&& \mt{table} \; x : c & \textrm{SQL table} \\
adamc@784	488 &&& \mt{view} \; x : c & \textrm{SQL view} \\
adamc@528	489 &&& \mt{sequence} \; x & \textrm{SQL sequence} \\
adamc@535	490 &&& \mt{cookie} \; x : \tau & \textrm{HTTP cookie} \\
adamc@784	491 &&& \mt{style} \; x : \tau & \textrm{CSS class} \\
adamc@654	492 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@1085	493 &&& \mt{task} \; e = e & \textrm{recurring task} \\
adamc@528	494 \\
adamc@529	495 \textrm{Modules} & M &::=& \mt{struct} \; d^* \; \mt{end} & \textrm{constant} \\
adamc@529	496 &&& X & \textrm{variable} \\
adamc@529	497 &&& M.X & \textrm{projection} \\
adamc@529	498 &&& M(M) & \textrm{functor application} \\
adamc@529	499 &&& \mt{functor}(X : S) : S = M & \textrm{functor abstraction} \\
adamc@528	500 \end{array}$$
adamc@528	501
adamc@528	502 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	503
adamc@784	504 We omit some extra possibilities in $\mt{table}$ syntax, deferring them to Section \ref{tables}.
adamc@784	505
adamc@529	506 \subsection{Shorthands}
adamc@529	507
adamc@529	508 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	509
adamc@529	510 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	511
adamc@529	512 A record type may be written $\{(c = c,)^\}$, which elaborates to $\$[(c = c,)^]$.
adamc@529	513
adamc@533	514 The notation $[c_1, \ldots, c_n]$ is shorthand for $[c_1 = (), \ldots, c_n = ()]$.
adamc@533	515
adam@1350	516 A tuple type $\tau_1 \times \ldots \times \tau_n$ expands to a record type $\{1 : \tau_1, \ldots, n : \tau_n\}$, with natural numbers as field names. A tuple expression $(e_1, \ldots, e_n)$ expands to a record expression $\{1 = e_1, \ldots, n = e_n\}$. A tuple pattern $(p_1, \ldots, p_n)$ expands to a rigid record pattern $\{1 = p_1, \ldots, n = p_n\}$. Positive natural numbers may be used in most places where field names would be allowed.
adamc@529	517
adamc@852	518 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	519
adam@1306	520 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	521
adamc@529	522 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	523
adamc@529	524 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	525
adamc@654	526 A signature item or declaration $\mt{class} \; x = \lambda y \Rightarrow c$ may be abbreviated $\mt{class} \; x \; y = c$.
adamc@529	527
adam@1354	528 Handling of implicit and explicit constructor arguments may be tweaked with some prefixes to variable references. An expression $@x$ is a version of $x$ where all type class instance and disjointness arguments have been made explicit. An expression $@@x$ achieves the same effect, additionally making explicit all implicit constructor arguments. The default is that implicit arguments are inserted automatically after any reference to a non-local variable, or after any application of a non-local variable to one or more arguments. For such an expression, implicit wildcard arguments are added for the longest prefix of the expression's type consisting only of implicit polymorphism, type class instances, and disjointness obligations. The same syntax works for variables projected out of modules and for capitalized variables (datatype constructors).
adamc@529	529
adamc@852	530 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	531
adamc@852	532 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	533
adamc@852	534 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	535
adamc@529	536 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	537
adamc@852	538 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	539
adamc@853	540 A declaration $\mt{table} \; x : \{(c = c,)^\}$ is elaborated into $\mt{table} \; x : [(c = c,)^]$.
adamc@529	541
adamc@529	542 The syntax $\mt{where} \; \mt{type}$ is an alternate form of $\mt{where} \; \mt{con}$.
adamc@529	543
adamc@529	544 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	545
adamc@529	546 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	547
adamc@784	548 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	549
adamc@530	550
adamc@530	551 \section{Static Semantics}
adamc@530	552
adamc@530	553 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	554
adamc@530	555 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	556 \begin{itemize}
adamc@655	557 \item $\Gamma \vdash \kappa$ expresses kind well-formedness.
adamc@530	558 \item $\Gamma \vdash c :: \kappa$ assigns a kind to a constructor in a context.
adamc@530	559 \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	560 \item $\Gamma \vdash c \hookrightarrow C$ proves that record constructor $c$ decomposes into set $C$ of field names and record constructors.
adamc@530	561 \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	562 \item $\Gamma \vdash e : \tau$ is a standard typing judgment.
adamc@534	563 \item $\Gamma \vdash p \leadsto \Gamma; \tau$ combines typing of patterns with calculation of which new variables they bind.
adamc@537	564 \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	565 \item $\Gamma \vdash S \equiv S$ is the signature equivalence judgment.
adamc@536	566 \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	567 \item $\Gamma \vdash M : S$ is the module signature checking judgment.
adamc@537	568 \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	569 \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	570 \end{itemize}
adamc@530	571
adamc@655	572
adamc@655	573 \subsection{Kind Well-Formedness}
adamc@655	574
adamc@655	575 $$\infer{\Gamma \vdash \mt{Type}}{}
adamc@655	576 \quad \infer{\Gamma \vdash \mt{Unit}}{}
adamc@655	577 \quad \infer{\Gamma \vdash \mt{Name}}{}
adamc@655	578 \quad \infer{\Gamma \vdash \kappa_1 \to \kappa_2}{
adamc@655	579 \Gamma \vdash \kappa_1
adamc@655	580 & \Gamma \vdash \kappa_2
adamc@655	581 }
adamc@655	582 \quad \infer{\Gamma \vdash \{\kappa\}}{
adamc@655	583 \Gamma \vdash \kappa
adamc@655	584 }
adamc@655	585 \quad \infer{\Gamma \vdash (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@655	586 \forall i: \Gamma \vdash \kappa_i
adamc@655	587 }$$
adamc@655	588
adamc@655	589 $$\infer{\Gamma \vdash X}{
adamc@655	590 X \in \Gamma
adamc@655	591 }
adamc@655	592 \quad \infer{\Gamma \vdash X \longrightarrow \kappa}{
adamc@655	593 \Gamma, X \vdash \kappa
adamc@655	594 }$$
adamc@655	595
adamc@530	596 \subsection{Kinding}
adamc@530	597
adamc@655	598 We write $[X \mapsto \kappa_1]\kappa_2$ for capture-avoiding substitution of $\kappa_1$ for $X$ in $\kappa_2$.
adamc@655	599
adamc@530	600 $$\infer{\Gamma \vdash (c) :: \kappa :: \kappa}{
adamc@530	601 \Gamma \vdash c :: \kappa
adamc@530	602 }
adamc@530	603 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530	604 x :: \kappa \in \Gamma
adamc@530	605 }
adamc@530	606 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530	607 x :: \kappa = c \in \Gamma
adamc@530	608 }$$
adamc@530	609
adamc@530	610 $$\infer{\Gamma \vdash M.x :: \kappa}{
adamc@537	611 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	612 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = \kappa
adamc@530	613 }
adamc@530	614 \quad \infer{\Gamma \vdash M.x :: \kappa}{
adamc@537	615 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	616 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@530	617 }$$
adamc@530	618
adamc@530	619 $$\infer{\Gamma \vdash \tau_1 \to \tau_2 :: \mt{Type}}{
adamc@530	620 \Gamma \vdash \tau_1 :: \mt{Type}
adamc@530	621 & \Gamma \vdash \tau_2 :: \mt{Type}
adamc@530	622 }
adamc@530	623 \quad \infer{\Gamma \vdash x \; ? \: \kappa \to \tau :: \mt{Type}}{
adamc@530	624 \Gamma, x :: \kappa \vdash \tau :: \mt{Type}
adamc@530	625 }
adamc@655	626 \quad \infer{\Gamma \vdash X \longrightarrow \tau :: \mt{Type}}{
adamc@655	627 \Gamma, X \vdash \tau :: \mt{Type}
adamc@655	628 }
adamc@530	629 \quad \infer{\Gamma \vdash \$c :: \mt{Type}}{
adamc@530	630 \Gamma \vdash c :: \{\mt{Type}\}
adamc@530	631 }$$
adamc@530	632
adamc@530	633 $$\infer{\Gamma \vdash c_1 \; c_2 :: \kappa_2}{
adamc@530	634 \Gamma \vdash c_1 :: \kappa_1 \to \kappa_2
adamc@530	635 & \Gamma \vdash c_2 :: \kappa_1
adamc@530	636 }
adamc@530	637 \quad \infer{\Gamma \vdash \lambda x \; :: \; \kappa_1 \Rightarrow c :: \kappa_1 \to \kappa_2}{
adamc@530	638 \Gamma, x :: \kappa_1 \vdash c :: \kappa_2
adamc@530	639 }$$
adamc@530	640
adamc@655	641 $$\infer{\Gamma \vdash c[\kappa'] :: [X \mapsto \kappa']\kappa}{
adamc@655	642 \Gamma \vdash c :: X \to \kappa
adamc@655	643 & \Gamma \vdash \kappa'
adamc@655	644 }
adamc@655	645 \quad \infer{\Gamma \vdash X \Longrightarrow c :: X \to \kappa}{
adamc@655	646 \Gamma, X \vdash c :: \kappa
adamc@655	647 }$$
adamc@655	648
adamc@530	649 $$\infer{\Gamma \vdash () :: \mt{Unit}}{}
adamc@530	650 \quad \infer{\Gamma \vdash \#X :: \mt{Name}}{}$$
adamc@530	651
adamc@530	652 $$\infer{\Gamma \vdash [\overline{c_i = c'_i}] :: \{\kappa\}}{
adamc@530	653 \forall i: \Gamma \vdash c_i : \mt{Name}
adamc@530	654 & \Gamma \vdash c'_i :: \kappa
adamc@530	655 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@530	656 }
adamc@530	657 \quad \infer{\Gamma \vdash c_1 \rc c_2 :: \{\kappa\}}{
adamc@530	658 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530	659 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@530	660 & \Gamma \vdash c_1 \sim c_2
adamc@530	661 }$$
adamc@530	662
adamc@655	663 $$\infer{\Gamma \vdash \mt{map} :: (\kappa_1 \to \kappa_2) \to \{\kappa_1\} \to \{\kappa_2\}}{}$$
adamc@530	664
adamc@573	665 $$\infer{\Gamma \vdash (\overline c) :: (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@573	666 \forall i: \Gamma \vdash c_i :: \kappa_i
adamc@530	667 }
adamc@573	668 \quad \infer{\Gamma \vdash c.i :: \kappa_i}{
adamc@573	669 \Gamma \vdash c :: (\kappa_1 \times \ldots \times \kappa_n)
adamc@530	670 }$$
adamc@530	671
adamc@655	672 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow \tau :: \mt{Type}}{
adamc@655	673 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530	674 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@655	675 & \Gamma, c_1 \sim c_2 \vdash \tau :: \mt{Type}
adamc@530	676 }$$
adamc@530	677
adamc@531	678 \subsection{Record Disjointness}
adamc@531	679
adamc@531	680 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@558	681 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@558	682 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@558	683 & \forall c'_1 \in C_1, c'_2 \in C_2: \Gamma \vdash c'_1 \sim c'_2
adamc@531	684 }
adamc@531	685 \quad \infer{\Gamma \vdash X \sim X'}{
adamc@531	686 X \neq X'
adamc@531	687 }$$
adamc@531	688
adamc@531	689 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@531	690 c'_1 \sim c'_2 \in \Gamma
adamc@558	691 & \Gamma \vdash c'_1 \hookrightarrow C_1
adamc@558	692 & \Gamma \vdash c'_2 \hookrightarrow C_2
adamc@558	693 & c_1 \in C_1
adamc@558	694 & c_2 \in C_2
adamc@531	695 }$$
adamc@531	696
adamc@531	697 $$\infer{\Gamma \vdash c \hookrightarrow \{c\}}{}
adamc@531	698 \quad \infer{\Gamma \vdash [\overline{c = c'}] \hookrightarrow \{\overline{c}\}}{}
adamc@531	699 \quad \infer{\Gamma \vdash c_1 \rc c_2 \hookrightarrow C_1 \cup C_2}{
adamc@531	700 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@531	701 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@531	702 }
adamc@531	703 \quad \infer{\Gamma \vdash c \hookrightarrow C}{
adamc@531	704 \Gamma \vdash c \equiv c'
adamc@531	705 & \Gamma \vdash c' \hookrightarrow C
adamc@531	706 }
adamc@531	707 \quad \infer{\Gamma \vdash \mt{map} \; f \; c \hookrightarrow C}{
adamc@531	708 \Gamma \vdash c \hookrightarrow C
adamc@531	709 }$$
adamc@531	710
adamc@541	711 \subsection{\label{definitional}Definitional Equality}
adamc@532	712
adamc@655	713 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	714
adamc@532	715 $$\infer{\Gamma \vdash c \equiv c}{}
adamc@532	716 \quad \infer{\Gamma \vdash c_1 \equiv c_2}{
adamc@532	717 \Gamma \vdash c_2 \equiv c_1
adamc@532	718 }
adamc@532	719 \quad \infer{\Gamma \vdash c_1 \equiv c_3}{
adamc@532	720 \Gamma \vdash c_1 \equiv c_2
adamc@532	721 & \Gamma \vdash c_2 \equiv c_3
adamc@532	722 }
adamc@532	723 \quad \infer{\Gamma \vdash \mathcal C[c_1] \equiv \mathcal C[c_2]}{
adamc@532	724 \Gamma \vdash c_1 \equiv c_2
adamc@532	725 }$$
adamc@532	726
adamc@532	727 $$\infer{\Gamma \vdash x \equiv c}{
adamc@532	728 x :: \kappa = c \in \Gamma
adamc@532	729 }
adamc@532	730 \quad \infer{\Gamma \vdash M.x \equiv c}{
adamc@537	731 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	732 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@532	733 }
adamc@532	734 \quad \infer{\Gamma \vdash (\overline c).i \equiv c_i}{}$$
adamc@532	735
adamc@532	736 $$\infer{\Gamma \vdash (\lambda x :: \kappa \Rightarrow c) \; c' \equiv [x \mapsto c'] c}{}
adamc@655	737 \quad \infer{\Gamma \vdash (X \Longrightarrow c) [\kappa] \equiv [X \mapsto \kappa] c}{}$$
adamc@655	738
adamc@655	739 $$\infer{\Gamma \vdash c_1 \rc c_2 \equiv c_2 \rc c_1}{}
adamc@532	740 \quad \infer{\Gamma \vdash c_1 \rc (c_2 \rc c_3) \equiv (c_1 \rc c_2) \rc c_3}{}$$
adamc@532	741
adamc@532	742 $$\infer{\Gamma \vdash [] \rc c \equiv c}{}
adamc@532	743 \quad \infer{\Gamma \vdash [\overline{c_1 = c'_1}] \rc [\overline{c_2 = c'_2}] \equiv [\overline{c_1 = c'_1}, \overline{c_2 = c'_2}]}{}$$
adamc@532	744
adamc@655	745 $$\infer{\Gamma \vdash \mt{map} \; f \; [] \equiv []}{}
adamc@655	746 \quad \infer{\Gamma \vdash \mt{map} \; f \; ([c_1 = c_2] \rc c) \equiv [c_1 = f \; c_2] \rc \mt{map} \; f \; c}{}$$
adamc@532	747
adamc@532	748 $$\infer{\Gamma \vdash \mt{map} \; (\lambda x \Rightarrow x) \; c \equiv c}{}
adamc@655	749 \quad \infer{\Gamma \vdash \mt{map} \; f \; (\mt{map} \; f' \; c)
adamc@655	750 \equiv \mt{map} \; (\lambda x \Rightarrow f \; (f' \; x)) \; c}{}$$
adamc@532	751
adamc@532	752 $$\infer{\Gamma \vdash \mt{map} \; f \; (c_1 \rc c_2) \equiv \mt{map} \; f \; c_1 \rc \mt{map} \; f \; c_2}{}$$
adamc@531	753
adamc@534	754 \subsection{Expression Typing}
adamc@533	755
adamc@873	756 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	757
adamc@533	758 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	759
adamc@533	760 $$\infer{\Gamma \vdash e : \tau : \tau}{
adamc@533	761 \Gamma \vdash e : \tau
adamc@533	762 }
adamc@533	763 \quad \infer{\Gamma \vdash e : \tau}{
adamc@533	764 \Gamma \vdash e : \tau'
adamc@533	765 & \Gamma \vdash \tau' \equiv \tau
adamc@533	766 }
adamc@533	767 \quad \infer{\Gamma \vdash \ell : T(\ell)}{}$$
adamc@533	768
adamc@533	769 $$\infer{\Gamma \vdash x : \mathcal I(\tau)}{
adamc@533	770 x : \tau \in \Gamma
adamc@533	771 }
adamc@533	772 \quad \infer{\Gamma \vdash M.x : \mathcal I(\tau)}{
adamc@537	773 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	774 & \mt{proj}(M, \overline{s}, \mt{val} \; x) = \tau
adamc@533	775 }
adamc@533	776 \quad \infer{\Gamma \vdash X : \mathcal I(\tau)}{
adamc@533	777 X : \tau \in \Gamma
adamc@533	778 }
adamc@533	779 \quad \infer{\Gamma \vdash M.X : \mathcal I(\tau)}{
adamc@537	780 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	781 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \tau
adamc@533	782 }$$
adamc@533	783
adamc@533	784 $$\infer{\Gamma \vdash e_1 \; e_2 : \tau_2}{
adamc@533	785 \Gamma \vdash e_1 : \tau_1 \to \tau_2
adamc@533	786 & \Gamma \vdash e_2 : \tau_1
adamc@533	787 }
adamc@533	788 \quad \infer{\Gamma \vdash \lambda x : \tau_1 \Rightarrow e : \tau_1 \to \tau_2}{
adamc@533	789 \Gamma, x : \tau_1 \vdash e : \tau_2
adamc@533	790 }$$
adamc@533	791
adamc@533	792 $$\infer{\Gamma \vdash e [c] : [x \mapsto c]\tau}{
adamc@533	793 \Gamma \vdash e : x :: \kappa \to \tau
adamc@533	794 & \Gamma \vdash c :: \kappa
adamc@533	795 }
adamc@852	796 \quad \infer{\Gamma \vdash \lambda [x \; ? \; \kappa] \Rightarrow e : x \; ? \; \kappa \to \tau}{
adamc@533	797 \Gamma, x :: \kappa \vdash e : \tau
adamc@533	798 }$$
adamc@533	799
adamc@655	800 $$\infer{\Gamma \vdash e [\kappa] : [X \mapsto \kappa]\tau}{
adamc@655	801 \Gamma \vdash e : X \longrightarrow \tau
adamc@655	802 & \Gamma \vdash \kappa
adamc@655	803 }
adamc@655	804 \quad \infer{\Gamma \vdash X \Longrightarrow e : X \longrightarrow \tau}{
adamc@655	805 \Gamma, X \vdash e : \tau
adamc@655	806 }$$
adamc@655	807
adamc@533	808 $$\infer{\Gamma \vdash \{\overline{c = e}\} : \{\overline{c : \tau}\}}{
adamc@533	809 \forall i: \Gamma \vdash c_i :: \mt{Name}
adamc@533	810 & \Gamma \vdash e_i : \tau_i
adamc@533	811 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@533	812 }
adamc@533	813 \quad \infer{\Gamma \vdash e.c : \tau}{
adamc@533	814 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533	815 }
adamc@533	816 \quad \infer{\Gamma \vdash e_1 \rc e_2 : \$(c_1 \rc c_2)}{
adamc@533	817 \Gamma \vdash e_1 : \$c_1
adamc@533	818 & \Gamma \vdash e_2 : \$c_2
adamc@573	819 & \Gamma \vdash c_1 \sim c_2
adamc@533	820 }$$
adamc@533	821
adamc@533	822 $$\infer{\Gamma \vdash e \rcut c : \$c'}{
adamc@533	823 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533	824 }
adamc@533	825 \quad \infer{\Gamma \vdash e \rcutM c : \$c'}{
adamc@533	826 \Gamma \vdash e : \$(c \rc c')
adamc@533	827 }$$
adamc@533	828
adamc@533	829 $$\infer{\Gamma \vdash \mt{let} \; \overline{ed} \; \mt{in} \; e \; \mt{end} : \tau}{
adamc@533	830 \Gamma \vdash \overline{ed} \leadsto \Gamma'
adamc@533	831 & \Gamma' \vdash e : \tau
adamc@533	832 }
adamc@533	833 \quad \infer{\Gamma \vdash \mt{case} \; e \; \mt{of} \; \overline{p \Rightarrow e} : \tau}{
adamc@533	834 \forall i: \Gamma \vdash p_i \leadsto \Gamma_i, \tau'
adamc@533	835 & \Gamma_i \vdash e_i : \tau
adamc@533	836 }$$
adamc@533	837
adamc@573	838 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow e : \lambda [c_1 \sim c_2] \Rightarrow \tau}{
adamc@533	839 \Gamma \vdash c_1 :: \{\kappa\}
adamc@655	840 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@533	841 & \Gamma, c_1 \sim c_2 \vdash e : \tau
adamc@662	842 }
adamc@662	843 \quad \infer{\Gamma \vdash e \; ! : \tau}{
adamc@662	844 \Gamma \vdash e : [c_1 \sim c_2] \Rightarrow \tau
adamc@662	845 & \Gamma \vdash c_1 \sim c_2
adamc@533	846 }$$
adamc@533	847
adamc@534	848 \subsection{Pattern Typing}
adamc@534	849
adamc@534	850 $$\infer{\Gamma \vdash \_ \leadsto \Gamma; \tau}{}
adamc@534	851 \quad \infer{\Gamma \vdash x \leadsto \Gamma, x : \tau; \tau}{}
adamc@534	852 \quad \infer{\Gamma \vdash \ell \leadsto \Gamma; T(\ell)}{}$$
adamc@534	853
adamc@534	854 $$\infer{\Gamma \vdash X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534	855 X : \overline{x ::: \mt{Type}} \to \tau \in \Gamma
adamc@534	856 & \textrm{$\tau$ not a function type}
adamc@534	857 }
adamc@534	858 \quad \infer{\Gamma \vdash X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534	859 X : \overline{x ::: \mt{Type}} \to \tau'' \to \tau \in \Gamma
adamc@534	860 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534	861 }$$
adamc@534	862
adamc@534	863 $$\infer{\Gamma \vdash M.X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537	864 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	865 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau
adamc@534	866 & \textrm{$\tau$ not a function type}
adamc@534	867 }$$
adamc@534	868
adamc@534	869 $$\infer{\Gamma \vdash M.X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537	870 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	871 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau'' \to \tau
adamc@534	872 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534	873 }$$
adamc@534	874
adamc@534	875 $$\infer{\Gamma \vdash \{\overline{x = p}\} \leadsto \Gamma_n; \{\overline{x = \tau}\}}{
adamc@534	876 \Gamma_0 = \Gamma
adamc@534	877 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534	878 }
adamc@534	879 \quad \infer{\Gamma \vdash \{\overline{x = p}, \ldots\} \leadsto \Gamma_n; \$([\overline{x = \tau}] \rc c)}{
adamc@534	880 \Gamma_0 = \Gamma
adamc@534	881 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534	882 }$$
adamc@534	883
adamc@852	884 $$\infer{\Gamma \vdash p : \tau \leadsto \Gamma'; \tau}{
adamc@852	885 \Gamma \vdash p \leadsto \Gamma'; \tau'
adamc@852	886 & \Gamma \vdash \tau' \equiv \tau
adamc@852	887 }$$
adamc@852	888
adamc@535	889 \subsection{Declaration Typing}
adamc@535	890
adamc@535	891 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	892
adamc@655	893 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	894
adamc@558	895 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	896 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	897
adamc@535	898 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535	899 \quad \infer{\Gamma \vdash d, \overline{d} \leadsto \Gamma''}{
adamc@535	900 \Gamma \vdash d \leadsto \Gamma'
adamc@535	901 & \Gamma' \vdash \overline{d} \leadsto \Gamma''
adamc@535	902 }$$
adamc@535	903
adamc@535	904 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@535	905 \Gamma \vdash c :: \kappa
adamc@535	906 }
adamc@535	907 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@535	908 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@535	909 }$$
adamc@535	910
adamc@535	911 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537	912 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	913 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@535	914 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@535	915 }$$
adamc@535	916
adamc@535	917 $$\infer{\Gamma \vdash \mt{val} \; x : \tau = e \leadsto \Gamma, x : \tau}{
adamc@535	918 \Gamma \vdash e : \tau
adamc@535	919 }$$
adamc@535	920
adamc@535	921 $$\infer{\Gamma \vdash \mt{val} \; \mt{rec} \; \overline{x : \tau = e} \leadsto \Gamma, \overline{x : \tau}}{
adamc@535	922 \forall i: \Gamma, \overline{x : \tau} \vdash e_i : \tau_i
adamc@535	923 & \textrm{$e_i$ starts with an expression $\lambda$, optionally preceded by constructor and disjointness $\lambda$s}
adamc@535	924 }$$
adamc@535	925
adamc@535	926 $$\infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : S}{
adamc@535	927 \Gamma \vdash M : S
adamc@558	928 & \textrm{ $M$ not a constant or application}
adamc@535	929 }
adamc@558	930 \quad \infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : \mt{selfify}(X, \overline{s})}{
adamc@558	931 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@539	932 }$$
adamc@539	933
adamc@539	934 $$\infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@535	935 \Gamma \vdash S
adamc@535	936 }$$
adamc@535	937
adamc@537	938 $$\infer{\Gamma \vdash \mt{open} \; M \leadsto \Gamma, \mathcal O(M, \overline{s})}{
adamc@537	939 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535	940 }$$
adamc@535	941
adamc@535	942 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma}{
adamc@535	943 \Gamma \vdash c_1 :: \{\kappa\}
adamc@535	944 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@535	945 & \Gamma \vdash c_1 \sim c_2
adamc@535	946 }
adamc@537	947 \quad \infer{\Gamma \vdash \mt{open} \; \mt{constraints} \; M \leadsto \Gamma, \mathcal O_c(M, \overline{s})}{
adamc@537	948 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535	949 }$$
adamc@535	950
adamc@784	951 $$\infer{\Gamma \vdash \mt{table} \; x : c \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_table} \; c \; []}{
adamc@535	952 \Gamma \vdash c :: \{\mt{Type}\}
adamc@535	953 }
adamc@784	954 \quad \infer{\Gamma \vdash \mt{view} \; x : c \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_view} \; c}{
adamc@784	955 \Gamma \vdash c :: \{\mt{Type}\}
adamc@784	956 }$$
adamc@784	957
adamc@784	958 $$\infer{\Gamma \vdash \mt{sequence} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_sequence}}{}$$
adamc@535	959
adamc@535	960 $$\infer{\Gamma \vdash \mt{cookie} \; x : \tau \leadsto \Gamma, x : \mt{Basis}.\mt{http\_cookie} \; \tau}{
adamc@535	961 \Gamma \vdash \tau :: \mt{Type}
adamc@784	962 }
adamc@784	963 \quad \infer{\Gamma \vdash \mt{style} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{css\_class}}{}$$
adamc@535	964
adamc@1085	965 $$\infer{\Gamma \vdash \mt{task} \; e_1 = e_2 \leadsto \Gamma}{
adam@1348	966 \Gamma \vdash e_1 :: \mt{Basis}.\mt{task\_kind} \; \tau
adam@1348	967 & \Gamma \vdash e_2 :: \tau \to \mt{Basis}.\mt{transaction} \; \{\}
adamc@1085	968 }$$
adamc@1085	969
adamc@784	970 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784	971 \Gamma \vdash c :: \kappa
adamc@535	972 }$$
adamc@535	973
adamc@535	974 $$\infer{\overline{y}; x; \Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535	975 \quad \infer{\overline{y}; x; \Gamma \vdash X \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to x \; \overline{y}}{
adamc@535	976 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535	977 }
adamc@535	978 \quad \infer{\overline{y}; x; \Gamma \vdash X \; \mt{of} \; \tau \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to \tau \to x \; \overline{y}}{
adamc@535	979 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535	980 }$$
adamc@535	981
adamc@537	982 \subsection{Signature Item Typing}
adamc@537	983
adamc@537	984 We appeal to a signature item analogue of the $\mathcal O$ function from the last subsection.
adamc@537	985
adamc@537	986 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@537	987 \quad \infer{\Gamma \vdash s, \overline{s} \leadsto \Gamma''}{
adamc@537	988 \Gamma \vdash s \leadsto \Gamma'
adamc@537	989 & \Gamma' \vdash \overline{s} \leadsto \Gamma''
adamc@537	990 }$$
adamc@537	991
adamc@537	992 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}
adamc@537	993 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@537	994 \Gamma \vdash c :: \kappa
adamc@537	995 }
adamc@537	996 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@537	997 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@537	998 }$$
adamc@537	999
adamc@537	1000 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537	1001 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1002 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537	1003 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@537	1004 }$$
adamc@537	1005
adamc@537	1006 $$\infer{\Gamma \vdash \mt{val} \; x : \tau \leadsto \Gamma, x : \tau}{
adamc@537	1007 \Gamma \vdash \tau :: \mt{Type}
adamc@537	1008 }$$
adamc@537	1009
adamc@537	1010 $$\infer{\Gamma \vdash \mt{structure} \; X : S \leadsto \Gamma, X : S}{
adamc@537	1011 \Gamma \vdash S
adamc@537	1012 }
adamc@537	1013 \quad \infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@537	1014 \Gamma \vdash S
adamc@537	1015 }$$
adamc@537	1016
adamc@537	1017 $$\infer{\Gamma \vdash \mt{include} \; S \leadsto \Gamma, \mathcal O(\overline{s})}{
adamc@537	1018 \Gamma \vdash S
adamc@537	1019 & \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1020 }$$
adamc@537	1021
adamc@537	1022 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma, c_1 \sim c_2}{
adamc@537	1023 \Gamma \vdash c_1 :: \{\kappa\}
adamc@537	1024 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@537	1025 }$$
adamc@537	1026
adamc@784	1027 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784	1028 \Gamma \vdash c :: \kappa
adamc@537	1029 }
adamc@784	1030 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}$$
adamc@537	1031
adamc@536	1032 \subsection{Signature Compatibility}
adamc@536	1033
adamc@558	1034 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	1035
adamc@537	1036 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	1037
adamc@536	1038 $$\infer{\Gamma \vdash S \equiv S}{}
adamc@536	1039 \quad \infer{\Gamma \vdash S_1 \equiv S_2}{
adamc@536	1040 \Gamma \vdash S_2 \equiv S_1
adamc@536	1041 }
adamc@536	1042 \quad \infer{\Gamma \vdash X \equiv S}{
adamc@536	1043 X = S \in \Gamma
adamc@536	1044 }
adamc@536	1045 \quad \infer{\Gamma \vdash M.X \equiv S}{
adamc@537	1046 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1047 & \mt{proj}(M, \overline{s}, \mt{signature} \; X) = S
adamc@536	1048 }$$
adamc@536	1049
adamc@536	1050 $$\infer{\Gamma \vdash S \; \mt{where} \; \mt{con} \; x = c \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa = c \; \overline{s_2} \; \mt{end}}{
adamc@536	1051 \Gamma \vdash S \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa \; \overline{s_2} \; \mt{end}
adamc@536	1052 & \Gamma \vdash c :: \kappa
adamc@537	1053 }
adamc@537	1054 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s^1} \; \mt{include} \; S \; \overline{s^2} \; \mt{end} \equiv \mt{sig} \; \overline{s^1} \; \overline{s} \; \overline{s^2} \; \mt{end}}{
adamc@537	1055 \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@536	1056 }$$
adamc@536	1057
adamc@536	1058 $$\infer{\Gamma \vdash S_1 \leq S_2}{
adamc@536	1059 \Gamma \vdash S_1 \equiv S_2
adamc@536	1060 }
adamc@536	1061 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \mt{end}}{}
adamc@537	1062 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; s' \; \overline{s'} \; \mt{end}}{
adamc@537	1063 \Gamma \vdash \overline{s} \leq s'
adamc@537	1064 & \Gamma \vdash s' \leadsto \Gamma'
adamc@537	1065 & \Gamma' \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \overline{s'} \; \mt{end}
adamc@537	1066 }$$
adamc@537	1067
adamc@537	1068 $$\infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537	1069 \Gamma \vdash s \leq s'
adamc@537	1070 }
adamc@537	1071 \quad \infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537	1072 \Gamma \vdash s \leadsto \Gamma'
adamc@537	1073 & \Gamma' \vdash \overline{s} \leq s'
adamc@536	1074 }$$
adamc@536	1075
adamc@536	1076 $$\infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 \leq \mt{functor} (X : S'_1) : S'_2}{
adamc@536	1077 \Gamma \vdash S'_1 \leq S_1
adamc@536	1078 & \Gamma, X : S'_1 \vdash S_2 \leq S'_2
adamc@536	1079 }$$
adamc@536	1080
adamc@537	1081 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@537	1082 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}
adamc@558	1083 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type}}{}$$
adamc@537	1084
adamc@537	1085 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(y)} \to \mt{Type}}{
adamc@537	1086 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1087 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537	1088 }$$
adamc@537	1089
adamc@784	1090 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@784	1091 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}$$
adamc@537	1092
adamc@537	1093 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \mt{\kappa} = c_2}{
adamc@537	1094 \Gamma \vdash c_1 \equiv c_2
adamc@537	1095 }
adamc@784	1096 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \kappa = c_2}{
adamc@537	1097 \Gamma \vdash c_1 \equiv c_2
adamc@537	1098 }$$
adamc@537	1099
adamc@537	1100 $$\infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537	1101 \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537	1102 }$$
adamc@537	1103
adamc@537	1104 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537	1105 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1106 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537	1107 & \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537	1108 }$$
adamc@537	1109
adamc@537	1110 $$\infer{\Gamma \vdash \cdot \leq \cdot}{}
adamc@537	1111 \quad \infer{\Gamma \vdash X; \overline{dc} \leq X; \overline{dc'}}{
adamc@537	1112 \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537	1113 }
adamc@537	1114 \quad \infer{\Gamma \vdash X \; \mt{of} \; \tau_1; \overline{dc} \leq X \; \mt{of} \; \tau_2; \overline{dc'}}{
adamc@537	1115 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537	1116 & \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537	1117 }$$
adamc@537	1118
adamc@537	1119 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x = \mt{datatype} \; M'.z'}{
adamc@537	1120 \Gamma \vdash M.z \equiv M'.z'
adamc@537	1121 }$$
adamc@537	1122
adamc@537	1123 $$\infer{\Gamma \vdash \mt{val} \; x : \tau_1 \leq \mt{val} \; x : \tau_2}{
adamc@537	1124 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537	1125 }
adamc@537	1126 \quad \infer{\Gamma \vdash \mt{structure} \; X : S_1 \leq \mt{structure} \; X : S_2}{
adamc@537	1127 \Gamma \vdash S_1 \leq S_2
adamc@537	1128 }
adamc@537	1129 \quad \infer{\Gamma \vdash \mt{signature} \; X = S_1 \leq \mt{signature} \; X = S_2}{
adamc@537	1130 \Gamma \vdash S_1 \leq S_2
adamc@537	1131 & \Gamma \vdash S_2 \leq S_1
adamc@537	1132 }$$
adamc@537	1133
adamc@537	1134 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leq \mt{constraint} \; c'_1 \sim c'_2}{
adamc@537	1135 \Gamma \vdash c_1 \equiv c'_1
adamc@537	1136 & \Gamma \vdash c_2 \equiv c'_2
adamc@537	1137 }$$
adamc@537	1138
adamc@655	1139 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{class} \; x :: \kappa}{}
adamc@655	1140 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{class} \; x :: \kappa}{}
adamc@655	1141 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{class} \; x :: \kappa = c_2}{
adamc@537	1142 \Gamma \vdash c_1 \equiv c_2
adamc@537	1143 }$$
adamc@537	1144
adamc@538	1145 \subsection{Module Typing}
adamc@538	1146
adamc@538	1147 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	1148
adamc@538	1149 $$\infer{\Gamma \vdash M : S}{
adamc@538	1150 \Gamma \vdash M : S'
adamc@538	1151 & \Gamma \vdash S' \leq S
adamc@538	1152 }
adamc@538	1153 \quad \infer{\Gamma \vdash \mt{struct} \; \overline{d} \; \mt{end} : \mt{sig} \; \mt{sigOf}(\overline{d}) \; \mt{end}}{
adamc@538	1154 \Gamma \vdash \overline{d} \leadsto \Gamma'
adamc@538	1155 }
adamc@538	1156 \quad \infer{\Gamma \vdash X : S}{
adamc@538	1157 X : S \in \Gamma
adamc@538	1158 }$$
adamc@538	1159
adamc@538	1160 $$\infer{\Gamma \vdash M.X : S}{
adamc@538	1161 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@538	1162 & \mt{proj}(M, \overline{s}, \mt{structure} \; X) = S
adamc@538	1163 }$$
adamc@538	1164
adamc@538	1165 $$\infer{\Gamma \vdash M_1(M_2) : [X \mapsto M_2]S_2}{
adamc@538	1166 \Gamma \vdash M_1 : \mt{functor}(X : S_1) : S_2
adamc@538	1167 & \Gamma \vdash M_2 : S_1
adamc@538	1168 }
adamc@538	1169 \quad \infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 = M : \mt{functor} (X : S_1) : S_2}{
adamc@538	1170 \Gamma \vdash S_1
adamc@538	1171 & \Gamma, X : S_1 \vdash S_2
adamc@538	1172 & \Gamma, X : S_1 \vdash M : S_2
adamc@538	1173 }$$
adamc@538	1174
adamc@538	1175 \begin{eqnarray*}
adamc@538	1176 \mt{sigOf}(\cdot) &=& \cdot \\
adamc@538	1177 \mt{sigOf}(s \; \overline{s'}) &=& \mt{sigOf}(s) \; \mt{sigOf}(\overline{s'}) \\
adamc@538	1178 \\
adamc@538	1179 \mt{sigOf}(\mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@538	1180 \mt{sigOf}(\mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \overline{dc} \\
adamc@538	1181 \mt{sigOf}(\mt{datatype} \; x = \mt{datatype} \; M.z) &=& \mt{datatype} \; x = \mt{datatype} \; M.z \\
adamc@538	1182 \mt{sigOf}(\mt{val} \; x : \tau = e) &=& \mt{val} \; x : \tau \\
adamc@538	1183 \mt{sigOf}(\mt{val} \; \mt{rec} \; \overline{x : \tau = e}) &=& \overline{\mt{val} \; x : \tau} \\
adamc@538	1184 \mt{sigOf}(\mt{structure} \; X : S = M) &=& \mt{structure} \; X : S \\
adamc@538	1185 \mt{sigOf}(\mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@538	1186 \mt{sigOf}(\mt{open} \; M) &=& \mt{include} \; S \textrm{ (where $\Gamma \vdash M : S$)} \\
adamc@538	1187 \mt{sigOf}(\mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@538	1188 \mt{sigOf}(\mt{open} \; \mt{constraints} \; M) &=& \cdot \\
adamc@538	1189 \mt{sigOf}(\mt{table} \; x : c) &=& \mt{table} \; x : c \\
adamc@784	1190 \mt{sigOf}(\mt{view} \; x : c) &=& \mt{view} \; x : c \\
adamc@538	1191 \mt{sigOf}(\mt{sequence} \; x) &=& \mt{sequence} \; x \\
adamc@538	1192 \mt{sigOf}(\mt{cookie} \; x : \tau) &=& \mt{cookie} \; x : \tau \\
adamc@784	1193 \mt{sigOf}(\mt{style} \; x) &=& \mt{style} \; x \\
adamc@655	1194 \mt{sigOf}(\mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@538	1195 \end{eqnarray*}
adamc@539	1196 \begin{eqnarray*}
adamc@539	1197 \mt{selfify}(M, \cdot) &=& \cdot \\
adamc@558	1198 \mt{selfify}(M, s \; \overline{s'}) &=& \mt{selfify}(M, s) \; \mt{selfify}(M, \overline{s'}) \\
adamc@539	1199 \\
adamc@539	1200 \mt{selfify}(M, \mt{con} \; x :: \kappa) &=& \mt{con} \; x :: \kappa = M.x \\
adamc@539	1201 \mt{selfify}(M, \mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@539	1202 \mt{selfify}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \mt{datatype} \; M.x \\
adamc@539	1203 \mt{selfify}(M, \mt{datatype} \; x = \mt{datatype} \; M'.z) &=& \mt{datatype} \; x = \mt{datatype} \; M'.z \\
adamc@539	1204 \mt{selfify}(M, \mt{val} \; x : \tau) &=& \mt{val} \; x : \tau \\
adamc@539	1205 \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	1206 \mt{selfify}(M, \mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@539	1207 \mt{selfify}(M, \mt{include} \; S) &=& \mt{include} \; S \\
adamc@539	1208 \mt{selfify}(M, \mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@655	1209 \mt{selfify}(M, \mt{class} \; x :: \kappa) &=& \mt{class} \; x :: \kappa = M.x \\
adamc@655	1210 \mt{selfify}(M, \mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@539	1211 \end{eqnarray*}
adamc@539	1212
adamc@540	1213 \subsection{Module Projection}
adamc@540	1214
adamc@540	1215 \begin{eqnarray*}
adamc@540	1216 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \\
adamc@540	1217 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa, c) \\
adamc@540	1218 \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	1219 \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	1220 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})$)} \\
adamc@655	1221 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \to \mt{Type} \\
adamc@655	1222 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa \to \mt{Type}, c) \\
adamc@540	1223 \\
adamc@540	1224 \mt{proj}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc} \; \overline{s}, \mt{datatype} \; x) &=& (\overline{y}, \overline{dc}) \\
adamc@540	1225 \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	1226 \\
adamc@540	1227 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, \mt{val} \; x) &=& \tau \\
adamc@540	1228 \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	1229 \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	1230 \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	1231 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \in \overline{dc}$)} \\
adamc@540	1232 \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	1233 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \; \mt{of} \; \tau \in \overline{dc}$)} \\
adamc@540	1234 \\
adamc@540	1235 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, \mt{structure} \; X) &=& S \\
adamc@540	1236 \\
adamc@540	1237 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, \mt{signature} \; X) &=& S \\
adamc@540	1238 \\
adamc@540	1239 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1240 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1241 \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	1242 \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	1243 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@540	1244 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1245 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1246 \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	1247 \mt{proj}(M, \mt{constraint} \; c_1 \sim c_2 \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@655	1248 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@655	1249 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1250 \end{eqnarray*}
adamc@540	1251
adamc@541	1252
adamc@541	1253 \section{Type Inference}
adamc@541	1254
adamc@541	1255 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	1256
adamc@541	1257 \subsection{Basic Unification}
adamc@541	1258
adamc@560	1259 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	1260
adamc@656	1261 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	1262
adamc@541	1263 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	1264
adamc@541	1265 \subsection{Unifying Record Types}
adamc@541	1266
adamc@570	1267 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	1268
adamc@656	1269 \subsection{\label{typeclasses}Constructor Classes}
adamc@541	1270
adamc@784	1271 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	1272
adamc@784	1273 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	1274
adamc@656	1275 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	1276
adamc@656	1277 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	1278
adamc@541	1279 \subsection{Reverse-Engineering Record Types}
adamc@541	1280
adamc@656	1281 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	1282
adamc@541	1283 \subsection{Implicit Arguments in Functor Applications}
adamc@541	1284
adamc@656	1285 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	1286
adamc@541	1287
adamc@542	1288 \section{The Ur Standard Library}
adamc@542	1289
adamc@542	1290 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	1291
adamc@542	1292 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	1293
adamc@542	1294 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	1295 $$\begin{array}{l}
adamc@542	1296 \mt{type} \; \mt{int} \\
adamc@542	1297 \mt{type} \; \mt{float} \\
adamc@873	1298 \mt{type} \; \mt{char} \\
adamc@542	1299 \mt{type} \; \mt{string} \\
adamc@542	1300 \mt{type} \; \mt{time} \\
adamc@785	1301 \mt{type} \; \mt{blob} \\
adamc@542	1302 \\
adamc@542	1303 \mt{type} \; \mt{unit} = \{\} \\
adamc@542	1304 \\
adamc@542	1305 \mt{datatype} \; \mt{bool} = \mt{False} \mid \mt{True} \\
adamc@542	1306 \\
adamc@785	1307 \mt{datatype} \; \mt{option} \; \mt{t} = \mt{None} \mid \mt{Some} \; \mt{of} \; \mt{t} \\
adamc@785	1308 \\
adamc@785	1309 \mt{datatype} \; \mt{list} \; \mt{t} = \mt{Nil} \mid \mt{Cons} \; \mt{of} \; \mt{t} \times \mt{list} \; \mt{t}
adamc@542	1310 \end{array}$$
adamc@542	1311
adamc@1123	1312 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	1313
adam@1297	1314 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	1315 $$\begin{array}{l}
adam@1297	1316 \mt{con} \; \mt{variant} :: \{\mt{Type}\} \to \mt{Type} \\
adam@1297	1317 \mt{val} \; \mt{make} : \mt{nm} :: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{ts} ::: \{\mt{Type}\} \to [[\mt{nm}] \sim \mt{ts}] \Rightarrow \mt{t} \to \mt{variant} \; ([\mt{nm} = \mt{t}] \rc \mt{ts}) \\
adam@1297	1318 \mt{val} \; \mt{match} : \mt{ts} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{variant} \; \mt{ts} \to \$(\mt{map} \; (\lambda \mt{t'} \Rightarrow \mt{t'} \to \mt{t}) \; \mt{ts}) \to \mt{t}
adam@1297	1319 \end{array}$$
adam@1297	1320
adamc@657	1321 Another important generic Ur element comes at the beginning of \texttt{top.urs}.
adamc@657	1322
adamc@657	1323 $$\begin{array}{l}
adamc@657	1324 \mt{con} \; \mt{folder} :: \mt{K} \longrightarrow \{\mt{K}\} \to \mt{Type} \\
adamc@657	1325 \\
adamc@657	1326 \mt{val} \; \mt{fold} : \mt{K} \longrightarrow \mt{tf} :: (\{\mt{K}\} \to \mt{Type}) \\
adamc@657	1327 \hspace{.1in} \to (\mt{nm} :: \mt{Name} \to \mt{v} :: \mt{K} \to \mt{r} :: \{\mt{K}\} \to [[\mt{nm}] \sim \mt{r}] \Rightarrow \\
adamc@657	1328 \hspace{.2in} \mt{tf} \; \mt{r} \to \mt{tf} \; ([\mt{nm} = \mt{v}] \rc \mt{r})) \\
adamc@657	1329 \hspace{.1in} \to \mt{tf} \; [] \\
adamc@657	1330 \hspace{.1in} \to \mt{r} :: \{\mt{K}\} \to \mt{folder} \; \mt{r} \to \mt{tf} \; \mt{r}
adamc@657	1331 \end{array}$$
adamc@657	1332
adamc@657	1333 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	1334
adamc@664	1335 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	1336
adamc@542	1337
adamc@542	1338 \section{The Ur/Web Standard Library}
adamc@542	1339
adam@1400	1340 Some operations are only allowed in server-side code or only in client-side code. The type system does not enforce such restrictions, but the compiler enforces them in the process of whole-program compilation. In the discussion below, we note when a set of operations has a location restriction.
adam@1400	1341
adamc@658	1342 \subsection{Monads}
adamc@658	1343
adamc@658	1344 The Ur Basis defines the monad constructor class from Haskell.
adamc@658	1345
adamc@658	1346 $$\begin{array}{l}
adamc@658	1347 \mt{class} \; \mt{monad} :: \mt{Type} \to \mt{Type} \\
adamc@658	1348 \mt{val} \; \mt{return} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t} ::: \mt{Type} \\
adamc@658	1349 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658	1350 \hspace{.1in} \to \mt{t} \to \mt{m} \; \mt{t} \\
adamc@658	1351 \mt{val} \; \mt{bind} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t1} ::: \mt{Type} \to \mt{t2} ::: \mt{Type} \\
adamc@658	1352 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658	1353 \hspace{.1in} \to \mt{m} \; \mt{t1} \to (\mt{t1} \to \mt{m} \; \mt{t2}) \\
adamc@658	1354 \hspace{.1in} \to \mt{m} \; \mt{t2}
adamc@658	1355 \end{array}$$
adamc@658	1356
adamc@542	1357 \subsection{Transactions}
adamc@542	1358
adamc@542	1359 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	1360 $$\begin{array}{l}
adamc@542	1361 \mt{con} \; \mt{transaction} :: \mt{Type} \to \mt{Type} \\
adamc@658	1362 \mt{val} \; \mt{transaction\_monad} : \mt{monad} \; \mt{transaction}
adamc@542	1363 \end{array}$$
adamc@542	1364
adamc@1123	1365 For debugging purposes, a transactional function is provided for outputting a string on the server process' \texttt{stderr}.
adamc@1123	1366 $$\begin{array}{l}
adamc@1123	1367 \mt{val} \; \mt{debug} : \mt{string} \to \mt{transaction} \; \mt{unit}
adamc@1123	1368 \end{array}$$
adamc@1123	1369
adamc@542	1370 \subsection{HTTP}
adamc@542	1371
adam@1400	1372 There are transactions for reading an HTTP header by name and for getting and setting strongly-typed cookies. Cookies may only be created by the $\mt{cookie}$ declaration form, ensuring that they be named consistently based on module structure. For now, cookie operations are server-side only.
adamc@542	1373 $$\begin{array}{l}
adamc@786	1374 \mt{con} \; \mt{http\_cookie} :: \mt{Type} \to \mt{Type} \\
adamc@786	1375 \mt{val} \; \mt{getCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; (\mt{option} \; \mt{t}) \\
adamc@1050	1376 \mt{val} \; \mt{setCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \{\mt{Value} : \mt{t}, \mt{Expires} : \mt{option} \; \mt{time}, \mt{Secure} : \mt{bool}\} \to \mt{transaction} \; \mt{unit} \\
adamc@1050	1377 \mt{val} \; \mt{clearCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; \mt{unit}
adamc@786	1378 \end{array}$$
adamc@786	1379
adamc@786	1380 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	1381 $$\begin{array}{l}
adamc@786	1382 \mt{type} \; \mt{url} \\
adamc@786	1383 \mt{val} \; \mt{bless} : \mt{string} \to \mt{url} \\
adamc@786	1384 \mt{val} \; \mt{checkUrl} : \mt{string} \to \mt{option} \; \mt{url}
adamc@786	1385 \end{array}$$
adamc@786	1386 $\mt{bless}$ raises a runtime error if the string passed to it fails the URL policy.
adamc@786	1387
adam@1400	1388 It is possible to grab the current page's URL or to build a URL for an arbitrary transaction that would also be an acceptable value of a \texttt{link} attribute of the \texttt{a} tag. These are server-side operations.
adamc@1085	1389 $$\begin{array}{l}
adamc@1085	1390 \mt{val} \; \mt{currentUrl} : \mt{transaction} \; \mt{url} \\
adamc@1085	1391 \mt{val} \; \mt{url} : \mt{transaction} \; \mt{page} \to \mt{url}
adamc@1085	1392 \end{array}$$
adamc@1085	1393
adamc@1085	1394 Page generation may be interrupted at any time with a request to redirect to a particular URL instead.
adamc@1085	1395 $$\begin{array}{l}
adamc@1085	1396 \mt{val} \; \mt{redirect} : \mt{t} ::: \mt{Type} \to \mt{url} \to \mt{transaction} \; \mt{t}
adamc@1085	1397 \end{array}$$
adamc@1085	1398
adam@1400	1399 It's possible for pages to return files of arbitrary MIME types. A file can be input from the user using this data type, along with the $\mt{upload}$ form tag. These functions and those described in the following paragraph are server-side.
adamc@786	1400 $$\begin{array}{l}
adamc@786	1401 \mt{type} \; \mt{file} \\
adamc@786	1402 \mt{val} \; \mt{fileName} : \mt{file} \to \mt{option} \; \mt{string} \\
adamc@786	1403 \mt{val} \; \mt{fileMimeType} : \mt{file} \to \mt{string} \\
adamc@786	1404 \mt{val} \; \mt{fileData} : \mt{file} \to \mt{blob}
adamc@786	1405 \end{array}$$
adamc@786	1406
adamc@786	1407 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	1408 $$\begin{array}{l}
adamc@786	1409 \mt{type} \; \mt{mimeType} \\
adamc@786	1410 \mt{val} \; \mt{blessMime} : \mt{string} \to \mt{mimeType} \\
adamc@786	1411 \mt{val} \; \mt{checkMime} : \mt{string} \to \mt{option} \; \mt{mimeType} \\
adamc@786	1412 \mt{val} \; \mt{returnBlob} : \mt{t} ::: \mt{Type} \to \mt{blob} \to \mt{mimeType} \to \mt{transaction} \; \mt{t}
adamc@542	1413 \end{array}$$
adamc@542	1414
adamc@543	1415 \subsection{SQL}
adamc@543	1416
adam@1400	1417 Everything about SQL database access is restricted to server-side code.
adam@1400	1418
adamc@543	1419 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	1420 $$\begin{array}{l}
adamc@785	1421 \mt{con} \; \mt{sql\_table} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785	1422 \end{array}$$
adamc@785	1423 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	1424
adamc@785	1425 We also have the simpler type family of SQL views, which have no keys.
adamc@785	1426 $$\begin{array}{l}
adamc@785	1427 \mt{con} \; \mt{sql\_view} :: \{\mt{Type}\} \to \mt{Type}
adamc@543	1428 \end{array}$$
adamc@543	1429
adamc@785	1430 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	1431 $$\begin{array}{l}
adamc@785	1432 \mt{class} \; \mt{fieldsOf} :: \mt{Type} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785	1433 \mt{val} \; \mt{fieldsOf\_table} : \mt{fs} ::: \{\mt{Type}\} \to \mt{keys} ::: \{\{\mt{Unit}\}\} \to \mt{fieldsOf} \; (\mt{sql\_table} \; \mt{fs} \; \mt{keys}) \; \mt{fs} \\
adamc@785	1434 \mt{val} \; \mt{fieldsOf\_view} : \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; (\mt{sql\_view} \; \mt{fs}) \; \mt{fs}
adamc@785	1435 \end{array}$$
adamc@785	1436
adamc@785	1437 \subsubsection{Table Constraints}
adamc@785	1438
adamc@785	1439 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	1440
adamc@785	1441 $$\begin{array}{l}
adamc@785	1442 \mt{con} \; \mt{primary\_key} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type} \\
adamc@785	1443 \mt{val} \; \mt{no\_primary\_key} : \mt{fs} ::: \{\mt{Type}\} \to \mt{primary\_key} \; \mt{fs} \; [] \\
adamc@785	1444 \mt{val} \; \mt{primary\_key} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{key1} :: \mt{Name} \to \mt{keys} :: \{\mt{Type}\} \\
adamc@785	1445 \hspace{.1in} \to [[\mt{key1}] \sim \mt{keys}] \Rightarrow [[\mt{key1} = \mt{t}] \rc \mt{keys} \sim \mt{rest}] \\
adamc@785	1446 \hspace{.1in} \Rightarrow \$([\mt{key1} = \mt{sql\_injectable\_prim} \; \mt{t}] \rc \mt{map} \; \mt{sql\_injectable\_prim} \; \mt{keys}) \\
adamc@785	1447 \hspace{.1in} \to \mt{primary\_key} \; ([\mt{key1} = \mt{t}] \rc \mt{keys} \rc \mt{rest}) \; [\mt{Pkey} = [\mt{key1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{keys}]
adamc@785	1448 \end{array}$$
adamc@785	1449 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	1450
adamc@785	1451 A type family stands for sets of named constraints of the remaining varieties.
adamc@785	1452 $$\begin{array}{l}
adamc@785	1453 \mt{con} \; \mt{sql\_constraints} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785	1454 \end{array}$$
adamc@785	1455 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	1456
adamc@785	1457 There is a type family of individual, unnamed constraints.
adamc@785	1458 $$\begin{array}{l}
adamc@785	1459 \mt{con} \; \mt{sql\_constraint} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \mt{Type}
adamc@785	1460 \end{array}$$
adamc@785	1461 The first argument is the same as above, and the second argument gives the key columns for just this constraint.
adamc@785	1462
adamc@785	1463 We have operations for assembling constraints into constraint sets.
adamc@785	1464 $$\begin{array}{l}
adamc@785	1465 \mt{val} \; \mt{no\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_constraints} \; \mt{fs} \; [] \\
adamc@785	1466 \mt{val} \; \mt{one\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{unique} ::: \{\mt{Unit}\} \to \mt{name} :: \mt{Name} \\
adamc@785	1467 \hspace{.1in} \to \mt{sql\_constraint} \; \mt{fs} \; \mt{unique} \to \mt{sql\_constraints} \; \mt{fs} \; [\mt{name} = \mt{unique}] \\
adamc@785	1468 \mt{val} \; \mt{join\_constraints} : \mt{fs} ::: \{\mt{Type}\} \to \mt{uniques1} ::: \{\{\mt{Unit}\}\} \to \mt{uniques2} ::: \{\{\mt{Unit}\}\} \to [\mt{uniques1} \sim \mt{uniques2}] \\
adamc@785	1469 \hspace{.1in} \Rightarrow \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques1} \to \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques2} \to \mt{sql\_constraints} \; \mt{fs} \; (\mt{uniques1} \rc \mt{uniques2})
adamc@785	1470 \end{array}$$
adamc@785	1471
adamc@785	1472 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	1473 $$\begin{array}{l}
adamc@785	1474 \mt{val} \; \mt{unique} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{unique1} :: \mt{Name} \to \mt{unique} :: \{\mt{Type}\} \\
adamc@785	1475 \hspace{.1in} \to [[\mt{unique1}] \sim \mt{unique}] \Rightarrow [[\mt{unique1} = \mt{t}] \rc \mt{unique} \sim \mt{rest}] \\
adamc@785	1476 \hspace{.1in} \Rightarrow \mt{sql\_constraint} \; ([\mt{unique1} = \mt{t}] \rc \mt{unique} \rc \mt{rest}) \; ([\mt{unique1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{unique})
adamc@785	1477 \end{array}$$
adamc@785	1478
adamc@785	1479 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	1480 $$\begin{array}{l}
adamc@785	1481 \mt{class} \; \mt{linkable} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@785	1482 \mt{val} \; \mt{linkable\_same} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; \mt{t} \\
adamc@785	1483 \mt{val} \; \mt{linkable\_from\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; (\mt{option} \; \mt{t}) \; \mt{t} \\
adamc@785	1484 \mt{val} \; \mt{linkable\_to\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@785	1485 \end{array}$$
adamc@785	1486
adamc@785	1487 The $\mt{matching}$ type family uses $\mt{linkable}$ to define when two keys match up type-wise.
adamc@785	1488 $$\begin{array}{l}
adamc@785	1489 \mt{con} \; \mt{matching} :: \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785	1490 \mt{val} \; \mt{mat\_nil} : \mt{matching} \; [] \; [] \\
adamc@785	1491 \mt{val} \; \mt{mat\_cons} : \mt{t1} ::: \mt{Type} \to \mt{rest1} ::: \{\mt{Type}\} \to \mt{t2} ::: \mt{Type} \to \mt{rest2} ::: \{\mt{Type}\} \to \mt{nm1} :: \mt{Name} \to \mt{nm2} :: \mt{Name} \\
adamc@785	1492 \hspace{.1in} \to [[\mt{nm1}] \sim \mt{rest1}] \Rightarrow [[\mt{nm2}] \sim \mt{rest2}] \Rightarrow \mt{linkable} \; \mt{t1} \; \mt{t2} \to \mt{matching} \; \mt{rest1} \; \mt{rest2} \\
adamc@785	1493 \hspace{.1in} \to \mt{matching} \; ([\mt{nm1} = \mt{t1}] \rc \mt{rest1}) \; ([\mt{nm2} = \mt{t2}] \rc \mt{rest2})
adamc@785	1494 \end{array}$$
adamc@785	1495
adamc@785	1496 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	1497 $$\begin{array}{l}
adamc@785	1498 \mt{con} \; \mt{propagation\_mode} :: \{\mt{Type}\} \to \mt{Type} \\
adamc@785	1499 \mt{val} \; \mt{restrict} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785	1500 \mt{val} \; \mt{cascade} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785	1501 \mt{val} \; \mt{no\_action} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785	1502 \mt{val} \; \mt{set\_null} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; (\mt{map} \; \mt{option} \; \mt{fs})
adamc@785	1503 \end{array}$$
adamc@785	1504
adamc@785	1505 Finally, we put these ingredient together to define the \texttt{FOREIGN KEY} constraint function.
adamc@785	1506 $$\begin{array}{l}
adamc@785	1507 \mt{val} \; \mt{foreign\_key} : \mt{mine1} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{mine} ::: \{\mt{Type}\} \to \mt{munused} ::: \{\mt{Type}\} \to \mt{foreign} ::: \{\mt{Type}\} \\
adamc@785	1508 \hspace{.1in} \to \mt{funused} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{uniques} ::: \{\{\mt{Unit}\}\} \\
adamc@785	1509 \hspace{.1in} \to [[\mt{mine1}] \sim \mt{mine}] \Rightarrow [[\mt{mine1} = \mt{t}] \rc \mt{mine} \sim \mt{munused}] \Rightarrow [\mt{foreign} \sim \mt{funused}] \Rightarrow [[\mt{nm}] \sim \mt{uniques}] \\
adamc@785	1510 \hspace{.1in} \Rightarrow \mt{matching} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}) \; \mt{foreign} \\
adamc@785	1511 \hspace{.1in} \to \mt{sql\_table} \; (\mt{foreign} \rc \mt{funused}) \; ([\mt{nm} = \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{foreign}] \rc \mt{uniques}) \\
adamc@785	1512 \hspace{.1in} \to \{\mt{OnDelete} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}), \\
adamc@785	1513 \hspace{.2in} \mt{OnUpdate} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine})\} \\
adamc@785	1514 \hspace{.1in} \to \mt{sql\_constraint} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine} \rc \mt{munused}) \; []
adamc@785	1515 \end{array}$$
adamc@785	1516
adamc@785	1517 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	1518 $$\begin{array}{l}
adamc@785	1519 \mt{val} \; \mt{check} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; [] \; [] \; \mt{fs} \; \mt{bool} \to \mt{sql\_constraint} \; \mt{fs} \; []
adamc@785	1520 \end{array}$$
adamc@785	1521
adamc@785	1522 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	1523
adamc@784	1524
adamc@543	1525 \subsubsection{Queries}
adamc@543	1526
adam@1400	1527 A final query is constructed via the $\mt{sql\_query}$ function. Constructor arguments respectively specify the unrestricted free table variables (which will only be available in subqueries), the free table variables that may only be mentioned within arguments to aggregate functions, table fields we select (as records mapping tables to the subsets of their fields that we choose), and the (always named) extra expressions that we select.
adamc@543	1528 $$\begin{array}{l}
adam@1400	1529 \mt{con} \; \mt{sql\_query} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@1193	1530 \mt{val} \; \mt{sql\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400	1531 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adamc@1193	1532 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543	1533 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543	1534 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1193	1535 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adam@1400	1536 \hspace{.1in} \Rightarrow \{\mt{Rows} : \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}, \\
adamc@1193	1537 \hspace{.2in} \mt{OrderBy} : \mt{sql\_order\_by} \; (\mt{free} \rc \mt{tables}) \; \mt{selectedExps}, \\
adamc@543	1538 \hspace{.2in} \mt{Limit} : \mt{sql\_limit}, \\
adamc@543	1539 \hspace{.2in} \mt{Offset} : \mt{sql\_offset}\} \\
adam@1400	1540 \hspace{.1in} \to \mt{sql\_query} \; \mt{free} \; \mt{afree} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543	1541 \end{array}$$
adamc@543	1542
adamc@545	1543 Queries are used by folding over their results inside transactions.
adamc@545	1544 $$\begin{array}{l}
adam@1400	1545 \mt{val} \; \mt{query} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to [\mt{tables} \sim \mt{exps}] \Rightarrow \mt{state} ::: \mt{Type} \to \mt{sql\_query} \; [] \; [] \; \mt{tables} \; \mt{exps} \\
adamc@658	1546 \hspace{.1in} \to (\$(\mt{exps} \rc \mt{map} \; (\lambda \mt{fields} :: \{\mt{Type}\} \Rightarrow \$\mt{fields}) \; \mt{tables}) \\
adamc@545	1547 \hspace{.2in} \to \mt{state} \to \mt{transaction} \; \mt{state}) \\
adamc@545	1548 \hspace{.1in} \to \mt{state} \to \mt{transaction} \; \mt{state}
adamc@545	1549 \end{array}$$
adamc@545	1550
adam@1400	1551 Most of the complexity of the query encoding is in the type $\mt{sql\_query1}$, which includes simple queries and derived queries based on relational operators. Constructor arguments respectively specify the unrestricted free table veriables, the aggregate-only free table variables, the tables we select from, the subset of fields that we keep from each table for the result rows, and the extra expressions that we select.
adamc@543	1552 $$\begin{array}{l}
adam@1400	1553 \mt{con} \; \mt{sql\_query1} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@543	1554 \\
adamc@543	1555 \mt{type} \; \mt{sql\_relop} \\
adamc@543	1556 \mt{val} \; \mt{sql\_union} : \mt{sql\_relop} \\
adamc@543	1557 \mt{val} \; \mt{sql\_intersect} : \mt{sql\_relop} \\
adamc@543	1558 \mt{val} \; \mt{sql\_except} : \mt{sql\_relop} \\
adam@1400	1559 \mt{val} \; \mt{sql\_relop} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400	1560 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adam@1400	1561 \hspace{.1in} \to \mt{tables1} ::: \{\{\mt{Type}\}\} \\
adamc@543	1562 \hspace{.1in} \to \mt{tables2} ::: \{\{\mt{Type}\}\} \\
adamc@543	1563 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543	1564 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@543	1565 \hspace{.1in} \to \mt{sql\_relop} \\
adam@1400	1566 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables1} \; \mt{selectedFields} \; \mt{selectedExps} \\
adam@1400	1567 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables2} \; \mt{selectedFields} \; \mt{selectedExps} \\
adam@1400	1568 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{selectedFields} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543	1569 \end{array}$$
adamc@543	1570
adamc@543	1571 $$\begin{array}{l}
adamc@1193	1572 \mt{val} \; \mt{sql\_query1} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400	1573 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adamc@1193	1574 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543	1575 \hspace{.1in} \to \mt{grouped} ::: \{\{\mt{Type}\}\} \\
adamc@543	1576 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543	1577 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1085	1578 \hspace{.1in} \to \mt{empties} :: \{\mt{Unit}\} \\
adamc@1193	1579 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adamc@1193	1580 \hspace{.1in} \Rightarrow [\mt{free} \sim \mt{grouped}] \\
adam@1400	1581 \hspace{.1in} \Rightarrow [\mt{afree} \sim \mt{tables}] \\
adamc@1193	1582 \hspace{.1in} \Rightarrow [\mt{empties} \sim \mt{selectedFields}] \\
adamc@1085	1583 \hspace{.1in} \Rightarrow \{\mt{Distinct} : \mt{bool}, \\
adamc@1193	1584 \hspace{.2in} \mt{From} : \mt{sql\_from\_items} \; \mt{free} \; \mt{tables}, \\
adam@1400	1585 \hspace{.2in} \mt{Where} : \mt{sql\_exp} \; (\mt{free} \rc \mt{tables}) \; \mt{afree} \; [] \; \mt{bool}, \\
adamc@543	1586 \hspace{.2in} \mt{GroupBy} : \mt{sql\_subset} \; \mt{tables} \; \mt{grouped}, \\
adam@1400	1587 \hspace{.2in} \mt{Having} : \mt{sql\_exp} \; (\mt{free} \rc \mt{grouped}) \; (\mt{afree} \rc \mt{tables}) \; [] \; \mt{bool}, \\
adamc@1085	1588 \hspace{.2in} \mt{SelectFields} : \mt{sql\_subset} \; \mt{grouped} \; (\mt{map} \; (\lambda \_ \Rightarrow []) \; \mt{empties} \rc \mt{selectedFields}), \\
adam@1400	1589 \hspace{.2in} \mt {SelectExps} : \$(\mt{map} \; (\mt{sql\_exp} \; (\mt{free} \rc \mt{grouped}) \; (\mt{afree} \rc \mt{tables}) \; []) \; \mt{selectedExps}) \} \\
adam@1400	1590 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543	1591 \end{array}$$
adamc@543	1592
adamc@543	1593 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	1594 $$\begin{array}{l}
adamc@543	1595 \mt{con} \; \mt{sql\_subset} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@543	1596 \mt{val} \; \mt{sql\_subset} : \mt{keep\_drop} :: \{(\{\mt{Type}\} \times \{\mt{Type}\})\} \\
adamc@543	1597 \hspace{.1in} \to \mt{sql\_subset} \\
adamc@658	1598 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1 \rc \mt{fields}.2)\; \mt{keep\_drop}) \\
adamc@658	1599 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1) \; \mt{keep\_drop}) \\
adamc@543	1600 \mt{val} \; \mt{sql\_subset\_all} : \mt{tables} :: \{\{\mt{Type}\}\} \to \mt{sql\_subset} \; \mt{tables} \; \mt{tables}
adamc@543	1601 \end{array}$$
adamc@543	1602
adamc@560	1603 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	1604 $$\begin{array}{l}
adamc@543	1605 \mt{con} \; \mt{sql\_exp} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}
adamc@543	1606 \end{array}$$
adamc@543	1607
adamc@543	1608 Any field in scope may be converted to an expression.
adamc@543	1609 $$\begin{array}{l}
adamc@543	1610 \mt{val} \; \mt{sql\_field} : \mt{otherTabs} ::: \{\{\mt{Type}\}\} \to \mt{otherFields} ::: \{\mt{Type}\} \\
adamc@543	1611 \hspace{.1in} \to \mt{fieldType} ::: \mt{Type} \to \mt{agg} ::: \{\{\mt{Type}\}\} \\
adamc@543	1612 \hspace{.1in} \to \mt{exps} ::: \{\mt{Type}\} \\
adamc@543	1613 \hspace{.1in} \to \mt{tab} :: \mt{Name} \to \mt{field} :: \mt{Name} \\
adamc@543	1614 \hspace{.1in} \to \mt{sql\_exp} \; ([\mt{tab} = [\mt{field} = \mt{fieldType}] \rc \mt{otherFields}] \rc \mt{otherTabs}) \; \mt{agg} \; \mt{exps} \; \mt{fieldType}
adamc@543	1615 \end{array}$$
adamc@543	1616
adamc@544	1617 There is an analogous function for referencing named expressions.
adamc@544	1618 $$\begin{array}{l}
adamc@544	1619 \mt{val} \; \mt{sql\_exp} : \mt{tabs} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{t} ::: \mt{Type} \to \mt{rest} ::: \{\mt{Type}\} \to \mt{nm} :: \mt{Name} \\
adamc@544	1620 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tabs} \; \mt{agg} \; ([\mt{nm} = \mt{t}] \rc \mt{rest}) \; \mt{t}
adamc@544	1621 \end{array}$$
adamc@544	1622
adamc@544	1623 Ur values of appropriate types may be injected into SQL expressions.
adamc@544	1624 $$\begin{array}{l}
adamc@786	1625 \mt{class} \; \mt{sql\_injectable\_prim} \\
adamc@786	1626 \mt{val} \; \mt{sql\_bool} : \mt{sql\_injectable\_prim} \; \mt{bool} \\
adamc@786	1627 \mt{val} \; \mt{sql\_int} : \mt{sql\_injectable\_prim} \; \mt{int} \\
adamc@786	1628 \mt{val} \; \mt{sql\_float} : \mt{sql\_injectable\_prim} \; \mt{float} \\
adamc@786	1629 \mt{val} \; \mt{sql\_string} : \mt{sql\_injectable\_prim} \; \mt{string} \\
adamc@786	1630 \mt{val} \; \mt{sql\_time} : \mt{sql\_injectable\_prim} \; \mt{time} \\
adamc@786	1631 \mt{val} \; \mt{sql\_blob} : \mt{sql\_injectable\_prim} \; \mt{blob} \\
adamc@786	1632 \mt{val} \; \mt{sql\_channel} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{channel} \; \mt{t}) \\
adamc@786	1633 \mt{val} \; \mt{sql\_client} : \mt{sql\_injectable\_prim} \; \mt{client} \\
adamc@786	1634 \\
adamc@544	1635 \mt{class} \; \mt{sql\_injectable} \\
adamc@786	1636 \mt{val} \; \mt{sql\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@786	1637 \mt{val} \; \mt{sql\_option\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; (\mt{option} \; \mt{t}) \\
adamc@786	1638 \\
adamc@544	1639 \mt{val} \; \mt{sql\_inject} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@544	1640 \hspace{.1in} \to \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adamc@544	1641 \end{array}$$
adamc@544	1642
adamc@1123	1643 Additionally, most function-free types may be injected safely, via the $\mt{serialized}$ type family.
adamc@1123	1644 $$\begin{array}{l}
adamc@1123	1645 \mt{con} \; \mt{serialized} :: \mt{Type} \to \mt{Type} \\
adamc@1123	1646 \mt{val} \; \mt{serialize} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{serialized} \; \mt{t} \\
adamc@1123	1647 \mt{val} \; \mt{deserialize} : \mt{t} ::: \mt{Type} \to \mt{serialized} \; \mt{t} \to \mt{t} \\
adamc@1123	1648 \mt{val} \; \mt{sql\_serialized} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{serialized} \; \mt{t})
adamc@1123	1649 \end{array}$$
adamc@1123	1650
adamc@544	1651 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	1652 $$\begin{array}{l}
adamc@544	1653 \mt{val} \; \mt{sql\_is\_null} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544	1654 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; (\mt{option} \; \mt{t}) \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{bool}
adamc@544	1655 \end{array}$$
adamc@544	1656
adamc@559	1657 We have generic nullary, unary, and binary operators.
adamc@544	1658 $$\begin{array}{l}
adamc@544	1659 \mt{con} \; \mt{sql\_nfunc} :: \mt{Type} \to \mt{Type} \\
adamc@544	1660 \mt{val} \; \mt{sql\_current\_timestamp} : \mt{sql\_nfunc} \; \mt{time} \\
adamc@544	1661 \mt{val} \; \mt{sql\_nfunc} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544	1662 \hspace{.1in} \to \mt{sql\_nfunc} \; \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\\end{array}$$
adamc@544	1663
adamc@544	1664 $$\begin{array}{l}
adamc@544	1665 \mt{con} \; \mt{sql\_unary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544	1666 \mt{val} \; \mt{sql\_not} : \mt{sql\_unary} \; \mt{bool} \; \mt{bool} \\
adamc@544	1667 \mt{val} \; \mt{sql\_unary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adamc@544	1668 \hspace{.1in} \to \mt{sql\_unary} \; \mt{arg} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res} \\
adamc@544	1669 \end{array}$$
adamc@544	1670
adamc@544	1671 $$\begin{array}{l}
adamc@544	1672 \mt{con} \; \mt{sql\_binary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544	1673 \mt{val} \; \mt{sql\_and} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544	1674 \mt{val} \; \mt{sql\_or} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544	1675 \mt{val} \; \mt{sql\_binary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg_1} ::: \mt{Type} \to \mt{arg_2} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adamc@544	1676 \hspace{.1in} \to \mt{sql\_binary} \; \mt{arg_1} \; \mt{arg_2} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_1} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_2} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res}
adamc@544	1677 \end{array}$$
adamc@544	1678
adamc@544	1679 $$\begin{array}{l}
adamc@559	1680 \mt{class} \; \mt{sql\_arith} \\
adamc@559	1681 \mt{val} \; \mt{sql\_int\_arith} : \mt{sql\_arith} \; \mt{int} \\
adamc@559	1682 \mt{val} \; \mt{sql\_float\_arith} : \mt{sql\_arith} \; \mt{float} \\
adamc@559	1683 \mt{val} \; \mt{sql\_neg} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_unary} \; \mt{t} \; \mt{t} \\
adamc@559	1684 \mt{val} \; \mt{sql\_plus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559	1685 \mt{val} \; \mt{sql\_minus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559	1686 \mt{val} \; \mt{sql\_times} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559	1687 \mt{val} \; \mt{sql\_div} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559	1688 \mt{val} \; \mt{sql\_mod} : \mt{sql\_binary} \; \mt{int} \; \mt{int} \; \mt{int}
adamc@559	1689 \end{array}$$
adamc@544	1690
adamc@656	1691 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	1692 $$\begin{array}{l}
adamc@544	1693 \mt{val} \; \mt{sql\_count} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int}
adamc@544	1694 \end{array}$$
adamc@544	1695
adamc@544	1696 $$\begin{array}{l}
adamc@1188	1697 \mt{con} \; \mt{sql\_aggregate} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@1188	1698 \mt{val} \; \mt{sql\_aggregate} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{dom} ::: \mt{Type} \to \mt{ran} ::: \mt{Type} \\
adamc@1188	1699 \hspace{.1in} \to \mt{sql\_aggregate} \; \mt{dom} \; \mt{ran} \to \mt{sql\_exp} \; \mt{agg} \; \mt{agg} \; \mt{exps} \; \mt{dom} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{ran}
adamc@1188	1700 \end{array}$$
adamc@1188	1701
adamc@1188	1702 $$\begin{array}{l}
adamc@1188	1703 \mt{val} \; \mt{sql\_count\_col} : \mt{t} ::: \mt{Type} \to \mt{sql\_aggregate} \; (\mt{option} \; \mt{t}) \; \mt{int}
adamc@544	1704 \end{array}$$
adam@1400	1705
adam@1400	1706 Most aggregate functions are typed using a two-parameter constructor class $\mt{nullify}$ which maps $\mt{option}$ types to themselves and adds $\mt{option}$ to others. That is, this constructor class represents the process of making an SQL type ``nullable.''
adamc@544	1707
adamc@544	1708 $$\begin{array}{l}
adamc@544	1709 \mt{class} \; \mt{sql\_summable} \\
adamc@544	1710 \mt{val} \; \mt{sql\_summable\_int} : \mt{sql\_summable} \; \mt{int} \\
adamc@544	1711 \mt{val} \; \mt{sql\_summable\_float} : \mt{sql\_summable} \; \mt{float} \\
adam@1400	1712 \mt{val} \; \mt{sql\_avg} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt} \\
adam@1400	1713 \mt{val} \; \mt{sql\_sum} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt}
adamc@544	1714 \end{array}$$
adamc@544	1715
adamc@544	1716 $$\begin{array}{l}
adamc@544	1717 \mt{class} \; \mt{sql\_maxable} \\
adamc@544	1718 \mt{val} \; \mt{sql\_maxable\_int} : \mt{sql\_maxable} \; \mt{int} \\
adamc@544	1719 \mt{val} \; \mt{sql\_maxable\_float} : \mt{sql\_maxable} \; \mt{float} \\
adamc@544	1720 \mt{val} \; \mt{sql\_maxable\_string} : \mt{sql\_maxable} \; \mt{string} \\
adamc@544	1721 \mt{val} \; \mt{sql\_maxable\_time} : \mt{sql\_maxable} \; \mt{time} \\
adam@1400	1722 \mt{val} \; \mt{sql\_max} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt} \\
adam@1400	1723 \mt{val} \; \mt{sql\_min} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt}
adamc@544	1724 \end{array}$$
adamc@544	1725
adamc@1193	1726 Any SQL query that returns single columns may be turned into a subquery expression.
adamc@1193	1727
adamc@786	1728 $$\begin{array}{l}
adamc@1193	1729 \mt{val} \; \mt{sql\_subquery} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \\
adam@1400	1730 \hspace{.1in} \to \mt{sql\_query} \; \mt{tables} \; \mt{agg} \; [\mt{nm} = \mt{t}] \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adamc@1193	1731 \end{array}$$
adamc@1193	1732
adamc@1193	1733 \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	1734 $$\begin{array}{l}
adamc@1193	1735 \mt{con} \; \mt{sql\_from\_items} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@1193	1736 \mt{val} \; \mt{sql\_from\_table} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adamc@1193	1737 \hspace{.1in} \to \mt{t} ::: \mt{Type} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; \mt{t} \; \mt{fs} \to \mt{name} :: \mt{Name} \to \mt{t} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193	1738 \mt{val} \; \mt{sql\_from\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{name} :: \mt{Name} \to \mt{sql\_query} \; \mt{free} \; [] \; \mt{fs} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193	1739 \mt{val} \; \mt{sql\_from\_comma} : \mt{free} ::: \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \to [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193	1740 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adamc@1193	1741 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2}) \\
adamc@1193	1742 \mt{val} \; \mt{sql\_inner\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \\
adamc@1193	1743 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193	1744 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adamc@1193	1745 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193	1746 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2})
adamc@786	1747 \end{array}$$
adamc@786	1748
adamc@786	1749 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	1750 $$\begin{array}{l}
adamc@786	1751 \mt{class} \; \mt{nullify} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@786	1752 \mt{val} \; \mt{nullify\_option} : \mt{t} ::: \mt{Type} \to \mt{nullify} \; (\mt{option} \; \mt{t}) \; (\mt{option} \; \mt{t}) \\
adamc@786	1753 \mt{val} \; \mt{nullify\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{nullify} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@786	1754 \end{array}$$
adamc@786	1755
adamc@786	1756 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	1757
adamc@786	1758 $$\begin{array}{l}
adamc@1193	1759 \mt{val} \; \mt{sql\_left\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{(\mt{Type} \times \mt{Type})\}\} \\
adamc@1193	1760 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@786	1761 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\lambda \mt{r} \Rightarrow \$(\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{nullify} \; \mt{p}.1 \; \mt{p}.2) \; \mt{r})) \; \mt{tabs2}) \\
adamc@1193	1762 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \\
adamc@1193	1763 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193	1764 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.2)) \; \mt{tabs2})
adamc@786	1765 \end{array}$$
adamc@786	1766
adamc@544	1767 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	1768 $$\begin{array}{l}
adamc@544	1769 \mt{type} \; \mt{sql\_direction} \\
adamc@544	1770 \mt{val} \; \mt{sql\_asc} : \mt{sql\_direction} \\
adamc@544	1771 \mt{val} \; \mt{sql\_desc} : \mt{sql\_direction} \\
adamc@544	1772 \\
adamc@544	1773 \mt{con} \; \mt{sql\_order\_by} :: \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@544	1774 \mt{val} \; \mt{sql\_order\_by\_Nil} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} :: \{\mt{Type}\} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544	1775 \mt{val} \; \mt{sql\_order\_by\_Cons} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544	1776 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; [] \; \mt{exps} \; \mt{t} \to \mt{sql\_direction} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544	1777 \\
adamc@544	1778 \mt{type} \; \mt{sql\_limit} \\
adamc@544	1779 \mt{val} \; \mt{sql\_no\_limit} : \mt{sql\_limit} \\
adamc@544	1780 \mt{val} \; \mt{sql\_limit} : \mt{int} \to \mt{sql\_limit} \\
adamc@544	1781 \\
adamc@544	1782 \mt{type} \; \mt{sql\_offset} \\
adamc@544	1783 \mt{val} \; \mt{sql\_no\_offset} : \mt{sql\_offset} \\
adamc@544	1784 \mt{val} \; \mt{sql\_offset} : \mt{int} \to \mt{sql\_offset}
adamc@544	1785 \end{array}$$
adamc@544	1786
adamc@545	1787
adamc@545	1788 \subsubsection{DML}
adamc@545	1789
adamc@545	1790 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	1791
adamc@545	1792 $$\begin{array}{l}
adamc@545	1793 \mt{type} \; \mt{dml} \\
adamc@545	1794 \mt{val} \; \mt{dml} : \mt{dml} \to \mt{transaction} \; \mt{unit}
adamc@545	1795 \end{array}$$
adamc@545	1796
adam@1297	1797 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	1798
adam@1297	1799 $$\begin{array}{l}
adam@1297	1800 \mt{val} \; \mt{tryDml} : \mt{dml} \to \mt{transaction} \; (\mt{option} \; \mt{string})
adam@1297	1801 \end{array}$$
adam@1297	1802
adamc@545	1803 Properly-typed records may be used to form $\mt{INSERT}$ commands.
adamc@545	1804 $$\begin{array}{l}
adamc@545	1805 \mt{val} \; \mt{insert} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \\
adamc@658	1806 \hspace{.1in} \to \$(\mt{map} \; (\mt{sql\_exp} \; [] \; [] \; []) \; \mt{fields}) \to \mt{dml}
adamc@545	1807 \end{array}$$
adamc@545	1808
adamc@545	1809 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	1810 $$\begin{array}{l}
adam@1380	1811 \mt{val} \; \mt{update} : \mt{unchanged} ::: \{\mt{Type}\} \to \mt{changed} :: \{\mt{Type}\} \to [\mt{changed} \sim \mt{unchanged}] \\
adamc@658	1812 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; []) \; \mt{changed}) \\
adamc@545	1813 \hspace{.1in} \to \mt{sql\_table} \; (\mt{changed} \rc \mt{unchanged}) \to \mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545	1814 \end{array}$$
adamc@545	1815
adamc@545	1816 A $\mt{DELETE}$ command is formed from a table and a $\mt{WHERE}$ clause.
adamc@545	1817 $$\begin{array}{l}
adamc@545	1818 \mt{val} \; \mt{delete} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \to \mt{sql\_exp} \; [\mt{T} = \mt{fields}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545	1819 \end{array}$$
adamc@545	1820
adamc@546	1821 \subsubsection{Sequences}
adamc@546	1822
adamc@546	1823 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	1824
adamc@546	1825 $$\begin{array}{l}
adamc@546	1826 \mt{type} \; \mt{sql\_sequence} \\
adamc@1085	1827 \mt{val} \; \mt{nextval} : \mt{sql\_sequence} \to \mt{transaction} \; \mt{int} \\
adamc@1085	1828 \mt{val} \; \mt{setval} : \mt{sql\_sequence} \to \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@546	1829 \end{array}$$
adamc@546	1830
adamc@546	1831
adamc@547	1832 \subsection{XML}
adamc@547	1833
adam@1333	1834 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	1835
adam@1345	1836 The basic XML type family has arguments respectively indicating the \emph{context} of a fragment, the fields that the fragment expects to be bound on entry (and their types), and the fields that the fragment will bind (and their types). Contexts are a record-based ``poor man's subtyping'' encoding, with each possible set of valid tags corresponding to a different context record. For instance, the context for the \texttt{<td>} tag is $[\mt{Body}, \mt{Tr}]$, to indicate a kind of nesting inside \texttt{<body>} and \texttt{<tr>}. Contexts are maintained in a somewhat ad-hoc way; the only definitive reference for their meanings is the types of the tag values in \texttt{basis.urs}. The arguments dealing with field binding are only relevant to HTML forms.
adamc@547	1837 $$\begin{array}{l}
adamc@547	1838 \mt{con} \; \mt{xml} :: \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547	1839 \end{array}$$
adamc@547	1840
adamc@547	1841 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	1842 $$\begin{array}{l}
adamc@547	1843 \mt{con} \; \mt{tag} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547	1844 \end{array}$$
adamc@547	1845
adamc@547	1846 Literal text may be injected into XML as ``CDATA.''
adamc@547	1847 $$\begin{array}{l}
adamc@547	1848 \mt{val} \; \mt{cdata} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{string} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adamc@547	1849 \end{array}$$
adamc@547	1850
adam@1358	1851 There is also a function to insert the literal value of a character. Since Ur/Web uses the UTF-8 text encoding, the $\mt{cdata}$ function is only sufficient to encode characters with ASCII codes below 128. Higher codes have alternate meanings in UTF-8 than in usual ASCII, so this alternate function should be used with them.
adam@1358	1852 $$\begin{array}{l}
adam@1358	1853 \mt{val} \; \mt{cdataChar} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{char} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adam@1358	1854 \end{array}$$
adam@1358	1855
adamc@547	1856 There is a function for producing an XML tree with a particular tag at its root.
adamc@547	1857 $$\begin{array}{l}
adamc@547	1858 \mt{val} \; \mt{tag} : \mt{attrsGiven} ::: \{\mt{Type}\} \to \mt{attrsAbsent} ::: \{\mt{Type}\} \to \mt{ctxOuter} ::: \{\mt{Unit}\} \to \mt{ctxInner} ::: \{\mt{Unit}\} \\
adamc@547	1859 \hspace{.1in} \to \mt{useOuter} ::: \{\mt{Type}\} \to \mt{useInner} ::: \{\mt{Type}\} \to \mt{bindOuter} ::: \{\mt{Type}\} \to \mt{bindInner} ::: \{\mt{Type}\} \\
adam@1380	1860 \hspace{.1in} \to [\mt{attrsGiven} \sim \mt{attrsAbsent}] \Rightarrow [\mt{useOuter} \sim \mt{useInner}] \Rightarrow [\mt{bindOuter} \sim \mt{bindInner}] \\
adamc@787	1861 \hspace{.1in} \Rightarrow \mt{option} \; \mt{css\_class} \\
adamc@787	1862 \hspace{.1in} \to \$\mt{attrsGiven} \\
adamc@547	1863 \hspace{.1in} \to \mt{tag} \; (\mt{attrsGiven} \rc \mt{attrsAbsent}) \; \mt{ctxOuter} \; \mt{ctxInner} \; \mt{useOuter} \; \mt{bindOuter} \\
adamc@547	1864 \hspace{.1in} \to \mt{xml} \; \mt{ctxInner} \; \mt{useInner} \; \mt{bindInner} \to \mt{xml} \; \mt{ctxOuter} \; (\mt{useOuter} \rc \mt{useInner}) \; (\mt{bindOuter} \rc \mt{bindInner})
adamc@547	1865 \end{array}$$
adam@1297	1866 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	1867
adamc@547	1868 Two XML fragments may be concatenated.
adamc@547	1869 $$\begin{array}{l}
adamc@547	1870 \mt{val} \; \mt{join} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{bind_1} ::: \{\mt{Type}\} \to \mt{bind_2} ::: \{\mt{Type}\} \\
adam@1380	1871 \hspace{.1in} \to [\mt{use_1} \sim \mt{bind_1}] \Rightarrow [\mt{bind_1} \sim \mt{bind_2}] \\
adamc@547	1872 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind_1} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{bind_1}) \; \mt{bind_2} \to \mt{xml} \; \mt{ctx} \; \mt{use_1} \; (\mt{bind_1} \rc \mt{bind_2})
adamc@547	1873 \end{array}$$
adamc@547	1874
adamc@547	1875 Finally, any XML fragment may be updated to ``claim'' to use more form fields than it does.
adamc@547	1876 $$\begin{array}{l}
adam@1380	1877 \mt{val} \; \mt{useMore} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{use_2} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to [\mt{use_1} \sim \mt{use_2}] \\
adamc@547	1878 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{use_2}) \; \mt{bind}
adamc@547	1879 \end{array}$$
adamc@547	1880
adam@1344	1881 We will not list here the different HTML tags and related functions from the standard library. They should be easy enough to understand from the code in \texttt{basis.urs}. The set of tags in the library is not yet claimed to be complete for HTML standards. Also note that there is currently no way for the programmer to add his own tags. It \emph{is} possible to add new tags directly to \texttt{basis.urs}, but this should only be done as a prelude to suggesting a patch to the main distribution.
adamc@547	1882
adamc@547	1883 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	1884 $$\begin{array}{l}
adamc@547	1885 \mt{val} \; \mt{error} : \mt{t} ::: \mt{Type} \to \mt{xml} \; [\mt{Body}] \; [] \; [] \to \mt{t}
adamc@547	1886 \end{array}$$
adamc@547	1887
adamc@549	1888
adamc@701	1889 \subsection{Client-Side Programming}
adamc@659	1890
adamc@701	1891 Ur/Web supports running code on web browsers, via automatic compilation to JavaScript.
adamc@701	1892
adamc@701	1893 \subsubsection{The Basics}
adamc@701	1894
adam@1400	1895 All of the functions in this subsection are client-side only.
adam@1400	1896
adam@1297	1897 Clients can open alert and confirm dialog boxes, in the usual annoying JavaScript way.
adamc@701	1898 $$\begin{array}{l}
adam@1297	1899 \mt{val} \; \mt{alert} : \mt{string} \to \mt{transaction} \; \mt{unit} \\
adam@1297	1900 \mt{val} \; \mt{confirm} : \mt{string} \to \mt{transaction} \; \mt{bool}
adamc@701	1901 \end{array}$$
adamc@701	1902
adamc@701	1903 Any transaction may be run in a new thread with the $\mt{spawn}$ function.
adamc@701	1904 $$\begin{array}{l}
adamc@701	1905 \mt{val} \; \mt{spawn} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit}
adamc@701	1906 \end{array}$$
adamc@701	1907
adamc@701	1908 The current thread can be paused for at least a specified number of milliseconds.
adamc@701	1909 $$\begin{array}{l}
adamc@701	1910 \mt{val} \; \mt{sleep} : \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@701	1911 \end{array}$$
adamc@701	1912
adamc@787	1913 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	1914 $$\begin{array}{l}
adamc@787	1915 \mt{val} \; \mt{onError} : (\mt{xbody} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787	1916 \mt{val} \; \mt{onFail} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787	1917 \mt{val} \; \mt{onConnectFail} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787	1918 \mt{val} \; \mt{onDisconnect} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787	1919 \mt{val} \; \mt{onServerError} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit}
adamc@787	1920 \end{array}$$
adamc@787	1921
adamc@701	1922 \subsubsection{Functional-Reactive Page Generation}
adamc@701	1923
adamc@701	1924 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	1925
adam@1403	1926 More operationally, you can think of a source as a mutable cell with facilities for subscription to change notifications. That level of detail is hidden behind a monadic facility to be described below. First, there are three primitive operations for working with sources just as if they were ML \cd{ref} cells, corresponding to ML's \cd{ref}, \cd{:=}, and \cd{!} operations.
adam@1403	1927
adamc@659	1928 $$\begin{array}{l}
adamc@659	1929 \mt{con} \; \mt{source} :: \mt{Type} \to \mt{Type} \\
adamc@659	1930 \mt{val} \; \mt{source} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{transaction} \; (\mt{source} \; \mt{t}) \\
adamc@659	1931 \mt{val} \; \mt{set} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@659	1932 \mt{val} \; \mt{get} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@659	1933 \end{array}$$
adamc@659	1934
adam@1400	1935 Only source creation and setting are supported server-side, as a convenience to help in setting up a page, where you may wish to allocate many sources that will be referenced through the page. All server-side storage of values inside sources uses string serializations of values, while client-side storage uses normal JavaScript values.
adam@1400	1936
adam@1403	1937 Pure functions over arbitrary numbers of sources are represented in a monad of \emph{signals}, which may only be used in client-side code. This is presented to the programmer in the form of a monad $\mt{signal}$, each of whose values represents (conceptually) some pure function over all sources that may be allocated in the course of program execution. A monad operation $\mt{signal}$ denotes the identity function over a particular source. By using $\mt{signal}$ on a source, you implicitly subscribe to change notifications for that source. That is, your signal will automatically be recomputed as that source changes. The usual monad operators make it possible to build up complex signals that depend on multiple sources; automatic updating upon source-value changes still happens automatically.
adamc@659	1938
adamc@659	1939 $$\begin{array}{l}
adamc@659	1940 \mt{con} \; \mt{signal} :: \mt{Type} \to \mt{Type} \\
adamc@659	1941 \mt{val} \; \mt{signal\_monad} : \mt{monad} \; \mt{signal} \\
adamc@659	1942 \mt{val} \; \mt{signal} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{signal} \; \mt{t}
adamc@659	1943 \end{array}$$
adamc@659	1944
adamc@659	1945 A reactive portion of an HTML page is injected with a $\mt{dyn}$ tag, which has a signal-valued attribute $\mt{Signal}$.
adamc@659	1946
adamc@659	1947 $$\begin{array}{l}
adamc@701	1948 \mt{val} \; \mt{dyn} : \mt{use} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to \mt{unit} \\
adamc@701	1949 \hspace{.1in} \to \mt{tag} \; [\mt{Signal} = \mt{signal} \; (\mt{xml} \; \mt{body} \; \mt{use} \; \mt{bind})] \; \mt{body} \; [] \; \mt{use} \; \mt{bind}
adamc@659	1950 \end{array}$$
adamc@659	1951
adamc@701	1952 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	1953
adamc@914	1954 \subsubsection{Remote Procedure Calls}
adamc@914	1955
adamc@914	1956 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	1957
adamc@914	1958 $$\begin{array}{l}
adamc@914	1959 \mt{val} \; \mt{rpc} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@914	1960 \end{array}$$
adamc@914	1961
adamc@701	1962 \subsubsection{Asynchronous Message-Passing}
adamc@701	1963
adamc@701	1964 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	1965
adamc@701	1966 $$\begin{array}{l}
adamc@701	1967 \mt{type} \; \mt{client} \\
adamc@701	1968 \mt{val} \; \mt{self} : \mt{transaction} \; \mt{client}
adamc@701	1969 \end{array}$$
adamc@701	1970
adamc@701	1971 \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	1972
adamc@701	1973 $$\begin{array}{l}
adamc@701	1974 \mt{con} \; \mt{channel} :: \mt{Type} \to \mt{Type} \\
adamc@701	1975 \mt{val} \; \mt{channel} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; (\mt{channel} \; \mt{t}) \\
adamc@701	1976 \mt{val} \; \mt{send} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@701	1977 \mt{val} \; \mt{recv} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@701	1978 \end{array}$$
adamc@701	1979
adamc@701	1980 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	1981
adamc@701	1982 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	1983
adamc@659	1984
adamc@549	1985 \section{Ur/Web Syntax Extensions}
adamc@549	1986
adamc@549	1987 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	1988
adamc@549	1989 \subsection{SQL}
adamc@549	1990
adamc@786	1991 \subsubsection{\label{tables}Table Declarations}
adamc@786	1992
adamc@788	1993 $\mt{table}$ declarations may include constraints, via these grammar rules.
adamc@788	1994 $$\begin{array}{rrcll}
adamc@788	1995 \textrm{Declarations} & d &::=& \mt{table} \; x : c \; [pk[,]] \; cts \\
adamc@788	1996 \textrm{Primary key constraints} & pk &::=& \mt{PRIMARY} \; \mt{KEY} \; K \\
adamc@788	1997 \textrm{Keys} & K &::=& f \mid (f, (f,)^+) \\
adamc@788	1998 \textrm{Constraint sets} & cts &::=& \mt{CONSTRAINT} f \; ct \mid cts, cts \mid \{\{e\}\} \\
adamc@788	1999 \textrm{Constraints} & ct &::=& \mt{UNIQUE} \; K \mid \mt{CHECK} \; E \\
adamc@788	2000 &&& \mid \mt{FOREIGN} \; \mt{KEY} \; K \; \mt{REFERENCES} \; F \; (K) \; [\mt{ON} \; \mt{DELETE} \; pr] \; [\mt{ON} \; \mt{UPDATE} \; pr] \\
adamc@788	2001 \textrm{Foreign tables} & F &::=& x \mid \{\{e\}\} \\
adamc@788	2002 \textrm{Propagation modes} & pr &::=& \mt{NO} \; \mt{ACTION} \mid \mt{RESTRICT} \mid \mt{CASCADE} \mid \mt{SET} \; \mt{NULL}
adamc@788	2003 \end{array}$$
adamc@788	2004
adamc@788	2005 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	2006
adamc@788	2007
adamc@549	2008 \subsubsection{Queries}
adamc@549	2009
adamc@550	2010 Queries $Q$ are added to the rules for expressions $e$.
adamc@550	2011
adamc@549	2012 $$\begin{array}{rrcll}
adamc@550	2013 \textrm{Queries} & Q &::=& (q \; [\mt{ORDER} \; \mt{BY} \; (E \; [o],)^+] \; [\mt{LIMIT} \; N] \; [\mt{OFFSET} \; N]) \\
adamc@1085	2014 \textrm{Pre-queries} & q &::=& \mt{SELECT} \; [\mt{DISTINCT}] \; P \; \mt{FROM} \; F,^+ \; [\mt{WHERE} \; E] \; [\mt{GROUP} \; \mt{BY} \; p,^+] \; [\mt{HAVING} \; E] \\
adamc@1085	2015 &&& \mid q \; R \; q \mid \{\{\{e\}\}\} \\
adamc@549	2016 \textrm{Relational operators} & R &::=& \mt{UNION} \mid \mt{INTERSECT} \mid \mt{EXCEPT}
adamc@549	2017 \end{array}$$
adamc@549	2018
adamc@549	2019 $$\begin{array}{rrcll}
adamc@549	2020 \textrm{Projections} & P &::=& \ast & \textrm{all columns} \\
adamc@549	2021 &&& p,^+ & \textrm{particular columns} \\
adamc@549	2022 \textrm{Pre-projections} & p &::=& t.f & \textrm{one column from a table} \\
adamc@558	2023 &&& t.\{\{c\}\} & \textrm{a record of columns from a table (of kind $\{\mt{Type}\}$)} \\
adamc@1194	2024 &&& E \; [\mt{AS} \; f] & \textrm{expression column} \\
adamc@549	2025 \textrm{Table names} & t &::=& x & \textrm{constant table name (automatically capitalized)} \\
adamc@549	2026 &&& X & \textrm{constant table name} \\
adamc@549	2027 &&& \{\{c\}\} & \textrm{computed table name (of kind $\mt{Name}$)} \\
adamc@549	2028 \textrm{Column names} & f &::=& X & \textrm{constant column name} \\
adamc@549	2029 &&& \{c\} & \textrm{computed column name (of kind $\mt{Name}$)} \\
adamc@549	2030 \textrm{Tables} & T &::=& x & \textrm{table variable, named locally by its own capitalization} \\
adamc@549	2031 &&& x \; \mt{AS} \; t & \textrm{table variable, with local name} \\
adamc@549	2032 &&& \{\{e\}\} \; \mt{AS} \; t & \textrm{computed table expression, with local name} \\
adamc@1085	2033 \textrm{$\mt{FROM}$ items} & F &::=& T \mid \{\{e\}\} \mid F \; J \; \mt{JOIN} \; F \; \mt{ON} \; E \\
adamc@1085	2034 &&& \mid F \; \mt{CROSS} \; \mt{JOIN} \ F \\
adamc@1193	2035 &&& \mid (Q) \; \mt{AS} \; t \\
adamc@1085	2036 \textrm{Joins} & J &::=& [\mt{INNER}] \\
adamc@1085	2037 &&& \mid [\mt{LEFT} \mid \mt{RIGHT} \mid \mt{FULL}] \; [\mt{OUTER}] \\
adamc@549	2038 \textrm{SQL expressions} & E &::=& p & \textrm{column references} \\
adamc@549	2039 &&& X & \textrm{named expression references} \\
adamc@549	2040 &&& \{\{e\}\} & \textrm{injected native Ur expressions} \\
adamc@549	2041 &&& \{e\} & \textrm{computed expressions, probably using $\mt{sql\_exp}$ directly} \\
adamc@549	2042 &&& \mt{TRUE} \mid \mt{FALSE} & \textrm{boolean constants} \\
adamc@549	2043 &&& \ell & \textrm{primitive type literals} \\
adamc@549	2044 &&& \mt{NULL} & \textrm{null value (injection of $\mt{None}$)} \\
adamc@549	2045 &&& E \; \mt{IS} \; \mt{NULL} & \textrm{nullness test} \\
adamc@549	2046 &&& n & \textrm{nullary operators} \\
adamc@549	2047 &&& u \; E & \textrm{unary operators} \\
adamc@549	2048 &&& E \; b \; E & \textrm{binary operators} \\
adamc@549	2049 &&& \mt{COUNT}(\ast) & \textrm{count number of rows} \\
adamc@549	2050 &&& a(E) & \textrm{other aggregate function} \\
adamc@1193	2051 &&& (Q) & \textrm{subquery (must return a single expression column)} \\
adamc@549	2052 &&& (E) & \textrm{explicit precedence} \\
adamc@549	2053 \textrm{Nullary operators} & n &::=& \mt{CURRENT\_TIMESTAMP} \\
adamc@549	2054 \textrm{Unary operators} & u &::=& \mt{NOT} \\
adamc@549	2055 \textrm{Binary operators} & b &::=& \mt{AND} \mid \mt{OR} \mid \neq \mid < \mid \leq \mid > \mid \geq \\
adamc@1188	2056 \textrm{Aggregate functions} & a &::=& \mt{COUNT} \mid \mt{AVG} \mid \mt{SUM} \mid \mt{MIN} \mid \mt{MAX} \\
adamc@550	2057 \textrm{Directions} & o &::=& \mt{ASC} \mid \mt{DESC} \\
adamc@549	2058 \textrm{SQL integer} & N &::=& n \mid \{e\} \\
adamc@549	2059 \end{array}$$
adamc@549	2060
adamc@1085	2061 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	2062
adamc@1194	2063 Unnamed expression columns in $\mt{SELECT}$ clauses are assigned consecutive natural numbers, starting with 1.
adamc@1194	2064
adamc@550	2065 \subsubsection{DML}
adamc@550	2066
adamc@550	2067 DML commands $D$ are added to the rules for expressions $e$.
adamc@550	2068
adamc@550	2069 $$\begin{array}{rrcll}
adamc@550	2070 \textrm{Commands} & D &::=& (\mt{INSERT} \; \mt{INTO} \; T^E \; (f,^+) \; \mt{VALUES} \; (E,^+)) \\
adamc@550	2071 &&& (\mt{UPDATE} \; T^E \; \mt{SET} \; (f = E,)^+ \; \mt{WHERE} \; E) \\
adamc@550	2072 &&& (\mt{DELETE} \; \mt{FROM} \; T^E \; \mt{WHERE} \; E) \\
adamc@550	2073 \textrm{Table expressions} & T^E &::=& x \mid \{\{e\}\}
adamc@550	2074 \end{array}$$
adamc@550	2075
adamc@550	2076 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	2077
adamc@551	2078 \subsection{XML}
adamc@551	2079
adamc@551	2080 XML fragments $L$ are added to the rules for expressions $e$.
adamc@551	2081
adamc@551	2082 $$\begin{array}{rrcll}
adamc@551	2083 \textrm{XML fragments} & L &::=& \texttt{<xml/>} \mid \texttt{<xml>}l^*\texttt{</xml>} \\
adamc@551	2084 \textrm{XML pieces} & l &::=& \textrm{text} & \textrm{cdata} \\
adamc@551	2085 &&& \texttt{<}g\texttt{/>} & \textrm{tag with no children} \\
adamc@551	2086 &&& \texttt{<}g\texttt{>}l^*\texttt{</}x\texttt{>} & \textrm{tag with children} \\
adamc@559	2087 &&& \{e\} & \textrm{computed XML fragment} \\
adamc@559	2088 &&& \{[e]\} & \textrm{injection of an Ur expression, via the $\mt{Top}.\mt{txt}$ function} \\
adamc@551	2089 \textrm{Tag} & g &::=& h \; (x = v)^* \\
adamc@551	2090 \textrm{Tag head} & h &::=& x & \textrm{tag name} \\
adamc@551	2091 &&& h\{c\} & \textrm{constructor parameter} \\
adamc@551	2092 \textrm{Attribute value} & v &::=& \ell & \textrm{literal value} \\
adamc@551	2093 &&& \{e\} & \textrm{computed value} \\
adamc@551	2094 \end{array}$$
adamc@551	2095
adamc@552	2096
adamc@1198	2097 \section{\label{structure}The Structure of Web Applications}
adamc@553	2098
adamc@1127	2099 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	2100
adam@1347	2101 Normal links are accessible via HTTP \texttt{GET}, which the relevant standard says should never cause side effects. To export a page which may cause side effects, accessible only via HTTP \texttt{POST}, include one argument of the page handler of type $\mt{Basis.postBody}$. When the handler is called, this argument will receive a value that can be deconstructed into a MIME type (with $\mt{Basis.postType}$) and payload (with $\mt{Basis.postData}$). This kind of handler will only work with \texttt{POST} payloads of MIME types besides those associated with HTML forms; for these, use Ur/Web's built-in support, as described below.
adam@1347	2102
adam@1370	2103 Any normal page handler may also include arguments of type $\mt{option \; Basis.queryString}$, which will be handled specially. Rather than being deserialized from the current URI, such an argument is passed the whole query string that the handler received. The string may be analyzed by calling $\mt{Basis.show}$ on it. A handler of this kind may be passed as an argument to $\mt{Basis.effectfulUrl}$ to generate a URL to a page that may be used as a ``callback'' by an external service, such that the handler is allowed to cause side effects.
adam@1370	2104
adamc@553	2105 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	2106
adamc@553	2107 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	2108
adamc@558	2109 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	2110
adamc@660	2111 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	2112
adamc@789	2113 \medskip
adamc@789	2114
adam@1347	2115 The HTTP standard suggests that GET requests only be used in ways that generate no side effects. Side effecting operations should use POST requests instead. The Ur/Web compiler enforces this rule strictly, via a simple conservative program analysis. Any page that may have a side effect must be accessed through a form, all of which use POST requests, or via a direct call to a page handler with some argument of type $\mt{Basis.postBody}$. A page is judged to have a side effect if its code depends syntactically on any of the side-effecting, server-side FFI functions. Links, forms, and most client-side event handlers are not followed during this syntactic traversal, but \texttt{<body onload=\{...\}>} handlers \emph{are} examined, since they run right away and could just as well be considered parts of main page handlers.
adamc@789	2116
adamc@789	2117 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	2118
adam@1348	2119 \subsection{Tasks}
adam@1348	2120
adam@1348	2121 In many web applications, it's useful to run code at points other than requests from browsers. Ur/Web's \emph{task} mechanism facilitates this. A type family of \emph{task kinds} is in the standard library:
adam@1348	2122
adam@1348	2123 $$\begin{array}{l}
adam@1348	2124 \mt{con} \; \mt{task\_kind} :: \mt{Type} \to \mt{Type} \\
adam@1348	2125 \mt{val} \; \mt{initialize} : \mt{task\_kind} \; \mt{unit} \\
adam@1349	2126 \mt{val} \; \mt{clientLeaves} : \mt{task\_kind} \; \mt{client} \\
adam@1349	2127 \mt{val} \; \mt{periodic} : \mt{int} \to \mt{task\_kind} \; \mt{unit}
adam@1348	2128 \end{array}$$
adam@1348	2129
adam@1348	2130 A task kind names a particular extension point of generated applications, where the type parameter of a task kind describes which extra input data is available at that extension point. Add task code with the special declaration form $\mt{task} \; e_1 = e_2$, where $e_1$ is a task kind with data $\tau$, and $e_2$ is a function from $\tau$ to $\mt{transaction} \; \mt{unit}$.
adam@1348	2131
adam@1348	2132 The currently supported task kinds are:
adam@1348	2133 \begin{itemize}
adam@1349	2134 \item $\mt{initialize}$: Code that is run when the application starts up.
adam@1348	2135 \item $\mt{clientLeaves}$: Code that is run for each client that the runtime system decides has surfed away. When a request that generates a new client handle is aborted, that handle will still eventually be passed to $\mt{clientLeaves}$ task code, even though the corresponding browser was never informed of the client handle's existence. In other words, in general, $\mt{clientLeaves}$ handlers will be called more times than there are actual clients.
adam@1349	2136 \item $\mt{periodic} \; n$: Code that is run when the application starts up and then every $n$ seconds thereafter.
adam@1348	2137 \end{itemize}
adam@1348	2138
adamc@553	2139
adamc@897	2140 \section{The Foreign Function Interface}
adamc@897	2141
adamc@897	2142 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	2143
adamc@897	2144 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	2145
adamc@897	2146 \begin{itemize}
adamc@897	2147 \item \texttt{clientOnly Module.ident} registers a value as being allowed only in client-side code.
adamc@897	2148 \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	2149 \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	2150 \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	2151 \item \texttt{include FILE} requests inclusion of a C header file.
adamc@897	2152 \item \texttt{jsFunc Module.ident=name} gives a mapping from an Ur name for a value to a JavaScript name.
adamc@897	2153 \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	2154 \item \texttt{script URL} requests inclusion of a JavaScript source file within application HTML.
adamc@897	2155 \item \texttt{serverOnly Module.ident} registers a value as being allowed only in server-side code.
adamc@897	2156 \end{itemize}
adamc@897	2157
adamc@897	2158 \subsection{Writing C FFI Code}
adamc@897	2159
adamc@897	2160 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	2161
adamc@897	2162 \begin{itemize}
adamc@897	2163 \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	2164 \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	2165 \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	2166 \end{itemize}
adamc@897	2167
adamc@897	2168 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	2169 \begin{itemize}
adamc@897	2170 \item \begin{verbatim}
adamc@897	2171 void uw_error(uw_context, failure_kind, const char *fmt, ...);
adamc@897	2172 \end{verbatim}
adamc@897	2173 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	2174
adam@1329	2175 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	2176
adamc@897	2177 \item \begin{verbatim}
adamc@897	2178 void uw_push_cleanup(uw_context, void (func)(void ), void *arg);
adamc@897	2179 void uw_pop_cleanup(uw_context);
adamc@897	2180 \end{verbatim}
adam@1329	2181 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	2182
adam@1329	2183 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	2184
adamc@897	2185 \item \begin{verbatim}
adamc@897	2186 void *uw_malloc(uw_context, size_t);
adamc@897	2187 \end{verbatim}
adam@1329	2188 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	2189
adam@1329	2190 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	2191
adamc@897	2192 \item \begin{verbatim}
adamc@897	2193 typedef void (uw_callback)(void );
adam@1328	2194 typedef void (uw_callback_with_retry)(void , int will_retry);
adamc@897	2195 void uw_register_transactional(uw_context, void *data, uw_callback commit,
adam@1328	2196 uw_callback rollback, uw_callback_with_retry free);
adamc@897	2197 \end{verbatim}
adam@1328	2198 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	2199
adamc@1085	2200 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	2201
adam@1329	2202 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	2203
adam@1329	2204 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	2205
adamc@1085	2206 \item \begin{verbatim}
adamc@1085	2207 void uw_get_global(uw_context, char name);
adamc@1085	2208 void uw_set_global(uw_context, char name, void data, uw_callback free);
adamc@1085	2209 \end{verbatim}
adam@1329	2210 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	2211
adamc@897	2212 \end{itemize}
adamc@897	2213
adamc@897	2214 \subsection{Writing JavaScript FFI Code}
adamc@897	2215
adamc@897	2216 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	2217
adamc@897	2218 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	2219
adamc@897	2220 \begin{itemize}
adamc@897	2221 \item Integers, floats, strings, characters, and booleans are represented in the usual JavaScript way.
adamc@985	2222 \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	2223 \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	2224 \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	2225 \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	2226 \end{itemize}
adamc@897	2227
adamc@897	2228 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	2229
adamc@897	2230
adamc@552	2231 \section{Compiler Phases}
adamc@552	2232
adamc@552	2233 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	2234
adamc@552	2235 In this section, we step through the main phases of compilation, noting what consequences each phase has for effective programming.
adamc@552	2236
adamc@552	2237 \subsection{Parse}
adamc@552	2238
adamc@552	2239 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	2240
adamc@552	2241 \subsection{Elaborate}
adamc@552	2242
adamc@552	2243 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	2244
adam@1378	2245 Those crawling through the compiler source will also want to be aware of another compiler phase, Explify, that occurs immediately afterward. This phase just translates from an AST language that includes unification variables to a very similar language that doesn't; all variables should have been determined by the end of Elaborate, anyway. The new AST language also drops some features that are used only for static checking and that have no influence on runtime behavior, like disjointness constraints.
adam@1378	2246
adamc@552	2247 \subsection{Unnest}
adamc@552	2248
adamc@552	2249 Named local function definitions are moved to the top level, to avoid the need to generate closures.
adamc@552	2250
adamc@552	2251 \subsection{Corify}
adamc@552	2252
adamc@552	2253 Module system features are compiled away, through inlining of functor definitions at application sites. Afterward, most abstraction boundaries are broken, facilitating optimization.
adamc@552	2254
adamc@552	2255 \subsection{Especialize}
adamc@552	2256
adam@1356	2257 Functions are specialized to particular argument patterns. This is an important trick for avoiding the need to maintain any closures at runtime. Currently, specialization only happens for prefixes of a function's full list of parameters, so you may need to take care to put arguments of function types before other arguments. The optimizer will not be effective enough if you use arguments that mix functions and values that must be calculated at run-time. For instance, a tuple of a function and an integer counter would not lead to successful code generation; these should be split into separate arguments via currying.
adamc@552	2258
adamc@552	2259 \subsection{Untangle}
adamc@552	2260
adamc@552	2261 Remove unnecessary mutual recursion, splitting recursive groups into strongly-connected components.
adamc@552	2262
adamc@552	2263 \subsection{Shake}
adamc@552	2264
adamc@552	2265 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	2266
adamc@661	2267 \subsection{Rpcify}
adamc@661	2268
adamc@661	2269 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	2270
adamc@661	2271 \subsection{Untangle, Shake}
adamc@661	2272
adamc@661	2273 Repeat these simplifications.
adamc@661	2274
adamc@553	2275 \subsection{\label{tag}Tag}
adamc@552	2276
adamc@552	2277 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	2278
adamc@552	2279 \subsection{Reduce}
adamc@552	2280
adamc@552	2281 Apply definitional equality rules to simplify the program as much as possible. This effectively includes inlining of every non-recursive definition.
adamc@552	2282
adamc@552	2283 \subsection{Unpoly}
adamc@552	2284
adamc@552	2285 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	2286
adamc@552	2287 \subsection{Specialize}
adamc@552	2288
adamc@558	2289 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	2290
adamc@552	2291 \subsection{Shake}
adamc@552	2292
adamc@558	2293 Here the compiler repeats the earlier Shake phase.
adamc@552	2294
adamc@552	2295 \subsection{Monoize}
adamc@552	2296
adamc@552	2297 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	2298
adamc@552	2299 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	2300
adamc@552	2301 \subsection{MonoOpt}
adamc@552	2302
adamc@552	2303 Simple algebraic laws are applied to simplify the program, focusing especially on efficient imperative generation of HTML pages.
adamc@552	2304
adamc@552	2305 \subsection{MonoUntangle}
adamc@552	2306
adamc@552	2307 Unnecessary mutual recursion is broken up again.
adamc@552	2308
adamc@552	2309 \subsection{MonoReduce}
adamc@552	2310
adamc@552	2311 Equivalents of the definitional equality rules are applied to simplify programs, with inlining again playing a major role.
adamc@552	2312
adamc@552	2313 \subsection{MonoShake, MonoOpt}
adamc@552	2314
adamc@552	2315 Unneeded declarations are removed, and basic optimizations are repeated.
adamc@552	2316
adamc@552	2317 \subsection{Fuse}
adamc@552	2318
adamc@552	2319 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	2320
adamc@552	2321 \subsection{MonoUntangle, MonoShake}
adamc@552	2322
adamc@552	2323 Fuse often creates more opportunities to remove spurious mutual recursion.
adamc@552	2324
adamc@552	2325 \subsection{Pathcheck}
adamc@552	2326
adamc@552	2327 The compiler checks that no link or action name has been used more than once.
adamc@552	2328
adamc@552	2329 \subsection{Cjrize}
adamc@552	2330
adamc@552	2331 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	2332
adamc@552	2333 \subsection{C Compilation and Linking}
adamc@552	2334
adamc@552	2335 The output of the last phase is pretty-printed as C source code and passed to GCC.
adamc@552	2336
adamc@552	2337
adamc@524	2338 \end{document}

Mercurial > urweb

annotate doc/manual.tex @ 1415:e65082d76d26