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author	Adam Chlipala <adam@chlipala.net>
date	Sat, 05 Dec 2015 12:12:40 -0500
parents	3acaaff30c85
children	9083b44bad0a

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} + \;}
adam@2107	9 \newcommand{\rcut}{\; \texttt{-{}-} \;}
adam@2107	10 \newcommand{\rcutM}{\; \texttt{-{}-{}-} \;}
adamc@524	11
julian@2134	12 \usepackage{hyperref}
julian@2134	13
adamc@524	14 \begin{document}
adamc@524	15
adamc@524	16 \title{The Ur/Web Manual}
adamc@524	17 \author{Adam Chlipala}
adamc@524	18
adamc@524	19 \maketitle
adamc@524	20
adamc@540	21 \tableofcontents
adamc@540	22
adamc@554	23
adamc@554	24 \section{Introduction}
adamc@554	25
adam@1797	26 \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	27
adamc@554	28 \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	29
adamc@554	30 \begin{itemize}
adamc@554	31 \item Suffer from any kinds of code-injection attacks
adamc@554	32 \item Return invalid HTML
adamc@554	33 \item Contain dead intra-application links
adamc@554	34 \item Have mismatches between HTML forms and the fields expected by their handlers
adamc@652	35 \item Include client-side code that makes incorrect assumptions about the ``AJAX''-style services that the remote web server provides
adamc@554	36 \item Attempt invalid SQL queries
adamc@652	37 \item Use improper marshaling or unmarshaling in communication with SQL databases or between browsers and web servers
adamc@554	38 \end{itemize}
adamc@554	39
adamc@554	40 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	41
adamc@652	42 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	43
adamc@554	44 \medskip
adamc@554	45
adamc@554	46 The official web site for Ur is:
adamc@554	47 \begin{center}
adamc@554	48 \url{http://www.impredicative.com/ur/}
adamc@554	49 \end{center}
adamc@554	50
adamc@555	51
adamc@555	52 \section{Installation}
adamc@555	53
adamc@555	54 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	55
adamc@555	56 \begin{verbatim}
adamc@555	57 ./configure
adamc@555	58 make
adamc@555	59 sudo make install
adamc@555	60 \end{verbatim}
adamc@555	61
adam@1523	62 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	63 \begin{verbatim}
adam@1368	64 apt-get install mlton libssl-dev
adamc@896	65 \end{verbatim}
adamc@555	66
adam@2016	67 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	68
adamc@896	69 To build programs that access SQL databases, you also need one of these client libraries for supported backends.
adamc@555	70 \begin{verbatim}
adam@1960	71 apt-get install libpq-dev libmysqlclient-dev libsqlite3-dev
adamc@555	72 \end{verbatim}
adamc@555	73
adamc@555	74 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	75 \begin{verbatim}
adamc@555	76 apt-get install smlnj libsmlnj-smlnj ml-yacc ml-lpt
adamc@555	77 \end{verbatim}
adamc@555	78
adam@2016	79 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	80
adamc@896	81 To run an SQL-backed application with a backend besides SQLite, you will probably want to install one of these servers.
adamc@555	82
adamc@555	83 \begin{verbatim}
adam@1960	84 apt-get install postgresql mysql-server
adamc@555	85 \end{verbatim}
adamc@555	86
adamc@555	87 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	88
adamc@555	89 \begin{verbatim}
adamc@555	90 apt-get install emacs-goodies-el
adamc@555	91 \end{verbatim}
adamc@555	92
adam@1441	93 If you don't want to install the Emacs mode, run \texttt{./configure} with the argument \texttt{--without-emacs}.
adam@1441	94
adam@1523	95 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	96
adamc@555	97 \begin{verbatim}
adam@1523	98 CCARGS=-fno-inline ./configure
adamc@555	99 \end{verbatim}
adamc@555	100
adam@1523	101 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	102
adamc@555	103 The Emacs mode can be set to autoload by adding the following to your \texttt{.emacs} file.
adamc@555	104
adamc@555	105 \begin{verbatim}
adamc@555	106 (add-to-list 'load-path "/usr/local/share/emacs/site-lisp/urweb-mode")
adamc@555	107 (load "urweb-mode-startup")
adamc@555	108 \end{verbatim}
adamc@555	109
adamc@555	110 Change the path in the first line if you chose a different Emacs installation path during configuration.
adamc@555	111
adamc@555	112
adamc@556	113 \section{Command-Line Compiler}
adamc@556	114
adam@1604	115 \subsection{\label{cl}Project Files}
adamc@556	116
adamc@556	117 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	118
adamc@556	119 \begin{verbatim}
adamc@556	120 database dbname=test
adamc@556	121 sql crud1.sql
adamc@556	122
adamc@556	123 crud
adamc@556	124 crud1
adamc@556	125 \end{verbatim}
adamc@556	126
adamc@556	127 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	128
adamc@556	129 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	130
adamc@556	131 \begin{verbatim}
adamc@556	132 createdb test
adamc@556	133 psql -f crud1.sql test
adamc@556	134 \end{verbatim}
adamc@556	135
adam@1331	136 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	137
adamc@556	138 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	139
adamc@783	140 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	141 \begin{itemize}
adam@1799	142 \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	143 \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	144 \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	145 \item \texttt{clientOnly Module.ident} registers an FFI function or transaction that may only be run in client browsers.
adam@1881	146 \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	147 \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	148 \item \texttt{database DBSTRING} sets the string to pass to libpq to open a database connection.
adamc@783	149 \item \texttt{debug} saves some intermediate C files, which is mostly useful to help in debugging the compiler itself.
adam@1878	150 \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	151 \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	152 \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	153 \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	154 \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	155 \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.
adam@2198	156 \item \texttt{jsFile FILENAME} asks to serve the contents of a file as JavaScript. All such content is concatenated into a single file, included via a \texttt{<script>} tag on every page that needs client-side scripting.
adamc@783	157 \item \texttt{jsFunc Module.ident=name} gives the JavaScript name of an FFI value.
adamc@1089	158 \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	159 \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	160 \begin{itemize}
adam@1309	161 \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	162 \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	163 \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	164 \item \texttt{deltas}: maximum number of messages sendable in a single request handler with \texttt{Basis.send}
adam@1309	165 \item \texttt{globals}: maximum number of global variables that FFI libraries may set in a single request context
adam@1309	166 \item \texttt{headers}: maximum size (in bytes) of per-request buffer used to hold HTTP headers for generated pages
adam@1797	167 \item \texttt{heap}: maximum size (in bytes) of per-request heap for dynamically allocated data
adam@1309	168 \item \texttt{inputs}: maximum number of top-level form fields per request
adam@1309	169 \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	170 \item \texttt{page}: maximum size (in bytes) of per-request buffer used to hold HTML content of generated pages
adam@1309	171 \item \texttt{script}: maximum size (in bytes) of per-request buffer used to hold JavaScript content of generated pages
adam@1309	172 \item \texttt{subinputs}: maximum number of form fields per request, excluding top-level fields
adam@1309	173 \item \texttt{time}: maximum running time of a single page request, in units of approximately 0.1 seconds
adam@1309	174 \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	175 \end{itemize}
adam@1523	176 \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	177 \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	178 \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	179 \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	180 \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	181 \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	182 \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	183 \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	184 \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	185 \item \texttt{prefix PREFIX} sets the prefix included before every URI within the generated application. The default is \texttt{/}.
adamc@783	186 \item \texttt{profile} generates an executable that may be used with gprof.
adam@1752	187 \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	188 \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	189 \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	190 \item \texttt{serverOnly Module.ident} registers an FFI function or transaction that may only be run on the server.
adamc@1164	191 \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	192 \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	193 \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	194 \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	195 \end{itemize}
adamc@701	196
adamc@701	197
adamc@557	198 \subsection{Building an Application}
adamc@557	199
adamc@557	200 To compile project \texttt{P.urp}, simply run
adamc@557	201 \begin{verbatim}
adamc@557	202 urweb P
adamc@557	203 \end{verbatim}
adamc@1198	204 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	205
adamc@557	206 To time how long the different compiler phases run, without generating an executable, run
adamc@557	207 \begin{verbatim}
adamc@557	208 urweb -timing P
adamc@557	209 \end{verbatim}
adamc@557	210
adamc@1086	211 To stop the compilation process after type-checking, run
adamc@1086	212 \begin{verbatim}
adamc@1086	213 urweb -tc P
adamc@1086	214 \end{verbatim}
adam@1530	215 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	216
adam@1745	217 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	218
adam@1723	219 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	220
adamc@1170	221 To output information relevant to CSS stylesheets (and not finish regular compilation), run
adamc@1170	222 \begin{verbatim}
adamc@1170	223 urweb -css P
adamc@1170	224 \end{verbatim}
adamc@1170	225 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	226
adam@1733	227 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	228 \begin{verbatim}
adam@1733	229 urweb daemon start
adam@1733	230 \end{verbatim}
adam@1733	231 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	232 \begin{verbatim}
adam@1733	233 urweb daemon stop
adam@1733	234 \end{verbatim}
adam@1733	235 Communication happens via a UNIX domain socket in file \cd{.urweb\_daemon} in the working directory.
adam@1733	236
adam@1733	237 \medskip
adam@1733	238
adamc@896	239 Some other command-line parameters are accepted:
adamc@896	240 \begin{itemize}
ezyang@1739	241 \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	242
adam@1875	243 \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	244
adamc@896	245 \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	246
adamc@896	247 \item \texttt{-dbms [postgres\|mysql\|sqlite]}: Sets the database backend to use.
adamc@896	248 \begin{itemize}
adamc@896	249 \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	250
adamc@896	251 A command sequence like this can initialize a Postgres database, using a file \texttt{app.sql} generated by the compiler:
adamc@896	252 \begin{verbatim}
adamc@896	253 createdb app
adamc@896	254 psql -f app.sql app
adamc@896	255 \end{verbatim}
adamc@896	256
adamc@896	257 \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	258
adamc@896	259 A command sequence like this can initialize a MySQL database:
adamc@896	260 \begin{verbatim}
adamc@896	261 echo "CREATE DATABASE app" \| mysql
adamc@896	262 mysql -D app <app.sql
adamc@896	263 \end{verbatim}
adamc@896	264
adamc@896	265 \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	266
adamc@896	267 A command like this can initialize an SQLite database:
adamc@896	268 \begin{verbatim}
adamc@896	269 sqlite3 path/to/database/file <app.sql
adamc@896	270 \end{verbatim}
adamc@896	271 \end{itemize}
adamc@896	272
adam@1693	273 \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	274
adam@1995	275 \item \texttt{-explainEmbed}: Trigger more verbose error messages about inability to embed server-side values in client-side code.
adam@1995	276
adam@1309	277 \item \texttt{-limit class num}: Equivalent to the \texttt{limit} directive from \texttt{.urp} files
adam@1309	278
adam@1850	279 \item \texttt{-moduleOf FILENAME}: Prints the Ur/Web module name corresponding to source file \texttt{FILENAME}, exiting immediately afterward.
adam@1850	280
adamc@896	281 \item \texttt{-output FILENAME}: Set where the application executable is written.
adamc@896	282
adamc@1127	283 \item \texttt{-path NAME VALUE}: Set the value of path variable \texttt{\$NAME} to \texttt{VALUE}, for use in \texttt{.urp} files.
adamc@1127	284
adam@1335	285 \item \texttt{-prefix PREFIX}: Equivalent to the \texttt{prefix} directive from \texttt{.urp} files
adam@1335	286
adam@1875	287 \item \texttt{-print-ccompiler}: Print the C compiler being used.
adam@1875	288
adam@1923	289 \item \texttt{-print-cinclude}: Print the name of the directory where C/C++ header files are installed.
adam@1923	290
adam@1753	291 \item \texttt{-protocol [http\|cgi\|fastcgi\|static]}: Set the protocol that the generated application speaks.
adamc@896	292 \begin{itemize}
adamc@896	293 \item \texttt{http}: This is the default. It is for building standalone web servers that can be accessed by web browsers directly.
adamc@896	294
adamc@896	295 \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	296
adamc@896	297 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	298 \begin{verbatim}
adamc@896	299 ScriptAlias /Hello /path/to/hello.exe
adamc@896	300 \end{verbatim}
adamc@896	301
adamc@1163	302 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	303 \begin{verbatim}
adamc@1163	304 Options +ExecCGI
adamc@1163	305 AddHandler cgi-script .exe
adamc@1163	306 \end{verbatim}
adamc@1163	307
adamc@1163	308 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	309 \begin{verbatim}
adamc@1163	310 prefix /dir/script.exe/
adamc@1163	311 \end{verbatim}
adamc@1163	312
adamc@1163	313 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	314
adamc@1164	315 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	316
adamc@896	317 \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	318
adamc@896	319 To configure a FastCGI program with Apache, one could combine the above \texttt{ScriptAlias} line with a line like this:
adamc@896	320 \begin{verbatim}
adamc@896	321 FastCgiServer /path/to/hello.exe -idle-timeout 99999
adamc@896	322 \end{verbatim}
adamc@896	323 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	324
adam@1753	325 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	326
adamc@896	327 Here is some lighttpd configuration for the same application.
adamc@896	328 \begin{verbatim}
adamc@896	329 fastcgi.server = (
adamc@896	330 "/Hello/" =>
adamc@896	331 (( "bin-path" => "/path/to/hello.exe",
adamc@896	332 "socket" => "/tmp/hello",
adamc@896	333 "check-local" => "disable",
adamc@896	334 "docroot" => "/",
adamc@896	335 "max-procs" => "1"
adamc@896	336 ))
adamc@896	337 )
adamc@896	338 \end{verbatim}
adamc@896	339 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	340
adamc@896	341 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	342
adam@1509	343 \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	344 \end{itemize}
adamc@896	345
adamc@1127	346 \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	347
adamc@1164	348 \item \texttt{-sigfile PATH}: Same as the \texttt{sigfile} directive in \texttt{.urp} files
adamc@1164	349
adamc@896	350 \item \texttt{-sql FILENAME}: Set where a database set-up SQL script is written.
adamc@1095	351
adamc@1095	352 \item \texttt{-static}: Link the runtime system statically. The default is to link against dynamic libraries.
adam@1961	353
adam@1961	354 \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	355 \end{itemize}
adamc@896	356
adam@1297	357 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	358
adam@1509	359 \subsection{Tutorial Formatting}
adam@1509	360
adam@1509	361 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	362
adam@1509	363 These input files follow normal Ur syntax, with a few exceptions:
adam@1509	364 \begin{itemize}
adam@1509	365 \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	366 \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	367 \item A comment like \cd{(* * HEADING *)} introduces a section heading, with text \cd{HEADING} of your choice.
adam@1509	368 \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	369 \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	370 \end{itemize}
adam@1509	371
adam@1509	372 A word of warning: as for demo generation, tutorial generation calls Emacs to syntax-highlight Ur code.
adam@1509	373
adam@1522	374 \subsection{Run-Time Options}
adam@1522	375
adam@1522	376 Compiled applications consult a few environment variables to modify their behavior:
adam@1522	377
adam@1522	378 \begin{itemize}
adam@1522	379 \item \cd{URWEB\_NUM\_THREADS}: alternative to the \cd{-t} command-line argument (currently used only by FastCGI)
adam@1522	380 \item \cd{URWEB\_STACK\_SIZE}: size of per-thread stacks, in bytes
as@1564	381 \item \cd{URWEB\_PQ\_CON}: when using PostgreSQL, overrides the compiled-in connection string
adam@1522	382 \end{itemize}
adam@1522	383
adam@2042	384 \subsection{A Word of Warning on Heuristic Compilation}
adam@2042	385
adam@2042	386 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	387
adam@1509	388
adamc@529	389 \section{Ur Syntax}
adamc@529	390
adamc@784	391 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	392
adamc@524	393 \subsection{Lexical Conventions}
adamc@524	394
adamc@524	395 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	396
adamc@524	397 \begin{center}
adamc@524	398 \begin{tabular}{rl}
adamc@524	399 \textbf{\LaTeX} & \textbf{ASCII} \\
adamc@524	400 $\to$ & \cd{->} \\
adam@1687	401 $\longrightarrow$ & \cd{-{}->} \\
adamc@524	402 $\times$ & \cd{*} \\
adamc@524	403 $\lambda$ & \cd{fn} \\
adamc@524	404 $\Rightarrow$ & \cd{=>} \\
adamc@652	405 $\Longrightarrow$ & \cd{==>} \\
adamc@529	406 $\neq$ & \cd{<>} \\
adamc@529	407 $\leq$ & \cd{<=} \\
adamc@529	408 $\geq$ & \cd{>=} \\
adamc@524	409 \\
adamc@524	410 $x$ & Normal textual identifier, not beginning with an uppercase letter \\
adamc@525	411 $X$ & Normal textual identifier, beginning with an uppercase letter \\
adamc@524	412 \end{tabular}
adamc@524	413 \end{center}
adamc@524	414
adamc@525	415 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	416
adamc@873	417 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	418
adamc@527	419 This version of the manual doesn't include operator precedences; see \texttt{src/urweb.grm} for that.
adamc@527	420
adam@1297	421 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	422
adamc@552	423 \subsection{\label{core}Core Syntax}
adamc@524	424
adamc@524	425 \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	426 $$\begin{array}{rrcll}
adamc@524	427 \textrm{Kinds} & \kappa &::=& \mt{Type} & \textrm{proper types} \\
adamc@525	428 &&& \mt{Unit} & \textrm{the trivial constructor} \\
adamc@525	429 &&& \mt{Name} & \textrm{field names} \\
adamc@525	430 &&& \kappa \to \kappa & \textrm{type-level functions} \\
adamc@525	431 &&& \{\kappa\} & \textrm{type-level records} \\
adamc@525	432 &&& (\kappa\times^+) & \textrm{type-level tuples} \\
adamc@652	433 &&& X & \textrm{variable} \\
adam@1574	434 &&& X \longrightarrow \kappa & \textrm{kind-polymorphic type-level function} \\
adamc@529	435 &&& \_\_ & \textrm{wildcard} \\
adamc@525	436 &&& (\kappa) & \textrm{explicit precedence} \\
adamc@524	437 \end{array}$$
adamc@524	438
adamc@524	439 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	440 $$\begin{array}{rrcll}
adamc@524	441 \textrm{Explicitness} & ? &::=& :: & \textrm{explicit} \\
adamc@558	442 &&& ::: & \textrm{implicit}
adamc@524	443 \end{array}$$
adamc@524	444
adamc@524	445 \emph{Constructors} are the main class of compile-time-only data. They include proper types and are classified by kinds.
adamc@524	446 $$\begin{array}{rrcll}
adamc@524	447 \textrm{Constructors} & c, \tau &::=& (c) :: \kappa & \textrm{kind annotation} \\
adamc@530	448 &&& \hat{x} & \textrm{constructor variable} \\
adamc@524	449 \\
adamc@525	450 &&& \tau \to \tau & \textrm{function type} \\
adamc@525	451 &&& x \; ? \; \kappa \to \tau & \textrm{polymorphic function type} \\
adamc@652	452 &&& X \longrightarrow \tau & \textrm{kind-polymorphic function type} \\
adamc@525	453 &&& \$ c & \textrm{record type} \\
adamc@524	454 \\
adamc@525	455 &&& c \; c & \textrm{type-level function application} \\
adamc@530	456 &&& \lambda x \; :: \; \kappa \Rightarrow c & \textrm{type-level function abstraction} \\
adamc@524	457 \\
adamc@652	458 &&& X \Longrightarrow c & \textrm{type-level kind-polymorphic function abstraction} \\
adamc@655	459 &&& c [\kappa] & \textrm{type-level kind-polymorphic function application} \\
adamc@652	460 \\
adamc@525	461 &&& () & \textrm{type-level unit} \\
adamc@525	462 &&& \#X & \textrm{field name} \\
adamc@524	463 \\
adamc@525	464 &&& [(c = c)^*] & \textrm{known-length type-level record} \\
adamc@525	465 &&& c \rc c & \textrm{type-level record concatenation} \\
adamc@652	466 &&& \mt{map} & \textrm{type-level record map} \\
adamc@524	467 \\
adamc@558	468 &&& (c,^+) & \textrm{type-level tuple} \\
adamc@525	469 &&& c.n & \textrm{type-level tuple projection ($n \in \mathbb N^+$)} \\
adamc@524	470 \\
adamc@652	471 &&& [c \sim c] \Rightarrow \tau & \textrm{guarded type} \\
adamc@524	472 \\
adamc@529	473 &&& \_ :: \kappa & \textrm{wildcard} \\
adamc@525	474 &&& (c) & \textrm{explicit precedence} \\
adamc@530	475 \\
adamc@530	476 \textrm{Qualified uncapitalized variables} & \hat{x} &::=& x & \textrm{not from a module} \\
adamc@530	477 &&& M.x & \textrm{projection from a module} \\
adamc@525	478 \end{array}$$
adamc@525	479
adam@1579	480 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	481
adamc@525	482 Modules of the module system are described by \emph{signatures}.
adamc@525	483 $$\begin{array}{rrcll}
adamc@525	484 \textrm{Signatures} & S &::=& \mt{sig} \; s^* \; \mt{end} & \textrm{constant} \\
adamc@525	485 &&& X & \textrm{variable} \\
adamc@525	486 &&& \mt{functor}(X : S) : S & \textrm{functor} \\
adamc@529	487 &&& S \; \mt{where} \; \mt{con} \; x = c & \textrm{concretizing an abstract constructor} \\
adamc@525	488 &&& M.X & \textrm{projection from a module} \\
adamc@525	489 \\
adamc@525	490 \textrm{Signature items} & s &::=& \mt{con} \; x :: \kappa & \textrm{abstract constructor} \\
adamc@525	491 &&& \mt{con} \; x :: \kappa = c & \textrm{concrete constructor} \\
adamc@528	492 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529	493 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@525	494 &&& \mt{val} \; x : \tau & \textrm{value} \\
adamc@525	495 &&& \mt{structure} \; X : S & \textrm{sub-module} \\
adamc@525	496 &&& \mt{signature} \; X = S & \textrm{sub-signature} \\
adamc@525	497 &&& \mt{include} \; S & \textrm{signature inclusion} \\
adamc@525	498 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@654	499 &&& \mt{class} \; x :: \kappa & \textrm{abstract constructor class} \\
adamc@654	500 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@525	501 \\
adamc@525	502 \textrm{Datatype constructors} & dc &::=& X & \textrm{nullary constructor} \\
adamc@525	503 &&& X \; \mt{of} \; \tau & \textrm{unary constructor} \\
adamc@524	504 \end{array}$$
adamc@524	505
adamc@526	506 \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	507 $$\begin{array}{rrcll}
adamc@526	508 \textrm{Patterns} & p &::=& \_ & \textrm{wildcard} \\
adamc@526	509 &&& x & \textrm{variable} \\
adamc@526	510 &&& \ell & \textrm{constant} \\
adamc@526	511 &&& \hat{X} & \textrm{nullary constructor} \\
adamc@526	512 &&& \hat{X} \; p & \textrm{unary constructor} \\
adam@2155	513 &&& \{(X = p,)^*\} & \textrm{rigid record pattern} \\
adam@2155	514 &&& \{(X = p,)^+, \ldots\} & \textrm{flexible record pattern} \\
adamc@852	515 &&& p : \tau & \textrm{type annotation} \\
adamc@527	516 &&& (p) & \textrm{explicit precedence} \\
adamc@526	517 \\
adamc@529	518 \textrm{Qualified capitalized variables} & \hat{X} &::=& X & \textrm{not from a module} \\
adamc@526	519 &&& M.X & \textrm{projection from a module} \\
adamc@526	520 \end{array}$$
adamc@526	521
adamc@527	522 \emph{Expressions} are the main run-time entities, corresponding to both ``expressions'' and ``statements'' in mainstream imperative languages.
adamc@527	523 $$\begin{array}{rrcll}
adamc@527	524 \textrm{Expressions} & e &::=& e : \tau & \textrm{type annotation} \\
adamc@529	525 &&& \hat{x} & \textrm{variable} \\
adamc@529	526 &&& \hat{X} & \textrm{datatype constructor} \\
adamc@527	527 &&& \ell & \textrm{constant} \\
adamc@527	528 \\
adamc@527	529 &&& e \; e & \textrm{function application} \\
adamc@527	530 &&& \lambda x : \tau \Rightarrow e & \textrm{function abstraction} \\
adamc@527	531 &&& e [c] & \textrm{polymorphic function application} \\
adamc@852	532 &&& \lambda [x \; ? \; \kappa] \Rightarrow e & \textrm{polymorphic function abstraction} \\
adamc@655	533 &&& e [\kappa] & \textrm{kind-polymorphic function application} \\
adamc@652	534 &&& X \Longrightarrow e & \textrm{kind-polymorphic function abstraction} \\
adamc@527	535 \\
adamc@527	536 &&& \{(c = e,)^*\} & \textrm{known-length record} \\
adamc@527	537 &&& e.c & \textrm{record field projection} \\
adamc@527	538 &&& e \rc e & \textrm{record concatenation} \\
adamc@527	539 &&& e \rcut c & \textrm{removal of a single record field} \\
adamc@527	540 &&& e \rcutM c & \textrm{removal of multiple record fields} \\
adamc@527	541 \\
adamc@527	542 &&& \mt{let} \; ed^* \; \mt{in} \; e \; \mt{end} & \textrm{local definitions} \\
adamc@527	543 \\
adamc@527	544 &&& \mt{case} \; e \; \mt{of} \; (p \Rightarrow e\|)^+ & \textrm{pattern matching} \\
adamc@527	545 \\
adamc@654	546 &&& \lambda [c \sim c] \Rightarrow e & \textrm{guarded expression abstraction} \\
adamc@654	547 &&& e \; ! & \textrm{guarded expression application} \\
adamc@527	548 \\
adamc@527	549 &&& \_ & \textrm{wildcard} \\
adamc@527	550 &&& (e) & \textrm{explicit precedence} \\
adamc@527	551 \\
adamc@527	552 \textrm{Local declarations} & ed &::=& \cd{val} \; x : \tau = e & \textrm{non-recursive value} \\
adam@1797	553 &&& \cd{val} \; \cd{rec} \; (x : \tau = e \; \cd{and})^+ & \textrm{mutually recursive values} \\
adamc@527	554 \end{array}$$
adamc@527	555
adamc@655	556 As with constructors, we include both abstraction and application for kind polymorphism, but applications are only inferred internally.
adamc@655	557
adamc@528	558 \emph{Declarations} primarily bring new symbols into context.
adamc@528	559 $$\begin{array}{rrcll}
adamc@528	560 \textrm{Declarations} & d &::=& \mt{con} \; x :: \kappa = c & \textrm{constructor synonym} \\
adamc@528	561 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529	562 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@528	563 &&& \mt{val} \; x : \tau = e & \textrm{value} \\
adam@1797	564 &&& \mt{val} \; \cd{rec} \; (x : \tau = e \; \mt{and})^+ & \textrm{mutually recursive values} \\
adamc@528	565 &&& \mt{structure} \; X : S = M & \textrm{module definition} \\
adamc@528	566 &&& \mt{signature} \; X = S & \textrm{signature definition} \\
adamc@528	567 &&& \mt{open} \; M & \textrm{module inclusion} \\
adamc@528	568 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@528	569 &&& \mt{open} \; \mt{constraints} \; M & \textrm{inclusion of just the constraints from a module} \\
adamc@528	570 &&& \mt{table} \; x : c & \textrm{SQL table} \\
adam@1594	571 &&& \mt{view} \; x = e & \textrm{SQL view} \\
adamc@528	572 &&& \mt{sequence} \; x & \textrm{SQL sequence} \\
adamc@535	573 &&& \mt{cookie} \; x : \tau & \textrm{HTTP cookie} \\
adamc@784	574 &&& \mt{style} \; x : \tau & \textrm{CSS class} \\
adamc@1085	575 &&& \mt{task} \; e = e & \textrm{recurring task} \\
adamc@528	576 \\
adamc@529	577 \textrm{Modules} & M &::=& \mt{struct} \; d^* \; \mt{end} & \textrm{constant} \\
adamc@529	578 &&& X & \textrm{variable} \\
adamc@529	579 &&& M.X & \textrm{projection} \\
adamc@529	580 &&& M(M) & \textrm{functor application} \\
adamc@529	581 &&& \mt{functor}(X : S) : S = M & \textrm{functor abstraction} \\
adamc@528	582 \end{array}$$
adamc@528	583
adamc@528	584 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	585
adam@1594	586 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	587
adamc@529	588 \subsection{Shorthands}
adamc@529	589
adamc@529	590 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	591
adamc@529	592 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	593
adamc@529	594 A record type may be written $\{(c = c,)^\}$, which elaborates to $\$[(c = c,)^]$.
adamc@529	595
adamc@533	596 The notation $[c_1, \ldots, c_n]$ is shorthand for $[c_1 = (), \ldots, c_n = ()]$.
adamc@533	597
adam@1350	598 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	599
adam@1687	600 The syntax $()$ expands to $\{\}$ as a pattern or expression.
adam@1687	601
adamc@852	602 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	603
adam@1574	604 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	605
adam@1306	606 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	607
adamc@529	608 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	609
adamc@529	610 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	611
adamc@654	612 A signature item or declaration $\mt{class} \; x = \lambda y \Rightarrow c$ may be abbreviated $\mt{class} \; x \; y = c$.
adamc@529	613
adam@1738	614 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	615
adamc@852	616 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	617
adamc@852	618 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	619
adam@1797	620 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	621
adamc@529	622 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	623
adamc@852	624 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	625
adamc@853	626 A declaration $\mt{table} \; x : \{(c = c,)^\}$ is elaborated into $\mt{table} \; x : [(c = c,)^]$.
adamc@529	627
adamc@529	628 The syntax $\mt{where} \; \mt{type}$ is an alternate form of $\mt{where} \; \mt{con}$.
adamc@529	629
adamc@529	630 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	631
adamc@529	632 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	633
adamc@784	634 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	635
adam@2025	636 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	637
adam@2123	638 Ur/Web also includes a few more infix operators: $f \; \texttt{<\|} \; x$ desugars to $f \; x$, $x \; \texttt{\|>} \; f$ to $f \; x$, $f \; \texttt{<{}<{}<} \; g$ to $\mt{Top}.\mt{compose} \; f \; g$, and $g \; \texttt{>{}>{}>} \; f$ to $\mt{Top}.\mt{compose} \; f \; g$. (The latter two are doing function composition in the usual way.) Furthermore, any identifier may be changed into an infix operator by placing it between backticks, e.g. a silly way to do addition is $x \; \texttt{`}\mt{plus}\texttt{`} \; y$ instead of $x + y$.
adam@2123	639
adam@2125	640 Hexadecimal integer literals are supported like \texttt{0xDEADBEEF}. Only capital letters are allowed.
adam@2125	641
adamc@530	642
adamc@530	643 \section{Static Semantics}
adamc@530	644
adamc@530	645 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	646
adam@1891	647 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	648 \begin{quote}
adam@1891	649 Benjamin C. Pierce, \emph{Types and Programming Languages}, MIT Press, 2002.
adam@1891	650 \end{quote}
adam@1891	651
adamc@530	652 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	653 \begin{itemize}
adamc@655	654 \item $\Gamma \vdash \kappa$ expresses kind well-formedness.
adamc@530	655 \item $\Gamma \vdash c :: \kappa$ assigns a kind to a constructor in a context.
adamc@530	656 \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	657 \item $\Gamma \vdash c \hookrightarrow C$ proves that record constructor $c$ decomposes into set $C$ of field names and record constructors.
adamc@530	658 \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	659 \item $\Gamma \vdash e : \tau$ is a standard typing judgment.
adamc@534	660 \item $\Gamma \vdash p \leadsto \Gamma; \tau$ combines typing of patterns with calculation of which new variables they bind.
adamc@537	661 \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	662 \item $\Gamma \vdash S \equiv S$ is the signature equivalence judgment.
adamc@536	663 \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	664 \item $\Gamma \vdash M : S$ is the module signature checking judgment.
adamc@537	665 \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	666 \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	667 \end{itemize}
adamc@530	668
adamc@655	669
adamc@655	670 \subsection{Kind Well-Formedness}
adamc@655	671
adamc@655	672 $$\infer{\Gamma \vdash \mt{Type}}{}
adamc@655	673 \quad \infer{\Gamma \vdash \mt{Unit}}{}
adamc@655	674 \quad \infer{\Gamma \vdash \mt{Name}}{}
adamc@655	675 \quad \infer{\Gamma \vdash \kappa_1 \to \kappa_2}{
adamc@655	676 \Gamma \vdash \kappa_1
adamc@655	677 & \Gamma \vdash \kappa_2
adamc@655	678 }
adamc@655	679 \quad \infer{\Gamma \vdash \{\kappa\}}{
adamc@655	680 \Gamma \vdash \kappa
adamc@655	681 }
adamc@655	682 \quad \infer{\Gamma \vdash (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@655	683 \forall i: \Gamma \vdash \kappa_i
adamc@655	684 }$$
adamc@655	685
adamc@655	686 $$\infer{\Gamma \vdash X}{
adamc@655	687 X \in \Gamma
adamc@655	688 }
adamc@655	689 \quad \infer{\Gamma \vdash X \longrightarrow \kappa}{
adamc@655	690 \Gamma, X \vdash \kappa
adamc@655	691 }$$
adamc@655	692
adamc@530	693 \subsection{Kinding}
adamc@530	694
adamc@655	695 We write $[X \mapsto \kappa_1]\kappa_2$ for capture-avoiding substitution of $\kappa_1$ for $X$ in $\kappa_2$.
adamc@655	696
adamc@530	697 $$\infer{\Gamma \vdash (c) :: \kappa :: \kappa}{
adamc@530	698 \Gamma \vdash c :: \kappa
adamc@530	699 }
adamc@530	700 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530	701 x :: \kappa \in \Gamma
adamc@530	702 }
adamc@530	703 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530	704 x :: \kappa = c \in \Gamma
adamc@530	705 }$$
adamc@530	706
adamc@530	707 $$\infer{\Gamma \vdash M.x :: \kappa}{
adamc@537	708 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	709 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = \kappa
adamc@530	710 }
adamc@530	711 \quad \infer{\Gamma \vdash M.x :: \kappa}{
adamc@537	712 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	713 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@530	714 }$$
adamc@530	715
adamc@530	716 $$\infer{\Gamma \vdash \tau_1 \to \tau_2 :: \mt{Type}}{
adamc@530	717 \Gamma \vdash \tau_1 :: \mt{Type}
adamc@530	718 & \Gamma \vdash \tau_2 :: \mt{Type}
adamc@530	719 }
adamc@530	720 \quad \infer{\Gamma \vdash x \; ? \: \kappa \to \tau :: \mt{Type}}{
adamc@530	721 \Gamma, x :: \kappa \vdash \tau :: \mt{Type}
adamc@530	722 }
adamc@655	723 \quad \infer{\Gamma \vdash X \longrightarrow \tau :: \mt{Type}}{
adamc@655	724 \Gamma, X \vdash \tau :: \mt{Type}
adamc@655	725 }
adamc@530	726 \quad \infer{\Gamma \vdash \$c :: \mt{Type}}{
adamc@530	727 \Gamma \vdash c :: \{\mt{Type}\}
adamc@530	728 }$$
adamc@530	729
adamc@530	730 $$\infer{\Gamma \vdash c_1 \; c_2 :: \kappa_2}{
adamc@530	731 \Gamma \vdash c_1 :: \kappa_1 \to \kappa_2
adamc@530	732 & \Gamma \vdash c_2 :: \kappa_1
adamc@530	733 }
adamc@530	734 \quad \infer{\Gamma \vdash \lambda x \; :: \; \kappa_1 \Rightarrow c :: \kappa_1 \to \kappa_2}{
adamc@530	735 \Gamma, x :: \kappa_1 \vdash c :: \kappa_2
adamc@530	736 }$$
adamc@530	737
adamc@655	738 $$\infer{\Gamma \vdash c[\kappa'] :: [X \mapsto \kappa']\kappa}{
adamc@655	739 \Gamma \vdash c :: X \to \kappa
adamc@655	740 & \Gamma \vdash \kappa'
adamc@655	741 }
adamc@655	742 \quad \infer{\Gamma \vdash X \Longrightarrow c :: X \to \kappa}{
adamc@655	743 \Gamma, X \vdash c :: \kappa
adamc@655	744 }$$
adamc@655	745
adamc@530	746 $$\infer{\Gamma \vdash () :: \mt{Unit}}{}
adamc@530	747 \quad \infer{\Gamma \vdash \#X :: \mt{Name}}{}$$
adamc@530	748
adamc@530	749 $$\infer{\Gamma \vdash [\overline{c_i = c'_i}] :: \{\kappa\}}{
adamc@530	750 \forall i: \Gamma \vdash c_i : \mt{Name}
adamc@530	751 & \Gamma \vdash c'_i :: \kappa
adamc@530	752 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@530	753 }
adamc@530	754 \quad \infer{\Gamma \vdash c_1 \rc c_2 :: \{\kappa\}}{
adamc@530	755 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530	756 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@530	757 & \Gamma \vdash c_1 \sim c_2
adamc@530	758 }$$
adamc@530	759
adamc@655	760 $$\infer{\Gamma \vdash \mt{map} :: (\kappa_1 \to \kappa_2) \to \{\kappa_1\} \to \{\kappa_2\}}{}$$
adamc@530	761
adamc@573	762 $$\infer{\Gamma \vdash (\overline c) :: (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@573	763 \forall i: \Gamma \vdash c_i :: \kappa_i
adamc@530	764 }
adamc@573	765 \quad \infer{\Gamma \vdash c.i :: \kappa_i}{
adamc@573	766 \Gamma \vdash c :: (\kappa_1 \times \ldots \times \kappa_n)
adamc@530	767 }$$
adamc@530	768
adamc@655	769 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow \tau :: \mt{Type}}{
adamc@655	770 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530	771 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@655	772 & \Gamma, c_1 \sim c_2 \vdash \tau :: \mt{Type}
adamc@530	773 }$$
adamc@530	774
adamc@531	775 \subsection{Record Disjointness}
adamc@531	776
adamc@531	777 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@558	778 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@558	779 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@558	780 & \forall c'_1 \in C_1, c'_2 \in C_2: \Gamma \vdash c'_1 \sim c'_2
adamc@531	781 }
adamc@531	782 \quad \infer{\Gamma \vdash X \sim X'}{
adamc@531	783 X \neq X'
adamc@531	784 }$$
adamc@531	785
adamc@531	786 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@531	787 c'_1 \sim c'_2 \in \Gamma
adamc@558	788 & \Gamma \vdash c'_1 \hookrightarrow C_1
adamc@558	789 & \Gamma \vdash c'_2 \hookrightarrow C_2
adamc@558	790 & c_1 \in C_1
adamc@558	791 & c_2 \in C_2
adamc@531	792 }$$
adamc@531	793
adamc@531	794 $$\infer{\Gamma \vdash c \hookrightarrow \{c\}}{}
adamc@531	795 \quad \infer{\Gamma \vdash [\overline{c = c'}] \hookrightarrow \{\overline{c}\}}{}
adamc@531	796 \quad \infer{\Gamma \vdash c_1 \rc c_2 \hookrightarrow C_1 \cup C_2}{
adamc@531	797 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@531	798 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@531	799 }
adamc@531	800 \quad \infer{\Gamma \vdash c \hookrightarrow C}{
adamc@531	801 \Gamma \vdash c \equiv c'
adamc@531	802 & \Gamma \vdash c' \hookrightarrow C
adamc@531	803 }
adamc@531	804 \quad \infer{\Gamma \vdash \mt{map} \; f \; c \hookrightarrow C}{
adamc@531	805 \Gamma \vdash c \hookrightarrow C
adamc@531	806 }$$
adamc@531	807
adamc@541	808 \subsection{\label{definitional}Definitional Equality}
adamc@532	809
adamc@655	810 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	811
adamc@532	812 $$\infer{\Gamma \vdash c \equiv c}{}
adamc@532	813 \quad \infer{\Gamma \vdash c_1 \equiv c_2}{
adamc@532	814 \Gamma \vdash c_2 \equiv c_1
adamc@532	815 }
adamc@532	816 \quad \infer{\Gamma \vdash c_1 \equiv c_3}{
adamc@532	817 \Gamma \vdash c_1 \equiv c_2
adamc@532	818 & \Gamma \vdash c_2 \equiv c_3
adamc@532	819 }
adamc@532	820 \quad \infer{\Gamma \vdash \mathcal C[c_1] \equiv \mathcal C[c_2]}{
adamc@532	821 \Gamma \vdash c_1 \equiv c_2
adamc@532	822 }$$
adamc@532	823
adamc@532	824 $$\infer{\Gamma \vdash x \equiv c}{
adamc@532	825 x :: \kappa = c \in \Gamma
adamc@532	826 }
adamc@532	827 \quad \infer{\Gamma \vdash M.x \equiv c}{
adamc@537	828 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	829 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@532	830 }
adamc@532	831 \quad \infer{\Gamma \vdash (\overline c).i \equiv c_i}{}$$
adamc@532	832
adamc@532	833 $$\infer{\Gamma \vdash (\lambda x :: \kappa \Rightarrow c) \; c' \equiv [x \mapsto c'] c}{}
adamc@655	834 \quad \infer{\Gamma \vdash (X \Longrightarrow c) [\kappa] \equiv [X \mapsto \kappa] c}{}$$
adamc@655	835
adamc@655	836 $$\infer{\Gamma \vdash c_1 \rc c_2 \equiv c_2 \rc c_1}{}
adamc@532	837 \quad \infer{\Gamma \vdash c_1 \rc (c_2 \rc c_3) \equiv (c_1 \rc c_2) \rc c_3}{}$$
adamc@532	838
adamc@532	839 $$\infer{\Gamma \vdash [] \rc c \equiv c}{}
adamc@532	840 \quad \infer{\Gamma \vdash [\overline{c_1 = c'_1}] \rc [\overline{c_2 = c'_2}] \equiv [\overline{c_1 = c'_1}, \overline{c_2 = c'_2}]}{}$$
adamc@532	841
adamc@655	842 $$\infer{\Gamma \vdash \mt{map} \; f \; [] \equiv []}{}
adamc@655	843 \quad \infer{\Gamma \vdash \mt{map} \; f \; ([c_1 = c_2] \rc c) \equiv [c_1 = f \; c_2] \rc \mt{map} \; f \; c}{}$$
adamc@532	844
adamc@532	845 $$\infer{\Gamma \vdash \mt{map} \; (\lambda x \Rightarrow x) \; c \equiv c}{}
adamc@655	846 \quad \infer{\Gamma \vdash \mt{map} \; f \; (\mt{map} \; f' \; c)
adamc@655	847 \equiv \mt{map} \; (\lambda x \Rightarrow f \; (f' \; x)) \; c}{}$$
adamc@532	848
adamc@532	849 $$\infer{\Gamma \vdash \mt{map} \; f \; (c_1 \rc c_2) \equiv \mt{map} \; f \; c_1 \rc \mt{map} \; f \; c_2}{}$$
adamc@531	850
adamc@534	851 \subsection{Expression Typing}
adamc@533	852
adamc@873	853 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	854
adamc@533	855 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	856
adamc@533	857 $$\infer{\Gamma \vdash e : \tau : \tau}{
adamc@533	858 \Gamma \vdash e : \tau
adamc@533	859 }
adamc@533	860 \quad \infer{\Gamma \vdash e : \tau}{
adamc@533	861 \Gamma \vdash e : \tau'
adamc@533	862 & \Gamma \vdash \tau' \equiv \tau
adamc@533	863 }
adamc@533	864 \quad \infer{\Gamma \vdash \ell : T(\ell)}{}$$
adamc@533	865
adamc@533	866 $$\infer{\Gamma \vdash x : \mathcal I(\tau)}{
adamc@533	867 x : \tau \in \Gamma
adamc@533	868 }
adamc@533	869 \quad \infer{\Gamma \vdash M.x : \mathcal I(\tau)}{
adamc@537	870 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	871 & \mt{proj}(M, \overline{s}, \mt{val} \; x) = \tau
adamc@533	872 }
adamc@533	873 \quad \infer{\Gamma \vdash X : \mathcal I(\tau)}{
adamc@533	874 X : \tau \in \Gamma
adamc@533	875 }
adamc@533	876 \quad \infer{\Gamma \vdash M.X : \mathcal I(\tau)}{
adamc@537	877 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	878 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \tau
adamc@533	879 }$$
adamc@533	880
adamc@533	881 $$\infer{\Gamma \vdash e_1 \; e_2 : \tau_2}{
adamc@533	882 \Gamma \vdash e_1 : \tau_1 \to \tau_2
adamc@533	883 & \Gamma \vdash e_2 : \tau_1
adamc@533	884 }
adamc@533	885 \quad \infer{\Gamma \vdash \lambda x : \tau_1 \Rightarrow e : \tau_1 \to \tau_2}{
adamc@533	886 \Gamma, x : \tau_1 \vdash e : \tau_2
adamc@533	887 }$$
adamc@533	888
adamc@533	889 $$\infer{\Gamma \vdash e [c] : [x \mapsto c]\tau}{
adamc@533	890 \Gamma \vdash e : x :: \kappa \to \tau
adamc@533	891 & \Gamma \vdash c :: \kappa
adamc@533	892 }
adamc@852	893 \quad \infer{\Gamma \vdash \lambda [x \; ? \; \kappa] \Rightarrow e : x \; ? \; \kappa \to \tau}{
adamc@533	894 \Gamma, x :: \kappa \vdash e : \tau
adamc@533	895 }$$
adamc@533	896
adamc@655	897 $$\infer{\Gamma \vdash e [\kappa] : [X \mapsto \kappa]\tau}{
adamc@655	898 \Gamma \vdash e : X \longrightarrow \tau
adamc@655	899 & \Gamma \vdash \kappa
adamc@655	900 }
adamc@655	901 \quad \infer{\Gamma \vdash X \Longrightarrow e : X \longrightarrow \tau}{
adamc@655	902 \Gamma, X \vdash e : \tau
adamc@655	903 }$$
adamc@655	904
adamc@533	905 $$\infer{\Gamma \vdash \{\overline{c = e}\} : \{\overline{c : \tau}\}}{
adamc@533	906 \forall i: \Gamma \vdash c_i :: \mt{Name}
adamc@533	907 & \Gamma \vdash e_i : \tau_i
adamc@533	908 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@533	909 }
adamc@533	910 \quad \infer{\Gamma \vdash e.c : \tau}{
adamc@533	911 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533	912 }
adamc@533	913 \quad \infer{\Gamma \vdash e_1 \rc e_2 : \$(c_1 \rc c_2)}{
adamc@533	914 \Gamma \vdash e_1 : \$c_1
adamc@533	915 & \Gamma \vdash e_2 : \$c_2
adamc@573	916 & \Gamma \vdash c_1 \sim c_2
adamc@533	917 }$$
adamc@533	918
adamc@533	919 $$\infer{\Gamma \vdash e \rcut c : \$c'}{
adamc@533	920 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533	921 }
adamc@533	922 \quad \infer{\Gamma \vdash e \rcutM c : \$c'}{
adamc@533	923 \Gamma \vdash e : \$(c \rc c')
adamc@533	924 }$$
adamc@533	925
adamc@533	926 $$\infer{\Gamma \vdash \mt{let} \; \overline{ed} \; \mt{in} \; e \; \mt{end} : \tau}{
adamc@533	927 \Gamma \vdash \overline{ed} \leadsto \Gamma'
adamc@533	928 & \Gamma' \vdash e : \tau
adamc@533	929 }
adamc@533	930 \quad \infer{\Gamma \vdash \mt{case} \; e \; \mt{of} \; \overline{p \Rightarrow e} : \tau}{
adamc@533	931 \forall i: \Gamma \vdash p_i \leadsto \Gamma_i, \tau'
adamc@533	932 & \Gamma_i \vdash e_i : \tau
adamc@533	933 }$$
adamc@533	934
adamc@573	935 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow e : \lambda [c_1 \sim c_2] \Rightarrow \tau}{
adamc@533	936 \Gamma \vdash c_1 :: \{\kappa\}
adamc@655	937 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@533	938 & \Gamma, c_1 \sim c_2 \vdash e : \tau
adamc@662	939 }
adamc@662	940 \quad \infer{\Gamma \vdash e \; ! : \tau}{
adamc@662	941 \Gamma \vdash e : [c_1 \sim c_2] \Rightarrow \tau
adamc@662	942 & \Gamma \vdash c_1 \sim c_2
adamc@533	943 }$$
adamc@533	944
adamc@534	945 \subsection{Pattern Typing}
adamc@534	946
adamc@534	947 $$\infer{\Gamma \vdash \_ \leadsto \Gamma; \tau}{}
adamc@534	948 \quad \infer{\Gamma \vdash x \leadsto \Gamma, x : \tau; \tau}{}
adamc@534	949 \quad \infer{\Gamma \vdash \ell \leadsto \Gamma; T(\ell)}{}$$
adamc@534	950
adamc@534	951 $$\infer{\Gamma \vdash X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534	952 X : \overline{x ::: \mt{Type}} \to \tau \in \Gamma
adamc@534	953 & \textrm{$\tau$ not a function type}
adamc@534	954 }
adamc@534	955 \quad \infer{\Gamma \vdash X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534	956 X : \overline{x ::: \mt{Type}} \to \tau'' \to \tau \in \Gamma
adamc@534	957 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534	958 }$$
adamc@534	959
adamc@534	960 $$\infer{\Gamma \vdash M.X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537	961 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	962 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau
adamc@534	963 & \textrm{$\tau$ not a function type}
adamc@534	964 }$$
adamc@534	965
adamc@534	966 $$\infer{\Gamma \vdash M.X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537	967 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	968 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau'' \to \tau
adamc@534	969 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534	970 }$$
adamc@534	971
adam@2155	972 $$\infer{\Gamma \vdash \{\overline{X = p}\} \leadsto \Gamma_n; \{\overline{X = \tau}\}}{
adamc@534	973 \Gamma_0 = \Gamma
adamc@534	974 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534	975 }
adam@2155	976 \quad \infer{\Gamma \vdash \{\overline{X = p}, \ldots\} \leadsto \Gamma_n; \$([\overline{X = \tau}] \rc c)}{
adamc@534	977 \Gamma_0 = \Gamma
adamc@534	978 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534	979 }$$
adamc@534	980
adamc@852	981 $$\infer{\Gamma \vdash p : \tau \leadsto \Gamma'; \tau}{
adamc@852	982 \Gamma \vdash p \leadsto \Gamma'; \tau'
adamc@852	983 & \Gamma \vdash \tau' \equiv \tau
adamc@852	984 }$$
adamc@852	985
adamc@535	986 \subsection{Declaration Typing}
adamc@535	987
adamc@535	988 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	989
adamc@558	990 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	991 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	992
adamc@535	993 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535	994 \quad \infer{\Gamma \vdash d, \overline{d} \leadsto \Gamma''}{
adamc@535	995 \Gamma \vdash d \leadsto \Gamma'
adamc@535	996 & \Gamma' \vdash \overline{d} \leadsto \Gamma''
adamc@535	997 }$$
adamc@535	998
adamc@535	999 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@535	1000 \Gamma \vdash c :: \kappa
adamc@535	1001 }
adamc@535	1002 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@535	1003 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@535	1004 }$$
adamc@535	1005
adamc@535	1006 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537	1007 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1008 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@535	1009 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@535	1010 }$$
adamc@535	1011
adamc@535	1012 $$\infer{\Gamma \vdash \mt{val} \; x : \tau = e \leadsto \Gamma, x : \tau}{
adamc@535	1013 \Gamma \vdash e : \tau
adamc@535	1014 }$$
adamc@535	1015
adamc@535	1016 $$\infer{\Gamma \vdash \mt{val} \; \mt{rec} \; \overline{x : \tau = e} \leadsto \Gamma, \overline{x : \tau}}{
adamc@535	1017 \forall i: \Gamma, \overline{x : \tau} \vdash e_i : \tau_i
adamc@535	1018 & \textrm{$e_i$ starts with an expression $\lambda$, optionally preceded by constructor and disjointness $\lambda$s}
adamc@535	1019 }$$
adamc@535	1020
adamc@535	1021 $$\infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : S}{
adamc@535	1022 \Gamma \vdash M : S
adamc@558	1023 & \textrm{ $M$ not a constant or application}
adamc@535	1024 }
adamc@558	1025 \quad \infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : \mt{selfify}(X, \overline{s})}{
adamc@558	1026 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@539	1027 }$$
adamc@539	1028
adamc@539	1029 $$\infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@535	1030 \Gamma \vdash S
adamc@535	1031 }$$
adamc@535	1032
adamc@537	1033 $$\infer{\Gamma \vdash \mt{open} \; M \leadsto \Gamma, \mathcal O(M, \overline{s})}{
adamc@537	1034 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535	1035 }$$
adamc@535	1036
adamc@535	1037 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma}{
adamc@535	1038 \Gamma \vdash c_1 :: \{\kappa\}
adamc@535	1039 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@535	1040 & \Gamma \vdash c_1 \sim c_2
adamc@535	1041 }
adamc@537	1042 \quad \infer{\Gamma \vdash \mt{open} \; \mt{constraints} \; M \leadsto \Gamma, \mathcal O_c(M, \overline{s})}{
adamc@537	1043 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535	1044 }$$
adamc@535	1045
adamc@784	1046 $$\infer{\Gamma \vdash \mt{table} \; x : c \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_table} \; c \; []}{
adamc@535	1047 \Gamma \vdash c :: \{\mt{Type}\}
adamc@535	1048 }
adam@1594	1049 \quad \infer{\Gamma \vdash \mt{view} \; x = e \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_view} \; c}{
adam@1594	1050 \Gamma \vdash e :: \mt{Basis}.\mt{sql\_query} \; [] \; [] \; (\mt{map} \; (\lambda \_ \Rightarrow []) \; c') \; c
adamc@784	1051 }$$
adamc@784	1052
adamc@784	1053 $$\infer{\Gamma \vdash \mt{sequence} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_sequence}}{}$$
adamc@535	1054
adamc@535	1055 $$\infer{\Gamma \vdash \mt{cookie} \; x : \tau \leadsto \Gamma, x : \mt{Basis}.\mt{http\_cookie} \; \tau}{
adamc@535	1056 \Gamma \vdash \tau :: \mt{Type}
adamc@784	1057 }
adamc@784	1058 \quad \infer{\Gamma \vdash \mt{style} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{css\_class}}{}$$
adamc@535	1059
adamc@1085	1060 $$\infer{\Gamma \vdash \mt{task} \; e_1 = e_2 \leadsto \Gamma}{
adam@1348	1061 \Gamma \vdash e_1 :: \mt{Basis}.\mt{task\_kind} \; \tau
adam@1348	1062 & \Gamma \vdash e_2 :: \tau \to \mt{Basis}.\mt{transaction} \; \{\}
adamc@1085	1063 }$$
adamc@1085	1064
adamc@535	1065 $$\infer{\overline{y}; x; \Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535	1066 \quad \infer{\overline{y}; x; \Gamma \vdash X \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to x \; \overline{y}}{
adamc@535	1067 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535	1068 }
adamc@535	1069 \quad \infer{\overline{y}; x; \Gamma \vdash X \; \mt{of} \; \tau \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to \tau \to x \; \overline{y}}{
adamc@535	1070 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535	1071 }$$
adamc@535	1072
adamc@537	1073 \subsection{Signature Item Typing}
adamc@537	1074
adamc@537	1075 We appeal to a signature item analogue of the $\mathcal O$ function from the last subsection.
adamc@537	1076
adam@1797	1077 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	1078
adamc@537	1079 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@537	1080 \quad \infer{\Gamma \vdash s, \overline{s} \leadsto \Gamma''}{
adamc@537	1081 \Gamma \vdash s \leadsto \Gamma'
adamc@537	1082 & \Gamma' \vdash \overline{s} \leadsto \Gamma''
adamc@537	1083 }$$
adamc@537	1084
adamc@537	1085 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}
adamc@537	1086 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@537	1087 \Gamma \vdash c :: \kappa
adamc@537	1088 }
adamc@537	1089 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@537	1090 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@537	1091 }$$
adamc@537	1092
adamc@537	1093 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537	1094 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1095 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537	1096 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@537	1097 }$$
adamc@537	1098
adamc@537	1099 $$\infer{\Gamma \vdash \mt{val} \; x : \tau \leadsto \Gamma, x : \tau}{
adamc@537	1100 \Gamma \vdash \tau :: \mt{Type}
adamc@537	1101 }$$
adamc@537	1102
adamc@537	1103 $$\infer{\Gamma \vdash \mt{structure} \; X : S \leadsto \Gamma, X : S}{
adamc@537	1104 \Gamma \vdash S
adamc@537	1105 }
adamc@537	1106 \quad \infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@537	1107 \Gamma \vdash S
adamc@537	1108 }$$
adamc@537	1109
adamc@537	1110 $$\infer{\Gamma \vdash \mt{include} \; S \leadsto \Gamma, \mathcal O(\overline{s})}{
adamc@537	1111 \Gamma \vdash S
adamc@537	1112 & \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1113 }$$
adamc@537	1114
adamc@537	1115 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma, c_1 \sim c_2}{
adamc@537	1116 \Gamma \vdash c_1 :: \{\kappa\}
adamc@537	1117 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@537	1118 }$$
adamc@537	1119
adamc@784	1120 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784	1121 \Gamma \vdash c :: \kappa
adamc@537	1122 }
adamc@784	1123 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}$$
adamc@537	1124
adamc@536	1125 \subsection{Signature Compatibility}
adamc@536	1126
adam@1797	1127 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	1128
adamc@537	1129 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	1130
adamc@536	1131 $$\infer{\Gamma \vdash S \equiv S}{}
adamc@536	1132 \quad \infer{\Gamma \vdash S_1 \equiv S_2}{
adamc@536	1133 \Gamma \vdash S_2 \equiv S_1
adamc@536	1134 }
adamc@536	1135 \quad \infer{\Gamma \vdash X \equiv S}{
adamc@536	1136 X = S \in \Gamma
adamc@536	1137 }
adamc@536	1138 \quad \infer{\Gamma \vdash M.X \equiv S}{
adamc@537	1139 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1140 & \mt{proj}(M, \overline{s}, \mt{signature} \; X) = S
adamc@536	1141 }$$
adamc@536	1142
adamc@536	1143 $$\infer{\Gamma \vdash S \; \mt{where} \; \mt{con} \; x = c \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa = c \; \overline{s_2} \; \mt{end}}{
adamc@536	1144 \Gamma \vdash S \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa \; \overline{s_2} \; \mt{end}
adamc@536	1145 & \Gamma \vdash c :: \kappa
adamc@537	1146 }
adamc@537	1147 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s^1} \; \mt{include} \; S \; \overline{s^2} \; \mt{end} \equiv \mt{sig} \; \overline{s^1} \; \overline{s} \; \overline{s^2} \; \mt{end}}{
adamc@537	1148 \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@536	1149 }$$
adamc@536	1150
adamc@536	1151 $$\infer{\Gamma \vdash S_1 \leq S_2}{
adamc@536	1152 \Gamma \vdash S_1 \equiv S_2
adamc@536	1153 }
adamc@536	1154 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \mt{end}}{}
adamc@537	1155 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; s' \; \overline{s'} \; \mt{end}}{
adamc@537	1156 \Gamma \vdash \overline{s} \leq s'
adamc@537	1157 & \Gamma \vdash s' \leadsto \Gamma'
adamc@537	1158 & \Gamma' \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \overline{s'} \; \mt{end}
adamc@537	1159 }$$
adamc@537	1160
adamc@537	1161 $$\infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537	1162 \Gamma \vdash s \leq s'
adamc@537	1163 }
adamc@537	1164 \quad \infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537	1165 \Gamma \vdash s \leadsto \Gamma'
adamc@537	1166 & \Gamma' \vdash \overline{s} \leq s'
adamc@536	1167 }$$
adamc@536	1168
adamc@536	1169 $$\infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 \leq \mt{functor} (X : S'_1) : S'_2}{
adamc@536	1170 \Gamma \vdash S'_1 \leq S_1
adamc@536	1171 & \Gamma, X : S'_1 \vdash S_2 \leq S'_2
adamc@536	1172 }$$
adamc@536	1173
adamc@537	1174 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@537	1175 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}
adamc@558	1176 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type}}{}$$
adamc@537	1177
adamc@537	1178 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(y)} \to \mt{Type}}{
adamc@537	1179 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1180 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537	1181 }$$
adamc@537	1182
adamc@784	1183 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@784	1184 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}$$
adamc@537	1185
adamc@537	1186 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \mt{\kappa} = c_2}{
adamc@537	1187 \Gamma \vdash c_1 \equiv c_2
adamc@537	1188 }
adamc@784	1189 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \kappa = c_2}{
adamc@537	1190 \Gamma \vdash c_1 \equiv c_2
adamc@537	1191 }$$
adamc@537	1192
adamc@537	1193 $$\infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537	1194 \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537	1195 }$$
adamc@537	1196
adamc@537	1197 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537	1198 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1199 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537	1200 & \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537	1201 }$$
adamc@537	1202
adamc@537	1203 $$\infer{\Gamma \vdash \cdot \leq \cdot}{}
adamc@537	1204 \quad \infer{\Gamma \vdash X; \overline{dc} \leq X; \overline{dc'}}{
adamc@537	1205 \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537	1206 }
adamc@537	1207 \quad \infer{\Gamma \vdash X \; \mt{of} \; \tau_1; \overline{dc} \leq X \; \mt{of} \; \tau_2; \overline{dc'}}{
adamc@537	1208 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537	1209 & \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537	1210 }$$
adamc@537	1211
adamc@537	1212 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x = \mt{datatype} \; M'.z'}{
adamc@537	1213 \Gamma \vdash M.z \equiv M'.z'
adamc@537	1214 }$$
adamc@537	1215
adamc@537	1216 $$\infer{\Gamma \vdash \mt{val} \; x : \tau_1 \leq \mt{val} \; x : \tau_2}{
adamc@537	1217 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537	1218 }
adamc@537	1219 \quad \infer{\Gamma \vdash \mt{structure} \; X : S_1 \leq \mt{structure} \; X : S_2}{
adamc@537	1220 \Gamma \vdash S_1 \leq S_2
adamc@537	1221 }
adamc@537	1222 \quad \infer{\Gamma \vdash \mt{signature} \; X = S_1 \leq \mt{signature} \; X = S_2}{
adamc@537	1223 \Gamma \vdash S_1 \leq S_2
adamc@537	1224 & \Gamma \vdash S_2 \leq S_1
adamc@537	1225 }$$
adamc@537	1226
adamc@537	1227 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leq \mt{constraint} \; c'_1 \sim c'_2}{
adamc@537	1228 \Gamma \vdash c_1 \equiv c'_1
adamc@537	1229 & \Gamma \vdash c_2 \equiv c'_2
adamc@537	1230 }$$
adamc@537	1231
adamc@655	1232 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{class} \; x :: \kappa}{}
adamc@655	1233 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{class} \; x :: \kappa}{}
adamc@655	1234 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{class} \; x :: \kappa = c_2}{
adamc@537	1235 \Gamma \vdash c_1 \equiv c_2
adamc@537	1236 }$$
adamc@537	1237
adam@1797	1238 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leq \mt{class} \; x :: \kappa}{}
adam@1797	1239 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leq \mt{class} \; x :: \kappa}{}
adam@1797	1240 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c_1 \leq \mt{class} \; x :: \kappa = c_2}{
adam@1797	1241 \Gamma \vdash c_1 \equiv c_2
adam@1797	1242 }$$
adam@1797	1243
adamc@538	1244 \subsection{Module Typing}
adamc@538	1245
adamc@538	1246 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	1247
adamc@538	1248 $$\infer{\Gamma \vdash M : S}{
adamc@538	1249 \Gamma \vdash M : S'
adamc@538	1250 & \Gamma \vdash S' \leq S
adamc@538	1251 }
adamc@538	1252 \quad \infer{\Gamma \vdash \mt{struct} \; \overline{d} \; \mt{end} : \mt{sig} \; \mt{sigOf}(\overline{d}) \; \mt{end}}{
adamc@538	1253 \Gamma \vdash \overline{d} \leadsto \Gamma'
adamc@538	1254 }
adamc@538	1255 \quad \infer{\Gamma \vdash X : S}{
adamc@538	1256 X : S \in \Gamma
adamc@538	1257 }$$
adamc@538	1258
adamc@538	1259 $$\infer{\Gamma \vdash M.X : S}{
adamc@538	1260 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@538	1261 & \mt{proj}(M, \overline{s}, \mt{structure} \; X) = S
adamc@538	1262 }$$
adamc@538	1263
adamc@538	1264 $$\infer{\Gamma \vdash M_1(M_2) : [X \mapsto M_2]S_2}{
adamc@538	1265 \Gamma \vdash M_1 : \mt{functor}(X : S_1) : S_2
adamc@538	1266 & \Gamma \vdash M_2 : S_1
adamc@538	1267 }
adamc@538	1268 \quad \infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 = M : \mt{functor} (X : S_1) : S_2}{
adamc@538	1269 \Gamma \vdash S_1
adamc@538	1270 & \Gamma, X : S_1 \vdash S_2
adamc@538	1271 & \Gamma, X : S_1 \vdash M : S_2
adamc@538	1272 }$$
adamc@538	1273
adamc@538	1274 \begin{eqnarray*}
adamc@538	1275 \mt{sigOf}(\cdot) &=& \cdot \\
adamc@538	1276 \mt{sigOf}(s \; \overline{s'}) &=& \mt{sigOf}(s) \; \mt{sigOf}(\overline{s'}) \\
adamc@538	1277 \\
adamc@538	1278 \mt{sigOf}(\mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@538	1279 \mt{sigOf}(\mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \overline{dc} \\
adamc@538	1280 \mt{sigOf}(\mt{datatype} \; x = \mt{datatype} \; M.z) &=& \mt{datatype} \; x = \mt{datatype} \; M.z \\
adamc@538	1281 \mt{sigOf}(\mt{val} \; x : \tau = e) &=& \mt{val} \; x : \tau \\
adamc@538	1282 \mt{sigOf}(\mt{val} \; \mt{rec} \; \overline{x : \tau = e}) &=& \overline{\mt{val} \; x : \tau} \\
adamc@538	1283 \mt{sigOf}(\mt{structure} \; X : S = M) &=& \mt{structure} \; X : S \\
adamc@538	1284 \mt{sigOf}(\mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@538	1285 \mt{sigOf}(\mt{open} \; M) &=& \mt{include} \; S \textrm{ (where $\Gamma \vdash M : S$)} \\
adamc@538	1286 \mt{sigOf}(\mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@538	1287 \mt{sigOf}(\mt{open} \; \mt{constraints} \; M) &=& \cdot \\
adamc@538	1288 \mt{sigOf}(\mt{table} \; x : c) &=& \mt{table} \; x : c \\
adam@1594	1289 \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	1290 \mt{sigOf}(\mt{sequence} \; x) &=& \mt{sequence} \; x \\
adamc@538	1291 \mt{sigOf}(\mt{cookie} \; x : \tau) &=& \mt{cookie} \; x : \tau \\
adam@1797	1292 \mt{sigOf}(\mt{style} \; x) &=& \mt{style} \; x
adamc@538	1293 \end{eqnarray*}
adamc@539	1294 \begin{eqnarray*}
adamc@539	1295 \mt{selfify}(M, \cdot) &=& \cdot \\
adamc@558	1296 \mt{selfify}(M, s \; \overline{s'}) &=& \mt{selfify}(M, s) \; \mt{selfify}(M, \overline{s'}) \\
adamc@539	1297 \\
adamc@539	1298 \mt{selfify}(M, \mt{con} \; x :: \kappa) &=& \mt{con} \; x :: \kappa = M.x \\
adamc@539	1299 \mt{selfify}(M, \mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@539	1300 \mt{selfify}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \mt{datatype} \; M.x \\
adamc@539	1301 \mt{selfify}(M, \mt{datatype} \; x = \mt{datatype} \; M'.z) &=& \mt{datatype} \; x = \mt{datatype} \; M'.z \\
adamc@539	1302 \mt{selfify}(M, \mt{val} \; x : \tau) &=& \mt{val} \; x : \tau \\
adamc@539	1303 \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	1304 \mt{selfify}(M, \mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@539	1305 \mt{selfify}(M, \mt{include} \; S) &=& \mt{include} \; S \\
adamc@539	1306 \mt{selfify}(M, \mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@655	1307 \mt{selfify}(M, \mt{class} \; x :: \kappa) &=& \mt{class} \; x :: \kappa = M.x \\
adamc@655	1308 \mt{selfify}(M, \mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@539	1309 \end{eqnarray*}
adamc@539	1310
adamc@540	1311 \subsection{Module Projection}
adamc@540	1312
adamc@540	1313 \begin{eqnarray*}
adamc@540	1314 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \\
adamc@540	1315 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa, c) \\
adamc@540	1316 \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	1317 \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	1318 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})$)} \\
adamc@655	1319 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \to \mt{Type} \\
adamc@655	1320 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa \to \mt{Type}, c) \\
adamc@540	1321 \\
adamc@540	1322 \mt{proj}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc} \; \overline{s}, \mt{datatype} \; x) &=& (\overline{y}, \overline{dc}) \\
adamc@540	1323 \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	1324 \\
adamc@540	1325 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, \mt{val} \; x) &=& \tau \\
adamc@540	1326 \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	1327 \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	1328 \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	1329 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \in \overline{dc}$)} \\
adamc@540	1330 \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	1331 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \; \mt{of} \; \tau \in \overline{dc}$)} \\
adamc@540	1332 \\
adamc@540	1333 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, \mt{structure} \; X) &=& S \\
adamc@540	1334 \\
adamc@540	1335 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, \mt{signature} \; X) &=& S \\
adamc@540	1336 \\
adamc@540	1337 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1338 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1339 \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	1340 \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	1341 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@540	1342 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1343 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1344 \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	1345 \mt{proj}(M, \mt{constraint} \; c_1 \sim c_2 \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@655	1346 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@655	1347 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1348 \end{eqnarray*}
adamc@540	1349
adamc@541	1350
adamc@541	1351 \section{Type Inference}
adamc@541	1352
adamc@541	1353 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	1354
adamc@541	1355 \subsection{Basic Unification}
adamc@541	1356
adamc@560	1357 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	1358
adamc@656	1359 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	1360
adamc@541	1361 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	1362
adamc@541	1363 \subsection{Unifying Record Types}
adamc@541	1364
adamc@570	1365 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	1366
adamc@656	1367 \subsection{\label{typeclasses}Constructor Classes}
adamc@541	1368
adamc@784	1369 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	1370
adam@1797	1371 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	1372
adam@1797	1373 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	1374
adam@1797	1375 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	1376
adamc@541	1377 \subsection{Reverse-Engineering Record Types}
adamc@541	1378
adamc@656	1379 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	1380
adamc@541	1381 \subsection{Implicit Arguments in Functor Applications}
adamc@541	1382
adamc@656	1383 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	1384
adamc@541	1385
adamc@542	1386 \section{The Ur Standard Library}
adamc@542	1387
adamc@542	1388 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	1389
adamc@542	1390 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	1391
adamc@542	1392 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	1393 $$\begin{array}{l}
adamc@542	1394 \mt{type} \; \mt{int} \\
adamc@542	1395 \mt{type} \; \mt{float} \\
adamc@873	1396 \mt{type} \; \mt{char} \\
adamc@542	1397 \mt{type} \; \mt{string} \\
adamc@542	1398 \mt{type} \; \mt{time} \\
adamc@785	1399 \mt{type} \; \mt{blob} \\
adamc@542	1400 \\
adamc@542	1401 \mt{type} \; \mt{unit} = \{\} \\
adamc@542	1402 \\
adamc@542	1403 \mt{datatype} \; \mt{bool} = \mt{False} \mid \mt{True} \\
adamc@542	1404 \\
adamc@785	1405 \mt{datatype} \; \mt{option} \; \mt{t} = \mt{None} \mid \mt{Some} \; \mt{of} \; \mt{t} \\
adamc@785	1406 \\
adamc@785	1407 \mt{datatype} \; \mt{list} \; \mt{t} = \mt{Nil} \mid \mt{Cons} \; \mt{of} \; \mt{t} \times \mt{list} \; \mt{t}
adamc@542	1408 \end{array}$$
adamc@542	1409
adamc@1123	1410 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	1411
adam@1297	1412 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	1413 $$\begin{array}{l}
adam@1297	1414 \mt{con} \; \mt{variant} :: \{\mt{Type}\} \to \mt{Type} \\
adam@1297	1415 \mt{val} \; \mt{make} : \mt{nm} :: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{ts} ::: \{\mt{Type}\} \to [[\mt{nm}] \sim \mt{ts}] \Rightarrow \mt{t} \to \mt{variant} \; ([\mt{nm} = \mt{t}] \rc \mt{ts}) \\
adam@1297	1416 \mt{val} \; \mt{match} : \mt{ts} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{variant} \; \mt{ts} \to \$(\mt{map} \; (\lambda \mt{t'} \Rightarrow \mt{t'} \to \mt{t}) \; \mt{ts}) \to \mt{t}
adam@1297	1417 \end{array}$$
adam@1297	1418
adamc@657	1419 Another important generic Ur element comes at the beginning of \texttt{top.urs}.
adamc@657	1420
adamc@657	1421 $$\begin{array}{l}
adamc@657	1422 \mt{con} \; \mt{folder} :: \mt{K} \longrightarrow \{\mt{K}\} \to \mt{Type} \\
adamc@657	1423 \\
adamc@657	1424 \mt{val} \; \mt{fold} : \mt{K} \longrightarrow \mt{tf} :: (\{\mt{K}\} \to \mt{Type}) \\
adamc@657	1425 \hspace{.1in} \to (\mt{nm} :: \mt{Name} \to \mt{v} :: \mt{K} \to \mt{r} :: \{\mt{K}\} \to [[\mt{nm}] \sim \mt{r}] \Rightarrow \\
adamc@657	1426 \hspace{.2in} \mt{tf} \; \mt{r} \to \mt{tf} \; ([\mt{nm} = \mt{v}] \rc \mt{r})) \\
adamc@657	1427 \hspace{.1in} \to \mt{tf} \; [] \\
adam@2155	1428 \hspace{.1in} \to \mt{r} ::: \{\mt{K}\} \to \mt{folder} \; \mt{r} \to \mt{tf} \; \mt{r}
adamc@657	1429 \end{array}$$
adamc@657	1430
adamc@657	1431 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	1432
adamc@664	1433 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	1434
adamc@542	1435
adamc@542	1436 \section{The Ur/Web Standard Library}
adamc@542	1437
adam@1400	1438 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	1439
adamc@658	1440 \subsection{Monads}
adamc@658	1441
adamc@658	1442 The Ur Basis defines the monad constructor class from Haskell.
adamc@658	1443
adamc@658	1444 $$\begin{array}{l}
adamc@658	1445 \mt{class} \; \mt{monad} :: \mt{Type} \to \mt{Type} \\
adamc@658	1446 \mt{val} \; \mt{return} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t} ::: \mt{Type} \\
adamc@658	1447 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658	1448 \hspace{.1in} \to \mt{t} \to \mt{m} \; \mt{t} \\
adamc@658	1449 \mt{val} \; \mt{bind} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t1} ::: \mt{Type} \to \mt{t2} ::: \mt{Type} \\
adamc@658	1450 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658	1451 \hspace{.1in} \to \mt{m} \; \mt{t1} \to (\mt{t1} \to \mt{m} \; \mt{t2}) \\
adam@1544	1452 \hspace{.1in} \to \mt{m} \; \mt{t2} \\
adam@1544	1453 \mt{val} \; \mt{mkMonad} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \\
adam@1544	1454 \hspace{.1in} \to \{\mt{Return} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{m} \; \mt{t}, \\
adam@1544	1455 \hspace{.3in} \mt{Bind} : \mt{t1} ::: \mt{Type} \to \mt{t2} ::: \mt{Type} \to \mt{m} \; \mt{t1} \to (\mt{t1} \to \mt{m} \; \mt{t2}) \to \mt{m} \; \mt{t2}\} \\
adam@1544	1456 \hspace{.1in} \to \mt{monad} \; \mt{m}
adamc@658	1457 \end{array}$$
adamc@658	1458
adam@1687	1459 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	1460
adam@2009	1461 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	1462
adamc@542	1463 \subsection{Transactions}
adamc@542	1464
adamc@542	1465 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	1466 $$\begin{array}{l}
adamc@542	1467 \mt{con} \; \mt{transaction} :: \mt{Type} \to \mt{Type} \\
adamc@658	1468 \mt{val} \; \mt{transaction\_monad} : \mt{monad} \; \mt{transaction}
adamc@542	1469 \end{array}$$
adamc@542	1470
adamc@1123	1471 For debugging purposes, a transactional function is provided for outputting a string on the server process' \texttt{stderr}.
adamc@1123	1472 $$\begin{array}{l}
adamc@1123	1473 \mt{val} \; \mt{debug} : \mt{string} \to \mt{transaction} \; \mt{unit}
adamc@1123	1474 \end{array}$$
adamc@1123	1475
adamc@542	1476 \subsection{HTTP}
adamc@542	1477
adam@1797	1478 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	1479 $$\begin{array}{l}
adamc@786	1480 \mt{con} \; \mt{http\_cookie} :: \mt{Type} \to \mt{Type} \\
adamc@786	1481 \mt{val} \; \mt{getCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; (\mt{option} \; \mt{t}) \\
adamc@1050	1482 \mt{val} \; \mt{setCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \{\mt{Value} : \mt{t}, \mt{Expires} : \mt{option} \; \mt{time}, \mt{Secure} : \mt{bool}\} \to \mt{transaction} \; \mt{unit} \\
adamc@1050	1483 \mt{val} \; \mt{clearCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; \mt{unit}
adamc@786	1484 \end{array}$$
adamc@786	1485
adamc@786	1486 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	1487 $$\begin{array}{l}
adamc@786	1488 \mt{type} \; \mt{url} \\
adamc@786	1489 \mt{val} \; \mt{bless} : \mt{string} \to \mt{url} \\
adamc@786	1490 \mt{val} \; \mt{checkUrl} : \mt{string} \to \mt{option} \; \mt{url}
adamc@786	1491 \end{array}$$
adamc@786	1492 $\mt{bless}$ raises a runtime error if the string passed to it fails the URL policy.
adamc@786	1493
adam@1400	1494 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	1495 $$\begin{array}{l}
adamc@1085	1496 \mt{val} \; \mt{currentUrl} : \mt{transaction} \; \mt{url} \\
adamc@1085	1497 \mt{val} \; \mt{url} : \mt{transaction} \; \mt{page} \to \mt{url}
adamc@1085	1498 \end{array}$$
adamc@1085	1499
adamc@1085	1500 Page generation may be interrupted at any time with a request to redirect to a particular URL instead.
adamc@1085	1501 $$\begin{array}{l}
adamc@1085	1502 \mt{val} \; \mt{redirect} : \mt{t} ::: \mt{Type} \to \mt{url} \to \mt{transaction} \; \mt{t}
adamc@1085	1503 \end{array}$$
adamc@1085	1504
adam@1400	1505 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	1506 $$\begin{array}{l}
adamc@786	1507 \mt{type} \; \mt{file} \\
adamc@786	1508 \mt{val} \; \mt{fileName} : \mt{file} \to \mt{option} \; \mt{string} \\
adamc@786	1509 \mt{val} \; \mt{fileMimeType} : \mt{file} \to \mt{string} \\
adamc@786	1510 \mt{val} \; \mt{fileData} : \mt{file} \to \mt{blob}
adamc@786	1511 \end{array}$$
adamc@786	1512
adam@1799	1513 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	1514
adam@1465	1515 $$\begin{array}{l}
adam@1465	1516 \mt{type} \; \mt{requestHeader} \\
adam@1465	1517 \mt{val} \; \mt{blessRequestHeader} : \mt{string} \to \mt{requestHeader} \\
adam@1465	1518 \mt{val} \; \mt{checkRequestHeader} : \mt{string} \to \mt{option} \; \mt{requestHeader} \\
adam@1465	1519 \mt{val} \; \mt{getHeader} : \mt{requestHeader} \to \mt{transaction} \; (\mt{option} \; \mt{string}) \\
adam@1465	1520 \\
adam@1799	1521 \mt{type} \; \mt{envVar} \\
adam@1799	1522 \mt{val} \; \mt{blessEnvVar} : \mt{string} \to \mt{envVar} \\
adam@1799	1523 \mt{val} \; \mt{checkEnvVar} : \mt{string} \to \mt{option} \; \mt{envVar} \\
adam@1799	1524 \mt{val} \; \mt{getenv} : \mt{envVar} \to \mt{transaction} \; (\mt{option} \; \mt{string}) \\
adam@1799	1525 \\
adam@1465	1526 \mt{type} \; \mt{responseHeader} \\
adam@1465	1527 \mt{val} \; \mt{blessResponseHeader} : \mt{string} \to \mt{responseHeader} \\
adam@1465	1528 \mt{val} \; \mt{checkResponseHeader} : \mt{string} \to \mt{option} \; \mt{responseHeader} \\
adam@1465	1529 \mt{val} \; \mt{setHeader} : \mt{responseHeader} \to \mt{string} \to \mt{transaction} \; \mt{unit}
adam@1465	1530 \end{array}$$
adam@1465	1531
adamc@786	1532 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	1533 $$\begin{array}{l}
adamc@786	1534 \mt{type} \; \mt{mimeType} \\
adamc@786	1535 \mt{val} \; \mt{blessMime} : \mt{string} \to \mt{mimeType} \\
adamc@786	1536 \mt{val} \; \mt{checkMime} : \mt{string} \to \mt{option} \; \mt{mimeType} \\
adamc@786	1537 \mt{val} \; \mt{returnBlob} : \mt{t} ::: \mt{Type} \to \mt{blob} \to \mt{mimeType} \to \mt{transaction} \; \mt{t}
adamc@542	1538 \end{array}$$
adamc@542	1539
adamc@543	1540 \subsection{SQL}
adamc@543	1541
adam@1400	1542 Everything about SQL database access is restricted to server-side code.
adam@1400	1543
adamc@543	1544 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	1545 $$\begin{array}{l}
adamc@785	1546 \mt{con} \; \mt{sql\_table} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785	1547 \end{array}$$
adamc@785	1548 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	1549
adamc@785	1550 We also have the simpler type family of SQL views, which have no keys.
adamc@785	1551 $$\begin{array}{l}
adamc@785	1552 \mt{con} \; \mt{sql\_view} :: \{\mt{Type}\} \to \mt{Type}
adamc@543	1553 \end{array}$$
adamc@543	1554
adamc@785	1555 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	1556 $$\begin{array}{l}
adamc@785	1557 \mt{class} \; \mt{fieldsOf} :: \mt{Type} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785	1558 \mt{val} \; \mt{fieldsOf\_table} : \mt{fs} ::: \{\mt{Type}\} \to \mt{keys} ::: \{\{\mt{Unit}\}\} \to \mt{fieldsOf} \; (\mt{sql\_table} \; \mt{fs} \; \mt{keys}) \; \mt{fs} \\
adamc@785	1559 \mt{val} \; \mt{fieldsOf\_view} : \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; (\mt{sql\_view} \; \mt{fs}) \; \mt{fs}
adamc@785	1560 \end{array}$$
adamc@785	1561
adamc@785	1562 \subsubsection{Table Constraints}
adamc@785	1563
adamc@785	1564 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	1565
adamc@785	1566 $$\begin{array}{l}
adamc@785	1567 \mt{con} \; \mt{primary\_key} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type} \\
adamc@785	1568 \mt{val} \; \mt{no\_primary\_key} : \mt{fs} ::: \{\mt{Type}\} \to \mt{primary\_key} \; \mt{fs} \; [] \\
adamc@785	1569 \mt{val} \; \mt{primary\_key} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{key1} :: \mt{Name} \to \mt{keys} :: \{\mt{Type}\} \\
adamc@785	1570 \hspace{.1in} \to [[\mt{key1}] \sim \mt{keys}] \Rightarrow [[\mt{key1} = \mt{t}] \rc \mt{keys} \sim \mt{rest}] \\
adamc@785	1571 \hspace{.1in} \Rightarrow \$([\mt{key1} = \mt{sql\_injectable\_prim} \; \mt{t}] \rc \mt{map} \; \mt{sql\_injectable\_prim} \; \mt{keys}) \\
adamc@785	1572 \hspace{.1in} \to \mt{primary\_key} \; ([\mt{key1} = \mt{t}] \rc \mt{keys} \rc \mt{rest}) \; [\mt{Pkey} = [\mt{key1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{keys}]
adamc@785	1573 \end{array}$$
adamc@785	1574 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	1575
adamc@785	1576 A type family stands for sets of named constraints of the remaining varieties.
adamc@785	1577 $$\begin{array}{l}
adamc@785	1578 \mt{con} \; \mt{sql\_constraints} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785	1579 \end{array}$$
adamc@785	1580 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	1581
adamc@785	1582 There is a type family of individual, unnamed constraints.
adamc@785	1583 $$\begin{array}{l}
adamc@785	1584 \mt{con} \; \mt{sql\_constraint} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \mt{Type}
adamc@785	1585 \end{array}$$
adamc@785	1586 The first argument is the same as above, and the second argument gives the key columns for just this constraint.
adamc@785	1587
adamc@785	1588 We have operations for assembling constraints into constraint sets.
adamc@785	1589 $$\begin{array}{l}
adamc@785	1590 \mt{val} \; \mt{no\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_constraints} \; \mt{fs} \; [] \\
adamc@785	1591 \mt{val} \; \mt{one\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{unique} ::: \{\mt{Unit}\} \to \mt{name} :: \mt{Name} \\
adamc@785	1592 \hspace{.1in} \to \mt{sql\_constraint} \; \mt{fs} \; \mt{unique} \to \mt{sql\_constraints} \; \mt{fs} \; [\mt{name} = \mt{unique}] \\
adamc@785	1593 \mt{val} \; \mt{join\_constraints} : \mt{fs} ::: \{\mt{Type}\} \to \mt{uniques1} ::: \{\{\mt{Unit}\}\} \to \mt{uniques2} ::: \{\{\mt{Unit}\}\} \to [\mt{uniques1} \sim \mt{uniques2}] \\
adamc@785	1594 \hspace{.1in} \Rightarrow \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques1} \to \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques2} \to \mt{sql\_constraints} \; \mt{fs} \; (\mt{uniques1} \rc \mt{uniques2})
adamc@785	1595 \end{array}$$
adamc@785	1596
adamc@785	1597 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	1598 $$\begin{array}{l}
adamc@785	1599 \mt{val} \; \mt{unique} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{unique1} :: \mt{Name} \to \mt{unique} :: \{\mt{Type}\} \\
adamc@785	1600 \hspace{.1in} \to [[\mt{unique1}] \sim \mt{unique}] \Rightarrow [[\mt{unique1} = \mt{t}] \rc \mt{unique} \sim \mt{rest}] \\
adamc@785	1601 \hspace{.1in} \Rightarrow \mt{sql\_constraint} \; ([\mt{unique1} = \mt{t}] \rc \mt{unique} \rc \mt{rest}) \; ([\mt{unique1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{unique})
adamc@785	1602 \end{array}$$
adamc@785	1603
adamc@785	1604 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	1605 $$\begin{array}{l}
adamc@785	1606 \mt{class} \; \mt{linkable} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@785	1607 \mt{val} \; \mt{linkable\_same} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; \mt{t} \\
adamc@785	1608 \mt{val} \; \mt{linkable\_from\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; (\mt{option} \; \mt{t}) \; \mt{t} \\
adamc@785	1609 \mt{val} \; \mt{linkable\_to\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@785	1610 \end{array}$$
adamc@785	1611
adamc@785	1612 The $\mt{matching}$ type family uses $\mt{linkable}$ to define when two keys match up type-wise.
adamc@785	1613 $$\begin{array}{l}
adamc@785	1614 \mt{con} \; \mt{matching} :: \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785	1615 \mt{val} \; \mt{mat\_nil} : \mt{matching} \; [] \; [] \\
adamc@785	1616 \mt{val} \; \mt{mat\_cons} : \mt{t1} ::: \mt{Type} \to \mt{rest1} ::: \{\mt{Type}\} \to \mt{t2} ::: \mt{Type} \to \mt{rest2} ::: \{\mt{Type}\} \to \mt{nm1} :: \mt{Name} \to \mt{nm2} :: \mt{Name} \\
adamc@785	1617 \hspace{.1in} \to [[\mt{nm1}] \sim \mt{rest1}] \Rightarrow [[\mt{nm2}] \sim \mt{rest2}] \Rightarrow \mt{linkable} \; \mt{t1} \; \mt{t2} \to \mt{matching} \; \mt{rest1} \; \mt{rest2} \\
adamc@785	1618 \hspace{.1in} \to \mt{matching} \; ([\mt{nm1} = \mt{t1}] \rc \mt{rest1}) \; ([\mt{nm2} = \mt{t2}] \rc \mt{rest2})
adamc@785	1619 \end{array}$$
adamc@785	1620
adamc@785	1621 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	1622 $$\begin{array}{l}
adamc@785	1623 \mt{con} \; \mt{propagation\_mode} :: \{\mt{Type}\} \to \mt{Type} \\
adamc@785	1624 \mt{val} \; \mt{restrict} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785	1625 \mt{val} \; \mt{cascade} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785	1626 \mt{val} \; \mt{no\_action} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785	1627 \mt{val} \; \mt{set\_null} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; (\mt{map} \; \mt{option} \; \mt{fs})
adamc@785	1628 \end{array}$$
adamc@785	1629
adamc@785	1630 Finally, we put these ingredient together to define the \texttt{FOREIGN KEY} constraint function.
adamc@785	1631 $$\begin{array}{l}
adamc@785	1632 \mt{val} \; \mt{foreign\_key} : \mt{mine1} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{mine} ::: \{\mt{Type}\} \to \mt{munused} ::: \{\mt{Type}\} \to \mt{foreign} ::: \{\mt{Type}\} \\
adamc@785	1633 \hspace{.1in} \to \mt{funused} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{uniques} ::: \{\{\mt{Unit}\}\} \\
adamc@785	1634 \hspace{.1in} \to [[\mt{mine1}] \sim \mt{mine}] \Rightarrow [[\mt{mine1} = \mt{t}] \rc \mt{mine} \sim \mt{munused}] \Rightarrow [\mt{foreign} \sim \mt{funused}] \Rightarrow [[\mt{nm}] \sim \mt{uniques}] \\
adamc@785	1635 \hspace{.1in} \Rightarrow \mt{matching} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}) \; \mt{foreign} \\
adamc@785	1636 \hspace{.1in} \to \mt{sql\_table} \; (\mt{foreign} \rc \mt{funused}) \; ([\mt{nm} = \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{foreign}] \rc \mt{uniques}) \\
adamc@785	1637 \hspace{.1in} \to \{\mt{OnDelete} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}), \\
adamc@785	1638 \hspace{.2in} \mt{OnUpdate} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine})\} \\
adamc@785	1639 \hspace{.1in} \to \mt{sql\_constraint} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine} \rc \mt{munused}) \; []
adamc@785	1640 \end{array}$$
adamc@785	1641
adamc@785	1642 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	1643 $$\begin{array}{l}
adam@1778	1644 \mt{val} \; \mt{check} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; [] \; [] \; \mt{fs} \; \mt{bool} \to \mt{sql\_constraint} \; \mt{fs} \; []
adamc@785	1645 \end{array}$$
adamc@785	1646
adamc@785	1647 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	1648
adamc@784	1649
adamc@543	1650 \subsubsection{Queries}
adamc@543	1651
adam@1400	1652 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	1653 $$\begin{array}{l}
adam@1400	1654 \mt{con} \; \mt{sql\_query} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@1193	1655 \mt{val} \; \mt{sql\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400	1656 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adamc@1193	1657 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543	1658 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543	1659 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1193	1660 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adam@1400	1661 \hspace{.1in} \Rightarrow \{\mt{Rows} : \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}, \\
adamc@1193	1662 \hspace{.2in} \mt{OrderBy} : \mt{sql\_order\_by} \; (\mt{free} \rc \mt{tables}) \; \mt{selectedExps}, \\
adamc@543	1663 \hspace{.2in} \mt{Limit} : \mt{sql\_limit}, \\
adamc@543	1664 \hspace{.2in} \mt{Offset} : \mt{sql\_offset}\} \\
adam@1400	1665 \hspace{.1in} \to \mt{sql\_query} \; \mt{free} \; \mt{afree} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543	1666 \end{array}$$
adamc@543	1667
adamc@545	1668 Queries are used by folding over their results inside transactions.
adamc@545	1669 $$\begin{array}{l}
adam@1400	1670 \mt{val} \; \mt{query} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to [\mt{tables} \sim \mt{exps}] \Rightarrow \mt{state} ::: \mt{Type} \to \mt{sql\_query} \; [] \; [] \; \mt{tables} \; \mt{exps} \\
adamc@658	1671 \hspace{.1in} \to (\$(\mt{exps} \rc \mt{map} \; (\lambda \mt{fields} :: \{\mt{Type}\} \Rightarrow \$\mt{fields}) \; \mt{tables}) \\
adamc@545	1672 \hspace{.2in} \to \mt{state} \to \mt{transaction} \; \mt{state}) \\
adamc@545	1673 \hspace{.1in} \to \mt{state} \to \mt{transaction} \; \mt{state}
adamc@545	1674 \end{array}$$
adamc@545	1675
adam@1400	1676 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	1677 $$\begin{array}{l}
adam@1400	1678 \mt{con} \; \mt{sql\_query1} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@543	1679 \\
adamc@543	1680 \mt{type} \; \mt{sql\_relop} \\
adamc@543	1681 \mt{val} \; \mt{sql\_union} : \mt{sql\_relop} \\
adamc@543	1682 \mt{val} \; \mt{sql\_intersect} : \mt{sql\_relop} \\
adamc@543	1683 \mt{val} \; \mt{sql\_except} : \mt{sql\_relop} \\
adam@1400	1684 \mt{val} \; \mt{sql\_relop} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400	1685 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adam@1400	1686 \hspace{.1in} \to \mt{tables1} ::: \{\{\mt{Type}\}\} \\
adamc@543	1687 \hspace{.1in} \to \mt{tables2} ::: \{\{\mt{Type}\}\} \\
adamc@543	1688 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543	1689 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@543	1690 \hspace{.1in} \to \mt{sql\_relop} \\
adam@1458	1691 \hspace{.1in} \to \mt{bool} \; (* \; \mt{ALL} \; *) \\
adam@1400	1692 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables1} \; \mt{selectedFields} \; \mt{selectedExps} \\
adam@1400	1693 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables2} \; \mt{selectedFields} \; \mt{selectedExps} \\
adam@1400	1694 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{selectedFields} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543	1695 \end{array}$$
adamc@543	1696
adamc@543	1697 $$\begin{array}{l}
adamc@1193	1698 \mt{val} \; \mt{sql\_query1} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400	1699 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adamc@1193	1700 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543	1701 \hspace{.1in} \to \mt{grouped} ::: \{\{\mt{Type}\}\} \\
adamc@543	1702 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543	1703 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1085	1704 \hspace{.1in} \to \mt{empties} :: \{\mt{Unit}\} \\
adamc@1193	1705 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adamc@1193	1706 \hspace{.1in} \Rightarrow [\mt{free} \sim \mt{grouped}] \\
adam@1400	1707 \hspace{.1in} \Rightarrow [\mt{afree} \sim \mt{tables}] \\
adamc@1193	1708 \hspace{.1in} \Rightarrow [\mt{empties} \sim \mt{selectedFields}] \\
adamc@1085	1709 \hspace{.1in} \Rightarrow \{\mt{Distinct} : \mt{bool}, \\
adamc@1193	1710 \hspace{.2in} \mt{From} : \mt{sql\_from\_items} \; \mt{free} \; \mt{tables}, \\
adam@1778	1711 \hspace{.2in} \mt{Where} : \mt{sql\_exp} \; (\mt{free} \rc \mt{tables}) \; \mt{afree} \; [] \; \mt{bool}, \\
adamc@543	1712 \hspace{.2in} \mt{GroupBy} : \mt{sql\_subset} \; \mt{tables} \; \mt{grouped}, \\
adam@1778	1713 \hspace{.2in} \mt{Having} : \mt{sql\_exp} \; (\mt{free} \rc \mt{grouped}) \; (\mt{afree} \rc \mt{tables}) \; [] \; \mt{bool}, \\
adamc@1085	1714 \hspace{.2in} \mt{SelectFields} : \mt{sql\_subset} \; \mt{grouped} \; (\mt{map} \; (\lambda \_ \Rightarrow []) \; \mt{empties} \rc \mt{selectedFields}), \\
adam@1778	1715 \hspace{.2in} \mt {SelectExps} : \$(\mt{map} \; (\mt{sql\_expw} \; (\mt{free} \rc \mt{grouped}) \; (\mt{afree} \rc \mt{tables}) \; []) \; \mt{selectedExps}) \} \\
adam@1400	1716 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543	1717 \end{array}$$
adamc@543	1718
adamc@543	1719 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	1720 $$\begin{array}{l}
adamc@543	1721 \mt{con} \; \mt{sql\_subset} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@543	1722 \mt{val} \; \mt{sql\_subset} : \mt{keep\_drop} :: \{(\{\mt{Type}\} \times \{\mt{Type}\})\} \\
adamc@543	1723 \hspace{.1in} \to \mt{sql\_subset} \\
adamc@658	1724 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1 \rc \mt{fields}.2)\; \mt{keep\_drop}) \\
adamc@658	1725 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1) \; \mt{keep\_drop}) \\
adamc@543	1726 \mt{val} \; \mt{sql\_subset\_all} : \mt{tables} :: \{\{\mt{Type}\}\} \to \mt{sql\_subset} \; \mt{tables} \; \mt{tables}
adamc@543	1727 \end{array}$$
adamc@543	1728
adam@1778	1729 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	1730 $$\begin{array}{l}
adam@1778	1731 \mt{con} \; \mt{sql\_exp} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}
adamc@543	1732 \end{array}$$
adamc@543	1733
adamc@543	1734 Any field in scope may be converted to an expression.
adamc@543	1735 $$\begin{array}{l}
adamc@543	1736 \mt{val} \; \mt{sql\_field} : \mt{otherTabs} ::: \{\{\mt{Type}\}\} \to \mt{otherFields} ::: \{\mt{Type}\} \\
adam@1778	1737 \hspace{.1in} \to \mt{fieldType} ::: \mt{Type} \to \mt{agg} ::: \{\{\mt{Type}\}\} \\
adamc@543	1738 \hspace{.1in} \to \mt{exps} ::: \{\mt{Type}\} \\
adamc@543	1739 \hspace{.1in} \to \mt{tab} :: \mt{Name} \to \mt{field} :: \mt{Name} \\
adam@1778	1740 \hspace{.1in} \to \mt{sql\_exp} \; ([\mt{tab} = [\mt{field} = \mt{fieldType}] \rc \mt{otherFields}] \rc \mt{otherTabs}) \; \mt{agg} \; \mt{exps} \; \mt{fieldType}
adamc@543	1741 \end{array}$$
adamc@543	1742
adamc@544	1743 There is an analogous function for referencing named expressions.
adamc@544	1744 $$\begin{array}{l}
adam@1778	1745 \mt{val} \; \mt{sql\_exp} : \mt{tabs} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{t} ::: \mt{Type} \to \mt{rest} ::: \{\mt{Type}\} \to \mt{nm} :: \mt{Name} \\
adam@1778	1746 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tabs} \; \mt{agg} \; ([\mt{nm} = \mt{t}] \rc \mt{rest}) \; \mt{t}
adamc@544	1747 \end{array}$$
adamc@544	1748
adamc@544	1749 Ur values of appropriate types may be injected into SQL expressions.
adamc@544	1750 $$\begin{array}{l}
adamc@786	1751 \mt{class} \; \mt{sql\_injectable\_prim} \\
adamc@786	1752 \mt{val} \; \mt{sql\_bool} : \mt{sql\_injectable\_prim} \; \mt{bool} \\
adamc@786	1753 \mt{val} \; \mt{sql\_int} : \mt{sql\_injectable\_prim} \; \mt{int} \\
adamc@786	1754 \mt{val} \; \mt{sql\_float} : \mt{sql\_injectable\_prim} \; \mt{float} \\
adamc@786	1755 \mt{val} \; \mt{sql\_string} : \mt{sql\_injectable\_prim} \; \mt{string} \\
adamc@786	1756 \mt{val} \; \mt{sql\_time} : \mt{sql\_injectable\_prim} \; \mt{time} \\
adamc@786	1757 \mt{val} \; \mt{sql\_blob} : \mt{sql\_injectable\_prim} \; \mt{blob} \\
adamc@786	1758 \mt{val} \; \mt{sql\_channel} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{channel} \; \mt{t}) \\
adamc@786	1759 \mt{val} \; \mt{sql\_client} : \mt{sql\_injectable\_prim} \; \mt{client} \\
adamc@786	1760 \\
adamc@544	1761 \mt{class} \; \mt{sql\_injectable} \\
adamc@786	1762 \mt{val} \; \mt{sql\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@786	1763 \mt{val} \; \mt{sql\_option\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; (\mt{option} \; \mt{t}) \\
adamc@786	1764 \\
adam@1778	1765 \mt{val} \; \mt{sql\_inject} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{sql\_injectable} \; \mt{t} \\
adam@1778	1766 \hspace{.1in} \to \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adamc@544	1767 \end{array}$$
adamc@544	1768
adamc@1123	1769 Additionally, most function-free types may be injected safely, via the $\mt{serialized}$ type family.
adamc@1123	1770 $$\begin{array}{l}
adamc@1123	1771 \mt{con} \; \mt{serialized} :: \mt{Type} \to \mt{Type} \\
adamc@1123	1772 \mt{val} \; \mt{serialize} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{serialized} \; \mt{t} \\
adamc@1123	1773 \mt{val} \; \mt{deserialize} : \mt{t} ::: \mt{Type} \to \mt{serialized} \; \mt{t} \to \mt{t} \\
adamc@1123	1774 \mt{val} \; \mt{sql\_serialized} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{serialized} \; \mt{t})
adamc@1123	1775 \end{array}$$
adamc@1123	1776
adamc@544	1777 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	1778 $$\begin{array}{l}
adam@1778	1779 \mt{val} \; \mt{sql\_is\_null} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778	1780 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; (\mt{option} \; \mt{t}) \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{bool}
adamc@544	1781 \end{array}$$
adamc@544	1782
adam@1602	1783 As another way of dealing with null values, there is also a restricted form of the standard \cd{COALESCE} function.
adam@1602	1784 $$\begin{array}{l}
adam@1602	1785 \mt{val} \; \mt{sql\_coalesce} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778	1786 \hspace{.1in} \to \mt{t} ::: \mt{Type} \\
adam@1778	1787 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; (\mt{option} \; \mt{t}) \\
adam@1778	1788 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778	1789 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adam@1602	1790 \end{array}$$
adam@1602	1791
adamc@559	1792 We have generic nullary, unary, and binary operators.
adamc@544	1793 $$\begin{array}{l}
adamc@544	1794 \mt{con} \; \mt{sql\_nfunc} :: \mt{Type} \to \mt{Type} \\
adamc@544	1795 \mt{val} \; \mt{sql\_current\_timestamp} : \mt{sql\_nfunc} \; \mt{time} \\
adam@1778	1796 \mt{val} \; \mt{sql\_nfunc} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778	1797 \hspace{.1in} \to \mt{sql\_nfunc} \; \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\\end{array}$$
adamc@544	1798
adamc@544	1799 $$\begin{array}{l}
adamc@544	1800 \mt{con} \; \mt{sql\_unary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544	1801 \mt{val} \; \mt{sql\_not} : \mt{sql\_unary} \; \mt{bool} \; \mt{bool} \\
adam@1778	1802 \mt{val} \; \mt{sql\_unary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adam@1778	1803 \hspace{.1in} \to \mt{sql\_unary} \; \mt{arg} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res} \\
adamc@544	1804 \end{array}$$
adamc@544	1805
adamc@544	1806 $$\begin{array}{l}
adamc@544	1807 \mt{con} \; \mt{sql\_binary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544	1808 \mt{val} \; \mt{sql\_and} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544	1809 \mt{val} \; \mt{sql\_or} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adam@1778	1810 \mt{val} \; \mt{sql\_binary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg_1} ::: \mt{Type} \to \mt{arg_2} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adam@1778	1811 \hspace{.1in} \to \mt{sql\_binary} \; \mt{arg_1} \; \mt{arg_2} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_1} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_2} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res}
adamc@544	1812 \end{array}$$
adamc@544	1813
adamc@544	1814 $$\begin{array}{l}
adamc@559	1815 \mt{class} \; \mt{sql\_arith} \\
adamc@559	1816 \mt{val} \; \mt{sql\_int\_arith} : \mt{sql\_arith} \; \mt{int} \\
adamc@559	1817 \mt{val} \; \mt{sql\_float\_arith} : \mt{sql\_arith} \; \mt{float} \\
adamc@559	1818 \mt{val} \; \mt{sql\_neg} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_unary} \; \mt{t} \; \mt{t} \\
adamc@559	1819 \mt{val} \; \mt{sql\_plus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559	1820 \mt{val} \; \mt{sql\_minus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559	1821 \mt{val} \; \mt{sql\_times} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559	1822 \mt{val} \; \mt{sql\_div} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559	1823 \mt{val} \; \mt{sql\_mod} : \mt{sql\_binary} \; \mt{int} \; \mt{int} \; \mt{int}
adamc@559	1824 \end{array}$$
adamc@544	1825
adam@1797	1826 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	1827 $$\begin{array}{l}
adam@1778	1828 \mt{val} \; \mt{sql\_count} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int}
adamc@544	1829 \end{array}$$
adamc@544	1830
adamc@544	1831 $$\begin{array}{l}
adamc@1188	1832 \mt{con} \; \mt{sql\_aggregate} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adam@1778	1833 \mt{val} \; \mt{sql\_aggregate} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{dom} ::: \mt{Type} \to \mt{ran} ::: \mt{Type} \\
adam@1778	1834 \hspace{.1in} \to \mt{sql\_aggregate} \; \mt{dom} \; \mt{ran} \to \mt{sql\_exp} \; \mt{agg} \; \mt{agg} \; \mt{exps} \; \mt{dom} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{ran}
adamc@1188	1835 \end{array}$$
adamc@1188	1836
adamc@1188	1837 $$\begin{array}{l}
adamc@1188	1838 \mt{val} \; \mt{sql\_count\_col} : \mt{t} ::: \mt{Type} \to \mt{sql\_aggregate} \; (\mt{option} \; \mt{t}) \; \mt{int}
adamc@544	1839 \end{array}$$
adam@1400	1840
adam@1400	1841 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	1842
adamc@544	1843 $$\begin{array}{l}
adamc@544	1844 \mt{class} \; \mt{sql\_summable} \\
adamc@544	1845 \mt{val} \; \mt{sql\_summable\_int} : \mt{sql\_summable} \; \mt{int} \\
adamc@544	1846 \mt{val} \; \mt{sql\_summable\_float} : \mt{sql\_summable} \; \mt{float} \\
adam@1777	1847 \mt{val} \; \mt{sql\_avg} : \mt{t} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{sql\_aggregate} \; \mt{t} \; (\mt{option} \; \mt{float}) \\
adam@1400	1848 \mt{val} \; \mt{sql\_sum} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt}
adamc@544	1849 \end{array}$$
adamc@544	1850
adamc@544	1851 $$\begin{array}{l}
adamc@544	1852 \mt{class} \; \mt{sql\_maxable} \\
adamc@544	1853 \mt{val} \; \mt{sql\_maxable\_int} : \mt{sql\_maxable} \; \mt{int} \\
adamc@544	1854 \mt{val} \; \mt{sql\_maxable\_float} : \mt{sql\_maxable} \; \mt{float} \\
adamc@544	1855 \mt{val} \; \mt{sql\_maxable\_string} : \mt{sql\_maxable} \; \mt{string} \\
adamc@544	1856 \mt{val} \; \mt{sql\_maxable\_time} : \mt{sql\_maxable} \; \mt{time} \\
adam@1400	1857 \mt{val} \; \mt{sql\_max} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt} \\
adam@1400	1858 \mt{val} \; \mt{sql\_min} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt}
adamc@544	1859 \end{array}$$
adamc@544	1860
adam@1778	1861 Any SQL query that returns single columns may be turned into a subquery expression.
adam@1777	1862
adam@1777	1863 $$\begin{array}{l}
adam@1778	1864 \mt{val} \; \mt{sql\_subquery} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \\
adam@2155	1865 \hspace{.1in} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_query} \; \mt{tables} \; \mt{agg} \; [] \; [\mt{nm} = \mt{t}] \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{nt}
adamc@1193	1866 \end{array}$$
adamc@1193	1867
adam@1573	1868 There is also an \cd{IF..THEN..ELSE..} construct that is compiled into standard SQL \cd{CASE} expressions.
adam@1573	1869 $$\begin{array}{l}
adam@1778	1870 \mt{val} \; \mt{sql\_if\_then\_else} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778	1871 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{bool} \\
adam@1778	1872 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778	1873 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778	1874 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adam@1573	1875 \end{array}$$
adam@1573	1876
adamc@1193	1877 \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	1878 $$\begin{array}{l}
adamc@1193	1879 \mt{con} \; \mt{sql\_from\_items} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@1193	1880 \mt{val} \; \mt{sql\_from\_table} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adamc@1193	1881 \hspace{.1in} \to \mt{t} ::: \mt{Type} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; \mt{t} \; \mt{fs} \to \mt{name} :: \mt{Name} \to \mt{t} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193	1882 \mt{val} \; \mt{sql\_from\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{name} :: \mt{Name} \to \mt{sql\_query} \; \mt{free} \; [] \; \mt{fs} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193	1883 \mt{val} \; \mt{sql\_from\_comma} : \mt{free} ::: \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \to [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193	1884 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adamc@1193	1885 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2}) \\
adamc@1193	1886 \mt{val} \; \mt{sql\_inner\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \\
adamc@1193	1887 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193	1888 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adam@1778	1889 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193	1890 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2})
adamc@786	1891 \end{array}$$
adamc@786	1892
adamc@786	1893 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	1894 $$\begin{array}{l}
adamc@786	1895 \mt{class} \; \mt{nullify} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@786	1896 \mt{val} \; \mt{nullify\_option} : \mt{t} ::: \mt{Type} \to \mt{nullify} \; (\mt{option} \; \mt{t}) \; (\mt{option} \; \mt{t}) \\
adamc@786	1897 \mt{val} \; \mt{nullify\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{nullify} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@786	1898 \end{array}$$
adamc@786	1899
adamc@786	1900 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	1901
adamc@786	1902 $$\begin{array}{l}
adamc@1193	1903 \mt{val} \; \mt{sql\_left\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{(\mt{Type} \times \mt{Type})\}\} \\
adamc@1193	1904 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@786	1905 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\lambda \mt{r} \Rightarrow \$(\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{nullify} \; \mt{p}.1 \; \mt{p}.2) \; \mt{r})) \; \mt{tabs2}) \\
adamc@1193	1906 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \\
adam@1778	1907 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193	1908 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.2)) \; \mt{tabs2})
adamc@786	1909 \end{array}$$
adamc@786	1910
adamc@544	1911 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	1912 $$\begin{array}{l}
adamc@544	1913 \mt{type} \; \mt{sql\_direction} \\
adamc@544	1914 \mt{val} \; \mt{sql\_asc} : \mt{sql\_direction} \\
adamc@544	1915 \mt{val} \; \mt{sql\_desc} : \mt{sql\_direction} \\
adamc@544	1916 \\
adamc@544	1917 \mt{con} \; \mt{sql\_order\_by} :: \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@544	1918 \mt{val} \; \mt{sql\_order\_by\_Nil} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} :: \{\mt{Type}\} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adam@1778	1919 \mt{val} \; \mt{sql\_order\_by\_Cons} : \mt{tf} ::: (\{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}) \\
adam@1778	1920 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778	1921 \hspace{.1in} \to \mt{sql\_window} \; \mt{tf} \to \mt{tf} \; \mt{tables} \; [] \; \mt{exps} \; \mt{t} \to \mt{sql\_direction} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adam@1684	1922 \mt{val} \; \mt{sql\_order\_by\_random} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544	1923 \\
adamc@544	1924 \mt{type} \; \mt{sql\_limit} \\
adamc@544	1925 \mt{val} \; \mt{sql\_no\_limit} : \mt{sql\_limit} \\
adamc@544	1926 \mt{val} \; \mt{sql\_limit} : \mt{int} \to \mt{sql\_limit} \\
adamc@544	1927 \\
adamc@544	1928 \mt{type} \; \mt{sql\_offset} \\
adamc@544	1929 \mt{val} \; \mt{sql\_no\_offset} : \mt{sql\_offset} \\
adamc@544	1930 \mt{val} \; \mt{sql\_offset} : \mt{int} \to \mt{sql\_offset}
adamc@544	1931 \end{array}$$
adamc@544	1932
adam@1778	1933 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	1934 $$\begin{array}{l}
adam@1778	1935 \mt{con} \; \mt{sql\_expw} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type} \\
adam@1778	1936 \\
adam@1778	1937 \mt{class} \; \mt{sql\_window} :: (\{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}) \to \mt{Type} \\
adam@1778	1938 \mt{val} \; \mt{sql\_window\_normal} : \mt{sql\_window} \; \mt{sql\_exp} \\
adam@1778	1939 \mt{val} \; \mt{sql\_window\_fancy} : \mt{sql\_window} \; \mt{sql\_expw} \\
adam@1778	1940 \mt{val} \; \mt{sql\_window} : \mt{tf} ::: (\{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}) \\
adam@1778	1941 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778	1942 \hspace{.1in} \to \mt{sql\_window} \; \mt{tf} \\
adam@1778	1943 \hspace{.1in} \to \mt{tf} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778	1944 \hspace{.1in} \to \mt{sql\_expw} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778	1945 \\
adam@1778	1946 \mt{con} \; \mt{sql\_partition} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adam@1778	1947 \mt{val} \; \mt{sql\_no\_partition} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778	1948 \hspace{.1in} \to \mt{sql\_partition} \; \mt{tables} \; \mt{agg} \; \mt{exps} \\
adam@1778	1949 \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	1950 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778	1951 \hspace{.1in} \to \mt{sql\_partition} \; \mt{tables} \; \mt{agg} \; \mt{exps} \\
adam@1778	1952 \\
adam@1778	1953 \mt{con} \; \mt{sql\_window\_function} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type} \\
adam@1778	1954 \mt{val} \; \mt{sql\_window\_function} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778	1955 \hspace{.1in} \to \mt{t} ::: \mt{Type} \\
adam@1778	1956 \hspace{.1in} \to \mt{sql\_window\_function} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778	1957 \hspace{.1in} \to \mt{sql\_partition} \; \mt{tables} \; \mt{agg} \; \mt{exps} \\
adam@1778	1958 \hspace{.1in} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adam@1778	1959 \hspace{.1in} \to \mt{sql\_expw} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778	1960 \\
adam@1778	1961 \mt{val} \; \mt{sql\_window\_aggregate} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778	1962 \hspace{.1in} \to \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \\
adam@1778	1963 \hspace{.1in} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt} \\
adam@1778	1964 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778	1965 \hspace{.1in} \to \mt{sql\_window\_function} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{nt} \\
adam@1778	1966 \mt{val} \; \mt{sql\_window\_count} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778	1967 \hspace{.1in} \to \mt{sql\_window\_function} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int} \\
adam@1778	1968 \mt{val} \; \mt{sql\_rank} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778	1969 \hspace{.1in} \to \mt{sql\_window\_function} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int}
adam@1778	1970 \end{array}$$
adam@1778	1971
adamc@545	1972
adamc@545	1973 \subsubsection{DML}
adamc@545	1974
adamc@545	1975 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	1976
adamc@545	1977 $$\begin{array}{l}
adamc@545	1978 \mt{type} \; \mt{dml} \\
adamc@545	1979 \mt{val} \; \mt{dml} : \mt{dml} \to \mt{transaction} \; \mt{unit}
adamc@545	1980 \end{array}$$
adamc@545	1981
adam@1297	1982 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	1983
adam@1297	1984 $$\begin{array}{l}
adam@1297	1985 \mt{val} \; \mt{tryDml} : \mt{dml} \to \mt{transaction} \; (\mt{option} \; \mt{string})
adam@1297	1986 \end{array}$$
adam@1297	1987
adam@1797	1988 Properly typed records may be used to form $\mt{INSERT}$ commands.
adamc@545	1989 $$\begin{array}{l}
adamc@545	1990 \mt{val} \; \mt{insert} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \\
adam@1778	1991 \hspace{.1in} \to \$(\mt{map} \; (\mt{sql\_exp} \; [] \; [] \; []) \; \mt{fields}) \to \mt{dml}
adamc@545	1992 \end{array}$$
adamc@545	1993
adam@2155	1994 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 constant table name $\mt{T}$.
adamc@545	1995 $$\begin{array}{l}
adam@1380	1996 \mt{val} \; \mt{update} : \mt{unchanged} ::: \{\mt{Type}\} \to \mt{changed} :: \{\mt{Type}\} \to [\mt{changed} \sim \mt{unchanged}] \\
adam@1778	1997 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; []) \; \mt{changed}) \\
adam@1778	1998 \hspace{.1in} \to \mt{sql\_table} \; (\mt{changed} \rc \mt{unchanged}) \to \mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545	1999 \end{array}$$
adamc@545	2000
adam@1578	2001 A $\mt{DELETE}$ command is formed from a table and a $\mt{WHERE}$ clause. The above use of $\mt{T}$ is repeated.
adamc@545	2002 $$\begin{array}{l}
adam@1778	2003 \mt{val} \; \mt{delete} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \to \mt{sql\_exp} \; [\mt{T} = \mt{fields}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545	2004 \end{array}$$
adamc@545	2005
adamc@546	2006 \subsubsection{Sequences}
adamc@546	2007
adamc@546	2008 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	2009
adamc@546	2010 $$\begin{array}{l}
adamc@546	2011 \mt{type} \; \mt{sql\_sequence} \\
adamc@1085	2012 \mt{val} \; \mt{nextval} : \mt{sql\_sequence} \to \mt{transaction} \; \mt{int} \\
adamc@1085	2013 \mt{val} \; \mt{setval} : \mt{sql\_sequence} \to \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@546	2014 \end{array}$$
adamc@546	2015
adamc@546	2016
adam@1648	2017 \subsection{\label{xml}XML}
adamc@547	2018
adam@1333	2019 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	2020
adam@1642	2021 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	2022 $$\begin{array}{l}
adamc@547	2023 \mt{con} \; \mt{xml} :: \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547	2024 \end{array}$$
adamc@547	2025
adamc@547	2026 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	2027 $$\begin{array}{l}
adamc@547	2028 \mt{con} \; \mt{tag} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547	2029 \end{array}$$
adamc@547	2030
adamc@547	2031 Literal text may be injected into XML as ``CDATA.''
adamc@547	2032 $$\begin{array}{l}
adamc@547	2033 \mt{val} \; \mt{cdata} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{string} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adamc@547	2034 \end{array}$$
adamc@547	2035
adam@1358	2036 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	2037 $$\begin{array}{l}
adam@1358	2038 \mt{val} \; \mt{cdataChar} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{char} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adam@1358	2039 \end{array}$$
adam@1358	2040
adamc@547	2041 There is a function for producing an XML tree with a particular tag at its root.
adamc@547	2042 $$\begin{array}{l}
adamc@547	2043 \mt{val} \; \mt{tag} : \mt{attrsGiven} ::: \{\mt{Type}\} \to \mt{attrsAbsent} ::: \{\mt{Type}\} \to \mt{ctxOuter} ::: \{\mt{Unit}\} \to \mt{ctxInner} ::: \{\mt{Unit}\} \\
adamc@547	2044 \hspace{.1in} \to \mt{useOuter} ::: \{\mt{Type}\} \to \mt{useInner} ::: \{\mt{Type}\} \to \mt{bindOuter} ::: \{\mt{Type}\} \to \mt{bindInner} ::: \{\mt{Type}\} \\
adam@1380	2045 \hspace{.1in} \to [\mt{attrsGiven} \sim \mt{attrsAbsent}] \Rightarrow [\mt{useOuter} \sim \mt{useInner}] \Rightarrow [\mt{bindOuter} \sim \mt{bindInner}] \\
adam@1749	2046 \hspace{.1in} \Rightarrow \mt{css\_class} \\
adam@1643	2047 \hspace{.1in} \to \mt{option} \; (\mt{signal} \; \mt{css\_class}) \\
adam@1750	2048 \hspace{.1in} \to \mt{css\_style} \\
adam@1751	2049 \hspace{.1in} \to \mt{option} \; (\mt{signal} \; \mt{css\_style}) \\
adamc@787	2050 \hspace{.1in} \to \$\mt{attrsGiven} \\
adamc@547	2051 \hspace{.1in} \to \mt{tag} \; (\mt{attrsGiven} \rc \mt{attrsAbsent}) \; \mt{ctxOuter} \; \mt{ctxInner} \; \mt{useOuter} \; \mt{bindOuter} \\
adamc@547	2052 \hspace{.1in} \to \mt{xml} \; \mt{ctxInner} \; \mt{useInner} \; \mt{bindInner} \to \mt{xml} \; \mt{ctxOuter} \; (\mt{useOuter} \rc \mt{useInner}) \; (\mt{bindOuter} \rc \mt{bindInner})
adamc@547	2053 \end{array}$$
adam@1750	2054 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	2055
adam@1643	2056 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	2057
adam@1751	2058 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	2059
adamc@547	2060 Two XML fragments may be concatenated.
adamc@547	2061 $$\begin{array}{l}
adamc@547	2062 \mt{val} \; \mt{join} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{bind_1} ::: \{\mt{Type}\} \to \mt{bind_2} ::: \{\mt{Type}\} \\
adam@1380	2063 \hspace{.1in} \to [\mt{use_1} \sim \mt{bind_1}] \Rightarrow [\mt{bind_1} \sim \mt{bind_2}] \\
adamc@547	2064 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind_1} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{bind_1}) \; \mt{bind_2} \to \mt{xml} \; \mt{ctx} \; \mt{use_1} \; (\mt{bind_1} \rc \mt{bind_2})
adamc@547	2065 \end{array}$$
adamc@547	2066
adamc@547	2067 Finally, any XML fragment may be updated to ``claim'' to use more form fields than it does.
adamc@547	2068 $$\begin{array}{l}
adam@1380	2069 \mt{val} \; \mt{useMore} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{use_2} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to [\mt{use_1} \sim \mt{use_2}] \\
adamc@547	2070 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{use_2}) \; \mt{bind}
adamc@547	2071 \end{array}$$
adamc@547	2072
adam@2008	2073 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	2074
adam@2047	2075 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	2076
adamc@547	2077 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	2078 $$\begin{array}{l}
adam@1641	2079 \mt{val} \; \mt{error} : \mt{t} ::: \mt{Type} \to \mt{xbody} \to \mt{t}
adamc@547	2080 \end{array}$$
adamc@547	2081
adamc@549	2082
adamc@701	2083 \subsection{Client-Side Programming}
adamc@659	2084
adamc@701	2085 Ur/Web supports running code on web browsers, via automatic compilation to JavaScript.
adamc@701	2086
adamc@701	2087 \subsubsection{The Basics}
adamc@701	2088
adam@1400	2089 All of the functions in this subsection are client-side only.
adam@1400	2090
adam@1297	2091 Clients can open alert and confirm dialog boxes, in the usual annoying JavaScript way.
adamc@701	2092 $$\begin{array}{l}
adam@1297	2093 \mt{val} \; \mt{alert} : \mt{string} \to \mt{transaction} \; \mt{unit} \\
adam@1297	2094 \mt{val} \; \mt{confirm} : \mt{string} \to \mt{transaction} \; \mt{bool}
adamc@701	2095 \end{array}$$
adamc@701	2096
adamc@701	2097 Any transaction may be run in a new thread with the $\mt{spawn}$ function.
adamc@701	2098 $$\begin{array}{l}
adamc@701	2099 \mt{val} \; \mt{spawn} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit}
adamc@701	2100 \end{array}$$
adamc@701	2101
adamc@701	2102 The current thread can be paused for at least a specified number of milliseconds.
adamc@701	2103 $$\begin{array}{l}
adamc@701	2104 \mt{val} \; \mt{sleep} : \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@701	2105 \end{array}$$
adamc@701	2106
adam@1770	2107 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	2108 $$\begin{array}{l}
adamc@787	2109 \mt{val} \; \mt{onError} : (\mt{xbody} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787	2110 \mt{val} \; \mt{onFail} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787	2111 \mt{val} \; \mt{onConnectFail} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787	2112 \mt{val} \; \mt{onDisconnect} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787	2113 \mt{val} \; \mt{onServerError} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit}
adamc@787	2114 \end{array}$$
adamc@787	2115
adam@1555	2116 There are also functions to register standard document-level event handlers.
adam@1555	2117
adam@1555	2118 $$\begin{array}{l}
adam@1783	2119 \mt{val} \; \mt{onClick} : (\mt{mouseEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783	2120 \mt{val} \; \mt{onDblclick} : (\mt{mouseEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783	2121 \mt{val} \; \mt{onKeydown} : (\mt{keyEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783	2122 \mt{val} \; \mt{onKeypress} : (\mt{keyEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783	2123 \mt{val} \; \mt{onKeyup} : (\mt{keyEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783	2124 \mt{val} \; \mt{onMousedown} : (\mt{mouseEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783	2125 \mt{val} \; \mt{onMouseup} : (\mt{mouseEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit}
adam@1555	2126 \end{array}$$
adam@1555	2127
adam@1559	2128 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	2129
adam@1559	2130 $$\begin{array}{l}
adam@1559	2131 \mt{val} \; \mt{preventDefault} : \mt{transaction} \; \mt{unit} \\
adam@1559	2132 \mt{val} \; \mt{stopPropagation} : \mt{transaction} \; \mt{unit}
adam@1559	2133 \end{array}$$
adam@1559	2134
adam@1926	2135 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	2136
adam@1926	2137 $$\begin{array}{l}
adam@1926	2138 \mt{val} \; \mt{script} : \mt{unit} \to \mt{tag} \; [\mt{Code} = \mt{transaction} \; \mt{unit}] \; \mt{head} \; [] \; [] \; []
adam@1926	2139 \end{array}$$
adam@1926	2140
adam@1926	2141 Note that the Ur/Web version of \cd{<script>} is used like \cd{<script code=\{...\}/>}, rather than \cd{<script>...</script>}.
adam@1926	2142
adam@1556	2143 \subsubsection{Node IDs}
adam@1556	2144
adam@1556	2145 There is an abstract type of node IDs that may be assigned to \cd{id} attributes of most HTML tags.
adam@1556	2146
adam@1556	2147 $$\begin{array}{l}
adam@1556	2148 \mt{type} \; \mt{id} \\
adam@1556	2149 \mt{val} \; \mt{fresh} : \mt{transaction} \; \mt{id}
adam@1556	2150 \end{array}$$
adam@1556	2151
adam@1785	2152 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	2153
adam@1785	2154 One further use of IDs is as handles for requesting that \emph{focus} be given to specific tags.
adam@1785	2155
adam@1785	2156 $$\begin{array}{l}
adam@1785	2157 \mt{val} \; \mt{giveFocus} : \mt{id} \to \mt{transaction} \; \mt{unit}
adam@1785	2158 \end{array}$$
adam@1556	2159
adam@1643	2160 \subsubsection{\label{signals}Functional-Reactive Page Generation}
adamc@701	2161
adamc@701	2162 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	2163
adam@1403	2164 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	2165
adamc@659	2166 $$\begin{array}{l}
adamc@659	2167 \mt{con} \; \mt{source} :: \mt{Type} \to \mt{Type} \\
adamc@659	2168 \mt{val} \; \mt{source} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{transaction} \; (\mt{source} \; \mt{t}) \\
adamc@659	2169 \mt{val} \; \mt{set} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@659	2170 \mt{val} \; \mt{get} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@659	2171 \end{array}$$
adamc@659	2172
adam@1400	2173 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	2174
adam@1608	2175 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	2176
adamc@659	2177 $$\begin{array}{l}
adamc@659	2178 \mt{con} \; \mt{signal} :: \mt{Type} \to \mt{Type} \\
adamc@659	2179 \mt{val} \; \mt{signal\_monad} : \mt{monad} \; \mt{signal} \\
adam@1608	2180 \mt{val} \; \mt{signal} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{signal} \; \mt{t} \\
adam@1608	2181 \mt{val} \; \mt{current} : \mt{t} ::: \mt{Type} \to \mt{signal} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@659	2182 \end{array}$$
adamc@659	2183
adamc@659	2184 A reactive portion of an HTML page is injected with a $\mt{dyn}$ tag, which has a signal-valued attribute $\mt{Signal}$.
adamc@659	2185
adamc@659	2186 $$\begin{array}{l}
adam@1641	2187 \mt{val} \; \mt{dyn} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to [\mt{ctx} \sim [\mt{Dyn}]] \Rightarrow \mt{unit} \\
adam@1641	2188 \hspace{.1in} \to \mt{tag} \; [\mt{Signal} = \mt{signal} \; (\mt{xml} \; ([\mt{Dyn}] \rc \mt{ctx}) \; \mt{use} \; \mt{bind})] \; ([\mt{Dyn}] \rc \mt{ctx}) \; [] \; \mt{use} \; \mt{bind}
adamc@659	2189 \end{array}$$
adamc@659	2190
adam@1648	2191 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	2192
adam@1648	2193 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	2194
adam@1786	2195 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	2196
adam@1786	2197 $$\begin{array}{l}
adam@1786	2198 \mt{val} \; \mt{active} : \mt{unit} \to \mt{tag} \; [\mt{Code} = \mt{transaction} \; \mt{xbody}] \; \mt{body} \; [] \; [] \; []
adam@1786	2199 \end{array}$$
adamc@701	2200
adamc@914	2201 \subsubsection{Remote Procedure Calls}
adamc@914	2202
adamc@914	2203 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	2204
adamc@914	2205 $$\begin{array}{l}
adamc@914	2206 \mt{val} \; \mt{rpc} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@914	2207 \end{array}$$
adamc@914	2208
adam@1848	2209 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	2210
adam@1848	2211 $$\begin{array}{l}
adam@1848	2212 \mt{val} \; \mt{tryRpc} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; \mt{t} \to \mt{transaction} \; (\mt{option} \; \mt{t})
adam@1848	2213 \end{array}$$
adam@1848	2214
adamc@701	2215 \subsubsection{Asynchronous Message-Passing}
adamc@701	2216
adamc@701	2217 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	2218
adamc@701	2219 $$\begin{array}{l}
adamc@701	2220 \mt{type} \; \mt{client} \\
adamc@701	2221 \mt{val} \; \mt{self} : \mt{transaction} \; \mt{client}
adamc@701	2222 \end{array}$$
adamc@701	2223
adam@1940	2224 \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	2225
adamc@701	2226 $$\begin{array}{l}
adamc@701	2227 \mt{con} \; \mt{channel} :: \mt{Type} \to \mt{Type} \\
adamc@701	2228 \mt{val} \; \mt{channel} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; (\mt{channel} \; \mt{t}) \\
adamc@701	2229 \mt{val} \; \mt{send} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@701	2230 \mt{val} \; \mt{recv} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@701	2231 \end{array}$$
adamc@701	2232
adamc@701	2233 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	2234
adamc@701	2235 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	2236
adam@1551	2237 \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	2238
adamc@659	2239
adamc@549	2240 \section{Ur/Web Syntax Extensions}
adamc@549	2241
adamc@549	2242 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	2243
adamc@549	2244 \subsection{SQL}
adamc@549	2245
adamc@786	2246 \subsubsection{\label{tables}Table Declarations}
adamc@786	2247
adamc@788	2248 $\mt{table}$ declarations may include constraints, via these grammar rules.
adamc@788	2249 $$\begin{array}{rrcll}
adam@1594	2250 \textrm{Declarations} & d &::=& \mt{table} \; x : c \; [pk[,]] \; cts \mid \mt{view} \; x = V \\
adamc@788	2251 \textrm{Primary key constraints} & pk &::=& \mt{PRIMARY} \; \mt{KEY} \; K \\
adam@1722	2252 \textrm{Keys} & K &::=& f \mid (f, (f,)^+) \mid \{\{e\}\} \\
adamc@788	2253 \textrm{Constraint sets} & cts &::=& \mt{CONSTRAINT} f \; ct \mid cts, cts \mid \{\{e\}\} \\
adamc@788	2254 \textrm{Constraints} & ct &::=& \mt{UNIQUE} \; K \mid \mt{CHECK} \; E \\
adamc@788	2255 &&& \mid \mt{FOREIGN} \; \mt{KEY} \; K \; \mt{REFERENCES} \; F \; (K) \; [\mt{ON} \; \mt{DELETE} \; pr] \; [\mt{ON} \; \mt{UPDATE} \; pr] \\
adamc@788	2256 \textrm{Foreign tables} & F &::=& x \mid \{\{e\}\} \\
adam@1594	2257 \textrm{Propagation modes} & pr &::=& \mt{NO} \; \mt{ACTION} \mid \mt{RESTRICT} \mid \mt{CASCADE} \mid \mt{SET} \; \mt{NULL} \\
adam@1594	2258 \textrm{View expressions} & V &::=& Q \mid \{e\}
adamc@788	2259 \end{array}$$
adamc@788	2260
adamc@788	2261 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	2262
adamc@788	2263
adamc@549	2264 \subsubsection{Queries}
adamc@549	2265
adamc@550	2266 Queries $Q$ are added to the rules for expressions $e$.
adamc@550	2267
adamc@549	2268 $$\begin{array}{rrcll}
adam@1684	2269 \textrm{Queries} & Q &::=& (q \; [\mt{ORDER} \; \mt{BY} \; O] \; [\mt{LIMIT} \; N] \; [\mt{OFFSET} \; N]) \\
adamc@1085	2270 \textrm{Pre-queries} & q &::=& \mt{SELECT} \; [\mt{DISTINCT}] \; P \; \mt{FROM} \; F,^+ \; [\mt{WHERE} \; E] \; [\mt{GROUP} \; \mt{BY} \; p,^+] \; [\mt{HAVING} \; E] \\
adamc@1085	2271 &&& \mid q \; R \; q \mid \{\{\{e\}\}\} \\
adam@1684	2272 \textrm{Relational operators} & R &::=& \mt{UNION} \mid \mt{INTERSECT} \mid \mt{EXCEPT} \\
adam@2093	2273 \textrm{$\mt{ORDER \; BY}$ items} & O &::=& \mt{RANDOM} [()] \mid \hat{E} \; [o] \mid \hat{E} \; [o], O \mid \{\{\{e\}\}\}
adamc@549	2274 \end{array}$$
adamc@549	2275
adamc@549	2276 $$\begin{array}{rrcll}
adamc@549	2277 \textrm{Projections} & P &::=& \ast & \textrm{all columns} \\
adamc@549	2278 &&& p,^+ & \textrm{particular columns} \\
adamc@549	2279 \textrm{Pre-projections} & p &::=& t.f & \textrm{one column from a table} \\
adamc@558	2280 &&& t.\{\{c\}\} & \textrm{a record of columns from a table (of kind $\{\mt{Type}\}$)} \\
adam@1627	2281 &&& t.* & \textrm{all columns from a table} \\
adam@1778	2282 &&& \hat{E} \; [\mt{AS} \; f] & \textrm{expression column} \\
adamc@549	2283 \textrm{Table names} & t &::=& x & \textrm{constant table name (automatically capitalized)} \\
adamc@549	2284 &&& X & \textrm{constant table name} \\
adamc@549	2285 &&& \{\{c\}\} & \textrm{computed table name (of kind $\mt{Name}$)} \\
adamc@549	2286 \textrm{Column names} & f &::=& X & \textrm{constant column name} \\
adamc@549	2287 &&& \{c\} & \textrm{computed column name (of kind $\mt{Name}$)} \\
adamc@549	2288 \textrm{Tables} & T &::=& x & \textrm{table variable, named locally by its own capitalization} \\
adam@1756	2289 &&& x \; \mt{AS} \; X & \textrm{table variable, with local name} \\
adam@1756	2290 &&& x \; \mt{AS} \; \{c\} & \textrm{table variable, with computed local name} \\
adam@2155	2291 &&& \{\{e\}\} \; \mt{AS} \; X & \textrm{computed table expression, with local name} \\
adam@1756	2292 &&& \{\{e\}\} \; \mt{AS} \; \{c\} & \textrm{computed table expression, with computed local name} \\
adamc@1085	2293 \textrm{$\mt{FROM}$ items} & F &::=& T \mid \{\{e\}\} \mid F \; J \; \mt{JOIN} \; F \; \mt{ON} \; E \\
adamc@1085	2294 &&& \mid F \; \mt{CROSS} \; \mt{JOIN} \ F \\
adam@2155	2295 &&& \mid (Q) \; \mt{AS} \; X \mid (Q) \; \mt{AS} \; \{c\} \\
adam@2155	2296 &&& \mid (\{\{e\}\}) \; \mt{AS} \; t \\
adamc@1085	2297 \textrm{Joins} & J &::=& [\mt{INNER}] \\
adamc@1085	2298 &&& \mid [\mt{LEFT} \mid \mt{RIGHT} \mid \mt{FULL}] \; [\mt{OUTER}] \\
adam@1587	2299 \textrm{SQL expressions} & E &::=& t.f & \textrm{column references} \\
adamc@549	2300 &&& X & \textrm{named expression references} \\
adam@1490	2301 &&& \{[e]\} & \textrm{injected native Ur expressions} \\
adam@1778	2302 &&& \{e\} & \textrm{computed expressions, probably using $\mt{sql\_exp}$ directly} \\
adamc@549	2303 &&& \mt{TRUE} \mid \mt{FALSE} & \textrm{boolean constants} \\
adamc@549	2304 &&& \ell & \textrm{primitive type literals} \\
adamc@549	2305 &&& \mt{NULL} & \textrm{null value (injection of $\mt{None}$)} \\
adamc@549	2306 &&& E \; \mt{IS} \; \mt{NULL} & \textrm{nullness test} \\
adam@1602	2307 &&& \mt{COALESCE}(E, E) & \textrm{take first non-null value} \\
adamc@549	2308 &&& n & \textrm{nullary operators} \\
adamc@549	2309 &&& u \; E & \textrm{unary operators} \\
adamc@549	2310 &&& E \; b \; E & \textrm{binary operators} \\
adam@1778	2311 &&& \mt{COUNT}(\ast) & \textrm{count number of rows} \\
adam@1778	2312 &&& a(E) & \textrm{other aggregate function} \\
adam@1573	2313 &&& \mt{IF} \; E \; \mt{THEN} \; E \; \mt{ELSE} \; E & \textrm{conditional} \\
adam@1778	2314 &&& (Q) & \textrm{subquery (must return a single expression column)} \\
adamc@549	2315 &&& (E) & \textrm{explicit precedence} \\
adamc@549	2316 \textrm{Nullary operators} & n &::=& \mt{CURRENT\_TIMESTAMP} \\
adamc@549	2317 \textrm{Unary operators} & u &::=& \mt{NOT} \\
adam@2169	2318 \textrm{Binary operators} & b &::=& \mt{AND} \mid \mt{OR} \mid = \mid \neq \mid < \mid \leq \mid > \mid \geq \mid \mt{LIKE} \\
adamc@1188	2319 \textrm{Aggregate functions} & a &::=& \mt{COUNT} \mid \mt{AVG} \mid \mt{SUM} \mid \mt{MIN} \mid \mt{MAX} \\
adam@1543	2320 \textrm{Directions} & o &::=& \mt{ASC} \mid \mt{DESC} \mid \{e\} \\
adamc@549	2321 \textrm{SQL integer} & N &::=& n \mid \{e\} \\
adam@1778	2322 \textrm{Windowable expressions} & \hat{E} &::=& E \\
adam@1778	2323 &&& w \; [\mt{OVER} \; ( & \textrm{(Postgres only)} \\
adam@1778	2324 &&& \hspace{.1in} [\mt{PARTITION} \; \mt{BY} \; E] \\
adam@1778	2325 &&& \hspace{.1in} [\mt{ORDER} \; \mt{BY} \; O])] \\
adam@1778	2326 \textrm{Window function} & w &::=& \mt{RANK}() \\
adam@1778	2327 &&& \mt{COUNT}(*) \\
adam@1778	2328 &&& a(E)
adamc@549	2329 \end{array}$$
adamc@549	2330
adamc@1085	2331 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	2332
adam@1683	2333 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	2334
adamc@550	2335 \subsubsection{DML}
adamc@550	2336
adamc@550	2337 DML commands $D$ are added to the rules for expressions $e$.
adamc@550	2338
adamc@550	2339 $$\begin{array}{rrcll}
adamc@550	2340 \textrm{Commands} & D &::=& (\mt{INSERT} \; \mt{INTO} \; T^E \; (f,^+) \; \mt{VALUES} \; (E,^+)) \\
adamc@550	2341 &&& (\mt{UPDATE} \; T^E \; \mt{SET} \; (f = E,)^+ \; \mt{WHERE} \; E) \\
adamc@550	2342 &&& (\mt{DELETE} \; \mt{FROM} \; T^E \; \mt{WHERE} \; E) \\
adamc@550	2343 \textrm{Table expressions} & T^E &::=& x \mid \{\{e\}\}
adamc@550	2344 \end{array}$$
adamc@550	2345
adamc@550	2346 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	2347
adamc@551	2348 \subsection{XML}
adamc@551	2349
adamc@551	2350 XML fragments $L$ are added to the rules for expressions $e$.
adamc@551	2351
adamc@551	2352 $$\begin{array}{rrcll}
adamc@551	2353 \textrm{XML fragments} & L &::=& \texttt{<xml/>} \mid \texttt{<xml>}l^*\texttt{</xml>} \\
adamc@551	2354 \textrm{XML pieces} & l &::=& \textrm{text} & \textrm{cdata} \\
adamc@551	2355 &&& \texttt{<}g\texttt{/>} & \textrm{tag with no children} \\
adamc@551	2356 &&& \texttt{<}g\texttt{>}l^*\texttt{</}x\texttt{>} & \textrm{tag with children} \\
adamc@559	2357 &&& \{e\} & \textrm{computed XML fragment} \\
adamc@559	2358 &&& \{[e]\} & \textrm{injection of an Ur expression, via the $\mt{Top}.\mt{txt}$ function} \\
adam@2075	2359 \textrm{Tag} & g &::=& h \; (x [= v])^* \\
adamc@551	2360 \textrm{Tag head} & h &::=& x & \textrm{tag name} \\
adamc@551	2361 &&& h\{c\} & \textrm{constructor parameter} \\
adamc@551	2362 \textrm{Attribute value} & v &::=& \ell & \textrm{literal value} \\
adamc@551	2363 &&& \{e\} & \textrm{computed value} \\
adamc@551	2364 \end{array}$$
adamc@551	2365
adam@2075	2366 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	2367
adam@1751	2368 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	2369
adam@1751	2370 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	2371
adamc@1198	2372 \section{\label{structure}The Structure of Web Applications}
adamc@553	2373
adam@1797	2374 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	2375
adam@1532	2376 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	2377
adam@1787	2378 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	2379
adam@1370	2380 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	2381
adamc@553	2382 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	2383
adamc@553	2384 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	2385
adam@1653	2386 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	2387 \begin{itemize}
adam@1653	2388 \item Functions are disallowed, since there is no obvious way to serialize them safely.
adam@1653	2389 \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	2390 \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	2391 \end{itemize}
adamc@553	2392
adamc@660	2393 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	2394
adamc@789	2395 \medskip
adamc@789	2396
adam@1347	2397 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	2398
adamc@789	2399 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	2400
adam@1348	2401 \subsection{Tasks}
adam@1348	2402
adam@1348	2403 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	2404
adam@1348	2405 $$\begin{array}{l}
adam@1348	2406 \mt{con} \; \mt{task\_kind} :: \mt{Type} \to \mt{Type} \\
adam@1348	2407 \mt{val} \; \mt{initialize} : \mt{task\_kind} \; \mt{unit} \\
adam@1349	2408 \mt{val} \; \mt{clientLeaves} : \mt{task\_kind} \; \mt{client} \\
adam@1349	2409 \mt{val} \; \mt{periodic} : \mt{int} \to \mt{task\_kind} \; \mt{unit}
adam@1348	2410 \end{array}$$
adam@1348	2411
adam@1348	2412 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	2413
adam@1348	2414 The currently supported task kinds are:
adam@1348	2415 \begin{itemize}
adam@1349	2416 \item $\mt{initialize}$: Code that is run when the application starts up.
adam@1348	2417 \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	2418 \item $\mt{periodic} \; n$: Code that is run when the application starts up and then every $n$ seconds thereafter.
adam@1348	2419 \end{itemize}
adam@1348	2420
adamc@553	2421
adam@2008	2422 \section{\label{ffi}The Foreign Function Interface}
adamc@897	2423
adamc@897	2424 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	2425
adamc@897	2426 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	2427
adamc@897	2428 \begin{itemize}
adamc@897	2429 \item \texttt{clientOnly Module.ident} registers a value as being allowed only in client-side code.
adamc@897	2430 \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	2431 \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	2432 \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	2433 \item \texttt{include FILE} requests inclusion of a C header file.
adam@2198	2434 \item \texttt{jsFile FILE} requests inclusion of a JavaScript source file.
adamc@897	2435 \item \texttt{jsFunc Module.ident=name} gives a mapping from an Ur name for a value to a JavaScript name.
adamc@897	2436 \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	2437 \item \texttt{script URL} requests inclusion of a JavaScript source file within application HTML.
adamc@897	2438 \item \texttt{serverOnly Module.ident} registers a value as being allowed only in server-side code.
adamc@897	2439 \end{itemize}
adamc@897	2440
adamc@897	2441 \subsection{Writing C FFI Code}
adamc@897	2442
adam@1881	2443 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	2444
adamc@897	2445 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	2446
adamc@897	2447 \begin{itemize}
adam@1881	2448 \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	2449 \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	2450 \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	2451 \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	2452 \end{itemize}
adamc@897	2453
adam@1881	2454 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	2455 \begin{itemize}
adamc@897	2456 \item \begin{verbatim}
adamc@897	2457 void uw_error(uw_context, failure_kind, const char *fmt, ...);
adamc@897	2458 \end{verbatim}
adamc@897	2459 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	2460
adam@1329	2461 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	2462
adamc@897	2463 \item \begin{verbatim}
adam@1469	2464 void uw_set_error_message(uw_context, const char *fmt, ...);
adam@1469	2465 \end{verbatim}
adam@1469	2466 This simpler form of \texttt{uw\_error()} saves an error message without immediately aborting execution.
adam@1469	2467
adam@1469	2468 \item \begin{verbatim}
adamc@897	2469 void uw_push_cleanup(uw_context, void (func)(void ), void *arg);
adamc@897	2470 void uw_pop_cleanup(uw_context);
adamc@897	2471 \end{verbatim}
adam@1329	2472 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	2473
adam@1329	2474 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	2475
adamc@897	2476 \item \begin{verbatim}
adamc@897	2477 void *uw_malloc(uw_context, size_t);
adamc@897	2478 \end{verbatim}
adam@1329	2479 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	2480
adam@1329	2481 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	2482
adamc@897	2483 \item \begin{verbatim}
adamc@897	2484 typedef void (uw_callback)(void );
adam@1328	2485 typedef void (uw_callback_with_retry)(void , int will_retry);
adam@2001	2486 int uw_register_transactional(uw_context, void *data, uw_callback commit,
adam@2001	2487 uw_callback rollback, uw_callback_with_retry free);
adamc@897	2488 \end{verbatim}
adam@2001	2489 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	2490
adam@2000	2491 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	2492
adam@1329	2493 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	2494
adam@1329	2495 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	2496
adam@1469	2497 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	2498
adamc@1085	2499 \item \begin{verbatim}
adamc@1085	2500 void uw_get_global(uw_context, char name);
adamc@1085	2501 void uw_set_global(uw_context, char name, void data, uw_callback free);
adamc@1085	2502 \end{verbatim}
adam@1329	2503 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	2504
adamc@897	2505 \end{itemize}
adamc@897	2506
adamc@897	2507 \subsection{Writing JavaScript FFI Code}
adamc@897	2508
adam@2198	2509 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, and one easy way to get code included is with the \texttt{jsFile} directive.
adamc@897	2510
adamc@897	2511 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	2512
adamc@897	2513 \begin{itemize}
adamc@897	2514 \item Integers, floats, strings, characters, and booleans are represented in the usual JavaScript way.
adam@1996	2515 \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	2516 \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	2517 \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	2518 \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	2519 \item As in the C FFI, all abstract types of program syntax are implemented with strings in JavaScript.
adam@1996	2520 \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	2521 \end{itemize}
adamc@897	2522
adam@1644	2523 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	2524
adam@1644	2525 \begin{itemize}
adam@1644	2526 \item Sources should be treated as an abstract type, manipulated via:
adam@1644	2527 \begin{itemize}
adam@1644	2528 \item \cd{sc(v)}, to create a source initialized to \cd{v}
adam@1644	2529 \item \cd{sg(s)}, to retrieve the current value of source \cd{s}
adam@1644	2530 \item \cd{sv(s, v)}, to set source \cd{s} to value \cd{v}
adam@1644	2531 \end{itemize}
adam@1644	2532
adam@1644	2533 \item Signals should be treated as an abstract type, manipulated via:
adam@1644	2534 \begin{itemize}
adam@1644	2535 \item \cd{sr(v)} and \cd{sb(s, f)}, the ``return'' and ``bind'' monad operators, respectively
adam@1644	2536 \item \cd{ss(s)}, to produce the signal corresponding to source \cd{s}
adam@1644	2537 \item \cd{scur(s)}, to get the current value of signal \cd{s}
adam@1644	2538 \end{itemize}
adam@1644	2539
adam@1644	2540 \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	2541
adam@1702	2542 \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	2543
adam@1644	2544 \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	2545 \end{itemize}
adamc@897	2546
adam@1833	2547 \subsection{Introducing New HTML Tags}
adam@1833	2548
adam@1833	2549 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	2550
adam@1833	2551 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	2552
adam@2010	2553 \subsection{The Less Safe FFI}
adam@2010	2554
adam@2010	2555 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	2556
adam@2010	2557 When the less safe mode is enabled, declarations like this one are accepted, at the top level of a \texttt{.ur} file:
adam@2010	2558 \begin{verbatim}
adam@2010	2559 ffi foo : int -> int
adam@2010	2560 \end{verbatim}
adam@2010	2561
adam@2010	2562 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	2563 \begin{itemize}
adam@2010	2564 \item \texttt{effectful}
adam@2010	2565 \item \texttt{benignEffectful}
adam@2010	2566 \item \texttt{clientOnly}
adam@2010	2567 \item \texttt{serverOnly}
adam@2010	2568 \item \texttt{jsFunc "putJsFuncNameHere"}
adam@2010	2569 \end{itemize}
adam@2010	2570
adam@2039	2571 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	2572
adamc@897	2573
adam@2042	2574 \section{\label{phases}Compiler Phases}
adam@2042	2575
adam@2042	2576 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	2577
adamc@552	2578 In this section, we step through the main phases of compilation, noting what consequences each phase has for effective programming.
adamc@552	2579
adamc@552	2580 \subsection{Parse}
adamc@552	2581
adamc@552	2582 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	2583
adamc@552	2584 \subsection{Elaborate}
adamc@552	2585
adamc@552	2586 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	2587
adam@1378	2588 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	2589
adamc@552	2590 \subsection{Unnest}
adamc@552	2591
adamc@552	2592 Named local function definitions are moved to the top level, to avoid the need to generate closures.
adamc@552	2593
adamc@552	2594 \subsection{Corify}
adamc@552	2595
adamc@552	2596 Module system features are compiled away, through inlining of functor definitions at application sites. Afterward, most abstraction boundaries are broken, facilitating optimization.
adamc@552	2597
adamc@552	2598 \subsection{Especialize}
adamc@552	2599
adam@1356	2600 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	2601
adamc@552	2602 \subsection{Untangle}
adamc@552	2603
adam@1797	2604 Remove unnecessary mutual recursion, splitting recursive groups into strongly connected components.
adamc@552	2605
adamc@552	2606 \subsection{Shake}
adamc@552	2607
adamc@552	2608 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	2609
adamc@661	2610 \subsection{Rpcify}
adamc@661	2611
adamc@661	2612 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	2613
adamc@661	2614 \subsection{Untangle, Shake}
adamc@661	2615
adamc@661	2616 Repeat these simplifications.
adamc@661	2617
adamc@553	2618 \subsection{\label{tag}Tag}
adamc@552	2619
adamc@552	2620 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	2621
adamc@552	2622 \subsection{Reduce}
adamc@552	2623
adamc@552	2624 Apply definitional equality rules to simplify the program as much as possible. This effectively includes inlining of every non-recursive definition.
adamc@552	2625
adamc@552	2626 \subsection{Unpoly}
adamc@552	2627
adamc@552	2628 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	2629
adamc@552	2630 \subsection{Specialize}
adamc@552	2631
adamc@558	2632 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	2633
adamc@552	2634 \subsection{Shake}
adamc@552	2635
adamc@558	2636 Here the compiler repeats the earlier Shake phase.
adamc@552	2637
adamc@552	2638 \subsection{Monoize}
adamc@552	2639
adamc@552	2640 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	2641
adamc@552	2642 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	2643
adamc@552	2644 \subsection{MonoOpt}
adamc@552	2645
adamc@552	2646 Simple algebraic laws are applied to simplify the program, focusing especially on efficient imperative generation of HTML pages.
adamc@552	2647
adamc@552	2648 \subsection{MonoUntangle}
adamc@552	2649
adamc@552	2650 Unnecessary mutual recursion is broken up again.
adamc@552	2651
adamc@552	2652 \subsection{MonoReduce}
adamc@552	2653
adamc@552	2654 Equivalents of the definitional equality rules are applied to simplify programs, with inlining again playing a major role.
adamc@552	2655
adamc@552	2656 \subsection{MonoShake, MonoOpt}
adamc@552	2657
adamc@552	2658 Unneeded declarations are removed, and basic optimizations are repeated.
adamc@552	2659
adamc@552	2660 \subsection{Fuse}
adamc@552	2661
adamc@552	2662 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	2663
adamc@552	2664 \subsection{MonoUntangle, MonoShake}
adamc@552	2665
adamc@552	2666 Fuse often creates more opportunities to remove spurious mutual recursion.
adamc@552	2667
adamc@552	2668 \subsection{Pathcheck}
adamc@552	2669
adamc@552	2670 The compiler checks that no link or action name has been used more than once.
adamc@552	2671
adamc@552	2672 \subsection{Cjrize}
adamc@552	2673
adamc@552	2674 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	2675
adamc@552	2676 \subsection{C Compilation and Linking}
adamc@552	2677
adam@1523	2678 The output of the last phase is pretty-printed as C source code and passed to the C compiler.
adamc@552	2679
adamc@552	2680
as@1564	2681 \end{document}

Mercurial > urweb

annotate doc/manual.tex @ 2198:cf2abef213d8