Ur/Web: doc/manual.tex annotate

annotate doc/manual.tex @ 1844:2c5e6f78560c

Manual: Reveal JavaScript representation of transaction type family

author	Adam Chlipala <adam@chlipala.net>
date	Tue, 12 Mar 2013 16:21:20 -0400
parents	be0c4e2e488a
children	e15234fbb163

rev	line source
adamc@524	1 \documentclass{article}
adamc@554	2 \usepackage{fullpage,amsmath,amssymb,proof,url}
rmbruijn@1568	3 \usepackage[T1]{fontenc}
vshabanoff@1765	4 \usepackage{ae,aecompl}
adamc@524	5 \newcommand{\cd}[1]{\texttt{#1}}
adamc@524	6 \newcommand{\mt}[1]{\mathsf{#1}}
adamc@524	7
adamc@524	8 \newcommand{\rc}{+ \hspace{-.075in} + \;}
adamc@527	9 \newcommand{\rcut}{\; \texttt{--} \;}
adamc@527	10 \newcommand{\rcutM}{\; \texttt{---} \;}
adamc@524	11
adamc@524	12 \begin{document}
adamc@524	13
adamc@524	14 \title{The Ur/Web Manual}
adamc@524	15 \author{Adam Chlipala}
adamc@524	16
adamc@524	17 \maketitle
adamc@524	18
adamc@540	19 \tableofcontents
adamc@540	20
adamc@554	21
adamc@554	22 \section{Introduction}
adamc@554	23
adam@1797	24 \emph{Ur} is a programming language designed to introduce richer type system features into functional programming in the tradition of ML and Haskell. Ur is functional, pure, statically typed, and strict. Ur supports a powerful kind of \emph{metaprogramming} based on \emph{type-level computation with type-level records}.
adamc@554	25
adamc@554	26 \emph{Ur/Web} is Ur plus a special standard library and associated rules for parsing and optimization. Ur/Web supports construction of dynamic web applications backed by SQL databases. The signature of the standard library is such that well-typed Ur/Web programs ``don't go wrong'' in a very broad sense. Not only do they not crash during particular page generations, but they also may not:
adamc@554	27
adamc@554	28 \begin{itemize}
adamc@554	29 \item Suffer from any kinds of code-injection attacks
adamc@554	30 \item Return invalid HTML
adamc@554	31 \item Contain dead intra-application links
adamc@554	32 \item Have mismatches between HTML forms and the fields expected by their handlers
adamc@652	33 \item Include client-side code that makes incorrect assumptions about the ``AJAX''-style services that the remote web server provides
adamc@554	34 \item Attempt invalid SQL queries
adamc@652	35 \item Use improper marshaling or unmarshaling in communication with SQL databases or between browsers and web servers
adamc@554	36 \end{itemize}
adamc@554	37
adamc@554	38 This type safety is just the foundation of the Ur/Web methodology. It is also possible to use metaprogramming to build significant application pieces by analysis of type structure. For instance, the demo includes an ML-style functor for building an admin interface for an arbitrary SQL table. The type system guarantees that the admin interface sub-application that comes out will always be free of the above-listed bugs, no matter which well-typed table description is given as input.
adamc@554	39
adamc@652	40 The Ur/Web compiler also produces very efficient object code that does not use garbage collection. These compiled programs will often be even more efficient than what most programmers would bother to write in C. The compiler also generates JavaScript versions of client-side code, with no need to write those parts of applications in a different language.
adamc@554	41
adamc@554	42 \medskip
adamc@554	43
adamc@554	44 The official web site for Ur is:
adamc@554	45 \begin{center}
adamc@554	46 \url{http://www.impredicative.com/ur/}
adamc@554	47 \end{center}
adamc@554	48
adamc@555	49
adamc@555	50 \section{Installation}
adamc@555	51
adamc@555	52 If you are lucky, then the following standard command sequence will suffice for installation, in a directory to which you have unpacked the latest distribution tarball.
adamc@555	53
adamc@555	54 \begin{verbatim}
adamc@555	55 ./configure
adamc@555	56 make
adamc@555	57 sudo make install
adamc@555	58 \end{verbatim}
adamc@555	59
adam@1523	60 Some other packages must be installed for the above to work. At a minimum, you need a standard UNIX shell, with standard UNIX tools like sed and GCC (or an alternate C compiler) in your execution path; MLton, the whole-program optimizing compiler for Standard ML; and the development files for the OpenSSL C library. As of this writing, in the ``testing'' version of Debian Linux, this command will install the more uncommon of these dependencies:
adamc@896	61 \begin{verbatim}
adam@1368	62 apt-get install mlton libssl-dev
adamc@896	63 \end{verbatim}
adamc@555	64
adamc@896	65 To build programs that access SQL databases, you also need one of these client libraries for supported backends.
adamc@555	66 \begin{verbatim}
adamc@896	67 apt-get install libpq-dev libmysqlclient15-dev libsqlite3-dev
adamc@555	68 \end{verbatim}
adamc@555	69
adamc@555	70 It is also possible to access the modules of the Ur/Web compiler interactively, within Standard ML of New Jersey. To install the prerequisites in Debian testing:
adamc@555	71 \begin{verbatim}
adamc@555	72 apt-get install smlnj libsmlnj-smlnj ml-yacc ml-lpt
adamc@555	73 \end{verbatim}
adamc@555	74
adamc@555	75 To begin an interactive session with the Ur compiler modules, run \texttt{make smlnj}, and then, from within an \texttt{sml} session, run \texttt{CM.make "src/urweb.cm";}. The \texttt{Compiler} module is the main entry point.
adamc@555	76
adamc@896	77 To run an SQL-backed application with a backend besides SQLite, you will probably want to install one of these servers.
adamc@555	78
adamc@555	79 \begin{verbatim}
adam@1400	80 apt-get install postgresql-8.4 mysql-server-5.1
adamc@555	81 \end{verbatim}
adamc@555	82
adamc@555	83 To use the Emacs mode, you must have a modern Emacs installed. We assume that you already know how to do this, if you're in the business of looking for an Emacs mode. The demo generation facility of the compiler will also call out to Emacs to syntax-highlight code, and that process depends on the \texttt{htmlize} module, which can be installed in Debian testing via:
adamc@555	84
adamc@555	85 \begin{verbatim}
adamc@555	86 apt-get install emacs-goodies-el
adamc@555	87 \end{verbatim}
adamc@555	88
adam@1441	89 If you don't want to install the Emacs mode, run \texttt{./configure} with the argument \texttt{--without-emacs}.
adam@1441	90
adam@1523	91 Even with the right packages installed, configuration and building might fail to work. After you run \texttt{./configure}, you will see the values of some named environment variables printed. You may need to adjust these values to get proper installation for your system. To change a value, store your preferred alternative in the corresponding UNIX environment variable, before running \texttt{./configure}. For instance, here is how to change the list of extra arguments that the Ur/Web compiler will pass to the C compiler and linker on every invocation. Some older GCC versions need this setting to mask a bug in function inlining.
adamc@555	92
adamc@555	93 \begin{verbatim}
adam@1523	94 CCARGS=-fno-inline ./configure
adamc@555	95 \end{verbatim}
adamc@555	96
adam@1523	97 Since the author is still getting a handle on the GNU Autotools that provide the build system, you may need to do some further work to get started, especially in environments with significant differences from Linux (where most testing is done). The variables \texttt{PGHEADER}, \texttt{MSHEADER}, and \texttt{SQHEADER} may be used to set the proper C header files to include for the development libraries of PostgreSQL, MySQL, and SQLite, respectively. To get libpq to link, one OS X user reported setting \texttt{CCARGS="-I/opt/local/include -L/opt/local/lib/postgresql84"}, after creating a symbolic link with \texttt{ln -s /opt/local/include/postgresql84 /opt/local/include/postgresql}.
adamc@555	98
adamc@555	99 The Emacs mode can be set to autoload by adding the following to your \texttt{.emacs} file.
adamc@555	100
adamc@555	101 \begin{verbatim}
adamc@555	102 (add-to-list 'load-path "/usr/local/share/emacs/site-lisp/urweb-mode")
adamc@555	103 (load "urweb-mode-startup")
adamc@555	104 \end{verbatim}
adamc@555	105
adamc@555	106 Change the path in the first line if you chose a different Emacs installation path during configuration.
adamc@555	107
adamc@555	108
adamc@556	109 \section{Command-Line Compiler}
adamc@556	110
adam@1604	111 \subsection{\label{cl}Project Files}
adamc@556	112
adamc@556	113 The basic inputs to the \texttt{urweb} compiler are project files, which have the extension \texttt{.urp}. Here is a sample \texttt{.urp} file.
adamc@556	114
adamc@556	115 \begin{verbatim}
adamc@556	116 database dbname=test
adamc@556	117 sql crud1.sql
adamc@556	118
adamc@556	119 crud
adamc@556	120 crud1
adamc@556	121 \end{verbatim}
adamc@556	122
adamc@556	123 The \texttt{database} line gives the database information string to pass to libpq. In this case, the string only says to connect to a local database named \texttt{test}.
adamc@556	124
adamc@556	125 The \texttt{sql} line asks for an SQL source file to be generated, giving the commands to run to create the tables and sequences that this application expects to find. After building this \texttt{.urp} file, the following commands could be used to initialize the database, assuming that the current UNIX user exists as a Postgres user with database creation privileges:
adamc@556	126
adamc@556	127 \begin{verbatim}
adamc@556	128 createdb test
adamc@556	129 psql -f crud1.sql test
adamc@556	130 \end{verbatim}
adamc@556	131
adam@1331	132 A blank line separates the named directives from a list of modules to include in the project. Any line may contain a shell-script-style comment, where any suffix of a line starting at a hash character \texttt{\#} is ignored.
adamc@556	133
adamc@556	134 For each entry \texttt{M} in the module list, the file \texttt{M.urs} is included in the project if it exists, and the file \texttt{M.ur} must exist and is always included.
adamc@556	135
adamc@783	136 Here is the complete list of directive forms. ``FFI'' stands for ``foreign function interface,'' Ur's facility for interaction between Ur programs and C and JavaScript libraries.
adamc@783	137 \begin{itemize}
adam@1799	138 \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	139 \item \texttt{alwaysInline PATH} requests that every call to the referenced function be inlined. Section \ref{structure} explains how functions are assigned path strings.
adam@1462	140 \item \texttt{benignEffectful Module.ident} registers an FFI function or transaction as having side effects. The optimizer avoids removing, moving, or duplicating calls to such functions. Every effectful FFI function must be registered, or the optimizer may make invalid transformations. This version of the \texttt{effectful} directive registers that this function only has side effects that remain local to a single page generation.
adamc@783	141 \item \texttt{clientOnly Module.ident} registers an FFI function or transaction that may only be run in client browsers.
adamc@783	142 \item \texttt{clientToServer Module.ident} adds FFI type \texttt{Module.ident} to the list of types that are OK to marshal from clients to servers. Values like XML trees and SQL queries are hard to marshal without introducing expensive validity checks, so it's easier to ensure that the server never trusts clients to send such values. The file \texttt{include/urweb.h} shows examples of the C support functions that are required of any type that may be marshalled. These include \texttt{attrify}, \texttt{urlify}, and \texttt{unurlify} functions.
adam@1816	143 \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	144 \item \texttt{database DBSTRING} sets the string to pass to libpq to open a database connection.
adamc@783	145 \item \texttt{debug} saves some intermediate C files, which is mostly useful to help in debugging the compiler itself.
adam@1699	146 \item \texttt{effectful Module.ident} registers an FFI function or transaction as having side effects. The optimizer avoids removing, moving, or duplicating calls to such functions. Every effectful FFI function must be registered, or the optimizer may make invalid transformations. (Note that merely assigning a function a \texttt{transaction}-based type does not mark it as effectful in this way!)
adamc@783	147 \item \texttt{exe FILENAME} sets the filename to which to write the output executable. The default for file \texttt{P.urp} is \texttt{P.exe}.
adamc@783	148 \item \texttt{ffi FILENAME} reads the file \texttt{FILENAME.urs} to determine the interface to a new FFI module. The name of the module is calculated from \texttt{FILENAME} in the same way as for normal source files. See the files \texttt{include/urweb.h} and \texttt{src/c/urweb.c} for examples of C headers and implementations for FFI modules. In general, every type or value \texttt{Module.ident} becomes \texttt{uw\_Module\_ident} in C.
adamc@1099	149 \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	150 \item \texttt{jsFunc Module.ident=name} gives the JavaScript name of an FFI value.
adamc@1089	151 \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	152 \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	153 \begin{itemize}
adam@1309	154 \item \texttt{cleanup}: maximum number of cleanup operations (e.g., entries recording the need to deallocate certain temporary objects) that may be active at once per request
adam@1309	155 \item \texttt{database}: maximum size of database files (currently only used by SQLite)
adam@1309	156 \item \texttt{deltas}: maximum number of messages sendable in a single request handler with \texttt{Basis.send}
adam@1309	157 \item \texttt{globals}: maximum number of global variables that FFI libraries may set in a single request context
adam@1309	158 \item \texttt{headers}: maximum size (in bytes) of per-request buffer used to hold HTTP headers for generated pages
adam@1797	159 \item \texttt{heap}: maximum size (in bytes) of per-request heap for dynamically allocated data
adam@1309	160 \item \texttt{inputs}: maximum number of top-level form fields per request
adam@1309	161 \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	162 \item \texttt{page}: maximum size (in bytes) of per-request buffer used to hold HTML content of generated pages
adam@1309	163 \item \texttt{script}: maximum size (in bytes) of per-request buffer used to hold JavaScript content of generated pages
adam@1309	164 \item \texttt{subinputs}: maximum number of form fields per request, excluding top-level fields
adam@1309	165 \item \texttt{time}: maximum running time of a single page request, in units of approximately 0.1 seconds
adam@1309	166 \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	167 \end{itemize}
adam@1523	168 \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	169 \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	170 \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	171 \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@1478	172 \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	173 \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	174 \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	175 \item \texttt{prefix PREFIX} sets the prefix included before every URI within the generated application. The default is \texttt{/}.
adamc@783	176 \item \texttt{profile} generates an executable that may be used with gprof.
adam@1752	177 \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	178 \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	179 \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	180 \item \texttt{serverOnly Module.ident} registers an FFI function or transaction that may only be run on the server.
adamc@1164	181 \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	182 \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	183 \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	184 \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	185 \end{itemize}
adamc@701	186
adamc@701	187
adamc@557	188 \subsection{Building an Application}
adamc@557	189
adamc@557	190 To compile project \texttt{P.urp}, simply run
adamc@557	191 \begin{verbatim}
adamc@557	192 urweb P
adamc@557	193 \end{verbatim}
adamc@1198	194 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	195
adamc@557	196 To time how long the different compiler phases run, without generating an executable, run
adamc@557	197 \begin{verbatim}
adamc@557	198 urweb -timing P
adamc@557	199 \end{verbatim}
adamc@557	200
adamc@1086	201 To stop the compilation process after type-checking, run
adamc@1086	202 \begin{verbatim}
adamc@1086	203 urweb -tc P
adamc@1086	204 \end{verbatim}
adam@1530	205 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	206
adam@1745	207 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	208
adam@1723	209 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	210
adamc@1170	211 To output information relevant to CSS stylesheets (and not finish regular compilation), run
adamc@1170	212 \begin{verbatim}
adamc@1170	213 urweb -css P
adamc@1170	214 \end{verbatim}
adamc@1170	215 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	216
adam@1733	217 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	218 \begin{verbatim}
adam@1733	219 urweb daemon start
adam@1733	220 \end{verbatim}
adam@1733	221 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	222 \begin{verbatim}
adam@1733	223 urweb daemon stop
adam@1733	224 \end{verbatim}
adam@1733	225 Communication happens via a UNIX domain socket in file \cd{.urweb\_daemon} in the working directory.
adam@1733	226
adam@1733	227 \medskip
adam@1733	228
adamc@896	229 Some other command-line parameters are accepted:
adamc@896	230 \begin{itemize}
ezyang@1739	231 \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	232
adamc@896	233 \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	234
adamc@896	235 \item \texttt{-dbms [postgres\|mysql\|sqlite]}: Sets the database backend to use.
adamc@896	236 \begin{itemize}
adamc@896	237 \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	238
adamc@896	239 A command sequence like this can initialize a Postgres database, using a file \texttt{app.sql} generated by the compiler:
adamc@896	240 \begin{verbatim}
adamc@896	241 createdb app
adamc@896	242 psql -f app.sql app
adamc@896	243 \end{verbatim}
adamc@896	244
adamc@896	245 \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	246
adamc@896	247 A command sequence like this can initialize a MySQL database:
adamc@896	248 \begin{verbatim}
adamc@896	249 echo "CREATE DATABASE app" \| mysql
adamc@896	250 mysql -D app <app.sql
adamc@896	251 \end{verbatim}
adamc@896	252
adamc@896	253 \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	254
adamc@896	255 A command like this can initialize an SQLite database:
adamc@896	256 \begin{verbatim}
adamc@896	257 sqlite3 path/to/database/file <app.sql
adamc@896	258 \end{verbatim}
adamc@896	259 \end{itemize}
adamc@896	260
adam@1693	261 \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	262
adam@1309	263 \item \texttt{-limit class num}: Equivalent to the \texttt{limit} directive from \texttt{.urp} files
adam@1309	264
adamc@896	265 \item \texttt{-output FILENAME}: Set where the application executable is written.
adamc@896	266
adamc@1127	267 \item \texttt{-path NAME VALUE}: Set the value of path variable \texttt{\$NAME} to \texttt{VALUE}, for use in \texttt{.urp} files.
adamc@1127	268
adam@1335	269 \item \texttt{-prefix PREFIX}: Equivalent to the \texttt{prefix} directive from \texttt{.urp} files
adam@1335	270
adam@1753	271 \item \texttt{-protocol [http\|cgi\|fastcgi\|static]}: Set the protocol that the generated application speaks.
adamc@896	272 \begin{itemize}
adamc@896	273 \item \texttt{http}: This is the default. It is for building standalone web servers that can be accessed by web browsers directly.
adamc@896	274
adamc@896	275 \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	276
adamc@896	277 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	278 \begin{verbatim}
adamc@896	279 ScriptAlias /Hello /path/to/hello.exe
adamc@896	280 \end{verbatim}
adamc@896	281
adamc@1163	282 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	283 \begin{verbatim}
adamc@1163	284 Options +ExecCGI
adamc@1163	285 AddHandler cgi-script .exe
adamc@1163	286 \end{verbatim}
adamc@1163	287
adamc@1163	288 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	289 \begin{verbatim}
adamc@1163	290 prefix /dir/script.exe/
adamc@1163	291 \end{verbatim}
adamc@1163	292
adamc@1163	293 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	294
adamc@1164	295 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	296
adamc@896	297 \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	298
adamc@896	299 To configure a FastCGI program with Apache, one could combine the above \texttt{ScriptAlias} line with a line like this:
adamc@896	300 \begin{verbatim}
adamc@896	301 FastCgiServer /path/to/hello.exe -idle-timeout 99999
adamc@896	302 \end{verbatim}
adamc@896	303 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	304
adam@1753	305 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	306
adamc@896	307 Here is some lighttpd configuration for the same application.
adamc@896	308 \begin{verbatim}
adamc@896	309 fastcgi.server = (
adamc@896	310 "/Hello/" =>
adamc@896	311 (( "bin-path" => "/path/to/hello.exe",
adamc@896	312 "socket" => "/tmp/hello",
adamc@896	313 "check-local" => "disable",
adamc@896	314 "docroot" => "/",
adamc@896	315 "max-procs" => "1"
adamc@896	316 ))
adamc@896	317 )
adamc@896	318 \end{verbatim}
adamc@896	319 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	320
adamc@896	321 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	322
adam@1509	323 \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	324 \end{itemize}
adamc@896	325
adamc@1127	326 \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	327
adamc@1164	328 \item \texttt{-sigfile PATH}: Same as the \texttt{sigfile} directive in \texttt{.urp} files
adamc@1164	329
adamc@896	330 \item \texttt{-sql FILENAME}: Set where a database set-up SQL script is written.
adamc@1095	331
adamc@1095	332 \item \texttt{-static}: Link the runtime system statically. The default is to link against dynamic libraries.
adamc@896	333 \end{itemize}
adamc@896	334
adam@1297	335 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	336
adam@1509	337 \subsection{Tutorial Formatting}
adam@1509	338
adam@1509	339 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	340
adam@1509	341 These input files follow normal Ur syntax, with a few exceptions:
adam@1509	342 \begin{itemize}
adam@1509	343 \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	344 \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	345 \item A comment like \cd{(* * HEADING *)} introduces a section heading, with text \cd{HEADING} of your choice.
adam@1509	346 \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	347 \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	348 \end{itemize}
adam@1509	349
adam@1509	350 A word of warning: as for demo generation, tutorial generation calls Emacs to syntax-highlight Ur code.
adam@1509	351
adam@1522	352 \subsection{Run-Time Options}
adam@1522	353
adam@1522	354 Compiled applications consult a few environment variables to modify their behavior:
adam@1522	355
adam@1522	356 \begin{itemize}
adam@1522	357 \item \cd{URWEB\_NUM\_THREADS}: alternative to the \cd{-t} command-line argument (currently used only by FastCGI)
adam@1522	358 \item \cd{URWEB\_STACK\_SIZE}: size of per-thread stacks, in bytes
as@1564	359 \item \cd{URWEB\_PQ\_CON}: when using PostgreSQL, overrides the compiled-in connection string
adam@1522	360 \end{itemize}
adam@1522	361
adam@1509	362
adamc@529	363 \section{Ur Syntax}
adamc@529	364
adamc@784	365 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	366
adamc@524	367 \subsection{Lexical Conventions}
adamc@524	368
adamc@524	369 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	370
adamc@524	371 \begin{center}
adamc@524	372 \begin{tabular}{rl}
adamc@524	373 \textbf{\LaTeX} & \textbf{ASCII} \\
adamc@524	374 $\to$ & \cd{->} \\
adam@1687	375 $\longrightarrow$ & \cd{-{}->} \\
adamc@524	376 $\times$ & \cd{*} \\
adamc@524	377 $\lambda$ & \cd{fn} \\
adamc@524	378 $\Rightarrow$ & \cd{=>} \\
adamc@652	379 $\Longrightarrow$ & \cd{==>} \\
adamc@529	380 $\neq$ & \cd{<>} \\
adamc@529	381 $\leq$ & \cd{<=} \\
adamc@529	382 $\geq$ & \cd{>=} \\
adamc@524	383 \\
adamc@524	384 $x$ & Normal textual identifier, not beginning with an uppercase letter \\
adamc@525	385 $X$ & Normal textual identifier, beginning with an uppercase letter \\
adamc@524	386 \end{tabular}
adamc@524	387 \end{center}
adamc@524	388
adamc@525	389 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	390
adamc@873	391 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	392
adamc@527	393 This version of the manual doesn't include operator precedences; see \texttt{src/urweb.grm} for that.
adamc@527	394
adam@1297	395 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	396
adamc@552	397 \subsection{\label{core}Core Syntax}
adamc@524	398
adamc@524	399 \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	400 $$\begin{array}{rrcll}
adamc@524	401 \textrm{Kinds} & \kappa &::=& \mt{Type} & \textrm{proper types} \\
adamc@525	402 &&& \mt{Unit} & \textrm{the trivial constructor} \\
adamc@525	403 &&& \mt{Name} & \textrm{field names} \\
adamc@525	404 &&& \kappa \to \kappa & \textrm{type-level functions} \\
adamc@525	405 &&& \{\kappa\} & \textrm{type-level records} \\
adamc@525	406 &&& (\kappa\times^+) & \textrm{type-level tuples} \\
adamc@652	407 &&& X & \textrm{variable} \\
adam@1574	408 &&& X \longrightarrow \kappa & \textrm{kind-polymorphic type-level function} \\
adamc@529	409 &&& \_\_ & \textrm{wildcard} \\
adamc@525	410 &&& (\kappa) & \textrm{explicit precedence} \\
adamc@524	411 \end{array}$$
adamc@524	412
adamc@524	413 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	414 $$\begin{array}{rrcll}
adamc@524	415 \textrm{Explicitness} & ? &::=& :: & \textrm{explicit} \\
adamc@558	416 &&& ::: & \textrm{implicit}
adamc@524	417 \end{array}$$
adamc@524	418
adamc@524	419 \emph{Constructors} are the main class of compile-time-only data. They include proper types and are classified by kinds.
adamc@524	420 $$\begin{array}{rrcll}
adamc@524	421 \textrm{Constructors} & c, \tau &::=& (c) :: \kappa & \textrm{kind annotation} \\
adamc@530	422 &&& \hat{x} & \textrm{constructor variable} \\
adamc@524	423 \\
adamc@525	424 &&& \tau \to \tau & \textrm{function type} \\
adamc@525	425 &&& x \; ? \; \kappa \to \tau & \textrm{polymorphic function type} \\
adamc@652	426 &&& X \longrightarrow \tau & \textrm{kind-polymorphic function type} \\
adamc@525	427 &&& \$ c & \textrm{record type} \\
adamc@524	428 \\
adamc@525	429 &&& c \; c & \textrm{type-level function application} \\
adamc@530	430 &&& \lambda x \; :: \; \kappa \Rightarrow c & \textrm{type-level function abstraction} \\
adamc@524	431 \\
adamc@652	432 &&& X \Longrightarrow c & \textrm{type-level kind-polymorphic function abstraction} \\
adamc@655	433 &&& c [\kappa] & \textrm{type-level kind-polymorphic function application} \\
adamc@652	434 \\
adamc@525	435 &&& () & \textrm{type-level unit} \\
adamc@525	436 &&& \#X & \textrm{field name} \\
adamc@524	437 \\
adamc@525	438 &&& [(c = c)^*] & \textrm{known-length type-level record} \\
adamc@525	439 &&& c \rc c & \textrm{type-level record concatenation} \\
adamc@652	440 &&& \mt{map} & \textrm{type-level record map} \\
adamc@524	441 \\
adamc@558	442 &&& (c,^+) & \textrm{type-level tuple} \\
adamc@525	443 &&& c.n & \textrm{type-level tuple projection ($n \in \mathbb N^+$)} \\
adamc@524	444 \\
adamc@652	445 &&& [c \sim c] \Rightarrow \tau & \textrm{guarded type} \\
adamc@524	446 \\
adamc@529	447 &&& \_ :: \kappa & \textrm{wildcard} \\
adamc@525	448 &&& (c) & \textrm{explicit precedence} \\
adamc@530	449 \\
adamc@530	450 \textrm{Qualified uncapitalized variables} & \hat{x} &::=& x & \textrm{not from a module} \\
adamc@530	451 &&& M.x & \textrm{projection from a module} \\
adamc@525	452 \end{array}$$
adamc@525	453
adam@1579	454 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	455
adamc@525	456 Modules of the module system are described by \emph{signatures}.
adamc@525	457 $$\begin{array}{rrcll}
adamc@525	458 \textrm{Signatures} & S &::=& \mt{sig} \; s^* \; \mt{end} & \textrm{constant} \\
adamc@525	459 &&& X & \textrm{variable} \\
adamc@525	460 &&& \mt{functor}(X : S) : S & \textrm{functor} \\
adamc@529	461 &&& S \; \mt{where} \; \mt{con} \; x = c & \textrm{concretizing an abstract constructor} \\
adamc@525	462 &&& M.X & \textrm{projection from a module} \\
adamc@525	463 \\
adamc@525	464 \textrm{Signature items} & s &::=& \mt{con} \; x :: \kappa & \textrm{abstract constructor} \\
adamc@525	465 &&& \mt{con} \; x :: \kappa = c & \textrm{concrete constructor} \\
adamc@528	466 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529	467 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@525	468 &&& \mt{val} \; x : \tau & \textrm{value} \\
adamc@525	469 &&& \mt{structure} \; X : S & \textrm{sub-module} \\
adamc@525	470 &&& \mt{signature} \; X = S & \textrm{sub-signature} \\
adamc@525	471 &&& \mt{include} \; S & \textrm{signature inclusion} \\
adamc@525	472 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@654	473 &&& \mt{class} \; x :: \kappa & \textrm{abstract constructor class} \\
adamc@654	474 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@525	475 \\
adamc@525	476 \textrm{Datatype constructors} & dc &::=& X & \textrm{nullary constructor} \\
adamc@525	477 &&& X \; \mt{of} \; \tau & \textrm{unary constructor} \\
adamc@524	478 \end{array}$$
adamc@524	479
adamc@526	480 \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	481 $$\begin{array}{rrcll}
adamc@526	482 \textrm{Patterns} & p &::=& \_ & \textrm{wildcard} \\
adamc@526	483 &&& x & \textrm{variable} \\
adamc@526	484 &&& \ell & \textrm{constant} \\
adamc@526	485 &&& \hat{X} & \textrm{nullary constructor} \\
adamc@526	486 &&& \hat{X} \; p & \textrm{unary constructor} \\
adamc@526	487 &&& \{(x = p,)^*\} & \textrm{rigid record pattern} \\
adamc@526	488 &&& \{(x = p,)^+, \ldots\} & \textrm{flexible record pattern} \\
adamc@852	489 &&& p : \tau & \textrm{type annotation} \\
adamc@527	490 &&& (p) & \textrm{explicit precedence} \\
adamc@526	491 \\
adamc@529	492 \textrm{Qualified capitalized variables} & \hat{X} &::=& X & \textrm{not from a module} \\
adamc@526	493 &&& M.X & \textrm{projection from a module} \\
adamc@526	494 \end{array}$$
adamc@526	495
adamc@527	496 \emph{Expressions} are the main run-time entities, corresponding to both ``expressions'' and ``statements'' in mainstream imperative languages.
adamc@527	497 $$\begin{array}{rrcll}
adamc@527	498 \textrm{Expressions} & e &::=& e : \tau & \textrm{type annotation} \\
adamc@529	499 &&& \hat{x} & \textrm{variable} \\
adamc@529	500 &&& \hat{X} & \textrm{datatype constructor} \\
adamc@527	501 &&& \ell & \textrm{constant} \\
adamc@527	502 \\
adamc@527	503 &&& e \; e & \textrm{function application} \\
adamc@527	504 &&& \lambda x : \tau \Rightarrow e & \textrm{function abstraction} \\
adamc@527	505 &&& e [c] & \textrm{polymorphic function application} \\
adamc@852	506 &&& \lambda [x \; ? \; \kappa] \Rightarrow e & \textrm{polymorphic function abstraction} \\
adamc@655	507 &&& e [\kappa] & \textrm{kind-polymorphic function application} \\
adamc@652	508 &&& X \Longrightarrow e & \textrm{kind-polymorphic function abstraction} \\
adamc@527	509 \\
adamc@527	510 &&& \{(c = e,)^*\} & \textrm{known-length record} \\
adamc@527	511 &&& e.c & \textrm{record field projection} \\
adamc@527	512 &&& e \rc e & \textrm{record concatenation} \\
adamc@527	513 &&& e \rcut c & \textrm{removal of a single record field} \\
adamc@527	514 &&& e \rcutM c & \textrm{removal of multiple record fields} \\
adamc@527	515 \\
adamc@527	516 &&& \mt{let} \; ed^* \; \mt{in} \; e \; \mt{end} & \textrm{local definitions} \\
adamc@527	517 \\
adamc@527	518 &&& \mt{case} \; e \; \mt{of} \; (p \Rightarrow e\|)^+ & \textrm{pattern matching} \\
adamc@527	519 \\
adamc@654	520 &&& \lambda [c \sim c] \Rightarrow e & \textrm{guarded expression abstraction} \\
adamc@654	521 &&& e \; ! & \textrm{guarded expression application} \\
adamc@527	522 \\
adamc@527	523 &&& \_ & \textrm{wildcard} \\
adamc@527	524 &&& (e) & \textrm{explicit precedence} \\
adamc@527	525 \\
adamc@527	526 \textrm{Local declarations} & ed &::=& \cd{val} \; x : \tau = e & \textrm{non-recursive value} \\
adam@1797	527 &&& \cd{val} \; \cd{rec} \; (x : \tau = e \; \cd{and})^+ & \textrm{mutually recursive values} \\
adamc@527	528 \end{array}$$
adamc@527	529
adamc@655	530 As with constructors, we include both abstraction and application for kind polymorphism, but applications are only inferred internally.
adamc@655	531
adamc@528	532 \emph{Declarations} primarily bring new symbols into context.
adamc@528	533 $$\begin{array}{rrcll}
adamc@528	534 \textrm{Declarations} & d &::=& \mt{con} \; x :: \kappa = c & \textrm{constructor synonym} \\
adamc@528	535 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529	536 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@528	537 &&& \mt{val} \; x : \tau = e & \textrm{value} \\
adam@1797	538 &&& \mt{val} \; \cd{rec} \; (x : \tau = e \; \mt{and})^+ & \textrm{mutually recursive values} \\
adamc@528	539 &&& \mt{structure} \; X : S = M & \textrm{module definition} \\
adamc@528	540 &&& \mt{signature} \; X = S & \textrm{signature definition} \\
adamc@528	541 &&& \mt{open} \; M & \textrm{module inclusion} \\
adamc@528	542 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@528	543 &&& \mt{open} \; \mt{constraints} \; M & \textrm{inclusion of just the constraints from a module} \\
adamc@528	544 &&& \mt{table} \; x : c & \textrm{SQL table} \\
adam@1594	545 &&& \mt{view} \; x = e & \textrm{SQL view} \\
adamc@528	546 &&& \mt{sequence} \; x & \textrm{SQL sequence} \\
adamc@535	547 &&& \mt{cookie} \; x : \tau & \textrm{HTTP cookie} \\
adamc@784	548 &&& \mt{style} \; x : \tau & \textrm{CSS class} \\
adamc@1085	549 &&& \mt{task} \; e = e & \textrm{recurring task} \\
adamc@528	550 \\
adamc@529	551 \textrm{Modules} & M &::=& \mt{struct} \; d^* \; \mt{end} & \textrm{constant} \\
adamc@529	552 &&& X & \textrm{variable} \\
adamc@529	553 &&& M.X & \textrm{projection} \\
adamc@529	554 &&& M(M) & \textrm{functor application} \\
adamc@529	555 &&& \mt{functor}(X : S) : S = M & \textrm{functor abstraction} \\
adamc@528	556 \end{array}$$
adamc@528	557
adamc@528	558 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	559
adam@1594	560 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	561
adamc@529	562 \subsection{Shorthands}
adamc@529	563
adamc@529	564 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	565
adamc@529	566 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	567
adamc@529	568 A record type may be written $\{(c = c,)^\}$, which elaborates to $\$[(c = c,)^]$.
adamc@529	569
adamc@533	570 The notation $[c_1, \ldots, c_n]$ is shorthand for $[c_1 = (), \ldots, c_n = ()]$.
adamc@533	571
adam@1350	572 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	573
adam@1687	574 The syntax $()$ expands to $\{\}$ as a pattern or expression.
adam@1687	575
adamc@852	576 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	577
adam@1574	578 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	579
adam@1306	580 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	581
adamc@529	582 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	583
adamc@529	584 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	585
adamc@654	586 A signature item or declaration $\mt{class} \; x = \lambda y \Rightarrow c$ may be abbreviated $\mt{class} \; x \; y = c$.
adamc@529	587
adam@1738	588 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	589
adamc@852	590 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	591
adamc@852	592 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	593
adam@1797	594 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	595
adamc@529	596 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	597
adamc@852	598 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	599
adamc@853	600 A declaration $\mt{table} \; x : \{(c = c,)^\}$ is elaborated into $\mt{table} \; x : [(c = c,)^]$.
adamc@529	601
adamc@529	602 The syntax $\mt{where} \; \mt{type}$ is an alternate form of $\mt{where} \; \mt{con}$.
adamc@529	603
adamc@529	604 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	605
adamc@529	606 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	607
adamc@784	608 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	609
adamc@530	610
adamc@530	611 \section{Static Semantics}
adamc@530	612
adamc@530	613 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	614
adamc@530	615 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	616 \begin{itemize}
adamc@655	617 \item $\Gamma \vdash \kappa$ expresses kind well-formedness.
adamc@530	618 \item $\Gamma \vdash c :: \kappa$ assigns a kind to a constructor in a context.
adamc@530	619 \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	620 \item $\Gamma \vdash c \hookrightarrow C$ proves that record constructor $c$ decomposes into set $C$ of field names and record constructors.
adamc@530	621 \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	622 \item $\Gamma \vdash e : \tau$ is a standard typing judgment.
adamc@534	623 \item $\Gamma \vdash p \leadsto \Gamma; \tau$ combines typing of patterns with calculation of which new variables they bind.
adamc@537	624 \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	625 \item $\Gamma \vdash S \equiv S$ is the signature equivalence judgment.
adamc@536	626 \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	627 \item $\Gamma \vdash M : S$ is the module signature checking judgment.
adamc@537	628 \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	629 \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	630 \end{itemize}
adamc@530	631
adamc@655	632
adamc@655	633 \subsection{Kind Well-Formedness}
adamc@655	634
adamc@655	635 $$\infer{\Gamma \vdash \mt{Type}}{}
adamc@655	636 \quad \infer{\Gamma \vdash \mt{Unit}}{}
adamc@655	637 \quad \infer{\Gamma \vdash \mt{Name}}{}
adamc@655	638 \quad \infer{\Gamma \vdash \kappa_1 \to \kappa_2}{
adamc@655	639 \Gamma \vdash \kappa_1
adamc@655	640 & \Gamma \vdash \kappa_2
adamc@655	641 }
adamc@655	642 \quad \infer{\Gamma \vdash \{\kappa\}}{
adamc@655	643 \Gamma \vdash \kappa
adamc@655	644 }
adamc@655	645 \quad \infer{\Gamma \vdash (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@655	646 \forall i: \Gamma \vdash \kappa_i
adamc@655	647 }$$
adamc@655	648
adamc@655	649 $$\infer{\Gamma \vdash X}{
adamc@655	650 X \in \Gamma
adamc@655	651 }
adamc@655	652 \quad \infer{\Gamma \vdash X \longrightarrow \kappa}{
adamc@655	653 \Gamma, X \vdash \kappa
adamc@655	654 }$$
adamc@655	655
adamc@530	656 \subsection{Kinding}
adamc@530	657
adamc@655	658 We write $[X \mapsto \kappa_1]\kappa_2$ for capture-avoiding substitution of $\kappa_1$ for $X$ in $\kappa_2$.
adamc@655	659
adamc@530	660 $$\infer{\Gamma \vdash (c) :: \kappa :: \kappa}{
adamc@530	661 \Gamma \vdash c :: \kappa
adamc@530	662 }
adamc@530	663 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530	664 x :: \kappa \in \Gamma
adamc@530	665 }
adamc@530	666 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530	667 x :: \kappa = c \in \Gamma
adamc@530	668 }$$
adamc@530	669
adamc@530	670 $$\infer{\Gamma \vdash M.x :: \kappa}{
adamc@537	671 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	672 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = \kappa
adamc@530	673 }
adamc@530	674 \quad \infer{\Gamma \vdash M.x :: \kappa}{
adamc@537	675 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	676 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@530	677 }$$
adamc@530	678
adamc@530	679 $$\infer{\Gamma \vdash \tau_1 \to \tau_2 :: \mt{Type}}{
adamc@530	680 \Gamma \vdash \tau_1 :: \mt{Type}
adamc@530	681 & \Gamma \vdash \tau_2 :: \mt{Type}
adamc@530	682 }
adamc@530	683 \quad \infer{\Gamma \vdash x \; ? \: \kappa \to \tau :: \mt{Type}}{
adamc@530	684 \Gamma, x :: \kappa \vdash \tau :: \mt{Type}
adamc@530	685 }
adamc@655	686 \quad \infer{\Gamma \vdash X \longrightarrow \tau :: \mt{Type}}{
adamc@655	687 \Gamma, X \vdash \tau :: \mt{Type}
adamc@655	688 }
adamc@530	689 \quad \infer{\Gamma \vdash \$c :: \mt{Type}}{
adamc@530	690 \Gamma \vdash c :: \{\mt{Type}\}
adamc@530	691 }$$
adamc@530	692
adamc@530	693 $$\infer{\Gamma \vdash c_1 \; c_2 :: \kappa_2}{
adamc@530	694 \Gamma \vdash c_1 :: \kappa_1 \to \kappa_2
adamc@530	695 & \Gamma \vdash c_2 :: \kappa_1
adamc@530	696 }
adamc@530	697 \quad \infer{\Gamma \vdash \lambda x \; :: \; \kappa_1 \Rightarrow c :: \kappa_1 \to \kappa_2}{
adamc@530	698 \Gamma, x :: \kappa_1 \vdash c :: \kappa_2
adamc@530	699 }$$
adamc@530	700
adamc@655	701 $$\infer{\Gamma \vdash c[\kappa'] :: [X \mapsto \kappa']\kappa}{
adamc@655	702 \Gamma \vdash c :: X \to \kappa
adamc@655	703 & \Gamma \vdash \kappa'
adamc@655	704 }
adamc@655	705 \quad \infer{\Gamma \vdash X \Longrightarrow c :: X \to \kappa}{
adamc@655	706 \Gamma, X \vdash c :: \kappa
adamc@655	707 }$$
adamc@655	708
adamc@530	709 $$\infer{\Gamma \vdash () :: \mt{Unit}}{}
adamc@530	710 \quad \infer{\Gamma \vdash \#X :: \mt{Name}}{}$$
adamc@530	711
adamc@530	712 $$\infer{\Gamma \vdash [\overline{c_i = c'_i}] :: \{\kappa\}}{
adamc@530	713 \forall i: \Gamma \vdash c_i : \mt{Name}
adamc@530	714 & \Gamma \vdash c'_i :: \kappa
adamc@530	715 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@530	716 }
adamc@530	717 \quad \infer{\Gamma \vdash c_1 \rc c_2 :: \{\kappa\}}{
adamc@530	718 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530	719 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@530	720 & \Gamma \vdash c_1 \sim c_2
adamc@530	721 }$$
adamc@530	722
adamc@655	723 $$\infer{\Gamma \vdash \mt{map} :: (\kappa_1 \to \kappa_2) \to \{\kappa_1\} \to \{\kappa_2\}}{}$$
adamc@530	724
adamc@573	725 $$\infer{\Gamma \vdash (\overline c) :: (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@573	726 \forall i: \Gamma \vdash c_i :: \kappa_i
adamc@530	727 }
adamc@573	728 \quad \infer{\Gamma \vdash c.i :: \kappa_i}{
adamc@573	729 \Gamma \vdash c :: (\kappa_1 \times \ldots \times \kappa_n)
adamc@530	730 }$$
adamc@530	731
adamc@655	732 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow \tau :: \mt{Type}}{
adamc@655	733 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530	734 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@655	735 & \Gamma, c_1 \sim c_2 \vdash \tau :: \mt{Type}
adamc@530	736 }$$
adamc@530	737
adamc@531	738 \subsection{Record Disjointness}
adamc@531	739
adamc@531	740 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@558	741 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@558	742 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@558	743 & \forall c'_1 \in C_1, c'_2 \in C_2: \Gamma \vdash c'_1 \sim c'_2
adamc@531	744 }
adamc@531	745 \quad \infer{\Gamma \vdash X \sim X'}{
adamc@531	746 X \neq X'
adamc@531	747 }$$
adamc@531	748
adamc@531	749 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@531	750 c'_1 \sim c'_2 \in \Gamma
adamc@558	751 & \Gamma \vdash c'_1 \hookrightarrow C_1
adamc@558	752 & \Gamma \vdash c'_2 \hookrightarrow C_2
adamc@558	753 & c_1 \in C_1
adamc@558	754 & c_2 \in C_2
adamc@531	755 }$$
adamc@531	756
adamc@531	757 $$\infer{\Gamma \vdash c \hookrightarrow \{c\}}{}
adamc@531	758 \quad \infer{\Gamma \vdash [\overline{c = c'}] \hookrightarrow \{\overline{c}\}}{}
adamc@531	759 \quad \infer{\Gamma \vdash c_1 \rc c_2 \hookrightarrow C_1 \cup C_2}{
adamc@531	760 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@531	761 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@531	762 }
adamc@531	763 \quad \infer{\Gamma \vdash c \hookrightarrow C}{
adamc@531	764 \Gamma \vdash c \equiv c'
adamc@531	765 & \Gamma \vdash c' \hookrightarrow C
adamc@531	766 }
adamc@531	767 \quad \infer{\Gamma \vdash \mt{map} \; f \; c \hookrightarrow C}{
adamc@531	768 \Gamma \vdash c \hookrightarrow C
adamc@531	769 }$$
adamc@531	770
adamc@541	771 \subsection{\label{definitional}Definitional Equality}
adamc@532	772
adamc@655	773 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	774
adamc@532	775 $$\infer{\Gamma \vdash c \equiv c}{}
adamc@532	776 \quad \infer{\Gamma \vdash c_1 \equiv c_2}{
adamc@532	777 \Gamma \vdash c_2 \equiv c_1
adamc@532	778 }
adamc@532	779 \quad \infer{\Gamma \vdash c_1 \equiv c_3}{
adamc@532	780 \Gamma \vdash c_1 \equiv c_2
adamc@532	781 & \Gamma \vdash c_2 \equiv c_3
adamc@532	782 }
adamc@532	783 \quad \infer{\Gamma \vdash \mathcal C[c_1] \equiv \mathcal C[c_2]}{
adamc@532	784 \Gamma \vdash c_1 \equiv c_2
adamc@532	785 }$$
adamc@532	786
adamc@532	787 $$\infer{\Gamma \vdash x \equiv c}{
adamc@532	788 x :: \kappa = c \in \Gamma
adamc@532	789 }
adamc@532	790 \quad \infer{\Gamma \vdash M.x \equiv c}{
adamc@537	791 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	792 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@532	793 }
adamc@532	794 \quad \infer{\Gamma \vdash (\overline c).i \equiv c_i}{}$$
adamc@532	795
adamc@532	796 $$\infer{\Gamma \vdash (\lambda x :: \kappa \Rightarrow c) \; c' \equiv [x \mapsto c'] c}{}
adamc@655	797 \quad \infer{\Gamma \vdash (X \Longrightarrow c) [\kappa] \equiv [X \mapsto \kappa] c}{}$$
adamc@655	798
adamc@655	799 $$\infer{\Gamma \vdash c_1 \rc c_2 \equiv c_2 \rc c_1}{}
adamc@532	800 \quad \infer{\Gamma \vdash c_1 \rc (c_2 \rc c_3) \equiv (c_1 \rc c_2) \rc c_3}{}$$
adamc@532	801
adamc@532	802 $$\infer{\Gamma \vdash [] \rc c \equiv c}{}
adamc@532	803 \quad \infer{\Gamma \vdash [\overline{c_1 = c'_1}] \rc [\overline{c_2 = c'_2}] \equiv [\overline{c_1 = c'_1}, \overline{c_2 = c'_2}]}{}$$
adamc@532	804
adamc@655	805 $$\infer{\Gamma \vdash \mt{map} \; f \; [] \equiv []}{}
adamc@655	806 \quad \infer{\Gamma \vdash \mt{map} \; f \; ([c_1 = c_2] \rc c) \equiv [c_1 = f \; c_2] \rc \mt{map} \; f \; c}{}$$
adamc@532	807
adamc@532	808 $$\infer{\Gamma \vdash \mt{map} \; (\lambda x \Rightarrow x) \; c \equiv c}{}
adamc@655	809 \quad \infer{\Gamma \vdash \mt{map} \; f \; (\mt{map} \; f' \; c)
adamc@655	810 \equiv \mt{map} \; (\lambda x \Rightarrow f \; (f' \; x)) \; c}{}$$
adamc@532	811
adamc@532	812 $$\infer{\Gamma \vdash \mt{map} \; f \; (c_1 \rc c_2) \equiv \mt{map} \; f \; c_1 \rc \mt{map} \; f \; c_2}{}$$
adamc@531	813
adamc@534	814 \subsection{Expression Typing}
adamc@533	815
adamc@873	816 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	817
adamc@533	818 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	819
adamc@533	820 $$\infer{\Gamma \vdash e : \tau : \tau}{
adamc@533	821 \Gamma \vdash e : \tau
adamc@533	822 }
adamc@533	823 \quad \infer{\Gamma \vdash e : \tau}{
adamc@533	824 \Gamma \vdash e : \tau'
adamc@533	825 & \Gamma \vdash \tau' \equiv \tau
adamc@533	826 }
adamc@533	827 \quad \infer{\Gamma \vdash \ell : T(\ell)}{}$$
adamc@533	828
adamc@533	829 $$\infer{\Gamma \vdash x : \mathcal I(\tau)}{
adamc@533	830 x : \tau \in \Gamma
adamc@533	831 }
adamc@533	832 \quad \infer{\Gamma \vdash M.x : \mathcal I(\tau)}{
adamc@537	833 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	834 & \mt{proj}(M, \overline{s}, \mt{val} \; x) = \tau
adamc@533	835 }
adamc@533	836 \quad \infer{\Gamma \vdash X : \mathcal I(\tau)}{
adamc@533	837 X : \tau \in \Gamma
adamc@533	838 }
adamc@533	839 \quad \infer{\Gamma \vdash M.X : \mathcal I(\tau)}{
adamc@537	840 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	841 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \tau
adamc@533	842 }$$
adamc@533	843
adamc@533	844 $$\infer{\Gamma \vdash e_1 \; e_2 : \tau_2}{
adamc@533	845 \Gamma \vdash e_1 : \tau_1 \to \tau_2
adamc@533	846 & \Gamma \vdash e_2 : \tau_1
adamc@533	847 }
adamc@533	848 \quad \infer{\Gamma \vdash \lambda x : \tau_1 \Rightarrow e : \tau_1 \to \tau_2}{
adamc@533	849 \Gamma, x : \tau_1 \vdash e : \tau_2
adamc@533	850 }$$
adamc@533	851
adamc@533	852 $$\infer{\Gamma \vdash e [c] : [x \mapsto c]\tau}{
adamc@533	853 \Gamma \vdash e : x :: \kappa \to \tau
adamc@533	854 & \Gamma \vdash c :: \kappa
adamc@533	855 }
adamc@852	856 \quad \infer{\Gamma \vdash \lambda [x \; ? \; \kappa] \Rightarrow e : x \; ? \; \kappa \to \tau}{
adamc@533	857 \Gamma, x :: \kappa \vdash e : \tau
adamc@533	858 }$$
adamc@533	859
adamc@655	860 $$\infer{\Gamma \vdash e [\kappa] : [X \mapsto \kappa]\tau}{
adamc@655	861 \Gamma \vdash e : X \longrightarrow \tau
adamc@655	862 & \Gamma \vdash \kappa
adamc@655	863 }
adamc@655	864 \quad \infer{\Gamma \vdash X \Longrightarrow e : X \longrightarrow \tau}{
adamc@655	865 \Gamma, X \vdash e : \tau
adamc@655	866 }$$
adamc@655	867
adamc@533	868 $$\infer{\Gamma \vdash \{\overline{c = e}\} : \{\overline{c : \tau}\}}{
adamc@533	869 \forall i: \Gamma \vdash c_i :: \mt{Name}
adamc@533	870 & \Gamma \vdash e_i : \tau_i
adamc@533	871 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@533	872 }
adamc@533	873 \quad \infer{\Gamma \vdash e.c : \tau}{
adamc@533	874 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533	875 }
adamc@533	876 \quad \infer{\Gamma \vdash e_1 \rc e_2 : \$(c_1 \rc c_2)}{
adamc@533	877 \Gamma \vdash e_1 : \$c_1
adamc@533	878 & \Gamma \vdash e_2 : \$c_2
adamc@573	879 & \Gamma \vdash c_1 \sim c_2
adamc@533	880 }$$
adamc@533	881
adamc@533	882 $$\infer{\Gamma \vdash e \rcut c : \$c'}{
adamc@533	883 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533	884 }
adamc@533	885 \quad \infer{\Gamma \vdash e \rcutM c : \$c'}{
adamc@533	886 \Gamma \vdash e : \$(c \rc c')
adamc@533	887 }$$
adamc@533	888
adamc@533	889 $$\infer{\Gamma \vdash \mt{let} \; \overline{ed} \; \mt{in} \; e \; \mt{end} : \tau}{
adamc@533	890 \Gamma \vdash \overline{ed} \leadsto \Gamma'
adamc@533	891 & \Gamma' \vdash e : \tau
adamc@533	892 }
adamc@533	893 \quad \infer{\Gamma \vdash \mt{case} \; e \; \mt{of} \; \overline{p \Rightarrow e} : \tau}{
adamc@533	894 \forall i: \Gamma \vdash p_i \leadsto \Gamma_i, \tau'
adamc@533	895 & \Gamma_i \vdash e_i : \tau
adamc@533	896 }$$
adamc@533	897
adamc@573	898 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow e : \lambda [c_1 \sim c_2] \Rightarrow \tau}{
adamc@533	899 \Gamma \vdash c_1 :: \{\kappa\}
adamc@655	900 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@533	901 & \Gamma, c_1 \sim c_2 \vdash e : \tau
adamc@662	902 }
adamc@662	903 \quad \infer{\Gamma \vdash e \; ! : \tau}{
adamc@662	904 \Gamma \vdash e : [c_1 \sim c_2] \Rightarrow \tau
adamc@662	905 & \Gamma \vdash c_1 \sim c_2
adamc@533	906 }$$
adamc@533	907
adamc@534	908 \subsection{Pattern Typing}
adamc@534	909
adamc@534	910 $$\infer{\Gamma \vdash \_ \leadsto \Gamma; \tau}{}
adamc@534	911 \quad \infer{\Gamma \vdash x \leadsto \Gamma, x : \tau; \tau}{}
adamc@534	912 \quad \infer{\Gamma \vdash \ell \leadsto \Gamma; T(\ell)}{}$$
adamc@534	913
adamc@534	914 $$\infer{\Gamma \vdash X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534	915 X : \overline{x ::: \mt{Type}} \to \tau \in \Gamma
adamc@534	916 & \textrm{$\tau$ not a function type}
adamc@534	917 }
adamc@534	918 \quad \infer{\Gamma \vdash X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534	919 X : \overline{x ::: \mt{Type}} \to \tau'' \to \tau \in \Gamma
adamc@534	920 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534	921 }$$
adamc@534	922
adamc@534	923 $$\infer{\Gamma \vdash M.X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537	924 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	925 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau
adamc@534	926 & \textrm{$\tau$ not a function type}
adamc@534	927 }$$
adamc@534	928
adamc@534	929 $$\infer{\Gamma \vdash M.X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537	930 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	931 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau'' \to \tau
adamc@534	932 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534	933 }$$
adamc@534	934
adamc@534	935 $$\infer{\Gamma \vdash \{\overline{x = p}\} \leadsto \Gamma_n; \{\overline{x = \tau}\}}{
adamc@534	936 \Gamma_0 = \Gamma
adamc@534	937 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534	938 }
adamc@534	939 \quad \infer{\Gamma \vdash \{\overline{x = p}, \ldots\} \leadsto \Gamma_n; \$([\overline{x = \tau}] \rc c)}{
adamc@534	940 \Gamma_0 = \Gamma
adamc@534	941 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534	942 }$$
adamc@534	943
adamc@852	944 $$\infer{\Gamma \vdash p : \tau \leadsto \Gamma'; \tau}{
adamc@852	945 \Gamma \vdash p \leadsto \Gamma'; \tau'
adamc@852	946 & \Gamma \vdash \tau' \equiv \tau
adamc@852	947 }$$
adamc@852	948
adamc@535	949 \subsection{Declaration Typing}
adamc@535	950
adamc@535	951 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	952
adamc@558	953 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	954 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	955
adamc@535	956 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535	957 \quad \infer{\Gamma \vdash d, \overline{d} \leadsto \Gamma''}{
adamc@535	958 \Gamma \vdash d \leadsto \Gamma'
adamc@535	959 & \Gamma' \vdash \overline{d} \leadsto \Gamma''
adamc@535	960 }$$
adamc@535	961
adamc@535	962 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@535	963 \Gamma \vdash c :: \kappa
adamc@535	964 }
adamc@535	965 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@535	966 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@535	967 }$$
adamc@535	968
adamc@535	969 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537	970 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	971 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@535	972 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@535	973 }$$
adamc@535	974
adamc@535	975 $$\infer{\Gamma \vdash \mt{val} \; x : \tau = e \leadsto \Gamma, x : \tau}{
adamc@535	976 \Gamma \vdash e : \tau
adamc@535	977 }$$
adamc@535	978
adamc@535	979 $$\infer{\Gamma \vdash \mt{val} \; \mt{rec} \; \overline{x : \tau = e} \leadsto \Gamma, \overline{x : \tau}}{
adamc@535	980 \forall i: \Gamma, \overline{x : \tau} \vdash e_i : \tau_i
adamc@535	981 & \textrm{$e_i$ starts with an expression $\lambda$, optionally preceded by constructor and disjointness $\lambda$s}
adamc@535	982 }$$
adamc@535	983
adamc@535	984 $$\infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : S}{
adamc@535	985 \Gamma \vdash M : S
adamc@558	986 & \textrm{ $M$ not a constant or application}
adamc@535	987 }
adamc@558	988 \quad \infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : \mt{selfify}(X, \overline{s})}{
adamc@558	989 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@539	990 }$$
adamc@539	991
adamc@539	992 $$\infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@535	993 \Gamma \vdash S
adamc@535	994 }$$
adamc@535	995
adamc@537	996 $$\infer{\Gamma \vdash \mt{open} \; M \leadsto \Gamma, \mathcal O(M, \overline{s})}{
adamc@537	997 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535	998 }$$
adamc@535	999
adamc@535	1000 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma}{
adamc@535	1001 \Gamma \vdash c_1 :: \{\kappa\}
adamc@535	1002 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@535	1003 & \Gamma \vdash c_1 \sim c_2
adamc@535	1004 }
adamc@537	1005 \quad \infer{\Gamma \vdash \mt{open} \; \mt{constraints} \; M \leadsto \Gamma, \mathcal O_c(M, \overline{s})}{
adamc@537	1006 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535	1007 }$$
adamc@535	1008
adamc@784	1009 $$\infer{\Gamma \vdash \mt{table} \; x : c \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_table} \; c \; []}{
adamc@535	1010 \Gamma \vdash c :: \{\mt{Type}\}
adamc@535	1011 }
adam@1594	1012 \quad \infer{\Gamma \vdash \mt{view} \; x = e \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_view} \; c}{
adam@1594	1013 \Gamma \vdash e :: \mt{Basis}.\mt{sql\_query} \; [] \; [] \; (\mt{map} \; (\lambda \_ \Rightarrow []) \; c') \; c
adamc@784	1014 }$$
adamc@784	1015
adamc@784	1016 $$\infer{\Gamma \vdash \mt{sequence} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_sequence}}{}$$
adamc@535	1017
adamc@535	1018 $$\infer{\Gamma \vdash \mt{cookie} \; x : \tau \leadsto \Gamma, x : \mt{Basis}.\mt{http\_cookie} \; \tau}{
adamc@535	1019 \Gamma \vdash \tau :: \mt{Type}
adamc@784	1020 }
adamc@784	1021 \quad \infer{\Gamma \vdash \mt{style} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{css\_class}}{}$$
adamc@535	1022
adamc@1085	1023 $$\infer{\Gamma \vdash \mt{task} \; e_1 = e_2 \leadsto \Gamma}{
adam@1348	1024 \Gamma \vdash e_1 :: \mt{Basis}.\mt{task\_kind} \; \tau
adam@1348	1025 & \Gamma \vdash e_2 :: \tau \to \mt{Basis}.\mt{transaction} \; \{\}
adamc@1085	1026 }$$
adamc@1085	1027
adamc@535	1028 $$\infer{\overline{y}; x; \Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535	1029 \quad \infer{\overline{y}; x; \Gamma \vdash X \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to x \; \overline{y}}{
adamc@535	1030 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535	1031 }
adamc@535	1032 \quad \infer{\overline{y}; x; \Gamma \vdash X \; \mt{of} \; \tau \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to \tau \to x \; \overline{y}}{
adamc@535	1033 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535	1034 }$$
adamc@535	1035
adamc@537	1036 \subsection{Signature Item Typing}
adamc@537	1037
adamc@537	1038 We appeal to a signature item analogue of the $\mathcal O$ function from the last subsection.
adamc@537	1039
adam@1797	1040 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	1041
adamc@537	1042 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@537	1043 \quad \infer{\Gamma \vdash s, \overline{s} \leadsto \Gamma''}{
adamc@537	1044 \Gamma \vdash s \leadsto \Gamma'
adamc@537	1045 & \Gamma' \vdash \overline{s} \leadsto \Gamma''
adamc@537	1046 }$$
adamc@537	1047
adamc@537	1048 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}
adamc@537	1049 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@537	1050 \Gamma \vdash c :: \kappa
adamc@537	1051 }
adamc@537	1052 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@537	1053 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@537	1054 }$$
adamc@537	1055
adamc@537	1056 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537	1057 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1058 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537	1059 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@537	1060 }$$
adamc@537	1061
adamc@537	1062 $$\infer{\Gamma \vdash \mt{val} \; x : \tau \leadsto \Gamma, x : \tau}{
adamc@537	1063 \Gamma \vdash \tau :: \mt{Type}
adamc@537	1064 }$$
adamc@537	1065
adamc@537	1066 $$\infer{\Gamma \vdash \mt{structure} \; X : S \leadsto \Gamma, X : S}{
adamc@537	1067 \Gamma \vdash S
adamc@537	1068 }
adamc@537	1069 \quad \infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@537	1070 \Gamma \vdash S
adamc@537	1071 }$$
adamc@537	1072
adamc@537	1073 $$\infer{\Gamma \vdash \mt{include} \; S \leadsto \Gamma, \mathcal O(\overline{s})}{
adamc@537	1074 \Gamma \vdash S
adamc@537	1075 & \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1076 }$$
adamc@537	1077
adamc@537	1078 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma, c_1 \sim c_2}{
adamc@537	1079 \Gamma \vdash c_1 :: \{\kappa\}
adamc@537	1080 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@537	1081 }$$
adamc@537	1082
adamc@784	1083 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784	1084 \Gamma \vdash c :: \kappa
adamc@537	1085 }
adamc@784	1086 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}$$
adamc@537	1087
adamc@536	1088 \subsection{Signature Compatibility}
adamc@536	1089
adam@1797	1090 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	1091
adamc@537	1092 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	1093
adamc@536	1094 $$\infer{\Gamma \vdash S \equiv S}{}
adamc@536	1095 \quad \infer{\Gamma \vdash S_1 \equiv S_2}{
adamc@536	1096 \Gamma \vdash S_2 \equiv S_1
adamc@536	1097 }
adamc@536	1098 \quad \infer{\Gamma \vdash X \equiv S}{
adamc@536	1099 X = S \in \Gamma
adamc@536	1100 }
adamc@536	1101 \quad \infer{\Gamma \vdash M.X \equiv S}{
adamc@537	1102 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1103 & \mt{proj}(M, \overline{s}, \mt{signature} \; X) = S
adamc@536	1104 }$$
adamc@536	1105
adamc@536	1106 $$\infer{\Gamma \vdash S \; \mt{where} \; \mt{con} \; x = c \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa = c \; \overline{s_2} \; \mt{end}}{
adamc@536	1107 \Gamma \vdash S \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa \; \overline{s_2} \; \mt{end}
adamc@536	1108 & \Gamma \vdash c :: \kappa
adamc@537	1109 }
adamc@537	1110 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s^1} \; \mt{include} \; S \; \overline{s^2} \; \mt{end} \equiv \mt{sig} \; \overline{s^1} \; \overline{s} \; \overline{s^2} \; \mt{end}}{
adamc@537	1111 \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@536	1112 }$$
adamc@536	1113
adamc@536	1114 $$\infer{\Gamma \vdash S_1 \leq S_2}{
adamc@536	1115 \Gamma \vdash S_1 \equiv S_2
adamc@536	1116 }
adamc@536	1117 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \mt{end}}{}
adamc@537	1118 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; s' \; \overline{s'} \; \mt{end}}{
adamc@537	1119 \Gamma \vdash \overline{s} \leq s'
adamc@537	1120 & \Gamma \vdash s' \leadsto \Gamma'
adamc@537	1121 & \Gamma' \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \overline{s'} \; \mt{end}
adamc@537	1122 }$$
adamc@537	1123
adamc@537	1124 $$\infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537	1125 \Gamma \vdash s \leq s'
adamc@537	1126 }
adamc@537	1127 \quad \infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537	1128 \Gamma \vdash s \leadsto \Gamma'
adamc@537	1129 & \Gamma' \vdash \overline{s} \leq s'
adamc@536	1130 }$$
adamc@536	1131
adamc@536	1132 $$\infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 \leq \mt{functor} (X : S'_1) : S'_2}{
adamc@536	1133 \Gamma \vdash S'_1 \leq S_1
adamc@536	1134 & \Gamma, X : S'_1 \vdash S_2 \leq S'_2
adamc@536	1135 }$$
adamc@536	1136
adamc@537	1137 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@537	1138 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}
adamc@558	1139 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type}}{}$$
adamc@537	1140
adamc@537	1141 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(y)} \to \mt{Type}}{
adamc@537	1142 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1143 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537	1144 }$$
adamc@537	1145
adamc@784	1146 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@784	1147 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}$$
adamc@537	1148
adamc@537	1149 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \mt{\kappa} = c_2}{
adamc@537	1150 \Gamma \vdash c_1 \equiv c_2
adamc@537	1151 }
adamc@784	1152 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \kappa = c_2}{
adamc@537	1153 \Gamma \vdash c_1 \equiv c_2
adamc@537	1154 }$$
adamc@537	1155
adamc@537	1156 $$\infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537	1157 \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537	1158 }$$
adamc@537	1159
adamc@537	1160 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537	1161 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1162 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537	1163 & \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537	1164 }$$
adamc@537	1165
adamc@537	1166 $$\infer{\Gamma \vdash \cdot \leq \cdot}{}
adamc@537	1167 \quad \infer{\Gamma \vdash X; \overline{dc} \leq X; \overline{dc'}}{
adamc@537	1168 \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537	1169 }
adamc@537	1170 \quad \infer{\Gamma \vdash X \; \mt{of} \; \tau_1; \overline{dc} \leq X \; \mt{of} \; \tau_2; \overline{dc'}}{
adamc@537	1171 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537	1172 & \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537	1173 }$$
adamc@537	1174
adamc@537	1175 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x = \mt{datatype} \; M'.z'}{
adamc@537	1176 \Gamma \vdash M.z \equiv M'.z'
adamc@537	1177 }$$
adamc@537	1178
adamc@537	1179 $$\infer{\Gamma \vdash \mt{val} \; x : \tau_1 \leq \mt{val} \; x : \tau_2}{
adamc@537	1180 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537	1181 }
adamc@537	1182 \quad \infer{\Gamma \vdash \mt{structure} \; X : S_1 \leq \mt{structure} \; X : S_2}{
adamc@537	1183 \Gamma \vdash S_1 \leq S_2
adamc@537	1184 }
adamc@537	1185 \quad \infer{\Gamma \vdash \mt{signature} \; X = S_1 \leq \mt{signature} \; X = S_2}{
adamc@537	1186 \Gamma \vdash S_1 \leq S_2
adamc@537	1187 & \Gamma \vdash S_2 \leq S_1
adamc@537	1188 }$$
adamc@537	1189
adamc@537	1190 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leq \mt{constraint} \; c'_1 \sim c'_2}{
adamc@537	1191 \Gamma \vdash c_1 \equiv c'_1
adamc@537	1192 & \Gamma \vdash c_2 \equiv c'_2
adamc@537	1193 }$$
adamc@537	1194
adamc@655	1195 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{class} \; x :: \kappa}{}
adamc@655	1196 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{class} \; x :: \kappa}{}
adamc@655	1197 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{class} \; x :: \kappa = c_2}{
adamc@537	1198 \Gamma \vdash c_1 \equiv c_2
adamc@537	1199 }$$
adamc@537	1200
adam@1797	1201 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leq \mt{class} \; x :: \kappa}{}
adam@1797	1202 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leq \mt{class} \; x :: \kappa}{}
adam@1797	1203 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c_1 \leq \mt{class} \; x :: \kappa = c_2}{
adam@1797	1204 \Gamma \vdash c_1 \equiv c_2
adam@1797	1205 }$$
adam@1797	1206
adamc@538	1207 \subsection{Module Typing}
adamc@538	1208
adamc@538	1209 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	1210
adamc@538	1211 $$\infer{\Gamma \vdash M : S}{
adamc@538	1212 \Gamma \vdash M : S'
adamc@538	1213 & \Gamma \vdash S' \leq S
adamc@538	1214 }
adamc@538	1215 \quad \infer{\Gamma \vdash \mt{struct} \; \overline{d} \; \mt{end} : \mt{sig} \; \mt{sigOf}(\overline{d}) \; \mt{end}}{
adamc@538	1216 \Gamma \vdash \overline{d} \leadsto \Gamma'
adamc@538	1217 }
adamc@538	1218 \quad \infer{\Gamma \vdash X : S}{
adamc@538	1219 X : S \in \Gamma
adamc@538	1220 }$$
adamc@538	1221
adamc@538	1222 $$\infer{\Gamma \vdash M.X : S}{
adamc@538	1223 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@538	1224 & \mt{proj}(M, \overline{s}, \mt{structure} \; X) = S
adamc@538	1225 }$$
adamc@538	1226
adamc@538	1227 $$\infer{\Gamma \vdash M_1(M_2) : [X \mapsto M_2]S_2}{
adamc@538	1228 \Gamma \vdash M_1 : \mt{functor}(X : S_1) : S_2
adamc@538	1229 & \Gamma \vdash M_2 : S_1
adamc@538	1230 }
adamc@538	1231 \quad \infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 = M : \mt{functor} (X : S_1) : S_2}{
adamc@538	1232 \Gamma \vdash S_1
adamc@538	1233 & \Gamma, X : S_1 \vdash S_2
adamc@538	1234 & \Gamma, X : S_1 \vdash M : S_2
adamc@538	1235 }$$
adamc@538	1236
adamc@538	1237 \begin{eqnarray*}
adamc@538	1238 \mt{sigOf}(\cdot) &=& \cdot \\
adamc@538	1239 \mt{sigOf}(s \; \overline{s'}) &=& \mt{sigOf}(s) \; \mt{sigOf}(\overline{s'}) \\
adamc@538	1240 \\
adamc@538	1241 \mt{sigOf}(\mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@538	1242 \mt{sigOf}(\mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \overline{dc} \\
adamc@538	1243 \mt{sigOf}(\mt{datatype} \; x = \mt{datatype} \; M.z) &=& \mt{datatype} \; x = \mt{datatype} \; M.z \\
adamc@538	1244 \mt{sigOf}(\mt{val} \; x : \tau = e) &=& \mt{val} \; x : \tau \\
adamc@538	1245 \mt{sigOf}(\mt{val} \; \mt{rec} \; \overline{x : \tau = e}) &=& \overline{\mt{val} \; x : \tau} \\
adamc@538	1246 \mt{sigOf}(\mt{structure} \; X : S = M) &=& \mt{structure} \; X : S \\
adamc@538	1247 \mt{sigOf}(\mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@538	1248 \mt{sigOf}(\mt{open} \; M) &=& \mt{include} \; S \textrm{ (where $\Gamma \vdash M : S$)} \\
adamc@538	1249 \mt{sigOf}(\mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@538	1250 \mt{sigOf}(\mt{open} \; \mt{constraints} \; M) &=& \cdot \\
adamc@538	1251 \mt{sigOf}(\mt{table} \; x : c) &=& \mt{table} \; x : c \\
adam@1594	1252 \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	1253 \mt{sigOf}(\mt{sequence} \; x) &=& \mt{sequence} \; x \\
adamc@538	1254 \mt{sigOf}(\mt{cookie} \; x : \tau) &=& \mt{cookie} \; x : \tau \\
adam@1797	1255 \mt{sigOf}(\mt{style} \; x) &=& \mt{style} \; x
adamc@538	1256 \end{eqnarray*}
adamc@539	1257 \begin{eqnarray*}
adamc@539	1258 \mt{selfify}(M, \cdot) &=& \cdot \\
adamc@558	1259 \mt{selfify}(M, s \; \overline{s'}) &=& \mt{selfify}(M, s) \; \mt{selfify}(M, \overline{s'}) \\
adamc@539	1260 \\
adamc@539	1261 \mt{selfify}(M, \mt{con} \; x :: \kappa) &=& \mt{con} \; x :: \kappa = M.x \\
adamc@539	1262 \mt{selfify}(M, \mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@539	1263 \mt{selfify}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \mt{datatype} \; M.x \\
adamc@539	1264 \mt{selfify}(M, \mt{datatype} \; x = \mt{datatype} \; M'.z) &=& \mt{datatype} \; x = \mt{datatype} \; M'.z \\
adamc@539	1265 \mt{selfify}(M, \mt{val} \; x : \tau) &=& \mt{val} \; x : \tau \\
adamc@539	1266 \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	1267 \mt{selfify}(M, \mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@539	1268 \mt{selfify}(M, \mt{include} \; S) &=& \mt{include} \; S \\
adamc@539	1269 \mt{selfify}(M, \mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@655	1270 \mt{selfify}(M, \mt{class} \; x :: \kappa) &=& \mt{class} \; x :: \kappa = M.x \\
adamc@655	1271 \mt{selfify}(M, \mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@539	1272 \end{eqnarray*}
adamc@539	1273
adamc@540	1274 \subsection{Module Projection}
adamc@540	1275
adamc@540	1276 \begin{eqnarray*}
adamc@540	1277 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \\
adamc@540	1278 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa, c) \\
adamc@540	1279 \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	1280 \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	1281 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})$)} \\
adamc@655	1282 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \to \mt{Type} \\
adamc@655	1283 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa \to \mt{Type}, c) \\
adamc@540	1284 \\
adamc@540	1285 \mt{proj}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc} \; \overline{s}, \mt{datatype} \; x) &=& (\overline{y}, \overline{dc}) \\
adamc@540	1286 \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	1287 \\
adamc@540	1288 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, \mt{val} \; x) &=& \tau \\
adamc@540	1289 \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	1290 \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	1291 \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	1292 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \in \overline{dc}$)} \\
adamc@540	1293 \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	1294 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \; \mt{of} \; \tau \in \overline{dc}$)} \\
adamc@540	1295 \\
adamc@540	1296 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, \mt{structure} \; X) &=& S \\
adamc@540	1297 \\
adamc@540	1298 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, \mt{signature} \; X) &=& S \\
adamc@540	1299 \\
adamc@540	1300 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1301 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1302 \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	1303 \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	1304 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@540	1305 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1306 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1307 \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	1308 \mt{proj}(M, \mt{constraint} \; c_1 \sim c_2 \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@655	1309 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@655	1310 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1311 \end{eqnarray*}
adamc@540	1312
adamc@541	1313
adamc@541	1314 \section{Type Inference}
adamc@541	1315
adamc@541	1316 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	1317
adamc@541	1318 \subsection{Basic Unification}
adamc@541	1319
adamc@560	1320 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	1321
adamc@656	1322 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	1323
adamc@541	1324 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	1325
adamc@541	1326 \subsection{Unifying Record Types}
adamc@541	1327
adamc@570	1328 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	1329
adamc@656	1330 \subsection{\label{typeclasses}Constructor Classes}
adamc@541	1331
adamc@784	1332 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	1333
adam@1797	1334 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	1335
adam@1797	1336 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	1337
adam@1797	1338 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	1339
adamc@541	1340 \subsection{Reverse-Engineering Record Types}
adamc@541	1341
adamc@656	1342 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	1343
adamc@541	1344 \subsection{Implicit Arguments in Functor Applications}
adamc@541	1345
adamc@656	1346 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	1347
adamc@541	1348
adamc@542	1349 \section{The Ur Standard Library}
adamc@542	1350
adamc@542	1351 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	1352
adamc@542	1353 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	1354
adamc@542	1355 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	1356 $$\begin{array}{l}
adamc@542	1357 \mt{type} \; \mt{int} \\
adamc@542	1358 \mt{type} \; \mt{float} \\
adamc@873	1359 \mt{type} \; \mt{char} \\
adamc@542	1360 \mt{type} \; \mt{string} \\
adamc@542	1361 \mt{type} \; \mt{time} \\
adamc@785	1362 \mt{type} \; \mt{blob} \\
adamc@542	1363 \\
adamc@542	1364 \mt{type} \; \mt{unit} = \{\} \\
adamc@542	1365 \\
adamc@542	1366 \mt{datatype} \; \mt{bool} = \mt{False} \mid \mt{True} \\
adamc@542	1367 \\
adamc@785	1368 \mt{datatype} \; \mt{option} \; \mt{t} = \mt{None} \mid \mt{Some} \; \mt{of} \; \mt{t} \\
adamc@785	1369 \\
adamc@785	1370 \mt{datatype} \; \mt{list} \; \mt{t} = \mt{Nil} \mid \mt{Cons} \; \mt{of} \; \mt{t} \times \mt{list} \; \mt{t}
adamc@542	1371 \end{array}$$
adamc@542	1372
adamc@1123	1373 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	1374
adam@1297	1375 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	1376 $$\begin{array}{l}
adam@1297	1377 \mt{con} \; \mt{variant} :: \{\mt{Type}\} \to \mt{Type} \\
adam@1297	1378 \mt{val} \; \mt{make} : \mt{nm} :: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{ts} ::: \{\mt{Type}\} \to [[\mt{nm}] \sim \mt{ts}] \Rightarrow \mt{t} \to \mt{variant} \; ([\mt{nm} = \mt{t}] \rc \mt{ts}) \\
adam@1297	1379 \mt{val} \; \mt{match} : \mt{ts} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{variant} \; \mt{ts} \to \$(\mt{map} \; (\lambda \mt{t'} \Rightarrow \mt{t'} \to \mt{t}) \; \mt{ts}) \to \mt{t}
adam@1297	1380 \end{array}$$
adam@1297	1381
adamc@657	1382 Another important generic Ur element comes at the beginning of \texttt{top.urs}.
adamc@657	1383
adamc@657	1384 $$\begin{array}{l}
adamc@657	1385 \mt{con} \; \mt{folder} :: \mt{K} \longrightarrow \{\mt{K}\} \to \mt{Type} \\
adamc@657	1386 \\
adamc@657	1387 \mt{val} \; \mt{fold} : \mt{K} \longrightarrow \mt{tf} :: (\{\mt{K}\} \to \mt{Type}) \\
adamc@657	1388 \hspace{.1in} \to (\mt{nm} :: \mt{Name} \to \mt{v} :: \mt{K} \to \mt{r} :: \{\mt{K}\} \to [[\mt{nm}] \sim \mt{r}] \Rightarrow \\
adamc@657	1389 \hspace{.2in} \mt{tf} \; \mt{r} \to \mt{tf} \; ([\mt{nm} = \mt{v}] \rc \mt{r})) \\
adamc@657	1390 \hspace{.1in} \to \mt{tf} \; [] \\
adamc@657	1391 \hspace{.1in} \to \mt{r} :: \{\mt{K}\} \to \mt{folder} \; \mt{r} \to \mt{tf} \; \mt{r}
adamc@657	1392 \end{array}$$
adamc@657	1393
adamc@657	1394 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	1395
adamc@664	1396 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	1397
adamc@542	1398
adamc@542	1399 \section{The Ur/Web Standard Library}
adamc@542	1400
adam@1400	1401 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	1402
adamc@658	1403 \subsection{Monads}
adamc@658	1404
adamc@658	1405 The Ur Basis defines the monad constructor class from Haskell.
adamc@658	1406
adamc@658	1407 $$\begin{array}{l}
adamc@658	1408 \mt{class} \; \mt{monad} :: \mt{Type} \to \mt{Type} \\
adamc@658	1409 \mt{val} \; \mt{return} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t} ::: \mt{Type} \\
adamc@658	1410 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658	1411 \hspace{.1in} \to \mt{t} \to \mt{m} \; \mt{t} \\
adamc@658	1412 \mt{val} \; \mt{bind} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t1} ::: \mt{Type} \to \mt{t2} ::: \mt{Type} \\
adamc@658	1413 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658	1414 \hspace{.1in} \to \mt{m} \; \mt{t1} \to (\mt{t1} \to \mt{m} \; \mt{t2}) \\
adam@1544	1415 \hspace{.1in} \to \mt{m} \; \mt{t2} \\
adam@1544	1416 \mt{val} \; \mt{mkMonad} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \\
adam@1544	1417 \hspace{.1in} \to \{\mt{Return} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{m} \; \mt{t}, \\
adam@1544	1418 \hspace{.3in} \mt{Bind} : \mt{t1} ::: \mt{Type} \to \mt{t2} ::: \mt{Type} \to \mt{m} \; \mt{t1} \to (\mt{t1} \to \mt{m} \; \mt{t2}) \to \mt{m} \; \mt{t2}\} \\
adam@1544	1419 \hspace{.1in} \to \mt{monad} \; \mt{m}
adamc@658	1420 \end{array}$$
adamc@658	1421
adam@1687	1422 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	1423
adamc@542	1424 \subsection{Transactions}
adamc@542	1425
adamc@542	1426 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	1427 $$\begin{array}{l}
adamc@542	1428 \mt{con} \; \mt{transaction} :: \mt{Type} \to \mt{Type} \\
adamc@658	1429 \mt{val} \; \mt{transaction\_monad} : \mt{monad} \; \mt{transaction}
adamc@542	1430 \end{array}$$
adamc@542	1431
adamc@1123	1432 For debugging purposes, a transactional function is provided for outputting a string on the server process' \texttt{stderr}.
adamc@1123	1433 $$\begin{array}{l}
adamc@1123	1434 \mt{val} \; \mt{debug} : \mt{string} \to \mt{transaction} \; \mt{unit}
adamc@1123	1435 \end{array}$$
adamc@1123	1436
adamc@542	1437 \subsection{HTTP}
adamc@542	1438
adam@1797	1439 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	1440 $$\begin{array}{l}
adamc@786	1441 \mt{con} \; \mt{http\_cookie} :: \mt{Type} \to \mt{Type} \\
adamc@786	1442 \mt{val} \; \mt{getCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; (\mt{option} \; \mt{t}) \\
adamc@1050	1443 \mt{val} \; \mt{setCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \{\mt{Value} : \mt{t}, \mt{Expires} : \mt{option} \; \mt{time}, \mt{Secure} : \mt{bool}\} \to \mt{transaction} \; \mt{unit} \\
adamc@1050	1444 \mt{val} \; \mt{clearCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; \mt{unit}
adamc@786	1445 \end{array}$$
adamc@786	1446
adamc@786	1447 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	1448 $$\begin{array}{l}
adamc@786	1449 \mt{type} \; \mt{url} \\
adamc@786	1450 \mt{val} \; \mt{bless} : \mt{string} \to \mt{url} \\
adamc@786	1451 \mt{val} \; \mt{checkUrl} : \mt{string} \to \mt{option} \; \mt{url}
adamc@786	1452 \end{array}$$
adamc@786	1453 $\mt{bless}$ raises a runtime error if the string passed to it fails the URL policy.
adamc@786	1454
adam@1400	1455 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	1456 $$\begin{array}{l}
adamc@1085	1457 \mt{val} \; \mt{currentUrl} : \mt{transaction} \; \mt{url} \\
adamc@1085	1458 \mt{val} \; \mt{url} : \mt{transaction} \; \mt{page} \to \mt{url}
adamc@1085	1459 \end{array}$$
adamc@1085	1460
adamc@1085	1461 Page generation may be interrupted at any time with a request to redirect to a particular URL instead.
adamc@1085	1462 $$\begin{array}{l}
adamc@1085	1463 \mt{val} \; \mt{redirect} : \mt{t} ::: \mt{Type} \to \mt{url} \to \mt{transaction} \; \mt{t}
adamc@1085	1464 \end{array}$$
adamc@1085	1465
adam@1400	1466 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	1467 $$\begin{array}{l}
adamc@786	1468 \mt{type} \; \mt{file} \\
adamc@786	1469 \mt{val} \; \mt{fileName} : \mt{file} \to \mt{option} \; \mt{string} \\
adamc@786	1470 \mt{val} \; \mt{fileMimeType} : \mt{file} \to \mt{string} \\
adamc@786	1471 \mt{val} \; \mt{fileData} : \mt{file} \to \mt{blob}
adamc@786	1472 \end{array}$$
adamc@786	1473
adam@1799	1474 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	1475
adam@1465	1476 $$\begin{array}{l}
adam@1465	1477 \mt{type} \; \mt{requestHeader} \\
adam@1465	1478 \mt{val} \; \mt{blessRequestHeader} : \mt{string} \to \mt{requestHeader} \\
adam@1465	1479 \mt{val} \; \mt{checkRequestHeader} : \mt{string} \to \mt{option} \; \mt{requestHeader} \\
adam@1465	1480 \mt{val} \; \mt{getHeader} : \mt{requestHeader} \to \mt{transaction} \; (\mt{option} \; \mt{string}) \\
adam@1465	1481 \\
adam@1799	1482 \mt{type} \; \mt{envVar} \\
adam@1799	1483 \mt{val} \; \mt{blessEnvVar} : \mt{string} \to \mt{envVar} \\
adam@1799	1484 \mt{val} \; \mt{checkEnvVar} : \mt{string} \to \mt{option} \; \mt{envVar} \\
adam@1799	1485 \mt{val} \; \mt{getenv} : \mt{envVar} \to \mt{transaction} \; (\mt{option} \; \mt{string}) \\
adam@1799	1486 \\
adam@1465	1487 \mt{type} \; \mt{responseHeader} \\
adam@1465	1488 \mt{val} \; \mt{blessResponseHeader} : \mt{string} \to \mt{responseHeader} \\
adam@1465	1489 \mt{val} \; \mt{checkResponseHeader} : \mt{string} \to \mt{option} \; \mt{responseHeader} \\
adam@1465	1490 \mt{val} \; \mt{setHeader} : \mt{responseHeader} \to \mt{string} \to \mt{transaction} \; \mt{unit}
adam@1465	1491 \end{array}$$
adam@1465	1492
adamc@786	1493 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	1494 $$\begin{array}{l}
adamc@786	1495 \mt{type} \; \mt{mimeType} \\
adamc@786	1496 \mt{val} \; \mt{blessMime} : \mt{string} \to \mt{mimeType} \\
adamc@786	1497 \mt{val} \; \mt{checkMime} : \mt{string} \to \mt{option} \; \mt{mimeType} \\
adamc@786	1498 \mt{val} \; \mt{returnBlob} : \mt{t} ::: \mt{Type} \to \mt{blob} \to \mt{mimeType} \to \mt{transaction} \; \mt{t}
adamc@542	1499 \end{array}$$
adamc@542	1500
adamc@543	1501 \subsection{SQL}
adamc@543	1502
adam@1400	1503 Everything about SQL database access is restricted to server-side code.
adam@1400	1504
adamc@543	1505 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	1506 $$\begin{array}{l}
adamc@785	1507 \mt{con} \; \mt{sql\_table} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785	1508 \end{array}$$
adamc@785	1509 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	1510
adamc@785	1511 We also have the simpler type family of SQL views, which have no keys.
adamc@785	1512 $$\begin{array}{l}
adamc@785	1513 \mt{con} \; \mt{sql\_view} :: \{\mt{Type}\} \to \mt{Type}
adamc@543	1514 \end{array}$$
adamc@543	1515
adamc@785	1516 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	1517 $$\begin{array}{l}
adamc@785	1518 \mt{class} \; \mt{fieldsOf} :: \mt{Type} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785	1519 \mt{val} \; \mt{fieldsOf\_table} : \mt{fs} ::: \{\mt{Type}\} \to \mt{keys} ::: \{\{\mt{Unit}\}\} \to \mt{fieldsOf} \; (\mt{sql\_table} \; \mt{fs} \; \mt{keys}) \; \mt{fs} \\
adamc@785	1520 \mt{val} \; \mt{fieldsOf\_view} : \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; (\mt{sql\_view} \; \mt{fs}) \; \mt{fs}
adamc@785	1521 \end{array}$$
adamc@785	1522
adamc@785	1523 \subsubsection{Table Constraints}
adamc@785	1524
adamc@785	1525 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	1526
adamc@785	1527 $$\begin{array}{l}
adamc@785	1528 \mt{con} \; \mt{primary\_key} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type} \\
adamc@785	1529 \mt{val} \; \mt{no\_primary\_key} : \mt{fs} ::: \{\mt{Type}\} \to \mt{primary\_key} \; \mt{fs} \; [] \\
adamc@785	1530 \mt{val} \; \mt{primary\_key} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{key1} :: \mt{Name} \to \mt{keys} :: \{\mt{Type}\} \\
adamc@785	1531 \hspace{.1in} \to [[\mt{key1}] \sim \mt{keys}] \Rightarrow [[\mt{key1} = \mt{t}] \rc \mt{keys} \sim \mt{rest}] \\
adamc@785	1532 \hspace{.1in} \Rightarrow \$([\mt{key1} = \mt{sql\_injectable\_prim} \; \mt{t}] \rc \mt{map} \; \mt{sql\_injectable\_prim} \; \mt{keys}) \\
adamc@785	1533 \hspace{.1in} \to \mt{primary\_key} \; ([\mt{key1} = \mt{t}] \rc \mt{keys} \rc \mt{rest}) \; [\mt{Pkey} = [\mt{key1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{keys}]
adamc@785	1534 \end{array}$$
adamc@785	1535 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	1536
adamc@785	1537 A type family stands for sets of named constraints of the remaining varieties.
adamc@785	1538 $$\begin{array}{l}
adamc@785	1539 \mt{con} \; \mt{sql\_constraints} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785	1540 \end{array}$$
adamc@785	1541 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	1542
adamc@785	1543 There is a type family of individual, unnamed constraints.
adamc@785	1544 $$\begin{array}{l}
adamc@785	1545 \mt{con} \; \mt{sql\_constraint} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \mt{Type}
adamc@785	1546 \end{array}$$
adamc@785	1547 The first argument is the same as above, and the second argument gives the key columns for just this constraint.
adamc@785	1548
adamc@785	1549 We have operations for assembling constraints into constraint sets.
adamc@785	1550 $$\begin{array}{l}
adamc@785	1551 \mt{val} \; \mt{no\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_constraints} \; \mt{fs} \; [] \\
adamc@785	1552 \mt{val} \; \mt{one\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{unique} ::: \{\mt{Unit}\} \to \mt{name} :: \mt{Name} \\
adamc@785	1553 \hspace{.1in} \to \mt{sql\_constraint} \; \mt{fs} \; \mt{unique} \to \mt{sql\_constraints} \; \mt{fs} \; [\mt{name} = \mt{unique}] \\
adamc@785	1554 \mt{val} \; \mt{join\_constraints} : \mt{fs} ::: \{\mt{Type}\} \to \mt{uniques1} ::: \{\{\mt{Unit}\}\} \to \mt{uniques2} ::: \{\{\mt{Unit}\}\} \to [\mt{uniques1} \sim \mt{uniques2}] \\
adamc@785	1555 \hspace{.1in} \Rightarrow \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques1} \to \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques2} \to \mt{sql\_constraints} \; \mt{fs} \; (\mt{uniques1} \rc \mt{uniques2})
adamc@785	1556 \end{array}$$
adamc@785	1557
adamc@785	1558 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	1559 $$\begin{array}{l}
adamc@785	1560 \mt{val} \; \mt{unique} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{unique1} :: \mt{Name} \to \mt{unique} :: \{\mt{Type}\} \\
adamc@785	1561 \hspace{.1in} \to [[\mt{unique1}] \sim \mt{unique}] \Rightarrow [[\mt{unique1} = \mt{t}] \rc \mt{unique} \sim \mt{rest}] \\
adamc@785	1562 \hspace{.1in} \Rightarrow \mt{sql\_constraint} \; ([\mt{unique1} = \mt{t}] \rc \mt{unique} \rc \mt{rest}) \; ([\mt{unique1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{unique})
adamc@785	1563 \end{array}$$
adamc@785	1564
adamc@785	1565 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	1566 $$\begin{array}{l}
adamc@785	1567 \mt{class} \; \mt{linkable} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@785	1568 \mt{val} \; \mt{linkable\_same} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; \mt{t} \\
adamc@785	1569 \mt{val} \; \mt{linkable\_from\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; (\mt{option} \; \mt{t}) \; \mt{t} \\
adamc@785	1570 \mt{val} \; \mt{linkable\_to\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@785	1571 \end{array}$$
adamc@785	1572
adamc@785	1573 The $\mt{matching}$ type family uses $\mt{linkable}$ to define when two keys match up type-wise.
adamc@785	1574 $$\begin{array}{l}
adamc@785	1575 \mt{con} \; \mt{matching} :: \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785	1576 \mt{val} \; \mt{mat\_nil} : \mt{matching} \; [] \; [] \\
adamc@785	1577 \mt{val} \; \mt{mat\_cons} : \mt{t1} ::: \mt{Type} \to \mt{rest1} ::: \{\mt{Type}\} \to \mt{t2} ::: \mt{Type} \to \mt{rest2} ::: \{\mt{Type}\} \to \mt{nm1} :: \mt{Name} \to \mt{nm2} :: \mt{Name} \\
adamc@785	1578 \hspace{.1in} \to [[\mt{nm1}] \sim \mt{rest1}] \Rightarrow [[\mt{nm2}] \sim \mt{rest2}] \Rightarrow \mt{linkable} \; \mt{t1} \; \mt{t2} \to \mt{matching} \; \mt{rest1} \; \mt{rest2} \\
adamc@785	1579 \hspace{.1in} \to \mt{matching} \; ([\mt{nm1} = \mt{t1}] \rc \mt{rest1}) \; ([\mt{nm2} = \mt{t2}] \rc \mt{rest2})
adamc@785	1580 \end{array}$$
adamc@785	1581
adamc@785	1582 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	1583 $$\begin{array}{l}
adamc@785	1584 \mt{con} \; \mt{propagation\_mode} :: \{\mt{Type}\} \to \mt{Type} \\
adamc@785	1585 \mt{val} \; \mt{restrict} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785	1586 \mt{val} \; \mt{cascade} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785	1587 \mt{val} \; \mt{no\_action} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785	1588 \mt{val} \; \mt{set\_null} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; (\mt{map} \; \mt{option} \; \mt{fs})
adamc@785	1589 \end{array}$$
adamc@785	1590
adamc@785	1591 Finally, we put these ingredient together to define the \texttt{FOREIGN KEY} constraint function.
adamc@785	1592 $$\begin{array}{l}
adamc@785	1593 \mt{val} \; \mt{foreign\_key} : \mt{mine1} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{mine} ::: \{\mt{Type}\} \to \mt{munused} ::: \{\mt{Type}\} \to \mt{foreign} ::: \{\mt{Type}\} \\
adamc@785	1594 \hspace{.1in} \to \mt{funused} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{uniques} ::: \{\{\mt{Unit}\}\} \\
adamc@785	1595 \hspace{.1in} \to [[\mt{mine1}] \sim \mt{mine}] \Rightarrow [[\mt{mine1} = \mt{t}] \rc \mt{mine} \sim \mt{munused}] \Rightarrow [\mt{foreign} \sim \mt{funused}] \Rightarrow [[\mt{nm}] \sim \mt{uniques}] \\
adamc@785	1596 \hspace{.1in} \Rightarrow \mt{matching} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}) \; \mt{foreign} \\
adamc@785	1597 \hspace{.1in} \to \mt{sql\_table} \; (\mt{foreign} \rc \mt{funused}) \; ([\mt{nm} = \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{foreign}] \rc \mt{uniques}) \\
adamc@785	1598 \hspace{.1in} \to \{\mt{OnDelete} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}), \\
adamc@785	1599 \hspace{.2in} \mt{OnUpdate} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine})\} \\
adamc@785	1600 \hspace{.1in} \to \mt{sql\_constraint} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine} \rc \mt{munused}) \; []
adamc@785	1601 \end{array}$$
adamc@785	1602
adamc@785	1603 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	1604 $$\begin{array}{l}
adam@1778	1605 \mt{val} \; \mt{check} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; [] \; [] \; \mt{fs} \; \mt{bool} \to \mt{sql\_constraint} \; \mt{fs} \; []
adamc@785	1606 \end{array}$$
adamc@785	1607
adamc@785	1608 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	1609
adamc@784	1610
adamc@543	1611 \subsubsection{Queries}
adamc@543	1612
adam@1400	1613 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	1614 $$\begin{array}{l}
adam@1400	1615 \mt{con} \; \mt{sql\_query} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@1193	1616 \mt{val} \; \mt{sql\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400	1617 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adamc@1193	1618 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543	1619 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543	1620 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1193	1621 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adam@1400	1622 \hspace{.1in} \Rightarrow \{\mt{Rows} : \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}, \\
adamc@1193	1623 \hspace{.2in} \mt{OrderBy} : \mt{sql\_order\_by} \; (\mt{free} \rc \mt{tables}) \; \mt{selectedExps}, \\
adamc@543	1624 \hspace{.2in} \mt{Limit} : \mt{sql\_limit}, \\
adamc@543	1625 \hspace{.2in} \mt{Offset} : \mt{sql\_offset}\} \\
adam@1400	1626 \hspace{.1in} \to \mt{sql\_query} \; \mt{free} \; \mt{afree} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543	1627 \end{array}$$
adamc@543	1628
adamc@545	1629 Queries are used by folding over their results inside transactions.
adamc@545	1630 $$\begin{array}{l}
adam@1400	1631 \mt{val} \; \mt{query} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to [\mt{tables} \sim \mt{exps}] \Rightarrow \mt{state} ::: \mt{Type} \to \mt{sql\_query} \; [] \; [] \; \mt{tables} \; \mt{exps} \\
adamc@658	1632 \hspace{.1in} \to (\$(\mt{exps} \rc \mt{map} \; (\lambda \mt{fields} :: \{\mt{Type}\} \Rightarrow \$\mt{fields}) \; \mt{tables}) \\
adamc@545	1633 \hspace{.2in} \to \mt{state} \to \mt{transaction} \; \mt{state}) \\
adamc@545	1634 \hspace{.1in} \to \mt{state} \to \mt{transaction} \; \mt{state}
adamc@545	1635 \end{array}$$
adamc@545	1636
adam@1400	1637 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	1638 $$\begin{array}{l}
adam@1400	1639 \mt{con} \; \mt{sql\_query1} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@543	1640 \\
adamc@543	1641 \mt{type} \; \mt{sql\_relop} \\
adamc@543	1642 \mt{val} \; \mt{sql\_union} : \mt{sql\_relop} \\
adamc@543	1643 \mt{val} \; \mt{sql\_intersect} : \mt{sql\_relop} \\
adamc@543	1644 \mt{val} \; \mt{sql\_except} : \mt{sql\_relop} \\
adam@1400	1645 \mt{val} \; \mt{sql\_relop} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400	1646 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adam@1400	1647 \hspace{.1in} \to \mt{tables1} ::: \{\{\mt{Type}\}\} \\
adamc@543	1648 \hspace{.1in} \to \mt{tables2} ::: \{\{\mt{Type}\}\} \\
adamc@543	1649 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543	1650 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@543	1651 \hspace{.1in} \to \mt{sql\_relop} \\
adam@1458	1652 \hspace{.1in} \to \mt{bool} \; (* \; \mt{ALL} \; *) \\
adam@1400	1653 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables1} \; \mt{selectedFields} \; \mt{selectedExps} \\
adam@1400	1654 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables2} \; \mt{selectedFields} \; \mt{selectedExps} \\
adam@1400	1655 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{selectedFields} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543	1656 \end{array}$$
adamc@543	1657
adamc@543	1658 $$\begin{array}{l}
adamc@1193	1659 \mt{val} \; \mt{sql\_query1} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400	1660 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adamc@1193	1661 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543	1662 \hspace{.1in} \to \mt{grouped} ::: \{\{\mt{Type}\}\} \\
adamc@543	1663 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543	1664 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1085	1665 \hspace{.1in} \to \mt{empties} :: \{\mt{Unit}\} \\
adamc@1193	1666 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adamc@1193	1667 \hspace{.1in} \Rightarrow [\mt{free} \sim \mt{grouped}] \\
adam@1400	1668 \hspace{.1in} \Rightarrow [\mt{afree} \sim \mt{tables}] \\
adamc@1193	1669 \hspace{.1in} \Rightarrow [\mt{empties} \sim \mt{selectedFields}] \\
adamc@1085	1670 \hspace{.1in} \Rightarrow \{\mt{Distinct} : \mt{bool}, \\
adamc@1193	1671 \hspace{.2in} \mt{From} : \mt{sql\_from\_items} \; \mt{free} \; \mt{tables}, \\
adam@1778	1672 \hspace{.2in} \mt{Where} : \mt{sql\_exp} \; (\mt{free} \rc \mt{tables}) \; \mt{afree} \; [] \; \mt{bool}, \\
adamc@543	1673 \hspace{.2in} \mt{GroupBy} : \mt{sql\_subset} \; \mt{tables} \; \mt{grouped}, \\
adam@1778	1674 \hspace{.2in} \mt{Having} : \mt{sql\_exp} \; (\mt{free} \rc \mt{grouped}) \; (\mt{afree} \rc \mt{tables}) \; [] \; \mt{bool}, \\
adamc@1085	1675 \hspace{.2in} \mt{SelectFields} : \mt{sql\_subset} \; \mt{grouped} \; (\mt{map} \; (\lambda \_ \Rightarrow []) \; \mt{empties} \rc \mt{selectedFields}), \\
adam@1778	1676 \hspace{.2in} \mt {SelectExps} : \$(\mt{map} \; (\mt{sql\_expw} \; (\mt{free} \rc \mt{grouped}) \; (\mt{afree} \rc \mt{tables}) \; []) \; \mt{selectedExps}) \} \\
adam@1400	1677 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543	1678 \end{array}$$
adamc@543	1679
adamc@543	1680 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	1681 $$\begin{array}{l}
adamc@543	1682 \mt{con} \; \mt{sql\_subset} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@543	1683 \mt{val} \; \mt{sql\_subset} : \mt{keep\_drop} :: \{(\{\mt{Type}\} \times \{\mt{Type}\})\} \\
adamc@543	1684 \hspace{.1in} \to \mt{sql\_subset} \\
adamc@658	1685 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1 \rc \mt{fields}.2)\; \mt{keep\_drop}) \\
adamc@658	1686 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1) \; \mt{keep\_drop}) \\
adamc@543	1687 \mt{val} \; \mt{sql\_subset\_all} : \mt{tables} :: \{\{\mt{Type}\}\} \to \mt{sql\_subset} \; \mt{tables} \; \mt{tables}
adamc@543	1688 \end{array}$$
adamc@543	1689
adam@1778	1690 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	1691 $$\begin{array}{l}
adam@1778	1692 \mt{con} \; \mt{sql\_exp} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}
adamc@543	1693 \end{array}$$
adamc@543	1694
adamc@543	1695 Any field in scope may be converted to an expression.
adamc@543	1696 $$\begin{array}{l}
adamc@543	1697 \mt{val} \; \mt{sql\_field} : \mt{otherTabs} ::: \{\{\mt{Type}\}\} \to \mt{otherFields} ::: \{\mt{Type}\} \\
adam@1778	1698 \hspace{.1in} \to \mt{fieldType} ::: \mt{Type} \to \mt{agg} ::: \{\{\mt{Type}\}\} \\
adamc@543	1699 \hspace{.1in} \to \mt{exps} ::: \{\mt{Type}\} \\
adamc@543	1700 \hspace{.1in} \to \mt{tab} :: \mt{Name} \to \mt{field} :: \mt{Name} \\
adam@1778	1701 \hspace{.1in} \to \mt{sql\_exp} \; ([\mt{tab} = [\mt{field} = \mt{fieldType}] \rc \mt{otherFields}] \rc \mt{otherTabs}) \; \mt{agg} \; \mt{exps} \; \mt{fieldType}
adamc@543	1702 \end{array}$$
adamc@543	1703
adamc@544	1704 There is an analogous function for referencing named expressions.
adamc@544	1705 $$\begin{array}{l}
adam@1778	1706 \mt{val} \; \mt{sql\_exp} : \mt{tabs} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{t} ::: \mt{Type} \to \mt{rest} ::: \{\mt{Type}\} \to \mt{nm} :: \mt{Name} \\
adam@1778	1707 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tabs} \; \mt{agg} \; ([\mt{nm} = \mt{t}] \rc \mt{rest}) \; \mt{t}
adamc@544	1708 \end{array}$$
adamc@544	1709
adamc@544	1710 Ur values of appropriate types may be injected into SQL expressions.
adamc@544	1711 $$\begin{array}{l}
adamc@786	1712 \mt{class} \; \mt{sql\_injectable\_prim} \\
adamc@786	1713 \mt{val} \; \mt{sql\_bool} : \mt{sql\_injectable\_prim} \; \mt{bool} \\
adamc@786	1714 \mt{val} \; \mt{sql\_int} : \mt{sql\_injectable\_prim} \; \mt{int} \\
adamc@786	1715 \mt{val} \; \mt{sql\_float} : \mt{sql\_injectable\_prim} \; \mt{float} \\
adamc@786	1716 \mt{val} \; \mt{sql\_string} : \mt{sql\_injectable\_prim} \; \mt{string} \\
adamc@786	1717 \mt{val} \; \mt{sql\_time} : \mt{sql\_injectable\_prim} \; \mt{time} \\
adamc@786	1718 \mt{val} \; \mt{sql\_blob} : \mt{sql\_injectable\_prim} \; \mt{blob} \\
adamc@786	1719 \mt{val} \; \mt{sql\_channel} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{channel} \; \mt{t}) \\
adamc@786	1720 \mt{val} \; \mt{sql\_client} : \mt{sql\_injectable\_prim} \; \mt{client} \\
adamc@786	1721 \\
adamc@544	1722 \mt{class} \; \mt{sql\_injectable} \\
adamc@786	1723 \mt{val} \; \mt{sql\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@786	1724 \mt{val} \; \mt{sql\_option\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; (\mt{option} \; \mt{t}) \\
adamc@786	1725 \\
adam@1778	1726 \mt{val} \; \mt{sql\_inject} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{sql\_injectable} \; \mt{t} \\
adam@1778	1727 \hspace{.1in} \to \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adamc@544	1728 \end{array}$$
adamc@544	1729
adamc@1123	1730 Additionally, most function-free types may be injected safely, via the $\mt{serialized}$ type family.
adamc@1123	1731 $$\begin{array}{l}
adamc@1123	1732 \mt{con} \; \mt{serialized} :: \mt{Type} \to \mt{Type} \\
adamc@1123	1733 \mt{val} \; \mt{serialize} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{serialized} \; \mt{t} \\
adamc@1123	1734 \mt{val} \; \mt{deserialize} : \mt{t} ::: \mt{Type} \to \mt{serialized} \; \mt{t} \to \mt{t} \\
adamc@1123	1735 \mt{val} \; \mt{sql\_serialized} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{serialized} \; \mt{t})
adamc@1123	1736 \end{array}$$
adamc@1123	1737
adamc@544	1738 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	1739 $$\begin{array}{l}
adam@1778	1740 \mt{val} \; \mt{sql\_is\_null} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778	1741 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; (\mt{option} \; \mt{t}) \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{bool}
adamc@544	1742 \end{array}$$
adamc@544	1743
adam@1602	1744 As another way of dealing with null values, there is also a restricted form of the standard \cd{COALESCE} function.
adam@1602	1745 $$\begin{array}{l}
adam@1602	1746 \mt{val} \; \mt{sql\_coalesce} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778	1747 \hspace{.1in} \to \mt{t} ::: \mt{Type} \\
adam@1778	1748 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; (\mt{option} \; \mt{t}) \\
adam@1778	1749 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778	1750 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adam@1602	1751 \end{array}$$
adam@1602	1752
adamc@559	1753 We have generic nullary, unary, and binary operators.
adamc@544	1754 $$\begin{array}{l}
adamc@544	1755 \mt{con} \; \mt{sql\_nfunc} :: \mt{Type} \to \mt{Type} \\
adamc@544	1756 \mt{val} \; \mt{sql\_current\_timestamp} : \mt{sql\_nfunc} \; \mt{time} \\
adam@1778	1757 \mt{val} \; \mt{sql\_nfunc} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778	1758 \hspace{.1in} \to \mt{sql\_nfunc} \; \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\\end{array}$$
adamc@544	1759
adamc@544	1760 $$\begin{array}{l}
adamc@544	1761 \mt{con} \; \mt{sql\_unary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544	1762 \mt{val} \; \mt{sql\_not} : \mt{sql\_unary} \; \mt{bool} \; \mt{bool} \\
adam@1778	1763 \mt{val} \; \mt{sql\_unary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adam@1778	1764 \hspace{.1in} \to \mt{sql\_unary} \; \mt{arg} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res} \\
adamc@544	1765 \end{array}$$
adamc@544	1766
adamc@544	1767 $$\begin{array}{l}
adamc@544	1768 \mt{con} \; \mt{sql\_binary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544	1769 \mt{val} \; \mt{sql\_and} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544	1770 \mt{val} \; \mt{sql\_or} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adam@1778	1771 \mt{val} \; \mt{sql\_binary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg_1} ::: \mt{Type} \to \mt{arg_2} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adam@1778	1772 \hspace{.1in} \to \mt{sql\_binary} \; \mt{arg_1} \; \mt{arg_2} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_1} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_2} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res}
adamc@544	1773 \end{array}$$
adamc@544	1774
adamc@544	1775 $$\begin{array}{l}
adamc@559	1776 \mt{class} \; \mt{sql\_arith} \\
adamc@559	1777 \mt{val} \; \mt{sql\_int\_arith} : \mt{sql\_arith} \; \mt{int} \\
adamc@559	1778 \mt{val} \; \mt{sql\_float\_arith} : \mt{sql\_arith} \; \mt{float} \\
adamc@559	1779 \mt{val} \; \mt{sql\_neg} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_unary} \; \mt{t} \; \mt{t} \\
adamc@559	1780 \mt{val} \; \mt{sql\_plus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559	1781 \mt{val} \; \mt{sql\_minus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559	1782 \mt{val} \; \mt{sql\_times} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559	1783 \mt{val} \; \mt{sql\_div} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559	1784 \mt{val} \; \mt{sql\_mod} : \mt{sql\_binary} \; \mt{int} \; \mt{int} \; \mt{int}
adamc@559	1785 \end{array}$$
adamc@544	1786
adam@1797	1787 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	1788 $$\begin{array}{l}
adam@1778	1789 \mt{val} \; \mt{sql\_count} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int}
adamc@544	1790 \end{array}$$
adamc@544	1791
adamc@544	1792 $$\begin{array}{l}
adamc@1188	1793 \mt{con} \; \mt{sql\_aggregate} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adam@1778	1794 \mt{val} \; \mt{sql\_aggregate} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{dom} ::: \mt{Type} \to \mt{ran} ::: \mt{Type} \\
adam@1778	1795 \hspace{.1in} \to \mt{sql\_aggregate} \; \mt{dom} \; \mt{ran} \to \mt{sql\_exp} \; \mt{agg} \; \mt{agg} \; \mt{exps} \; \mt{dom} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{ran}
adamc@1188	1796 \end{array}$$
adamc@1188	1797
adamc@1188	1798 $$\begin{array}{l}
adamc@1188	1799 \mt{val} \; \mt{sql\_count\_col} : \mt{t} ::: \mt{Type} \to \mt{sql\_aggregate} \; (\mt{option} \; \mt{t}) \; \mt{int}
adamc@544	1800 \end{array}$$
adam@1400	1801
adam@1400	1802 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	1803
adamc@544	1804 $$\begin{array}{l}
adamc@544	1805 \mt{class} \; \mt{sql\_summable} \\
adamc@544	1806 \mt{val} \; \mt{sql\_summable\_int} : \mt{sql\_summable} \; \mt{int} \\
adamc@544	1807 \mt{val} \; \mt{sql\_summable\_float} : \mt{sql\_summable} \; \mt{float} \\
adam@1777	1808 \mt{val} \; \mt{sql\_avg} : \mt{t} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{sql\_aggregate} \; \mt{t} \; (\mt{option} \; \mt{float}) \\
adam@1400	1809 \mt{val} \; \mt{sql\_sum} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt}
adamc@544	1810 \end{array}$$
adamc@544	1811
adamc@544	1812 $$\begin{array}{l}
adamc@544	1813 \mt{class} \; \mt{sql\_maxable} \\
adamc@544	1814 \mt{val} \; \mt{sql\_maxable\_int} : \mt{sql\_maxable} \; \mt{int} \\
adamc@544	1815 \mt{val} \; \mt{sql\_maxable\_float} : \mt{sql\_maxable} \; \mt{float} \\
adamc@544	1816 \mt{val} \; \mt{sql\_maxable\_string} : \mt{sql\_maxable} \; \mt{string} \\
adamc@544	1817 \mt{val} \; \mt{sql\_maxable\_time} : \mt{sql\_maxable} \; \mt{time} \\
adam@1400	1818 \mt{val} \; \mt{sql\_max} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt} \\
adam@1400	1819 \mt{val} \; \mt{sql\_min} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt}
adamc@544	1820 \end{array}$$
adamc@544	1821
adam@1778	1822 Any SQL query that returns single columns may be turned into a subquery expression.
adam@1777	1823
adam@1777	1824 $$\begin{array}{l}
adam@1778	1825 \mt{val} \; \mt{sql\_subquery} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \\
adam@1778	1826 \hspace{.1in} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_query} \; \mt{tables} \; \mt{agg} \; [\mt{nm} = \mt{t}] \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{nt}
adamc@1193	1827 \end{array}$$
adamc@1193	1828
adam@1573	1829 There is also an \cd{IF..THEN..ELSE..} construct that is compiled into standard SQL \cd{CASE} expressions.
adam@1573	1830 $$\begin{array}{l}
adam@1778	1831 \mt{val} \; \mt{sql\_if\_then\_else} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778	1832 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{bool} \\
adam@1778	1833 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778	1834 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778	1835 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adam@1573	1836 \end{array}$$
adam@1573	1837
adamc@1193	1838 \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	1839 $$\begin{array}{l}
adamc@1193	1840 \mt{con} \; \mt{sql\_from\_items} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@1193	1841 \mt{val} \; \mt{sql\_from\_table} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adamc@1193	1842 \hspace{.1in} \to \mt{t} ::: \mt{Type} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; \mt{t} \; \mt{fs} \to \mt{name} :: \mt{Name} \to \mt{t} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193	1843 \mt{val} \; \mt{sql\_from\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{name} :: \mt{Name} \to \mt{sql\_query} \; \mt{free} \; [] \; \mt{fs} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193	1844 \mt{val} \; \mt{sql\_from\_comma} : \mt{free} ::: \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \to [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193	1845 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adamc@1193	1846 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2}) \\
adamc@1193	1847 \mt{val} \; \mt{sql\_inner\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \\
adamc@1193	1848 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193	1849 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adam@1778	1850 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193	1851 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2})
adamc@786	1852 \end{array}$$
adamc@786	1853
adamc@786	1854 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	1855 $$\begin{array}{l}
adamc@786	1856 \mt{class} \; \mt{nullify} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@786	1857 \mt{val} \; \mt{nullify\_option} : \mt{t} ::: \mt{Type} \to \mt{nullify} \; (\mt{option} \; \mt{t}) \; (\mt{option} \; \mt{t}) \\
adamc@786	1858 \mt{val} \; \mt{nullify\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{nullify} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@786	1859 \end{array}$$
adamc@786	1860
adamc@786	1861 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	1862
adamc@786	1863 $$\begin{array}{l}
adamc@1193	1864 \mt{val} \; \mt{sql\_left\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{(\mt{Type} \times \mt{Type})\}\} \\
adamc@1193	1865 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@786	1866 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\lambda \mt{r} \Rightarrow \$(\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{nullify} \; \mt{p}.1 \; \mt{p}.2) \; \mt{r})) \; \mt{tabs2}) \\
adamc@1193	1867 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \\
adam@1778	1868 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193	1869 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.2)) \; \mt{tabs2})
adamc@786	1870 \end{array}$$
adamc@786	1871
adamc@544	1872 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	1873 $$\begin{array}{l}
adamc@544	1874 \mt{type} \; \mt{sql\_direction} \\
adamc@544	1875 \mt{val} \; \mt{sql\_asc} : \mt{sql\_direction} \\
adamc@544	1876 \mt{val} \; \mt{sql\_desc} : \mt{sql\_direction} \\
adamc@544	1877 \\
adamc@544	1878 \mt{con} \; \mt{sql\_order\_by} :: \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@544	1879 \mt{val} \; \mt{sql\_order\_by\_Nil} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} :: \{\mt{Type}\} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adam@1778	1880 \mt{val} \; \mt{sql\_order\_by\_Cons} : \mt{tf} ::: (\{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}) \\
adam@1778	1881 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778	1882 \hspace{.1in} \to \mt{sql\_window} \; \mt{tf} \to \mt{tf} \; \mt{tables} \; [] \; \mt{exps} \; \mt{t} \to \mt{sql\_direction} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adam@1684	1883 \mt{val} \; \mt{sql\_order\_by\_random} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544	1884 \\
adamc@544	1885 \mt{type} \; \mt{sql\_limit} \\
adamc@544	1886 \mt{val} \; \mt{sql\_no\_limit} : \mt{sql\_limit} \\
adamc@544	1887 \mt{val} \; \mt{sql\_limit} : \mt{int} \to \mt{sql\_limit} \\
adamc@544	1888 \\
adamc@544	1889 \mt{type} \; \mt{sql\_offset} \\
adamc@544	1890 \mt{val} \; \mt{sql\_no\_offset} : \mt{sql\_offset} \\
adamc@544	1891 \mt{val} \; \mt{sql\_offset} : \mt{int} \to \mt{sql\_offset}
adamc@544	1892 \end{array}$$
adamc@544	1893
adam@1778	1894 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	1895 $$\begin{array}{l}
adam@1778	1896 \mt{con} \; \mt{sql\_expw} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type} \\
adam@1778	1897 \\
adam@1778	1898 \mt{class} \; \mt{sql\_window} :: (\{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}) \to \mt{Type} \\
adam@1778	1899 \mt{val} \; \mt{sql\_window\_normal} : \mt{sql\_window} \; \mt{sql\_exp} \\
adam@1778	1900 \mt{val} \; \mt{sql\_window\_fancy} : \mt{sql\_window} \; \mt{sql\_expw} \\
adam@1778	1901 \mt{val} \; \mt{sql\_window} : \mt{tf} ::: (\{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}) \\
adam@1778	1902 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778	1903 \hspace{.1in} \to \mt{sql\_window} \; \mt{tf} \\
adam@1778	1904 \hspace{.1in} \to \mt{tf} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778	1905 \hspace{.1in} \to \mt{sql\_expw} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778	1906 \\
adam@1778	1907 \mt{con} \; \mt{sql\_partition} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adam@1778	1908 \mt{val} \; \mt{sql\_no\_partition} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778	1909 \hspace{.1in} \to \mt{sql\_partition} \; \mt{tables} \; \mt{agg} \; \mt{exps} \\
adam@1778	1910 \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	1911 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778	1912 \hspace{.1in} \to \mt{sql\_partition} \; \mt{tables} \; \mt{agg} \; \mt{exps} \\
adam@1778	1913 \\
adam@1778	1914 \mt{con} \; \mt{sql\_window\_function} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type} \\
adam@1778	1915 \mt{val} \; \mt{sql\_window\_function} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778	1916 \hspace{.1in} \to \mt{t} ::: \mt{Type} \\
adam@1778	1917 \hspace{.1in} \to \mt{sql\_window\_function} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778	1918 \hspace{.1in} \to \mt{sql\_partition} \; \mt{tables} \; \mt{agg} \; \mt{exps} \\
adam@1778	1919 \hspace{.1in} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adam@1778	1920 \hspace{.1in} \to \mt{sql\_expw} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778	1921 \\
adam@1778	1922 \mt{val} \; \mt{sql\_window\_aggregate} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778	1923 \hspace{.1in} \to \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \\
adam@1778	1924 \hspace{.1in} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt} \\
adam@1778	1925 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778	1926 \hspace{.1in} \to \mt{sql\_window\_function} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{nt} \\
adam@1778	1927 \mt{val} \; \mt{sql\_window\_count} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778	1928 \hspace{.1in} \to \mt{sql\_window\_function} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int} \\
adam@1778	1929 \mt{val} \; \mt{sql\_rank} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778	1930 \hspace{.1in} \to \mt{sql\_window\_function} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int}
adam@1778	1931 \end{array}$$
adam@1778	1932
adamc@545	1933
adamc@545	1934 \subsubsection{DML}
adamc@545	1935
adamc@545	1936 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	1937
adamc@545	1938 $$\begin{array}{l}
adamc@545	1939 \mt{type} \; \mt{dml} \\
adamc@545	1940 \mt{val} \; \mt{dml} : \mt{dml} \to \mt{transaction} \; \mt{unit}
adamc@545	1941 \end{array}$$
adamc@545	1942
adam@1297	1943 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	1944
adam@1297	1945 $$\begin{array}{l}
adam@1297	1946 \mt{val} \; \mt{tryDml} : \mt{dml} \to \mt{transaction} \; (\mt{option} \; \mt{string})
adam@1297	1947 \end{array}$$
adam@1297	1948
adam@1797	1949 Properly typed records may be used to form $\mt{INSERT}$ commands.
adamc@545	1950 $$\begin{array}{l}
adamc@545	1951 \mt{val} \; \mt{insert} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \\
adam@1778	1952 \hspace{.1in} \to \$(\mt{map} \; (\mt{sql\_exp} \; [] \; [] \; []) \; \mt{fields}) \to \mt{dml}
adamc@545	1953 \end{array}$$
adamc@545	1954
adam@1578	1955 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	1956 $$\begin{array}{l}
adam@1380	1957 \mt{val} \; \mt{update} : \mt{unchanged} ::: \{\mt{Type}\} \to \mt{changed} :: \{\mt{Type}\} \to [\mt{changed} \sim \mt{unchanged}] \\
adam@1778	1958 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; []) \; \mt{changed}) \\
adam@1778	1959 \hspace{.1in} \to \mt{sql\_table} \; (\mt{changed} \rc \mt{unchanged}) \to \mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545	1960 \end{array}$$
adamc@545	1961
adam@1578	1962 A $\mt{DELETE}$ command is formed from a table and a $\mt{WHERE}$ clause. The above use of $\mt{T}$ is repeated.
adamc@545	1963 $$\begin{array}{l}
adam@1778	1964 \mt{val} \; \mt{delete} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \to \mt{sql\_exp} \; [\mt{T} = \mt{fields}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545	1965 \end{array}$$
adamc@545	1966
adamc@546	1967 \subsubsection{Sequences}
adamc@546	1968
adamc@546	1969 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	1970
adamc@546	1971 $$\begin{array}{l}
adamc@546	1972 \mt{type} \; \mt{sql\_sequence} \\
adamc@1085	1973 \mt{val} \; \mt{nextval} : \mt{sql\_sequence} \to \mt{transaction} \; \mt{int} \\
adamc@1085	1974 \mt{val} \; \mt{setval} : \mt{sql\_sequence} \to \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@546	1975 \end{array}$$
adamc@546	1976
adamc@546	1977
adam@1648	1978 \subsection{\label{xml}XML}
adamc@547	1979
adam@1333	1980 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	1981
adam@1642	1982 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	1983 $$\begin{array}{l}
adamc@547	1984 \mt{con} \; \mt{xml} :: \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547	1985 \end{array}$$
adamc@547	1986
adamc@547	1987 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	1988 $$\begin{array}{l}
adamc@547	1989 \mt{con} \; \mt{tag} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547	1990 \end{array}$$
adamc@547	1991
adamc@547	1992 Literal text may be injected into XML as ``CDATA.''
adamc@547	1993 $$\begin{array}{l}
adamc@547	1994 \mt{val} \; \mt{cdata} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{string} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adamc@547	1995 \end{array}$$
adamc@547	1996
adam@1358	1997 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	1998 $$\begin{array}{l}
adam@1358	1999 \mt{val} \; \mt{cdataChar} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{char} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adam@1358	2000 \end{array}$$
adam@1358	2001
adamc@547	2002 There is a function for producing an XML tree with a particular tag at its root.
adamc@547	2003 $$\begin{array}{l}
adamc@547	2004 \mt{val} \; \mt{tag} : \mt{attrsGiven} ::: \{\mt{Type}\} \to \mt{attrsAbsent} ::: \{\mt{Type}\} \to \mt{ctxOuter} ::: \{\mt{Unit}\} \to \mt{ctxInner} ::: \{\mt{Unit}\} \\
adamc@547	2005 \hspace{.1in} \to \mt{useOuter} ::: \{\mt{Type}\} \to \mt{useInner} ::: \{\mt{Type}\} \to \mt{bindOuter} ::: \{\mt{Type}\} \to \mt{bindInner} ::: \{\mt{Type}\} \\
adam@1380	2006 \hspace{.1in} \to [\mt{attrsGiven} \sim \mt{attrsAbsent}] \Rightarrow [\mt{useOuter} \sim \mt{useInner}] \Rightarrow [\mt{bindOuter} \sim \mt{bindInner}] \\
adam@1749	2007 \hspace{.1in} \Rightarrow \mt{css\_class} \\
adam@1643	2008 \hspace{.1in} \to \mt{option} \; (\mt{signal} \; \mt{css\_class}) \\
adam@1750	2009 \hspace{.1in} \to \mt{css\_style} \\
adam@1751	2010 \hspace{.1in} \to \mt{option} \; (\mt{signal} \; \mt{css\_style}) \\
adamc@787	2011 \hspace{.1in} \to \$\mt{attrsGiven} \\
adamc@547	2012 \hspace{.1in} \to \mt{tag} \; (\mt{attrsGiven} \rc \mt{attrsAbsent}) \; \mt{ctxOuter} \; \mt{ctxInner} \; \mt{useOuter} \; \mt{bindOuter} \\
adamc@547	2013 \hspace{.1in} \to \mt{xml} \; \mt{ctxInner} \; \mt{useInner} \; \mt{bindInner} \to \mt{xml} \; \mt{ctxOuter} \; (\mt{useOuter} \rc \mt{useInner}) \; (\mt{bindOuter} \rc \mt{bindInner})
adamc@547	2014 \end{array}$$
adam@1750	2015 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	2016
adam@1643	2017 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	2018
adam@1751	2019 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	2020
adamc@547	2021 Two XML fragments may be concatenated.
adamc@547	2022 $$\begin{array}{l}
adamc@547	2023 \mt{val} \; \mt{join} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{bind_1} ::: \{\mt{Type}\} \to \mt{bind_2} ::: \{\mt{Type}\} \\
adam@1380	2024 \hspace{.1in} \to [\mt{use_1} \sim \mt{bind_1}] \Rightarrow [\mt{bind_1} \sim \mt{bind_2}] \\
adamc@547	2025 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind_1} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{bind_1}) \; \mt{bind_2} \to \mt{xml} \; \mt{ctx} \; \mt{use_1} \; (\mt{bind_1} \rc \mt{bind_2})
adamc@547	2026 \end{array}$$
adamc@547	2027
adamc@547	2028 Finally, any XML fragment may be updated to ``claim'' to use more form fields than it does.
adamc@547	2029 $$\begin{array}{l}
adam@1380	2030 \mt{val} \; \mt{useMore} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{use_2} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to [\mt{use_1} \sim \mt{use_2}] \\
adamc@547	2031 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{use_2}) \; \mt{bind}
adamc@547	2032 \end{array}$$
adamc@547	2033
adam@1344	2034 We will not list here the different HTML tags and related functions from the standard library. They should be easy enough to understand from the code in \texttt{basis.urs}. The set of tags in the library is not yet claimed to be complete for HTML standards. Also note that there is currently no way for the programmer to add his own tags. It \emph{is} possible to add new tags directly to \texttt{basis.urs}, but this should only be done as a prelude to suggesting a patch to the main distribution.
adamc@547	2035
adamc@547	2036 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	2037 $$\begin{array}{l}
adam@1641	2038 \mt{val} \; \mt{error} : \mt{t} ::: \mt{Type} \to \mt{xbody} \to \mt{t}
adamc@547	2039 \end{array}$$
adamc@547	2040
adamc@549	2041
adamc@701	2042 \subsection{Client-Side Programming}
adamc@659	2043
adamc@701	2044 Ur/Web supports running code on web browsers, via automatic compilation to JavaScript.
adamc@701	2045
adamc@701	2046 \subsubsection{The Basics}
adamc@701	2047
adam@1400	2048 All of the functions in this subsection are client-side only.
adam@1400	2049
adam@1297	2050 Clients can open alert and confirm dialog boxes, in the usual annoying JavaScript way.
adamc@701	2051 $$\begin{array}{l}
adam@1297	2052 \mt{val} \; \mt{alert} : \mt{string} \to \mt{transaction} \; \mt{unit} \\
adam@1297	2053 \mt{val} \; \mt{confirm} : \mt{string} \to \mt{transaction} \; \mt{bool}
adamc@701	2054 \end{array}$$
adamc@701	2055
adamc@701	2056 Any transaction may be run in a new thread with the $\mt{spawn}$ function.
adamc@701	2057 $$\begin{array}{l}
adamc@701	2058 \mt{val} \; \mt{spawn} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit}
adamc@701	2059 \end{array}$$
adamc@701	2060
adamc@701	2061 The current thread can be paused for at least a specified number of milliseconds.
adamc@701	2062 $$\begin{array}{l}
adamc@701	2063 \mt{val} \; \mt{sleep} : \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@701	2064 \end{array}$$
adamc@701	2065
adam@1770	2066 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	2067 $$\begin{array}{l}
adamc@787	2068 \mt{val} \; \mt{onError} : (\mt{xbody} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787	2069 \mt{val} \; \mt{onFail} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787	2070 \mt{val} \; \mt{onConnectFail} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787	2071 \mt{val} \; \mt{onDisconnect} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787	2072 \mt{val} \; \mt{onServerError} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit}
adamc@787	2073 \end{array}$$
adamc@787	2074
adam@1555	2075 There are also functions to register standard document-level event handlers.
adam@1555	2076
adam@1555	2077 $$\begin{array}{l}
adam@1783	2078 \mt{val} \; \mt{onClick} : (\mt{mouseEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783	2079 \mt{val} \; \mt{onDblclick} : (\mt{mouseEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783	2080 \mt{val} \; \mt{onKeydown} : (\mt{keyEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783	2081 \mt{val} \; \mt{onKeypress} : (\mt{keyEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783	2082 \mt{val} \; \mt{onKeyup} : (\mt{keyEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783	2083 \mt{val} \; \mt{onMousedown} : (\mt{mouseEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783	2084 \mt{val} \; \mt{onMouseup} : (\mt{mouseEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit}
adam@1555	2085 \end{array}$$
adam@1555	2086
adam@1559	2087 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	2088
adam@1559	2089 $$\begin{array}{l}
adam@1559	2090 \mt{val} \; \mt{preventDefault} : \mt{transaction} \; \mt{unit} \\
adam@1559	2091 \mt{val} \; \mt{stopPropagation} : \mt{transaction} \; \mt{unit}
adam@1559	2092 \end{array}$$
adam@1559	2093
adam@1556	2094 \subsubsection{Node IDs}
adam@1556	2095
adam@1556	2096 There is an abstract type of node IDs that may be assigned to \cd{id} attributes of most HTML tags.
adam@1556	2097
adam@1556	2098 $$\begin{array}{l}
adam@1556	2099 \mt{type} \; \mt{id} \\
adam@1556	2100 \mt{val} \; \mt{fresh} : \mt{transaction} \; \mt{id}
adam@1556	2101 \end{array}$$
adam@1556	2102
adam@1785	2103 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	2104
adam@1785	2105 One further use of IDs is as handles for requesting that \emph{focus} be given to specific tags.
adam@1785	2106
adam@1785	2107 $$\begin{array}{l}
adam@1785	2108 \mt{val} \; \mt{giveFocus} : \mt{id} \to \mt{transaction} \; \mt{unit}
adam@1785	2109 \end{array}$$
adam@1556	2110
adam@1643	2111 \subsubsection{\label{signals}Functional-Reactive Page Generation}
adamc@701	2112
adamc@701	2113 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	2114
adam@1403	2115 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	2116
adamc@659	2117 $$\begin{array}{l}
adamc@659	2118 \mt{con} \; \mt{source} :: \mt{Type} \to \mt{Type} \\
adamc@659	2119 \mt{val} \; \mt{source} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{transaction} \; (\mt{source} \; \mt{t}) \\
adamc@659	2120 \mt{val} \; \mt{set} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@659	2121 \mt{val} \; \mt{get} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@659	2122 \end{array}$$
adamc@659	2123
adam@1400	2124 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	2125
adam@1608	2126 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	2127
adamc@659	2128 $$\begin{array}{l}
adamc@659	2129 \mt{con} \; \mt{signal} :: \mt{Type} \to \mt{Type} \\
adamc@659	2130 \mt{val} \; \mt{signal\_monad} : \mt{monad} \; \mt{signal} \\
adam@1608	2131 \mt{val} \; \mt{signal} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{signal} \; \mt{t} \\
adam@1608	2132 \mt{val} \; \mt{current} : \mt{t} ::: \mt{Type} \to \mt{signal} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@659	2133 \end{array}$$
adamc@659	2134
adamc@659	2135 A reactive portion of an HTML page is injected with a $\mt{dyn}$ tag, which has a signal-valued attribute $\mt{Signal}$.
adamc@659	2136
adamc@659	2137 $$\begin{array}{l}
adam@1641	2138 \mt{val} \; \mt{dyn} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to [\mt{ctx} \sim [\mt{Dyn}]] \Rightarrow \mt{unit} \\
adam@1641	2139 \hspace{.1in} \to \mt{tag} \; [\mt{Signal} = \mt{signal} \; (\mt{xml} \; ([\mt{Dyn}] \rc \mt{ctx}) \; \mt{use} \; \mt{bind})] \; ([\mt{Dyn}] \rc \mt{ctx}) \; [] \; \mt{use} \; \mt{bind}
adamc@659	2140 \end{array}$$
adamc@659	2141
adam@1648	2142 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	2143
adam@1648	2144 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	2145
adam@1786	2146 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	2147
adam@1786	2148 $$\begin{array}{l}
adam@1786	2149 \mt{val} \; \mt{active} : \mt{unit} \to \mt{tag} \; [\mt{Code} = \mt{transaction} \; \mt{xbody}] \; \mt{body} \; [] \; [] \; []
adam@1786	2150 \end{array}$$
adamc@701	2151
adamc@914	2152 \subsubsection{Remote Procedure Calls}
adamc@914	2153
adamc@914	2154 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	2155
adamc@914	2156 $$\begin{array}{l}
adamc@914	2157 \mt{val} \; \mt{rpc} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@914	2158 \end{array}$$
adamc@914	2159
adamc@701	2160 \subsubsection{Asynchronous Message-Passing}
adamc@701	2161
adamc@701	2162 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	2163
adamc@701	2164 $$\begin{array}{l}
adamc@701	2165 \mt{type} \; \mt{client} \\
adamc@701	2166 \mt{val} \; \mt{self} : \mt{transaction} \; \mt{client}
adamc@701	2167 \end{array}$$
adamc@701	2168
adamc@701	2169 \emph{Channels} are the means of message-passing. Each channel is created in the context of a client and belongs to that client; no other client may receive the channel's messages. Each channel type includes the type of values that may be sent over the channel. Sending and receiving are asynchronous, in the sense that a client need not be ready to receive a message right away. Rather, sent messages may queue up, waiting to be processed.
adamc@701	2170
adamc@701	2171 $$\begin{array}{l}
adamc@701	2172 \mt{con} \; \mt{channel} :: \mt{Type} \to \mt{Type} \\
adamc@701	2173 \mt{val} \; \mt{channel} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; (\mt{channel} \; \mt{t}) \\
adamc@701	2174 \mt{val} \; \mt{send} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@701	2175 \mt{val} \; \mt{recv} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@701	2176 \end{array}$$
adamc@701	2177
adamc@701	2178 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	2179
adamc@701	2180 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	2181
adam@1551	2182 \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	2183
adamc@659	2184
adamc@549	2185 \section{Ur/Web Syntax Extensions}
adamc@549	2186
adamc@549	2187 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	2188
adamc@549	2189 \subsection{SQL}
adamc@549	2190
adamc@786	2191 \subsubsection{\label{tables}Table Declarations}
adamc@786	2192
adamc@788	2193 $\mt{table}$ declarations may include constraints, via these grammar rules.
adamc@788	2194 $$\begin{array}{rrcll}
adam@1594	2195 \textrm{Declarations} & d &::=& \mt{table} \; x : c \; [pk[,]] \; cts \mid \mt{view} \; x = V \\
adamc@788	2196 \textrm{Primary key constraints} & pk &::=& \mt{PRIMARY} \; \mt{KEY} \; K \\
adam@1722	2197 \textrm{Keys} & K &::=& f \mid (f, (f,)^+) \mid \{\{e\}\} \\
adamc@788	2198 \textrm{Constraint sets} & cts &::=& \mt{CONSTRAINT} f \; ct \mid cts, cts \mid \{\{e\}\} \\
adamc@788	2199 \textrm{Constraints} & ct &::=& \mt{UNIQUE} \; K \mid \mt{CHECK} \; E \\
adamc@788	2200 &&& \mid \mt{FOREIGN} \; \mt{KEY} \; K \; \mt{REFERENCES} \; F \; (K) \; [\mt{ON} \; \mt{DELETE} \; pr] \; [\mt{ON} \; \mt{UPDATE} \; pr] \\
adamc@788	2201 \textrm{Foreign tables} & F &::=& x \mid \{\{e\}\} \\
adam@1594	2202 \textrm{Propagation modes} & pr &::=& \mt{NO} \; \mt{ACTION} \mid \mt{RESTRICT} \mid \mt{CASCADE} \mid \mt{SET} \; \mt{NULL} \\
adam@1594	2203 \textrm{View expressions} & V &::=& Q \mid \{e\}
adamc@788	2204 \end{array}$$
adamc@788	2205
adamc@788	2206 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	2207
adamc@788	2208
adamc@549	2209 \subsubsection{Queries}
adamc@549	2210
adamc@550	2211 Queries $Q$ are added to the rules for expressions $e$.
adamc@550	2212
adamc@549	2213 $$\begin{array}{rrcll}
adam@1684	2214 \textrm{Queries} & Q &::=& (q \; [\mt{ORDER} \; \mt{BY} \; O] \; [\mt{LIMIT} \; N] \; [\mt{OFFSET} \; N]) \\
adamc@1085	2215 \textrm{Pre-queries} & q &::=& \mt{SELECT} \; [\mt{DISTINCT}] \; P \; \mt{FROM} \; F,^+ \; [\mt{WHERE} \; E] \; [\mt{GROUP} \; \mt{BY} \; p,^+] \; [\mt{HAVING} \; E] \\
adamc@1085	2216 &&& \mid q \; R \; q \mid \{\{\{e\}\}\} \\
adam@1684	2217 \textrm{Relational operators} & R &::=& \mt{UNION} \mid \mt{INTERSECT} \mid \mt{EXCEPT} \\
adam@1778	2218 \textrm{$\mt{ORDER \; BY}$ items} & O &::=& \mt{RANDOM} [()] \mid \hat{E} \; [o] \mid \hat{E} \; [o], O
adamc@549	2219 \end{array}$$
adamc@549	2220
adamc@549	2221 $$\begin{array}{rrcll}
adamc@549	2222 \textrm{Projections} & P &::=& \ast & \textrm{all columns} \\
adamc@549	2223 &&& p,^+ & \textrm{particular columns} \\
adamc@549	2224 \textrm{Pre-projections} & p &::=& t.f & \textrm{one column from a table} \\
adamc@558	2225 &&& t.\{\{c\}\} & \textrm{a record of columns from a table (of kind $\{\mt{Type}\}$)} \\
adam@1627	2226 &&& t.* & \textrm{all columns from a table} \\
adam@1778	2227 &&& \hat{E} \; [\mt{AS} \; f] & \textrm{expression column} \\
adamc@549	2228 \textrm{Table names} & t &::=& x & \textrm{constant table name (automatically capitalized)} \\
adamc@549	2229 &&& X & \textrm{constant table name} \\
adamc@549	2230 &&& \{\{c\}\} & \textrm{computed table name (of kind $\mt{Name}$)} \\
adamc@549	2231 \textrm{Column names} & f &::=& X & \textrm{constant column name} \\
adamc@549	2232 &&& \{c\} & \textrm{computed column name (of kind $\mt{Name}$)} \\
adamc@549	2233 \textrm{Tables} & T &::=& x & \textrm{table variable, named locally by its own capitalization} \\
adam@1756	2234 &&& x \; \mt{AS} \; X & \textrm{table variable, with local name} \\
adam@1756	2235 &&& x \; \mt{AS} \; \{c\} & \textrm{table variable, with computed local name} \\
adamc@549	2236 &&& \{\{e\}\} \; \mt{AS} \; t & \textrm{computed table expression, with local name} \\
adam@1756	2237 &&& \{\{e\}\} \; \mt{AS} \; \{c\} & \textrm{computed table expression, with computed local name} \\
adamc@1085	2238 \textrm{$\mt{FROM}$ items} & F &::=& T \mid \{\{e\}\} \mid F \; J \; \mt{JOIN} \; F \; \mt{ON} \; E \\
adamc@1085	2239 &&& \mid F \; \mt{CROSS} \; \mt{JOIN} \ F \\
adamc@1193	2240 &&& \mid (Q) \; \mt{AS} \; t \\
adamc@1085	2241 \textrm{Joins} & J &::=& [\mt{INNER}] \\
adamc@1085	2242 &&& \mid [\mt{LEFT} \mid \mt{RIGHT} \mid \mt{FULL}] \; [\mt{OUTER}] \\
adam@1587	2243 \textrm{SQL expressions} & E &::=& t.f & \textrm{column references} \\
adamc@549	2244 &&& X & \textrm{named expression references} \\
adam@1490	2245 &&& \{[e]\} & \textrm{injected native Ur expressions} \\
adam@1778	2246 &&& \{e\} & \textrm{computed expressions, probably using $\mt{sql\_exp}$ directly} \\
adamc@549	2247 &&& \mt{TRUE} \mid \mt{FALSE} & \textrm{boolean constants} \\
adamc@549	2248 &&& \ell & \textrm{primitive type literals} \\
adamc@549	2249 &&& \mt{NULL} & \textrm{null value (injection of $\mt{None}$)} \\
adamc@549	2250 &&& E \; \mt{IS} \; \mt{NULL} & \textrm{nullness test} \\
adam@1602	2251 &&& \mt{COALESCE}(E, E) & \textrm{take first non-null value} \\
adamc@549	2252 &&& n & \textrm{nullary operators} \\
adamc@549	2253 &&& u \; E & \textrm{unary operators} \\
adamc@549	2254 &&& E \; b \; E & \textrm{binary operators} \\
adam@1778	2255 &&& \mt{COUNT}(\ast) & \textrm{count number of rows} \\
adam@1778	2256 &&& a(E) & \textrm{other aggregate function} \\
adam@1573	2257 &&& \mt{IF} \; E \; \mt{THEN} \; E \; \mt{ELSE} \; E & \textrm{conditional} \\
adam@1778	2258 &&& (Q) & \textrm{subquery (must return a single expression column)} \\
adamc@549	2259 &&& (E) & \textrm{explicit precedence} \\
adamc@549	2260 \textrm{Nullary operators} & n &::=& \mt{CURRENT\_TIMESTAMP} \\
adamc@549	2261 \textrm{Unary operators} & u &::=& \mt{NOT} \\
adam@1688	2262 \textrm{Binary operators} & b &::=& \mt{AND} \mid \mt{OR} \mid = \mid \neq \mid < \mid \leq \mid > \mid \geq \\
adamc@1188	2263 \textrm{Aggregate functions} & a &::=& \mt{COUNT} \mid \mt{AVG} \mid \mt{SUM} \mid \mt{MIN} \mid \mt{MAX} \\
adam@1543	2264 \textrm{Directions} & o &::=& \mt{ASC} \mid \mt{DESC} \mid \{e\} \\
adamc@549	2265 \textrm{SQL integer} & N &::=& n \mid \{e\} \\
adam@1778	2266 \textrm{Windowable expressions} & \hat{E} &::=& E \\
adam@1778	2267 &&& w \; [\mt{OVER} \; ( & \textrm{(Postgres only)} \\
adam@1778	2268 &&& \hspace{.1in} [\mt{PARTITION} \; \mt{BY} \; E] \\
adam@1778	2269 &&& \hspace{.1in} [\mt{ORDER} \; \mt{BY} \; O])] \\
adam@1778	2270 \textrm{Window function} & w &::=& \mt{RANK}() \\
adam@1778	2271 &&& \mt{COUNT}(*) \\
adam@1778	2272 &&& a(E)
adamc@549	2273 \end{array}$$
adamc@549	2274
adamc@1085	2275 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	2276
adam@1683	2277 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	2278
adamc@550	2279 \subsubsection{DML}
adamc@550	2280
adamc@550	2281 DML commands $D$ are added to the rules for expressions $e$.
adamc@550	2282
adamc@550	2283 $$\begin{array}{rrcll}
adamc@550	2284 \textrm{Commands} & D &::=& (\mt{INSERT} \; \mt{INTO} \; T^E \; (f,^+) \; \mt{VALUES} \; (E,^+)) \\
adamc@550	2285 &&& (\mt{UPDATE} \; T^E \; \mt{SET} \; (f = E,)^+ \; \mt{WHERE} \; E) \\
adamc@550	2286 &&& (\mt{DELETE} \; \mt{FROM} \; T^E \; \mt{WHERE} \; E) \\
adamc@550	2287 \textrm{Table expressions} & T^E &::=& x \mid \{\{e\}\}
adamc@550	2288 \end{array}$$
adamc@550	2289
adamc@550	2290 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	2291
adamc@551	2292 \subsection{XML}
adamc@551	2293
adamc@551	2294 XML fragments $L$ are added to the rules for expressions $e$.
adamc@551	2295
adamc@551	2296 $$\begin{array}{rrcll}
adamc@551	2297 \textrm{XML fragments} & L &::=& \texttt{<xml/>} \mid \texttt{<xml>}l^*\texttt{</xml>} \\
adamc@551	2298 \textrm{XML pieces} & l &::=& \textrm{text} & \textrm{cdata} \\
adamc@551	2299 &&& \texttt{<}g\texttt{/>} & \textrm{tag with no children} \\
adamc@551	2300 &&& \texttt{<}g\texttt{>}l^*\texttt{</}x\texttt{>} & \textrm{tag with children} \\
adamc@559	2301 &&& \{e\} & \textrm{computed XML fragment} \\
adamc@559	2302 &&& \{[e]\} & \textrm{injection of an Ur expression, via the $\mt{Top}.\mt{txt}$ function} \\
adamc@551	2303 \textrm{Tag} & g &::=& h \; (x = v)^* \\
adamc@551	2304 \textrm{Tag head} & h &::=& x & \textrm{tag name} \\
adamc@551	2305 &&& h\{c\} & \textrm{constructor parameter} \\
adamc@551	2306 \textrm{Attribute value} & v &::=& \ell & \textrm{literal value} \\
adamc@551	2307 &&& \{e\} & \textrm{computed value} \\
adamc@551	2308 \end{array}$$
adamc@551	2309
adam@1751	2310 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	2311
adam@1751	2312 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	2313
adamc@1198	2314 \section{\label{structure}The Structure of Web Applications}
adamc@553	2315
adam@1797	2316 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	2317
adam@1532	2318 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	2319
adam@1787	2320 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	2321
adam@1370	2322 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	2323
adamc@553	2324 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	2325
adamc@553	2326 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	2327
adam@1653	2328 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	2329 \begin{itemize}
adam@1653	2330 \item Functions are disallowed, since there is no obvious way to serialize them safely.
adam@1653	2331 \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	2332 \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	2333 \end{itemize}
adamc@553	2334
adamc@660	2335 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	2336
adamc@789	2337 \medskip
adamc@789	2338
adam@1347	2339 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	2340
adamc@789	2341 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	2342
adam@1348	2343 \subsection{Tasks}
adam@1348	2344
adam@1348	2345 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	2346
adam@1348	2347 $$\begin{array}{l}
adam@1348	2348 \mt{con} \; \mt{task\_kind} :: \mt{Type} \to \mt{Type} \\
adam@1348	2349 \mt{val} \; \mt{initialize} : \mt{task\_kind} \; \mt{unit} \\
adam@1349	2350 \mt{val} \; \mt{clientLeaves} : \mt{task\_kind} \; \mt{client} \\
adam@1349	2351 \mt{val} \; \mt{periodic} : \mt{int} \to \mt{task\_kind} \; \mt{unit}
adam@1348	2352 \end{array}$$
adam@1348	2353
adam@1348	2354 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	2355
adam@1348	2356 The currently supported task kinds are:
adam@1348	2357 \begin{itemize}
adam@1349	2358 \item $\mt{initialize}$: Code that is run when the application starts up.
adam@1348	2359 \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	2360 \item $\mt{periodic} \; n$: Code that is run when the application starts up and then every $n$ seconds thereafter.
adam@1348	2361 \end{itemize}
adam@1348	2362
adamc@553	2363
adamc@897	2364 \section{The Foreign Function Interface}
adamc@897	2365
adamc@897	2366 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	2367
adamc@897	2368 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	2369
adamc@897	2370 \begin{itemize}
adamc@897	2371 \item \texttt{clientOnly Module.ident} registers a value as being allowed only in client-side code.
adamc@897	2372 \item \texttt{clientToServer Module.ident} declares a type as OK to marshal between clients and servers. By default, abstract FFI types are not allowed to be marshalled, since your library might be maintaining invariants that the simple serialization code doesn't check.
adam@1699	2373 \item \texttt{effectful Module.ident} registers a function that can have side effects. It is important to remember to use this directive for each such function, or else the optimizer might change program semantics. (Note that merely assigning a function a \texttt{transaction}-based type does not mark it as effectful in this way!)
adamc@897	2374 \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	2375 \item \texttt{include FILE} requests inclusion of a C header file.
adamc@897	2376 \item \texttt{jsFunc Module.ident=name} gives a mapping from an Ur name for a value to a JavaScript name.
adamc@897	2377 \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	2378 \item \texttt{script URL} requests inclusion of a JavaScript source file within application HTML.
adamc@897	2379 \item \texttt{serverOnly Module.ident} registers a value as being allowed only in server-side code.
adamc@897	2380 \end{itemize}
adamc@897	2381
adamc@897	2382 \subsection{Writing C FFI Code}
adamc@897	2383
adamc@897	2384 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	2385
adamc@897	2386 \begin{itemize}
adamc@897	2387 \item Primitive types defined in \texttt{Basis} are themselves using the standard FFI interface, so you may refer to them like \texttt{uw\_Basis\_t}. See \texttt{include/types.h} for their definitions.
adamc@897	2388 \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	2389 \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	2390 \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	2391 \end{itemize}
adamc@897	2392
adamc@897	2393 The C FFI version of a Ur function with type \texttt{T1 -> ... -> TN -> R} or \texttt{T1 -> ... -> TN -> transaction R} has a C prototype like \texttt{R uw\_Module\_ident(uw\_context, T1, ..., TN)}. Only functions with types of the second form may have side effects. \texttt{uw\_context} is the type of state that persists across handling a client request. Many functions that operate on contexts are prototyped in \texttt{include/urweb.h}. Most should only be used internally by the compiler. A few are useful in general FFI implementation:
adamc@897	2394 \begin{itemize}
adamc@897	2395 \item \begin{verbatim}
adamc@897	2396 void uw_error(uw_context, failure_kind, const char *fmt, ...);
adamc@897	2397 \end{verbatim}
adamc@897	2398 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	2399
adam@1329	2400 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	2401
adamc@897	2402 \item \begin{verbatim}
adam@1469	2403 void uw_set_error_message(uw_context, const char *fmt, ...);
adam@1469	2404 \end{verbatim}
adam@1469	2405 This simpler form of \texttt{uw\_error()} saves an error message without immediately aborting execution.
adam@1469	2406
adam@1469	2407 \item \begin{verbatim}
adamc@897	2408 void uw_push_cleanup(uw_context, void (func)(void ), void *arg);
adamc@897	2409 void uw_pop_cleanup(uw_context);
adamc@897	2410 \end{verbatim}
adam@1329	2411 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	2412
adam@1329	2413 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	2414
adamc@897	2415 \item \begin{verbatim}
adamc@897	2416 void *uw_malloc(uw_context, size_t);
adamc@897	2417 \end{verbatim}
adam@1329	2418 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	2419
adam@1329	2420 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	2421
adamc@897	2422 \item \begin{verbatim}
adamc@897	2423 typedef void (uw_callback)(void );
adam@1328	2424 typedef void (uw_callback_with_retry)(void , int will_retry);
adamc@897	2425 void uw_register_transactional(uw_context, void *data, uw_callback commit,
adam@1328	2426 uw_callback rollback, uw_callback_with_retry free);
adamc@897	2427 \end{verbatim}
adam@1328	2428 All side effects in Ur/Web programs need to be compatible with transactions, such that any set of actions can be undone at any time. Thus, you should not perform actions with non-local side effects directly; instead, register handlers to be called when the current transaction is committed or rolled back. The arguments here give an arbitary piece of data to be passed to callbacks, a function to call on commit, a function to call on rollback, and a function to call afterward in either case to clean up any allocated resources. A rollback handler may be called after the associated commit handler has already been called, if some later part of the commit process fails. A free handler is told whether the runtime system expects to retry the current page request after rollback finishes.
adamc@897	2429
adamc@1085	2430 Any of the callbacks may be \texttt{NULL}. To accommodate some stubbornly non-transactional real-world actions like sending an e-mail message, Ur/Web treats \texttt{NULL} \texttt{rollback} callbacks specially. When a transaction commits, all \texttt{commit} actions that have non-\texttt{NULL} rollback actions are tried before any \texttt{commit} actions that have \texttt{NULL} rollback actions. Thus, if a single execution uses only one non-transactional action, and if that action never fails partway through its execution while still causing an observable side effect, then Ur/Web can maintain the transactional abstraction.
adamc@1085	2431
adam@1329	2432 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	2433
adam@1329	2434 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	2435
adam@1469	2436 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	2437
adamc@1085	2438 \item \begin{verbatim}
adamc@1085	2439 void uw_get_global(uw_context, char name);
adamc@1085	2440 void uw_set_global(uw_context, char name, void data, uw_callback free);
adamc@1085	2441 \end{verbatim}
adam@1329	2442 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	2443
adamc@897	2444 \end{itemize}
adamc@897	2445
adamc@897	2446 \subsection{Writing JavaScript FFI Code}
adamc@897	2447
adamc@897	2448 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	2449
adamc@897	2450 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	2451
adamc@897	2452 \begin{itemize}
adamc@897	2453 \item Integers, floats, strings, characters, and booleans are represented in the usual JavaScript way.
adam@1644	2454 \item Ur functions are represented in an unspecified way. This means that you should not rely on any details of function representation. Named FFI functions are represented as JavaScript functions with as many arguments as their Ur types specify. To call a non-FFI function \texttt{f} on argument \texttt{x}, run \texttt{execF(f, x)}. To lift a normal JavaScript function \cd{f} into an Ur/Web JavaScript function, run \cd{flift(f)}.
adamc@897	2455 \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	2456 \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	2457 \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	2458 \item As in the C FFI, all abstract types of program syntax are implemented with strings in JavaScript.
adam@1844	2459 \item A value of Ur type \texttt{transaction t} is represented in the same way as for \texttt{unit -> t}.
adamc@897	2460 \end{itemize}
adamc@897	2461
adam@1644	2462 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	2463
adam@1644	2464 \begin{itemize}
adam@1644	2465 \item Sources should be treated as an abstract type, manipulated via:
adam@1644	2466 \begin{itemize}
adam@1644	2467 \item \cd{sc(v)}, to create a source initialized to \cd{v}
adam@1644	2468 \item \cd{sg(s)}, to retrieve the current value of source \cd{s}
adam@1644	2469 \item \cd{sv(s, v)}, to set source \cd{s} to value \cd{v}
adam@1644	2470 \end{itemize}
adam@1644	2471
adam@1644	2472 \item Signals should be treated as an abstract type, manipulated via:
adam@1644	2473 \begin{itemize}
adam@1644	2474 \item \cd{sr(v)} and \cd{sb(s, f)}, the ``return'' and ``bind'' monad operators, respectively
adam@1644	2475 \item \cd{ss(s)}, to produce the signal corresponding to source \cd{s}
adam@1644	2476 \item \cd{scur(s)}, to get the current value of signal \cd{s}
adam@1644	2477 \end{itemize}
adam@1644	2478
adam@1644	2479 \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	2480
adam@1702	2481 \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	2482
adam@1644	2483 \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	2484 \end{itemize}
adamc@897	2485
adam@1833	2486 \subsection{Introducing New HTML Tags}
adam@1833	2487
adam@1833	2488 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	2489
adam@1833	2490 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	2491
adamc@897	2492
adamc@552	2493 \section{Compiler Phases}
adamc@552	2494
adamc@552	2495 The Ur/Web compiler is unconventional in that it relies on a kind of \emph{heuristic compilation}. Not all valid programs will compile successfully. Informally, programs fail to compile when they are ``too higher order.'' Compiler phases do their best to eliminate different kinds of higher order-ness, but some programs just won't compile. This is a trade-off for producing very efficient executables. Compiled Ur/Web programs use native C representations and require no garbage collection.
adamc@552	2496
adamc@552	2497 In this section, we step through the main phases of compilation, noting what consequences each phase has for effective programming.
adamc@552	2498
adamc@552	2499 \subsection{Parse}
adamc@552	2500
adamc@552	2501 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	2502
adamc@552	2503 \subsection{Elaborate}
adamc@552	2504
adamc@552	2505 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	2506
adam@1378	2507 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	2508
adamc@552	2509 \subsection{Unnest}
adamc@552	2510
adamc@552	2511 Named local function definitions are moved to the top level, to avoid the need to generate closures.
adamc@552	2512
adamc@552	2513 \subsection{Corify}
adamc@552	2514
adamc@552	2515 Module system features are compiled away, through inlining of functor definitions at application sites. Afterward, most abstraction boundaries are broken, facilitating optimization.
adamc@552	2516
adamc@552	2517 \subsection{Especialize}
adamc@552	2518
adam@1356	2519 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	2520
adamc@552	2521 \subsection{Untangle}
adamc@552	2522
adam@1797	2523 Remove unnecessary mutual recursion, splitting recursive groups into strongly connected components.
adamc@552	2524
adamc@552	2525 \subsection{Shake}
adamc@552	2526
adamc@552	2527 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	2528
adamc@661	2529 \subsection{Rpcify}
adamc@661	2530
adamc@661	2531 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	2532
adamc@661	2533 \subsection{Untangle, Shake}
adamc@661	2534
adamc@661	2535 Repeat these simplifications.
adamc@661	2536
adamc@553	2537 \subsection{\label{tag}Tag}
adamc@552	2538
adamc@552	2539 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	2540
adamc@552	2541 \subsection{Reduce}
adamc@552	2542
adamc@552	2543 Apply definitional equality rules to simplify the program as much as possible. This effectively includes inlining of every non-recursive definition.
adamc@552	2544
adamc@552	2545 \subsection{Unpoly}
adamc@552	2546
adamc@552	2547 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	2548
adamc@552	2549 \subsection{Specialize}
adamc@552	2550
adamc@558	2551 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	2552
adamc@552	2553 \subsection{Shake}
adamc@552	2554
adamc@558	2555 Here the compiler repeats the earlier Shake phase.
adamc@552	2556
adamc@552	2557 \subsection{Monoize}
adamc@552	2558
adamc@552	2559 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	2560
adamc@552	2561 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	2562
adamc@552	2563 \subsection{MonoOpt}
adamc@552	2564
adamc@552	2565 Simple algebraic laws are applied to simplify the program, focusing especially on efficient imperative generation of HTML pages.
adamc@552	2566
adamc@552	2567 \subsection{MonoUntangle}
adamc@552	2568
adamc@552	2569 Unnecessary mutual recursion is broken up again.
adamc@552	2570
adamc@552	2571 \subsection{MonoReduce}
adamc@552	2572
adamc@552	2573 Equivalents of the definitional equality rules are applied to simplify programs, with inlining again playing a major role.
adamc@552	2574
adamc@552	2575 \subsection{MonoShake, MonoOpt}
adamc@552	2576
adamc@552	2577 Unneeded declarations are removed, and basic optimizations are repeated.
adamc@552	2578
adamc@552	2579 \subsection{Fuse}
adamc@552	2580
adamc@552	2581 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	2582
adamc@552	2583 \subsection{MonoUntangle, MonoShake}
adamc@552	2584
adamc@552	2585 Fuse often creates more opportunities to remove spurious mutual recursion.
adamc@552	2586
adamc@552	2587 \subsection{Pathcheck}
adamc@552	2588
adamc@552	2589 The compiler checks that no link or action name has been used more than once.
adamc@552	2590
adamc@552	2591 \subsection{Cjrize}
adamc@552	2592
adamc@552	2593 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	2594
adamc@552	2595 \subsection{C Compilation and Linking}
adamc@552	2596
adam@1523	2597 The output of the last phase is pretty-printed as C source code and passed to the C compiler.
adamc@552	2598
adamc@552	2599
as@1564	2600 \end{document}

Mercurial > urweb

annotate doc/manual.tex @ 1844:2c5e6f78560c