Ur/Web: doc/manual.tex annotate

annotate doc/manual.tex @ 2124:f3c24e6790ba

Hexadecimal integer literals, contributed by Gabriel Riba

author	Adam Chlipala <adam@chlipala.net>
date	Thu, 05 Mar 2015 15:03:04 -0500
parents	1218daa14279
children	15d46eb02570

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
adamc@524	12 \begin{document}
adamc@524	13
adamc@524	14 \title{The Ur/Web Manual}
adamc@524	15 \author{Adam Chlipala}
adamc@524	16
adamc@524	17 \maketitle
adamc@524	18
adamc@540	19 \tableofcontents
adamc@540	20
adamc@554	21
adamc@554	22 \section{Introduction}
adamc@554	23
adam@1797	24 \emph{Ur} is a programming language designed to introduce richer type system features into functional programming in the tradition of ML and Haskell. Ur is functional, pure, statically typed, and strict. Ur supports a powerful kind of \emph{metaprogramming} based on \emph{type-level computation with type-level records}.
adamc@554	25
adamc@554	26 \emph{Ur/Web} is Ur plus a special standard library and associated rules for parsing and optimization. Ur/Web supports construction of dynamic web applications backed by SQL databases. The signature of the standard library is such that well-typed Ur/Web programs ``don't go wrong'' in a very broad sense. Not only do they not crash during particular page generations, but they also may not:
adamc@554	27
adamc@554	28 \begin{itemize}
adamc@554	29 \item Suffer from any kinds of code-injection attacks
adamc@554	30 \item Return invalid HTML
adamc@554	31 \item Contain dead intra-application links
adamc@554	32 \item Have mismatches between HTML forms and the fields expected by their handlers
adamc@652	33 \item Include client-side code that makes incorrect assumptions about the ``AJAX''-style services that the remote web server provides
adamc@554	34 \item Attempt invalid SQL queries
adamc@652	35 \item Use improper marshaling or unmarshaling in communication with SQL databases or between browsers and web servers
adamc@554	36 \end{itemize}
adamc@554	37
adamc@554	38 This type safety is just the foundation of the Ur/Web methodology. It is also possible to use metaprogramming to build significant application pieces by analysis of type structure. For instance, the demo includes an ML-style functor for building an admin interface for an arbitrary SQL table. The type system guarantees that the admin interface sub-application that comes out will always be free of the above-listed bugs, no matter which well-typed table description is given as input.
adamc@554	39
adamc@652	40 The Ur/Web compiler also produces very efficient object code that does not use garbage collection. These compiled programs will often be even more efficient than what most programmers would bother to write in C. The compiler also generates JavaScript versions of client-side code, with no need to write those parts of applications in a different language.
adamc@554	41
adamc@554	42 \medskip
adamc@554	43
adamc@554	44 The official web site for Ur is:
adamc@554	45 \begin{center}
adamc@554	46 \url{http://www.impredicative.com/ur/}
adamc@554	47 \end{center}
adamc@554	48
adamc@555	49
adamc@555	50 \section{Installation}
adamc@555	51
adamc@555	52 If you are lucky, then the following standard command sequence will suffice for installation, in a directory to which you have unpacked the latest distribution tarball.
adamc@555	53
adamc@555	54 \begin{verbatim}
adamc@555	55 ./configure
adamc@555	56 make
adamc@555	57 sudo make install
adamc@555	58 \end{verbatim}
adamc@555	59
adam@1523	60 Some other packages must be installed for the above to work. At a minimum, you need a standard UNIX shell, with standard UNIX tools like sed and GCC (or an alternate C compiler) in your execution path; MLton, the whole-program optimizing compiler for Standard ML; and the development files for the OpenSSL C library. As of this writing, in the ``testing'' version of Debian Linux, this command will install the more uncommon of these dependencies:
adamc@896	61 \begin{verbatim}
adam@1368	62 apt-get install mlton libssl-dev
adamc@896	63 \end{verbatim}
adamc@555	64
adam@2016	65 Note that, like the Ur/Web compiler, MLton is a whole-program optimizing compiler, so it frequently requires much more memory than old-fashioned compilers do. Expect building Ur/Web with MLton to require not much less than a gigabyte of RAM. If a \texttt{mlton} invocation ends suspiciously, the most likely explanation is that it has exhausted available memory.
adam@2016	66
adamc@896	67 To build programs that access SQL databases, you also need one of these client libraries for supported backends.
adamc@555	68 \begin{verbatim}
adam@1960	69 apt-get install libpq-dev libmysqlclient-dev libsqlite3-dev
adamc@555	70 \end{verbatim}
adamc@555	71
adamc@555	72 It is also possible to access the modules of the Ur/Web compiler interactively, within Standard ML of New Jersey. To install the prerequisites in Debian testing:
adamc@555	73 \begin{verbatim}
adamc@555	74 apt-get install smlnj libsmlnj-smlnj ml-yacc ml-lpt
adamc@555	75 \end{verbatim}
adamc@555	76
adam@2016	77 To begin an interactive session with the Ur compiler modules, run \texttt{make smlnj}, and then, from within an \texttt{sml} session, run \texttt{CM.make "src/urweb.cm";}. The \texttt{Compiler} module is the main entry point, and you can find its signature in \texttt{src/compiler.sig}.
adamc@555	78
adamc@896	79 To run an SQL-backed application with a backend besides SQLite, you will probably want to install one of these servers.
adamc@555	80
adamc@555	81 \begin{verbatim}
adam@1960	82 apt-get install postgresql mysql-server
adamc@555	83 \end{verbatim}
adamc@555	84
adamc@555	85 To use the Emacs mode, you must have a modern Emacs installed. We assume that you already know how to do this, if you're in the business of looking for an Emacs mode. The demo generation facility of the compiler will also call out to Emacs to syntax-highlight code, and that process depends on the \texttt{htmlize} module, which can be installed in Debian testing via:
adamc@555	86
adamc@555	87 \begin{verbatim}
adamc@555	88 apt-get install emacs-goodies-el
adamc@555	89 \end{verbatim}
adamc@555	90
adam@1441	91 If you don't want to install the Emacs mode, run \texttt{./configure} with the argument \texttt{--without-emacs}.
adam@1441	92
adam@1523	93 Even with the right packages installed, configuration and building might fail to work. After you run \texttt{./configure}, you will see the values of some named environment variables printed. You may need to adjust these values to get proper installation for your system. To change a value, store your preferred alternative in the corresponding UNIX environment variable, before running \texttt{./configure}. For instance, here is how to change the list of extra arguments that the Ur/Web compiler will pass to the C compiler and linker on every invocation. Some older GCC versions need this setting to mask a bug in function inlining.
adamc@555	94
adamc@555	95 \begin{verbatim}
adam@1523	96 CCARGS=-fno-inline ./configure
adamc@555	97 \end{verbatim}
adamc@555	98
adam@1523	99 Since the author is still getting a handle on the GNU Autotools that provide the build system, you may need to do some further work to get started, especially in environments with significant differences from Linux (where most testing is done). The variables \texttt{PGHEADER}, \texttt{MSHEADER}, and \texttt{SQHEADER} may be used to set the proper C header files to include for the development libraries of PostgreSQL, MySQL, and SQLite, respectively. To get libpq to link, one OS X user reported setting \texttt{CCARGS="-I/opt/local/include -L/opt/local/lib/postgresql84"}, after creating a symbolic link with \texttt{ln -s /opt/local/include/postgresql84 /opt/local/include/postgresql}.
adamc@555	100
adamc@555	101 The Emacs mode can be set to autoload by adding the following to your \texttt{.emacs} file.
adamc@555	102
adamc@555	103 \begin{verbatim}
adamc@555	104 (add-to-list 'load-path "/usr/local/share/emacs/site-lisp/urweb-mode")
adamc@555	105 (load "urweb-mode-startup")
adamc@555	106 \end{verbatim}
adamc@555	107
adamc@555	108 Change the path in the first line if you chose a different Emacs installation path during configuration.
adamc@555	109
adamc@555	110
adamc@556	111 \section{Command-Line Compiler}
adamc@556	112
adam@1604	113 \subsection{\label{cl}Project Files}
adamc@556	114
adamc@556	115 The basic inputs to the \texttt{urweb} compiler are project files, which have the extension \texttt{.urp}. Here is a sample \texttt{.urp} file.
adamc@556	116
adamc@556	117 \begin{verbatim}
adamc@556	118 database dbname=test
adamc@556	119 sql crud1.sql
adamc@556	120
adamc@556	121 crud
adamc@556	122 crud1
adamc@556	123 \end{verbatim}
adamc@556	124
adamc@556	125 The \texttt{database} line gives the database information string to pass to libpq. In this case, the string only says to connect to a local database named \texttt{test}.
adamc@556	126
adamc@556	127 The \texttt{sql} line asks for an SQL source file to be generated, giving the commands to run to create the tables and sequences that this application expects to find. After building this \texttt{.urp} file, the following commands could be used to initialize the database, assuming that the current UNIX user exists as a Postgres user with database creation privileges:
adamc@556	128
adamc@556	129 \begin{verbatim}
adamc@556	130 createdb test
adamc@556	131 psql -f crud1.sql test
adamc@556	132 \end{verbatim}
adamc@556	133
adam@1331	134 A blank line separates the named directives from a list of modules to include in the project. Any line may contain a shell-script-style comment, where any suffix of a line starting at a hash character \texttt{\#} is ignored.
adamc@556	135
adamc@556	136 For each entry \texttt{M} in the module list, the file \texttt{M.urs} is included in the project if it exists, and the file \texttt{M.ur} must exist and is always included.
adamc@556	137
adamc@783	138 Here is the complete list of directive forms. ``FFI'' stands for ``foreign function interface,'' Ur's facility for interaction between Ur programs and C and JavaScript libraries.
adamc@783	139 \begin{itemize}
adam@1799	140 \item \texttt{[allow\|deny] [url\|mime\|requestHeader\|responseHeader\|env] PATTERN} registers a rule governing which URLs, MIME types, HTTP request headers, HTTP response headers, or environment variable names are allowed to appear explicitly in this application. The first such rule to match a name determines the verdict. If \texttt{PATTERN} ends in \texttt{*}, it is interpreted as a prefix rule. Otherwise, a string must match it exactly.
adam@1400	141 \item \texttt{alwaysInline PATH} requests that every call to the referenced function be inlined. Section \ref{structure} explains how functions are assigned path strings.
adam@1462	142 \item \texttt{benignEffectful Module.ident} registers an FFI function or transaction as having side effects. The optimizer avoids removing, moving, or duplicating calls to such functions. Every effectful FFI function must be registered, or the optimizer may make invalid transformations. This version of the \texttt{effectful} directive registers that this function only has side effects that remain local to a single page generation.
adamc@783	143 \item \texttt{clientOnly Module.ident} registers an FFI function or transaction that may only be run in client browsers.
adam@1881	144 \item \texttt{clientToServer Module.ident} adds FFI type \texttt{Module.ident} to the list of types that are OK to marshal from clients to servers. Values like XML trees and SQL queries are hard to marshal without introducing expensive validity checks, so it's easier to ensure that the server never trusts clients to send such values. The file \texttt{include/urweb/urweb\_cpp.h} shows examples of the C support functions that are required of any type that may be marshalled. These include \texttt{attrify}, \texttt{urlify}, and \texttt{unurlify} functions.
adam@1816	145 \item \texttt{coreInline TREESIZE} sets how many nodes the AST of a function definition may have before the optimizer stops trying hard to inline calls to that function. (This is one of two options for one of two intermediate languages within the compiler.)
adamc@783	146 \item \texttt{database DBSTRING} sets the string to pass to libpq to open a database connection.
adamc@783	147 \item \texttt{debug} saves some intermediate C files, which is mostly useful to help in debugging the compiler itself.
adam@1878	148 \item \texttt{effectful Module.ident} registers an FFI function or transaction as having side effects. The optimizer avoids removing, moving, or duplicating calls to such functions. This is the default behavior for \texttt{transaction}-based types.
adam@2046	149 \item \texttt{exe FILENAME} sets the filename to which to write the output executable. The default for file \texttt{P.urp} is \texttt{P.exe}.
adam@2046	150 \item \texttt{file URI FILENAME} asks for the application executable to respond to requests for \texttt{URI} by serving a snapshot of the contents of \texttt{FILENAME} as of compile time. That is, the file contents are baked into the executable. System file \texttt{/etc/mime.types} is consulted (again, at compile time) to figure out the right MIME type to suggest in the HTTP response.
adam@1881	151 \item \texttt{ffi FILENAME} reads the file \texttt{FILENAME.urs} to determine the interface to a new FFI module. The name of the module is calculated from \texttt{FILENAME} in the same way as for normal source files. See the files \texttt{include/urweb/urweb\_cpp.h} and \texttt{src/c/urweb.c} for examples of C headers and implementations for FFI modules. In general, every type or value \texttt{Module.ident} becomes \texttt{uw\_Module\_ident} in C.
adam@1956	152 \item \texttt{html5} activates work-in-progress support for generating HTML5 instead of XHTML. For now, this option only affects the first few tokens on any page, which are always the same.
adamc@1099	153 \item \texttt{include FILENAME} adds \texttt{FILENAME} to the list of files to be \texttt{\#include}d in C sources. This is most useful for interfacing with new FFI modules.
adamc@783	154 \item \texttt{jsFunc Module.ident=name} gives the JavaScript name of an FFI value.
adamc@1089	155 \item \texttt{library FILENAME} parses \texttt{FILENAME.urp} and merges its contents with the rest of the current file's contents. If \texttt{FILENAME.urp} doesn't exist, the compiler also tries \texttt{FILENAME/lib.urp}.
adam@1309	156 \item \texttt{limit class num} sets a resource usage limit for generated applications. The limit \texttt{class} will be set to the non-negative integer \texttt{num}. The classes are:
adam@1309	157 \begin{itemize}
adam@1309	158 \item \texttt{cleanup}: maximum number of cleanup operations (e.g., entries recording the need to deallocate certain temporary objects) that may be active at once per request
adam@1850	159 \item \texttt{clients}: maximum number of simultaneous connections to one application by web clients waiting for new asynchronous messages sent with \texttt{Basis.send}
adam@1850	160 \item \texttt{database}: maximum size of a database file (currently only used by SQLite, which interprets the parameter as a number of pages, where page size is itself a quantity configurable in SQLite)
adam@1309	161 \item \texttt{deltas}: maximum number of messages sendable in a single request handler with \texttt{Basis.send}
adam@1309	162 \item \texttt{globals}: maximum number of global variables that FFI libraries may set in a single request context
adam@1309	163 \item \texttt{headers}: maximum size (in bytes) of per-request buffer used to hold HTTP headers for generated pages
adam@1797	164 \item \texttt{heap}: maximum size (in bytes) of per-request heap for dynamically allocated data
adam@1309	165 \item \texttt{inputs}: maximum number of top-level form fields per request
adam@1309	166 \item \texttt{messages}: maximum size (in bytes) of per-request buffer used to hold a single outgoing message sent with \texttt{Basis.send}
adam@1309	167 \item \texttt{page}: maximum size (in bytes) of per-request buffer used to hold HTML content of generated pages
adam@1309	168 \item \texttt{script}: maximum size (in bytes) of per-request buffer used to hold JavaScript content of generated pages
adam@1309	169 \item \texttt{subinputs}: maximum number of form fields per request, excluding top-level fields
adam@1309	170 \item \texttt{time}: maximum running time of a single page request, in units of approximately 0.1 seconds
adam@1309	171 \item \texttt{transactionals}: maximum number of custom transactional actions (e.g., sending an e-mail) that may be run in a single page generation
adam@1309	172 \end{itemize}
adam@1523	173 \item \texttt{link FILENAME} adds \texttt{FILENAME} to the list of files to be passed to the linker at the end of compilation. This is most useful for importing extra libraries needed by new FFI modules.
adam@1725	174 \item \texttt{linker CMD} sets \texttt{CMD} as the command line prefix to use for linking C object files. The command line will be completed with a space-separated list of \texttt{.o} and \texttt{.a} files, \texttt{-L} and \texttt{-l} flags, and finally with a \texttt{-o} flag to set the location where the executable should be written.
adam@1332	175 \item \texttt{minHeap NUMBYTES} sets the initial size for thread-local heaps used in handling requests. These heaps grow automatically as needed (up to any maximum set with \texttt{limit}), but each regrow requires restarting the request handling process.
adam@1816	176 \item \texttt{monoInline TREESIZE} sets how many nodes the AST of a function definition may have before the optimizer stops trying hard to inline calls to that function. (This is one of two options for one of two intermediate languages within the compiler.)
adam@1966	177 \item \texttt{neverInline PATH} requests that no call to the referenced function be inlined. Section \ref{structure} explains how functions are assigned path strings.
adam@1953	178 \item \texttt{noMangleSql} avoids adding a \texttt{uw\_} prefix in front of each identifier in SQL. With this experimental feature, the burden is on the programmer to avoid naming tables or columns after SQL keywords!
adam@1478	179 \item \texttt{noXsrfProtection URIPREFIX} turns off automatic cross-site request forgery protection for the page handler identified by the given URI prefix. This will avoid checking cryptographic signatures on cookies, which is generally a reasonable idea for some pages, such as login pages that are going to discard all old cookie values, anyway.
adam@1297	180 \item \texttt{onError Module.var} changes the handling of fatal application errors. Instead of displaying a default, ugly error 500 page, the error page will be generated by calling function \texttt{Module.var} on a piece of XML representing the error message. The error handler should have type $\mt{xbody} \to \mt{transaction} \; \mt{page}$. Note that the error handler \emph{cannot} be in the application's main module, since that would register it as explicitly callable via URLs.
adamc@852	181 \item \texttt{path NAME=VALUE} creates a mapping from \texttt{NAME} to \texttt{VALUE}. This mapping may be used at the beginnings of filesystem paths given to various other configuration directives. A path like \texttt{\$NAME/rest} is expanded to \texttt{VALUE/rest}. There is an initial mapping from the empty name (for paths like \texttt{\$/list}) to the directory where the Ur/Web standard library is installed. If you accept the default \texttt{configure} options, this directory is \texttt{/usr/local/lib/urweb/ur}.
adamc@783	182 \item \texttt{prefix PREFIX} sets the prefix included before every URI within the generated application. The default is \texttt{/}.
adamc@783	183 \item \texttt{profile} generates an executable that may be used with gprof.
adam@1752	184 \item \texttt{rewrite KIND FROM TO} gives a rule for rewriting canonical module paths. For instance, the canonical path of a page may be \texttt{Mod1.Mod2.mypage}, while you would rather the page were accessed via a URL containing only \texttt{page}. The directive \texttt{rewrite url Mod1/Mod2/mypage page} would accomplish that. The possible values of \texttt{KIND} determine which kinds of objects are affected. The kind \texttt{all} matches any object, and \texttt{url} matches page URLs. The kinds \texttt{table}, \texttt{sequence}, and \texttt{view} match those sorts of SQL entities, and \texttt{relation} matches any of those three. \texttt{cookie} matches HTTP cookies, and \texttt{style} matches CSS class names. If \texttt{FROM} ends in \texttt{/}, it is interpreted as a prefix matching rule, and rewriting occurs by replacing only the appropriate prefix of a path with \texttt{TO}. The \texttt{TO} field may be left empty to express the idea of deleting a prefix. For instance, \texttt{rewrite url Main/} will strip all \texttt{Main/} prefixes from URLs. While the actual external names of relations and styles have parts separated by underscores instead of slashes, all rewrite rules must be written in terms of slashes. An optional suffix of \cd{[-]} for a \cd{rewrite} directive asks to additionally replace all \cd{\_} characters with \cd{-} characters, which can be handy for, e.g., interfacing with an off-the-shelf CSS library that prefers hyphens over underscores.
adamc@1183	185 \item \texttt{safeGet URI} asks to allow the page handler assigned this canonical URI prefix to cause persistent side effects, even if accessed via an HTTP \cd{GET} request.
adamc@783	186 \item \texttt{script URL} adds \texttt{URL} to the list of extra JavaScript files to be included at the beginning of any page that uses JavaScript. This is most useful for importing JavaScript versions of functions found in new FFI modules.
adamc@783	187 \item \texttt{serverOnly Module.ident} registers an FFI function or transaction that may only be run on the server.
adamc@1164	188 \item \texttt{sigfile PATH} sets a path where your application should look for a key to use in cryptographic signing. This is used to prevent cross-site request forgery attacks for any form handler that both reads a cookie and creates side effects. If the referenced file doesn't exist, an application will create it and read its saved data on future invocations. You can also initialize the file manually with any contents at least 16 bytes long; the first 16 bytes will be treated as the key.
adamc@783	189 \item \texttt{sql FILENAME} sets where to write an SQL file with the commands to create the expected database schema. The default is not to create such a file.
adam@1629	190 \item \texttt{timeFormat FMT} accepts a time format string, as processed by the POSIX C function \texttt{strftime()}. This controls the default rendering of $\mt{time}$ values, via the $\mt{show}$ instance for $\mt{time}$.
adamc@783	191 \item \texttt{timeout N} sets to \texttt{N} seconds the amount of time that the generated server will wait after the last contact from a client before determining that that client has exited the application. Clients that remain active will take the timeout setting into account in determining how often to ping the server, so it only makes sense to set a high timeout to cope with browser and network delays and failures. Higher timeouts can lead to more unnecessary client information taking up memory on the server. The timeout goes unused by any page that doesn't involve the \texttt{recv} function, since the server only needs to store per-client information for clients that receive asynchronous messages.
adamc@783	192 \end{itemize}
adamc@701	193
adamc@701	194
adamc@557	195 \subsection{Building an Application}
adamc@557	196
adamc@557	197 To compile project \texttt{P.urp}, simply run
adamc@557	198 \begin{verbatim}
adamc@557	199 urweb P
adamc@557	200 \end{verbatim}
adamc@1198	201 The output executable is a standalone web server. Run it with the command-line argument \texttt{-h} to see which options it takes. If the project file lists a database, the web server will attempt to connect to that database on startup. See Section \ref{structure} for an explanation of the URI mapping convention, which determines how each page of your application may be accessed via URLs.
adamc@557	202
adamc@557	203 To time how long the different compiler phases run, without generating an executable, run
adamc@557	204 \begin{verbatim}
adamc@557	205 urweb -timing P
adamc@557	206 \end{verbatim}
adamc@557	207
adamc@1086	208 To stop the compilation process after type-checking, run
adamc@1086	209 \begin{verbatim}
adamc@1086	210 urweb -tc P
adamc@1086	211 \end{verbatim}
adam@1530	212 It is often worthwhile to run \cd{urweb} in this mode, because later phases of compilation can take significantly longer than type-checking alone, and the type checker catches many errors that would traditionally be found through debugging a running application.
adamc@1086	213
adam@1745	214 A related option is \cd{-dumpTypes}, which, as long as parsing succeeds, outputs to stdout a summary of the kinds of all identifiers declared with \cd{con} and the types of all identifiers declared with \cd{val} or \cd{val rec}. This information is dumped even if there are errors during type inference. Compiler error messages go to stderr, not stdout, so it is easy to distinguish the two kinds of output programmatically. A refined version of this option is \cd{-dumpTypesOnError}, which only has an effect when there are compilation errors.
adam@1531	215
adam@1723	216 It may be useful to combine another option \cd{-unifyMore} with \cd{-dumpTypes}. Ur/Web type inference proceeds in a series of stages, where the first is standard Hindley-Milner type inference as in ML, and the later phases add more complex aspects. By default, an error detected in one phase cuts off the execution of later phases. However, the later phases might still determine more values of unification variables. These value choices might be ``misguided,'' since earlier phases have not come up with reasonable types at a coarser detail level; but the unification decisions may still be useful for debugging and program understanding. So, if a run with \cd{-dumpTypes} leaves unification variables undetermined in positions where you would like to see best-effort guesses instead, consider \cd{-unifyMore}. Note that \cd{-unifyMore} has no effect when type inference succeeds fully, but it may lead to many more error messages when inference fails.
adam@1723	217
adamc@1170	218 To output information relevant to CSS stylesheets (and not finish regular compilation), run
adamc@1170	219 \begin{verbatim}
adamc@1170	220 urweb -css P
adamc@1170	221 \end{verbatim}
adamc@1170	222 The first output line is a list of categories of CSS properties that would be worth setting on the document body. The remaining lines are space-separated pairs of CSS class names and categories of properties that would be worth setting for that class. The category codes are divided into two varieties. Codes that reveal properties of a tag or its (recursive) children are \cd{B} for block-level elements, \cd{C} for table captions, \cd{D} for table cells, \cd{L} for lists, and \cd{T} for tables. Codes that reveal properties of the precise tag that uses a class are \cd{b} for block-level elements, \cd{t} for tables, \cd{d} for table cells, \cd{-} for table rows, \cd{H} for the possibility to set a height, \cd{N} for non-replaced inline-level elements, \cd{R} for replaced inline elements, and \cd{W} for the possibility to set a width.
adamc@1170	223
adam@1733	224 Ur/Web type inference can take a significant amount of time, so it can be helpful to cache type-inferred versions of source files. This mode can be activated by running
adam@1733	225 \begin{verbatim}
adam@1733	226 urweb daemon start
adam@1733	227 \end{verbatim}
adam@1733	228 Further \cd{urweb} invocations in the same working directory will send requests to a background daemon process that reuses type inference results whenever possible, tracking source file dependencies and modification times. To stop the background daemon, run
adam@1733	229 \begin{verbatim}
adam@1733	230 urweb daemon stop
adam@1733	231 \end{verbatim}
adam@1733	232 Communication happens via a UNIX domain socket in file \cd{.urweb\_daemon} in the working directory.
adam@1733	233
adam@1733	234 \medskip
adam@1733	235
adamc@896	236 Some other command-line parameters are accepted:
adamc@896	237 \begin{itemize}
ezyang@1739	238 \item \texttt{-boot}: Run Ur/Web from a build tree (and not from a system install). This is useful if you're testing the compiler and don't want to install it. It forces generation of statically linked executables.
ezyang@1739	239
adam@1875	240 \item \texttt{-ccompiler <PROGRAM>}: Select an alternative C compiler to call with command lines in compiling Ur/Web applications. (It's possible to set the default compiler as part of the \texttt{configure} process, but it may sometimes be useful to override the default.)
adam@1875	241
adamc@896	242 \item \texttt{-db <DBSTRING>}: Set database connection information, using the format expected by Postgres's \texttt{PQconnectdb()}, which is \texttt{name1=value1 ... nameN=valueN}. The same format is also parsed and used to discover connection parameters for MySQL and SQLite. The only significant settings for MySQL are \texttt{host}, \texttt{hostaddr}, \texttt{port}, \texttt{dbname}, \texttt{user}, and \texttt{password}. The only significant setting for SQLite is \texttt{dbname}, which is interpreted as the filesystem path to the database. Additionally, when using SQLite, a database string may be just a file path.
adamc@896	243
adamc@896	244 \item \texttt{-dbms [postgres\|mysql\|sqlite]}: Sets the database backend to use.
adamc@896	245 \begin{itemize}
adamc@896	246 \item \texttt{postgres}: This is PostgreSQL, the default. Among the supported engines, Postgres best matches the design philosophy behind Ur, with a focus on consistent views of data, even in the face of much concurrency. Different database engines have different quirks of SQL syntax. Ur/Web tends to use Postgres idioms where there are choices to be made, though the compiler translates SQL as needed to support other backends.
adamc@896	247
adamc@896	248 A command sequence like this can initialize a Postgres database, using a file \texttt{app.sql} generated by the compiler:
adamc@896	249 \begin{verbatim}
adamc@896	250 createdb app
adamc@896	251 psql -f app.sql app
adamc@896	252 \end{verbatim}
adamc@896	253
adamc@896	254 \item \texttt{mysql}: This is MySQL, another popular relational database engine that uses persistent server processes. Ur/Web needs transactions to function properly. Many installations of MySQL use non-transactional storage engines by default. Ur/Web generates table definitions that try to use MySQL's InnoDB engine, which supports transactions. You can edit the first line of a generated \texttt{.sql} file to change this behavior, but it really is true that Ur/Web applications will exhibit bizarre behavior if you choose an engine that ignores transaction commands.
adamc@896	255
adamc@896	256 A command sequence like this can initialize a MySQL database:
adamc@896	257 \begin{verbatim}
adamc@896	258 echo "CREATE DATABASE app" \| mysql
adamc@896	259 mysql -D app <app.sql
adamc@896	260 \end{verbatim}
adamc@896	261
adamc@896	262 \item \texttt{sqlite}: This is SQLite, a simple filesystem-based transactional database engine. With this backend, Ur/Web applications can run without any additional server processes. The other engines are generally preferred for large-workload performance and full admin feature sets, while SQLite is popular for its low resource footprint and ease of set-up.
adamc@896	263
adamc@896	264 A command like this can initialize an SQLite database:
adamc@896	265 \begin{verbatim}
adamc@896	266 sqlite3 path/to/database/file <app.sql
adamc@896	267 \end{verbatim}
adamc@896	268 \end{itemize}
adamc@896	269
adam@1693	270 \item \texttt{-dumpSource}: When compilation fails, output to stderr the complete source code of the last intermediate program before the compilation phase that signaled the error. (Warning: these outputs can be very long and aren't especially optimized for readability!)
adam@1693	271
adam@1995	272 \item \texttt{-explainEmbed}: Trigger more verbose error messages about inability to embed server-side values in client-side code.
adam@1995	273
adam@1309	274 \item \texttt{-limit class num}: Equivalent to the \texttt{limit} directive from \texttt{.urp} files
adam@1309	275
adam@1850	276 \item \texttt{-moduleOf FILENAME}: Prints the Ur/Web module name corresponding to source file \texttt{FILENAME}, exiting immediately afterward.
adam@1850	277
adamc@896	278 \item \texttt{-output FILENAME}: Set where the application executable is written.
adamc@896	279
adamc@1127	280 \item \texttt{-path NAME VALUE}: Set the value of path variable \texttt{\$NAME} to \texttt{VALUE}, for use in \texttt{.urp} files.
adamc@1127	281
adam@1335	282 \item \texttt{-prefix PREFIX}: Equivalent to the \texttt{prefix} directive from \texttt{.urp} files
adam@1335	283
adam@1875	284 \item \texttt{-print-ccompiler}: Print the C compiler being used.
adam@1875	285
adam@1923	286 \item \texttt{-print-cinclude}: Print the name of the directory where C/C++ header files are installed.
adam@1923	287
adam@1753	288 \item \texttt{-protocol [http\|cgi\|fastcgi\|static]}: Set the protocol that the generated application speaks.
adamc@896	289 \begin{itemize}
adamc@896	290 \item \texttt{http}: This is the default. It is for building standalone web servers that can be accessed by web browsers directly.
adamc@896	291
adamc@896	292 \item \texttt{cgi}: This is the classic protocol that web servers use to generate dynamic content by spawning new processes. While Ur/Web programs may in general use message-passing with the \texttt{send} and \texttt{recv} functions, that functionality is not yet supported in CGI, since CGI needs a fresh process for each request, and message-passing needs to use persistent sockets to deliver messages.
adamc@896	293
adamc@896	294 Since Ur/Web treats paths in an unusual way, a configuration line like this one can be used to configure an application that was built with URL prefix \texttt{/Hello}:
adamc@896	295 \begin{verbatim}
adamc@896	296 ScriptAlias /Hello /path/to/hello.exe
adamc@896	297 \end{verbatim}
adamc@896	298
adamc@1163	299 A different method can be used for, e.g., a shared host, where you can only configure Apache via \texttt{.htaccess} files. Drop the generated executable into your web space and mark it as CGI somehow. For instance, if the script ends in \texttt{.exe}, you might put this in \texttt{.htaccess} in the directory containing the script:
adamc@1163	300 \begin{verbatim}
adamc@1163	301 Options +ExecCGI
adamc@1163	302 AddHandler cgi-script .exe
adamc@1163	303 \end{verbatim}
adamc@1163	304
adamc@1163	305 Additionally, make sure that Ur/Web knows the proper URI prefix for your script. For instance, if the script is accessed via \texttt{http://somewhere/dir/script.exe}, then include this line in your \texttt{.urp} file:
adamc@1163	306 \begin{verbatim}
adamc@1163	307 prefix /dir/script.exe/
adamc@1163	308 \end{verbatim}
adamc@1163	309
adamc@1163	310 To access the \texttt{foo} function in the \texttt{Bar} module, you would then hit \texttt{http://somewhere/dir/script.exe/Bar/foo}.
adamc@1163	311
adamc@1164	312 If your application contains form handlers that read cookies before causing side effects, then you will need to use the \texttt{sigfile} \texttt{.urp} directive, too.
adamc@1164	313
adamc@896	314 \item \texttt{fastcgi}: This is a newer protocol inspired by CGI, wherein web servers can start and reuse persistent external processes to generate dynamic content. Ur/Web doesn't implement the whole protocol, but Ur/Web's support has been tested to work with the \texttt{mod\_fastcgi}s of Apache and lighttpd.
adamc@896	315
adamc@896	316 To configure a FastCGI program with Apache, one could combine the above \texttt{ScriptAlias} line with a line like this:
adamc@896	317 \begin{verbatim}
adamc@896	318 FastCgiServer /path/to/hello.exe -idle-timeout 99999
adamc@896	319 \end{verbatim}
adamc@896	320 The idle timeout is only important for applications that use message-passing. Client connections may go long periods without receiving messages, and Apache tries to be helpful and garbage collect them in such cases. To prevent that behavior, we specify how long a connection must be idle to be collected.
adamc@896	321
adam@1753	322 Also see the discussion of the \cd{prefix} directive for CGI above; similar configuration is likely to be necessary for FastCGI. An Ur/Web application won't generally run correctly if it doesn't have a unique URI prefix assigned to it and configured with \cd{prefix}.
adam@1753	323
adamc@896	324 Here is some lighttpd configuration for the same application.
adamc@896	325 \begin{verbatim}
adamc@896	326 fastcgi.server = (
adamc@896	327 "/Hello/" =>
adamc@896	328 (( "bin-path" => "/path/to/hello.exe",
adamc@896	329 "socket" => "/tmp/hello",
adamc@896	330 "check-local" => "disable",
adamc@896	331 "docroot" => "/",
adamc@896	332 "max-procs" => "1"
adamc@896	333 ))
adamc@896	334 )
adamc@896	335 \end{verbatim}
adamc@896	336 The least obvious requirement is setting \texttt{max-procs} to 1, so that lighttpd doesn't try to multiplex requests across multiple external processes. This is required for message-passing applications, where a single database of client connections is maintained within a multi-threaded server process. Multiple processes may, however, be used safely with applications that don't use message-passing.
adamc@896	337
adamc@896	338 A FastCGI process reads the environment variable \texttt{URWEB\_NUM\_THREADS} to determine how many threads to spawn for handling client requests. The default is 1.
adam@1509	339
adam@1509	340 \item \texttt{static}: This protocol may be used to generate static web pages from Ur/Web code. The output executable expects a single command-line argument, giving the URI of a page to generate. For instance, this argument might be \cd{/main}, in which case a static HTTP response for that page will be written to stdout.
adamc@896	341 \end{itemize}
adamc@896	342
adamc@1127	343 \item \texttt{-root Name PATH}: Trigger an alternate module convention for all source files found in directory \texttt{PATH} or any of its subdirectories. Any file \texttt{PATH/foo.ur} defines a module \texttt{Name.Foo} instead of the usual \texttt{Foo}. Any file \texttt{PATH/subdir/foo.ur} defines a module \texttt{Name.Subdir.Foo}, and so on for arbitrary nesting of subdirectories.
adamc@1127	344
adamc@1164	345 \item \texttt{-sigfile PATH}: Same as the \texttt{sigfile} directive in \texttt{.urp} files
adamc@1164	346
adamc@896	347 \item \texttt{-sql FILENAME}: Set where a database set-up SQL script is written.
adamc@1095	348
adamc@1095	349 \item \texttt{-static}: Link the runtime system statically. The default is to link against dynamic libraries.
adam@1961	350
adam@1961	351 \item \texttt{-stop PHASE}: Stop compilation after the named phase, printing the intermediate program to stderr. This flag is mainly useful for debugging the Ur/Web compiler itself.
adamc@896	352 \end{itemize}
adamc@896	353
adam@1297	354 There is an additional convenience method for invoking \texttt{urweb}. If the main argument is \texttt{FOO}, and \texttt{FOO.ur} exists but \texttt{FOO.urp} doesn't, then the invocation is interpreted as if called on a \texttt{.urp} file containing \texttt{FOO} as its only main entry, with an additional \texttt{rewrite all FOO/*} directive.
adamc@556	355
adam@1509	356 \subsection{Tutorial Formatting}
adam@1509	357
adam@1509	358 The Ur/Web compiler also supports rendering of nice HTML tutorials from Ur source files, when invoked like \cd{urweb -tutorial DIR}. The directory \cd{DIR} is examined for files whose names end in \cd{.ur}. Every such file is translated into a \cd{.html} version.
adam@1509	359
adam@1509	360 These input files follow normal Ur syntax, with a few exceptions:
adam@1509	361 \begin{itemize}
adam@1509	362 \item The first line must be a comment like \cd{(* TITLE *)}, where \cd{TITLE} is a string of your choice that will be used as the title of the output page.
adam@1509	363 \item While most code in the output HTML will be formatted as a monospaced code listing, text in regular Ur comments is formatted as normal English text.
adam@1509	364 \item A comment like \cd{(* * HEADING *)} introduces a section heading, with text \cd{HEADING} of your choice.
adam@1509	365 \item To include both a rendering of an Ur expression and a pretty-printed version of its value, bracket the expression with \cd{(* begin eval )} and \cd{( end *)}. The result of expression evaluation is pretty-printed with \cd{show}, so the expression type must belong to that type class.
adam@1509	366 \item To include code that should not be shown in the tutorial (e.g., to add a \cd{show} instance to use with \cd{eval}), bracket the code with \cd{(* begin hide )} and \cd{( end *)}.
adam@1509	367 \end{itemize}
adam@1509	368
adam@1509	369 A word of warning: as for demo generation, tutorial generation calls Emacs to syntax-highlight Ur code.
adam@1509	370
adam@1522	371 \subsection{Run-Time Options}
adam@1522	372
adam@1522	373 Compiled applications consult a few environment variables to modify their behavior:
adam@1522	374
adam@1522	375 \begin{itemize}
adam@1522	376 \item \cd{URWEB\_NUM\_THREADS}: alternative to the \cd{-t} command-line argument (currently used only by FastCGI)
adam@1522	377 \item \cd{URWEB\_STACK\_SIZE}: size of per-thread stacks, in bytes
as@1564	378 \item \cd{URWEB\_PQ\_CON}: when using PostgreSQL, overrides the compiled-in connection string
adam@1522	379 \end{itemize}
adam@1522	380
adam@2042	381 \subsection{A Word of Warning on Heuristic Compilation}
adam@2042	382
adam@2042	383 For server-side code, Ur/Web follows an unusual compilation model, where not all type-correct programs can be compiled successfully, especially when using functions as data not known until runtime. See Section \ref{phases} for more detail.
adam@2042	384
adam@1509	385
adamc@529	386 \section{Ur Syntax}
adamc@529	387
adamc@784	388 In this section, we describe the syntax of Ur, deferring to a later section discussion of most of the syntax specific to SQL and XML. The sole exceptions are the declaration forms for relations, cookies, and styles.
adamc@524	389
adamc@524	390 \subsection{Lexical Conventions}
adamc@524	391
adamc@524	392 We give the Ur language definition in \LaTeX $\;$ math mode, since that is prettier than monospaced ASCII. The corresponding ASCII syntax can be read off directly. Here is the key for mapping math symbols to ASCII character sequences.
adamc@524	393
adamc@524	394 \begin{center}
adamc@524	395 \begin{tabular}{rl}
adamc@524	396 \textbf{\LaTeX} & \textbf{ASCII} \\
adamc@524	397 $\to$ & \cd{->} \\
adam@1687	398 $\longrightarrow$ & \cd{-{}->} \\
adamc@524	399 $\times$ & \cd{*} \\
adamc@524	400 $\lambda$ & \cd{fn} \\
adamc@524	401 $\Rightarrow$ & \cd{=>} \\
adamc@652	402 $\Longrightarrow$ & \cd{==>} \\
adamc@529	403 $\neq$ & \cd{<>} \\
adamc@529	404 $\leq$ & \cd{<=} \\
adamc@529	405 $\geq$ & \cd{>=} \\
adamc@524	406 \\
adamc@524	407 $x$ & Normal textual identifier, not beginning with an uppercase letter \\
adamc@525	408 $X$ & Normal textual identifier, beginning with an uppercase letter \\
adamc@524	409 \end{tabular}
adamc@524	410 \end{center}
adamc@524	411
adamc@525	412 We often write syntax like $e^$ to indicate zero or more copies of $e$, $e^+$ to indicate one or more copies, and $e,^$ and $e,^+$ to indicate multiple copies separated by commas. Another separator may be used in place of a comma. The $e$ term may be surrounded by parentheses to indicate grouping; those parentheses should not be included in the actual ASCII.
adamc@524	413
adamc@873	414 We write $\ell$ for literals of the primitive types, for the most part following C conventions. There are $\mt{int}$, $\mt{float}$, $\mt{char}$, and $\mt{string}$ literals. Character literals follow the SML convention instead of the C convention, written like \texttt{\#"a"} instead of \texttt{'a'}.
adamc@526	415
adamc@527	416 This version of the manual doesn't include operator precedences; see \texttt{src/urweb.grm} for that.
adamc@527	417
adam@1297	418 As in the ML language family, the syntax \texttt{(* ... *)} is used for (nestable) comments. Within XML literals, Ur/Web also supports the usual \texttt{<!-- ... -->} XML comments.
adam@1297	419
adamc@552	420 \subsection{\label{core}Core Syntax}
adamc@524	421
adamc@524	422 \emph{Kinds} classify types and other compile-time-only entities. Each kind in the grammar is listed with a description of the sort of data it classifies.
adamc@524	423 $$\begin{array}{rrcll}
adamc@524	424 \textrm{Kinds} & \kappa &::=& \mt{Type} & \textrm{proper types} \\
adamc@525	425 &&& \mt{Unit} & \textrm{the trivial constructor} \\
adamc@525	426 &&& \mt{Name} & \textrm{field names} \\
adamc@525	427 &&& \kappa \to \kappa & \textrm{type-level functions} \\
adamc@525	428 &&& \{\kappa\} & \textrm{type-level records} \\
adamc@525	429 &&& (\kappa\times^+) & \textrm{type-level tuples} \\
adamc@652	430 &&& X & \textrm{variable} \\
adam@1574	431 &&& X \longrightarrow \kappa & \textrm{kind-polymorphic type-level function} \\
adamc@529	432 &&& \_\_ & \textrm{wildcard} \\
adamc@525	433 &&& (\kappa) & \textrm{explicit precedence} \\
adamc@524	434 \end{array}$$
adamc@524	435
adamc@524	436 Ur supports several different notions of functions that take types as arguments. These arguments can be either implicit, causing them to be inferred at use sites; or explicit, forcing them to be specified manually at use sites. There is a common explicitness annotation convention applied at the definitions of and in the types of such functions.
adamc@524	437 $$\begin{array}{rrcll}
adamc@524	438 \textrm{Explicitness} & ? &::=& :: & \textrm{explicit} \\
adamc@558	439 &&& ::: & \textrm{implicit}
adamc@524	440 \end{array}$$
adamc@524	441
adamc@524	442 \emph{Constructors} are the main class of compile-time-only data. They include proper types and are classified by kinds.
adamc@524	443 $$\begin{array}{rrcll}
adamc@524	444 \textrm{Constructors} & c, \tau &::=& (c) :: \kappa & \textrm{kind annotation} \\
adamc@530	445 &&& \hat{x} & \textrm{constructor variable} \\
adamc@524	446 \\
adamc@525	447 &&& \tau \to \tau & \textrm{function type} \\
adamc@525	448 &&& x \; ? \; \kappa \to \tau & \textrm{polymorphic function type} \\
adamc@652	449 &&& X \longrightarrow \tau & \textrm{kind-polymorphic function type} \\
adamc@525	450 &&& \$ c & \textrm{record type} \\
adamc@524	451 \\
adamc@525	452 &&& c \; c & \textrm{type-level function application} \\
adamc@530	453 &&& \lambda x \; :: \; \kappa \Rightarrow c & \textrm{type-level function abstraction} \\
adamc@524	454 \\
adamc@652	455 &&& X \Longrightarrow c & \textrm{type-level kind-polymorphic function abstraction} \\
adamc@655	456 &&& c [\kappa] & \textrm{type-level kind-polymorphic function application} \\
adamc@652	457 \\
adamc@525	458 &&& () & \textrm{type-level unit} \\
adamc@525	459 &&& \#X & \textrm{field name} \\
adamc@524	460 \\
adamc@525	461 &&& [(c = c)^*] & \textrm{known-length type-level record} \\
adamc@525	462 &&& c \rc c & \textrm{type-level record concatenation} \\
adamc@652	463 &&& \mt{map} & \textrm{type-level record map} \\
adamc@524	464 \\
adamc@558	465 &&& (c,^+) & \textrm{type-level tuple} \\
adamc@525	466 &&& c.n & \textrm{type-level tuple projection ($n \in \mathbb N^+$)} \\
adamc@524	467 \\
adamc@652	468 &&& [c \sim c] \Rightarrow \tau & \textrm{guarded type} \\
adamc@524	469 \\
adamc@529	470 &&& \_ :: \kappa & \textrm{wildcard} \\
adamc@525	471 &&& (c) & \textrm{explicit precedence} \\
adamc@530	472 \\
adamc@530	473 \textrm{Qualified uncapitalized variables} & \hat{x} &::=& x & \textrm{not from a module} \\
adamc@530	474 &&& M.x & \textrm{projection from a module} \\
adamc@525	475 \end{array}$$
adamc@525	476
adam@1579	477 We include both abstraction and application for kind polymorphism, but applications are only inferred internally; they may not be written explicitly in source programs. Also, in the ``known-length type-level record'' form, in $c_1 = c_2$ terms, the parser currently only allows $c_1$ to be of the forms $X$ (as a shorthand for $\#X$) or $x$, or a natural number to stand for the corresponding field name (e.g., for tuples).
adamc@655	478
adamc@525	479 Modules of the module system are described by \emph{signatures}.
adamc@525	480 $$\begin{array}{rrcll}
adamc@525	481 \textrm{Signatures} & S &::=& \mt{sig} \; s^* \; \mt{end} & \textrm{constant} \\
adamc@525	482 &&& X & \textrm{variable} \\
adamc@525	483 &&& \mt{functor}(X : S) : S & \textrm{functor} \\
adamc@529	484 &&& S \; \mt{where} \; \mt{con} \; x = c & \textrm{concretizing an abstract constructor} \\
adamc@525	485 &&& M.X & \textrm{projection from a module} \\
adamc@525	486 \\
adamc@525	487 \textrm{Signature items} & s &::=& \mt{con} \; x :: \kappa & \textrm{abstract constructor} \\
adamc@525	488 &&& \mt{con} \; x :: \kappa = c & \textrm{concrete constructor} \\
adamc@528	489 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529	490 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@525	491 &&& \mt{val} \; x : \tau & \textrm{value} \\
adamc@525	492 &&& \mt{structure} \; X : S & \textrm{sub-module} \\
adamc@525	493 &&& \mt{signature} \; X = S & \textrm{sub-signature} \\
adamc@525	494 &&& \mt{include} \; S & \textrm{signature inclusion} \\
adamc@525	495 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@654	496 &&& \mt{class} \; x :: \kappa & \textrm{abstract constructor class} \\
adamc@654	497 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@525	498 \\
adamc@525	499 \textrm{Datatype constructors} & dc &::=& X & \textrm{nullary constructor} \\
adamc@525	500 &&& X \; \mt{of} \; \tau & \textrm{unary constructor} \\
adamc@524	501 \end{array}$$
adamc@524	502
adamc@526	503 \emph{Patterns} are used to describe structural conditions on expressions, such that expressions may be tested against patterns, generating assignments to pattern variables if successful.
adamc@526	504 $$\begin{array}{rrcll}
adamc@526	505 \textrm{Patterns} & p &::=& \_ & \textrm{wildcard} \\
adamc@526	506 &&& x & \textrm{variable} \\
adamc@526	507 &&& \ell & \textrm{constant} \\
adamc@526	508 &&& \hat{X} & \textrm{nullary constructor} \\
adamc@526	509 &&& \hat{X} \; p & \textrm{unary constructor} \\
adamc@526	510 &&& \{(x = p,)^*\} & \textrm{rigid record pattern} \\
adamc@526	511 &&& \{(x = p,)^+, \ldots\} & \textrm{flexible record pattern} \\
adamc@852	512 &&& p : \tau & \textrm{type annotation} \\
adamc@527	513 &&& (p) & \textrm{explicit precedence} \\
adamc@526	514 \\
adamc@529	515 \textrm{Qualified capitalized variables} & \hat{X} &::=& X & \textrm{not from a module} \\
adamc@526	516 &&& M.X & \textrm{projection from a module} \\
adamc@526	517 \end{array}$$
adamc@526	518
adamc@527	519 \emph{Expressions} are the main run-time entities, corresponding to both ``expressions'' and ``statements'' in mainstream imperative languages.
adamc@527	520 $$\begin{array}{rrcll}
adamc@527	521 \textrm{Expressions} & e &::=& e : \tau & \textrm{type annotation} \\
adamc@529	522 &&& \hat{x} & \textrm{variable} \\
adamc@529	523 &&& \hat{X} & \textrm{datatype constructor} \\
adamc@527	524 &&& \ell & \textrm{constant} \\
adamc@527	525 \\
adamc@527	526 &&& e \; e & \textrm{function application} \\
adamc@527	527 &&& \lambda x : \tau \Rightarrow e & \textrm{function abstraction} \\
adamc@527	528 &&& e [c] & \textrm{polymorphic function application} \\
adamc@852	529 &&& \lambda [x \; ? \; \kappa] \Rightarrow e & \textrm{polymorphic function abstraction} \\
adamc@655	530 &&& e [\kappa] & \textrm{kind-polymorphic function application} \\
adamc@652	531 &&& X \Longrightarrow e & \textrm{kind-polymorphic function abstraction} \\
adamc@527	532 \\
adamc@527	533 &&& \{(c = e,)^*\} & \textrm{known-length record} \\
adamc@527	534 &&& e.c & \textrm{record field projection} \\
adamc@527	535 &&& e \rc e & \textrm{record concatenation} \\
adamc@527	536 &&& e \rcut c & \textrm{removal of a single record field} \\
adamc@527	537 &&& e \rcutM c & \textrm{removal of multiple record fields} \\
adamc@527	538 \\
adamc@527	539 &&& \mt{let} \; ed^* \; \mt{in} \; e \; \mt{end} & \textrm{local definitions} \\
adamc@527	540 \\
adamc@527	541 &&& \mt{case} \; e \; \mt{of} \; (p \Rightarrow e\|)^+ & \textrm{pattern matching} \\
adamc@527	542 \\
adamc@654	543 &&& \lambda [c \sim c] \Rightarrow e & \textrm{guarded expression abstraction} \\
adamc@654	544 &&& e \; ! & \textrm{guarded expression application} \\
adamc@527	545 \\
adamc@527	546 &&& \_ & \textrm{wildcard} \\
adamc@527	547 &&& (e) & \textrm{explicit precedence} \\
adamc@527	548 \\
adamc@527	549 \textrm{Local declarations} & ed &::=& \cd{val} \; x : \tau = e & \textrm{non-recursive value} \\
adam@1797	550 &&& \cd{val} \; \cd{rec} \; (x : \tau = e \; \cd{and})^+ & \textrm{mutually recursive values} \\
adamc@527	551 \end{array}$$
adamc@527	552
adamc@655	553 As with constructors, we include both abstraction and application for kind polymorphism, but applications are only inferred internally.
adamc@655	554
adamc@528	555 \emph{Declarations} primarily bring new symbols into context.
adamc@528	556 $$\begin{array}{rrcll}
adamc@528	557 \textrm{Declarations} & d &::=& \mt{con} \; x :: \kappa = c & \textrm{constructor synonym} \\
adamc@528	558 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529	559 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@528	560 &&& \mt{val} \; x : \tau = e & \textrm{value} \\
adam@1797	561 &&& \mt{val} \; \cd{rec} \; (x : \tau = e \; \mt{and})^+ & \textrm{mutually recursive values} \\
adamc@528	562 &&& \mt{structure} \; X : S = M & \textrm{module definition} \\
adamc@528	563 &&& \mt{signature} \; X = S & \textrm{signature definition} \\
adamc@528	564 &&& \mt{open} \; M & \textrm{module inclusion} \\
adamc@528	565 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@528	566 &&& \mt{open} \; \mt{constraints} \; M & \textrm{inclusion of just the constraints from a module} \\
adamc@528	567 &&& \mt{table} \; x : c & \textrm{SQL table} \\
adam@1594	568 &&& \mt{view} \; x = e & \textrm{SQL view} \\
adamc@528	569 &&& \mt{sequence} \; x & \textrm{SQL sequence} \\
adamc@535	570 &&& \mt{cookie} \; x : \tau & \textrm{HTTP cookie} \\
adamc@784	571 &&& \mt{style} \; x : \tau & \textrm{CSS class} \\
adamc@1085	572 &&& \mt{task} \; e = e & \textrm{recurring task} \\
adamc@528	573 \\
adamc@529	574 \textrm{Modules} & M &::=& \mt{struct} \; d^* \; \mt{end} & \textrm{constant} \\
adamc@529	575 &&& X & \textrm{variable} \\
adamc@529	576 &&& M.X & \textrm{projection} \\
adamc@529	577 &&& M(M) & \textrm{functor application} \\
adamc@529	578 &&& \mt{functor}(X : S) : S = M & \textrm{functor abstraction} \\
adamc@528	579 \end{array}$$
adamc@528	580
adamc@528	581 There are two kinds of Ur files. A file named $M\texttt{.ur}$ is an \emph{implementation file}, and it should contain a sequence of declarations $d^$. A file named $M\texttt{.urs}$ is an \emph{interface file}; it must always have a matching $M\texttt{.ur}$ and should contain a sequence of signature items $s^$. When both files are present, the overall effect is the same as a monolithic declaration $\mt{structure} \; M : \mt{sig} \; s^* \; \mt{end} = \mt{struct} \; d^* \; \mt{end}$. When no interface file is included, the overall effect is similar, with a signature for module $M$ being inferred rather than just checked against an interface.
adamc@527	582
adam@1594	583 We omit some extra possibilities in $\mt{table}$ syntax, deferring them to Section \ref{tables}. The concrete syntax of $\mt{view}$ declarations is also more complex than shown in the table above, with details deferred to Section \ref{tables}.
adamc@784	584
adamc@529	585 \subsection{Shorthands}
adamc@529	586
adamc@529	587 There are a variety of derived syntactic forms that elaborate into the core syntax from the last subsection. We will present the additional forms roughly following the order in which we presented the constructs that they elaborate into.
adamc@529	588
adamc@529	589 In many contexts where record fields are expected, like in a projection $e.c$, a constant field may be written as simply $X$, rather than $\#X$.
adamc@529	590
adamc@529	591 A record type may be written $\{(c = c,)^\}$, which elaborates to $\$[(c = c,)^]$.
adamc@529	592
adamc@533	593 The notation $[c_1, \ldots, c_n]$ is shorthand for $[c_1 = (), \ldots, c_n = ()]$.
adamc@533	594
adam@1350	595 A tuple type $\tau_1 \times \ldots \times \tau_n$ expands to a record type $\{1 : \tau_1, \ldots, n : \tau_n\}$, with natural numbers as field names. A tuple expression $(e_1, \ldots, e_n)$ expands to a record expression $\{1 = e_1, \ldots, n = e_n\}$. A tuple pattern $(p_1, \ldots, p_n)$ expands to a rigid record pattern $\{1 = p_1, \ldots, n = p_n\}$. Positive natural numbers may be used in most places where field names would be allowed.
adamc@529	596
adam@1687	597 The syntax $()$ expands to $\{\}$ as a pattern or expression.
adam@1687	598
adamc@852	599 In general, several adjacent $\lambda$ forms may be combined into one, and kind and type annotations may be omitted, in which case they are implicitly included as wildcards. More formally, for constructor-level abstractions, we can define a new non-terminal $b ::= x \mid (x :: \kappa) \mid X$ and allow composite abstractions of the form $\lambda b^+ \Rightarrow c$, elaborating into the obvious sequence of one core $\lambda$ per element of $b^+$.
adamc@529	600
adam@1574	601 Further, the signature item or declaration syntax $\mt{con} \; x \; b^+ = c$ is shorthand for wrapping of the appropriate $\lambda$s around the righthand side $c$. The $b$ elements may not include $X$, and there may also be an optional $:: \kappa$ before the $=$.
adam@1574	602
adam@1306	603 In some contexts, the parser isn't happy with token sequences like $x :: \_$, to indicate a constructor variable of wildcard kind. In such cases, write the second two tokens as $::\hspace{-.05in}\_$, with no intervening spaces. Analogous syntax $:::\hspace{-.05in}\_$ is available for implicit constructor arguments.
adam@1302	604
adamc@529	605 For any signature item or declaration that defines some entity to be equal to $A$ with classification annotation $B$ (e.g., $\mt{val} \; x : B = A$), $B$ and the preceding colon (or similar punctuation) may be omitted, in which case it is filled in as a wildcard.
adamc@529	606
adamc@529	607 A signature item or declaration $\mt{type} \; x$ or $\mt{type} \; x = \tau$ is elaborated into $\mt{con} \; x :: \mt{Type}$ or $\mt{con} \; x :: \mt{Type} = \tau$, respectively.
adamc@529	608
adamc@654	609 A signature item or declaration $\mt{class} \; x = \lambda y \Rightarrow c$ may be abbreviated $\mt{class} \; x \; y = c$.
adamc@529	610
adam@1738	611 Handling of implicit and explicit constructor arguments may be tweaked with some prefixes to variable references. An expression $@x$ is a version of $x$ where all type class instance and disjointness arguments have been made explicit. (For the purposes of this paragraph, the type family $\mt{Top.folder}$ is a type class, though it isn't marked as one by the usual means; and any record type is considered to be a type class instance type when every field's type is a type class instance type.) An expression $@@x$ achieves the same effect, additionally making explicit all implicit constructor arguments. The default is that implicit arguments are inserted automatically after any reference to a variable, or after any application of a variable to one or more arguments. For such an expression, implicit wildcard arguments are added for the longest prefix of the expression's type consisting only of implicit polymorphism, type class instances, and disjointness obligations. The same syntax works for variables projected out of modules and for capitalized variables (datatype constructors).
adamc@529	612
adamc@852	613 At the expression level, an analogue is available of the composite $\lambda$ form for constructors. We define the language of binders as $b ::= p \mid [x] \mid [x \; ? \; \kappa] \mid X \mid [c \sim c]$. A lone variable $[x]$ stands for an implicit constructor variable of unspecified kind. The standard value-level function binder is recovered as the type-annotated pattern form $x : \tau$. It is a compile-time error to include a pattern $p$ that does not match every value of the appropriate type.
adamc@529	614
adamc@852	615 A local $\mt{val}$ declaration may bind a pattern instead of just a plain variable. As for function arguments, only irrefutable patterns are legal.
adamc@852	616
adam@1797	617 The keyword $\mt{fun}$ is a shorthand for $\mt{val} \; \mt{rec}$ that allows arguments to be specified before the equal sign in the definition of each mutually recursive function, as in SML. Each curried argument must follow the grammar of the $b$ non-terminal introduced two paragraphs ago. A $\mt{fun}$ declaration is elaborated into a version that adds additional $\lambda$s to the fronts of the righthand sides, as appropriate.
adamc@529	618
adamc@529	619 A signature item $\mt{functor} \; X_1 \; (X_2 : S_1) : S_2$ is elaborated into $\mt{structure} \; X_1 : \mt{functor}(X_2 : S_1) : S_2$. A declaration $\mt{functor} \; X_1 \; (X_2 : S_1) : S_2 = M$ is elaborated into $\mt{structure} \; X_1 : \mt{functor}(X_2 : S_1) : S_2 = \mt{functor}(X_2 : S_1) : S_2 = M$.
adamc@529	620
adamc@852	621 An $\mt{open} \; \mt{constraints}$ declaration is implicitly inserted for the argument of every functor at the beginning of the functor body. For every declaration of the form $\mt{structure} \; X : S = \mt{struct} \ldots \mt{end}$, an $\mt{open} \; \mt{constraints} \; X$ declaration is implicitly inserted immediately afterward.
adamc@852	622
adamc@853	623 A declaration $\mt{table} \; x : \{(c = c,)^\}$ is elaborated into $\mt{table} \; x : [(c = c,)^]$.
adamc@529	624
adamc@529	625 The syntax $\mt{where} \; \mt{type}$ is an alternate form of $\mt{where} \; \mt{con}$.
adamc@529	626
adamc@529	627 The syntax $\mt{if} \; e \; \mt{then} \; e_1 \; \mt{else} \; e_2$ expands to $\mt{case} \; e \; \mt{of} \; \mt{Basis}.\mt{True} \Rightarrow e_1 \mid \mt{Basis}.\mt{False} \Rightarrow e_2$.
adamc@529	628
adamc@529	629 There are infix operator syntaxes for a number of functions defined in the $\mt{Basis}$ module. There is $=$ for $\mt{eq}$, $\neq$ for $\mt{neq}$, $-$ for $\mt{neg}$ (as a prefix operator) and $\mt{minus}$, $+$ for $\mt{plus}$, $\times$ for $\mt{times}$, $/$ for $\mt{div}$, $\%$ for $\mt{mod}$, $<$ for $\mt{lt}$, $\leq$ for $\mt{le}$, $>$ for $\mt{gt}$, and $\geq$ for $\mt{ge}$.
adamc@529	630
adamc@784	631 A signature item $\mt{table} \; x : c$ is shorthand for $\mt{val} \; x : \mt{Basis}.\mt{sql\_table} \; c \; []$. $\mt{view} \; x : c$ is shorthand for $\mt{val} \; x : \mt{Basis}.\mt{sql\_view} \; c$, $\mt{sequence} \; x$ is short for $\mt{val} \; x : \mt{Basis}.\mt{sql\_sequence}$. $\mt{cookie} \; x : \tau$ is shorthand for $\mt{val} \; x : \mt{Basis}.\mt{http\_cookie} \; \tau$, and $\mt{style} \; x$ is shorthand for $\mt{val} \; x : \mt{Basis}.\mt{css\_class}$.
adamc@529	632
adam@2025	633 It is possible to write a $\mt{let}$ expression with its constituents in reverse order, along the lines of Haskell's \cd{where}. An expression $\mt{let} \; e \; \mt{where} \; ed^* \; \mt{end}$ desugars to $\mt{let} \; ed^* \; \mt{in} \; e \; \mt{end}$.
adam@2025	634
adam@2123	635 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	636
adamc@530	637
adamc@530	638 \section{Static Semantics}
adamc@530	639
adamc@530	640 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	641
adam@1891	642 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	643 \begin{quote}
adam@1891	644 Benjamin C. Pierce, \emph{Types and Programming Languages}, MIT Press, 2002.
adam@1891	645 \end{quote}
adam@1891	646
adamc@530	647 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	648 \begin{itemize}
adamc@655	649 \item $\Gamma \vdash \kappa$ expresses kind well-formedness.
adamc@530	650 \item $\Gamma \vdash c :: \kappa$ assigns a kind to a constructor in a context.
adamc@530	651 \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	652 \item $\Gamma \vdash c \hookrightarrow C$ proves that record constructor $c$ decomposes into set $C$ of field names and record constructors.
adamc@530	653 \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	654 \item $\Gamma \vdash e : \tau$ is a standard typing judgment.
adamc@534	655 \item $\Gamma \vdash p \leadsto \Gamma; \tau$ combines typing of patterns with calculation of which new variables they bind.
adamc@537	656 \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	657 \item $\Gamma \vdash S \equiv S$ is the signature equivalence judgment.
adamc@536	658 \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	659 \item $\Gamma \vdash M : S$ is the module signature checking judgment.
adamc@537	660 \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	661 \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	662 \end{itemize}
adamc@530	663
adamc@655	664
adamc@655	665 \subsection{Kind Well-Formedness}
adamc@655	666
adamc@655	667 $$\infer{\Gamma \vdash \mt{Type}}{}
adamc@655	668 \quad \infer{\Gamma \vdash \mt{Unit}}{}
adamc@655	669 \quad \infer{\Gamma \vdash \mt{Name}}{}
adamc@655	670 \quad \infer{\Gamma \vdash \kappa_1 \to \kappa_2}{
adamc@655	671 \Gamma \vdash \kappa_1
adamc@655	672 & \Gamma \vdash \kappa_2
adamc@655	673 }
adamc@655	674 \quad \infer{\Gamma \vdash \{\kappa\}}{
adamc@655	675 \Gamma \vdash \kappa
adamc@655	676 }
adamc@655	677 \quad \infer{\Gamma \vdash (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@655	678 \forall i: \Gamma \vdash \kappa_i
adamc@655	679 }$$
adamc@655	680
adamc@655	681 $$\infer{\Gamma \vdash X}{
adamc@655	682 X \in \Gamma
adamc@655	683 }
adamc@655	684 \quad \infer{\Gamma \vdash X \longrightarrow \kappa}{
adamc@655	685 \Gamma, X \vdash \kappa
adamc@655	686 }$$
adamc@655	687
adamc@530	688 \subsection{Kinding}
adamc@530	689
adamc@655	690 We write $[X \mapsto \kappa_1]\kappa_2$ for capture-avoiding substitution of $\kappa_1$ for $X$ in $\kappa_2$.
adamc@655	691
adamc@530	692 $$\infer{\Gamma \vdash (c) :: \kappa :: \kappa}{
adamc@530	693 \Gamma \vdash c :: \kappa
adamc@530	694 }
adamc@530	695 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530	696 x :: \kappa \in \Gamma
adamc@530	697 }
adamc@530	698 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530	699 x :: \kappa = c \in \Gamma
adamc@530	700 }$$
adamc@530	701
adamc@530	702 $$\infer{\Gamma \vdash M.x :: \kappa}{
adamc@537	703 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	704 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = \kappa
adamc@530	705 }
adamc@530	706 \quad \infer{\Gamma \vdash M.x :: \kappa}{
adamc@537	707 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	708 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@530	709 }$$
adamc@530	710
adamc@530	711 $$\infer{\Gamma \vdash \tau_1 \to \tau_2 :: \mt{Type}}{
adamc@530	712 \Gamma \vdash \tau_1 :: \mt{Type}
adamc@530	713 & \Gamma \vdash \tau_2 :: \mt{Type}
adamc@530	714 }
adamc@530	715 \quad \infer{\Gamma \vdash x \; ? \: \kappa \to \tau :: \mt{Type}}{
adamc@530	716 \Gamma, x :: \kappa \vdash \tau :: \mt{Type}
adamc@530	717 }
adamc@655	718 \quad \infer{\Gamma \vdash X \longrightarrow \tau :: \mt{Type}}{
adamc@655	719 \Gamma, X \vdash \tau :: \mt{Type}
adamc@655	720 }
adamc@530	721 \quad \infer{\Gamma \vdash \$c :: \mt{Type}}{
adamc@530	722 \Gamma \vdash c :: \{\mt{Type}\}
adamc@530	723 }$$
adamc@530	724
adamc@530	725 $$\infer{\Gamma \vdash c_1 \; c_2 :: \kappa_2}{
adamc@530	726 \Gamma \vdash c_1 :: \kappa_1 \to \kappa_2
adamc@530	727 & \Gamma \vdash c_2 :: \kappa_1
adamc@530	728 }
adamc@530	729 \quad \infer{\Gamma \vdash \lambda x \; :: \; \kappa_1 \Rightarrow c :: \kappa_1 \to \kappa_2}{
adamc@530	730 \Gamma, x :: \kappa_1 \vdash c :: \kappa_2
adamc@530	731 }$$
adamc@530	732
adamc@655	733 $$\infer{\Gamma \vdash c[\kappa'] :: [X \mapsto \kappa']\kappa}{
adamc@655	734 \Gamma \vdash c :: X \to \kappa
adamc@655	735 & \Gamma \vdash \kappa'
adamc@655	736 }
adamc@655	737 \quad \infer{\Gamma \vdash X \Longrightarrow c :: X \to \kappa}{
adamc@655	738 \Gamma, X \vdash c :: \kappa
adamc@655	739 }$$
adamc@655	740
adamc@530	741 $$\infer{\Gamma \vdash () :: \mt{Unit}}{}
adamc@530	742 \quad \infer{\Gamma \vdash \#X :: \mt{Name}}{}$$
adamc@530	743
adamc@530	744 $$\infer{\Gamma \vdash [\overline{c_i = c'_i}] :: \{\kappa\}}{
adamc@530	745 \forall i: \Gamma \vdash c_i : \mt{Name}
adamc@530	746 & \Gamma \vdash c'_i :: \kappa
adamc@530	747 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@530	748 }
adamc@530	749 \quad \infer{\Gamma \vdash c_1 \rc c_2 :: \{\kappa\}}{
adamc@530	750 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530	751 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@530	752 & \Gamma \vdash c_1 \sim c_2
adamc@530	753 }$$
adamc@530	754
adamc@655	755 $$\infer{\Gamma \vdash \mt{map} :: (\kappa_1 \to \kappa_2) \to \{\kappa_1\} \to \{\kappa_2\}}{}$$
adamc@530	756
adamc@573	757 $$\infer{\Gamma \vdash (\overline c) :: (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@573	758 \forall i: \Gamma \vdash c_i :: \kappa_i
adamc@530	759 }
adamc@573	760 \quad \infer{\Gamma \vdash c.i :: \kappa_i}{
adamc@573	761 \Gamma \vdash c :: (\kappa_1 \times \ldots \times \kappa_n)
adamc@530	762 }$$
adamc@530	763
adamc@655	764 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow \tau :: \mt{Type}}{
adamc@655	765 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530	766 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@655	767 & \Gamma, c_1 \sim c_2 \vdash \tau :: \mt{Type}
adamc@530	768 }$$
adamc@530	769
adamc@531	770 \subsection{Record Disjointness}
adamc@531	771
adamc@531	772 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@558	773 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@558	774 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@558	775 & \forall c'_1 \in C_1, c'_2 \in C_2: \Gamma \vdash c'_1 \sim c'_2
adamc@531	776 }
adamc@531	777 \quad \infer{\Gamma \vdash X \sim X'}{
adamc@531	778 X \neq X'
adamc@531	779 }$$
adamc@531	780
adamc@531	781 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@531	782 c'_1 \sim c'_2 \in \Gamma
adamc@558	783 & \Gamma \vdash c'_1 \hookrightarrow C_1
adamc@558	784 & \Gamma \vdash c'_2 \hookrightarrow C_2
adamc@558	785 & c_1 \in C_1
adamc@558	786 & c_2 \in C_2
adamc@531	787 }$$
adamc@531	788
adamc@531	789 $$\infer{\Gamma \vdash c \hookrightarrow \{c\}}{}
adamc@531	790 \quad \infer{\Gamma \vdash [\overline{c = c'}] \hookrightarrow \{\overline{c}\}}{}
adamc@531	791 \quad \infer{\Gamma \vdash c_1 \rc c_2 \hookrightarrow C_1 \cup C_2}{
adamc@531	792 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@531	793 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@531	794 }
adamc@531	795 \quad \infer{\Gamma \vdash c \hookrightarrow C}{
adamc@531	796 \Gamma \vdash c \equiv c'
adamc@531	797 & \Gamma \vdash c' \hookrightarrow C
adamc@531	798 }
adamc@531	799 \quad \infer{\Gamma \vdash \mt{map} \; f \; c \hookrightarrow C}{
adamc@531	800 \Gamma \vdash c \hookrightarrow C
adamc@531	801 }$$
adamc@531	802
adamc@541	803 \subsection{\label{definitional}Definitional Equality}
adamc@532	804
adamc@655	805 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	806
adamc@532	807 $$\infer{\Gamma \vdash c \equiv c}{}
adamc@532	808 \quad \infer{\Gamma \vdash c_1 \equiv c_2}{
adamc@532	809 \Gamma \vdash c_2 \equiv c_1
adamc@532	810 }
adamc@532	811 \quad \infer{\Gamma \vdash c_1 \equiv c_3}{
adamc@532	812 \Gamma \vdash c_1 \equiv c_2
adamc@532	813 & \Gamma \vdash c_2 \equiv c_3
adamc@532	814 }
adamc@532	815 \quad \infer{\Gamma \vdash \mathcal C[c_1] \equiv \mathcal C[c_2]}{
adamc@532	816 \Gamma \vdash c_1 \equiv c_2
adamc@532	817 }$$
adamc@532	818
adamc@532	819 $$\infer{\Gamma \vdash x \equiv c}{
adamc@532	820 x :: \kappa = c \in \Gamma
adamc@532	821 }
adamc@532	822 \quad \infer{\Gamma \vdash M.x \equiv c}{
adamc@537	823 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	824 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@532	825 }
adamc@532	826 \quad \infer{\Gamma \vdash (\overline c).i \equiv c_i}{}$$
adamc@532	827
adamc@532	828 $$\infer{\Gamma \vdash (\lambda x :: \kappa \Rightarrow c) \; c' \equiv [x \mapsto c'] c}{}
adamc@655	829 \quad \infer{\Gamma \vdash (X \Longrightarrow c) [\kappa] \equiv [X \mapsto \kappa] c}{}$$
adamc@655	830
adamc@655	831 $$\infer{\Gamma \vdash c_1 \rc c_2 \equiv c_2 \rc c_1}{}
adamc@532	832 \quad \infer{\Gamma \vdash c_1 \rc (c_2 \rc c_3) \equiv (c_1 \rc c_2) \rc c_3}{}$$
adamc@532	833
adamc@532	834 $$\infer{\Gamma \vdash [] \rc c \equiv c}{}
adamc@532	835 \quad \infer{\Gamma \vdash [\overline{c_1 = c'_1}] \rc [\overline{c_2 = c'_2}] \equiv [\overline{c_1 = c'_1}, \overline{c_2 = c'_2}]}{}$$
adamc@532	836
adamc@655	837 $$\infer{\Gamma \vdash \mt{map} \; f \; [] \equiv []}{}
adamc@655	838 \quad \infer{\Gamma \vdash \mt{map} \; f \; ([c_1 = c_2] \rc c) \equiv [c_1 = f \; c_2] \rc \mt{map} \; f \; c}{}$$
adamc@532	839
adamc@532	840 $$\infer{\Gamma \vdash \mt{map} \; (\lambda x \Rightarrow x) \; c \equiv c}{}
adamc@655	841 \quad \infer{\Gamma \vdash \mt{map} \; f \; (\mt{map} \; f' \; c)
adamc@655	842 \equiv \mt{map} \; (\lambda x \Rightarrow f \; (f' \; x)) \; c}{}$$
adamc@532	843
adamc@532	844 $$\infer{\Gamma \vdash \mt{map} \; f \; (c_1 \rc c_2) \equiv \mt{map} \; f \; c_1 \rc \mt{map} \; f \; c_2}{}$$
adamc@531	845
adamc@534	846 \subsection{Expression Typing}
adamc@533	847
adamc@873	848 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	849
adamc@533	850 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	851
adamc@533	852 $$\infer{\Gamma \vdash e : \tau : \tau}{
adamc@533	853 \Gamma \vdash e : \tau
adamc@533	854 }
adamc@533	855 \quad \infer{\Gamma \vdash e : \tau}{
adamc@533	856 \Gamma \vdash e : \tau'
adamc@533	857 & \Gamma \vdash \tau' \equiv \tau
adamc@533	858 }
adamc@533	859 \quad \infer{\Gamma \vdash \ell : T(\ell)}{}$$
adamc@533	860
adamc@533	861 $$\infer{\Gamma \vdash x : \mathcal I(\tau)}{
adamc@533	862 x : \tau \in \Gamma
adamc@533	863 }
adamc@533	864 \quad \infer{\Gamma \vdash M.x : \mathcal I(\tau)}{
adamc@537	865 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	866 & \mt{proj}(M, \overline{s}, \mt{val} \; x) = \tau
adamc@533	867 }
adamc@533	868 \quad \infer{\Gamma \vdash X : \mathcal I(\tau)}{
adamc@533	869 X : \tau \in \Gamma
adamc@533	870 }
adamc@533	871 \quad \infer{\Gamma \vdash M.X : \mathcal I(\tau)}{
adamc@537	872 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	873 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \tau
adamc@533	874 }$$
adamc@533	875
adamc@533	876 $$\infer{\Gamma \vdash e_1 \; e_2 : \tau_2}{
adamc@533	877 \Gamma \vdash e_1 : \tau_1 \to \tau_2
adamc@533	878 & \Gamma \vdash e_2 : \tau_1
adamc@533	879 }
adamc@533	880 \quad \infer{\Gamma \vdash \lambda x : \tau_1 \Rightarrow e : \tau_1 \to \tau_2}{
adamc@533	881 \Gamma, x : \tau_1 \vdash e : \tau_2
adamc@533	882 }$$
adamc@533	883
adamc@533	884 $$\infer{\Gamma \vdash e [c] : [x \mapsto c]\tau}{
adamc@533	885 \Gamma \vdash e : x :: \kappa \to \tau
adamc@533	886 & \Gamma \vdash c :: \kappa
adamc@533	887 }
adamc@852	888 \quad \infer{\Gamma \vdash \lambda [x \; ? \; \kappa] \Rightarrow e : x \; ? \; \kappa \to \tau}{
adamc@533	889 \Gamma, x :: \kappa \vdash e : \tau
adamc@533	890 }$$
adamc@533	891
adamc@655	892 $$\infer{\Gamma \vdash e [\kappa] : [X \mapsto \kappa]\tau}{
adamc@655	893 \Gamma \vdash e : X \longrightarrow \tau
adamc@655	894 & \Gamma \vdash \kappa
adamc@655	895 }
adamc@655	896 \quad \infer{\Gamma \vdash X \Longrightarrow e : X \longrightarrow \tau}{
adamc@655	897 \Gamma, X \vdash e : \tau
adamc@655	898 }$$
adamc@655	899
adamc@533	900 $$\infer{\Gamma \vdash \{\overline{c = e}\} : \{\overline{c : \tau}\}}{
adamc@533	901 \forall i: \Gamma \vdash c_i :: \mt{Name}
adamc@533	902 & \Gamma \vdash e_i : \tau_i
adamc@533	903 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@533	904 }
adamc@533	905 \quad \infer{\Gamma \vdash e.c : \tau}{
adamc@533	906 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533	907 }
adamc@533	908 \quad \infer{\Gamma \vdash e_1 \rc e_2 : \$(c_1 \rc c_2)}{
adamc@533	909 \Gamma \vdash e_1 : \$c_1
adamc@533	910 & \Gamma \vdash e_2 : \$c_2
adamc@573	911 & \Gamma \vdash c_1 \sim c_2
adamc@533	912 }$$
adamc@533	913
adamc@533	914 $$\infer{\Gamma \vdash e \rcut c : \$c'}{
adamc@533	915 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533	916 }
adamc@533	917 \quad \infer{\Gamma \vdash e \rcutM c : \$c'}{
adamc@533	918 \Gamma \vdash e : \$(c \rc c')
adamc@533	919 }$$
adamc@533	920
adamc@533	921 $$\infer{\Gamma \vdash \mt{let} \; \overline{ed} \; \mt{in} \; e \; \mt{end} : \tau}{
adamc@533	922 \Gamma \vdash \overline{ed} \leadsto \Gamma'
adamc@533	923 & \Gamma' \vdash e : \tau
adamc@533	924 }
adamc@533	925 \quad \infer{\Gamma \vdash \mt{case} \; e \; \mt{of} \; \overline{p \Rightarrow e} : \tau}{
adamc@533	926 \forall i: \Gamma \vdash p_i \leadsto \Gamma_i, \tau'
adamc@533	927 & \Gamma_i \vdash e_i : \tau
adamc@533	928 }$$
adamc@533	929
adamc@573	930 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow e : \lambda [c_1 \sim c_2] \Rightarrow \tau}{
adamc@533	931 \Gamma \vdash c_1 :: \{\kappa\}
adamc@655	932 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@533	933 & \Gamma, c_1 \sim c_2 \vdash e : \tau
adamc@662	934 }
adamc@662	935 \quad \infer{\Gamma \vdash e \; ! : \tau}{
adamc@662	936 \Gamma \vdash e : [c_1 \sim c_2] \Rightarrow \tau
adamc@662	937 & \Gamma \vdash c_1 \sim c_2
adamc@533	938 }$$
adamc@533	939
adamc@534	940 \subsection{Pattern Typing}
adamc@534	941
adamc@534	942 $$\infer{\Gamma \vdash \_ \leadsto \Gamma; \tau}{}
adamc@534	943 \quad \infer{\Gamma \vdash x \leadsto \Gamma, x : \tau; \tau}{}
adamc@534	944 \quad \infer{\Gamma \vdash \ell \leadsto \Gamma; T(\ell)}{}$$
adamc@534	945
adamc@534	946 $$\infer{\Gamma \vdash X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534	947 X : \overline{x ::: \mt{Type}} \to \tau \in \Gamma
adamc@534	948 & \textrm{$\tau$ not a function type}
adamc@534	949 }
adamc@534	950 \quad \infer{\Gamma \vdash X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534	951 X : \overline{x ::: \mt{Type}} \to \tau'' \to \tau \in \Gamma
adamc@534	952 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534	953 }$$
adamc@534	954
adamc@534	955 $$\infer{\Gamma \vdash M.X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537	956 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	957 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau
adamc@534	958 & \textrm{$\tau$ not a function type}
adamc@534	959 }$$
adamc@534	960
adamc@534	961 $$\infer{\Gamma \vdash M.X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537	962 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	963 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau'' \to \tau
adamc@534	964 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534	965 }$$
adamc@534	966
adamc@534	967 $$\infer{\Gamma \vdash \{\overline{x = p}\} \leadsto \Gamma_n; \{\overline{x = \tau}\}}{
adamc@534	968 \Gamma_0 = \Gamma
adamc@534	969 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534	970 }
adamc@534	971 \quad \infer{\Gamma \vdash \{\overline{x = p}, \ldots\} \leadsto \Gamma_n; \$([\overline{x = \tau}] \rc c)}{
adamc@534	972 \Gamma_0 = \Gamma
adamc@534	973 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534	974 }$$
adamc@534	975
adamc@852	976 $$\infer{\Gamma \vdash p : \tau \leadsto \Gamma'; \tau}{
adamc@852	977 \Gamma \vdash p \leadsto \Gamma'; \tau'
adamc@852	978 & \Gamma \vdash \tau' \equiv \tau
adamc@852	979 }$$
adamc@852	980
adamc@535	981 \subsection{Declaration Typing}
adamc@535	982
adamc@535	983 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	984
adamc@558	985 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	986 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	987
adamc@535	988 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535	989 \quad \infer{\Gamma \vdash d, \overline{d} \leadsto \Gamma''}{
adamc@535	990 \Gamma \vdash d \leadsto \Gamma'
adamc@535	991 & \Gamma' \vdash \overline{d} \leadsto \Gamma''
adamc@535	992 }$$
adamc@535	993
adamc@535	994 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@535	995 \Gamma \vdash c :: \kappa
adamc@535	996 }
adamc@535	997 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@535	998 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@535	999 }$$
adamc@535	1000
adamc@535	1001 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537	1002 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1003 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@535	1004 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@535	1005 }$$
adamc@535	1006
adamc@535	1007 $$\infer{\Gamma \vdash \mt{val} \; x : \tau = e \leadsto \Gamma, x : \tau}{
adamc@535	1008 \Gamma \vdash e : \tau
adamc@535	1009 }$$
adamc@535	1010
adamc@535	1011 $$\infer{\Gamma \vdash \mt{val} \; \mt{rec} \; \overline{x : \tau = e} \leadsto \Gamma, \overline{x : \tau}}{
adamc@535	1012 \forall i: \Gamma, \overline{x : \tau} \vdash e_i : \tau_i
adamc@535	1013 & \textrm{$e_i$ starts with an expression $\lambda$, optionally preceded by constructor and disjointness $\lambda$s}
adamc@535	1014 }$$
adamc@535	1015
adamc@535	1016 $$\infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : S}{
adamc@535	1017 \Gamma \vdash M : S
adamc@558	1018 & \textrm{ $M$ not a constant or application}
adamc@535	1019 }
adamc@558	1020 \quad \infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : \mt{selfify}(X, \overline{s})}{
adamc@558	1021 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@539	1022 }$$
adamc@539	1023
adamc@539	1024 $$\infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@535	1025 \Gamma \vdash S
adamc@535	1026 }$$
adamc@535	1027
adamc@537	1028 $$\infer{\Gamma \vdash \mt{open} \; M \leadsto \Gamma, \mathcal O(M, \overline{s})}{
adamc@537	1029 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535	1030 }$$
adamc@535	1031
adamc@535	1032 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma}{
adamc@535	1033 \Gamma \vdash c_1 :: \{\kappa\}
adamc@535	1034 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@535	1035 & \Gamma \vdash c_1 \sim c_2
adamc@535	1036 }
adamc@537	1037 \quad \infer{\Gamma \vdash \mt{open} \; \mt{constraints} \; M \leadsto \Gamma, \mathcal O_c(M, \overline{s})}{
adamc@537	1038 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535	1039 }$$
adamc@535	1040
adamc@784	1041 $$\infer{\Gamma \vdash \mt{table} \; x : c \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_table} \; c \; []}{
adamc@535	1042 \Gamma \vdash c :: \{\mt{Type}\}
adamc@535	1043 }
adam@1594	1044 \quad \infer{\Gamma \vdash \mt{view} \; x = e \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_view} \; c}{
adam@1594	1045 \Gamma \vdash e :: \mt{Basis}.\mt{sql\_query} \; [] \; [] \; (\mt{map} \; (\lambda \_ \Rightarrow []) \; c') \; c
adamc@784	1046 }$$
adamc@784	1047
adamc@784	1048 $$\infer{\Gamma \vdash \mt{sequence} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_sequence}}{}$$
adamc@535	1049
adamc@535	1050 $$\infer{\Gamma \vdash \mt{cookie} \; x : \tau \leadsto \Gamma, x : \mt{Basis}.\mt{http\_cookie} \; \tau}{
adamc@535	1051 \Gamma \vdash \tau :: \mt{Type}
adamc@784	1052 }
adamc@784	1053 \quad \infer{\Gamma \vdash \mt{style} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{css\_class}}{}$$
adamc@535	1054
adamc@1085	1055 $$\infer{\Gamma \vdash \mt{task} \; e_1 = e_2 \leadsto \Gamma}{
adam@1348	1056 \Gamma \vdash e_1 :: \mt{Basis}.\mt{task\_kind} \; \tau
adam@1348	1057 & \Gamma \vdash e_2 :: \tau \to \mt{Basis}.\mt{transaction} \; \{\}
adamc@1085	1058 }$$
adamc@1085	1059
adamc@535	1060 $$\infer{\overline{y}; x; \Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535	1061 \quad \infer{\overline{y}; x; \Gamma \vdash X \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to x \; \overline{y}}{
adamc@535	1062 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535	1063 }
adamc@535	1064 \quad \infer{\overline{y}; x; \Gamma \vdash X \; \mt{of} \; \tau \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to \tau \to x \; \overline{y}}{
adamc@535	1065 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535	1066 }$$
adamc@535	1067
adamc@537	1068 \subsection{Signature Item Typing}
adamc@537	1069
adamc@537	1070 We appeal to a signature item analogue of the $\mathcal O$ function from the last subsection.
adamc@537	1071
adam@1797	1072 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	1073
adamc@537	1074 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@537	1075 \quad \infer{\Gamma \vdash s, \overline{s} \leadsto \Gamma''}{
adamc@537	1076 \Gamma \vdash s \leadsto \Gamma'
adamc@537	1077 & \Gamma' \vdash \overline{s} \leadsto \Gamma''
adamc@537	1078 }$$
adamc@537	1079
adamc@537	1080 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}
adamc@537	1081 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@537	1082 \Gamma \vdash c :: \kappa
adamc@537	1083 }
adamc@537	1084 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@537	1085 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@537	1086 }$$
adamc@537	1087
adamc@537	1088 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537	1089 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1090 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537	1091 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@537	1092 }$$
adamc@537	1093
adamc@537	1094 $$\infer{\Gamma \vdash \mt{val} \; x : \tau \leadsto \Gamma, x : \tau}{
adamc@537	1095 \Gamma \vdash \tau :: \mt{Type}
adamc@537	1096 }$$
adamc@537	1097
adamc@537	1098 $$\infer{\Gamma \vdash \mt{structure} \; X : S \leadsto \Gamma, X : S}{
adamc@537	1099 \Gamma \vdash S
adamc@537	1100 }
adamc@537	1101 \quad \infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@537	1102 \Gamma \vdash S
adamc@537	1103 }$$
adamc@537	1104
adamc@537	1105 $$\infer{\Gamma \vdash \mt{include} \; S \leadsto \Gamma, \mathcal O(\overline{s})}{
adamc@537	1106 \Gamma \vdash S
adamc@537	1107 & \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1108 }$$
adamc@537	1109
adamc@537	1110 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma, c_1 \sim c_2}{
adamc@537	1111 \Gamma \vdash c_1 :: \{\kappa\}
adamc@537	1112 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@537	1113 }$$
adamc@537	1114
adamc@784	1115 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784	1116 \Gamma \vdash c :: \kappa
adamc@537	1117 }
adamc@784	1118 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}$$
adamc@537	1119
adamc@536	1120 \subsection{Signature Compatibility}
adamc@536	1121
adam@1797	1122 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	1123
adamc@537	1124 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	1125
adamc@536	1126 $$\infer{\Gamma \vdash S \equiv S}{}
adamc@536	1127 \quad \infer{\Gamma \vdash S_1 \equiv S_2}{
adamc@536	1128 \Gamma \vdash S_2 \equiv S_1
adamc@536	1129 }
adamc@536	1130 \quad \infer{\Gamma \vdash X \equiv S}{
adamc@536	1131 X = S \in \Gamma
adamc@536	1132 }
adamc@536	1133 \quad \infer{\Gamma \vdash M.X \equiv S}{
adamc@537	1134 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1135 & \mt{proj}(M, \overline{s}, \mt{signature} \; X) = S
adamc@536	1136 }$$
adamc@536	1137
adamc@536	1138 $$\infer{\Gamma \vdash S \; \mt{where} \; \mt{con} \; x = c \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa = c \; \overline{s_2} \; \mt{end}}{
adamc@536	1139 \Gamma \vdash S \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa \; \overline{s_2} \; \mt{end}
adamc@536	1140 & \Gamma \vdash c :: \kappa
adamc@537	1141 }
adamc@537	1142 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s^1} \; \mt{include} \; S \; \overline{s^2} \; \mt{end} \equiv \mt{sig} \; \overline{s^1} \; \overline{s} \; \overline{s^2} \; \mt{end}}{
adamc@537	1143 \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@536	1144 }$$
adamc@536	1145
adamc@536	1146 $$\infer{\Gamma \vdash S_1 \leq S_2}{
adamc@536	1147 \Gamma \vdash S_1 \equiv S_2
adamc@536	1148 }
adamc@536	1149 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \mt{end}}{}
adamc@537	1150 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; s' \; \overline{s'} \; \mt{end}}{
adamc@537	1151 \Gamma \vdash \overline{s} \leq s'
adamc@537	1152 & \Gamma \vdash s' \leadsto \Gamma'
adamc@537	1153 & \Gamma' \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \overline{s'} \; \mt{end}
adamc@537	1154 }$$
adamc@537	1155
adamc@537	1156 $$\infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537	1157 \Gamma \vdash s \leq s'
adamc@537	1158 }
adamc@537	1159 \quad \infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537	1160 \Gamma \vdash s \leadsto \Gamma'
adamc@537	1161 & \Gamma' \vdash \overline{s} \leq s'
adamc@536	1162 }$$
adamc@536	1163
adamc@536	1164 $$\infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 \leq \mt{functor} (X : S'_1) : S'_2}{
adamc@536	1165 \Gamma \vdash S'_1 \leq S_1
adamc@536	1166 & \Gamma, X : S'_1 \vdash S_2 \leq S'_2
adamc@536	1167 }$$
adamc@536	1168
adamc@537	1169 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@537	1170 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}
adamc@558	1171 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type}}{}$$
adamc@537	1172
adamc@537	1173 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(y)} \to \mt{Type}}{
adamc@537	1174 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1175 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537	1176 }$$
adamc@537	1177
adamc@784	1178 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@784	1179 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}$$
adamc@537	1180
adamc@537	1181 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \mt{\kappa} = c_2}{
adamc@537	1182 \Gamma \vdash c_1 \equiv c_2
adamc@537	1183 }
adamc@784	1184 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \kappa = c_2}{
adamc@537	1185 \Gamma \vdash c_1 \equiv c_2
adamc@537	1186 }$$
adamc@537	1187
adamc@537	1188 $$\infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537	1189 \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537	1190 }$$
adamc@537	1191
adamc@537	1192 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537	1193 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1194 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537	1195 & \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537	1196 }$$
adamc@537	1197
adamc@537	1198 $$\infer{\Gamma \vdash \cdot \leq \cdot}{}
adamc@537	1199 \quad \infer{\Gamma \vdash X; \overline{dc} \leq X; \overline{dc'}}{
adamc@537	1200 \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537	1201 }
adamc@537	1202 \quad \infer{\Gamma \vdash X \; \mt{of} \; \tau_1; \overline{dc} \leq X \; \mt{of} \; \tau_2; \overline{dc'}}{
adamc@537	1203 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537	1204 & \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537	1205 }$$
adamc@537	1206
adamc@537	1207 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x = \mt{datatype} \; M'.z'}{
adamc@537	1208 \Gamma \vdash M.z \equiv M'.z'
adamc@537	1209 }$$
adamc@537	1210
adamc@537	1211 $$\infer{\Gamma \vdash \mt{val} \; x : \tau_1 \leq \mt{val} \; x : \tau_2}{
adamc@537	1212 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537	1213 }
adamc@537	1214 \quad \infer{\Gamma \vdash \mt{structure} \; X : S_1 \leq \mt{structure} \; X : S_2}{
adamc@537	1215 \Gamma \vdash S_1 \leq S_2
adamc@537	1216 }
adamc@537	1217 \quad \infer{\Gamma \vdash \mt{signature} \; X = S_1 \leq \mt{signature} \; X = S_2}{
adamc@537	1218 \Gamma \vdash S_1 \leq S_2
adamc@537	1219 & \Gamma \vdash S_2 \leq S_1
adamc@537	1220 }$$
adamc@537	1221
adamc@537	1222 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leq \mt{constraint} \; c'_1 \sim c'_2}{
adamc@537	1223 \Gamma \vdash c_1 \equiv c'_1
adamc@537	1224 & \Gamma \vdash c_2 \equiv c'_2
adamc@537	1225 }$$
adamc@537	1226
adamc@655	1227 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{class} \; x :: \kappa}{}
adamc@655	1228 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{class} \; x :: \kappa}{}
adamc@655	1229 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{class} \; x :: \kappa = c_2}{
adamc@537	1230 \Gamma \vdash c_1 \equiv c_2
adamc@537	1231 }$$
adamc@537	1232
adam@1797	1233 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leq \mt{class} \; x :: \kappa}{}
adam@1797	1234 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leq \mt{class} \; x :: \kappa}{}
adam@1797	1235 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c_1 \leq \mt{class} \; x :: \kappa = c_2}{
adam@1797	1236 \Gamma \vdash c_1 \equiv c_2
adam@1797	1237 }$$
adam@1797	1238
adamc@538	1239 \subsection{Module Typing}
adamc@538	1240
adamc@538	1241 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	1242
adamc@538	1243 $$\infer{\Gamma \vdash M : S}{
adamc@538	1244 \Gamma \vdash M : S'
adamc@538	1245 & \Gamma \vdash S' \leq S
adamc@538	1246 }
adamc@538	1247 \quad \infer{\Gamma \vdash \mt{struct} \; \overline{d} \; \mt{end} : \mt{sig} \; \mt{sigOf}(\overline{d}) \; \mt{end}}{
adamc@538	1248 \Gamma \vdash \overline{d} \leadsto \Gamma'
adamc@538	1249 }
adamc@538	1250 \quad \infer{\Gamma \vdash X : S}{
adamc@538	1251 X : S \in \Gamma
adamc@538	1252 }$$
adamc@538	1253
adamc@538	1254 $$\infer{\Gamma \vdash M.X : S}{
adamc@538	1255 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@538	1256 & \mt{proj}(M, \overline{s}, \mt{structure} \; X) = S
adamc@538	1257 }$$
adamc@538	1258
adamc@538	1259 $$\infer{\Gamma \vdash M_1(M_2) : [X \mapsto M_2]S_2}{
adamc@538	1260 \Gamma \vdash M_1 : \mt{functor}(X : S_1) : S_2
adamc@538	1261 & \Gamma \vdash M_2 : S_1
adamc@538	1262 }
adamc@538	1263 \quad \infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 = M : \mt{functor} (X : S_1) : S_2}{
adamc@538	1264 \Gamma \vdash S_1
adamc@538	1265 & \Gamma, X : S_1 \vdash S_2
adamc@538	1266 & \Gamma, X : S_1 \vdash M : S_2
adamc@538	1267 }$$
adamc@538	1268
adamc@538	1269 \begin{eqnarray*}
adamc@538	1270 \mt{sigOf}(\cdot) &=& \cdot \\
adamc@538	1271 \mt{sigOf}(s \; \overline{s'}) &=& \mt{sigOf}(s) \; \mt{sigOf}(\overline{s'}) \\
adamc@538	1272 \\
adamc@538	1273 \mt{sigOf}(\mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@538	1274 \mt{sigOf}(\mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \overline{dc} \\
adamc@538	1275 \mt{sigOf}(\mt{datatype} \; x = \mt{datatype} \; M.z) &=& \mt{datatype} \; x = \mt{datatype} \; M.z \\
adamc@538	1276 \mt{sigOf}(\mt{val} \; x : \tau = e) &=& \mt{val} \; x : \tau \\
adamc@538	1277 \mt{sigOf}(\mt{val} \; \mt{rec} \; \overline{x : \tau = e}) &=& \overline{\mt{val} \; x : \tau} \\
adamc@538	1278 \mt{sigOf}(\mt{structure} \; X : S = M) &=& \mt{structure} \; X : S \\
adamc@538	1279 \mt{sigOf}(\mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@538	1280 \mt{sigOf}(\mt{open} \; M) &=& \mt{include} \; S \textrm{ (where $\Gamma \vdash M : S$)} \\
adamc@538	1281 \mt{sigOf}(\mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@538	1282 \mt{sigOf}(\mt{open} \; \mt{constraints} \; M) &=& \cdot \\
adamc@538	1283 \mt{sigOf}(\mt{table} \; x : c) &=& \mt{table} \; x : c \\
adam@1594	1284 \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	1285 \mt{sigOf}(\mt{sequence} \; x) &=& \mt{sequence} \; x \\
adamc@538	1286 \mt{sigOf}(\mt{cookie} \; x : \tau) &=& \mt{cookie} \; x : \tau \\
adam@1797	1287 \mt{sigOf}(\mt{style} \; x) &=& \mt{style} \; x
adamc@538	1288 \end{eqnarray*}
adamc@539	1289 \begin{eqnarray*}
adamc@539	1290 \mt{selfify}(M, \cdot) &=& \cdot \\
adamc@558	1291 \mt{selfify}(M, s \; \overline{s'}) &=& \mt{selfify}(M, s) \; \mt{selfify}(M, \overline{s'}) \\
adamc@539	1292 \\
adamc@539	1293 \mt{selfify}(M, \mt{con} \; x :: \kappa) &=& \mt{con} \; x :: \kappa = M.x \\
adamc@539	1294 \mt{selfify}(M, \mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@539	1295 \mt{selfify}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \mt{datatype} \; M.x \\
adamc@539	1296 \mt{selfify}(M, \mt{datatype} \; x = \mt{datatype} \; M'.z) &=& \mt{datatype} \; x = \mt{datatype} \; M'.z \\
adamc@539	1297 \mt{selfify}(M, \mt{val} \; x : \tau) &=& \mt{val} \; x : \tau \\
adamc@539	1298 \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	1299 \mt{selfify}(M, \mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@539	1300 \mt{selfify}(M, \mt{include} \; S) &=& \mt{include} \; S \\
adamc@539	1301 \mt{selfify}(M, \mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@655	1302 \mt{selfify}(M, \mt{class} \; x :: \kappa) &=& \mt{class} \; x :: \kappa = M.x \\
adamc@655	1303 \mt{selfify}(M, \mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@539	1304 \end{eqnarray*}
adamc@539	1305
adamc@540	1306 \subsection{Module Projection}
adamc@540	1307
adamc@540	1308 \begin{eqnarray*}
adamc@540	1309 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \\
adamc@540	1310 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa, c) \\
adamc@540	1311 \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	1312 \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	1313 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})$)} \\
adamc@655	1314 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \to \mt{Type} \\
adamc@655	1315 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa \to \mt{Type}, c) \\
adamc@540	1316 \\
adamc@540	1317 \mt{proj}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc} \; \overline{s}, \mt{datatype} \; x) &=& (\overline{y}, \overline{dc}) \\
adamc@540	1318 \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	1319 \\
adamc@540	1320 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, \mt{val} \; x) &=& \tau \\
adamc@540	1321 \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	1322 \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	1323 \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	1324 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \in \overline{dc}$)} \\
adamc@540	1325 \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	1326 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \; \mt{of} \; \tau \in \overline{dc}$)} \\
adamc@540	1327 \\
adamc@540	1328 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, \mt{structure} \; X) &=& S \\
adamc@540	1329 \\
adamc@540	1330 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, \mt{signature} \; X) &=& S \\
adamc@540	1331 \\
adamc@540	1332 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1333 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1334 \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	1335 \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	1336 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@540	1337 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1338 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1339 \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	1340 \mt{proj}(M, \mt{constraint} \; c_1 \sim c_2 \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@655	1341 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@655	1342 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1343 \end{eqnarray*}
adamc@540	1344
adamc@541	1345
adamc@541	1346 \section{Type Inference}
adamc@541	1347
adamc@541	1348 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	1349
adamc@541	1350 \subsection{Basic Unification}
adamc@541	1351
adamc@560	1352 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	1353
adamc@656	1354 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	1355
adamc@541	1356 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	1357
adamc@541	1358 \subsection{Unifying Record Types}
adamc@541	1359
adamc@570	1360 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	1361
adamc@656	1362 \subsection{\label{typeclasses}Constructor Classes}
adamc@541	1363
adamc@784	1364 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	1365
adam@1797	1366 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	1367
adam@1797	1368 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	1369
adam@1797	1370 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	1371
adamc@541	1372 \subsection{Reverse-Engineering Record Types}
adamc@541	1373
adamc@656	1374 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	1375
adamc@541	1376 \subsection{Implicit Arguments in Functor Applications}
adamc@541	1377
adamc@656	1378 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	1379
adamc@541	1380
adamc@542	1381 \section{The Ur Standard Library}
adamc@542	1382
adamc@542	1383 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	1384
adamc@542	1385 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	1386
adamc@542	1387 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	1388 $$\begin{array}{l}
adamc@542	1389 \mt{type} \; \mt{int} \\
adamc@542	1390 \mt{type} \; \mt{float} \\
adamc@873	1391 \mt{type} \; \mt{char} \\
adamc@542	1392 \mt{type} \; \mt{string} \\
adamc@542	1393 \mt{type} \; \mt{time} \\
adamc@785	1394 \mt{type} \; \mt{blob} \\
adamc@542	1395 \\
adamc@542	1396 \mt{type} \; \mt{unit} = \{\} \\
adamc@542	1397 \\
adamc@542	1398 \mt{datatype} \; \mt{bool} = \mt{False} \mid \mt{True} \\
adamc@542	1399 \\
adamc@785	1400 \mt{datatype} \; \mt{option} \; \mt{t} = \mt{None} \mid \mt{Some} \; \mt{of} \; \mt{t} \\
adamc@785	1401 \\
adamc@785	1402 \mt{datatype} \; \mt{list} \; \mt{t} = \mt{Nil} \mid \mt{Cons} \; \mt{of} \; \mt{t} \times \mt{list} \; \mt{t}
adamc@542	1403 \end{array}$$
adamc@542	1404
adamc@1123	1405 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	1406
adam@1297	1407 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	1408 $$\begin{array}{l}
adam@1297	1409 \mt{con} \; \mt{variant} :: \{\mt{Type}\} \to \mt{Type} \\
adam@1297	1410 \mt{val} \; \mt{make} : \mt{nm} :: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{ts} ::: \{\mt{Type}\} \to [[\mt{nm}] \sim \mt{ts}] \Rightarrow \mt{t} \to \mt{variant} \; ([\mt{nm} = \mt{t}] \rc \mt{ts}) \\
adam@1297	1411 \mt{val} \; \mt{match} : \mt{ts} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{variant} \; \mt{ts} \to \$(\mt{map} \; (\lambda \mt{t'} \Rightarrow \mt{t'} \to \mt{t}) \; \mt{ts}) \to \mt{t}
adam@1297	1412 \end{array}$$
adam@1297	1413
adamc@657	1414 Another important generic Ur element comes at the beginning of \texttt{top.urs}.
adamc@657	1415
adamc@657	1416 $$\begin{array}{l}
adamc@657	1417 \mt{con} \; \mt{folder} :: \mt{K} \longrightarrow \{\mt{K}\} \to \mt{Type} \\
adamc@657	1418 \\
adamc@657	1419 \mt{val} \; \mt{fold} : \mt{K} \longrightarrow \mt{tf} :: (\{\mt{K}\} \to \mt{Type}) \\
adamc@657	1420 \hspace{.1in} \to (\mt{nm} :: \mt{Name} \to \mt{v} :: \mt{K} \to \mt{r} :: \{\mt{K}\} \to [[\mt{nm}] \sim \mt{r}] \Rightarrow \\
adamc@657	1421 \hspace{.2in} \mt{tf} \; \mt{r} \to \mt{tf} \; ([\mt{nm} = \mt{v}] \rc \mt{r})) \\
adamc@657	1422 \hspace{.1in} \to \mt{tf} \; [] \\
adamc@657	1423 \hspace{.1in} \to \mt{r} :: \{\mt{K}\} \to \mt{folder} \; \mt{r} \to \mt{tf} \; \mt{r}
adamc@657	1424 \end{array}$$
adamc@657	1425
adamc@657	1426 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	1427
adamc@664	1428 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	1429
adamc@542	1430
adamc@542	1431 \section{The Ur/Web Standard Library}
adamc@542	1432
adam@1400	1433 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	1434
adamc@658	1435 \subsection{Monads}
adamc@658	1436
adamc@658	1437 The Ur Basis defines the monad constructor class from Haskell.
adamc@658	1438
adamc@658	1439 $$\begin{array}{l}
adamc@658	1440 \mt{class} \; \mt{monad} :: \mt{Type} \to \mt{Type} \\
adamc@658	1441 \mt{val} \; \mt{return} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t} ::: \mt{Type} \\
adamc@658	1442 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658	1443 \hspace{.1in} \to \mt{t} \to \mt{m} \; \mt{t} \\
adamc@658	1444 \mt{val} \; \mt{bind} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t1} ::: \mt{Type} \to \mt{t2} ::: \mt{Type} \\
adamc@658	1445 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658	1446 \hspace{.1in} \to \mt{m} \; \mt{t1} \to (\mt{t1} \to \mt{m} \; \mt{t2}) \\
adam@1544	1447 \hspace{.1in} \to \mt{m} \; \mt{t2} \\
adam@1544	1448 \mt{val} \; \mt{mkMonad} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \\
adam@1544	1449 \hspace{.1in} \to \{\mt{Return} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{m} \; \mt{t}, \\
adam@1544	1450 \hspace{.3in} \mt{Bind} : \mt{t1} ::: \mt{Type} \to \mt{t2} ::: \mt{Type} \to \mt{m} \; \mt{t1} \to (\mt{t1} \to \mt{m} \; \mt{t2}) \to \mt{m} \; \mt{t2}\} \\
adam@1544	1451 \hspace{.1in} \to \mt{monad} \; \mt{m}
adamc@658	1452 \end{array}$$
adamc@658	1453
adam@1687	1454 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	1455
adam@2009	1456 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	1457
adamc@542	1458 \subsection{Transactions}
adamc@542	1459
adamc@542	1460 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	1461 $$\begin{array}{l}
adamc@542	1462 \mt{con} \; \mt{transaction} :: \mt{Type} \to \mt{Type} \\
adamc@658	1463 \mt{val} \; \mt{transaction\_monad} : \mt{monad} \; \mt{transaction}
adamc@542	1464 \end{array}$$
adamc@542	1465
adamc@1123	1466 For debugging purposes, a transactional function is provided for outputting a string on the server process' \texttt{stderr}.
adamc@1123	1467 $$\begin{array}{l}
adamc@1123	1468 \mt{val} \; \mt{debug} : \mt{string} \to \mt{transaction} \; \mt{unit}
adamc@1123	1469 \end{array}$$
adamc@1123	1470
adamc@542	1471 \subsection{HTTP}
adamc@542	1472
adam@1797	1473 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	1474 $$\begin{array}{l}
adamc@786	1475 \mt{con} \; \mt{http\_cookie} :: \mt{Type} \to \mt{Type} \\
adamc@786	1476 \mt{val} \; \mt{getCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; (\mt{option} \; \mt{t}) \\
adamc@1050	1477 \mt{val} \; \mt{setCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \{\mt{Value} : \mt{t}, \mt{Expires} : \mt{option} \; \mt{time}, \mt{Secure} : \mt{bool}\} \to \mt{transaction} \; \mt{unit} \\
adamc@1050	1478 \mt{val} \; \mt{clearCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; \mt{unit}
adamc@786	1479 \end{array}$$
adamc@786	1480
adamc@786	1481 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	1482 $$\begin{array}{l}
adamc@786	1483 \mt{type} \; \mt{url} \\
adamc@786	1484 \mt{val} \; \mt{bless} : \mt{string} \to \mt{url} \\
adamc@786	1485 \mt{val} \; \mt{checkUrl} : \mt{string} \to \mt{option} \; \mt{url}
adamc@786	1486 \end{array}$$
adamc@786	1487 $\mt{bless}$ raises a runtime error if the string passed to it fails the URL policy.
adamc@786	1488
adam@1400	1489 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	1490 $$\begin{array}{l}
adamc@1085	1491 \mt{val} \; \mt{currentUrl} : \mt{transaction} \; \mt{url} \\
adamc@1085	1492 \mt{val} \; \mt{url} : \mt{transaction} \; \mt{page} \to \mt{url}
adamc@1085	1493 \end{array}$$
adamc@1085	1494
adamc@1085	1495 Page generation may be interrupted at any time with a request to redirect to a particular URL instead.
adamc@1085	1496 $$\begin{array}{l}
adamc@1085	1497 \mt{val} \; \mt{redirect} : \mt{t} ::: \mt{Type} \to \mt{url} \to \mt{transaction} \; \mt{t}
adamc@1085	1498 \end{array}$$
adamc@1085	1499
adam@1400	1500 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	1501 $$\begin{array}{l}
adamc@786	1502 \mt{type} \; \mt{file} \\
adamc@786	1503 \mt{val} \; \mt{fileName} : \mt{file} \to \mt{option} \; \mt{string} \\
adamc@786	1504 \mt{val} \; \mt{fileMimeType} : \mt{file} \to \mt{string} \\
adamc@786	1505 \mt{val} \; \mt{fileData} : \mt{file} \to \mt{blob}
adamc@786	1506 \end{array}$$
adamc@786	1507
adam@1799	1508 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	1509
adam@1465	1510 $$\begin{array}{l}
adam@1465	1511 \mt{type} \; \mt{requestHeader} \\
adam@1465	1512 \mt{val} \; \mt{blessRequestHeader} : \mt{string} \to \mt{requestHeader} \\
adam@1465	1513 \mt{val} \; \mt{checkRequestHeader} : \mt{string} \to \mt{option} \; \mt{requestHeader} \\
adam@1465	1514 \mt{val} \; \mt{getHeader} : \mt{requestHeader} \to \mt{transaction} \; (\mt{option} \; \mt{string}) \\
adam@1465	1515 \\
adam@1799	1516 \mt{type} \; \mt{envVar} \\
adam@1799	1517 \mt{val} \; \mt{blessEnvVar} : \mt{string} \to \mt{envVar} \\
adam@1799	1518 \mt{val} \; \mt{checkEnvVar} : \mt{string} \to \mt{option} \; \mt{envVar} \\
adam@1799	1519 \mt{val} \; \mt{getenv} : \mt{envVar} \to \mt{transaction} \; (\mt{option} \; \mt{string}) \\
adam@1799	1520 \\
adam@1465	1521 \mt{type} \; \mt{responseHeader} \\
adam@1465	1522 \mt{val} \; \mt{blessResponseHeader} : \mt{string} \to \mt{responseHeader} \\
adam@1465	1523 \mt{val} \; \mt{checkResponseHeader} : \mt{string} \to \mt{option} \; \mt{responseHeader} \\
adam@1465	1524 \mt{val} \; \mt{setHeader} : \mt{responseHeader} \to \mt{string} \to \mt{transaction} \; \mt{unit}
adam@1465	1525 \end{array}$$
adam@1465	1526
adamc@786	1527 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	1528 $$\begin{array}{l}
adamc@786	1529 \mt{type} \; \mt{mimeType} \\
adamc@786	1530 \mt{val} \; \mt{blessMime} : \mt{string} \to \mt{mimeType} \\
adamc@786	1531 \mt{val} \; \mt{checkMime} : \mt{string} \to \mt{option} \; \mt{mimeType} \\
adamc@786	1532 \mt{val} \; \mt{returnBlob} : \mt{t} ::: \mt{Type} \to \mt{blob} \to \mt{mimeType} \to \mt{transaction} \; \mt{t}
adamc@542	1533 \end{array}$$
adamc@542	1534
adamc@543	1535 \subsection{SQL}
adamc@543	1536
adam@1400	1537 Everything about SQL database access is restricted to server-side code.
adam@1400	1538
adamc@543	1539 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	1540 $$\begin{array}{l}
adamc@785	1541 \mt{con} \; \mt{sql\_table} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785	1542 \end{array}$$
adamc@785	1543 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	1544
adamc@785	1545 We also have the simpler type family of SQL views, which have no keys.
adamc@785	1546 $$\begin{array}{l}
adamc@785	1547 \mt{con} \; \mt{sql\_view} :: \{\mt{Type}\} \to \mt{Type}
adamc@543	1548 \end{array}$$
adamc@543	1549
adamc@785	1550 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	1551 $$\begin{array}{l}
adamc@785	1552 \mt{class} \; \mt{fieldsOf} :: \mt{Type} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785	1553 \mt{val} \; \mt{fieldsOf\_table} : \mt{fs} ::: \{\mt{Type}\} \to \mt{keys} ::: \{\{\mt{Unit}\}\} \to \mt{fieldsOf} \; (\mt{sql\_table} \; \mt{fs} \; \mt{keys}) \; \mt{fs} \\
adamc@785	1554 \mt{val} \; \mt{fieldsOf\_view} : \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; (\mt{sql\_view} \; \mt{fs}) \; \mt{fs}
adamc@785	1555 \end{array}$$
adamc@785	1556
adamc@785	1557 \subsubsection{Table Constraints}
adamc@785	1558
adamc@785	1559 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	1560
adamc@785	1561 $$\begin{array}{l}
adamc@785	1562 \mt{con} \; \mt{primary\_key} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type} \\
adamc@785	1563 \mt{val} \; \mt{no\_primary\_key} : \mt{fs} ::: \{\mt{Type}\} \to \mt{primary\_key} \; \mt{fs} \; [] \\
adamc@785	1564 \mt{val} \; \mt{primary\_key} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{key1} :: \mt{Name} \to \mt{keys} :: \{\mt{Type}\} \\
adamc@785	1565 \hspace{.1in} \to [[\mt{key1}] \sim \mt{keys}] \Rightarrow [[\mt{key1} = \mt{t}] \rc \mt{keys} \sim \mt{rest}] \\
adamc@785	1566 \hspace{.1in} \Rightarrow \$([\mt{key1} = \mt{sql\_injectable\_prim} \; \mt{t}] \rc \mt{map} \; \mt{sql\_injectable\_prim} \; \mt{keys}) \\
adamc@785	1567 \hspace{.1in} \to \mt{primary\_key} \; ([\mt{key1} = \mt{t}] \rc \mt{keys} \rc \mt{rest}) \; [\mt{Pkey} = [\mt{key1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{keys}]
adamc@785	1568 \end{array}$$
adamc@785	1569 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	1570
adamc@785	1571 A type family stands for sets of named constraints of the remaining varieties.
adamc@785	1572 $$\begin{array}{l}
adamc@785	1573 \mt{con} \; \mt{sql\_constraints} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785	1574 \end{array}$$
adamc@785	1575 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	1576
adamc@785	1577 There is a type family of individual, unnamed constraints.
adamc@785	1578 $$\begin{array}{l}
adamc@785	1579 \mt{con} \; \mt{sql\_constraint} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \mt{Type}
adamc@785	1580 \end{array}$$
adamc@785	1581 The first argument is the same as above, and the second argument gives the key columns for just this constraint.
adamc@785	1582
adamc@785	1583 We have operations for assembling constraints into constraint sets.
adamc@785	1584 $$\begin{array}{l}
adamc@785	1585 \mt{val} \; \mt{no\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_constraints} \; \mt{fs} \; [] \\
adamc@785	1586 \mt{val} \; \mt{one\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{unique} ::: \{\mt{Unit}\} \to \mt{name} :: \mt{Name} \\
adamc@785	1587 \hspace{.1in} \to \mt{sql\_constraint} \; \mt{fs} \; \mt{unique} \to \mt{sql\_constraints} \; \mt{fs} \; [\mt{name} = \mt{unique}] \\
adamc@785	1588 \mt{val} \; \mt{join\_constraints} : \mt{fs} ::: \{\mt{Type}\} \to \mt{uniques1} ::: \{\{\mt{Unit}\}\} \to \mt{uniques2} ::: \{\{\mt{Unit}\}\} \to [\mt{uniques1} \sim \mt{uniques2}] \\
adamc@785	1589 \hspace{.1in} \Rightarrow \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques1} \to \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques2} \to \mt{sql\_constraints} \; \mt{fs} \; (\mt{uniques1} \rc \mt{uniques2})
adamc@785	1590 \end{array}$$
adamc@785	1591
adamc@785	1592 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	1593 $$\begin{array}{l}
adamc@785	1594 \mt{val} \; \mt{unique} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{unique1} :: \mt{Name} \to \mt{unique} :: \{\mt{Type}\} \\
adamc@785	1595 \hspace{.1in} \to [[\mt{unique1}] \sim \mt{unique}] \Rightarrow [[\mt{unique1} = \mt{t}] \rc \mt{unique} \sim \mt{rest}] \\
adamc@785	1596 \hspace{.1in} \Rightarrow \mt{sql\_constraint} \; ([\mt{unique1} = \mt{t}] \rc \mt{unique} \rc \mt{rest}) \; ([\mt{unique1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{unique})
adamc@785	1597 \end{array}$$
adamc@785	1598
adamc@785	1599 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	1600 $$\begin{array}{l}
adamc@785	1601 \mt{class} \; \mt{linkable} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@785	1602 \mt{val} \; \mt{linkable\_same} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; \mt{t} \\
adamc@785	1603 \mt{val} \; \mt{linkable\_from\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; (\mt{option} \; \mt{t}) \; \mt{t} \\
adamc@785	1604 \mt{val} \; \mt{linkable\_to\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@785	1605 \end{array}$$
adamc@785	1606
adamc@785	1607 The $\mt{matching}$ type family uses $\mt{linkable}$ to define when two keys match up type-wise.
adamc@785	1608 $$\begin{array}{l}
adamc@785	1609 \mt{con} \; \mt{matching} :: \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785	1610 \mt{val} \; \mt{mat\_nil} : \mt{matching} \; [] \; [] \\
adamc@785	1611 \mt{val} \; \mt{mat\_cons} : \mt{t1} ::: \mt{Type} \to \mt{rest1} ::: \{\mt{Type}\} \to \mt{t2} ::: \mt{Type} \to \mt{rest2} ::: \{\mt{Type}\} \to \mt{nm1} :: \mt{Name} \to \mt{nm2} :: \mt{Name} \\
adamc@785	1612 \hspace{.1in} \to [[\mt{nm1}] \sim \mt{rest1}] \Rightarrow [[\mt{nm2}] \sim \mt{rest2}] \Rightarrow \mt{linkable} \; \mt{t1} \; \mt{t2} \to \mt{matching} \; \mt{rest1} \; \mt{rest2} \\
adamc@785	1613 \hspace{.1in} \to \mt{matching} \; ([\mt{nm1} = \mt{t1}] \rc \mt{rest1}) \; ([\mt{nm2} = \mt{t2}] \rc \mt{rest2})
adamc@785	1614 \end{array}$$
adamc@785	1615
adamc@785	1616 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	1617 $$\begin{array}{l}
adamc@785	1618 \mt{con} \; \mt{propagation\_mode} :: \{\mt{Type}\} \to \mt{Type} \\
adamc@785	1619 \mt{val} \; \mt{restrict} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785	1620 \mt{val} \; \mt{cascade} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785	1621 \mt{val} \; \mt{no\_action} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785	1622 \mt{val} \; \mt{set\_null} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; (\mt{map} \; \mt{option} \; \mt{fs})
adamc@785	1623 \end{array}$$
adamc@785	1624
adamc@785	1625 Finally, we put these ingredient together to define the \texttt{FOREIGN KEY} constraint function.
adamc@785	1626 $$\begin{array}{l}
adamc@785	1627 \mt{val} \; \mt{foreign\_key} : \mt{mine1} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{mine} ::: \{\mt{Type}\} \to \mt{munused} ::: \{\mt{Type}\} \to \mt{foreign} ::: \{\mt{Type}\} \\
adamc@785	1628 \hspace{.1in} \to \mt{funused} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{uniques} ::: \{\{\mt{Unit}\}\} \\
adamc@785	1629 \hspace{.1in} \to [[\mt{mine1}] \sim \mt{mine}] \Rightarrow [[\mt{mine1} = \mt{t}] \rc \mt{mine} \sim \mt{munused}] \Rightarrow [\mt{foreign} \sim \mt{funused}] \Rightarrow [[\mt{nm}] \sim \mt{uniques}] \\
adamc@785	1630 \hspace{.1in} \Rightarrow \mt{matching} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}) \; \mt{foreign} \\
adamc@785	1631 \hspace{.1in} \to \mt{sql\_table} \; (\mt{foreign} \rc \mt{funused}) \; ([\mt{nm} = \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{foreign}] \rc \mt{uniques}) \\
adamc@785	1632 \hspace{.1in} \to \{\mt{OnDelete} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}), \\
adamc@785	1633 \hspace{.2in} \mt{OnUpdate} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine})\} \\
adamc@785	1634 \hspace{.1in} \to \mt{sql\_constraint} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine} \rc \mt{munused}) \; []
adamc@785	1635 \end{array}$$
adamc@785	1636
adamc@785	1637 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	1638 $$\begin{array}{l}
adam@1778	1639 \mt{val} \; \mt{check} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; [] \; [] \; \mt{fs} \; \mt{bool} \to \mt{sql\_constraint} \; \mt{fs} \; []
adamc@785	1640 \end{array}$$
adamc@785	1641
adamc@785	1642 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	1643
adamc@784	1644
adamc@543	1645 \subsubsection{Queries}
adamc@543	1646
adam@1400	1647 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	1648 $$\begin{array}{l}
adam@1400	1649 \mt{con} \; \mt{sql\_query} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@1193	1650 \mt{val} \; \mt{sql\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400	1651 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adamc@1193	1652 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543	1653 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543	1654 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1193	1655 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adam@1400	1656 \hspace{.1in} \Rightarrow \{\mt{Rows} : \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}, \\
adamc@1193	1657 \hspace{.2in} \mt{OrderBy} : \mt{sql\_order\_by} \; (\mt{free} \rc \mt{tables}) \; \mt{selectedExps}, \\
adamc@543	1658 \hspace{.2in} \mt{Limit} : \mt{sql\_limit}, \\
adamc@543	1659 \hspace{.2in} \mt{Offset} : \mt{sql\_offset}\} \\
adam@1400	1660 \hspace{.1in} \to \mt{sql\_query} \; \mt{free} \; \mt{afree} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543	1661 \end{array}$$
adamc@543	1662
adamc@545	1663 Queries are used by folding over their results inside transactions.
adamc@545	1664 $$\begin{array}{l}
adam@1400	1665 \mt{val} \; \mt{query} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to [\mt{tables} \sim \mt{exps}] \Rightarrow \mt{state} ::: \mt{Type} \to \mt{sql\_query} \; [] \; [] \; \mt{tables} \; \mt{exps} \\
adamc@658	1666 \hspace{.1in} \to (\$(\mt{exps} \rc \mt{map} \; (\lambda \mt{fields} :: \{\mt{Type}\} \Rightarrow \$\mt{fields}) \; \mt{tables}) \\
adamc@545	1667 \hspace{.2in} \to \mt{state} \to \mt{transaction} \; \mt{state}) \\
adamc@545	1668 \hspace{.1in} \to \mt{state} \to \mt{transaction} \; \mt{state}
adamc@545	1669 \end{array}$$
adamc@545	1670
adam@1400	1671 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	1672 $$\begin{array}{l}
adam@1400	1673 \mt{con} \; \mt{sql\_query1} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@543	1674 \\
adamc@543	1675 \mt{type} \; \mt{sql\_relop} \\
adamc@543	1676 \mt{val} \; \mt{sql\_union} : \mt{sql\_relop} \\
adamc@543	1677 \mt{val} \; \mt{sql\_intersect} : \mt{sql\_relop} \\
adamc@543	1678 \mt{val} \; \mt{sql\_except} : \mt{sql\_relop} \\
adam@1400	1679 \mt{val} \; \mt{sql\_relop} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400	1680 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adam@1400	1681 \hspace{.1in} \to \mt{tables1} ::: \{\{\mt{Type}\}\} \\
adamc@543	1682 \hspace{.1in} \to \mt{tables2} ::: \{\{\mt{Type}\}\} \\
adamc@543	1683 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543	1684 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@543	1685 \hspace{.1in} \to \mt{sql\_relop} \\
adam@1458	1686 \hspace{.1in} \to \mt{bool} \; (* \; \mt{ALL} \; *) \\
adam@1400	1687 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables1} \; \mt{selectedFields} \; \mt{selectedExps} \\
adam@1400	1688 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables2} \; \mt{selectedFields} \; \mt{selectedExps} \\
adam@1400	1689 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{selectedFields} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543	1690 \end{array}$$
adamc@543	1691
adamc@543	1692 $$\begin{array}{l}
adamc@1193	1693 \mt{val} \; \mt{sql\_query1} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400	1694 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adamc@1193	1695 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543	1696 \hspace{.1in} \to \mt{grouped} ::: \{\{\mt{Type}\}\} \\
adamc@543	1697 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543	1698 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1085	1699 \hspace{.1in} \to \mt{empties} :: \{\mt{Unit}\} \\
adamc@1193	1700 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adamc@1193	1701 \hspace{.1in} \Rightarrow [\mt{free} \sim \mt{grouped}] \\
adam@1400	1702 \hspace{.1in} \Rightarrow [\mt{afree} \sim \mt{tables}] \\
adamc@1193	1703 \hspace{.1in} \Rightarrow [\mt{empties} \sim \mt{selectedFields}] \\
adamc@1085	1704 \hspace{.1in} \Rightarrow \{\mt{Distinct} : \mt{bool}, \\
adamc@1193	1705 \hspace{.2in} \mt{From} : \mt{sql\_from\_items} \; \mt{free} \; \mt{tables}, \\
adam@1778	1706 \hspace{.2in} \mt{Where} : \mt{sql\_exp} \; (\mt{free} \rc \mt{tables}) \; \mt{afree} \; [] \; \mt{bool}, \\
adamc@543	1707 \hspace{.2in} \mt{GroupBy} : \mt{sql\_subset} \; \mt{tables} \; \mt{grouped}, \\
adam@1778	1708 \hspace{.2in} \mt{Having} : \mt{sql\_exp} \; (\mt{free} \rc \mt{grouped}) \; (\mt{afree} \rc \mt{tables}) \; [] \; \mt{bool}, \\
adamc@1085	1709 \hspace{.2in} \mt{SelectFields} : \mt{sql\_subset} \; \mt{grouped} \; (\mt{map} \; (\lambda \_ \Rightarrow []) \; \mt{empties} \rc \mt{selectedFields}), \\
adam@1778	1710 \hspace{.2in} \mt {SelectExps} : \$(\mt{map} \; (\mt{sql\_expw} \; (\mt{free} \rc \mt{grouped}) \; (\mt{afree} \rc \mt{tables}) \; []) \; \mt{selectedExps}) \} \\
adam@1400	1711 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543	1712 \end{array}$$
adamc@543	1713
adamc@543	1714 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	1715 $$\begin{array}{l}
adamc@543	1716 \mt{con} \; \mt{sql\_subset} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@543	1717 \mt{val} \; \mt{sql\_subset} : \mt{keep\_drop} :: \{(\{\mt{Type}\} \times \{\mt{Type}\})\} \\
adamc@543	1718 \hspace{.1in} \to \mt{sql\_subset} \\
adamc@658	1719 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1 \rc \mt{fields}.2)\; \mt{keep\_drop}) \\
adamc@658	1720 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1) \; \mt{keep\_drop}) \\
adamc@543	1721 \mt{val} \; \mt{sql\_subset\_all} : \mt{tables} :: \{\{\mt{Type}\}\} \to \mt{sql\_subset} \; \mt{tables} \; \mt{tables}
adamc@543	1722 \end{array}$$
adamc@543	1723
adam@1778	1724 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	1725 $$\begin{array}{l}
adam@1778	1726 \mt{con} \; \mt{sql\_exp} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}
adamc@543	1727 \end{array}$$
adamc@543	1728
adamc@543	1729 Any field in scope may be converted to an expression.
adamc@543	1730 $$\begin{array}{l}
adamc@543	1731 \mt{val} \; \mt{sql\_field} : \mt{otherTabs} ::: \{\{\mt{Type}\}\} \to \mt{otherFields} ::: \{\mt{Type}\} \\
adam@1778	1732 \hspace{.1in} \to \mt{fieldType} ::: \mt{Type} \to \mt{agg} ::: \{\{\mt{Type}\}\} \\
adamc@543	1733 \hspace{.1in} \to \mt{exps} ::: \{\mt{Type}\} \\
adamc@543	1734 \hspace{.1in} \to \mt{tab} :: \mt{Name} \to \mt{field} :: \mt{Name} \\
adam@1778	1735 \hspace{.1in} \to \mt{sql\_exp} \; ([\mt{tab} = [\mt{field} = \mt{fieldType}] \rc \mt{otherFields}] \rc \mt{otherTabs}) \; \mt{agg} \; \mt{exps} \; \mt{fieldType}
adamc@543	1736 \end{array}$$
adamc@543	1737
adamc@544	1738 There is an analogous function for referencing named expressions.
adamc@544	1739 $$\begin{array}{l}
adam@1778	1740 \mt{val} \; \mt{sql\_exp} : \mt{tabs} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{t} ::: \mt{Type} \to \mt{rest} ::: \{\mt{Type}\} \to \mt{nm} :: \mt{Name} \\
adam@1778	1741 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tabs} \; \mt{agg} \; ([\mt{nm} = \mt{t}] \rc \mt{rest}) \; \mt{t}
adamc@544	1742 \end{array}$$
adamc@544	1743
adamc@544	1744 Ur values of appropriate types may be injected into SQL expressions.
adamc@544	1745 $$\begin{array}{l}
adamc@786	1746 \mt{class} \; \mt{sql\_injectable\_prim} \\
adamc@786	1747 \mt{val} \; \mt{sql\_bool} : \mt{sql\_injectable\_prim} \; \mt{bool} \\
adamc@786	1748 \mt{val} \; \mt{sql\_int} : \mt{sql\_injectable\_prim} \; \mt{int} \\
adamc@786	1749 \mt{val} \; \mt{sql\_float} : \mt{sql\_injectable\_prim} \; \mt{float} \\
adamc@786	1750 \mt{val} \; \mt{sql\_string} : \mt{sql\_injectable\_prim} \; \mt{string} \\
adamc@786	1751 \mt{val} \; \mt{sql\_time} : \mt{sql\_injectable\_prim} \; \mt{time} \\
adamc@786	1752 \mt{val} \; \mt{sql\_blob} : \mt{sql\_injectable\_prim} \; \mt{blob} \\
adamc@786	1753 \mt{val} \; \mt{sql\_channel} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{channel} \; \mt{t}) \\
adamc@786	1754 \mt{val} \; \mt{sql\_client} : \mt{sql\_injectable\_prim} \; \mt{client} \\
adamc@786	1755 \\
adamc@544	1756 \mt{class} \; \mt{sql\_injectable} \\
adamc@786	1757 \mt{val} \; \mt{sql\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@786	1758 \mt{val} \; \mt{sql\_option\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; (\mt{option} \; \mt{t}) \\
adamc@786	1759 \\
adam@1778	1760 \mt{val} \; \mt{sql\_inject} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{sql\_injectable} \; \mt{t} \\
adam@1778	1761 \hspace{.1in} \to \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adamc@544	1762 \end{array}$$
adamc@544	1763
adamc@1123	1764 Additionally, most function-free types may be injected safely, via the $\mt{serialized}$ type family.
adamc@1123	1765 $$\begin{array}{l}
adamc@1123	1766 \mt{con} \; \mt{serialized} :: \mt{Type} \to \mt{Type} \\
adamc@1123	1767 \mt{val} \; \mt{serialize} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{serialized} \; \mt{t} \\
adamc@1123	1768 \mt{val} \; \mt{deserialize} : \mt{t} ::: \mt{Type} \to \mt{serialized} \; \mt{t} \to \mt{t} \\
adamc@1123	1769 \mt{val} \; \mt{sql\_serialized} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{serialized} \; \mt{t})
adamc@1123	1770 \end{array}$$
adamc@1123	1771
adamc@544	1772 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	1773 $$\begin{array}{l}
adam@1778	1774 \mt{val} \; \mt{sql\_is\_null} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778	1775 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; (\mt{option} \; \mt{t}) \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{bool}
adamc@544	1776 \end{array}$$
adamc@544	1777
adam@1602	1778 As another way of dealing with null values, there is also a restricted form of the standard \cd{COALESCE} function.
adam@1602	1779 $$\begin{array}{l}
adam@1602	1780 \mt{val} \; \mt{sql\_coalesce} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778	1781 \hspace{.1in} \to \mt{t} ::: \mt{Type} \\
adam@1778	1782 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; (\mt{option} \; \mt{t}) \\
adam@1778	1783 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778	1784 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adam@1602	1785 \end{array}$$
adam@1602	1786
adamc@559	1787 We have generic nullary, unary, and binary operators.
adamc@544	1788 $$\begin{array}{l}
adamc@544	1789 \mt{con} \; \mt{sql\_nfunc} :: \mt{Type} \to \mt{Type} \\
adamc@544	1790 \mt{val} \; \mt{sql\_current\_timestamp} : \mt{sql\_nfunc} \; \mt{time} \\
adam@1778	1791 \mt{val} \; \mt{sql\_nfunc} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778	1792 \hspace{.1in} \to \mt{sql\_nfunc} \; \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\\end{array}$$
adamc@544	1793
adamc@544	1794 $$\begin{array}{l}
adamc@544	1795 \mt{con} \; \mt{sql\_unary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544	1796 \mt{val} \; \mt{sql\_not} : \mt{sql\_unary} \; \mt{bool} \; \mt{bool} \\
adam@1778	1797 \mt{val} \; \mt{sql\_unary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adam@1778	1798 \hspace{.1in} \to \mt{sql\_unary} \; \mt{arg} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res} \\
adamc@544	1799 \end{array}$$
adamc@544	1800
adamc@544	1801 $$\begin{array}{l}
adamc@544	1802 \mt{con} \; \mt{sql\_binary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544	1803 \mt{val} \; \mt{sql\_and} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544	1804 \mt{val} \; \mt{sql\_or} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adam@1778	1805 \mt{val} \; \mt{sql\_binary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg_1} ::: \mt{Type} \to \mt{arg_2} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adam@1778	1806 \hspace{.1in} \to \mt{sql\_binary} \; \mt{arg_1} \; \mt{arg_2} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_1} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_2} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res}
adamc@544	1807 \end{array}$$
adamc@544	1808
adamc@544	1809 $$\begin{array}{l}
adamc@559	1810 \mt{class} \; \mt{sql\_arith} \\
adamc@559	1811 \mt{val} \; \mt{sql\_int\_arith} : \mt{sql\_arith} \; \mt{int} \\
adamc@559	1812 \mt{val} \; \mt{sql\_float\_arith} : \mt{sql\_arith} \; \mt{float} \\
adamc@559	1813 \mt{val} \; \mt{sql\_neg} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_unary} \; \mt{t} \; \mt{t} \\
adamc@559	1814 \mt{val} \; \mt{sql\_plus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559	1815 \mt{val} \; \mt{sql\_minus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559	1816 \mt{val} \; \mt{sql\_times} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559	1817 \mt{val} \; \mt{sql\_div} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559	1818 \mt{val} \; \mt{sql\_mod} : \mt{sql\_binary} \; \mt{int} \; \mt{int} \; \mt{int}
adamc@559	1819 \end{array}$$
adamc@544	1820
adam@1797	1821 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	1822 $$\begin{array}{l}
adam@1778	1823 \mt{val} \; \mt{sql\_count} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int}
adamc@544	1824 \end{array}$$
adamc@544	1825
adamc@544	1826 $$\begin{array}{l}
adamc@1188	1827 \mt{con} \; \mt{sql\_aggregate} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adam@1778	1828 \mt{val} \; \mt{sql\_aggregate} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{dom} ::: \mt{Type} \to \mt{ran} ::: \mt{Type} \\
adam@1778	1829 \hspace{.1in} \to \mt{sql\_aggregate} \; \mt{dom} \; \mt{ran} \to \mt{sql\_exp} \; \mt{agg} \; \mt{agg} \; \mt{exps} \; \mt{dom} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{ran}
adamc@1188	1830 \end{array}$$
adamc@1188	1831
adamc@1188	1832 $$\begin{array}{l}
adamc@1188	1833 \mt{val} \; \mt{sql\_count\_col} : \mt{t} ::: \mt{Type} \to \mt{sql\_aggregate} \; (\mt{option} \; \mt{t}) \; \mt{int}
adamc@544	1834 \end{array}$$
adam@1400	1835
adam@1400	1836 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	1837
adamc@544	1838 $$\begin{array}{l}
adamc@544	1839 \mt{class} \; \mt{sql\_summable} \\
adamc@544	1840 \mt{val} \; \mt{sql\_summable\_int} : \mt{sql\_summable} \; \mt{int} \\
adamc@544	1841 \mt{val} \; \mt{sql\_summable\_float} : \mt{sql\_summable} \; \mt{float} \\
adam@1777	1842 \mt{val} \; \mt{sql\_avg} : \mt{t} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{sql\_aggregate} \; \mt{t} \; (\mt{option} \; \mt{float}) \\
adam@1400	1843 \mt{val} \; \mt{sql\_sum} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt}
adamc@544	1844 \end{array}$$
adamc@544	1845
adamc@544	1846 $$\begin{array}{l}
adamc@544	1847 \mt{class} \; \mt{sql\_maxable} \\
adamc@544	1848 \mt{val} \; \mt{sql\_maxable\_int} : \mt{sql\_maxable} \; \mt{int} \\
adamc@544	1849 \mt{val} \; \mt{sql\_maxable\_float} : \mt{sql\_maxable} \; \mt{float} \\
adamc@544	1850 \mt{val} \; \mt{sql\_maxable\_string} : \mt{sql\_maxable} \; \mt{string} \\
adamc@544	1851 \mt{val} \; \mt{sql\_maxable\_time} : \mt{sql\_maxable} \; \mt{time} \\
adam@1400	1852 \mt{val} \; \mt{sql\_max} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt} \\
adam@1400	1853 \mt{val} \; \mt{sql\_min} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt}
adamc@544	1854 \end{array}$$
adamc@544	1855
adam@1778	1856 Any SQL query that returns single columns may be turned into a subquery expression.
adam@1777	1857
adam@1777	1858 $$\begin{array}{l}
adam@1778	1859 \mt{val} \; \mt{sql\_subquery} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \\
adam@1778	1860 \hspace{.1in} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_query} \; \mt{tables} \; \mt{agg} \; [\mt{nm} = \mt{t}] \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{nt}
adamc@1193	1861 \end{array}$$
adamc@1193	1862
adam@1573	1863 There is also an \cd{IF..THEN..ELSE..} construct that is compiled into standard SQL \cd{CASE} expressions.
adam@1573	1864 $$\begin{array}{l}
adam@1778	1865 \mt{val} \; \mt{sql\_if\_then\_else} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778	1866 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{bool} \\
adam@1778	1867 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778	1868 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778	1869 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adam@1573	1870 \end{array}$$
adam@1573	1871
adamc@1193	1872 \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	1873 $$\begin{array}{l}
adamc@1193	1874 \mt{con} \; \mt{sql\_from\_items} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@1193	1875 \mt{val} \; \mt{sql\_from\_table} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adamc@1193	1876 \hspace{.1in} \to \mt{t} ::: \mt{Type} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; \mt{t} \; \mt{fs} \to \mt{name} :: \mt{Name} \to \mt{t} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193	1877 \mt{val} \; \mt{sql\_from\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{name} :: \mt{Name} \to \mt{sql\_query} \; \mt{free} \; [] \; \mt{fs} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193	1878 \mt{val} \; \mt{sql\_from\_comma} : \mt{free} ::: \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \to [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193	1879 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adamc@1193	1880 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2}) \\
adamc@1193	1881 \mt{val} \; \mt{sql\_inner\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \\
adamc@1193	1882 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193	1883 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adam@1778	1884 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193	1885 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2})
adamc@786	1886 \end{array}$$
adamc@786	1887
adamc@786	1888 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	1889 $$\begin{array}{l}
adamc@786	1890 \mt{class} \; \mt{nullify} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@786	1891 \mt{val} \; \mt{nullify\_option} : \mt{t} ::: \mt{Type} \to \mt{nullify} \; (\mt{option} \; \mt{t}) \; (\mt{option} \; \mt{t}) \\
adamc@786	1892 \mt{val} \; \mt{nullify\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{nullify} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@786	1893 \end{array}$$
adamc@786	1894
adamc@786	1895 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	1896
adamc@786	1897 $$\begin{array}{l}
adamc@1193	1898 \mt{val} \; \mt{sql\_left\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{(\mt{Type} \times \mt{Type})\}\} \\
adamc@1193	1899 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@786	1900 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\lambda \mt{r} \Rightarrow \$(\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{nullify} \; \mt{p}.1 \; \mt{p}.2) \; \mt{r})) \; \mt{tabs2}) \\
adamc@1193	1901 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \\
adam@1778	1902 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193	1903 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.2)) \; \mt{tabs2})
adamc@786	1904 \end{array}$$
adamc@786	1905
adamc@544	1906 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	1907 $$\begin{array}{l}
adamc@544	1908 \mt{type} \; \mt{sql\_direction} \\
adamc@544	1909 \mt{val} \; \mt{sql\_asc} : \mt{sql\_direction} \\
adamc@544	1910 \mt{val} \; \mt{sql\_desc} : \mt{sql\_direction} \\
adamc@544	1911 \\
adamc@544	1912 \mt{con} \; \mt{sql\_order\_by} :: \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@544	1913 \mt{val} \; \mt{sql\_order\_by\_Nil} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} :: \{\mt{Type}\} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adam@1778	1914 \mt{val} \; \mt{sql\_order\_by\_Cons} : \mt{tf} ::: (\{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}) \\
adam@1778	1915 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778	1916 \hspace{.1in} \to \mt{sql\_window} \; \mt{tf} \to \mt{tf} \; \mt{tables} \; [] \; \mt{exps} \; \mt{t} \to \mt{sql\_direction} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adam@1684	1917 \mt{val} \; \mt{sql\_order\_by\_random} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544	1918 \\
adamc@544	1919 \mt{type} \; \mt{sql\_limit} \\
adamc@544	1920 \mt{val} \; \mt{sql\_no\_limit} : \mt{sql\_limit} \\
adamc@544	1921 \mt{val} \; \mt{sql\_limit} : \mt{int} \to \mt{sql\_limit} \\
adamc@544	1922 \\
adamc@544	1923 \mt{type} \; \mt{sql\_offset} \\
adamc@544	1924 \mt{val} \; \mt{sql\_no\_offset} : \mt{sql\_offset} \\
adamc@544	1925 \mt{val} \; \mt{sql\_offset} : \mt{int} \to \mt{sql\_offset}
adamc@544	1926 \end{array}$$
adamc@544	1927
adam@1778	1928 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	1929 $$\begin{array}{l}
adam@1778	1930 \mt{con} \; \mt{sql\_expw} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type} \\
adam@1778	1931 \\
adam@1778	1932 \mt{class} \; \mt{sql\_window} :: (\{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}) \to \mt{Type} \\
adam@1778	1933 \mt{val} \; \mt{sql\_window\_normal} : \mt{sql\_window} \; \mt{sql\_exp} \\
adam@1778	1934 \mt{val} \; \mt{sql\_window\_fancy} : \mt{sql\_window} \; \mt{sql\_expw} \\
adam@1778	1935 \mt{val} \; \mt{sql\_window} : \mt{tf} ::: (\{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}) \\
adam@1778	1936 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778	1937 \hspace{.1in} \to \mt{sql\_window} \; \mt{tf} \\
adam@1778	1938 \hspace{.1in} \to \mt{tf} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778	1939 \hspace{.1in} \to \mt{sql\_expw} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778	1940 \\
adam@1778	1941 \mt{con} \; \mt{sql\_partition} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adam@1778	1942 \mt{val} \; \mt{sql\_no\_partition} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778	1943 \hspace{.1in} \to \mt{sql\_partition} \; \mt{tables} \; \mt{agg} \; \mt{exps} \\
adam@1778	1944 \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	1945 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778	1946 \hspace{.1in} \to \mt{sql\_partition} \; \mt{tables} \; \mt{agg} \; \mt{exps} \\
adam@1778	1947 \\
adam@1778	1948 \mt{con} \; \mt{sql\_window\_function} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type} \\
adam@1778	1949 \mt{val} \; \mt{sql\_window\_function} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778	1950 \hspace{.1in} \to \mt{t} ::: \mt{Type} \\
adam@1778	1951 \hspace{.1in} \to \mt{sql\_window\_function} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778	1952 \hspace{.1in} \to \mt{sql\_partition} \; \mt{tables} \; \mt{agg} \; \mt{exps} \\
adam@1778	1953 \hspace{.1in} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adam@1778	1954 \hspace{.1in} \to \mt{sql\_expw} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778	1955 \\
adam@1778	1956 \mt{val} \; \mt{sql\_window\_aggregate} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778	1957 \hspace{.1in} \to \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \\
adam@1778	1958 \hspace{.1in} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt} \\
adam@1778	1959 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778	1960 \hspace{.1in} \to \mt{sql\_window\_function} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{nt} \\
adam@1778	1961 \mt{val} \; \mt{sql\_window\_count} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778	1962 \hspace{.1in} \to \mt{sql\_window\_function} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int} \\
adam@1778	1963 \mt{val} \; \mt{sql\_rank} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778	1964 \hspace{.1in} \to \mt{sql\_window\_function} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int}
adam@1778	1965 \end{array}$$
adam@1778	1966
adamc@545	1967
adamc@545	1968 \subsubsection{DML}
adamc@545	1969
adamc@545	1970 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	1971
adamc@545	1972 $$\begin{array}{l}
adamc@545	1973 \mt{type} \; \mt{dml} \\
adamc@545	1974 \mt{val} \; \mt{dml} : \mt{dml} \to \mt{transaction} \; \mt{unit}
adamc@545	1975 \end{array}$$
adamc@545	1976
adam@1297	1977 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	1978
adam@1297	1979 $$\begin{array}{l}
adam@1297	1980 \mt{val} \; \mt{tryDml} : \mt{dml} \to \mt{transaction} \; (\mt{option} \; \mt{string})
adam@1297	1981 \end{array}$$
adam@1297	1982
adam@1797	1983 Properly typed records may be used to form $\mt{INSERT}$ commands.
adamc@545	1984 $$\begin{array}{l}
adamc@545	1985 \mt{val} \; \mt{insert} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \\
adam@1778	1986 \hspace{.1in} \to \$(\mt{map} \; (\mt{sql\_exp} \; [] \; [] \; []) \; \mt{fields}) \to \mt{dml}
adamc@545	1987 \end{array}$$
adamc@545	1988
adam@1578	1989 An $\mt{UPDATE}$ command is formed from a choice of which table fields to leave alone and which to change, along with an expression to use to compute the new value of each changed field and a $\mt{WHERE}$ clause. Note that, in the table environment applied to expressions, the table being updated is hardcoded at the name $\mt{T}$. The parsing extension for $\mt{UPDATE}$ will elaborate all table-free field references to use table variable $\mt{T}$.
adamc@545	1990 $$\begin{array}{l}
adam@1380	1991 \mt{val} \; \mt{update} : \mt{unchanged} ::: \{\mt{Type}\} \to \mt{changed} :: \{\mt{Type}\} \to [\mt{changed} \sim \mt{unchanged}] \\
adam@1778	1992 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; []) \; \mt{changed}) \\
adam@1778	1993 \hspace{.1in} \to \mt{sql\_table} \; (\mt{changed} \rc \mt{unchanged}) \to \mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545	1994 \end{array}$$
adamc@545	1995
adam@1578	1996 A $\mt{DELETE}$ command is formed from a table and a $\mt{WHERE}$ clause. The above use of $\mt{T}$ is repeated.
adamc@545	1997 $$\begin{array}{l}
adam@1778	1998 \mt{val} \; \mt{delete} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \to \mt{sql\_exp} \; [\mt{T} = \mt{fields}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545	1999 \end{array}$$
adamc@545	2000
adamc@546	2001 \subsubsection{Sequences}
adamc@546	2002
adamc@546	2003 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	2004
adamc@546	2005 $$\begin{array}{l}
adamc@546	2006 \mt{type} \; \mt{sql\_sequence} \\
adamc@1085	2007 \mt{val} \; \mt{nextval} : \mt{sql\_sequence} \to \mt{transaction} \; \mt{int} \\
adamc@1085	2008 \mt{val} \; \mt{setval} : \mt{sql\_sequence} \to \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@546	2009 \end{array}$$
adamc@546	2010
adamc@546	2011
adam@1648	2012 \subsection{\label{xml}XML}
adamc@547	2013
adam@1333	2014 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	2015
adam@1642	2016 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	2017 $$\begin{array}{l}
adamc@547	2018 \mt{con} \; \mt{xml} :: \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547	2019 \end{array}$$
adamc@547	2020
adamc@547	2021 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	2022 $$\begin{array}{l}
adamc@547	2023 \mt{con} \; \mt{tag} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547	2024 \end{array}$$
adamc@547	2025
adamc@547	2026 Literal text may be injected into XML as ``CDATA.''
adamc@547	2027 $$\begin{array}{l}
adamc@547	2028 \mt{val} \; \mt{cdata} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{string} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adamc@547	2029 \end{array}$$
adamc@547	2030
adam@1358	2031 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	2032 $$\begin{array}{l}
adam@1358	2033 \mt{val} \; \mt{cdataChar} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{char} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adam@1358	2034 \end{array}$$
adam@1358	2035
adamc@547	2036 There is a function for producing an XML tree with a particular tag at its root.
adamc@547	2037 $$\begin{array}{l}
adamc@547	2038 \mt{val} \; \mt{tag} : \mt{attrsGiven} ::: \{\mt{Type}\} \to \mt{attrsAbsent} ::: \{\mt{Type}\} \to \mt{ctxOuter} ::: \{\mt{Unit}\} \to \mt{ctxInner} ::: \{\mt{Unit}\} \\
adamc@547	2039 \hspace{.1in} \to \mt{useOuter} ::: \{\mt{Type}\} \to \mt{useInner} ::: \{\mt{Type}\} \to \mt{bindOuter} ::: \{\mt{Type}\} \to \mt{bindInner} ::: \{\mt{Type}\} \\
adam@1380	2040 \hspace{.1in} \to [\mt{attrsGiven} \sim \mt{attrsAbsent}] \Rightarrow [\mt{useOuter} \sim \mt{useInner}] \Rightarrow [\mt{bindOuter} \sim \mt{bindInner}] \\
adam@1749	2041 \hspace{.1in} \Rightarrow \mt{css\_class} \\
adam@1643	2042 \hspace{.1in} \to \mt{option} \; (\mt{signal} \; \mt{css\_class}) \\
adam@1750	2043 \hspace{.1in} \to \mt{css\_style} \\
adam@1751	2044 \hspace{.1in} \to \mt{option} \; (\mt{signal} \; \mt{css\_style}) \\
adamc@787	2045 \hspace{.1in} \to \$\mt{attrsGiven} \\
adamc@547	2046 \hspace{.1in} \to \mt{tag} \; (\mt{attrsGiven} \rc \mt{attrsAbsent}) \; \mt{ctxOuter} \; \mt{ctxInner} \; \mt{useOuter} \; \mt{bindOuter} \\
adamc@547	2047 \hspace{.1in} \to \mt{xml} \; \mt{ctxInner} \; \mt{useInner} \; \mt{bindInner} \to \mt{xml} \; \mt{ctxOuter} \; (\mt{useOuter} \rc \mt{useInner}) \; (\mt{bindOuter} \rc \mt{bindInner})
adamc@547	2048 \end{array}$$
adam@1750	2049 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	2050
adam@1643	2051 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	2052
adam@1751	2053 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	2054
adamc@547	2055 Two XML fragments may be concatenated.
adamc@547	2056 $$\begin{array}{l}
adamc@547	2057 \mt{val} \; \mt{join} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{bind_1} ::: \{\mt{Type}\} \to \mt{bind_2} ::: \{\mt{Type}\} \\
adam@1380	2058 \hspace{.1in} \to [\mt{use_1} \sim \mt{bind_1}] \Rightarrow [\mt{bind_1} \sim \mt{bind_2}] \\
adamc@547	2059 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind_1} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{bind_1}) \; \mt{bind_2} \to \mt{xml} \; \mt{ctx} \; \mt{use_1} \; (\mt{bind_1} \rc \mt{bind_2})
adamc@547	2060 \end{array}$$
adamc@547	2061
adamc@547	2062 Finally, any XML fragment may be updated to ``claim'' to use more form fields than it does.
adamc@547	2063 $$\begin{array}{l}
adam@1380	2064 \mt{val} \; \mt{useMore} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{use_2} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to [\mt{use_1} \sim \mt{use_2}] \\
adamc@547	2065 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{use_2}) \; \mt{bind}
adamc@547	2066 \end{array}$$
adamc@547	2067
adam@2008	2068 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	2069
adam@2047	2070 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	2071
adamc@547	2072 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	2073 $$\begin{array}{l}
adam@1641	2074 \mt{val} \; \mt{error} : \mt{t} ::: \mt{Type} \to \mt{xbody} \to \mt{t}
adamc@547	2075 \end{array}$$
adamc@547	2076
adamc@549	2077
adamc@701	2078 \subsection{Client-Side Programming}
adamc@659	2079
adamc@701	2080 Ur/Web supports running code on web browsers, via automatic compilation to JavaScript.
adamc@701	2081
adamc@701	2082 \subsubsection{The Basics}
adamc@701	2083
adam@1400	2084 All of the functions in this subsection are client-side only.
adam@1400	2085
adam@1297	2086 Clients can open alert and confirm dialog boxes, in the usual annoying JavaScript way.
adamc@701	2087 $$\begin{array}{l}
adam@1297	2088 \mt{val} \; \mt{alert} : \mt{string} \to \mt{transaction} \; \mt{unit} \\
adam@1297	2089 \mt{val} \; \mt{confirm} : \mt{string} \to \mt{transaction} \; \mt{bool}
adamc@701	2090 \end{array}$$
adamc@701	2091
adamc@701	2092 Any transaction may be run in a new thread with the $\mt{spawn}$ function.
adamc@701	2093 $$\begin{array}{l}
adamc@701	2094 \mt{val} \; \mt{spawn} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit}
adamc@701	2095 \end{array}$$
adamc@701	2096
adamc@701	2097 The current thread can be paused for at least a specified number of milliseconds.
adamc@701	2098 $$\begin{array}{l}
adamc@701	2099 \mt{val} \; \mt{sleep} : \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@701	2100 \end{array}$$
adamc@701	2101
adam@1770	2102 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	2103 $$\begin{array}{l}
adamc@787	2104 \mt{val} \; \mt{onError} : (\mt{xbody} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787	2105 \mt{val} \; \mt{onFail} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787	2106 \mt{val} \; \mt{onConnectFail} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787	2107 \mt{val} \; \mt{onDisconnect} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787	2108 \mt{val} \; \mt{onServerError} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit}
adamc@787	2109 \end{array}$$
adamc@787	2110
adam@1555	2111 There are also functions to register standard document-level event handlers.
adam@1555	2112
adam@1555	2113 $$\begin{array}{l}
adam@1783	2114 \mt{val} \; \mt{onClick} : (\mt{mouseEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783	2115 \mt{val} \; \mt{onDblclick} : (\mt{mouseEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783	2116 \mt{val} \; \mt{onKeydown} : (\mt{keyEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783	2117 \mt{val} \; \mt{onKeypress} : (\mt{keyEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783	2118 \mt{val} \; \mt{onKeyup} : (\mt{keyEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783	2119 \mt{val} \; \mt{onMousedown} : (\mt{mouseEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783	2120 \mt{val} \; \mt{onMouseup} : (\mt{mouseEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit}
adam@1555	2121 \end{array}$$
adam@1555	2122
adam@1559	2123 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	2124
adam@1559	2125 $$\begin{array}{l}
adam@1559	2126 \mt{val} \; \mt{preventDefault} : \mt{transaction} \; \mt{unit} \\
adam@1559	2127 \mt{val} \; \mt{stopPropagation} : \mt{transaction} \; \mt{unit}
adam@1559	2128 \end{array}$$
adam@1559	2129
adam@1926	2130 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	2131
adam@1926	2132 $$\begin{array}{l}
adam@1926	2133 \mt{val} \; \mt{script} : \mt{unit} \to \mt{tag} \; [\mt{Code} = \mt{transaction} \; \mt{unit}] \; \mt{head} \; [] \; [] \; []
adam@1926	2134 \end{array}$$
adam@1926	2135
adam@1926	2136 Note that the Ur/Web version of \cd{<script>} is used like \cd{<script code=\{...\}/>}, rather than \cd{<script>...</script>}.
adam@1926	2137
adam@1556	2138 \subsubsection{Node IDs}
adam@1556	2139
adam@1556	2140 There is an abstract type of node IDs that may be assigned to \cd{id} attributes of most HTML tags.
adam@1556	2141
adam@1556	2142 $$\begin{array}{l}
adam@1556	2143 \mt{type} \; \mt{id} \\
adam@1556	2144 \mt{val} \; \mt{fresh} : \mt{transaction} \; \mt{id}
adam@1556	2145 \end{array}$$
adam@1556	2146
adam@1785	2147 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	2148
adam@1785	2149 One further use of IDs is as handles for requesting that \emph{focus} be given to specific tags.
adam@1785	2150
adam@1785	2151 $$\begin{array}{l}
adam@1785	2152 \mt{val} \; \mt{giveFocus} : \mt{id} \to \mt{transaction} \; \mt{unit}
adam@1785	2153 \end{array}$$
adam@1556	2154
adam@1643	2155 \subsubsection{\label{signals}Functional-Reactive Page Generation}
adamc@701	2156
adamc@701	2157 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	2158
adam@1403	2159 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	2160
adamc@659	2161 $$\begin{array}{l}
adamc@659	2162 \mt{con} \; \mt{source} :: \mt{Type} \to \mt{Type} \\
adamc@659	2163 \mt{val} \; \mt{source} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{transaction} \; (\mt{source} \; \mt{t}) \\
adamc@659	2164 \mt{val} \; \mt{set} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@659	2165 \mt{val} \; \mt{get} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@659	2166 \end{array}$$
adamc@659	2167
adam@1400	2168 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	2169
adam@1608	2170 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	2171
adamc@659	2172 $$\begin{array}{l}
adamc@659	2173 \mt{con} \; \mt{signal} :: \mt{Type} \to \mt{Type} \\
adamc@659	2174 \mt{val} \; \mt{signal\_monad} : \mt{monad} \; \mt{signal} \\
adam@1608	2175 \mt{val} \; \mt{signal} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{signal} \; \mt{t} \\
adam@1608	2176 \mt{val} \; \mt{current} : \mt{t} ::: \mt{Type} \to \mt{signal} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@659	2177 \end{array}$$
adamc@659	2178
adamc@659	2179 A reactive portion of an HTML page is injected with a $\mt{dyn}$ tag, which has a signal-valued attribute $\mt{Signal}$.
adamc@659	2180
adamc@659	2181 $$\begin{array}{l}
adam@1641	2182 \mt{val} \; \mt{dyn} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to [\mt{ctx} \sim [\mt{Dyn}]] \Rightarrow \mt{unit} \\
adam@1641	2183 \hspace{.1in} \to \mt{tag} \; [\mt{Signal} = \mt{signal} \; (\mt{xml} \; ([\mt{Dyn}] \rc \mt{ctx}) \; \mt{use} \; \mt{bind})] \; ([\mt{Dyn}] \rc \mt{ctx}) \; [] \; \mt{use} \; \mt{bind}
adamc@659	2184 \end{array}$$
adamc@659	2185
adam@1648	2186 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	2187
adam@1648	2188 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	2189
adam@1786	2190 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	2191
adam@1786	2192 $$\begin{array}{l}
adam@1786	2193 \mt{val} \; \mt{active} : \mt{unit} \to \mt{tag} \; [\mt{Code} = \mt{transaction} \; \mt{xbody}] \; \mt{body} \; [] \; [] \; []
adam@1786	2194 \end{array}$$
adamc@701	2195
adamc@914	2196 \subsubsection{Remote Procedure Calls}
adamc@914	2197
adamc@914	2198 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	2199
adamc@914	2200 $$\begin{array}{l}
adamc@914	2201 \mt{val} \; \mt{rpc} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@914	2202 \end{array}$$
adamc@914	2203
adam@1848	2204 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	2205
adam@1848	2206 $$\begin{array}{l}
adam@1848	2207 \mt{val} \; \mt{tryRpc} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; \mt{t} \to \mt{transaction} \; (\mt{option} \; \mt{t})
adam@1848	2208 \end{array}$$
adam@1848	2209
adamc@701	2210 \subsubsection{Asynchronous Message-Passing}
adamc@701	2211
adamc@701	2212 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	2213
adamc@701	2214 $$\begin{array}{l}
adamc@701	2215 \mt{type} \; \mt{client} \\
adamc@701	2216 \mt{val} \; \mt{self} : \mt{transaction} \; \mt{client}
adamc@701	2217 \end{array}$$
adamc@701	2218
adam@1940	2219 \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	2220
adamc@701	2221 $$\begin{array}{l}
adamc@701	2222 \mt{con} \; \mt{channel} :: \mt{Type} \to \mt{Type} \\
adamc@701	2223 \mt{val} \; \mt{channel} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; (\mt{channel} \; \mt{t}) \\
adamc@701	2224 \mt{val} \; \mt{send} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@701	2225 \mt{val} \; \mt{recv} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@701	2226 \end{array}$$
adamc@701	2227
adamc@701	2228 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	2229
adamc@701	2230 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	2231
adam@1551	2232 \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	2233
adamc@659	2234
adamc@549	2235 \section{Ur/Web Syntax Extensions}
adamc@549	2236
adamc@549	2237 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	2238
adamc@549	2239 \subsection{SQL}
adamc@549	2240
adamc@786	2241 \subsubsection{\label{tables}Table Declarations}
adamc@786	2242
adamc@788	2243 $\mt{table}$ declarations may include constraints, via these grammar rules.
adamc@788	2244 $$\begin{array}{rrcll}
adam@1594	2245 \textrm{Declarations} & d &::=& \mt{table} \; x : c \; [pk[,]] \; cts \mid \mt{view} \; x = V \\
adamc@788	2246 \textrm{Primary key constraints} & pk &::=& \mt{PRIMARY} \; \mt{KEY} \; K \\
adam@1722	2247 \textrm{Keys} & K &::=& f \mid (f, (f,)^+) \mid \{\{e\}\} \\
adamc@788	2248 \textrm{Constraint sets} & cts &::=& \mt{CONSTRAINT} f \; ct \mid cts, cts \mid \{\{e\}\} \\
adamc@788	2249 \textrm{Constraints} & ct &::=& \mt{UNIQUE} \; K \mid \mt{CHECK} \; E \\
adamc@788	2250 &&& \mid \mt{FOREIGN} \; \mt{KEY} \; K \; \mt{REFERENCES} \; F \; (K) \; [\mt{ON} \; \mt{DELETE} \; pr] \; [\mt{ON} \; \mt{UPDATE} \; pr] \\
adamc@788	2251 \textrm{Foreign tables} & F &::=& x \mid \{\{e\}\} \\
adam@1594	2252 \textrm{Propagation modes} & pr &::=& \mt{NO} \; \mt{ACTION} \mid \mt{RESTRICT} \mid \mt{CASCADE} \mid \mt{SET} \; \mt{NULL} \\
adam@1594	2253 \textrm{View expressions} & V &::=& Q \mid \{e\}
adamc@788	2254 \end{array}$$
adamc@788	2255
adamc@788	2256 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	2257
adamc@788	2258
adamc@549	2259 \subsubsection{Queries}
adamc@549	2260
adamc@550	2261 Queries $Q$ are added to the rules for expressions $e$.
adamc@550	2262
adamc@549	2263 $$\begin{array}{rrcll}
adam@1684	2264 \textrm{Queries} & Q &::=& (q \; [\mt{ORDER} \; \mt{BY} \; O] \; [\mt{LIMIT} \; N] \; [\mt{OFFSET} \; N]) \\
adamc@1085	2265 \textrm{Pre-queries} & q &::=& \mt{SELECT} \; [\mt{DISTINCT}] \; P \; \mt{FROM} \; F,^+ \; [\mt{WHERE} \; E] \; [\mt{GROUP} \; \mt{BY} \; p,^+] \; [\mt{HAVING} \; E] \\
adamc@1085	2266 &&& \mid q \; R \; q \mid \{\{\{e\}\}\} \\
adam@1684	2267 \textrm{Relational operators} & R &::=& \mt{UNION} \mid \mt{INTERSECT} \mid \mt{EXCEPT} \\
adam@2093	2268 \textrm{$\mt{ORDER \; BY}$ items} & O &::=& \mt{RANDOM} [()] \mid \hat{E} \; [o] \mid \hat{E} \; [o], O \mid \{\{\{e\}\}\}
adamc@549	2269 \end{array}$$
adamc@549	2270
adamc@549	2271 $$\begin{array}{rrcll}
adamc@549	2272 \textrm{Projections} & P &::=& \ast & \textrm{all columns} \\
adamc@549	2273 &&& p,^+ & \textrm{particular columns} \\
adamc@549	2274 \textrm{Pre-projections} & p &::=& t.f & \textrm{one column from a table} \\
adamc@558	2275 &&& t.\{\{c\}\} & \textrm{a record of columns from a table (of kind $\{\mt{Type}\}$)} \\
adam@1627	2276 &&& t.* & \textrm{all columns from a table} \\
adam@1778	2277 &&& \hat{E} \; [\mt{AS} \; f] & \textrm{expression column} \\
adamc@549	2278 \textrm{Table names} & t &::=& x & \textrm{constant table name (automatically capitalized)} \\
adamc@549	2279 &&& X & \textrm{constant table name} \\
adamc@549	2280 &&& \{\{c\}\} & \textrm{computed table name (of kind $\mt{Name}$)} \\
adamc@549	2281 \textrm{Column names} & f &::=& X & \textrm{constant column name} \\
adamc@549	2282 &&& \{c\} & \textrm{computed column name (of kind $\mt{Name}$)} \\
adamc@549	2283 \textrm{Tables} & T &::=& x & \textrm{table variable, named locally by its own capitalization} \\
adam@1756	2284 &&& x \; \mt{AS} \; X & \textrm{table variable, with local name} \\
adam@1756	2285 &&& x \; \mt{AS} \; \{c\} & \textrm{table variable, with computed local name} \\
adamc@549	2286 &&& \{\{e\}\} \; \mt{AS} \; t & \textrm{computed table expression, with local name} \\
adam@1756	2287 &&& \{\{e\}\} \; \mt{AS} \; \{c\} & \textrm{computed table expression, with computed local name} \\
adamc@1085	2288 \textrm{$\mt{FROM}$ items} & F &::=& T \mid \{\{e\}\} \mid F \; J \; \mt{JOIN} \; F \; \mt{ON} \; E \\
adamc@1085	2289 &&& \mid F \; \mt{CROSS} \; \mt{JOIN} \ F \\
adam@2031	2290 &&& \mid (Q) \; \mt{AS} \; t \mid (\{\{e\}\}) \; \mt{AS} \; t \\
adamc@1085	2291 \textrm{Joins} & J &::=& [\mt{INNER}] \\
adamc@1085	2292 &&& \mid [\mt{LEFT} \mid \mt{RIGHT} \mid \mt{FULL}] \; [\mt{OUTER}] \\
adam@1587	2293 \textrm{SQL expressions} & E &::=& t.f & \textrm{column references} \\
adamc@549	2294 &&& X & \textrm{named expression references} \\
adam@1490	2295 &&& \{[e]\} & \textrm{injected native Ur expressions} \\
adam@1778	2296 &&& \{e\} & \textrm{computed expressions, probably using $\mt{sql\_exp}$ directly} \\
adamc@549	2297 &&& \mt{TRUE} \mid \mt{FALSE} & \textrm{boolean constants} \\
adamc@549	2298 &&& \ell & \textrm{primitive type literals} \\
adamc@549	2299 &&& \mt{NULL} & \textrm{null value (injection of $\mt{None}$)} \\
adamc@549	2300 &&& E \; \mt{IS} \; \mt{NULL} & \textrm{nullness test} \\
adam@1602	2301 &&& \mt{COALESCE}(E, E) & \textrm{take first non-null value} \\
adamc@549	2302 &&& n & \textrm{nullary operators} \\
adamc@549	2303 &&& u \; E & \textrm{unary operators} \\
adamc@549	2304 &&& E \; b \; E & \textrm{binary operators} \\
adam@1778	2305 &&& \mt{COUNT}(\ast) & \textrm{count number of rows} \\
adam@1778	2306 &&& a(E) & \textrm{other aggregate function} \\
adam@1573	2307 &&& \mt{IF} \; E \; \mt{THEN} \; E \; \mt{ELSE} \; E & \textrm{conditional} \\
adam@1778	2308 &&& (Q) & \textrm{subquery (must return a single expression column)} \\
adamc@549	2309 &&& (E) & \textrm{explicit precedence} \\
adamc@549	2310 \textrm{Nullary operators} & n &::=& \mt{CURRENT\_TIMESTAMP} \\
adamc@549	2311 \textrm{Unary operators} & u &::=& \mt{NOT} \\
adam@1688	2312 \textrm{Binary operators} & b &::=& \mt{AND} \mid \mt{OR} \mid = \mid \neq \mid < \mid \leq \mid > \mid \geq \\
adamc@1188	2313 \textrm{Aggregate functions} & a &::=& \mt{COUNT} \mid \mt{AVG} \mid \mt{SUM} \mid \mt{MIN} \mid \mt{MAX} \\
adam@1543	2314 \textrm{Directions} & o &::=& \mt{ASC} \mid \mt{DESC} \mid \{e\} \\
adamc@549	2315 \textrm{SQL integer} & N &::=& n \mid \{e\} \\
adam@1778	2316 \textrm{Windowable expressions} & \hat{E} &::=& E \\
adam@1778	2317 &&& w \; [\mt{OVER} \; ( & \textrm{(Postgres only)} \\
adam@1778	2318 &&& \hspace{.1in} [\mt{PARTITION} \; \mt{BY} \; E] \\
adam@1778	2319 &&& \hspace{.1in} [\mt{ORDER} \; \mt{BY} \; O])] \\
adam@1778	2320 \textrm{Window function} & w &::=& \mt{RANK}() \\
adam@1778	2321 &&& \mt{COUNT}(*) \\
adam@1778	2322 &&& a(E)
adamc@549	2323 \end{array}$$
adamc@549	2324
adamc@1085	2325 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	2326
adam@1683	2327 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	2328
adamc@550	2329 \subsubsection{DML}
adamc@550	2330
adamc@550	2331 DML commands $D$ are added to the rules for expressions $e$.
adamc@550	2332
adamc@550	2333 $$\begin{array}{rrcll}
adamc@550	2334 \textrm{Commands} & D &::=& (\mt{INSERT} \; \mt{INTO} \; T^E \; (f,^+) \; \mt{VALUES} \; (E,^+)) \\
adamc@550	2335 &&& (\mt{UPDATE} \; T^E \; \mt{SET} \; (f = E,)^+ \; \mt{WHERE} \; E) \\
adamc@550	2336 &&& (\mt{DELETE} \; \mt{FROM} \; T^E \; \mt{WHERE} \; E) \\
adamc@550	2337 \textrm{Table expressions} & T^E &::=& x \mid \{\{e\}\}
adamc@550	2338 \end{array}$$
adamc@550	2339
adamc@550	2340 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	2341
adamc@551	2342 \subsection{XML}
adamc@551	2343
adamc@551	2344 XML fragments $L$ are added to the rules for expressions $e$.
adamc@551	2345
adamc@551	2346 $$\begin{array}{rrcll}
adamc@551	2347 \textrm{XML fragments} & L &::=& \texttt{<xml/>} \mid \texttt{<xml>}l^*\texttt{</xml>} \\
adamc@551	2348 \textrm{XML pieces} & l &::=& \textrm{text} & \textrm{cdata} \\
adamc@551	2349 &&& \texttt{<}g\texttt{/>} & \textrm{tag with no children} \\
adamc@551	2350 &&& \texttt{<}g\texttt{>}l^*\texttt{</}x\texttt{>} & \textrm{tag with children} \\
adamc@559	2351 &&& \{e\} & \textrm{computed XML fragment} \\
adamc@559	2352 &&& \{[e]\} & \textrm{injection of an Ur expression, via the $\mt{Top}.\mt{txt}$ function} \\
adam@2075	2353 \textrm{Tag} & g &::=& h \; (x [= v])^* \\
adamc@551	2354 \textrm{Tag head} & h &::=& x & \textrm{tag name} \\
adamc@551	2355 &&& h\{c\} & \textrm{constructor parameter} \\
adamc@551	2356 \textrm{Attribute value} & v &::=& \ell & \textrm{literal value} \\
adamc@551	2357 &&& \{e\} & \textrm{computed value} \\
adamc@551	2358 \end{array}$$
adamc@551	2359
adam@2075	2360 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	2361
adam@1751	2362 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	2363
adam@1751	2364 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	2365
adamc@1198	2366 \section{\label{structure}The Structure of Web Applications}
adamc@553	2367
adam@1797	2368 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	2369
adam@1532	2370 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	2371
adam@1787	2372 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	2373
adam@1370	2374 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	2375
adamc@553	2376 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	2377
adamc@553	2378 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	2379
adam@1653	2380 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	2381 \begin{itemize}
adam@1653	2382 \item Functions are disallowed, since there is no obvious way to serialize them safely.
adam@1653	2383 \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	2384 \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	2385 \end{itemize}
adamc@553	2386
adamc@660	2387 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	2388
adamc@789	2389 \medskip
adamc@789	2390
adam@1347	2391 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	2392
adamc@789	2393 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	2394
adam@1348	2395 \subsection{Tasks}
adam@1348	2396
adam@1348	2397 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	2398
adam@1348	2399 $$\begin{array}{l}
adam@1348	2400 \mt{con} \; \mt{task\_kind} :: \mt{Type} \to \mt{Type} \\
adam@1348	2401 \mt{val} \; \mt{initialize} : \mt{task\_kind} \; \mt{unit} \\
adam@1349	2402 \mt{val} \; \mt{clientLeaves} : \mt{task\_kind} \; \mt{client} \\
adam@1349	2403 \mt{val} \; \mt{periodic} : \mt{int} \to \mt{task\_kind} \; \mt{unit}
adam@1348	2404 \end{array}$$
adam@1348	2405
adam@1348	2406 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	2407
adam@1348	2408 The currently supported task kinds are:
adam@1348	2409 \begin{itemize}
adam@1349	2410 \item $\mt{initialize}$: Code that is run when the application starts up.
adam@1348	2411 \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	2412 \item $\mt{periodic} \; n$: Code that is run when the application starts up and then every $n$ seconds thereafter.
adam@1348	2413 \end{itemize}
adam@1348	2414
adamc@553	2415
adam@2008	2416 \section{\label{ffi}The Foreign Function Interface}
adamc@897	2417
adamc@897	2418 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	2419
adamc@897	2420 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	2421
adamc@897	2422 \begin{itemize}
adamc@897	2423 \item \texttt{clientOnly Module.ident} registers a value as being allowed only in client-side code.
adamc@897	2424 \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	2425 \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	2426 \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	2427 \item \texttt{include FILE} requests inclusion of a C header file.
adamc@897	2428 \item \texttt{jsFunc Module.ident=name} gives a mapping from an Ur name for a value to a JavaScript name.
adamc@897	2429 \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	2430 \item \texttt{script URL} requests inclusion of a JavaScript source file within application HTML.
adamc@897	2431 \item \texttt{serverOnly Module.ident} registers a value as being allowed only in server-side code.
adamc@897	2432 \end{itemize}
adamc@897	2433
adamc@897	2434 \subsection{Writing C FFI Code}
adamc@897	2435
adam@1881	2436 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	2437
adamc@897	2438 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	2439
adamc@897	2440 \begin{itemize}
adam@1881	2441 \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	2442 \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	2443 \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	2444 \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	2445 \end{itemize}
adamc@897	2446
adam@1881	2447 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	2448 \begin{itemize}
adamc@897	2449 \item \begin{verbatim}
adamc@897	2450 void uw_error(uw_context, failure_kind, const char *fmt, ...);
adamc@897	2451 \end{verbatim}
adamc@897	2452 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	2453
adam@1329	2454 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	2455
adamc@897	2456 \item \begin{verbatim}
adam@1469	2457 void uw_set_error_message(uw_context, const char *fmt, ...);
adam@1469	2458 \end{verbatim}
adam@1469	2459 This simpler form of \texttt{uw\_error()} saves an error message without immediately aborting execution.
adam@1469	2460
adam@1469	2461 \item \begin{verbatim}
adamc@897	2462 void uw_push_cleanup(uw_context, void (func)(void ), void *arg);
adamc@897	2463 void uw_pop_cleanup(uw_context);
adamc@897	2464 \end{verbatim}
adam@1329	2465 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	2466
adam@1329	2467 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	2468
adamc@897	2469 \item \begin{verbatim}
adamc@897	2470 void *uw_malloc(uw_context, size_t);
adamc@897	2471 \end{verbatim}
adam@1329	2472 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	2473
adam@1329	2474 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	2475
adamc@897	2476 \item \begin{verbatim}
adamc@897	2477 typedef void (uw_callback)(void );
adam@1328	2478 typedef void (uw_callback_with_retry)(void , int will_retry);
adam@2001	2479 int uw_register_transactional(uw_context, void *data, uw_callback commit,
adam@2001	2480 uw_callback rollback, uw_callback_with_retry free);
adamc@897	2481 \end{verbatim}
adam@2001	2482 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	2483
adam@2000	2484 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	2485
adam@1329	2486 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	2487
adam@1329	2488 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	2489
adam@1469	2490 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	2491
adamc@1085	2492 \item \begin{verbatim}
adamc@1085	2493 void uw_get_global(uw_context, char name);
adamc@1085	2494 void uw_set_global(uw_context, char name, void data, uw_callback free);
adamc@1085	2495 \end{verbatim}
adam@1329	2496 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	2497
adamc@897	2498 \end{itemize}
adamc@897	2499
adamc@897	2500 \subsection{Writing JavaScript FFI Code}
adamc@897	2501
adamc@897	2502 JavaScript is dynamically typed, so Ur/Web type definitions imply no JavaScript code. The JavaScript identifier for each FFI function is set with the \texttt{jsFunc} directive. Each identifier can be defined in any JavaScript file that you ask to include with the \texttt{script} directive.
adamc@897	2503
adamc@897	2504 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	2505
adamc@897	2506 \begin{itemize}
adamc@897	2507 \item Integers, floats, strings, characters, and booleans are represented in the usual JavaScript way.
adam@1996	2508 \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	2509 \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	2510 \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	2511 \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	2512 \item As in the C FFI, all abstract types of program syntax are implemented with strings in JavaScript.
adam@1996	2513 \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	2514 \end{itemize}
adamc@897	2515
adam@1644	2516 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	2517
adam@1644	2518 \begin{itemize}
adam@1644	2519 \item Sources should be treated as an abstract type, manipulated via:
adam@1644	2520 \begin{itemize}
adam@1644	2521 \item \cd{sc(v)}, to create a source initialized to \cd{v}
adam@1644	2522 \item \cd{sg(s)}, to retrieve the current value of source \cd{s}
adam@1644	2523 \item \cd{sv(s, v)}, to set source \cd{s} to value \cd{v}
adam@1644	2524 \end{itemize}
adam@1644	2525
adam@1644	2526 \item Signals should be treated as an abstract type, manipulated via:
adam@1644	2527 \begin{itemize}
adam@1644	2528 \item \cd{sr(v)} and \cd{sb(s, f)}, the ``return'' and ``bind'' monad operators, respectively
adam@1644	2529 \item \cd{ss(s)}, to produce the signal corresponding to source \cd{s}
adam@1644	2530 \item \cd{scur(s)}, to get the current value of signal \cd{s}
adam@1644	2531 \end{itemize}
adam@1644	2532
adam@1644	2533 \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	2534
adam@1702	2535 \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	2536
adam@1644	2537 \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	2538 \end{itemize}
adamc@897	2539
adam@1833	2540 \subsection{Introducing New HTML Tags}
adam@1833	2541
adam@1833	2542 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	2543
adam@1833	2544 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	2545
adam@2010	2546 \subsection{The Less Safe FFI}
adam@2010	2547
adam@2010	2548 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	2549
adam@2010	2550 When the less safe mode is enabled, declarations like this one are accepted, at the top level of a \texttt{.ur} file:
adam@2010	2551 \begin{verbatim}
adam@2010	2552 ffi foo : int -> int
adam@2010	2553 \end{verbatim}
adam@2010	2554
adam@2010	2555 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	2556 \begin{itemize}
adam@2010	2557 \item \texttt{effectful}
adam@2010	2558 \item \texttt{benignEffectful}
adam@2010	2559 \item \texttt{clientOnly}
adam@2010	2560 \item \texttt{serverOnly}
adam@2010	2561 \item \texttt{jsFunc "putJsFuncNameHere"}
adam@2010	2562 \end{itemize}
adam@2010	2563
adam@2039	2564 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	2565
adamc@897	2566
adam@2042	2567 \section{\label{phases}Compiler Phases}
adam@2042	2568
adam@2042	2569 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	2570
adamc@552	2571 In this section, we step through the main phases of compilation, noting what consequences each phase has for effective programming.
adamc@552	2572
adamc@552	2573 \subsection{Parse}
adamc@552	2574
adamc@552	2575 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	2576
adamc@552	2577 \subsection{Elaborate}
adamc@552	2578
adamc@552	2579 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	2580
adam@1378	2581 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	2582
adamc@552	2583 \subsection{Unnest}
adamc@552	2584
adamc@552	2585 Named local function definitions are moved to the top level, to avoid the need to generate closures.
adamc@552	2586
adamc@552	2587 \subsection{Corify}
adamc@552	2588
adamc@552	2589 Module system features are compiled away, through inlining of functor definitions at application sites. Afterward, most abstraction boundaries are broken, facilitating optimization.
adamc@552	2590
adamc@552	2591 \subsection{Especialize}
adamc@552	2592
adam@1356	2593 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	2594
adamc@552	2595 \subsection{Untangle}
adamc@552	2596
adam@1797	2597 Remove unnecessary mutual recursion, splitting recursive groups into strongly connected components.
adamc@552	2598
adamc@552	2599 \subsection{Shake}
adamc@552	2600
adamc@552	2601 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	2602
adamc@661	2603 \subsection{Rpcify}
adamc@661	2604
adamc@661	2605 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	2606
adamc@661	2607 \subsection{Untangle, Shake}
adamc@661	2608
adamc@661	2609 Repeat these simplifications.
adamc@661	2610
adamc@553	2611 \subsection{\label{tag}Tag}
adamc@552	2612
adamc@552	2613 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	2614
adamc@552	2615 \subsection{Reduce}
adamc@552	2616
adamc@552	2617 Apply definitional equality rules to simplify the program as much as possible. This effectively includes inlining of every non-recursive definition.
adamc@552	2618
adamc@552	2619 \subsection{Unpoly}
adamc@552	2620
adamc@552	2621 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	2622
adamc@552	2623 \subsection{Specialize}
adamc@552	2624
adamc@558	2625 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	2626
adamc@552	2627 \subsection{Shake}
adamc@552	2628
adamc@558	2629 Here the compiler repeats the earlier Shake phase.
adamc@552	2630
adamc@552	2631 \subsection{Monoize}
adamc@552	2632
adamc@552	2633 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	2634
adamc@552	2635 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	2636
adamc@552	2637 \subsection{MonoOpt}
adamc@552	2638
adamc@552	2639 Simple algebraic laws are applied to simplify the program, focusing especially on efficient imperative generation of HTML pages.
adamc@552	2640
adamc@552	2641 \subsection{MonoUntangle}
adamc@552	2642
adamc@552	2643 Unnecessary mutual recursion is broken up again.
adamc@552	2644
adamc@552	2645 \subsection{MonoReduce}
adamc@552	2646
adamc@552	2647 Equivalents of the definitional equality rules are applied to simplify programs, with inlining again playing a major role.
adamc@552	2648
adamc@552	2649 \subsection{MonoShake, MonoOpt}
adamc@552	2650
adamc@552	2651 Unneeded declarations are removed, and basic optimizations are repeated.
adamc@552	2652
adamc@552	2653 \subsection{Fuse}
adamc@552	2654
adamc@552	2655 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	2656
adamc@552	2657 \subsection{MonoUntangle, MonoShake}
adamc@552	2658
adamc@552	2659 Fuse often creates more opportunities to remove spurious mutual recursion.
adamc@552	2660
adamc@552	2661 \subsection{Pathcheck}
adamc@552	2662
adamc@552	2663 The compiler checks that no link or action name has been used more than once.
adamc@552	2664
adamc@552	2665 \subsection{Cjrize}
adamc@552	2666
adamc@552	2667 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	2668
adamc@552	2669 \subsection{C Compilation and Linking}
adamc@552	2670
adam@1523	2671 The output of the last phase is pretty-printed as C source code and passed to the C compiler.
adamc@552	2672
adamc@552	2673
as@1564	2674 \end{document}

Mercurial > urweb

annotate doc/manual.tex @ 2124:f3c24e6790ba