Ur/Web: doc/manual.tex annotate

annotate doc/manual.tex @ 1891:779c390382b9

Manual: add a pointer to background reading on inference rule notation

author	Adam Chlipala <adam@chlipala.net>
date	Sun, 17 Nov 2013 07:54:59 -0500
parents	a5b08bdfa450
children	afdc823563de 44f607a7f4cd

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.
adam@1881	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/urweb\_cpp.h} shows examples of the C support functions that are required of any type that may be marshalled. These include \texttt{attrify}, \texttt{urlify}, and \texttt{unurlify} functions.
adam@1816	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@1878	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. This is the default behavior for \texttt{transaction}-based types.
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}.
adam@1881	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/urweb\_cpp.h} and \texttt{src/c/urweb.c} for examples of C headers and implementations for FFI modules. In general, every type or value \texttt{Module.ident} becomes \texttt{uw\_Module\_ident} in C.
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@1850	155 \item \texttt{clients}: maximum number of simultaneous connections to one application by web clients waiting for new asynchronous messages sent with \texttt{Basis.send}
adam@1850	156 \item \texttt{database}: maximum size of a database file (currently only used by SQLite, which interprets the parameter as a number of pages, where page size is itself a quantity configurable in SQLite)
adam@1309	157 \item \texttt{deltas}: maximum number of messages sendable in a single request handler with \texttt{Basis.send}
adam@1309	158 \item \texttt{globals}: maximum number of global variables that FFI libraries may set in a single request context
adam@1309	159 \item \texttt{headers}: maximum size (in bytes) of per-request buffer used to hold HTTP headers for generated pages
adam@1797	160 \item \texttt{heap}: maximum size (in bytes) of per-request heap for dynamically allocated data
adam@1309	161 \item \texttt{inputs}: maximum number of top-level form fields per request
adam@1309	162 \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	163 \item \texttt{page}: maximum size (in bytes) of per-request buffer used to hold HTML content of generated pages
adam@1309	164 \item \texttt{script}: maximum size (in bytes) of per-request buffer used to hold JavaScript content of generated pages
adam@1309	165 \item \texttt{subinputs}: maximum number of form fields per request, excluding top-level fields
adam@1309	166 \item \texttt{time}: maximum running time of a single page request, in units of approximately 0.1 seconds
adam@1309	167 \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	168 \end{itemize}
adam@1523	169 \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	170 \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	171 \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	172 \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	173 \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	174 \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	175 \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	176 \item \texttt{prefix PREFIX} sets the prefix included before every URI within the generated application. The default is \texttt{/}.
adamc@783	177 \item \texttt{profile} generates an executable that may be used with gprof.
adam@1752	178 \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	179 \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	180 \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	181 \item \texttt{serverOnly Module.ident} registers an FFI function or transaction that may only be run on the server.
adamc@1164	182 \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	183 \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	184 \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	185 \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	186 \end{itemize}
adamc@701	187
adamc@701	188
adamc@557	189 \subsection{Building an Application}
adamc@557	190
adamc@557	191 To compile project \texttt{P.urp}, simply run
adamc@557	192 \begin{verbatim}
adamc@557	193 urweb P
adamc@557	194 \end{verbatim}
adamc@1198	195 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	196
adamc@557	197 To time how long the different compiler phases run, without generating an executable, run
adamc@557	198 \begin{verbatim}
adamc@557	199 urweb -timing P
adamc@557	200 \end{verbatim}
adamc@557	201
adamc@1086	202 To stop the compilation process after type-checking, run
adamc@1086	203 \begin{verbatim}
adamc@1086	204 urweb -tc P
adamc@1086	205 \end{verbatim}
adam@1530	206 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	207
adam@1745	208 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	209
adam@1723	210 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	211
adamc@1170	212 To output information relevant to CSS stylesheets (and not finish regular compilation), run
adamc@1170	213 \begin{verbatim}
adamc@1170	214 urweb -css P
adamc@1170	215 \end{verbatim}
adamc@1170	216 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	217
adam@1733	218 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	219 \begin{verbatim}
adam@1733	220 urweb daemon start
adam@1733	221 \end{verbatim}
adam@1733	222 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	223 \begin{verbatim}
adam@1733	224 urweb daemon stop
adam@1733	225 \end{verbatim}
adam@1733	226 Communication happens via a UNIX domain socket in file \cd{.urweb\_daemon} in the working directory.
adam@1733	227
adam@1733	228 \medskip
adam@1733	229
adamc@896	230 Some other command-line parameters are accepted:
adamc@896	231 \begin{itemize}
ezyang@1739	232 \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	233
adam@1875	234 \item \texttt{-ccompiler <PROGRAM>}: Select an alternative C compiler to call with command lines in compiling Ur/Web applications. (It's possible to set the default compiler as part of the \texttt{configure} process, but it may sometimes be useful to override the default.)
adam@1875	235
adamc@896	236 \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	237
adamc@896	238 \item \texttt{-dbms [postgres\|mysql\|sqlite]}: Sets the database backend to use.
adamc@896	239 \begin{itemize}
adamc@896	240 \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	241
adamc@896	242 A command sequence like this can initialize a Postgres database, using a file \texttt{app.sql} generated by the compiler:
adamc@896	243 \begin{verbatim}
adamc@896	244 createdb app
adamc@896	245 psql -f app.sql app
adamc@896	246 \end{verbatim}
adamc@896	247
adamc@896	248 \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	249
adamc@896	250 A command sequence like this can initialize a MySQL database:
adamc@896	251 \begin{verbatim}
adamc@896	252 echo "CREATE DATABASE app" \| mysql
adamc@896	253 mysql -D app <app.sql
adamc@896	254 \end{verbatim}
adamc@896	255
adamc@896	256 \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	257
adamc@896	258 A command like this can initialize an SQLite database:
adamc@896	259 \begin{verbatim}
adamc@896	260 sqlite3 path/to/database/file <app.sql
adamc@896	261 \end{verbatim}
adamc@896	262 \end{itemize}
adamc@896	263
adam@1693	264 \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	265
adam@1309	266 \item \texttt{-limit class num}: Equivalent to the \texttt{limit} directive from \texttt{.urp} files
adam@1309	267
adam@1850	268 \item \texttt{-moduleOf FILENAME}: Prints the Ur/Web module name corresponding to source file \texttt{FILENAME}, exiting immediately afterward.
adam@1850	269
adamc@896	270 \item \texttt{-output FILENAME}: Set where the application executable is written.
adamc@896	271
adamc@1127	272 \item \texttt{-path NAME VALUE}: Set the value of path variable \texttt{\$NAME} to \texttt{VALUE}, for use in \texttt{.urp} files.
adamc@1127	273
adam@1335	274 \item \texttt{-prefix PREFIX}: Equivalent to the \texttt{prefix} directive from \texttt{.urp} files
adam@1335	275
adam@1875	276 \item \texttt{-print-ccompiler}: Print the C compiler being used.
adam@1875	277
adam@1753	278 \item \texttt{-protocol [http\|cgi\|fastcgi\|static]}: Set the protocol that the generated application speaks.
adamc@896	279 \begin{itemize}
adamc@896	280 \item \texttt{http}: This is the default. It is for building standalone web servers that can be accessed by web browsers directly.
adamc@896	281
adamc@896	282 \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	283
adamc@896	284 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	285 \begin{verbatim}
adamc@896	286 ScriptAlias /Hello /path/to/hello.exe
adamc@896	287 \end{verbatim}
adamc@896	288
adamc@1163	289 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	290 \begin{verbatim}
adamc@1163	291 Options +ExecCGI
adamc@1163	292 AddHandler cgi-script .exe
adamc@1163	293 \end{verbatim}
adamc@1163	294
adamc@1163	295 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	296 \begin{verbatim}
adamc@1163	297 prefix /dir/script.exe/
adamc@1163	298 \end{verbatim}
adamc@1163	299
adamc@1163	300 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	301
adamc@1164	302 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	303
adamc@896	304 \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	305
adamc@896	306 To configure a FastCGI program with Apache, one could combine the above \texttt{ScriptAlias} line with a line like this:
adamc@896	307 \begin{verbatim}
adamc@896	308 FastCgiServer /path/to/hello.exe -idle-timeout 99999
adamc@896	309 \end{verbatim}
adamc@896	310 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	311
adam@1753	312 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	313
adamc@896	314 Here is some lighttpd configuration for the same application.
adamc@896	315 \begin{verbatim}
adamc@896	316 fastcgi.server = (
adamc@896	317 "/Hello/" =>
adamc@896	318 (( "bin-path" => "/path/to/hello.exe",
adamc@896	319 "socket" => "/tmp/hello",
adamc@896	320 "check-local" => "disable",
adamc@896	321 "docroot" => "/",
adamc@896	322 "max-procs" => "1"
adamc@896	323 ))
adamc@896	324 )
adamc@896	325 \end{verbatim}
adamc@896	326 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	327
adamc@896	328 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	329
adam@1509	330 \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	331 \end{itemize}
adamc@896	332
adamc@1127	333 \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	334
adamc@1164	335 \item \texttt{-sigfile PATH}: Same as the \texttt{sigfile} directive in \texttt{.urp} files
adamc@1164	336
adamc@896	337 \item \texttt{-sql FILENAME}: Set where a database set-up SQL script is written.
adamc@1095	338
adamc@1095	339 \item \texttt{-static}: Link the runtime system statically. The default is to link against dynamic libraries.
adamc@896	340 \end{itemize}
adamc@896	341
adam@1297	342 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	343
adam@1509	344 \subsection{Tutorial Formatting}
adam@1509	345
adam@1509	346 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	347
adam@1509	348 These input files follow normal Ur syntax, with a few exceptions:
adam@1509	349 \begin{itemize}
adam@1509	350 \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	351 \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	352 \item A comment like \cd{(* * HEADING *)} introduces a section heading, with text \cd{HEADING} of your choice.
adam@1509	353 \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	354 \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	355 \end{itemize}
adam@1509	356
adam@1509	357 A word of warning: as for demo generation, tutorial generation calls Emacs to syntax-highlight Ur code.
adam@1509	358
adam@1522	359 \subsection{Run-Time Options}
adam@1522	360
adam@1522	361 Compiled applications consult a few environment variables to modify their behavior:
adam@1522	362
adam@1522	363 \begin{itemize}
adam@1522	364 \item \cd{URWEB\_NUM\_THREADS}: alternative to the \cd{-t} command-line argument (currently used only by FastCGI)
adam@1522	365 \item \cd{URWEB\_STACK\_SIZE}: size of per-thread stacks, in bytes
as@1564	366 \item \cd{URWEB\_PQ\_CON}: when using PostgreSQL, overrides the compiled-in connection string
adam@1522	367 \end{itemize}
adam@1522	368
adam@1509	369
adamc@529	370 \section{Ur Syntax}
adamc@529	371
adamc@784	372 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	373
adamc@524	374 \subsection{Lexical Conventions}
adamc@524	375
adamc@524	376 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	377
adamc@524	378 \begin{center}
adamc@524	379 \begin{tabular}{rl}
adamc@524	380 \textbf{\LaTeX} & \textbf{ASCII} \\
adamc@524	381 $\to$ & \cd{->} \\
adam@1687	382 $\longrightarrow$ & \cd{-{}->} \\
adamc@524	383 $\times$ & \cd{*} \\
adamc@524	384 $\lambda$ & \cd{fn} \\
adamc@524	385 $\Rightarrow$ & \cd{=>} \\
adamc@652	386 $\Longrightarrow$ & \cd{==>} \\
adamc@529	387 $\neq$ & \cd{<>} \\
adamc@529	388 $\leq$ & \cd{<=} \\
adamc@529	389 $\geq$ & \cd{>=} \\
adamc@524	390 \\
adamc@524	391 $x$ & Normal textual identifier, not beginning with an uppercase letter \\
adamc@525	392 $X$ & Normal textual identifier, beginning with an uppercase letter \\
adamc@524	393 \end{tabular}
adamc@524	394 \end{center}
adamc@524	395
adamc@525	396 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	397
adamc@873	398 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	399
adamc@527	400 This version of the manual doesn't include operator precedences; see \texttt{src/urweb.grm} for that.
adamc@527	401
adam@1297	402 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	403
adamc@552	404 \subsection{\label{core}Core Syntax}
adamc@524	405
adamc@524	406 \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	407 $$\begin{array}{rrcll}
adamc@524	408 \textrm{Kinds} & \kappa &::=& \mt{Type} & \textrm{proper types} \\
adamc@525	409 &&& \mt{Unit} & \textrm{the trivial constructor} \\
adamc@525	410 &&& \mt{Name} & \textrm{field names} \\
adamc@525	411 &&& \kappa \to \kappa & \textrm{type-level functions} \\
adamc@525	412 &&& \{\kappa\} & \textrm{type-level records} \\
adamc@525	413 &&& (\kappa\times^+) & \textrm{type-level tuples} \\
adamc@652	414 &&& X & \textrm{variable} \\
adam@1574	415 &&& X \longrightarrow \kappa & \textrm{kind-polymorphic type-level function} \\
adamc@529	416 &&& \_\_ & \textrm{wildcard} \\
adamc@525	417 &&& (\kappa) & \textrm{explicit precedence} \\
adamc@524	418 \end{array}$$
adamc@524	419
adamc@524	420 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	421 $$\begin{array}{rrcll}
adamc@524	422 \textrm{Explicitness} & ? &::=& :: & \textrm{explicit} \\
adamc@558	423 &&& ::: & \textrm{implicit}
adamc@524	424 \end{array}$$
adamc@524	425
adamc@524	426 \emph{Constructors} are the main class of compile-time-only data. They include proper types and are classified by kinds.
adamc@524	427 $$\begin{array}{rrcll}
adamc@524	428 \textrm{Constructors} & c, \tau &::=& (c) :: \kappa & \textrm{kind annotation} \\
adamc@530	429 &&& \hat{x} & \textrm{constructor variable} \\
adamc@524	430 \\
adamc@525	431 &&& \tau \to \tau & \textrm{function type} \\
adamc@525	432 &&& x \; ? \; \kappa \to \tau & \textrm{polymorphic function type} \\
adamc@652	433 &&& X \longrightarrow \tau & \textrm{kind-polymorphic function type} \\
adamc@525	434 &&& \$ c & \textrm{record type} \\
adamc@524	435 \\
adamc@525	436 &&& c \; c & \textrm{type-level function application} \\
adamc@530	437 &&& \lambda x \; :: \; \kappa \Rightarrow c & \textrm{type-level function abstraction} \\
adamc@524	438 \\
adamc@652	439 &&& X \Longrightarrow c & \textrm{type-level kind-polymorphic function abstraction} \\
adamc@655	440 &&& c [\kappa] & \textrm{type-level kind-polymorphic function application} \\
adamc@652	441 \\
adamc@525	442 &&& () & \textrm{type-level unit} \\
adamc@525	443 &&& \#X & \textrm{field name} \\
adamc@524	444 \\
adamc@525	445 &&& [(c = c)^*] & \textrm{known-length type-level record} \\
adamc@525	446 &&& c \rc c & \textrm{type-level record concatenation} \\
adamc@652	447 &&& \mt{map} & \textrm{type-level record map} \\
adamc@524	448 \\
adamc@558	449 &&& (c,^+) & \textrm{type-level tuple} \\
adamc@525	450 &&& c.n & \textrm{type-level tuple projection ($n \in \mathbb N^+$)} \\
adamc@524	451 \\
adamc@652	452 &&& [c \sim c] \Rightarrow \tau & \textrm{guarded type} \\
adamc@524	453 \\
adamc@529	454 &&& \_ :: \kappa & \textrm{wildcard} \\
adamc@525	455 &&& (c) & \textrm{explicit precedence} \\
adamc@530	456 \\
adamc@530	457 \textrm{Qualified uncapitalized variables} & \hat{x} &::=& x & \textrm{not from a module} \\
adamc@530	458 &&& M.x & \textrm{projection from a module} \\
adamc@525	459 \end{array}$$
adamc@525	460
adam@1579	461 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	462
adamc@525	463 Modules of the module system are described by \emph{signatures}.
adamc@525	464 $$\begin{array}{rrcll}
adamc@525	465 \textrm{Signatures} & S &::=& \mt{sig} \; s^* \; \mt{end} & \textrm{constant} \\
adamc@525	466 &&& X & \textrm{variable} \\
adamc@525	467 &&& \mt{functor}(X : S) : S & \textrm{functor} \\
adamc@529	468 &&& S \; \mt{where} \; \mt{con} \; x = c & \textrm{concretizing an abstract constructor} \\
adamc@525	469 &&& M.X & \textrm{projection from a module} \\
adamc@525	470 \\
adamc@525	471 \textrm{Signature items} & s &::=& \mt{con} \; x :: \kappa & \textrm{abstract constructor} \\
adamc@525	472 &&& \mt{con} \; x :: \kappa = c & \textrm{concrete constructor} \\
adamc@528	473 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529	474 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@525	475 &&& \mt{val} \; x : \tau & \textrm{value} \\
adamc@525	476 &&& \mt{structure} \; X : S & \textrm{sub-module} \\
adamc@525	477 &&& \mt{signature} \; X = S & \textrm{sub-signature} \\
adamc@525	478 &&& \mt{include} \; S & \textrm{signature inclusion} \\
adamc@525	479 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@654	480 &&& \mt{class} \; x :: \kappa & \textrm{abstract constructor class} \\
adamc@654	481 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@525	482 \\
adamc@525	483 \textrm{Datatype constructors} & dc &::=& X & \textrm{nullary constructor} \\
adamc@525	484 &&& X \; \mt{of} \; \tau & \textrm{unary constructor} \\
adamc@524	485 \end{array}$$
adamc@524	486
adamc@526	487 \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	488 $$\begin{array}{rrcll}
adamc@526	489 \textrm{Patterns} & p &::=& \_ & \textrm{wildcard} \\
adamc@526	490 &&& x & \textrm{variable} \\
adamc@526	491 &&& \ell & \textrm{constant} \\
adamc@526	492 &&& \hat{X} & \textrm{nullary constructor} \\
adamc@526	493 &&& \hat{X} \; p & \textrm{unary constructor} \\
adamc@526	494 &&& \{(x = p,)^*\} & \textrm{rigid record pattern} \\
adamc@526	495 &&& \{(x = p,)^+, \ldots\} & \textrm{flexible record pattern} \\
adamc@852	496 &&& p : \tau & \textrm{type annotation} \\
adamc@527	497 &&& (p) & \textrm{explicit precedence} \\
adamc@526	498 \\
adamc@529	499 \textrm{Qualified capitalized variables} & \hat{X} &::=& X & \textrm{not from a module} \\
adamc@526	500 &&& M.X & \textrm{projection from a module} \\
adamc@526	501 \end{array}$$
adamc@526	502
adamc@527	503 \emph{Expressions} are the main run-time entities, corresponding to both ``expressions'' and ``statements'' in mainstream imperative languages.
adamc@527	504 $$\begin{array}{rrcll}
adamc@527	505 \textrm{Expressions} & e &::=& e : \tau & \textrm{type annotation} \\
adamc@529	506 &&& \hat{x} & \textrm{variable} \\
adamc@529	507 &&& \hat{X} & \textrm{datatype constructor} \\
adamc@527	508 &&& \ell & \textrm{constant} \\
adamc@527	509 \\
adamc@527	510 &&& e \; e & \textrm{function application} \\
adamc@527	511 &&& \lambda x : \tau \Rightarrow e & \textrm{function abstraction} \\
adamc@527	512 &&& e [c] & \textrm{polymorphic function application} \\
adamc@852	513 &&& \lambda [x \; ? \; \kappa] \Rightarrow e & \textrm{polymorphic function abstraction} \\
adamc@655	514 &&& e [\kappa] & \textrm{kind-polymorphic function application} \\
adamc@652	515 &&& X \Longrightarrow e & \textrm{kind-polymorphic function abstraction} \\
adamc@527	516 \\
adamc@527	517 &&& \{(c = e,)^*\} & \textrm{known-length record} \\
adamc@527	518 &&& e.c & \textrm{record field projection} \\
adamc@527	519 &&& e \rc e & \textrm{record concatenation} \\
adamc@527	520 &&& e \rcut c & \textrm{removal of a single record field} \\
adamc@527	521 &&& e \rcutM c & \textrm{removal of multiple record fields} \\
adamc@527	522 \\
adamc@527	523 &&& \mt{let} \; ed^* \; \mt{in} \; e \; \mt{end} & \textrm{local definitions} \\
adamc@527	524 \\
adamc@527	525 &&& \mt{case} \; e \; \mt{of} \; (p \Rightarrow e\|)^+ & \textrm{pattern matching} \\
adamc@527	526 \\
adamc@654	527 &&& \lambda [c \sim c] \Rightarrow e & \textrm{guarded expression abstraction} \\
adamc@654	528 &&& e \; ! & \textrm{guarded expression application} \\
adamc@527	529 \\
adamc@527	530 &&& \_ & \textrm{wildcard} \\
adamc@527	531 &&& (e) & \textrm{explicit precedence} \\
adamc@527	532 \\
adamc@527	533 \textrm{Local declarations} & ed &::=& \cd{val} \; x : \tau = e & \textrm{non-recursive value} \\
adam@1797	534 &&& \cd{val} \; \cd{rec} \; (x : \tau = e \; \cd{and})^+ & \textrm{mutually recursive values} \\
adamc@527	535 \end{array}$$
adamc@527	536
adamc@655	537 As with constructors, we include both abstraction and application for kind polymorphism, but applications are only inferred internally.
adamc@655	538
adamc@528	539 \emph{Declarations} primarily bring new symbols into context.
adamc@528	540 $$\begin{array}{rrcll}
adamc@528	541 \textrm{Declarations} & d &::=& \mt{con} \; x :: \kappa = c & \textrm{constructor synonym} \\
adamc@528	542 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529	543 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@528	544 &&& \mt{val} \; x : \tau = e & \textrm{value} \\
adam@1797	545 &&& \mt{val} \; \cd{rec} \; (x : \tau = e \; \mt{and})^+ & \textrm{mutually recursive values} \\
adamc@528	546 &&& \mt{structure} \; X : S = M & \textrm{module definition} \\
adamc@528	547 &&& \mt{signature} \; X = S & \textrm{signature definition} \\
adamc@528	548 &&& \mt{open} \; M & \textrm{module inclusion} \\
adamc@528	549 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@528	550 &&& \mt{open} \; \mt{constraints} \; M & \textrm{inclusion of just the constraints from a module} \\
adamc@528	551 &&& \mt{table} \; x : c & \textrm{SQL table} \\
adam@1594	552 &&& \mt{view} \; x = e & \textrm{SQL view} \\
adamc@528	553 &&& \mt{sequence} \; x & \textrm{SQL sequence} \\
adamc@535	554 &&& \mt{cookie} \; x : \tau & \textrm{HTTP cookie} \\
adamc@784	555 &&& \mt{style} \; x : \tau & \textrm{CSS class} \\
adamc@1085	556 &&& \mt{task} \; e = e & \textrm{recurring task} \\
adamc@528	557 \\
adamc@529	558 \textrm{Modules} & M &::=& \mt{struct} \; d^* \; \mt{end} & \textrm{constant} \\
adamc@529	559 &&& X & \textrm{variable} \\
adamc@529	560 &&& M.X & \textrm{projection} \\
adamc@529	561 &&& M(M) & \textrm{functor application} \\
adamc@529	562 &&& \mt{functor}(X : S) : S = M & \textrm{functor abstraction} \\
adamc@528	563 \end{array}$$
adamc@528	564
adamc@528	565 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	566
adam@1594	567 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	568
adamc@529	569 \subsection{Shorthands}
adamc@529	570
adamc@529	571 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	572
adamc@529	573 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	574
adamc@529	575 A record type may be written $\{(c = c,)^\}$, which elaborates to $\$[(c = c,)^]$.
adamc@529	576
adamc@533	577 The notation $[c_1, \ldots, c_n]$ is shorthand for $[c_1 = (), \ldots, c_n = ()]$.
adamc@533	578
adam@1350	579 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	580
adam@1687	581 The syntax $()$ expands to $\{\}$ as a pattern or expression.
adam@1687	582
adamc@852	583 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	584
adam@1574	585 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	586
adam@1306	587 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	588
adamc@529	589 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	590
adamc@529	591 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	592
adamc@654	593 A signature item or declaration $\mt{class} \; x = \lambda y \Rightarrow c$ may be abbreviated $\mt{class} \; x \; y = c$.
adamc@529	594
adam@1738	595 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	596
adamc@852	597 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	598
adamc@852	599 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	600
adam@1797	601 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	602
adamc@529	603 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	604
adamc@852	605 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	606
adamc@853	607 A declaration $\mt{table} \; x : \{(c = c,)^\}$ is elaborated into $\mt{table} \; x : [(c = c,)^]$.
adamc@529	608
adamc@529	609 The syntax $\mt{where} \; \mt{type}$ is an alternate form of $\mt{where} \; \mt{con}$.
adamc@529	610
adamc@529	611 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	612
adamc@529	613 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	614
adamc@784	615 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	616
adamc@530	617
adamc@530	618 \section{Static Semantics}
adamc@530	619
adamc@530	620 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	621
adam@1891	622 The notations used here are the standard ones of programming language semantics. They are probably the most effective way to convey this information. At the same time, most Ur/Web users can probably get by \emph{without} knowing the contents of this section! If you're interested in diving into the details of Ur typing but are unfamiliar with ``inference rule notation,'' I recommend the following book:
adam@1891	623 \begin{quote}
adam@1891	624 Benjamin C. Pierce, \emph{Types and Programming Languages}, MIT Press, 2002.
adam@1891	625 \end{quote}
adam@1891	626
adamc@530	627 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	628 \begin{itemize}
adamc@655	629 \item $\Gamma \vdash \kappa$ expresses kind well-formedness.
adamc@530	630 \item $\Gamma \vdash c :: \kappa$ assigns a kind to a constructor in a context.
adamc@530	631 \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	632 \item $\Gamma \vdash c \hookrightarrow C$ proves that record constructor $c$ decomposes into set $C$ of field names and record constructors.
adamc@530	633 \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	634 \item $\Gamma \vdash e : \tau$ is a standard typing judgment.
adamc@534	635 \item $\Gamma \vdash p \leadsto \Gamma; \tau$ combines typing of patterns with calculation of which new variables they bind.
adamc@537	636 \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	637 \item $\Gamma \vdash S \equiv S$ is the signature equivalence judgment.
adamc@536	638 \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	639 \item $\Gamma \vdash M : S$ is the module signature checking judgment.
adamc@537	640 \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	641 \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	642 \end{itemize}
adamc@530	643
adamc@655	644
adamc@655	645 \subsection{Kind Well-Formedness}
adamc@655	646
adamc@655	647 $$\infer{\Gamma \vdash \mt{Type}}{}
adamc@655	648 \quad \infer{\Gamma \vdash \mt{Unit}}{}
adamc@655	649 \quad \infer{\Gamma \vdash \mt{Name}}{}
adamc@655	650 \quad \infer{\Gamma \vdash \kappa_1 \to \kappa_2}{
adamc@655	651 \Gamma \vdash \kappa_1
adamc@655	652 & \Gamma \vdash \kappa_2
adamc@655	653 }
adamc@655	654 \quad \infer{\Gamma \vdash \{\kappa\}}{
adamc@655	655 \Gamma \vdash \kappa
adamc@655	656 }
adamc@655	657 \quad \infer{\Gamma \vdash (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@655	658 \forall i: \Gamma \vdash \kappa_i
adamc@655	659 }$$
adamc@655	660
adamc@655	661 $$\infer{\Gamma \vdash X}{
adamc@655	662 X \in \Gamma
adamc@655	663 }
adamc@655	664 \quad \infer{\Gamma \vdash X \longrightarrow \kappa}{
adamc@655	665 \Gamma, X \vdash \kappa
adamc@655	666 }$$
adamc@655	667
adamc@530	668 \subsection{Kinding}
adamc@530	669
adamc@655	670 We write $[X \mapsto \kappa_1]\kappa_2$ for capture-avoiding substitution of $\kappa_1$ for $X$ in $\kappa_2$.
adamc@655	671
adamc@530	672 $$\infer{\Gamma \vdash (c) :: \kappa :: \kappa}{
adamc@530	673 \Gamma \vdash c :: \kappa
adamc@530	674 }
adamc@530	675 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530	676 x :: \kappa \in \Gamma
adamc@530	677 }
adamc@530	678 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530	679 x :: \kappa = c \in \Gamma
adamc@530	680 }$$
adamc@530	681
adamc@530	682 $$\infer{\Gamma \vdash M.x :: \kappa}{
adamc@537	683 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	684 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = \kappa
adamc@530	685 }
adamc@530	686 \quad \infer{\Gamma \vdash M.x :: \kappa}{
adamc@537	687 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	688 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@530	689 }$$
adamc@530	690
adamc@530	691 $$\infer{\Gamma \vdash \tau_1 \to \tau_2 :: \mt{Type}}{
adamc@530	692 \Gamma \vdash \tau_1 :: \mt{Type}
adamc@530	693 & \Gamma \vdash \tau_2 :: \mt{Type}
adamc@530	694 }
adamc@530	695 \quad \infer{\Gamma \vdash x \; ? \: \kappa \to \tau :: \mt{Type}}{
adamc@530	696 \Gamma, x :: \kappa \vdash \tau :: \mt{Type}
adamc@530	697 }
adamc@655	698 \quad \infer{\Gamma \vdash X \longrightarrow \tau :: \mt{Type}}{
adamc@655	699 \Gamma, X \vdash \tau :: \mt{Type}
adamc@655	700 }
adamc@530	701 \quad \infer{\Gamma \vdash \$c :: \mt{Type}}{
adamc@530	702 \Gamma \vdash c :: \{\mt{Type}\}
adamc@530	703 }$$
adamc@530	704
adamc@530	705 $$\infer{\Gamma \vdash c_1 \; c_2 :: \kappa_2}{
adamc@530	706 \Gamma \vdash c_1 :: \kappa_1 \to \kappa_2
adamc@530	707 & \Gamma \vdash c_2 :: \kappa_1
adamc@530	708 }
adamc@530	709 \quad \infer{\Gamma \vdash \lambda x \; :: \; \kappa_1 \Rightarrow c :: \kappa_1 \to \kappa_2}{
adamc@530	710 \Gamma, x :: \kappa_1 \vdash c :: \kappa_2
adamc@530	711 }$$
adamc@530	712
adamc@655	713 $$\infer{\Gamma \vdash c[\kappa'] :: [X \mapsto \kappa']\kappa}{
adamc@655	714 \Gamma \vdash c :: X \to \kappa
adamc@655	715 & \Gamma \vdash \kappa'
adamc@655	716 }
adamc@655	717 \quad \infer{\Gamma \vdash X \Longrightarrow c :: X \to \kappa}{
adamc@655	718 \Gamma, X \vdash c :: \kappa
adamc@655	719 }$$
adamc@655	720
adamc@530	721 $$\infer{\Gamma \vdash () :: \mt{Unit}}{}
adamc@530	722 \quad \infer{\Gamma \vdash \#X :: \mt{Name}}{}$$
adamc@530	723
adamc@530	724 $$\infer{\Gamma \vdash [\overline{c_i = c'_i}] :: \{\kappa\}}{
adamc@530	725 \forall i: \Gamma \vdash c_i : \mt{Name}
adamc@530	726 & \Gamma \vdash c'_i :: \kappa
adamc@530	727 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@530	728 }
adamc@530	729 \quad \infer{\Gamma \vdash c_1 \rc c_2 :: \{\kappa\}}{
adamc@530	730 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530	731 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@530	732 & \Gamma \vdash c_1 \sim c_2
adamc@530	733 }$$
adamc@530	734
adamc@655	735 $$\infer{\Gamma \vdash \mt{map} :: (\kappa_1 \to \kappa_2) \to \{\kappa_1\} \to \{\kappa_2\}}{}$$
adamc@530	736
adamc@573	737 $$\infer{\Gamma \vdash (\overline c) :: (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@573	738 \forall i: \Gamma \vdash c_i :: \kappa_i
adamc@530	739 }
adamc@573	740 \quad \infer{\Gamma \vdash c.i :: \kappa_i}{
adamc@573	741 \Gamma \vdash c :: (\kappa_1 \times \ldots \times \kappa_n)
adamc@530	742 }$$
adamc@530	743
adamc@655	744 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow \tau :: \mt{Type}}{
adamc@655	745 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530	746 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@655	747 & \Gamma, c_1 \sim c_2 \vdash \tau :: \mt{Type}
adamc@530	748 }$$
adamc@530	749
adamc@531	750 \subsection{Record Disjointness}
adamc@531	751
adamc@531	752 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@558	753 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@558	754 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@558	755 & \forall c'_1 \in C_1, c'_2 \in C_2: \Gamma \vdash c'_1 \sim c'_2
adamc@531	756 }
adamc@531	757 \quad \infer{\Gamma \vdash X \sim X'}{
adamc@531	758 X \neq X'
adamc@531	759 }$$
adamc@531	760
adamc@531	761 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@531	762 c'_1 \sim c'_2 \in \Gamma
adamc@558	763 & \Gamma \vdash c'_1 \hookrightarrow C_1
adamc@558	764 & \Gamma \vdash c'_2 \hookrightarrow C_2
adamc@558	765 & c_1 \in C_1
adamc@558	766 & c_2 \in C_2
adamc@531	767 }$$
adamc@531	768
adamc@531	769 $$\infer{\Gamma \vdash c \hookrightarrow \{c\}}{}
adamc@531	770 \quad \infer{\Gamma \vdash [\overline{c = c'}] \hookrightarrow \{\overline{c}\}}{}
adamc@531	771 \quad \infer{\Gamma \vdash c_1 \rc c_2 \hookrightarrow C_1 \cup C_2}{
adamc@531	772 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@531	773 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@531	774 }
adamc@531	775 \quad \infer{\Gamma \vdash c \hookrightarrow C}{
adamc@531	776 \Gamma \vdash c \equiv c'
adamc@531	777 & \Gamma \vdash c' \hookrightarrow C
adamc@531	778 }
adamc@531	779 \quad \infer{\Gamma \vdash \mt{map} \; f \; c \hookrightarrow C}{
adamc@531	780 \Gamma \vdash c \hookrightarrow C
adamc@531	781 }$$
adamc@531	782
adamc@541	783 \subsection{\label{definitional}Definitional Equality}
adamc@532	784
adamc@655	785 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	786
adamc@532	787 $$\infer{\Gamma \vdash c \equiv c}{}
adamc@532	788 \quad \infer{\Gamma \vdash c_1 \equiv c_2}{
adamc@532	789 \Gamma \vdash c_2 \equiv c_1
adamc@532	790 }
adamc@532	791 \quad \infer{\Gamma \vdash c_1 \equiv c_3}{
adamc@532	792 \Gamma \vdash c_1 \equiv c_2
adamc@532	793 & \Gamma \vdash c_2 \equiv c_3
adamc@532	794 }
adamc@532	795 \quad \infer{\Gamma \vdash \mathcal C[c_1] \equiv \mathcal C[c_2]}{
adamc@532	796 \Gamma \vdash c_1 \equiv c_2
adamc@532	797 }$$
adamc@532	798
adamc@532	799 $$\infer{\Gamma \vdash x \equiv c}{
adamc@532	800 x :: \kappa = c \in \Gamma
adamc@532	801 }
adamc@532	802 \quad \infer{\Gamma \vdash M.x \equiv c}{
adamc@537	803 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	804 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@532	805 }
adamc@532	806 \quad \infer{\Gamma \vdash (\overline c).i \equiv c_i}{}$$
adamc@532	807
adamc@532	808 $$\infer{\Gamma \vdash (\lambda x :: \kappa \Rightarrow c) \; c' \equiv [x \mapsto c'] c}{}
adamc@655	809 \quad \infer{\Gamma \vdash (X \Longrightarrow c) [\kappa] \equiv [X \mapsto \kappa] c}{}$$
adamc@655	810
adamc@655	811 $$\infer{\Gamma \vdash c_1 \rc c_2 \equiv c_2 \rc c_1}{}
adamc@532	812 \quad \infer{\Gamma \vdash c_1 \rc (c_2 \rc c_3) \equiv (c_1 \rc c_2) \rc c_3}{}$$
adamc@532	813
adamc@532	814 $$\infer{\Gamma \vdash [] \rc c \equiv c}{}
adamc@532	815 \quad \infer{\Gamma \vdash [\overline{c_1 = c'_1}] \rc [\overline{c_2 = c'_2}] \equiv [\overline{c_1 = c'_1}, \overline{c_2 = c'_2}]}{}$$
adamc@532	816
adamc@655	817 $$\infer{\Gamma \vdash \mt{map} \; f \; [] \equiv []}{}
adamc@655	818 \quad \infer{\Gamma \vdash \mt{map} \; f \; ([c_1 = c_2] \rc c) \equiv [c_1 = f \; c_2] \rc \mt{map} \; f \; c}{}$$
adamc@532	819
adamc@532	820 $$\infer{\Gamma \vdash \mt{map} \; (\lambda x \Rightarrow x) \; c \equiv c}{}
adamc@655	821 \quad \infer{\Gamma \vdash \mt{map} \; f \; (\mt{map} \; f' \; c)
adamc@655	822 \equiv \mt{map} \; (\lambda x \Rightarrow f \; (f' \; x)) \; c}{}$$
adamc@532	823
adamc@532	824 $$\infer{\Gamma \vdash \mt{map} \; f \; (c_1 \rc c_2) \equiv \mt{map} \; f \; c_1 \rc \mt{map} \; f \; c_2}{}$$
adamc@531	825
adamc@534	826 \subsection{Expression Typing}
adamc@533	827
adamc@873	828 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	829
adamc@533	830 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	831
adamc@533	832 $$\infer{\Gamma \vdash e : \tau : \tau}{
adamc@533	833 \Gamma \vdash e : \tau
adamc@533	834 }
adamc@533	835 \quad \infer{\Gamma \vdash e : \tau}{
adamc@533	836 \Gamma \vdash e : \tau'
adamc@533	837 & \Gamma \vdash \tau' \equiv \tau
adamc@533	838 }
adamc@533	839 \quad \infer{\Gamma \vdash \ell : T(\ell)}{}$$
adamc@533	840
adamc@533	841 $$\infer{\Gamma \vdash x : \mathcal I(\tau)}{
adamc@533	842 x : \tau \in \Gamma
adamc@533	843 }
adamc@533	844 \quad \infer{\Gamma \vdash M.x : \mathcal I(\tau)}{
adamc@537	845 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	846 & \mt{proj}(M, \overline{s}, \mt{val} \; x) = \tau
adamc@533	847 }
adamc@533	848 \quad \infer{\Gamma \vdash X : \mathcal I(\tau)}{
adamc@533	849 X : \tau \in \Gamma
adamc@533	850 }
adamc@533	851 \quad \infer{\Gamma \vdash M.X : \mathcal I(\tau)}{
adamc@537	852 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	853 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \tau
adamc@533	854 }$$
adamc@533	855
adamc@533	856 $$\infer{\Gamma \vdash e_1 \; e_2 : \tau_2}{
adamc@533	857 \Gamma \vdash e_1 : \tau_1 \to \tau_2
adamc@533	858 & \Gamma \vdash e_2 : \tau_1
adamc@533	859 }
adamc@533	860 \quad \infer{\Gamma \vdash \lambda x : \tau_1 \Rightarrow e : \tau_1 \to \tau_2}{
adamc@533	861 \Gamma, x : \tau_1 \vdash e : \tau_2
adamc@533	862 }$$
adamc@533	863
adamc@533	864 $$\infer{\Gamma \vdash e [c] : [x \mapsto c]\tau}{
adamc@533	865 \Gamma \vdash e : x :: \kappa \to \tau
adamc@533	866 & \Gamma \vdash c :: \kappa
adamc@533	867 }
adamc@852	868 \quad \infer{\Gamma \vdash \lambda [x \; ? \; \kappa] \Rightarrow e : x \; ? \; \kappa \to \tau}{
adamc@533	869 \Gamma, x :: \kappa \vdash e : \tau
adamc@533	870 }$$
adamc@533	871
adamc@655	872 $$\infer{\Gamma \vdash e [\kappa] : [X \mapsto \kappa]\tau}{
adamc@655	873 \Gamma \vdash e : X \longrightarrow \tau
adamc@655	874 & \Gamma \vdash \kappa
adamc@655	875 }
adamc@655	876 \quad \infer{\Gamma \vdash X \Longrightarrow e : X \longrightarrow \tau}{
adamc@655	877 \Gamma, X \vdash e : \tau
adamc@655	878 }$$
adamc@655	879
adamc@533	880 $$\infer{\Gamma \vdash \{\overline{c = e}\} : \{\overline{c : \tau}\}}{
adamc@533	881 \forall i: \Gamma \vdash c_i :: \mt{Name}
adamc@533	882 & \Gamma \vdash e_i : \tau_i
adamc@533	883 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@533	884 }
adamc@533	885 \quad \infer{\Gamma \vdash e.c : \tau}{
adamc@533	886 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533	887 }
adamc@533	888 \quad \infer{\Gamma \vdash e_1 \rc e_2 : \$(c_1 \rc c_2)}{
adamc@533	889 \Gamma \vdash e_1 : \$c_1
adamc@533	890 & \Gamma \vdash e_2 : \$c_2
adamc@573	891 & \Gamma \vdash c_1 \sim c_2
adamc@533	892 }$$
adamc@533	893
adamc@533	894 $$\infer{\Gamma \vdash e \rcut c : \$c'}{
adamc@533	895 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533	896 }
adamc@533	897 \quad \infer{\Gamma \vdash e \rcutM c : \$c'}{
adamc@533	898 \Gamma \vdash e : \$(c \rc c')
adamc@533	899 }$$
adamc@533	900
adamc@533	901 $$\infer{\Gamma \vdash \mt{let} \; \overline{ed} \; \mt{in} \; e \; \mt{end} : \tau}{
adamc@533	902 \Gamma \vdash \overline{ed} \leadsto \Gamma'
adamc@533	903 & \Gamma' \vdash e : \tau
adamc@533	904 }
adamc@533	905 \quad \infer{\Gamma \vdash \mt{case} \; e \; \mt{of} \; \overline{p \Rightarrow e} : \tau}{
adamc@533	906 \forall i: \Gamma \vdash p_i \leadsto \Gamma_i, \tau'
adamc@533	907 & \Gamma_i \vdash e_i : \tau
adamc@533	908 }$$
adamc@533	909
adamc@573	910 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow e : \lambda [c_1 \sim c_2] \Rightarrow \tau}{
adamc@533	911 \Gamma \vdash c_1 :: \{\kappa\}
adamc@655	912 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@533	913 & \Gamma, c_1 \sim c_2 \vdash e : \tau
adamc@662	914 }
adamc@662	915 \quad \infer{\Gamma \vdash e \; ! : \tau}{
adamc@662	916 \Gamma \vdash e : [c_1 \sim c_2] \Rightarrow \tau
adamc@662	917 & \Gamma \vdash c_1 \sim c_2
adamc@533	918 }$$
adamc@533	919
adamc@534	920 \subsection{Pattern Typing}
adamc@534	921
adamc@534	922 $$\infer{\Gamma \vdash \_ \leadsto \Gamma; \tau}{}
adamc@534	923 \quad \infer{\Gamma \vdash x \leadsto \Gamma, x : \tau; \tau}{}
adamc@534	924 \quad \infer{\Gamma \vdash \ell \leadsto \Gamma; T(\ell)}{}$$
adamc@534	925
adamc@534	926 $$\infer{\Gamma \vdash X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534	927 X : \overline{x ::: \mt{Type}} \to \tau \in \Gamma
adamc@534	928 & \textrm{$\tau$ not a function type}
adamc@534	929 }
adamc@534	930 \quad \infer{\Gamma \vdash X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534	931 X : \overline{x ::: \mt{Type}} \to \tau'' \to \tau \in \Gamma
adamc@534	932 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534	933 }$$
adamc@534	934
adamc@534	935 $$\infer{\Gamma \vdash M.X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537	936 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	937 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau
adamc@534	938 & \textrm{$\tau$ not a function type}
adamc@534	939 }$$
adamc@534	940
adamc@534	941 $$\infer{\Gamma \vdash M.X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537	942 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	943 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau'' \to \tau
adamc@534	944 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534	945 }$$
adamc@534	946
adamc@534	947 $$\infer{\Gamma \vdash \{\overline{x = p}\} \leadsto \Gamma_n; \{\overline{x = \tau}\}}{
adamc@534	948 \Gamma_0 = \Gamma
adamc@534	949 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534	950 }
adamc@534	951 \quad \infer{\Gamma \vdash \{\overline{x = p}, \ldots\} \leadsto \Gamma_n; \$([\overline{x = \tau}] \rc c)}{
adamc@534	952 \Gamma_0 = \Gamma
adamc@534	953 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534	954 }$$
adamc@534	955
adamc@852	956 $$\infer{\Gamma \vdash p : \tau \leadsto \Gamma'; \tau}{
adamc@852	957 \Gamma \vdash p \leadsto \Gamma'; \tau'
adamc@852	958 & \Gamma \vdash \tau' \equiv \tau
adamc@852	959 }$$
adamc@852	960
adamc@535	961 \subsection{Declaration Typing}
adamc@535	962
adamc@535	963 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	964
adamc@558	965 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	966 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	967
adamc@535	968 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535	969 \quad \infer{\Gamma \vdash d, \overline{d} \leadsto \Gamma''}{
adamc@535	970 \Gamma \vdash d \leadsto \Gamma'
adamc@535	971 & \Gamma' \vdash \overline{d} \leadsto \Gamma''
adamc@535	972 }$$
adamc@535	973
adamc@535	974 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@535	975 \Gamma \vdash c :: \kappa
adamc@535	976 }
adamc@535	977 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@535	978 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@535	979 }$$
adamc@535	980
adamc@535	981 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537	982 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	983 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@535	984 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@535	985 }$$
adamc@535	986
adamc@535	987 $$\infer{\Gamma \vdash \mt{val} \; x : \tau = e \leadsto \Gamma, x : \tau}{
adamc@535	988 \Gamma \vdash e : \tau
adamc@535	989 }$$
adamc@535	990
adamc@535	991 $$\infer{\Gamma \vdash \mt{val} \; \mt{rec} \; \overline{x : \tau = e} \leadsto \Gamma, \overline{x : \tau}}{
adamc@535	992 \forall i: \Gamma, \overline{x : \tau} \vdash e_i : \tau_i
adamc@535	993 & \textrm{$e_i$ starts with an expression $\lambda$, optionally preceded by constructor and disjointness $\lambda$s}
adamc@535	994 }$$
adamc@535	995
adamc@535	996 $$\infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : S}{
adamc@535	997 \Gamma \vdash M : S
adamc@558	998 & \textrm{ $M$ not a constant or application}
adamc@535	999 }
adamc@558	1000 \quad \infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : \mt{selfify}(X, \overline{s})}{
adamc@558	1001 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@539	1002 }$$
adamc@539	1003
adamc@539	1004 $$\infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@535	1005 \Gamma \vdash S
adamc@535	1006 }$$
adamc@535	1007
adamc@537	1008 $$\infer{\Gamma \vdash \mt{open} \; M \leadsto \Gamma, \mathcal O(M, \overline{s})}{
adamc@537	1009 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535	1010 }$$
adamc@535	1011
adamc@535	1012 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma}{
adamc@535	1013 \Gamma \vdash c_1 :: \{\kappa\}
adamc@535	1014 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@535	1015 & \Gamma \vdash c_1 \sim c_2
adamc@535	1016 }
adamc@537	1017 \quad \infer{\Gamma \vdash \mt{open} \; \mt{constraints} \; M \leadsto \Gamma, \mathcal O_c(M, \overline{s})}{
adamc@537	1018 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535	1019 }$$
adamc@535	1020
adamc@784	1021 $$\infer{\Gamma \vdash \mt{table} \; x : c \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_table} \; c \; []}{
adamc@535	1022 \Gamma \vdash c :: \{\mt{Type}\}
adamc@535	1023 }
adam@1594	1024 \quad \infer{\Gamma \vdash \mt{view} \; x = e \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_view} \; c}{
adam@1594	1025 \Gamma \vdash e :: \mt{Basis}.\mt{sql\_query} \; [] \; [] \; (\mt{map} \; (\lambda \_ \Rightarrow []) \; c') \; c
adamc@784	1026 }$$
adamc@784	1027
adamc@784	1028 $$\infer{\Gamma \vdash \mt{sequence} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_sequence}}{}$$
adamc@535	1029
adamc@535	1030 $$\infer{\Gamma \vdash \mt{cookie} \; x : \tau \leadsto \Gamma, x : \mt{Basis}.\mt{http\_cookie} \; \tau}{
adamc@535	1031 \Gamma \vdash \tau :: \mt{Type}
adamc@784	1032 }
adamc@784	1033 \quad \infer{\Gamma \vdash \mt{style} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{css\_class}}{}$$
adamc@535	1034
adamc@1085	1035 $$\infer{\Gamma \vdash \mt{task} \; e_1 = e_2 \leadsto \Gamma}{
adam@1348	1036 \Gamma \vdash e_1 :: \mt{Basis}.\mt{task\_kind} \; \tau
adam@1348	1037 & \Gamma \vdash e_2 :: \tau \to \mt{Basis}.\mt{transaction} \; \{\}
adamc@1085	1038 }$$
adamc@1085	1039
adamc@535	1040 $$\infer{\overline{y}; x; \Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535	1041 \quad \infer{\overline{y}; x; \Gamma \vdash X \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to x \; \overline{y}}{
adamc@535	1042 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535	1043 }
adamc@535	1044 \quad \infer{\overline{y}; x; \Gamma \vdash X \; \mt{of} \; \tau \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to \tau \to x \; \overline{y}}{
adamc@535	1045 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535	1046 }$$
adamc@535	1047
adamc@537	1048 \subsection{Signature Item Typing}
adamc@537	1049
adamc@537	1050 We appeal to a signature item analogue of the $\mathcal O$ function from the last subsection.
adamc@537	1051
adam@1797	1052 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	1053
adamc@537	1054 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@537	1055 \quad \infer{\Gamma \vdash s, \overline{s} \leadsto \Gamma''}{
adamc@537	1056 \Gamma \vdash s \leadsto \Gamma'
adamc@537	1057 & \Gamma' \vdash \overline{s} \leadsto \Gamma''
adamc@537	1058 }$$
adamc@537	1059
adamc@537	1060 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}
adamc@537	1061 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@537	1062 \Gamma \vdash c :: \kappa
adamc@537	1063 }
adamc@537	1064 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@537	1065 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@537	1066 }$$
adamc@537	1067
adamc@537	1068 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537	1069 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1070 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537	1071 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@537	1072 }$$
adamc@537	1073
adamc@537	1074 $$\infer{\Gamma \vdash \mt{val} \; x : \tau \leadsto \Gamma, x : \tau}{
adamc@537	1075 \Gamma \vdash \tau :: \mt{Type}
adamc@537	1076 }$$
adamc@537	1077
adamc@537	1078 $$\infer{\Gamma \vdash \mt{structure} \; X : S \leadsto \Gamma, X : S}{
adamc@537	1079 \Gamma \vdash S
adamc@537	1080 }
adamc@537	1081 \quad \infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@537	1082 \Gamma \vdash S
adamc@537	1083 }$$
adamc@537	1084
adamc@537	1085 $$\infer{\Gamma \vdash \mt{include} \; S \leadsto \Gamma, \mathcal O(\overline{s})}{
adamc@537	1086 \Gamma \vdash S
adamc@537	1087 & \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1088 }$$
adamc@537	1089
adamc@537	1090 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma, c_1 \sim c_2}{
adamc@537	1091 \Gamma \vdash c_1 :: \{\kappa\}
adamc@537	1092 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@537	1093 }$$
adamc@537	1094
adamc@784	1095 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784	1096 \Gamma \vdash c :: \kappa
adamc@537	1097 }
adamc@784	1098 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}$$
adamc@537	1099
adamc@536	1100 \subsection{Signature Compatibility}
adamc@536	1101
adam@1797	1102 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	1103
adamc@537	1104 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	1105
adamc@536	1106 $$\infer{\Gamma \vdash S \equiv S}{}
adamc@536	1107 \quad \infer{\Gamma \vdash S_1 \equiv S_2}{
adamc@536	1108 \Gamma \vdash S_2 \equiv S_1
adamc@536	1109 }
adamc@536	1110 \quad \infer{\Gamma \vdash X \equiv S}{
adamc@536	1111 X = S \in \Gamma
adamc@536	1112 }
adamc@536	1113 \quad \infer{\Gamma \vdash M.X \equiv S}{
adamc@537	1114 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1115 & \mt{proj}(M, \overline{s}, \mt{signature} \; X) = S
adamc@536	1116 }$$
adamc@536	1117
adamc@536	1118 $$\infer{\Gamma \vdash S \; \mt{where} \; \mt{con} \; x = c \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa = c \; \overline{s_2} \; \mt{end}}{
adamc@536	1119 \Gamma \vdash S \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa \; \overline{s_2} \; \mt{end}
adamc@536	1120 & \Gamma \vdash c :: \kappa
adamc@537	1121 }
adamc@537	1122 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s^1} \; \mt{include} \; S \; \overline{s^2} \; \mt{end} \equiv \mt{sig} \; \overline{s^1} \; \overline{s} \; \overline{s^2} \; \mt{end}}{
adamc@537	1123 \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@536	1124 }$$
adamc@536	1125
adamc@536	1126 $$\infer{\Gamma \vdash S_1 \leq S_2}{
adamc@536	1127 \Gamma \vdash S_1 \equiv S_2
adamc@536	1128 }
adamc@536	1129 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \mt{end}}{}
adamc@537	1130 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; s' \; \overline{s'} \; \mt{end}}{
adamc@537	1131 \Gamma \vdash \overline{s} \leq s'
adamc@537	1132 & \Gamma \vdash s' \leadsto \Gamma'
adamc@537	1133 & \Gamma' \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \overline{s'} \; \mt{end}
adamc@537	1134 }$$
adamc@537	1135
adamc@537	1136 $$\infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537	1137 \Gamma \vdash s \leq s'
adamc@537	1138 }
adamc@537	1139 \quad \infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537	1140 \Gamma \vdash s \leadsto \Gamma'
adamc@537	1141 & \Gamma' \vdash \overline{s} \leq s'
adamc@536	1142 }$$
adamc@536	1143
adamc@536	1144 $$\infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 \leq \mt{functor} (X : S'_1) : S'_2}{
adamc@536	1145 \Gamma \vdash S'_1 \leq S_1
adamc@536	1146 & \Gamma, X : S'_1 \vdash S_2 \leq S'_2
adamc@536	1147 }$$
adamc@536	1148
adamc@537	1149 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@537	1150 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}
adamc@558	1151 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type}}{}$$
adamc@537	1152
adamc@537	1153 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(y)} \to \mt{Type}}{
adamc@537	1154 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1155 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537	1156 }$$
adamc@537	1157
adamc@784	1158 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@784	1159 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}$$
adamc@537	1160
adamc@537	1161 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \mt{\kappa} = c_2}{
adamc@537	1162 \Gamma \vdash c_1 \equiv c_2
adamc@537	1163 }
adamc@784	1164 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \kappa = c_2}{
adamc@537	1165 \Gamma \vdash c_1 \equiv c_2
adamc@537	1166 }$$
adamc@537	1167
adamc@537	1168 $$\infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537	1169 \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537	1170 }$$
adamc@537	1171
adamc@537	1172 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537	1173 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537	1174 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537	1175 & \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537	1176 }$$
adamc@537	1177
adamc@537	1178 $$\infer{\Gamma \vdash \cdot \leq \cdot}{}
adamc@537	1179 \quad \infer{\Gamma \vdash X; \overline{dc} \leq X; \overline{dc'}}{
adamc@537	1180 \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537	1181 }
adamc@537	1182 \quad \infer{\Gamma \vdash X \; \mt{of} \; \tau_1; \overline{dc} \leq X \; \mt{of} \; \tau_2; \overline{dc'}}{
adamc@537	1183 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537	1184 & \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537	1185 }$$
adamc@537	1186
adamc@537	1187 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x = \mt{datatype} \; M'.z'}{
adamc@537	1188 \Gamma \vdash M.z \equiv M'.z'
adamc@537	1189 }$$
adamc@537	1190
adamc@537	1191 $$\infer{\Gamma \vdash \mt{val} \; x : \tau_1 \leq \mt{val} \; x : \tau_2}{
adamc@537	1192 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537	1193 }
adamc@537	1194 \quad \infer{\Gamma \vdash \mt{structure} \; X : S_1 \leq \mt{structure} \; X : S_2}{
adamc@537	1195 \Gamma \vdash S_1 \leq S_2
adamc@537	1196 }
adamc@537	1197 \quad \infer{\Gamma \vdash \mt{signature} \; X = S_1 \leq \mt{signature} \; X = S_2}{
adamc@537	1198 \Gamma \vdash S_1 \leq S_2
adamc@537	1199 & \Gamma \vdash S_2 \leq S_1
adamc@537	1200 }$$
adamc@537	1201
adamc@537	1202 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leq \mt{constraint} \; c'_1 \sim c'_2}{
adamc@537	1203 \Gamma \vdash c_1 \equiv c'_1
adamc@537	1204 & \Gamma \vdash c_2 \equiv c'_2
adamc@537	1205 }$$
adamc@537	1206
adamc@655	1207 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{class} \; x :: \kappa}{}
adamc@655	1208 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{class} \; x :: \kappa}{}
adamc@655	1209 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{class} \; x :: \kappa = c_2}{
adamc@537	1210 \Gamma \vdash c_1 \equiv c_2
adamc@537	1211 }$$
adamc@537	1212
adam@1797	1213 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leq \mt{class} \; x :: \kappa}{}
adam@1797	1214 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leq \mt{class} \; x :: \kappa}{}
adam@1797	1215 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c_1 \leq \mt{class} \; x :: \kappa = c_2}{
adam@1797	1216 \Gamma \vdash c_1 \equiv c_2
adam@1797	1217 }$$
adam@1797	1218
adamc@538	1219 \subsection{Module Typing}
adamc@538	1220
adamc@538	1221 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	1222
adamc@538	1223 $$\infer{\Gamma \vdash M : S}{
adamc@538	1224 \Gamma \vdash M : S'
adamc@538	1225 & \Gamma \vdash S' \leq S
adamc@538	1226 }
adamc@538	1227 \quad \infer{\Gamma \vdash \mt{struct} \; \overline{d} \; \mt{end} : \mt{sig} \; \mt{sigOf}(\overline{d}) \; \mt{end}}{
adamc@538	1228 \Gamma \vdash \overline{d} \leadsto \Gamma'
adamc@538	1229 }
adamc@538	1230 \quad \infer{\Gamma \vdash X : S}{
adamc@538	1231 X : S \in \Gamma
adamc@538	1232 }$$
adamc@538	1233
adamc@538	1234 $$\infer{\Gamma \vdash M.X : S}{
adamc@538	1235 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@538	1236 & \mt{proj}(M, \overline{s}, \mt{structure} \; X) = S
adamc@538	1237 }$$
adamc@538	1238
adamc@538	1239 $$\infer{\Gamma \vdash M_1(M_2) : [X \mapsto M_2]S_2}{
adamc@538	1240 \Gamma \vdash M_1 : \mt{functor}(X : S_1) : S_2
adamc@538	1241 & \Gamma \vdash M_2 : S_1
adamc@538	1242 }
adamc@538	1243 \quad \infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 = M : \mt{functor} (X : S_1) : S_2}{
adamc@538	1244 \Gamma \vdash S_1
adamc@538	1245 & \Gamma, X : S_1 \vdash S_2
adamc@538	1246 & \Gamma, X : S_1 \vdash M : S_2
adamc@538	1247 }$$
adamc@538	1248
adamc@538	1249 \begin{eqnarray*}
adamc@538	1250 \mt{sigOf}(\cdot) &=& \cdot \\
adamc@538	1251 \mt{sigOf}(s \; \overline{s'}) &=& \mt{sigOf}(s) \; \mt{sigOf}(\overline{s'}) \\
adamc@538	1252 \\
adamc@538	1253 \mt{sigOf}(\mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@538	1254 \mt{sigOf}(\mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \overline{dc} \\
adamc@538	1255 \mt{sigOf}(\mt{datatype} \; x = \mt{datatype} \; M.z) &=& \mt{datatype} \; x = \mt{datatype} \; M.z \\
adamc@538	1256 \mt{sigOf}(\mt{val} \; x : \tau = e) &=& \mt{val} \; x : \tau \\
adamc@538	1257 \mt{sigOf}(\mt{val} \; \mt{rec} \; \overline{x : \tau = e}) &=& \overline{\mt{val} \; x : \tau} \\
adamc@538	1258 \mt{sigOf}(\mt{structure} \; X : S = M) &=& \mt{structure} \; X : S \\
adamc@538	1259 \mt{sigOf}(\mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@538	1260 \mt{sigOf}(\mt{open} \; M) &=& \mt{include} \; S \textrm{ (where $\Gamma \vdash M : S$)} \\
adamc@538	1261 \mt{sigOf}(\mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@538	1262 \mt{sigOf}(\mt{open} \; \mt{constraints} \; M) &=& \cdot \\
adamc@538	1263 \mt{sigOf}(\mt{table} \; x : c) &=& \mt{table} \; x : c \\
adam@1594	1264 \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	1265 \mt{sigOf}(\mt{sequence} \; x) &=& \mt{sequence} \; x \\
adamc@538	1266 \mt{sigOf}(\mt{cookie} \; x : \tau) &=& \mt{cookie} \; x : \tau \\
adam@1797	1267 \mt{sigOf}(\mt{style} \; x) &=& \mt{style} \; x
adamc@538	1268 \end{eqnarray*}
adamc@539	1269 \begin{eqnarray*}
adamc@539	1270 \mt{selfify}(M, \cdot) &=& \cdot \\
adamc@558	1271 \mt{selfify}(M, s \; \overline{s'}) &=& \mt{selfify}(M, s) \; \mt{selfify}(M, \overline{s'}) \\
adamc@539	1272 \\
adamc@539	1273 \mt{selfify}(M, \mt{con} \; x :: \kappa) &=& \mt{con} \; x :: \kappa = M.x \\
adamc@539	1274 \mt{selfify}(M, \mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@539	1275 \mt{selfify}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \mt{datatype} \; M.x \\
adamc@539	1276 \mt{selfify}(M, \mt{datatype} \; x = \mt{datatype} \; M'.z) &=& \mt{datatype} \; x = \mt{datatype} \; M'.z \\
adamc@539	1277 \mt{selfify}(M, \mt{val} \; x : \tau) &=& \mt{val} \; x : \tau \\
adamc@539	1278 \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	1279 \mt{selfify}(M, \mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@539	1280 \mt{selfify}(M, \mt{include} \; S) &=& \mt{include} \; S \\
adamc@539	1281 \mt{selfify}(M, \mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@655	1282 \mt{selfify}(M, \mt{class} \; x :: \kappa) &=& \mt{class} \; x :: \kappa = M.x \\
adamc@655	1283 \mt{selfify}(M, \mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@539	1284 \end{eqnarray*}
adamc@539	1285
adamc@540	1286 \subsection{Module Projection}
adamc@540	1287
adamc@540	1288 \begin{eqnarray*}
adamc@540	1289 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \\
adamc@540	1290 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa, c) \\
adamc@540	1291 \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	1292 \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	1293 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})$)} \\
adamc@655	1294 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \to \mt{Type} \\
adamc@655	1295 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa \to \mt{Type}, c) \\
adamc@540	1296 \\
adamc@540	1297 \mt{proj}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc} \; \overline{s}, \mt{datatype} \; x) &=& (\overline{y}, \overline{dc}) \\
adamc@540	1298 \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	1299 \\
adamc@540	1300 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, \mt{val} \; x) &=& \tau \\
adamc@540	1301 \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	1302 \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	1303 \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	1304 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \in \overline{dc}$)} \\
adamc@540	1305 \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	1306 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \; \mt{of} \; \tau \in \overline{dc}$)} \\
adamc@540	1307 \\
adamc@540	1308 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, \mt{structure} \; X) &=& S \\
adamc@540	1309 \\
adamc@540	1310 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, \mt{signature} \; X) &=& S \\
adamc@540	1311 \\
adamc@540	1312 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1313 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1314 \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	1315 \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	1316 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@540	1317 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1318 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1319 \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	1320 \mt{proj}(M, \mt{constraint} \; c_1 \sim c_2 \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@655	1321 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@655	1322 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540	1323 \end{eqnarray*}
adamc@540	1324
adamc@541	1325
adamc@541	1326 \section{Type Inference}
adamc@541	1327
adamc@541	1328 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	1329
adamc@541	1330 \subsection{Basic Unification}
adamc@541	1331
adamc@560	1332 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	1333
adamc@656	1334 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	1335
adamc@541	1336 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	1337
adamc@541	1338 \subsection{Unifying Record Types}
adamc@541	1339
adamc@570	1340 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	1341
adamc@656	1342 \subsection{\label{typeclasses}Constructor Classes}
adamc@541	1343
adamc@784	1344 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	1345
adam@1797	1346 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	1347
adam@1797	1348 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	1349
adam@1797	1350 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	1351
adamc@541	1352 \subsection{Reverse-Engineering Record Types}
adamc@541	1353
adamc@656	1354 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	1355
adamc@541	1356 \subsection{Implicit Arguments in Functor Applications}
adamc@541	1357
adamc@656	1358 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	1359
adamc@541	1360
adamc@542	1361 \section{The Ur Standard Library}
adamc@542	1362
adamc@542	1363 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	1364
adamc@542	1365 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	1366
adamc@542	1367 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	1368 $$\begin{array}{l}
adamc@542	1369 \mt{type} \; \mt{int} \\
adamc@542	1370 \mt{type} \; \mt{float} \\
adamc@873	1371 \mt{type} \; \mt{char} \\
adamc@542	1372 \mt{type} \; \mt{string} \\
adamc@542	1373 \mt{type} \; \mt{time} \\
adamc@785	1374 \mt{type} \; \mt{blob} \\
adamc@542	1375 \\
adamc@542	1376 \mt{type} \; \mt{unit} = \{\} \\
adamc@542	1377 \\
adamc@542	1378 \mt{datatype} \; \mt{bool} = \mt{False} \mid \mt{True} \\
adamc@542	1379 \\
adamc@785	1380 \mt{datatype} \; \mt{option} \; \mt{t} = \mt{None} \mid \mt{Some} \; \mt{of} \; \mt{t} \\
adamc@785	1381 \\
adamc@785	1382 \mt{datatype} \; \mt{list} \; \mt{t} = \mt{Nil} \mid \mt{Cons} \; \mt{of} \; \mt{t} \times \mt{list} \; \mt{t}
adamc@542	1383 \end{array}$$
adamc@542	1384
adamc@1123	1385 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	1386
adam@1297	1387 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	1388 $$\begin{array}{l}
adam@1297	1389 \mt{con} \; \mt{variant} :: \{\mt{Type}\} \to \mt{Type} \\
adam@1297	1390 \mt{val} \; \mt{make} : \mt{nm} :: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{ts} ::: \{\mt{Type}\} \to [[\mt{nm}] \sim \mt{ts}] \Rightarrow \mt{t} \to \mt{variant} \; ([\mt{nm} = \mt{t}] \rc \mt{ts}) \\
adam@1297	1391 \mt{val} \; \mt{match} : \mt{ts} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{variant} \; \mt{ts} \to \$(\mt{map} \; (\lambda \mt{t'} \Rightarrow \mt{t'} \to \mt{t}) \; \mt{ts}) \to \mt{t}
adam@1297	1392 \end{array}$$
adam@1297	1393
adamc@657	1394 Another important generic Ur element comes at the beginning of \texttt{top.urs}.
adamc@657	1395
adamc@657	1396 $$\begin{array}{l}
adamc@657	1397 \mt{con} \; \mt{folder} :: \mt{K} \longrightarrow \{\mt{K}\} \to \mt{Type} \\
adamc@657	1398 \\
adamc@657	1399 \mt{val} \; \mt{fold} : \mt{K} \longrightarrow \mt{tf} :: (\{\mt{K}\} \to \mt{Type}) \\
adamc@657	1400 \hspace{.1in} \to (\mt{nm} :: \mt{Name} \to \mt{v} :: \mt{K} \to \mt{r} :: \{\mt{K}\} \to [[\mt{nm}] \sim \mt{r}] \Rightarrow \\
adamc@657	1401 \hspace{.2in} \mt{tf} \; \mt{r} \to \mt{tf} \; ([\mt{nm} = \mt{v}] \rc \mt{r})) \\
adamc@657	1402 \hspace{.1in} \to \mt{tf} \; [] \\
adamc@657	1403 \hspace{.1in} \to \mt{r} :: \{\mt{K}\} \to \mt{folder} \; \mt{r} \to \mt{tf} \; \mt{r}
adamc@657	1404 \end{array}$$
adamc@657	1405
adamc@657	1406 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	1407
adamc@664	1408 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	1409
adamc@542	1410
adamc@542	1411 \section{The Ur/Web Standard Library}
adamc@542	1412
adam@1400	1413 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	1414
adamc@658	1415 \subsection{Monads}
adamc@658	1416
adamc@658	1417 The Ur Basis defines the monad constructor class from Haskell.
adamc@658	1418
adamc@658	1419 $$\begin{array}{l}
adamc@658	1420 \mt{class} \; \mt{monad} :: \mt{Type} \to \mt{Type} \\
adamc@658	1421 \mt{val} \; \mt{return} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t} ::: \mt{Type} \\
adamc@658	1422 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658	1423 \hspace{.1in} \to \mt{t} \to \mt{m} \; \mt{t} \\
adamc@658	1424 \mt{val} \; \mt{bind} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t1} ::: \mt{Type} \to \mt{t2} ::: \mt{Type} \\
adamc@658	1425 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658	1426 \hspace{.1in} \to \mt{m} \; \mt{t1} \to (\mt{t1} \to \mt{m} \; \mt{t2}) \\
adam@1544	1427 \hspace{.1in} \to \mt{m} \; \mt{t2} \\
adam@1544	1428 \mt{val} \; \mt{mkMonad} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \\
adam@1544	1429 \hspace{.1in} \to \{\mt{Return} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{m} \; \mt{t}, \\
adam@1544	1430 \hspace{.3in} \mt{Bind} : \mt{t1} ::: \mt{Type} \to \mt{t2} ::: \mt{Type} \to \mt{m} \; \mt{t1} \to (\mt{t1} \to \mt{m} \; \mt{t2}) \to \mt{m} \; \mt{t2}\} \\
adam@1544	1431 \hspace{.1in} \to \mt{monad} \; \mt{m}
adamc@658	1432 \end{array}$$
adamc@658	1433
adam@1687	1434 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	1435
adamc@542	1436 \subsection{Transactions}
adamc@542	1437
adamc@542	1438 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	1439 $$\begin{array}{l}
adamc@542	1440 \mt{con} \; \mt{transaction} :: \mt{Type} \to \mt{Type} \\
adamc@658	1441 \mt{val} \; \mt{transaction\_monad} : \mt{monad} \; \mt{transaction}
adamc@542	1442 \end{array}$$
adamc@542	1443
adamc@1123	1444 For debugging purposes, a transactional function is provided for outputting a string on the server process' \texttt{stderr}.
adamc@1123	1445 $$\begin{array}{l}
adamc@1123	1446 \mt{val} \; \mt{debug} : \mt{string} \to \mt{transaction} \; \mt{unit}
adamc@1123	1447 \end{array}$$
adamc@1123	1448
adamc@542	1449 \subsection{HTTP}
adamc@542	1450
adam@1797	1451 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	1452 $$\begin{array}{l}
adamc@786	1453 \mt{con} \; \mt{http\_cookie} :: \mt{Type} \to \mt{Type} \\
adamc@786	1454 \mt{val} \; \mt{getCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; (\mt{option} \; \mt{t}) \\
adamc@1050	1455 \mt{val} \; \mt{setCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \{\mt{Value} : \mt{t}, \mt{Expires} : \mt{option} \; \mt{time}, \mt{Secure} : \mt{bool}\} \to \mt{transaction} \; \mt{unit} \\
adamc@1050	1456 \mt{val} \; \mt{clearCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; \mt{unit}
adamc@786	1457 \end{array}$$
adamc@786	1458
adamc@786	1459 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	1460 $$\begin{array}{l}
adamc@786	1461 \mt{type} \; \mt{url} \\
adamc@786	1462 \mt{val} \; \mt{bless} : \mt{string} \to \mt{url} \\
adamc@786	1463 \mt{val} \; \mt{checkUrl} : \mt{string} \to \mt{option} \; \mt{url}
adamc@786	1464 \end{array}$$
adamc@786	1465 $\mt{bless}$ raises a runtime error if the string passed to it fails the URL policy.
adamc@786	1466
adam@1400	1467 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	1468 $$\begin{array}{l}
adamc@1085	1469 \mt{val} \; \mt{currentUrl} : \mt{transaction} \; \mt{url} \\
adamc@1085	1470 \mt{val} \; \mt{url} : \mt{transaction} \; \mt{page} \to \mt{url}
adamc@1085	1471 \end{array}$$
adamc@1085	1472
adamc@1085	1473 Page generation may be interrupted at any time with a request to redirect to a particular URL instead.
adamc@1085	1474 $$\begin{array}{l}
adamc@1085	1475 \mt{val} \; \mt{redirect} : \mt{t} ::: \mt{Type} \to \mt{url} \to \mt{transaction} \; \mt{t}
adamc@1085	1476 \end{array}$$
adamc@1085	1477
adam@1400	1478 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	1479 $$\begin{array}{l}
adamc@786	1480 \mt{type} \; \mt{file} \\
adamc@786	1481 \mt{val} \; \mt{fileName} : \mt{file} \to \mt{option} \; \mt{string} \\
adamc@786	1482 \mt{val} \; \mt{fileMimeType} : \mt{file} \to \mt{string} \\
adamc@786	1483 \mt{val} \; \mt{fileData} : \mt{file} \to \mt{blob}
adamc@786	1484 \end{array}$$
adamc@786	1485
adam@1799	1486 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	1487
adam@1465	1488 $$\begin{array}{l}
adam@1465	1489 \mt{type} \; \mt{requestHeader} \\
adam@1465	1490 \mt{val} \; \mt{blessRequestHeader} : \mt{string} \to \mt{requestHeader} \\
adam@1465	1491 \mt{val} \; \mt{checkRequestHeader} : \mt{string} \to \mt{option} \; \mt{requestHeader} \\
adam@1465	1492 \mt{val} \; \mt{getHeader} : \mt{requestHeader} \to \mt{transaction} \; (\mt{option} \; \mt{string}) \\
adam@1465	1493 \\
adam@1799	1494 \mt{type} \; \mt{envVar} \\
adam@1799	1495 \mt{val} \; \mt{blessEnvVar} : \mt{string} \to \mt{envVar} \\
adam@1799	1496 \mt{val} \; \mt{checkEnvVar} : \mt{string} \to \mt{option} \; \mt{envVar} \\
adam@1799	1497 \mt{val} \; \mt{getenv} : \mt{envVar} \to \mt{transaction} \; (\mt{option} \; \mt{string}) \\
adam@1799	1498 \\
adam@1465	1499 \mt{type} \; \mt{responseHeader} \\
adam@1465	1500 \mt{val} \; \mt{blessResponseHeader} : \mt{string} \to \mt{responseHeader} \\
adam@1465	1501 \mt{val} \; \mt{checkResponseHeader} : \mt{string} \to \mt{option} \; \mt{responseHeader} \\
adam@1465	1502 \mt{val} \; \mt{setHeader} : \mt{responseHeader} \to \mt{string} \to \mt{transaction} \; \mt{unit}
adam@1465	1503 \end{array}$$
adam@1465	1504
adamc@786	1505 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	1506 $$\begin{array}{l}
adamc@786	1507 \mt{type} \; \mt{mimeType} \\
adamc@786	1508 \mt{val} \; \mt{blessMime} : \mt{string} \to \mt{mimeType} \\
adamc@786	1509 \mt{val} \; \mt{checkMime} : \mt{string} \to \mt{option} \; \mt{mimeType} \\
adamc@786	1510 \mt{val} \; \mt{returnBlob} : \mt{t} ::: \mt{Type} \to \mt{blob} \to \mt{mimeType} \to \mt{transaction} \; \mt{t}
adamc@542	1511 \end{array}$$
adamc@542	1512
adamc@543	1513 \subsection{SQL}
adamc@543	1514
adam@1400	1515 Everything about SQL database access is restricted to server-side code.
adam@1400	1516
adamc@543	1517 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	1518 $$\begin{array}{l}
adamc@785	1519 \mt{con} \; \mt{sql\_table} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785	1520 \end{array}$$
adamc@785	1521 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	1522
adamc@785	1523 We also have the simpler type family of SQL views, which have no keys.
adamc@785	1524 $$\begin{array}{l}
adamc@785	1525 \mt{con} \; \mt{sql\_view} :: \{\mt{Type}\} \to \mt{Type}
adamc@543	1526 \end{array}$$
adamc@543	1527
adamc@785	1528 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	1529 $$\begin{array}{l}
adamc@785	1530 \mt{class} \; \mt{fieldsOf} :: \mt{Type} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785	1531 \mt{val} \; \mt{fieldsOf\_table} : \mt{fs} ::: \{\mt{Type}\} \to \mt{keys} ::: \{\{\mt{Unit}\}\} \to \mt{fieldsOf} \; (\mt{sql\_table} \; \mt{fs} \; \mt{keys}) \; \mt{fs} \\
adamc@785	1532 \mt{val} \; \mt{fieldsOf\_view} : \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; (\mt{sql\_view} \; \mt{fs}) \; \mt{fs}
adamc@785	1533 \end{array}$$
adamc@785	1534
adamc@785	1535 \subsubsection{Table Constraints}
adamc@785	1536
adamc@785	1537 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	1538
adamc@785	1539 $$\begin{array}{l}
adamc@785	1540 \mt{con} \; \mt{primary\_key} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type} \\
adamc@785	1541 \mt{val} \; \mt{no\_primary\_key} : \mt{fs} ::: \{\mt{Type}\} \to \mt{primary\_key} \; \mt{fs} \; [] \\
adamc@785	1542 \mt{val} \; \mt{primary\_key} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{key1} :: \mt{Name} \to \mt{keys} :: \{\mt{Type}\} \\
adamc@785	1543 \hspace{.1in} \to [[\mt{key1}] \sim \mt{keys}] \Rightarrow [[\mt{key1} = \mt{t}] \rc \mt{keys} \sim \mt{rest}] \\
adamc@785	1544 \hspace{.1in} \Rightarrow \$([\mt{key1} = \mt{sql\_injectable\_prim} \; \mt{t}] \rc \mt{map} \; \mt{sql\_injectable\_prim} \; \mt{keys}) \\
adamc@785	1545 \hspace{.1in} \to \mt{primary\_key} \; ([\mt{key1} = \mt{t}] \rc \mt{keys} \rc \mt{rest}) \; [\mt{Pkey} = [\mt{key1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{keys}]
adamc@785	1546 \end{array}$$
adamc@785	1547 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	1548
adamc@785	1549 A type family stands for sets of named constraints of the remaining varieties.
adamc@785	1550 $$\begin{array}{l}
adamc@785	1551 \mt{con} \; \mt{sql\_constraints} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785	1552 \end{array}$$
adamc@785	1553 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	1554
adamc@785	1555 There is a type family of individual, unnamed constraints.
adamc@785	1556 $$\begin{array}{l}
adamc@785	1557 \mt{con} \; \mt{sql\_constraint} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \mt{Type}
adamc@785	1558 \end{array}$$
adamc@785	1559 The first argument is the same as above, and the second argument gives the key columns for just this constraint.
adamc@785	1560
adamc@785	1561 We have operations for assembling constraints into constraint sets.
adamc@785	1562 $$\begin{array}{l}
adamc@785	1563 \mt{val} \; \mt{no\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_constraints} \; \mt{fs} \; [] \\
adamc@785	1564 \mt{val} \; \mt{one\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{unique} ::: \{\mt{Unit}\} \to \mt{name} :: \mt{Name} \\
adamc@785	1565 \hspace{.1in} \to \mt{sql\_constraint} \; \mt{fs} \; \mt{unique} \to \mt{sql\_constraints} \; \mt{fs} \; [\mt{name} = \mt{unique}] \\
adamc@785	1566 \mt{val} \; \mt{join\_constraints} : \mt{fs} ::: \{\mt{Type}\} \to \mt{uniques1} ::: \{\{\mt{Unit}\}\} \to \mt{uniques2} ::: \{\{\mt{Unit}\}\} \to [\mt{uniques1} \sim \mt{uniques2}] \\
adamc@785	1567 \hspace{.1in} \Rightarrow \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques1} \to \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques2} \to \mt{sql\_constraints} \; \mt{fs} \; (\mt{uniques1} \rc \mt{uniques2})
adamc@785	1568 \end{array}$$
adamc@785	1569
adamc@785	1570 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	1571 $$\begin{array}{l}
adamc@785	1572 \mt{val} \; \mt{unique} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{unique1} :: \mt{Name} \to \mt{unique} :: \{\mt{Type}\} \\
adamc@785	1573 \hspace{.1in} \to [[\mt{unique1}] \sim \mt{unique}] \Rightarrow [[\mt{unique1} = \mt{t}] \rc \mt{unique} \sim \mt{rest}] \\
adamc@785	1574 \hspace{.1in} \Rightarrow \mt{sql\_constraint} \; ([\mt{unique1} = \mt{t}] \rc \mt{unique} \rc \mt{rest}) \; ([\mt{unique1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{unique})
adamc@785	1575 \end{array}$$
adamc@785	1576
adamc@785	1577 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	1578 $$\begin{array}{l}
adamc@785	1579 \mt{class} \; \mt{linkable} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@785	1580 \mt{val} \; \mt{linkable\_same} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; \mt{t} \\
adamc@785	1581 \mt{val} \; \mt{linkable\_from\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; (\mt{option} \; \mt{t}) \; \mt{t} \\
adamc@785	1582 \mt{val} \; \mt{linkable\_to\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@785	1583 \end{array}$$
adamc@785	1584
adamc@785	1585 The $\mt{matching}$ type family uses $\mt{linkable}$ to define when two keys match up type-wise.
adamc@785	1586 $$\begin{array}{l}
adamc@785	1587 \mt{con} \; \mt{matching} :: \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785	1588 \mt{val} \; \mt{mat\_nil} : \mt{matching} \; [] \; [] \\
adamc@785	1589 \mt{val} \; \mt{mat\_cons} : \mt{t1} ::: \mt{Type} \to \mt{rest1} ::: \{\mt{Type}\} \to \mt{t2} ::: \mt{Type} \to \mt{rest2} ::: \{\mt{Type}\} \to \mt{nm1} :: \mt{Name} \to \mt{nm2} :: \mt{Name} \\
adamc@785	1590 \hspace{.1in} \to [[\mt{nm1}] \sim \mt{rest1}] \Rightarrow [[\mt{nm2}] \sim \mt{rest2}] \Rightarrow \mt{linkable} \; \mt{t1} \; \mt{t2} \to \mt{matching} \; \mt{rest1} \; \mt{rest2} \\
adamc@785	1591 \hspace{.1in} \to \mt{matching} \; ([\mt{nm1} = \mt{t1}] \rc \mt{rest1}) \; ([\mt{nm2} = \mt{t2}] \rc \mt{rest2})
adamc@785	1592 \end{array}$$
adamc@785	1593
adamc@785	1594 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	1595 $$\begin{array}{l}
adamc@785	1596 \mt{con} \; \mt{propagation\_mode} :: \{\mt{Type}\} \to \mt{Type} \\
adamc@785	1597 \mt{val} \; \mt{restrict} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785	1598 \mt{val} \; \mt{cascade} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785	1599 \mt{val} \; \mt{no\_action} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785	1600 \mt{val} \; \mt{set\_null} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; (\mt{map} \; \mt{option} \; \mt{fs})
adamc@785	1601 \end{array}$$
adamc@785	1602
adamc@785	1603 Finally, we put these ingredient together to define the \texttt{FOREIGN KEY} constraint function.
adamc@785	1604 $$\begin{array}{l}
adamc@785	1605 \mt{val} \; \mt{foreign\_key} : \mt{mine1} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{mine} ::: \{\mt{Type}\} \to \mt{munused} ::: \{\mt{Type}\} \to \mt{foreign} ::: \{\mt{Type}\} \\
adamc@785	1606 \hspace{.1in} \to \mt{funused} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{uniques} ::: \{\{\mt{Unit}\}\} \\
adamc@785	1607 \hspace{.1in} \to [[\mt{mine1}] \sim \mt{mine}] \Rightarrow [[\mt{mine1} = \mt{t}] \rc \mt{mine} \sim \mt{munused}] \Rightarrow [\mt{foreign} \sim \mt{funused}] \Rightarrow [[\mt{nm}] \sim \mt{uniques}] \\
adamc@785	1608 \hspace{.1in} \Rightarrow \mt{matching} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}) \; \mt{foreign} \\
adamc@785	1609 \hspace{.1in} \to \mt{sql\_table} \; (\mt{foreign} \rc \mt{funused}) \; ([\mt{nm} = \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{foreign}] \rc \mt{uniques}) \\
adamc@785	1610 \hspace{.1in} \to \{\mt{OnDelete} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}), \\
adamc@785	1611 \hspace{.2in} \mt{OnUpdate} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine})\} \\
adamc@785	1612 \hspace{.1in} \to \mt{sql\_constraint} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine} \rc \mt{munused}) \; []
adamc@785	1613 \end{array}$$
adamc@785	1614
adamc@785	1615 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	1616 $$\begin{array}{l}
adam@1778	1617 \mt{val} \; \mt{check} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; [] \; [] \; \mt{fs} \; \mt{bool} \to \mt{sql\_constraint} \; \mt{fs} \; []
adamc@785	1618 \end{array}$$
adamc@785	1619
adamc@785	1620 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	1621
adamc@784	1622
adamc@543	1623 \subsubsection{Queries}
adamc@543	1624
adam@1400	1625 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	1626 $$\begin{array}{l}
adam@1400	1627 \mt{con} \; \mt{sql\_query} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@1193	1628 \mt{val} \; \mt{sql\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400	1629 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adamc@1193	1630 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543	1631 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543	1632 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1193	1633 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adam@1400	1634 \hspace{.1in} \Rightarrow \{\mt{Rows} : \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}, \\
adamc@1193	1635 \hspace{.2in} \mt{OrderBy} : \mt{sql\_order\_by} \; (\mt{free} \rc \mt{tables}) \; \mt{selectedExps}, \\
adamc@543	1636 \hspace{.2in} \mt{Limit} : \mt{sql\_limit}, \\
adamc@543	1637 \hspace{.2in} \mt{Offset} : \mt{sql\_offset}\} \\
adam@1400	1638 \hspace{.1in} \to \mt{sql\_query} \; \mt{free} \; \mt{afree} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543	1639 \end{array}$$
adamc@543	1640
adamc@545	1641 Queries are used by folding over their results inside transactions.
adamc@545	1642 $$\begin{array}{l}
adam@1400	1643 \mt{val} \; \mt{query} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to [\mt{tables} \sim \mt{exps}] \Rightarrow \mt{state} ::: \mt{Type} \to \mt{sql\_query} \; [] \; [] \; \mt{tables} \; \mt{exps} \\
adamc@658	1644 \hspace{.1in} \to (\$(\mt{exps} \rc \mt{map} \; (\lambda \mt{fields} :: \{\mt{Type}\} \Rightarrow \$\mt{fields}) \; \mt{tables}) \\
adamc@545	1645 \hspace{.2in} \to \mt{state} \to \mt{transaction} \; \mt{state}) \\
adamc@545	1646 \hspace{.1in} \to \mt{state} \to \mt{transaction} \; \mt{state}
adamc@545	1647 \end{array}$$
adamc@545	1648
adam@1400	1649 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	1650 $$\begin{array}{l}
adam@1400	1651 \mt{con} \; \mt{sql\_query1} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@543	1652 \\
adamc@543	1653 \mt{type} \; \mt{sql\_relop} \\
adamc@543	1654 \mt{val} \; \mt{sql\_union} : \mt{sql\_relop} \\
adamc@543	1655 \mt{val} \; \mt{sql\_intersect} : \mt{sql\_relop} \\
adamc@543	1656 \mt{val} \; \mt{sql\_except} : \mt{sql\_relop} \\
adam@1400	1657 \mt{val} \; \mt{sql\_relop} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400	1658 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adam@1400	1659 \hspace{.1in} \to \mt{tables1} ::: \{\{\mt{Type}\}\} \\
adamc@543	1660 \hspace{.1in} \to \mt{tables2} ::: \{\{\mt{Type}\}\} \\
adamc@543	1661 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543	1662 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@543	1663 \hspace{.1in} \to \mt{sql\_relop} \\
adam@1458	1664 \hspace{.1in} \to \mt{bool} \; (* \; \mt{ALL} \; *) \\
adam@1400	1665 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables1} \; \mt{selectedFields} \; \mt{selectedExps} \\
adam@1400	1666 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables2} \; \mt{selectedFields} \; \mt{selectedExps} \\
adam@1400	1667 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{selectedFields} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543	1668 \end{array}$$
adamc@543	1669
adamc@543	1670 $$\begin{array}{l}
adamc@1193	1671 \mt{val} \; \mt{sql\_query1} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400	1672 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adamc@1193	1673 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543	1674 \hspace{.1in} \to \mt{grouped} ::: \{\{\mt{Type}\}\} \\
adamc@543	1675 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543	1676 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1085	1677 \hspace{.1in} \to \mt{empties} :: \{\mt{Unit}\} \\
adamc@1193	1678 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adamc@1193	1679 \hspace{.1in} \Rightarrow [\mt{free} \sim \mt{grouped}] \\
adam@1400	1680 \hspace{.1in} \Rightarrow [\mt{afree} \sim \mt{tables}] \\
adamc@1193	1681 \hspace{.1in} \Rightarrow [\mt{empties} \sim \mt{selectedFields}] \\
adamc@1085	1682 \hspace{.1in} \Rightarrow \{\mt{Distinct} : \mt{bool}, \\
adamc@1193	1683 \hspace{.2in} \mt{From} : \mt{sql\_from\_items} \; \mt{free} \; \mt{tables}, \\
adam@1778	1684 \hspace{.2in} \mt{Where} : \mt{sql\_exp} \; (\mt{free} \rc \mt{tables}) \; \mt{afree} \; [] \; \mt{bool}, \\
adamc@543	1685 \hspace{.2in} \mt{GroupBy} : \mt{sql\_subset} \; \mt{tables} \; \mt{grouped}, \\
adam@1778	1686 \hspace{.2in} \mt{Having} : \mt{sql\_exp} \; (\mt{free} \rc \mt{grouped}) \; (\mt{afree} \rc \mt{tables}) \; [] \; \mt{bool}, \\
adamc@1085	1687 \hspace{.2in} \mt{SelectFields} : \mt{sql\_subset} \; \mt{grouped} \; (\mt{map} \; (\lambda \_ \Rightarrow []) \; \mt{empties} \rc \mt{selectedFields}), \\
adam@1778	1688 \hspace{.2in} \mt {SelectExps} : \$(\mt{map} \; (\mt{sql\_expw} \; (\mt{free} \rc \mt{grouped}) \; (\mt{afree} \rc \mt{tables}) \; []) \; \mt{selectedExps}) \} \\
adam@1400	1689 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543	1690 \end{array}$$
adamc@543	1691
adamc@543	1692 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	1693 $$\begin{array}{l}
adamc@543	1694 \mt{con} \; \mt{sql\_subset} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@543	1695 \mt{val} \; \mt{sql\_subset} : \mt{keep\_drop} :: \{(\{\mt{Type}\} \times \{\mt{Type}\})\} \\
adamc@543	1696 \hspace{.1in} \to \mt{sql\_subset} \\
adamc@658	1697 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1 \rc \mt{fields}.2)\; \mt{keep\_drop}) \\
adamc@658	1698 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1) \; \mt{keep\_drop}) \\
adamc@543	1699 \mt{val} \; \mt{sql\_subset\_all} : \mt{tables} :: \{\{\mt{Type}\}\} \to \mt{sql\_subset} \; \mt{tables} \; \mt{tables}
adamc@543	1700 \end{array}$$
adamc@543	1701
adam@1778	1702 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	1703 $$\begin{array}{l}
adam@1778	1704 \mt{con} \; \mt{sql\_exp} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}
adamc@543	1705 \end{array}$$
adamc@543	1706
adamc@543	1707 Any field in scope may be converted to an expression.
adamc@543	1708 $$\begin{array}{l}
adamc@543	1709 \mt{val} \; \mt{sql\_field} : \mt{otherTabs} ::: \{\{\mt{Type}\}\} \to \mt{otherFields} ::: \{\mt{Type}\} \\
adam@1778	1710 \hspace{.1in} \to \mt{fieldType} ::: \mt{Type} \to \mt{agg} ::: \{\{\mt{Type}\}\} \\
adamc@543	1711 \hspace{.1in} \to \mt{exps} ::: \{\mt{Type}\} \\
adamc@543	1712 \hspace{.1in} \to \mt{tab} :: \mt{Name} \to \mt{field} :: \mt{Name} \\
adam@1778	1713 \hspace{.1in} \to \mt{sql\_exp} \; ([\mt{tab} = [\mt{field} = \mt{fieldType}] \rc \mt{otherFields}] \rc \mt{otherTabs}) \; \mt{agg} \; \mt{exps} \; \mt{fieldType}
adamc@543	1714 \end{array}$$
adamc@543	1715
adamc@544	1716 There is an analogous function for referencing named expressions.
adamc@544	1717 $$\begin{array}{l}
adam@1778	1718 \mt{val} \; \mt{sql\_exp} : \mt{tabs} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{t} ::: \mt{Type} \to \mt{rest} ::: \{\mt{Type}\} \to \mt{nm} :: \mt{Name} \\
adam@1778	1719 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tabs} \; \mt{agg} \; ([\mt{nm} = \mt{t}] \rc \mt{rest}) \; \mt{t}
adamc@544	1720 \end{array}$$
adamc@544	1721
adamc@544	1722 Ur values of appropriate types may be injected into SQL expressions.
adamc@544	1723 $$\begin{array}{l}
adamc@786	1724 \mt{class} \; \mt{sql\_injectable\_prim} \\
adamc@786	1725 \mt{val} \; \mt{sql\_bool} : \mt{sql\_injectable\_prim} \; \mt{bool} \\
adamc@786	1726 \mt{val} \; \mt{sql\_int} : \mt{sql\_injectable\_prim} \; \mt{int} \\
adamc@786	1727 \mt{val} \; \mt{sql\_float} : \mt{sql\_injectable\_prim} \; \mt{float} \\
adamc@786	1728 \mt{val} \; \mt{sql\_string} : \mt{sql\_injectable\_prim} \; \mt{string} \\
adamc@786	1729 \mt{val} \; \mt{sql\_time} : \mt{sql\_injectable\_prim} \; \mt{time} \\
adamc@786	1730 \mt{val} \; \mt{sql\_blob} : \mt{sql\_injectable\_prim} \; \mt{blob} \\
adamc@786	1731 \mt{val} \; \mt{sql\_channel} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{channel} \; \mt{t}) \\
adamc@786	1732 \mt{val} \; \mt{sql\_client} : \mt{sql\_injectable\_prim} \; \mt{client} \\
adamc@786	1733 \\
adamc@544	1734 \mt{class} \; \mt{sql\_injectable} \\
adamc@786	1735 \mt{val} \; \mt{sql\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@786	1736 \mt{val} \; \mt{sql\_option\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; (\mt{option} \; \mt{t}) \\
adamc@786	1737 \\
adam@1778	1738 \mt{val} \; \mt{sql\_inject} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{sql\_injectable} \; \mt{t} \\
adam@1778	1739 \hspace{.1in} \to \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adamc@544	1740 \end{array}$$
adamc@544	1741
adamc@1123	1742 Additionally, most function-free types may be injected safely, via the $\mt{serialized}$ type family.
adamc@1123	1743 $$\begin{array}{l}
adamc@1123	1744 \mt{con} \; \mt{serialized} :: \mt{Type} \to \mt{Type} \\
adamc@1123	1745 \mt{val} \; \mt{serialize} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{serialized} \; \mt{t} \\
adamc@1123	1746 \mt{val} \; \mt{deserialize} : \mt{t} ::: \mt{Type} \to \mt{serialized} \; \mt{t} \to \mt{t} \\
adamc@1123	1747 \mt{val} \; \mt{sql\_serialized} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{serialized} \; \mt{t})
adamc@1123	1748 \end{array}$$
adamc@1123	1749
adamc@544	1750 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	1751 $$\begin{array}{l}
adam@1778	1752 \mt{val} \; \mt{sql\_is\_null} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778	1753 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; (\mt{option} \; \mt{t}) \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{bool}
adamc@544	1754 \end{array}$$
adamc@544	1755
adam@1602	1756 As another way of dealing with null values, there is also a restricted form of the standard \cd{COALESCE} function.
adam@1602	1757 $$\begin{array}{l}
adam@1602	1758 \mt{val} \; \mt{sql\_coalesce} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778	1759 \hspace{.1in} \to \mt{t} ::: \mt{Type} \\
adam@1778	1760 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; (\mt{option} \; \mt{t}) \\
adam@1778	1761 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778	1762 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adam@1602	1763 \end{array}$$
adam@1602	1764
adamc@559	1765 We have generic nullary, unary, and binary operators.
adamc@544	1766 $$\begin{array}{l}
adamc@544	1767 \mt{con} \; \mt{sql\_nfunc} :: \mt{Type} \to \mt{Type} \\
adamc@544	1768 \mt{val} \; \mt{sql\_current\_timestamp} : \mt{sql\_nfunc} \; \mt{time} \\
adam@1778	1769 \mt{val} \; \mt{sql\_nfunc} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778	1770 \hspace{.1in} \to \mt{sql\_nfunc} \; \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\\end{array}$$
adamc@544	1771
adamc@544	1772 $$\begin{array}{l}
adamc@544	1773 \mt{con} \; \mt{sql\_unary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544	1774 \mt{val} \; \mt{sql\_not} : \mt{sql\_unary} \; \mt{bool} \; \mt{bool} \\
adam@1778	1775 \mt{val} \; \mt{sql\_unary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adam@1778	1776 \hspace{.1in} \to \mt{sql\_unary} \; \mt{arg} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res} \\
adamc@544	1777 \end{array}$$
adamc@544	1778
adamc@544	1779 $$\begin{array}{l}
adamc@544	1780 \mt{con} \; \mt{sql\_binary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544	1781 \mt{val} \; \mt{sql\_and} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544	1782 \mt{val} \; \mt{sql\_or} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adam@1778	1783 \mt{val} \; \mt{sql\_binary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg_1} ::: \mt{Type} \to \mt{arg_2} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adam@1778	1784 \hspace{.1in} \to \mt{sql\_binary} \; \mt{arg_1} \; \mt{arg_2} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_1} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_2} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res}
adamc@544	1785 \end{array}$$
adamc@544	1786
adamc@544	1787 $$\begin{array}{l}
adamc@559	1788 \mt{class} \; \mt{sql\_arith} \\
adamc@559	1789 \mt{val} \; \mt{sql\_int\_arith} : \mt{sql\_arith} \; \mt{int} \\
adamc@559	1790 \mt{val} \; \mt{sql\_float\_arith} : \mt{sql\_arith} \; \mt{float} \\
adamc@559	1791 \mt{val} \; \mt{sql\_neg} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_unary} \; \mt{t} \; \mt{t} \\
adamc@559	1792 \mt{val} \; \mt{sql\_plus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559	1793 \mt{val} \; \mt{sql\_minus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559	1794 \mt{val} \; \mt{sql\_times} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559	1795 \mt{val} \; \mt{sql\_div} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559	1796 \mt{val} \; \mt{sql\_mod} : \mt{sql\_binary} \; \mt{int} \; \mt{int} \; \mt{int}
adamc@559	1797 \end{array}$$
adamc@544	1798
adam@1797	1799 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	1800 $$\begin{array}{l}
adam@1778	1801 \mt{val} \; \mt{sql\_count} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int}
adamc@544	1802 \end{array}$$
adamc@544	1803
adamc@544	1804 $$\begin{array}{l}
adamc@1188	1805 \mt{con} \; \mt{sql\_aggregate} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adam@1778	1806 \mt{val} \; \mt{sql\_aggregate} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{dom} ::: \mt{Type} \to \mt{ran} ::: \mt{Type} \\
adam@1778	1807 \hspace{.1in} \to \mt{sql\_aggregate} \; \mt{dom} \; \mt{ran} \to \mt{sql\_exp} \; \mt{agg} \; \mt{agg} \; \mt{exps} \; \mt{dom} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{ran}
adamc@1188	1808 \end{array}$$
adamc@1188	1809
adamc@1188	1810 $$\begin{array}{l}
adamc@1188	1811 \mt{val} \; \mt{sql\_count\_col} : \mt{t} ::: \mt{Type} \to \mt{sql\_aggregate} \; (\mt{option} \; \mt{t}) \; \mt{int}
adamc@544	1812 \end{array}$$
adam@1400	1813
adam@1400	1814 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	1815
adamc@544	1816 $$\begin{array}{l}
adamc@544	1817 \mt{class} \; \mt{sql\_summable} \\
adamc@544	1818 \mt{val} \; \mt{sql\_summable\_int} : \mt{sql\_summable} \; \mt{int} \\
adamc@544	1819 \mt{val} \; \mt{sql\_summable\_float} : \mt{sql\_summable} \; \mt{float} \\
adam@1777	1820 \mt{val} \; \mt{sql\_avg} : \mt{t} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{sql\_aggregate} \; \mt{t} \; (\mt{option} \; \mt{float}) \\
adam@1400	1821 \mt{val} \; \mt{sql\_sum} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt}
adamc@544	1822 \end{array}$$
adamc@544	1823
adamc@544	1824 $$\begin{array}{l}
adamc@544	1825 \mt{class} \; \mt{sql\_maxable} \\
adamc@544	1826 \mt{val} \; \mt{sql\_maxable\_int} : \mt{sql\_maxable} \; \mt{int} \\
adamc@544	1827 \mt{val} \; \mt{sql\_maxable\_float} : \mt{sql\_maxable} \; \mt{float} \\
adamc@544	1828 \mt{val} \; \mt{sql\_maxable\_string} : \mt{sql\_maxable} \; \mt{string} \\
adamc@544	1829 \mt{val} \; \mt{sql\_maxable\_time} : \mt{sql\_maxable} \; \mt{time} \\
adam@1400	1830 \mt{val} \; \mt{sql\_max} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt} \\
adam@1400	1831 \mt{val} \; \mt{sql\_min} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt}
adamc@544	1832 \end{array}$$
adamc@544	1833
adam@1778	1834 Any SQL query that returns single columns may be turned into a subquery expression.
adam@1777	1835
adam@1777	1836 $$\begin{array}{l}
adam@1778	1837 \mt{val} \; \mt{sql\_subquery} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \\
adam@1778	1838 \hspace{.1in} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_query} \; \mt{tables} \; \mt{agg} \; [\mt{nm} = \mt{t}] \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{nt}
adamc@1193	1839 \end{array}$$
adamc@1193	1840
adam@1573	1841 There is also an \cd{IF..THEN..ELSE..} construct that is compiled into standard SQL \cd{CASE} expressions.
adam@1573	1842 $$\begin{array}{l}
adam@1778	1843 \mt{val} \; \mt{sql\_if\_then\_else} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778	1844 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{bool} \\
adam@1778	1845 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778	1846 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778	1847 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adam@1573	1848 \end{array}$$
adam@1573	1849
adamc@1193	1850 \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	1851 $$\begin{array}{l}
adamc@1193	1852 \mt{con} \; \mt{sql\_from\_items} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@1193	1853 \mt{val} \; \mt{sql\_from\_table} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adamc@1193	1854 \hspace{.1in} \to \mt{t} ::: \mt{Type} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; \mt{t} \; \mt{fs} \to \mt{name} :: \mt{Name} \to \mt{t} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193	1855 \mt{val} \; \mt{sql\_from\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{name} :: \mt{Name} \to \mt{sql\_query} \; \mt{free} \; [] \; \mt{fs} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193	1856 \mt{val} \; \mt{sql\_from\_comma} : \mt{free} ::: \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \to [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193	1857 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adamc@1193	1858 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2}) \\
adamc@1193	1859 \mt{val} \; \mt{sql\_inner\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \\
adamc@1193	1860 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193	1861 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adam@1778	1862 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193	1863 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2})
adamc@786	1864 \end{array}$$
adamc@786	1865
adamc@786	1866 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	1867 $$\begin{array}{l}
adamc@786	1868 \mt{class} \; \mt{nullify} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@786	1869 \mt{val} \; \mt{nullify\_option} : \mt{t} ::: \mt{Type} \to \mt{nullify} \; (\mt{option} \; \mt{t}) \; (\mt{option} \; \mt{t}) \\
adamc@786	1870 \mt{val} \; \mt{nullify\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{nullify} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@786	1871 \end{array}$$
adamc@786	1872
adamc@786	1873 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	1874
adamc@786	1875 $$\begin{array}{l}
adamc@1193	1876 \mt{val} \; \mt{sql\_left\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{(\mt{Type} \times \mt{Type})\}\} \\
adamc@1193	1877 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@786	1878 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\lambda \mt{r} \Rightarrow \$(\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{nullify} \; \mt{p}.1 \; \mt{p}.2) \; \mt{r})) \; \mt{tabs2}) \\
adamc@1193	1879 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \\
adam@1778	1880 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193	1881 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.2)) \; \mt{tabs2})
adamc@786	1882 \end{array}$$
adamc@786	1883
adamc@544	1884 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	1885 $$\begin{array}{l}
adamc@544	1886 \mt{type} \; \mt{sql\_direction} \\
adamc@544	1887 \mt{val} \; \mt{sql\_asc} : \mt{sql\_direction} \\
adamc@544	1888 \mt{val} \; \mt{sql\_desc} : \mt{sql\_direction} \\
adamc@544	1889 \\
adamc@544	1890 \mt{con} \; \mt{sql\_order\_by} :: \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@544	1891 \mt{val} \; \mt{sql\_order\_by\_Nil} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} :: \{\mt{Type}\} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adam@1778	1892 \mt{val} \; \mt{sql\_order\_by\_Cons} : \mt{tf} ::: (\{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}) \\
adam@1778	1893 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778	1894 \hspace{.1in} \to \mt{sql\_window} \; \mt{tf} \to \mt{tf} \; \mt{tables} \; [] \; \mt{exps} \; \mt{t} \to \mt{sql\_direction} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adam@1684	1895 \mt{val} \; \mt{sql\_order\_by\_random} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544	1896 \\
adamc@544	1897 \mt{type} \; \mt{sql\_limit} \\
adamc@544	1898 \mt{val} \; \mt{sql\_no\_limit} : \mt{sql\_limit} \\
adamc@544	1899 \mt{val} \; \mt{sql\_limit} : \mt{int} \to \mt{sql\_limit} \\
adamc@544	1900 \\
adamc@544	1901 \mt{type} \; \mt{sql\_offset} \\
adamc@544	1902 \mt{val} \; \mt{sql\_no\_offset} : \mt{sql\_offset} \\
adamc@544	1903 \mt{val} \; \mt{sql\_offset} : \mt{int} \to \mt{sql\_offset}
adamc@544	1904 \end{array}$$
adamc@544	1905
adam@1778	1906 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	1907 $$\begin{array}{l}
adam@1778	1908 \mt{con} \; \mt{sql\_expw} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type} \\
adam@1778	1909 \\
adam@1778	1910 \mt{class} \; \mt{sql\_window} :: (\{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}) \to \mt{Type} \\
adam@1778	1911 \mt{val} \; \mt{sql\_window\_normal} : \mt{sql\_window} \; \mt{sql\_exp} \\
adam@1778	1912 \mt{val} \; \mt{sql\_window\_fancy} : \mt{sql\_window} \; \mt{sql\_expw} \\
adam@1778	1913 \mt{val} \; \mt{sql\_window} : \mt{tf} ::: (\{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}) \\
adam@1778	1914 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778	1915 \hspace{.1in} \to \mt{sql\_window} \; \mt{tf} \\
adam@1778	1916 \hspace{.1in} \to \mt{tf} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778	1917 \hspace{.1in} \to \mt{sql\_expw} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778	1918 \\
adam@1778	1919 \mt{con} \; \mt{sql\_partition} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adam@1778	1920 \mt{val} \; \mt{sql\_no\_partition} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778	1921 \hspace{.1in} \to \mt{sql\_partition} \; \mt{tables} \; \mt{agg} \; \mt{exps} \\
adam@1778	1922 \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	1923 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778	1924 \hspace{.1in} \to \mt{sql\_partition} \; \mt{tables} \; \mt{agg} \; \mt{exps} \\
adam@1778	1925 \\
adam@1778	1926 \mt{con} \; \mt{sql\_window\_function} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type} \\
adam@1778	1927 \mt{val} \; \mt{sql\_window\_function} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778	1928 \hspace{.1in} \to \mt{t} ::: \mt{Type} \\
adam@1778	1929 \hspace{.1in} \to \mt{sql\_window\_function} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778	1930 \hspace{.1in} \to \mt{sql\_partition} \; \mt{tables} \; \mt{agg} \; \mt{exps} \\
adam@1778	1931 \hspace{.1in} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adam@1778	1932 \hspace{.1in} \to \mt{sql\_expw} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778	1933 \\
adam@1778	1934 \mt{val} \; \mt{sql\_window\_aggregate} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778	1935 \hspace{.1in} \to \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \\
adam@1778	1936 \hspace{.1in} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt} \\
adam@1778	1937 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778	1938 \hspace{.1in} \to \mt{sql\_window\_function} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{nt} \\
adam@1778	1939 \mt{val} \; \mt{sql\_window\_count} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778	1940 \hspace{.1in} \to \mt{sql\_window\_function} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int} \\
adam@1778	1941 \mt{val} \; \mt{sql\_rank} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778	1942 \hspace{.1in} \to \mt{sql\_window\_function} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int}
adam@1778	1943 \end{array}$$
adam@1778	1944
adamc@545	1945
adamc@545	1946 \subsubsection{DML}
adamc@545	1947
adamc@545	1948 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	1949
adamc@545	1950 $$\begin{array}{l}
adamc@545	1951 \mt{type} \; \mt{dml} \\
adamc@545	1952 \mt{val} \; \mt{dml} : \mt{dml} \to \mt{transaction} \; \mt{unit}
adamc@545	1953 \end{array}$$
adamc@545	1954
adam@1297	1955 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	1956
adam@1297	1957 $$\begin{array}{l}
adam@1297	1958 \mt{val} \; \mt{tryDml} : \mt{dml} \to \mt{transaction} \; (\mt{option} \; \mt{string})
adam@1297	1959 \end{array}$$
adam@1297	1960
adam@1797	1961 Properly typed records may be used to form $\mt{INSERT}$ commands.
adamc@545	1962 $$\begin{array}{l}
adamc@545	1963 \mt{val} \; \mt{insert} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \\
adam@1778	1964 \hspace{.1in} \to \$(\mt{map} \; (\mt{sql\_exp} \; [] \; [] \; []) \; \mt{fields}) \to \mt{dml}
adamc@545	1965 \end{array}$$
adamc@545	1966
adam@1578	1967 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	1968 $$\begin{array}{l}
adam@1380	1969 \mt{val} \; \mt{update} : \mt{unchanged} ::: \{\mt{Type}\} \to \mt{changed} :: \{\mt{Type}\} \to [\mt{changed} \sim \mt{unchanged}] \\
adam@1778	1970 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; []) \; \mt{changed}) \\
adam@1778	1971 \hspace{.1in} \to \mt{sql\_table} \; (\mt{changed} \rc \mt{unchanged}) \to \mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545	1972 \end{array}$$
adamc@545	1973
adam@1578	1974 A $\mt{DELETE}$ command is formed from a table and a $\mt{WHERE}$ clause. The above use of $\mt{T}$ is repeated.
adamc@545	1975 $$\begin{array}{l}
adam@1778	1976 \mt{val} \; \mt{delete} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \to \mt{sql\_exp} \; [\mt{T} = \mt{fields}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545	1977 \end{array}$$
adamc@545	1978
adamc@546	1979 \subsubsection{Sequences}
adamc@546	1980
adamc@546	1981 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	1982
adamc@546	1983 $$\begin{array}{l}
adamc@546	1984 \mt{type} \; \mt{sql\_sequence} \\
adamc@1085	1985 \mt{val} \; \mt{nextval} : \mt{sql\_sequence} \to \mt{transaction} \; \mt{int} \\
adamc@1085	1986 \mt{val} \; \mt{setval} : \mt{sql\_sequence} \to \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@546	1987 \end{array}$$
adamc@546	1988
adamc@546	1989
adam@1648	1990 \subsection{\label{xml}XML}
adamc@547	1991
adam@1333	1992 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	1993
adam@1642	1994 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	1995 $$\begin{array}{l}
adamc@547	1996 \mt{con} \; \mt{xml} :: \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547	1997 \end{array}$$
adamc@547	1998
adamc@547	1999 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	2000 $$\begin{array}{l}
adamc@547	2001 \mt{con} \; \mt{tag} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547	2002 \end{array}$$
adamc@547	2003
adamc@547	2004 Literal text may be injected into XML as ``CDATA.''
adamc@547	2005 $$\begin{array}{l}
adamc@547	2006 \mt{val} \; \mt{cdata} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{string} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adamc@547	2007 \end{array}$$
adamc@547	2008
adam@1358	2009 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	2010 $$\begin{array}{l}
adam@1358	2011 \mt{val} \; \mt{cdataChar} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{char} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adam@1358	2012 \end{array}$$
adam@1358	2013
adamc@547	2014 There is a function for producing an XML tree with a particular tag at its root.
adamc@547	2015 $$\begin{array}{l}
adamc@547	2016 \mt{val} \; \mt{tag} : \mt{attrsGiven} ::: \{\mt{Type}\} \to \mt{attrsAbsent} ::: \{\mt{Type}\} \to \mt{ctxOuter} ::: \{\mt{Unit}\} \to \mt{ctxInner} ::: \{\mt{Unit}\} \\
adamc@547	2017 \hspace{.1in} \to \mt{useOuter} ::: \{\mt{Type}\} \to \mt{useInner} ::: \{\mt{Type}\} \to \mt{bindOuter} ::: \{\mt{Type}\} \to \mt{bindInner} ::: \{\mt{Type}\} \\
adam@1380	2018 \hspace{.1in} \to [\mt{attrsGiven} \sim \mt{attrsAbsent}] \Rightarrow [\mt{useOuter} \sim \mt{useInner}] \Rightarrow [\mt{bindOuter} \sim \mt{bindInner}] \\
adam@1749	2019 \hspace{.1in} \Rightarrow \mt{css\_class} \\
adam@1643	2020 \hspace{.1in} \to \mt{option} \; (\mt{signal} \; \mt{css\_class}) \\
adam@1750	2021 \hspace{.1in} \to \mt{css\_style} \\
adam@1751	2022 \hspace{.1in} \to \mt{option} \; (\mt{signal} \; \mt{css\_style}) \\
adamc@787	2023 \hspace{.1in} \to \$\mt{attrsGiven} \\
adamc@547	2024 \hspace{.1in} \to \mt{tag} \; (\mt{attrsGiven} \rc \mt{attrsAbsent}) \; \mt{ctxOuter} \; \mt{ctxInner} \; \mt{useOuter} \; \mt{bindOuter} \\
adamc@547	2025 \hspace{.1in} \to \mt{xml} \; \mt{ctxInner} \; \mt{useInner} \; \mt{bindInner} \to \mt{xml} \; \mt{ctxOuter} \; (\mt{useOuter} \rc \mt{useInner}) \; (\mt{bindOuter} \rc \mt{bindInner})
adamc@547	2026 \end{array}$$
adam@1750	2027 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	2028
adam@1643	2029 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	2030
adam@1751	2031 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	2032
adamc@547	2033 Two XML fragments may be concatenated.
adamc@547	2034 $$\begin{array}{l}
adamc@547	2035 \mt{val} \; \mt{join} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{bind_1} ::: \{\mt{Type}\} \to \mt{bind_2} ::: \{\mt{Type}\} \\
adam@1380	2036 \hspace{.1in} \to [\mt{use_1} \sim \mt{bind_1}] \Rightarrow [\mt{bind_1} \sim \mt{bind_2}] \\
adamc@547	2037 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind_1} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{bind_1}) \; \mt{bind_2} \to \mt{xml} \; \mt{ctx} \; \mt{use_1} \; (\mt{bind_1} \rc \mt{bind_2})
adamc@547	2038 \end{array}$$
adamc@547	2039
adamc@547	2040 Finally, any XML fragment may be updated to ``claim'' to use more form fields than it does.
adamc@547	2041 $$\begin{array}{l}
adam@1380	2042 \mt{val} \; \mt{useMore} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{use_2} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to [\mt{use_1} \sim \mt{use_2}] \\
adamc@547	2043 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{use_2}) \; \mt{bind}
adamc@547	2044 \end{array}$$
adamc@547	2045
adam@1344	2046 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	2047
adamc@547	2048 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	2049 $$\begin{array}{l}
adam@1641	2050 \mt{val} \; \mt{error} : \mt{t} ::: \mt{Type} \to \mt{xbody} \to \mt{t}
adamc@547	2051 \end{array}$$
adamc@547	2052
adamc@549	2053
adamc@701	2054 \subsection{Client-Side Programming}
adamc@659	2055
adamc@701	2056 Ur/Web supports running code on web browsers, via automatic compilation to JavaScript.
adamc@701	2057
adamc@701	2058 \subsubsection{The Basics}
adamc@701	2059
adam@1400	2060 All of the functions in this subsection are client-side only.
adam@1400	2061
adam@1297	2062 Clients can open alert and confirm dialog boxes, in the usual annoying JavaScript way.
adamc@701	2063 $$\begin{array}{l}
adam@1297	2064 \mt{val} \; \mt{alert} : \mt{string} \to \mt{transaction} \; \mt{unit} \\
adam@1297	2065 \mt{val} \; \mt{confirm} : \mt{string} \to \mt{transaction} \; \mt{bool}
adamc@701	2066 \end{array}$$
adamc@701	2067
adamc@701	2068 Any transaction may be run in a new thread with the $\mt{spawn}$ function.
adamc@701	2069 $$\begin{array}{l}
adamc@701	2070 \mt{val} \; \mt{spawn} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit}
adamc@701	2071 \end{array}$$
adamc@701	2072
adamc@701	2073 The current thread can be paused for at least a specified number of milliseconds.
adamc@701	2074 $$\begin{array}{l}
adamc@701	2075 \mt{val} \; \mt{sleep} : \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@701	2076 \end{array}$$
adamc@701	2077
adam@1770	2078 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	2079 $$\begin{array}{l}
adamc@787	2080 \mt{val} \; \mt{onError} : (\mt{xbody} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787	2081 \mt{val} \; \mt{onFail} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787	2082 \mt{val} \; \mt{onConnectFail} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787	2083 \mt{val} \; \mt{onDisconnect} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787	2084 \mt{val} \; \mt{onServerError} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit}
adamc@787	2085 \end{array}$$
adamc@787	2086
adam@1555	2087 There are also functions to register standard document-level event handlers.
adam@1555	2088
adam@1555	2089 $$\begin{array}{l}
adam@1783	2090 \mt{val} \; \mt{onClick} : (\mt{mouseEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783	2091 \mt{val} \; \mt{onDblclick} : (\mt{mouseEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783	2092 \mt{val} \; \mt{onKeydown} : (\mt{keyEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783	2093 \mt{val} \; \mt{onKeypress} : (\mt{keyEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783	2094 \mt{val} \; \mt{onKeyup} : (\mt{keyEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783	2095 \mt{val} \; \mt{onMousedown} : (\mt{mouseEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783	2096 \mt{val} \; \mt{onMouseup} : (\mt{mouseEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit}
adam@1555	2097 \end{array}$$
adam@1555	2098
adam@1559	2099 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	2100
adam@1559	2101 $$\begin{array}{l}
adam@1559	2102 \mt{val} \; \mt{preventDefault} : \mt{transaction} \; \mt{unit} \\
adam@1559	2103 \mt{val} \; \mt{stopPropagation} : \mt{transaction} \; \mt{unit}
adam@1559	2104 \end{array}$$
adam@1559	2105
adam@1556	2106 \subsubsection{Node IDs}
adam@1556	2107
adam@1556	2108 There is an abstract type of node IDs that may be assigned to \cd{id} attributes of most HTML tags.
adam@1556	2109
adam@1556	2110 $$\begin{array}{l}
adam@1556	2111 \mt{type} \; \mt{id} \\
adam@1556	2112 \mt{val} \; \mt{fresh} : \mt{transaction} \; \mt{id}
adam@1556	2113 \end{array}$$
adam@1556	2114
adam@1785	2115 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	2116
adam@1785	2117 One further use of IDs is as handles for requesting that \emph{focus} be given to specific tags.
adam@1785	2118
adam@1785	2119 $$\begin{array}{l}
adam@1785	2120 \mt{val} \; \mt{giveFocus} : \mt{id} \to \mt{transaction} \; \mt{unit}
adam@1785	2121 \end{array}$$
adam@1556	2122
adam@1643	2123 \subsubsection{\label{signals}Functional-Reactive Page Generation}
adamc@701	2124
adamc@701	2125 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	2126
adam@1403	2127 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	2128
adamc@659	2129 $$\begin{array}{l}
adamc@659	2130 \mt{con} \; \mt{source} :: \mt{Type} \to \mt{Type} \\
adamc@659	2131 \mt{val} \; \mt{source} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{transaction} \; (\mt{source} \; \mt{t}) \\
adamc@659	2132 \mt{val} \; \mt{set} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@659	2133 \mt{val} \; \mt{get} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@659	2134 \end{array}$$
adamc@659	2135
adam@1400	2136 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	2137
adam@1608	2138 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	2139
adamc@659	2140 $$\begin{array}{l}
adamc@659	2141 \mt{con} \; \mt{signal} :: \mt{Type} \to \mt{Type} \\
adamc@659	2142 \mt{val} \; \mt{signal\_monad} : \mt{monad} \; \mt{signal} \\
adam@1608	2143 \mt{val} \; \mt{signal} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{signal} \; \mt{t} \\
adam@1608	2144 \mt{val} \; \mt{current} : \mt{t} ::: \mt{Type} \to \mt{signal} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@659	2145 \end{array}$$
adamc@659	2146
adamc@659	2147 A reactive portion of an HTML page is injected with a $\mt{dyn}$ tag, which has a signal-valued attribute $\mt{Signal}$.
adamc@659	2148
adamc@659	2149 $$\begin{array}{l}
adam@1641	2150 \mt{val} \; \mt{dyn} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to [\mt{ctx} \sim [\mt{Dyn}]] \Rightarrow \mt{unit} \\
adam@1641	2151 \hspace{.1in} \to \mt{tag} \; [\mt{Signal} = \mt{signal} \; (\mt{xml} \; ([\mt{Dyn}] \rc \mt{ctx}) \; \mt{use} \; \mt{bind})] \; ([\mt{Dyn}] \rc \mt{ctx}) \; [] \; \mt{use} \; \mt{bind}
adamc@659	2152 \end{array}$$
adamc@659	2153
adam@1648	2154 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	2155
adam@1648	2156 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	2157
adam@1786	2158 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	2159
adam@1786	2160 $$\begin{array}{l}
adam@1786	2161 \mt{val} \; \mt{active} : \mt{unit} \to \mt{tag} \; [\mt{Code} = \mt{transaction} \; \mt{xbody}] \; \mt{body} \; [] \; [] \; []
adam@1786	2162 \end{array}$$
adamc@701	2163
adamc@914	2164 \subsubsection{Remote Procedure Calls}
adamc@914	2165
adamc@914	2166 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	2167
adamc@914	2168 $$\begin{array}{l}
adamc@914	2169 \mt{val} \; \mt{rpc} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@914	2170 \end{array}$$
adamc@914	2171
adam@1848	2172 There is an alternate form that uses $\mt{None}$ to indicate that an error occurred during RPC processing, rather than raising an exception to abort this branch of control flow.
adam@1848	2173
adam@1848	2174 $$\begin{array}{l}
adam@1848	2175 \mt{val} \; \mt{tryRpc} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; \mt{t} \to \mt{transaction} \; (\mt{option} \; \mt{t})
adam@1848	2176 \end{array}$$
adam@1848	2177
adamc@701	2178 \subsubsection{Asynchronous Message-Passing}
adamc@701	2179
adamc@701	2180 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	2181
adamc@701	2182 $$\begin{array}{l}
adamc@701	2183 \mt{type} \; \mt{client} \\
adamc@701	2184 \mt{val} \; \mt{self} : \mt{transaction} \; \mt{client}
adamc@701	2185 \end{array}$$
adamc@701	2186
adamc@701	2187 \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	2188
adamc@701	2189 $$\begin{array}{l}
adamc@701	2190 \mt{con} \; \mt{channel} :: \mt{Type} \to \mt{Type} \\
adamc@701	2191 \mt{val} \; \mt{channel} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; (\mt{channel} \; \mt{t}) \\
adamc@701	2192 \mt{val} \; \mt{send} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@701	2193 \mt{val} \; \mt{recv} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@701	2194 \end{array}$$
adamc@701	2195
adamc@701	2196 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	2197
adamc@701	2198 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	2199
adam@1551	2200 \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	2201
adamc@659	2202
adamc@549	2203 \section{Ur/Web Syntax Extensions}
adamc@549	2204
adamc@549	2205 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	2206
adamc@549	2207 \subsection{SQL}
adamc@549	2208
adamc@786	2209 \subsubsection{\label{tables}Table Declarations}
adamc@786	2210
adamc@788	2211 $\mt{table}$ declarations may include constraints, via these grammar rules.
adamc@788	2212 $$\begin{array}{rrcll}
adam@1594	2213 \textrm{Declarations} & d &::=& \mt{table} \; x : c \; [pk[,]] \; cts \mid \mt{view} \; x = V \\
adamc@788	2214 \textrm{Primary key constraints} & pk &::=& \mt{PRIMARY} \; \mt{KEY} \; K \\
adam@1722	2215 \textrm{Keys} & K &::=& f \mid (f, (f,)^+) \mid \{\{e\}\} \\
adamc@788	2216 \textrm{Constraint sets} & cts &::=& \mt{CONSTRAINT} f \; ct \mid cts, cts \mid \{\{e\}\} \\
adamc@788	2217 \textrm{Constraints} & ct &::=& \mt{UNIQUE} \; K \mid \mt{CHECK} \; E \\
adamc@788	2218 &&& \mid \mt{FOREIGN} \; \mt{KEY} \; K \; \mt{REFERENCES} \; F \; (K) \; [\mt{ON} \; \mt{DELETE} \; pr] \; [\mt{ON} \; \mt{UPDATE} \; pr] \\
adamc@788	2219 \textrm{Foreign tables} & F &::=& x \mid \{\{e\}\} \\
adam@1594	2220 \textrm{Propagation modes} & pr &::=& \mt{NO} \; \mt{ACTION} \mid \mt{RESTRICT} \mid \mt{CASCADE} \mid \mt{SET} \; \mt{NULL} \\
adam@1594	2221 \textrm{View expressions} & V &::=& Q \mid \{e\}
adamc@788	2222 \end{array}$$
adamc@788	2223
adamc@788	2224 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	2225
adamc@788	2226
adamc@549	2227 \subsubsection{Queries}
adamc@549	2228
adamc@550	2229 Queries $Q$ are added to the rules for expressions $e$.
adamc@550	2230
adamc@549	2231 $$\begin{array}{rrcll}
adam@1684	2232 \textrm{Queries} & Q &::=& (q \; [\mt{ORDER} \; \mt{BY} \; O] \; [\mt{LIMIT} \; N] \; [\mt{OFFSET} \; N]) \\
adamc@1085	2233 \textrm{Pre-queries} & q &::=& \mt{SELECT} \; [\mt{DISTINCT}] \; P \; \mt{FROM} \; F,^+ \; [\mt{WHERE} \; E] \; [\mt{GROUP} \; \mt{BY} \; p,^+] \; [\mt{HAVING} \; E] \\
adamc@1085	2234 &&& \mid q \; R \; q \mid \{\{\{e\}\}\} \\
adam@1684	2235 \textrm{Relational operators} & R &::=& \mt{UNION} \mid \mt{INTERSECT} \mid \mt{EXCEPT} \\
adam@1778	2236 \textrm{$\mt{ORDER \; BY}$ items} & O &::=& \mt{RANDOM} [()] \mid \hat{E} \; [o] \mid \hat{E} \; [o], O
adamc@549	2237 \end{array}$$
adamc@549	2238
adamc@549	2239 $$\begin{array}{rrcll}
adamc@549	2240 \textrm{Projections} & P &::=& \ast & \textrm{all columns} \\
adamc@549	2241 &&& p,^+ & \textrm{particular columns} \\
adamc@549	2242 \textrm{Pre-projections} & p &::=& t.f & \textrm{one column from a table} \\
adamc@558	2243 &&& t.\{\{c\}\} & \textrm{a record of columns from a table (of kind $\{\mt{Type}\}$)} \\
adam@1627	2244 &&& t.* & \textrm{all columns from a table} \\
adam@1778	2245 &&& \hat{E} \; [\mt{AS} \; f] & \textrm{expression column} \\
adamc@549	2246 \textrm{Table names} & t &::=& x & \textrm{constant table name (automatically capitalized)} \\
adamc@549	2247 &&& X & \textrm{constant table name} \\
adamc@549	2248 &&& \{\{c\}\} & \textrm{computed table name (of kind $\mt{Name}$)} \\
adamc@549	2249 \textrm{Column names} & f &::=& X & \textrm{constant column name} \\
adamc@549	2250 &&& \{c\} & \textrm{computed column name (of kind $\mt{Name}$)} \\
adamc@549	2251 \textrm{Tables} & T &::=& x & \textrm{table variable, named locally by its own capitalization} \\
adam@1756	2252 &&& x \; \mt{AS} \; X & \textrm{table variable, with local name} \\
adam@1756	2253 &&& x \; \mt{AS} \; \{c\} & \textrm{table variable, with computed local name} \\
adamc@549	2254 &&& \{\{e\}\} \; \mt{AS} \; t & \textrm{computed table expression, with local name} \\
adam@1756	2255 &&& \{\{e\}\} \; \mt{AS} \; \{c\} & \textrm{computed table expression, with computed local name} \\
adamc@1085	2256 \textrm{$\mt{FROM}$ items} & F &::=& T \mid \{\{e\}\} \mid F \; J \; \mt{JOIN} \; F \; \mt{ON} \; E \\
adamc@1085	2257 &&& \mid F \; \mt{CROSS} \; \mt{JOIN} \ F \\
adamc@1193	2258 &&& \mid (Q) \; \mt{AS} \; t \\
adamc@1085	2259 \textrm{Joins} & J &::=& [\mt{INNER}] \\
adamc@1085	2260 &&& \mid [\mt{LEFT} \mid \mt{RIGHT} \mid \mt{FULL}] \; [\mt{OUTER}] \\
adam@1587	2261 \textrm{SQL expressions} & E &::=& t.f & \textrm{column references} \\
adamc@549	2262 &&& X & \textrm{named expression references} \\
adam@1490	2263 &&& \{[e]\} & \textrm{injected native Ur expressions} \\
adam@1778	2264 &&& \{e\} & \textrm{computed expressions, probably using $\mt{sql\_exp}$ directly} \\
adamc@549	2265 &&& \mt{TRUE} \mid \mt{FALSE} & \textrm{boolean constants} \\
adamc@549	2266 &&& \ell & \textrm{primitive type literals} \\
adamc@549	2267 &&& \mt{NULL} & \textrm{null value (injection of $\mt{None}$)} \\
adamc@549	2268 &&& E \; \mt{IS} \; \mt{NULL} & \textrm{nullness test} \\
adam@1602	2269 &&& \mt{COALESCE}(E, E) & \textrm{take first non-null value} \\
adamc@549	2270 &&& n & \textrm{nullary operators} \\
adamc@549	2271 &&& u \; E & \textrm{unary operators} \\
adamc@549	2272 &&& E \; b \; E & \textrm{binary operators} \\
adam@1778	2273 &&& \mt{COUNT}(\ast) & \textrm{count number of rows} \\
adam@1778	2274 &&& a(E) & \textrm{other aggregate function} \\
adam@1573	2275 &&& \mt{IF} \; E \; \mt{THEN} \; E \; \mt{ELSE} \; E & \textrm{conditional} \\
adam@1778	2276 &&& (Q) & \textrm{subquery (must return a single expression column)} \\
adamc@549	2277 &&& (E) & \textrm{explicit precedence} \\
adamc@549	2278 \textrm{Nullary operators} & n &::=& \mt{CURRENT\_TIMESTAMP} \\
adamc@549	2279 \textrm{Unary operators} & u &::=& \mt{NOT} \\
adam@1688	2280 \textrm{Binary operators} & b &::=& \mt{AND} \mid \mt{OR} \mid = \mid \neq \mid < \mid \leq \mid > \mid \geq \\
adamc@1188	2281 \textrm{Aggregate functions} & a &::=& \mt{COUNT} \mid \mt{AVG} \mid \mt{SUM} \mid \mt{MIN} \mid \mt{MAX} \\
adam@1543	2282 \textrm{Directions} & o &::=& \mt{ASC} \mid \mt{DESC} \mid \{e\} \\
adamc@549	2283 \textrm{SQL integer} & N &::=& n \mid \{e\} \\
adam@1778	2284 \textrm{Windowable expressions} & \hat{E} &::=& E \\
adam@1778	2285 &&& w \; [\mt{OVER} \; ( & \textrm{(Postgres only)} \\
adam@1778	2286 &&& \hspace{.1in} [\mt{PARTITION} \; \mt{BY} \; E] \\
adam@1778	2287 &&& \hspace{.1in} [\mt{ORDER} \; \mt{BY} \; O])] \\
adam@1778	2288 \textrm{Window function} & w &::=& \mt{RANK}() \\
adam@1778	2289 &&& \mt{COUNT}(*) \\
adam@1778	2290 &&& a(E)
adamc@549	2291 \end{array}$$
adamc@549	2292
adamc@1085	2293 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	2294
adam@1683	2295 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	2296
adamc@550	2297 \subsubsection{DML}
adamc@550	2298
adamc@550	2299 DML commands $D$ are added to the rules for expressions $e$.
adamc@550	2300
adamc@550	2301 $$\begin{array}{rrcll}
adamc@550	2302 \textrm{Commands} & D &::=& (\mt{INSERT} \; \mt{INTO} \; T^E \; (f,^+) \; \mt{VALUES} \; (E,^+)) \\
adamc@550	2303 &&& (\mt{UPDATE} \; T^E \; \mt{SET} \; (f = E,)^+ \; \mt{WHERE} \; E) \\
adamc@550	2304 &&& (\mt{DELETE} \; \mt{FROM} \; T^E \; \mt{WHERE} \; E) \\
adamc@550	2305 \textrm{Table expressions} & T^E &::=& x \mid \{\{e\}\}
adamc@550	2306 \end{array}$$
adamc@550	2307
adamc@550	2308 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	2309
adamc@551	2310 \subsection{XML}
adamc@551	2311
adamc@551	2312 XML fragments $L$ are added to the rules for expressions $e$.
adamc@551	2313
adamc@551	2314 $$\begin{array}{rrcll}
adamc@551	2315 \textrm{XML fragments} & L &::=& \texttt{<xml/>} \mid \texttt{<xml>}l^*\texttt{</xml>} \\
adamc@551	2316 \textrm{XML pieces} & l &::=& \textrm{text} & \textrm{cdata} \\
adamc@551	2317 &&& \texttt{<}g\texttt{/>} & \textrm{tag with no children} \\
adamc@551	2318 &&& \texttt{<}g\texttt{>}l^*\texttt{</}x\texttt{>} & \textrm{tag with children} \\
adamc@559	2319 &&& \{e\} & \textrm{computed XML fragment} \\
adamc@559	2320 &&& \{[e]\} & \textrm{injection of an Ur expression, via the $\mt{Top}.\mt{txt}$ function} \\
adamc@551	2321 \textrm{Tag} & g &::=& h \; (x = v)^* \\
adamc@551	2322 \textrm{Tag head} & h &::=& x & \textrm{tag name} \\
adamc@551	2323 &&& h\{c\} & \textrm{constructor parameter} \\
adamc@551	2324 \textrm{Attribute value} & v &::=& \ell & \textrm{literal value} \\
adamc@551	2325 &&& \{e\} & \textrm{computed value} \\
adamc@551	2326 \end{array}$$
adamc@551	2327
adam@1751	2328 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	2329
adam@1751	2330 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	2331
adamc@1198	2332 \section{\label{structure}The Structure of Web Applications}
adamc@553	2333
adam@1797	2334 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	2335
adam@1532	2336 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	2337
adam@1787	2338 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	2339
adam@1370	2340 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	2341
adamc@553	2342 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	2343
adamc@553	2344 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	2345
adam@1653	2346 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	2347 \begin{itemize}
adam@1653	2348 \item Functions are disallowed, since there is no obvious way to serialize them safely.
adam@1653	2349 \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	2350 \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	2351 \end{itemize}
adamc@553	2352
adamc@660	2353 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	2354
adamc@789	2355 \medskip
adamc@789	2356
adam@1347	2357 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	2358
adamc@789	2359 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	2360
adam@1348	2361 \subsection{Tasks}
adam@1348	2362
adam@1348	2363 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	2364
adam@1348	2365 $$\begin{array}{l}
adam@1348	2366 \mt{con} \; \mt{task\_kind} :: \mt{Type} \to \mt{Type} \\
adam@1348	2367 \mt{val} \; \mt{initialize} : \mt{task\_kind} \; \mt{unit} \\
adam@1349	2368 \mt{val} \; \mt{clientLeaves} : \mt{task\_kind} \; \mt{client} \\
adam@1349	2369 \mt{val} \; \mt{periodic} : \mt{int} \to \mt{task\_kind} \; \mt{unit}
adam@1348	2370 \end{array}$$
adam@1348	2371
adam@1348	2372 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	2373
adam@1348	2374 The currently supported task kinds are:
adam@1348	2375 \begin{itemize}
adam@1349	2376 \item $\mt{initialize}$: Code that is run when the application starts up.
adam@1348	2377 \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	2378 \item $\mt{periodic} \; n$: Code that is run when the application starts up and then every $n$ seconds thereafter.
adam@1348	2379 \end{itemize}
adam@1348	2380
adamc@553	2381
adamc@897	2382 \section{The Foreign Function Interface}
adamc@897	2383
adamc@897	2384 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	2385
adamc@897	2386 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	2387
adamc@897	2388 \begin{itemize}
adamc@897	2389 \item \texttt{clientOnly Module.ident} registers a value as being allowed only in client-side code.
adamc@897	2390 \item \texttt{clientToServer Module.ident} declares a type as OK to marshal between clients and servers. By default, abstract FFI types are not allowed to be marshalled, since your library might be maintaining invariants that the simple serialization code doesn't check.
adam@1878	2391 \item \texttt{effectful Module.ident} registers a function that can have side effects. This is the default for \texttt{transaction}-based types, and, actually, this directive is mostly present for legacy compatibility reasons, since it used to be required explicitly for each \texttt{transaction}al function.
adamc@897	2392 \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	2393 \item \texttt{include FILE} requests inclusion of a C header file.
adamc@897	2394 \item \texttt{jsFunc Module.ident=name} gives a mapping from an Ur name for a value to a JavaScript name.
adamc@897	2395 \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	2396 \item \texttt{script URL} requests inclusion of a JavaScript source file within application HTML.
adamc@897	2397 \item \texttt{serverOnly Module.ident} registers a value as being allowed only in server-side code.
adamc@897	2398 \end{itemize}
adamc@897	2399
adamc@897	2400 \subsection{Writing C FFI Code}
adamc@897	2401
adam@1881	2402 C source files connecting to the Ur/Web FFI should include \texttt{urweb.h}, and C++ source files should include \texttt{urweb\_cpp.h}.
adam@1881	2403
adamc@897	2404 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	2405
adamc@897	2406 \begin{itemize}
adam@1881	2407 \item Primitive types defined in \texttt{Basis} are themselves using the standard FFI interface, so you may refer to them like \texttt{uw\_Basis\_t}. See \texttt{include/urweb/types.h} for their definitions.
adamc@897	2408 \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	2409 \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	2410 \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	2411 \end{itemize}
adamc@897	2412
adam@1881	2413 The C FFI version of a Ur function with type \texttt{T1 -> ... -> TN -> R} or \texttt{T1 -> ... -> TN -> transaction R} has a C prototype like \texttt{R uw\_Module\_ident(uw\_context, T1, ..., TN)}. Only functions with types of the second form may have side effects. \texttt{uw\_context} is the type of state that persists across handling a client request. Many functions that operate on contexts are prototyped in \texttt{include/urweb/urweb\_cpp.h}. Most should only be used internally by the compiler. A few are useful in general FFI implementation:
adamc@897	2414 \begin{itemize}
adamc@897	2415 \item \begin{verbatim}
adamc@897	2416 void uw_error(uw_context, failure_kind, const char *fmt, ...);
adamc@897	2417 \end{verbatim}
adamc@897	2418 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	2419
adam@1329	2420 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	2421
adamc@897	2422 \item \begin{verbatim}
adam@1469	2423 void uw_set_error_message(uw_context, const char *fmt, ...);
adam@1469	2424 \end{verbatim}
adam@1469	2425 This simpler form of \texttt{uw\_error()} saves an error message without immediately aborting execution.
adam@1469	2426
adam@1469	2427 \item \begin{verbatim}
adamc@897	2428 void uw_push_cleanup(uw_context, void (func)(void ), void *arg);
adamc@897	2429 void uw_pop_cleanup(uw_context);
adamc@897	2430 \end{verbatim}
adam@1329	2431 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	2432
adam@1329	2433 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	2434
adamc@897	2435 \item \begin{verbatim}
adamc@897	2436 void *uw_malloc(uw_context, size_t);
adamc@897	2437 \end{verbatim}
adam@1329	2438 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	2439
adam@1329	2440 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	2441
adamc@897	2442 \item \begin{verbatim}
adamc@897	2443 typedef void (uw_callback)(void );
adam@1328	2444 typedef void (uw_callback_with_retry)(void , int will_retry);
adamc@897	2445 void uw_register_transactional(uw_context, void *data, uw_callback commit,
adam@1328	2446 uw_callback rollback, uw_callback_with_retry free);
adamc@897	2447 \end{verbatim}
adam@1328	2448 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	2449
adamc@1085	2450 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	2451
adam@1329	2452 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	2453
adam@1329	2454 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	2455
adam@1469	2456 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	2457
adamc@1085	2458 \item \begin{verbatim}
adamc@1085	2459 void uw_get_global(uw_context, char name);
adamc@1085	2460 void uw_set_global(uw_context, char name, void data, uw_callback free);
adamc@1085	2461 \end{verbatim}
adam@1329	2462 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	2463
adamc@897	2464 \end{itemize}
adamc@897	2465
adamc@897	2466 \subsection{Writing JavaScript FFI Code}
adamc@897	2467
adamc@897	2468 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	2469
adamc@897	2470 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	2471
adamc@897	2472 \begin{itemize}
adamc@897	2473 \item Integers, floats, strings, characters, and booleans are represented in the usual JavaScript way.
adam@1644	2474 \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	2475 \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	2476 \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	2477 \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	2478 \item As in the C FFI, all abstract types of program syntax are implemented with strings in JavaScript.
adam@1844	2479 \item A value of Ur type \texttt{transaction t} is represented in the same way as for \texttt{unit -> t}.
adamc@897	2480 \end{itemize}
adamc@897	2481
adam@1644	2482 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	2483
adam@1644	2484 \begin{itemize}
adam@1644	2485 \item Sources should be treated as an abstract type, manipulated via:
adam@1644	2486 \begin{itemize}
adam@1644	2487 \item \cd{sc(v)}, to create a source initialized to \cd{v}
adam@1644	2488 \item \cd{sg(s)}, to retrieve the current value of source \cd{s}
adam@1644	2489 \item \cd{sv(s, v)}, to set source \cd{s} to value \cd{v}
adam@1644	2490 \end{itemize}
adam@1644	2491
adam@1644	2492 \item Signals should be treated as an abstract type, manipulated via:
adam@1644	2493 \begin{itemize}
adam@1644	2494 \item \cd{sr(v)} and \cd{sb(s, f)}, the ``return'' and ``bind'' monad operators, respectively
adam@1644	2495 \item \cd{ss(s)}, to produce the signal corresponding to source \cd{s}
adam@1644	2496 \item \cd{scur(s)}, to get the current value of signal \cd{s}
adam@1644	2497 \end{itemize}
adam@1644	2498
adam@1644	2499 \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	2500
adam@1702	2501 \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	2502
adam@1644	2503 \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	2504 \end{itemize}
adamc@897	2505
adam@1833	2506 \subsection{Introducing New HTML Tags}
adam@1833	2507
adam@1833	2508 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	2509
adam@1833	2510 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	2511
adamc@897	2512
adamc@552	2513 \section{Compiler Phases}
adamc@552	2514
adamc@552	2515 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	2516
adamc@552	2517 In this section, we step through the main phases of compilation, noting what consequences each phase has for effective programming.
adamc@552	2518
adamc@552	2519 \subsection{Parse}
adamc@552	2520
adamc@552	2521 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	2522
adamc@552	2523 \subsection{Elaborate}
adamc@552	2524
adamc@552	2525 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	2526
adam@1378	2527 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	2528
adamc@552	2529 \subsection{Unnest}
adamc@552	2530
adamc@552	2531 Named local function definitions are moved to the top level, to avoid the need to generate closures.
adamc@552	2532
adamc@552	2533 \subsection{Corify}
adamc@552	2534
adamc@552	2535 Module system features are compiled away, through inlining of functor definitions at application sites. Afterward, most abstraction boundaries are broken, facilitating optimization.
adamc@552	2536
adamc@552	2537 \subsection{Especialize}
adamc@552	2538
adam@1356	2539 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	2540
adamc@552	2541 \subsection{Untangle}
adamc@552	2542
adam@1797	2543 Remove unnecessary mutual recursion, splitting recursive groups into strongly connected components.
adamc@552	2544
adamc@552	2545 \subsection{Shake}
adamc@552	2546
adamc@552	2547 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	2548
adamc@661	2549 \subsection{Rpcify}
adamc@661	2550
adamc@661	2551 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	2552
adamc@661	2553 \subsection{Untangle, Shake}
adamc@661	2554
adamc@661	2555 Repeat these simplifications.
adamc@661	2556
adamc@553	2557 \subsection{\label{tag}Tag}
adamc@552	2558
adamc@552	2559 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	2560
adamc@552	2561 \subsection{Reduce}
adamc@552	2562
adamc@552	2563 Apply definitional equality rules to simplify the program as much as possible. This effectively includes inlining of every non-recursive definition.
adamc@552	2564
adamc@552	2565 \subsection{Unpoly}
adamc@552	2566
adamc@552	2567 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	2568
adamc@552	2569 \subsection{Specialize}
adamc@552	2570
adamc@558	2571 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	2572
adamc@552	2573 \subsection{Shake}
adamc@552	2574
adamc@558	2575 Here the compiler repeats the earlier Shake phase.
adamc@552	2576
adamc@552	2577 \subsection{Monoize}
adamc@552	2578
adamc@552	2579 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	2580
adamc@552	2581 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	2582
adamc@552	2583 \subsection{MonoOpt}
adamc@552	2584
adamc@552	2585 Simple algebraic laws are applied to simplify the program, focusing especially on efficient imperative generation of HTML pages.
adamc@552	2586
adamc@552	2587 \subsection{MonoUntangle}
adamc@552	2588
adamc@552	2589 Unnecessary mutual recursion is broken up again.
adamc@552	2590
adamc@552	2591 \subsection{MonoReduce}
adamc@552	2592
adamc@552	2593 Equivalents of the definitional equality rules are applied to simplify programs, with inlining again playing a major role.
adamc@552	2594
adamc@552	2595 \subsection{MonoShake, MonoOpt}
adamc@552	2596
adamc@552	2597 Unneeded declarations are removed, and basic optimizations are repeated.
adamc@552	2598
adamc@552	2599 \subsection{Fuse}
adamc@552	2600
adamc@552	2601 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	2602
adamc@552	2603 \subsection{MonoUntangle, MonoShake}
adamc@552	2604
adamc@552	2605 Fuse often creates more opportunities to remove spurious mutual recursion.
adamc@552	2606
adamc@552	2607 \subsection{Pathcheck}
adamc@552	2608
adamc@552	2609 The compiler checks that no link or action name has been used more than once.
adamc@552	2610
adamc@552	2611 \subsection{Cjrize}
adamc@552	2612
adamc@552	2613 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	2614
adamc@552	2615 \subsection{C Compilation and Linking}
adamc@552	2616
adam@1523	2617 The output of the last phase is pretty-printed as C source code and passed to the C compiler.
adamc@552	2618
adamc@552	2619
as@1564	2620 \end{document}

Mercurial > urweb

annotate doc/manual.tex @ 1891:779c390382b9