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Tweaking treatment of function application: substitute or introduce a 'let'?
author Adam Chlipala <adam@chlipala.net>
date Sun, 05 Aug 2012 14:55:28 -0400
parents 3d922a28370b
children ae8b0e05522a
rev   line source
adamc@524 1 \documentclass{article}
adamc@554 2 \usepackage{fullpage,amsmath,amssymb,proof,url}
rmbruijn@1568 3 \usepackage[T1]{fontenc}
vshabanoff@1765 4 \usepackage{ae,aecompl}
adamc@524 5 \newcommand{\cd}[1]{\texttt{#1}}
adamc@524 6 \newcommand{\mt}[1]{\mathsf{#1}}
adamc@524 7
adamc@524 8 \newcommand{\rc}{+ \hspace{-.075in} + \;}
adamc@527 9 \newcommand{\rcut}{\; \texttt{--} \;}
adamc@527 10 \newcommand{\rcutM}{\; \texttt{---} \;}
adamc@524 11
adamc@524 12 \begin{document}
adamc@524 13
adamc@524 14 \title{The Ur/Web Manual}
adamc@524 15 \author{Adam Chlipala}
adamc@524 16
adamc@524 17 \maketitle
adamc@524 18
adamc@540 19 \tableofcontents
adamc@540 20
adamc@554 21
adamc@554 22 \section{Introduction}
adamc@554 23
adam@1797 24 \emph{Ur} is a programming language designed to introduce richer type system features into functional programming in the tradition of ML and Haskell. Ur is functional, pure, statically typed, and strict. Ur supports a powerful kind of \emph{metaprogramming} based on \emph{type-level computation with type-level records}.
adamc@554 25
adamc@554 26 \emph{Ur/Web} is Ur plus a special standard library and associated rules for parsing and optimization. Ur/Web supports construction of dynamic web applications backed by SQL databases. The signature of the standard library is such that well-typed Ur/Web programs ``don't go wrong'' in a very broad sense. Not only do they not crash during particular page generations, but they also may not:
adamc@554 27
adamc@554 28 \begin{itemize}
adamc@554 29 \item Suffer from any kinds of code-injection attacks
adamc@554 30 \item Return invalid HTML
adamc@554 31 \item Contain dead intra-application links
adamc@554 32 \item Have mismatches between HTML forms and the fields expected by their handlers
adamc@652 33 \item Include client-side code that makes incorrect assumptions about the ``AJAX''-style services that the remote web server provides
adamc@554 34 \item Attempt invalid SQL queries
adamc@652 35 \item Use improper marshaling or unmarshaling in communication with SQL databases or between browsers and web servers
adamc@554 36 \end{itemize}
adamc@554 37
adamc@554 38 This type safety is just the foundation of the Ur/Web methodology. It is also possible to use metaprogramming to build significant application pieces by analysis of type structure. For instance, the demo includes an ML-style functor for building an admin interface for an arbitrary SQL table. The type system guarantees that the admin interface sub-application that comes out will always be free of the above-listed bugs, no matter which well-typed table description is given as input.
adamc@554 39
adamc@652 40 The Ur/Web compiler also produces very efficient object code that does not use garbage collection. These compiled programs will often be even more efficient than what most programmers would bother to write in C. The compiler also generates JavaScript versions of client-side code, with no need to write those parts of applications in a different language.
adamc@554 41
adamc@554 42 \medskip
adamc@554 43
adamc@554 44 The official web site for Ur is:
adamc@554 45 \begin{center}
adamc@554 46 \url{http://www.impredicative.com/ur/}
adamc@554 47 \end{center}
adamc@554 48
adamc@555 49
adamc@555 50 \section{Installation}
adamc@555 51
adamc@555 52 If you are lucky, then the following standard command sequence will suffice for installation, in a directory to which you have unpacked the latest distribution tarball.
adamc@555 53
adamc@555 54 \begin{verbatim}
adamc@555 55 ./configure
adamc@555 56 make
adamc@555 57 sudo make install
adamc@555 58 \end{verbatim}
adamc@555 59
adam@1523 60 Some other packages must be installed for the above to work. At a minimum, you need a standard UNIX shell, with standard UNIX tools like sed and GCC (or an alternate C compiler) in your execution path; MLton, the whole-program optimizing compiler for Standard ML; and the development files for the OpenSSL C library. As of this writing, in the ``testing'' version of Debian Linux, this command will install the more uncommon of these dependencies:
adamc@896 61 \begin{verbatim}
adam@1368 62 apt-get install mlton libssl-dev
adamc@896 63 \end{verbatim}
adamc@555 64
adamc@896 65 To build programs that access SQL databases, you also need one of these client libraries for supported backends.
adamc@555 66 \begin{verbatim}
adamc@896 67 apt-get install libpq-dev libmysqlclient15-dev libsqlite3-dev
adamc@555 68 \end{verbatim}
adamc@555 69
adamc@555 70 It is also possible to access the modules of the Ur/Web compiler interactively, within Standard ML of New Jersey. To install the prerequisites in Debian testing:
adamc@555 71 \begin{verbatim}
adamc@555 72 apt-get install smlnj libsmlnj-smlnj ml-yacc ml-lpt
adamc@555 73 \end{verbatim}
adamc@555 74
adamc@555 75 To begin an interactive session with the Ur compiler modules, run \texttt{make smlnj}, and then, from within an \texttt{sml} session, run \texttt{CM.make "src/urweb.cm";}. The \texttt{Compiler} module is the main entry point.
adamc@555 76
adamc@896 77 To run an SQL-backed application with a backend besides SQLite, you will probably want to install one of these servers.
adamc@555 78
adamc@555 79 \begin{verbatim}
adam@1400 80 apt-get install postgresql-8.4 mysql-server-5.1
adamc@555 81 \end{verbatim}
adamc@555 82
adamc@555 83 To use the Emacs mode, you must have a modern Emacs installed. We assume that you already know how to do this, if you're in the business of looking for an Emacs mode. The demo generation facility of the compiler will also call out to Emacs to syntax-highlight code, and that process depends on the \texttt{htmlize} module, which can be installed in Debian testing via:
adamc@555 84
adamc@555 85 \begin{verbatim}
adamc@555 86 apt-get install emacs-goodies-el
adamc@555 87 \end{verbatim}
adamc@555 88
adam@1441 89 If you don't want to install the Emacs mode, run \texttt{./configure} with the argument \texttt{--without-emacs}.
adam@1441 90
adam@1523 91 Even with the right packages installed, configuration and building might fail to work. After you run \texttt{./configure}, you will see the values of some named environment variables printed. You may need to adjust these values to get proper installation for your system. To change a value, store your preferred alternative in the corresponding UNIX environment variable, before running \texttt{./configure}. For instance, here is how to change the list of extra arguments that the Ur/Web compiler will pass to the C compiler and linker on every invocation. Some older GCC versions need this setting to mask a bug in function inlining.
adamc@555 92
adamc@555 93 \begin{verbatim}
adam@1523 94 CCARGS=-fno-inline ./configure
adamc@555 95 \end{verbatim}
adamc@555 96
adam@1523 97 Since the author is still getting a handle on the GNU Autotools that provide the build system, you may need to do some further work to get started, especially in environments with significant differences from Linux (where most testing is done). The variables \texttt{PGHEADER}, \texttt{MSHEADER}, and \texttt{SQHEADER} may be used to set the proper C header files to include for the development libraries of PostgreSQL, MySQL, and SQLite, respectively. To get libpq to link, one OS X user reported setting \texttt{CCARGS="-I/opt/local/include -L/opt/local/lib/postgresql84"}, after creating a symbolic link with \texttt{ln -s /opt/local/include/postgresql84 /opt/local/include/postgresql}.
adamc@555 98
adamc@555 99 The Emacs mode can be set to autoload by adding the following to your \texttt{.emacs} file.
adamc@555 100
adamc@555 101 \begin{verbatim}
adamc@555 102 (add-to-list 'load-path "/usr/local/share/emacs/site-lisp/urweb-mode")
adamc@555 103 (load "urweb-mode-startup")
adamc@555 104 \end{verbatim}
adamc@555 105
adamc@555 106 Change the path in the first line if you chose a different Emacs installation path during configuration.
adamc@555 107
adamc@555 108
adamc@556 109 \section{Command-Line Compiler}
adamc@556 110
adam@1604 111 \subsection{\label{cl}Project Files}
adamc@556 112
adamc@556 113 The basic inputs to the \texttt{urweb} compiler are project files, which have the extension \texttt{.urp}. Here is a sample \texttt{.urp} file.
adamc@556 114
adamc@556 115 \begin{verbatim}
adamc@556 116 database dbname=test
adamc@556 117 sql crud1.sql
adamc@556 118
adamc@556 119 crud
adamc@556 120 crud1
adamc@556 121 \end{verbatim}
adamc@556 122
adamc@556 123 The \texttt{database} line gives the database information string to pass to libpq. In this case, the string only says to connect to a local database named \texttt{test}.
adamc@556 124
adamc@556 125 The \texttt{sql} line asks for an SQL source file to be generated, giving the commands to run to create the tables and sequences that this application expects to find. After building this \texttt{.urp} file, the following commands could be used to initialize the database, assuming that the current UNIX user exists as a Postgres user with database creation privileges:
adamc@556 126
adamc@556 127 \begin{verbatim}
adamc@556 128 createdb test
adamc@556 129 psql -f crud1.sql test
adamc@556 130 \end{verbatim}
adamc@556 131
adam@1331 132 A blank line separates the named directives from a list of modules to include in the project. Any line may contain a shell-script-style comment, where any suffix of a line starting at a hash character \texttt{\#} is ignored.
adamc@556 133
adamc@556 134 For each entry \texttt{M} in the module list, the file \texttt{M.urs} is included in the project if it exists, and the file \texttt{M.ur} must exist and is always included.
adamc@556 135
adamc@783 136 Here is the complete list of directive forms. ``FFI'' stands for ``foreign function interface,'' Ur's facility for interaction between Ur programs and C and JavaScript libraries.
adamc@783 137 \begin{itemize}
adam@1799 138 \item \texttt{[allow|deny] [url|mime|requestHeader|responseHeader|env] PATTERN} registers a rule governing which URLs, MIME types, HTTP request headers, HTTP response headers, or environment variable names are allowed to appear explicitly in this application. The first such rule to match a name determines the verdict. If \texttt{PATTERN} ends in \texttt{*}, it is interpreted as a prefix rule. Otherwise, a string must match it exactly.
adam@1400 139 \item \texttt{alwaysInline PATH} requests that every call to the referenced function be inlined. Section \ref{structure} explains how functions are assigned path strings.
adam@1462 140 \item \texttt{benignEffectful Module.ident} registers an FFI function or transaction as having side effects. The optimizer avoids removing, moving, or duplicating calls to such functions. Every effectful FFI function must be registered, or the optimizer may make invalid transformations. This version of the \texttt{effectful} directive registers that this function only has side effects that remain local to a single page generation.
adamc@783 141 \item \texttt{clientOnly Module.ident} registers an FFI function or transaction that may only be run in client browsers.
adamc@783 142 \item \texttt{clientToServer Module.ident} adds FFI type \texttt{Module.ident} to the list of types that are OK to marshal from clients to servers. Values like XML trees and SQL queries are hard to marshal without introducing expensive validity checks, so it's easier to ensure that the server never trusts clients to send such values. The file \texttt{include/urweb.h} shows examples of the C support functions that are required of any type that may be marshalled. These include \texttt{attrify}, \texttt{urlify}, and \texttt{unurlify} functions.
adamc@783 143 \item \texttt{database DBSTRING} sets the string to pass to libpq to open a database connection.
adamc@783 144 \item \texttt{debug} saves some intermediate C files, which is mostly useful to help in debugging the compiler itself.
adam@1699 145 \item \texttt{effectful Module.ident} registers an FFI function or transaction as having side effects. The optimizer avoids removing, moving, or duplicating calls to such functions. Every effectful FFI function must be registered, or the optimizer may make invalid transformations. (Note that merely assigning a function a \texttt{transaction}-based type does not mark it as effectful in this way!)
adamc@783 146 \item \texttt{exe FILENAME} sets the filename to which to write the output executable. The default for file \texttt{P.urp} is \texttt{P.exe}.
adamc@783 147 \item \texttt{ffi FILENAME} reads the file \texttt{FILENAME.urs} to determine the interface to a new FFI module. The name of the module is calculated from \texttt{FILENAME} in the same way as for normal source files. See the files \texttt{include/urweb.h} and \texttt{src/c/urweb.c} for examples of C headers and implementations for FFI modules. In general, every type or value \texttt{Module.ident} becomes \texttt{uw\_Module\_ident} in C.
adamc@1099 148 \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@783 149 \item \texttt{jsFunc Module.ident=name} gives the JavaScript name of an FFI value.
adamc@1089 150 \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 151 \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 152 \begin{itemize}
adam@1309 153 \item \texttt{cleanup}: maximum number of cleanup operations (e.g., entries recording the need to deallocate certain temporary objects) that may be active at once per request
adam@1309 154 \item \texttt{database}: maximum size of database files (currently only used by SQLite)
adam@1309 155 \item \texttt{deltas}: maximum number of messages sendable in a single request handler with \texttt{Basis.send}
adam@1309 156 \item \texttt{globals}: maximum number of global variables that FFI libraries may set in a single request context
adam@1309 157 \item \texttt{headers}: maximum size (in bytes) of per-request buffer used to hold HTTP headers for generated pages
adam@1797 158 \item \texttt{heap}: maximum size (in bytes) of per-request heap for dynamically allocated data
adam@1309 159 \item \texttt{inputs}: maximum number of top-level form fields per request
adam@1309 160 \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 161 \item \texttt{page}: maximum size (in bytes) of per-request buffer used to hold HTML content of generated pages
adam@1309 162 \item \texttt{script}: maximum size (in bytes) of per-request buffer used to hold JavaScript content of generated pages
adam@1309 163 \item \texttt{subinputs}: maximum number of form fields per request, excluding top-level fields
adam@1309 164 \item \texttt{time}: maximum running time of a single page request, in units of approximately 0.1 seconds
adam@1309 165 \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 166 \end{itemize}
adam@1523 167 \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 168 \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 169 \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@1478 170 \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 171 \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@852 172 \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@783 173 \item \texttt{prefix PREFIX} sets the prefix included before every URI within the generated application. The default is \texttt{/}.
adamc@783 174 \item \texttt{profile} generates an executable that may be used with gprof.
adam@1752 175 \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 176 \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@783 177 \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@783 178 \item \texttt{serverOnly Module.ident} registers an FFI function or transaction that may only be run on the server.
adamc@1164 179 \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@783 180 \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 181 \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@783 182 \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@783 183 \end{itemize}
adamc@701 184
adamc@701 185
adamc@557 186 \subsection{Building an Application}
adamc@557 187
adamc@557 188 To compile project \texttt{P.urp}, simply run
adamc@557 189 \begin{verbatim}
adamc@557 190 urweb P
adamc@557 191 \end{verbatim}
adamc@1198 192 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@557 193
adamc@557 194 To time how long the different compiler phases run, without generating an executable, run
adamc@557 195 \begin{verbatim}
adamc@557 196 urweb -timing P
adamc@557 197 \end{verbatim}
adamc@557 198
adamc@1086 199 To stop the compilation process after type-checking, run
adamc@1086 200 \begin{verbatim}
adamc@1086 201 urweb -tc P
adamc@1086 202 \end{verbatim}
adam@1530 203 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 204
adam@1745 205 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 206
adam@1723 207 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 208
adamc@1170 209 To output information relevant to CSS stylesheets (and not finish regular compilation), run
adamc@1170 210 \begin{verbatim}
adamc@1170 211 urweb -css P
adamc@1170 212 \end{verbatim}
adamc@1170 213 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 214
adam@1733 215 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 216 \begin{verbatim}
adam@1733 217 urweb daemon start
adam@1733 218 \end{verbatim}
adam@1733 219 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 220 \begin{verbatim}
adam@1733 221 urweb daemon stop
adam@1733 222 \end{verbatim}
adam@1733 223 Communication happens via a UNIX domain socket in file \cd{.urweb\_daemon} in the working directory.
adam@1733 224
adam@1733 225 \medskip
adam@1733 226
adamc@896 227 Some other command-line parameters are accepted:
adamc@896 228 \begin{itemize}
ezyang@1739 229 \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 230
adamc@896 231 \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@896 232
adamc@896 233 \item \texttt{-dbms [postgres|mysql|sqlite]}: Sets the database backend to use.
adamc@896 234 \begin{itemize}
adamc@896 235 \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@896 236
adamc@896 237 A command sequence like this can initialize a Postgres database, using a file \texttt{app.sql} generated by the compiler:
adamc@896 238 \begin{verbatim}
adamc@896 239 createdb app
adamc@896 240 psql -f app.sql app
adamc@896 241 \end{verbatim}
adamc@896 242
adamc@896 243 \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@896 244
adamc@896 245 A command sequence like this can initialize a MySQL database:
adamc@896 246 \begin{verbatim}
adamc@896 247 echo "CREATE DATABASE app" | mysql
adamc@896 248 mysql -D app <app.sql
adamc@896 249 \end{verbatim}
adamc@896 250
adamc@896 251 \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@896 252
adamc@896 253 A command like this can initialize an SQLite database:
adamc@896 254 \begin{verbatim}
adamc@896 255 sqlite3 path/to/database/file <app.sql
adamc@896 256 \end{verbatim}
adamc@896 257 \end{itemize}
adamc@896 258
adam@1693 259 \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 260
adam@1309 261 \item \texttt{-limit class num}: Equivalent to the \texttt{limit} directive from \texttt{.urp} files
adam@1309 262
adamc@896 263 \item \texttt{-output FILENAME}: Set where the application executable is written.
adamc@896 264
adamc@1127 265 \item \texttt{-path NAME VALUE}: Set the value of path variable \texttt{\$NAME} to \texttt{VALUE}, for use in \texttt{.urp} files.
adamc@1127 266
adam@1335 267 \item \texttt{-prefix PREFIX}: Equivalent to the \texttt{prefix} directive from \texttt{.urp} files
adam@1335 268
adam@1753 269 \item \texttt{-protocol [http|cgi|fastcgi|static]}: Set the protocol that the generated application speaks.
adamc@896 270 \begin{itemize}
adamc@896 271 \item \texttt{http}: This is the default. It is for building standalone web servers that can be accessed by web browsers directly.
adamc@896 272
adamc@896 273 \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@896 274
adamc@896 275 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@896 276 \begin{verbatim}
adamc@896 277 ScriptAlias /Hello /path/to/hello.exe
adamc@896 278 \end{verbatim}
adamc@896 279
adamc@1163 280 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 281 \begin{verbatim}
adamc@1163 282 Options +ExecCGI
adamc@1163 283 AddHandler cgi-script .exe
adamc@1163 284 \end{verbatim}
adamc@1163 285
adamc@1163 286 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 287 \begin{verbatim}
adamc@1163 288 prefix /dir/script.exe/
adamc@1163 289 \end{verbatim}
adamc@1163 290
adamc@1163 291 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 292
adamc@1164 293 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 294
adamc@896 295 \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@896 296
adamc@896 297 To configure a FastCGI program with Apache, one could combine the above \texttt{ScriptAlias} line with a line like this:
adamc@896 298 \begin{verbatim}
adamc@896 299 FastCgiServer /path/to/hello.exe -idle-timeout 99999
adamc@896 300 \end{verbatim}
adamc@896 301 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@896 302
adam@1753 303 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 304
adamc@896 305 Here is some lighttpd configuration for the same application.
adamc@896 306 \begin{verbatim}
adamc@896 307 fastcgi.server = (
adamc@896 308 "/Hello/" =>
adamc@896 309 (( "bin-path" => "/path/to/hello.exe",
adamc@896 310 "socket" => "/tmp/hello",
adamc@896 311 "check-local" => "disable",
adamc@896 312 "docroot" => "/",
adamc@896 313 "max-procs" => "1"
adamc@896 314 ))
adamc@896 315 )
adamc@896 316 \end{verbatim}
adamc@896 317 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@896 318
adamc@896 319 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 320
adam@1509 321 \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@896 322 \end{itemize}
adamc@896 323
adamc@1127 324 \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 325
adamc@1164 326 \item \texttt{-sigfile PATH}: Same as the \texttt{sigfile} directive in \texttt{.urp} files
adamc@1164 327
adamc@896 328 \item \texttt{-sql FILENAME}: Set where a database set-up SQL script is written.
adamc@1095 329
adamc@1095 330 \item \texttt{-static}: Link the runtime system statically. The default is to link against dynamic libraries.
adamc@896 331 \end{itemize}
adamc@896 332
adam@1297 333 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@556 334
adam@1509 335 \subsection{Tutorial Formatting}
adam@1509 336
adam@1509 337 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 338
adam@1509 339 These input files follow normal Ur syntax, with a few exceptions:
adam@1509 340 \begin{itemize}
adam@1509 341 \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 342 \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 343 \item A comment like \cd{(* * HEADING *)} introduces a section heading, with text \cd{HEADING} of your choice.
adam@1509 344 \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 345 \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 346 \end{itemize}
adam@1509 347
adam@1509 348 A word of warning: as for demo generation, tutorial generation calls Emacs to syntax-highlight Ur code.
adam@1509 349
adam@1522 350 \subsection{Run-Time Options}
adam@1522 351
adam@1522 352 Compiled applications consult a few environment variables to modify their behavior:
adam@1522 353
adam@1522 354 \begin{itemize}
adam@1522 355 \item \cd{URWEB\_NUM\_THREADS}: alternative to the \cd{-t} command-line argument (currently used only by FastCGI)
adam@1522 356 \item \cd{URWEB\_STACK\_SIZE}: size of per-thread stacks, in bytes
as@1564 357 \item \cd{URWEB\_PQ\_CON}: when using PostgreSQL, overrides the compiled-in connection string
adam@1522 358 \end{itemize}
adam@1522 359
adam@1509 360
adamc@529 361 \section{Ur Syntax}
adamc@529 362
adamc@784 363 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@524 364
adamc@524 365 \subsection{Lexical Conventions}
adamc@524 366
adamc@524 367 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@524 368
adamc@524 369 \begin{center}
adamc@524 370 \begin{tabular}{rl}
adamc@524 371 \textbf{\LaTeX} & \textbf{ASCII} \\
adamc@524 372 $\to$ & \cd{->} \\
adam@1687 373 $\longrightarrow$ & \cd{-{}->} \\
adamc@524 374 $\times$ & \cd{*} \\
adamc@524 375 $\lambda$ & \cd{fn} \\
adamc@524 376 $\Rightarrow$ & \cd{=>} \\
adamc@652 377 $\Longrightarrow$ & \cd{==>} \\
adamc@529 378 $\neq$ & \cd{<>} \\
adamc@529 379 $\leq$ & \cd{<=} \\
adamc@529 380 $\geq$ & \cd{>=} \\
adamc@524 381 \\
adamc@524 382 $x$ & Normal textual identifier, not beginning with an uppercase letter \\
adamc@525 383 $X$ & Normal textual identifier, beginning with an uppercase letter \\
adamc@524 384 \end{tabular}
adamc@524 385 \end{center}
adamc@524 386
adamc@525 387 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@524 388
adamc@873 389 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@526 390
adamc@527 391 This version of the manual doesn't include operator precedences; see \texttt{src/urweb.grm} for that.
adamc@527 392
adam@1297 393 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 394
adamc@552 395 \subsection{\label{core}Core Syntax}
adamc@524 396
adamc@524 397 \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@524 398 $$\begin{array}{rrcll}
adamc@524 399 \textrm{Kinds} & \kappa &::=& \mt{Type} & \textrm{proper types} \\
adamc@525 400 &&& \mt{Unit} & \textrm{the trivial constructor} \\
adamc@525 401 &&& \mt{Name} & \textrm{field names} \\
adamc@525 402 &&& \kappa \to \kappa & \textrm{type-level functions} \\
adamc@525 403 &&& \{\kappa\} & \textrm{type-level records} \\
adamc@525 404 &&& (\kappa\times^+) & \textrm{type-level tuples} \\
adamc@652 405 &&& X & \textrm{variable} \\
adam@1574 406 &&& X \longrightarrow \kappa & \textrm{kind-polymorphic type-level function} \\
adamc@529 407 &&& \_\_ & \textrm{wildcard} \\
adamc@525 408 &&& (\kappa) & \textrm{explicit precedence} \\
adamc@524 409 \end{array}$$
adamc@524 410
adamc@524 411 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@524 412 $$\begin{array}{rrcll}
adamc@524 413 \textrm{Explicitness} & ? &::=& :: & \textrm{explicit} \\
adamc@558 414 &&& ::: & \textrm{implicit}
adamc@524 415 \end{array}$$
adamc@524 416
adamc@524 417 \emph{Constructors} are the main class of compile-time-only data. They include proper types and are classified by kinds.
adamc@524 418 $$\begin{array}{rrcll}
adamc@524 419 \textrm{Constructors} & c, \tau &::=& (c) :: \kappa & \textrm{kind annotation} \\
adamc@530 420 &&& \hat{x} & \textrm{constructor variable} \\
adamc@524 421 \\
adamc@525 422 &&& \tau \to \tau & \textrm{function type} \\
adamc@525 423 &&& x \; ? \; \kappa \to \tau & \textrm{polymorphic function type} \\
adamc@652 424 &&& X \longrightarrow \tau & \textrm{kind-polymorphic function type} \\
adamc@525 425 &&& \$ c & \textrm{record type} \\
adamc@524 426 \\
adamc@525 427 &&& c \; c & \textrm{type-level function application} \\
adamc@530 428 &&& \lambda x \; :: \; \kappa \Rightarrow c & \textrm{type-level function abstraction} \\
adamc@524 429 \\
adamc@652 430 &&& X \Longrightarrow c & \textrm{type-level kind-polymorphic function abstraction} \\
adamc@655 431 &&& c [\kappa] & \textrm{type-level kind-polymorphic function application} \\
adamc@652 432 \\
adamc@525 433 &&& () & \textrm{type-level unit} \\
adamc@525 434 &&& \#X & \textrm{field name} \\
adamc@524 435 \\
adamc@525 436 &&& [(c = c)^*] & \textrm{known-length type-level record} \\
adamc@525 437 &&& c \rc c & \textrm{type-level record concatenation} \\
adamc@652 438 &&& \mt{map} & \textrm{type-level record map} \\
adamc@524 439 \\
adamc@558 440 &&& (c,^+) & \textrm{type-level tuple} \\
adamc@525 441 &&& c.n & \textrm{type-level tuple projection ($n \in \mathbb N^+$)} \\
adamc@524 442 \\
adamc@652 443 &&& [c \sim c] \Rightarrow \tau & \textrm{guarded type} \\
adamc@524 444 \\
adamc@529 445 &&& \_ :: \kappa & \textrm{wildcard} \\
adamc@525 446 &&& (c) & \textrm{explicit precedence} \\
adamc@530 447 \\
adamc@530 448 \textrm{Qualified uncapitalized variables} & \hat{x} &::=& x & \textrm{not from a module} \\
adamc@530 449 &&& M.x & \textrm{projection from a module} \\
adamc@525 450 \end{array}$$
adamc@525 451
adam@1579 452 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@655 453
adamc@525 454 Modules of the module system are described by \emph{signatures}.
adamc@525 455 $$\begin{array}{rrcll}
adamc@525 456 \textrm{Signatures} & S &::=& \mt{sig} \; s^* \; \mt{end} & \textrm{constant} \\
adamc@525 457 &&& X & \textrm{variable} \\
adamc@525 458 &&& \mt{functor}(X : S) : S & \textrm{functor} \\
adamc@529 459 &&& S \; \mt{where} \; \mt{con} \; x = c & \textrm{concretizing an abstract constructor} \\
adamc@525 460 &&& M.X & \textrm{projection from a module} \\
adamc@525 461 \\
adamc@525 462 \textrm{Signature items} & s &::=& \mt{con} \; x :: \kappa & \textrm{abstract constructor} \\
adamc@525 463 &&& \mt{con} \; x :: \kappa = c & \textrm{concrete constructor} \\
adamc@528 464 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529 465 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@525 466 &&& \mt{val} \; x : \tau & \textrm{value} \\
adamc@525 467 &&& \mt{structure} \; X : S & \textrm{sub-module} \\
adamc@525 468 &&& \mt{signature} \; X = S & \textrm{sub-signature} \\
adamc@525 469 &&& \mt{include} \; S & \textrm{signature inclusion} \\
adamc@525 470 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@654 471 &&& \mt{class} \; x :: \kappa & \textrm{abstract constructor class} \\
adamc@654 472 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@525 473 \\
adamc@525 474 \textrm{Datatype constructors} & dc &::=& X & \textrm{nullary constructor} \\
adamc@525 475 &&& X \; \mt{of} \; \tau & \textrm{unary constructor} \\
adamc@524 476 \end{array}$$
adamc@524 477
adamc@526 478 \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@526 479 $$\begin{array}{rrcll}
adamc@526 480 \textrm{Patterns} & p &::=& \_ & \textrm{wildcard} \\
adamc@526 481 &&& x & \textrm{variable} \\
adamc@526 482 &&& \ell & \textrm{constant} \\
adamc@526 483 &&& \hat{X} & \textrm{nullary constructor} \\
adamc@526 484 &&& \hat{X} \; p & \textrm{unary constructor} \\
adamc@526 485 &&& \{(x = p,)^*\} & \textrm{rigid record pattern} \\
adamc@526 486 &&& \{(x = p,)^+, \ldots\} & \textrm{flexible record pattern} \\
adamc@852 487 &&& p : \tau & \textrm{type annotation} \\
adamc@527 488 &&& (p) & \textrm{explicit precedence} \\
adamc@526 489 \\
adamc@529 490 \textrm{Qualified capitalized variables} & \hat{X} &::=& X & \textrm{not from a module} \\
adamc@526 491 &&& M.X & \textrm{projection from a module} \\
adamc@526 492 \end{array}$$
adamc@526 493
adamc@527 494 \emph{Expressions} are the main run-time entities, corresponding to both ``expressions'' and ``statements'' in mainstream imperative languages.
adamc@527 495 $$\begin{array}{rrcll}
adamc@527 496 \textrm{Expressions} & e &::=& e : \tau & \textrm{type annotation} \\
adamc@529 497 &&& \hat{x} & \textrm{variable} \\
adamc@529 498 &&& \hat{X} & \textrm{datatype constructor} \\
adamc@527 499 &&& \ell & \textrm{constant} \\
adamc@527 500 \\
adamc@527 501 &&& e \; e & \textrm{function application} \\
adamc@527 502 &&& \lambda x : \tau \Rightarrow e & \textrm{function abstraction} \\
adamc@527 503 &&& e [c] & \textrm{polymorphic function application} \\
adamc@852 504 &&& \lambda [x \; ? \; \kappa] \Rightarrow e & \textrm{polymorphic function abstraction} \\
adamc@655 505 &&& e [\kappa] & \textrm{kind-polymorphic function application} \\
adamc@652 506 &&& X \Longrightarrow e & \textrm{kind-polymorphic function abstraction} \\
adamc@527 507 \\
adamc@527 508 &&& \{(c = e,)^*\} & \textrm{known-length record} \\
adamc@527 509 &&& e.c & \textrm{record field projection} \\
adamc@527 510 &&& e \rc e & \textrm{record concatenation} \\
adamc@527 511 &&& e \rcut c & \textrm{removal of a single record field} \\
adamc@527 512 &&& e \rcutM c & \textrm{removal of multiple record fields} \\
adamc@527 513 \\
adamc@527 514 &&& \mt{let} \; ed^* \; \mt{in} \; e \; \mt{end} & \textrm{local definitions} \\
adamc@527 515 \\
adamc@527 516 &&& \mt{case} \; e \; \mt{of} \; (p \Rightarrow e|)^+ & \textrm{pattern matching} \\
adamc@527 517 \\
adamc@654 518 &&& \lambda [c \sim c] \Rightarrow e & \textrm{guarded expression abstraction} \\
adamc@654 519 &&& e \; ! & \textrm{guarded expression application} \\
adamc@527 520 \\
adamc@527 521 &&& \_ & \textrm{wildcard} \\
adamc@527 522 &&& (e) & \textrm{explicit precedence} \\
adamc@527 523 \\
adamc@527 524 \textrm{Local declarations} & ed &::=& \cd{val} \; x : \tau = e & \textrm{non-recursive value} \\
adam@1797 525 &&& \cd{val} \; \cd{rec} \; (x : \tau = e \; \cd{and})^+ & \textrm{mutually recursive values} \\
adamc@527 526 \end{array}$$
adamc@527 527
adamc@655 528 As with constructors, we include both abstraction and application for kind polymorphism, but applications are only inferred internally.
adamc@655 529
adamc@528 530 \emph{Declarations} primarily bring new symbols into context.
adamc@528 531 $$\begin{array}{rrcll}
adamc@528 532 \textrm{Declarations} & d &::=& \mt{con} \; x :: \kappa = c & \textrm{constructor synonym} \\
adamc@528 533 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529 534 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@528 535 &&& \mt{val} \; x : \tau = e & \textrm{value} \\
adam@1797 536 &&& \mt{val} \; \cd{rec} \; (x : \tau = e \; \mt{and})^+ & \textrm{mutually recursive values} \\
adamc@528 537 &&& \mt{structure} \; X : S = M & \textrm{module definition} \\
adamc@528 538 &&& \mt{signature} \; X = S & \textrm{signature definition} \\
adamc@528 539 &&& \mt{open} \; M & \textrm{module inclusion} \\
adamc@528 540 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@528 541 &&& \mt{open} \; \mt{constraints} \; M & \textrm{inclusion of just the constraints from a module} \\
adamc@528 542 &&& \mt{table} \; x : c & \textrm{SQL table} \\
adam@1594 543 &&& \mt{view} \; x = e & \textrm{SQL view} \\
adamc@528 544 &&& \mt{sequence} \; x & \textrm{SQL sequence} \\
adamc@535 545 &&& \mt{cookie} \; x : \tau & \textrm{HTTP cookie} \\
adamc@784 546 &&& \mt{style} \; x : \tau & \textrm{CSS class} \\
adamc@1085 547 &&& \mt{task} \; e = e & \textrm{recurring task} \\
adamc@528 548 \\
adamc@529 549 \textrm{Modules} & M &::=& \mt{struct} \; d^* \; \mt{end} & \textrm{constant} \\
adamc@529 550 &&& X & \textrm{variable} \\
adamc@529 551 &&& M.X & \textrm{projection} \\
adamc@529 552 &&& M(M) & \textrm{functor application} \\
adamc@529 553 &&& \mt{functor}(X : S) : S = M & \textrm{functor abstraction} \\
adamc@528 554 \end{array}$$
adamc@528 555
adamc@528 556 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@527 557
adam@1594 558 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@784 559
adamc@529 560 \subsection{Shorthands}
adamc@529 561
adamc@529 562 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@529 563
adamc@529 564 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@529 565
adamc@529 566 A record type may be written $\{(c = c,)^*\}$, which elaborates to $\$[(c = c,)^*]$.
adamc@529 567
adamc@533 568 The notation $[c_1, \ldots, c_n]$ is shorthand for $[c_1 = (), \ldots, c_n = ()]$.
adamc@533 569
adam@1350 570 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@529 571
adam@1687 572 The syntax $()$ expands to $\{\}$ as a pattern or expression.
adam@1687 573
adamc@852 574 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@529 575
adam@1574 576 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 577
adam@1306 578 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 579
adamc@529 580 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@529 581
adamc@529 582 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@529 583
adamc@654 584 A signature item or declaration $\mt{class} \; x = \lambda y \Rightarrow c$ may be abbreviated $\mt{class} \; x \; y = c$.
adamc@529 585
adam@1738 586 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@529 587
adamc@852 588 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@529 589
adamc@852 590 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@852 591
adam@1797 592 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@529 593
adamc@529 594 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@529 595
adamc@852 596 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@852 597
adamc@853 598 A declaration $\mt{table} \; x : \{(c = c,)^*\}$ is elaborated into $\mt{table} \; x : [(c = c,)^*]$.
adamc@529 599
adamc@529 600 The syntax $\mt{where} \; \mt{type}$ is an alternate form of $\mt{where} \; \mt{con}$.
adamc@529 601
adamc@529 602 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@529 603
adamc@529 604 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@529 605
adamc@784 606 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@529 607
adamc@530 608
adamc@530 609 \section{Static Semantics}
adamc@530 610
adamc@530 611 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@530 612
adamc@530 613 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@530 614 \begin{itemize}
adamc@655 615 \item $\Gamma \vdash \kappa$ expresses kind well-formedness.
adamc@530 616 \item $\Gamma \vdash c :: \kappa$ assigns a kind to a constructor in a context.
adamc@530 617 \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@531 618 \item $\Gamma \vdash c \hookrightarrow C$ proves that record constructor $c$ decomposes into set $C$ of field names and record constructors.
adamc@530 619 \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@530 620 \item $\Gamma \vdash e : \tau$ is a standard typing judgment.
adamc@534 621 \item $\Gamma \vdash p \leadsto \Gamma; \tau$ combines typing of patterns with calculation of which new variables they bind.
adamc@537 622 \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@537 623 \item $\Gamma \vdash S \equiv S$ is the signature equivalence judgment.
adamc@536 624 \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@530 625 \item $\Gamma \vdash M : S$ is the module signature checking judgment.
adamc@537 626 \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@539 627 \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@530 628 \end{itemize}
adamc@530 629
adamc@655 630
adamc@655 631 \subsection{Kind Well-Formedness}
adamc@655 632
adamc@655 633 $$\infer{\Gamma \vdash \mt{Type}}{}
adamc@655 634 \quad \infer{\Gamma \vdash \mt{Unit}}{}
adamc@655 635 \quad \infer{\Gamma \vdash \mt{Name}}{}
adamc@655 636 \quad \infer{\Gamma \vdash \kappa_1 \to \kappa_2}{
adamc@655 637 \Gamma \vdash \kappa_1
adamc@655 638 & \Gamma \vdash \kappa_2
adamc@655 639 }
adamc@655 640 \quad \infer{\Gamma \vdash \{\kappa\}}{
adamc@655 641 \Gamma \vdash \kappa
adamc@655 642 }
adamc@655 643 \quad \infer{\Gamma \vdash (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@655 644 \forall i: \Gamma \vdash \kappa_i
adamc@655 645 }$$
adamc@655 646
adamc@655 647 $$\infer{\Gamma \vdash X}{
adamc@655 648 X \in \Gamma
adamc@655 649 }
adamc@655 650 \quad \infer{\Gamma \vdash X \longrightarrow \kappa}{
adamc@655 651 \Gamma, X \vdash \kappa
adamc@655 652 }$$
adamc@655 653
adamc@530 654 \subsection{Kinding}
adamc@530 655
adamc@655 656 We write $[X \mapsto \kappa_1]\kappa_2$ for capture-avoiding substitution of $\kappa_1$ for $X$ in $\kappa_2$.
adamc@655 657
adamc@530 658 $$\infer{\Gamma \vdash (c) :: \kappa :: \kappa}{
adamc@530 659 \Gamma \vdash c :: \kappa
adamc@530 660 }
adamc@530 661 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530 662 x :: \kappa \in \Gamma
adamc@530 663 }
adamc@530 664 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530 665 x :: \kappa = c \in \Gamma
adamc@530 666 }$$
adamc@530 667
adamc@530 668 $$\infer{\Gamma \vdash M.x :: \kappa}{
adamc@537 669 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 670 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = \kappa
adamc@530 671 }
adamc@530 672 \quad \infer{\Gamma \vdash M.x :: \kappa}{
adamc@537 673 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 674 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@530 675 }$$
adamc@530 676
adamc@530 677 $$\infer{\Gamma \vdash \tau_1 \to \tau_2 :: \mt{Type}}{
adamc@530 678 \Gamma \vdash \tau_1 :: \mt{Type}
adamc@530 679 & \Gamma \vdash \tau_2 :: \mt{Type}
adamc@530 680 }
adamc@530 681 \quad \infer{\Gamma \vdash x \; ? \: \kappa \to \tau :: \mt{Type}}{
adamc@530 682 \Gamma, x :: \kappa \vdash \tau :: \mt{Type}
adamc@530 683 }
adamc@655 684 \quad \infer{\Gamma \vdash X \longrightarrow \tau :: \mt{Type}}{
adamc@655 685 \Gamma, X \vdash \tau :: \mt{Type}
adamc@655 686 }
adamc@530 687 \quad \infer{\Gamma \vdash \$c :: \mt{Type}}{
adamc@530 688 \Gamma \vdash c :: \{\mt{Type}\}
adamc@530 689 }$$
adamc@530 690
adamc@530 691 $$\infer{\Gamma \vdash c_1 \; c_2 :: \kappa_2}{
adamc@530 692 \Gamma \vdash c_1 :: \kappa_1 \to \kappa_2
adamc@530 693 & \Gamma \vdash c_2 :: \kappa_1
adamc@530 694 }
adamc@530 695 \quad \infer{\Gamma \vdash \lambda x \; :: \; \kappa_1 \Rightarrow c :: \kappa_1 \to \kappa_2}{
adamc@530 696 \Gamma, x :: \kappa_1 \vdash c :: \kappa_2
adamc@530 697 }$$
adamc@530 698
adamc@655 699 $$\infer{\Gamma \vdash c[\kappa'] :: [X \mapsto \kappa']\kappa}{
adamc@655 700 \Gamma \vdash c :: X \to \kappa
adamc@655 701 & \Gamma \vdash \kappa'
adamc@655 702 }
adamc@655 703 \quad \infer{\Gamma \vdash X \Longrightarrow c :: X \to \kappa}{
adamc@655 704 \Gamma, X \vdash c :: \kappa
adamc@655 705 }$$
adamc@655 706
adamc@530 707 $$\infer{\Gamma \vdash () :: \mt{Unit}}{}
adamc@530 708 \quad \infer{\Gamma \vdash \#X :: \mt{Name}}{}$$
adamc@530 709
adamc@530 710 $$\infer{\Gamma \vdash [\overline{c_i = c'_i}] :: \{\kappa\}}{
adamc@530 711 \forall i: \Gamma \vdash c_i : \mt{Name}
adamc@530 712 & \Gamma \vdash c'_i :: \kappa
adamc@530 713 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@530 714 }
adamc@530 715 \quad \infer{\Gamma \vdash c_1 \rc c_2 :: \{\kappa\}}{
adamc@530 716 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530 717 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@530 718 & \Gamma \vdash c_1 \sim c_2
adamc@530 719 }$$
adamc@530 720
adamc@655 721 $$\infer{\Gamma \vdash \mt{map} :: (\kappa_1 \to \kappa_2) \to \{\kappa_1\} \to \{\kappa_2\}}{}$$
adamc@530 722
adamc@573 723 $$\infer{\Gamma \vdash (\overline c) :: (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@573 724 \forall i: \Gamma \vdash c_i :: \kappa_i
adamc@530 725 }
adamc@573 726 \quad \infer{\Gamma \vdash c.i :: \kappa_i}{
adamc@573 727 \Gamma \vdash c :: (\kappa_1 \times \ldots \times \kappa_n)
adamc@530 728 }$$
adamc@530 729
adamc@655 730 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow \tau :: \mt{Type}}{
adamc@655 731 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530 732 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@655 733 & \Gamma, c_1 \sim c_2 \vdash \tau :: \mt{Type}
adamc@530 734 }$$
adamc@530 735
adamc@531 736 \subsection{Record Disjointness}
adamc@531 737
adamc@531 738 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@558 739 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@558 740 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@558 741 & \forall c'_1 \in C_1, c'_2 \in C_2: \Gamma \vdash c'_1 \sim c'_2
adamc@531 742 }
adamc@531 743 \quad \infer{\Gamma \vdash X \sim X'}{
adamc@531 744 X \neq X'
adamc@531 745 }$$
adamc@531 746
adamc@531 747 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@531 748 c'_1 \sim c'_2 \in \Gamma
adamc@558 749 & \Gamma \vdash c'_1 \hookrightarrow C_1
adamc@558 750 & \Gamma \vdash c'_2 \hookrightarrow C_2
adamc@558 751 & c_1 \in C_1
adamc@558 752 & c_2 \in C_2
adamc@531 753 }$$
adamc@531 754
adamc@531 755 $$\infer{\Gamma \vdash c \hookrightarrow \{c\}}{}
adamc@531 756 \quad \infer{\Gamma \vdash [\overline{c = c'}] \hookrightarrow \{\overline{c}\}}{}
adamc@531 757 \quad \infer{\Gamma \vdash c_1 \rc c_2 \hookrightarrow C_1 \cup C_2}{
adamc@531 758 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@531 759 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@531 760 }
adamc@531 761 \quad \infer{\Gamma \vdash c \hookrightarrow C}{
adamc@531 762 \Gamma \vdash c \equiv c'
adamc@531 763 & \Gamma \vdash c' \hookrightarrow C
adamc@531 764 }
adamc@531 765 \quad \infer{\Gamma \vdash \mt{map} \; f \; c \hookrightarrow C}{
adamc@531 766 \Gamma \vdash c \hookrightarrow C
adamc@531 767 }$$
adamc@531 768
adamc@541 769 \subsection{\label{definitional}Definitional Equality}
adamc@532 770
adamc@655 771 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@532 772
adamc@532 773 $$\infer{\Gamma \vdash c \equiv c}{}
adamc@532 774 \quad \infer{\Gamma \vdash c_1 \equiv c_2}{
adamc@532 775 \Gamma \vdash c_2 \equiv c_1
adamc@532 776 }
adamc@532 777 \quad \infer{\Gamma \vdash c_1 \equiv c_3}{
adamc@532 778 \Gamma \vdash c_1 \equiv c_2
adamc@532 779 & \Gamma \vdash c_2 \equiv c_3
adamc@532 780 }
adamc@532 781 \quad \infer{\Gamma \vdash \mathcal C[c_1] \equiv \mathcal C[c_2]}{
adamc@532 782 \Gamma \vdash c_1 \equiv c_2
adamc@532 783 }$$
adamc@532 784
adamc@532 785 $$\infer{\Gamma \vdash x \equiv c}{
adamc@532 786 x :: \kappa = c \in \Gamma
adamc@532 787 }
adamc@532 788 \quad \infer{\Gamma \vdash M.x \equiv c}{
adamc@537 789 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 790 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@532 791 }
adamc@532 792 \quad \infer{\Gamma \vdash (\overline c).i \equiv c_i}{}$$
adamc@532 793
adamc@532 794 $$\infer{\Gamma \vdash (\lambda x :: \kappa \Rightarrow c) \; c' \equiv [x \mapsto c'] c}{}
adamc@655 795 \quad \infer{\Gamma \vdash (X \Longrightarrow c) [\kappa] \equiv [X \mapsto \kappa] c}{}$$
adamc@655 796
adamc@655 797 $$\infer{\Gamma \vdash c_1 \rc c_2 \equiv c_2 \rc c_1}{}
adamc@532 798 \quad \infer{\Gamma \vdash c_1 \rc (c_2 \rc c_3) \equiv (c_1 \rc c_2) \rc c_3}{}$$
adamc@532 799
adamc@532 800 $$\infer{\Gamma \vdash [] \rc c \equiv c}{}
adamc@532 801 \quad \infer{\Gamma \vdash [\overline{c_1 = c'_1}] \rc [\overline{c_2 = c'_2}] \equiv [\overline{c_1 = c'_1}, \overline{c_2 = c'_2}]}{}$$
adamc@532 802
adamc@655 803 $$\infer{\Gamma \vdash \mt{map} \; f \; [] \equiv []}{}
adamc@655 804 \quad \infer{\Gamma \vdash \mt{map} \; f \; ([c_1 = c_2] \rc c) \equiv [c_1 = f \; c_2] \rc \mt{map} \; f \; c}{}$$
adamc@532 805
adamc@532 806 $$\infer{\Gamma \vdash \mt{map} \; (\lambda x \Rightarrow x) \; c \equiv c}{}
adamc@655 807 \quad \infer{\Gamma \vdash \mt{map} \; f \; (\mt{map} \; f' \; c)
adamc@655 808 \equiv \mt{map} \; (\lambda x \Rightarrow f \; (f' \; x)) \; c}{}$$
adamc@532 809
adamc@532 810 $$\infer{\Gamma \vdash \mt{map} \; f \; (c_1 \rc c_2) \equiv \mt{map} \; f \; c_1 \rc \mt{map} \; f \; c_2}{}$$
adamc@531 811
adamc@534 812 \subsection{Expression Typing}
adamc@533 813
adamc@873 814 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@533 815
adamc@533 816 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@533 817
adamc@533 818 $$\infer{\Gamma \vdash e : \tau : \tau}{
adamc@533 819 \Gamma \vdash e : \tau
adamc@533 820 }
adamc@533 821 \quad \infer{\Gamma \vdash e : \tau}{
adamc@533 822 \Gamma \vdash e : \tau'
adamc@533 823 & \Gamma \vdash \tau' \equiv \tau
adamc@533 824 }
adamc@533 825 \quad \infer{\Gamma \vdash \ell : T(\ell)}{}$$
adamc@533 826
adamc@533 827 $$\infer{\Gamma \vdash x : \mathcal I(\tau)}{
adamc@533 828 x : \tau \in \Gamma
adamc@533 829 }
adamc@533 830 \quad \infer{\Gamma \vdash M.x : \mathcal I(\tau)}{
adamc@537 831 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 832 & \mt{proj}(M, \overline{s}, \mt{val} \; x) = \tau
adamc@533 833 }
adamc@533 834 \quad \infer{\Gamma \vdash X : \mathcal I(\tau)}{
adamc@533 835 X : \tau \in \Gamma
adamc@533 836 }
adamc@533 837 \quad \infer{\Gamma \vdash M.X : \mathcal I(\tau)}{
adamc@537 838 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 839 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \tau
adamc@533 840 }$$
adamc@533 841
adamc@533 842 $$\infer{\Gamma \vdash e_1 \; e_2 : \tau_2}{
adamc@533 843 \Gamma \vdash e_1 : \tau_1 \to \tau_2
adamc@533 844 & \Gamma \vdash e_2 : \tau_1
adamc@533 845 }
adamc@533 846 \quad \infer{\Gamma \vdash \lambda x : \tau_1 \Rightarrow e : \tau_1 \to \tau_2}{
adamc@533 847 \Gamma, x : \tau_1 \vdash e : \tau_2
adamc@533 848 }$$
adamc@533 849
adamc@533 850 $$\infer{\Gamma \vdash e [c] : [x \mapsto c]\tau}{
adamc@533 851 \Gamma \vdash e : x :: \kappa \to \tau
adamc@533 852 & \Gamma \vdash c :: \kappa
adamc@533 853 }
adamc@852 854 \quad \infer{\Gamma \vdash \lambda [x \; ? \; \kappa] \Rightarrow e : x \; ? \; \kappa \to \tau}{
adamc@533 855 \Gamma, x :: \kappa \vdash e : \tau
adamc@533 856 }$$
adamc@533 857
adamc@655 858 $$\infer{\Gamma \vdash e [\kappa] : [X \mapsto \kappa]\tau}{
adamc@655 859 \Gamma \vdash e : X \longrightarrow \tau
adamc@655 860 & \Gamma \vdash \kappa
adamc@655 861 }
adamc@655 862 \quad \infer{\Gamma \vdash X \Longrightarrow e : X \longrightarrow \tau}{
adamc@655 863 \Gamma, X \vdash e : \tau
adamc@655 864 }$$
adamc@655 865
adamc@533 866 $$\infer{\Gamma \vdash \{\overline{c = e}\} : \{\overline{c : \tau}\}}{
adamc@533 867 \forall i: \Gamma \vdash c_i :: \mt{Name}
adamc@533 868 & \Gamma \vdash e_i : \tau_i
adamc@533 869 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@533 870 }
adamc@533 871 \quad \infer{\Gamma \vdash e.c : \tau}{
adamc@533 872 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533 873 }
adamc@533 874 \quad \infer{\Gamma \vdash e_1 \rc e_2 : \$(c_1 \rc c_2)}{
adamc@533 875 \Gamma \vdash e_1 : \$c_1
adamc@533 876 & \Gamma \vdash e_2 : \$c_2
adamc@573 877 & \Gamma \vdash c_1 \sim c_2
adamc@533 878 }$$
adamc@533 879
adamc@533 880 $$\infer{\Gamma \vdash e \rcut c : \$c'}{
adamc@533 881 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533 882 }
adamc@533 883 \quad \infer{\Gamma \vdash e \rcutM c : \$c'}{
adamc@533 884 \Gamma \vdash e : \$(c \rc c')
adamc@533 885 }$$
adamc@533 886
adamc@533 887 $$\infer{\Gamma \vdash \mt{let} \; \overline{ed} \; \mt{in} \; e \; \mt{end} : \tau}{
adamc@533 888 \Gamma \vdash \overline{ed} \leadsto \Gamma'
adamc@533 889 & \Gamma' \vdash e : \tau
adamc@533 890 }
adamc@533 891 \quad \infer{\Gamma \vdash \mt{case} \; e \; \mt{of} \; \overline{p \Rightarrow e} : \tau}{
adamc@533 892 \forall i: \Gamma \vdash p_i \leadsto \Gamma_i, \tau'
adamc@533 893 & \Gamma_i \vdash e_i : \tau
adamc@533 894 }$$
adamc@533 895
adamc@573 896 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow e : \lambda [c_1 \sim c_2] \Rightarrow \tau}{
adamc@533 897 \Gamma \vdash c_1 :: \{\kappa\}
adamc@655 898 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@533 899 & \Gamma, c_1 \sim c_2 \vdash e : \tau
adamc@662 900 }
adamc@662 901 \quad \infer{\Gamma \vdash e \; ! : \tau}{
adamc@662 902 \Gamma \vdash e : [c_1 \sim c_2] \Rightarrow \tau
adamc@662 903 & \Gamma \vdash c_1 \sim c_2
adamc@533 904 }$$
adamc@533 905
adamc@534 906 \subsection{Pattern Typing}
adamc@534 907
adamc@534 908 $$\infer{\Gamma \vdash \_ \leadsto \Gamma; \tau}{}
adamc@534 909 \quad \infer{\Gamma \vdash x \leadsto \Gamma, x : \tau; \tau}{}
adamc@534 910 \quad \infer{\Gamma \vdash \ell \leadsto \Gamma; T(\ell)}{}$$
adamc@534 911
adamc@534 912 $$\infer{\Gamma \vdash X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534 913 X : \overline{x ::: \mt{Type}} \to \tau \in \Gamma
adamc@534 914 & \textrm{$\tau$ not a function type}
adamc@534 915 }
adamc@534 916 \quad \infer{\Gamma \vdash X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534 917 X : \overline{x ::: \mt{Type}} \to \tau'' \to \tau \in \Gamma
adamc@534 918 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534 919 }$$
adamc@534 920
adamc@534 921 $$\infer{\Gamma \vdash M.X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537 922 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 923 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau
adamc@534 924 & \textrm{$\tau$ not a function type}
adamc@534 925 }$$
adamc@534 926
adamc@534 927 $$\infer{\Gamma \vdash M.X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537 928 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 929 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau'' \to \tau
adamc@534 930 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534 931 }$$
adamc@534 932
adamc@534 933 $$\infer{\Gamma \vdash \{\overline{x = p}\} \leadsto \Gamma_n; \{\overline{x = \tau}\}}{
adamc@534 934 \Gamma_0 = \Gamma
adamc@534 935 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534 936 }
adamc@534 937 \quad \infer{\Gamma \vdash \{\overline{x = p}, \ldots\} \leadsto \Gamma_n; \$([\overline{x = \tau}] \rc c)}{
adamc@534 938 \Gamma_0 = \Gamma
adamc@534 939 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534 940 }$$
adamc@534 941
adamc@852 942 $$\infer{\Gamma \vdash p : \tau \leadsto \Gamma'; \tau}{
adamc@852 943 \Gamma \vdash p \leadsto \Gamma'; \tau'
adamc@852 944 & \Gamma \vdash \tau' \equiv \tau
adamc@852 945 }$$
adamc@852 946
adamc@535 947 \subsection{Declaration Typing}
adamc@535 948
adamc@535 949 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@535 950
adamc@558 951 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@537 952 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@535 953
adamc@535 954 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535 955 \quad \infer{\Gamma \vdash d, \overline{d} \leadsto \Gamma''}{
adamc@535 956 \Gamma \vdash d \leadsto \Gamma'
adamc@535 957 & \Gamma' \vdash \overline{d} \leadsto \Gamma''
adamc@535 958 }$$
adamc@535 959
adamc@535 960 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@535 961 \Gamma \vdash c :: \kappa
adamc@535 962 }
adamc@535 963 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@535 964 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@535 965 }$$
adamc@535 966
adamc@535 967 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537 968 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 969 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@535 970 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@535 971 }$$
adamc@535 972
adamc@535 973 $$\infer{\Gamma \vdash \mt{val} \; x : \tau = e \leadsto \Gamma, x : \tau}{
adamc@535 974 \Gamma \vdash e : \tau
adamc@535 975 }$$
adamc@535 976
adamc@535 977 $$\infer{\Gamma \vdash \mt{val} \; \mt{rec} \; \overline{x : \tau = e} \leadsto \Gamma, \overline{x : \tau}}{
adamc@535 978 \forall i: \Gamma, \overline{x : \tau} \vdash e_i : \tau_i
adamc@535 979 & \textrm{$e_i$ starts with an expression $\lambda$, optionally preceded by constructor and disjointness $\lambda$s}
adamc@535 980 }$$
adamc@535 981
adamc@535 982 $$\infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : S}{
adamc@535 983 \Gamma \vdash M : S
adamc@558 984 & \textrm{ $M$ not a constant or application}
adamc@535 985 }
adamc@558 986 \quad \infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : \mt{selfify}(X, \overline{s})}{
adamc@558 987 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@539 988 }$$
adamc@539 989
adamc@539 990 $$\infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@535 991 \Gamma \vdash S
adamc@535 992 }$$
adamc@535 993
adamc@537 994 $$\infer{\Gamma \vdash \mt{open} \; M \leadsto \Gamma, \mathcal O(M, \overline{s})}{
adamc@537 995 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535 996 }$$
adamc@535 997
adamc@535 998 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma}{
adamc@535 999 \Gamma \vdash c_1 :: \{\kappa\}
adamc@535 1000 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@535 1001 & \Gamma \vdash c_1 \sim c_2
adamc@535 1002 }
adamc@537 1003 \quad \infer{\Gamma \vdash \mt{open} \; \mt{constraints} \; M \leadsto \Gamma, \mathcal O_c(M, \overline{s})}{
adamc@537 1004 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535 1005 }$$
adamc@535 1006
adamc@784 1007 $$\infer{\Gamma \vdash \mt{table} \; x : c \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_table} \; c \; []}{
adamc@535 1008 \Gamma \vdash c :: \{\mt{Type}\}
adamc@535 1009 }
adam@1594 1010 \quad \infer{\Gamma \vdash \mt{view} \; x = e \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_view} \; c}{
adam@1594 1011 \Gamma \vdash e :: \mt{Basis}.\mt{sql\_query} \; [] \; [] \; (\mt{map} \; (\lambda \_ \Rightarrow []) \; c') \; c
adamc@784 1012 }$$
adamc@784 1013
adamc@784 1014 $$\infer{\Gamma \vdash \mt{sequence} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_sequence}}{}$$
adamc@535 1015
adamc@535 1016 $$\infer{\Gamma \vdash \mt{cookie} \; x : \tau \leadsto \Gamma, x : \mt{Basis}.\mt{http\_cookie} \; \tau}{
adamc@535 1017 \Gamma \vdash \tau :: \mt{Type}
adamc@784 1018 }
adamc@784 1019 \quad \infer{\Gamma \vdash \mt{style} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{css\_class}}{}$$
adamc@535 1020
adamc@1085 1021 $$\infer{\Gamma \vdash \mt{task} \; e_1 = e_2 \leadsto \Gamma}{
adam@1348 1022 \Gamma \vdash e_1 :: \mt{Basis}.\mt{task\_kind} \; \tau
adam@1348 1023 & \Gamma \vdash e_2 :: \tau \to \mt{Basis}.\mt{transaction} \; \{\}
adamc@1085 1024 }$$
adamc@1085 1025
adamc@535 1026 $$\infer{\overline{y}; x; \Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535 1027 \quad \infer{\overline{y}; x; \Gamma \vdash X \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to x \; \overline{y}}{
adamc@535 1028 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535 1029 }
adamc@535 1030 \quad \infer{\overline{y}; x; \Gamma \vdash X \; \mt{of} \; \tau \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to \tau \to x \; \overline{y}}{
adamc@535 1031 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535 1032 }$$
adamc@535 1033
adamc@537 1034 \subsection{Signature Item Typing}
adamc@537 1035
adamc@537 1036 We appeal to a signature item analogue of the $\mathcal O$ function from the last subsection.
adamc@537 1037
adam@1797 1038 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 1039
adamc@537 1040 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@537 1041 \quad \infer{\Gamma \vdash s, \overline{s} \leadsto \Gamma''}{
adamc@537 1042 \Gamma \vdash s \leadsto \Gamma'
adamc@537 1043 & \Gamma' \vdash \overline{s} \leadsto \Gamma''
adamc@537 1044 }$$
adamc@537 1045
adamc@537 1046 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}
adamc@537 1047 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@537 1048 \Gamma \vdash c :: \kappa
adamc@537 1049 }
adamc@537 1050 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@537 1051 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@537 1052 }$$
adamc@537 1053
adamc@537 1054 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537 1055 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1056 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1057 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@537 1058 }$$
adamc@537 1059
adamc@537 1060 $$\infer{\Gamma \vdash \mt{val} \; x : \tau \leadsto \Gamma, x : \tau}{
adamc@537 1061 \Gamma \vdash \tau :: \mt{Type}
adamc@537 1062 }$$
adamc@537 1063
adamc@537 1064 $$\infer{\Gamma \vdash \mt{structure} \; X : S \leadsto \Gamma, X : S}{
adamc@537 1065 \Gamma \vdash S
adamc@537 1066 }
adamc@537 1067 \quad \infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@537 1068 \Gamma \vdash S
adamc@537 1069 }$$
adamc@537 1070
adamc@537 1071 $$\infer{\Gamma \vdash \mt{include} \; S \leadsto \Gamma, \mathcal O(\overline{s})}{
adamc@537 1072 \Gamma \vdash S
adamc@537 1073 & \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1074 }$$
adamc@537 1075
adamc@537 1076 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma, c_1 \sim c_2}{
adamc@537 1077 \Gamma \vdash c_1 :: \{\kappa\}
adamc@537 1078 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@537 1079 }$$
adamc@537 1080
adamc@784 1081 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784 1082 \Gamma \vdash c :: \kappa
adamc@537 1083 }
adamc@784 1084 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}$$
adamc@537 1085
adamc@536 1086 \subsection{Signature Compatibility}
adamc@536 1087
adam@1797 1088 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 1089
adamc@537 1090 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 1091
adamc@536 1092 $$\infer{\Gamma \vdash S \equiv S}{}
adamc@536 1093 \quad \infer{\Gamma \vdash S_1 \equiv S_2}{
adamc@536 1094 \Gamma \vdash S_2 \equiv S_1
adamc@536 1095 }
adamc@536 1096 \quad \infer{\Gamma \vdash X \equiv S}{
adamc@536 1097 X = S \in \Gamma
adamc@536 1098 }
adamc@536 1099 \quad \infer{\Gamma \vdash M.X \equiv S}{
adamc@537 1100 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1101 & \mt{proj}(M, \overline{s}, \mt{signature} \; X) = S
adamc@536 1102 }$$
adamc@536 1103
adamc@536 1104 $$\infer{\Gamma \vdash S \; \mt{where} \; \mt{con} \; x = c \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa = c \; \overline{s_2} \; \mt{end}}{
adamc@536 1105 \Gamma \vdash S \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa \; \overline{s_2} \; \mt{end}
adamc@536 1106 & \Gamma \vdash c :: \kappa
adamc@537 1107 }
adamc@537 1108 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s^1} \; \mt{include} \; S \; \overline{s^2} \; \mt{end} \equiv \mt{sig} \; \overline{s^1} \; \overline{s} \; \overline{s^2} \; \mt{end}}{
adamc@537 1109 \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@536 1110 }$$
adamc@536 1111
adamc@536 1112 $$\infer{\Gamma \vdash S_1 \leq S_2}{
adamc@536 1113 \Gamma \vdash S_1 \equiv S_2
adamc@536 1114 }
adamc@536 1115 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \mt{end}}{}
adamc@537 1116 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; s' \; \overline{s'} \; \mt{end}}{
adamc@537 1117 \Gamma \vdash \overline{s} \leq s'
adamc@537 1118 & \Gamma \vdash s' \leadsto \Gamma'
adamc@537 1119 & \Gamma' \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \overline{s'} \; \mt{end}
adamc@537 1120 }$$
adamc@537 1121
adamc@537 1122 $$\infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537 1123 \Gamma \vdash s \leq s'
adamc@537 1124 }
adamc@537 1125 \quad \infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537 1126 \Gamma \vdash s \leadsto \Gamma'
adamc@537 1127 & \Gamma' \vdash \overline{s} \leq s'
adamc@536 1128 }$$
adamc@536 1129
adamc@536 1130 $$\infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 \leq \mt{functor} (X : S'_1) : S'_2}{
adamc@536 1131 \Gamma \vdash S'_1 \leq S_1
adamc@536 1132 & \Gamma, X : S'_1 \vdash S_2 \leq S'_2
adamc@536 1133 }$$
adamc@536 1134
adamc@537 1135 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@537 1136 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}
adamc@558 1137 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type}}{}$$
adamc@537 1138
adamc@537 1139 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(y)} \to \mt{Type}}{
adamc@537 1140 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1141 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1142 }$$
adamc@537 1143
adamc@784 1144 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@784 1145 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}$$
adamc@537 1146
adamc@537 1147 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \mt{\kappa} = c_2}{
adamc@537 1148 \Gamma \vdash c_1 \equiv c_2
adamc@537 1149 }
adamc@784 1150 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \kappa = c_2}{
adamc@537 1151 \Gamma \vdash c_1 \equiv c_2
adamc@537 1152 }$$
adamc@537 1153
adamc@537 1154 $$\infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537 1155 \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1156 }$$
adamc@537 1157
adamc@537 1158 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537 1159 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1160 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1161 & \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1162 }$$
adamc@537 1163
adamc@537 1164 $$\infer{\Gamma \vdash \cdot \leq \cdot}{}
adamc@537 1165 \quad \infer{\Gamma \vdash X; \overline{dc} \leq X; \overline{dc'}}{
adamc@537 1166 \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1167 }
adamc@537 1168 \quad \infer{\Gamma \vdash X \; \mt{of} \; \tau_1; \overline{dc} \leq X \; \mt{of} \; \tau_2; \overline{dc'}}{
adamc@537 1169 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537 1170 & \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1171 }$$
adamc@537 1172
adamc@537 1173 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x = \mt{datatype} \; M'.z'}{
adamc@537 1174 \Gamma \vdash M.z \equiv M'.z'
adamc@537 1175 }$$
adamc@537 1176
adamc@537 1177 $$\infer{\Gamma \vdash \mt{val} \; x : \tau_1 \leq \mt{val} \; x : \tau_2}{
adamc@537 1178 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537 1179 }
adamc@537 1180 \quad \infer{\Gamma \vdash \mt{structure} \; X : S_1 \leq \mt{structure} \; X : S_2}{
adamc@537 1181 \Gamma \vdash S_1 \leq S_2
adamc@537 1182 }
adamc@537 1183 \quad \infer{\Gamma \vdash \mt{signature} \; X = S_1 \leq \mt{signature} \; X = S_2}{
adamc@537 1184 \Gamma \vdash S_1 \leq S_2
adamc@537 1185 & \Gamma \vdash S_2 \leq S_1
adamc@537 1186 }$$
adamc@537 1187
adamc@537 1188 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leq \mt{constraint} \; c'_1 \sim c'_2}{
adamc@537 1189 \Gamma \vdash c_1 \equiv c'_1
adamc@537 1190 & \Gamma \vdash c_2 \equiv c'_2
adamc@537 1191 }$$
adamc@537 1192
adamc@655 1193 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{class} \; x :: \kappa}{}
adamc@655 1194 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{class} \; x :: \kappa}{}
adamc@655 1195 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{class} \; x :: \kappa = c_2}{
adamc@537 1196 \Gamma \vdash c_1 \equiv c_2
adamc@537 1197 }$$
adamc@537 1198
adam@1797 1199 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leq \mt{class} \; x :: \kappa}{}
adam@1797 1200 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leq \mt{class} \; x :: \kappa}{}
adam@1797 1201 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c_1 \leq \mt{class} \; x :: \kappa = c_2}{
adam@1797 1202 \Gamma \vdash c_1 \equiv c_2
adam@1797 1203 }$$
adam@1797 1204
adamc@538 1205 \subsection{Module Typing}
adamc@538 1206
adamc@538 1207 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 1208
adamc@538 1209 $$\infer{\Gamma \vdash M : S}{
adamc@538 1210 \Gamma \vdash M : S'
adamc@538 1211 & \Gamma \vdash S' \leq S
adamc@538 1212 }
adamc@538 1213 \quad \infer{\Gamma \vdash \mt{struct} \; \overline{d} \; \mt{end} : \mt{sig} \; \mt{sigOf}(\overline{d}) \; \mt{end}}{
adamc@538 1214 \Gamma \vdash \overline{d} \leadsto \Gamma'
adamc@538 1215 }
adamc@538 1216 \quad \infer{\Gamma \vdash X : S}{
adamc@538 1217 X : S \in \Gamma
adamc@538 1218 }$$
adamc@538 1219
adamc@538 1220 $$\infer{\Gamma \vdash M.X : S}{
adamc@538 1221 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@538 1222 & \mt{proj}(M, \overline{s}, \mt{structure} \; X) = S
adamc@538 1223 }$$
adamc@538 1224
adamc@538 1225 $$\infer{\Gamma \vdash M_1(M_2) : [X \mapsto M_2]S_2}{
adamc@538 1226 \Gamma \vdash M_1 : \mt{functor}(X : S_1) : S_2
adamc@538 1227 & \Gamma \vdash M_2 : S_1
adamc@538 1228 }
adamc@538 1229 \quad \infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 = M : \mt{functor} (X : S_1) : S_2}{
adamc@538 1230 \Gamma \vdash S_1
adamc@538 1231 & \Gamma, X : S_1 \vdash S_2
adamc@538 1232 & \Gamma, X : S_1 \vdash M : S_2
adamc@538 1233 }$$
adamc@538 1234
adamc@538 1235 \begin{eqnarray*}
adamc@538 1236 \mt{sigOf}(\cdot) &=& \cdot \\
adamc@538 1237 \mt{sigOf}(s \; \overline{s'}) &=& \mt{sigOf}(s) \; \mt{sigOf}(\overline{s'}) \\
adamc@538 1238 \\
adamc@538 1239 \mt{sigOf}(\mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@538 1240 \mt{sigOf}(\mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \overline{dc} \\
adamc@538 1241 \mt{sigOf}(\mt{datatype} \; x = \mt{datatype} \; M.z) &=& \mt{datatype} \; x = \mt{datatype} \; M.z \\
adamc@538 1242 \mt{sigOf}(\mt{val} \; x : \tau = e) &=& \mt{val} \; x : \tau \\
adamc@538 1243 \mt{sigOf}(\mt{val} \; \mt{rec} \; \overline{x : \tau = e}) &=& \overline{\mt{val} \; x : \tau} \\
adamc@538 1244 \mt{sigOf}(\mt{structure} \; X : S = M) &=& \mt{structure} \; X : S \\
adamc@538 1245 \mt{sigOf}(\mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@538 1246 \mt{sigOf}(\mt{open} \; M) &=& \mt{include} \; S \textrm{ (where $\Gamma \vdash M : S$)} \\
adamc@538 1247 \mt{sigOf}(\mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@538 1248 \mt{sigOf}(\mt{open} \; \mt{constraints} \; M) &=& \cdot \\
adamc@538 1249 \mt{sigOf}(\mt{table} \; x : c) &=& \mt{table} \; x : c \\
adam@1594 1250 \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 1251 \mt{sigOf}(\mt{sequence} \; x) &=& \mt{sequence} \; x \\
adamc@538 1252 \mt{sigOf}(\mt{cookie} \; x : \tau) &=& \mt{cookie} \; x : \tau \\
adam@1797 1253 \mt{sigOf}(\mt{style} \; x) &=& \mt{style} \; x
adamc@538 1254 \end{eqnarray*}
adamc@539 1255 \begin{eqnarray*}
adamc@539 1256 \mt{selfify}(M, \cdot) &=& \cdot \\
adamc@558 1257 \mt{selfify}(M, s \; \overline{s'}) &=& \mt{selfify}(M, s) \; \mt{selfify}(M, \overline{s'}) \\
adamc@539 1258 \\
adamc@539 1259 \mt{selfify}(M, \mt{con} \; x :: \kappa) &=& \mt{con} \; x :: \kappa = M.x \\
adamc@539 1260 \mt{selfify}(M, \mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@539 1261 \mt{selfify}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \mt{datatype} \; M.x \\
adamc@539 1262 \mt{selfify}(M, \mt{datatype} \; x = \mt{datatype} \; M'.z) &=& \mt{datatype} \; x = \mt{datatype} \; M'.z \\
adamc@539 1263 \mt{selfify}(M, \mt{val} \; x : \tau) &=& \mt{val} \; x : \tau \\
adamc@539 1264 \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 1265 \mt{selfify}(M, \mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@539 1266 \mt{selfify}(M, \mt{include} \; S) &=& \mt{include} \; S \\
adamc@539 1267 \mt{selfify}(M, \mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@655 1268 \mt{selfify}(M, \mt{class} \; x :: \kappa) &=& \mt{class} \; x :: \kappa = M.x \\
adamc@655 1269 \mt{selfify}(M, \mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@539 1270 \end{eqnarray*}
adamc@539 1271
adamc@540 1272 \subsection{Module Projection}
adamc@540 1273
adamc@540 1274 \begin{eqnarray*}
adamc@540 1275 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \\
adamc@540 1276 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa, c) \\
adamc@540 1277 \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 1278 \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 1279 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})$)} \\
adamc@655 1280 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \to \mt{Type} \\
adamc@655 1281 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa \to \mt{Type}, c) \\
adamc@540 1282 \\
adamc@540 1283 \mt{proj}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc} \; \overline{s}, \mt{datatype} \; x) &=& (\overline{y}, \overline{dc}) \\
adamc@540 1284 \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 1285 \\
adamc@540 1286 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, \mt{val} \; x) &=& \tau \\
adamc@540 1287 \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 1288 \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 1289 \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 1290 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \in \overline{dc}$)} \\
adamc@540 1291 \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 1292 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \; \mt{of} \; \tau \in \overline{dc}$)} \\
adamc@540 1293 \\
adamc@540 1294 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, \mt{structure} \; X) &=& S \\
adamc@540 1295 \\
adamc@540 1296 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, \mt{signature} \; X) &=& S \\
adamc@540 1297 \\
adamc@540 1298 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1299 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1300 \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 1301 \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 1302 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@540 1303 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1304 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1305 \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 1306 \mt{proj}(M, \mt{constraint} \; c_1 \sim c_2 \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@655 1307 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@655 1308 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1309 \end{eqnarray*}
adamc@540 1310
adamc@541 1311
adamc@541 1312 \section{Type Inference}
adamc@541 1313
adamc@541 1314 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 1315
adamc@541 1316 \subsection{Basic Unification}
adamc@541 1317
adamc@560 1318 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 1319
adamc@656 1320 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 1321
adamc@541 1322 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 1323
adamc@541 1324 \subsection{Unifying Record Types}
adamc@541 1325
adamc@570 1326 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 1327
adamc@656 1328 \subsection{\label{typeclasses}Constructor Classes}
adamc@541 1329
adamc@784 1330 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 1331
adam@1797 1332 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 1333
adam@1797 1334 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 1335
adam@1797 1336 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 1337
adamc@541 1338 \subsection{Reverse-Engineering Record Types}
adamc@541 1339
adamc@656 1340 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 1341
adamc@541 1342 \subsection{Implicit Arguments in Functor Applications}
adamc@541 1343
adamc@656 1344 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 1345
adamc@541 1346
adamc@542 1347 \section{The Ur Standard Library}
adamc@542 1348
adamc@542 1349 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 1350
adamc@542 1351 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 1352
adamc@542 1353 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 1354 $$\begin{array}{l}
adamc@542 1355 \mt{type} \; \mt{int} \\
adamc@542 1356 \mt{type} \; \mt{float} \\
adamc@873 1357 \mt{type} \; \mt{char} \\
adamc@542 1358 \mt{type} \; \mt{string} \\
adamc@542 1359 \mt{type} \; \mt{time} \\
adamc@785 1360 \mt{type} \; \mt{blob} \\
adamc@542 1361 \\
adamc@542 1362 \mt{type} \; \mt{unit} = \{\} \\
adamc@542 1363 \\
adamc@542 1364 \mt{datatype} \; \mt{bool} = \mt{False} \mid \mt{True} \\
adamc@542 1365 \\
adamc@785 1366 \mt{datatype} \; \mt{option} \; \mt{t} = \mt{None} \mid \mt{Some} \; \mt{of} \; \mt{t} \\
adamc@785 1367 \\
adamc@785 1368 \mt{datatype} \; \mt{list} \; \mt{t} = \mt{Nil} \mid \mt{Cons} \; \mt{of} \; \mt{t} \times \mt{list} \; \mt{t}
adamc@542 1369 \end{array}$$
adamc@542 1370
adamc@1123 1371 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 1372
adam@1297 1373 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 1374 $$\begin{array}{l}
adam@1297 1375 \mt{con} \; \mt{variant} :: \{\mt{Type}\} \to \mt{Type} \\
adam@1297 1376 \mt{val} \; \mt{make} : \mt{nm} :: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{ts} ::: \{\mt{Type}\} \to [[\mt{nm}] \sim \mt{ts}] \Rightarrow \mt{t} \to \mt{variant} \; ([\mt{nm} = \mt{t}] \rc \mt{ts}) \\
adam@1297 1377 \mt{val} \; \mt{match} : \mt{ts} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{variant} \; \mt{ts} \to \$(\mt{map} \; (\lambda \mt{t'} \Rightarrow \mt{t'} \to \mt{t}) \; \mt{ts}) \to \mt{t}
adam@1297 1378 \end{array}$$
adam@1297 1379
adamc@657 1380 Another important generic Ur element comes at the beginning of \texttt{top.urs}.
adamc@657 1381
adamc@657 1382 $$\begin{array}{l}
adamc@657 1383 \mt{con} \; \mt{folder} :: \mt{K} \longrightarrow \{\mt{K}\} \to \mt{Type} \\
adamc@657 1384 \\
adamc@657 1385 \mt{val} \; \mt{fold} : \mt{K} \longrightarrow \mt{tf} :: (\{\mt{K}\} \to \mt{Type}) \\
adamc@657 1386 \hspace{.1in} \to (\mt{nm} :: \mt{Name} \to \mt{v} :: \mt{K} \to \mt{r} :: \{\mt{K}\} \to [[\mt{nm}] \sim \mt{r}] \Rightarrow \\
adamc@657 1387 \hspace{.2in} \mt{tf} \; \mt{r} \to \mt{tf} \; ([\mt{nm} = \mt{v}] \rc \mt{r})) \\
adamc@657 1388 \hspace{.1in} \to \mt{tf} \; [] \\
adamc@657 1389 \hspace{.1in} \to \mt{r} :: \{\mt{K}\} \to \mt{folder} \; \mt{r} \to \mt{tf} \; \mt{r}
adamc@657 1390 \end{array}$$
adamc@657 1391
adamc@657 1392 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 1393
adamc@664 1394 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 1395
adamc@542 1396
adamc@542 1397 \section{The Ur/Web Standard Library}
adamc@542 1398
adam@1400 1399 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 1400
adamc@658 1401 \subsection{Monads}
adamc@658 1402
adamc@658 1403 The Ur Basis defines the monad constructor class from Haskell.
adamc@658 1404
adamc@658 1405 $$\begin{array}{l}
adamc@658 1406 \mt{class} \; \mt{monad} :: \mt{Type} \to \mt{Type} \\
adamc@658 1407 \mt{val} \; \mt{return} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t} ::: \mt{Type} \\
adamc@658 1408 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658 1409 \hspace{.1in} \to \mt{t} \to \mt{m} \; \mt{t} \\
adamc@658 1410 \mt{val} \; \mt{bind} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t1} ::: \mt{Type} \to \mt{t2} ::: \mt{Type} \\
adamc@658 1411 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658 1412 \hspace{.1in} \to \mt{m} \; \mt{t1} \to (\mt{t1} \to \mt{m} \; \mt{t2}) \\
adam@1544 1413 \hspace{.1in} \to \mt{m} \; \mt{t2} \\
adam@1544 1414 \mt{val} \; \mt{mkMonad} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \\
adam@1544 1415 \hspace{.1in} \to \{\mt{Return} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{m} \; \mt{t}, \\
adam@1544 1416 \hspace{.3in} \mt{Bind} : \mt{t1} ::: \mt{Type} \to \mt{t2} ::: \mt{Type} \to \mt{m} \; \mt{t1} \to (\mt{t1} \to \mt{m} \; \mt{t2}) \to \mt{m} \; \mt{t2}\} \\
adam@1544 1417 \hspace{.1in} \to \mt{monad} \; \mt{m}
adamc@658 1418 \end{array}$$
adamc@658 1419
adam@1687 1420 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 1421
adamc@542 1422 \subsection{Transactions}
adamc@542 1423
adamc@542 1424 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 1425 $$\begin{array}{l}
adamc@542 1426 \mt{con} \; \mt{transaction} :: \mt{Type} \to \mt{Type} \\
adamc@658 1427 \mt{val} \; \mt{transaction\_monad} : \mt{monad} \; \mt{transaction}
adamc@542 1428 \end{array}$$
adamc@542 1429
adamc@1123 1430 For debugging purposes, a transactional function is provided for outputting a string on the server process' \texttt{stderr}.
adamc@1123 1431 $$\begin{array}{l}
adamc@1123 1432 \mt{val} \; \mt{debug} : \mt{string} \to \mt{transaction} \; \mt{unit}
adamc@1123 1433 \end{array}$$
adamc@1123 1434
adamc@542 1435 \subsection{HTTP}
adamc@542 1436
adam@1797 1437 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 1438 $$\begin{array}{l}
adamc@786 1439 \mt{con} \; \mt{http\_cookie} :: \mt{Type} \to \mt{Type} \\
adamc@786 1440 \mt{val} \; \mt{getCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; (\mt{option} \; \mt{t}) \\
adamc@1050 1441 \mt{val} \; \mt{setCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \{\mt{Value} : \mt{t}, \mt{Expires} : \mt{option} \; \mt{time}, \mt{Secure} : \mt{bool}\} \to \mt{transaction} \; \mt{unit} \\
adamc@1050 1442 \mt{val} \; \mt{clearCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; \mt{unit}
adamc@786 1443 \end{array}$$
adamc@786 1444
adamc@786 1445 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 1446 $$\begin{array}{l}
adamc@786 1447 \mt{type} \; \mt{url} \\
adamc@786 1448 \mt{val} \; \mt{bless} : \mt{string} \to \mt{url} \\
adamc@786 1449 \mt{val} \; \mt{checkUrl} : \mt{string} \to \mt{option} \; \mt{url}
adamc@786 1450 \end{array}$$
adamc@786 1451 $\mt{bless}$ raises a runtime error if the string passed to it fails the URL policy.
adamc@786 1452
adam@1400 1453 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 1454 $$\begin{array}{l}
adamc@1085 1455 \mt{val} \; \mt{currentUrl} : \mt{transaction} \; \mt{url} \\
adamc@1085 1456 \mt{val} \; \mt{url} : \mt{transaction} \; \mt{page} \to \mt{url}
adamc@1085 1457 \end{array}$$
adamc@1085 1458
adamc@1085 1459 Page generation may be interrupted at any time with a request to redirect to a particular URL instead.
adamc@1085 1460 $$\begin{array}{l}
adamc@1085 1461 \mt{val} \; \mt{redirect} : \mt{t} ::: \mt{Type} \to \mt{url} \to \mt{transaction} \; \mt{t}
adamc@1085 1462 \end{array}$$
adamc@1085 1463
adam@1400 1464 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 1465 $$\begin{array}{l}
adamc@786 1466 \mt{type} \; \mt{file} \\
adamc@786 1467 \mt{val} \; \mt{fileName} : \mt{file} \to \mt{option} \; \mt{string} \\
adamc@786 1468 \mt{val} \; \mt{fileMimeType} : \mt{file} \to \mt{string} \\
adamc@786 1469 \mt{val} \; \mt{fileData} : \mt{file} \to \mt{blob}
adamc@786 1470 \end{array}$$
adamc@786 1471
adam@1799 1472 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 1473
adam@1465 1474 $$\begin{array}{l}
adam@1465 1475 \mt{type} \; \mt{requestHeader} \\
adam@1465 1476 \mt{val} \; \mt{blessRequestHeader} : \mt{string} \to \mt{requestHeader} \\
adam@1465 1477 \mt{val} \; \mt{checkRequestHeader} : \mt{string} \to \mt{option} \; \mt{requestHeader} \\
adam@1465 1478 \mt{val} \; \mt{getHeader} : \mt{requestHeader} \to \mt{transaction} \; (\mt{option} \; \mt{string}) \\
adam@1465 1479 \\
adam@1799 1480 \mt{type} \; \mt{envVar} \\
adam@1799 1481 \mt{val} \; \mt{blessEnvVar} : \mt{string} \to \mt{envVar} \\
adam@1799 1482 \mt{val} \; \mt{checkEnvVar} : \mt{string} \to \mt{option} \; \mt{envVar} \\
adam@1799 1483 \mt{val} \; \mt{getenv} : \mt{envVar} \to \mt{transaction} \; (\mt{option} \; \mt{string}) \\
adam@1799 1484 \\
adam@1465 1485 \mt{type} \; \mt{responseHeader} \\
adam@1465 1486 \mt{val} \; \mt{blessResponseHeader} : \mt{string} \to \mt{responseHeader} \\
adam@1465 1487 \mt{val} \; \mt{checkResponseHeader} : \mt{string} \to \mt{option} \; \mt{responseHeader} \\
adam@1465 1488 \mt{val} \; \mt{setHeader} : \mt{responseHeader} \to \mt{string} \to \mt{transaction} \; \mt{unit}
adam@1465 1489 \end{array}$$
adam@1465 1490
adamc@786 1491 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 1492 $$\begin{array}{l}
adamc@786 1493 \mt{type} \; \mt{mimeType} \\
adamc@786 1494 \mt{val} \; \mt{blessMime} : \mt{string} \to \mt{mimeType} \\
adamc@786 1495 \mt{val} \; \mt{checkMime} : \mt{string} \to \mt{option} \; \mt{mimeType} \\
adamc@786 1496 \mt{val} \; \mt{returnBlob} : \mt{t} ::: \mt{Type} \to \mt{blob} \to \mt{mimeType} \to \mt{transaction} \; \mt{t}
adamc@542 1497 \end{array}$$
adamc@542 1498
adamc@543 1499 \subsection{SQL}
adamc@543 1500
adam@1400 1501 Everything about SQL database access is restricted to server-side code.
adam@1400 1502
adamc@543 1503 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 1504 $$\begin{array}{l}
adamc@785 1505 \mt{con} \; \mt{sql\_table} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785 1506 \end{array}$$
adamc@785 1507 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 1508
adamc@785 1509 We also have the simpler type family of SQL views, which have no keys.
adamc@785 1510 $$\begin{array}{l}
adamc@785 1511 \mt{con} \; \mt{sql\_view} :: \{\mt{Type}\} \to \mt{Type}
adamc@543 1512 \end{array}$$
adamc@543 1513
adamc@785 1514 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 1515 $$\begin{array}{l}
adamc@785 1516 \mt{class} \; \mt{fieldsOf} :: \mt{Type} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1517 \mt{val} \; \mt{fieldsOf\_table} : \mt{fs} ::: \{\mt{Type}\} \to \mt{keys} ::: \{\{\mt{Unit}\}\} \to \mt{fieldsOf} \; (\mt{sql\_table} \; \mt{fs} \; \mt{keys}) \; \mt{fs} \\
adamc@785 1518 \mt{val} \; \mt{fieldsOf\_view} : \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; (\mt{sql\_view} \; \mt{fs}) \; \mt{fs}
adamc@785 1519 \end{array}$$
adamc@785 1520
adamc@785 1521 \subsubsection{Table Constraints}
adamc@785 1522
adamc@785 1523 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 1524
adamc@785 1525 $$\begin{array}{l}
adamc@785 1526 \mt{con} \; \mt{primary\_key} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type} \\
adamc@785 1527 \mt{val} \; \mt{no\_primary\_key} : \mt{fs} ::: \{\mt{Type}\} \to \mt{primary\_key} \; \mt{fs} \; [] \\
adamc@785 1528 \mt{val} \; \mt{primary\_key} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{key1} :: \mt{Name} \to \mt{keys} :: \{\mt{Type}\} \\
adamc@785 1529 \hspace{.1in} \to [[\mt{key1}] \sim \mt{keys}] \Rightarrow [[\mt{key1} = \mt{t}] \rc \mt{keys} \sim \mt{rest}] \\
adamc@785 1530 \hspace{.1in} \Rightarrow \$([\mt{key1} = \mt{sql\_injectable\_prim} \; \mt{t}] \rc \mt{map} \; \mt{sql\_injectable\_prim} \; \mt{keys}) \\
adamc@785 1531 \hspace{.1in} \to \mt{primary\_key} \; ([\mt{key1} = \mt{t}] \rc \mt{keys} \rc \mt{rest}) \; [\mt{Pkey} = [\mt{key1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{keys}]
adamc@785 1532 \end{array}$$
adamc@785 1533 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 1534
adamc@785 1535 A type family stands for sets of named constraints of the remaining varieties.
adamc@785 1536 $$\begin{array}{l}
adamc@785 1537 \mt{con} \; \mt{sql\_constraints} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785 1538 \end{array}$$
adamc@785 1539 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 1540
adamc@785 1541 There is a type family of individual, unnamed constraints.
adamc@785 1542 $$\begin{array}{l}
adamc@785 1543 \mt{con} \; \mt{sql\_constraint} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \mt{Type}
adamc@785 1544 \end{array}$$
adamc@785 1545 The first argument is the same as above, and the second argument gives the key columns for just this constraint.
adamc@785 1546
adamc@785 1547 We have operations for assembling constraints into constraint sets.
adamc@785 1548 $$\begin{array}{l}
adamc@785 1549 \mt{val} \; \mt{no\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_constraints} \; \mt{fs} \; [] \\
adamc@785 1550 \mt{val} \; \mt{one\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{unique} ::: \{\mt{Unit}\} \to \mt{name} :: \mt{Name} \\
adamc@785 1551 \hspace{.1in} \to \mt{sql\_constraint} \; \mt{fs} \; \mt{unique} \to \mt{sql\_constraints} \; \mt{fs} \; [\mt{name} = \mt{unique}] \\
adamc@785 1552 \mt{val} \; \mt{join\_constraints} : \mt{fs} ::: \{\mt{Type}\} \to \mt{uniques1} ::: \{\{\mt{Unit}\}\} \to \mt{uniques2} ::: \{\{\mt{Unit}\}\} \to [\mt{uniques1} \sim \mt{uniques2}] \\
adamc@785 1553 \hspace{.1in} \Rightarrow \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques1} \to \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques2} \to \mt{sql\_constraints} \; \mt{fs} \; (\mt{uniques1} \rc \mt{uniques2})
adamc@785 1554 \end{array}$$
adamc@785 1555
adamc@785 1556 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 1557 $$\begin{array}{l}
adamc@785 1558 \mt{val} \; \mt{unique} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{unique1} :: \mt{Name} \to \mt{unique} :: \{\mt{Type}\} \\
adamc@785 1559 \hspace{.1in} \to [[\mt{unique1}] \sim \mt{unique}] \Rightarrow [[\mt{unique1} = \mt{t}] \rc \mt{unique} \sim \mt{rest}] \\
adamc@785 1560 \hspace{.1in} \Rightarrow \mt{sql\_constraint} \; ([\mt{unique1} = \mt{t}] \rc \mt{unique} \rc \mt{rest}) \; ([\mt{unique1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{unique})
adamc@785 1561 \end{array}$$
adamc@785 1562
adamc@785 1563 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 1564 $$\begin{array}{l}
adamc@785 1565 \mt{class} \; \mt{linkable} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@785 1566 \mt{val} \; \mt{linkable\_same} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; \mt{t} \\
adamc@785 1567 \mt{val} \; \mt{linkable\_from\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; (\mt{option} \; \mt{t}) \; \mt{t} \\
adamc@785 1568 \mt{val} \; \mt{linkable\_to\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@785 1569 \end{array}$$
adamc@785 1570
adamc@785 1571 The $\mt{matching}$ type family uses $\mt{linkable}$ to define when two keys match up type-wise.
adamc@785 1572 $$\begin{array}{l}
adamc@785 1573 \mt{con} \; \mt{matching} :: \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1574 \mt{val} \; \mt{mat\_nil} : \mt{matching} \; [] \; [] \\
adamc@785 1575 \mt{val} \; \mt{mat\_cons} : \mt{t1} ::: \mt{Type} \to \mt{rest1} ::: \{\mt{Type}\} \to \mt{t2} ::: \mt{Type} \to \mt{rest2} ::: \{\mt{Type}\} \to \mt{nm1} :: \mt{Name} \to \mt{nm2} :: \mt{Name} \\
adamc@785 1576 \hspace{.1in} \to [[\mt{nm1}] \sim \mt{rest1}] \Rightarrow [[\mt{nm2}] \sim \mt{rest2}] \Rightarrow \mt{linkable} \; \mt{t1} \; \mt{t2} \to \mt{matching} \; \mt{rest1} \; \mt{rest2} \\
adamc@785 1577 \hspace{.1in} \to \mt{matching} \; ([\mt{nm1} = \mt{t1}] \rc \mt{rest1}) \; ([\mt{nm2} = \mt{t2}] \rc \mt{rest2})
adamc@785 1578 \end{array}$$
adamc@785 1579
adamc@785 1580 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 1581 $$\begin{array}{l}
adamc@785 1582 \mt{con} \; \mt{propagation\_mode} :: \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1583 \mt{val} \; \mt{restrict} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1584 \mt{val} \; \mt{cascade} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1585 \mt{val} \; \mt{no\_action} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1586 \mt{val} \; \mt{set\_null} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; (\mt{map} \; \mt{option} \; \mt{fs})
adamc@785 1587 \end{array}$$
adamc@785 1588
adamc@785 1589 Finally, we put these ingredient together to define the \texttt{FOREIGN KEY} constraint function.
adamc@785 1590 $$\begin{array}{l}
adamc@785 1591 \mt{val} \; \mt{foreign\_key} : \mt{mine1} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{mine} ::: \{\mt{Type}\} \to \mt{munused} ::: \{\mt{Type}\} \to \mt{foreign} ::: \{\mt{Type}\} \\
adamc@785 1592 \hspace{.1in} \to \mt{funused} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{uniques} ::: \{\{\mt{Unit}\}\} \\
adamc@785 1593 \hspace{.1in} \to [[\mt{mine1}] \sim \mt{mine}] \Rightarrow [[\mt{mine1} = \mt{t}] \rc \mt{mine} \sim \mt{munused}] \Rightarrow [\mt{foreign} \sim \mt{funused}] \Rightarrow [[\mt{nm}] \sim \mt{uniques}] \\
adamc@785 1594 \hspace{.1in} \Rightarrow \mt{matching} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}) \; \mt{foreign} \\
adamc@785 1595 \hspace{.1in} \to \mt{sql\_table} \; (\mt{foreign} \rc \mt{funused}) \; ([\mt{nm} = \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{foreign}] \rc \mt{uniques}) \\
adamc@785 1596 \hspace{.1in} \to \{\mt{OnDelete} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}), \\
adamc@785 1597 \hspace{.2in} \mt{OnUpdate} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine})\} \\
adamc@785 1598 \hspace{.1in} \to \mt{sql\_constraint} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine} \rc \mt{munused}) \; []
adamc@785 1599 \end{array}$$
adamc@785 1600
adamc@785 1601 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 1602 $$\begin{array}{l}
adam@1778 1603 \mt{val} \; \mt{check} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; [] \; [] \; \mt{fs} \; \mt{bool} \to \mt{sql\_constraint} \; \mt{fs} \; []
adamc@785 1604 \end{array}$$
adamc@785 1605
adamc@785 1606 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 1607
adamc@784 1608
adamc@543 1609 \subsubsection{Queries}
adamc@543 1610
adam@1400 1611 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 1612 $$\begin{array}{l}
adam@1400 1613 \mt{con} \; \mt{sql\_query} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@1193 1614 \mt{val} \; \mt{sql\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400 1615 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1616 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543 1617 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1618 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1193 1619 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adam@1400 1620 \hspace{.1in} \Rightarrow \{\mt{Rows} : \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}, \\
adamc@1193 1621 \hspace{.2in} \mt{OrderBy} : \mt{sql\_order\_by} \; (\mt{free} \rc \mt{tables}) \; \mt{selectedExps}, \\
adamc@543 1622 \hspace{.2in} \mt{Limit} : \mt{sql\_limit}, \\
adamc@543 1623 \hspace{.2in} \mt{Offset} : \mt{sql\_offset}\} \\
adam@1400 1624 \hspace{.1in} \to \mt{sql\_query} \; \mt{free} \; \mt{afree} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1625 \end{array}$$
adamc@543 1626
adamc@545 1627 Queries are used by folding over their results inside transactions.
adamc@545 1628 $$\begin{array}{l}
adam@1400 1629 \mt{val} \; \mt{query} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to [\mt{tables} \sim \mt{exps}] \Rightarrow \mt{state} ::: \mt{Type} \to \mt{sql\_query} \; [] \; [] \; \mt{tables} \; \mt{exps} \\
adamc@658 1630 \hspace{.1in} \to (\$(\mt{exps} \rc \mt{map} \; (\lambda \mt{fields} :: \{\mt{Type}\} \Rightarrow \$\mt{fields}) \; \mt{tables}) \\
adamc@545 1631 \hspace{.2in} \to \mt{state} \to \mt{transaction} \; \mt{state}) \\
adamc@545 1632 \hspace{.1in} \to \mt{state} \to \mt{transaction} \; \mt{state}
adamc@545 1633 \end{array}$$
adamc@545 1634
adam@1400 1635 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 1636 $$\begin{array}{l}
adam@1400 1637 \mt{con} \; \mt{sql\_query1} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@543 1638 \\
adamc@543 1639 \mt{type} \; \mt{sql\_relop} \\
adamc@543 1640 \mt{val} \; \mt{sql\_union} : \mt{sql\_relop} \\
adamc@543 1641 \mt{val} \; \mt{sql\_intersect} : \mt{sql\_relop} \\
adamc@543 1642 \mt{val} \; \mt{sql\_except} : \mt{sql\_relop} \\
adam@1400 1643 \mt{val} \; \mt{sql\_relop} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400 1644 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adam@1400 1645 \hspace{.1in} \to \mt{tables1} ::: \{\{\mt{Type}\}\} \\
adamc@543 1646 \hspace{.1in} \to \mt{tables2} ::: \{\{\mt{Type}\}\} \\
adamc@543 1647 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1648 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@543 1649 \hspace{.1in} \to \mt{sql\_relop} \\
adam@1458 1650 \hspace{.1in} \to \mt{bool} \; (* \; \mt{ALL} \; *) \\
adam@1400 1651 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables1} \; \mt{selectedFields} \; \mt{selectedExps} \\
adam@1400 1652 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables2} \; \mt{selectedFields} \; \mt{selectedExps} \\
adam@1400 1653 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{selectedFields} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1654 \end{array}$$
adamc@543 1655
adamc@543 1656 $$\begin{array}{l}
adamc@1193 1657 \mt{val} \; \mt{sql\_query1} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400 1658 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1659 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543 1660 \hspace{.1in} \to \mt{grouped} ::: \{\{\mt{Type}\}\} \\
adamc@543 1661 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1662 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1085 1663 \hspace{.1in} \to \mt{empties} :: \{\mt{Unit}\} \\
adamc@1193 1664 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adamc@1193 1665 \hspace{.1in} \Rightarrow [\mt{free} \sim \mt{grouped}] \\
adam@1400 1666 \hspace{.1in} \Rightarrow [\mt{afree} \sim \mt{tables}] \\
adamc@1193 1667 \hspace{.1in} \Rightarrow [\mt{empties} \sim \mt{selectedFields}] \\
adamc@1085 1668 \hspace{.1in} \Rightarrow \{\mt{Distinct} : \mt{bool}, \\
adamc@1193 1669 \hspace{.2in} \mt{From} : \mt{sql\_from\_items} \; \mt{free} \; \mt{tables}, \\
adam@1778 1670 \hspace{.2in} \mt{Where} : \mt{sql\_exp} \; (\mt{free} \rc \mt{tables}) \; \mt{afree} \; [] \; \mt{bool}, \\
adamc@543 1671 \hspace{.2in} \mt{GroupBy} : \mt{sql\_subset} \; \mt{tables} \; \mt{grouped}, \\
adam@1778 1672 \hspace{.2in} \mt{Having} : \mt{sql\_exp} \; (\mt{free} \rc \mt{grouped}) \; (\mt{afree} \rc \mt{tables}) \; [] \; \mt{bool}, \\
adamc@1085 1673 \hspace{.2in} \mt{SelectFields} : \mt{sql\_subset} \; \mt{grouped} \; (\mt{map} \; (\lambda \_ \Rightarrow []) \; \mt{empties} \rc \mt{selectedFields}), \\
adam@1778 1674 \hspace{.2in} \mt {SelectExps} : \$(\mt{map} \; (\mt{sql\_expw} \; (\mt{free} \rc \mt{grouped}) \; (\mt{afree} \rc \mt{tables}) \; []) \; \mt{selectedExps}) \} \\
adam@1400 1675 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1676 \end{array}$$
adamc@543 1677
adamc@543 1678 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 1679 $$\begin{array}{l}
adamc@543 1680 \mt{con} \; \mt{sql\_subset} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@543 1681 \mt{val} \; \mt{sql\_subset} : \mt{keep\_drop} :: \{(\{\mt{Type}\} \times \{\mt{Type}\})\} \\
adamc@543 1682 \hspace{.1in} \to \mt{sql\_subset} \\
adamc@658 1683 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1 \rc \mt{fields}.2)\; \mt{keep\_drop}) \\
adamc@658 1684 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1) \; \mt{keep\_drop}) \\
adamc@543 1685 \mt{val} \; \mt{sql\_subset\_all} : \mt{tables} :: \{\{\mt{Type}\}\} \to \mt{sql\_subset} \; \mt{tables} \; \mt{tables}
adamc@543 1686 \end{array}$$
adamc@543 1687
adam@1778 1688 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 1689 $$\begin{array}{l}
adam@1778 1690 \mt{con} \; \mt{sql\_exp} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}
adamc@543 1691 \end{array}$$
adamc@543 1692
adamc@543 1693 Any field in scope may be converted to an expression.
adamc@543 1694 $$\begin{array}{l}
adamc@543 1695 \mt{val} \; \mt{sql\_field} : \mt{otherTabs} ::: \{\{\mt{Type}\}\} \to \mt{otherFields} ::: \{\mt{Type}\} \\
adam@1778 1696 \hspace{.1in} \to \mt{fieldType} ::: \mt{Type} \to \mt{agg} ::: \{\{\mt{Type}\}\} \\
adamc@543 1697 \hspace{.1in} \to \mt{exps} ::: \{\mt{Type}\} \\
adamc@543 1698 \hspace{.1in} \to \mt{tab} :: \mt{Name} \to \mt{field} :: \mt{Name} \\
adam@1778 1699 \hspace{.1in} \to \mt{sql\_exp} \; ([\mt{tab} = [\mt{field} = \mt{fieldType}] \rc \mt{otherFields}] \rc \mt{otherTabs}) \; \mt{agg} \; \mt{exps} \; \mt{fieldType}
adamc@543 1700 \end{array}$$
adamc@543 1701
adamc@544 1702 There is an analogous function for referencing named expressions.
adamc@544 1703 $$\begin{array}{l}
adam@1778 1704 \mt{val} \; \mt{sql\_exp} : \mt{tabs} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{t} ::: \mt{Type} \to \mt{rest} ::: \{\mt{Type}\} \to \mt{nm} :: \mt{Name} \\
adam@1778 1705 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tabs} \; \mt{agg} \; ([\mt{nm} = \mt{t}] \rc \mt{rest}) \; \mt{t}
adamc@544 1706 \end{array}$$
adamc@544 1707
adamc@544 1708 Ur values of appropriate types may be injected into SQL expressions.
adamc@544 1709 $$\begin{array}{l}
adamc@786 1710 \mt{class} \; \mt{sql\_injectable\_prim} \\
adamc@786 1711 \mt{val} \; \mt{sql\_bool} : \mt{sql\_injectable\_prim} \; \mt{bool} \\
adamc@786 1712 \mt{val} \; \mt{sql\_int} : \mt{sql\_injectable\_prim} \; \mt{int} \\
adamc@786 1713 \mt{val} \; \mt{sql\_float} : \mt{sql\_injectable\_prim} \; \mt{float} \\
adamc@786 1714 \mt{val} \; \mt{sql\_string} : \mt{sql\_injectable\_prim} \; \mt{string} \\
adamc@786 1715 \mt{val} \; \mt{sql\_time} : \mt{sql\_injectable\_prim} \; \mt{time} \\
adamc@786 1716 \mt{val} \; \mt{sql\_blob} : \mt{sql\_injectable\_prim} \; \mt{blob} \\
adamc@786 1717 \mt{val} \; \mt{sql\_channel} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{channel} \; \mt{t}) \\
adamc@786 1718 \mt{val} \; \mt{sql\_client} : \mt{sql\_injectable\_prim} \; \mt{client} \\
adamc@786 1719 \\
adamc@544 1720 \mt{class} \; \mt{sql\_injectable} \\
adamc@786 1721 \mt{val} \; \mt{sql\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@786 1722 \mt{val} \; \mt{sql\_option\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; (\mt{option} \; \mt{t}) \\
adamc@786 1723 \\
adam@1778 1724 \mt{val} \; \mt{sql\_inject} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{sql\_injectable} \; \mt{t} \\
adam@1778 1725 \hspace{.1in} \to \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adamc@544 1726 \end{array}$$
adamc@544 1727
adamc@1123 1728 Additionally, most function-free types may be injected safely, via the $\mt{serialized}$ type family.
adamc@1123 1729 $$\begin{array}{l}
adamc@1123 1730 \mt{con} \; \mt{serialized} :: \mt{Type} \to \mt{Type} \\
adamc@1123 1731 \mt{val} \; \mt{serialize} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{serialized} \; \mt{t} \\
adamc@1123 1732 \mt{val} \; \mt{deserialize} : \mt{t} ::: \mt{Type} \to \mt{serialized} \; \mt{t} \to \mt{t} \\
adamc@1123 1733 \mt{val} \; \mt{sql\_serialized} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{serialized} \; \mt{t})
adamc@1123 1734 \end{array}$$
adamc@1123 1735
adamc@544 1736 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 1737 $$\begin{array}{l}
adam@1778 1738 \mt{val} \; \mt{sql\_is\_null} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778 1739 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; (\mt{option} \; \mt{t}) \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{bool}
adamc@544 1740 \end{array}$$
adamc@544 1741
adam@1602 1742 As another way of dealing with null values, there is also a restricted form of the standard \cd{COALESCE} function.
adam@1602 1743 $$\begin{array}{l}
adam@1602 1744 \mt{val} \; \mt{sql\_coalesce} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778 1745 \hspace{.1in} \to \mt{t} ::: \mt{Type} \\
adam@1778 1746 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; (\mt{option} \; \mt{t}) \\
adam@1778 1747 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1748 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adam@1602 1749 \end{array}$$
adam@1602 1750
adamc@559 1751 We have generic nullary, unary, and binary operators.
adamc@544 1752 $$\begin{array}{l}
adamc@544 1753 \mt{con} \; \mt{sql\_nfunc} :: \mt{Type} \to \mt{Type} \\
adamc@544 1754 \mt{val} \; \mt{sql\_current\_timestamp} : \mt{sql\_nfunc} \; \mt{time} \\
adam@1778 1755 \mt{val} \; \mt{sql\_nfunc} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778 1756 \hspace{.1in} \to \mt{sql\_nfunc} \; \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\\end{array}$$
adamc@544 1757
adamc@544 1758 $$\begin{array}{l}
adamc@544 1759 \mt{con} \; \mt{sql\_unary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544 1760 \mt{val} \; \mt{sql\_not} : \mt{sql\_unary} \; \mt{bool} \; \mt{bool} \\
adam@1778 1761 \mt{val} \; \mt{sql\_unary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adam@1778 1762 \hspace{.1in} \to \mt{sql\_unary} \; \mt{arg} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res} \\
adamc@544 1763 \end{array}$$
adamc@544 1764
adamc@544 1765 $$\begin{array}{l}
adamc@544 1766 \mt{con} \; \mt{sql\_binary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544 1767 \mt{val} \; \mt{sql\_and} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544 1768 \mt{val} \; \mt{sql\_or} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adam@1778 1769 \mt{val} \; \mt{sql\_binary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg_1} ::: \mt{Type} \to \mt{arg_2} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adam@1778 1770 \hspace{.1in} \to \mt{sql\_binary} \; \mt{arg_1} \; \mt{arg_2} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_1} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_2} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res}
adamc@544 1771 \end{array}$$
adamc@544 1772
adamc@544 1773 $$\begin{array}{l}
adamc@559 1774 \mt{class} \; \mt{sql\_arith} \\
adamc@559 1775 \mt{val} \; \mt{sql\_int\_arith} : \mt{sql\_arith} \; \mt{int} \\
adamc@559 1776 \mt{val} \; \mt{sql\_float\_arith} : \mt{sql\_arith} \; \mt{float} \\
adamc@559 1777 \mt{val} \; \mt{sql\_neg} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_unary} \; \mt{t} \; \mt{t} \\
adamc@559 1778 \mt{val} \; \mt{sql\_plus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1779 \mt{val} \; \mt{sql\_minus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1780 \mt{val} \; \mt{sql\_times} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1781 \mt{val} \; \mt{sql\_div} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1782 \mt{val} \; \mt{sql\_mod} : \mt{sql\_binary} \; \mt{int} \; \mt{int} \; \mt{int}
adamc@559 1783 \end{array}$$
adamc@544 1784
adam@1797 1785 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 1786 $$\begin{array}{l}
adam@1778 1787 \mt{val} \; \mt{sql\_count} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int}
adamc@544 1788 \end{array}$$
adamc@544 1789
adamc@544 1790 $$\begin{array}{l}
adamc@1188 1791 \mt{con} \; \mt{sql\_aggregate} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adam@1778 1792 \mt{val} \; \mt{sql\_aggregate} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{dom} ::: \mt{Type} \to \mt{ran} ::: \mt{Type} \\
adam@1778 1793 \hspace{.1in} \to \mt{sql\_aggregate} \; \mt{dom} \; \mt{ran} \to \mt{sql\_exp} \; \mt{agg} \; \mt{agg} \; \mt{exps} \; \mt{dom} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{ran}
adamc@1188 1794 \end{array}$$
adamc@1188 1795
adamc@1188 1796 $$\begin{array}{l}
adamc@1188 1797 \mt{val} \; \mt{sql\_count\_col} : \mt{t} ::: \mt{Type} \to \mt{sql\_aggregate} \; (\mt{option} \; \mt{t}) \; \mt{int}
adamc@544 1798 \end{array}$$
adam@1400 1799
adam@1400 1800 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 1801
adamc@544 1802 $$\begin{array}{l}
adamc@544 1803 \mt{class} \; \mt{sql\_summable} \\
adamc@544 1804 \mt{val} \; \mt{sql\_summable\_int} : \mt{sql\_summable} \; \mt{int} \\
adamc@544 1805 \mt{val} \; \mt{sql\_summable\_float} : \mt{sql\_summable} \; \mt{float} \\
adam@1777 1806 \mt{val} \; \mt{sql\_avg} : \mt{t} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{sql\_aggregate} \; \mt{t} \; (\mt{option} \; \mt{float}) \\
adam@1400 1807 \mt{val} \; \mt{sql\_sum} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt}
adamc@544 1808 \end{array}$$
adamc@544 1809
adamc@544 1810 $$\begin{array}{l}
adamc@544 1811 \mt{class} \; \mt{sql\_maxable} \\
adamc@544 1812 \mt{val} \; \mt{sql\_maxable\_int} : \mt{sql\_maxable} \; \mt{int} \\
adamc@544 1813 \mt{val} \; \mt{sql\_maxable\_float} : \mt{sql\_maxable} \; \mt{float} \\
adamc@544 1814 \mt{val} \; \mt{sql\_maxable\_string} : \mt{sql\_maxable} \; \mt{string} \\
adamc@544 1815 \mt{val} \; \mt{sql\_maxable\_time} : \mt{sql\_maxable} \; \mt{time} \\
adam@1400 1816 \mt{val} \; \mt{sql\_max} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt} \\
adam@1400 1817 \mt{val} \; \mt{sql\_min} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt}
adamc@544 1818 \end{array}$$
adamc@544 1819
adam@1778 1820 Any SQL query that returns single columns may be turned into a subquery expression.
adam@1777 1821
adam@1777 1822 $$\begin{array}{l}
adam@1778 1823 \mt{val} \; \mt{sql\_subquery} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \\
adam@1778 1824 \hspace{.1in} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_query} \; \mt{tables} \; \mt{agg} \; [\mt{nm} = \mt{t}] \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{nt}
adamc@1193 1825 \end{array}$$
adamc@1193 1826
adam@1573 1827 There is also an \cd{IF..THEN..ELSE..} construct that is compiled into standard SQL \cd{CASE} expressions.
adam@1573 1828 $$\begin{array}{l}
adam@1778 1829 \mt{val} \; \mt{sql\_if\_then\_else} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778 1830 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{bool} \\
adam@1778 1831 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1832 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1833 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adam@1573 1834 \end{array}$$
adam@1573 1835
adamc@1193 1836 \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 1837 $$\begin{array}{l}
adamc@1193 1838 \mt{con} \; \mt{sql\_from\_items} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@1193 1839 \mt{val} \; \mt{sql\_from\_table} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1840 \hspace{.1in} \to \mt{t} ::: \mt{Type} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; \mt{t} \; \mt{fs} \to \mt{name} :: \mt{Name} \to \mt{t} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193 1841 \mt{val} \; \mt{sql\_from\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{name} :: \mt{Name} \to \mt{sql\_query} \; \mt{free} \; [] \; \mt{fs} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193 1842 \mt{val} \; \mt{sql\_from\_comma} : \mt{free} ::: \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \to [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193 1843 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adamc@1193 1844 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2}) \\
adamc@1193 1845 \mt{val} \; \mt{sql\_inner\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1846 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193 1847 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adam@1778 1848 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193 1849 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2})
adamc@786 1850 \end{array}$$
adamc@786 1851
adamc@786 1852 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 1853 $$\begin{array}{l}
adamc@786 1854 \mt{class} \; \mt{nullify} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@786 1855 \mt{val} \; \mt{nullify\_option} : \mt{t} ::: \mt{Type} \to \mt{nullify} \; (\mt{option} \; \mt{t}) \; (\mt{option} \; \mt{t}) \\
adamc@786 1856 \mt{val} \; \mt{nullify\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{nullify} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@786 1857 \end{array}$$
adamc@786 1858
adamc@786 1859 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 1860
adamc@786 1861 $$\begin{array}{l}
adamc@1193 1862 \mt{val} \; \mt{sql\_left\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{(\mt{Type} \times \mt{Type})\}\} \\
adamc@1193 1863 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@786 1864 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\lambda \mt{r} \Rightarrow \$(\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{nullify} \; \mt{p}.1 \; \mt{p}.2) \; \mt{r})) \; \mt{tabs2}) \\
adamc@1193 1865 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \\
adam@1778 1866 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193 1867 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.2)) \; \mt{tabs2})
adamc@786 1868 \end{array}$$
adamc@786 1869
adamc@544 1870 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 1871 $$\begin{array}{l}
adamc@544 1872 \mt{type} \; \mt{sql\_direction} \\
adamc@544 1873 \mt{val} \; \mt{sql\_asc} : \mt{sql\_direction} \\
adamc@544 1874 \mt{val} \; \mt{sql\_desc} : \mt{sql\_direction} \\
adamc@544 1875 \\
adamc@544 1876 \mt{con} \; \mt{sql\_order\_by} :: \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@544 1877 \mt{val} \; \mt{sql\_order\_by\_Nil} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} :: \{\mt{Type}\} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adam@1778 1878 \mt{val} \; \mt{sql\_order\_by\_Cons} : \mt{tf} ::: (\{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}) \\
adam@1778 1879 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778 1880 \hspace{.1in} \to \mt{sql\_window} \; \mt{tf} \to \mt{tf} \; \mt{tables} \; [] \; \mt{exps} \; \mt{t} \to \mt{sql\_direction} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adam@1684 1881 \mt{val} \; \mt{sql\_order\_by\_random} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544 1882 \\
adamc@544 1883 \mt{type} \; \mt{sql\_limit} \\
adamc@544 1884 \mt{val} \; \mt{sql\_no\_limit} : \mt{sql\_limit} \\
adamc@544 1885 \mt{val} \; \mt{sql\_limit} : \mt{int} \to \mt{sql\_limit} \\
adamc@544 1886 \\
adamc@544 1887 \mt{type} \; \mt{sql\_offset} \\
adamc@544 1888 \mt{val} \; \mt{sql\_no\_offset} : \mt{sql\_offset} \\
adamc@544 1889 \mt{val} \; \mt{sql\_offset} : \mt{int} \to \mt{sql\_offset}
adamc@544 1890 \end{array}$$
adamc@544 1891
adam@1778 1892 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 1893 $$\begin{array}{l}
adam@1778 1894 \mt{con} \; \mt{sql\_expw} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type} \\
adam@1778 1895 \\
adam@1778 1896 \mt{class} \; \mt{sql\_window} :: (\{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}) \to \mt{Type} \\
adam@1778 1897 \mt{val} \; \mt{sql\_window\_normal} : \mt{sql\_window} \; \mt{sql\_exp} \\
adam@1778 1898 \mt{val} \; \mt{sql\_window\_fancy} : \mt{sql\_window} \; \mt{sql\_expw} \\
adam@1778 1899 \mt{val} \; \mt{sql\_window} : \mt{tf} ::: (\{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}) \\
adam@1778 1900 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778 1901 \hspace{.1in} \to \mt{sql\_window} \; \mt{tf} \\
adam@1778 1902 \hspace{.1in} \to \mt{tf} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1903 \hspace{.1in} \to \mt{sql\_expw} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1904 \\
adam@1778 1905 \mt{con} \; \mt{sql\_partition} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adam@1778 1906 \mt{val} \; \mt{sql\_no\_partition} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778 1907 \hspace{.1in} \to \mt{sql\_partition} \; \mt{tables} \; \mt{agg} \; \mt{exps} \\
adam@1778 1908 \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 1909 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1910 \hspace{.1in} \to \mt{sql\_partition} \; \mt{tables} \; \mt{agg} \; \mt{exps} \\
adam@1778 1911 \\
adam@1778 1912 \mt{con} \; \mt{sql\_window\_function} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type} \\
adam@1778 1913 \mt{val} \; \mt{sql\_window\_function} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778 1914 \hspace{.1in} \to \mt{t} ::: \mt{Type} \\
adam@1778 1915 \hspace{.1in} \to \mt{sql\_window\_function} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1916 \hspace{.1in} \to \mt{sql\_partition} \; \mt{tables} \; \mt{agg} \; \mt{exps} \\
adam@1778 1917 \hspace{.1in} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adam@1778 1918 \hspace{.1in} \to \mt{sql\_expw} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1919 \\
adam@1778 1920 \mt{val} \; \mt{sql\_window\_aggregate} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778 1921 \hspace{.1in} \to \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \\
adam@1778 1922 \hspace{.1in} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt} \\
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\_window\_function} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{nt} \\
adam@1778 1925 \mt{val} \; \mt{sql\_window\_count} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778 1926 \hspace{.1in} \to \mt{sql\_window\_function} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int} \\
adam@1778 1927 \mt{val} \; \mt{sql\_rank} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778 1928 \hspace{.1in} \to \mt{sql\_window\_function} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int}
adam@1778 1929 \end{array}$$
adam@1778 1930
adamc@545 1931
adamc@545 1932 \subsubsection{DML}
adamc@545 1933
adamc@545 1934 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 1935
adamc@545 1936 $$\begin{array}{l}
adamc@545 1937 \mt{type} \; \mt{dml} \\
adamc@545 1938 \mt{val} \; \mt{dml} : \mt{dml} \to \mt{transaction} \; \mt{unit}
adamc@545 1939 \end{array}$$
adamc@545 1940
adam@1297 1941 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 1942
adam@1297 1943 $$\begin{array}{l}
adam@1297 1944 \mt{val} \; \mt{tryDml} : \mt{dml} \to \mt{transaction} \; (\mt{option} \; \mt{string})
adam@1297 1945 \end{array}$$
adam@1297 1946
adam@1797 1947 Properly typed records may be used to form $\mt{INSERT}$ commands.
adamc@545 1948 $$\begin{array}{l}
adamc@545 1949 \mt{val} \; \mt{insert} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \\
adam@1778 1950 \hspace{.1in} \to \$(\mt{map} \; (\mt{sql\_exp} \; [] \; [] \; []) \; \mt{fields}) \to \mt{dml}
adamc@545 1951 \end{array}$$
adamc@545 1952
adam@1578 1953 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 1954 $$\begin{array}{l}
adam@1380 1955 \mt{val} \; \mt{update} : \mt{unchanged} ::: \{\mt{Type}\} \to \mt{changed} :: \{\mt{Type}\} \to [\mt{changed} \sim \mt{unchanged}] \\
adam@1778 1956 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; []) \; \mt{changed}) \\
adam@1778 1957 \hspace{.1in} \to \mt{sql\_table} \; (\mt{changed} \rc \mt{unchanged}) \to \mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545 1958 \end{array}$$
adamc@545 1959
adam@1578 1960 A $\mt{DELETE}$ command is formed from a table and a $\mt{WHERE}$ clause. The above use of $\mt{T}$ is repeated.
adamc@545 1961 $$\begin{array}{l}
adam@1778 1962 \mt{val} \; \mt{delete} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \to \mt{sql\_exp} \; [\mt{T} = \mt{fields}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545 1963 \end{array}$$
adamc@545 1964
adamc@546 1965 \subsubsection{Sequences}
adamc@546 1966
adamc@546 1967 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 1968
adamc@546 1969 $$\begin{array}{l}
adamc@546 1970 \mt{type} \; \mt{sql\_sequence} \\
adamc@1085 1971 \mt{val} \; \mt{nextval} : \mt{sql\_sequence} \to \mt{transaction} \; \mt{int} \\
adamc@1085 1972 \mt{val} \; \mt{setval} : \mt{sql\_sequence} \to \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@546 1973 \end{array}$$
adamc@546 1974
adamc@546 1975
adam@1648 1976 \subsection{\label{xml}XML}
adamc@547 1977
adam@1333 1978 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 1979
adam@1642 1980 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 1981 $$\begin{array}{l}
adamc@547 1982 \mt{con} \; \mt{xml} :: \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547 1983 \end{array}$$
adamc@547 1984
adamc@547 1985 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 1986 $$\begin{array}{l}
adamc@547 1987 \mt{con} \; \mt{tag} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547 1988 \end{array}$$
adamc@547 1989
adamc@547 1990 Literal text may be injected into XML as ``CDATA.''
adamc@547 1991 $$\begin{array}{l}
adamc@547 1992 \mt{val} \; \mt{cdata} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{string} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adamc@547 1993 \end{array}$$
adamc@547 1994
adam@1358 1995 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 1996 $$\begin{array}{l}
adam@1358 1997 \mt{val} \; \mt{cdataChar} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{char} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adam@1358 1998 \end{array}$$
adam@1358 1999
adamc@547 2000 There is a function for producing an XML tree with a particular tag at its root.
adamc@547 2001 $$\begin{array}{l}
adamc@547 2002 \mt{val} \; \mt{tag} : \mt{attrsGiven} ::: \{\mt{Type}\} \to \mt{attrsAbsent} ::: \{\mt{Type}\} \to \mt{ctxOuter} ::: \{\mt{Unit}\} \to \mt{ctxInner} ::: \{\mt{Unit}\} \\
adamc@547 2003 \hspace{.1in} \to \mt{useOuter} ::: \{\mt{Type}\} \to \mt{useInner} ::: \{\mt{Type}\} \to \mt{bindOuter} ::: \{\mt{Type}\} \to \mt{bindInner} ::: \{\mt{Type}\} \\
adam@1380 2004 \hspace{.1in} \to [\mt{attrsGiven} \sim \mt{attrsAbsent}] \Rightarrow [\mt{useOuter} \sim \mt{useInner}] \Rightarrow [\mt{bindOuter} \sim \mt{bindInner}] \\
adam@1749 2005 \hspace{.1in} \Rightarrow \mt{css\_class} \\
adam@1643 2006 \hspace{.1in} \to \mt{option} \; (\mt{signal} \; \mt{css\_class}) \\
adam@1750 2007 \hspace{.1in} \to \mt{css\_style} \\
adam@1751 2008 \hspace{.1in} \to \mt{option} \; (\mt{signal} \; \mt{css\_style}) \\
adamc@787 2009 \hspace{.1in} \to \$\mt{attrsGiven} \\
adamc@547 2010 \hspace{.1in} \to \mt{tag} \; (\mt{attrsGiven} \rc \mt{attrsAbsent}) \; \mt{ctxOuter} \; \mt{ctxInner} \; \mt{useOuter} \; \mt{bindOuter} \\
adamc@547 2011 \hspace{.1in} \to \mt{xml} \; \mt{ctxInner} \; \mt{useInner} \; \mt{bindInner} \to \mt{xml} \; \mt{ctxOuter} \; (\mt{useOuter} \rc \mt{useInner}) \; (\mt{bindOuter} \rc \mt{bindInner})
adamc@547 2012 \end{array}$$
adam@1750 2013 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 2014
adam@1643 2015 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 2016
adam@1751 2017 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 2018
adamc@547 2019 Two XML fragments may be concatenated.
adamc@547 2020 $$\begin{array}{l}
adamc@547 2021 \mt{val} \; \mt{join} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{bind_1} ::: \{\mt{Type}\} \to \mt{bind_2} ::: \{\mt{Type}\} \\
adam@1380 2022 \hspace{.1in} \to [\mt{use_1} \sim \mt{bind_1}] \Rightarrow [\mt{bind_1} \sim \mt{bind_2}] \\
adamc@547 2023 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind_1} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{bind_1}) \; \mt{bind_2} \to \mt{xml} \; \mt{ctx} \; \mt{use_1} \; (\mt{bind_1} \rc \mt{bind_2})
adamc@547 2024 \end{array}$$
adamc@547 2025
adamc@547 2026 Finally, any XML fragment may be updated to ``claim'' to use more form fields than it does.
adamc@547 2027 $$\begin{array}{l}
adam@1380 2028 \mt{val} \; \mt{useMore} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{use_2} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to [\mt{use_1} \sim \mt{use_2}] \\
adamc@547 2029 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{use_2}) \; \mt{bind}
adamc@547 2030 \end{array}$$
adamc@547 2031
adam@1344 2032 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 2033
adamc@547 2034 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 2035 $$\begin{array}{l}
adam@1641 2036 \mt{val} \; \mt{error} : \mt{t} ::: \mt{Type} \to \mt{xbody} \to \mt{t}
adamc@547 2037 \end{array}$$
adamc@547 2038
adamc@549 2039
adamc@701 2040 \subsection{Client-Side Programming}
adamc@659 2041
adamc@701 2042 Ur/Web supports running code on web browsers, via automatic compilation to JavaScript.
adamc@701 2043
adamc@701 2044 \subsubsection{The Basics}
adamc@701 2045
adam@1400 2046 All of the functions in this subsection are client-side only.
adam@1400 2047
adam@1297 2048 Clients can open alert and confirm dialog boxes, in the usual annoying JavaScript way.
adamc@701 2049 $$\begin{array}{l}
adam@1297 2050 \mt{val} \; \mt{alert} : \mt{string} \to \mt{transaction} \; \mt{unit} \\
adam@1297 2051 \mt{val} \; \mt{confirm} : \mt{string} \to \mt{transaction} \; \mt{bool}
adamc@701 2052 \end{array}$$
adamc@701 2053
adamc@701 2054 Any transaction may be run in a new thread with the $\mt{spawn}$ function.
adamc@701 2055 $$\begin{array}{l}
adamc@701 2056 \mt{val} \; \mt{spawn} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit}
adamc@701 2057 \end{array}$$
adamc@701 2058
adamc@701 2059 The current thread can be paused for at least a specified number of milliseconds.
adamc@701 2060 $$\begin{array}{l}
adamc@701 2061 \mt{val} \; \mt{sleep} : \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@701 2062 \end{array}$$
adamc@701 2063
adam@1770 2064 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 2065 $$\begin{array}{l}
adamc@787 2066 \mt{val} \; \mt{onError} : (\mt{xbody} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787 2067 \mt{val} \; \mt{onFail} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787 2068 \mt{val} \; \mt{onConnectFail} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787 2069 \mt{val} \; \mt{onDisconnect} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787 2070 \mt{val} \; \mt{onServerError} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit}
adamc@787 2071 \end{array}$$
adamc@787 2072
adam@1555 2073 There are also functions to register standard document-level event handlers.
adam@1555 2074
adam@1555 2075 $$\begin{array}{l}
adam@1783 2076 \mt{val} \; \mt{onClick} : (\mt{mouseEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783 2077 \mt{val} \; \mt{onDblclick} : (\mt{mouseEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783 2078 \mt{val} \; \mt{onKeydown} : (\mt{keyEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783 2079 \mt{val} \; \mt{onKeypress} : (\mt{keyEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783 2080 \mt{val} \; \mt{onKeyup} : (\mt{keyEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783 2081 \mt{val} \; \mt{onMousedown} : (\mt{mouseEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783 2082 \mt{val} \; \mt{onMouseup} : (\mt{mouseEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit}
adam@1555 2083 \end{array}$$
adam@1555 2084
adam@1559 2085 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 2086
adam@1559 2087 $$\begin{array}{l}
adam@1559 2088 \mt{val} \; \mt{preventDefault} : \mt{transaction} \; \mt{unit} \\
adam@1559 2089 \mt{val} \; \mt{stopPropagation} : \mt{transaction} \; \mt{unit}
adam@1559 2090 \end{array}$$
adam@1559 2091
adam@1556 2092 \subsubsection{Node IDs}
adam@1556 2093
adam@1556 2094 There is an abstract type of node IDs that may be assigned to \cd{id} attributes of most HTML tags.
adam@1556 2095
adam@1556 2096 $$\begin{array}{l}
adam@1556 2097 \mt{type} \; \mt{id} \\
adam@1556 2098 \mt{val} \; \mt{fresh} : \mt{transaction} \; \mt{id}
adam@1556 2099 \end{array}$$
adam@1556 2100
adam@1785 2101 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 2102
adam@1785 2103 One further use of IDs is as handles for requesting that \emph{focus} be given to specific tags.
adam@1785 2104
adam@1785 2105 $$\begin{array}{l}
adam@1785 2106 \mt{val} \; \mt{giveFocus} : \mt{id} \to \mt{transaction} \; \mt{unit}
adam@1785 2107 \end{array}$$
adam@1556 2108
adam@1643 2109 \subsubsection{\label{signals}Functional-Reactive Page Generation}
adamc@701 2110
adamc@701 2111 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 2112
adam@1403 2113 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 2114
adamc@659 2115 $$\begin{array}{l}
adamc@659 2116 \mt{con} \; \mt{source} :: \mt{Type} \to \mt{Type} \\
adamc@659 2117 \mt{val} \; \mt{source} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{transaction} \; (\mt{source} \; \mt{t}) \\
adamc@659 2118 \mt{val} \; \mt{set} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@659 2119 \mt{val} \; \mt{get} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@659 2120 \end{array}$$
adamc@659 2121
adam@1400 2122 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 2123
adam@1608 2124 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 2125
adamc@659 2126 $$\begin{array}{l}
adamc@659 2127 \mt{con} \; \mt{signal} :: \mt{Type} \to \mt{Type} \\
adamc@659 2128 \mt{val} \; \mt{signal\_monad} : \mt{monad} \; \mt{signal} \\
adam@1608 2129 \mt{val} \; \mt{signal} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{signal} \; \mt{t} \\
adam@1608 2130 \mt{val} \; \mt{current} : \mt{t} ::: \mt{Type} \to \mt{signal} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@659 2131 \end{array}$$
adamc@659 2132
adamc@659 2133 A reactive portion of an HTML page is injected with a $\mt{dyn}$ tag, which has a signal-valued attribute $\mt{Signal}$.
adamc@659 2134
adamc@659 2135 $$\begin{array}{l}
adam@1641 2136 \mt{val} \; \mt{dyn} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to [\mt{ctx} \sim [\mt{Dyn}]] \Rightarrow \mt{unit} \\
adam@1641 2137 \hspace{.1in} \to \mt{tag} \; [\mt{Signal} = \mt{signal} \; (\mt{xml} \; ([\mt{Dyn}] \rc \mt{ctx}) \; \mt{use} \; \mt{bind})] \; ([\mt{Dyn}] \rc \mt{ctx}) \; [] \; \mt{use} \; \mt{bind}
adamc@659 2138 \end{array}$$
adamc@659 2139
adam@1648 2140 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 2141
adam@1648 2142 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 2143
adam@1786 2144 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 2145
adam@1786 2146 $$\begin{array}{l}
adam@1786 2147 \mt{val} \; \mt{active} : \mt{unit} \to \mt{tag} \; [\mt{Code} = \mt{transaction} \; \mt{xbody}] \; \mt{body} \; [] \; [] \; []
adam@1786 2148 \end{array}$$
adamc@701 2149
adamc@914 2150 \subsubsection{Remote Procedure Calls}
adamc@914 2151
adamc@914 2152 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 2153
adamc@914 2154 $$\begin{array}{l}
adamc@914 2155 \mt{val} \; \mt{rpc} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@914 2156 \end{array}$$
adamc@914 2157
adamc@701 2158 \subsubsection{Asynchronous Message-Passing}
adamc@701 2159
adamc@701 2160 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 2161
adamc@701 2162 $$\begin{array}{l}
adamc@701 2163 \mt{type} \; \mt{client} \\
adamc@701 2164 \mt{val} \; \mt{self} : \mt{transaction} \; \mt{client}
adamc@701 2165 \end{array}$$
adamc@701 2166
adamc@701 2167 \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 2168
adamc@701 2169 $$\begin{array}{l}
adamc@701 2170 \mt{con} \; \mt{channel} :: \mt{Type} \to \mt{Type} \\
adamc@701 2171 \mt{val} \; \mt{channel} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; (\mt{channel} \; \mt{t}) \\
adamc@701 2172 \mt{val} \; \mt{send} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@701 2173 \mt{val} \; \mt{recv} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@701 2174 \end{array}$$
adamc@701 2175
adamc@701 2176 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 2177
adamc@701 2178 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 2179
adam@1551 2180 \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 2181
adamc@659 2182
adamc@549 2183 \section{Ur/Web Syntax Extensions}
adamc@549 2184
adamc@549 2185 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 2186
adamc@549 2187 \subsection{SQL}
adamc@549 2188
adamc@786 2189 \subsubsection{\label{tables}Table Declarations}
adamc@786 2190
adamc@788 2191 $\mt{table}$ declarations may include constraints, via these grammar rules.
adamc@788 2192 $$\begin{array}{rrcll}
adam@1594 2193 \textrm{Declarations} & d &::=& \mt{table} \; x : c \; [pk[,]] \; cts \mid \mt{view} \; x = V \\
adamc@788 2194 \textrm{Primary key constraints} & pk &::=& \mt{PRIMARY} \; \mt{KEY} \; K \\
adam@1722 2195 \textrm{Keys} & K &::=& f \mid (f, (f,)^+) \mid \{\{e\}\} \\
adamc@788 2196 \textrm{Constraint sets} & cts &::=& \mt{CONSTRAINT} f \; ct \mid cts, cts \mid \{\{e\}\} \\
adamc@788 2197 \textrm{Constraints} & ct &::=& \mt{UNIQUE} \; K \mid \mt{CHECK} \; E \\
adamc@788 2198 &&& \mid \mt{FOREIGN} \; \mt{KEY} \; K \; \mt{REFERENCES} \; F \; (K) \; [\mt{ON} \; \mt{DELETE} \; pr] \; [\mt{ON} \; \mt{UPDATE} \; pr] \\
adamc@788 2199 \textrm{Foreign tables} & F &::=& x \mid \{\{e\}\} \\
adam@1594 2200 \textrm{Propagation modes} & pr &::=& \mt{NO} \; \mt{ACTION} \mid \mt{RESTRICT} \mid \mt{CASCADE} \mid \mt{SET} \; \mt{NULL} \\
adam@1594 2201 \textrm{View expressions} & V &::=& Q \mid \{e\}
adamc@788 2202 \end{array}$$
adamc@788 2203
adamc@788 2204 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 2205
adamc@788 2206
adamc@549 2207 \subsubsection{Queries}
adamc@549 2208
adamc@550 2209 Queries $Q$ are added to the rules for expressions $e$.
adamc@550 2210
adamc@549 2211 $$\begin{array}{rrcll}
adam@1684 2212 \textrm{Queries} & Q &::=& (q \; [\mt{ORDER} \; \mt{BY} \; O] \; [\mt{LIMIT} \; N] \; [\mt{OFFSET} \; N]) \\
adamc@1085 2213 \textrm{Pre-queries} & q &::=& \mt{SELECT} \; [\mt{DISTINCT}] \; P \; \mt{FROM} \; F,^+ \; [\mt{WHERE} \; E] \; [\mt{GROUP} \; \mt{BY} \; p,^+] \; [\mt{HAVING} \; E] \\
adamc@1085 2214 &&& \mid q \; R \; q \mid \{\{\{e\}\}\} \\
adam@1684 2215 \textrm{Relational operators} & R &::=& \mt{UNION} \mid \mt{INTERSECT} \mid \mt{EXCEPT} \\
adam@1778 2216 \textrm{$\mt{ORDER \; BY}$ items} & O &::=& \mt{RANDOM} [()] \mid \hat{E} \; [o] \mid \hat{E} \; [o], O
adamc@549 2217 \end{array}$$
adamc@549 2218
adamc@549 2219 $$\begin{array}{rrcll}
adamc@549 2220 \textrm{Projections} & P &::=& \ast & \textrm{all columns} \\
adamc@549 2221 &&& p,^+ & \textrm{particular columns} \\
adamc@549 2222 \textrm{Pre-projections} & p &::=& t.f & \textrm{one column from a table} \\
adamc@558 2223 &&& t.\{\{c\}\} & \textrm{a record of columns from a table (of kind $\{\mt{Type}\}$)} \\
adam@1627 2224 &&& t.* & \textrm{all columns from a table} \\
adam@1778 2225 &&& \hat{E} \; [\mt{AS} \; f] & \textrm{expression column} \\
adamc@549 2226 \textrm{Table names} & t &::=& x & \textrm{constant table name (automatically capitalized)} \\
adamc@549 2227 &&& X & \textrm{constant table name} \\
adamc@549 2228 &&& \{\{c\}\} & \textrm{computed table name (of kind $\mt{Name}$)} \\
adamc@549 2229 \textrm{Column names} & f &::=& X & \textrm{constant column name} \\
adamc@549 2230 &&& \{c\} & \textrm{computed column name (of kind $\mt{Name}$)} \\
adamc@549 2231 \textrm{Tables} & T &::=& x & \textrm{table variable, named locally by its own capitalization} \\
adam@1756 2232 &&& x \; \mt{AS} \; X & \textrm{table variable, with local name} \\
adam@1756 2233 &&& x \; \mt{AS} \; \{c\} & \textrm{table variable, with computed local name} \\
adamc@549 2234 &&& \{\{e\}\} \; \mt{AS} \; t & \textrm{computed table expression, with local name} \\
adam@1756 2235 &&& \{\{e\}\} \; \mt{AS} \; \{c\} & \textrm{computed table expression, with computed local name} \\
adamc@1085 2236 \textrm{$\mt{FROM}$ items} & F &::=& T \mid \{\{e\}\} \mid F \; J \; \mt{JOIN} \; F \; \mt{ON} \; E \\
adamc@1085 2237 &&& \mid F \; \mt{CROSS} \; \mt{JOIN} \ F \\
adamc@1193 2238 &&& \mid (Q) \; \mt{AS} \; t \\
adamc@1085 2239 \textrm{Joins} & J &::=& [\mt{INNER}] \\
adamc@1085 2240 &&& \mid [\mt{LEFT} \mid \mt{RIGHT} \mid \mt{FULL}] \; [\mt{OUTER}] \\
adam@1587 2241 \textrm{SQL expressions} & E &::=& t.f & \textrm{column references} \\
adamc@549 2242 &&& X & \textrm{named expression references} \\
adam@1490 2243 &&& \{[e]\} & \textrm{injected native Ur expressions} \\
adam@1778 2244 &&& \{e\} & \textrm{computed expressions, probably using $\mt{sql\_exp}$ directly} \\
adamc@549 2245 &&& \mt{TRUE} \mid \mt{FALSE} & \textrm{boolean constants} \\
adamc@549 2246 &&& \ell & \textrm{primitive type literals} \\
adamc@549 2247 &&& \mt{NULL} & \textrm{null value (injection of $\mt{None}$)} \\
adamc@549 2248 &&& E \; \mt{IS} \; \mt{NULL} & \textrm{nullness test} \\
adam@1602 2249 &&& \mt{COALESCE}(E, E) & \textrm{take first non-null value} \\
adamc@549 2250 &&& n & \textrm{nullary operators} \\
adamc@549 2251 &&& u \; E & \textrm{unary operators} \\
adamc@549 2252 &&& E \; b \; E & \textrm{binary operators} \\
adam@1778 2253 &&& \mt{COUNT}(\ast) & \textrm{count number of rows} \\
adam@1778 2254 &&& a(E) & \textrm{other aggregate function} \\
adam@1573 2255 &&& \mt{IF} \; E \; \mt{THEN} \; E \; \mt{ELSE} \; E & \textrm{conditional} \\
adam@1778 2256 &&& (Q) & \textrm{subquery (must return a single expression column)} \\
adamc@549 2257 &&& (E) & \textrm{explicit precedence} \\
adamc@549 2258 \textrm{Nullary operators} & n &::=& \mt{CURRENT\_TIMESTAMP} \\
adamc@549 2259 \textrm{Unary operators} & u &::=& \mt{NOT} \\
adam@1688 2260 \textrm{Binary operators} & b &::=& \mt{AND} \mid \mt{OR} \mid = \mid \neq \mid < \mid \leq \mid > \mid \geq \\
adamc@1188 2261 \textrm{Aggregate functions} & a &::=& \mt{COUNT} \mid \mt{AVG} \mid \mt{SUM} \mid \mt{MIN} \mid \mt{MAX} \\
adam@1543 2262 \textrm{Directions} & o &::=& \mt{ASC} \mid \mt{DESC} \mid \{e\} \\
adamc@549 2263 \textrm{SQL integer} & N &::=& n \mid \{e\} \\
adam@1778 2264 \textrm{Windowable expressions} & \hat{E} &::=& E \\
adam@1778 2265 &&& w \; [\mt{OVER} \; ( & \textrm{(Postgres only)} \\
adam@1778 2266 &&& \hspace{.1in} [\mt{PARTITION} \; \mt{BY} \; E] \\
adam@1778 2267 &&& \hspace{.1in} [\mt{ORDER} \; \mt{BY} \; O])] \\
adam@1778 2268 \textrm{Window function} & w &::=& \mt{RANK}() \\
adam@1778 2269 &&& \mt{COUNT}(*) \\
adam@1778 2270 &&& a(E)
adamc@549 2271 \end{array}$$
adamc@549 2272
adamc@1085 2273 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 2274
adam@1683 2275 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 2276
adamc@550 2277 \subsubsection{DML}
adamc@550 2278
adamc@550 2279 DML commands $D$ are added to the rules for expressions $e$.
adamc@550 2280
adamc@550 2281 $$\begin{array}{rrcll}
adamc@550 2282 \textrm{Commands} & D &::=& (\mt{INSERT} \; \mt{INTO} \; T^E \; (f,^+) \; \mt{VALUES} \; (E,^+)) \\
adamc@550 2283 &&& (\mt{UPDATE} \; T^E \; \mt{SET} \; (f = E,)^+ \; \mt{WHERE} \; E) \\
adamc@550 2284 &&& (\mt{DELETE} \; \mt{FROM} \; T^E \; \mt{WHERE} \; E) \\
adamc@550 2285 \textrm{Table expressions} & T^E &::=& x \mid \{\{e\}\}
adamc@550 2286 \end{array}$$
adamc@550 2287
adamc@550 2288 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 2289
adamc@551 2290 \subsection{XML}
adamc@551 2291
adamc@551 2292 XML fragments $L$ are added to the rules for expressions $e$.
adamc@551 2293
adamc@551 2294 $$\begin{array}{rrcll}
adamc@551 2295 \textrm{XML fragments} & L &::=& \texttt{<xml/>} \mid \texttt{<xml>}l^*\texttt{</xml>} \\
adamc@551 2296 \textrm{XML pieces} & l &::=& \textrm{text} & \textrm{cdata} \\
adamc@551 2297 &&& \texttt{<}g\texttt{/>} & \textrm{tag with no children} \\
adamc@551 2298 &&& \texttt{<}g\texttt{>}l^*\texttt{</}x\texttt{>} & \textrm{tag with children} \\
adamc@559 2299 &&& \{e\} & \textrm{computed XML fragment} \\
adamc@559 2300 &&& \{[e]\} & \textrm{injection of an Ur expression, via the $\mt{Top}.\mt{txt}$ function} \\
adamc@551 2301 \textrm{Tag} & g &::=& h \; (x = v)^* \\
adamc@551 2302 \textrm{Tag head} & h &::=& x & \textrm{tag name} \\
adamc@551 2303 &&& h\{c\} & \textrm{constructor parameter} \\
adamc@551 2304 \textrm{Attribute value} & v &::=& \ell & \textrm{literal value} \\
adamc@551 2305 &&& \{e\} & \textrm{computed value} \\
adamc@551 2306 \end{array}$$
adamc@551 2307
adam@1751 2308 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 2309
adam@1751 2310 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 2311
adamc@1198 2312 \section{\label{structure}The Structure of Web Applications}
adamc@553 2313
adam@1797 2314 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 2315
adam@1532 2316 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 2317
adam@1787 2318 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 2319
adam@1370 2320 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 2321
adamc@553 2322 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 2323
adamc@553 2324 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 2325
adam@1653 2326 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 2327 \begin{itemize}
adam@1653 2328 \item Functions are disallowed, since there is no obvious way to serialize them safely.
adam@1653 2329 \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 2330 \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 2331 \end{itemize}
adamc@553 2332
adamc@660 2333 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 2334
adamc@789 2335 \medskip
adamc@789 2336
adam@1347 2337 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 2338
adamc@789 2339 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 2340
adam@1348 2341 \subsection{Tasks}
adam@1348 2342
adam@1348 2343 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 2344
adam@1348 2345 $$\begin{array}{l}
adam@1348 2346 \mt{con} \; \mt{task\_kind} :: \mt{Type} \to \mt{Type} \\
adam@1348 2347 \mt{val} \; \mt{initialize} : \mt{task\_kind} \; \mt{unit} \\
adam@1349 2348 \mt{val} \; \mt{clientLeaves} : \mt{task\_kind} \; \mt{client} \\
adam@1349 2349 \mt{val} \; \mt{periodic} : \mt{int} \to \mt{task\_kind} \; \mt{unit}
adam@1348 2350 \end{array}$$
adam@1348 2351
adam@1348 2352 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 2353
adam@1348 2354 The currently supported task kinds are:
adam@1348 2355 \begin{itemize}
adam@1349 2356 \item $\mt{initialize}$: Code that is run when the application starts up.
adam@1348 2357 \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 2358 \item $\mt{periodic} \; n$: Code that is run when the application starts up and then every $n$ seconds thereafter.
adam@1348 2359 \end{itemize}
adam@1348 2360
adamc@553 2361
adamc@897 2362 \section{The Foreign Function Interface}
adamc@897 2363
adamc@897 2364 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 2365
adamc@897 2366 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 2367
adamc@897 2368 \begin{itemize}
adamc@897 2369 \item \texttt{clientOnly Module.ident} registers a value as being allowed only in client-side code.
adamc@897 2370 \item \texttt{clientToServer Module.ident} declares a type as OK to marshal between clients and servers. By default, abstract FFI types are not allowed to be marshalled, since your library might be maintaining invariants that the simple serialization code doesn't check.
adam@1699 2371 \item \texttt{effectful Module.ident} registers a function that can have side effects. It is important to remember to use this directive for each such function, or else the optimizer might change program semantics. (Note that merely assigning a function a \texttt{transaction}-based type does not mark it as effectful in this way!)
adamc@897 2372 \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 2373 \item \texttt{include FILE} requests inclusion of a C header file.
adamc@897 2374 \item \texttt{jsFunc Module.ident=name} gives a mapping from an Ur name for a value to a JavaScript name.
adamc@897 2375 \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 2376 \item \texttt{script URL} requests inclusion of a JavaScript source file within application HTML.
adamc@897 2377 \item \texttt{serverOnly Module.ident} registers a value as being allowed only in server-side code.
adamc@897 2378 \end{itemize}
adamc@897 2379
adamc@897 2380 \subsection{Writing C FFI Code}
adamc@897 2381
adamc@897 2382 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 2383
adamc@897 2384 \begin{itemize}
adamc@897 2385 \item Primitive types defined in \texttt{Basis} are themselves using the standard FFI interface, so you may refer to them like \texttt{uw\_Basis\_t}. See \texttt{include/types.h} for their definitions.
adamc@897 2386 \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 2387 \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 2388 \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 2389 \end{itemize}
adamc@897 2390
adamc@897 2391 The C FFI version of a Ur function with type \texttt{T1 -> ... -> TN -> R} or \texttt{T1 -> ... -> TN -> transaction R} has a C prototype like \texttt{R uw\_Module\_ident(uw\_context, T1, ..., TN)}. Only functions with types of the second form may have side effects. \texttt{uw\_context} is the type of state that persists across handling a client request. Many functions that operate on contexts are prototyped in \texttt{include/urweb.h}. Most should only be used internally by the compiler. A few are useful in general FFI implementation:
adamc@897 2392 \begin{itemize}
adamc@897 2393 \item \begin{verbatim}
adamc@897 2394 void uw_error(uw_context, failure_kind, const char *fmt, ...);
adamc@897 2395 \end{verbatim}
adamc@897 2396 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 2397
adam@1329 2398 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 2399
adamc@897 2400 \item \begin{verbatim}
adam@1469 2401 void uw_set_error_message(uw_context, const char *fmt, ...);
adam@1469 2402 \end{verbatim}
adam@1469 2403 This simpler form of \texttt{uw\_error()} saves an error message without immediately aborting execution.
adam@1469 2404
adam@1469 2405 \item \begin{verbatim}
adamc@897 2406 void uw_push_cleanup(uw_context, void (*func)(void *), void *arg);
adamc@897 2407 void uw_pop_cleanup(uw_context);
adamc@897 2408 \end{verbatim}
adam@1329 2409 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 2410
adam@1329 2411 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 2412
adamc@897 2413 \item \begin{verbatim}
adamc@897 2414 void *uw_malloc(uw_context, size_t);
adamc@897 2415 \end{verbatim}
adam@1329 2416 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 2417
adam@1329 2418 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 2419
adamc@897 2420 \item \begin{verbatim}
adamc@897 2421 typedef void (*uw_callback)(void *);
adam@1328 2422 typedef void (*uw_callback_with_retry)(void *, int will_retry);
adamc@897 2423 void uw_register_transactional(uw_context, void *data, uw_callback commit,
adam@1328 2424 uw_callback rollback, uw_callback_with_retry free);
adamc@897 2425 \end{verbatim}
adam@1328 2426 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 2427
adamc@1085 2428 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 2429
adam@1329 2430 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 2431
adam@1329 2432 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 2433
adam@1469 2434 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 2435
adamc@1085 2436 \item \begin{verbatim}
adamc@1085 2437 void *uw_get_global(uw_context, char *name);
adamc@1085 2438 void uw_set_global(uw_context, char *name, void *data, uw_callback free);
adamc@1085 2439 \end{verbatim}
adam@1329 2440 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 2441
adamc@897 2442 \end{itemize}
adamc@897 2443
adamc@897 2444 \subsection{Writing JavaScript FFI Code}
adamc@897 2445
adamc@897 2446 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 2447
adamc@897 2448 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 2449
adamc@897 2450 \begin{itemize}
adamc@897 2451 \item Integers, floats, strings, characters, and booleans are represented in the usual JavaScript way.
adam@1644 2452 \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 2453 \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 2454 \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 2455 \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 2456 \item As in the C FFI, all abstract types of program syntax are implemented with strings in JavaScript.
adamc@897 2457 \end{itemize}
adamc@897 2458
adam@1644 2459 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 2460
adam@1644 2461 \begin{itemize}
adam@1644 2462 \item Sources should be treated as an abstract type, manipulated via:
adam@1644 2463 \begin{itemize}
adam@1644 2464 \item \cd{sc(v)}, to create a source initialized to \cd{v}
adam@1644 2465 \item \cd{sg(s)}, to retrieve the current value of source \cd{s}
adam@1644 2466 \item \cd{sv(s, v)}, to set source \cd{s} to value \cd{v}
adam@1644 2467 \end{itemize}
adam@1644 2468
adam@1644 2469 \item Signals should be treated as an abstract type, manipulated via:
adam@1644 2470 \begin{itemize}
adam@1644 2471 \item \cd{sr(v)} and \cd{sb(s, f)}, the ``return'' and ``bind'' monad operators, respectively
adam@1644 2472 \item \cd{ss(s)}, to produce the signal corresponding to source \cd{s}
adam@1644 2473 \item \cd{scur(s)}, to get the current value of signal \cd{s}
adam@1644 2474 \end{itemize}
adam@1644 2475
adam@1644 2476 \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 2477
adam@1702 2478 \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 2479
adam@1644 2480 \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 2481 \end{itemize}
adamc@897 2482
adamc@897 2483
adamc@552 2484 \section{Compiler Phases}
adamc@552 2485
adamc@552 2486 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 2487
adamc@552 2488 In this section, we step through the main phases of compilation, noting what consequences each phase has for effective programming.
adamc@552 2489
adamc@552 2490 \subsection{Parse}
adamc@552 2491
adamc@552 2492 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 2493
adamc@552 2494 \subsection{Elaborate}
adamc@552 2495
adamc@552 2496 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 2497
adam@1378 2498 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 2499
adamc@552 2500 \subsection{Unnest}
adamc@552 2501
adamc@552 2502 Named local function definitions are moved to the top level, to avoid the need to generate closures.
adamc@552 2503
adamc@552 2504 \subsection{Corify}
adamc@552 2505
adamc@552 2506 Module system features are compiled away, through inlining of functor definitions at application sites. Afterward, most abstraction boundaries are broken, facilitating optimization.
adamc@552 2507
adamc@552 2508 \subsection{Especialize}
adamc@552 2509
adam@1356 2510 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 2511
adamc@552 2512 \subsection{Untangle}
adamc@552 2513
adam@1797 2514 Remove unnecessary mutual recursion, splitting recursive groups into strongly connected components.
adamc@552 2515
adamc@552 2516 \subsection{Shake}
adamc@552 2517
adamc@552 2518 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 2519
adamc@661 2520 \subsection{Rpcify}
adamc@661 2521
adamc@661 2522 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 2523
adamc@661 2524 \subsection{Untangle, Shake}
adamc@661 2525
adamc@661 2526 Repeat these simplifications.
adamc@661 2527
adamc@553 2528 \subsection{\label{tag}Tag}
adamc@552 2529
adamc@552 2530 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 2531
adamc@552 2532 \subsection{Reduce}
adamc@552 2533
adamc@552 2534 Apply definitional equality rules to simplify the program as much as possible. This effectively includes inlining of every non-recursive definition.
adamc@552 2535
adamc@552 2536 \subsection{Unpoly}
adamc@552 2537
adamc@552 2538 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 2539
adamc@552 2540 \subsection{Specialize}
adamc@552 2541
adamc@558 2542 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 2543
adamc@552 2544 \subsection{Shake}
adamc@552 2545
adamc@558 2546 Here the compiler repeats the earlier Shake phase.
adamc@552 2547
adamc@552 2548 \subsection{Monoize}
adamc@552 2549
adamc@552 2550 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 2551
adamc@552 2552 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 2553
adamc@552 2554 \subsection{MonoOpt}
adamc@552 2555
adamc@552 2556 Simple algebraic laws are applied to simplify the program, focusing especially on efficient imperative generation of HTML pages.
adamc@552 2557
adamc@552 2558 \subsection{MonoUntangle}
adamc@552 2559
adamc@552 2560 Unnecessary mutual recursion is broken up again.
adamc@552 2561
adamc@552 2562 \subsection{MonoReduce}
adamc@552 2563
adamc@552 2564 Equivalents of the definitional equality rules are applied to simplify programs, with inlining again playing a major role.
adamc@552 2565
adamc@552 2566 \subsection{MonoShake, MonoOpt}
adamc@552 2567
adamc@552 2568 Unneeded declarations are removed, and basic optimizations are repeated.
adamc@552 2569
adamc@552 2570 \subsection{Fuse}
adamc@552 2571
adamc@552 2572 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 2573
adamc@552 2574 \subsection{MonoUntangle, MonoShake}
adamc@552 2575
adamc@552 2576 Fuse often creates more opportunities to remove spurious mutual recursion.
adamc@552 2577
adamc@552 2578 \subsection{Pathcheck}
adamc@552 2579
adamc@552 2580 The compiler checks that no link or action name has been used more than once.
adamc@552 2581
adamc@552 2582 \subsection{Cjrize}
adamc@552 2583
adamc@552 2584 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 2585
adamc@552 2586 \subsection{C Compilation and Linking}
adamc@552 2587
adam@1523 2588 The output of the last phase is pretty-printed as C source code and passed to the C compiler.
adamc@552 2589
adamc@552 2590
as@1564 2591 \end{document}