Ur/Web: doc/manual.tex annotate

annotate doc/manual.tex @ 1771:4cca386e5766

New release

author	Adam Chlipala <adam@chlipala.net>
date	Sat, 19 May 2012 11:46:29 -0400
parents	53d56d87fbd2
children	6bc2a8cb3a67

rev	line source
adamc@524	1 \documentclass{article}
adamc@554	2 \usepackage{fullpage,amsmath,amssymb,proof,url}
rmbruijn@1568	3 \usepackage[T1]{fontenc}
vshabanoff@1765	4 \usepackage{ae,aecompl}
adamc@524	5 \newcommand{\cd}[1]{\texttt{#1}}
adamc@524	6 \newcommand{\mt}[1]{\mathsf{#1}}
adamc@524	7
adamc@524	8 \newcommand{\rc}{+ \hspace{-.075in} + \;}
adamc@527	9 \newcommand{\rcut}{\; \texttt{--} \;}
adamc@527	10 \newcommand{\rcutM}{\; \texttt{---} \;}
adamc@524	11
adamc@524	12 \begin{document}
adamc@524	13
adamc@524	14 \title{The Ur/Web Manual}
adamc@524	15 \author{Adam Chlipala}
adamc@524	16
adamc@524	17 \maketitle
adamc@524	18
adamc@540	19 \tableofcontents
adamc@540	20
adamc@554	21
adamc@554	22 \section{Introduction}
adamc@554	23
adamc@1160	24 \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	25
adamc@554	26 \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	27
adamc@554	28 \begin{itemize}
adamc@554	29 \item Suffer from any kinds of code-injection attacks
adamc@554	30 \item Return invalid HTML
adamc@554	31 \item Contain dead intra-application links
adamc@554	32 \item Have mismatches between HTML forms and the fields expected by their handlers
adamc@652	33 \item Include client-side code that makes incorrect assumptions about the ``AJAX''-style services that the remote web server provides
adamc@554	34 \item Attempt invalid SQL queries
adamc@652	35 \item Use improper marshaling or unmarshaling in communication with SQL databases or between browsers and web servers
adamc@554	36 \end{itemize}
adamc@554	37
adamc@554	38 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	39
adamc@652	40 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	41
adamc@554	42 \medskip
adamc@554	43
adamc@554	44 The official web site for Ur is:
adamc@554	45 \begin{center}
adamc@554	46 \url{http://www.impredicative.com/ur/}
adamc@554	47 \end{center}
adamc@554	48
adamc@555	49
adamc@555	50 \section{Installation}
adamc@555	51
adamc@555	52 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	53
adamc@555	54 \begin{verbatim}
adamc@555	55 ./configure
adamc@555	56 make
adamc@555	57 sudo make install
adamc@555	58 \end{verbatim}
adamc@555	59
adam@1523	60 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	61 \begin{verbatim}
adam@1368	62 apt-get install mlton libssl-dev
adamc@896	63 \end{verbatim}
adamc@555	64
adamc@896	65 To build programs that access SQL databases, you also need one of these client libraries for supported backends.
adamc@555	66 \begin{verbatim}
adamc@896	67 apt-get install libpq-dev libmysqlclient15-dev libsqlite3-dev
adamc@555	68 \end{verbatim}
adamc@555	69
adamc@555	70 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	71 \begin{verbatim}
adamc@555	72 apt-get install smlnj libsmlnj-smlnj ml-yacc ml-lpt
adamc@555	73 \end{verbatim}
adamc@555	74
adamc@555	75 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	76
adamc@896	77 To run an SQL-backed application with a backend besides SQLite, you will probably want to install one of these servers.
adamc@555	78
adamc@555	79 \begin{verbatim}
adam@1400	80 apt-get install postgresql-8.4 mysql-server-5.1
adamc@555	81 \end{verbatim}
adamc@555	82
adamc@555	83 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	84
adamc@555	85 \begin{verbatim}
adamc@555	86 apt-get install emacs-goodies-el
adamc@555	87 \end{verbatim}
adamc@555	88
adam@1441	89 If you don't want to install the Emacs mode, run \texttt{./configure} with the argument \texttt{--without-emacs}.
adam@1441	90
adam@1523	91 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	92
adamc@555	93 \begin{verbatim}
adam@1523	94 CCARGS=-fno-inline ./configure
adamc@555	95 \end{verbatim}
adamc@555	96
adam@1523	97 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	98
adamc@555	99 The Emacs mode can be set to autoload by adding the following to your \texttt{.emacs} file.
adamc@555	100
adamc@555	101 \begin{verbatim}
adamc@555	102 (add-to-list 'load-path "/usr/local/share/emacs/site-lisp/urweb-mode")
adamc@555	103 (load "urweb-mode-startup")
adamc@555	104 \end{verbatim}
adamc@555	105
adamc@555	106 Change the path in the first line if you chose a different Emacs installation path during configuration.
adamc@555	107
adamc@555	108
adamc@556	109 \section{Command-Line Compiler}
adamc@556	110
adam@1604	111 \subsection{\label{cl}Project Files}
adamc@556	112
adamc@556	113 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	114
adamc@556	115 \begin{verbatim}
adamc@556	116 database dbname=test
adamc@556	117 sql crud1.sql
adamc@556	118
adamc@556	119 crud
adamc@556	120 crud1
adamc@556	121 \end{verbatim}
adamc@556	122
adamc@556	123 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	124
adamc@556	125 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	126
adamc@556	127 \begin{verbatim}
adamc@556	128 createdb test
adamc@556	129 psql -f crud1.sql test
adamc@556	130 \end{verbatim}
adamc@556	131
adam@1331	132 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	133
adamc@556	134 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	135
adamc@783	136 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	137 \begin{itemize}
adam@1465	138 \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	139 \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	140 \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	141 \item \texttt{clientOnly Module.ident} registers an FFI function or transaction that may only be run in client browsers.
adamc@783	142 \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	143 \item \texttt{database DBSTRING} sets the string to pass to libpq to open a database connection.
adamc@783	144 \item \texttt{debug} saves some intermediate C files, which is mostly useful to help in debugging the compiler itself.
adam@1699	145 \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	146 \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	147 \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	148 \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	149 \item \texttt{jsFunc Module.ident=name} gives the JavaScript name of an FFI value.
adamc@1089	150 \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	151 \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	152 \begin{itemize}
adam@1309	153 \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	154 \item \texttt{database}: maximum size of database files (currently only used by SQLite)
adam@1309	155 \item \texttt{deltas}: maximum number of messages sendable in a single request handler with \texttt{Basis.send}
adam@1309	156 \item \texttt{globals}: maximum number of global variables that FFI libraries may set in a single request context
adam@1309	157 \item \texttt{headers}: maximum size (in bytes) of per-request buffer used to hold HTTP headers for generated pages
adam@1309	158 \item \texttt{heap}: maximum size (in bytes) of per-request heap for dynamically-allocated data
adam@1309	159 \item \texttt{inputs}: maximum number of top-level form fields per request
adam@1309	160 \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	161 \item \texttt{page}: maximum size (in bytes) of per-request buffer used to hold HTML content of generated pages
adam@1309	162 \item \texttt{script}: maximum size (in bytes) of per-request buffer used to hold JavaScript content of generated pages
adam@1309	163 \item \texttt{subinputs}: maximum number of form fields per request, excluding top-level fields
adam@1309	164 \item \texttt{time}: maximum running time of a single page request, in units of approximately 0.1 seconds
adam@1309	165 \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	166 \end{itemize}
adam@1523	167 \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	168 \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	169 \item \texttt{minHeap NUMBYTES} sets the initial size for thread-local heaps used in handling requests. These heaps grow automatically as needed (up to any maximum set with \texttt{limit}), but each regrow requires restarting the request handling process.
adam@1478	170 \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	171 \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	172 \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	173 \item \texttt{prefix PREFIX} sets the prefix included before every URI within the generated application. The default is \texttt{/}.
adamc@783	174 \item \texttt{profile} generates an executable that may be used with gprof.
adam@1752	175 \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. An optional suffix of \cd{[-]} for a \cd{rewrite} directive asks to additionally replace all \cd{\_} characters with \cd{-} characters, which can be handy for, e.g., interfacing with an off-the-shelf CSS library that prefers hyphens over underscores.
adamc@1183	176 \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	177 \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	178 \item \texttt{serverOnly Module.ident} registers an FFI function or transaction that may only be run on the server.
adamc@1164	179 \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	180 \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	181 \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	182 \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	183 \end{itemize}
adamc@701	184
adamc@701	185
adamc@557	186 \subsection{Building an Application}
adamc@557	187
adamc@557	188 To compile project \texttt{P.urp}, simply run
adamc@557	189 \begin{verbatim}
adamc@557	190 urweb P
adamc@557	191 \end{verbatim}
adamc@1198	192 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	193
adamc@557	194 To time how long the different compiler phases run, without generating an executable, run
adamc@557	195 \begin{verbatim}
adamc@557	196 urweb -timing P
adamc@557	197 \end{verbatim}
adamc@557	198
adamc@1086	199 To stop the compilation process after type-checking, run
adamc@1086	200 \begin{verbatim}
adamc@1086	201 urweb -tc P
adamc@1086	202 \end{verbatim}
adam@1530	203 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	204
adam@1745	205 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. A refined version of this option is \cd{-dumpTypesOnError}, which only has an effect when there are compilation errors.
adam@1531	206
adam@1723	207 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	208
adamc@1170	209 To output information relevant to CSS stylesheets (and not finish regular compilation), run
adamc@1170	210 \begin{verbatim}
adamc@1170	211 urweb -css P
adamc@1170	212 \end{verbatim}
adamc@1170	213 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	214
adam@1733	215 Ur/Web type inference can take a significant amount of time, so it can be helpful to cache type-inferred versions of source files. This mode can be activated by running
adam@1733	216 \begin{verbatim}
adam@1733	217 urweb daemon start
adam@1733	218 \end{verbatim}
adam@1733	219 Further \cd{urweb} invocations in the same working directory will send requests to a background daemon process that reuses type inference results whenever possible, tracking source file dependencies and modification times. To stop the background daemon, run
adam@1733	220 \begin{verbatim}
adam@1733	221 urweb daemon stop
adam@1733	222 \end{verbatim}
adam@1733	223 Communication happens via a UNIX domain socket in file \cd{.urweb\_daemon} in the working directory.
adam@1733	224
adam@1733	225 \medskip
adam@1733	226
adamc@896	227 Some other command-line parameters are accepted:
adamc@896	228 \begin{itemize}
ezyang@1739	229 \item \texttt{-boot}: Run Ur/Web from a build tree (and not from a system install). This is useful if you're testing the compiler and don't want to install it. It forces generation of statically linked executables.
ezyang@1739	230
adamc@896	231 \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	232
adamc@896	233 \item \texttt{-dbms [postgres\|mysql\|sqlite]}: Sets the database backend to use.
adamc@896	234 \begin{itemize}
adamc@896	235 \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	236
adamc@896	237 A command sequence like this can initialize a Postgres database, using a file \texttt{app.sql} generated by the compiler:
adamc@896	238 \begin{verbatim}
adamc@896	239 createdb app
adamc@896	240 psql -f app.sql app
adamc@896	241 \end{verbatim}
adamc@896	242
adamc@896	243 \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	244
adamc@896	245 A command sequence like this can initialize a MySQL database:
adamc@896	246 \begin{verbatim}
adamc@896	247 echo "CREATE DATABASE app" \| mysql
adamc@896	248 mysql -D app <app.sql
adamc@896	249 \end{verbatim}
adamc@896	250
adamc@896	251 \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	252
adamc@896	253 A command like this can initialize an SQLite database:
adamc@896	254 \begin{verbatim}
adamc@896	255 sqlite3 path/to/database/file <app.sql
adamc@896	256 \end{verbatim}
adamc@896	257 \end{itemize}
adamc@896	258
adam@1693	259 \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	260
adam@1309	261 \item \texttt{-limit class num}: Equivalent to the \texttt{limit} directive from \texttt{.urp} files
adam@1309	262
adamc@896	263 \item \texttt{-output FILENAME}: Set where the application executable is written.
adamc@896	264
adamc@1127	265 \item \texttt{-path NAME VALUE}: Set the value of path variable \texttt{\$NAME} to \texttt{VALUE}, for use in \texttt{.urp} files.
adamc@1127	266
adam@1335	267 \item \texttt{-prefix PREFIX}: Equivalent to the \texttt{prefix} directive from \texttt{.urp} files
adam@1335	268
adam@1753	269 \item \texttt{-protocol [http\|cgi\|fastcgi\|static]}: Set the protocol that the generated application speaks.
adamc@896	270 \begin{itemize}
adamc@896	271 \item \texttt{http}: This is the default. It is for building standalone web servers that can be accessed by web browsers directly.
adamc@896	272
adamc@896	273 \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	274
adamc@896	275 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	276 \begin{verbatim}
adamc@896	277 ScriptAlias /Hello /path/to/hello.exe
adamc@896	278 \end{verbatim}
adamc@896	279
adamc@1163	280 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	281 \begin{verbatim}
adamc@1163	282 Options +ExecCGI
adamc@1163	283 AddHandler cgi-script .exe
adamc@1163	284 \end{verbatim}
adamc@1163	285
adamc@1163	286 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	287 \begin{verbatim}
adamc@1163	288 prefix /dir/script.exe/
adamc@1163	289 \end{verbatim}
adamc@1163	290
adamc@1163	291 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	292
adamc@1164	293 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	294
adamc@896	295 \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	296
adamc@896	297 To configure a FastCGI program with Apache, one could combine the above \texttt{ScriptAlias} line with a line like this:
adamc@896	298 \begin{verbatim}
adamc@896	299 FastCgiServer /path/to/hello.exe -idle-timeout 99999
adamc@896	300 \end{verbatim}
adamc@896	301 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	302
adam@1753	303 Also see the discussion of the \cd{prefix} directive for CGI above; similar configuration is likely to be necessary for FastCGI. An Ur/Web application won't generally run correctly if it doesn't have a unique URI prefix assigned to it and configured with \cd{prefix}.
adam@1753	304
adamc@896	305 Here is some lighttpd configuration for the same application.
adamc@896	306 \begin{verbatim}
adamc@896	307 fastcgi.server = (
adamc@896	308 "/Hello/" =>
adamc@896	309 (( "bin-path" => "/path/to/hello.exe",
adamc@896	310 "socket" => "/tmp/hello",
adamc@896	311 "check-local" => "disable",
adamc@896	312 "docroot" => "/",
adamc@896	313 "max-procs" => "1"
adamc@896	314 ))
adamc@896	315 )
adamc@896	316 \end{verbatim}
adamc@896	317 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	318
adamc@896	319 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	320
adam@1509	321 \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	322 \end{itemize}
adamc@896	323
adamc@1127	324 \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	325
adamc@1164	326 \item \texttt{-sigfile PATH}: Same as the \texttt{sigfile} directive in \texttt{.urp} files
adamc@1164	327
adamc@896	328 \item \texttt{-sql FILENAME}: Set where a database set-up SQL script is written.
adamc@1095	329
adamc@1095	330 \item \texttt{-static}: Link the runtime system statically. The default is to link against dynamic libraries.
adamc@896	331 \end{itemize}
adamc@896	332
adam@1297	333 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	334
adam@1509	335 \subsection{Tutorial Formatting}
adam@1509	336
adam@1509	337 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	338
adam@1509	339 These input files follow normal Ur syntax, with a few exceptions:
adam@1509	340 \begin{itemize}
adam@1509	341 \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	342 \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	343 \item A comment like \cd{(* * HEADING *)} introduces a section heading, with text \cd{HEADING} of your choice.
adam@1509	344 \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	345 \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	346 \end{itemize}
adam@1509	347
adam@1509	348 A word of warning: as for demo generation, tutorial generation calls Emacs to syntax-highlight Ur code.
adam@1509	349
adam@1522	350 \subsection{Run-Time Options}
adam@1522	351
adam@1522	352 Compiled applications consult a few environment variables to modify their behavior:
adam@1522	353
adam@1522	354 \begin{itemize}
adam@1522	355 \item \cd{URWEB\_NUM\_THREADS}: alternative to the \cd{-t} command-line argument (currently used only by FastCGI)
adam@1522	356 \item \cd{URWEB\_STACK\_SIZE}: size of per-thread stacks, in bytes
as@1564	357 \item \cd{URWEB\_PQ\_CON}: when using PostgreSQL, overrides the compiled-in connection string
adam@1522	358 \end{itemize}
adam@1522	359
adam@1509	360
adamc@529	361 \section{Ur Syntax}
adamc@529	362
adamc@784	363 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	364
adamc@524	365 \subsection{Lexical Conventions}
adamc@524	366
adamc@524	367 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	368
adamc@524	369 \begin{center}
adamc@524	370 \begin{tabular}{rl}
adamc@524	371 \textbf{\LaTeX} & \textbf{ASCII} \\
adamc@524	372 $\to$ & \cd{->} \\
adam@1687	373 $\longrightarrow$ & \cd{-{}->} \\
adamc@524	374 $\times$ & \cd{*} \\
adamc@524	375 $\lambda$ & \cd{fn} \\
adamc@524	376 $\Rightarrow$ & \cd{=>} \\
adamc@652	377 $\Longrightarrow$ & \cd{==>} \\
adamc@529	378 $\neq$ & \cd{<>} \\
adamc@529	379 $\leq$ & \cd{<=} \\
adamc@529	380 $\geq$ & \cd{>=} \\
adamc@524	381 \\
adamc@524	382 $x$ & Normal textual identifier, not beginning with an uppercase letter \\
adamc@525	383 $X$ & Normal textual identifier, beginning with an uppercase letter \\
adamc@524	384 \end{tabular}
adamc@524	385 \end{center}
adamc@524	386
adamc@525	387 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	388
adamc@873	389 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	390
adamc@527	391 This version of the manual doesn't include operator precedences; see \texttt{src/urweb.grm} for that.
adamc@527	392
adam@1297	393 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	394
adamc@552	395 \subsection{\label{core}Core Syntax}
adamc@524	396
adamc@524	397 \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	398 $$\begin{array}{rrcll}
adamc@524	399 \textrm{Kinds} & \kappa &::=& \mt{Type} & \textrm{proper types} \\
adamc@525	400 &&& \mt{Unit} & \textrm{the trivial constructor} \\
adamc@525	401 &&& \mt{Name} & \textrm{field names} \\
adamc@525	402 &&& \kappa \to \kappa & \textrm{type-level functions} \\
adamc@525	403 &&& \{\kappa\} & \textrm{type-level records} \\
adamc@525	404 &&& (\kappa\times^+) & \textrm{type-level tuples} \\
adamc@652	405 &&& X & \textrm{variable} \\
adam@1574	406 &&& X \longrightarrow \kappa & \textrm{kind-polymorphic type-level function} \\
adamc@529	407 &&& \_\_ & \textrm{wildcard} \\
adamc@525	408 &&& (\kappa) & \textrm{explicit precedence} \\
adamc@524	409 \end{array}$$
adamc@524	410
adamc@524	411 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	412 $$\begin{array}{rrcll}
adamc@524	413 \textrm{Explicitness} & ? &::=& :: & \textrm{explicit} \\
adamc@558	414 &&& ::: & \textrm{implicit}
adamc@524	415 \end{array}$$
adamc@524	416
adamc@524	417 \emph{Constructors} are the main class of compile-time-only data. They include proper types and are classified by kinds.
adamc@524	418 $$\begin{array}{rrcll}
adamc@524	419 \textrm{Constructors} & c, \tau &::=& (c) :: \kappa & \textrm{kind annotation} \\
adamc@530	420 &&& \hat{x} & \textrm{constructor variable} \\
adamc@524	421 \\
adamc@525	422 &&& \tau \to \tau & \textrm{function type} \\
adamc@525	423 &&& x \; ? \; \kappa \to \tau & \textrm{polymorphic function type} \\
adamc@652	424 &&& X \longrightarrow \tau & \textrm{kind-polymorphic function type} \\
adamc@525	425 &&& \$ c & \textrm{record type} \\
adamc@524	426 \\
adamc@525	427 &&& c \; c & \textrm{type-level function application} \\
adamc@530	428 &&& \lambda x \; :: \; \kappa \Rightarrow c & \textrm{type-level function abstraction} \\
adamc@524	429 \\
adamc@652	430 &&& X \Longrightarrow c & \textrm{type-level kind-polymorphic function abstraction} \\
adamc@655	431 &&& c [\kappa] & \textrm{type-level kind-polymorphic function application} \\
adamc@652	432 \\
adamc@525	433 &&& () & \textrm{type-level unit} \\
adamc@525	434 &&& \#X & \textrm{field name} \\
adamc@524	435 \\
adamc@525	436 &&& [(c = c)^*] & \textrm{known-length type-level record} \\
adamc@525	437 &&& c \rc c & \textrm{type-level record concatenation} \\
adamc@652	438 &&& \mt{map} & \textrm{type-level record map} \\
adamc@524	439 \\
adamc@558	440 &&& (c,^+) & \textrm{type-level tuple} \\
adamc@525	441 &&& c.n & \textrm{type-level tuple projection ($n \in \mathbb N^+$)} \\
adamc@524	442 \\
adamc@652	443 &&& [c \sim c] \Rightarrow \tau & \textrm{guarded type} \\
adamc@524	444 \\
adamc@529	445 &&& \_ :: \kappa & \textrm{wildcard} \\
adamc@525	446 &&& (c) & \textrm{explicit precedence} \\
adamc@530	447 \\
adamc@530	448 \textrm{Qualified uncapitalized variables} & \hat{x} &::=& x & \textrm{not from a module} \\
adamc@530	449 &&& M.x & \textrm{projection from a module} \\
adamc@525	450 \end{array}$$
adamc@525	451
adam@1579	452 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	453
adamc@525	454 Modules of the module system are described by \emph{signatures}.
adamc@525	455 $$\begin{array}{rrcll}
adamc@525	456 \textrm{Signatures} & S &::=& \mt{sig} \; s^* \; \mt{end} & \textrm{constant} \\
adamc@525	457 &&& X & \textrm{variable} \\
adamc@525	458 &&& \mt{functor}(X : S) : S & \textrm{functor} \\
adamc@529	459 &&& S \; \mt{where} \; \mt{con} \; x = c & \textrm{concretizing an abstract constructor} \\
adamc@525	460 &&& M.X & \textrm{projection from a module} \\
adamc@525	461 \\
adamc@525	462 \textrm{Signature items} & s &::=& \mt{con} \; x :: \kappa & \textrm{abstract constructor} \\
adamc@525	463 &&& \mt{con} \; x :: \kappa = c & \textrm{concrete constructor} \\
adamc@528	464 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529	465 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@525	466 &&& \mt{val} \; x : \tau & \textrm{value} \\
adamc@525	467 &&& \mt{structure} \; X : S & \textrm{sub-module} \\
adamc@525	468 &&& \mt{signature} \; X = S & \textrm{sub-signature} \\
adamc@525	469 &&& \mt{include} \; S & \textrm{signature inclusion} \\
adamc@525	470 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@654	471 &&& \mt{class} \; x :: \kappa & \textrm{abstract constructor class} \\
adamc@654	472 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@525	473 \\
adamc@525	474 \textrm{Datatype constructors} & dc &::=& X & \textrm{nullary constructor} \\
adamc@525	475 &&& X \; \mt{of} \; \tau & \textrm{unary constructor} \\
adamc@524	476 \end{array}$$
adamc@524	477
adamc@526	478 \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	479 $$\begin{array}{rrcll}
adamc@526	480 \textrm{Patterns} & p &::=& \_ & \textrm{wildcard} \\
adamc@526	481 &&& x & \textrm{variable} \\
adamc@526	482 &&& \ell & \textrm{constant} \\
adamc@526	483 &&& \hat{X} & \textrm{nullary constructor} \\
adamc@526	484 &&& \hat{X} \; p & \textrm{unary constructor} \\
adamc@526	485 &&& \{(x = p,)^*\} & \textrm{rigid record pattern} \\
adamc@526	486 &&& \{(x = p,)^+, \ldots\} & \textrm{flexible record pattern} \\
adamc@852	487 &&& p : \tau & \textrm{type annotation} \\
adamc@527	488 &&& (p) & \textrm{explicit precedence} \\
adamc@526	489 \\
adamc@529	490 \textrm{Qualified capitalized variables} & \hat{X} &::=& X & \textrm{not from a module} \\
adamc@526	491 &&& M.X & \textrm{projection from a module} \\
adamc@526	492 \end{array}$$
adamc@526	493
adamc@527	494 \emph{Expressions} are the main run-time entities, corresponding to both ``expressions'' and ``statements'' in mainstream imperative languages.
adamc@527	495 $$\begin{array}{rrcll}
adamc@527	496 \textrm{Expressions} & e &::=& e : \tau & \textrm{type annotation} \\
adamc@529	497 &&& \hat{x} & \textrm{variable} \\
adamc@529	498 &&& \hat{X} & \textrm{datatype constructor} \\
adamc@527	499 &&& \ell & \textrm{constant} \\
adamc@527	500 \\
adamc@527	501 &&& e \; e & \textrm{function application} \\
adamc@527	502 &&& \lambda x : \tau \Rightarrow e & \textrm{function abstraction} \\
adamc@527	503 &&& e [c] & \textrm{polymorphic function application} \\
adamc@852	504 &&& \lambda [x \; ? \; \kappa] \Rightarrow e & \textrm{polymorphic function abstraction} \\
adamc@655	505 &&& e [\kappa] & \textrm{kind-polymorphic function application} \\
adamc@652	506 &&& X \Longrightarrow e & \textrm{kind-polymorphic function abstraction} \\
adamc@527	507 \\
adamc@527	508 &&& \{(c = e,)^*\} & \textrm{known-length record} \\
adamc@527	509 &&& e.c & \textrm{record field projection} \\
adamc@527	510 &&& e \rc e & \textrm{record concatenation} \\
adamc@527	511 &&& e \rcut c & \textrm{removal of a single record field} \\
adamc@527	512 &&& e \rcutM c & \textrm{removal of multiple record fields} \\
adamc@527	513 \\
adamc@527	514 &&& \mt{let} \; ed^* \; \mt{in} \; e \; \mt{end} & \textrm{local definitions} \\
adamc@527	515 \\
adamc@527	516 &&& \mt{case} \; e \; \mt{of} \; (p \Rightarrow e\|)^+ & \textrm{pattern matching} \\
adamc@527	517 \\
adamc@654	518 &&& \lambda [c \sim c] \Rightarrow e & \textrm{guarded expression abstraction} \\
adamc@654	519 &&& e \; ! & \textrm{guarded expression application} \\
adamc@527	520 \\
adamc@527	521 &&& \_ & \textrm{wildcard} \\
adamc@527	522 &&& (e) & \textrm{explicit precedence} \\
adamc@527	523 \\
adamc@527	524 \textrm{Local declarations} & ed &::=& \cd{val} \; x : \tau = e & \textrm{non-recursive value} \\
adamc@527	525 &&& \cd{val} \; \cd{rec} \; (x : \tau = e \; \cd{and})^+ & \textrm{mutually-recursive values} \\
adamc@527	526 \end{array}$$
adamc@527	527
adamc@655	528 As with constructors, we include both abstraction and application for kind polymorphism, but applications are only inferred internally.
adamc@655	529
adamc@528	530 \emph{Declarations} primarily bring new symbols into context.
adamc@528	531 $$\begin{array}{rrcll}
adamc@528	532 \textrm{Declarations} & d &::=& \mt{con} \; x :: \kappa = c & \textrm{constructor synonym} \\
adamc@528	533 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529	534 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@528	535 &&& \mt{val} \; x : \tau = e & \textrm{value} \\
adamc@528	536 &&& \mt{val} \; \cd{rec} \; (x : \tau = e \; \mt{and})^+ & \textrm{mutually-recursive values} \\
adamc@528	537 &&& \mt{structure} \; X : S = M & \textrm{module definition} \\
adamc@528	538 &&& \mt{signature} \; X = S & \textrm{signature definition} \\
adamc@528	539 &&& \mt{open} \; M & \textrm{module inclusion} \\
adamc@528	540 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@528	541 &&& \mt{open} \; \mt{constraints} \; M & \textrm{inclusion of just the constraints from a module} \\
adamc@528	542 &&& \mt{table} \; x : c & \textrm{SQL table} \\
adam@1594	543 &&& \mt{view} \; x = e & \textrm{SQL view} \\
adamc@528	544 &&& \mt{sequence} \; x & \textrm{SQL sequence} \\
adamc@535	545 &&& \mt{cookie} \; x : \tau & \textrm{HTTP cookie} \\
adamc@784	546 &&& \mt{style} \; x : \tau & \textrm{CSS class} \\
adamc@654	547 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@1085	548 &&& \mt{task} \; e = e & \textrm{recurring task} \\
adamc@528	549 \\
adamc@529	550 \textrm{Modules} & M &::=& \mt{struct} \; d^* \; \mt{end} & \textrm{constant} \\
adamc@529	551 &&& X & \textrm{variable} \\
adamc@529	552 &&& M.X & \textrm{projection} \\
adamc@529	553 &&& M(M) & \textrm{functor application} \\
adamc@529	554 &&& \mt{functor}(X : S) : S = M & \textrm{functor abstraction} \\
adamc@528	555 \end{array}$$
adamc@528	556
adamc@528	557 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	558
adam@1594	559 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	560
adamc@529	561 \subsection{Shorthands}
adamc@529	562
adamc@529	563 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	564
adamc@529	565 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	566
adamc@529	567 A record type may be written $\{(c = c,)^\}$, which elaborates to $\$[(c = c,)^]$.
adamc@529	568
adamc@533	569 The notation $[c_1, \ldots, c_n]$ is shorthand for $[c_1 = (), \ldots, c_n = ()]$.
adamc@533	570
adam@1350	571 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	572
adam@1687	573 The syntax $()$ expands to $\{\}$ as a pattern or expression.
adam@1687	574
adamc@852	575 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	576
adam@1574	577 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	578
adam@1306	579 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	580
adamc@529	581 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	582
adamc@529	583 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	584
adamc@654	585 A signature item or declaration $\mt{class} \; x = \lambda y \Rightarrow c$ may be abbreviated $\mt{class} \; x \; y = c$.
adamc@529	586
adam@1738	587 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; and any record type is considered to be a type class instance type when every field's type is a type class instance type.) 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	588
adamc@852	589 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	590
adamc@852	591 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	592
adamc@852	593 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	594
adamc@529	595 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	596
adamc@852	597 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	598
adamc@853	599 A declaration $\mt{table} \; x : \{(c = c,)^\}$ is elaborated into $\mt{table} \; x : [(c = c,)^]$.
adamc@529	600
adamc@529	601 The syntax $\mt{where} \; \mt{type}$ is an alternate form of $\mt{where} \; \mt{con}$.
adamc@529	602
adamc@529	603 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	604
adamc@529	605 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	606
adamc@784	607 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	608
adamc@530	609
adamc@530	610 \section{Static Semantics}
adamc@530	611
adamc@530	612 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	613
adamc@530	614 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	615 \begin{itemize}
adamc@655	616 \item $\Gamma \vdash \kappa$ expresses kind well-formedness.
adamc@530	617 \item $\Gamma \vdash c :: \kappa$ assigns a kind to a constructor in a context.
adamc@530	618 \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	619 \item $\Gamma \vdash c \hookrightarrow C$ proves that record constructor $c$ decomposes into set $C$ of field names and record constructors.
adamc@530	620 \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	621 \item $\Gamma \vdash e : \tau$ is a standard typing judgment.
adamc@534	622 \item $\Gamma \vdash p \leadsto \Gamma; \tau$ combines typing of patterns with calculation of which new variables they bind.
adamc@537	623 \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	624 \item $\Gamma \vdash S \equiv S$ is the signature equivalence judgment.
adamc@536	625 \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	626 \item $\Gamma \vdash M : S$ is the module signature checking judgment.
adamc@537	627 \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	628 \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	629 \end{itemize}
adamc@530	630
adamc@655	631
adamc@655	632 \subsection{Kind Well-Formedness}
adamc@655	633
adamc@655	634 $$\infer{\Gamma \vdash \mt{Type}}{}
adamc@655	635 \quad \infer{\Gamma \vdash \mt{Unit}}{}
adamc@655	636 \quad \infer{\Gamma \vdash \mt{Name}}{}
adamc@655	637 \quad \infer{\Gamma \vdash \kappa_1 \to \kappa_2}{
adamc@655	638 \Gamma \vdash \kappa_1
adamc@655	639 & \Gamma \vdash \kappa_2
adamc@655	640 }
adamc@655	641 \quad \infer{\Gamma \vdash \{\kappa\}}{
adamc@655	642 \Gamma \vdash \kappa
adamc@655	643 }
adamc@655	644 \quad \infer{\Gamma \vdash (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@655	645 \forall i: \Gamma \vdash \kappa_i
adamc@655	646 }$$
adamc@655	647
adamc@655	648 $$\infer{\Gamma \vdash X}{
adamc@655	649 X \in \Gamma
adamc@655	650 }
adamc@655	651 \quad \infer{\Gamma \vdash X \longrightarrow \kappa}{
adamc@655	652 \Gamma, X \vdash \kappa
adamc@655	653 }$$
adamc@655	654
adamc@530	655 \subsection{Kinding}
adamc@530	656
adamc@655	657 We write $[X \mapsto \kappa_1]\kappa_2$ for capture-avoiding substitution of $\kappa_1$ for $X$ in $\kappa_2$.
adamc@655	658
adamc@530	659 $$\infer{\Gamma \vdash (c) :: \kappa :: \kappa}{
adamc@530	660 \Gamma \vdash c :: \kappa
adamc@530	661 }
adamc@530	662 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530	663 x :: \kappa \in \Gamma
adamc@530	664 }
adamc@530	665 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530	666 x :: \kappa = c \in \Gamma
adamc@530	667 }$$
adamc@530	668
adamc@530	669 $$\infer{\Gamma \vdash M.x :: \kappa}{
adamc@537	670 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	671 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = \kappa
adamc@530	672 }
adamc@530	673 \quad \infer{\Gamma \vdash M.x :: \kappa}{
adamc@537	674 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	675 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@530	676 }$$
adamc@530	677
adamc@530	678 $$\infer{\Gamma \vdash \tau_1 \to \tau_2 :: \mt{Type}}{
adamc@530	679 \Gamma \vdash \tau_1 :: \mt{Type}
adamc@530	680 & \Gamma \vdash \tau_2 :: \mt{Type}
adamc@530	681 }
adamc@530	682 \quad \infer{\Gamma \vdash x \; ? \: \kappa \to \tau :: \mt{Type}}{
adamc@530	683 \Gamma, x :: \kappa \vdash \tau :: \mt{Type}
adamc@530	684 }
adamc@655	685 \quad \infer{\Gamma \vdash X \longrightarrow \tau :: \mt{Type}}{
adamc@655	686 \Gamma, X \vdash \tau :: \mt{Type}
adamc@655	687 }
adamc@530	688 \quad \infer{\Gamma \vdash \$c :: \mt{Type}}{
adamc@530	689 \Gamma \vdash c :: \{\mt{Type}\}
adamc@530	690 }$$
adamc@530	691
adamc@530	692 $$\infer{\Gamma \vdash c_1 \; c_2 :: \kappa_2}{
adamc@530	693 \Gamma \vdash c_1 :: \kappa_1 \to \kappa_2
adamc@530	694 & \Gamma \vdash c_2 :: \kappa_1
adamc@530	695 }
adamc@530	696 \quad \infer{\Gamma \vdash \lambda x \; :: \; \kappa_1 \Rightarrow c :: \kappa_1 \to \kappa_2}{
adamc@530	697 \Gamma, x :: \kappa_1 \vdash c :: \kappa_2
adamc@530	698 }$$
adamc@530	699
adamc@655	700 $$\infer{\Gamma \vdash c[\kappa'] :: [X \mapsto \kappa']\kappa}{
adamc@655	701 \Gamma \vdash c :: X \to \kappa
adamc@655	702 & \Gamma \vdash \kappa'
adamc@655	703 }
adamc@655	704 \quad \infer{\Gamma \vdash X \Longrightarrow c :: X \to \kappa}{
adamc@655	705 \Gamma, X \vdash c :: \kappa
adamc@655	706 }$$
adamc@655	707
adamc@530	708 $$\infer{\Gamma \vdash () :: \mt{Unit}}{}
adamc@530	709 \quad \infer{\Gamma \vdash \#X :: \mt{Name}}{}$$
adamc@530	710
adamc@530	711 $$\infer{\Gamma \vdash [\overline{c_i = c'_i}] :: \{\kappa\}}{
adamc@530	712 \forall i: \Gamma \vdash c_i : \mt{Name}
adamc@530	713 & \Gamma \vdash c'_i :: \kappa
adamc@530	714 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@530	715 }
adamc@530	716 \quad \infer{\Gamma \vdash c_1 \rc c_2 :: \{\kappa\}}{
adamc@530	717 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530	718 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@530	719 & \Gamma \vdash c_1 \sim c_2
adamc@530	720 }$$
adamc@530	721
adamc@655	722 $$\infer{\Gamma \vdash \mt{map} :: (\kappa_1 \to \kappa_2) \to \{\kappa_1\} \to \{\kappa_2\}}{}$$
adamc@530	723
adamc@573	724 $$\infer{\Gamma \vdash (\overline c) :: (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@573	725 \forall i: \Gamma \vdash c_i :: \kappa_i
adamc@530	726 }
adamc@573	727 \quad \infer{\Gamma \vdash c.i :: \kappa_i}{
adamc@573	728 \Gamma \vdash c :: (\kappa_1 \times \ldots \times \kappa_n)
adamc@530	729 }$$
adamc@530	730
adamc@655	731 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow \tau :: \mt{Type}}{
adamc@655	732 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530	733 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@655	734 & \Gamma, c_1 \sim c_2 \vdash \tau :: \mt{Type}
adamc@530	735 }$$
adamc@530	736
adamc@531	737 \subsection{Record Disjointness}
adamc@531	738
adamc@531	739 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@558	740 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@558	741 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@558	742 & \forall c'_1 \in C_1, c'_2 \in C_2: \Gamma \vdash c'_1 \sim c'_2
adamc@531	743 }
adamc@531	744 \quad \infer{\Gamma \vdash X \sim X'}{
adamc@531	745 X \neq X'
adamc@531	746 }$$
adamc@531	747
adamc@531	748 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@531	749 c'_1 \sim c'_2 \in \Gamma
adamc@558	750 & \Gamma \vdash c'_1 \hookrightarrow C_1
adamc@558	751 & \Gamma \vdash c'_2 \hookrightarrow C_2
adamc@558	752 & c_1 \in C_1
adamc@558	753 & c_2 \in C_2
adamc@531	754 }$$
adamc@531	755
adamc@531	756 $$\infer{\Gamma \vdash c \hookrightarrow \{c\}}{}
adamc@531	757 \quad \infer{\Gamma \vdash [\overline{c = c'}] \hookrightarrow \{\overline{c}\}}{}
adamc@531	758 \quad \infer{\Gamma \vdash c_1 \rc c_2 \hookrightarrow C_1 \cup C_2}{
adamc@531	759 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@531	760 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@531	761 }
adamc@531	762 \quad \infer{\Gamma \vdash c \hookrightarrow C}{
adamc@531	763 \Gamma \vdash c \equiv c'
adamc@531	764 & \Gamma \vdash c' \hookrightarrow C
adamc@531	765 }
adamc@531	766 \quad \infer{\Gamma \vdash \mt{map} \; f \; c \hookrightarrow C}{
adamc@531	767 \Gamma \vdash c \hookrightarrow C
adamc@531	768 }$$
adamc@531	769
adamc@541	770 \subsection{\label{definitional}Definitional Equality}
adamc@532	771
adamc@655	772 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	773
adamc@532	774 $$\infer{\Gamma \vdash c \equiv c}{}
adamc@532	775 \quad \infer{\Gamma \vdash c_1 \equiv c_2}{
adamc@532	776 \Gamma \vdash c_2 \equiv c_1
adamc@532	777 }
adamc@532	778 \quad \infer{\Gamma \vdash c_1 \equiv c_3}{
adamc@532	779 \Gamma \vdash c_1 \equiv c_2
adamc@532	780 & \Gamma \vdash c_2 \equiv c_3
adamc@532	781 }
adamc@532	782 \quad \infer{\Gamma \vdash \mathcal C[c_1] \equiv \mathcal C[c_2]}{
adamc@532	783 \Gamma \vdash c_1 \equiv c_2
adamc@532	784 }$$
adamc@532	785
adamc@532	786 $$\infer{\Gamma \vdash x \equiv c}{
adamc@532	787 x :: \kappa = c \in \Gamma
adamc@532	788 }
adamc@532	789 \quad \infer{\Gamma \vdash M.x \equiv c}{
adamc@537	790 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	791 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@532	792 }
adamc@532	793 \quad \infer{\Gamma \vdash (\overline c).i \equiv c_i}{}$$
adamc@532	794
adamc@532	795 $$\infer{\Gamma \vdash (\lambda x :: \kappa \Rightarrow c) \; c' \equiv [x \mapsto c'] c}{}
adamc@655	796 \quad \infer{\Gamma \vdash (X \Longrightarrow c) [\kappa] \equiv [X \mapsto \kappa] c}{}$$
adamc@655	797
adamc@655	798 $$\infer{\Gamma \vdash c_1 \rc c_2 \equiv c_2 \rc c_1}{}
adamc@532	799 \quad \infer{\Gamma \vdash c_1 \rc (c_2 \rc c_3) \equiv (c_1 \rc c_2) \rc c_3}{}$$
adamc@532	800
adamc@532	801 $$\infer{\Gamma \vdash [] \rc c \equiv c}{}
adamc@532	802 \quad \infer{\Gamma \vdash [\overline{c_1 = c'_1}] \rc [\overline{c_2 = c'_2}] \equiv [\overline{c_1 = c'_1}, \overline{c_2 = c'_2}]}{}$$
adamc@532	803
adamc@655	804 $$\infer{\Gamma \vdash \mt{map} \; f \; [] \equiv []}{}
adamc@655	805 \quad \infer{\Gamma \vdash \mt{map} \; f \; ([c_1 = c_2] \rc c) \equiv [c_1 = f \; c_2] \rc \mt{map} \; f \; c}{}$$
adamc@532	806
adamc@532	807 $$\infer{\Gamma \vdash \mt{map} \; (\lambda x \Rightarrow x) \; c \equiv c}{}
adamc@655	808 \quad \infer{\Gamma \vdash \mt{map} \; f \; (\mt{map} \; f' \; c)
adamc@655	809 \equiv \mt{map} \; (\lambda x \Rightarrow f \; (f' \; x)) \; c}{}$$
adamc@532	810
adamc@532	811 $$\infer{\Gamma \vdash \mt{map} \; f \; (c_1 \rc c_2) \equiv \mt{map} \; f \; c_1 \rc \mt{map} \; f \; c_2}{}$$
adamc@531	812
adamc@534	813 \subsection{Expression Typing}
adamc@533	814
adamc@873	815 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	816
adamc@533	817 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	818
adamc@533	819 $$\infer{\Gamma \vdash e : \tau : \tau}{
adamc@533	820 \Gamma \vdash e : \tau
adamc@533	821 }
adamc@533	822 \quad \infer{\Gamma \vdash e : \tau}{
adamc@533	823 \Gamma \vdash e : \tau'
adamc@533	824 & \Gamma \vdash \tau' \equiv \tau
adamc@533	825 }
adamc@533	826 \quad \infer{\Gamma \vdash \ell : T(\ell)}{}$$
adamc@533	827
adamc@533	828 $$\infer{\Gamma \vdash x : \mathcal I(\tau)}{
adamc@533	829 x : \tau \in \Gamma
adamc@533	830 }
adamc@533	831 \quad \infer{\Gamma \vdash M.x : \mathcal I(\tau)}{
adamc@537	832 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	833 & \mt{proj}(M, \overline{s}, \mt{val} \; x) = \tau
adamc@533	834 }
adamc@533	835 \quad \infer{\Gamma \vdash X : \mathcal I(\tau)}{
adamc@533	836 X : \tau \in \Gamma
adamc@533	837 }
adamc@533	838 \quad \infer{\Gamma \vdash M.X : \mathcal I(\tau)}{
adamc@537	839 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	840 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \tau
adamc@533	841 }$$
adamc@533	842
adamc@533	843 $$\infer{\Gamma \vdash e_1 \; e_2 : \tau_2}{
adamc@533	844 \Gamma \vdash e_1 : \tau_1 \to \tau_2
adamc@533	845 & \Gamma \vdash e_2 : \tau_1
adamc@533	846 }
adamc@533	847 \quad \infer{\Gamma \vdash \lambda x : \tau_1 \Rightarrow e : \tau_1 \to \tau_2}{
adamc@533	848 \Gamma, x : \tau_1 \vdash e : \tau_2
adamc@533	849 }$$
adamc@533	850
adamc@533	851 $$\infer{\Gamma \vdash e [c] : [x \mapsto c]\tau}{
adamc@533	852 \Gamma \vdash e : x :: \kappa \to \tau
adamc@533	853 & \Gamma \vdash c :: \kappa
adamc@533	854 }
adamc@852	855 \quad \infer{\Gamma \vdash \lambda [x \; ? \; \kappa] \Rightarrow e : x \; ? \; \kappa \to \tau}{
adamc@533	856 \Gamma, x :: \kappa \vdash e : \tau
adamc@533	857 }$$
adamc@533	858
adamc@655	859 $$\infer{\Gamma \vdash e [\kappa] : [X \mapsto \kappa]\tau}{
adamc@655	860 \Gamma \vdash e : X \longrightarrow \tau
adamc@655	861 & \Gamma \vdash \kappa
adamc@655	862 }
adamc@655	863 \quad \infer{\Gamma \vdash X \Longrightarrow e : X \longrightarrow \tau}{
adamc@655	864 \Gamma, X \vdash e : \tau
adamc@655	865 }$$
adamc@655	866
adamc@533	867 $$\infer{\Gamma \vdash \{\overline{c = e}\} : \{\overline{c : \tau}\}}{
adamc@533	868 \forall i: \Gamma \vdash c_i :: \mt{Name}
adamc@533	869 & \Gamma \vdash e_i : \tau_i
adamc@533	870 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@533	871 }
adamc@533	872 \quad \infer{\Gamma \vdash e.c : \tau}{
adamc@533	873 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533	874 }
adamc@533	875 \quad \infer{\Gamma \vdash e_1 \rc e_2 : \$(c_1 \rc c_2)}{
adamc@533	876 \Gamma \vdash e_1 : \$c_1
adamc@533	877 & \Gamma \vdash e_2 : \$c_2
adamc@573	878 & \Gamma \vdash c_1 \sim c_2
adamc@533	879 }$$
adamc@533	880
adamc@533	881 $$\infer{\Gamma \vdash e \rcut c : \$c'}{
adamc@533	882 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533	883 }
adamc@533	884 \quad \infer{\Gamma \vdash e \rcutM c : \$c'}{
adamc@533	885 \Gamma \vdash e : \$(c \rc c')
adamc@533	886 }$$
adamc@533	887
adamc@533	888 $$\infer{\Gamma \vdash \mt{let} \; \overline{ed} \; \mt{in} \; e \; \mt{end} : \tau}{
adamc@533	889 \Gamma \vdash \overline{ed} \leadsto \Gamma'
adamc@533	890 & \Gamma' \vdash e : \tau
adamc@533	891 }
adamc@533	892 \quad \infer{\Gamma \vdash \mt{case} \; e \; \mt{of} \; \overline{p \Rightarrow e} : \tau}{
adamc@533	893 \forall i: \Gamma \vdash p_i \leadsto \Gamma_i, \tau'
adamc@533	894 & \Gamma_i \vdash e_i : \tau
adamc@533	895 }$$
adamc@533	896
adamc@573	897 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow e : \lambda [c_1 \sim c_2] \Rightarrow \tau}{
adamc@533	898 \Gamma \vdash c_1 :: \{\kappa\}
adamc@655	899 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@533	900 & \Gamma, c_1 \sim c_2 \vdash e : \tau
adamc@662	901 }
adamc@662	902 \quad \infer{\Gamma \vdash e \; ! : \tau}{
adamc@662	903 \Gamma \vdash e : [c_1 \sim c_2] \Rightarrow \tau
adamc@662	904 & \Gamma \vdash c_1 \sim c_2
adamc@533	905 }$$
adamc@533	906
adamc@534	907 \subsection{Pattern Typing}
adamc@534	908
adamc@534	909 $$\infer{\Gamma \vdash \_ \leadsto \Gamma; \tau}{}
adamc@534	910 \quad \infer{\Gamma \vdash x \leadsto \Gamma, x : \tau; \tau}{}
adamc@534	911 \quad \infer{\Gamma \vdash \ell \leadsto \Gamma; T(\ell)}{}$$
adamc@534	912
adamc@534	913 $$\infer{\Gamma \vdash X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534	914 X : \overline{x ::: \mt{Type}} \to \tau \in \Gamma
adamc@534	915 & \textrm{$\tau$ not a function type}
adamc@534	916 }
adamc@534	917 \quad \infer{\Gamma \vdash X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534	918 X : \overline{x ::: \mt{Type}} \to \tau'' \to \tau \in \Gamma
adamc@534	919 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534	920 }$$
adamc@534	921
adamc@534	922 $$\infer{\Gamma \vdash M.X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537	923 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	924 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau
adamc@534	925 & \textrm{$\tau$ not a function type}
adamc@534	926 }$$
adamc@534	927
adamc@534	928 $$\infer{\Gamma \vdash M.X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537	929 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	930 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau'' \to \tau
adamc@534	931 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534	932 }$$
adamc@534	933
adamc@534	934 $$\infer{\Gamma \vdash \{\overline{x = p}\} \leadsto \Gamma_n; \{\overline{x = \tau}\}}{
adamc@534	935 \Gamma_0 = \Gamma
adamc@534	936 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534	937 }
adamc@534	938 \quad \infer{\Gamma \vdash \{\overline{x = p}, \ldots\} \leadsto \Gamma_n; \$([\overline{x = \tau}] \rc c)}{
adamc@534	939 \Gamma_0 = \Gamma
adamc@534	940 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534	941 }$$
adamc@534	942
adamc@852	943 $$\infer{\Gamma \vdash p : \tau \leadsto \Gamma'; \tau}{
adamc@852	944 \Gamma \vdash p \leadsto \Gamma'; \tau'
adamc@852	945 & \Gamma \vdash \tau' \equiv \tau
adamc@852	946 }$$
adamc@852	947
adamc@535	948 \subsection{Declaration Typing}
adamc@535	949
adamc@535	950 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	951
adamc@655	952 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	953
adamc@558	954 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	955 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	956
adamc@535	957 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535	958 \quad \infer{\Gamma \vdash d, \overline{d} \leadsto \Gamma''}{
adamc@535	959 \Gamma \vdash d \leadsto \Gamma'
adamc@535	960 & \Gamma' \vdash \overline{d} \leadsto \Gamma''
adamc@535	961 }$$
adamc@535	962
adamc@535	963 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@535	964 \Gamma \vdash c :: \kappa
adamc@535	965 }
adamc@535	966 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@535	967 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@535	968 }$$
adamc@535	969
adamc@535	970 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537	971 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	972 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@535	973 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@535	974 }$$
adamc@535	975
adamc@535	976 $$\infer{\Gamma \vdash \mt{val} \; x : \tau = e \leadsto \Gamma, x : \tau}{
adamc@535	977 \Gamma \vdash e : \tau
adamc@535	978 }$$
adamc@535	979
adamc@535	980 $$\infer{\Gamma \vdash \mt{val} \; \mt{rec} \; \overline{x : \tau = e} \leadsto \Gamma, \overline{x : \tau}}{
adamc@535	981 \forall i: \Gamma, \overline{x : \tau} \vdash e_i : \tau_i
adamc@535	982 & \textrm{$e_i$ starts with an expression $\lambda$, optionally preceded by constructor and disjointness $\lambda$s}
adamc@535	983 }$$
adamc@535	984
adamc@535	985 $$\infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : S}{
adamc@535	986 \Gamma \vdash M : S
adamc@558	987 & \textrm{ $M$ not a constant or application}
adamc@535	988 }
adamc@558	989 \quad \infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : \mt{selfify}(X, \overline{s})}{
adamc@558	990 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@539	991 }$$
adamc@539	992
adamc@539	993 $$\infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@535	994 \Gamma \vdash S
adamc@535	995 }$$
adamc@535	996
adamc@537	997 $$\infer{\Gamma \vdash \mt{open} \; M \leadsto \Gamma, \mathcal O(M, \overline{s})}{
adamc@537	998 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535	999 }$$
adamc@535	1000
adamc@535	1001 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma}{
adamc@535	1002 \Gamma \vdash c_1 :: \{\kappa\}
adamc@535	1003 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@535	1004 & \Gamma \vdash c_1 \sim c_2
adamc@535	1005 }
adamc@537	1006 \quad \infer{\Gamma \vdash \mt{open} \; \mt{constraints} \; M \leadsto \Gamma, \mathcal O_c(M, \overline{s})}{
adamc@537	1007 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535	1008 }$$
adamc@535	1009
adamc@784	1010 $$\infer{\Gamma \vdash \mt{table} \; x : c \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_table} \; c \; []}{
adamc@535	1011 \Gamma \vdash c :: \{\mt{Type}\}
adamc@535	1012 }
adam@1594	1013 \quad \infer{\Gamma \vdash \mt{view} \; x = e \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_view} \; c}{
adam@1594	1014 \Gamma \vdash e :: \mt{Basis}.\mt{sql\_query} \; [] \; [] \; (\mt{map} \; (\lambda \_ \Rightarrow []) \; c') \; c
adamc@784	1015 }$$
adamc@784	1016
adamc@784	1017 $$\infer{\Gamma \vdash \mt{sequence} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_sequence}}{}$$
adamc@535	1018
adamc@535	1019 $$\infer{\Gamma \vdash \mt{cookie} \; x : \tau \leadsto \Gamma, x : \mt{Basis}.\mt{http\_cookie} \; \tau}{
adamc@535	1020 \Gamma \vdash \tau :: \mt{Type}
adamc@784	1021 }
adamc@784	1022 \quad \infer{\Gamma \vdash \mt{style} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{css\_class}}{}$$
adamc@535	1023
adamc@1085	1024 $$\infer{\Gamma \vdash \mt{task} \; e_1 = e_2 \leadsto \Gamma}{
adam@1348	1025 \Gamma \vdash e_1 :: \mt{Basis}.\mt{task\_kind} \; \tau
adam@1348	1026 & \Gamma \vdash e_2 :: \tau \to \mt{Basis}.\mt{transaction} \; \{\}
adamc@1085	1027 }$$
adamc@1085	1028
adamc@784	1029 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784	1030 \Gamma \vdash c :: \kappa
adamc@535	1031 }$$
adamc@535	1032
adamc@535	1033 $$\infer{\overline{y}; x; \Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535	1034 \quad \infer{\overline{y}; x; \Gamma \vdash X \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to x \; \overline{y}}{
adamc@535	1035 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535	1036 }
adamc@535	1037 \quad \infer{\overline{y}; x; \Gamma \vdash X \; \mt{of} \; \tau \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to \tau \to x \; \overline{y}}{
adamc@535	1038 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535	1039 }$$
adamc@535	1040
adamc@537	1041 \subsection{Signature Item Typing}
adamc@537	1042
adamc@537	1043 We appeal to a signature item analogue of the $\mathcal O$ function from the last subsection.
adamc@537	1044
adamc@537	1045 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@537	1046 \quad \infer{\Gamma \vdash s, \overline{s} \leadsto \Gamma''}{
adamc@537	1047 \Gamma \vdash s \leadsto \Gamma'
adamc@537	1048 & \Gamma' \vdash \overline{s} \leadsto \Gamma''
adamc@537	1049 }$$
adamc@537	1050
adamc@537	1051 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}
adamc@537	1052 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@537	1053 \Gamma \vdash c :: \kappa
adamc@537	1054 }
adamc@537	1055 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@537	1056 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@537	1057 }$$
adamc@537	1058
adamc@537	1059 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537	1060 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1061 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537	1062 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@537	1063 }$$
adamc@537	1064
adamc@537	1065 $$\infer{\Gamma \vdash \mt{val} \; x : \tau \leadsto \Gamma, x : \tau}{
adamc@537	1066 \Gamma \vdash \tau :: \mt{Type}
adamc@537	1067 }$$
adamc@537	1068
adamc@537	1069 $$\infer{\Gamma \vdash \mt{structure} \; X : S \leadsto \Gamma, X : S}{
adamc@537	1070 \Gamma \vdash S
adamc@537	1071 }
adamc@537	1072 \quad \infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@537	1073 \Gamma \vdash S
adamc@537	1074 }$$
adamc@537	1075
adamc@537	1076 $$\infer{\Gamma \vdash \mt{include} \; S \leadsto \Gamma, \mathcal O(\overline{s})}{
adamc@537	1077 \Gamma \vdash S
adamc@537	1078 & \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1079 }$$
adamc@537	1080
adamc@537	1081 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma, c_1 \sim c_2}{
adamc@537	1082 \Gamma \vdash c_1 :: \{\kappa\}
adamc@537	1083 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@537	1084 }$$
adamc@537	1085
adamc@784	1086 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784	1087 \Gamma \vdash c :: \kappa
adamc@537	1088 }
adamc@784	1089 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}$$
adamc@537	1090
adamc@536	1091 \subsection{Signature Compatibility}
adamc@536	1092
adamc@558	1093 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	1094
adamc@537	1095 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	1096
adamc@536	1097 $$\infer{\Gamma \vdash S \equiv S}{}
adamc@536	1098 \quad \infer{\Gamma \vdash S_1 \equiv S_2}{
adamc@536	1099 \Gamma \vdash S_2 \equiv S_1
adamc@536	1100 }
adamc@536	1101 \quad \infer{\Gamma \vdash X \equiv S}{
adamc@536	1102 X = S \in \Gamma
adamc@536	1103 }
adamc@536	1104 \quad \infer{\Gamma \vdash M.X \equiv S}{
adamc@537	1105 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1106 & \mt{proj}(M, \overline{s}, \mt{signature} \; X) = S
adamc@536	1107 }$$
adamc@536	1108
adamc@536	1109 $$\infer{\Gamma \vdash S \; \mt{where} \; \mt{con} \; x = c \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa = c \; \overline{s_2} \; \mt{end}}{
adamc@536	1110 \Gamma \vdash S \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa \; \overline{s_2} \; \mt{end}
adamc@536	1111 & \Gamma \vdash c :: \kappa
adamc@537	1112 }
adamc@537	1113 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s^1} \; \mt{include} \; S \; \overline{s^2} \; \mt{end} \equiv \mt{sig} \; \overline{s^1} \; \overline{s} \; \overline{s^2} \; \mt{end}}{
adamc@537	1114 \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@536	1115 }$$
adamc@536	1116
adamc@536	1117 $$\infer{\Gamma \vdash S_1 \leq S_2}{
adamc@536	1118 \Gamma \vdash S_1 \equiv S_2
adamc@536	1119 }
adamc@536	1120 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \mt{end}}{}
adamc@537	1121 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; s' \; \overline{s'} \; \mt{end}}{
adamc@537	1122 \Gamma \vdash \overline{s} \leq s'
adamc@537	1123 & \Gamma \vdash s' \leadsto \Gamma'
adamc@537	1124 & \Gamma' \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \overline{s'} \; \mt{end}
adamc@537	1125 }$$
adamc@537	1126
adamc@537	1127 $$\infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537	1128 \Gamma \vdash s \leq s'
adamc@537	1129 }
adamc@537	1130 \quad \infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537	1131 \Gamma \vdash s \leadsto \Gamma'
adamc@537	1132 & \Gamma' \vdash \overline{s} \leq s'
adamc@536	1133 }$$
adamc@536	1134
adamc@536	1135 $$\infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 \leq \mt{functor} (X : S'_1) : S'_2}{
adamc@536	1136 \Gamma \vdash S'_1 \leq S_1
adamc@536	1137 & \Gamma, X : S'_1 \vdash S_2 \leq S'_2
adamc@536	1138 }$$
adamc@536	1139
adamc@537	1140 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@537	1141 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}
adamc@558	1142 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type}}{}$$
adamc@537	1143
adamc@537	1144 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(y)} \to \mt{Type}}{
adamc@537	1145 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1146 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537	1147 }$$
adamc@537	1148
adamc@784	1149 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@784	1150 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}$$
adamc@537	1151
adamc@537	1152 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \mt{\kappa} = c_2}{
adamc@537	1153 \Gamma \vdash c_1 \equiv c_2
adamc@537	1154 }
adamc@784	1155 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \kappa = c_2}{
adamc@537	1156 \Gamma \vdash c_1 \equiv c_2
adamc@537	1157 }$$
adamc@537	1158
adamc@537	1159 $$\infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537	1160 \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537	1161 }$$
adamc@537	1162
adamc@537	1163 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537	1164 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1165 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537	1166 & \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537	1167 }$$
adamc@537	1168
adamc@537	1169 $$\infer{\Gamma \vdash \cdot \leq \cdot}{}
adamc@537	1170 \quad \infer{\Gamma \vdash X; \overline{dc} \leq X; \overline{dc'}}{
adamc@537	1171 \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537	1172 }
adamc@537	1173 \quad \infer{\Gamma \vdash X \; \mt{of} \; \tau_1; \overline{dc} \leq X \; \mt{of} \; \tau_2; \overline{dc'}}{
adamc@537	1174 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537	1175 & \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537	1176 }$$
adamc@537	1177
adamc@537	1178 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x = \mt{datatype} \; M'.z'}{
adamc@537	1179 \Gamma \vdash M.z \equiv M'.z'
adamc@537	1180 }$$
adamc@537	1181
adamc@537	1182 $$\infer{\Gamma \vdash \mt{val} \; x : \tau_1 \leq \mt{val} \; x : \tau_2}{
adamc@537	1183 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537	1184 }
adamc@537	1185 \quad \infer{\Gamma \vdash \mt{structure} \; X : S_1 \leq \mt{structure} \; X : S_2}{
adamc@537	1186 \Gamma \vdash S_1 \leq S_2
adamc@537	1187 }
adamc@537	1188 \quad \infer{\Gamma \vdash \mt{signature} \; X = S_1 \leq \mt{signature} \; X = S_2}{
adamc@537	1189 \Gamma \vdash S_1 \leq S_2
adamc@537	1190 & \Gamma \vdash S_2 \leq S_1
adamc@537	1191 }$$
adamc@537	1192
adamc@537	1193 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leq \mt{constraint} \; c'_1 \sim c'_2}{
adamc@537	1194 \Gamma \vdash c_1 \equiv c'_1
adamc@537	1195 & \Gamma \vdash c_2 \equiv c'_2
adamc@537	1196 }$$
adamc@537	1197
adamc@655	1198 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{class} \; x :: \kappa}{}
adamc@655	1199 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{class} \; x :: \kappa}{}
adamc@655	1200 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{class} \; x :: \kappa = c_2}{
adamc@537	1201 \Gamma \vdash c_1 \equiv c_2
adamc@537	1202 }$$
adamc@537	1203
adamc@538	1204 \subsection{Module Typing}
adamc@538	1205
adamc@538	1206 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	1207
adamc@538	1208 $$\infer{\Gamma \vdash M : S}{
adamc@538	1209 \Gamma \vdash M : S'
adamc@538	1210 & \Gamma \vdash S' \leq S
adamc@538	1211 }
adamc@538	1212 \quad \infer{\Gamma \vdash \mt{struct} \; \overline{d} \; \mt{end} : \mt{sig} \; \mt{sigOf}(\overline{d}) \; \mt{end}}{
adamc@538	1213 \Gamma \vdash \overline{d} \leadsto \Gamma'
adamc@538	1214 }
adamc@538	1215 \quad \infer{\Gamma \vdash X : S}{
adamc@538	1216 X : S \in \Gamma
adamc@538	1217 }$$
adamc@538	1218
adamc@538	1219 $$\infer{\Gamma \vdash M.X : S}{
adamc@538	1220 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@538	1221 & \mt{proj}(M, \overline{s}, \mt{structure} \; X) = S
adamc@538	1222 }$$
adamc@538	1223
adamc@538	1224 $$\infer{\Gamma \vdash M_1(M_2) : [X \mapsto M_2]S_2}{
adamc@538	1225 \Gamma \vdash M_1 : \mt{functor}(X : S_1) : S_2
adamc@538	1226 & \Gamma \vdash M_2 : S_1
adamc@538	1227 }
adamc@538	1228 \quad \infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 = M : \mt{functor} (X : S_1) : S_2}{
adamc@538	1229 \Gamma \vdash S_1
adamc@538	1230 & \Gamma, X : S_1 \vdash S_2
adamc@538	1231 & \Gamma, X : S_1 \vdash M : S_2
adamc@538	1232 }$$
adamc@538	1233
adamc@538	1234 \begin{eqnarray*}
adamc@538	1235 \mt{sigOf}(\cdot) &=& \cdot \\
adamc@538	1236 \mt{sigOf}(s \; \overline{s'}) &=& \mt{sigOf}(s) \; \mt{sigOf}(\overline{s'}) \\
adamc@538	1237 \\
adamc@538	1238 \mt{sigOf}(\mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@538	1239 \mt{sigOf}(\mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \overline{dc} \\
adamc@538	1240 \mt{sigOf}(\mt{datatype} \; x = \mt{datatype} \; M.z) &=& \mt{datatype} \; x = \mt{datatype} \; M.z \\
adamc@538	1241 \mt{sigOf}(\mt{val} \; x : \tau = e) &=& \mt{val} \; x : \tau \\
adamc@538	1242 \mt{sigOf}(\mt{val} \; \mt{rec} \; \overline{x : \tau = e}) &=& \overline{\mt{val} \; x : \tau} \\
adamc@538	1243 \mt{sigOf}(\mt{structure} \; X : S = M) &=& \mt{structure} \; X : S \\
adamc@538	1244 \mt{sigOf}(\mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@538	1245 \mt{sigOf}(\mt{open} \; M) &=& \mt{include} \; S \textrm{ (where $\Gamma \vdash M : S$)} \\
adamc@538	1246 \mt{sigOf}(\mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@538	1247 \mt{sigOf}(\mt{open} \; \mt{constraints} \; M) &=& \cdot \\
adamc@538	1248 \mt{sigOf}(\mt{table} \; x : c) &=& \mt{table} \; x : c \\
adam@1594	1249 \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	1250 \mt{sigOf}(\mt{sequence} \; x) &=& \mt{sequence} \; x \\
adamc@538	1251 \mt{sigOf}(\mt{cookie} \; x : \tau) &=& \mt{cookie} \; x : \tau \\
adamc@784	1252 \mt{sigOf}(\mt{style} \; x) &=& \mt{style} \; x \\
adamc@655	1253 \mt{sigOf}(\mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@538	1254 \end{eqnarray*}
adamc@539	1255 \begin{eqnarray*}
adamc@539	1256 \mt{selfify}(M, \cdot) &=& \cdot \\
adamc@558	1257 \mt{selfify}(M, s \; \overline{s'}) &=& \mt{selfify}(M, s) \; \mt{selfify}(M, \overline{s'}) \\
adamc@539	1258 \\
adamc@539	1259 \mt{selfify}(M, \mt{con} \; x :: \kappa) &=& \mt{con} \; x :: \kappa = M.x \\
adamc@539	1260 \mt{selfify}(M, \mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@539	1261 \mt{selfify}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \mt{datatype} \; M.x \\
adamc@539	1262 \mt{selfify}(M, \mt{datatype} \; x = \mt{datatype} \; M'.z) &=& \mt{datatype} \; x = \mt{datatype} \; M'.z \\
adamc@539	1263 \mt{selfify}(M, \mt{val} \; x : \tau) &=& \mt{val} \; x : \tau \\
adamc@539	1264 \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	1265 \mt{selfify}(M, \mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@539	1266 \mt{selfify}(M, \mt{include} \; S) &=& \mt{include} \; S \\
adamc@539	1267 \mt{selfify}(M, \mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@655	1268 \mt{selfify}(M, \mt{class} \; x :: \kappa) &=& \mt{class} \; x :: \kappa = M.x \\
adamc@655	1269 \mt{selfify}(M, \mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@539	1270 \end{eqnarray*}
adamc@539	1271
adamc@540	1272 \subsection{Module Projection}
adamc@540	1273
adamc@540	1274 \begin{eqnarray*}
adamc@540	1275 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \\
adamc@540	1276 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa, c) \\
adamc@540	1277 \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	1278 \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	1279 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})$)} \\
adamc@655	1280 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \to \mt{Type} \\
adamc@655	1281 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa \to \mt{Type}, c) \\
adamc@540	1282 \\
adamc@540	1283 \mt{proj}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc} \; \overline{s}, \mt{datatype} \; x) &=& (\overline{y}, \overline{dc}) \\
adamc@540	1284 \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	1285 \\
adamc@540	1286 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, \mt{val} \; x) &=& \tau \\
adamc@540	1287 \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	1288 \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	1289 \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	1290 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \in \overline{dc}$)} \\
adamc@540	1291 \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	1292 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \; \mt{of} \; \tau \in \overline{dc}$)} \\
adamc@540	1293 \\
adamc@540	1294 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, \mt{structure} \; X) &=& S \\
adamc@540	1295 \\
adamc@540	1296 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, \mt{signature} \; X) &=& S \\
adamc@540	1297 \\
adamc@540	1298 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1299 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1300 \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	1301 \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	1302 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@540	1303 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1304 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1305 \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	1306 \mt{proj}(M, \mt{constraint} \; c_1 \sim c_2 \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@655	1307 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@655	1308 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1309 \end{eqnarray*}
adamc@540	1310
adamc@541	1311
adamc@541	1312 \section{Type Inference}
adamc@541	1313
adamc@541	1314 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	1315
adamc@541	1316 \subsection{Basic Unification}
adamc@541	1317
adamc@560	1318 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	1319
adamc@656	1320 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	1321
adamc@541	1322 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	1323
adamc@541	1324 \subsection{Unifying Record Types}
adamc@541	1325
adamc@570	1326 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	1327
adamc@656	1328 \subsection{\label{typeclasses}Constructor Classes}
adamc@541	1329
adamc@784	1330 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	1331
adamc@784	1332 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	1333
adamc@656	1334 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	1335
adamc@656	1336 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	1337
adamc@541	1338 \subsection{Reverse-Engineering Record Types}
adamc@541	1339
adamc@656	1340 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	1341
adamc@541	1342 \subsection{Implicit Arguments in Functor Applications}
adamc@541	1343
adamc@656	1344 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	1345
adamc@541	1346
adamc@542	1347 \section{The Ur Standard Library}
adamc@542	1348
adamc@542	1349 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	1350
adamc@542	1351 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	1352
adamc@542	1353 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	1354 $$\begin{array}{l}
adamc@542	1355 \mt{type} \; \mt{int} \\
adamc@542	1356 \mt{type} \; \mt{float} \\
adamc@873	1357 \mt{type} \; \mt{char} \\
adamc@542	1358 \mt{type} \; \mt{string} \\
adamc@542	1359 \mt{type} \; \mt{time} \\
adamc@785	1360 \mt{type} \; \mt{blob} \\
adamc@542	1361 \\
adamc@542	1362 \mt{type} \; \mt{unit} = \{\} \\
adamc@542	1363 \\
adamc@542	1364 \mt{datatype} \; \mt{bool} = \mt{False} \mid \mt{True} \\
adamc@542	1365 \\
adamc@785	1366 \mt{datatype} \; \mt{option} \; \mt{t} = \mt{None} \mid \mt{Some} \; \mt{of} \; \mt{t} \\
adamc@785	1367 \\
adamc@785	1368 \mt{datatype} \; \mt{list} \; \mt{t} = \mt{Nil} \mid \mt{Cons} \; \mt{of} \; \mt{t} \times \mt{list} \; \mt{t}
adamc@542	1369 \end{array}$$
adamc@542	1370
adamc@1123	1371 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	1372
adam@1297	1373 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	1374 $$\begin{array}{l}
adam@1297	1375 \mt{con} \; \mt{variant} :: \{\mt{Type}\} \to \mt{Type} \\
adam@1297	1376 \mt{val} \; \mt{make} : \mt{nm} :: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{ts} ::: \{\mt{Type}\} \to [[\mt{nm}] \sim \mt{ts}] \Rightarrow \mt{t} \to \mt{variant} \; ([\mt{nm} = \mt{t}] \rc \mt{ts}) \\
adam@1297	1377 \mt{val} \; \mt{match} : \mt{ts} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{variant} \; \mt{ts} \to \$(\mt{map} \; (\lambda \mt{t'} \Rightarrow \mt{t'} \to \mt{t}) \; \mt{ts}) \to \mt{t}
adam@1297	1378 \end{array}$$
adam@1297	1379
adamc@657	1380 Another important generic Ur element comes at the beginning of \texttt{top.urs}.
adamc@657	1381
adamc@657	1382 $$\begin{array}{l}
adamc@657	1383 \mt{con} \; \mt{folder} :: \mt{K} \longrightarrow \{\mt{K}\} \to \mt{Type} \\
adamc@657	1384 \\
adamc@657	1385 \mt{val} \; \mt{fold} : \mt{K} \longrightarrow \mt{tf} :: (\{\mt{K}\} \to \mt{Type}) \\
adamc@657	1386 \hspace{.1in} \to (\mt{nm} :: \mt{Name} \to \mt{v} :: \mt{K} \to \mt{r} :: \{\mt{K}\} \to [[\mt{nm}] \sim \mt{r}] \Rightarrow \\
adamc@657	1387 \hspace{.2in} \mt{tf} \; \mt{r} \to \mt{tf} \; ([\mt{nm} = \mt{v}] \rc \mt{r})) \\
adamc@657	1388 \hspace{.1in} \to \mt{tf} \; [] \\
adamc@657	1389 \hspace{.1in} \to \mt{r} :: \{\mt{K}\} \to \mt{folder} \; \mt{r} \to \mt{tf} \; \mt{r}
adamc@657	1390 \end{array}$$
adamc@657	1391
adamc@657	1392 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	1393
adamc@664	1394 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	1395
adamc@542	1396
adamc@542	1397 \section{The Ur/Web Standard Library}
adamc@542	1398
adam@1400	1399 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	1400
adamc@658	1401 \subsection{Monads}
adamc@658	1402
adamc@658	1403 The Ur Basis defines the monad constructor class from Haskell.
adamc@658	1404
adamc@658	1405 $$\begin{array}{l}
adamc@658	1406 \mt{class} \; \mt{monad} :: \mt{Type} \to \mt{Type} \\
adamc@658	1407 \mt{val} \; \mt{return} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t} ::: \mt{Type} \\
adamc@658	1408 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658	1409 \hspace{.1in} \to \mt{t} \to \mt{m} \; \mt{t} \\
adamc@658	1410 \mt{val} \; \mt{bind} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t1} ::: \mt{Type} \to \mt{t2} ::: \mt{Type} \\
adamc@658	1411 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658	1412 \hspace{.1in} \to \mt{m} \; \mt{t1} \to (\mt{t1} \to \mt{m} \; \mt{t2}) \\
adam@1544	1413 \hspace{.1in} \to \mt{m} \; \mt{t2} \\
adam@1544	1414 \mt{val} \; \mt{mkMonad} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \\
adam@1544	1415 \hspace{.1in} \to \{\mt{Return} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{m} \; \mt{t}, \\
adam@1544	1416 \hspace{.3in} \mt{Bind} : \mt{t1} ::: \mt{Type} \to \mt{t2} ::: \mt{Type} \to \mt{m} \; \mt{t1} \to (\mt{t1} \to \mt{m} \; \mt{t2}) \to \mt{m} \; \mt{t2}\} \\
adam@1544	1417 \hspace{.1in} \to \mt{monad} \; \mt{m}
adamc@658	1418 \end{array}$$
adamc@658	1419
adam@1687	1420 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	1421
adamc@542	1422 \subsection{Transactions}
adamc@542	1423
adamc@542	1424 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	1425 $$\begin{array}{l}
adamc@542	1426 \mt{con} \; \mt{transaction} :: \mt{Type} \to \mt{Type} \\
adamc@658	1427 \mt{val} \; \mt{transaction\_monad} : \mt{monad} \; \mt{transaction}
adamc@542	1428 \end{array}$$
adamc@542	1429
adamc@1123	1430 For debugging purposes, a transactional function is provided for outputting a string on the server process' \texttt{stderr}.
adamc@1123	1431 $$\begin{array}{l}
adamc@1123	1432 \mt{val} \; \mt{debug} : \mt{string} \to \mt{transaction} \; \mt{unit}
adamc@1123	1433 \end{array}$$
adamc@1123	1434
adamc@542	1435 \subsection{HTTP}
adamc@542	1436
adam@1400	1437 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	1438 $$\begin{array}{l}
adamc@786	1439 \mt{con} \; \mt{http\_cookie} :: \mt{Type} \to \mt{Type} \\
adamc@786	1440 \mt{val} \; \mt{getCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; (\mt{option} \; \mt{t}) \\
adamc@1050	1441 \mt{val} \; \mt{setCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \{\mt{Value} : \mt{t}, \mt{Expires} : \mt{option} \; \mt{time}, \mt{Secure} : \mt{bool}\} \to \mt{transaction} \; \mt{unit} \\
adamc@1050	1442 \mt{val} \; \mt{clearCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; \mt{unit}
adamc@786	1443 \end{array}$$
adamc@786	1444
adamc@786	1445 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	1446 $$\begin{array}{l}
adamc@786	1447 \mt{type} \; \mt{url} \\
adamc@786	1448 \mt{val} \; \mt{bless} : \mt{string} \to \mt{url} \\
adamc@786	1449 \mt{val} \; \mt{checkUrl} : \mt{string} \to \mt{option} \; \mt{url}
adamc@786	1450 \end{array}$$
adamc@786	1451 $\mt{bless}$ raises a runtime error if the string passed to it fails the URL policy.
adamc@786	1452
adam@1400	1453 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	1454 $$\begin{array}{l}
adamc@1085	1455 \mt{val} \; \mt{currentUrl} : \mt{transaction} \; \mt{url} \\
adamc@1085	1456 \mt{val} \; \mt{url} : \mt{transaction} \; \mt{page} \to \mt{url}
adamc@1085	1457 \end{array}$$
adamc@1085	1458
adamc@1085	1459 Page generation may be interrupted at any time with a request to redirect to a particular URL instead.
adamc@1085	1460 $$\begin{array}{l}
adamc@1085	1461 \mt{val} \; \mt{redirect} : \mt{t} ::: \mt{Type} \to \mt{url} \to \mt{transaction} \; \mt{t}
adamc@1085	1462 \end{array}$$
adamc@1085	1463
adam@1400	1464 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	1465 $$\begin{array}{l}
adamc@786	1466 \mt{type} \; \mt{file} \\
adamc@786	1467 \mt{val} \; \mt{fileName} : \mt{file} \to \mt{option} \; \mt{string} \\
adamc@786	1468 \mt{val} \; \mt{fileMimeType} : \mt{file} \to \mt{string} \\
adamc@786	1469 \mt{val} \; \mt{fileData} : \mt{file} \to \mt{blob}
adamc@786	1470 \end{array}$$
adamc@786	1471
adam@1465	1472 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	1473
adam@1465	1474 $$\begin{array}{l}
adam@1465	1475 \mt{type} \; \mt{requestHeader} \\
adam@1465	1476 \mt{val} \; \mt{blessRequestHeader} : \mt{string} \to \mt{requestHeader} \\
adam@1465	1477 \mt{val} \; \mt{checkRequestHeader} : \mt{string} \to \mt{option} \; \mt{requestHeader} \\
adam@1465	1478 \mt{val} \; \mt{getHeader} : \mt{requestHeader} \to \mt{transaction} \; (\mt{option} \; \mt{string}) \\
adam@1465	1479 \\
adam@1465	1480 \mt{type} \; \mt{responseHeader} \\
adam@1465	1481 \mt{val} \; \mt{blessResponseHeader} : \mt{string} \to \mt{responseHeader} \\
adam@1465	1482 \mt{val} \; \mt{checkResponseHeader} : \mt{string} \to \mt{option} \; \mt{responseHeader} \\
adam@1465	1483 \mt{val} \; \mt{setHeader} : \mt{responseHeader} \to \mt{string} \to \mt{transaction} \; \mt{unit}
adam@1465	1484 \end{array}$$
adam@1465	1485
adamc@786	1486 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	1487 $$\begin{array}{l}
adamc@786	1488 \mt{type} \; \mt{mimeType} \\
adamc@786	1489 \mt{val} \; \mt{blessMime} : \mt{string} \to \mt{mimeType} \\
adamc@786	1490 \mt{val} \; \mt{checkMime} : \mt{string} \to \mt{option} \; \mt{mimeType} \\
adamc@786	1491 \mt{val} \; \mt{returnBlob} : \mt{t} ::: \mt{Type} \to \mt{blob} \to \mt{mimeType} \to \mt{transaction} \; \mt{t}
adamc@542	1492 \end{array}$$
adamc@542	1493
adamc@543	1494 \subsection{SQL}
adamc@543	1495
adam@1400	1496 Everything about SQL database access is restricted to server-side code.
adam@1400	1497
adamc@543	1498 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	1499 $$\begin{array}{l}
adamc@785	1500 \mt{con} \; \mt{sql\_table} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785	1501 \end{array}$$
adamc@785	1502 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	1503
adamc@785	1504 We also have the simpler type family of SQL views, which have no keys.
adamc@785	1505 $$\begin{array}{l}
adamc@785	1506 \mt{con} \; \mt{sql\_view} :: \{\mt{Type}\} \to \mt{Type}
adamc@543	1507 \end{array}$$
adamc@543	1508
adamc@785	1509 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	1510 $$\begin{array}{l}
adamc@785	1511 \mt{class} \; \mt{fieldsOf} :: \mt{Type} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785	1512 \mt{val} \; \mt{fieldsOf\_table} : \mt{fs} ::: \{\mt{Type}\} \to \mt{keys} ::: \{\{\mt{Unit}\}\} \to \mt{fieldsOf} \; (\mt{sql\_table} \; \mt{fs} \; \mt{keys}) \; \mt{fs} \\
adamc@785	1513 \mt{val} \; \mt{fieldsOf\_view} : \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; (\mt{sql\_view} \; \mt{fs}) \; \mt{fs}
adamc@785	1514 \end{array}$$
adamc@785	1515
adamc@785	1516 \subsubsection{Table Constraints}
adamc@785	1517
adamc@785	1518 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	1519
adamc@785	1520 $$\begin{array}{l}
adamc@785	1521 \mt{con} \; \mt{primary\_key} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type} \\
adamc@785	1522 \mt{val} \; \mt{no\_primary\_key} : \mt{fs} ::: \{\mt{Type}\} \to \mt{primary\_key} \; \mt{fs} \; [] \\
adamc@785	1523 \mt{val} \; \mt{primary\_key} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{key1} :: \mt{Name} \to \mt{keys} :: \{\mt{Type}\} \\
adamc@785	1524 \hspace{.1in} \to [[\mt{key1}] \sim \mt{keys}] \Rightarrow [[\mt{key1} = \mt{t}] \rc \mt{keys} \sim \mt{rest}] \\
adamc@785	1525 \hspace{.1in} \Rightarrow \$([\mt{key1} = \mt{sql\_injectable\_prim} \; \mt{t}] \rc \mt{map} \; \mt{sql\_injectable\_prim} \; \mt{keys}) \\
adamc@785	1526 \hspace{.1in} \to \mt{primary\_key} \; ([\mt{key1} = \mt{t}] \rc \mt{keys} \rc \mt{rest}) \; [\mt{Pkey} = [\mt{key1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{keys}]
adamc@785	1527 \end{array}$$
adamc@785	1528 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	1529
adamc@785	1530 A type family stands for sets of named constraints of the remaining varieties.
adamc@785	1531 $$\begin{array}{l}
adamc@785	1532 \mt{con} \; \mt{sql\_constraints} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785	1533 \end{array}$$
adamc@785	1534 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	1535
adamc@785	1536 There is a type family of individual, unnamed constraints.
adamc@785	1537 $$\begin{array}{l}
adamc@785	1538 \mt{con} \; \mt{sql\_constraint} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \mt{Type}
adamc@785	1539 \end{array}$$
adamc@785	1540 The first argument is the same as above, and the second argument gives the key columns for just this constraint.
adamc@785	1541
adamc@785	1542 We have operations for assembling constraints into constraint sets.
adamc@785	1543 $$\begin{array}{l}
adamc@785	1544 \mt{val} \; \mt{no\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_constraints} \; \mt{fs} \; [] \\
adamc@785	1545 \mt{val} \; \mt{one\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{unique} ::: \{\mt{Unit}\} \to \mt{name} :: \mt{Name} \\
adamc@785	1546 \hspace{.1in} \to \mt{sql\_constraint} \; \mt{fs} \; \mt{unique} \to \mt{sql\_constraints} \; \mt{fs} \; [\mt{name} = \mt{unique}] \\
adamc@785	1547 \mt{val} \; \mt{join\_constraints} : \mt{fs} ::: \{\mt{Type}\} \to \mt{uniques1} ::: \{\{\mt{Unit}\}\} \to \mt{uniques2} ::: \{\{\mt{Unit}\}\} \to [\mt{uniques1} \sim \mt{uniques2}] \\
adamc@785	1548 \hspace{.1in} \Rightarrow \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques1} \to \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques2} \to \mt{sql\_constraints} \; \mt{fs} \; (\mt{uniques1} \rc \mt{uniques2})
adamc@785	1549 \end{array}$$
adamc@785	1550
adamc@785	1551 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	1552 $$\begin{array}{l}
adamc@785	1553 \mt{val} \; \mt{unique} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{unique1} :: \mt{Name} \to \mt{unique} :: \{\mt{Type}\} \\
adamc@785	1554 \hspace{.1in} \to [[\mt{unique1}] \sim \mt{unique}] \Rightarrow [[\mt{unique1} = \mt{t}] \rc \mt{unique} \sim \mt{rest}] \\
adamc@785	1555 \hspace{.1in} \Rightarrow \mt{sql\_constraint} \; ([\mt{unique1} = \mt{t}] \rc \mt{unique} \rc \mt{rest}) \; ([\mt{unique1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{unique})
adamc@785	1556 \end{array}$$
adamc@785	1557
adamc@785	1558 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	1559 $$\begin{array}{l}
adamc@785	1560 \mt{class} \; \mt{linkable} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@785	1561 \mt{val} \; \mt{linkable\_same} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; \mt{t} \\
adamc@785	1562 \mt{val} \; \mt{linkable\_from\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; (\mt{option} \; \mt{t}) \; \mt{t} \\
adamc@785	1563 \mt{val} \; \mt{linkable\_to\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@785	1564 \end{array}$$
adamc@785	1565
adamc@785	1566 The $\mt{matching}$ type family uses $\mt{linkable}$ to define when two keys match up type-wise.
adamc@785	1567 $$\begin{array}{l}
adamc@785	1568 \mt{con} \; \mt{matching} :: \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785	1569 \mt{val} \; \mt{mat\_nil} : \mt{matching} \; [] \; [] \\
adamc@785	1570 \mt{val} \; \mt{mat\_cons} : \mt{t1} ::: \mt{Type} \to \mt{rest1} ::: \{\mt{Type}\} \to \mt{t2} ::: \mt{Type} \to \mt{rest2} ::: \{\mt{Type}\} \to \mt{nm1} :: \mt{Name} \to \mt{nm2} :: \mt{Name} \\
adamc@785	1571 \hspace{.1in} \to [[\mt{nm1}] \sim \mt{rest1}] \Rightarrow [[\mt{nm2}] \sim \mt{rest2}] \Rightarrow \mt{linkable} \; \mt{t1} \; \mt{t2} \to \mt{matching} \; \mt{rest1} \; \mt{rest2} \\
adamc@785	1572 \hspace{.1in} \to \mt{matching} \; ([\mt{nm1} = \mt{t1}] \rc \mt{rest1}) \; ([\mt{nm2} = \mt{t2}] \rc \mt{rest2})
adamc@785	1573 \end{array}$$
adamc@785	1574
adamc@785	1575 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	1576 $$\begin{array}{l}
adamc@785	1577 \mt{con} \; \mt{propagation\_mode} :: \{\mt{Type}\} \to \mt{Type} \\
adamc@785	1578 \mt{val} \; \mt{restrict} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785	1579 \mt{val} \; \mt{cascade} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785	1580 \mt{val} \; \mt{no\_action} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785	1581 \mt{val} \; \mt{set\_null} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; (\mt{map} \; \mt{option} \; \mt{fs})
adamc@785	1582 \end{array}$$
adamc@785	1583
adamc@785	1584 Finally, we put these ingredient together to define the \texttt{FOREIGN KEY} constraint function.
adamc@785	1585 $$\begin{array}{l}
adamc@785	1586 \mt{val} \; \mt{foreign\_key} : \mt{mine1} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{mine} ::: \{\mt{Type}\} \to \mt{munused} ::: \{\mt{Type}\} \to \mt{foreign} ::: \{\mt{Type}\} \\
adamc@785	1587 \hspace{.1in} \to \mt{funused} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{uniques} ::: \{\{\mt{Unit}\}\} \\
adamc@785	1588 \hspace{.1in} \to [[\mt{mine1}] \sim \mt{mine}] \Rightarrow [[\mt{mine1} = \mt{t}] \rc \mt{mine} \sim \mt{munused}] \Rightarrow [\mt{foreign} \sim \mt{funused}] \Rightarrow [[\mt{nm}] \sim \mt{uniques}] \\
adamc@785	1589 \hspace{.1in} \Rightarrow \mt{matching} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}) \; \mt{foreign} \\
adamc@785	1590 \hspace{.1in} \to \mt{sql\_table} \; (\mt{foreign} \rc \mt{funused}) \; ([\mt{nm} = \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{foreign}] \rc \mt{uniques}) \\
adamc@785	1591 \hspace{.1in} \to \{\mt{OnDelete} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}), \\
adamc@785	1592 \hspace{.2in} \mt{OnUpdate} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine})\} \\
adamc@785	1593 \hspace{.1in} \to \mt{sql\_constraint} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine} \rc \mt{munused}) \; []
adamc@785	1594 \end{array}$$
adamc@785	1595
adamc@785	1596 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	1597 $$\begin{array}{l}
adamc@785	1598 \mt{val} \; \mt{check} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; [] \; [] \; \mt{fs} \; \mt{bool} \to \mt{sql\_constraint} \; \mt{fs} \; []
adamc@785	1599 \end{array}$$
adamc@785	1600
adamc@785	1601 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	1602
adamc@784	1603
adamc@543	1604 \subsubsection{Queries}
adamc@543	1605
adam@1400	1606 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	1607 $$\begin{array}{l}
adam@1400	1608 \mt{con} \; \mt{sql\_query} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@1193	1609 \mt{val} \; \mt{sql\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400	1610 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adamc@1193	1611 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543	1612 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543	1613 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1193	1614 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adam@1400	1615 \hspace{.1in} \Rightarrow \{\mt{Rows} : \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}, \\
adamc@1193	1616 \hspace{.2in} \mt{OrderBy} : \mt{sql\_order\_by} \; (\mt{free} \rc \mt{tables}) \; \mt{selectedExps}, \\
adamc@543	1617 \hspace{.2in} \mt{Limit} : \mt{sql\_limit}, \\
adamc@543	1618 \hspace{.2in} \mt{Offset} : \mt{sql\_offset}\} \\
adam@1400	1619 \hspace{.1in} \to \mt{sql\_query} \; \mt{free} \; \mt{afree} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543	1620 \end{array}$$
adamc@543	1621
adamc@545	1622 Queries are used by folding over their results inside transactions.
adamc@545	1623 $$\begin{array}{l}
adam@1400	1624 \mt{val} \; \mt{query} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to [\mt{tables} \sim \mt{exps}] \Rightarrow \mt{state} ::: \mt{Type} \to \mt{sql\_query} \; [] \; [] \; \mt{tables} \; \mt{exps} \\
adamc@658	1625 \hspace{.1in} \to (\$(\mt{exps} \rc \mt{map} \; (\lambda \mt{fields} :: \{\mt{Type}\} \Rightarrow \$\mt{fields}) \; \mt{tables}) \\
adamc@545	1626 \hspace{.2in} \to \mt{state} \to \mt{transaction} \; \mt{state}) \\
adamc@545	1627 \hspace{.1in} \to \mt{state} \to \mt{transaction} \; \mt{state}
adamc@545	1628 \end{array}$$
adamc@545	1629
adam@1400	1630 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	1631 $$\begin{array}{l}
adam@1400	1632 \mt{con} \; \mt{sql\_query1} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@543	1633 \\
adamc@543	1634 \mt{type} \; \mt{sql\_relop} \\
adamc@543	1635 \mt{val} \; \mt{sql\_union} : \mt{sql\_relop} \\
adamc@543	1636 \mt{val} \; \mt{sql\_intersect} : \mt{sql\_relop} \\
adamc@543	1637 \mt{val} \; \mt{sql\_except} : \mt{sql\_relop} \\
adam@1400	1638 \mt{val} \; \mt{sql\_relop} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400	1639 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adam@1400	1640 \hspace{.1in} \to \mt{tables1} ::: \{\{\mt{Type}\}\} \\
adamc@543	1641 \hspace{.1in} \to \mt{tables2} ::: \{\{\mt{Type}\}\} \\
adamc@543	1642 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543	1643 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@543	1644 \hspace{.1in} \to \mt{sql\_relop} \\
adam@1458	1645 \hspace{.1in} \to \mt{bool} \; (* \; \mt{ALL} \; *) \\
adam@1400	1646 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables1} \; \mt{selectedFields} \; \mt{selectedExps} \\
adam@1400	1647 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables2} \; \mt{selectedFields} \; \mt{selectedExps} \\
adam@1400	1648 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{selectedFields} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543	1649 \end{array}$$
adamc@543	1650
adamc@543	1651 $$\begin{array}{l}
adamc@1193	1652 \mt{val} \; \mt{sql\_query1} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400	1653 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adamc@1193	1654 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543	1655 \hspace{.1in} \to \mt{grouped} ::: \{\{\mt{Type}\}\} \\
adamc@543	1656 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543	1657 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1085	1658 \hspace{.1in} \to \mt{empties} :: \{\mt{Unit}\} \\
adamc@1193	1659 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adamc@1193	1660 \hspace{.1in} \Rightarrow [\mt{free} \sim \mt{grouped}] \\
adam@1400	1661 \hspace{.1in} \Rightarrow [\mt{afree} \sim \mt{tables}] \\
adamc@1193	1662 \hspace{.1in} \Rightarrow [\mt{empties} \sim \mt{selectedFields}] \\
adamc@1085	1663 \hspace{.1in} \Rightarrow \{\mt{Distinct} : \mt{bool}, \\
adamc@1193	1664 \hspace{.2in} \mt{From} : \mt{sql\_from\_items} \; \mt{free} \; \mt{tables}, \\
adam@1400	1665 \hspace{.2in} \mt{Where} : \mt{sql\_exp} \; (\mt{free} \rc \mt{tables}) \; \mt{afree} \; [] \; \mt{bool}, \\
adamc@543	1666 \hspace{.2in} \mt{GroupBy} : \mt{sql\_subset} \; \mt{tables} \; \mt{grouped}, \\
adam@1400	1667 \hspace{.2in} \mt{Having} : \mt{sql\_exp} \; (\mt{free} \rc \mt{grouped}) \; (\mt{afree} \rc \mt{tables}) \; [] \; \mt{bool}, \\
adamc@1085	1668 \hspace{.2in} \mt{SelectFields} : \mt{sql\_subset} \; \mt{grouped} \; (\mt{map} \; (\lambda \_ \Rightarrow []) \; \mt{empties} \rc \mt{selectedFields}), \\
adam@1400	1669 \hspace{.2in} \mt {SelectExps} : \$(\mt{map} \; (\mt{sql\_exp} \; (\mt{free} \rc \mt{grouped}) \; (\mt{afree} \rc \mt{tables}) \; []) \; \mt{selectedExps}) \} \\
adam@1400	1670 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543	1671 \end{array}$$
adamc@543	1672
adamc@543	1673 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	1674 $$\begin{array}{l}
adamc@543	1675 \mt{con} \; \mt{sql\_subset} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@543	1676 \mt{val} \; \mt{sql\_subset} : \mt{keep\_drop} :: \{(\{\mt{Type}\} \times \{\mt{Type}\})\} \\
adamc@543	1677 \hspace{.1in} \to \mt{sql\_subset} \\
adamc@658	1678 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1 \rc \mt{fields}.2)\; \mt{keep\_drop}) \\
adamc@658	1679 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1) \; \mt{keep\_drop}) \\
adamc@543	1680 \mt{val} \; \mt{sql\_subset\_all} : \mt{tables} :: \{\{\mt{Type}\}\} \to \mt{sql\_subset} \; \mt{tables} \; \mt{tables}
adamc@543	1681 \end{array}$$
adamc@543	1682
adamc@560	1683 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	1684 $$\begin{array}{l}
adamc@543	1685 \mt{con} \; \mt{sql\_exp} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}
adamc@543	1686 \end{array}$$
adamc@543	1687
adamc@543	1688 Any field in scope may be converted to an expression.
adamc@543	1689 $$\begin{array}{l}
adamc@543	1690 \mt{val} \; \mt{sql\_field} : \mt{otherTabs} ::: \{\{\mt{Type}\}\} \to \mt{otherFields} ::: \{\mt{Type}\} \\
adamc@543	1691 \hspace{.1in} \to \mt{fieldType} ::: \mt{Type} \to \mt{agg} ::: \{\{\mt{Type}\}\} \\
adamc@543	1692 \hspace{.1in} \to \mt{exps} ::: \{\mt{Type}\} \\
adamc@543	1693 \hspace{.1in} \to \mt{tab} :: \mt{Name} \to \mt{field} :: \mt{Name} \\
adamc@543	1694 \hspace{.1in} \to \mt{sql\_exp} \; ([\mt{tab} = [\mt{field} = \mt{fieldType}] \rc \mt{otherFields}] \rc \mt{otherTabs}) \; \mt{agg} \; \mt{exps} \; \mt{fieldType}
adamc@543	1695 \end{array}$$
adamc@543	1696
adamc@544	1697 There is an analogous function for referencing named expressions.
adamc@544	1698 $$\begin{array}{l}
adamc@544	1699 \mt{val} \; \mt{sql\_exp} : \mt{tabs} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{t} ::: \mt{Type} \to \mt{rest} ::: \{\mt{Type}\} \to \mt{nm} :: \mt{Name} \\
adamc@544	1700 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tabs} \; \mt{agg} \; ([\mt{nm} = \mt{t}] \rc \mt{rest}) \; \mt{t}
adamc@544	1701 \end{array}$$
adamc@544	1702
adamc@544	1703 Ur values of appropriate types may be injected into SQL expressions.
adamc@544	1704 $$\begin{array}{l}
adamc@786	1705 \mt{class} \; \mt{sql\_injectable\_prim} \\
adamc@786	1706 \mt{val} \; \mt{sql\_bool} : \mt{sql\_injectable\_prim} \; \mt{bool} \\
adamc@786	1707 \mt{val} \; \mt{sql\_int} : \mt{sql\_injectable\_prim} \; \mt{int} \\
adamc@786	1708 \mt{val} \; \mt{sql\_float} : \mt{sql\_injectable\_prim} \; \mt{float} \\
adamc@786	1709 \mt{val} \; \mt{sql\_string} : \mt{sql\_injectable\_prim} \; \mt{string} \\
adamc@786	1710 \mt{val} \; \mt{sql\_time} : \mt{sql\_injectable\_prim} \; \mt{time} \\
adamc@786	1711 \mt{val} \; \mt{sql\_blob} : \mt{sql\_injectable\_prim} \; \mt{blob} \\
adamc@786	1712 \mt{val} \; \mt{sql\_channel} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{channel} \; \mt{t}) \\
adamc@786	1713 \mt{val} \; \mt{sql\_client} : \mt{sql\_injectable\_prim} \; \mt{client} \\
adamc@786	1714 \\
adamc@544	1715 \mt{class} \; \mt{sql\_injectable} \\
adamc@786	1716 \mt{val} \; \mt{sql\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@786	1717 \mt{val} \; \mt{sql\_option\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; (\mt{option} \; \mt{t}) \\
adamc@786	1718 \\
adamc@544	1719 \mt{val} \; \mt{sql\_inject} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@544	1720 \hspace{.1in} \to \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adamc@544	1721 \end{array}$$
adamc@544	1722
adamc@1123	1723 Additionally, most function-free types may be injected safely, via the $\mt{serialized}$ type family.
adamc@1123	1724 $$\begin{array}{l}
adamc@1123	1725 \mt{con} \; \mt{serialized} :: \mt{Type} \to \mt{Type} \\
adamc@1123	1726 \mt{val} \; \mt{serialize} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{serialized} \; \mt{t} \\
adamc@1123	1727 \mt{val} \; \mt{deserialize} : \mt{t} ::: \mt{Type} \to \mt{serialized} \; \mt{t} \to \mt{t} \\
adamc@1123	1728 \mt{val} \; \mt{sql\_serialized} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{serialized} \; \mt{t})
adamc@1123	1729 \end{array}$$
adamc@1123	1730
adamc@544	1731 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	1732 $$\begin{array}{l}
adamc@544	1733 \mt{val} \; \mt{sql\_is\_null} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544	1734 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; (\mt{option} \; \mt{t}) \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{bool}
adamc@544	1735 \end{array}$$
adamc@544	1736
adam@1602	1737 As another way of dealing with null values, there is also a restricted form of the standard \cd{COALESCE} function.
adam@1602	1738 $$\begin{array}{l}
adam@1602	1739 \mt{val} \; \mt{sql\_coalesce} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1602	1740 \hspace{.1in} \to \mt{t} ::: \mt{Type} \\
adam@1602	1741 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; (\mt{option} \; \mt{t}) \\
adam@1602	1742 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1602	1743 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adam@1602	1744 \end{array}$$
adam@1602	1745
adamc@559	1746 We have generic nullary, unary, and binary operators.
adamc@544	1747 $$\begin{array}{l}
adamc@544	1748 \mt{con} \; \mt{sql\_nfunc} :: \mt{Type} \to \mt{Type} \\
adamc@544	1749 \mt{val} \; \mt{sql\_current\_timestamp} : \mt{sql\_nfunc} \; \mt{time} \\
adamc@544	1750 \mt{val} \; \mt{sql\_nfunc} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544	1751 \hspace{.1in} \to \mt{sql\_nfunc} \; \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\\end{array}$$
adamc@544	1752
adamc@544	1753 $$\begin{array}{l}
adamc@544	1754 \mt{con} \; \mt{sql\_unary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544	1755 \mt{val} \; \mt{sql\_not} : \mt{sql\_unary} \; \mt{bool} \; \mt{bool} \\
adamc@544	1756 \mt{val} \; \mt{sql\_unary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adamc@544	1757 \hspace{.1in} \to \mt{sql\_unary} \; \mt{arg} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res} \\
adamc@544	1758 \end{array}$$
adamc@544	1759
adamc@544	1760 $$\begin{array}{l}
adamc@544	1761 \mt{con} \; \mt{sql\_binary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544	1762 \mt{val} \; \mt{sql\_and} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544	1763 \mt{val} \; \mt{sql\_or} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544	1764 \mt{val} \; \mt{sql\_binary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg_1} ::: \mt{Type} \to \mt{arg_2} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adamc@544	1765 \hspace{.1in} \to \mt{sql\_binary} \; \mt{arg_1} \; \mt{arg_2} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_1} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_2} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res}
adamc@544	1766 \end{array}$$
adamc@544	1767
adamc@544	1768 $$\begin{array}{l}
adamc@559	1769 \mt{class} \; \mt{sql\_arith} \\
adamc@559	1770 \mt{val} \; \mt{sql\_int\_arith} : \mt{sql\_arith} \; \mt{int} \\
adamc@559	1771 \mt{val} \; \mt{sql\_float\_arith} : \mt{sql\_arith} \; \mt{float} \\
adamc@559	1772 \mt{val} \; \mt{sql\_neg} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_unary} \; \mt{t} \; \mt{t} \\
adamc@559	1773 \mt{val} \; \mt{sql\_plus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559	1774 \mt{val} \; \mt{sql\_minus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559	1775 \mt{val} \; \mt{sql\_times} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559	1776 \mt{val} \; \mt{sql\_div} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559	1777 \mt{val} \; \mt{sql\_mod} : \mt{sql\_binary} \; \mt{int} \; \mt{int} \; \mt{int}
adamc@559	1778 \end{array}$$
adamc@544	1779
adamc@656	1780 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	1781 $$\begin{array}{l}
adamc@544	1782 \mt{val} \; \mt{sql\_count} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int}
adamc@544	1783 \end{array}$$
adamc@544	1784
adamc@544	1785 $$\begin{array}{l}
adamc@1188	1786 \mt{con} \; \mt{sql\_aggregate} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@1188	1787 \mt{val} \; \mt{sql\_aggregate} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{dom} ::: \mt{Type} \to \mt{ran} ::: \mt{Type} \\
adamc@1188	1788 \hspace{.1in} \to \mt{sql\_aggregate} \; \mt{dom} \; \mt{ran} \to \mt{sql\_exp} \; \mt{agg} \; \mt{agg} \; \mt{exps} \; \mt{dom} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{ran}
adamc@1188	1789 \end{array}$$
adamc@1188	1790
adamc@1188	1791 $$\begin{array}{l}
adamc@1188	1792 \mt{val} \; \mt{sql\_count\_col} : \mt{t} ::: \mt{Type} \to \mt{sql\_aggregate} \; (\mt{option} \; \mt{t}) \; \mt{int}
adamc@544	1793 \end{array}$$
adam@1400	1794
adam@1400	1795 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	1796
adamc@544	1797 $$\begin{array}{l}
adamc@544	1798 \mt{class} \; \mt{sql\_summable} \\
adamc@544	1799 \mt{val} \; \mt{sql\_summable\_int} : \mt{sql\_summable} \; \mt{int} \\
adamc@544	1800 \mt{val} \; \mt{sql\_summable\_float} : \mt{sql\_summable} \; \mt{float} \\
adam@1400	1801 \mt{val} \; \mt{sql\_avg} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt} \\
adam@1400	1802 \mt{val} \; \mt{sql\_sum} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt}
adamc@544	1803 \end{array}$$
adamc@544	1804
adamc@544	1805 $$\begin{array}{l}
adamc@544	1806 \mt{class} \; \mt{sql\_maxable} \\
adamc@544	1807 \mt{val} \; \mt{sql\_maxable\_int} : \mt{sql\_maxable} \; \mt{int} \\
adamc@544	1808 \mt{val} \; \mt{sql\_maxable\_float} : \mt{sql\_maxable} \; \mt{float} \\
adamc@544	1809 \mt{val} \; \mt{sql\_maxable\_string} : \mt{sql\_maxable} \; \mt{string} \\
adamc@544	1810 \mt{val} \; \mt{sql\_maxable\_time} : \mt{sql\_maxable} \; \mt{time} \\
adam@1400	1811 \mt{val} \; \mt{sql\_max} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt} \\
adam@1400	1812 \mt{val} \; \mt{sql\_min} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt}
adamc@544	1813 \end{array}$$
adamc@544	1814
adamc@1193	1815 Any SQL query that returns single columns may be turned into a subquery expression.
adamc@1193	1816
adamc@786	1817 $$\begin{array}{l}
adam@1421	1818 \mt{val} \; \mt{sql\_subquery} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \\
adam@1421	1819 \hspace{.1in} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_query} \; \mt{tables} \; \mt{agg} \; [\mt{nm} = \mt{t}] \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{nt}
adamc@1193	1820 \end{array}$$
adamc@1193	1821
adam@1573	1822 There is also an \cd{IF..THEN..ELSE..} construct that is compiled into standard SQL \cd{CASE} expressions.
adam@1573	1823 $$\begin{array}{l}
adam@1573	1824 \mt{val} \; \mt{sql\_if\_then\_else} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1573	1825 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{bool} \\
adam@1573	1826 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1573	1827 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1573	1828 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adam@1573	1829 \end{array}$$
adam@1573	1830
adamc@1193	1831 \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	1832 $$\begin{array}{l}
adamc@1193	1833 \mt{con} \; \mt{sql\_from\_items} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@1193	1834 \mt{val} \; \mt{sql\_from\_table} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adamc@1193	1835 \hspace{.1in} \to \mt{t} ::: \mt{Type} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; \mt{t} \; \mt{fs} \to \mt{name} :: \mt{Name} \to \mt{t} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193	1836 \mt{val} \; \mt{sql\_from\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{name} :: \mt{Name} \to \mt{sql\_query} \; \mt{free} \; [] \; \mt{fs} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193	1837 \mt{val} \; \mt{sql\_from\_comma} : \mt{free} ::: \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \to [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193	1838 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adamc@1193	1839 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2}) \\
adamc@1193	1840 \mt{val} \; \mt{sql\_inner\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \\
adamc@1193	1841 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193	1842 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adamc@1193	1843 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193	1844 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2})
adamc@786	1845 \end{array}$$
adamc@786	1846
adamc@786	1847 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	1848 $$\begin{array}{l}
adamc@786	1849 \mt{class} \; \mt{nullify} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@786	1850 \mt{val} \; \mt{nullify\_option} : \mt{t} ::: \mt{Type} \to \mt{nullify} \; (\mt{option} \; \mt{t}) \; (\mt{option} \; \mt{t}) \\
adamc@786	1851 \mt{val} \; \mt{nullify\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{nullify} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@786	1852 \end{array}$$
adamc@786	1853
adamc@786	1854 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	1855
adamc@786	1856 $$\begin{array}{l}
adamc@1193	1857 \mt{val} \; \mt{sql\_left\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{(\mt{Type} \times \mt{Type})\}\} \\
adamc@1193	1858 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@786	1859 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\lambda \mt{r} \Rightarrow \$(\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{nullify} \; \mt{p}.1 \; \mt{p}.2) \; \mt{r})) \; \mt{tabs2}) \\
adamc@1193	1860 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \\
adamc@1193	1861 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193	1862 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.2)) \; \mt{tabs2})
adamc@786	1863 \end{array}$$
adamc@786	1864
adamc@544	1865 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	1866 $$\begin{array}{l}
adamc@544	1867 \mt{type} \; \mt{sql\_direction} \\
adamc@544	1868 \mt{val} \; \mt{sql\_asc} : \mt{sql\_direction} \\
adamc@544	1869 \mt{val} \; \mt{sql\_desc} : \mt{sql\_direction} \\
adamc@544	1870 \\
adamc@544	1871 \mt{con} \; \mt{sql\_order\_by} :: \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@544	1872 \mt{val} \; \mt{sql\_order\_by\_Nil} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} :: \{\mt{Type}\} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544	1873 \mt{val} \; \mt{sql\_order\_by\_Cons} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544	1874 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; [] \; \mt{exps} \; \mt{t} \to \mt{sql\_direction} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adam@1684	1875 \mt{val} \; \mt{sql\_order\_by\_random} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544	1876 \\
adamc@544	1877 \mt{type} \; \mt{sql\_limit} \\
adamc@544	1878 \mt{val} \; \mt{sql\_no\_limit} : \mt{sql\_limit} \\
adamc@544	1879 \mt{val} \; \mt{sql\_limit} : \mt{int} \to \mt{sql\_limit} \\
adamc@544	1880 \\
adamc@544	1881 \mt{type} \; \mt{sql\_offset} \\
adamc@544	1882 \mt{val} \; \mt{sql\_no\_offset} : \mt{sql\_offset} \\
adamc@544	1883 \mt{val} \; \mt{sql\_offset} : \mt{int} \to \mt{sql\_offset}
adamc@544	1884 \end{array}$$
adamc@544	1885
adamc@545	1886
adamc@545	1887 \subsubsection{DML}
adamc@545	1888
adamc@545	1889 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	1890
adamc@545	1891 $$\begin{array}{l}
adamc@545	1892 \mt{type} \; \mt{dml} \\
adamc@545	1893 \mt{val} \; \mt{dml} : \mt{dml} \to \mt{transaction} \; \mt{unit}
adamc@545	1894 \end{array}$$
adamc@545	1895
adam@1297	1896 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	1897
adam@1297	1898 $$\begin{array}{l}
adam@1297	1899 \mt{val} \; \mt{tryDml} : \mt{dml} \to \mt{transaction} \; (\mt{option} \; \mt{string})
adam@1297	1900 \end{array}$$
adam@1297	1901
adamc@545	1902 Properly-typed records may be used to form $\mt{INSERT}$ commands.
adamc@545	1903 $$\begin{array}{l}
adamc@545	1904 \mt{val} \; \mt{insert} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \\
adamc@658	1905 \hspace{.1in} \to \$(\mt{map} \; (\mt{sql\_exp} \; [] \; [] \; []) \; \mt{fields}) \to \mt{dml}
adamc@545	1906 \end{array}$$
adamc@545	1907
adam@1578	1908 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	1909 $$\begin{array}{l}
adam@1380	1910 \mt{val} \; \mt{update} : \mt{unchanged} ::: \{\mt{Type}\} \to \mt{changed} :: \{\mt{Type}\} \to [\mt{changed} \sim \mt{unchanged}] \\
adamc@658	1911 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; []) \; \mt{changed}) \\
adamc@545	1912 \hspace{.1in} \to \mt{sql\_table} \; (\mt{changed} \rc \mt{unchanged}) \to \mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545	1913 \end{array}$$
adamc@545	1914
adam@1578	1915 A $\mt{DELETE}$ command is formed from a table and a $\mt{WHERE}$ clause. The above use of $\mt{T}$ is repeated.
adamc@545	1916 $$\begin{array}{l}
adamc@545	1917 \mt{val} \; \mt{delete} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \to \mt{sql\_exp} \; [\mt{T} = \mt{fields}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545	1918 \end{array}$$
adamc@545	1919
adamc@546	1920 \subsubsection{Sequences}
adamc@546	1921
adamc@546	1922 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	1923
adamc@546	1924 $$\begin{array}{l}
adamc@546	1925 \mt{type} \; \mt{sql\_sequence} \\
adamc@1085	1926 \mt{val} \; \mt{nextval} : \mt{sql\_sequence} \to \mt{transaction} \; \mt{int} \\
adamc@1085	1927 \mt{val} \; \mt{setval} : \mt{sql\_sequence} \to \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@546	1928 \end{array}$$
adamc@546	1929
adamc@546	1930
adam@1648	1931 \subsection{\label{xml}XML}
adamc@547	1932
adam@1333	1933 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	1934
adam@1642	1935 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	1936 $$\begin{array}{l}
adamc@547	1937 \mt{con} \; \mt{xml} :: \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547	1938 \end{array}$$
adamc@547	1939
adamc@547	1940 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	1941 $$\begin{array}{l}
adamc@547	1942 \mt{con} \; \mt{tag} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547	1943 \end{array}$$
adamc@547	1944
adamc@547	1945 Literal text may be injected into XML as ``CDATA.''
adamc@547	1946 $$\begin{array}{l}
adamc@547	1947 \mt{val} \; \mt{cdata} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{string} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adamc@547	1948 \end{array}$$
adamc@547	1949
adam@1358	1950 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	1951 $$\begin{array}{l}
adam@1358	1952 \mt{val} \; \mt{cdataChar} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{char} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adam@1358	1953 \end{array}$$
adam@1358	1954
adamc@547	1955 There is a function for producing an XML tree with a particular tag at its root.
adamc@547	1956 $$\begin{array}{l}
adamc@547	1957 \mt{val} \; \mt{tag} : \mt{attrsGiven} ::: \{\mt{Type}\} \to \mt{attrsAbsent} ::: \{\mt{Type}\} \to \mt{ctxOuter} ::: \{\mt{Unit}\} \to \mt{ctxInner} ::: \{\mt{Unit}\} \\
adamc@547	1958 \hspace{.1in} \to \mt{useOuter} ::: \{\mt{Type}\} \to \mt{useInner} ::: \{\mt{Type}\} \to \mt{bindOuter} ::: \{\mt{Type}\} \to \mt{bindInner} ::: \{\mt{Type}\} \\
adam@1380	1959 \hspace{.1in} \to [\mt{attrsGiven} \sim \mt{attrsAbsent}] \Rightarrow [\mt{useOuter} \sim \mt{useInner}] \Rightarrow [\mt{bindOuter} \sim \mt{bindInner}] \\
adam@1749	1960 \hspace{.1in} \Rightarrow \mt{css\_class} \\
adam@1643	1961 \hspace{.1in} \to \mt{option} \; (\mt{signal} \; \mt{css\_class}) \\
adam@1750	1962 \hspace{.1in} \to \mt{css\_style} \\
adam@1751	1963 \hspace{.1in} \to \mt{option} \; (\mt{signal} \; \mt{css\_style}) \\
adamc@787	1964 \hspace{.1in} \to \$\mt{attrsGiven} \\
adamc@547	1965 \hspace{.1in} \to \mt{tag} \; (\mt{attrsGiven} \rc \mt{attrsAbsent}) \; \mt{ctxOuter} \; \mt{ctxInner} \; \mt{useOuter} \; \mt{bindOuter} \\
adamc@547	1966 \hspace{.1in} \to \mt{xml} \; \mt{ctxInner} \; \mt{useInner} \; \mt{bindInner} \to \mt{xml} \; \mt{ctxOuter} \; (\mt{useOuter} \rc \mt{useInner}) \; (\mt{bindOuter} \rc \mt{bindInner})
adamc@547	1967 \end{array}$$
adam@1750	1968 Note that any tag may be assigned a CSS class, or left without a class by passing $\mt{Basis.null}$ as the first value-level argument. This is the sole way of making use of the values produced by $\mt{style}$ declarations. The function $\mt{Basis.classes}$ can be used to specify a list of CSS classes for a single tag. Stylesheets to assign properties to the classes can be linked via URL's with \texttt{link} tags. Ur/Web makes it easy to calculate upper bounds on usage of CSS classes through program analysis, with the \cd{-css} command-line flag.
adamc@547	1969
adam@1643	1970 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	1971
adam@1751	1972 The third and fourth value-level arguments makes it possible to generate HTML \cd{style} attributes, either with fixed content (\cd{style} attribute) or dynamic content (\cd{dynStyle} pseudo-attribute).
adam@1750	1973
adamc@547	1974 Two XML fragments may be concatenated.
adamc@547	1975 $$\begin{array}{l}
adamc@547	1976 \mt{val} \; \mt{join} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{bind_1} ::: \{\mt{Type}\} \to \mt{bind_2} ::: \{\mt{Type}\} \\
adam@1380	1977 \hspace{.1in} \to [\mt{use_1} \sim \mt{bind_1}] \Rightarrow [\mt{bind_1} \sim \mt{bind_2}] \\
adamc@547	1978 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind_1} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{bind_1}) \; \mt{bind_2} \to \mt{xml} \; \mt{ctx} \; \mt{use_1} \; (\mt{bind_1} \rc \mt{bind_2})
adamc@547	1979 \end{array}$$
adamc@547	1980
adamc@547	1981 Finally, any XML fragment may be updated to ``claim'' to use more form fields than it does.
adamc@547	1982 $$\begin{array}{l}
adam@1380	1983 \mt{val} \; \mt{useMore} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{use_2} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to [\mt{use_1} \sim \mt{use_2}] \\
adamc@547	1984 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{use_2}) \; \mt{bind}
adamc@547	1985 \end{array}$$
adamc@547	1986
adam@1344	1987 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	1988
adamc@547	1989 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	1990 $$\begin{array}{l}
adam@1641	1991 \mt{val} \; \mt{error} : \mt{t} ::: \mt{Type} \to \mt{xbody} \to \mt{t}
adamc@547	1992 \end{array}$$
adamc@547	1993
adamc@549	1994
adamc@701	1995 \subsection{Client-Side Programming}
adamc@659	1996
adamc@701	1997 Ur/Web supports running code on web browsers, via automatic compilation to JavaScript.
adamc@701	1998
adamc@701	1999 \subsubsection{The Basics}
adamc@701	2000
adam@1400	2001 All of the functions in this subsection are client-side only.
adam@1400	2002
adam@1297	2003 Clients can open alert and confirm dialog boxes, in the usual annoying JavaScript way.
adamc@701	2004 $$\begin{array}{l}
adam@1297	2005 \mt{val} \; \mt{alert} : \mt{string} \to \mt{transaction} \; \mt{unit} \\
adam@1297	2006 \mt{val} \; \mt{confirm} : \mt{string} \to \mt{transaction} \; \mt{bool}
adamc@701	2007 \end{array}$$
adamc@701	2008
adamc@701	2009 Any transaction may be run in a new thread with the $\mt{spawn}$ function.
adamc@701	2010 $$\begin{array}{l}
adamc@701	2011 \mt{val} \; \mt{spawn} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit}
adamc@701	2012 \end{array}$$
adamc@701	2013
adamc@701	2014 The current thread can be paused for at least a specified number of milliseconds.
adamc@701	2015 $$\begin{array}{l}
adamc@701	2016 \mt{val} \; \mt{sleep} : \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@701	2017 \end{array}$$
adamc@701	2018
adam@1770	2019 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 a JavaScript \cd{alert()} is used to announce its occurrence. When one of these functions is called multiple times within a single page, all registered handlers are run when appropriate events occur, with handlers run in the reverse of their registration order.
adamc@787	2020 $$\begin{array}{l}
adamc@787	2021 \mt{val} \; \mt{onError} : (\mt{xbody} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787	2022 \mt{val} \; \mt{onFail} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787	2023 \mt{val} \; \mt{onConnectFail} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787	2024 \mt{val} \; \mt{onDisconnect} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787	2025 \mt{val} \; \mt{onServerError} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit}
adamc@787	2026 \end{array}$$
adamc@787	2027
adam@1555	2028 There are also functions to register standard document-level event handlers.
adam@1555	2029
adam@1555	2030 $$\begin{array}{l}
adam@1555	2031 \mt{val} \; \mt{onClick} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adam@1555	2032 \mt{val} \; \mt{onDblclick} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adam@1555	2033 \mt{val} \; \mt{onKeydown} : (\mt{int} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1555	2034 \mt{val} \; \mt{onKeypress} : (\mt{int} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1555	2035 \mt{val} \; \mt{onKeyup} : (\mt{int} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1555	2036 \mt{val} \; \mt{onMousedown} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adam@1555	2037 \mt{val} \; \mt{onMouseup} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit}
adam@1555	2038 \end{array}$$
adam@1555	2039
adam@1559	2040 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	2041
adam@1559	2042 $$\begin{array}{l}
adam@1559	2043 \mt{val} \; \mt{preventDefault} : \mt{transaction} \; \mt{unit} \\
adam@1559	2044 \mt{val} \; \mt{stopPropagation} : \mt{transaction} \; \mt{unit}
adam@1559	2045 \end{array}$$
adam@1559	2046
adam@1556	2047 \subsubsection{Node IDs}
adam@1556	2048
adam@1556	2049 There is an abstract type of node IDs that may be assigned to \cd{id} attributes of most HTML tags.
adam@1556	2050
adam@1556	2051 $$\begin{array}{l}
adam@1556	2052 \mt{type} \; \mt{id} \\
adam@1556	2053 \mt{val} \; \mt{fresh} : \mt{transaction} \; \mt{id}
adam@1556	2054 \end{array}$$
adam@1556	2055
adam@1556	2056 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	2057
adam@1643	2058 \subsubsection{\label{signals}Functional-Reactive Page Generation}
adamc@701	2059
adamc@701	2060 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	2061
adam@1403	2062 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	2063
adamc@659	2064 $$\begin{array}{l}
adamc@659	2065 \mt{con} \; \mt{source} :: \mt{Type} \to \mt{Type} \\
adamc@659	2066 \mt{val} \; \mt{source} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{transaction} \; (\mt{source} \; \mt{t}) \\
adamc@659	2067 \mt{val} \; \mt{set} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@659	2068 \mt{val} \; \mt{get} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@659	2069 \end{array}$$
adamc@659	2070
adam@1400	2071 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	2072
adam@1608	2073 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	2074
adamc@659	2075 $$\begin{array}{l}
adamc@659	2076 \mt{con} \; \mt{signal} :: \mt{Type} \to \mt{Type} \\
adamc@659	2077 \mt{val} \; \mt{signal\_monad} : \mt{monad} \; \mt{signal} \\
adam@1608	2078 \mt{val} \; \mt{signal} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{signal} \; \mt{t} \\
adam@1608	2079 \mt{val} \; \mt{current} : \mt{t} ::: \mt{Type} \to \mt{signal} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@659	2080 \end{array}$$
adamc@659	2081
adamc@659	2082 A reactive portion of an HTML page is injected with a $\mt{dyn}$ tag, which has a signal-valued attribute $\mt{Signal}$.
adamc@659	2083
adamc@659	2084 $$\begin{array}{l}
adam@1641	2085 \mt{val} \; \mt{dyn} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to [\mt{ctx} \sim [\mt{Dyn}]] \Rightarrow \mt{unit} \\
adam@1641	2086 \hspace{.1in} \to \mt{tag} \; [\mt{Signal} = \mt{signal} \; (\mt{xml} \; ([\mt{Dyn}] \rc \mt{ctx}) \; \mt{use} \; \mt{bind})] \; ([\mt{Dyn}] \rc \mt{ctx}) \; [] \; \mt{use} \; \mt{bind}
adamc@659	2087 \end{array}$$
adamc@659	2088
adam@1648	2089 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	2090
adam@1648	2091 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	2092
adamc@701	2093 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	2094
adamc@914	2095 \subsubsection{Remote Procedure Calls}
adamc@914	2096
adamc@914	2097 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	2098
adamc@914	2099 $$\begin{array}{l}
adamc@914	2100 \mt{val} \; \mt{rpc} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@914	2101 \end{array}$$
adamc@914	2102
adamc@701	2103 \subsubsection{Asynchronous Message-Passing}
adamc@701	2104
adamc@701	2105 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	2106
adamc@701	2107 $$\begin{array}{l}
adamc@701	2108 \mt{type} \; \mt{client} \\
adamc@701	2109 \mt{val} \; \mt{self} : \mt{transaction} \; \mt{client}
adamc@701	2110 \end{array}$$
adamc@701	2111
adamc@701	2112 \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	2113
adamc@701	2114 $$\begin{array}{l}
adamc@701	2115 \mt{con} \; \mt{channel} :: \mt{Type} \to \mt{Type} \\
adamc@701	2116 \mt{val} \; \mt{channel} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; (\mt{channel} \; \mt{t}) \\
adamc@701	2117 \mt{val} \; \mt{send} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@701	2118 \mt{val} \; \mt{recv} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@701	2119 \end{array}$$
adamc@701	2120
adamc@701	2121 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	2122
adamc@701	2123 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	2124
adam@1551	2125 \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	2126
adamc@659	2127
adamc@549	2128 \section{Ur/Web Syntax Extensions}
adamc@549	2129
adamc@549	2130 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	2131
adamc@549	2132 \subsection{SQL}
adamc@549	2133
adamc@786	2134 \subsubsection{\label{tables}Table Declarations}
adamc@786	2135
adamc@788	2136 $\mt{table}$ declarations may include constraints, via these grammar rules.
adamc@788	2137 $$\begin{array}{rrcll}
adam@1594	2138 \textrm{Declarations} & d &::=& \mt{table} \; x : c \; [pk[,]] \; cts \mid \mt{view} \; x = V \\
adamc@788	2139 \textrm{Primary key constraints} & pk &::=& \mt{PRIMARY} \; \mt{KEY} \; K \\
adam@1722	2140 \textrm{Keys} & K &::=& f \mid (f, (f,)^+) \mid \{\{e\}\} \\
adamc@788	2141 \textrm{Constraint sets} & cts &::=& \mt{CONSTRAINT} f \; ct \mid cts, cts \mid \{\{e\}\} \\
adamc@788	2142 \textrm{Constraints} & ct &::=& \mt{UNIQUE} \; K \mid \mt{CHECK} \; E \\
adamc@788	2143 &&& \mid \mt{FOREIGN} \; \mt{KEY} \; K \; \mt{REFERENCES} \; F \; (K) \; [\mt{ON} \; \mt{DELETE} \; pr] \; [\mt{ON} \; \mt{UPDATE} \; pr] \\
adamc@788	2144 \textrm{Foreign tables} & F &::=& x \mid \{\{e\}\} \\
adam@1594	2145 \textrm{Propagation modes} & pr &::=& \mt{NO} \; \mt{ACTION} \mid \mt{RESTRICT} \mid \mt{CASCADE} \mid \mt{SET} \; \mt{NULL} \\
adam@1594	2146 \textrm{View expressions} & V &::=& Q \mid \{e\}
adamc@788	2147 \end{array}$$
adamc@788	2148
adamc@788	2149 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	2150
adamc@788	2151
adamc@549	2152 \subsubsection{Queries}
adamc@549	2153
adamc@550	2154 Queries $Q$ are added to the rules for expressions $e$.
adamc@550	2155
adamc@549	2156 $$\begin{array}{rrcll}
adam@1684	2157 \textrm{Queries} & Q &::=& (q \; [\mt{ORDER} \; \mt{BY} \; O] \; [\mt{LIMIT} \; N] \; [\mt{OFFSET} \; N]) \\
adamc@1085	2158 \textrm{Pre-queries} & q &::=& \mt{SELECT} \; [\mt{DISTINCT}] \; P \; \mt{FROM} \; F,^+ \; [\mt{WHERE} \; E] \; [\mt{GROUP} \; \mt{BY} \; p,^+] \; [\mt{HAVING} \; E] \\
adamc@1085	2159 &&& \mid q \; R \; q \mid \{\{\{e\}\}\} \\
adam@1684	2160 \textrm{Relational operators} & R &::=& \mt{UNION} \mid \mt{INTERSECT} \mid \mt{EXCEPT} \\
adam@1684	2161 \textrm{$\mt{ORDER \; BY}$ items} & O &::=& \mt{RANDOM} [()] \mid E \; [o] \mid E \; [o], O
adamc@549	2162 \end{array}$$
adamc@549	2163
adamc@549	2164 $$\begin{array}{rrcll}
adamc@549	2165 \textrm{Projections} & P &::=& \ast & \textrm{all columns} \\
adamc@549	2166 &&& p,^+ & \textrm{particular columns} \\
adamc@549	2167 \textrm{Pre-projections} & p &::=& t.f & \textrm{one column from a table} \\
adamc@558	2168 &&& t.\{\{c\}\} & \textrm{a record of columns from a table (of kind $\{\mt{Type}\}$)} \\
adam@1627	2169 &&& t.* & \textrm{all columns from a table} \\
adamc@1194	2170 &&& E \; [\mt{AS} \; f] & \textrm{expression column} \\
adamc@549	2171 \textrm{Table names} & t &::=& x & \textrm{constant table name (automatically capitalized)} \\
adamc@549	2172 &&& X & \textrm{constant table name} \\
adamc@549	2173 &&& \{\{c\}\} & \textrm{computed table name (of kind $\mt{Name}$)} \\
adamc@549	2174 \textrm{Column names} & f &::=& X & \textrm{constant column name} \\
adamc@549	2175 &&& \{c\} & \textrm{computed column name (of kind $\mt{Name}$)} \\
adamc@549	2176 \textrm{Tables} & T &::=& x & \textrm{table variable, named locally by its own capitalization} \\
adam@1756	2177 &&& x \; \mt{AS} \; X & \textrm{table variable, with local name} \\
adam@1756	2178 &&& x \; \mt{AS} \; \{c\} & \textrm{table variable, with computed local name} \\
adamc@549	2179 &&& \{\{e\}\} \; \mt{AS} \; t & \textrm{computed table expression, with local name} \\
adam@1756	2180 &&& \{\{e\}\} \; \mt{AS} \; \{c\} & \textrm{computed table expression, with computed local name} \\
adamc@1085	2181 \textrm{$\mt{FROM}$ items} & F &::=& T \mid \{\{e\}\} \mid F \; J \; \mt{JOIN} \; F \; \mt{ON} \; E \\
adamc@1085	2182 &&& \mid F \; \mt{CROSS} \; \mt{JOIN} \ F \\
adamc@1193	2183 &&& \mid (Q) \; \mt{AS} \; t \\
adamc@1085	2184 \textrm{Joins} & J &::=& [\mt{INNER}] \\
adamc@1085	2185 &&& \mid [\mt{LEFT} \mid \mt{RIGHT} \mid \mt{FULL}] \; [\mt{OUTER}] \\
adam@1587	2186 \textrm{SQL expressions} & E &::=& t.f & \textrm{column references} \\
adamc@549	2187 &&& X & \textrm{named expression references} \\
adam@1490	2188 &&& \{[e]\} & \textrm{injected native Ur expressions} \\
adamc@549	2189 &&& \{e\} & \textrm{computed expressions, probably using $\mt{sql\_exp}$ directly} \\
adamc@549	2190 &&& \mt{TRUE} \mid \mt{FALSE} & \textrm{boolean constants} \\
adamc@549	2191 &&& \ell & \textrm{primitive type literals} \\
adamc@549	2192 &&& \mt{NULL} & \textrm{null value (injection of $\mt{None}$)} \\
adamc@549	2193 &&& E \; \mt{IS} \; \mt{NULL} & \textrm{nullness test} \\
adam@1602	2194 &&& \mt{COALESCE}(E, E) & \textrm{take first non-null value} \\
adamc@549	2195 &&& n & \textrm{nullary operators} \\
adamc@549	2196 &&& u \; E & \textrm{unary operators} \\
adamc@549	2197 &&& E \; b \; E & \textrm{binary operators} \\
adamc@549	2198 &&& \mt{COUNT}(\ast) & \textrm{count number of rows} \\
adamc@549	2199 &&& a(E) & \textrm{other aggregate function} \\
adam@1573	2200 &&& \mt{IF} \; E \; \mt{THEN} \; E \; \mt{ELSE} \; E & \textrm{conditional} \\
adamc@1193	2201 &&& (Q) & \textrm{subquery (must return a single expression column)} \\
adamc@549	2202 &&& (E) & \textrm{explicit precedence} \\
adamc@549	2203 \textrm{Nullary operators} & n &::=& \mt{CURRENT\_TIMESTAMP} \\
adamc@549	2204 \textrm{Unary operators} & u &::=& \mt{NOT} \\
adam@1688	2205 \textrm{Binary operators} & b &::=& \mt{AND} \mid \mt{OR} \mid = \mid \neq \mid < \mid \leq \mid > \mid \geq \\
adamc@1188	2206 \textrm{Aggregate functions} & a &::=& \mt{COUNT} \mid \mt{AVG} \mid \mt{SUM} \mid \mt{MIN} \mid \mt{MAX} \\
adam@1543	2207 \textrm{Directions} & o &::=& \mt{ASC} \mid \mt{DESC} \mid \{e\} \\
adamc@549	2208 \textrm{SQL integer} & N &::=& n \mid \{e\} \\
adamc@549	2209 \end{array}$$
adamc@549	2210
adamc@1085	2211 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	2212
adam@1683	2213 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	2214
adamc@550	2215 \subsubsection{DML}
adamc@550	2216
adamc@550	2217 DML commands $D$ are added to the rules for expressions $e$.
adamc@550	2218
adamc@550	2219 $$\begin{array}{rrcll}
adamc@550	2220 \textrm{Commands} & D &::=& (\mt{INSERT} \; \mt{INTO} \; T^E \; (f,^+) \; \mt{VALUES} \; (E,^+)) \\
adamc@550	2221 &&& (\mt{UPDATE} \; T^E \; \mt{SET} \; (f = E,)^+ \; \mt{WHERE} \; E) \\
adamc@550	2222 &&& (\mt{DELETE} \; \mt{FROM} \; T^E \; \mt{WHERE} \; E) \\
adamc@550	2223 \textrm{Table expressions} & T^E &::=& x \mid \{\{e\}\}
adamc@550	2224 \end{array}$$
adamc@550	2225
adamc@550	2226 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	2227
adamc@551	2228 \subsection{XML}
adamc@551	2229
adamc@551	2230 XML fragments $L$ are added to the rules for expressions $e$.
adamc@551	2231
adamc@551	2232 $$\begin{array}{rrcll}
adamc@551	2233 \textrm{XML fragments} & L &::=& \texttt{<xml/>} \mid \texttt{<xml>}l^*\texttt{</xml>} \\
adamc@551	2234 \textrm{XML pieces} & l &::=& \textrm{text} & \textrm{cdata} \\
adamc@551	2235 &&& \texttt{<}g\texttt{/>} & \textrm{tag with no children} \\
adamc@551	2236 &&& \texttt{<}g\texttt{>}l^*\texttt{</}x\texttt{>} & \textrm{tag with children} \\
adamc@559	2237 &&& \{e\} & \textrm{computed XML fragment} \\
adamc@559	2238 &&& \{[e]\} & \textrm{injection of an Ur expression, via the $\mt{Top}.\mt{txt}$ function} \\
adamc@551	2239 \textrm{Tag} & g &::=& h \; (x = v)^* \\
adamc@551	2240 \textrm{Tag head} & h &::=& x & \textrm{tag name} \\
adamc@551	2241 &&& h\{c\} & \textrm{constructor parameter} \\
adamc@551	2242 \textrm{Attribute value} & v &::=& \ell & \textrm{literal value} \\
adamc@551	2243 &&& \{e\} & \textrm{computed value} \\
adamc@551	2244 \end{array}$$
adamc@551	2245
adam@1751	2246 Further, there is a special convenience and compatibility form for setting CSS classes of tags. If a \cd{class} attribute has a value that is a string literal, the literal is parsed in the usual HTML way and replaced with calls to appropriate Ur/Web combinators. Any dashes in the text are replaced with underscores to determine Ur identifiers. The same desugaring can be accessed in a normal expression context by calling the pseudo-function \cd{CLASS} on a string literal.
adam@1751	2247
adam@1751	2248 Similar support is provided for \cd{style} attributes. Normal CSS syntax may be used in string literals that are \cd{style} attribute values, and the desugaring may be accessed elsewhere with the pseudo-function \cd{STYLE}.
adamc@552	2249
adamc@1198	2250 \section{\label{structure}The Structure of Web Applications}
adamc@553	2251
adam@1604	2252 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	2253
adam@1532	2254 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	2255
adam@1347	2256 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	2257
adam@1370	2258 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	2259
adamc@553	2260 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	2261
adamc@553	2262 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	2263
adam@1653	2264 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	2265 \begin{itemize}
adam@1653	2266 \item Functions are disallowed, since there is no obvious way to serialize them safely.
adam@1653	2267 \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	2268 \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	2269 \end{itemize}
adamc@553	2270
adamc@660	2271 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	2272
adamc@789	2273 \medskip
adamc@789	2274
adam@1347	2275 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	2276
adamc@789	2277 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	2278
adam@1348	2279 \subsection{Tasks}
adam@1348	2280
adam@1348	2281 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	2282
adam@1348	2283 $$\begin{array}{l}
adam@1348	2284 \mt{con} \; \mt{task\_kind} :: \mt{Type} \to \mt{Type} \\
adam@1348	2285 \mt{val} \; \mt{initialize} : \mt{task\_kind} \; \mt{unit} \\
adam@1349	2286 \mt{val} \; \mt{clientLeaves} : \mt{task\_kind} \; \mt{client} \\
adam@1349	2287 \mt{val} \; \mt{periodic} : \mt{int} \to \mt{task\_kind} \; \mt{unit}
adam@1348	2288 \end{array}$$
adam@1348	2289
adam@1348	2290 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	2291
adam@1348	2292 The currently supported task kinds are:
adam@1348	2293 \begin{itemize}
adam@1349	2294 \item $\mt{initialize}$: Code that is run when the application starts up.
adam@1348	2295 \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	2296 \item $\mt{periodic} \; n$: Code that is run when the application starts up and then every $n$ seconds thereafter.
adam@1348	2297 \end{itemize}
adam@1348	2298
adamc@553	2299
adamc@897	2300 \section{The Foreign Function Interface}
adamc@897	2301
adamc@897	2302 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	2303
adamc@897	2304 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	2305
adamc@897	2306 \begin{itemize}
adamc@897	2307 \item \texttt{clientOnly Module.ident} registers a value as being allowed only in client-side code.
adamc@897	2308 \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	2309 \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	2310 \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	2311 \item \texttt{include FILE} requests inclusion of a C header file.
adamc@897	2312 \item \texttt{jsFunc Module.ident=name} gives a mapping from an Ur name for a value to a JavaScript name.
adamc@897	2313 \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	2314 \item \texttt{script URL} requests inclusion of a JavaScript source file within application HTML.
adamc@897	2315 \item \texttt{serverOnly Module.ident} registers a value as being allowed only in server-side code.
adamc@897	2316 \end{itemize}
adamc@897	2317
adamc@897	2318 \subsection{Writing C FFI Code}
adamc@897	2319
adamc@897	2320 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	2321
adamc@897	2322 \begin{itemize}
adamc@897	2323 \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	2324 \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	2325 \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	2326 \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	2327 \end{itemize}
adamc@897	2328
adamc@897	2329 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	2330 \begin{itemize}
adamc@897	2331 \item \begin{verbatim}
adamc@897	2332 void uw_error(uw_context, failure_kind, const char *fmt, ...);
adamc@897	2333 \end{verbatim}
adamc@897	2334 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	2335
adam@1329	2336 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	2337
adamc@897	2338 \item \begin{verbatim}
adam@1469	2339 void uw_set_error_message(uw_context, const char *fmt, ...);
adam@1469	2340 \end{verbatim}
adam@1469	2341 This simpler form of \texttt{uw\_error()} saves an error message without immediately aborting execution.
adam@1469	2342
adam@1469	2343 \item \begin{verbatim}
adamc@897	2344 void uw_push_cleanup(uw_context, void (func)(void ), void *arg);
adamc@897	2345 void uw_pop_cleanup(uw_context);
adamc@897	2346 \end{verbatim}
adam@1329	2347 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	2348
adam@1329	2349 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	2350
adamc@897	2351 \item \begin{verbatim}
adamc@897	2352 void *uw_malloc(uw_context, size_t);
adamc@897	2353 \end{verbatim}
adam@1329	2354 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	2355
adam@1329	2356 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	2357
adamc@897	2358 \item \begin{verbatim}
adamc@897	2359 typedef void (uw_callback)(void );
adam@1328	2360 typedef void (uw_callback_with_retry)(void , int will_retry);
adamc@897	2361 void uw_register_transactional(uw_context, void *data, uw_callback commit,
adam@1328	2362 uw_callback rollback, uw_callback_with_retry free);
adamc@897	2363 \end{verbatim}
adam@1328	2364 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	2365
adamc@1085	2366 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	2367
adam@1329	2368 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	2369
adam@1329	2370 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	2371
adam@1469	2372 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	2373
adamc@1085	2374 \item \begin{verbatim}
adamc@1085	2375 void uw_get_global(uw_context, char name);
adamc@1085	2376 void uw_set_global(uw_context, char name, void data, uw_callback free);
adamc@1085	2377 \end{verbatim}
adam@1329	2378 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	2379
adamc@897	2380 \end{itemize}
adamc@897	2381
adamc@897	2382 \subsection{Writing JavaScript FFI Code}
adamc@897	2383
adamc@897	2384 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	2385
adamc@897	2386 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	2387
adamc@897	2388 \begin{itemize}
adamc@897	2389 \item Integers, floats, strings, characters, and booleans are represented in the usual JavaScript way.
adam@1644	2390 \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	2391 \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	2392 \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	2393 \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	2394 \item As in the C FFI, all abstract types of program syntax are implemented with strings in JavaScript.
adamc@897	2395 \end{itemize}
adamc@897	2396
adam@1644	2397 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	2398
adam@1644	2399 \begin{itemize}
adam@1644	2400 \item Sources should be treated as an abstract type, manipulated via:
adam@1644	2401 \begin{itemize}
adam@1644	2402 \item \cd{sc(v)}, to create a source initialized to \cd{v}
adam@1644	2403 \item \cd{sg(s)}, to retrieve the current value of source \cd{s}
adam@1644	2404 \item \cd{sv(s, v)}, to set source \cd{s} to value \cd{v}
adam@1644	2405 \end{itemize}
adam@1644	2406
adam@1644	2407 \item Signals should be treated as an abstract type, manipulated via:
adam@1644	2408 \begin{itemize}
adam@1644	2409 \item \cd{sr(v)} and \cd{sb(s, f)}, the ``return'' and ``bind'' monad operators, respectively
adam@1644	2410 \item \cd{ss(s)}, to produce the signal corresponding to source \cd{s}
adam@1644	2411 \item \cd{scur(s)}, to get the current value of signal \cd{s}
adam@1644	2412 \end{itemize}
adam@1644	2413
adam@1644	2414 \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	2415
adam@1702	2416 \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	2417
adam@1644	2418 \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	2419 \end{itemize}
adamc@897	2420
adamc@897	2421
adamc@552	2422 \section{Compiler Phases}
adamc@552	2423
adamc@552	2424 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	2425
adamc@552	2426 In this section, we step through the main phases of compilation, noting what consequences each phase has for effective programming.
adamc@552	2427
adamc@552	2428 \subsection{Parse}
adamc@552	2429
adamc@552	2430 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	2431
adamc@552	2432 \subsection{Elaborate}
adamc@552	2433
adamc@552	2434 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	2435
adam@1378	2436 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	2437
adamc@552	2438 \subsection{Unnest}
adamc@552	2439
adamc@552	2440 Named local function definitions are moved to the top level, to avoid the need to generate closures.
adamc@552	2441
adamc@552	2442 \subsection{Corify}
adamc@552	2443
adamc@552	2444 Module system features are compiled away, through inlining of functor definitions at application sites. Afterward, most abstraction boundaries are broken, facilitating optimization.
adamc@552	2445
adamc@552	2446 \subsection{Especialize}
adamc@552	2447
adam@1356	2448 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	2449
adamc@552	2450 \subsection{Untangle}
adamc@552	2451
adamc@552	2452 Remove unnecessary mutual recursion, splitting recursive groups into strongly-connected components.
adamc@552	2453
adamc@552	2454 \subsection{Shake}
adamc@552	2455
adamc@552	2456 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	2457
adamc@661	2458 \subsection{Rpcify}
adamc@661	2459
adamc@661	2460 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	2461
adamc@661	2462 \subsection{Untangle, Shake}
adamc@661	2463
adamc@661	2464 Repeat these simplifications.
adamc@661	2465
adamc@553	2466 \subsection{\label{tag}Tag}
adamc@552	2467
adamc@552	2468 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	2469
adamc@552	2470 \subsection{Reduce}
adamc@552	2471
adamc@552	2472 Apply definitional equality rules to simplify the program as much as possible. This effectively includes inlining of every non-recursive definition.
adamc@552	2473
adamc@552	2474 \subsection{Unpoly}
adamc@552	2475
adamc@552	2476 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	2477
adamc@552	2478 \subsection{Specialize}
adamc@552	2479
adamc@558	2480 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	2481
adamc@552	2482 \subsection{Shake}
adamc@552	2483
adamc@558	2484 Here the compiler repeats the earlier Shake phase.
adamc@552	2485
adamc@552	2486 \subsection{Monoize}
adamc@552	2487
adamc@552	2488 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	2489
adamc@552	2490 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	2491
adamc@552	2492 \subsection{MonoOpt}
adamc@552	2493
adamc@552	2494 Simple algebraic laws are applied to simplify the program, focusing especially on efficient imperative generation of HTML pages.
adamc@552	2495
adamc@552	2496 \subsection{MonoUntangle}
adamc@552	2497
adamc@552	2498 Unnecessary mutual recursion is broken up again.
adamc@552	2499
adamc@552	2500 \subsection{MonoReduce}
adamc@552	2501
adamc@552	2502 Equivalents of the definitional equality rules are applied to simplify programs, with inlining again playing a major role.
adamc@552	2503
adamc@552	2504 \subsection{MonoShake, MonoOpt}
adamc@552	2505
adamc@552	2506 Unneeded declarations are removed, and basic optimizations are repeated.
adamc@552	2507
adamc@552	2508 \subsection{Fuse}
adamc@552	2509
adamc@552	2510 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	2511
adamc@552	2512 \subsection{MonoUntangle, MonoShake}
adamc@552	2513
adamc@552	2514 Fuse often creates more opportunities to remove spurious mutual recursion.
adamc@552	2515
adamc@552	2516 \subsection{Pathcheck}
adamc@552	2517
adamc@552	2518 The compiler checks that no link or action name has been used more than once.
adamc@552	2519
adamc@552	2520 \subsection{Cjrize}
adamc@552	2521
adamc@552	2522 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	2523
adamc@552	2524 \subsection{C Compilation and Linking}
adamc@552	2525
adam@1523	2526 The output of the last phase is pretty-printed as C source code and passed to the C compiler.
adamc@552	2527
adamc@552	2528
as@1564	2529 \end{document}

Mercurial > urweb

annotate doc/manual.tex @ 1771:4cca386e5766