Ur/Web: doc/manual.tex annotate

annotate doc/manual.tex @ 2094:0d898b086bbe

Improve wildify heuristic for finding record type-class witnesses

author	Adam Chlipala <adam@chlipala.net>
date	Tue, 23 Dec 2014 13:42:20 -0500
parents	c647f113ba3e
children	6700f3700328

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
adam@1797	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
adam@2016	65 Note that, like the Ur/Web compiler, MLton is a whole-program optimizing compiler, so it frequently requires much more memory than old-fashioned compilers do. Expect building Ur/Web with MLton to require not much less than a gigabyte of RAM. If a \texttt{mlton} invocation ends suspiciously, the most likely explanation is that it has exhausted available memory.
adam@2016	66
adamc@896	67 To build programs that access SQL databases, you also need one of these client libraries for supported backends.
adamc@555	68 \begin{verbatim}
adam@1960	69 apt-get install libpq-dev libmysqlclient-dev libsqlite3-dev
adamc@555	70 \end{verbatim}
adamc@555	71
adamc@555	72 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	73 \begin{verbatim}
adamc@555	74 apt-get install smlnj libsmlnj-smlnj ml-yacc ml-lpt
adamc@555	75 \end{verbatim}
adamc@555	76
adam@2016	77 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, and you can find its signature in \texttt{src/compiler.sig}.
adamc@555	78
adamc@896	79 To run an SQL-backed application with a backend besides SQLite, you will probably want to install one of these servers.
adamc@555	80
adamc@555	81 \begin{verbatim}
adam@1960	82 apt-get install postgresql mysql-server
adamc@555	83 \end{verbatim}
adamc@555	84
adamc@555	85 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	86
adamc@555	87 \begin{verbatim}
adamc@555	88 apt-get install emacs-goodies-el
adamc@555	89 \end{verbatim}
adamc@555	90
adam@1441	91 If you don't want to install the Emacs mode, run \texttt{./configure} with the argument \texttt{--without-emacs}.
adam@1441	92
adam@1523	93 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	94
adamc@555	95 \begin{verbatim}
adam@1523	96 CCARGS=-fno-inline ./configure
adamc@555	97 \end{verbatim}
adamc@555	98
adam@1523	99 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	100
adamc@555	101 The Emacs mode can be set to autoload by adding the following to your \texttt{.emacs} file.
adamc@555	102
adamc@555	103 \begin{verbatim}
adamc@555	104 (add-to-list 'load-path "/usr/local/share/emacs/site-lisp/urweb-mode")
adamc@555	105 (load "urweb-mode-startup")
adamc@555	106 \end{verbatim}
adamc@555	107
adamc@555	108 Change the path in the first line if you chose a different Emacs installation path during configuration.
adamc@555	109
adamc@555	110
adamc@556	111 \section{Command-Line Compiler}
adamc@556	112
adam@1604	113 \subsection{\label{cl}Project Files}
adamc@556	114
adamc@556	115 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	116
adamc@556	117 \begin{verbatim}
adamc@556	118 database dbname=test
adamc@556	119 sql crud1.sql
adamc@556	120
adamc@556	121 crud
adamc@556	122 crud1
adamc@556	123 \end{verbatim}
adamc@556	124
adamc@556	125 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	126
adamc@556	127 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	128
adamc@556	129 \begin{verbatim}
adamc@556	130 createdb test
adamc@556	131 psql -f crud1.sql test
adamc@556	132 \end{verbatim}
adamc@556	133
adam@1331	134 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	135
adamc@556	136 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	137
adamc@783	138 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	139 \begin{itemize}
adam@1799	140 \item \texttt{[allow\|deny] [url\|mime\|requestHeader\|responseHeader\|env] PATTERN} registers a rule governing which URLs, MIME types, HTTP request headers, HTTP response headers, or environment variable names 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	141 \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	142 \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	143 \item \texttt{clientOnly Module.ident} registers an FFI function or transaction that may only be run in client browsers.
adam@1881	144 \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/urweb\_cpp.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.
adam@1816	145 \item \texttt{coreInline TREESIZE} sets how many nodes the AST of a function definition may have before the optimizer stops trying hard to inline calls to that function. (This is one of two options for one of two intermediate languages within the compiler.)
adamc@783	146 \item \texttt{database DBSTRING} sets the string to pass to libpq to open a database connection.
adamc@783	147 \item \texttt{debug} saves some intermediate C files, which is mostly useful to help in debugging the compiler itself.
adam@1878	148 \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. This is the default behavior for \texttt{transaction}-based types.
adam@2046	149 \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}.
adam@2046	150 \item \texttt{file URI FILENAME} asks for the application executable to respond to requests for \texttt{URI} by serving a snapshot of the contents of \texttt{FILENAME} as of compile time. That is, the file contents are baked into the executable. System file \texttt{/etc/mime.types} is consulted (again, at compile time) to figure out the right MIME type to suggest in the HTTP response.
adam@1881	151 \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/urweb\_cpp.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.
adam@1956	152 \item \texttt{html5} activates work-in-progress support for generating HTML5 instead of XHTML. For now, this option only affects the first few tokens on any page, which are always the same.
adamc@1099	153 \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	154 \item \texttt{jsFunc Module.ident=name} gives the JavaScript name of an FFI value.
adamc@1089	155 \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	156 \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	157 \begin{itemize}
adam@1309	158 \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@1850	159 \item \texttt{clients}: maximum number of simultaneous connections to one application by web clients waiting for new asynchronous messages sent with \texttt{Basis.send}
adam@1850	160 \item \texttt{database}: maximum size of a database file (currently only used by SQLite, which interprets the parameter as a number of pages, where page size is itself a quantity configurable in SQLite)
adam@1309	161 \item \texttt{deltas}: maximum number of messages sendable in a single request handler with \texttt{Basis.send}
adam@1309	162 \item \texttt{globals}: maximum number of global variables that FFI libraries may set in a single request context
adam@1309	163 \item \texttt{headers}: maximum size (in bytes) of per-request buffer used to hold HTTP headers for generated pages
adam@1797	164 \item \texttt{heap}: maximum size (in bytes) of per-request heap for dynamically allocated data
adam@1309	165 \item \texttt{inputs}: maximum number of top-level form fields per request
adam@1309	166 \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	167 \item \texttt{page}: maximum size (in bytes) of per-request buffer used to hold HTML content of generated pages
adam@1309	168 \item \texttt{script}: maximum size (in bytes) of per-request buffer used to hold JavaScript content of generated pages
adam@1309	169 \item \texttt{subinputs}: maximum number of form fields per request, excluding top-level fields
adam@1309	170 \item \texttt{time}: maximum running time of a single page request, in units of approximately 0.1 seconds
adam@1309	171 \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	172 \end{itemize}
adam@1523	173 \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	174 \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	175 \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@1816	176 \item \texttt{monoInline TREESIZE} sets how many nodes the AST of a function definition may have before the optimizer stops trying hard to inline calls to that function. (This is one of two options for one of two intermediate languages within the compiler.)
adam@1966	177 \item \texttt{neverInline PATH} requests that no call to the referenced function be inlined. Section \ref{structure} explains how functions are assigned path strings.
adam@1953	178 \item \texttt{noMangleSql} avoids adding a \texttt{uw\_} prefix in front of each identifier in SQL. With this experimental feature, the burden is on the programmer to avoid naming tables or columns after SQL keywords!
adam@1478	179 \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	180 \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	181 \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	182 \item \texttt{prefix PREFIX} sets the prefix included before every URI within the generated application. The default is \texttt{/}.
adamc@783	183 \item \texttt{profile} generates an executable that may be used with gprof.
adam@1752	184 \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	185 \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	186 \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	187 \item \texttt{serverOnly Module.ident} registers an FFI function or transaction that may only be run on the server.
adamc@1164	188 \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	189 \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	190 \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	191 \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	192 \end{itemize}
adamc@701	193
adamc@701	194
adamc@557	195 \subsection{Building an Application}
adamc@557	196
adamc@557	197 To compile project \texttt{P.urp}, simply run
adamc@557	198 \begin{verbatim}
adamc@557	199 urweb P
adamc@557	200 \end{verbatim}
adamc@1198	201 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	202
adamc@557	203 To time how long the different compiler phases run, without generating an executable, run
adamc@557	204 \begin{verbatim}
adamc@557	205 urweb -timing P
adamc@557	206 \end{verbatim}
adamc@557	207
adamc@1086	208 To stop the compilation process after type-checking, run
adamc@1086	209 \begin{verbatim}
adamc@1086	210 urweb -tc P
adamc@1086	211 \end{verbatim}
adam@1530	212 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	213
adam@1745	214 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	215
adam@1723	216 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	217
adamc@1170	218 To output information relevant to CSS stylesheets (and not finish regular compilation), run
adamc@1170	219 \begin{verbatim}
adamc@1170	220 urweb -css P
adamc@1170	221 \end{verbatim}
adamc@1170	222 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	223
adam@1733	224 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	225 \begin{verbatim}
adam@1733	226 urweb daemon start
adam@1733	227 \end{verbatim}
adam@1733	228 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	229 \begin{verbatim}
adam@1733	230 urweb daemon stop
adam@1733	231 \end{verbatim}
adam@1733	232 Communication happens via a UNIX domain socket in file \cd{.urweb\_daemon} in the working directory.
adam@1733	233
adam@1733	234 \medskip
adam@1733	235
adamc@896	236 Some other command-line parameters are accepted:
adamc@896	237 \begin{itemize}
ezyang@1739	238 \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	239
adam@1875	240 \item \texttt{-ccompiler <PROGRAM>}: Select an alternative C compiler to call with command lines in compiling Ur/Web applications. (It's possible to set the default compiler as part of the \texttt{configure} process, but it may sometimes be useful to override the default.)
adam@1875	241
adamc@896	242 \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	243
adamc@896	244 \item \texttt{-dbms [postgres\|mysql\|sqlite]}: Sets the database backend to use.
adamc@896	245 \begin{itemize}
adamc@896	246 \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	247
adamc@896	248 A command sequence like this can initialize a Postgres database, using a file \texttt{app.sql} generated by the compiler:
adamc@896	249 \begin{verbatim}
adamc@896	250 createdb app
adamc@896	251 psql -f app.sql app
adamc@896	252 \end{verbatim}
adamc@896	253
adamc@896	254 \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	255
adamc@896	256 A command sequence like this can initialize a MySQL database:
adamc@896	257 \begin{verbatim}
adamc@896	258 echo "CREATE DATABASE app" \| mysql
adamc@896	259 mysql -D app <app.sql
adamc@896	260 \end{verbatim}
adamc@896	261
adamc@896	262 \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	263
adamc@896	264 A command like this can initialize an SQLite database:
adamc@896	265 \begin{verbatim}
adamc@896	266 sqlite3 path/to/database/file <app.sql
adamc@896	267 \end{verbatim}
adamc@896	268 \end{itemize}
adamc@896	269
adam@1693	270 \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	271
adam@1995	272 \item \texttt{-explainEmbed}: Trigger more verbose error messages about inability to embed server-side values in client-side code.
adam@1995	273
adam@1309	274 \item \texttt{-limit class num}: Equivalent to the \texttt{limit} directive from \texttt{.urp} files
adam@1309	275
adam@1850	276 \item \texttt{-moduleOf FILENAME}: Prints the Ur/Web module name corresponding to source file \texttt{FILENAME}, exiting immediately afterward.
adam@1850	277
adamc@896	278 \item \texttt{-output FILENAME}: Set where the application executable is written.
adamc@896	279
adamc@1127	280 \item \texttt{-path NAME VALUE}: Set the value of path variable \texttt{\$NAME} to \texttt{VALUE}, for use in \texttt{.urp} files.
adamc@1127	281
adam@1335	282 \item \texttt{-prefix PREFIX}: Equivalent to the \texttt{prefix} directive from \texttt{.urp} files
adam@1335	283
adam@1875	284 \item \texttt{-print-ccompiler}: Print the C compiler being used.
adam@1875	285
adam@1923	286 \item \texttt{-print-cinclude}: Print the name of the directory where C/C++ header files are installed.
adam@1923	287
adam@1753	288 \item \texttt{-protocol [http\|cgi\|fastcgi\|static]}: Set the protocol that the generated application speaks.
adamc@896	289 \begin{itemize}
adamc@896	290 \item \texttt{http}: This is the default. It is for building standalone web servers that can be accessed by web browsers directly.
adamc@896	291
adamc@896	292 \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	293
adamc@896	294 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	295 \begin{verbatim}
adamc@896	296 ScriptAlias /Hello /path/to/hello.exe
adamc@896	297 \end{verbatim}
adamc@896	298
adamc@1163	299 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	300 \begin{verbatim}
adamc@1163	301 Options +ExecCGI
adamc@1163	302 AddHandler cgi-script .exe
adamc@1163	303 \end{verbatim}
adamc@1163	304
adamc@1163	305 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	306 \begin{verbatim}
adamc@1163	307 prefix /dir/script.exe/
adamc@1163	308 \end{verbatim}
adamc@1163	309
adamc@1163	310 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	311
adamc@1164	312 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	313
adamc@896	314 \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	315
adamc@896	316 To configure a FastCGI program with Apache, one could combine the above \texttt{ScriptAlias} line with a line like this:
adamc@896	317 \begin{verbatim}
adamc@896	318 FastCgiServer /path/to/hello.exe -idle-timeout 99999
adamc@896	319 \end{verbatim}
adamc@896	320 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	321
adam@1753	322 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	323
adamc@896	324 Here is some lighttpd configuration for the same application.
adamc@896	325 \begin{verbatim}
adamc@896	326 fastcgi.server = (
adamc@896	327 "/Hello/" =>
adamc@896	328 (( "bin-path" => "/path/to/hello.exe",
adamc@896	329 "socket" => "/tmp/hello",
adamc@896	330 "check-local" => "disable",
adamc@896	331 "docroot" => "/",
adamc@896	332 "max-procs" => "1"
adamc@896	333 ))
adamc@896	334 )
adamc@896	335 \end{verbatim}
adamc@896	336 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	337
adamc@896	338 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	339
adam@1509	340 \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	341 \end{itemize}
adamc@896	342
adamc@1127	343 \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	344
adamc@1164	345 \item \texttt{-sigfile PATH}: Same as the \texttt{sigfile} directive in \texttt{.urp} files
adamc@1164	346
adamc@896	347 \item \texttt{-sql FILENAME}: Set where a database set-up SQL script is written.
adamc@1095	348
adamc@1095	349 \item \texttt{-static}: Link the runtime system statically. The default is to link against dynamic libraries.
adam@1961	350
adam@1961	351 \item \texttt{-stop PHASE}: Stop compilation after the named phase, printing the intermediate program to stderr. This flag is mainly useful for debugging the Ur/Web compiler itself.
adamc@896	352 \end{itemize}
adamc@896	353
adam@1297	354 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	355
adam@1509	356 \subsection{Tutorial Formatting}
adam@1509	357
adam@1509	358 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	359
adam@1509	360 These input files follow normal Ur syntax, with a few exceptions:
adam@1509	361 \begin{itemize}
adam@1509	362 \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	363 \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	364 \item A comment like \cd{(* * HEADING *)} introduces a section heading, with text \cd{HEADING} of your choice.
adam@1509	365 \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	366 \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	367 \end{itemize}
adam@1509	368
adam@1509	369 A word of warning: as for demo generation, tutorial generation calls Emacs to syntax-highlight Ur code.
adam@1509	370
adam@1522	371 \subsection{Run-Time Options}
adam@1522	372
adam@1522	373 Compiled applications consult a few environment variables to modify their behavior:
adam@1522	374
adam@1522	375 \begin{itemize}
adam@1522	376 \item \cd{URWEB\_NUM\_THREADS}: alternative to the \cd{-t} command-line argument (currently used only by FastCGI)
adam@1522	377 \item \cd{URWEB\_STACK\_SIZE}: size of per-thread stacks, in bytes
as@1564	378 \item \cd{URWEB\_PQ\_CON}: when using PostgreSQL, overrides the compiled-in connection string
adam@1522	379 \end{itemize}
adam@1522	380
adam@2042	381 \subsection{A Word of Warning on Heuristic Compilation}
adam@2042	382
adam@2042	383 For server-side code, Ur/Web follows an unusual compilation model, where not all type-correct programs can be compiled successfully, especially when using functions as data not known until runtime. See Section \ref{phases} for more detail.
adam@2042	384
adam@1509	385
adamc@529	386 \section{Ur Syntax}
adamc@529	387
adamc@784	388 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	389
adamc@524	390 \subsection{Lexical Conventions}
adamc@524	391
adamc@524	392 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	393
adamc@524	394 \begin{center}
adamc@524	395 \begin{tabular}{rl}
adamc@524	396 \textbf{\LaTeX} & \textbf{ASCII} \\
adamc@524	397 $\to$ & \cd{->} \\
adam@1687	398 $\longrightarrow$ & \cd{-{}->} \\
adamc@524	399 $\times$ & \cd{*} \\
adamc@524	400 $\lambda$ & \cd{fn} \\
adamc@524	401 $\Rightarrow$ & \cd{=>} \\
adamc@652	402 $\Longrightarrow$ & \cd{==>} \\
adamc@529	403 $\neq$ & \cd{<>} \\
adamc@529	404 $\leq$ & \cd{<=} \\
adamc@529	405 $\geq$ & \cd{>=} \\
adamc@524	406 \\
adamc@524	407 $x$ & Normal textual identifier, not beginning with an uppercase letter \\
adamc@525	408 $X$ & Normal textual identifier, beginning with an uppercase letter \\
adamc@524	409 \end{tabular}
adamc@524	410 \end{center}
adamc@524	411
adamc@525	412 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	413
adamc@873	414 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	415
adamc@527	416 This version of the manual doesn't include operator precedences; see \texttt{src/urweb.grm} for that.
adamc@527	417
adam@1297	418 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	419
adamc@552	420 \subsection{\label{core}Core Syntax}
adamc@524	421
adamc@524	422 \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	423 $$\begin{array}{rrcll}
adamc@524	424 \textrm{Kinds} & \kappa &::=& \mt{Type} & \textrm{proper types} \\
adamc@525	425 &&& \mt{Unit} & \textrm{the trivial constructor} \\
adamc@525	426 &&& \mt{Name} & \textrm{field names} \\
adamc@525	427 &&& \kappa \to \kappa & \textrm{type-level functions} \\
adamc@525	428 &&& \{\kappa\} & \textrm{type-level records} \\
adamc@525	429 &&& (\kappa\times^+) & \textrm{type-level tuples} \\
adamc@652	430 &&& X & \textrm{variable} \\
adam@1574	431 &&& X \longrightarrow \kappa & \textrm{kind-polymorphic type-level function} \\
adamc@529	432 &&& \_\_ & \textrm{wildcard} \\
adamc@525	433 &&& (\kappa) & \textrm{explicit precedence} \\
adamc@524	434 \end{array}$$
adamc@524	435
adamc@524	436 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	437 $$\begin{array}{rrcll}
adamc@524	438 \textrm{Explicitness} & ? &::=& :: & \textrm{explicit} \\
adamc@558	439 &&& ::: & \textrm{implicit}
adamc@524	440 \end{array}$$
adamc@524	441
adamc@524	442 \emph{Constructors} are the main class of compile-time-only data. They include proper types and are classified by kinds.
adamc@524	443 $$\begin{array}{rrcll}
adamc@524	444 \textrm{Constructors} & c, \tau &::=& (c) :: \kappa & \textrm{kind annotation} \\
adamc@530	445 &&& \hat{x} & \textrm{constructor variable} \\
adamc@524	446 \\
adamc@525	447 &&& \tau \to \tau & \textrm{function type} \\
adamc@525	448 &&& x \; ? \; \kappa \to \tau & \textrm{polymorphic function type} \\
adamc@652	449 &&& X \longrightarrow \tau & \textrm{kind-polymorphic function type} \\
adamc@525	450 &&& \$ c & \textrm{record type} \\
adamc@524	451 \\
adamc@525	452 &&& c \; c & \textrm{type-level function application} \\
adamc@530	453 &&& \lambda x \; :: \; \kappa \Rightarrow c & \textrm{type-level function abstraction} \\
adamc@524	454 \\
adamc@652	455 &&& X \Longrightarrow c & \textrm{type-level kind-polymorphic function abstraction} \\
adamc@655	456 &&& c [\kappa] & \textrm{type-level kind-polymorphic function application} \\
adamc@652	457 \\
adamc@525	458 &&& () & \textrm{type-level unit} \\
adamc@525	459 &&& \#X & \textrm{field name} \\
adamc@524	460 \\
adamc@525	461 &&& [(c = c)^*] & \textrm{known-length type-level record} \\
adamc@525	462 &&& c \rc c & \textrm{type-level record concatenation} \\
adamc@652	463 &&& \mt{map} & \textrm{type-level record map} \\
adamc@524	464 \\
adamc@558	465 &&& (c,^+) & \textrm{type-level tuple} \\
adamc@525	466 &&& c.n & \textrm{type-level tuple projection ($n \in \mathbb N^+$)} \\
adamc@524	467 \\
adamc@652	468 &&& [c \sim c] \Rightarrow \tau & \textrm{guarded type} \\
adamc@524	469 \\
adamc@529	470 &&& \_ :: \kappa & \textrm{wildcard} \\
adamc@525	471 &&& (c) & \textrm{explicit precedence} \\
adamc@530	472 \\
adamc@530	473 \textrm{Qualified uncapitalized variables} & \hat{x} &::=& x & \textrm{not from a module} \\
adamc@530	474 &&& M.x & \textrm{projection from a module} \\
adamc@525	475 \end{array}$$
adamc@525	476
adam@1579	477 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	478
adamc@525	479 Modules of the module system are described by \emph{signatures}.
adamc@525	480 $$\begin{array}{rrcll}
adamc@525	481 \textrm{Signatures} & S &::=& \mt{sig} \; s^* \; \mt{end} & \textrm{constant} \\
adamc@525	482 &&& X & \textrm{variable} \\
adamc@525	483 &&& \mt{functor}(X : S) : S & \textrm{functor} \\
adamc@529	484 &&& S \; \mt{where} \; \mt{con} \; x = c & \textrm{concretizing an abstract constructor} \\
adamc@525	485 &&& M.X & \textrm{projection from a module} \\
adamc@525	486 \\
adamc@525	487 \textrm{Signature items} & s &::=& \mt{con} \; x :: \kappa & \textrm{abstract constructor} \\
adamc@525	488 &&& \mt{con} \; x :: \kappa = c & \textrm{concrete constructor} \\
adamc@528	489 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529	490 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@525	491 &&& \mt{val} \; x : \tau & \textrm{value} \\
adamc@525	492 &&& \mt{structure} \; X : S & \textrm{sub-module} \\
adamc@525	493 &&& \mt{signature} \; X = S & \textrm{sub-signature} \\
adamc@525	494 &&& \mt{include} \; S & \textrm{signature inclusion} \\
adamc@525	495 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@654	496 &&& \mt{class} \; x :: \kappa & \textrm{abstract constructor class} \\
adamc@654	497 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@525	498 \\
adamc@525	499 \textrm{Datatype constructors} & dc &::=& X & \textrm{nullary constructor} \\
adamc@525	500 &&& X \; \mt{of} \; \tau & \textrm{unary constructor} \\
adamc@524	501 \end{array}$$
adamc@524	502
adamc@526	503 \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	504 $$\begin{array}{rrcll}
adamc@526	505 \textrm{Patterns} & p &::=& \_ & \textrm{wildcard} \\
adamc@526	506 &&& x & \textrm{variable} \\
adamc@526	507 &&& \ell & \textrm{constant} \\
adamc@526	508 &&& \hat{X} & \textrm{nullary constructor} \\
adamc@526	509 &&& \hat{X} \; p & \textrm{unary constructor} \\
adamc@526	510 &&& \{(x = p,)^*\} & \textrm{rigid record pattern} \\
adamc@526	511 &&& \{(x = p,)^+, \ldots\} & \textrm{flexible record pattern} \\
adamc@852	512 &&& p : \tau & \textrm{type annotation} \\
adamc@527	513 &&& (p) & \textrm{explicit precedence} \\
adamc@526	514 \\
adamc@529	515 \textrm{Qualified capitalized variables} & \hat{X} &::=& X & \textrm{not from a module} \\
adamc@526	516 &&& M.X & \textrm{projection from a module} \\
adamc@526	517 \end{array}$$
adamc@526	518
adamc@527	519 \emph{Expressions} are the main run-time entities, corresponding to both ``expressions'' and ``statements'' in mainstream imperative languages.
adamc@527	520 $$\begin{array}{rrcll}
adamc@527	521 \textrm{Expressions} & e &::=& e : \tau & \textrm{type annotation} \\
adamc@529	522 &&& \hat{x} & \textrm{variable} \\
adamc@529	523 &&& \hat{X} & \textrm{datatype constructor} \\
adamc@527	524 &&& \ell & \textrm{constant} \\
adamc@527	525 \\
adamc@527	526 &&& e \; e & \textrm{function application} \\
adamc@527	527 &&& \lambda x : \tau \Rightarrow e & \textrm{function abstraction} \\
adamc@527	528 &&& e [c] & \textrm{polymorphic function application} \\
adamc@852	529 &&& \lambda [x \; ? \; \kappa] \Rightarrow e & \textrm{polymorphic function abstraction} \\
adamc@655	530 &&& e [\kappa] & \textrm{kind-polymorphic function application} \\
adamc@652	531 &&& X \Longrightarrow e & \textrm{kind-polymorphic function abstraction} \\
adamc@527	532 \\
adamc@527	533 &&& \{(c = e,)^*\} & \textrm{known-length record} \\
adamc@527	534 &&& e.c & \textrm{record field projection} \\
adamc@527	535 &&& e \rc e & \textrm{record concatenation} \\
adamc@527	536 &&& e \rcut c & \textrm{removal of a single record field} \\
adamc@527	537 &&& e \rcutM c & \textrm{removal of multiple record fields} \\
adamc@527	538 \\
adamc@527	539 &&& \mt{let} \; ed^* \; \mt{in} \; e \; \mt{end} & \textrm{local definitions} \\
adamc@527	540 \\
adamc@527	541 &&& \mt{case} \; e \; \mt{of} \; (p \Rightarrow e\|)^+ & \textrm{pattern matching} \\
adamc@527	542 \\
adamc@654	543 &&& \lambda [c \sim c] \Rightarrow e & \textrm{guarded expression abstraction} \\
adamc@654	544 &&& e \; ! & \textrm{guarded expression application} \\
adamc@527	545 \\
adamc@527	546 &&& \_ & \textrm{wildcard} \\
adamc@527	547 &&& (e) & \textrm{explicit precedence} \\
adamc@527	548 \\
adamc@527	549 \textrm{Local declarations} & ed &::=& \cd{val} \; x : \tau = e & \textrm{non-recursive value} \\
adam@1797	550 &&& \cd{val} \; \cd{rec} \; (x : \tau = e \; \cd{and})^+ & \textrm{mutually recursive values} \\
adamc@527	551 \end{array}$$
adamc@527	552
adamc@655	553 As with constructors, we include both abstraction and application for kind polymorphism, but applications are only inferred internally.
adamc@655	554
adamc@528	555 \emph{Declarations} primarily bring new symbols into context.
adamc@528	556 $$\begin{array}{rrcll}
adamc@528	557 \textrm{Declarations} & d &::=& \mt{con} \; x :: \kappa = c & \textrm{constructor synonym} \\
adamc@528	558 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529	559 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@528	560 &&& \mt{val} \; x : \tau = e & \textrm{value} \\
adam@1797	561 &&& \mt{val} \; \cd{rec} \; (x : \tau = e \; \mt{and})^+ & \textrm{mutually recursive values} \\
adamc@528	562 &&& \mt{structure} \; X : S = M & \textrm{module definition} \\
adamc@528	563 &&& \mt{signature} \; X = S & \textrm{signature definition} \\
adamc@528	564 &&& \mt{open} \; M & \textrm{module inclusion} \\
adamc@528	565 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@528	566 &&& \mt{open} \; \mt{constraints} \; M & \textrm{inclusion of just the constraints from a module} \\
adamc@528	567 &&& \mt{table} \; x : c & \textrm{SQL table} \\
adam@1594	568 &&& \mt{view} \; x = e & \textrm{SQL view} \\
adamc@528	569 &&& \mt{sequence} \; x & \textrm{SQL sequence} \\
adamc@535	570 &&& \mt{cookie} \; x : \tau & \textrm{HTTP cookie} \\
adamc@784	571 &&& \mt{style} \; x : \tau & \textrm{CSS class} \\
adamc@1085	572 &&& \mt{task} \; e = e & \textrm{recurring task} \\
adamc@528	573 \\
adamc@529	574 \textrm{Modules} & M &::=& \mt{struct} \; d^* \; \mt{end} & \textrm{constant} \\
adamc@529	575 &&& X & \textrm{variable} \\
adamc@529	576 &&& M.X & \textrm{projection} \\
adamc@529	577 &&& M(M) & \textrm{functor application} \\
adamc@529	578 &&& \mt{functor}(X : S) : S = M & \textrm{functor abstraction} \\
adamc@528	579 \end{array}$$
adamc@528	580
adamc@528	581 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	582
adam@1594	583 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	584
adamc@529	585 \subsection{Shorthands}
adamc@529	586
adamc@529	587 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	588
adamc@529	589 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	590
adamc@529	591 A record type may be written $\{(c = c,)^\}$, which elaborates to $\$[(c = c,)^]$.
adamc@529	592
adamc@533	593 The notation $[c_1, \ldots, c_n]$ is shorthand for $[c_1 = (), \ldots, c_n = ()]$.
adamc@533	594
adam@1350	595 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	596
adam@1687	597 The syntax $()$ expands to $\{\}$ as a pattern or expression.
adam@1687	598
adamc@852	599 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	600
adam@1574	601 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	602
adam@1306	603 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	604
adamc@529	605 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	606
adamc@529	607 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	608
adamc@654	609 A signature item or declaration $\mt{class} \; x = \lambda y \Rightarrow c$ may be abbreviated $\mt{class} \; x \; y = c$.
adamc@529	610
adam@1738	611 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	612
adamc@852	613 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	614
adamc@852	615 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	616
adam@1797	617 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	618
adamc@529	619 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	620
adamc@852	621 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	622
adamc@853	623 A declaration $\mt{table} \; x : \{(c = c,)^\}$ is elaborated into $\mt{table} \; x : [(c = c,)^]$.
adamc@529	624
adamc@529	625 The syntax $\mt{where} \; \mt{type}$ is an alternate form of $\mt{where} \; \mt{con}$.
adamc@529	626
adamc@529	627 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	628
adamc@529	629 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	630
adamc@784	631 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	632
adam@2025	633 It is possible to write a $\mt{let}$ expression with its constituents in reverse order, along the lines of Haskell's \cd{where}. An expression $\mt{let} \; e \; \mt{where} \; ed^* \; \mt{end}$ desugars to $\mt{let} \; ed^* \; \mt{in} \; e \; \mt{end}$.
adam@2025	634
adamc@530	635
adamc@530	636 \section{Static Semantics}
adamc@530	637
adamc@530	638 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	639
adam@1891	640 The notations used here are the standard ones of programming language semantics. They are probably the most effective way to convey this information. At the same time, most Ur/Web users can probably get by \emph{without} knowing the contents of this section! If you're interested in diving into the details of Ur typing but are unfamiliar with ``inference rule notation,'' I recommend the following book:
adam@1891	641 \begin{quote}
adam@1891	642 Benjamin C. Pierce, \emph{Types and Programming Languages}, MIT Press, 2002.
adam@1891	643 \end{quote}
adam@1891	644
adamc@530	645 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	646 \begin{itemize}
adamc@655	647 \item $\Gamma \vdash \kappa$ expresses kind well-formedness.
adamc@530	648 \item $\Gamma \vdash c :: \kappa$ assigns a kind to a constructor in a context.
adamc@530	649 \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	650 \item $\Gamma \vdash c \hookrightarrow C$ proves that record constructor $c$ decomposes into set $C$ of field names and record constructors.
adamc@530	651 \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	652 \item $\Gamma \vdash e : \tau$ is a standard typing judgment.
adamc@534	653 \item $\Gamma \vdash p \leadsto \Gamma; \tau$ combines typing of patterns with calculation of which new variables they bind.
adamc@537	654 \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	655 \item $\Gamma \vdash S \equiv S$ is the signature equivalence judgment.
adamc@536	656 \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	657 \item $\Gamma \vdash M : S$ is the module signature checking judgment.
adamc@537	658 \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	659 \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	660 \end{itemize}
adamc@530	661
adamc@655	662
adamc@655	663 \subsection{Kind Well-Formedness}
adamc@655	664
adamc@655	665 $$\infer{\Gamma \vdash \mt{Type}}{}
adamc@655	666 \quad \infer{\Gamma \vdash \mt{Unit}}{}
adamc@655	667 \quad \infer{\Gamma \vdash \mt{Name}}{}
adamc@655	668 \quad \infer{\Gamma \vdash \kappa_1 \to \kappa_2}{
adamc@655	669 \Gamma \vdash \kappa_1
adamc@655	670 & \Gamma \vdash \kappa_2
adamc@655	671 }
adamc@655	672 \quad \infer{\Gamma \vdash \{\kappa\}}{
adamc@655	673 \Gamma \vdash \kappa
adamc@655	674 }
adamc@655	675 \quad \infer{\Gamma \vdash (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@655	676 \forall i: \Gamma \vdash \kappa_i
adamc@655	677 }$$
adamc@655	678
adamc@655	679 $$\infer{\Gamma \vdash X}{
adamc@655	680 X \in \Gamma
adamc@655	681 }
adamc@655	682 \quad \infer{\Gamma \vdash X \longrightarrow \kappa}{
adamc@655	683 \Gamma, X \vdash \kappa
adamc@655	684 }$$
adamc@655	685
adamc@530	686 \subsection{Kinding}
adamc@530	687
adamc@655	688 We write $[X \mapsto \kappa_1]\kappa_2$ for capture-avoiding substitution of $\kappa_1$ for $X$ in $\kappa_2$.
adamc@655	689
adamc@530	690 $$\infer{\Gamma \vdash (c) :: \kappa :: \kappa}{
adamc@530	691 \Gamma \vdash c :: \kappa
adamc@530	692 }
adamc@530	693 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530	694 x :: \kappa \in \Gamma
adamc@530	695 }
adamc@530	696 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530	697 x :: \kappa = c \in \Gamma
adamc@530	698 }$$
adamc@530	699
adamc@530	700 $$\infer{\Gamma \vdash M.x :: \kappa}{
adamc@537	701 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	702 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = \kappa
adamc@530	703 }
adamc@530	704 \quad \infer{\Gamma \vdash M.x :: \kappa}{
adamc@537	705 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	706 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@530	707 }$$
adamc@530	708
adamc@530	709 $$\infer{\Gamma \vdash \tau_1 \to \tau_2 :: \mt{Type}}{
adamc@530	710 \Gamma \vdash \tau_1 :: \mt{Type}
adamc@530	711 & \Gamma \vdash \tau_2 :: \mt{Type}
adamc@530	712 }
adamc@530	713 \quad \infer{\Gamma \vdash x \; ? \: \kappa \to \tau :: \mt{Type}}{
adamc@530	714 \Gamma, x :: \kappa \vdash \tau :: \mt{Type}
adamc@530	715 }
adamc@655	716 \quad \infer{\Gamma \vdash X \longrightarrow \tau :: \mt{Type}}{
adamc@655	717 \Gamma, X \vdash \tau :: \mt{Type}
adamc@655	718 }
adamc@530	719 \quad \infer{\Gamma \vdash \$c :: \mt{Type}}{
adamc@530	720 \Gamma \vdash c :: \{\mt{Type}\}
adamc@530	721 }$$
adamc@530	722
adamc@530	723 $$\infer{\Gamma \vdash c_1 \; c_2 :: \kappa_2}{
adamc@530	724 \Gamma \vdash c_1 :: \kappa_1 \to \kappa_2
adamc@530	725 & \Gamma \vdash c_2 :: \kappa_1
adamc@530	726 }
adamc@530	727 \quad \infer{\Gamma \vdash \lambda x \; :: \; \kappa_1 \Rightarrow c :: \kappa_1 \to \kappa_2}{
adamc@530	728 \Gamma, x :: \kappa_1 \vdash c :: \kappa_2
adamc@530	729 }$$
adamc@530	730
adamc@655	731 $$\infer{\Gamma \vdash c[\kappa'] :: [X \mapsto \kappa']\kappa}{
adamc@655	732 \Gamma \vdash c :: X \to \kappa
adamc@655	733 & \Gamma \vdash \kappa'
adamc@655	734 }
adamc@655	735 \quad \infer{\Gamma \vdash X \Longrightarrow c :: X \to \kappa}{
adamc@655	736 \Gamma, X \vdash c :: \kappa
adamc@655	737 }$$
adamc@655	738
adamc@530	739 $$\infer{\Gamma \vdash () :: \mt{Unit}}{}
adamc@530	740 \quad \infer{\Gamma \vdash \#X :: \mt{Name}}{}$$
adamc@530	741
adamc@530	742 $$\infer{\Gamma \vdash [\overline{c_i = c'_i}] :: \{\kappa\}}{
adamc@530	743 \forall i: \Gamma \vdash c_i : \mt{Name}
adamc@530	744 & \Gamma \vdash c'_i :: \kappa
adamc@530	745 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@530	746 }
adamc@530	747 \quad \infer{\Gamma \vdash c_1 \rc c_2 :: \{\kappa\}}{
adamc@530	748 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530	749 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@530	750 & \Gamma \vdash c_1 \sim c_2
adamc@530	751 }$$
adamc@530	752
adamc@655	753 $$\infer{\Gamma \vdash \mt{map} :: (\kappa_1 \to \kappa_2) \to \{\kappa_1\} \to \{\kappa_2\}}{}$$
adamc@530	754
adamc@573	755 $$\infer{\Gamma \vdash (\overline c) :: (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@573	756 \forall i: \Gamma \vdash c_i :: \kappa_i
adamc@530	757 }
adamc@573	758 \quad \infer{\Gamma \vdash c.i :: \kappa_i}{
adamc@573	759 \Gamma \vdash c :: (\kappa_1 \times \ldots \times \kappa_n)
adamc@530	760 }$$
adamc@530	761
adamc@655	762 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow \tau :: \mt{Type}}{
adamc@655	763 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530	764 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@655	765 & \Gamma, c_1 \sim c_2 \vdash \tau :: \mt{Type}
adamc@530	766 }$$
adamc@530	767
adamc@531	768 \subsection{Record Disjointness}
adamc@531	769
adamc@531	770 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@558	771 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@558	772 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@558	773 & \forall c'_1 \in C_1, c'_2 \in C_2: \Gamma \vdash c'_1 \sim c'_2
adamc@531	774 }
adamc@531	775 \quad \infer{\Gamma \vdash X \sim X'}{
adamc@531	776 X \neq X'
adamc@531	777 }$$
adamc@531	778
adamc@531	779 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@531	780 c'_1 \sim c'_2 \in \Gamma
adamc@558	781 & \Gamma \vdash c'_1 \hookrightarrow C_1
adamc@558	782 & \Gamma \vdash c'_2 \hookrightarrow C_2
adamc@558	783 & c_1 \in C_1
adamc@558	784 & c_2 \in C_2
adamc@531	785 }$$
adamc@531	786
adamc@531	787 $$\infer{\Gamma \vdash c \hookrightarrow \{c\}}{}
adamc@531	788 \quad \infer{\Gamma \vdash [\overline{c = c'}] \hookrightarrow \{\overline{c}\}}{}
adamc@531	789 \quad \infer{\Gamma \vdash c_1 \rc c_2 \hookrightarrow C_1 \cup C_2}{
adamc@531	790 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@531	791 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@531	792 }
adamc@531	793 \quad \infer{\Gamma \vdash c \hookrightarrow C}{
adamc@531	794 \Gamma \vdash c \equiv c'
adamc@531	795 & \Gamma \vdash c' \hookrightarrow C
adamc@531	796 }
adamc@531	797 \quad \infer{\Gamma \vdash \mt{map} \; f \; c \hookrightarrow C}{
adamc@531	798 \Gamma \vdash c \hookrightarrow C
adamc@531	799 }$$
adamc@531	800
adamc@541	801 \subsection{\label{definitional}Definitional Equality}
adamc@532	802
adamc@655	803 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	804
adamc@532	805 $$\infer{\Gamma \vdash c \equiv c}{}
adamc@532	806 \quad \infer{\Gamma \vdash c_1 \equiv c_2}{
adamc@532	807 \Gamma \vdash c_2 \equiv c_1
adamc@532	808 }
adamc@532	809 \quad \infer{\Gamma \vdash c_1 \equiv c_3}{
adamc@532	810 \Gamma \vdash c_1 \equiv c_2
adamc@532	811 & \Gamma \vdash c_2 \equiv c_3
adamc@532	812 }
adamc@532	813 \quad \infer{\Gamma \vdash \mathcal C[c_1] \equiv \mathcal C[c_2]}{
adamc@532	814 \Gamma \vdash c_1 \equiv c_2
adamc@532	815 }$$
adamc@532	816
adamc@532	817 $$\infer{\Gamma \vdash x \equiv c}{
adamc@532	818 x :: \kappa = c \in \Gamma
adamc@532	819 }
adamc@532	820 \quad \infer{\Gamma \vdash M.x \equiv c}{
adamc@537	821 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	822 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@532	823 }
adamc@532	824 \quad \infer{\Gamma \vdash (\overline c).i \equiv c_i}{}$$
adamc@532	825
adamc@532	826 $$\infer{\Gamma \vdash (\lambda x :: \kappa \Rightarrow c) \; c' \equiv [x \mapsto c'] c}{}
adamc@655	827 \quad \infer{\Gamma \vdash (X \Longrightarrow c) [\kappa] \equiv [X \mapsto \kappa] c}{}$$
adamc@655	828
adamc@655	829 $$\infer{\Gamma \vdash c_1 \rc c_2 \equiv c_2 \rc c_1}{}
adamc@532	830 \quad \infer{\Gamma \vdash c_1 \rc (c_2 \rc c_3) \equiv (c_1 \rc c_2) \rc c_3}{}$$
adamc@532	831
adamc@532	832 $$\infer{\Gamma \vdash [] \rc c \equiv c}{}
adamc@532	833 \quad \infer{\Gamma \vdash [\overline{c_1 = c'_1}] \rc [\overline{c_2 = c'_2}] \equiv [\overline{c_1 = c'_1}, \overline{c_2 = c'_2}]}{}$$
adamc@532	834
adamc@655	835 $$\infer{\Gamma \vdash \mt{map} \; f \; [] \equiv []}{}
adamc@655	836 \quad \infer{\Gamma \vdash \mt{map} \; f \; ([c_1 = c_2] \rc c) \equiv [c_1 = f \; c_2] \rc \mt{map} \; f \; c}{}$$
adamc@532	837
adamc@532	838 $$\infer{\Gamma \vdash \mt{map} \; (\lambda x \Rightarrow x) \; c \equiv c}{}
adamc@655	839 \quad \infer{\Gamma \vdash \mt{map} \; f \; (\mt{map} \; f' \; c)
adamc@655	840 \equiv \mt{map} \; (\lambda x \Rightarrow f \; (f' \; x)) \; c}{}$$
adamc@532	841
adamc@532	842 $$\infer{\Gamma \vdash \mt{map} \; f \; (c_1 \rc c_2) \equiv \mt{map} \; f \; c_1 \rc \mt{map} \; f \; c_2}{}$$
adamc@531	843
adamc@534	844 \subsection{Expression Typing}
adamc@533	845
adamc@873	846 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	847
adamc@533	848 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	849
adamc@533	850 $$\infer{\Gamma \vdash e : \tau : \tau}{
adamc@533	851 \Gamma \vdash e : \tau
adamc@533	852 }
adamc@533	853 \quad \infer{\Gamma \vdash e : \tau}{
adamc@533	854 \Gamma \vdash e : \tau'
adamc@533	855 & \Gamma \vdash \tau' \equiv \tau
adamc@533	856 }
adamc@533	857 \quad \infer{\Gamma \vdash \ell : T(\ell)}{}$$
adamc@533	858
adamc@533	859 $$\infer{\Gamma \vdash x : \mathcal I(\tau)}{
adamc@533	860 x : \tau \in \Gamma
adamc@533	861 }
adamc@533	862 \quad \infer{\Gamma \vdash M.x : \mathcal I(\tau)}{
adamc@537	863 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	864 & \mt{proj}(M, \overline{s}, \mt{val} \; x) = \tau
adamc@533	865 }
adamc@533	866 \quad \infer{\Gamma \vdash X : \mathcal I(\tau)}{
adamc@533	867 X : \tau \in \Gamma
adamc@533	868 }
adamc@533	869 \quad \infer{\Gamma \vdash M.X : \mathcal I(\tau)}{
adamc@537	870 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	871 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \tau
adamc@533	872 }$$
adamc@533	873
adamc@533	874 $$\infer{\Gamma \vdash e_1 \; e_2 : \tau_2}{
adamc@533	875 \Gamma \vdash e_1 : \tau_1 \to \tau_2
adamc@533	876 & \Gamma \vdash e_2 : \tau_1
adamc@533	877 }
adamc@533	878 \quad \infer{\Gamma \vdash \lambda x : \tau_1 \Rightarrow e : \tau_1 \to \tau_2}{
adamc@533	879 \Gamma, x : \tau_1 \vdash e : \tau_2
adamc@533	880 }$$
adamc@533	881
adamc@533	882 $$\infer{\Gamma \vdash e [c] : [x \mapsto c]\tau}{
adamc@533	883 \Gamma \vdash e : x :: \kappa \to \tau
adamc@533	884 & \Gamma \vdash c :: \kappa
adamc@533	885 }
adamc@852	886 \quad \infer{\Gamma \vdash \lambda [x \; ? \; \kappa] \Rightarrow e : x \; ? \; \kappa \to \tau}{
adamc@533	887 \Gamma, x :: \kappa \vdash e : \tau
adamc@533	888 }$$
adamc@533	889
adamc@655	890 $$\infer{\Gamma \vdash e [\kappa] : [X \mapsto \kappa]\tau}{
adamc@655	891 \Gamma \vdash e : X \longrightarrow \tau
adamc@655	892 & \Gamma \vdash \kappa
adamc@655	893 }
adamc@655	894 \quad \infer{\Gamma \vdash X \Longrightarrow e : X \longrightarrow \tau}{
adamc@655	895 \Gamma, X \vdash e : \tau
adamc@655	896 }$$
adamc@655	897
adamc@533	898 $$\infer{\Gamma \vdash \{\overline{c = e}\} : \{\overline{c : \tau}\}}{
adamc@533	899 \forall i: \Gamma \vdash c_i :: \mt{Name}
adamc@533	900 & \Gamma \vdash e_i : \tau_i
adamc@533	901 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@533	902 }
adamc@533	903 \quad \infer{\Gamma \vdash e.c : \tau}{
adamc@533	904 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533	905 }
adamc@533	906 \quad \infer{\Gamma \vdash e_1 \rc e_2 : \$(c_1 \rc c_2)}{
adamc@533	907 \Gamma \vdash e_1 : \$c_1
adamc@533	908 & \Gamma \vdash e_2 : \$c_2
adamc@573	909 & \Gamma \vdash c_1 \sim c_2
adamc@533	910 }$$
adamc@533	911
adamc@533	912 $$\infer{\Gamma \vdash e \rcut c : \$c'}{
adamc@533	913 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533	914 }
adamc@533	915 \quad \infer{\Gamma \vdash e \rcutM c : \$c'}{
adamc@533	916 \Gamma \vdash e : \$(c \rc c')
adamc@533	917 }$$
adamc@533	918
adamc@533	919 $$\infer{\Gamma \vdash \mt{let} \; \overline{ed} \; \mt{in} \; e \; \mt{end} : \tau}{
adamc@533	920 \Gamma \vdash \overline{ed} \leadsto \Gamma'
adamc@533	921 & \Gamma' \vdash e : \tau
adamc@533	922 }
adamc@533	923 \quad \infer{\Gamma \vdash \mt{case} \; e \; \mt{of} \; \overline{p \Rightarrow e} : \tau}{
adamc@533	924 \forall i: \Gamma \vdash p_i \leadsto \Gamma_i, \tau'
adamc@533	925 & \Gamma_i \vdash e_i : \tau
adamc@533	926 }$$
adamc@533	927
adamc@573	928 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow e : \lambda [c_1 \sim c_2] \Rightarrow \tau}{
adamc@533	929 \Gamma \vdash c_1 :: \{\kappa\}
adamc@655	930 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@533	931 & \Gamma, c_1 \sim c_2 \vdash e : \tau
adamc@662	932 }
adamc@662	933 \quad \infer{\Gamma \vdash e \; ! : \tau}{
adamc@662	934 \Gamma \vdash e : [c_1 \sim c_2] \Rightarrow \tau
adamc@662	935 & \Gamma \vdash c_1 \sim c_2
adamc@533	936 }$$
adamc@533	937
adamc@534	938 \subsection{Pattern Typing}
adamc@534	939
adamc@534	940 $$\infer{\Gamma \vdash \_ \leadsto \Gamma; \tau}{}
adamc@534	941 \quad \infer{\Gamma \vdash x \leadsto \Gamma, x : \tau; \tau}{}
adamc@534	942 \quad \infer{\Gamma \vdash \ell \leadsto \Gamma; T(\ell)}{}$$
adamc@534	943
adamc@534	944 $$\infer{\Gamma \vdash X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534	945 X : \overline{x ::: \mt{Type}} \to \tau \in \Gamma
adamc@534	946 & \textrm{$\tau$ not a function type}
adamc@534	947 }
adamc@534	948 \quad \infer{\Gamma \vdash X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534	949 X : \overline{x ::: \mt{Type}} \to \tau'' \to \tau \in \Gamma
adamc@534	950 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534	951 }$$
adamc@534	952
adamc@534	953 $$\infer{\Gamma \vdash M.X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537	954 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	955 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau
adamc@534	956 & \textrm{$\tau$ not a function type}
adamc@534	957 }$$
adamc@534	958
adamc@534	959 $$\infer{\Gamma \vdash M.X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537	960 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	961 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau'' \to \tau
adamc@534	962 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534	963 }$$
adamc@534	964
adamc@534	965 $$\infer{\Gamma \vdash \{\overline{x = p}\} \leadsto \Gamma_n; \{\overline{x = \tau}\}}{
adamc@534	966 \Gamma_0 = \Gamma
adamc@534	967 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534	968 }
adamc@534	969 \quad \infer{\Gamma \vdash \{\overline{x = p}, \ldots\} \leadsto \Gamma_n; \$([\overline{x = \tau}] \rc c)}{
adamc@534	970 \Gamma_0 = \Gamma
adamc@534	971 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534	972 }$$
adamc@534	973
adamc@852	974 $$\infer{\Gamma \vdash p : \tau \leadsto \Gamma'; \tau}{
adamc@852	975 \Gamma \vdash p \leadsto \Gamma'; \tau'
adamc@852	976 & \Gamma \vdash \tau' \equiv \tau
adamc@852	977 }$$
adamc@852	978
adamc@535	979 \subsection{Declaration Typing}
adamc@535	980
adamc@535	981 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	982
adamc@558	983 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	984 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	985
adamc@535	986 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535	987 \quad \infer{\Gamma \vdash d, \overline{d} \leadsto \Gamma''}{
adamc@535	988 \Gamma \vdash d \leadsto \Gamma'
adamc@535	989 & \Gamma' \vdash \overline{d} \leadsto \Gamma''
adamc@535	990 }$$
adamc@535	991
adamc@535	992 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@535	993 \Gamma \vdash c :: \kappa
adamc@535	994 }
adamc@535	995 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@535	996 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@535	997 }$$
adamc@535	998
adamc@535	999 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537	1000 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1001 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@535	1002 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@535	1003 }$$
adamc@535	1004
adamc@535	1005 $$\infer{\Gamma \vdash \mt{val} \; x : \tau = e \leadsto \Gamma, x : \tau}{
adamc@535	1006 \Gamma \vdash e : \tau
adamc@535	1007 }$$
adamc@535	1008
adamc@535	1009 $$\infer{\Gamma \vdash \mt{val} \; \mt{rec} \; \overline{x : \tau = e} \leadsto \Gamma, \overline{x : \tau}}{
adamc@535	1010 \forall i: \Gamma, \overline{x : \tau} \vdash e_i : \tau_i
adamc@535	1011 & \textrm{$e_i$ starts with an expression $\lambda$, optionally preceded by constructor and disjointness $\lambda$s}
adamc@535	1012 }$$
adamc@535	1013
adamc@535	1014 $$\infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : S}{
adamc@535	1015 \Gamma \vdash M : S
adamc@558	1016 & \textrm{ $M$ not a constant or application}
adamc@535	1017 }
adamc@558	1018 \quad \infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : \mt{selfify}(X, \overline{s})}{
adamc@558	1019 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@539	1020 }$$
adamc@539	1021
adamc@539	1022 $$\infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@535	1023 \Gamma \vdash S
adamc@535	1024 }$$
adamc@535	1025
adamc@537	1026 $$\infer{\Gamma \vdash \mt{open} \; M \leadsto \Gamma, \mathcal O(M, \overline{s})}{
adamc@537	1027 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535	1028 }$$
adamc@535	1029
adamc@535	1030 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma}{
adamc@535	1031 \Gamma \vdash c_1 :: \{\kappa\}
adamc@535	1032 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@535	1033 & \Gamma \vdash c_1 \sim c_2
adamc@535	1034 }
adamc@537	1035 \quad \infer{\Gamma \vdash \mt{open} \; \mt{constraints} \; M \leadsto \Gamma, \mathcal O_c(M, \overline{s})}{
adamc@537	1036 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535	1037 }$$
adamc@535	1038
adamc@784	1039 $$\infer{\Gamma \vdash \mt{table} \; x : c \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_table} \; c \; []}{
adamc@535	1040 \Gamma \vdash c :: \{\mt{Type}\}
adamc@535	1041 }
adam@1594	1042 \quad \infer{\Gamma \vdash \mt{view} \; x = e \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_view} \; c}{
adam@1594	1043 \Gamma \vdash e :: \mt{Basis}.\mt{sql\_query} \; [] \; [] \; (\mt{map} \; (\lambda \_ \Rightarrow []) \; c') \; c
adamc@784	1044 }$$
adamc@784	1045
adamc@784	1046 $$\infer{\Gamma \vdash \mt{sequence} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_sequence}}{}$$
adamc@535	1047
adamc@535	1048 $$\infer{\Gamma \vdash \mt{cookie} \; x : \tau \leadsto \Gamma, x : \mt{Basis}.\mt{http\_cookie} \; \tau}{
adamc@535	1049 \Gamma \vdash \tau :: \mt{Type}
adamc@784	1050 }
adamc@784	1051 \quad \infer{\Gamma \vdash \mt{style} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{css\_class}}{}$$
adamc@535	1052
adamc@1085	1053 $$\infer{\Gamma \vdash \mt{task} \; e_1 = e_2 \leadsto \Gamma}{
adam@1348	1054 \Gamma \vdash e_1 :: \mt{Basis}.\mt{task\_kind} \; \tau
adam@1348	1055 & \Gamma \vdash e_2 :: \tau \to \mt{Basis}.\mt{transaction} \; \{\}
adamc@1085	1056 }$$
adamc@1085	1057
adamc@535	1058 $$\infer{\overline{y}; x; \Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535	1059 \quad \infer{\overline{y}; x; \Gamma \vdash X \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to x \; \overline{y}}{
adamc@535	1060 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535	1061 }
adamc@535	1062 \quad \infer{\overline{y}; x; \Gamma \vdash X \; \mt{of} \; \tau \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to \tau \to x \; \overline{y}}{
adamc@535	1063 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535	1064 }$$
adamc@535	1065
adamc@537	1066 \subsection{Signature Item Typing}
adamc@537	1067
adamc@537	1068 We appeal to a signature item analogue of the $\mathcal O$ function from the last subsection.
adamc@537	1069
adam@1797	1070 This is the first judgment where we deal with constructor classes, for the $\mt{class}$ forms. We will omit their special handling in this formal specification. Section \ref{typeclasses} gives an informal description of how constructor classes influence type inference.
adam@1797	1071
adamc@537	1072 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@537	1073 \quad \infer{\Gamma \vdash s, \overline{s} \leadsto \Gamma''}{
adamc@537	1074 \Gamma \vdash s \leadsto \Gamma'
adamc@537	1075 & \Gamma' \vdash \overline{s} \leadsto \Gamma''
adamc@537	1076 }$$
adamc@537	1077
adamc@537	1078 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}
adamc@537	1079 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@537	1080 \Gamma \vdash c :: \kappa
adamc@537	1081 }
adamc@537	1082 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@537	1083 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@537	1084 }$$
adamc@537	1085
adamc@537	1086 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537	1087 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1088 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537	1089 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@537	1090 }$$
adamc@537	1091
adamc@537	1092 $$\infer{\Gamma \vdash \mt{val} \; x : \tau \leadsto \Gamma, x : \tau}{
adamc@537	1093 \Gamma \vdash \tau :: \mt{Type}
adamc@537	1094 }$$
adamc@537	1095
adamc@537	1096 $$\infer{\Gamma \vdash \mt{structure} \; X : S \leadsto \Gamma, X : S}{
adamc@537	1097 \Gamma \vdash S
adamc@537	1098 }
adamc@537	1099 \quad \infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@537	1100 \Gamma \vdash S
adamc@537	1101 }$$
adamc@537	1102
adamc@537	1103 $$\infer{\Gamma \vdash \mt{include} \; S \leadsto \Gamma, \mathcal O(\overline{s})}{
adamc@537	1104 \Gamma \vdash S
adamc@537	1105 & \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1106 }$$
adamc@537	1107
adamc@537	1108 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma, c_1 \sim c_2}{
adamc@537	1109 \Gamma \vdash c_1 :: \{\kappa\}
adamc@537	1110 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@537	1111 }$$
adamc@537	1112
adamc@784	1113 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784	1114 \Gamma \vdash c :: \kappa
adamc@537	1115 }
adamc@784	1116 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}$$
adamc@537	1117
adamc@536	1118 \subsection{Signature Compatibility}
adamc@536	1119
adam@1797	1120 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	1121
adamc@537	1122 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	1123
adamc@536	1124 $$\infer{\Gamma \vdash S \equiv S}{}
adamc@536	1125 \quad \infer{\Gamma \vdash S_1 \equiv S_2}{
adamc@536	1126 \Gamma \vdash S_2 \equiv S_1
adamc@536	1127 }
adamc@536	1128 \quad \infer{\Gamma \vdash X \equiv S}{
adamc@536	1129 X = S \in \Gamma
adamc@536	1130 }
adamc@536	1131 \quad \infer{\Gamma \vdash M.X \equiv S}{
adamc@537	1132 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1133 & \mt{proj}(M, \overline{s}, \mt{signature} \; X) = S
adamc@536	1134 }$$
adamc@536	1135
adamc@536	1136 $$\infer{\Gamma \vdash S \; \mt{where} \; \mt{con} \; x = c \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa = c \; \overline{s_2} \; \mt{end}}{
adamc@536	1137 \Gamma \vdash S \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa \; \overline{s_2} \; \mt{end}
adamc@536	1138 & \Gamma \vdash c :: \kappa
adamc@537	1139 }
adamc@537	1140 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s^1} \; \mt{include} \; S \; \overline{s^2} \; \mt{end} \equiv \mt{sig} \; \overline{s^1} \; \overline{s} \; \overline{s^2} \; \mt{end}}{
adamc@537	1141 \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@536	1142 }$$
adamc@536	1143
adamc@536	1144 $$\infer{\Gamma \vdash S_1 \leq S_2}{
adamc@536	1145 \Gamma \vdash S_1 \equiv S_2
adamc@536	1146 }
adamc@536	1147 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \mt{end}}{}
adamc@537	1148 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; s' \; \overline{s'} \; \mt{end}}{
adamc@537	1149 \Gamma \vdash \overline{s} \leq s'
adamc@537	1150 & \Gamma \vdash s' \leadsto \Gamma'
adamc@537	1151 & \Gamma' \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \overline{s'} \; \mt{end}
adamc@537	1152 }$$
adamc@537	1153
adamc@537	1154 $$\infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537	1155 \Gamma \vdash s \leq s'
adamc@537	1156 }
adamc@537	1157 \quad \infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537	1158 \Gamma \vdash s \leadsto \Gamma'
adamc@537	1159 & \Gamma' \vdash \overline{s} \leq s'
adamc@536	1160 }$$
adamc@536	1161
adamc@536	1162 $$\infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 \leq \mt{functor} (X : S'_1) : S'_2}{
adamc@536	1163 \Gamma \vdash S'_1 \leq S_1
adamc@536	1164 & \Gamma, X : S'_1 \vdash S_2 \leq S'_2
adamc@536	1165 }$$
adamc@536	1166
adamc@537	1167 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@537	1168 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}
adamc@558	1169 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type}}{}$$
adamc@537	1170
adamc@537	1171 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(y)} \to \mt{Type}}{
adamc@537	1172 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1173 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537	1174 }$$
adamc@537	1175
adamc@784	1176 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@784	1177 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}$$
adamc@537	1178
adamc@537	1179 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \mt{\kappa} = c_2}{
adamc@537	1180 \Gamma \vdash c_1 \equiv c_2
adamc@537	1181 }
adamc@784	1182 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \kappa = c_2}{
adamc@537	1183 \Gamma \vdash c_1 \equiv c_2
adamc@537	1184 }$$
adamc@537	1185
adamc@537	1186 $$\infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537	1187 \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537	1188 }$$
adamc@537	1189
adamc@537	1190 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537	1191 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1192 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537	1193 & \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537	1194 }$$
adamc@537	1195
adamc@537	1196 $$\infer{\Gamma \vdash \cdot \leq \cdot}{}
adamc@537	1197 \quad \infer{\Gamma \vdash X; \overline{dc} \leq X; \overline{dc'}}{
adamc@537	1198 \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537	1199 }
adamc@537	1200 \quad \infer{\Gamma \vdash X \; \mt{of} \; \tau_1; \overline{dc} \leq X \; \mt{of} \; \tau_2; \overline{dc'}}{
adamc@537	1201 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537	1202 & \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537	1203 }$$
adamc@537	1204
adamc@537	1205 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x = \mt{datatype} \; M'.z'}{
adamc@537	1206 \Gamma \vdash M.z \equiv M'.z'
adamc@537	1207 }$$
adamc@537	1208
adamc@537	1209 $$\infer{\Gamma \vdash \mt{val} \; x : \tau_1 \leq \mt{val} \; x : \tau_2}{
adamc@537	1210 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537	1211 }
adamc@537	1212 \quad \infer{\Gamma \vdash \mt{structure} \; X : S_1 \leq \mt{structure} \; X : S_2}{
adamc@537	1213 \Gamma \vdash S_1 \leq S_2
adamc@537	1214 }
adamc@537	1215 \quad \infer{\Gamma \vdash \mt{signature} \; X = S_1 \leq \mt{signature} \; X = S_2}{
adamc@537	1216 \Gamma \vdash S_1 \leq S_2
adamc@537	1217 & \Gamma \vdash S_2 \leq S_1
adamc@537	1218 }$$
adamc@537	1219
adamc@537	1220 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leq \mt{constraint} \; c'_1 \sim c'_2}{
adamc@537	1221 \Gamma \vdash c_1 \equiv c'_1
adamc@537	1222 & \Gamma \vdash c_2 \equiv c'_2
adamc@537	1223 }$$
adamc@537	1224
adamc@655	1225 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{class} \; x :: \kappa}{}
adamc@655	1226 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{class} \; x :: \kappa}{}
adamc@655	1227 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{class} \; x :: \kappa = c_2}{
adamc@537	1228 \Gamma \vdash c_1 \equiv c_2
adamc@537	1229 }$$
adamc@537	1230
adam@1797	1231 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leq \mt{class} \; x :: \kappa}{}
adam@1797	1232 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leq \mt{class} \; x :: \kappa}{}
adam@1797	1233 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c_1 \leq \mt{class} \; x :: \kappa = c_2}{
adam@1797	1234 \Gamma \vdash c_1 \equiv c_2
adam@1797	1235 }$$
adam@1797	1236
adamc@538	1237 \subsection{Module Typing}
adamc@538	1238
adamc@538	1239 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	1240
adamc@538	1241 $$\infer{\Gamma \vdash M : S}{
adamc@538	1242 \Gamma \vdash M : S'
adamc@538	1243 & \Gamma \vdash S' \leq S
adamc@538	1244 }
adamc@538	1245 \quad \infer{\Gamma \vdash \mt{struct} \; \overline{d} \; \mt{end} : \mt{sig} \; \mt{sigOf}(\overline{d}) \; \mt{end}}{
adamc@538	1246 \Gamma \vdash \overline{d} \leadsto \Gamma'
adamc@538	1247 }
adamc@538	1248 \quad \infer{\Gamma \vdash X : S}{
adamc@538	1249 X : S \in \Gamma
adamc@538	1250 }$$
adamc@538	1251
adamc@538	1252 $$\infer{\Gamma \vdash M.X : S}{
adamc@538	1253 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@538	1254 & \mt{proj}(M, \overline{s}, \mt{structure} \; X) = S
adamc@538	1255 }$$
adamc@538	1256
adamc@538	1257 $$\infer{\Gamma \vdash M_1(M_2) : [X \mapsto M_2]S_2}{
adamc@538	1258 \Gamma \vdash M_1 : \mt{functor}(X : S_1) : S_2
adamc@538	1259 & \Gamma \vdash M_2 : S_1
adamc@538	1260 }
adamc@538	1261 \quad \infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 = M : \mt{functor} (X : S_1) : S_2}{
adamc@538	1262 \Gamma \vdash S_1
adamc@538	1263 & \Gamma, X : S_1 \vdash S_2
adamc@538	1264 & \Gamma, X : S_1 \vdash M : S_2
adamc@538	1265 }$$
adamc@538	1266
adamc@538	1267 \begin{eqnarray*}
adamc@538	1268 \mt{sigOf}(\cdot) &=& \cdot \\
adamc@538	1269 \mt{sigOf}(s \; \overline{s'}) &=& \mt{sigOf}(s) \; \mt{sigOf}(\overline{s'}) \\
adamc@538	1270 \\
adamc@538	1271 \mt{sigOf}(\mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@538	1272 \mt{sigOf}(\mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \overline{dc} \\
adamc@538	1273 \mt{sigOf}(\mt{datatype} \; x = \mt{datatype} \; M.z) &=& \mt{datatype} \; x = \mt{datatype} \; M.z \\
adamc@538	1274 \mt{sigOf}(\mt{val} \; x : \tau = e) &=& \mt{val} \; x : \tau \\
adamc@538	1275 \mt{sigOf}(\mt{val} \; \mt{rec} \; \overline{x : \tau = e}) &=& \overline{\mt{val} \; x : \tau} \\
adamc@538	1276 \mt{sigOf}(\mt{structure} \; X : S = M) &=& \mt{structure} \; X : S \\
adamc@538	1277 \mt{sigOf}(\mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@538	1278 \mt{sigOf}(\mt{open} \; M) &=& \mt{include} \; S \textrm{ (where $\Gamma \vdash M : S$)} \\
adamc@538	1279 \mt{sigOf}(\mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@538	1280 \mt{sigOf}(\mt{open} \; \mt{constraints} \; M) &=& \cdot \\
adamc@538	1281 \mt{sigOf}(\mt{table} \; x : c) &=& \mt{table} \; x : c \\
adam@1594	1282 \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	1283 \mt{sigOf}(\mt{sequence} \; x) &=& \mt{sequence} \; x \\
adamc@538	1284 \mt{sigOf}(\mt{cookie} \; x : \tau) &=& \mt{cookie} \; x : \tau \\
adam@1797	1285 \mt{sigOf}(\mt{style} \; x) &=& \mt{style} \; x
adamc@538	1286 \end{eqnarray*}
adamc@539	1287 \begin{eqnarray*}
adamc@539	1288 \mt{selfify}(M, \cdot) &=& \cdot \\
adamc@558	1289 \mt{selfify}(M, s \; \overline{s'}) &=& \mt{selfify}(M, s) \; \mt{selfify}(M, \overline{s'}) \\
adamc@539	1290 \\
adamc@539	1291 \mt{selfify}(M, \mt{con} \; x :: \kappa) &=& \mt{con} \; x :: \kappa = M.x \\
adamc@539	1292 \mt{selfify}(M, \mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@539	1293 \mt{selfify}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \mt{datatype} \; M.x \\
adamc@539	1294 \mt{selfify}(M, \mt{datatype} \; x = \mt{datatype} \; M'.z) &=& \mt{datatype} \; x = \mt{datatype} \; M'.z \\
adamc@539	1295 \mt{selfify}(M, \mt{val} \; x : \tau) &=& \mt{val} \; x : \tau \\
adamc@539	1296 \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	1297 \mt{selfify}(M, \mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@539	1298 \mt{selfify}(M, \mt{include} \; S) &=& \mt{include} \; S \\
adamc@539	1299 \mt{selfify}(M, \mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@655	1300 \mt{selfify}(M, \mt{class} \; x :: \kappa) &=& \mt{class} \; x :: \kappa = M.x \\
adamc@655	1301 \mt{selfify}(M, \mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@539	1302 \end{eqnarray*}
adamc@539	1303
adamc@540	1304 \subsection{Module Projection}
adamc@540	1305
adamc@540	1306 \begin{eqnarray*}
adamc@540	1307 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \\
adamc@540	1308 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa, c) \\
adamc@540	1309 \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	1310 \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	1311 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})$)} \\
adamc@655	1312 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \to \mt{Type} \\
adamc@655	1313 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa \to \mt{Type}, c) \\
adamc@540	1314 \\
adamc@540	1315 \mt{proj}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc} \; \overline{s}, \mt{datatype} \; x) &=& (\overline{y}, \overline{dc}) \\
adamc@540	1316 \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	1317 \\
adamc@540	1318 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, \mt{val} \; x) &=& \tau \\
adamc@540	1319 \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	1320 \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	1321 \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	1322 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \in \overline{dc}$)} \\
adamc@540	1323 \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	1324 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \; \mt{of} \; \tau \in \overline{dc}$)} \\
adamc@540	1325 \\
adamc@540	1326 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, \mt{structure} \; X) &=& S \\
adamc@540	1327 \\
adamc@540	1328 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, \mt{signature} \; X) &=& S \\
adamc@540	1329 \\
adamc@540	1330 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1331 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1332 \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	1333 \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	1334 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@540	1335 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1336 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1337 \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	1338 \mt{proj}(M, \mt{constraint} \; c_1 \sim c_2 \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@655	1339 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@655	1340 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1341 \end{eqnarray*}
adamc@540	1342
adamc@541	1343
adamc@541	1344 \section{Type Inference}
adamc@541	1345
adamc@541	1346 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	1347
adamc@541	1348 \subsection{Basic Unification}
adamc@541	1349
adamc@560	1350 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	1351
adamc@656	1352 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	1353
adamc@541	1354 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	1355
adamc@541	1356 \subsection{Unifying Record Types}
adamc@541	1357
adamc@570	1358 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	1359
adamc@656	1360 \subsection{\label{typeclasses}Constructor Classes}
adamc@541	1361
adamc@784	1362 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	1363
adam@1797	1364 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. Any suitably kinded constructor within a module may be exposed as a constructor class from outside the module, simply by using a $\mt{class}$ signature item instead of a $\mt{con}$ signature item in the module's signature.
adam@1797	1365
adam@1797	1366 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.
adam@1797	1367
adam@1797	1368 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. Automatic inference of concrete class instances will not generally work, so abstract classes are almost always the right choice. They 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. Free extension of a concrete class is easily supported by exporting a constructor function from a module, since the class implementation will be concrete within the module.
adamc@541	1369
adamc@541	1370 \subsection{Reverse-Engineering Record Types}
adamc@541	1371
adamc@656	1372 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	1373
adamc@541	1374 \subsection{Implicit Arguments in Functor Applications}
adamc@541	1375
adamc@656	1376 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	1377
adamc@541	1378
adamc@542	1379 \section{The Ur Standard Library}
adamc@542	1380
adamc@542	1381 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	1382
adamc@542	1383 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	1384
adamc@542	1385 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	1386 $$\begin{array}{l}
adamc@542	1387 \mt{type} \; \mt{int} \\
adamc@542	1388 \mt{type} \; \mt{float} \\
adamc@873	1389 \mt{type} \; \mt{char} \\
adamc@542	1390 \mt{type} \; \mt{string} \\
adamc@542	1391 \mt{type} \; \mt{time} \\
adamc@785	1392 \mt{type} \; \mt{blob} \\
adamc@542	1393 \\
adamc@542	1394 \mt{type} \; \mt{unit} = \{\} \\
adamc@542	1395 \\
adamc@542	1396 \mt{datatype} \; \mt{bool} = \mt{False} \mid \mt{True} \\
adamc@542	1397 \\
adamc@785	1398 \mt{datatype} \; \mt{option} \; \mt{t} = \mt{None} \mid \mt{Some} \; \mt{of} \; \mt{t} \\
adamc@785	1399 \\
adamc@785	1400 \mt{datatype} \; \mt{list} \; \mt{t} = \mt{Nil} \mid \mt{Cons} \; \mt{of} \; \mt{t} \times \mt{list} \; \mt{t}
adamc@542	1401 \end{array}$$
adamc@542	1402
adamc@1123	1403 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	1404
adam@1297	1405 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	1406 $$\begin{array}{l}
adam@1297	1407 \mt{con} \; \mt{variant} :: \{\mt{Type}\} \to \mt{Type} \\
adam@1297	1408 \mt{val} \; \mt{make} : \mt{nm} :: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{ts} ::: \{\mt{Type}\} \to [[\mt{nm}] \sim \mt{ts}] \Rightarrow \mt{t} \to \mt{variant} \; ([\mt{nm} = \mt{t}] \rc \mt{ts}) \\
adam@1297	1409 \mt{val} \; \mt{match} : \mt{ts} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{variant} \; \mt{ts} \to \$(\mt{map} \; (\lambda \mt{t'} \Rightarrow \mt{t'} \to \mt{t}) \; \mt{ts}) \to \mt{t}
adam@1297	1410 \end{array}$$
adam@1297	1411
adamc@657	1412 Another important generic Ur element comes at the beginning of \texttt{top.urs}.
adamc@657	1413
adamc@657	1414 $$\begin{array}{l}
adamc@657	1415 \mt{con} \; \mt{folder} :: \mt{K} \longrightarrow \{\mt{K}\} \to \mt{Type} \\
adamc@657	1416 \\
adamc@657	1417 \mt{val} \; \mt{fold} : \mt{K} \longrightarrow \mt{tf} :: (\{\mt{K}\} \to \mt{Type}) \\
adamc@657	1418 \hspace{.1in} \to (\mt{nm} :: \mt{Name} \to \mt{v} :: \mt{K} \to \mt{r} :: \{\mt{K}\} \to [[\mt{nm}] \sim \mt{r}] \Rightarrow \\
adamc@657	1419 \hspace{.2in} \mt{tf} \; \mt{r} \to \mt{tf} \; ([\mt{nm} = \mt{v}] \rc \mt{r})) \\
adamc@657	1420 \hspace{.1in} \to \mt{tf} \; [] \\
adamc@657	1421 \hspace{.1in} \to \mt{r} :: \{\mt{K}\} \to \mt{folder} \; \mt{r} \to \mt{tf} \; \mt{r}
adamc@657	1422 \end{array}$$
adamc@657	1423
adamc@657	1424 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	1425
adamc@664	1426 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	1427
adamc@542	1428
adamc@542	1429 \section{The Ur/Web Standard Library}
adamc@542	1430
adam@1400	1431 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	1432
adamc@658	1433 \subsection{Monads}
adamc@658	1434
adamc@658	1435 The Ur Basis defines the monad constructor class from Haskell.
adamc@658	1436
adamc@658	1437 $$\begin{array}{l}
adamc@658	1438 \mt{class} \; \mt{monad} :: \mt{Type} \to \mt{Type} \\
adamc@658	1439 \mt{val} \; \mt{return} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t} ::: \mt{Type} \\
adamc@658	1440 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658	1441 \hspace{.1in} \to \mt{t} \to \mt{m} \; \mt{t} \\
adamc@658	1442 \mt{val} \; \mt{bind} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t1} ::: \mt{Type} \to \mt{t2} ::: \mt{Type} \\
adamc@658	1443 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658	1444 \hspace{.1in} \to \mt{m} \; \mt{t1} \to (\mt{t1} \to \mt{m} \; \mt{t2}) \\
adam@1544	1445 \hspace{.1in} \to \mt{m} \; \mt{t2} \\
adam@1544	1446 \mt{val} \; \mt{mkMonad} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \\
adam@1544	1447 \hspace{.1in} \to \{\mt{Return} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{m} \; \mt{t}, \\
adam@1544	1448 \hspace{.3in} \mt{Bind} : \mt{t1} ::: \mt{Type} \to \mt{t2} ::: \mt{Type} \to \mt{m} \; \mt{t1} \to (\mt{t1} \to \mt{m} \; \mt{t2}) \to \mt{m} \; \mt{t2}\} \\
adam@1544	1449 \hspace{.1in} \to \mt{monad} \; \mt{m}
adamc@658	1450 \end{array}$$
adamc@658	1451
adam@1687	1452 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	1453
adam@2009	1454 The syntactic sugar also allows $p \leftarrow e_1; e_2$ for $p$ a pattern. The pattern should be guaranteed to match any value of the corresponding type, or there will be a compile-time error.
adam@2009	1455
adamc@542	1456 \subsection{Transactions}
adamc@542	1457
adamc@542	1458 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	1459 $$\begin{array}{l}
adamc@542	1460 \mt{con} \; \mt{transaction} :: \mt{Type} \to \mt{Type} \\
adamc@658	1461 \mt{val} \; \mt{transaction\_monad} : \mt{monad} \; \mt{transaction}
adamc@542	1462 \end{array}$$
adamc@542	1463
adamc@1123	1464 For debugging purposes, a transactional function is provided for outputting a string on the server process' \texttt{stderr}.
adamc@1123	1465 $$\begin{array}{l}
adamc@1123	1466 \mt{val} \; \mt{debug} : \mt{string} \to \mt{transaction} \; \mt{unit}
adamc@1123	1467 \end{array}$$
adamc@1123	1468
adamc@542	1469 \subsection{HTTP}
adamc@542	1470
adam@1797	1471 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	1472 $$\begin{array}{l}
adamc@786	1473 \mt{con} \; \mt{http\_cookie} :: \mt{Type} \to \mt{Type} \\
adamc@786	1474 \mt{val} \; \mt{getCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; (\mt{option} \; \mt{t}) \\
adamc@1050	1475 \mt{val} \; \mt{setCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \{\mt{Value} : \mt{t}, \mt{Expires} : \mt{option} \; \mt{time}, \mt{Secure} : \mt{bool}\} \to \mt{transaction} \; \mt{unit} \\
adamc@1050	1476 \mt{val} \; \mt{clearCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; \mt{unit}
adamc@786	1477 \end{array}$$
adamc@786	1478
adamc@786	1479 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	1480 $$\begin{array}{l}
adamc@786	1481 \mt{type} \; \mt{url} \\
adamc@786	1482 \mt{val} \; \mt{bless} : \mt{string} \to \mt{url} \\
adamc@786	1483 \mt{val} \; \mt{checkUrl} : \mt{string} \to \mt{option} \; \mt{url}
adamc@786	1484 \end{array}$$
adamc@786	1485 $\mt{bless}$ raises a runtime error if the string passed to it fails the URL policy.
adamc@786	1486
adam@1400	1487 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	1488 $$\begin{array}{l}
adamc@1085	1489 \mt{val} \; \mt{currentUrl} : \mt{transaction} \; \mt{url} \\
adamc@1085	1490 \mt{val} \; \mt{url} : \mt{transaction} \; \mt{page} \to \mt{url}
adamc@1085	1491 \end{array}$$
adamc@1085	1492
adamc@1085	1493 Page generation may be interrupted at any time with a request to redirect to a particular URL instead.
adamc@1085	1494 $$\begin{array}{l}
adamc@1085	1495 \mt{val} \; \mt{redirect} : \mt{t} ::: \mt{Type} \to \mt{url} \to \mt{transaction} \; \mt{t}
adamc@1085	1496 \end{array}$$
adamc@1085	1497
adam@1400	1498 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	1499 $$\begin{array}{l}
adamc@786	1500 \mt{type} \; \mt{file} \\
adamc@786	1501 \mt{val} \; \mt{fileName} : \mt{file} \to \mt{option} \; \mt{string} \\
adamc@786	1502 \mt{val} \; \mt{fileMimeType} : \mt{file} \to \mt{string} \\
adamc@786	1503 \mt{val} \; \mt{fileData} : \mt{file} \to \mt{blob}
adamc@786	1504 \end{array}$$
adamc@786	1505
adam@1799	1506 It is also possible to get HTTP request headers and environment variables, and set HTTP response headers, using abstract types similar to the one for URLs.
adam@1465	1507
adam@1465	1508 $$\begin{array}{l}
adam@1465	1509 \mt{type} \; \mt{requestHeader} \\
adam@1465	1510 \mt{val} \; \mt{blessRequestHeader} : \mt{string} \to \mt{requestHeader} \\
adam@1465	1511 \mt{val} \; \mt{checkRequestHeader} : \mt{string} \to \mt{option} \; \mt{requestHeader} \\
adam@1465	1512 \mt{val} \; \mt{getHeader} : \mt{requestHeader} \to \mt{transaction} \; (\mt{option} \; \mt{string}) \\
adam@1465	1513 \\
adam@1799	1514 \mt{type} \; \mt{envVar} \\
adam@1799	1515 \mt{val} \; \mt{blessEnvVar} : \mt{string} \to \mt{envVar} \\
adam@1799	1516 \mt{val} \; \mt{checkEnvVar} : \mt{string} \to \mt{option} \; \mt{envVar} \\
adam@1799	1517 \mt{val} \; \mt{getenv} : \mt{envVar} \to \mt{transaction} \; (\mt{option} \; \mt{string}) \\
adam@1799	1518 \\
adam@1465	1519 \mt{type} \; \mt{responseHeader} \\
adam@1465	1520 \mt{val} \; \mt{blessResponseHeader} : \mt{string} \to \mt{responseHeader} \\
adam@1465	1521 \mt{val} \; \mt{checkResponseHeader} : \mt{string} \to \mt{option} \; \mt{responseHeader} \\
adam@1465	1522 \mt{val} \; \mt{setHeader} : \mt{responseHeader} \to \mt{string} \to \mt{transaction} \; \mt{unit}
adam@1465	1523 \end{array}$$
adam@1465	1524
adamc@786	1525 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	1526 $$\begin{array}{l}
adamc@786	1527 \mt{type} \; \mt{mimeType} \\
adamc@786	1528 \mt{val} \; \mt{blessMime} : \mt{string} \to \mt{mimeType} \\
adamc@786	1529 \mt{val} \; \mt{checkMime} : \mt{string} \to \mt{option} \; \mt{mimeType} \\
adamc@786	1530 \mt{val} \; \mt{returnBlob} : \mt{t} ::: \mt{Type} \to \mt{blob} \to \mt{mimeType} \to \mt{transaction} \; \mt{t}
adamc@542	1531 \end{array}$$
adamc@542	1532
adamc@543	1533 \subsection{SQL}
adamc@543	1534
adam@1400	1535 Everything about SQL database access is restricted to server-side code.
adam@1400	1536
adamc@543	1537 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	1538 $$\begin{array}{l}
adamc@785	1539 \mt{con} \; \mt{sql\_table} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785	1540 \end{array}$$
adamc@785	1541 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	1542
adamc@785	1543 We also have the simpler type family of SQL views, which have no keys.
adamc@785	1544 $$\begin{array}{l}
adamc@785	1545 \mt{con} \; \mt{sql\_view} :: \{\mt{Type}\} \to \mt{Type}
adamc@543	1546 \end{array}$$
adamc@543	1547
adamc@785	1548 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	1549 $$\begin{array}{l}
adamc@785	1550 \mt{class} \; \mt{fieldsOf} :: \mt{Type} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785	1551 \mt{val} \; \mt{fieldsOf\_table} : \mt{fs} ::: \{\mt{Type}\} \to \mt{keys} ::: \{\{\mt{Unit}\}\} \to \mt{fieldsOf} \; (\mt{sql\_table} \; \mt{fs} \; \mt{keys}) \; \mt{fs} \\
adamc@785	1552 \mt{val} \; \mt{fieldsOf\_view} : \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; (\mt{sql\_view} \; \mt{fs}) \; \mt{fs}
adamc@785	1553 \end{array}$$
adamc@785	1554
adamc@785	1555 \subsubsection{Table Constraints}
adamc@785	1556
adamc@785	1557 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	1558
adamc@785	1559 $$\begin{array}{l}
adamc@785	1560 \mt{con} \; \mt{primary\_key} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type} \\
adamc@785	1561 \mt{val} \; \mt{no\_primary\_key} : \mt{fs} ::: \{\mt{Type}\} \to \mt{primary\_key} \; \mt{fs} \; [] \\
adamc@785	1562 \mt{val} \; \mt{primary\_key} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{key1} :: \mt{Name} \to \mt{keys} :: \{\mt{Type}\} \\
adamc@785	1563 \hspace{.1in} \to [[\mt{key1}] \sim \mt{keys}] \Rightarrow [[\mt{key1} = \mt{t}] \rc \mt{keys} \sim \mt{rest}] \\
adamc@785	1564 \hspace{.1in} \Rightarrow \$([\mt{key1} = \mt{sql\_injectable\_prim} \; \mt{t}] \rc \mt{map} \; \mt{sql\_injectable\_prim} \; \mt{keys}) \\
adamc@785	1565 \hspace{.1in} \to \mt{primary\_key} \; ([\mt{key1} = \mt{t}] \rc \mt{keys} \rc \mt{rest}) \; [\mt{Pkey} = [\mt{key1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{keys}]
adamc@785	1566 \end{array}$$
adamc@785	1567 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	1568
adamc@785	1569 A type family stands for sets of named constraints of the remaining varieties.
adamc@785	1570 $$\begin{array}{l}
adamc@785	1571 \mt{con} \; \mt{sql\_constraints} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785	1572 \end{array}$$
adamc@785	1573 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	1574
adamc@785	1575 There is a type family of individual, unnamed constraints.
adamc@785	1576 $$\begin{array}{l}
adamc@785	1577 \mt{con} \; \mt{sql\_constraint} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \mt{Type}
adamc@785	1578 \end{array}$$
adamc@785	1579 The first argument is the same as above, and the second argument gives the key columns for just this constraint.
adamc@785	1580
adamc@785	1581 We have operations for assembling constraints into constraint sets.
adamc@785	1582 $$\begin{array}{l}
adamc@785	1583 \mt{val} \; \mt{no\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_constraints} \; \mt{fs} \; [] \\
adamc@785	1584 \mt{val} \; \mt{one\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{unique} ::: \{\mt{Unit}\} \to \mt{name} :: \mt{Name} \\
adamc@785	1585 \hspace{.1in} \to \mt{sql\_constraint} \; \mt{fs} \; \mt{unique} \to \mt{sql\_constraints} \; \mt{fs} \; [\mt{name} = \mt{unique}] \\
adamc@785	1586 \mt{val} \; \mt{join\_constraints} : \mt{fs} ::: \{\mt{Type}\} \to \mt{uniques1} ::: \{\{\mt{Unit}\}\} \to \mt{uniques2} ::: \{\{\mt{Unit}\}\} \to [\mt{uniques1} \sim \mt{uniques2}] \\
adamc@785	1587 \hspace{.1in} \Rightarrow \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques1} \to \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques2} \to \mt{sql\_constraints} \; \mt{fs} \; (\mt{uniques1} \rc \mt{uniques2})
adamc@785	1588 \end{array}$$
adamc@785	1589
adamc@785	1590 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	1591 $$\begin{array}{l}
adamc@785	1592 \mt{val} \; \mt{unique} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{unique1} :: \mt{Name} \to \mt{unique} :: \{\mt{Type}\} \\
adamc@785	1593 \hspace{.1in} \to [[\mt{unique1}] \sim \mt{unique}] \Rightarrow [[\mt{unique1} = \mt{t}] \rc \mt{unique} \sim \mt{rest}] \\
adamc@785	1594 \hspace{.1in} \Rightarrow \mt{sql\_constraint} \; ([\mt{unique1} = \mt{t}] \rc \mt{unique} \rc \mt{rest}) \; ([\mt{unique1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{unique})
adamc@785	1595 \end{array}$$
adamc@785	1596
adamc@785	1597 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	1598 $$\begin{array}{l}
adamc@785	1599 \mt{class} \; \mt{linkable} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@785	1600 \mt{val} \; \mt{linkable\_same} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; \mt{t} \\
adamc@785	1601 \mt{val} \; \mt{linkable\_from\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; (\mt{option} \; \mt{t}) \; \mt{t} \\
adamc@785	1602 \mt{val} \; \mt{linkable\_to\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@785	1603 \end{array}$$
adamc@785	1604
adamc@785	1605 The $\mt{matching}$ type family uses $\mt{linkable}$ to define when two keys match up type-wise.
adamc@785	1606 $$\begin{array}{l}
adamc@785	1607 \mt{con} \; \mt{matching} :: \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785	1608 \mt{val} \; \mt{mat\_nil} : \mt{matching} \; [] \; [] \\
adamc@785	1609 \mt{val} \; \mt{mat\_cons} : \mt{t1} ::: \mt{Type} \to \mt{rest1} ::: \{\mt{Type}\} \to \mt{t2} ::: \mt{Type} \to \mt{rest2} ::: \{\mt{Type}\} \to \mt{nm1} :: \mt{Name} \to \mt{nm2} :: \mt{Name} \\
adamc@785	1610 \hspace{.1in} \to [[\mt{nm1}] \sim \mt{rest1}] \Rightarrow [[\mt{nm2}] \sim \mt{rest2}] \Rightarrow \mt{linkable} \; \mt{t1} \; \mt{t2} \to \mt{matching} \; \mt{rest1} \; \mt{rest2} \\
adamc@785	1611 \hspace{.1in} \to \mt{matching} \; ([\mt{nm1} = \mt{t1}] \rc \mt{rest1}) \; ([\mt{nm2} = \mt{t2}] \rc \mt{rest2})
adamc@785	1612 \end{array}$$
adamc@785	1613
adamc@785	1614 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	1615 $$\begin{array}{l}
adamc@785	1616 \mt{con} \; \mt{propagation\_mode} :: \{\mt{Type}\} \to \mt{Type} \\
adamc@785	1617 \mt{val} \; \mt{restrict} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785	1618 \mt{val} \; \mt{cascade} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785	1619 \mt{val} \; \mt{no\_action} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785	1620 \mt{val} \; \mt{set\_null} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; (\mt{map} \; \mt{option} \; \mt{fs})
adamc@785	1621 \end{array}$$
adamc@785	1622
adamc@785	1623 Finally, we put these ingredient together to define the \texttt{FOREIGN KEY} constraint function.
adamc@785	1624 $$\begin{array}{l}
adamc@785	1625 \mt{val} \; \mt{foreign\_key} : \mt{mine1} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{mine} ::: \{\mt{Type}\} \to \mt{munused} ::: \{\mt{Type}\} \to \mt{foreign} ::: \{\mt{Type}\} \\
adamc@785	1626 \hspace{.1in} \to \mt{funused} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{uniques} ::: \{\{\mt{Unit}\}\} \\
adamc@785	1627 \hspace{.1in} \to [[\mt{mine1}] \sim \mt{mine}] \Rightarrow [[\mt{mine1} = \mt{t}] \rc \mt{mine} \sim \mt{munused}] \Rightarrow [\mt{foreign} \sim \mt{funused}] \Rightarrow [[\mt{nm}] \sim \mt{uniques}] \\
adamc@785	1628 \hspace{.1in} \Rightarrow \mt{matching} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}) \; \mt{foreign} \\
adamc@785	1629 \hspace{.1in} \to \mt{sql\_table} \; (\mt{foreign} \rc \mt{funused}) \; ([\mt{nm} = \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{foreign}] \rc \mt{uniques}) \\
adamc@785	1630 \hspace{.1in} \to \{\mt{OnDelete} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}), \\
adamc@785	1631 \hspace{.2in} \mt{OnUpdate} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine})\} \\
adamc@785	1632 \hspace{.1in} \to \mt{sql\_constraint} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine} \rc \mt{munused}) \; []
adamc@785	1633 \end{array}$$
adamc@785	1634
adamc@785	1635 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	1636 $$\begin{array}{l}
adam@1778	1637 \mt{val} \; \mt{check} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; [] \; [] \; \mt{fs} \; \mt{bool} \to \mt{sql\_constraint} \; \mt{fs} \; []
adamc@785	1638 \end{array}$$
adamc@785	1639
adamc@785	1640 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	1641
adamc@784	1642
adamc@543	1643 \subsubsection{Queries}
adamc@543	1644
adam@1400	1645 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	1646 $$\begin{array}{l}
adam@1400	1647 \mt{con} \; \mt{sql\_query} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@1193	1648 \mt{val} \; \mt{sql\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400	1649 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adamc@1193	1650 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543	1651 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543	1652 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1193	1653 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adam@1400	1654 \hspace{.1in} \Rightarrow \{\mt{Rows} : \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}, \\
adamc@1193	1655 \hspace{.2in} \mt{OrderBy} : \mt{sql\_order\_by} \; (\mt{free} \rc \mt{tables}) \; \mt{selectedExps}, \\
adamc@543	1656 \hspace{.2in} \mt{Limit} : \mt{sql\_limit}, \\
adamc@543	1657 \hspace{.2in} \mt{Offset} : \mt{sql\_offset}\} \\
adam@1400	1658 \hspace{.1in} \to \mt{sql\_query} \; \mt{free} \; \mt{afree} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543	1659 \end{array}$$
adamc@543	1660
adamc@545	1661 Queries are used by folding over their results inside transactions.
adamc@545	1662 $$\begin{array}{l}
adam@1400	1663 \mt{val} \; \mt{query} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to [\mt{tables} \sim \mt{exps}] \Rightarrow \mt{state} ::: \mt{Type} \to \mt{sql\_query} \; [] \; [] \; \mt{tables} \; \mt{exps} \\
adamc@658	1664 \hspace{.1in} \to (\$(\mt{exps} \rc \mt{map} \; (\lambda \mt{fields} :: \{\mt{Type}\} \Rightarrow \$\mt{fields}) \; \mt{tables}) \\
adamc@545	1665 \hspace{.2in} \to \mt{state} \to \mt{transaction} \; \mt{state}) \\
adamc@545	1666 \hspace{.1in} \to \mt{state} \to \mt{transaction} \; \mt{state}
adamc@545	1667 \end{array}$$
adamc@545	1668
adam@1400	1669 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	1670 $$\begin{array}{l}
adam@1400	1671 \mt{con} \; \mt{sql\_query1} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@543	1672 \\
adamc@543	1673 \mt{type} \; \mt{sql\_relop} \\
adamc@543	1674 \mt{val} \; \mt{sql\_union} : \mt{sql\_relop} \\
adamc@543	1675 \mt{val} \; \mt{sql\_intersect} : \mt{sql\_relop} \\
adamc@543	1676 \mt{val} \; \mt{sql\_except} : \mt{sql\_relop} \\
adam@1400	1677 \mt{val} \; \mt{sql\_relop} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400	1678 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adam@1400	1679 \hspace{.1in} \to \mt{tables1} ::: \{\{\mt{Type}\}\} \\
adamc@543	1680 \hspace{.1in} \to \mt{tables2} ::: \{\{\mt{Type}\}\} \\
adamc@543	1681 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543	1682 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@543	1683 \hspace{.1in} \to \mt{sql\_relop} \\
adam@1458	1684 \hspace{.1in} \to \mt{bool} \; (* \; \mt{ALL} \; *) \\
adam@1400	1685 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables1} \; \mt{selectedFields} \; \mt{selectedExps} \\
adam@1400	1686 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables2} \; \mt{selectedFields} \; \mt{selectedExps} \\
adam@1400	1687 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{selectedFields} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543	1688 \end{array}$$
adamc@543	1689
adamc@543	1690 $$\begin{array}{l}
adamc@1193	1691 \mt{val} \; \mt{sql\_query1} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400	1692 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adamc@1193	1693 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543	1694 \hspace{.1in} \to \mt{grouped} ::: \{\{\mt{Type}\}\} \\
adamc@543	1695 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543	1696 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1085	1697 \hspace{.1in} \to \mt{empties} :: \{\mt{Unit}\} \\
adamc@1193	1698 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adamc@1193	1699 \hspace{.1in} \Rightarrow [\mt{free} \sim \mt{grouped}] \\
adam@1400	1700 \hspace{.1in} \Rightarrow [\mt{afree} \sim \mt{tables}] \\
adamc@1193	1701 \hspace{.1in} \Rightarrow [\mt{empties} \sim \mt{selectedFields}] \\
adamc@1085	1702 \hspace{.1in} \Rightarrow \{\mt{Distinct} : \mt{bool}, \\
adamc@1193	1703 \hspace{.2in} \mt{From} : \mt{sql\_from\_items} \; \mt{free} \; \mt{tables}, \\
adam@1778	1704 \hspace{.2in} \mt{Where} : \mt{sql\_exp} \; (\mt{free} \rc \mt{tables}) \; \mt{afree} \; [] \; \mt{bool}, \\
adamc@543	1705 \hspace{.2in} \mt{GroupBy} : \mt{sql\_subset} \; \mt{tables} \; \mt{grouped}, \\
adam@1778	1706 \hspace{.2in} \mt{Having} : \mt{sql\_exp} \; (\mt{free} \rc \mt{grouped}) \; (\mt{afree} \rc \mt{tables}) \; [] \; \mt{bool}, \\
adamc@1085	1707 \hspace{.2in} \mt{SelectFields} : \mt{sql\_subset} \; \mt{grouped} \; (\mt{map} \; (\lambda \_ \Rightarrow []) \; \mt{empties} \rc \mt{selectedFields}), \\
adam@1778	1708 \hspace{.2in} \mt {SelectExps} : \$(\mt{map} \; (\mt{sql\_expw} \; (\mt{free} \rc \mt{grouped}) \; (\mt{afree} \rc \mt{tables}) \; []) \; \mt{selectedExps}) \} \\
adam@1400	1709 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543	1710 \end{array}$$
adamc@543	1711
adamc@543	1712 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	1713 $$\begin{array}{l}
adamc@543	1714 \mt{con} \; \mt{sql\_subset} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@543	1715 \mt{val} \; \mt{sql\_subset} : \mt{keep\_drop} :: \{(\{\mt{Type}\} \times \{\mt{Type}\})\} \\
adamc@543	1716 \hspace{.1in} \to \mt{sql\_subset} \\
adamc@658	1717 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1 \rc \mt{fields}.2)\; \mt{keep\_drop}) \\
adamc@658	1718 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1) \; \mt{keep\_drop}) \\
adamc@543	1719 \mt{val} \; \mt{sql\_subset\_all} : \mt{tables} :: \{\{\mt{Type}\}\} \to \mt{sql\_subset} \; \mt{tables} \; \mt{tables}
adamc@543	1720 \end{array}$$
adamc@543	1721
adam@1778	1722 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	1723 $$\begin{array}{l}
adam@1778	1724 \mt{con} \; \mt{sql\_exp} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}
adamc@543	1725 \end{array}$$
adamc@543	1726
adamc@543	1727 Any field in scope may be converted to an expression.
adamc@543	1728 $$\begin{array}{l}
adamc@543	1729 \mt{val} \; \mt{sql\_field} : \mt{otherTabs} ::: \{\{\mt{Type}\}\} \to \mt{otherFields} ::: \{\mt{Type}\} \\
adam@1778	1730 \hspace{.1in} \to \mt{fieldType} ::: \mt{Type} \to \mt{agg} ::: \{\{\mt{Type}\}\} \\
adamc@543	1731 \hspace{.1in} \to \mt{exps} ::: \{\mt{Type}\} \\
adamc@543	1732 \hspace{.1in} \to \mt{tab} :: \mt{Name} \to \mt{field} :: \mt{Name} \\
adam@1778	1733 \hspace{.1in} \to \mt{sql\_exp} \; ([\mt{tab} = [\mt{field} = \mt{fieldType}] \rc \mt{otherFields}] \rc \mt{otherTabs}) \; \mt{agg} \; \mt{exps} \; \mt{fieldType}
adamc@543	1734 \end{array}$$
adamc@543	1735
adamc@544	1736 There is an analogous function for referencing named expressions.
adamc@544	1737 $$\begin{array}{l}
adam@1778	1738 \mt{val} \; \mt{sql\_exp} : \mt{tabs} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{t} ::: \mt{Type} \to \mt{rest} ::: \{\mt{Type}\} \to \mt{nm} :: \mt{Name} \\
adam@1778	1739 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tabs} \; \mt{agg} \; ([\mt{nm} = \mt{t}] \rc \mt{rest}) \; \mt{t}
adamc@544	1740 \end{array}$$
adamc@544	1741
adamc@544	1742 Ur values of appropriate types may be injected into SQL expressions.
adamc@544	1743 $$\begin{array}{l}
adamc@786	1744 \mt{class} \; \mt{sql\_injectable\_prim} \\
adamc@786	1745 \mt{val} \; \mt{sql\_bool} : \mt{sql\_injectable\_prim} \; \mt{bool} \\
adamc@786	1746 \mt{val} \; \mt{sql\_int} : \mt{sql\_injectable\_prim} \; \mt{int} \\
adamc@786	1747 \mt{val} \; \mt{sql\_float} : \mt{sql\_injectable\_prim} \; \mt{float} \\
adamc@786	1748 \mt{val} \; \mt{sql\_string} : \mt{sql\_injectable\_prim} \; \mt{string} \\
adamc@786	1749 \mt{val} \; \mt{sql\_time} : \mt{sql\_injectable\_prim} \; \mt{time} \\
adamc@786	1750 \mt{val} \; \mt{sql\_blob} : \mt{sql\_injectable\_prim} \; \mt{blob} \\
adamc@786	1751 \mt{val} \; \mt{sql\_channel} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{channel} \; \mt{t}) \\
adamc@786	1752 \mt{val} \; \mt{sql\_client} : \mt{sql\_injectable\_prim} \; \mt{client} \\
adamc@786	1753 \\
adamc@544	1754 \mt{class} \; \mt{sql\_injectable} \\
adamc@786	1755 \mt{val} \; \mt{sql\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@786	1756 \mt{val} \; \mt{sql\_option\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; (\mt{option} \; \mt{t}) \\
adamc@786	1757 \\
adam@1778	1758 \mt{val} \; \mt{sql\_inject} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{sql\_injectable} \; \mt{t} \\
adam@1778	1759 \hspace{.1in} \to \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adamc@544	1760 \end{array}$$
adamc@544	1761
adamc@1123	1762 Additionally, most function-free types may be injected safely, via the $\mt{serialized}$ type family.
adamc@1123	1763 $$\begin{array}{l}
adamc@1123	1764 \mt{con} \; \mt{serialized} :: \mt{Type} \to \mt{Type} \\
adamc@1123	1765 \mt{val} \; \mt{serialize} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{serialized} \; \mt{t} \\
adamc@1123	1766 \mt{val} \; \mt{deserialize} : \mt{t} ::: \mt{Type} \to \mt{serialized} \; \mt{t} \to \mt{t} \\
adamc@1123	1767 \mt{val} \; \mt{sql\_serialized} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{serialized} \; \mt{t})
adamc@1123	1768 \end{array}$$
adamc@1123	1769
adamc@544	1770 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	1771 $$\begin{array}{l}
adam@1778	1772 \mt{val} \; \mt{sql\_is\_null} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778	1773 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; (\mt{option} \; \mt{t}) \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{bool}
adamc@544	1774 \end{array}$$
adamc@544	1775
adam@1602	1776 As another way of dealing with null values, there is also a restricted form of the standard \cd{COALESCE} function.
adam@1602	1777 $$\begin{array}{l}
adam@1602	1778 \mt{val} \; \mt{sql\_coalesce} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778	1779 \hspace{.1in} \to \mt{t} ::: \mt{Type} \\
adam@1778	1780 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; (\mt{option} \; \mt{t}) \\
adam@1778	1781 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778	1782 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adam@1602	1783 \end{array}$$
adam@1602	1784
adamc@559	1785 We have generic nullary, unary, and binary operators.
adamc@544	1786 $$\begin{array}{l}
adamc@544	1787 \mt{con} \; \mt{sql\_nfunc} :: \mt{Type} \to \mt{Type} \\
adamc@544	1788 \mt{val} \; \mt{sql\_current\_timestamp} : \mt{sql\_nfunc} \; \mt{time} \\
adam@1778	1789 \mt{val} \; \mt{sql\_nfunc} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778	1790 \hspace{.1in} \to \mt{sql\_nfunc} \; \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\\end{array}$$
adamc@544	1791
adamc@544	1792 $$\begin{array}{l}
adamc@544	1793 \mt{con} \; \mt{sql\_unary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544	1794 \mt{val} \; \mt{sql\_not} : \mt{sql\_unary} \; \mt{bool} \; \mt{bool} \\
adam@1778	1795 \mt{val} \; \mt{sql\_unary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adam@1778	1796 \hspace{.1in} \to \mt{sql\_unary} \; \mt{arg} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res} \\
adamc@544	1797 \end{array}$$
adamc@544	1798
adamc@544	1799 $$\begin{array}{l}
adamc@544	1800 \mt{con} \; \mt{sql\_binary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544	1801 \mt{val} \; \mt{sql\_and} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544	1802 \mt{val} \; \mt{sql\_or} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adam@1778	1803 \mt{val} \; \mt{sql\_binary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg_1} ::: \mt{Type} \to \mt{arg_2} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adam@1778	1804 \hspace{.1in} \to \mt{sql\_binary} \; \mt{arg_1} \; \mt{arg_2} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_1} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_2} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res}
adamc@544	1805 \end{array}$$
adamc@544	1806
adamc@544	1807 $$\begin{array}{l}
adamc@559	1808 \mt{class} \; \mt{sql\_arith} \\
adamc@559	1809 \mt{val} \; \mt{sql\_int\_arith} : \mt{sql\_arith} \; \mt{int} \\
adamc@559	1810 \mt{val} \; \mt{sql\_float\_arith} : \mt{sql\_arith} \; \mt{float} \\
adamc@559	1811 \mt{val} \; \mt{sql\_neg} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_unary} \; \mt{t} \; \mt{t} \\
adamc@559	1812 \mt{val} \; \mt{sql\_plus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559	1813 \mt{val} \; \mt{sql\_minus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559	1814 \mt{val} \; \mt{sql\_times} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559	1815 \mt{val} \; \mt{sql\_div} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559	1816 \mt{val} \; \mt{sql\_mod} : \mt{sql\_binary} \; \mt{int} \; \mt{int} \; \mt{int}
adamc@559	1817 \end{array}$$
adamc@544	1818
adam@1797	1819 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	1820 $$\begin{array}{l}
adam@1778	1821 \mt{val} \; \mt{sql\_count} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int}
adamc@544	1822 \end{array}$$
adamc@544	1823
adamc@544	1824 $$\begin{array}{l}
adamc@1188	1825 \mt{con} \; \mt{sql\_aggregate} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adam@1778	1826 \mt{val} \; \mt{sql\_aggregate} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{dom} ::: \mt{Type} \to \mt{ran} ::: \mt{Type} \\
adam@1778	1827 \hspace{.1in} \to \mt{sql\_aggregate} \; \mt{dom} \; \mt{ran} \to \mt{sql\_exp} \; \mt{agg} \; \mt{agg} \; \mt{exps} \; \mt{dom} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{ran}
adamc@1188	1828 \end{array}$$
adamc@1188	1829
adamc@1188	1830 $$\begin{array}{l}
adamc@1188	1831 \mt{val} \; \mt{sql\_count\_col} : \mt{t} ::: \mt{Type} \to \mt{sql\_aggregate} \; (\mt{option} \; \mt{t}) \; \mt{int}
adamc@544	1832 \end{array}$$
adam@1400	1833
adam@1400	1834 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	1835
adamc@544	1836 $$\begin{array}{l}
adamc@544	1837 \mt{class} \; \mt{sql\_summable} \\
adamc@544	1838 \mt{val} \; \mt{sql\_summable\_int} : \mt{sql\_summable} \; \mt{int} \\
adamc@544	1839 \mt{val} \; \mt{sql\_summable\_float} : \mt{sql\_summable} \; \mt{float} \\
adam@1777	1840 \mt{val} \; \mt{sql\_avg} : \mt{t} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{sql\_aggregate} \; \mt{t} \; (\mt{option} \; \mt{float}) \\
adam@1400	1841 \mt{val} \; \mt{sql\_sum} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt}
adamc@544	1842 \end{array}$$
adamc@544	1843
adamc@544	1844 $$\begin{array}{l}
adamc@544	1845 \mt{class} \; \mt{sql\_maxable} \\
adamc@544	1846 \mt{val} \; \mt{sql\_maxable\_int} : \mt{sql\_maxable} \; \mt{int} \\
adamc@544	1847 \mt{val} \; \mt{sql\_maxable\_float} : \mt{sql\_maxable} \; \mt{float} \\
adamc@544	1848 \mt{val} \; \mt{sql\_maxable\_string} : \mt{sql\_maxable} \; \mt{string} \\
adamc@544	1849 \mt{val} \; \mt{sql\_maxable\_time} : \mt{sql\_maxable} \; \mt{time} \\
adam@1400	1850 \mt{val} \; \mt{sql\_max} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt} \\
adam@1400	1851 \mt{val} \; \mt{sql\_min} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt}
adamc@544	1852 \end{array}$$
adamc@544	1853
adam@1778	1854 Any SQL query that returns single columns may be turned into a subquery expression.
adam@1777	1855
adam@1777	1856 $$\begin{array}{l}
adam@1778	1857 \mt{val} \; \mt{sql\_subquery} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \\
adam@1778	1858 \hspace{.1in} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_query} \; \mt{tables} \; \mt{agg} \; [\mt{nm} = \mt{t}] \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{nt}
adamc@1193	1859 \end{array}$$
adamc@1193	1860
adam@1573	1861 There is also an \cd{IF..THEN..ELSE..} construct that is compiled into standard SQL \cd{CASE} expressions.
adam@1573	1862 $$\begin{array}{l}
adam@1778	1863 \mt{val} \; \mt{sql\_if\_then\_else} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778	1864 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{bool} \\
adam@1778	1865 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778	1866 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778	1867 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adam@1573	1868 \end{array}$$
adam@1573	1869
adamc@1193	1870 \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	1871 $$\begin{array}{l}
adamc@1193	1872 \mt{con} \; \mt{sql\_from\_items} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@1193	1873 \mt{val} \; \mt{sql\_from\_table} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adamc@1193	1874 \hspace{.1in} \to \mt{t} ::: \mt{Type} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; \mt{t} \; \mt{fs} \to \mt{name} :: \mt{Name} \to \mt{t} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193	1875 \mt{val} \; \mt{sql\_from\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{name} :: \mt{Name} \to \mt{sql\_query} \; \mt{free} \; [] \; \mt{fs} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193	1876 \mt{val} \; \mt{sql\_from\_comma} : \mt{free} ::: \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \to [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193	1877 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adamc@1193	1878 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2}) \\
adamc@1193	1879 \mt{val} \; \mt{sql\_inner\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \\
adamc@1193	1880 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193	1881 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adam@1778	1882 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193	1883 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2})
adamc@786	1884 \end{array}$$
adamc@786	1885
adamc@786	1886 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	1887 $$\begin{array}{l}
adamc@786	1888 \mt{class} \; \mt{nullify} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@786	1889 \mt{val} \; \mt{nullify\_option} : \mt{t} ::: \mt{Type} \to \mt{nullify} \; (\mt{option} \; \mt{t}) \; (\mt{option} \; \mt{t}) \\
adamc@786	1890 \mt{val} \; \mt{nullify\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{nullify} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@786	1891 \end{array}$$
adamc@786	1892
adamc@786	1893 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	1894
adamc@786	1895 $$\begin{array}{l}
adamc@1193	1896 \mt{val} \; \mt{sql\_left\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{(\mt{Type} \times \mt{Type})\}\} \\
adamc@1193	1897 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@786	1898 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\lambda \mt{r} \Rightarrow \$(\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{nullify} \; \mt{p}.1 \; \mt{p}.2) \; \mt{r})) \; \mt{tabs2}) \\
adamc@1193	1899 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \\
adam@1778	1900 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193	1901 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.2)) \; \mt{tabs2})
adamc@786	1902 \end{array}$$
adamc@786	1903
adamc@544	1904 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	1905 $$\begin{array}{l}
adamc@544	1906 \mt{type} \; \mt{sql\_direction} \\
adamc@544	1907 \mt{val} \; \mt{sql\_asc} : \mt{sql\_direction} \\
adamc@544	1908 \mt{val} \; \mt{sql\_desc} : \mt{sql\_direction} \\
adamc@544	1909 \\
adamc@544	1910 \mt{con} \; \mt{sql\_order\_by} :: \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@544	1911 \mt{val} \; \mt{sql\_order\_by\_Nil} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} :: \{\mt{Type}\} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adam@1778	1912 \mt{val} \; \mt{sql\_order\_by\_Cons} : \mt{tf} ::: (\{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}) \\
adam@1778	1913 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778	1914 \hspace{.1in} \to \mt{sql\_window} \; \mt{tf} \to \mt{tf} \; \mt{tables} \; [] \; \mt{exps} \; \mt{t} \to \mt{sql\_direction} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adam@1684	1915 \mt{val} \; \mt{sql\_order\_by\_random} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544	1916 \\
adamc@544	1917 \mt{type} \; \mt{sql\_limit} \\
adamc@544	1918 \mt{val} \; \mt{sql\_no\_limit} : \mt{sql\_limit} \\
adamc@544	1919 \mt{val} \; \mt{sql\_limit} : \mt{int} \to \mt{sql\_limit} \\
adamc@544	1920 \\
adamc@544	1921 \mt{type} \; \mt{sql\_offset} \\
adamc@544	1922 \mt{val} \; \mt{sql\_no\_offset} : \mt{sql\_offset} \\
adamc@544	1923 \mt{val} \; \mt{sql\_offset} : \mt{int} \to \mt{sql\_offset}
adamc@544	1924 \end{array}$$
adamc@544	1925
adam@1778	1926 When using Postgres, \cd{SELECT} and \cd{ORDER BY} are allowed to contain top-level uses of \emph{window functions}. A separate type family \cd{sql\_expw} is provided for such cases, with some type class convenience for overloading between normal and window expressions.
adam@1778	1927 $$\begin{array}{l}
adam@1778	1928 \mt{con} \; \mt{sql\_expw} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type} \\
adam@1778	1929 \\
adam@1778	1930 \mt{class} \; \mt{sql\_window} :: (\{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}) \to \mt{Type} \\
adam@1778	1931 \mt{val} \; \mt{sql\_window\_normal} : \mt{sql\_window} \; \mt{sql\_exp} \\
adam@1778	1932 \mt{val} \; \mt{sql\_window\_fancy} : \mt{sql\_window} \; \mt{sql\_expw} \\
adam@1778	1933 \mt{val} \; \mt{sql\_window} : \mt{tf} ::: (\{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}) \\
adam@1778	1934 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778	1935 \hspace{.1in} \to \mt{sql\_window} \; \mt{tf} \\
adam@1778	1936 \hspace{.1in} \to \mt{tf} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778	1937 \hspace{.1in} \to \mt{sql\_expw} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778	1938 \\
adam@1778	1939 \mt{con} \; \mt{sql\_partition} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adam@1778	1940 \mt{val} \; \mt{sql\_no\_partition} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778	1941 \hspace{.1in} \to \mt{sql\_partition} \; \mt{tables} \; \mt{agg} \; \mt{exps} \\
adam@1778	1942 \mt{val} \; \mt{sql\_partition} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778	1943 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778	1944 \hspace{.1in} \to \mt{sql\_partition} \; \mt{tables} \; \mt{agg} \; \mt{exps} \\
adam@1778	1945 \\
adam@1778	1946 \mt{con} \; \mt{sql\_window\_function} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type} \\
adam@1778	1947 \mt{val} \; \mt{sql\_window\_function} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778	1948 \hspace{.1in} \to \mt{t} ::: \mt{Type} \\
adam@1778	1949 \hspace{.1in} \to \mt{sql\_window\_function} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778	1950 \hspace{.1in} \to \mt{sql\_partition} \; \mt{tables} \; \mt{agg} \; \mt{exps} \\
adam@1778	1951 \hspace{.1in} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adam@1778	1952 \hspace{.1in} \to \mt{sql\_expw} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778	1953 \\
adam@1778	1954 \mt{val} \; \mt{sql\_window\_aggregate} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778	1955 \hspace{.1in} \to \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \\
adam@1778	1956 \hspace{.1in} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt} \\
adam@1778	1957 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778	1958 \hspace{.1in} \to \mt{sql\_window\_function} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{nt} \\
adam@1778	1959 \mt{val} \; \mt{sql\_window\_count} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778	1960 \hspace{.1in} \to \mt{sql\_window\_function} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int} \\
adam@1778	1961 \mt{val} \; \mt{sql\_rank} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778	1962 \hspace{.1in} \to \mt{sql\_window\_function} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int}
adam@1778	1963 \end{array}$$
adam@1778	1964
adamc@545	1965
adamc@545	1966 \subsubsection{DML}
adamc@545	1967
adamc@545	1968 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	1969
adamc@545	1970 $$\begin{array}{l}
adamc@545	1971 \mt{type} \; \mt{dml} \\
adamc@545	1972 \mt{val} \; \mt{dml} : \mt{dml} \to \mt{transaction} \; \mt{unit}
adamc@545	1973 \end{array}$$
adamc@545	1974
adam@1297	1975 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	1976
adam@1297	1977 $$\begin{array}{l}
adam@1297	1978 \mt{val} \; \mt{tryDml} : \mt{dml} \to \mt{transaction} \; (\mt{option} \; \mt{string})
adam@1297	1979 \end{array}$$
adam@1297	1980
adam@1797	1981 Properly typed records may be used to form $\mt{INSERT}$ commands.
adamc@545	1982 $$\begin{array}{l}
adamc@545	1983 \mt{val} \; \mt{insert} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \\
adam@1778	1984 \hspace{.1in} \to \$(\mt{map} \; (\mt{sql\_exp} \; [] \; [] \; []) \; \mt{fields}) \to \mt{dml}
adamc@545	1985 \end{array}$$
adamc@545	1986
adam@1578	1987 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	1988 $$\begin{array}{l}
adam@1380	1989 \mt{val} \; \mt{update} : \mt{unchanged} ::: \{\mt{Type}\} \to \mt{changed} :: \{\mt{Type}\} \to [\mt{changed} \sim \mt{unchanged}] \\
adam@1778	1990 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; []) \; \mt{changed}) \\
adam@1778	1991 \hspace{.1in} \to \mt{sql\_table} \; (\mt{changed} \rc \mt{unchanged}) \to \mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545	1992 \end{array}$$
adamc@545	1993
adam@1578	1994 A $\mt{DELETE}$ command is formed from a table and a $\mt{WHERE}$ clause. The above use of $\mt{T}$ is repeated.
adamc@545	1995 $$\begin{array}{l}
adam@1778	1996 \mt{val} \; \mt{delete} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \to \mt{sql\_exp} \; [\mt{T} = \mt{fields}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545	1997 \end{array}$$
adamc@545	1998
adamc@546	1999 \subsubsection{Sequences}
adamc@546	2000
adamc@546	2001 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	2002
adamc@546	2003 $$\begin{array}{l}
adamc@546	2004 \mt{type} \; \mt{sql\_sequence} \\
adamc@1085	2005 \mt{val} \; \mt{nextval} : \mt{sql\_sequence} \to \mt{transaction} \; \mt{int} \\
adamc@1085	2006 \mt{val} \; \mt{setval} : \mt{sql\_sequence} \to \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@546	2007 \end{array}$$
adamc@546	2008
adamc@546	2009
adam@1648	2010 \subsection{\label{xml}XML}
adamc@547	2011
adam@1333	2012 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	2013
adam@1642	2014 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	2015 $$\begin{array}{l}
adamc@547	2016 \mt{con} \; \mt{xml} :: \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547	2017 \end{array}$$
adamc@547	2018
adamc@547	2019 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	2020 $$\begin{array}{l}
adamc@547	2021 \mt{con} \; \mt{tag} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547	2022 \end{array}$$
adamc@547	2023
adamc@547	2024 Literal text may be injected into XML as ``CDATA.''
adamc@547	2025 $$\begin{array}{l}
adamc@547	2026 \mt{val} \; \mt{cdata} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{string} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adamc@547	2027 \end{array}$$
adamc@547	2028
adam@1358	2029 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	2030 $$\begin{array}{l}
adam@1358	2031 \mt{val} \; \mt{cdataChar} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{char} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adam@1358	2032 \end{array}$$
adam@1358	2033
adamc@547	2034 There is a function for producing an XML tree with a particular tag at its root.
adamc@547	2035 $$\begin{array}{l}
adamc@547	2036 \mt{val} \; \mt{tag} : \mt{attrsGiven} ::: \{\mt{Type}\} \to \mt{attrsAbsent} ::: \{\mt{Type}\} \to \mt{ctxOuter} ::: \{\mt{Unit}\} \to \mt{ctxInner} ::: \{\mt{Unit}\} \\
adamc@547	2037 \hspace{.1in} \to \mt{useOuter} ::: \{\mt{Type}\} \to \mt{useInner} ::: \{\mt{Type}\} \to \mt{bindOuter} ::: \{\mt{Type}\} \to \mt{bindInner} ::: \{\mt{Type}\} \\
adam@1380	2038 \hspace{.1in} \to [\mt{attrsGiven} \sim \mt{attrsAbsent}] \Rightarrow [\mt{useOuter} \sim \mt{useInner}] \Rightarrow [\mt{bindOuter} \sim \mt{bindInner}] \\
adam@1749	2039 \hspace{.1in} \Rightarrow \mt{css\_class} \\
adam@1643	2040 \hspace{.1in} \to \mt{option} \; (\mt{signal} \; \mt{css\_class}) \\
adam@1750	2041 \hspace{.1in} \to \mt{css\_style} \\
adam@1751	2042 \hspace{.1in} \to \mt{option} \; (\mt{signal} \; \mt{css\_style}) \\
adamc@787	2043 \hspace{.1in} \to \$\mt{attrsGiven} \\
adamc@547	2044 \hspace{.1in} \to \mt{tag} \; (\mt{attrsGiven} \rc \mt{attrsAbsent}) \; \mt{ctxOuter} \; \mt{ctxInner} \; \mt{useOuter} \; \mt{bindOuter} \\
adamc@547	2045 \hspace{.1in} \to \mt{xml} \; \mt{ctxInner} \; \mt{useInner} \; \mt{bindInner} \to \mt{xml} \; \mt{ctxOuter} \; (\mt{useOuter} \rc \mt{useInner}) \; (\mt{bindOuter} \rc \mt{bindInner})
adamc@547	2046 \end{array}$$
adam@1750	2047 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	2048
adam@1643	2049 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	2050
adam@1751	2051 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	2052
adamc@547	2053 Two XML fragments may be concatenated.
adamc@547	2054 $$\begin{array}{l}
adamc@547	2055 \mt{val} \; \mt{join} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{bind_1} ::: \{\mt{Type}\} \to \mt{bind_2} ::: \{\mt{Type}\} \\
adam@1380	2056 \hspace{.1in} \to [\mt{use_1} \sim \mt{bind_1}] \Rightarrow [\mt{bind_1} \sim \mt{bind_2}] \\
adamc@547	2057 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind_1} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{bind_1}) \; \mt{bind_2} \to \mt{xml} \; \mt{ctx} \; \mt{use_1} \; (\mt{bind_1} \rc \mt{bind_2})
adamc@547	2058 \end{array}$$
adamc@547	2059
adamc@547	2060 Finally, any XML fragment may be updated to ``claim'' to use more form fields than it does.
adamc@547	2061 $$\begin{array}{l}
adam@1380	2062 \mt{val} \; \mt{useMore} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{use_2} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to [\mt{use_1} \sim \mt{use_2}] \\
adamc@547	2063 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{use_2}) \; \mt{bind}
adamc@547	2064 \end{array}$$
adamc@547	2065
adam@2008	2066 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, without using the foreign function interface (Section \ref{ffi}).
adam@2008	2067
adam@2047	2068 Some tags support HTML5 \texttt{data-} attributes, which in Ur/Web are encoded as a single attribute $\mt{Data}$ with type $\mt{data\_attrs}$ encoding one or more attributes of this kind. See \texttt{basis.urs} for details. The usual HTML5 syntax for these attributes is supported by the Ur/Web parser as syntactic sugar, and the same mechanism is reused to support \texttt{aria-} attributes.
adamc@547	2069
adamc@547	2070 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	2071 $$\begin{array}{l}
adam@1641	2072 \mt{val} \; \mt{error} : \mt{t} ::: \mt{Type} \to \mt{xbody} \to \mt{t}
adamc@547	2073 \end{array}$$
adamc@547	2074
adamc@549	2075
adamc@701	2076 \subsection{Client-Side Programming}
adamc@659	2077
adamc@701	2078 Ur/Web supports running code on web browsers, via automatic compilation to JavaScript.
adamc@701	2079
adamc@701	2080 \subsubsection{The Basics}
adamc@701	2081
adam@1400	2082 All of the functions in this subsection are client-side only.
adam@1400	2083
adam@1297	2084 Clients can open alert and confirm dialog boxes, in the usual annoying JavaScript way.
adamc@701	2085 $$\begin{array}{l}
adam@1297	2086 \mt{val} \; \mt{alert} : \mt{string} \to \mt{transaction} \; \mt{unit} \\
adam@1297	2087 \mt{val} \; \mt{confirm} : \mt{string} \to \mt{transaction} \; \mt{bool}
adamc@701	2088 \end{array}$$
adamc@701	2089
adamc@701	2090 Any transaction may be run in a new thread with the $\mt{spawn}$ function.
adamc@701	2091 $$\begin{array}{l}
adamc@701	2092 \mt{val} \; \mt{spawn} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit}
adamc@701	2093 \end{array}$$
adamc@701	2094
adamc@701	2095 The current thread can be paused for at least a specified number of milliseconds.
adamc@701	2096 $$\begin{array}{l}
adamc@701	2097 \mt{val} \; \mt{sleep} : \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@701	2098 \end{array}$$
adamc@701	2099
adam@1770	2100 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	2101 $$\begin{array}{l}
adamc@787	2102 \mt{val} \; \mt{onError} : (\mt{xbody} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787	2103 \mt{val} \; \mt{onFail} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787	2104 \mt{val} \; \mt{onConnectFail} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787	2105 \mt{val} \; \mt{onDisconnect} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787	2106 \mt{val} \; \mt{onServerError} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit}
adamc@787	2107 \end{array}$$
adamc@787	2108
adam@1555	2109 There are also functions to register standard document-level event handlers.
adam@1555	2110
adam@1555	2111 $$\begin{array}{l}
adam@1783	2112 \mt{val} \; \mt{onClick} : (\mt{mouseEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783	2113 \mt{val} \; \mt{onDblclick} : (\mt{mouseEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783	2114 \mt{val} \; \mt{onKeydown} : (\mt{keyEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783	2115 \mt{val} \; \mt{onKeypress} : (\mt{keyEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783	2116 \mt{val} \; \mt{onKeyup} : (\mt{keyEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783	2117 \mt{val} \; \mt{onMousedown} : (\mt{mouseEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783	2118 \mt{val} \; \mt{onMouseup} : (\mt{mouseEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit}
adam@1555	2119 \end{array}$$
adam@1555	2120
adam@1559	2121 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	2122
adam@1559	2123 $$\begin{array}{l}
adam@1559	2124 \mt{val} \; \mt{preventDefault} : \mt{transaction} \; \mt{unit} \\
adam@1559	2125 \mt{val} \; \mt{stopPropagation} : \mt{transaction} \; \mt{unit}
adam@1559	2126 \end{array}$$
adam@1559	2127
adam@1926	2128 Finally, here is an HTML tag to leave a marker in the \cd{<head>} of a document asking for some side-effecting code to be run. This pattern is \emph{much} less common in Ur/Web applications than in normal HTML/JavaScript applications; see Section \ref{signals} for the more idiomatic, functional way of manipulating the visible page.
adam@1926	2129
adam@1926	2130 $$\begin{array}{l}
adam@1926	2131 \mt{val} \; \mt{script} : \mt{unit} \to \mt{tag} \; [\mt{Code} = \mt{transaction} \; \mt{unit}] \; \mt{head} \; [] \; [] \; []
adam@1926	2132 \end{array}$$
adam@1926	2133
adam@1926	2134 Note that the Ur/Web version of \cd{<script>} is used like \cd{<script code=\{...\}/>}, rather than \cd{<script>...</script>}.
adam@1926	2135
adam@1556	2136 \subsubsection{Node IDs}
adam@1556	2137
adam@1556	2138 There is an abstract type of node IDs that may be assigned to \cd{id} attributes of most HTML tags.
adam@1556	2139
adam@1556	2140 $$\begin{array}{l}
adam@1556	2141 \mt{type} \; \mt{id} \\
adam@1556	2142 \mt{val} \; \mt{fresh} : \mt{transaction} \; \mt{id}
adam@1556	2143 \end{array}$$
adam@1556	2144
adam@1785	2145 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 main 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@1785	2146
adam@1785	2147 One further use of IDs is as handles for requesting that \emph{focus} be given to specific tags.
adam@1785	2148
adam@1785	2149 $$\begin{array}{l}
adam@1785	2150 \mt{val} \; \mt{giveFocus} : \mt{id} \to \mt{transaction} \; \mt{unit}
adam@1785	2151 \end{array}$$
adam@1556	2152
adam@1643	2153 \subsubsection{\label{signals}Functional-Reactive Page Generation}
adamc@701	2154
adamc@701	2155 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	2156
adam@1403	2157 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	2158
adamc@659	2159 $$\begin{array}{l}
adamc@659	2160 \mt{con} \; \mt{source} :: \mt{Type} \to \mt{Type} \\
adamc@659	2161 \mt{val} \; \mt{source} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{transaction} \; (\mt{source} \; \mt{t}) \\
adamc@659	2162 \mt{val} \; \mt{set} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@659	2163 \mt{val} \; \mt{get} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@659	2164 \end{array}$$
adamc@659	2165
adam@1400	2166 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	2167
adam@1608	2168 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	2169
adamc@659	2170 $$\begin{array}{l}
adamc@659	2171 \mt{con} \; \mt{signal} :: \mt{Type} \to \mt{Type} \\
adamc@659	2172 \mt{val} \; \mt{signal\_monad} : \mt{monad} \; \mt{signal} \\
adam@1608	2173 \mt{val} \; \mt{signal} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{signal} \; \mt{t} \\
adam@1608	2174 \mt{val} \; \mt{current} : \mt{t} ::: \mt{Type} \to \mt{signal} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@659	2175 \end{array}$$
adamc@659	2176
adamc@659	2177 A reactive portion of an HTML page is injected with a $\mt{dyn}$ tag, which has a signal-valued attribute $\mt{Signal}$.
adamc@659	2178
adamc@659	2179 $$\begin{array}{l}
adam@1641	2180 \mt{val} \; \mt{dyn} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to [\mt{ctx} \sim [\mt{Dyn}]] \Rightarrow \mt{unit} \\
adam@1641	2181 \hspace{.1in} \to \mt{tag} \; [\mt{Signal} = \mt{signal} \; (\mt{xml} \; ([\mt{Dyn}] \rc \mt{ctx}) \; \mt{use} \; \mt{bind})] \; ([\mt{Dyn}] \rc \mt{ctx}) \; [] \; \mt{use} \; \mt{bind}
adamc@659	2182 \end{array}$$
adamc@659	2183
adam@1648	2184 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	2185
adam@1648	2186 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	2187
adam@1786	2188 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. It is also possible to create an ``active'' HTML fragment that runs a $\mt{transaction}$ to determine its content, possibly allocating some sources in the process:
adam@1786	2189
adam@1786	2190 $$\begin{array}{l}
adam@1786	2191 \mt{val} \; \mt{active} : \mt{unit} \to \mt{tag} \; [\mt{Code} = \mt{transaction} \; \mt{xbody}] \; \mt{body} \; [] \; [] \; []
adam@1786	2192 \end{array}$$
adamc@701	2193
adamc@914	2194 \subsubsection{Remote Procedure Calls}
adamc@914	2195
adamc@914	2196 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	2197
adamc@914	2198 $$\begin{array}{l}
adamc@914	2199 \mt{val} \; \mt{rpc} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@914	2200 \end{array}$$
adamc@914	2201
adam@1848	2202 There is an alternate form that uses $\mt{None}$ to indicate that an error occurred during RPC processing, rather than raising an exception to abort this branch of control flow.
adam@1848	2203
adam@1848	2204 $$\begin{array}{l}
adam@1848	2205 \mt{val} \; \mt{tryRpc} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; \mt{t} \to \mt{transaction} \; (\mt{option} \; \mt{t})
adam@1848	2206 \end{array}$$
adam@1848	2207
adamc@701	2208 \subsubsection{Asynchronous Message-Passing}
adamc@701	2209
adamc@701	2210 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	2211
adamc@701	2212 $$\begin{array}{l}
adamc@701	2213 \mt{type} \; \mt{client} \\
adamc@701	2214 \mt{val} \; \mt{self} : \mt{transaction} \; \mt{client}
adamc@701	2215 \end{array}$$
adamc@701	2216
adam@1940	2217 \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. Note that here \emph{client} has a technical Ur/Web meaning so that it describes only \emph{single page views}, so a user following a traditional link within an application will remove the ability for \emph{any} code to receive messages on the channels associated with the previous client. 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	2218
adamc@701	2219 $$\begin{array}{l}
adamc@701	2220 \mt{con} \; \mt{channel} :: \mt{Type} \to \mt{Type} \\
adamc@701	2221 \mt{val} \; \mt{channel} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; (\mt{channel} \; \mt{t}) \\
adamc@701	2222 \mt{val} \; \mt{send} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@701	2223 \mt{val} \; \mt{recv} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@701	2224 \end{array}$$
adamc@701	2225
adamc@701	2226 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	2227
adamc@701	2228 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	2229
adam@1551	2230 \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	2231
adamc@659	2232
adamc@549	2233 \section{Ur/Web Syntax Extensions}
adamc@549	2234
adamc@549	2235 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	2236
adamc@549	2237 \subsection{SQL}
adamc@549	2238
adamc@786	2239 \subsubsection{\label{tables}Table Declarations}
adamc@786	2240
adamc@788	2241 $\mt{table}$ declarations may include constraints, via these grammar rules.
adamc@788	2242 $$\begin{array}{rrcll}
adam@1594	2243 \textrm{Declarations} & d &::=& \mt{table} \; x : c \; [pk[,]] \; cts \mid \mt{view} \; x = V \\
adamc@788	2244 \textrm{Primary key constraints} & pk &::=& \mt{PRIMARY} \; \mt{KEY} \; K \\
adam@1722	2245 \textrm{Keys} & K &::=& f \mid (f, (f,)^+) \mid \{\{e\}\} \\
adamc@788	2246 \textrm{Constraint sets} & cts &::=& \mt{CONSTRAINT} f \; ct \mid cts, cts \mid \{\{e\}\} \\
adamc@788	2247 \textrm{Constraints} & ct &::=& \mt{UNIQUE} \; K \mid \mt{CHECK} \; E \\
adamc@788	2248 &&& \mid \mt{FOREIGN} \; \mt{KEY} \; K \; \mt{REFERENCES} \; F \; (K) \; [\mt{ON} \; \mt{DELETE} \; pr] \; [\mt{ON} \; \mt{UPDATE} \; pr] \\
adamc@788	2249 \textrm{Foreign tables} & F &::=& x \mid \{\{e\}\} \\
adam@1594	2250 \textrm{Propagation modes} & pr &::=& \mt{NO} \; \mt{ACTION} \mid \mt{RESTRICT} \mid \mt{CASCADE} \mid \mt{SET} \; \mt{NULL} \\
adam@1594	2251 \textrm{View expressions} & V &::=& Q \mid \{e\}
adamc@788	2252 \end{array}$$
adamc@788	2253
adamc@788	2254 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	2255
adamc@788	2256
adamc@549	2257 \subsubsection{Queries}
adamc@549	2258
adamc@550	2259 Queries $Q$ are added to the rules for expressions $e$.
adamc@550	2260
adamc@549	2261 $$\begin{array}{rrcll}
adam@1684	2262 \textrm{Queries} & Q &::=& (q \; [\mt{ORDER} \; \mt{BY} \; O] \; [\mt{LIMIT} \; N] \; [\mt{OFFSET} \; N]) \\
adamc@1085	2263 \textrm{Pre-queries} & q &::=& \mt{SELECT} \; [\mt{DISTINCT}] \; P \; \mt{FROM} \; F,^+ \; [\mt{WHERE} \; E] \; [\mt{GROUP} \; \mt{BY} \; p,^+] \; [\mt{HAVING} \; E] \\
adamc@1085	2264 &&& \mid q \; R \; q \mid \{\{\{e\}\}\} \\
adam@1684	2265 \textrm{Relational operators} & R &::=& \mt{UNION} \mid \mt{INTERSECT} \mid \mt{EXCEPT} \\
adam@2093	2266 \textrm{$\mt{ORDER \; BY}$ items} & O &::=& \mt{RANDOM} [()] \mid \hat{E} \; [o] \mid \hat{E} \; [o], O \mid \{\{\{e\}\}\}
adamc@549	2267 \end{array}$$
adamc@549	2268
adamc@549	2269 $$\begin{array}{rrcll}
adamc@549	2270 \textrm{Projections} & P &::=& \ast & \textrm{all columns} \\
adamc@549	2271 &&& p,^+ & \textrm{particular columns} \\
adamc@549	2272 \textrm{Pre-projections} & p &::=& t.f & \textrm{one column from a table} \\
adamc@558	2273 &&& t.\{\{c\}\} & \textrm{a record of columns from a table (of kind $\{\mt{Type}\}$)} \\
adam@1627	2274 &&& t.* & \textrm{all columns from a table} \\
adam@1778	2275 &&& \hat{E} \; [\mt{AS} \; f] & \textrm{expression column} \\
adamc@549	2276 \textrm{Table names} & t &::=& x & \textrm{constant table name (automatically capitalized)} \\
adamc@549	2277 &&& X & \textrm{constant table name} \\
adamc@549	2278 &&& \{\{c\}\} & \textrm{computed table name (of kind $\mt{Name}$)} \\
adamc@549	2279 \textrm{Column names} & f &::=& X & \textrm{constant column name} \\
adamc@549	2280 &&& \{c\} & \textrm{computed column name (of kind $\mt{Name}$)} \\
adamc@549	2281 \textrm{Tables} & T &::=& x & \textrm{table variable, named locally by its own capitalization} \\
adam@1756	2282 &&& x \; \mt{AS} \; X & \textrm{table variable, with local name} \\
adam@1756	2283 &&& x \; \mt{AS} \; \{c\} & \textrm{table variable, with computed local name} \\
adamc@549	2284 &&& \{\{e\}\} \; \mt{AS} \; t & \textrm{computed table expression, with local name} \\
adam@1756	2285 &&& \{\{e\}\} \; \mt{AS} \; \{c\} & \textrm{computed table expression, with computed local name} \\
adamc@1085	2286 \textrm{$\mt{FROM}$ items} & F &::=& T \mid \{\{e\}\} \mid F \; J \; \mt{JOIN} \; F \; \mt{ON} \; E \\
adamc@1085	2287 &&& \mid F \; \mt{CROSS} \; \mt{JOIN} \ F \\
adam@2031	2288 &&& \mid (Q) \; \mt{AS} \; t \mid (\{\{e\}\}) \; \mt{AS} \; t \\
adamc@1085	2289 \textrm{Joins} & J &::=& [\mt{INNER}] \\
adamc@1085	2290 &&& \mid [\mt{LEFT} \mid \mt{RIGHT} \mid \mt{FULL}] \; [\mt{OUTER}] \\
adam@1587	2291 \textrm{SQL expressions} & E &::=& t.f & \textrm{column references} \\
adamc@549	2292 &&& X & \textrm{named expression references} \\
adam@1490	2293 &&& \{[e]\} & \textrm{injected native Ur expressions} \\
adam@1778	2294 &&& \{e\} & \textrm{computed expressions, probably using $\mt{sql\_exp}$ directly} \\
adamc@549	2295 &&& \mt{TRUE} \mid \mt{FALSE} & \textrm{boolean constants} \\
adamc@549	2296 &&& \ell & \textrm{primitive type literals} \\
adamc@549	2297 &&& \mt{NULL} & \textrm{null value (injection of $\mt{None}$)} \\
adamc@549	2298 &&& E \; \mt{IS} \; \mt{NULL} & \textrm{nullness test} \\
adam@1602	2299 &&& \mt{COALESCE}(E, E) & \textrm{take first non-null value} \\
adamc@549	2300 &&& n & \textrm{nullary operators} \\
adamc@549	2301 &&& u \; E & \textrm{unary operators} \\
adamc@549	2302 &&& E \; b \; E & \textrm{binary operators} \\
adam@1778	2303 &&& \mt{COUNT}(\ast) & \textrm{count number of rows} \\
adam@1778	2304 &&& a(E) & \textrm{other aggregate function} \\
adam@1573	2305 &&& \mt{IF} \; E \; \mt{THEN} \; E \; \mt{ELSE} \; E & \textrm{conditional} \\
adam@1778	2306 &&& (Q) & \textrm{subquery (must return a single expression column)} \\
adamc@549	2307 &&& (E) & \textrm{explicit precedence} \\
adamc@549	2308 \textrm{Nullary operators} & n &::=& \mt{CURRENT\_TIMESTAMP} \\
adamc@549	2309 \textrm{Unary operators} & u &::=& \mt{NOT} \\
adam@1688	2310 \textrm{Binary operators} & b &::=& \mt{AND} \mid \mt{OR} \mid = \mid \neq \mid < \mid \leq \mid > \mid \geq \\
adamc@1188	2311 \textrm{Aggregate functions} & a &::=& \mt{COUNT} \mid \mt{AVG} \mid \mt{SUM} \mid \mt{MIN} \mid \mt{MAX} \\
adam@1543	2312 \textrm{Directions} & o &::=& \mt{ASC} \mid \mt{DESC} \mid \{e\} \\
adamc@549	2313 \textrm{SQL integer} & N &::=& n \mid \{e\} \\
adam@1778	2314 \textrm{Windowable expressions} & \hat{E} &::=& E \\
adam@1778	2315 &&& w \; [\mt{OVER} \; ( & \textrm{(Postgres only)} \\
adam@1778	2316 &&& \hspace{.1in} [\mt{PARTITION} \; \mt{BY} \; E] \\
adam@1778	2317 &&& \hspace{.1in} [\mt{ORDER} \; \mt{BY} \; O])] \\
adam@1778	2318 \textrm{Window function} & w &::=& \mt{RANK}() \\
adam@1778	2319 &&& \mt{COUNT}(*) \\
adam@1778	2320 &&& a(E)
adamc@549	2321 \end{array}$$
adamc@549	2322
adamc@1085	2323 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	2324
adam@1683	2325 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	2326
adamc@550	2327 \subsubsection{DML}
adamc@550	2328
adamc@550	2329 DML commands $D$ are added to the rules for expressions $e$.
adamc@550	2330
adamc@550	2331 $$\begin{array}{rrcll}
adamc@550	2332 \textrm{Commands} & D &::=& (\mt{INSERT} \; \mt{INTO} \; T^E \; (f,^+) \; \mt{VALUES} \; (E,^+)) \\
adamc@550	2333 &&& (\mt{UPDATE} \; T^E \; \mt{SET} \; (f = E,)^+ \; \mt{WHERE} \; E) \\
adamc@550	2334 &&& (\mt{DELETE} \; \mt{FROM} \; T^E \; \mt{WHERE} \; E) \\
adamc@550	2335 \textrm{Table expressions} & T^E &::=& x \mid \{\{e\}\}
adamc@550	2336 \end{array}$$
adamc@550	2337
adamc@550	2338 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	2339
adamc@551	2340 \subsection{XML}
adamc@551	2341
adamc@551	2342 XML fragments $L$ are added to the rules for expressions $e$.
adamc@551	2343
adamc@551	2344 $$\begin{array}{rrcll}
adamc@551	2345 \textrm{XML fragments} & L &::=& \texttt{<xml/>} \mid \texttt{<xml>}l^*\texttt{</xml>} \\
adamc@551	2346 \textrm{XML pieces} & l &::=& \textrm{text} & \textrm{cdata} \\
adamc@551	2347 &&& \texttt{<}g\texttt{/>} & \textrm{tag with no children} \\
adamc@551	2348 &&& \texttt{<}g\texttt{>}l^*\texttt{</}x\texttt{>} & \textrm{tag with children} \\
adamc@559	2349 &&& \{e\} & \textrm{computed XML fragment} \\
adamc@559	2350 &&& \{[e]\} & \textrm{injection of an Ur expression, via the $\mt{Top}.\mt{txt}$ function} \\
adam@2075	2351 \textrm{Tag} & g &::=& h \; (x [= v])^* \\
adamc@551	2352 \textrm{Tag head} & h &::=& x & \textrm{tag name} \\
adamc@551	2353 &&& h\{c\} & \textrm{constructor parameter} \\
adamc@551	2354 \textrm{Attribute value} & v &::=& \ell & \textrm{literal value} \\
adamc@551	2355 &&& \{e\} & \textrm{computed value} \\
adamc@551	2356 \end{array}$$
adamc@551	2357
adam@2075	2358 When the optional $= v$ is omitted in an XML attribute, the attribute is assigned value $\mt{True}$ in Ur/Web, and it is rendered to HTML merely as including the attribute name without a value. If such a Boolean attribute is manually set to value $\mt{False}$, then it is omitted altogether in generating HTML.
adam@2075	2359
adam@1751	2360 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	2361
adam@1751	2362 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	2363
adamc@1198	2364 \section{\label{structure}The Structure of Web Applications}
adamc@553	2365
adam@1797	2366 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	2367
adam@1532	2368 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	2369
adam@1787	2370 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 should not be used with forms that exist solely within Ur/Web apps; for these, use Ur/Web's built-in support, as described below. It may still be useful to use $\mt{Basis.postBody}$ with form requests submitted by code outside an Ur/Web app. For such cases, the function $\mt{Top.postFields} : \mt{postBody} \to \mt{list} \; (\mt{string} \times \mt{string})$ may be useful, breaking a \texttt{POST} body of type \texttt{application/x-www-form-urlencoded} into its name-value pairs.
adam@1347	2371
adam@1370	2372 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	2373
adamc@553	2374 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	2375
adamc@553	2376 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	2377
adam@1653	2378 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	2379 \begin{itemize}
adam@1653	2380 \item Functions are disallowed, since there is no obvious way to serialize them safely.
adam@1653	2381 \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	2382 \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	2383 \end{itemize}
adamc@553	2384
adamc@660	2385 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	2386
adamc@789	2387 \medskip
adamc@789	2388
adam@1347	2389 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	2390
adamc@789	2391 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	2392
adam@1348	2393 \subsection{Tasks}
adam@1348	2394
adam@1348	2395 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	2396
adam@1348	2397 $$\begin{array}{l}
adam@1348	2398 \mt{con} \; \mt{task\_kind} :: \mt{Type} \to \mt{Type} \\
adam@1348	2399 \mt{val} \; \mt{initialize} : \mt{task\_kind} \; \mt{unit} \\
adam@1349	2400 \mt{val} \; \mt{clientLeaves} : \mt{task\_kind} \; \mt{client} \\
adam@1349	2401 \mt{val} \; \mt{periodic} : \mt{int} \to \mt{task\_kind} \; \mt{unit}
adam@1348	2402 \end{array}$$
adam@1348	2403
adam@1348	2404 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	2405
adam@1348	2406 The currently supported task kinds are:
adam@1348	2407 \begin{itemize}
adam@1349	2408 \item $\mt{initialize}$: Code that is run when the application starts up.
adam@1348	2409 \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	2410 \item $\mt{periodic} \; n$: Code that is run when the application starts up and then every $n$ seconds thereafter.
adam@1348	2411 \end{itemize}
adam@1348	2412
adamc@553	2413
adam@2008	2414 \section{\label{ffi}The Foreign Function Interface}
adamc@897	2415
adamc@897	2416 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	2417
adamc@897	2418 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	2419
adamc@897	2420 \begin{itemize}
adamc@897	2421 \item \texttt{clientOnly Module.ident} registers a value as being allowed only in client-side code.
adamc@897	2422 \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@1878	2423 \item \texttt{effectful Module.ident} registers a function that can have side effects. This is the default for \texttt{transaction}-based types, and, actually, this directive is mostly present for legacy compatibility reasons, since it used to be required explicitly for each \texttt{transaction}al function.
adamc@897	2424 \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	2425 \item \texttt{include FILE} requests inclusion of a C header file.
adamc@897	2426 \item \texttt{jsFunc Module.ident=name} gives a mapping from an Ur name for a value to a JavaScript name.
adamc@897	2427 \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	2428 \item \texttt{script URL} requests inclusion of a JavaScript source file within application HTML.
adamc@897	2429 \item \texttt{serverOnly Module.ident} registers a value as being allowed only in server-side code.
adamc@897	2430 \end{itemize}
adamc@897	2431
adamc@897	2432 \subsection{Writing C FFI Code}
adamc@897	2433
adam@1881	2434 C source files connecting to the Ur/Web FFI should include \texttt{urweb.h}, and C++ source files should include \texttt{urweb\_cpp.h}.
adam@1881	2435
adamc@897	2436 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	2437
adamc@897	2438 \begin{itemize}
adam@1881	2439 \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/urweb/types.h} for their definitions.
adamc@897	2440 \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	2441 \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	2442 \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	2443 \end{itemize}
adamc@897	2444
adam@1881	2445 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/urweb\_cpp.h}. Most should only be used internally by the compiler. A few are useful in general FFI implementation:
adamc@897	2446 \begin{itemize}
adamc@897	2447 \item \begin{verbatim}
adamc@897	2448 void uw_error(uw_context, failure_kind, const char *fmt, ...);
adamc@897	2449 \end{verbatim}
adamc@897	2450 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	2451
adam@1329	2452 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	2453
adamc@897	2454 \item \begin{verbatim}
adam@1469	2455 void uw_set_error_message(uw_context, const char *fmt, ...);
adam@1469	2456 \end{verbatim}
adam@1469	2457 This simpler form of \texttt{uw\_error()} saves an error message without immediately aborting execution.
adam@1469	2458
adam@1469	2459 \item \begin{verbatim}
adamc@897	2460 void uw_push_cleanup(uw_context, void (func)(void ), void *arg);
adamc@897	2461 void uw_pop_cleanup(uw_context);
adamc@897	2462 \end{verbatim}
adam@1329	2463 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	2464
adam@1329	2465 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	2466
adamc@897	2467 \item \begin{verbatim}
adamc@897	2468 void *uw_malloc(uw_context, size_t);
adamc@897	2469 \end{verbatim}
adam@1329	2470 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	2471
adam@1329	2472 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	2473
adamc@897	2474 \item \begin{verbatim}
adamc@897	2475 typedef void (uw_callback)(void );
adam@1328	2476 typedef void (uw_callback_with_retry)(void , int will_retry);
adam@2001	2477 int uw_register_transactional(uw_context, void *data, uw_callback commit,
adam@2001	2478 uw_callback rollback, uw_callback_with_retry free);
adamc@897	2479 \end{verbatim}
adam@2001	2480 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. The return value of \texttt{uw\_register\_transactional()} is 0 on success and nonzero on failure (where failure currently only happens when exceeding configured limits on number of transactionals).
adamc@897	2481
adam@2000	2482 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. Furthermore, an SQL \texttt{COMMIT} is also attempted in between the two phases, so the nicely transactional actions have a chance to influence whether data are committed to the database, while \texttt{NULL}-rollback actions only get run in the first place after committing data. The reason for all this is that it is \emph{expected} that concurrency interactions will cause database commits to fail in benign ways that call for transaction restart. A truly non-undoable action should only be run after we are sure the database transaction will commit.
adamc@1085	2483
adam@1329	2484 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	2485
adam@1329	2486 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	2487
adam@1469	2488 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	2489
adamc@1085	2490 \item \begin{verbatim}
adamc@1085	2491 void uw_get_global(uw_context, char name);
adamc@1085	2492 void uw_set_global(uw_context, char name, void data, uw_callback free);
adamc@1085	2493 \end{verbatim}
adam@1329	2494 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	2495
adamc@897	2496 \end{itemize}
adamc@897	2497
adamc@897	2498 \subsection{Writing JavaScript FFI Code}
adamc@897	2499
adamc@897	2500 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	2501
adamc@897	2502 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	2503
adamc@897	2504 \begin{itemize}
adamc@897	2505 \item Integers, floats, strings, characters, and booleans are represented in the usual JavaScript way.
adam@1996	2506 \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)}. A normal JavaScript function may also be used in a position where the Ur/Web runtime system expects an Ur/Web function.
adamc@897	2507 \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	2508 \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	2509 \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	2510 \item As in the C FFI, all abstract types of program syntax are implemented with strings in JavaScript.
adam@1996	2511 \item A value of Ur type \texttt{transaction t} is represented in the same way as for \texttt{unit -> t}. (Note that FFI functions skip this extra level of function encoding, which only applies to functions defined in Ur/Web.)
adamc@897	2512 \end{itemize}
adamc@897	2513
adam@1644	2514 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	2515
adam@1644	2516 \begin{itemize}
adam@1644	2517 \item Sources should be treated as an abstract type, manipulated via:
adam@1644	2518 \begin{itemize}
adam@1644	2519 \item \cd{sc(v)}, to create a source initialized to \cd{v}
adam@1644	2520 \item \cd{sg(s)}, to retrieve the current value of source \cd{s}
adam@1644	2521 \item \cd{sv(s, v)}, to set source \cd{s} to value \cd{v}
adam@1644	2522 \end{itemize}
adam@1644	2523
adam@1644	2524 \item Signals should be treated as an abstract type, manipulated via:
adam@1644	2525 \begin{itemize}
adam@1644	2526 \item \cd{sr(v)} and \cd{sb(s, f)}, the ``return'' and ``bind'' monad operators, respectively
adam@1644	2527 \item \cd{ss(s)}, to produce the signal corresponding to source \cd{s}
adam@1644	2528 \item \cd{scur(s)}, to get the current value of signal \cd{s}
adam@1644	2529 \end{itemize}
adam@1644	2530
adam@1644	2531 \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	2532
adam@1702	2533 \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	2534
adam@1644	2535 \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	2536 \end{itemize}
adamc@897	2537
adam@1833	2538 \subsection{Introducing New HTML Tags}
adam@1833	2539
adam@1833	2540 FFI modules may introduce new tags as values with $\mt{Basis.tag}$ types. See \texttt{basis.urs} for examples of how tags are declared. The identifier of a tag value is used as its rendering in HTML. The Ur/Web syntax sugar for XML literals desugars each use of a tag into a reference to an identifier with the same name. There is no need to provide implementations (i.e., in C or JavaScript code) for such identifiers.
adam@1833	2541
adam@1833	2542 The onus is on the coder of a new tag's interface to think about consequences for code injection attacks, messing with the DOM in ways that may break Ur/Web reactive programming, etc.
adam@1833	2543
adam@2010	2544 \subsection{The Less Safe FFI}
adam@2010	2545
adam@2010	2546 An alternative interface is provided for declaring FFI functions inline within normal Ur/Web modules. This facility must be opted into with the \texttt{lessSafeFfi} \texttt{.urp} directive, since it breaks a crucial property, allowing code in a \texttt{.ur} file to break basic invariants of the Ur/Web type system. Without this option, one only needs to audit \texttt{.urp} files to be sure an application obeys the type-system rules. The alternative interface may be more convenient for such purposes as declaring an FFI function typed in terms of some type local to a module.
adam@2010	2547
adam@2010	2548 When the less safe mode is enabled, declarations like this one are accepted, at the top level of a \texttt{.ur} file:
adam@2010	2549 \begin{verbatim}
adam@2010	2550 ffi foo : int -> int
adam@2010	2551 \end{verbatim}
adam@2010	2552
adam@2010	2553 Now \texttt{foo} is available as a normal function. If called in server-side code, and if the above declaration appeared in \texttt{bar.ur}, the C function will be linked as \texttt{uw\_Bar\_foo()}. It is also possible to declare an FFI function to be implemented in JavaScript, using a general facility for including modifiers in an FFI declaration. The modifiers appear before the colon, separated by spaces. Here are the available ones, which have the same semantics as corresponding \texttt{.urp} directives.
adam@2010	2554 \begin{itemize}
adam@2010	2555 \item \texttt{effectful}
adam@2010	2556 \item \texttt{benignEffectful}
adam@2010	2557 \item \texttt{clientOnly}
adam@2010	2558 \item \texttt{serverOnly}
adam@2010	2559 \item \texttt{jsFunc "putJsFuncNameHere"}
adam@2010	2560 \end{itemize}
adam@2010	2561
adam@2039	2562 When no \texttt{jsFunc} directive is present, the function is assumed to map to a JavaScript function of the same name, if used in a client-side context.
adam@2039	2563
adamc@897	2564
adam@2042	2565 \section{\label{phases}Compiler Phases}
adam@2042	2566
adam@2042	2567 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. Also, this warning only applies to server-side code, as client-side code runs in a normal JavaScript environment with garbage collection.
adamc@552	2568
adamc@552	2569 In this section, we step through the main phases of compilation, noting what consequences each phase has for effective programming.
adamc@552	2570
adamc@552	2571 \subsection{Parse}
adamc@552	2572
adamc@552	2573 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	2574
adamc@552	2575 \subsection{Elaborate}
adamc@552	2576
adamc@552	2577 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	2578
adam@1378	2579 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	2580
adamc@552	2581 \subsection{Unnest}
adamc@552	2582
adamc@552	2583 Named local function definitions are moved to the top level, to avoid the need to generate closures.
adamc@552	2584
adamc@552	2585 \subsection{Corify}
adamc@552	2586
adamc@552	2587 Module system features are compiled away, through inlining of functor definitions at application sites. Afterward, most abstraction boundaries are broken, facilitating optimization.
adamc@552	2588
adamc@552	2589 \subsection{Especialize}
adamc@552	2590
adam@1356	2591 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	2592
adamc@552	2593 \subsection{Untangle}
adamc@552	2594
adam@1797	2595 Remove unnecessary mutual recursion, splitting recursive groups into strongly connected components.
adamc@552	2596
adamc@552	2597 \subsection{Shake}
adamc@552	2598
adamc@552	2599 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	2600
adamc@661	2601 \subsection{Rpcify}
adamc@661	2602
adamc@661	2603 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	2604
adamc@661	2605 \subsection{Untangle, Shake}
adamc@661	2606
adamc@661	2607 Repeat these simplifications.
adamc@661	2608
adamc@553	2609 \subsection{\label{tag}Tag}
adamc@552	2610
adamc@552	2611 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	2612
adamc@552	2613 \subsection{Reduce}
adamc@552	2614
adamc@552	2615 Apply definitional equality rules to simplify the program as much as possible. This effectively includes inlining of every non-recursive definition.
adamc@552	2616
adamc@552	2617 \subsection{Unpoly}
adamc@552	2618
adamc@552	2619 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	2620
adamc@552	2621 \subsection{Specialize}
adamc@552	2622
adamc@558	2623 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	2624
adamc@552	2625 \subsection{Shake}
adamc@552	2626
adamc@558	2627 Here the compiler repeats the earlier Shake phase.
adamc@552	2628
adamc@552	2629 \subsection{Monoize}
adamc@552	2630
adamc@552	2631 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	2632
adamc@552	2633 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	2634
adamc@552	2635 \subsection{MonoOpt}
adamc@552	2636
adamc@552	2637 Simple algebraic laws are applied to simplify the program, focusing especially on efficient imperative generation of HTML pages.
adamc@552	2638
adamc@552	2639 \subsection{MonoUntangle}
adamc@552	2640
adamc@552	2641 Unnecessary mutual recursion is broken up again.
adamc@552	2642
adamc@552	2643 \subsection{MonoReduce}
adamc@552	2644
adamc@552	2645 Equivalents of the definitional equality rules are applied to simplify programs, with inlining again playing a major role.
adamc@552	2646
adamc@552	2647 \subsection{MonoShake, MonoOpt}
adamc@552	2648
adamc@552	2649 Unneeded declarations are removed, and basic optimizations are repeated.
adamc@552	2650
adamc@552	2651 \subsection{Fuse}
adamc@552	2652
adamc@552	2653 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	2654
adamc@552	2655 \subsection{MonoUntangle, MonoShake}
adamc@552	2656
adamc@552	2657 Fuse often creates more opportunities to remove spurious mutual recursion.
adamc@552	2658
adamc@552	2659 \subsection{Pathcheck}
adamc@552	2660
adamc@552	2661 The compiler checks that no link or action name has been used more than once.
adamc@552	2662
adamc@552	2663 \subsection{Cjrize}
adamc@552	2664
adamc@552	2665 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	2666
adamc@552	2667 \subsection{C Compilation and Linking}
adamc@552	2668
adam@1523	2669 The output of the last phase is pretty-printed as C source code and passed to the C compiler.
adamc@552	2670
adamc@552	2671
as@1564	2672 \end{document}

Mercurial > urweb

annotate doc/manual.tex @ 2094:0d898b086bbe