Ur/Web: doc/manual.tex annotate

annotate doc/manual.tex @ 1731:27e731a65934

Include JavaScript files properly in error handler pages

author	Adam Chlipala <adam@chlipala.net>
date	Sat, 28 Apr 2012 12:00:35 -0400
parents	7b9775d4a8ce
children	ab24a7cb2a64

rev	line source
adamc@524	1 \documentclass{article}
adamc@554	2 \usepackage{fullpage,amsmath,amssymb,proof,url}
rmbruijn@1568	3 \usepackage[T1]{fontenc}
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@1523	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 (or an alternate C compiler) in your execution path; MLton, the whole-program optimizing compiler for Standard ML; and the development files for the OpenSSL C library. As of this writing, in the ``testing'' version of Debian Linux, this command will install the more uncommon of these dependencies:
adamc@896	60 \begin{verbatim}
adam@1368	61 apt-get install mlton libssl-dev
adamc@896	62 \end{verbatim}
adamc@555	63
adamc@896	64 To build programs that access SQL databases, you also need one of these client libraries for supported backends.
adamc@555	65 \begin{verbatim}
adamc@896	66 apt-get install libpq-dev libmysqlclient15-dev libsqlite3-dev
adamc@555	67 \end{verbatim}
adamc@555	68
adamc@555	69 It is also possible to access the modules of the Ur/Web compiler interactively, within Standard ML of New Jersey. To install the prerequisites in Debian testing:
adamc@555	70 \begin{verbatim}
adamc@555	71 apt-get install smlnj libsmlnj-smlnj ml-yacc ml-lpt
adamc@555	72 \end{verbatim}
adamc@555	73
adamc@555	74 To begin an interactive session with the Ur compiler modules, run \texttt{make smlnj}, and then, from within an \texttt{sml} session, run \texttt{CM.make "src/urweb.cm";}. The \texttt{Compiler} module is the main entry point.
adamc@555	75
adamc@896	76 To run an SQL-backed application with a backend besides SQLite, you will probably want to install one of these servers.
adamc@555	77
adamc@555	78 \begin{verbatim}
adam@1400	79 apt-get install postgresql-8.4 mysql-server-5.1
adamc@555	80 \end{verbatim}
adamc@555	81
adamc@555	82 To use the Emacs mode, you must have a modern Emacs installed. We assume that you already know how to do this, if you're in the business of looking for an Emacs mode. The demo generation facility of the compiler will also call out to Emacs to syntax-highlight code, and that process depends on the \texttt{htmlize} module, which can be installed in Debian testing via:
adamc@555	83
adamc@555	84 \begin{verbatim}
adamc@555	85 apt-get install emacs-goodies-el
adamc@555	86 \end{verbatim}
adamc@555	87
adam@1441	88 If you don't want to install the Emacs mode, run \texttt{./configure} with the argument \texttt{--without-emacs}.
adam@1441	89
adam@1523	90 Even with the right packages installed, configuration and building might fail to work. After you run \texttt{./configure}, you will see the values of some named environment variables printed. You may need to adjust these values to get proper installation for your system. To change a value, store your preferred alternative in the corresponding UNIX environment variable, before running \texttt{./configure}. For instance, here is how to change the list of extra arguments that the Ur/Web compiler will pass to the C compiler and linker on every invocation. Some older GCC versions need this setting to mask a bug in function inlining.
adamc@555	91
adamc@555	92 \begin{verbatim}
adam@1523	93 CCARGS=-fno-inline ./configure
adamc@555	94 \end{verbatim}
adamc@555	95
adam@1523	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). The variables \texttt{PGHEADER}, \texttt{MSHEADER}, and \texttt{SQHEADER} may be used to set the proper C header files to include for the development libraries of PostgreSQL, MySQL, and SQLite, respectively. To get libpq to link, one OS X user reported setting \texttt{CCARGS="-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
adam@1604	110 \subsection{\label{cl}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}
adam@1465	137 \item \texttt{[allow\|deny] [url\|mime\|requestHeader\|responseHeader] PATTERN} registers a rule governing which URLs, MIME types, HTTP request headers, or HTTP response headers are allowed to appear explicitly in this application. The first such rule to match a name determines the verdict. If \texttt{PATTERN} ends in \texttt{*}, it is interpreted as a prefix rule. Otherwise, a string must match it exactly.
adam@1400	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.
adam@1462	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 only has side effects that remain local to a single page generation.
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.
adam@1699	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. (Note that merely assigning a function a \texttt{transaction}-based type does not mark it as effectful in this way!)
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}
adam@1523	166 \item \texttt{link FILENAME} adds \texttt{FILENAME} to the list of files to be passed to the linker at the end of compilation. This is most useful for importing extra libraries needed by new FFI modules.
adam@1725	167 \item \texttt{linker CMD} sets \texttt{CMD} as the command line prefix to use for linking C object files. The command line will be completed with a space-separated list of \texttt{.o} and \texttt{.a} files, \texttt{-L} and \texttt{-l} flags, and finally with a \texttt{-o} flag to set the location where the executable should be written.
adam@1332	168 \item \texttt{minHeap NUMBYTES} sets the initial size for thread-local heaps used in handling requests. These heaps grow automatically as needed (up to any maximum set with \texttt{limit}), but each regrow requires restarting the request handling process.
adam@1478	169 \item \texttt{noXsrfProtection URIPREFIX} turns off automatic cross-site request forgery protection for the page handler identified by the given URI prefix. This will avoid checking cryptographic signatures on cookies, which is generally a reasonable idea for some pages, such as login pages that are going to discard all old cookie values, anyway.
adam@1297	170 \item \texttt{onError Module.var} changes the handling of fatal application errors. Instead of displaying a default, ugly error 500 page, the error page will be generated by calling function \texttt{Module.var} on a piece of XML representing the error message. The error handler should have type $\mt{xbody} \to \mt{transaction} \; \mt{page}$. Note that the error handler \emph{cannot} be in the application's main module, since that would register it as explicitly callable via URLs.
adamc@852	171 \item \texttt{path NAME=VALUE} creates a mapping from \texttt{NAME} to \texttt{VALUE}. This mapping may be used at the beginnings of filesystem paths given to various other configuration directives. A path like \texttt{\$NAME/rest} is expanded to \texttt{VALUE/rest}. There is an initial mapping from the empty name (for paths like \texttt{\$/list}) to the directory where the Ur/Web standard library is installed. If you accept the default \texttt{configure} options, this directory is \texttt{/usr/local/lib/urweb/ur}.
adamc@783	172 \item \texttt{prefix PREFIX} sets the prefix included before every URI within the generated application. The default is \texttt{/}.
adamc@783	173 \item \texttt{profile} generates an executable that may be used with gprof.
adam@1300	174 \item \texttt{rewrite KIND FROM TO} gives a rule for rewriting canonical module paths. For instance, the canonical path of a page may be \texttt{Mod1.Mod2.mypage}, while you would rather the page were accessed via a URL containing only \texttt{page}. The directive \texttt{rewrite url Mod1/Mod2/mypage page} would accomplish that. The possible values of \texttt{KIND} determine which kinds of objects are affected. The kind \texttt{all} matches any object, and \texttt{url} matches page URLs. The kinds \texttt{table}, \texttt{sequence}, and \texttt{view} match those sorts of SQL entities, and \texttt{relation} matches any of those three. \texttt{cookie} matches HTTP cookies, and \texttt{style} matches CSS class names. If \texttt{FROM} ends in \texttt{/}, it is interpreted as a prefix matching rule, and rewriting occurs by replacing only the appropriate prefix of a path with \texttt{TO}. The \texttt{TO} field may be left empty to express the idea of deleting a prefix. For instance, \texttt{rewrite url Main/} will strip all \texttt{Main/} prefixes from URLs. While the actual external names of relations and styles have parts separated by underscores instead of slashes, all rewrite rules must be written in terms of slashes.
adamc@1183	175 \item \texttt{safeGet URI} asks to allow the page handler assigned this canonical URI prefix to cause persistent side effects, even if accessed via an HTTP \cd{GET} request.
adamc@783	176 \item \texttt{script URL} adds \texttt{URL} to the list of extra JavaScript files to be included at the beginning of any page that uses JavaScript. This is most useful for importing JavaScript versions of functions found in new FFI modules.
adamc@783	177 \item \texttt{serverOnly Module.ident} registers an FFI function or transaction that may only be run on the server.
adamc@1164	178 \item \texttt{sigfile PATH} sets a path where your application should look for a key to use in cryptographic signing. This is used to prevent cross-site request forgery attacks for any form handler that both reads a cookie and creates side effects. If the referenced file doesn't exist, an application will create it and read its saved data on future invocations. You can also initialize the file manually with any contents at least 16 bytes long; the first 16 bytes will be treated as the key.
adamc@783	179 \item \texttt{sql FILENAME} sets where to write an SQL file with the commands to create the expected database schema. The default is not to create such a file.
adam@1629	180 \item \texttt{timeFormat FMT} accepts a time format string, as processed by the POSIX C function \texttt{strftime()}. This controls the default rendering of $\mt{time}$ values, via the $\mt{show}$ instance for $\mt{time}$.
adamc@783	181 \item \texttt{timeout N} sets to \texttt{N} seconds the amount of time that the generated server will wait after the last contact from a client before determining that that client has exited the application. Clients that remain active will take the timeout setting into account in determining how often to ping the server, so it only makes sense to set a high timeout to cope with browser and network delays and failures. Higher timeouts can lead to more unnecessary client information taking up memory on the server. The timeout goes unused by any page that doesn't involve the \texttt{recv} function, since the server only needs to store per-client information for clients that receive asynchronous messages.
adamc@783	182 \end{itemize}
adamc@701	183
adamc@701	184
adamc@557	185 \subsection{Building an Application}
adamc@557	186
adamc@557	187 To compile project \texttt{P.urp}, simply run
adamc@557	188 \begin{verbatim}
adamc@557	189 urweb P
adamc@557	190 \end{verbatim}
adamc@1198	191 The output executable is a standalone web server. Run it with the command-line argument \texttt{-h} to see which options it takes. If the project file lists a database, the web server will attempt to connect to that database on startup. See Section \ref{structure} for an explanation of the URI mapping convention, which determines how each page of your application may be accessed via URLs.
adamc@557	192
adamc@557	193 To time how long the different compiler phases run, without generating an executable, run
adamc@557	194 \begin{verbatim}
adamc@557	195 urweb -timing P
adamc@557	196 \end{verbatim}
adamc@557	197
adamc@1086	198 To stop the compilation process after type-checking, run
adamc@1086	199 \begin{verbatim}
adamc@1086	200 urweb -tc P
adamc@1086	201 \end{verbatim}
adam@1530	202 It is often worthwhile to run \cd{urweb} in this mode, because later phases of compilation can take significantly longer than type-checking alone, and the type checker catches many errors that would traditionally be found through debugging a running application.
adamc@1086	203
adam@1531	204 A related option is \cd{-dumpTypes}, which, as long as parsing succeeds, outputs to stdout a summary of the kinds of all identifiers declared with \cd{con} and the types of all identifiers declared with \cd{val} or \cd{val rec}. This information is dumped even if there are errors during type inference. Compiler error messages go to stderr, not stdout, so it is easy to distinguish the two kinds of output programmatically.
adam@1531	205
adam@1723	206 It may be useful to combine another option \cd{-unifyMore} with \cd{-dumpTypes}. Ur/Web type inference proceeds in a series of stages, where the first is standard Hindley-Milner type inference as in ML, and the later phases add more complex aspects. By default, an error detected in one phase cuts off the execution of later phases. However, the later phases might still determine more values of unification variables. These value choices might be ``misguided,'' since earlier phases have not come up with reasonable types at a coarser detail level; but the unification decisions may still be useful for debugging and program understanding. So, if a run with \cd{-dumpTypes} leaves unification variables undetermined in positions where you would like to see best-effort guesses instead, consider \cd{-unifyMore}. Note that \cd{-unifyMore} has no effect when type inference succeeds fully, but it may lead to many more error messages when inference fails.
adam@1723	207
adamc@1170	208 To output information relevant to CSS stylesheets (and not finish regular compilation), run
adamc@1170	209 \begin{verbatim}
adamc@1170	210 urweb -css P
adamc@1170	211 \end{verbatim}
adamc@1170	212 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	213
adamc@896	214 Some other command-line parameters are accepted:
adamc@896	215 \begin{itemize}
adamc@896	216 \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	217
adamc@896	218 \item \texttt{-dbms [postgres\|mysql\|sqlite]}: Sets the database backend to use.
adamc@896	219 \begin{itemize}
adamc@896	220 \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	221
adamc@896	222 A command sequence like this can initialize a Postgres database, using a file \texttt{app.sql} generated by the compiler:
adamc@896	223 \begin{verbatim}
adamc@896	224 createdb app
adamc@896	225 psql -f app.sql app
adamc@896	226 \end{verbatim}
adamc@896	227
adamc@896	228 \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	229
adamc@896	230 A command sequence like this can initialize a MySQL database:
adamc@896	231 \begin{verbatim}
adamc@896	232 echo "CREATE DATABASE app" \| mysql
adamc@896	233 mysql -D app <app.sql
adamc@896	234 \end{verbatim}
adamc@896	235
adamc@896	236 \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	237
adamc@896	238 A command like this can initialize an SQLite database:
adamc@896	239 \begin{verbatim}
adamc@896	240 sqlite3 path/to/database/file <app.sql
adamc@896	241 \end{verbatim}
adamc@896	242 \end{itemize}
adamc@896	243
adam@1693	244 \item \texttt{-dumpSource}: When compilation fails, output to stderr the complete source code of the last intermediate program before the compilation phase that signaled the error. (Warning: these outputs can be very long and aren't especially optimized for readability!)
adam@1693	245
adam@1309	246 \item \texttt{-limit class num}: Equivalent to the \texttt{limit} directive from \texttt{.urp} files
adam@1309	247
adamc@896	248 \item \texttt{-output FILENAME}: Set where the application executable is written.
adamc@896	249
adamc@1127	250 \item \texttt{-path NAME VALUE}: Set the value of path variable \texttt{\$NAME} to \texttt{VALUE}, for use in \texttt{.urp} files.
adamc@1127	251
adam@1335	252 \item \texttt{-prefix PREFIX}: Equivalent to the \texttt{prefix} directive from \texttt{.urp} files
adam@1335	253
adamc@896	254 \item \texttt{-protocol [http\|cgi\|fastcgi]}: Set the protocol that the generated application speaks.
adamc@896	255 \begin{itemize}
adamc@896	256 \item \texttt{http}: This is the default. It is for building standalone web servers that can be accessed by web browsers directly.
adamc@896	257
adamc@896	258 \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	259
adamc@896	260 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	261 \begin{verbatim}
adamc@896	262 ScriptAlias /Hello /path/to/hello.exe
adamc@896	263 \end{verbatim}
adamc@896	264
adamc@1163	265 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	266 \begin{verbatim}
adamc@1163	267 Options +ExecCGI
adamc@1163	268 AddHandler cgi-script .exe
adamc@1163	269 \end{verbatim}
adamc@1163	270
adamc@1163	271 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	272 \begin{verbatim}
adamc@1163	273 prefix /dir/script.exe/
adamc@1163	274 \end{verbatim}
adamc@1163	275
adamc@1163	276 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	277
adamc@1164	278 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	279
adamc@896	280 \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	281
adamc@896	282 To configure a FastCGI program with Apache, one could combine the above \texttt{ScriptAlias} line with a line like this:
adamc@896	283 \begin{verbatim}
adamc@896	284 FastCgiServer /path/to/hello.exe -idle-timeout 99999
adamc@896	285 \end{verbatim}
adamc@896	286 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	287
adamc@896	288 Here is some lighttpd configuration for the same application.
adamc@896	289 \begin{verbatim}
adamc@896	290 fastcgi.server = (
adamc@896	291 "/Hello/" =>
adamc@896	292 (( "bin-path" => "/path/to/hello.exe",
adamc@896	293 "socket" => "/tmp/hello",
adamc@896	294 "check-local" => "disable",
adamc@896	295 "docroot" => "/",
adamc@896	296 "max-procs" => "1"
adamc@896	297 ))
adamc@896	298 )
adamc@896	299 \end{verbatim}
adamc@896	300 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	301
adamc@896	302 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.
adam@1509	303
adam@1509	304 \item \texttt{static}: This protocol may be used to generate static web pages from Ur/Web code. The output executable expects a single command-line argument, giving the URI of a page to generate. For instance, this argument might be \cd{/main}, in which case a static HTTP response for that page will be written to stdout.
adamc@896	305 \end{itemize}
adamc@896	306
adamc@1127	307 \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	308
adamc@1164	309 \item \texttt{-sigfile PATH}: Same as the \texttt{sigfile} directive in \texttt{.urp} files
adamc@1164	310
adamc@896	311 \item \texttt{-sql FILENAME}: Set where a database set-up SQL script is written.
adamc@1095	312
adamc@1095	313 \item \texttt{-static}: Link the runtime system statically. The default is to link against dynamic libraries.
adamc@896	314 \end{itemize}
adamc@896	315
adam@1297	316 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	317
adam@1509	318 \subsection{Tutorial Formatting}
adam@1509	319
adam@1509	320 The Ur/Web compiler also supports rendering of nice HTML tutorials from Ur source files, when invoked like \cd{urweb -tutorial DIR}. The directory \cd{DIR} is examined for files whose names end in \cd{.ur}. Every such file is translated into a \cd{.html} version.
adam@1509	321
adam@1509	322 These input files follow normal Ur syntax, with a few exceptions:
adam@1509	323 \begin{itemize}
adam@1509	324 \item The first line must be a comment like \cd{(* TITLE *)}, where \cd{TITLE} is a string of your choice that will be used as the title of the output page.
adam@1509	325 \item While most code in the output HTML will be formatted as a monospaced code listing, text in regular Ur comments is formatted as normal English text.
adam@1509	326 \item A comment like \cd{(* * HEADING *)} introduces a section heading, with text \cd{HEADING} of your choice.
adam@1509	327 \item To include both a rendering of an Ur expression and a pretty-printed version of its value, bracket the expression with \cd{(* begin eval )} and \cd{( end *)}. The result of expression evaluation is pretty-printed with \cd{show}, so the expression type must belong to that type class.
adam@1509	328 \item To include code that should not be shown in the tutorial (e.g., to add a \cd{show} instance to use with \cd{eval}), bracket the code with \cd{(* begin hide )} and \cd{( end *)}.
adam@1509	329 \end{itemize}
adam@1509	330
adam@1509	331 A word of warning: as for demo generation, tutorial generation calls Emacs to syntax-highlight Ur code.
adam@1509	332
adam@1522	333 \subsection{Run-Time Options}
adam@1522	334
adam@1522	335 Compiled applications consult a few environment variables to modify their behavior:
adam@1522	336
adam@1522	337 \begin{itemize}
adam@1522	338 \item \cd{URWEB\_NUM\_THREADS}: alternative to the \cd{-t} command-line argument (currently used only by FastCGI)
adam@1522	339 \item \cd{URWEB\_STACK\_SIZE}: size of per-thread stacks, in bytes
as@1564	340 \item \cd{URWEB\_PQ\_CON}: when using PostgreSQL, overrides the compiled-in connection string
adam@1522	341 \end{itemize}
adam@1522	342
adam@1509	343
adamc@529	344 \section{Ur Syntax}
adamc@529	345
adamc@784	346 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	347
adamc@524	348 \subsection{Lexical Conventions}
adamc@524	349
adamc@524	350 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	351
adamc@524	352 \begin{center}
adamc@524	353 \begin{tabular}{rl}
adamc@524	354 \textbf{\LaTeX} & \textbf{ASCII} \\
adamc@524	355 $\to$ & \cd{->} \\
adam@1687	356 $\longrightarrow$ & \cd{-{}->} \\
adamc@524	357 $\times$ & \cd{*} \\
adamc@524	358 $\lambda$ & \cd{fn} \\
adamc@524	359 $\Rightarrow$ & \cd{=>} \\
adamc@652	360 $\Longrightarrow$ & \cd{==>} \\
adamc@529	361 $\neq$ & \cd{<>} \\
adamc@529	362 $\leq$ & \cd{<=} \\
adamc@529	363 $\geq$ & \cd{>=} \\
adamc@524	364 \\
adamc@524	365 $x$ & Normal textual identifier, not beginning with an uppercase letter \\
adamc@525	366 $X$ & Normal textual identifier, beginning with an uppercase letter \\
adamc@524	367 \end{tabular}
adamc@524	368 \end{center}
adamc@524	369
adamc@525	370 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	371
adamc@873	372 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	373
adamc@527	374 This version of the manual doesn't include operator precedences; see \texttt{src/urweb.grm} for that.
adamc@527	375
adam@1297	376 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	377
adamc@552	378 \subsection{\label{core}Core Syntax}
adamc@524	379
adamc@524	380 \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	381 $$\begin{array}{rrcll}
adamc@524	382 \textrm{Kinds} & \kappa &::=& \mt{Type} & \textrm{proper types} \\
adamc@525	383 &&& \mt{Unit} & \textrm{the trivial constructor} \\
adamc@525	384 &&& \mt{Name} & \textrm{field names} \\
adamc@525	385 &&& \kappa \to \kappa & \textrm{type-level functions} \\
adamc@525	386 &&& \{\kappa\} & \textrm{type-level records} \\
adamc@525	387 &&& (\kappa\times^+) & \textrm{type-level tuples} \\
adamc@652	388 &&& X & \textrm{variable} \\
adam@1574	389 &&& X \longrightarrow \kappa & \textrm{kind-polymorphic type-level function} \\
adamc@529	390 &&& \_\_ & \textrm{wildcard} \\
adamc@525	391 &&& (\kappa) & \textrm{explicit precedence} \\
adamc@524	392 \end{array}$$
adamc@524	393
adamc@524	394 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	395 $$\begin{array}{rrcll}
adamc@524	396 \textrm{Explicitness} & ? &::=& :: & \textrm{explicit} \\
adamc@558	397 &&& ::: & \textrm{implicit}
adamc@524	398 \end{array}$$
adamc@524	399
adamc@524	400 \emph{Constructors} are the main class of compile-time-only data. They include proper types and are classified by kinds.
adamc@524	401 $$\begin{array}{rrcll}
adamc@524	402 \textrm{Constructors} & c, \tau &::=& (c) :: \kappa & \textrm{kind annotation} \\
adamc@530	403 &&& \hat{x} & \textrm{constructor variable} \\
adamc@524	404 \\
adamc@525	405 &&& \tau \to \tau & \textrm{function type} \\
adamc@525	406 &&& x \; ? \; \kappa \to \tau & \textrm{polymorphic function type} \\
adamc@652	407 &&& X \longrightarrow \tau & \textrm{kind-polymorphic function type} \\
adamc@525	408 &&& \$ c & \textrm{record type} \\
adamc@524	409 \\
adamc@525	410 &&& c \; c & \textrm{type-level function application} \\
adamc@530	411 &&& \lambda x \; :: \; \kappa \Rightarrow c & \textrm{type-level function abstraction} \\
adamc@524	412 \\
adamc@652	413 &&& X \Longrightarrow c & \textrm{type-level kind-polymorphic function abstraction} \\
adamc@655	414 &&& c [\kappa] & \textrm{type-level kind-polymorphic function application} \\
adamc@652	415 \\
adamc@525	416 &&& () & \textrm{type-level unit} \\
adamc@525	417 &&& \#X & \textrm{field name} \\
adamc@524	418 \\
adamc@525	419 &&& [(c = c)^*] & \textrm{known-length type-level record} \\
adamc@525	420 &&& c \rc c & \textrm{type-level record concatenation} \\
adamc@652	421 &&& \mt{map} & \textrm{type-level record map} \\
adamc@524	422 \\
adamc@558	423 &&& (c,^+) & \textrm{type-level tuple} \\
adamc@525	424 &&& c.n & \textrm{type-level tuple projection ($n \in \mathbb N^+$)} \\
adamc@524	425 \\
adamc@652	426 &&& [c \sim c] \Rightarrow \tau & \textrm{guarded type} \\
adamc@524	427 \\
adamc@529	428 &&& \_ :: \kappa & \textrm{wildcard} \\
adamc@525	429 &&& (c) & \textrm{explicit precedence} \\
adamc@530	430 \\
adamc@530	431 \textrm{Qualified uncapitalized variables} & \hat{x} &::=& x & \textrm{not from a module} \\
adamc@530	432 &&& M.x & \textrm{projection from a module} \\
adamc@525	433 \end{array}$$
adamc@525	434
adam@1579	435 We include both abstraction and application for kind polymorphism, but applications are only inferred internally; they may not be written explicitly in source programs. Also, in the ``known-length type-level record'' form, in $c_1 = c_2$ terms, the parser currently only allows $c_1$ to be of the forms $X$ (as a shorthand for $\#X$) or $x$, or a natural number to stand for the corresponding field name (e.g., for tuples).
adamc@655	436
adamc@525	437 Modules of the module system are described by \emph{signatures}.
adamc@525	438 $$\begin{array}{rrcll}
adamc@525	439 \textrm{Signatures} & S &::=& \mt{sig} \; s^* \; \mt{end} & \textrm{constant} \\
adamc@525	440 &&& X & \textrm{variable} \\
adamc@525	441 &&& \mt{functor}(X : S) : S & \textrm{functor} \\
adamc@529	442 &&& S \; \mt{where} \; \mt{con} \; x = c & \textrm{concretizing an abstract constructor} \\
adamc@525	443 &&& M.X & \textrm{projection from a module} \\
adamc@525	444 \\
adamc@525	445 \textrm{Signature items} & s &::=& \mt{con} \; x :: \kappa & \textrm{abstract constructor} \\
adamc@525	446 &&& \mt{con} \; x :: \kappa = c & \textrm{concrete constructor} \\
adamc@528	447 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529	448 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@525	449 &&& \mt{val} \; x : \tau & \textrm{value} \\
adamc@525	450 &&& \mt{structure} \; X : S & \textrm{sub-module} \\
adamc@525	451 &&& \mt{signature} \; X = S & \textrm{sub-signature} \\
adamc@525	452 &&& \mt{include} \; S & \textrm{signature inclusion} \\
adamc@525	453 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@654	454 &&& \mt{class} \; x :: \kappa & \textrm{abstract constructor class} \\
adamc@654	455 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@525	456 \\
adamc@525	457 \textrm{Datatype constructors} & dc &::=& X & \textrm{nullary constructor} \\
adamc@525	458 &&& X \; \mt{of} \; \tau & \textrm{unary constructor} \\
adamc@524	459 \end{array}$$
adamc@524	460
adamc@526	461 \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	462 $$\begin{array}{rrcll}
adamc@526	463 \textrm{Patterns} & p &::=& \_ & \textrm{wildcard} \\
adamc@526	464 &&& x & \textrm{variable} \\
adamc@526	465 &&& \ell & \textrm{constant} \\
adamc@526	466 &&& \hat{X} & \textrm{nullary constructor} \\
adamc@526	467 &&& \hat{X} \; p & \textrm{unary constructor} \\
adamc@526	468 &&& \{(x = p,)^*\} & \textrm{rigid record pattern} \\
adamc@526	469 &&& \{(x = p,)^+, \ldots\} & \textrm{flexible record pattern} \\
adamc@852	470 &&& p : \tau & \textrm{type annotation} \\
adamc@527	471 &&& (p) & \textrm{explicit precedence} \\
adamc@526	472 \\
adamc@529	473 \textrm{Qualified capitalized variables} & \hat{X} &::=& X & \textrm{not from a module} \\
adamc@526	474 &&& M.X & \textrm{projection from a module} \\
adamc@526	475 \end{array}$$
adamc@526	476
adamc@527	477 \emph{Expressions} are the main run-time entities, corresponding to both ``expressions'' and ``statements'' in mainstream imperative languages.
adamc@527	478 $$\begin{array}{rrcll}
adamc@527	479 \textrm{Expressions} & e &::=& e : \tau & \textrm{type annotation} \\
adamc@529	480 &&& \hat{x} & \textrm{variable} \\
adamc@529	481 &&& \hat{X} & \textrm{datatype constructor} \\
adamc@527	482 &&& \ell & \textrm{constant} \\
adamc@527	483 \\
adamc@527	484 &&& e \; e & \textrm{function application} \\
adamc@527	485 &&& \lambda x : \tau \Rightarrow e & \textrm{function abstraction} \\
adamc@527	486 &&& e [c] & \textrm{polymorphic function application} \\
adamc@852	487 &&& \lambda [x \; ? \; \kappa] \Rightarrow e & \textrm{polymorphic function abstraction} \\
adamc@655	488 &&& e [\kappa] & \textrm{kind-polymorphic function application} \\
adamc@652	489 &&& X \Longrightarrow e & \textrm{kind-polymorphic function abstraction} \\
adamc@527	490 \\
adamc@527	491 &&& \{(c = e,)^*\} & \textrm{known-length record} \\
adamc@527	492 &&& e.c & \textrm{record field projection} \\
adamc@527	493 &&& e \rc e & \textrm{record concatenation} \\
adamc@527	494 &&& e \rcut c & \textrm{removal of a single record field} \\
adamc@527	495 &&& e \rcutM c & \textrm{removal of multiple record fields} \\
adamc@527	496 \\
adamc@527	497 &&& \mt{let} \; ed^* \; \mt{in} \; e \; \mt{end} & \textrm{local definitions} \\
adamc@527	498 \\
adamc@527	499 &&& \mt{case} \; e \; \mt{of} \; (p \Rightarrow e\|)^+ & \textrm{pattern matching} \\
adamc@527	500 \\
adamc@654	501 &&& \lambda [c \sim c] \Rightarrow e & \textrm{guarded expression abstraction} \\
adamc@654	502 &&& e \; ! & \textrm{guarded expression application} \\
adamc@527	503 \\
adamc@527	504 &&& \_ & \textrm{wildcard} \\
adamc@527	505 &&& (e) & \textrm{explicit precedence} \\
adamc@527	506 \\
adamc@527	507 \textrm{Local declarations} & ed &::=& \cd{val} \; x : \tau = e & \textrm{non-recursive value} \\
adamc@527	508 &&& \cd{val} \; \cd{rec} \; (x : \tau = e \; \cd{and})^+ & \textrm{mutually-recursive values} \\
adamc@527	509 \end{array}$$
adamc@527	510
adamc@655	511 As with constructors, we include both abstraction and application for kind polymorphism, but applications are only inferred internally.
adamc@655	512
adamc@528	513 \emph{Declarations} primarily bring new symbols into context.
adamc@528	514 $$\begin{array}{rrcll}
adamc@528	515 \textrm{Declarations} & d &::=& \mt{con} \; x :: \kappa = c & \textrm{constructor synonym} \\
adamc@528	516 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529	517 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@528	518 &&& \mt{val} \; x : \tau = e & \textrm{value} \\
adamc@528	519 &&& \mt{val} \; \cd{rec} \; (x : \tau = e \; \mt{and})^+ & \textrm{mutually-recursive values} \\
adamc@528	520 &&& \mt{structure} \; X : S = M & \textrm{module definition} \\
adamc@528	521 &&& \mt{signature} \; X = S & \textrm{signature definition} \\
adamc@528	522 &&& \mt{open} \; M & \textrm{module inclusion} \\
adamc@528	523 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@528	524 &&& \mt{open} \; \mt{constraints} \; M & \textrm{inclusion of just the constraints from a module} \\
adamc@528	525 &&& \mt{table} \; x : c & \textrm{SQL table} \\
adam@1594	526 &&& \mt{view} \; x = e & \textrm{SQL view} \\
adamc@528	527 &&& \mt{sequence} \; x & \textrm{SQL sequence} \\
adamc@535	528 &&& \mt{cookie} \; x : \tau & \textrm{HTTP cookie} \\
adamc@784	529 &&& \mt{style} \; x : \tau & \textrm{CSS class} \\
adamc@654	530 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@1085	531 &&& \mt{task} \; e = e & \textrm{recurring task} \\
adamc@528	532 \\
adamc@529	533 \textrm{Modules} & M &::=& \mt{struct} \; d^* \; \mt{end} & \textrm{constant} \\
adamc@529	534 &&& X & \textrm{variable} \\
adamc@529	535 &&& M.X & \textrm{projection} \\
adamc@529	536 &&& M(M) & \textrm{functor application} \\
adamc@529	537 &&& \mt{functor}(X : S) : S = M & \textrm{functor abstraction} \\
adamc@528	538 \end{array}$$
adamc@528	539
adamc@528	540 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	541
adam@1594	542 We omit some extra possibilities in $\mt{table}$ syntax, deferring them to Section \ref{tables}. The concrete syntax of $\mt{view}$ declarations is also more complex than shown in the table above, with details deferred to Section \ref{tables}.
adamc@784	543
adamc@529	544 \subsection{Shorthands}
adamc@529	545
adamc@529	546 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	547
adamc@529	548 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	549
adamc@529	550 A record type may be written $\{(c = c,)^\}$, which elaborates to $\$[(c = c,)^]$.
adamc@529	551
adamc@533	552 The notation $[c_1, \ldots, c_n]$ is shorthand for $[c_1 = (), \ldots, c_n = ()]$.
adamc@533	553
adam@1350	554 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	555
adam@1687	556 The syntax $()$ expands to $\{\}$ as a pattern or expression.
adam@1687	557
adamc@852	558 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	559
adam@1574	560 Further, the signature item or declaration syntax $\mt{con} \; x \; b^+ = c$ is shorthand for wrapping of the appropriate $\lambda$s around the righthand side $c$. The $b$ elements may not include $X$, and there may also be an optional $:: \kappa$ before the $=$.
adam@1574	561
adam@1306	562 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	563
adamc@529	564 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	565
adamc@529	566 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	567
adamc@654	568 A signature item or declaration $\mt{class} \; x = \lambda y \Rightarrow c$ may be abbreviated $\mt{class} \; x \; y = c$.
adamc@529	569
adam@1482	570 Handling of implicit and explicit constructor arguments may be tweaked with some prefixes to variable references. An expression $@x$ is a version of $x$ where all type class instance and disjointness arguments have been made explicit. (For the purposes of this paragraph, the type family $\mt{Top.folder}$ is a type class, though it isn't marked as one by the usual means.) An expression $@@x$ achieves the same effect, additionally making explicit all implicit constructor arguments. The default is that implicit arguments are inserted automatically after any reference to a variable, or after any application of a variable to one or more arguments. For such an expression, implicit wildcard arguments are added for the longest prefix of the expression's type consisting only of implicit polymorphism, type class instances, and disjointness obligations. The same syntax works for variables projected out of modules and for capitalized variables (datatype constructors).
adamc@529	571
adamc@852	572 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	573
adamc@852	574 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	575
adamc@852	576 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	577
adamc@529	578 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	579
adamc@852	580 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	581
adamc@853	582 A declaration $\mt{table} \; x : \{(c = c,)^\}$ is elaborated into $\mt{table} \; x : [(c = c,)^]$.
adamc@529	583
adamc@529	584 The syntax $\mt{where} \; \mt{type}$ is an alternate form of $\mt{where} \; \mt{con}$.
adamc@529	585
adamc@529	586 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	587
adamc@529	588 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	589
adamc@784	590 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	591
adamc@530	592
adamc@530	593 \section{Static Semantics}
adamc@530	594
adamc@530	595 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	596
adamc@530	597 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	598 \begin{itemize}
adamc@655	599 \item $\Gamma \vdash \kappa$ expresses kind well-formedness.
adamc@530	600 \item $\Gamma \vdash c :: \kappa$ assigns a kind to a constructor in a context.
adamc@530	601 \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	602 \item $\Gamma \vdash c \hookrightarrow C$ proves that record constructor $c$ decomposes into set $C$ of field names and record constructors.
adamc@530	603 \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	604 \item $\Gamma \vdash e : \tau$ is a standard typing judgment.
adamc@534	605 \item $\Gamma \vdash p \leadsto \Gamma; \tau$ combines typing of patterns with calculation of which new variables they bind.
adamc@537	606 \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	607 \item $\Gamma \vdash S \equiv S$ is the signature equivalence judgment.
adamc@536	608 \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	609 \item $\Gamma \vdash M : S$ is the module signature checking judgment.
adamc@537	610 \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	611 \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	612 \end{itemize}
adamc@530	613
adamc@655	614
adamc@655	615 \subsection{Kind Well-Formedness}
adamc@655	616
adamc@655	617 $$\infer{\Gamma \vdash \mt{Type}}{}
adamc@655	618 \quad \infer{\Gamma \vdash \mt{Unit}}{}
adamc@655	619 \quad \infer{\Gamma \vdash \mt{Name}}{}
adamc@655	620 \quad \infer{\Gamma \vdash \kappa_1 \to \kappa_2}{
adamc@655	621 \Gamma \vdash \kappa_1
adamc@655	622 & \Gamma \vdash \kappa_2
adamc@655	623 }
adamc@655	624 \quad \infer{\Gamma \vdash \{\kappa\}}{
adamc@655	625 \Gamma \vdash \kappa
adamc@655	626 }
adamc@655	627 \quad \infer{\Gamma \vdash (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@655	628 \forall i: \Gamma \vdash \kappa_i
adamc@655	629 }$$
adamc@655	630
adamc@655	631 $$\infer{\Gamma \vdash X}{
adamc@655	632 X \in \Gamma
adamc@655	633 }
adamc@655	634 \quad \infer{\Gamma \vdash X \longrightarrow \kappa}{
adamc@655	635 \Gamma, X \vdash \kappa
adamc@655	636 }$$
adamc@655	637
adamc@530	638 \subsection{Kinding}
adamc@530	639
adamc@655	640 We write $[X \mapsto \kappa_1]\kappa_2$ for capture-avoiding substitution of $\kappa_1$ for $X$ in $\kappa_2$.
adamc@655	641
adamc@530	642 $$\infer{\Gamma \vdash (c) :: \kappa :: \kappa}{
adamc@530	643 \Gamma \vdash c :: \kappa
adamc@530	644 }
adamc@530	645 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530	646 x :: \kappa \in \Gamma
adamc@530	647 }
adamc@530	648 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530	649 x :: \kappa = c \in \Gamma
adamc@530	650 }$$
adamc@530	651
adamc@530	652 $$\infer{\Gamma \vdash M.x :: \kappa}{
adamc@537	653 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	654 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = \kappa
adamc@530	655 }
adamc@530	656 \quad \infer{\Gamma \vdash M.x :: \kappa}{
adamc@537	657 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	658 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@530	659 }$$
adamc@530	660
adamc@530	661 $$\infer{\Gamma \vdash \tau_1 \to \tau_2 :: \mt{Type}}{
adamc@530	662 \Gamma \vdash \tau_1 :: \mt{Type}
adamc@530	663 & \Gamma \vdash \tau_2 :: \mt{Type}
adamc@530	664 }
adamc@530	665 \quad \infer{\Gamma \vdash x \; ? \: \kappa \to \tau :: \mt{Type}}{
adamc@530	666 \Gamma, x :: \kappa \vdash \tau :: \mt{Type}
adamc@530	667 }
adamc@655	668 \quad \infer{\Gamma \vdash X \longrightarrow \tau :: \mt{Type}}{
adamc@655	669 \Gamma, X \vdash \tau :: \mt{Type}
adamc@655	670 }
adamc@530	671 \quad \infer{\Gamma \vdash \$c :: \mt{Type}}{
adamc@530	672 \Gamma \vdash c :: \{\mt{Type}\}
adamc@530	673 }$$
adamc@530	674
adamc@530	675 $$\infer{\Gamma \vdash c_1 \; c_2 :: \kappa_2}{
adamc@530	676 \Gamma \vdash c_1 :: \kappa_1 \to \kappa_2
adamc@530	677 & \Gamma \vdash c_2 :: \kappa_1
adamc@530	678 }
adamc@530	679 \quad \infer{\Gamma \vdash \lambda x \; :: \; \kappa_1 \Rightarrow c :: \kappa_1 \to \kappa_2}{
adamc@530	680 \Gamma, x :: \kappa_1 \vdash c :: \kappa_2
adamc@530	681 }$$
adamc@530	682
adamc@655	683 $$\infer{\Gamma \vdash c[\kappa'] :: [X \mapsto \kappa']\kappa}{
adamc@655	684 \Gamma \vdash c :: X \to \kappa
adamc@655	685 & \Gamma \vdash \kappa'
adamc@655	686 }
adamc@655	687 \quad \infer{\Gamma \vdash X \Longrightarrow c :: X \to \kappa}{
adamc@655	688 \Gamma, X \vdash c :: \kappa
adamc@655	689 }$$
adamc@655	690
adamc@530	691 $$\infer{\Gamma \vdash () :: \mt{Unit}}{}
adamc@530	692 \quad \infer{\Gamma \vdash \#X :: \mt{Name}}{}$$
adamc@530	693
adamc@530	694 $$\infer{\Gamma \vdash [\overline{c_i = c'_i}] :: \{\kappa\}}{
adamc@530	695 \forall i: \Gamma \vdash c_i : \mt{Name}
adamc@530	696 & \Gamma \vdash c'_i :: \kappa
adamc@530	697 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@530	698 }
adamc@530	699 \quad \infer{\Gamma \vdash c_1 \rc c_2 :: \{\kappa\}}{
adamc@530	700 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530	701 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@530	702 & \Gamma \vdash c_1 \sim c_2
adamc@530	703 }$$
adamc@530	704
adamc@655	705 $$\infer{\Gamma \vdash \mt{map} :: (\kappa_1 \to \kappa_2) \to \{\kappa_1\} \to \{\kappa_2\}}{}$$
adamc@530	706
adamc@573	707 $$\infer{\Gamma \vdash (\overline c) :: (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@573	708 \forall i: \Gamma \vdash c_i :: \kappa_i
adamc@530	709 }
adamc@573	710 \quad \infer{\Gamma \vdash c.i :: \kappa_i}{
adamc@573	711 \Gamma \vdash c :: (\kappa_1 \times \ldots \times \kappa_n)
adamc@530	712 }$$
adamc@530	713
adamc@655	714 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow \tau :: \mt{Type}}{
adamc@655	715 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530	716 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@655	717 & \Gamma, c_1 \sim c_2 \vdash \tau :: \mt{Type}
adamc@530	718 }$$
adamc@530	719
adamc@531	720 \subsection{Record Disjointness}
adamc@531	721
adamc@531	722 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@558	723 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@558	724 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@558	725 & \forall c'_1 \in C_1, c'_2 \in C_2: \Gamma \vdash c'_1 \sim c'_2
adamc@531	726 }
adamc@531	727 \quad \infer{\Gamma \vdash X \sim X'}{
adamc@531	728 X \neq X'
adamc@531	729 }$$
adamc@531	730
adamc@531	731 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@531	732 c'_1 \sim c'_2 \in \Gamma
adamc@558	733 & \Gamma \vdash c'_1 \hookrightarrow C_1
adamc@558	734 & \Gamma \vdash c'_2 \hookrightarrow C_2
adamc@558	735 & c_1 \in C_1
adamc@558	736 & c_2 \in C_2
adamc@531	737 }$$
adamc@531	738
adamc@531	739 $$\infer{\Gamma \vdash c \hookrightarrow \{c\}}{}
adamc@531	740 \quad \infer{\Gamma \vdash [\overline{c = c'}] \hookrightarrow \{\overline{c}\}}{}
adamc@531	741 \quad \infer{\Gamma \vdash c_1 \rc c_2 \hookrightarrow C_1 \cup C_2}{
adamc@531	742 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@531	743 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@531	744 }
adamc@531	745 \quad \infer{\Gamma \vdash c \hookrightarrow C}{
adamc@531	746 \Gamma \vdash c \equiv c'
adamc@531	747 & \Gamma \vdash c' \hookrightarrow C
adamc@531	748 }
adamc@531	749 \quad \infer{\Gamma \vdash \mt{map} \; f \; c \hookrightarrow C}{
adamc@531	750 \Gamma \vdash c \hookrightarrow C
adamc@531	751 }$$
adamc@531	752
adamc@541	753 \subsection{\label{definitional}Definitional Equality}
adamc@532	754
adamc@655	755 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	756
adamc@532	757 $$\infer{\Gamma \vdash c \equiv c}{}
adamc@532	758 \quad \infer{\Gamma \vdash c_1 \equiv c_2}{
adamc@532	759 \Gamma \vdash c_2 \equiv c_1
adamc@532	760 }
adamc@532	761 \quad \infer{\Gamma \vdash c_1 \equiv c_3}{
adamc@532	762 \Gamma \vdash c_1 \equiv c_2
adamc@532	763 & \Gamma \vdash c_2 \equiv c_3
adamc@532	764 }
adamc@532	765 \quad \infer{\Gamma \vdash \mathcal C[c_1] \equiv \mathcal C[c_2]}{
adamc@532	766 \Gamma \vdash c_1 \equiv c_2
adamc@532	767 }$$
adamc@532	768
adamc@532	769 $$\infer{\Gamma \vdash x \equiv c}{
adamc@532	770 x :: \kappa = c \in \Gamma
adamc@532	771 }
adamc@532	772 \quad \infer{\Gamma \vdash M.x \equiv c}{
adamc@537	773 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	774 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@532	775 }
adamc@532	776 \quad \infer{\Gamma \vdash (\overline c).i \equiv c_i}{}$$
adamc@532	777
adamc@532	778 $$\infer{\Gamma \vdash (\lambda x :: \kappa \Rightarrow c) \; c' \equiv [x \mapsto c'] c}{}
adamc@655	779 \quad \infer{\Gamma \vdash (X \Longrightarrow c) [\kappa] \equiv [X \mapsto \kappa] c}{}$$
adamc@655	780
adamc@655	781 $$\infer{\Gamma \vdash c_1 \rc c_2 \equiv c_2 \rc c_1}{}
adamc@532	782 \quad \infer{\Gamma \vdash c_1 \rc (c_2 \rc c_3) \equiv (c_1 \rc c_2) \rc c_3}{}$$
adamc@532	783
adamc@532	784 $$\infer{\Gamma \vdash [] \rc c \equiv c}{}
adamc@532	785 \quad \infer{\Gamma \vdash [\overline{c_1 = c'_1}] \rc [\overline{c_2 = c'_2}] \equiv [\overline{c_1 = c'_1}, \overline{c_2 = c'_2}]}{}$$
adamc@532	786
adamc@655	787 $$\infer{\Gamma \vdash \mt{map} \; f \; [] \equiv []}{}
adamc@655	788 \quad \infer{\Gamma \vdash \mt{map} \; f \; ([c_1 = c_2] \rc c) \equiv [c_1 = f \; c_2] \rc \mt{map} \; f \; c}{}$$
adamc@532	789
adamc@532	790 $$\infer{\Gamma \vdash \mt{map} \; (\lambda x \Rightarrow x) \; c \equiv c}{}
adamc@655	791 \quad \infer{\Gamma \vdash \mt{map} \; f \; (\mt{map} \; f' \; c)
adamc@655	792 \equiv \mt{map} \; (\lambda x \Rightarrow f \; (f' \; x)) \; c}{}$$
adamc@532	793
adamc@532	794 $$\infer{\Gamma \vdash \mt{map} \; f \; (c_1 \rc c_2) \equiv \mt{map} \; f \; c_1 \rc \mt{map} \; f \; c_2}{}$$
adamc@531	795
adamc@534	796 \subsection{Expression Typing}
adamc@533	797
adamc@873	798 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	799
adamc@533	800 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	801
adamc@533	802 $$\infer{\Gamma \vdash e : \tau : \tau}{
adamc@533	803 \Gamma \vdash e : \tau
adamc@533	804 }
adamc@533	805 \quad \infer{\Gamma \vdash e : \tau}{
adamc@533	806 \Gamma \vdash e : \tau'
adamc@533	807 & \Gamma \vdash \tau' \equiv \tau
adamc@533	808 }
adamc@533	809 \quad \infer{\Gamma \vdash \ell : T(\ell)}{}$$
adamc@533	810
adamc@533	811 $$\infer{\Gamma \vdash x : \mathcal I(\tau)}{
adamc@533	812 x : \tau \in \Gamma
adamc@533	813 }
adamc@533	814 \quad \infer{\Gamma \vdash M.x : \mathcal I(\tau)}{
adamc@537	815 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	816 & \mt{proj}(M, \overline{s}, \mt{val} \; x) = \tau
adamc@533	817 }
adamc@533	818 \quad \infer{\Gamma \vdash X : \mathcal I(\tau)}{
adamc@533	819 X : \tau \in \Gamma
adamc@533	820 }
adamc@533	821 \quad \infer{\Gamma \vdash M.X : \mathcal I(\tau)}{
adamc@537	822 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	823 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \tau
adamc@533	824 }$$
adamc@533	825
adamc@533	826 $$\infer{\Gamma \vdash e_1 \; e_2 : \tau_2}{
adamc@533	827 \Gamma \vdash e_1 : \tau_1 \to \tau_2
adamc@533	828 & \Gamma \vdash e_2 : \tau_1
adamc@533	829 }
adamc@533	830 \quad \infer{\Gamma \vdash \lambda x : \tau_1 \Rightarrow e : \tau_1 \to \tau_2}{
adamc@533	831 \Gamma, x : \tau_1 \vdash e : \tau_2
adamc@533	832 }$$
adamc@533	833
adamc@533	834 $$\infer{\Gamma \vdash e [c] : [x \mapsto c]\tau}{
adamc@533	835 \Gamma \vdash e : x :: \kappa \to \tau
adamc@533	836 & \Gamma \vdash c :: \kappa
adamc@533	837 }
adamc@852	838 \quad \infer{\Gamma \vdash \lambda [x \; ? \; \kappa] \Rightarrow e : x \; ? \; \kappa \to \tau}{
adamc@533	839 \Gamma, x :: \kappa \vdash e : \tau
adamc@533	840 }$$
adamc@533	841
adamc@655	842 $$\infer{\Gamma \vdash e [\kappa] : [X \mapsto \kappa]\tau}{
adamc@655	843 \Gamma \vdash e : X \longrightarrow \tau
adamc@655	844 & \Gamma \vdash \kappa
adamc@655	845 }
adamc@655	846 \quad \infer{\Gamma \vdash X \Longrightarrow e : X \longrightarrow \tau}{
adamc@655	847 \Gamma, X \vdash e : \tau
adamc@655	848 }$$
adamc@655	849
adamc@533	850 $$\infer{\Gamma \vdash \{\overline{c = e}\} : \{\overline{c : \tau}\}}{
adamc@533	851 \forall i: \Gamma \vdash c_i :: \mt{Name}
adamc@533	852 & \Gamma \vdash e_i : \tau_i
adamc@533	853 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@533	854 }
adamc@533	855 \quad \infer{\Gamma \vdash e.c : \tau}{
adamc@533	856 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533	857 }
adamc@533	858 \quad \infer{\Gamma \vdash e_1 \rc e_2 : \$(c_1 \rc c_2)}{
adamc@533	859 \Gamma \vdash e_1 : \$c_1
adamc@533	860 & \Gamma \vdash e_2 : \$c_2
adamc@573	861 & \Gamma \vdash c_1 \sim c_2
adamc@533	862 }$$
adamc@533	863
adamc@533	864 $$\infer{\Gamma \vdash e \rcut c : \$c'}{
adamc@533	865 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533	866 }
adamc@533	867 \quad \infer{\Gamma \vdash e \rcutM c : \$c'}{
adamc@533	868 \Gamma \vdash e : \$(c \rc c')
adamc@533	869 }$$
adamc@533	870
adamc@533	871 $$\infer{\Gamma \vdash \mt{let} \; \overline{ed} \; \mt{in} \; e \; \mt{end} : \tau}{
adamc@533	872 \Gamma \vdash \overline{ed} \leadsto \Gamma'
adamc@533	873 & \Gamma' \vdash e : \tau
adamc@533	874 }
adamc@533	875 \quad \infer{\Gamma \vdash \mt{case} \; e \; \mt{of} \; \overline{p \Rightarrow e} : \tau}{
adamc@533	876 \forall i: \Gamma \vdash p_i \leadsto \Gamma_i, \tau'
adamc@533	877 & \Gamma_i \vdash e_i : \tau
adamc@533	878 }$$
adamc@533	879
adamc@573	880 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow e : \lambda [c_1 \sim c_2] \Rightarrow \tau}{
adamc@533	881 \Gamma \vdash c_1 :: \{\kappa\}
adamc@655	882 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@533	883 & \Gamma, c_1 \sim c_2 \vdash e : \tau
adamc@662	884 }
adamc@662	885 \quad \infer{\Gamma \vdash e \; ! : \tau}{
adamc@662	886 \Gamma \vdash e : [c_1 \sim c_2] \Rightarrow \tau
adamc@662	887 & \Gamma \vdash c_1 \sim c_2
adamc@533	888 }$$
adamc@533	889
adamc@534	890 \subsection{Pattern Typing}
adamc@534	891
adamc@534	892 $$\infer{\Gamma \vdash \_ \leadsto \Gamma; \tau}{}
adamc@534	893 \quad \infer{\Gamma \vdash x \leadsto \Gamma, x : \tau; \tau}{}
adamc@534	894 \quad \infer{\Gamma \vdash \ell \leadsto \Gamma; T(\ell)}{}$$
adamc@534	895
adamc@534	896 $$\infer{\Gamma \vdash X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534	897 X : \overline{x ::: \mt{Type}} \to \tau \in \Gamma
adamc@534	898 & \textrm{$\tau$ not a function type}
adamc@534	899 }
adamc@534	900 \quad \infer{\Gamma \vdash X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534	901 X : \overline{x ::: \mt{Type}} \to \tau'' \to \tau \in \Gamma
adamc@534	902 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534	903 }$$
adamc@534	904
adamc@534	905 $$\infer{\Gamma \vdash M.X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537	906 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	907 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau
adamc@534	908 & \textrm{$\tau$ not a function type}
adamc@534	909 }$$
adamc@534	910
adamc@534	911 $$\infer{\Gamma \vdash M.X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537	912 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	913 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau'' \to \tau
adamc@534	914 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534	915 }$$
adamc@534	916
adamc@534	917 $$\infer{\Gamma \vdash \{\overline{x = p}\} \leadsto \Gamma_n; \{\overline{x = \tau}\}}{
adamc@534	918 \Gamma_0 = \Gamma
adamc@534	919 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534	920 }
adamc@534	921 \quad \infer{\Gamma \vdash \{\overline{x = p}, \ldots\} \leadsto \Gamma_n; \$([\overline{x = \tau}] \rc c)}{
adamc@534	922 \Gamma_0 = \Gamma
adamc@534	923 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534	924 }$$
adamc@534	925
adamc@852	926 $$\infer{\Gamma \vdash p : \tau \leadsto \Gamma'; \tau}{
adamc@852	927 \Gamma \vdash p \leadsto \Gamma'; \tau'
adamc@852	928 & \Gamma \vdash \tau' \equiv \tau
adamc@852	929 }$$
adamc@852	930
adamc@535	931 \subsection{Declaration Typing}
adamc@535	932
adamc@535	933 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	934
adamc@655	935 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	936
adamc@558	937 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	938 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	939
adamc@535	940 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535	941 \quad \infer{\Gamma \vdash d, \overline{d} \leadsto \Gamma''}{
adamc@535	942 \Gamma \vdash d \leadsto \Gamma'
adamc@535	943 & \Gamma' \vdash \overline{d} \leadsto \Gamma''
adamc@535	944 }$$
adamc@535	945
adamc@535	946 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@535	947 \Gamma \vdash c :: \kappa
adamc@535	948 }
adamc@535	949 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@535	950 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@535	951 }$$
adamc@535	952
adamc@535	953 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537	954 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	955 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@535	956 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@535	957 }$$
adamc@535	958
adamc@535	959 $$\infer{\Gamma \vdash \mt{val} \; x : \tau = e \leadsto \Gamma, x : \tau}{
adamc@535	960 \Gamma \vdash e : \tau
adamc@535	961 }$$
adamc@535	962
adamc@535	963 $$\infer{\Gamma \vdash \mt{val} \; \mt{rec} \; \overline{x : \tau = e} \leadsto \Gamma, \overline{x : \tau}}{
adamc@535	964 \forall i: \Gamma, \overline{x : \tau} \vdash e_i : \tau_i
adamc@535	965 & \textrm{$e_i$ starts with an expression $\lambda$, optionally preceded by constructor and disjointness $\lambda$s}
adamc@535	966 }$$
adamc@535	967
adamc@535	968 $$\infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : S}{
adamc@535	969 \Gamma \vdash M : S
adamc@558	970 & \textrm{ $M$ not a constant or application}
adamc@535	971 }
adamc@558	972 \quad \infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : \mt{selfify}(X, \overline{s})}{
adamc@558	973 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@539	974 }$$
adamc@539	975
adamc@539	976 $$\infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@535	977 \Gamma \vdash S
adamc@535	978 }$$
adamc@535	979
adamc@537	980 $$\infer{\Gamma \vdash \mt{open} \; M \leadsto \Gamma, \mathcal O(M, \overline{s})}{
adamc@537	981 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535	982 }$$
adamc@535	983
adamc@535	984 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma}{
adamc@535	985 \Gamma \vdash c_1 :: \{\kappa\}
adamc@535	986 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@535	987 & \Gamma \vdash c_1 \sim c_2
adamc@535	988 }
adamc@537	989 \quad \infer{\Gamma \vdash \mt{open} \; \mt{constraints} \; M \leadsto \Gamma, \mathcal O_c(M, \overline{s})}{
adamc@537	990 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535	991 }$$
adamc@535	992
adamc@784	993 $$\infer{\Gamma \vdash \mt{table} \; x : c \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_table} \; c \; []}{
adamc@535	994 \Gamma \vdash c :: \{\mt{Type}\}
adamc@535	995 }
adam@1594	996 \quad \infer{\Gamma \vdash \mt{view} \; x = e \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_view} \; c}{
adam@1594	997 \Gamma \vdash e :: \mt{Basis}.\mt{sql\_query} \; [] \; [] \; (\mt{map} \; (\lambda \_ \Rightarrow []) \; c') \; c
adamc@784	998 }$$
adamc@784	999
adamc@784	1000 $$\infer{\Gamma \vdash \mt{sequence} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_sequence}}{}$$
adamc@535	1001
adamc@535	1002 $$\infer{\Gamma \vdash \mt{cookie} \; x : \tau \leadsto \Gamma, x : \mt{Basis}.\mt{http\_cookie} \; \tau}{
adamc@535	1003 \Gamma \vdash \tau :: \mt{Type}
adamc@784	1004 }
adamc@784	1005 \quad \infer{\Gamma \vdash \mt{style} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{css\_class}}{}$$
adamc@535	1006
adamc@1085	1007 $$\infer{\Gamma \vdash \mt{task} \; e_1 = e_2 \leadsto \Gamma}{
adam@1348	1008 \Gamma \vdash e_1 :: \mt{Basis}.\mt{task\_kind} \; \tau
adam@1348	1009 & \Gamma \vdash e_2 :: \tau \to \mt{Basis}.\mt{transaction} \; \{\}
adamc@1085	1010 }$$
adamc@1085	1011
adamc@784	1012 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784	1013 \Gamma \vdash c :: \kappa
adamc@535	1014 }$$
adamc@535	1015
adamc@535	1016 $$\infer{\overline{y}; x; \Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535	1017 \quad \infer{\overline{y}; x; \Gamma \vdash X \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to x \; \overline{y}}{
adamc@535	1018 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535	1019 }
adamc@535	1020 \quad \infer{\overline{y}; x; \Gamma \vdash X \; \mt{of} \; \tau \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to \tau \to x \; \overline{y}}{
adamc@535	1021 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535	1022 }$$
adamc@535	1023
adamc@537	1024 \subsection{Signature Item Typing}
adamc@537	1025
adamc@537	1026 We appeal to a signature item analogue of the $\mathcal O$ function from the last subsection.
adamc@537	1027
adamc@537	1028 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@537	1029 \quad \infer{\Gamma \vdash s, \overline{s} \leadsto \Gamma''}{
adamc@537	1030 \Gamma \vdash s \leadsto \Gamma'
adamc@537	1031 & \Gamma' \vdash \overline{s} \leadsto \Gamma''
adamc@537	1032 }$$
adamc@537	1033
adamc@537	1034 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}
adamc@537	1035 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@537	1036 \Gamma \vdash c :: \kappa
adamc@537	1037 }
adamc@537	1038 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@537	1039 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@537	1040 }$$
adamc@537	1041
adamc@537	1042 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537	1043 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1044 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537	1045 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@537	1046 }$$
adamc@537	1047
adamc@537	1048 $$\infer{\Gamma \vdash \mt{val} \; x : \tau \leadsto \Gamma, x : \tau}{
adamc@537	1049 \Gamma \vdash \tau :: \mt{Type}
adamc@537	1050 }$$
adamc@537	1051
adamc@537	1052 $$\infer{\Gamma \vdash \mt{structure} \; X : S \leadsto \Gamma, X : S}{
adamc@537	1053 \Gamma \vdash S
adamc@537	1054 }
adamc@537	1055 \quad \infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@537	1056 \Gamma \vdash S
adamc@537	1057 }$$
adamc@537	1058
adamc@537	1059 $$\infer{\Gamma \vdash \mt{include} \; S \leadsto \Gamma, \mathcal O(\overline{s})}{
adamc@537	1060 \Gamma \vdash S
adamc@537	1061 & \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1062 }$$
adamc@537	1063
adamc@537	1064 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma, c_1 \sim c_2}{
adamc@537	1065 \Gamma \vdash c_1 :: \{\kappa\}
adamc@537	1066 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@537	1067 }$$
adamc@537	1068
adamc@784	1069 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784	1070 \Gamma \vdash c :: \kappa
adamc@537	1071 }
adamc@784	1072 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}$$
adamc@537	1073
adamc@536	1074 \subsection{Signature Compatibility}
adamc@536	1075
adamc@558	1076 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	1077
adamc@537	1078 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	1079
adamc@536	1080 $$\infer{\Gamma \vdash S \equiv S}{}
adamc@536	1081 \quad \infer{\Gamma \vdash S_1 \equiv S_2}{
adamc@536	1082 \Gamma \vdash S_2 \equiv S_1
adamc@536	1083 }
adamc@536	1084 \quad \infer{\Gamma \vdash X \equiv S}{
adamc@536	1085 X = S \in \Gamma
adamc@536	1086 }
adamc@536	1087 \quad \infer{\Gamma \vdash M.X \equiv S}{
adamc@537	1088 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1089 & \mt{proj}(M, \overline{s}, \mt{signature} \; X) = S
adamc@536	1090 }$$
adamc@536	1091
adamc@536	1092 $$\infer{\Gamma \vdash S \; \mt{where} \; \mt{con} \; x = c \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa = c \; \overline{s_2} \; \mt{end}}{
adamc@536	1093 \Gamma \vdash S \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa \; \overline{s_2} \; \mt{end}
adamc@536	1094 & \Gamma \vdash c :: \kappa
adamc@537	1095 }
adamc@537	1096 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s^1} \; \mt{include} \; S \; \overline{s^2} \; \mt{end} \equiv \mt{sig} \; \overline{s^1} \; \overline{s} \; \overline{s^2} \; \mt{end}}{
adamc@537	1097 \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@536	1098 }$$
adamc@536	1099
adamc@536	1100 $$\infer{\Gamma \vdash S_1 \leq S_2}{
adamc@536	1101 \Gamma \vdash S_1 \equiv S_2
adamc@536	1102 }
adamc@536	1103 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \mt{end}}{}
adamc@537	1104 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; s' \; \overline{s'} \; \mt{end}}{
adamc@537	1105 \Gamma \vdash \overline{s} \leq s'
adamc@537	1106 & \Gamma \vdash s' \leadsto \Gamma'
adamc@537	1107 & \Gamma' \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \overline{s'} \; \mt{end}
adamc@537	1108 }$$
adamc@537	1109
adamc@537	1110 $$\infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537	1111 \Gamma \vdash s \leq s'
adamc@537	1112 }
adamc@537	1113 \quad \infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537	1114 \Gamma \vdash s \leadsto \Gamma'
adamc@537	1115 & \Gamma' \vdash \overline{s} \leq s'
adamc@536	1116 }$$
adamc@536	1117
adamc@536	1118 $$\infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 \leq \mt{functor} (X : S'_1) : S'_2}{
adamc@536	1119 \Gamma \vdash S'_1 \leq S_1
adamc@536	1120 & \Gamma, X : S'_1 \vdash S_2 \leq S'_2
adamc@536	1121 }$$
adamc@536	1122
adamc@537	1123 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@537	1124 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}
adamc@558	1125 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type}}{}$$
adamc@537	1126
adamc@537	1127 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(y)} \to \mt{Type}}{
adamc@537	1128 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1129 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537	1130 }$$
adamc@537	1131
adamc@784	1132 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@784	1133 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}$$
adamc@537	1134
adamc@537	1135 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \mt{\kappa} = c_2}{
adamc@537	1136 \Gamma \vdash c_1 \equiv c_2
adamc@537	1137 }
adamc@784	1138 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \kappa = c_2}{
adamc@537	1139 \Gamma \vdash c_1 \equiv c_2
adamc@537	1140 }$$
adamc@537	1141
adamc@537	1142 $$\infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537	1143 \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537	1144 }$$
adamc@537	1145
adamc@537	1146 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537	1147 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1148 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537	1149 & \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537	1150 }$$
adamc@537	1151
adamc@537	1152 $$\infer{\Gamma \vdash \cdot \leq \cdot}{}
adamc@537	1153 \quad \infer{\Gamma \vdash X; \overline{dc} \leq X; \overline{dc'}}{
adamc@537	1154 \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537	1155 }
adamc@537	1156 \quad \infer{\Gamma \vdash X \; \mt{of} \; \tau_1; \overline{dc} \leq X \; \mt{of} \; \tau_2; \overline{dc'}}{
adamc@537	1157 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537	1158 & \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537	1159 }$$
adamc@537	1160
adamc@537	1161 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x = \mt{datatype} \; M'.z'}{
adamc@537	1162 \Gamma \vdash M.z \equiv M'.z'
adamc@537	1163 }$$
adamc@537	1164
adamc@537	1165 $$\infer{\Gamma \vdash \mt{val} \; x : \tau_1 \leq \mt{val} \; x : \tau_2}{
adamc@537	1166 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537	1167 }
adamc@537	1168 \quad \infer{\Gamma \vdash \mt{structure} \; X : S_1 \leq \mt{structure} \; X : S_2}{
adamc@537	1169 \Gamma \vdash S_1 \leq S_2
adamc@537	1170 }
adamc@537	1171 \quad \infer{\Gamma \vdash \mt{signature} \; X = S_1 \leq \mt{signature} \; X = S_2}{
adamc@537	1172 \Gamma \vdash S_1 \leq S_2
adamc@537	1173 & \Gamma \vdash S_2 \leq S_1
adamc@537	1174 }$$
adamc@537	1175
adamc@537	1176 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leq \mt{constraint} \; c'_1 \sim c'_2}{
adamc@537	1177 \Gamma \vdash c_1 \equiv c'_1
adamc@537	1178 & \Gamma \vdash c_2 \equiv c'_2
adamc@537	1179 }$$
adamc@537	1180
adamc@655	1181 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{class} \; x :: \kappa}{}
adamc@655	1182 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{class} \; x :: \kappa}{}
adamc@655	1183 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{class} \; x :: \kappa = c_2}{
adamc@537	1184 \Gamma \vdash c_1 \equiv c_2
adamc@537	1185 }$$
adamc@537	1186
adamc@538	1187 \subsection{Module Typing}
adamc@538	1188
adamc@538	1189 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	1190
adamc@538	1191 $$\infer{\Gamma \vdash M : S}{
adamc@538	1192 \Gamma \vdash M : S'
adamc@538	1193 & \Gamma \vdash S' \leq S
adamc@538	1194 }
adamc@538	1195 \quad \infer{\Gamma \vdash \mt{struct} \; \overline{d} \; \mt{end} : \mt{sig} \; \mt{sigOf}(\overline{d}) \; \mt{end}}{
adamc@538	1196 \Gamma \vdash \overline{d} \leadsto \Gamma'
adamc@538	1197 }
adamc@538	1198 \quad \infer{\Gamma \vdash X : S}{
adamc@538	1199 X : S \in \Gamma
adamc@538	1200 }$$
adamc@538	1201
adamc@538	1202 $$\infer{\Gamma \vdash M.X : S}{
adamc@538	1203 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@538	1204 & \mt{proj}(M, \overline{s}, \mt{structure} \; X) = S
adamc@538	1205 }$$
adamc@538	1206
adamc@538	1207 $$\infer{\Gamma \vdash M_1(M_2) : [X \mapsto M_2]S_2}{
adamc@538	1208 \Gamma \vdash M_1 : \mt{functor}(X : S_1) : S_2
adamc@538	1209 & \Gamma \vdash M_2 : S_1
adamc@538	1210 }
adamc@538	1211 \quad \infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 = M : \mt{functor} (X : S_1) : S_2}{
adamc@538	1212 \Gamma \vdash S_1
adamc@538	1213 & \Gamma, X : S_1 \vdash S_2
adamc@538	1214 & \Gamma, X : S_1 \vdash M : S_2
adamc@538	1215 }$$
adamc@538	1216
adamc@538	1217 \begin{eqnarray*}
adamc@538	1218 \mt{sigOf}(\cdot) &=& \cdot \\
adamc@538	1219 \mt{sigOf}(s \; \overline{s'}) &=& \mt{sigOf}(s) \; \mt{sigOf}(\overline{s'}) \\
adamc@538	1220 \\
adamc@538	1221 \mt{sigOf}(\mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@538	1222 \mt{sigOf}(\mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \overline{dc} \\
adamc@538	1223 \mt{sigOf}(\mt{datatype} \; x = \mt{datatype} \; M.z) &=& \mt{datatype} \; x = \mt{datatype} \; M.z \\
adamc@538	1224 \mt{sigOf}(\mt{val} \; x : \tau = e) &=& \mt{val} \; x : \tau \\
adamc@538	1225 \mt{sigOf}(\mt{val} \; \mt{rec} \; \overline{x : \tau = e}) &=& \overline{\mt{val} \; x : \tau} \\
adamc@538	1226 \mt{sigOf}(\mt{structure} \; X : S = M) &=& \mt{structure} \; X : S \\
adamc@538	1227 \mt{sigOf}(\mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@538	1228 \mt{sigOf}(\mt{open} \; M) &=& \mt{include} \; S \textrm{ (where $\Gamma \vdash M : S$)} \\
adamc@538	1229 \mt{sigOf}(\mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@538	1230 \mt{sigOf}(\mt{open} \; \mt{constraints} \; M) &=& \cdot \\
adamc@538	1231 \mt{sigOf}(\mt{table} \; x : c) &=& \mt{table} \; x : c \\
adam@1594	1232 \mt{sigOf}(\mt{view} \; x = e) &=& \mt{view} \; x : c \textrm{ (where $\Gamma \vdash e : \mt{Basis}.\mt{sql\_query} \; [] \; [] \; (\mt{map} \; (\lambda \_ \Rightarrow []) \; c') \; c$)} \\
adamc@538	1233 \mt{sigOf}(\mt{sequence} \; x) &=& \mt{sequence} \; x \\
adamc@538	1234 \mt{sigOf}(\mt{cookie} \; x : \tau) &=& \mt{cookie} \; x : \tau \\
adamc@784	1235 \mt{sigOf}(\mt{style} \; x) &=& \mt{style} \; x \\
adamc@655	1236 \mt{sigOf}(\mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@538	1237 \end{eqnarray*}
adamc@539	1238 \begin{eqnarray*}
adamc@539	1239 \mt{selfify}(M, \cdot) &=& \cdot \\
adamc@558	1240 \mt{selfify}(M, s \; \overline{s'}) &=& \mt{selfify}(M, s) \; \mt{selfify}(M, \overline{s'}) \\
adamc@539	1241 \\
adamc@539	1242 \mt{selfify}(M, \mt{con} \; x :: \kappa) &=& \mt{con} \; x :: \kappa = M.x \\
adamc@539	1243 \mt{selfify}(M, \mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@539	1244 \mt{selfify}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \mt{datatype} \; M.x \\
adamc@539	1245 \mt{selfify}(M, \mt{datatype} \; x = \mt{datatype} \; M'.z) &=& \mt{datatype} \; x = \mt{datatype} \; M'.z \\
adamc@539	1246 \mt{selfify}(M, \mt{val} \; x : \tau) &=& \mt{val} \; x : \tau \\
adamc@539	1247 \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	1248 \mt{selfify}(M, \mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@539	1249 \mt{selfify}(M, \mt{include} \; S) &=& \mt{include} \; S \\
adamc@539	1250 \mt{selfify}(M, \mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@655	1251 \mt{selfify}(M, \mt{class} \; x :: \kappa) &=& \mt{class} \; x :: \kappa = M.x \\
adamc@655	1252 \mt{selfify}(M, \mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@539	1253 \end{eqnarray*}
adamc@539	1254
adamc@540	1255 \subsection{Module Projection}
adamc@540	1256
adamc@540	1257 \begin{eqnarray*}
adamc@540	1258 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \\
adamc@540	1259 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa, c) \\
adamc@540	1260 \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	1261 \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	1262 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})$)} \\
adamc@655	1263 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \to \mt{Type} \\
adamc@655	1264 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa \to \mt{Type}, c) \\
adamc@540	1265 \\
adamc@540	1266 \mt{proj}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc} \; \overline{s}, \mt{datatype} \; x) &=& (\overline{y}, \overline{dc}) \\
adamc@540	1267 \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	1268 \\
adamc@540	1269 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, \mt{val} \; x) &=& \tau \\
adamc@540	1270 \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	1271 \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	1272 \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	1273 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \in \overline{dc}$)} \\
adamc@540	1274 \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	1275 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \; \mt{of} \; \tau \in \overline{dc}$)} \\
adamc@540	1276 \\
adamc@540	1277 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, \mt{structure} \; X) &=& S \\
adamc@540	1278 \\
adamc@540	1279 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, \mt{signature} \; X) &=& S \\
adamc@540	1280 \\
adamc@540	1281 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1282 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1283 \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	1284 \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	1285 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@540	1286 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1287 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1288 \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	1289 \mt{proj}(M, \mt{constraint} \; c_1 \sim c_2 \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@655	1290 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@655	1291 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1292 \end{eqnarray*}
adamc@540	1293
adamc@541	1294
adamc@541	1295 \section{Type Inference}
adamc@541	1296
adamc@541	1297 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	1298
adamc@541	1299 \subsection{Basic Unification}
adamc@541	1300
adamc@560	1301 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	1302
adamc@656	1303 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	1304
adamc@541	1305 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	1306
adamc@541	1307 \subsection{Unifying Record Types}
adamc@541	1308
adamc@570	1309 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	1310
adamc@656	1311 \subsection{\label{typeclasses}Constructor Classes}
adamc@541	1312
adamc@784	1313 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	1314
adamc@784	1315 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	1316
adamc@656	1317 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	1318
adamc@656	1319 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	1320
adamc@541	1321 \subsection{Reverse-Engineering Record Types}
adamc@541	1322
adamc@656	1323 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	1324
adamc@541	1325 \subsection{Implicit Arguments in Functor Applications}
adamc@541	1326
adamc@656	1327 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	1328
adamc@541	1329
adamc@542	1330 \section{The Ur Standard Library}
adamc@542	1331
adamc@542	1332 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	1333
adamc@542	1334 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	1335
adamc@542	1336 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	1337 $$\begin{array}{l}
adamc@542	1338 \mt{type} \; \mt{int} \\
adamc@542	1339 \mt{type} \; \mt{float} \\
adamc@873	1340 \mt{type} \; \mt{char} \\
adamc@542	1341 \mt{type} \; \mt{string} \\
adamc@542	1342 \mt{type} \; \mt{time} \\
adamc@785	1343 \mt{type} \; \mt{blob} \\
adamc@542	1344 \\
adamc@542	1345 \mt{type} \; \mt{unit} = \{\} \\
adamc@542	1346 \\
adamc@542	1347 \mt{datatype} \; \mt{bool} = \mt{False} \mid \mt{True} \\
adamc@542	1348 \\
adamc@785	1349 \mt{datatype} \; \mt{option} \; \mt{t} = \mt{None} \mid \mt{Some} \; \mt{of} \; \mt{t} \\
adamc@785	1350 \\
adamc@785	1351 \mt{datatype} \; \mt{list} \; \mt{t} = \mt{Nil} \mid \mt{Cons} \; \mt{of} \; \mt{t} \times \mt{list} \; \mt{t}
adamc@542	1352 \end{array}$$
adamc@542	1353
adamc@1123	1354 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	1355
adam@1297	1356 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	1357 $$\begin{array}{l}
adam@1297	1358 \mt{con} \; \mt{variant} :: \{\mt{Type}\} \to \mt{Type} \\
adam@1297	1359 \mt{val} \; \mt{make} : \mt{nm} :: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{ts} ::: \{\mt{Type}\} \to [[\mt{nm}] \sim \mt{ts}] \Rightarrow \mt{t} \to \mt{variant} \; ([\mt{nm} = \mt{t}] \rc \mt{ts}) \\
adam@1297	1360 \mt{val} \; \mt{match} : \mt{ts} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{variant} \; \mt{ts} \to \$(\mt{map} \; (\lambda \mt{t'} \Rightarrow \mt{t'} \to \mt{t}) \; \mt{ts}) \to \mt{t}
adam@1297	1361 \end{array}$$
adam@1297	1362
adamc@657	1363 Another important generic Ur element comes at the beginning of \texttt{top.urs}.
adamc@657	1364
adamc@657	1365 $$\begin{array}{l}
adamc@657	1366 \mt{con} \; \mt{folder} :: \mt{K} \longrightarrow \{\mt{K}\} \to \mt{Type} \\
adamc@657	1367 \\
adamc@657	1368 \mt{val} \; \mt{fold} : \mt{K} \longrightarrow \mt{tf} :: (\{\mt{K}\} \to \mt{Type}) \\
adamc@657	1369 \hspace{.1in} \to (\mt{nm} :: \mt{Name} \to \mt{v} :: \mt{K} \to \mt{r} :: \{\mt{K}\} \to [[\mt{nm}] \sim \mt{r}] \Rightarrow \\
adamc@657	1370 \hspace{.2in} \mt{tf} \; \mt{r} \to \mt{tf} \; ([\mt{nm} = \mt{v}] \rc \mt{r})) \\
adamc@657	1371 \hspace{.1in} \to \mt{tf} \; [] \\
adamc@657	1372 \hspace{.1in} \to \mt{r} :: \{\mt{K}\} \to \mt{folder} \; \mt{r} \to \mt{tf} \; \mt{r}
adamc@657	1373 \end{array}$$
adamc@657	1374
adamc@657	1375 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	1376
adamc@664	1377 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	1378
adamc@542	1379
adamc@542	1380 \section{The Ur/Web Standard Library}
adamc@542	1381
adam@1400	1382 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	1383
adamc@658	1384 \subsection{Monads}
adamc@658	1385
adamc@658	1386 The Ur Basis defines the monad constructor class from Haskell.
adamc@658	1387
adamc@658	1388 $$\begin{array}{l}
adamc@658	1389 \mt{class} \; \mt{monad} :: \mt{Type} \to \mt{Type} \\
adamc@658	1390 \mt{val} \; \mt{return} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t} ::: \mt{Type} \\
adamc@658	1391 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658	1392 \hspace{.1in} \to \mt{t} \to \mt{m} \; \mt{t} \\
adamc@658	1393 \mt{val} \; \mt{bind} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t1} ::: \mt{Type} \to \mt{t2} ::: \mt{Type} \\
adamc@658	1394 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658	1395 \hspace{.1in} \to \mt{m} \; \mt{t1} \to (\mt{t1} \to \mt{m} \; \mt{t2}) \\
adam@1544	1396 \hspace{.1in} \to \mt{m} \; \mt{t2} \\
adam@1544	1397 \mt{val} \; \mt{mkMonad} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \\
adam@1544	1398 \hspace{.1in} \to \{\mt{Return} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{m} \; \mt{t}, \\
adam@1544	1399 \hspace{.3in} \mt{Bind} : \mt{t1} ::: \mt{Type} \to \mt{t2} ::: \mt{Type} \to \mt{m} \; \mt{t1} \to (\mt{t1} \to \mt{m} \; \mt{t2}) \to \mt{m} \; \mt{t2}\} \\
adam@1544	1400 \hspace{.1in} \to \mt{monad} \; \mt{m}
adamc@658	1401 \end{array}$$
adamc@658	1402
adam@1687	1403 The Ur/Web compiler provides syntactic sugar for monads, similar to Haskell's \cd{do} notation. An expression $x \leftarrow e_1; e_2$ is desugared to $\mt{bind} \; e_1 \; (\lambda x \Rightarrow e_2)$, and an expression $e_1; e_2$ is desugared to $\mt{bind} \; e_1 \; (\lambda () \Rightarrow e_2)$. Note a difference from Haskell: as the $e_1; e_2$ case desugaring involves a function with $()$ as its formal argument, the type of $e_1$ must be of the form $m \; \{\}$, rather than some arbitrary $m \; t$.
adam@1548	1404
adamc@542	1405 \subsection{Transactions}
adamc@542	1406
adamc@542	1407 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	1408 $$\begin{array}{l}
adamc@542	1409 \mt{con} \; \mt{transaction} :: \mt{Type} \to \mt{Type} \\
adamc@658	1410 \mt{val} \; \mt{transaction\_monad} : \mt{monad} \; \mt{transaction}
adamc@542	1411 \end{array}$$
adamc@542	1412
adamc@1123	1413 For debugging purposes, a transactional function is provided for outputting a string on the server process' \texttt{stderr}.
adamc@1123	1414 $$\begin{array}{l}
adamc@1123	1415 \mt{val} \; \mt{debug} : \mt{string} \to \mt{transaction} \; \mt{unit}
adamc@1123	1416 \end{array}$$
adamc@1123	1417
adamc@542	1418 \subsection{HTTP}
adamc@542	1419
adam@1400	1420 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	1421 $$\begin{array}{l}
adamc@786	1422 \mt{con} \; \mt{http\_cookie} :: \mt{Type} \to \mt{Type} \\
adamc@786	1423 \mt{val} \; \mt{getCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; (\mt{option} \; \mt{t}) \\
adamc@1050	1424 \mt{val} \; \mt{setCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \{\mt{Value} : \mt{t}, \mt{Expires} : \mt{option} \; \mt{time}, \mt{Secure} : \mt{bool}\} \to \mt{transaction} \; \mt{unit} \\
adamc@1050	1425 \mt{val} \; \mt{clearCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; \mt{unit}
adamc@786	1426 \end{array}$$
adamc@786	1427
adamc@786	1428 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	1429 $$\begin{array}{l}
adamc@786	1430 \mt{type} \; \mt{url} \\
adamc@786	1431 \mt{val} \; \mt{bless} : \mt{string} \to \mt{url} \\
adamc@786	1432 \mt{val} \; \mt{checkUrl} : \mt{string} \to \mt{option} \; \mt{url}
adamc@786	1433 \end{array}$$
adamc@786	1434 $\mt{bless}$ raises a runtime error if the string passed to it fails the URL policy.
adamc@786	1435
adam@1400	1436 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	1437 $$\begin{array}{l}
adamc@1085	1438 \mt{val} \; \mt{currentUrl} : \mt{transaction} \; \mt{url} \\
adamc@1085	1439 \mt{val} \; \mt{url} : \mt{transaction} \; \mt{page} \to \mt{url}
adamc@1085	1440 \end{array}$$
adamc@1085	1441
adamc@1085	1442 Page generation may be interrupted at any time with a request to redirect to a particular URL instead.
adamc@1085	1443 $$\begin{array}{l}
adamc@1085	1444 \mt{val} \; \mt{redirect} : \mt{t} ::: \mt{Type} \to \mt{url} \to \mt{transaction} \; \mt{t}
adamc@1085	1445 \end{array}$$
adamc@1085	1446
adam@1400	1447 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	1448 $$\begin{array}{l}
adamc@786	1449 \mt{type} \; \mt{file} \\
adamc@786	1450 \mt{val} \; \mt{fileName} : \mt{file} \to \mt{option} \; \mt{string} \\
adamc@786	1451 \mt{val} \; \mt{fileMimeType} : \mt{file} \to \mt{string} \\
adamc@786	1452 \mt{val} \; \mt{fileData} : \mt{file} \to \mt{blob}
adamc@786	1453 \end{array}$$
adamc@786	1454
adam@1465	1455 It is also possible to get HTTP request headers and set HTTP response headers, using abstract types similar to the one for URLs.
adam@1465	1456
adam@1465	1457 $$\begin{array}{l}
adam@1465	1458 \mt{type} \; \mt{requestHeader} \\
adam@1465	1459 \mt{val} \; \mt{blessRequestHeader} : \mt{string} \to \mt{requestHeader} \\
adam@1465	1460 \mt{val} \; \mt{checkRequestHeader} : \mt{string} \to \mt{option} \; \mt{requestHeader} \\
adam@1465	1461 \mt{val} \; \mt{getHeader} : \mt{requestHeader} \to \mt{transaction} \; (\mt{option} \; \mt{string}) \\
adam@1465	1462 \\
adam@1465	1463 \mt{type} \; \mt{responseHeader} \\
adam@1465	1464 \mt{val} \; \mt{blessResponseHeader} : \mt{string} \to \mt{responseHeader} \\
adam@1465	1465 \mt{val} \; \mt{checkResponseHeader} : \mt{string} \to \mt{option} \; \mt{responseHeader} \\
adam@1465	1466 \mt{val} \; \mt{setHeader} : \mt{responseHeader} \to \mt{string} \to \mt{transaction} \; \mt{unit}
adam@1465	1467 \end{array}$$
adam@1465	1468
adamc@786	1469 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	1470 $$\begin{array}{l}
adamc@786	1471 \mt{type} \; \mt{mimeType} \\
adamc@786	1472 \mt{val} \; \mt{blessMime} : \mt{string} \to \mt{mimeType} \\
adamc@786	1473 \mt{val} \; \mt{checkMime} : \mt{string} \to \mt{option} \; \mt{mimeType} \\
adamc@786	1474 \mt{val} \; \mt{returnBlob} : \mt{t} ::: \mt{Type} \to \mt{blob} \to \mt{mimeType} \to \mt{transaction} \; \mt{t}
adamc@542	1475 \end{array}$$
adamc@542	1476
adamc@543	1477 \subsection{SQL}
adamc@543	1478
adam@1400	1479 Everything about SQL database access is restricted to server-side code.
adam@1400	1480
adamc@543	1481 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	1482 $$\begin{array}{l}
adamc@785	1483 \mt{con} \; \mt{sql\_table} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785	1484 \end{array}$$
adamc@785	1485 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	1486
adamc@785	1487 We also have the simpler type family of SQL views, which have no keys.
adamc@785	1488 $$\begin{array}{l}
adamc@785	1489 \mt{con} \; \mt{sql\_view} :: \{\mt{Type}\} \to \mt{Type}
adamc@543	1490 \end{array}$$
adamc@543	1491
adamc@785	1492 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	1493 $$\begin{array}{l}
adamc@785	1494 \mt{class} \; \mt{fieldsOf} :: \mt{Type} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785	1495 \mt{val} \; \mt{fieldsOf\_table} : \mt{fs} ::: \{\mt{Type}\} \to \mt{keys} ::: \{\{\mt{Unit}\}\} \to \mt{fieldsOf} \; (\mt{sql\_table} \; \mt{fs} \; \mt{keys}) \; \mt{fs} \\
adamc@785	1496 \mt{val} \; \mt{fieldsOf\_view} : \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; (\mt{sql\_view} \; \mt{fs}) \; \mt{fs}
adamc@785	1497 \end{array}$$
adamc@785	1498
adamc@785	1499 \subsubsection{Table Constraints}
adamc@785	1500
adamc@785	1501 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	1502
adamc@785	1503 $$\begin{array}{l}
adamc@785	1504 \mt{con} \; \mt{primary\_key} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type} \\
adamc@785	1505 \mt{val} \; \mt{no\_primary\_key} : \mt{fs} ::: \{\mt{Type}\} \to \mt{primary\_key} \; \mt{fs} \; [] \\
adamc@785	1506 \mt{val} \; \mt{primary\_key} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{key1} :: \mt{Name} \to \mt{keys} :: \{\mt{Type}\} \\
adamc@785	1507 \hspace{.1in} \to [[\mt{key1}] \sim \mt{keys}] \Rightarrow [[\mt{key1} = \mt{t}] \rc \mt{keys} \sim \mt{rest}] \\
adamc@785	1508 \hspace{.1in} \Rightarrow \$([\mt{key1} = \mt{sql\_injectable\_prim} \; \mt{t}] \rc \mt{map} \; \mt{sql\_injectable\_prim} \; \mt{keys}) \\
adamc@785	1509 \hspace{.1in} \to \mt{primary\_key} \; ([\mt{key1} = \mt{t}] \rc \mt{keys} \rc \mt{rest}) \; [\mt{Pkey} = [\mt{key1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{keys}]
adamc@785	1510 \end{array}$$
adamc@785	1511 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	1512
adamc@785	1513 A type family stands for sets of named constraints of the remaining varieties.
adamc@785	1514 $$\begin{array}{l}
adamc@785	1515 \mt{con} \; \mt{sql\_constraints} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785	1516 \end{array}$$
adamc@785	1517 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	1518
adamc@785	1519 There is a type family of individual, unnamed constraints.
adamc@785	1520 $$\begin{array}{l}
adamc@785	1521 \mt{con} \; \mt{sql\_constraint} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \mt{Type}
adamc@785	1522 \end{array}$$
adamc@785	1523 The first argument is the same as above, and the second argument gives the key columns for just this constraint.
adamc@785	1524
adamc@785	1525 We have operations for assembling constraints into constraint sets.
adamc@785	1526 $$\begin{array}{l}
adamc@785	1527 \mt{val} \; \mt{no\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_constraints} \; \mt{fs} \; [] \\
adamc@785	1528 \mt{val} \; \mt{one\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{unique} ::: \{\mt{Unit}\} \to \mt{name} :: \mt{Name} \\
adamc@785	1529 \hspace{.1in} \to \mt{sql\_constraint} \; \mt{fs} \; \mt{unique} \to \mt{sql\_constraints} \; \mt{fs} \; [\mt{name} = \mt{unique}] \\
adamc@785	1530 \mt{val} \; \mt{join\_constraints} : \mt{fs} ::: \{\mt{Type}\} \to \mt{uniques1} ::: \{\{\mt{Unit}\}\} \to \mt{uniques2} ::: \{\{\mt{Unit}\}\} \to [\mt{uniques1} \sim \mt{uniques2}] \\
adamc@785	1531 \hspace{.1in} \Rightarrow \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques1} \to \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques2} \to \mt{sql\_constraints} \; \mt{fs} \; (\mt{uniques1} \rc \mt{uniques2})
adamc@785	1532 \end{array}$$
adamc@785	1533
adamc@785	1534 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	1535 $$\begin{array}{l}
adamc@785	1536 \mt{val} \; \mt{unique} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{unique1} :: \mt{Name} \to \mt{unique} :: \{\mt{Type}\} \\
adamc@785	1537 \hspace{.1in} \to [[\mt{unique1}] \sim \mt{unique}] \Rightarrow [[\mt{unique1} = \mt{t}] \rc \mt{unique} \sim \mt{rest}] \\
adamc@785	1538 \hspace{.1in} \Rightarrow \mt{sql\_constraint} \; ([\mt{unique1} = \mt{t}] \rc \mt{unique} \rc \mt{rest}) \; ([\mt{unique1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{unique})
adamc@785	1539 \end{array}$$
adamc@785	1540
adamc@785	1541 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	1542 $$\begin{array}{l}
adamc@785	1543 \mt{class} \; \mt{linkable} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@785	1544 \mt{val} \; \mt{linkable\_same} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; \mt{t} \\
adamc@785	1545 \mt{val} \; \mt{linkable\_from\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; (\mt{option} \; \mt{t}) \; \mt{t} \\
adamc@785	1546 \mt{val} \; \mt{linkable\_to\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@785	1547 \end{array}$$
adamc@785	1548
adamc@785	1549 The $\mt{matching}$ type family uses $\mt{linkable}$ to define when two keys match up type-wise.
adamc@785	1550 $$\begin{array}{l}
adamc@785	1551 \mt{con} \; \mt{matching} :: \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785	1552 \mt{val} \; \mt{mat\_nil} : \mt{matching} \; [] \; [] \\
adamc@785	1553 \mt{val} \; \mt{mat\_cons} : \mt{t1} ::: \mt{Type} \to \mt{rest1} ::: \{\mt{Type}\} \to \mt{t2} ::: \mt{Type} \to \mt{rest2} ::: \{\mt{Type}\} \to \mt{nm1} :: \mt{Name} \to \mt{nm2} :: \mt{Name} \\
adamc@785	1554 \hspace{.1in} \to [[\mt{nm1}] \sim \mt{rest1}] \Rightarrow [[\mt{nm2}] \sim \mt{rest2}] \Rightarrow \mt{linkable} \; \mt{t1} \; \mt{t2} \to \mt{matching} \; \mt{rest1} \; \mt{rest2} \\
adamc@785	1555 \hspace{.1in} \to \mt{matching} \; ([\mt{nm1} = \mt{t1}] \rc \mt{rest1}) \; ([\mt{nm2} = \mt{t2}] \rc \mt{rest2})
adamc@785	1556 \end{array}$$
adamc@785	1557
adamc@785	1558 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	1559 $$\begin{array}{l}
adamc@785	1560 \mt{con} \; \mt{propagation\_mode} :: \{\mt{Type}\} \to \mt{Type} \\
adamc@785	1561 \mt{val} \; \mt{restrict} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785	1562 \mt{val} \; \mt{cascade} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785	1563 \mt{val} \; \mt{no\_action} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785	1564 \mt{val} \; \mt{set\_null} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; (\mt{map} \; \mt{option} \; \mt{fs})
adamc@785	1565 \end{array}$$
adamc@785	1566
adamc@785	1567 Finally, we put these ingredient together to define the \texttt{FOREIGN KEY} constraint function.
adamc@785	1568 $$\begin{array}{l}
adamc@785	1569 \mt{val} \; \mt{foreign\_key} : \mt{mine1} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{mine} ::: \{\mt{Type}\} \to \mt{munused} ::: \{\mt{Type}\} \to \mt{foreign} ::: \{\mt{Type}\} \\
adamc@785	1570 \hspace{.1in} \to \mt{funused} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{uniques} ::: \{\{\mt{Unit}\}\} \\
adamc@785	1571 \hspace{.1in} \to [[\mt{mine1}] \sim \mt{mine}] \Rightarrow [[\mt{mine1} = \mt{t}] \rc \mt{mine} \sim \mt{munused}] \Rightarrow [\mt{foreign} \sim \mt{funused}] \Rightarrow [[\mt{nm}] \sim \mt{uniques}] \\
adamc@785	1572 \hspace{.1in} \Rightarrow \mt{matching} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}) \; \mt{foreign} \\
adamc@785	1573 \hspace{.1in} \to \mt{sql\_table} \; (\mt{foreign} \rc \mt{funused}) \; ([\mt{nm} = \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{foreign}] \rc \mt{uniques}) \\
adamc@785	1574 \hspace{.1in} \to \{\mt{OnDelete} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}), \\
adamc@785	1575 \hspace{.2in} \mt{OnUpdate} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine})\} \\
adamc@785	1576 \hspace{.1in} \to \mt{sql\_constraint} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine} \rc \mt{munused}) \; []
adamc@785	1577 \end{array}$$
adamc@785	1578
adamc@785	1579 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	1580 $$\begin{array}{l}
adamc@785	1581 \mt{val} \; \mt{check} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; [] \; [] \; \mt{fs} \; \mt{bool} \to \mt{sql\_constraint} \; \mt{fs} \; []
adamc@785	1582 \end{array}$$
adamc@785	1583
adamc@785	1584 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	1585
adamc@784	1586
adamc@543	1587 \subsubsection{Queries}
adamc@543	1588
adam@1400	1589 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	1590 $$\begin{array}{l}
adam@1400	1591 \mt{con} \; \mt{sql\_query} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@1193	1592 \mt{val} \; \mt{sql\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400	1593 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adamc@1193	1594 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543	1595 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543	1596 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1193	1597 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adam@1400	1598 \hspace{.1in} \Rightarrow \{\mt{Rows} : \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}, \\
adamc@1193	1599 \hspace{.2in} \mt{OrderBy} : \mt{sql\_order\_by} \; (\mt{free} \rc \mt{tables}) \; \mt{selectedExps}, \\
adamc@543	1600 \hspace{.2in} \mt{Limit} : \mt{sql\_limit}, \\
adamc@543	1601 \hspace{.2in} \mt{Offset} : \mt{sql\_offset}\} \\
adam@1400	1602 \hspace{.1in} \to \mt{sql\_query} \; \mt{free} \; \mt{afree} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543	1603 \end{array}$$
adamc@543	1604
adamc@545	1605 Queries are used by folding over their results inside transactions.
adamc@545	1606 $$\begin{array}{l}
adam@1400	1607 \mt{val} \; \mt{query} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to [\mt{tables} \sim \mt{exps}] \Rightarrow \mt{state} ::: \mt{Type} \to \mt{sql\_query} \; [] \; [] \; \mt{tables} \; \mt{exps} \\
adamc@658	1608 \hspace{.1in} \to (\$(\mt{exps} \rc \mt{map} \; (\lambda \mt{fields} :: \{\mt{Type}\} \Rightarrow \$\mt{fields}) \; \mt{tables}) \\
adamc@545	1609 \hspace{.2in} \to \mt{state} \to \mt{transaction} \; \mt{state}) \\
adamc@545	1610 \hspace{.1in} \to \mt{state} \to \mt{transaction} \; \mt{state}
adamc@545	1611 \end{array}$$
adamc@545	1612
adam@1400	1613 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	1614 $$\begin{array}{l}
adam@1400	1615 \mt{con} \; \mt{sql\_query1} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@543	1616 \\
adamc@543	1617 \mt{type} \; \mt{sql\_relop} \\
adamc@543	1618 \mt{val} \; \mt{sql\_union} : \mt{sql\_relop} \\
adamc@543	1619 \mt{val} \; \mt{sql\_intersect} : \mt{sql\_relop} \\
adamc@543	1620 \mt{val} \; \mt{sql\_except} : \mt{sql\_relop} \\
adam@1400	1621 \mt{val} \; \mt{sql\_relop} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400	1622 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adam@1400	1623 \hspace{.1in} \to \mt{tables1} ::: \{\{\mt{Type}\}\} \\
adamc@543	1624 \hspace{.1in} \to \mt{tables2} ::: \{\{\mt{Type}\}\} \\
adamc@543	1625 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543	1626 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@543	1627 \hspace{.1in} \to \mt{sql\_relop} \\
adam@1458	1628 \hspace{.1in} \to \mt{bool} \; (* \; \mt{ALL} \; *) \\
adam@1400	1629 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables1} \; \mt{selectedFields} \; \mt{selectedExps} \\
adam@1400	1630 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables2} \; \mt{selectedFields} \; \mt{selectedExps} \\
adam@1400	1631 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{selectedFields} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543	1632 \end{array}$$
adamc@543	1633
adamc@543	1634 $$\begin{array}{l}
adamc@1193	1635 \mt{val} \; \mt{sql\_query1} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400	1636 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adamc@1193	1637 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543	1638 \hspace{.1in} \to \mt{grouped} ::: \{\{\mt{Type}\}\} \\
adamc@543	1639 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543	1640 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1085	1641 \hspace{.1in} \to \mt{empties} :: \{\mt{Unit}\} \\
adamc@1193	1642 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adamc@1193	1643 \hspace{.1in} \Rightarrow [\mt{free} \sim \mt{grouped}] \\
adam@1400	1644 \hspace{.1in} \Rightarrow [\mt{afree} \sim \mt{tables}] \\
adamc@1193	1645 \hspace{.1in} \Rightarrow [\mt{empties} \sim \mt{selectedFields}] \\
adamc@1085	1646 \hspace{.1in} \Rightarrow \{\mt{Distinct} : \mt{bool}, \\
adamc@1193	1647 \hspace{.2in} \mt{From} : \mt{sql\_from\_items} \; \mt{free} \; \mt{tables}, \\
adam@1400	1648 \hspace{.2in} \mt{Where} : \mt{sql\_exp} \; (\mt{free} \rc \mt{tables}) \; \mt{afree} \; [] \; \mt{bool}, \\
adamc@543	1649 \hspace{.2in} \mt{GroupBy} : \mt{sql\_subset} \; \mt{tables} \; \mt{grouped}, \\
adam@1400	1650 \hspace{.2in} \mt{Having} : \mt{sql\_exp} \; (\mt{free} \rc \mt{grouped}) \; (\mt{afree} \rc \mt{tables}) \; [] \; \mt{bool}, \\
adamc@1085	1651 \hspace{.2in} \mt{SelectFields} : \mt{sql\_subset} \; \mt{grouped} \; (\mt{map} \; (\lambda \_ \Rightarrow []) \; \mt{empties} \rc \mt{selectedFields}), \\
adam@1400	1652 \hspace{.2in} \mt {SelectExps} : \$(\mt{map} \; (\mt{sql\_exp} \; (\mt{free} \rc \mt{grouped}) \; (\mt{afree} \rc \mt{tables}) \; []) \; \mt{selectedExps}) \} \\
adam@1400	1653 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543	1654 \end{array}$$
adamc@543	1655
adamc@543	1656 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	1657 $$\begin{array}{l}
adamc@543	1658 \mt{con} \; \mt{sql\_subset} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@543	1659 \mt{val} \; \mt{sql\_subset} : \mt{keep\_drop} :: \{(\{\mt{Type}\} \times \{\mt{Type}\})\} \\
adamc@543	1660 \hspace{.1in} \to \mt{sql\_subset} \\
adamc@658	1661 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1 \rc \mt{fields}.2)\; \mt{keep\_drop}) \\
adamc@658	1662 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1) \; \mt{keep\_drop}) \\
adamc@543	1663 \mt{val} \; \mt{sql\_subset\_all} : \mt{tables} :: \{\{\mt{Type}\}\} \to \mt{sql\_subset} \; \mt{tables} \; \mt{tables}
adamc@543	1664 \end{array}$$
adamc@543	1665
adamc@560	1666 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	1667 $$\begin{array}{l}
adamc@543	1668 \mt{con} \; \mt{sql\_exp} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}
adamc@543	1669 \end{array}$$
adamc@543	1670
adamc@543	1671 Any field in scope may be converted to an expression.
adamc@543	1672 $$\begin{array}{l}
adamc@543	1673 \mt{val} \; \mt{sql\_field} : \mt{otherTabs} ::: \{\{\mt{Type}\}\} \to \mt{otherFields} ::: \{\mt{Type}\} \\
adamc@543	1674 \hspace{.1in} \to \mt{fieldType} ::: \mt{Type} \to \mt{agg} ::: \{\{\mt{Type}\}\} \\
adamc@543	1675 \hspace{.1in} \to \mt{exps} ::: \{\mt{Type}\} \\
adamc@543	1676 \hspace{.1in} \to \mt{tab} :: \mt{Name} \to \mt{field} :: \mt{Name} \\
adamc@543	1677 \hspace{.1in} \to \mt{sql\_exp} \; ([\mt{tab} = [\mt{field} = \mt{fieldType}] \rc \mt{otherFields}] \rc \mt{otherTabs}) \; \mt{agg} \; \mt{exps} \; \mt{fieldType}
adamc@543	1678 \end{array}$$
adamc@543	1679
adamc@544	1680 There is an analogous function for referencing named expressions.
adamc@544	1681 $$\begin{array}{l}
adamc@544	1682 \mt{val} \; \mt{sql\_exp} : \mt{tabs} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{t} ::: \mt{Type} \to \mt{rest} ::: \{\mt{Type}\} \to \mt{nm} :: \mt{Name} \\
adamc@544	1683 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tabs} \; \mt{agg} \; ([\mt{nm} = \mt{t}] \rc \mt{rest}) \; \mt{t}
adamc@544	1684 \end{array}$$
adamc@544	1685
adamc@544	1686 Ur values of appropriate types may be injected into SQL expressions.
adamc@544	1687 $$\begin{array}{l}
adamc@786	1688 \mt{class} \; \mt{sql\_injectable\_prim} \\
adamc@786	1689 \mt{val} \; \mt{sql\_bool} : \mt{sql\_injectable\_prim} \; \mt{bool} \\
adamc@786	1690 \mt{val} \; \mt{sql\_int} : \mt{sql\_injectable\_prim} \; \mt{int} \\
adamc@786	1691 \mt{val} \; \mt{sql\_float} : \mt{sql\_injectable\_prim} \; \mt{float} \\
adamc@786	1692 \mt{val} \; \mt{sql\_string} : \mt{sql\_injectable\_prim} \; \mt{string} \\
adamc@786	1693 \mt{val} \; \mt{sql\_time} : \mt{sql\_injectable\_prim} \; \mt{time} \\
adamc@786	1694 \mt{val} \; \mt{sql\_blob} : \mt{sql\_injectable\_prim} \; \mt{blob} \\
adamc@786	1695 \mt{val} \; \mt{sql\_channel} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{channel} \; \mt{t}) \\
adamc@786	1696 \mt{val} \; \mt{sql\_client} : \mt{sql\_injectable\_prim} \; \mt{client} \\
adamc@786	1697 \\
adamc@544	1698 \mt{class} \; \mt{sql\_injectable} \\
adamc@786	1699 \mt{val} \; \mt{sql\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@786	1700 \mt{val} \; \mt{sql\_option\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; (\mt{option} \; \mt{t}) \\
adamc@786	1701 \\
adamc@544	1702 \mt{val} \; \mt{sql\_inject} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@544	1703 \hspace{.1in} \to \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adamc@544	1704 \end{array}$$
adamc@544	1705
adamc@1123	1706 Additionally, most function-free types may be injected safely, via the $\mt{serialized}$ type family.
adamc@1123	1707 $$\begin{array}{l}
adamc@1123	1708 \mt{con} \; \mt{serialized} :: \mt{Type} \to \mt{Type} \\
adamc@1123	1709 \mt{val} \; \mt{serialize} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{serialized} \; \mt{t} \\
adamc@1123	1710 \mt{val} \; \mt{deserialize} : \mt{t} ::: \mt{Type} \to \mt{serialized} \; \mt{t} \to \mt{t} \\
adamc@1123	1711 \mt{val} \; \mt{sql\_serialized} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{serialized} \; \mt{t})
adamc@1123	1712 \end{array}$$
adamc@1123	1713
adamc@544	1714 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	1715 $$\begin{array}{l}
adamc@544	1716 \mt{val} \; \mt{sql\_is\_null} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544	1717 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; (\mt{option} \; \mt{t}) \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{bool}
adamc@544	1718 \end{array}$$
adamc@544	1719
adam@1602	1720 As another way of dealing with null values, there is also a restricted form of the standard \cd{COALESCE} function.
adam@1602	1721 $$\begin{array}{l}
adam@1602	1722 \mt{val} \; \mt{sql\_coalesce} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1602	1723 \hspace{.1in} \to \mt{t} ::: \mt{Type} \\
adam@1602	1724 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; (\mt{option} \; \mt{t}) \\
adam@1602	1725 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1602	1726 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adam@1602	1727 \end{array}$$
adam@1602	1728
adamc@559	1729 We have generic nullary, unary, and binary operators.
adamc@544	1730 $$\begin{array}{l}
adamc@544	1731 \mt{con} \; \mt{sql\_nfunc} :: \mt{Type} \to \mt{Type} \\
adamc@544	1732 \mt{val} \; \mt{sql\_current\_timestamp} : \mt{sql\_nfunc} \; \mt{time} \\
adamc@544	1733 \mt{val} \; \mt{sql\_nfunc} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544	1734 \hspace{.1in} \to \mt{sql\_nfunc} \; \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\\end{array}$$
adamc@544	1735
adamc@544	1736 $$\begin{array}{l}
adamc@544	1737 \mt{con} \; \mt{sql\_unary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544	1738 \mt{val} \; \mt{sql\_not} : \mt{sql\_unary} \; \mt{bool} \; \mt{bool} \\
adamc@544	1739 \mt{val} \; \mt{sql\_unary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adamc@544	1740 \hspace{.1in} \to \mt{sql\_unary} \; \mt{arg} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res} \\
adamc@544	1741 \end{array}$$
adamc@544	1742
adamc@544	1743 $$\begin{array}{l}
adamc@544	1744 \mt{con} \; \mt{sql\_binary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544	1745 \mt{val} \; \mt{sql\_and} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544	1746 \mt{val} \; \mt{sql\_or} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544	1747 \mt{val} \; \mt{sql\_binary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg_1} ::: \mt{Type} \to \mt{arg_2} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adamc@544	1748 \hspace{.1in} \to \mt{sql\_binary} \; \mt{arg_1} \; \mt{arg_2} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_1} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_2} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res}
adamc@544	1749 \end{array}$$
adamc@544	1750
adamc@544	1751 $$\begin{array}{l}
adamc@559	1752 \mt{class} \; \mt{sql\_arith} \\
adamc@559	1753 \mt{val} \; \mt{sql\_int\_arith} : \mt{sql\_arith} \; \mt{int} \\
adamc@559	1754 \mt{val} \; \mt{sql\_float\_arith} : \mt{sql\_arith} \; \mt{float} \\
adamc@559	1755 \mt{val} \; \mt{sql\_neg} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_unary} \; \mt{t} \; \mt{t} \\
adamc@559	1756 \mt{val} \; \mt{sql\_plus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559	1757 \mt{val} \; \mt{sql\_minus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559	1758 \mt{val} \; \mt{sql\_times} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559	1759 \mt{val} \; \mt{sql\_div} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559	1760 \mt{val} \; \mt{sql\_mod} : \mt{sql\_binary} \; \mt{int} \; \mt{int} \; \mt{int}
adamc@559	1761 \end{array}$$
adamc@544	1762
adamc@656	1763 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	1764 $$\begin{array}{l}
adamc@544	1765 \mt{val} \; \mt{sql\_count} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int}
adamc@544	1766 \end{array}$$
adamc@544	1767
adamc@544	1768 $$\begin{array}{l}
adamc@1188	1769 \mt{con} \; \mt{sql\_aggregate} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@1188	1770 \mt{val} \; \mt{sql\_aggregate} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{dom} ::: \mt{Type} \to \mt{ran} ::: \mt{Type} \\
adamc@1188	1771 \hspace{.1in} \to \mt{sql\_aggregate} \; \mt{dom} \; \mt{ran} \to \mt{sql\_exp} \; \mt{agg} \; \mt{agg} \; \mt{exps} \; \mt{dom} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{ran}
adamc@1188	1772 \end{array}$$
adamc@1188	1773
adamc@1188	1774 $$\begin{array}{l}
adamc@1188	1775 \mt{val} \; \mt{sql\_count\_col} : \mt{t} ::: \mt{Type} \to \mt{sql\_aggregate} \; (\mt{option} \; \mt{t}) \; \mt{int}
adamc@544	1776 \end{array}$$
adam@1400	1777
adam@1400	1778 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	1779
adamc@544	1780 $$\begin{array}{l}
adamc@544	1781 \mt{class} \; \mt{sql\_summable} \\
adamc@544	1782 \mt{val} \; \mt{sql\_summable\_int} : \mt{sql\_summable} \; \mt{int} \\
adamc@544	1783 \mt{val} \; \mt{sql\_summable\_float} : \mt{sql\_summable} \; \mt{float} \\
adam@1400	1784 \mt{val} \; \mt{sql\_avg} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt} \\
adam@1400	1785 \mt{val} \; \mt{sql\_sum} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt}
adamc@544	1786 \end{array}$$
adamc@544	1787
adamc@544	1788 $$\begin{array}{l}
adamc@544	1789 \mt{class} \; \mt{sql\_maxable} \\
adamc@544	1790 \mt{val} \; \mt{sql\_maxable\_int} : \mt{sql\_maxable} \; \mt{int} \\
adamc@544	1791 \mt{val} \; \mt{sql\_maxable\_float} : \mt{sql\_maxable} \; \mt{float} \\
adamc@544	1792 \mt{val} \; \mt{sql\_maxable\_string} : \mt{sql\_maxable} \; \mt{string} \\
adamc@544	1793 \mt{val} \; \mt{sql\_maxable\_time} : \mt{sql\_maxable} \; \mt{time} \\
adam@1400	1794 \mt{val} \; \mt{sql\_max} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt} \\
adam@1400	1795 \mt{val} \; \mt{sql\_min} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt}
adamc@544	1796 \end{array}$$
adamc@544	1797
adamc@1193	1798 Any SQL query that returns single columns may be turned into a subquery expression.
adamc@1193	1799
adamc@786	1800 $$\begin{array}{l}
adam@1421	1801 \mt{val} \; \mt{sql\_subquery} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \\
adam@1421	1802 \hspace{.1in} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_query} \; \mt{tables} \; \mt{agg} \; [\mt{nm} = \mt{t}] \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{nt}
adamc@1193	1803 \end{array}$$
adamc@1193	1804
adam@1573	1805 There is also an \cd{IF..THEN..ELSE..} construct that is compiled into standard SQL \cd{CASE} expressions.
adam@1573	1806 $$\begin{array}{l}
adam@1573	1807 \mt{val} \; \mt{sql\_if\_then\_else} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1573	1808 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{bool} \\
adam@1573	1809 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1573	1810 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1573	1811 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adam@1573	1812 \end{array}$$
adam@1573	1813
adamc@1193	1814 \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	1815 $$\begin{array}{l}
adamc@1193	1816 \mt{con} \; \mt{sql\_from\_items} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@1193	1817 \mt{val} \; \mt{sql\_from\_table} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adamc@1193	1818 \hspace{.1in} \to \mt{t} ::: \mt{Type} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; \mt{t} \; \mt{fs} \to \mt{name} :: \mt{Name} \to \mt{t} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193	1819 \mt{val} \; \mt{sql\_from\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{name} :: \mt{Name} \to \mt{sql\_query} \; \mt{free} \; [] \; \mt{fs} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193	1820 \mt{val} \; \mt{sql\_from\_comma} : \mt{free} ::: \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \to [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193	1821 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adamc@1193	1822 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2}) \\
adamc@1193	1823 \mt{val} \; \mt{sql\_inner\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \\
adamc@1193	1824 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193	1825 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adamc@1193	1826 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193	1827 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2})
adamc@786	1828 \end{array}$$
adamc@786	1829
adamc@786	1830 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	1831 $$\begin{array}{l}
adamc@786	1832 \mt{class} \; \mt{nullify} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@786	1833 \mt{val} \; \mt{nullify\_option} : \mt{t} ::: \mt{Type} \to \mt{nullify} \; (\mt{option} \; \mt{t}) \; (\mt{option} \; \mt{t}) \\
adamc@786	1834 \mt{val} \; \mt{nullify\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{nullify} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@786	1835 \end{array}$$
adamc@786	1836
adamc@786	1837 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	1838
adamc@786	1839 $$\begin{array}{l}
adamc@1193	1840 \mt{val} \; \mt{sql\_left\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{(\mt{Type} \times \mt{Type})\}\} \\
adamc@1193	1841 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@786	1842 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\lambda \mt{r} \Rightarrow \$(\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{nullify} \; \mt{p}.1 \; \mt{p}.2) \; \mt{r})) \; \mt{tabs2}) \\
adamc@1193	1843 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \\
adamc@1193	1844 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193	1845 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.2)) \; \mt{tabs2})
adamc@786	1846 \end{array}$$
adamc@786	1847
adamc@544	1848 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	1849 $$\begin{array}{l}
adamc@544	1850 \mt{type} \; \mt{sql\_direction} \\
adamc@544	1851 \mt{val} \; \mt{sql\_asc} : \mt{sql\_direction} \\
adamc@544	1852 \mt{val} \; \mt{sql\_desc} : \mt{sql\_direction} \\
adamc@544	1853 \\
adamc@544	1854 \mt{con} \; \mt{sql\_order\_by} :: \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@544	1855 \mt{val} \; \mt{sql\_order\_by\_Nil} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} :: \{\mt{Type}\} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544	1856 \mt{val} \; \mt{sql\_order\_by\_Cons} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544	1857 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; [] \; \mt{exps} \; \mt{t} \to \mt{sql\_direction} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adam@1684	1858 \mt{val} \; \mt{sql\_order\_by\_random} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544	1859 \\
adamc@544	1860 \mt{type} \; \mt{sql\_limit} \\
adamc@544	1861 \mt{val} \; \mt{sql\_no\_limit} : \mt{sql\_limit} \\
adamc@544	1862 \mt{val} \; \mt{sql\_limit} : \mt{int} \to \mt{sql\_limit} \\
adamc@544	1863 \\
adamc@544	1864 \mt{type} \; \mt{sql\_offset} \\
adamc@544	1865 \mt{val} \; \mt{sql\_no\_offset} : \mt{sql\_offset} \\
adamc@544	1866 \mt{val} \; \mt{sql\_offset} : \mt{int} \to \mt{sql\_offset}
adamc@544	1867 \end{array}$$
adamc@544	1868
adamc@545	1869
adamc@545	1870 \subsubsection{DML}
adamc@545	1871
adamc@545	1872 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	1873
adamc@545	1874 $$\begin{array}{l}
adamc@545	1875 \mt{type} \; \mt{dml} \\
adamc@545	1876 \mt{val} \; \mt{dml} : \mt{dml} \to \mt{transaction} \; \mt{unit}
adamc@545	1877 \end{array}$$
adamc@545	1878
adam@1297	1879 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	1880
adam@1297	1881 $$\begin{array}{l}
adam@1297	1882 \mt{val} \; \mt{tryDml} : \mt{dml} \to \mt{transaction} \; (\mt{option} \; \mt{string})
adam@1297	1883 \end{array}$$
adam@1297	1884
adamc@545	1885 Properly-typed records may be used to form $\mt{INSERT}$ commands.
adamc@545	1886 $$\begin{array}{l}
adamc@545	1887 \mt{val} \; \mt{insert} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \\
adamc@658	1888 \hspace{.1in} \to \$(\mt{map} \; (\mt{sql\_exp} \; [] \; [] \; []) \; \mt{fields}) \to \mt{dml}
adamc@545	1889 \end{array}$$
adamc@545	1890
adam@1578	1891 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. Note that, in the table environment applied to expressions, the table being updated is hardcoded at the name $\mt{T}$. The parsing extension for $\mt{UPDATE}$ will elaborate all table-free field references to use table variable $\mt{T}$.
adamc@545	1892 $$\begin{array}{l}
adam@1380	1893 \mt{val} \; \mt{update} : \mt{unchanged} ::: \{\mt{Type}\} \to \mt{changed} :: \{\mt{Type}\} \to [\mt{changed} \sim \mt{unchanged}] \\
adamc@658	1894 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; []) \; \mt{changed}) \\
adamc@545	1895 \hspace{.1in} \to \mt{sql\_table} \; (\mt{changed} \rc \mt{unchanged}) \to \mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545	1896 \end{array}$$
adamc@545	1897
adam@1578	1898 A $\mt{DELETE}$ command is formed from a table and a $\mt{WHERE}$ clause. The above use of $\mt{T}$ is repeated.
adamc@545	1899 $$\begin{array}{l}
adamc@545	1900 \mt{val} \; \mt{delete} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \to \mt{sql\_exp} \; [\mt{T} = \mt{fields}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545	1901 \end{array}$$
adamc@545	1902
adamc@546	1903 \subsubsection{Sequences}
adamc@546	1904
adamc@546	1905 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	1906
adamc@546	1907 $$\begin{array}{l}
adamc@546	1908 \mt{type} \; \mt{sql\_sequence} \\
adamc@1085	1909 \mt{val} \; \mt{nextval} : \mt{sql\_sequence} \to \mt{transaction} \; \mt{int} \\
adamc@1085	1910 \mt{val} \; \mt{setval} : \mt{sql\_sequence} \to \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@546	1911 \end{array}$$
adamc@546	1912
adamc@546	1913
adam@1648	1914 \subsection{\label{xml}XML}
adamc@547	1915
adam@1333	1916 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	1917
adam@1642	1918 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 $[\mt{Dyn}, \mt{MakeForm}, \mt{Tr}]$, to indicate nesting inside a \texttt{<tr>} tag with the ability to nest \texttt{<form>} and \texttt{<dyn>} tags (see below). 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	1919 $$\begin{array}{l}
adamc@547	1920 \mt{con} \; \mt{xml} :: \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547	1921 \end{array}$$
adamc@547	1922
adamc@547	1923 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	1924 $$\begin{array}{l}
adamc@547	1925 \mt{con} \; \mt{tag} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547	1926 \end{array}$$
adamc@547	1927
adamc@547	1928 Literal text may be injected into XML as ``CDATA.''
adamc@547	1929 $$\begin{array}{l}
adamc@547	1930 \mt{val} \; \mt{cdata} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{string} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adamc@547	1931 \end{array}$$
adamc@547	1932
adam@1358	1933 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	1934 $$\begin{array}{l}
adam@1358	1935 \mt{val} \; \mt{cdataChar} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{char} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adam@1358	1936 \end{array}$$
adam@1358	1937
adamc@547	1938 There is a function for producing an XML tree with a particular tag at its root.
adamc@547	1939 $$\begin{array}{l}
adamc@547	1940 \mt{val} \; \mt{tag} : \mt{attrsGiven} ::: \{\mt{Type}\} \to \mt{attrsAbsent} ::: \{\mt{Type}\} \to \mt{ctxOuter} ::: \{\mt{Unit}\} \to \mt{ctxInner} ::: \{\mt{Unit}\} \\
adamc@547	1941 \hspace{.1in} \to \mt{useOuter} ::: \{\mt{Type}\} \to \mt{useInner} ::: \{\mt{Type}\} \to \mt{bindOuter} ::: \{\mt{Type}\} \to \mt{bindInner} ::: \{\mt{Type}\} \\
adam@1380	1942 \hspace{.1in} \to [\mt{attrsGiven} \sim \mt{attrsAbsent}] \Rightarrow [\mt{useOuter} \sim \mt{useInner}] \Rightarrow [\mt{bindOuter} \sim \mt{bindInner}] \\
adamc@787	1943 \hspace{.1in} \Rightarrow \mt{option} \; \mt{css\_class} \\
adam@1643	1944 \hspace{.1in} \to \mt{option} \; (\mt{signal} \; \mt{css\_class}) \\
adamc@787	1945 \hspace{.1in} \to \$\mt{attrsGiven} \\
adamc@547	1946 \hspace{.1in} \to \mt{tag} \; (\mt{attrsGiven} \rc \mt{attrsAbsent}) \; \mt{ctxOuter} \; \mt{ctxInner} \; \mt{useOuter} \; \mt{bindOuter} \\
adamc@547	1947 \hspace{.1in} \to \mt{xml} \; \mt{ctxInner} \; \mt{useInner} \; \mt{bindInner} \to \mt{xml} \; \mt{ctxOuter} \; (\mt{useOuter} \rc \mt{useInner}) \; (\mt{bindOuter} \rc \mt{bindInner})
adamc@547	1948 \end{array}$$
adam@1297	1949 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	1950
adam@1643	1951 Also note that two different arguments are available for setting CSS classes: the first, associated with the \texttt{class} pseudo-attribute syntactic sugar, fixes the class of a tag for the duration of the tag's life; while the second, associated with the \texttt{dynClass} pseudo-attribute, allows the class to vary over the tag's life. See Section \ref{signals} for an introduction to the $\mt{signal}$ type family.
adam@1643	1952
adamc@547	1953 Two XML fragments may be concatenated.
adamc@547	1954 $$\begin{array}{l}
adamc@547	1955 \mt{val} \; \mt{join} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{bind_1} ::: \{\mt{Type}\} \to \mt{bind_2} ::: \{\mt{Type}\} \\
adam@1380	1956 \hspace{.1in} \to [\mt{use_1} \sim \mt{bind_1}] \Rightarrow [\mt{bind_1} \sim \mt{bind_2}] \\
adamc@547	1957 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind_1} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{bind_1}) \; \mt{bind_2} \to \mt{xml} \; \mt{ctx} \; \mt{use_1} \; (\mt{bind_1} \rc \mt{bind_2})
adamc@547	1958 \end{array}$$
adamc@547	1959
adamc@547	1960 Finally, any XML fragment may be updated to ``claim'' to use more form fields than it does.
adamc@547	1961 $$\begin{array}{l}
adam@1380	1962 \mt{val} \; \mt{useMore} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{use_2} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to [\mt{use_1} \sim \mt{use_2}] \\
adamc@547	1963 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{use_2}) \; \mt{bind}
adamc@547	1964 \end{array}$$
adamc@547	1965
adam@1344	1966 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	1967
adamc@547	1968 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	1969 $$\begin{array}{l}
adam@1641	1970 \mt{val} \; \mt{error} : \mt{t} ::: \mt{Type} \to \mt{xbody} \to \mt{t}
adamc@547	1971 \end{array}$$
adamc@547	1972
adamc@549	1973
adamc@701	1974 \subsection{Client-Side Programming}
adamc@659	1975
adamc@701	1976 Ur/Web supports running code on web browsers, via automatic compilation to JavaScript.
adamc@701	1977
adamc@701	1978 \subsubsection{The Basics}
adamc@701	1979
adam@1400	1980 All of the functions in this subsection are client-side only.
adam@1400	1981
adam@1297	1982 Clients can open alert and confirm dialog boxes, in the usual annoying JavaScript way.
adamc@701	1983 $$\begin{array}{l}
adam@1297	1984 \mt{val} \; \mt{alert} : \mt{string} \to \mt{transaction} \; \mt{unit} \\
adam@1297	1985 \mt{val} \; \mt{confirm} : \mt{string} \to \mt{transaction} \; \mt{bool}
adamc@701	1986 \end{array}$$
adamc@701	1987
adamc@701	1988 Any transaction may be run in a new thread with the $\mt{spawn}$ function.
adamc@701	1989 $$\begin{array}{l}
adamc@701	1990 \mt{val} \; \mt{spawn} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit}
adamc@701	1991 \end{array}$$
adamc@701	1992
adamc@701	1993 The current thread can be paused for at least a specified number of milliseconds.
adamc@701	1994 $$\begin{array}{l}
adamc@701	1995 \mt{val} \; \mt{sleep} : \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@701	1996 \end{array}$$
adamc@701	1997
adamc@787	1998 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	1999 $$\begin{array}{l}
adamc@787	2000 \mt{val} \; \mt{onError} : (\mt{xbody} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787	2001 \mt{val} \; \mt{onFail} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787	2002 \mt{val} \; \mt{onConnectFail} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787	2003 \mt{val} \; \mt{onDisconnect} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787	2004 \mt{val} \; \mt{onServerError} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit}
adamc@787	2005 \end{array}$$
adamc@787	2006
adam@1555	2007 There are also functions to register standard document-level event handlers.
adam@1555	2008
adam@1555	2009 $$\begin{array}{l}
adam@1555	2010 \mt{val} \; \mt{onClick} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adam@1555	2011 \mt{val} \; \mt{onDblclick} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adam@1555	2012 \mt{val} \; \mt{onKeydown} : (\mt{int} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1555	2013 \mt{val} \; \mt{onKeypress} : (\mt{int} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1555	2014 \mt{val} \; \mt{onKeyup} : (\mt{int} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1555	2015 \mt{val} \; \mt{onMousedown} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adam@1555	2016 \mt{val} \; \mt{onMouseup} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit}
adam@1555	2017 \end{array}$$
adam@1555	2018
adam@1559	2019 Versions of standard JavaScript functions are provided that event handlers may call to mask default handling or prevent bubbling of events up to parent DOM nodes, respectively.
adam@1559	2020
adam@1559	2021 $$\begin{array}{l}
adam@1559	2022 \mt{val} \; \mt{preventDefault} : \mt{transaction} \; \mt{unit} \\
adam@1559	2023 \mt{val} \; \mt{stopPropagation} : \mt{transaction} \; \mt{unit}
adam@1559	2024 \end{array}$$
adam@1559	2025
adam@1556	2026 \subsubsection{Node IDs}
adam@1556	2027
adam@1556	2028 There is an abstract type of node IDs that may be assigned to \cd{id} attributes of most HTML tags.
adam@1556	2029
adam@1556	2030 $$\begin{array}{l}
adam@1556	2031 \mt{type} \; \mt{id} \\
adam@1556	2032 \mt{val} \; \mt{fresh} : \mt{transaction} \; \mt{id}
adam@1556	2033 \end{array}$$
adam@1556	2034
adam@1556	2035 The \cd{fresh} function is allowed on both server and client, but there is no other way to create IDs, which includes lack of a way to force an ID to match a particular string. The only semantic importance of IDs within Ur/Web is in uses of the HTML \cd{<label>} tag. IDs play a much more central role in mainstream JavaScript programming, but Ur/Web uses a very different model to enable changes to particular nodes of a page tree, as the next manual subsection explains. IDs may still be useful in interfacing with JavaScript code (for instance, through Ur/Web's FFI).
adam@1556	2036
adam@1643	2037 \subsubsection{\label{signals}Functional-Reactive Page Generation}
adamc@701	2038
adamc@701	2039 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	2040
adam@1403	2041 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	2042
adamc@659	2043 $$\begin{array}{l}
adamc@659	2044 \mt{con} \; \mt{source} :: \mt{Type} \to \mt{Type} \\
adamc@659	2045 \mt{val} \; \mt{source} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{transaction} \; (\mt{source} \; \mt{t}) \\
adamc@659	2046 \mt{val} \; \mt{set} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@659	2047 \mt{val} \; \mt{get} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@659	2048 \end{array}$$
adamc@659	2049
adam@1400	2050 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	2051
adam@1608	2052 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. There is also an operator for computing a signal's current value within a transaction.
adamc@659	2053
adamc@659	2054 $$\begin{array}{l}
adamc@659	2055 \mt{con} \; \mt{signal} :: \mt{Type} \to \mt{Type} \\
adamc@659	2056 \mt{val} \; \mt{signal\_monad} : \mt{monad} \; \mt{signal} \\
adam@1608	2057 \mt{val} \; \mt{signal} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{signal} \; \mt{t} \\
adam@1608	2058 \mt{val} \; \mt{current} : \mt{t} ::: \mt{Type} \to \mt{signal} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@659	2059 \end{array}$$
adamc@659	2060
adamc@659	2061 A reactive portion of an HTML page is injected with a $\mt{dyn}$ tag, which has a signal-valued attribute $\mt{Signal}$.
adamc@659	2062
adamc@659	2063 $$\begin{array}{l}
adam@1641	2064 \mt{val} \; \mt{dyn} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to [\mt{ctx} \sim [\mt{Dyn}]] \Rightarrow \mt{unit} \\
adam@1641	2065 \hspace{.1in} \to \mt{tag} \; [\mt{Signal} = \mt{signal} \; (\mt{xml} \; ([\mt{Dyn}] \rc \mt{ctx}) \; \mt{use} \; \mt{bind})] \; ([\mt{Dyn}] \rc \mt{ctx}) \; [] \; \mt{use} \; \mt{bind}
adamc@659	2066 \end{array}$$
adamc@659	2067
adam@1648	2068 The semantics of \cd{<dyn>} tags is somewhat subtle. When the signal associated with such a tag changes value, the associated subtree of the HTML page is recreated. Some properties of the subtree, such as attributes and client-side widget values, are specified explicitly in the signal value, so these may be counted on to remain the same after recreation. Other properties, like focus and cursor position within textboxes, are \emph{not} specified by signal values, and these properties will be \emph{reset} upon subtree regeneration. Furthermore, user interaction with widgets may not work properly during regeneration. For instance, clicking a button while it is being regenerated may not trigger its \cd{onclick} event code.
adam@1648	2069
adam@1648	2070 Currently, the only way to avoid undesired resets is to avoid regeneration of containing subtrees. There are two main strategies for achieving that goal. First, when changes to a subtree can be confined to CSS classes of tags, the \texttt{dynClass} pseudo-attribute may be used instead (see Section \ref{xml}), as it does not regenerate subtrees. Second, a single \cd{<dyn>} tag may be broken into multiple tags, in a way that makes finer-grained dependency structure explicit. This latter strategy can avoid ``spurious'' regenerations that are not actually required to achieve the intended semantics.
adam@1648	2071
adamc@701	2072 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	2073
adamc@914	2074 \subsubsection{Remote Procedure Calls}
adamc@914	2075
adamc@914	2076 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	2077
adamc@914	2078 $$\begin{array}{l}
adamc@914	2079 \mt{val} \; \mt{rpc} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@914	2080 \end{array}$$
adamc@914	2081
adamc@701	2082 \subsubsection{Asynchronous Message-Passing}
adamc@701	2083
adamc@701	2084 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	2085
adamc@701	2086 $$\begin{array}{l}
adamc@701	2087 \mt{type} \; \mt{client} \\
adamc@701	2088 \mt{val} \; \mt{self} : \mt{transaction} \; \mt{client}
adamc@701	2089 \end{array}$$
adamc@701	2090
adamc@701	2091 \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	2092
adamc@701	2093 $$\begin{array}{l}
adamc@701	2094 \mt{con} \; \mt{channel} :: \mt{Type} \to \mt{Type} \\
adamc@701	2095 \mt{val} \; \mt{channel} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; (\mt{channel} \; \mt{t}) \\
adamc@701	2096 \mt{val} \; \mt{send} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@701	2097 \mt{val} \; \mt{recv} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@701	2098 \end{array}$$
adamc@701	2099
adamc@701	2100 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	2101
adamc@701	2102 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	2103
adam@1551	2104 \emph{Note}: Currently, there are known concurrency issues with multi-threaded applications that employ message-passing on top of database engines that don't support true serializable transactions. Postgres 9.1 is the only supported engine that does this properly.
adam@1551	2105
adamc@659	2106
adamc@549	2107 \section{Ur/Web Syntax Extensions}
adamc@549	2108
adamc@549	2109 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	2110
adamc@549	2111 \subsection{SQL}
adamc@549	2112
adamc@786	2113 \subsubsection{\label{tables}Table Declarations}
adamc@786	2114
adamc@788	2115 $\mt{table}$ declarations may include constraints, via these grammar rules.
adamc@788	2116 $$\begin{array}{rrcll}
adam@1594	2117 \textrm{Declarations} & d &::=& \mt{table} \; x : c \; [pk[,]] \; cts \mid \mt{view} \; x = V \\
adamc@788	2118 \textrm{Primary key constraints} & pk &::=& \mt{PRIMARY} \; \mt{KEY} \; K \\
adam@1722	2119 \textrm{Keys} & K &::=& f \mid (f, (f,)^+) \mid \{\{e\}\} \\
adamc@788	2120 \textrm{Constraint sets} & cts &::=& \mt{CONSTRAINT} f \; ct \mid cts, cts \mid \{\{e\}\} \\
adamc@788	2121 \textrm{Constraints} & ct &::=& \mt{UNIQUE} \; K \mid \mt{CHECK} \; E \\
adamc@788	2122 &&& \mid \mt{FOREIGN} \; \mt{KEY} \; K \; \mt{REFERENCES} \; F \; (K) \; [\mt{ON} \; \mt{DELETE} \; pr] \; [\mt{ON} \; \mt{UPDATE} \; pr] \\
adamc@788	2123 \textrm{Foreign tables} & F &::=& x \mid \{\{e\}\} \\
adam@1594	2124 \textrm{Propagation modes} & pr &::=& \mt{NO} \; \mt{ACTION} \mid \mt{RESTRICT} \mid \mt{CASCADE} \mid \mt{SET} \; \mt{NULL} \\
adam@1594	2125 \textrm{View expressions} & V &::=& Q \mid \{e\}
adamc@788	2126 \end{array}$$
adamc@788	2127
adamc@788	2128 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	2129
adamc@788	2130
adamc@549	2131 \subsubsection{Queries}
adamc@549	2132
adamc@550	2133 Queries $Q$ are added to the rules for expressions $e$.
adamc@550	2134
adamc@549	2135 $$\begin{array}{rrcll}
adam@1684	2136 \textrm{Queries} & Q &::=& (q \; [\mt{ORDER} \; \mt{BY} \; O] \; [\mt{LIMIT} \; N] \; [\mt{OFFSET} \; N]) \\
adamc@1085	2137 \textrm{Pre-queries} & q &::=& \mt{SELECT} \; [\mt{DISTINCT}] \; P \; \mt{FROM} \; F,^+ \; [\mt{WHERE} \; E] \; [\mt{GROUP} \; \mt{BY} \; p,^+] \; [\mt{HAVING} \; E] \\
adamc@1085	2138 &&& \mid q \; R \; q \mid \{\{\{e\}\}\} \\
adam@1684	2139 \textrm{Relational operators} & R &::=& \mt{UNION} \mid \mt{INTERSECT} \mid \mt{EXCEPT} \\
adam@1684	2140 \textrm{$\mt{ORDER \; BY}$ items} & O &::=& \mt{RANDOM} [()] \mid E \; [o] \mid E \; [o], O
adamc@549	2141 \end{array}$$
adamc@549	2142
adamc@549	2143 $$\begin{array}{rrcll}
adamc@549	2144 \textrm{Projections} & P &::=& \ast & \textrm{all columns} \\
adamc@549	2145 &&& p,^+ & \textrm{particular columns} \\
adamc@549	2146 \textrm{Pre-projections} & p &::=& t.f & \textrm{one column from a table} \\
adamc@558	2147 &&& t.\{\{c\}\} & \textrm{a record of columns from a table (of kind $\{\mt{Type}\}$)} \\
adam@1627	2148 &&& t.* & \textrm{all columns from a table} \\
adamc@1194	2149 &&& E \; [\mt{AS} \; f] & \textrm{expression column} \\
adamc@549	2150 \textrm{Table names} & t &::=& x & \textrm{constant table name (automatically capitalized)} \\
adamc@549	2151 &&& X & \textrm{constant table name} \\
adamc@549	2152 &&& \{\{c\}\} & \textrm{computed table name (of kind $\mt{Name}$)} \\
adamc@549	2153 \textrm{Column names} & f &::=& X & \textrm{constant column name} \\
adamc@549	2154 &&& \{c\} & \textrm{computed column name (of kind $\mt{Name}$)} \\
adamc@549	2155 \textrm{Tables} & T &::=& x & \textrm{table variable, named locally by its own capitalization} \\
adamc@549	2156 &&& x \; \mt{AS} \; t & \textrm{table variable, with local name} \\
adamc@549	2157 &&& \{\{e\}\} \; \mt{AS} \; t & \textrm{computed table expression, with local name} \\
adamc@1085	2158 \textrm{$\mt{FROM}$ items} & F &::=& T \mid \{\{e\}\} \mid F \; J \; \mt{JOIN} \; F \; \mt{ON} \; E \\
adamc@1085	2159 &&& \mid F \; \mt{CROSS} \; \mt{JOIN} \ F \\
adamc@1193	2160 &&& \mid (Q) \; \mt{AS} \; t \\
adamc@1085	2161 \textrm{Joins} & J &::=& [\mt{INNER}] \\
adamc@1085	2162 &&& \mid [\mt{LEFT} \mid \mt{RIGHT} \mid \mt{FULL}] \; [\mt{OUTER}] \\
adam@1587	2163 \textrm{SQL expressions} & E &::=& t.f & \textrm{column references} \\
adamc@549	2164 &&& X & \textrm{named expression references} \\
adam@1490	2165 &&& \{[e]\} & \textrm{injected native Ur expressions} \\
adamc@549	2166 &&& \{e\} & \textrm{computed expressions, probably using $\mt{sql\_exp}$ directly} \\
adamc@549	2167 &&& \mt{TRUE} \mid \mt{FALSE} & \textrm{boolean constants} \\
adamc@549	2168 &&& \ell & \textrm{primitive type literals} \\
adamc@549	2169 &&& \mt{NULL} & \textrm{null value (injection of $\mt{None}$)} \\
adamc@549	2170 &&& E \; \mt{IS} \; \mt{NULL} & \textrm{nullness test} \\
adam@1602	2171 &&& \mt{COALESCE}(E, E) & \textrm{take first non-null value} \\
adamc@549	2172 &&& n & \textrm{nullary operators} \\
adamc@549	2173 &&& u \; E & \textrm{unary operators} \\
adamc@549	2174 &&& E \; b \; E & \textrm{binary operators} \\
adamc@549	2175 &&& \mt{COUNT}(\ast) & \textrm{count number of rows} \\
adamc@549	2176 &&& a(E) & \textrm{other aggregate function} \\
adam@1573	2177 &&& \mt{IF} \; E \; \mt{THEN} \; E \; \mt{ELSE} \; E & \textrm{conditional} \\
adamc@1193	2178 &&& (Q) & \textrm{subquery (must return a single expression column)} \\
adamc@549	2179 &&& (E) & \textrm{explicit precedence} \\
adamc@549	2180 \textrm{Nullary operators} & n &::=& \mt{CURRENT\_TIMESTAMP} \\
adamc@549	2181 \textrm{Unary operators} & u &::=& \mt{NOT} \\
adam@1688	2182 \textrm{Binary operators} & b &::=& \mt{AND} \mid \mt{OR} \mid = \mid \neq \mid < \mid \leq \mid > \mid \geq \\
adamc@1188	2183 \textrm{Aggregate functions} & a &::=& \mt{COUNT} \mid \mt{AVG} \mid \mt{SUM} \mid \mt{MIN} \mid \mt{MAX} \\
adam@1543	2184 \textrm{Directions} & o &::=& \mt{ASC} \mid \mt{DESC} \mid \{e\} \\
adamc@549	2185 \textrm{SQL integer} & N &::=& n \mid \{e\} \\
adamc@549	2186 \end{array}$$
adamc@549	2187
adamc@1085	2188 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	2189
adam@1683	2190 Unnamed expression columns in $\mt{SELECT}$ clauses are assigned consecutive natural numbers, starting with 1. Any expression in a $p$ position that is enclosed in parentheses is treated as an expression column, rather than a column pulled directly out of a table, even if it is only a field projection. (This distinction affects the record type used to describe query results.)
adamc@1194	2191
adamc@550	2192 \subsubsection{DML}
adamc@550	2193
adamc@550	2194 DML commands $D$ are added to the rules for expressions $e$.
adamc@550	2195
adamc@550	2196 $$\begin{array}{rrcll}
adamc@550	2197 \textrm{Commands} & D &::=& (\mt{INSERT} \; \mt{INTO} \; T^E \; (f,^+) \; \mt{VALUES} \; (E,^+)) \\
adamc@550	2198 &&& (\mt{UPDATE} \; T^E \; \mt{SET} \; (f = E,)^+ \; \mt{WHERE} \; E) \\
adamc@550	2199 &&& (\mt{DELETE} \; \mt{FROM} \; T^E \; \mt{WHERE} \; E) \\
adamc@550	2200 \textrm{Table expressions} & T^E &::=& x \mid \{\{e\}\}
adamc@550	2201 \end{array}$$
adamc@550	2202
adamc@550	2203 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	2204
adamc@551	2205 \subsection{XML}
adamc@551	2206
adamc@551	2207 XML fragments $L$ are added to the rules for expressions $e$.
adamc@551	2208
adamc@551	2209 $$\begin{array}{rrcll}
adamc@551	2210 \textrm{XML fragments} & L &::=& \texttt{<xml/>} \mid \texttt{<xml>}l^*\texttt{</xml>} \\
adamc@551	2211 \textrm{XML pieces} & l &::=& \textrm{text} & \textrm{cdata} \\
adamc@551	2212 &&& \texttt{<}g\texttt{/>} & \textrm{tag with no children} \\
adamc@551	2213 &&& \texttt{<}g\texttt{>}l^*\texttt{</}x\texttt{>} & \textrm{tag with children} \\
adamc@559	2214 &&& \{e\} & \textrm{computed XML fragment} \\
adamc@559	2215 &&& \{[e]\} & \textrm{injection of an Ur expression, via the $\mt{Top}.\mt{txt}$ function} \\
adamc@551	2216 \textrm{Tag} & g &::=& h \; (x = v)^* \\
adamc@551	2217 \textrm{Tag head} & h &::=& x & \textrm{tag name} \\
adamc@551	2218 &&& h\{c\} & \textrm{constructor parameter} \\
adamc@551	2219 \textrm{Attribute value} & v &::=& \ell & \textrm{literal value} \\
adamc@551	2220 &&& \{e\} & \textrm{computed value} \\
adamc@551	2221 \end{array}$$
adamc@551	2222
adamc@552	2223
adamc@1198	2224 \section{\label{structure}The Structure of Web Applications}
adamc@553	2225
adam@1604	2226 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. See Section \ref{cl} for information on the \texttt{prefix} and \texttt{rewrite url} directives, which can be used to rewrite the default URIs of different entry point functions. The final URL of a function is its default module-based URI, with \texttt{rewrite url} rules applied, and with the \texttt{prefix} prepended. Arguments to an entry-point function are deserialized from the part of the URI following \texttt{f}.
adamc@553	2227
adam@1532	2228 Elements of modules beside the main module, including page handlers, will only be included in the final application if they are transitive dependencies of the handlers in the main module.
adam@1532	2229
adam@1347	2230 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	2231
adam@1370	2232 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	2233
adamc@553	2234 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	2235
adamc@553	2236 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	2237
adam@1653	2238 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. Such serialized values may only be drawn from a limited set of types, and programs will fail to compile when the (implicit or explicit) arguments of page handler functions involve disallowed types. (Keep in mind that every free variable of a function is an implicit argument if it was not defined at the top level of a module.) For instance:
adam@1653	2239 \begin{itemize}
adam@1653	2240 \item Functions are disallowed, since there is no obvious way to serialize them safely.
adam@1653	2241 \item XML fragments are disallowed, since it is unclear how to check client-provided XML to be sure it doesn't break the HTML invariants of the application (for instance, by mutating the DOM in the conventional way, interfering with Ur/Web's functional-reactive regime).
adam@1653	2242 \item Blobs (``files'') are disallowed, since they can easily have very large serializations that could not fit within most web servers' URL size limits. (And you probably don't want to be serializing, e.g., image files in URLs, anyway.)
adam@1653	2243 \end{itemize}
adamc@553	2244
adamc@660	2245 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	2246
adamc@789	2247 \medskip
adamc@789	2248
adam@1347	2249 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	2250
adamc@789	2251 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	2252
adam@1348	2253 \subsection{Tasks}
adam@1348	2254
adam@1348	2255 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	2256
adam@1348	2257 $$\begin{array}{l}
adam@1348	2258 \mt{con} \; \mt{task\_kind} :: \mt{Type} \to \mt{Type} \\
adam@1348	2259 \mt{val} \; \mt{initialize} : \mt{task\_kind} \; \mt{unit} \\
adam@1349	2260 \mt{val} \; \mt{clientLeaves} : \mt{task\_kind} \; \mt{client} \\
adam@1349	2261 \mt{val} \; \mt{periodic} : \mt{int} \to \mt{task\_kind} \; \mt{unit}
adam@1348	2262 \end{array}$$
adam@1348	2263
adam@1348	2264 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	2265
adam@1348	2266 The currently supported task kinds are:
adam@1348	2267 \begin{itemize}
adam@1349	2268 \item $\mt{initialize}$: Code that is run when the application starts up.
adam@1348	2269 \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	2270 \item $\mt{periodic} \; n$: Code that is run when the application starts up and then every $n$ seconds thereafter.
adam@1348	2271 \end{itemize}
adam@1348	2272
adamc@553	2273
adamc@897	2274 \section{The Foreign Function Interface}
adamc@897	2275
adamc@897	2276 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	2277
adamc@897	2278 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	2279
adamc@897	2280 \begin{itemize}
adamc@897	2281 \item \texttt{clientOnly Module.ident} registers a value as being allowed only in client-side code.
adamc@897	2282 \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.
adam@1699	2283 \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. (Note that merely assigning a function a \texttt{transaction}-based type does not mark it as effectful in this way!)
adamc@897	2284 \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	2285 \item \texttt{include FILE} requests inclusion of a C header file.
adamc@897	2286 \item \texttt{jsFunc Module.ident=name} gives a mapping from an Ur name for a value to a JavaScript name.
adamc@897	2287 \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	2288 \item \texttt{script URL} requests inclusion of a JavaScript source file within application HTML.
adamc@897	2289 \item \texttt{serverOnly Module.ident} registers a value as being allowed only in server-side code.
adamc@897	2290 \end{itemize}
adamc@897	2291
adamc@897	2292 \subsection{Writing C FFI Code}
adamc@897	2293
adamc@897	2294 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	2295
adamc@897	2296 \begin{itemize}
adamc@897	2297 \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	2298 \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	2299 \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*}.
adam@1686	2300 \item Ur/Web involves many types of program syntax, such as for HTML and SQL code. All of these types are implemented with normal C strings, and you may take advantage of that encoding to manipulate code as strings in C FFI code. Be mindful that, in writing such code, it is your responsibility to maintain the appropriate code invariants, or you may reintroduce the code injection vulnerabilities that Ur/Web rules out. The most convenient way to extend Ur/Web with functions that, e.g., use natively unsupported HTML tags is to generate the HTML code with the FFI.
adamc@897	2301 \end{itemize}
adamc@897	2302
adamc@897	2303 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	2304 \begin{itemize}
adamc@897	2305 \item \begin{verbatim}
adamc@897	2306 void uw_error(uw_context, failure_kind, const char *fmt, ...);
adamc@897	2307 \end{verbatim}
adamc@897	2308 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	2309
adam@1329	2310 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	2311
adamc@897	2312 \item \begin{verbatim}
adam@1469	2313 void uw_set_error_message(uw_context, const char *fmt, ...);
adam@1469	2314 \end{verbatim}
adam@1469	2315 This simpler form of \texttt{uw\_error()} saves an error message without immediately aborting execution.
adam@1469	2316
adam@1469	2317 \item \begin{verbatim}
adamc@897	2318 void uw_push_cleanup(uw_context, void (func)(void ), void *arg);
adamc@897	2319 void uw_pop_cleanup(uw_context);
adamc@897	2320 \end{verbatim}
adam@1329	2321 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	2322
adam@1329	2323 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	2324
adamc@897	2325 \item \begin{verbatim}
adamc@897	2326 void *uw_malloc(uw_context, size_t);
adamc@897	2327 \end{verbatim}
adam@1329	2328 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	2329
adam@1329	2330 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	2331
adamc@897	2332 \item \begin{verbatim}
adamc@897	2333 typedef void (uw_callback)(void );
adam@1328	2334 typedef void (uw_callback_with_retry)(void , int will_retry);
adamc@897	2335 void uw_register_transactional(uw_context, void *data, uw_callback commit,
adam@1328	2336 uw_callback rollback, uw_callback_with_retry free);
adamc@897	2337 \end{verbatim}
adam@1328	2338 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	2339
adamc@1085	2340 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	2341
adam@1329	2342 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	2343
adam@1329	2344 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	2345
adam@1469	2346 A handler may signal an error by calling \texttt{uw\_set\_error\_message()}, but it is not safe to call \texttt{uw\_error()} from a handler. Signaling an error in a commit handler will cause the runtime system to switch to aborting the transaction, immediately after the current commit handler returns.
adam@1469	2347
adamc@1085	2348 \item \begin{verbatim}
adamc@1085	2349 void uw_get_global(uw_context, char name);
adamc@1085	2350 void uw_set_global(uw_context, char name, void data, uw_callback free);
adamc@1085	2351 \end{verbatim}
adam@1329	2352 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	2353
adamc@897	2354 \end{itemize}
adamc@897	2355
adamc@897	2356 \subsection{Writing JavaScript FFI Code}
adamc@897	2357
adamc@897	2358 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	2359
adamc@897	2360 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	2361
adamc@897	2362 \begin{itemize}
adamc@897	2363 \item Integers, floats, strings, characters, and booleans are represented in the usual JavaScript way.
adam@1644	2364 \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)}. To lift a normal JavaScript function \cd{f} into an Ur/Web JavaScript function, run \cd{flift(f)}.
adamc@897	2365 \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	2366 \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	2367 \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.
adam@1686	2368 \item As in the C FFI, all abstract types of program syntax are implemented with strings in JavaScript.
adamc@897	2369 \end{itemize}
adamc@897	2370
adam@1644	2371 It is possible to write JavaScript FFI code that interacts with the functional-reactive structure of a document. Here is a quick summary of some of the simpler functions to use; descriptions of fancier stuff may be added later on request (and such stuff should be considered ``undocumented features'' until then).
adam@1644	2372
adam@1644	2373 \begin{itemize}
adam@1644	2374 \item Sources should be treated as an abstract type, manipulated via:
adam@1644	2375 \begin{itemize}
adam@1644	2376 \item \cd{sc(v)}, to create a source initialized to \cd{v}
adam@1644	2377 \item \cd{sg(s)}, to retrieve the current value of source \cd{s}
adam@1644	2378 \item \cd{sv(s, v)}, to set source \cd{s} to value \cd{v}
adam@1644	2379 \end{itemize}
adam@1644	2380
adam@1644	2381 \item Signals should be treated as an abstract type, manipulated via:
adam@1644	2382 \begin{itemize}
adam@1644	2383 \item \cd{sr(v)} and \cd{sb(s, f)}, the ``return'' and ``bind'' monad operators, respectively
adam@1644	2384 \item \cd{ss(s)}, to produce the signal corresponding to source \cd{s}
adam@1644	2385 \item \cd{scur(s)}, to get the current value of signal \cd{s}
adam@1644	2386 \end{itemize}
adam@1644	2387
adam@1644	2388 \item The behavior of the \cd{<dyn>} pseudo-tag may be mimicked by following the right convention in a piece of HTML source code with a type like $\mt{xbody}$. Such a piece of source code may be encoded with a JavaScript string. To insert a dynamic section, include a \cd{<script>} tag whose content is just a call \cd{dyn(pnode, s)}. The argument \cd{pnode} specifies what the relevant enclosing parent tag is. Use value \cd{"tr"} when the immediate parent is \cd{<tr>}, use \cd{"table"} when the immediate parent is \cd{<table>}, and use \cd{"span"} otherwise. The argument \cd{s} is a string-valued signal giving the HTML code to be inserted at this point. As with the usual \cd{<dyn>} tag, that HTML subtree is automatically updated as the value of \cd{s} changes.
adam@1644	2389
adam@1702	2390 \item There is only one supported method of taking HTML values generated in Ur/Web code and adding them to the DOM in FFI JavaScript code: call \cd{setInnerHTML(node, html)} to add HTML content \cd{html} within DOM node \cd{node}. Merely running \cd{node.innerHTML = html} is not guaranteed to get the job done, though programmers familiar with JavaScript will probably find it useful to think of \cd{setInnerHTML} as having this effect. The unusual idiom is required because Ur/Web uses a nonstandard representation of HTML, to support infinite nesting of code that may generate code that may generate code that.... The \cd{node} value must already be in the DOM tree at the point when \cd{setInnerHTML} is called, because some plumbing must be set up to interact sensibly with \cd{<dyn>} tags.
adam@1702	2391
adam@1644	2392 \item It is possible to use the more standard ``IDs and mutation'' style of JavaScript coding, though that style is unidiomatic for Ur/Web and should be avoided wherever possible. Recall the abstract type $\mt{id}$ and its constructor $\mt{fresh}$, which can be used to generate new unique IDs in Ur/Web code. Values of this type are represented as strings in JavaScript, and a function \cd{fresh()} is available to generate new unique IDs. Application-specific ID generation schemes may cause bad interactions with Ur/Web code that also generates IDs, so the recommended approach is to produce IDs only via calls to \cd{fresh()}. FFI code shouldn't depend on the ID generation scheme (on either server side or client side), but it is safe to include these IDs in tag attributes (in either server-side or client-side code) and manipulate the associated DOM nodes in the standard way (in client-side code). Be forewarned that this kind of imperative DOM manipulation may confuse the Ur/Web runtime system and interfere with proper behavior of tags like \cd{<dyn>}!
adam@1644	2393 \end{itemize}
adamc@897	2394
adamc@897	2395
adamc@552	2396 \section{Compiler Phases}
adamc@552	2397
adamc@552	2398 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	2399
adamc@552	2400 In this section, we step through the main phases of compilation, noting what consequences each phase has for effective programming.
adamc@552	2401
adamc@552	2402 \subsection{Parse}
adamc@552	2403
adamc@552	2404 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	2405
adamc@552	2406 \subsection{Elaborate}
adamc@552	2407
adamc@552	2408 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	2409
adam@1378	2410 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	2411
adamc@552	2412 \subsection{Unnest}
adamc@552	2413
adamc@552	2414 Named local function definitions are moved to the top level, to avoid the need to generate closures.
adamc@552	2415
adamc@552	2416 \subsection{Corify}
adamc@552	2417
adamc@552	2418 Module system features are compiled away, through inlining of functor definitions at application sites. Afterward, most abstraction boundaries are broken, facilitating optimization.
adamc@552	2419
adamc@552	2420 \subsection{Especialize}
adamc@552	2421
adam@1356	2422 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	2423
adamc@552	2424 \subsection{Untangle}
adamc@552	2425
adamc@552	2426 Remove unnecessary mutual recursion, splitting recursive groups into strongly-connected components.
adamc@552	2427
adamc@552	2428 \subsection{Shake}
adamc@552	2429
adamc@552	2430 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	2431
adamc@661	2432 \subsection{Rpcify}
adamc@661	2433
adamc@661	2434 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	2435
adamc@661	2436 \subsection{Untangle, Shake}
adamc@661	2437
adamc@661	2438 Repeat these simplifications.
adamc@661	2439
adamc@553	2440 \subsection{\label{tag}Tag}
adamc@552	2441
adamc@552	2442 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	2443
adamc@552	2444 \subsection{Reduce}
adamc@552	2445
adamc@552	2446 Apply definitional equality rules to simplify the program as much as possible. This effectively includes inlining of every non-recursive definition.
adamc@552	2447
adamc@552	2448 \subsection{Unpoly}
adamc@552	2449
adamc@552	2450 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	2451
adamc@552	2452 \subsection{Specialize}
adamc@552	2453
adamc@558	2454 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	2455
adamc@552	2456 \subsection{Shake}
adamc@552	2457
adamc@558	2458 Here the compiler repeats the earlier Shake phase.
adamc@552	2459
adamc@552	2460 \subsection{Monoize}
adamc@552	2461
adamc@552	2462 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	2463
adamc@552	2464 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	2465
adamc@552	2466 \subsection{MonoOpt}
adamc@552	2467
adamc@552	2468 Simple algebraic laws are applied to simplify the program, focusing especially on efficient imperative generation of HTML pages.
adamc@552	2469
adamc@552	2470 \subsection{MonoUntangle}
adamc@552	2471
adamc@552	2472 Unnecessary mutual recursion is broken up again.
adamc@552	2473
adamc@552	2474 \subsection{MonoReduce}
adamc@552	2475
adamc@552	2476 Equivalents of the definitional equality rules are applied to simplify programs, with inlining again playing a major role.
adamc@552	2477
adamc@552	2478 \subsection{MonoShake, MonoOpt}
adamc@552	2479
adamc@552	2480 Unneeded declarations are removed, and basic optimizations are repeated.
adamc@552	2481
adamc@552	2482 \subsection{Fuse}
adamc@552	2483
adamc@552	2484 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	2485
adamc@552	2486 \subsection{MonoUntangle, MonoShake}
adamc@552	2487
adamc@552	2488 Fuse often creates more opportunities to remove spurious mutual recursion.
adamc@552	2489
adamc@552	2490 \subsection{Pathcheck}
adamc@552	2491
adamc@552	2492 The compiler checks that no link or action name has been used more than once.
adamc@552	2493
adamc@552	2494 \subsection{Cjrize}
adamc@552	2495
adamc@552	2496 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	2497
adamc@552	2498 \subsection{C Compilation and Linking}
adamc@552	2499
adam@1523	2500 The output of the last phase is pretty-printed as C source code and passed to the C compiler.
adamc@552	2501
adamc@552	2502
as@1564	2503 \end{document}

Mercurial > urweb

annotate doc/manual.tex @ 1731:27e731a65934