annotate doc/manual.tex @ 1532:7ef09e91198b

Mention transitive dependency calculation for tree shaking
author Adam Chlipala <adam@chlipala.net>
date Wed, 10 Aug 2011 18:39:27 -0400
parents 7efcf8f4a44a
children 6f046b4bad24
rev   line source
adamc@524 1 \documentclass{article}
adamc@554 2 \usepackage{fullpage,amsmath,amssymb,proof,url}
adamc@524 3
adamc@524 4 \newcommand{\cd}[1]{\texttt{#1}}
adamc@524 5 \newcommand{\mt}[1]{\mathsf{#1}}
adamc@524 6
adamc@524 7 \newcommand{\rc}{+ \hspace{-.075in} + \;}
adamc@527 8 \newcommand{\rcut}{\; \texttt{--} \;}
adamc@527 9 \newcommand{\rcutM}{\; \texttt{---} \;}
adamc@524 10
adamc@524 11 \begin{document}
adamc@524 12
adamc@524 13 \title{The Ur/Web Manual}
adamc@524 14 \author{Adam Chlipala}
adamc@524 15
adamc@524 16 \maketitle
adamc@524 17
adamc@540 18 \tableofcontents
adamc@540 19
adamc@554 20
adamc@554 21 \section{Introduction}
adamc@554 22
adamc@1160 23 \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 24
adamc@554 25 \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 26
adamc@554 27 \begin{itemize}
adamc@554 28 \item Suffer from any kinds of code-injection attacks
adamc@554 29 \item Return invalid HTML
adamc@554 30 \item Contain dead intra-application links
adamc@554 31 \item Have mismatches between HTML forms and the fields expected by their handlers
adamc@652 32 \item Include client-side code that makes incorrect assumptions about the ``AJAX''-style services that the remote web server provides
adamc@554 33 \item Attempt invalid SQL queries
adamc@652 34 \item Use improper marshaling or unmarshaling in communication with SQL databases or between browsers and web servers
adamc@554 35 \end{itemize}
adamc@554 36
adamc@554 37 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 38
adamc@652 39 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 40
adamc@554 41 \medskip
adamc@554 42
adamc@554 43 The official web site for Ur is:
adamc@554 44 \begin{center}
adamc@554 45 \url{http://www.impredicative.com/ur/}
adamc@554 46 \end{center}
adamc@554 47
adamc@555 48
adamc@555 49 \section{Installation}
adamc@555 50
adamc@555 51 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 52
adamc@555 53 \begin{verbatim}
adamc@555 54 ./configure
adamc@555 55 make
adamc@555 56 sudo make install
adamc@555 57 \end{verbatim}
adamc@555 58
adam@1523 59 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 60 \begin{verbatim}
adam@1368 61 apt-get install mlton libssl-dev
adamc@896 62 \end{verbatim}
adamc@555 63
adamc@896 64 To build programs that access SQL databases, you also need one of these client libraries for supported backends.
adamc@555 65 \begin{verbatim}
adamc@896 66 apt-get install libpq-dev libmysqlclient15-dev libsqlite3-dev
adamc@555 67 \end{verbatim}
adamc@555 68
adamc@555 69 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 70 \begin{verbatim}
adamc@555 71 apt-get install smlnj libsmlnj-smlnj ml-yacc ml-lpt
adamc@555 72 \end{verbatim}
adamc@555 73
adamc@555 74 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 75
adamc@896 76 To run an SQL-backed application with a backend besides SQLite, you will probably want to install one of these servers.
adamc@555 77
adamc@555 78 \begin{verbatim}
adam@1400 79 apt-get install postgresql-8.4 mysql-server-5.1
adamc@555 80 \end{verbatim}
adamc@555 81
adamc@555 82 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 83
adamc@555 84 \begin{verbatim}
adamc@555 85 apt-get install emacs-goodies-el
adamc@555 86 \end{verbatim}
adamc@555 87
adam@1441 88 If you don't want to install the Emacs mode, run \texttt{./configure} with the argument \texttt{--without-emacs}.
adam@1441 89
adam@1523 90 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 91
adamc@555 92 \begin{verbatim}
adam@1523 93 CCARGS=-fno-inline ./configure
adamc@555 94 \end{verbatim}
adamc@555 95
adam@1523 96 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 97
adamc@555 98 The Emacs mode can be set to autoload by adding the following to your \texttt{.emacs} file.
adamc@555 99
adamc@555 100 \begin{verbatim}
adamc@555 101 (add-to-list 'load-path "/usr/local/share/emacs/site-lisp/urweb-mode")
adamc@555 102 (load "urweb-mode-startup")
adamc@555 103 \end{verbatim}
adamc@555 104
adamc@555 105 Change the path in the first line if you chose a different Emacs installation path during configuration.
adamc@555 106
adamc@555 107
adamc@556 108 \section{Command-Line Compiler}
adamc@556 109
adamc@556 110 \subsection{Project Files}
adamc@556 111
adamc@556 112 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@556 113
adamc@556 114 \begin{verbatim}
adamc@556 115 database dbname=test
adamc@556 116 sql crud1.sql
adamc@556 117
adamc@556 118 crud
adamc@556 119 crud1
adamc@556 120 \end{verbatim}
adamc@556 121
adamc@556 122 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@556 123
adamc@556 124 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@556 125
adamc@556 126 \begin{verbatim}
adamc@556 127 createdb test
adamc@556 128 psql -f crud1.sql test
adamc@556 129 \end{verbatim}
adamc@556 130
adam@1331 131 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@556 132
adamc@556 133 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@556 134
adamc@783 135 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@783 136 \begin{itemize}
adam@1465 137 \item \texttt{[allow|deny] [url|mime|requestHeader|responseHeader] PATTERN} registers a rule governing which URLs, MIME types, HTTP request headers, or HTTP response headers 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 138 \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 139 \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@783 140 \item \texttt{clientOnly Module.ident} registers an FFI function or transaction that may only be run in client browsers.
adamc@783 141 \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@783 142 \item \texttt{database DBSTRING} sets the string to pass to libpq to open a database connection.
adamc@783 143 \item \texttt{debug} saves some intermediate C files, which is mostly useful to help in debugging the compiler itself.
adamc@783 144 \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.
adamc@783 145 \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@783 146 \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 147 \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@783 148 \item \texttt{jsFunc Module.ident=name} gives the JavaScript name of an FFI value.
adamc@1089 149 \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 150 \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 151 \begin{itemize}
adam@1309 152 \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 153 \item \texttt{database}: maximum size of database files (currently only used by SQLite)
adam@1309 154 \item \texttt{deltas}: maximum number of messages sendable in a single request handler with \texttt{Basis.send}
adam@1309 155 \item \texttt{globals}: maximum number of global variables that FFI libraries may set in a single request context
adam@1309 156 \item \texttt{headers}: maximum size (in bytes) of per-request buffer used to hold HTTP headers for generated pages
adam@1309 157 \item \texttt{heap}: maximum size (in bytes) of per-request heap for dynamically-allocated data
adam@1309 158 \item \texttt{inputs}: maximum number of top-level form fields per request
adam@1309 159 \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 160 \item \texttt{page}: maximum size (in bytes) of per-request buffer used to hold HTML content of generated pages
adam@1309 161 \item \texttt{script}: maximum size (in bytes) of per-request buffer used to hold JavaScript content of generated pages
adam@1309 162 \item \texttt{subinputs}: maximum number of form fields per request, excluding top-level fields
adam@1309 163 \item \texttt{time}: maximum running time of a single page request, in units of approximately 0.1 seconds
adam@1309 164 \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 165 \end{itemize}
adam@1523 166 \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@1332 167 \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 168 \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 169 \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@852 170 \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@783 171 \item \texttt{prefix PREFIX} sets the prefix included before every URI within the generated application. The default is \texttt{/}.
adamc@783 172 \item \texttt{profile} generates an executable that may be used with gprof.
adam@1300 173 \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.
adamc@1183 174 \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@783 175 \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@783 176 \item \texttt{serverOnly Module.ident} registers an FFI function or transaction that may only be run on the server.
adamc@1164 177 \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@783 178 \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.
adamc@783 179 \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@783 180 \end{itemize}
adamc@701 181
adamc@701 182
adamc@557 183 \subsection{Building an Application}
adamc@557 184
adamc@557 185 To compile project \texttt{P.urp}, simply run
adamc@557 186 \begin{verbatim}
adamc@557 187 urweb P
adamc@557 188 \end{verbatim}
adamc@1198 189 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@557 190
adamc@557 191 To time how long the different compiler phases run, without generating an executable, run
adamc@557 192 \begin{verbatim}
adamc@557 193 urweb -timing P
adamc@557 194 \end{verbatim}
adamc@557 195
adamc@1086 196 To stop the compilation process after type-checking, run
adamc@1086 197 \begin{verbatim}
adamc@1086 198 urweb -tc P
adamc@1086 199 \end{verbatim}
adam@1530 200 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 201
adam@1531 202 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.
adam@1531 203
adamc@1170 204 To output information relevant to CSS stylesheets (and not finish regular compilation), run
adamc@1170 205 \begin{verbatim}
adamc@1170 206 urweb -css P
adamc@1170 207 \end{verbatim}
adamc@1170 208 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 209
adamc@896 210 Some other command-line parameters are accepted:
adamc@896 211 \begin{itemize}
adamc@896 212 \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@896 213
adamc@896 214 \item \texttt{-dbms [postgres|mysql|sqlite]}: Sets the database backend to use.
adamc@896 215 \begin{itemize}
adamc@896 216 \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@896 217
adamc@896 218 A command sequence like this can initialize a Postgres database, using a file \texttt{app.sql} generated by the compiler:
adamc@896 219 \begin{verbatim}
adamc@896 220 createdb app
adamc@896 221 psql -f app.sql app
adamc@896 222 \end{verbatim}
adamc@896 223
adamc@896 224 \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@896 225
adamc@896 226 A command sequence like this can initialize a MySQL database:
adamc@896 227 \begin{verbatim}
adamc@896 228 echo "CREATE DATABASE app" | mysql
adamc@896 229 mysql -D app <app.sql
adamc@896 230 \end{verbatim}
adamc@896 231
adamc@896 232 \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@896 233
adamc@896 234 A command like this can initialize an SQLite database:
adamc@896 235 \begin{verbatim}
adamc@896 236 sqlite3 path/to/database/file <app.sql
adamc@896 237 \end{verbatim}
adamc@896 238 \end{itemize}
adamc@896 239
adam@1309 240 \item \texttt{-limit class num}: Equivalent to the \texttt{limit} directive from \texttt{.urp} files
adam@1309 241
adamc@896 242 \item \texttt{-output FILENAME}: Set where the application executable is written.
adamc@896 243
adamc@1127 244 \item \texttt{-path NAME VALUE}: Set the value of path variable \texttt{\$NAME} to \texttt{VALUE}, for use in \texttt{.urp} files.
adamc@1127 245
adam@1335 246 \item \texttt{-prefix PREFIX}: Equivalent to the \texttt{prefix} directive from \texttt{.urp} files
adam@1335 247
adamc@896 248 \item \texttt{-protocol [http|cgi|fastcgi]}: Set the protocol that the generated application speaks.
adamc@896 249 \begin{itemize}
adamc@896 250 \item \texttt{http}: This is the default. It is for building standalone web servers that can be accessed by web browsers directly.
adamc@896 251
adamc@896 252 \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@896 253
adamc@896 254 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@896 255 \begin{verbatim}
adamc@896 256 ScriptAlias /Hello /path/to/hello.exe
adamc@896 257 \end{verbatim}
adamc@896 258
adamc@1163 259 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 260 \begin{verbatim}
adamc@1163 261 Options +ExecCGI
adamc@1163 262 AddHandler cgi-script .exe
adamc@1163 263 \end{verbatim}
adamc@1163 264
adamc@1163 265 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 266 \begin{verbatim}
adamc@1163 267 prefix /dir/script.exe/
adamc@1163 268 \end{verbatim}
adamc@1163 269
adamc@1163 270 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 271
adamc@1164 272 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 273
adamc@896 274 \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@896 275
adamc@896 276 To configure a FastCGI program with Apache, one could combine the above \texttt{ScriptAlias} line with a line like this:
adamc@896 277 \begin{verbatim}
adamc@896 278 FastCgiServer /path/to/hello.exe -idle-timeout 99999
adamc@896 279 \end{verbatim}
adamc@896 280 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@896 281
adamc@896 282 Here is some lighttpd configuration for the same application.
adamc@896 283 \begin{verbatim}
adamc@896 284 fastcgi.server = (
adamc@896 285 "/Hello/" =>
adamc@896 286 (( "bin-path" => "/path/to/hello.exe",
adamc@896 287 "socket" => "/tmp/hello",
adamc@896 288 "check-local" => "disable",
adamc@896 289 "docroot" => "/",
adamc@896 290 "max-procs" => "1"
adamc@896 291 ))
adamc@896 292 )
adamc@896 293 \end{verbatim}
adamc@896 294 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@896 295
adamc@896 296 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 297
adam@1509 298 \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@896 299 \end{itemize}
adamc@896 300
adamc@1127 301 \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 302
adamc@1164 303 \item \texttt{-sigfile PATH}: Same as the \texttt{sigfile} directive in \texttt{.urp} files
adamc@1164 304
adamc@896 305 \item \texttt{-sql FILENAME}: Set where a database set-up SQL script is written.
adamc@1095 306
adamc@1095 307 \item \texttt{-static}: Link the runtime system statically. The default is to link against dynamic libraries.
adamc@896 308 \end{itemize}
adamc@896 309
adam@1297 310 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@556 311
adam@1509 312 \subsection{Tutorial Formatting}
adam@1509 313
adam@1509 314 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 315
adam@1509 316 These input files follow normal Ur syntax, with a few exceptions:
adam@1509 317 \begin{itemize}
adam@1509 318 \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 319 \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 320 \item A comment like \cd{(* * HEADING *)} introduces a section heading, with text \cd{HEADING} of your choice.
adam@1509 321 \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 322 \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 323 \end{itemize}
adam@1509 324
adam@1509 325 A word of warning: as for demo generation, tutorial generation calls Emacs to syntax-highlight Ur code.
adam@1509 326
adam@1522 327 \subsection{Run-Time Options}
adam@1522 328
adam@1522 329 Compiled applications consult a few environment variables to modify their behavior:
adam@1522 330
adam@1522 331 \begin{itemize}
adam@1522 332 \item \cd{URWEB\_NUM\_THREADS}: alternative to the \cd{-t} command-line argument (currently used only by FastCGI)
adam@1522 333 \item \cd{URWEB\_STACK\_SIZE}: size of per-thread stacks, in bytes
adam@1522 334 \end{itemize}
adam@1522 335
adam@1509 336
adamc@529 337 \section{Ur Syntax}
adamc@529 338
adamc@784 339 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@524 340
adamc@524 341 \subsection{Lexical Conventions}
adamc@524 342
adamc@524 343 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@524 344
adamc@524 345 \begin{center}
adamc@524 346 \begin{tabular}{rl}
adamc@524 347 \textbf{\LaTeX} & \textbf{ASCII} \\
adamc@524 348 $\to$ & \cd{->} \\
adamc@652 349 $\longrightarrow$ & \cd{-->} \\
adamc@524 350 $\times$ & \cd{*} \\
adamc@524 351 $\lambda$ & \cd{fn} \\
adamc@524 352 $\Rightarrow$ & \cd{=>} \\
adamc@652 353 $\Longrightarrow$ & \cd{==>} \\
adamc@529 354 $\neq$ & \cd{<>} \\
adamc@529 355 $\leq$ & \cd{<=} \\
adamc@529 356 $\geq$ & \cd{>=} \\
adamc@524 357 \\
adamc@524 358 $x$ & Normal textual identifier, not beginning with an uppercase letter \\
adamc@525 359 $X$ & Normal textual identifier, beginning with an uppercase letter \\
adamc@524 360 \end{tabular}
adamc@524 361 \end{center}
adamc@524 362
adamc@525 363 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@524 364
adamc@873 365 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@526 366
adamc@527 367 This version of the manual doesn't include operator precedences; see \texttt{src/urweb.grm} for that.
adamc@527 368
adam@1297 369 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 370
adamc@552 371 \subsection{\label{core}Core Syntax}
adamc@524 372
adamc@524 373 \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@524 374 $$\begin{array}{rrcll}
adamc@524 375 \textrm{Kinds} & \kappa &::=& \mt{Type} & \textrm{proper types} \\
adamc@525 376 &&& \mt{Unit} & \textrm{the trivial constructor} \\
adamc@525 377 &&& \mt{Name} & \textrm{field names} \\
adamc@525 378 &&& \kappa \to \kappa & \textrm{type-level functions} \\
adamc@525 379 &&& \{\kappa\} & \textrm{type-level records} \\
adamc@525 380 &&& (\kappa\times^+) & \textrm{type-level tuples} \\
adamc@652 381 &&& X & \textrm{variable} \\
adamc@652 382 &&& X \longrightarrow k & \textrm{kind-polymorphic type-level function} \\
adamc@529 383 &&& \_\_ & \textrm{wildcard} \\
adamc@525 384 &&& (\kappa) & \textrm{explicit precedence} \\
adamc@524 385 \end{array}$$
adamc@524 386
adamc@524 387 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@524 388 $$\begin{array}{rrcll}
adamc@524 389 \textrm{Explicitness} & ? &::=& :: & \textrm{explicit} \\
adamc@558 390 &&& ::: & \textrm{implicit}
adamc@524 391 \end{array}$$
adamc@524 392
adamc@524 393 \emph{Constructors} are the main class of compile-time-only data. They include proper types and are classified by kinds.
adamc@524 394 $$\begin{array}{rrcll}
adamc@524 395 \textrm{Constructors} & c, \tau &::=& (c) :: \kappa & \textrm{kind annotation} \\
adamc@530 396 &&& \hat{x} & \textrm{constructor variable} \\
adamc@524 397 \\
adamc@525 398 &&& \tau \to \tau & \textrm{function type} \\
adamc@525 399 &&& x \; ? \; \kappa \to \tau & \textrm{polymorphic function type} \\
adamc@652 400 &&& X \longrightarrow \tau & \textrm{kind-polymorphic function type} \\
adamc@525 401 &&& \$ c & \textrm{record type} \\
adamc@524 402 \\
adamc@525 403 &&& c \; c & \textrm{type-level function application} \\
adamc@530 404 &&& \lambda x \; :: \; \kappa \Rightarrow c & \textrm{type-level function abstraction} \\
adamc@524 405 \\
adamc@652 406 &&& X \Longrightarrow c & \textrm{type-level kind-polymorphic function abstraction} \\
adamc@655 407 &&& c [\kappa] & \textrm{type-level kind-polymorphic function application} \\
adamc@652 408 \\
adamc@525 409 &&& () & \textrm{type-level unit} \\
adamc@525 410 &&& \#X & \textrm{field name} \\
adamc@524 411 \\
adamc@525 412 &&& [(c = c)^*] & \textrm{known-length type-level record} \\
adamc@525 413 &&& c \rc c & \textrm{type-level record concatenation} \\
adamc@652 414 &&& \mt{map} & \textrm{type-level record map} \\
adamc@524 415 \\
adamc@558 416 &&& (c,^+) & \textrm{type-level tuple} \\
adamc@525 417 &&& c.n & \textrm{type-level tuple projection ($n \in \mathbb N^+$)} \\
adamc@524 418 \\
adamc@652 419 &&& [c \sim c] \Rightarrow \tau & \textrm{guarded type} \\
adamc@524 420 \\
adamc@529 421 &&& \_ :: \kappa & \textrm{wildcard} \\
adamc@525 422 &&& (c) & \textrm{explicit precedence} \\
adamc@530 423 \\
adamc@530 424 \textrm{Qualified uncapitalized variables} & \hat{x} &::=& x & \textrm{not from a module} \\
adamc@530 425 &&& M.x & \textrm{projection from a module} \\
adamc@525 426 \end{array}$$
adamc@525 427
adamc@655 428 We include both abstraction and application for kind polymorphism, but applications are only inferred internally; they may not be written explicitly in source programs.
adamc@655 429
adamc@525 430 Modules of the module system are described by \emph{signatures}.
adamc@525 431 $$\begin{array}{rrcll}
adamc@525 432 \textrm{Signatures} & S &::=& \mt{sig} \; s^* \; \mt{end} & \textrm{constant} \\
adamc@525 433 &&& X & \textrm{variable} \\
adamc@525 434 &&& \mt{functor}(X : S) : S & \textrm{functor} \\
adamc@529 435 &&& S \; \mt{where} \; \mt{con} \; x = c & \textrm{concretizing an abstract constructor} \\
adamc@525 436 &&& M.X & \textrm{projection from a module} \\
adamc@525 437 \\
adamc@525 438 \textrm{Signature items} & s &::=& \mt{con} \; x :: \kappa & \textrm{abstract constructor} \\
adamc@525 439 &&& \mt{con} \; x :: \kappa = c & \textrm{concrete constructor} \\
adamc@528 440 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529 441 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@525 442 &&& \mt{val} \; x : \tau & \textrm{value} \\
adamc@525 443 &&& \mt{structure} \; X : S & \textrm{sub-module} \\
adamc@525 444 &&& \mt{signature} \; X = S & \textrm{sub-signature} \\
adamc@525 445 &&& \mt{include} \; S & \textrm{signature inclusion} \\
adamc@525 446 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@654 447 &&& \mt{class} \; x :: \kappa & \textrm{abstract constructor class} \\
adamc@654 448 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@525 449 \\
adamc@525 450 \textrm{Datatype constructors} & dc &::=& X & \textrm{nullary constructor} \\
adamc@525 451 &&& X \; \mt{of} \; \tau & \textrm{unary constructor} \\
adamc@524 452 \end{array}$$
adamc@524 453
adamc@526 454 \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@526 455 $$\begin{array}{rrcll}
adamc@526 456 \textrm{Patterns} & p &::=& \_ & \textrm{wildcard} \\
adamc@526 457 &&& x & \textrm{variable} \\
adamc@526 458 &&& \ell & \textrm{constant} \\
adamc@526 459 &&& \hat{X} & \textrm{nullary constructor} \\
adamc@526 460 &&& \hat{X} \; p & \textrm{unary constructor} \\
adamc@526 461 &&& \{(x = p,)^*\} & \textrm{rigid record pattern} \\
adamc@526 462 &&& \{(x = p,)^+, \ldots\} & \textrm{flexible record pattern} \\
adamc@852 463 &&& p : \tau & \textrm{type annotation} \\
adamc@527 464 &&& (p) & \textrm{explicit precedence} \\
adamc@526 465 \\
adamc@529 466 \textrm{Qualified capitalized variables} & \hat{X} &::=& X & \textrm{not from a module} \\
adamc@526 467 &&& M.X & \textrm{projection from a module} \\
adamc@526 468 \end{array}$$
adamc@526 469
adamc@527 470 \emph{Expressions} are the main run-time entities, corresponding to both ``expressions'' and ``statements'' in mainstream imperative languages.
adamc@527 471 $$\begin{array}{rrcll}
adamc@527 472 \textrm{Expressions} & e &::=& e : \tau & \textrm{type annotation} \\
adamc@529 473 &&& \hat{x} & \textrm{variable} \\
adamc@529 474 &&& \hat{X} & \textrm{datatype constructor} \\
adamc@527 475 &&& \ell & \textrm{constant} \\
adamc@527 476 \\
adamc@527 477 &&& e \; e & \textrm{function application} \\
adamc@527 478 &&& \lambda x : \tau \Rightarrow e & \textrm{function abstraction} \\
adamc@527 479 &&& e [c] & \textrm{polymorphic function application} \\
adamc@852 480 &&& \lambda [x \; ? \; \kappa] \Rightarrow e & \textrm{polymorphic function abstraction} \\
adamc@655 481 &&& e [\kappa] & \textrm{kind-polymorphic function application} \\
adamc@652 482 &&& X \Longrightarrow e & \textrm{kind-polymorphic function abstraction} \\
adamc@527 483 \\
adamc@527 484 &&& \{(c = e,)^*\} & \textrm{known-length record} \\
adamc@527 485 &&& e.c & \textrm{record field projection} \\
adamc@527 486 &&& e \rc e & \textrm{record concatenation} \\
adamc@527 487 &&& e \rcut c & \textrm{removal of a single record field} \\
adamc@527 488 &&& e \rcutM c & \textrm{removal of multiple record fields} \\
adamc@527 489 \\
adamc@527 490 &&& \mt{let} \; ed^* \; \mt{in} \; e \; \mt{end} & \textrm{local definitions} \\
adamc@527 491 \\
adamc@527 492 &&& \mt{case} \; e \; \mt{of} \; (p \Rightarrow e|)^+ & \textrm{pattern matching} \\
adamc@527 493 \\
adamc@654 494 &&& \lambda [c \sim c] \Rightarrow e & \textrm{guarded expression abstraction} \\
adamc@654 495 &&& e \; ! & \textrm{guarded expression application} \\
adamc@527 496 \\
adamc@527 497 &&& \_ & \textrm{wildcard} \\
adamc@527 498 &&& (e) & \textrm{explicit precedence} \\
adamc@527 499 \\
adamc@527 500 \textrm{Local declarations} & ed &::=& \cd{val} \; x : \tau = e & \textrm{non-recursive value} \\
adamc@527 501 &&& \cd{val} \; \cd{rec} \; (x : \tau = e \; \cd{and})^+ & \textrm{mutually-recursive values} \\
adamc@527 502 \end{array}$$
adamc@527 503
adamc@655 504 As with constructors, we include both abstraction and application for kind polymorphism, but applications are only inferred internally.
adamc@655 505
adamc@528 506 \emph{Declarations} primarily bring new symbols into context.
adamc@528 507 $$\begin{array}{rrcll}
adamc@528 508 \textrm{Declarations} & d &::=& \mt{con} \; x :: \kappa = c & \textrm{constructor synonym} \\
adamc@528 509 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529 510 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@528 511 &&& \mt{val} \; x : \tau = e & \textrm{value} \\
adamc@528 512 &&& \mt{val} \; \cd{rec} \; (x : \tau = e \; \mt{and})^+ & \textrm{mutually-recursive values} \\
adamc@528 513 &&& \mt{structure} \; X : S = M & \textrm{module definition} \\
adamc@528 514 &&& \mt{signature} \; X = S & \textrm{signature definition} \\
adamc@528 515 &&& \mt{open} \; M & \textrm{module inclusion} \\
adamc@528 516 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@528 517 &&& \mt{open} \; \mt{constraints} \; M & \textrm{inclusion of just the constraints from a module} \\
adamc@528 518 &&& \mt{table} \; x : c & \textrm{SQL table} \\
adamc@784 519 &&& \mt{view} \; x : c & \textrm{SQL view} \\
adamc@528 520 &&& \mt{sequence} \; x & \textrm{SQL sequence} \\
adamc@535 521 &&& \mt{cookie} \; x : \tau & \textrm{HTTP cookie} \\
adamc@784 522 &&& \mt{style} \; x : \tau & \textrm{CSS class} \\
adamc@654 523 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@1085 524 &&& \mt{task} \; e = e & \textrm{recurring task} \\
adamc@528 525 \\
adamc@529 526 \textrm{Modules} & M &::=& \mt{struct} \; d^* \; \mt{end} & \textrm{constant} \\
adamc@529 527 &&& X & \textrm{variable} \\
adamc@529 528 &&& M.X & \textrm{projection} \\
adamc@529 529 &&& M(M) & \textrm{functor application} \\
adamc@529 530 &&& \mt{functor}(X : S) : S = M & \textrm{functor abstraction} \\
adamc@528 531 \end{array}$$
adamc@528 532
adamc@528 533 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@527 534
adamc@784 535 We omit some extra possibilities in $\mt{table}$ syntax, deferring them to Section \ref{tables}.
adamc@784 536
adamc@529 537 \subsection{Shorthands}
adamc@529 538
adamc@529 539 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@529 540
adamc@529 541 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@529 542
adamc@529 543 A record type may be written $\{(c = c,)^*\}$, which elaborates to $\$[(c = c,)^*]$.
adamc@529 544
adamc@533 545 The notation $[c_1, \ldots, c_n]$ is shorthand for $[c_1 = (), \ldots, c_n = ()]$.
adamc@533 546
adam@1350 547 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@529 548
adamc@852 549 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@529 550
adam@1306 551 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 552
adamc@529 553 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@529 554
adamc@529 555 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@529 556
adamc@654 557 A signature item or declaration $\mt{class} \; x = \lambda y \Rightarrow c$ may be abbreviated $\mt{class} \; x \; y = c$.
adamc@529 558
adam@1482 559 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.) 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@529 560
adamc@852 561 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@529 562
adamc@852 563 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@852 564
adamc@852 565 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@529 566
adamc@529 567 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@529 568
adamc@852 569 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@852 570
adamc@853 571 A declaration $\mt{table} \; x : \{(c = c,)^*\}$ is elaborated into $\mt{table} \; x : [(c = c,)^*]$.
adamc@529 572
adamc@529 573 The syntax $\mt{where} \; \mt{type}$ is an alternate form of $\mt{where} \; \mt{con}$.
adamc@529 574
adamc@529 575 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@529 576
adamc@529 577 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@529 578
adamc@784 579 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@529 580
adamc@530 581
adamc@530 582 \section{Static Semantics}
adamc@530 583
adamc@530 584 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@530 585
adamc@530 586 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@530 587 \begin{itemize}
adamc@655 588 \item $\Gamma \vdash \kappa$ expresses kind well-formedness.
adamc@530 589 \item $\Gamma \vdash c :: \kappa$ assigns a kind to a constructor in a context.
adamc@530 590 \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@531 591 \item $\Gamma \vdash c \hookrightarrow C$ proves that record constructor $c$ decomposes into set $C$ of field names and record constructors.
adamc@530 592 \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@530 593 \item $\Gamma \vdash e : \tau$ is a standard typing judgment.
adamc@534 594 \item $\Gamma \vdash p \leadsto \Gamma; \tau$ combines typing of patterns with calculation of which new variables they bind.
adamc@537 595 \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@537 596 \item $\Gamma \vdash S \equiv S$ is the signature equivalence judgment.
adamc@536 597 \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@530 598 \item $\Gamma \vdash M : S$ is the module signature checking judgment.
adamc@537 599 \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@539 600 \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@530 601 \end{itemize}
adamc@530 602
adamc@655 603
adamc@655 604 \subsection{Kind Well-Formedness}
adamc@655 605
adamc@655 606 $$\infer{\Gamma \vdash \mt{Type}}{}
adamc@655 607 \quad \infer{\Gamma \vdash \mt{Unit}}{}
adamc@655 608 \quad \infer{\Gamma \vdash \mt{Name}}{}
adamc@655 609 \quad \infer{\Gamma \vdash \kappa_1 \to \kappa_2}{
adamc@655 610 \Gamma \vdash \kappa_1
adamc@655 611 & \Gamma \vdash \kappa_2
adamc@655 612 }
adamc@655 613 \quad \infer{\Gamma \vdash \{\kappa\}}{
adamc@655 614 \Gamma \vdash \kappa
adamc@655 615 }
adamc@655 616 \quad \infer{\Gamma \vdash (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@655 617 \forall i: \Gamma \vdash \kappa_i
adamc@655 618 }$$
adamc@655 619
adamc@655 620 $$\infer{\Gamma \vdash X}{
adamc@655 621 X \in \Gamma
adamc@655 622 }
adamc@655 623 \quad \infer{\Gamma \vdash X \longrightarrow \kappa}{
adamc@655 624 \Gamma, X \vdash \kappa
adamc@655 625 }$$
adamc@655 626
adamc@530 627 \subsection{Kinding}
adamc@530 628
adamc@655 629 We write $[X \mapsto \kappa_1]\kappa_2$ for capture-avoiding substitution of $\kappa_1$ for $X$ in $\kappa_2$.
adamc@655 630
adamc@530 631 $$\infer{\Gamma \vdash (c) :: \kappa :: \kappa}{
adamc@530 632 \Gamma \vdash c :: \kappa
adamc@530 633 }
adamc@530 634 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530 635 x :: \kappa \in \Gamma
adamc@530 636 }
adamc@530 637 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530 638 x :: \kappa = c \in \Gamma
adamc@530 639 }$$
adamc@530 640
adamc@530 641 $$\infer{\Gamma \vdash M.x :: \kappa}{
adamc@537 642 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 643 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = \kappa
adamc@530 644 }
adamc@530 645 \quad \infer{\Gamma \vdash M.x :: \kappa}{
adamc@537 646 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 647 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@530 648 }$$
adamc@530 649
adamc@530 650 $$\infer{\Gamma \vdash \tau_1 \to \tau_2 :: \mt{Type}}{
adamc@530 651 \Gamma \vdash \tau_1 :: \mt{Type}
adamc@530 652 & \Gamma \vdash \tau_2 :: \mt{Type}
adamc@530 653 }
adamc@530 654 \quad \infer{\Gamma \vdash x \; ? \: \kappa \to \tau :: \mt{Type}}{
adamc@530 655 \Gamma, x :: \kappa \vdash \tau :: \mt{Type}
adamc@530 656 }
adamc@655 657 \quad \infer{\Gamma \vdash X \longrightarrow \tau :: \mt{Type}}{
adamc@655 658 \Gamma, X \vdash \tau :: \mt{Type}
adamc@655 659 }
adamc@530 660 \quad \infer{\Gamma \vdash \$c :: \mt{Type}}{
adamc@530 661 \Gamma \vdash c :: \{\mt{Type}\}
adamc@530 662 }$$
adamc@530 663
adamc@530 664 $$\infer{\Gamma \vdash c_1 \; c_2 :: \kappa_2}{
adamc@530 665 \Gamma \vdash c_1 :: \kappa_1 \to \kappa_2
adamc@530 666 & \Gamma \vdash c_2 :: \kappa_1
adamc@530 667 }
adamc@530 668 \quad \infer{\Gamma \vdash \lambda x \; :: \; \kappa_1 \Rightarrow c :: \kappa_1 \to \kappa_2}{
adamc@530 669 \Gamma, x :: \kappa_1 \vdash c :: \kappa_2
adamc@530 670 }$$
adamc@530 671
adamc@655 672 $$\infer{\Gamma \vdash c[\kappa'] :: [X \mapsto \kappa']\kappa}{
adamc@655 673 \Gamma \vdash c :: X \to \kappa
adamc@655 674 & \Gamma \vdash \kappa'
adamc@655 675 }
adamc@655 676 \quad \infer{\Gamma \vdash X \Longrightarrow c :: X \to \kappa}{
adamc@655 677 \Gamma, X \vdash c :: \kappa
adamc@655 678 }$$
adamc@655 679
adamc@530 680 $$\infer{\Gamma \vdash () :: \mt{Unit}}{}
adamc@530 681 \quad \infer{\Gamma \vdash \#X :: \mt{Name}}{}$$
adamc@530 682
adamc@530 683 $$\infer{\Gamma \vdash [\overline{c_i = c'_i}] :: \{\kappa\}}{
adamc@530 684 \forall i: \Gamma \vdash c_i : \mt{Name}
adamc@530 685 & \Gamma \vdash c'_i :: \kappa
adamc@530 686 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@530 687 }
adamc@530 688 \quad \infer{\Gamma \vdash c_1 \rc c_2 :: \{\kappa\}}{
adamc@530 689 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530 690 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@530 691 & \Gamma \vdash c_1 \sim c_2
adamc@530 692 }$$
adamc@530 693
adamc@655 694 $$\infer{\Gamma \vdash \mt{map} :: (\kappa_1 \to \kappa_2) \to \{\kappa_1\} \to \{\kappa_2\}}{}$$
adamc@530 695
adamc@573 696 $$\infer{\Gamma \vdash (\overline c) :: (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@573 697 \forall i: \Gamma \vdash c_i :: \kappa_i
adamc@530 698 }
adamc@573 699 \quad \infer{\Gamma \vdash c.i :: \kappa_i}{
adamc@573 700 \Gamma \vdash c :: (\kappa_1 \times \ldots \times \kappa_n)
adamc@530 701 }$$
adamc@530 702
adamc@655 703 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow \tau :: \mt{Type}}{
adamc@655 704 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530 705 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@655 706 & \Gamma, c_1 \sim c_2 \vdash \tau :: \mt{Type}
adamc@530 707 }$$
adamc@530 708
adamc@531 709 \subsection{Record Disjointness}
adamc@531 710
adamc@531 711 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@558 712 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@558 713 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@558 714 & \forall c'_1 \in C_1, c'_2 \in C_2: \Gamma \vdash c'_1 \sim c'_2
adamc@531 715 }
adamc@531 716 \quad \infer{\Gamma \vdash X \sim X'}{
adamc@531 717 X \neq X'
adamc@531 718 }$$
adamc@531 719
adamc@531 720 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@531 721 c'_1 \sim c'_2 \in \Gamma
adamc@558 722 & \Gamma \vdash c'_1 \hookrightarrow C_1
adamc@558 723 & \Gamma \vdash c'_2 \hookrightarrow C_2
adamc@558 724 & c_1 \in C_1
adamc@558 725 & c_2 \in C_2
adamc@531 726 }$$
adamc@531 727
adamc@531 728 $$\infer{\Gamma \vdash c \hookrightarrow \{c\}}{}
adamc@531 729 \quad \infer{\Gamma \vdash [\overline{c = c'}] \hookrightarrow \{\overline{c}\}}{}
adamc@531 730 \quad \infer{\Gamma \vdash c_1 \rc c_2 \hookrightarrow C_1 \cup C_2}{
adamc@531 731 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@531 732 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@531 733 }
adamc@531 734 \quad \infer{\Gamma \vdash c \hookrightarrow C}{
adamc@531 735 \Gamma \vdash c \equiv c'
adamc@531 736 & \Gamma \vdash c' \hookrightarrow C
adamc@531 737 }
adamc@531 738 \quad \infer{\Gamma \vdash \mt{map} \; f \; c \hookrightarrow C}{
adamc@531 739 \Gamma \vdash c \hookrightarrow C
adamc@531 740 }$$
adamc@531 741
adamc@541 742 \subsection{\label{definitional}Definitional Equality}
adamc@532 743
adamc@655 744 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@532 745
adamc@532 746 $$\infer{\Gamma \vdash c \equiv c}{}
adamc@532 747 \quad \infer{\Gamma \vdash c_1 \equiv c_2}{
adamc@532 748 \Gamma \vdash c_2 \equiv c_1
adamc@532 749 }
adamc@532 750 \quad \infer{\Gamma \vdash c_1 \equiv c_3}{
adamc@532 751 \Gamma \vdash c_1 \equiv c_2
adamc@532 752 & \Gamma \vdash c_2 \equiv c_3
adamc@532 753 }
adamc@532 754 \quad \infer{\Gamma \vdash \mathcal C[c_1] \equiv \mathcal C[c_2]}{
adamc@532 755 \Gamma \vdash c_1 \equiv c_2
adamc@532 756 }$$
adamc@532 757
adamc@532 758 $$\infer{\Gamma \vdash x \equiv c}{
adamc@532 759 x :: \kappa = c \in \Gamma
adamc@532 760 }
adamc@532 761 \quad \infer{\Gamma \vdash M.x \equiv c}{
adamc@537 762 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 763 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@532 764 }
adamc@532 765 \quad \infer{\Gamma \vdash (\overline c).i \equiv c_i}{}$$
adamc@532 766
adamc@532 767 $$\infer{\Gamma \vdash (\lambda x :: \kappa \Rightarrow c) \; c' \equiv [x \mapsto c'] c}{}
adamc@655 768 \quad \infer{\Gamma \vdash (X \Longrightarrow c) [\kappa] \equiv [X \mapsto \kappa] c}{}$$
adamc@655 769
adamc@655 770 $$\infer{\Gamma \vdash c_1 \rc c_2 \equiv c_2 \rc c_1}{}
adamc@532 771 \quad \infer{\Gamma \vdash c_1 \rc (c_2 \rc c_3) \equiv (c_1 \rc c_2) \rc c_3}{}$$
adamc@532 772
adamc@532 773 $$\infer{\Gamma \vdash [] \rc c \equiv c}{}
adamc@532 774 \quad \infer{\Gamma \vdash [\overline{c_1 = c'_1}] \rc [\overline{c_2 = c'_2}] \equiv [\overline{c_1 = c'_1}, \overline{c_2 = c'_2}]}{}$$
adamc@532 775
adamc@655 776 $$\infer{\Gamma \vdash \mt{map} \; f \; [] \equiv []}{}
adamc@655 777 \quad \infer{\Gamma \vdash \mt{map} \; f \; ([c_1 = c_2] \rc c) \equiv [c_1 = f \; c_2] \rc \mt{map} \; f \; c}{}$$
adamc@532 778
adamc@532 779 $$\infer{\Gamma \vdash \mt{map} \; (\lambda x \Rightarrow x) \; c \equiv c}{}
adamc@655 780 \quad \infer{\Gamma \vdash \mt{map} \; f \; (\mt{map} \; f' \; c)
adamc@655 781 \equiv \mt{map} \; (\lambda x \Rightarrow f \; (f' \; x)) \; c}{}$$
adamc@532 782
adamc@532 783 $$\infer{\Gamma \vdash \mt{map} \; f \; (c_1 \rc c_2) \equiv \mt{map} \; f \; c_1 \rc \mt{map} \; f \; c_2}{}$$
adamc@531 784
adamc@534 785 \subsection{Expression Typing}
adamc@533 786
adamc@873 787 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@533 788
adamc@533 789 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@533 790
adamc@533 791 $$\infer{\Gamma \vdash e : \tau : \tau}{
adamc@533 792 \Gamma \vdash e : \tau
adamc@533 793 }
adamc@533 794 \quad \infer{\Gamma \vdash e : \tau}{
adamc@533 795 \Gamma \vdash e : \tau'
adamc@533 796 & \Gamma \vdash \tau' \equiv \tau
adamc@533 797 }
adamc@533 798 \quad \infer{\Gamma \vdash \ell : T(\ell)}{}$$
adamc@533 799
adamc@533 800 $$\infer{\Gamma \vdash x : \mathcal I(\tau)}{
adamc@533 801 x : \tau \in \Gamma
adamc@533 802 }
adamc@533 803 \quad \infer{\Gamma \vdash M.x : \mathcal I(\tau)}{
adamc@537 804 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 805 & \mt{proj}(M, \overline{s}, \mt{val} \; x) = \tau
adamc@533 806 }
adamc@533 807 \quad \infer{\Gamma \vdash X : \mathcal I(\tau)}{
adamc@533 808 X : \tau \in \Gamma
adamc@533 809 }
adamc@533 810 \quad \infer{\Gamma \vdash M.X : \mathcal I(\tau)}{
adamc@537 811 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 812 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \tau
adamc@533 813 }$$
adamc@533 814
adamc@533 815 $$\infer{\Gamma \vdash e_1 \; e_2 : \tau_2}{
adamc@533 816 \Gamma \vdash e_1 : \tau_1 \to \tau_2
adamc@533 817 & \Gamma \vdash e_2 : \tau_1
adamc@533 818 }
adamc@533 819 \quad \infer{\Gamma \vdash \lambda x : \tau_1 \Rightarrow e : \tau_1 \to \tau_2}{
adamc@533 820 \Gamma, x : \tau_1 \vdash e : \tau_2
adamc@533 821 }$$
adamc@533 822
adamc@533 823 $$\infer{\Gamma \vdash e [c] : [x \mapsto c]\tau}{
adamc@533 824 \Gamma \vdash e : x :: \kappa \to \tau
adamc@533 825 & \Gamma \vdash c :: \kappa
adamc@533 826 }
adamc@852 827 \quad \infer{\Gamma \vdash \lambda [x \; ? \; \kappa] \Rightarrow e : x \; ? \; \kappa \to \tau}{
adamc@533 828 \Gamma, x :: \kappa \vdash e : \tau
adamc@533 829 }$$
adamc@533 830
adamc@655 831 $$\infer{\Gamma \vdash e [\kappa] : [X \mapsto \kappa]\tau}{
adamc@655 832 \Gamma \vdash e : X \longrightarrow \tau
adamc@655 833 & \Gamma \vdash \kappa
adamc@655 834 }
adamc@655 835 \quad \infer{\Gamma \vdash X \Longrightarrow e : X \longrightarrow \tau}{
adamc@655 836 \Gamma, X \vdash e : \tau
adamc@655 837 }$$
adamc@655 838
adamc@533 839 $$\infer{\Gamma \vdash \{\overline{c = e}\} : \{\overline{c : \tau}\}}{
adamc@533 840 \forall i: \Gamma \vdash c_i :: \mt{Name}
adamc@533 841 & \Gamma \vdash e_i : \tau_i
adamc@533 842 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@533 843 }
adamc@533 844 \quad \infer{\Gamma \vdash e.c : \tau}{
adamc@533 845 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533 846 }
adamc@533 847 \quad \infer{\Gamma \vdash e_1 \rc e_2 : \$(c_1 \rc c_2)}{
adamc@533 848 \Gamma \vdash e_1 : \$c_1
adamc@533 849 & \Gamma \vdash e_2 : \$c_2
adamc@573 850 & \Gamma \vdash c_1 \sim c_2
adamc@533 851 }$$
adamc@533 852
adamc@533 853 $$\infer{\Gamma \vdash e \rcut c : \$c'}{
adamc@533 854 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533 855 }
adamc@533 856 \quad \infer{\Gamma \vdash e \rcutM c : \$c'}{
adamc@533 857 \Gamma \vdash e : \$(c \rc c')
adamc@533 858 }$$
adamc@533 859
adamc@533 860 $$\infer{\Gamma \vdash \mt{let} \; \overline{ed} \; \mt{in} \; e \; \mt{end} : \tau}{
adamc@533 861 \Gamma \vdash \overline{ed} \leadsto \Gamma'
adamc@533 862 & \Gamma' \vdash e : \tau
adamc@533 863 }
adamc@533 864 \quad \infer{\Gamma \vdash \mt{case} \; e \; \mt{of} \; \overline{p \Rightarrow e} : \tau}{
adamc@533 865 \forall i: \Gamma \vdash p_i \leadsto \Gamma_i, \tau'
adamc@533 866 & \Gamma_i \vdash e_i : \tau
adamc@533 867 }$$
adamc@533 868
adamc@573 869 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow e : \lambda [c_1 \sim c_2] \Rightarrow \tau}{
adamc@533 870 \Gamma \vdash c_1 :: \{\kappa\}
adamc@655 871 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@533 872 & \Gamma, c_1 \sim c_2 \vdash e : \tau
adamc@662 873 }
adamc@662 874 \quad \infer{\Gamma \vdash e \; ! : \tau}{
adamc@662 875 \Gamma \vdash e : [c_1 \sim c_2] \Rightarrow \tau
adamc@662 876 & \Gamma \vdash c_1 \sim c_2
adamc@533 877 }$$
adamc@533 878
adamc@534 879 \subsection{Pattern Typing}
adamc@534 880
adamc@534 881 $$\infer{\Gamma \vdash \_ \leadsto \Gamma; \tau}{}
adamc@534 882 \quad \infer{\Gamma \vdash x \leadsto \Gamma, x : \tau; \tau}{}
adamc@534 883 \quad \infer{\Gamma \vdash \ell \leadsto \Gamma; T(\ell)}{}$$
adamc@534 884
adamc@534 885 $$\infer{\Gamma \vdash X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534 886 X : \overline{x ::: \mt{Type}} \to \tau \in \Gamma
adamc@534 887 & \textrm{$\tau$ not a function type}
adamc@534 888 }
adamc@534 889 \quad \infer{\Gamma \vdash X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534 890 X : \overline{x ::: \mt{Type}} \to \tau'' \to \tau \in \Gamma
adamc@534 891 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534 892 }$$
adamc@534 893
adamc@534 894 $$\infer{\Gamma \vdash M.X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537 895 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 896 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau
adamc@534 897 & \textrm{$\tau$ not a function type}
adamc@534 898 }$$
adamc@534 899
adamc@534 900 $$\infer{\Gamma \vdash M.X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537 901 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 902 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau'' \to \tau
adamc@534 903 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534 904 }$$
adamc@534 905
adamc@534 906 $$\infer{\Gamma \vdash \{\overline{x = p}\} \leadsto \Gamma_n; \{\overline{x = \tau}\}}{
adamc@534 907 \Gamma_0 = \Gamma
adamc@534 908 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534 909 }
adamc@534 910 \quad \infer{\Gamma \vdash \{\overline{x = p}, \ldots\} \leadsto \Gamma_n; \$([\overline{x = \tau}] \rc c)}{
adamc@534 911 \Gamma_0 = \Gamma
adamc@534 912 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534 913 }$$
adamc@534 914
adamc@852 915 $$\infer{\Gamma \vdash p : \tau \leadsto \Gamma'; \tau}{
adamc@852 916 \Gamma \vdash p \leadsto \Gamma'; \tau'
adamc@852 917 & \Gamma \vdash \tau' \equiv \tau
adamc@852 918 }$$
adamc@852 919
adamc@535 920 \subsection{Declaration Typing}
adamc@535 921
adamc@535 922 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@535 923
adamc@655 924 This is the first judgment where we deal with constructor classes, for the $\mt{class}$ declaration form. We will omit their special handling in this formal specification. Section \ref{typeclasses} gives an informal description of how constructor classes influence type inference.
adamc@535 925
adamc@558 926 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@537 927 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@535 928
adamc@535 929 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535 930 \quad \infer{\Gamma \vdash d, \overline{d} \leadsto \Gamma''}{
adamc@535 931 \Gamma \vdash d \leadsto \Gamma'
adamc@535 932 & \Gamma' \vdash \overline{d} \leadsto \Gamma''
adamc@535 933 }$$
adamc@535 934
adamc@535 935 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@535 936 \Gamma \vdash c :: \kappa
adamc@535 937 }
adamc@535 938 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@535 939 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@535 940 }$$
adamc@535 941
adamc@535 942 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537 943 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 944 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@535 945 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@535 946 }$$
adamc@535 947
adamc@535 948 $$\infer{\Gamma \vdash \mt{val} \; x : \tau = e \leadsto \Gamma, x : \tau}{
adamc@535 949 \Gamma \vdash e : \tau
adamc@535 950 }$$
adamc@535 951
adamc@535 952 $$\infer{\Gamma \vdash \mt{val} \; \mt{rec} \; \overline{x : \tau = e} \leadsto \Gamma, \overline{x : \tau}}{
adamc@535 953 \forall i: \Gamma, \overline{x : \tau} \vdash e_i : \tau_i
adamc@535 954 & \textrm{$e_i$ starts with an expression $\lambda$, optionally preceded by constructor and disjointness $\lambda$s}
adamc@535 955 }$$
adamc@535 956
adamc@535 957 $$\infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : S}{
adamc@535 958 \Gamma \vdash M : S
adamc@558 959 & \textrm{ $M$ not a constant or application}
adamc@535 960 }
adamc@558 961 \quad \infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : \mt{selfify}(X, \overline{s})}{
adamc@558 962 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@539 963 }$$
adamc@539 964
adamc@539 965 $$\infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@535 966 \Gamma \vdash S
adamc@535 967 }$$
adamc@535 968
adamc@537 969 $$\infer{\Gamma \vdash \mt{open} \; M \leadsto \Gamma, \mathcal O(M, \overline{s})}{
adamc@537 970 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535 971 }$$
adamc@535 972
adamc@535 973 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma}{
adamc@535 974 \Gamma \vdash c_1 :: \{\kappa\}
adamc@535 975 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@535 976 & \Gamma \vdash c_1 \sim c_2
adamc@535 977 }
adamc@537 978 \quad \infer{\Gamma \vdash \mt{open} \; \mt{constraints} \; M \leadsto \Gamma, \mathcal O_c(M, \overline{s})}{
adamc@537 979 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535 980 }$$
adamc@535 981
adamc@784 982 $$\infer{\Gamma \vdash \mt{table} \; x : c \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_table} \; c \; []}{
adamc@535 983 \Gamma \vdash c :: \{\mt{Type}\}
adamc@535 984 }
adamc@784 985 \quad \infer{\Gamma \vdash \mt{view} \; x : c \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_view} \; c}{
adamc@784 986 \Gamma \vdash c :: \{\mt{Type}\}
adamc@784 987 }$$
adamc@784 988
adamc@784 989 $$\infer{\Gamma \vdash \mt{sequence} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_sequence}}{}$$
adamc@535 990
adamc@535 991 $$\infer{\Gamma \vdash \mt{cookie} \; x : \tau \leadsto \Gamma, x : \mt{Basis}.\mt{http\_cookie} \; \tau}{
adamc@535 992 \Gamma \vdash \tau :: \mt{Type}
adamc@784 993 }
adamc@784 994 \quad \infer{\Gamma \vdash \mt{style} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{css\_class}}{}$$
adamc@535 995
adamc@1085 996 $$\infer{\Gamma \vdash \mt{task} \; e_1 = e_2 \leadsto \Gamma}{
adam@1348 997 \Gamma \vdash e_1 :: \mt{Basis}.\mt{task\_kind} \; \tau
adam@1348 998 & \Gamma \vdash e_2 :: \tau \to \mt{Basis}.\mt{transaction} \; \{\}
adamc@1085 999 }$$
adamc@1085 1000
adamc@784 1001 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784 1002 \Gamma \vdash c :: \kappa
adamc@535 1003 }$$
adamc@535 1004
adamc@535 1005 $$\infer{\overline{y}; x; \Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535 1006 \quad \infer{\overline{y}; x; \Gamma \vdash X \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to x \; \overline{y}}{
adamc@535 1007 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535 1008 }
adamc@535 1009 \quad \infer{\overline{y}; x; \Gamma \vdash X \; \mt{of} \; \tau \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to \tau \to x \; \overline{y}}{
adamc@535 1010 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535 1011 }$$
adamc@535 1012
adamc@537 1013 \subsection{Signature Item Typing}
adamc@537 1014
adamc@537 1015 We appeal to a signature item analogue of the $\mathcal O$ function from the last subsection.
adamc@537 1016
adamc@537 1017 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@537 1018 \quad \infer{\Gamma \vdash s, \overline{s} \leadsto \Gamma''}{
adamc@537 1019 \Gamma \vdash s \leadsto \Gamma'
adamc@537 1020 & \Gamma' \vdash \overline{s} \leadsto \Gamma''
adamc@537 1021 }$$
adamc@537 1022
adamc@537 1023 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}
adamc@537 1024 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@537 1025 \Gamma \vdash c :: \kappa
adamc@537 1026 }
adamc@537 1027 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@537 1028 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@537 1029 }$$
adamc@537 1030
adamc@537 1031 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537 1032 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1033 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1034 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@537 1035 }$$
adamc@537 1036
adamc@537 1037 $$\infer{\Gamma \vdash \mt{val} \; x : \tau \leadsto \Gamma, x : \tau}{
adamc@537 1038 \Gamma \vdash \tau :: \mt{Type}
adamc@537 1039 }$$
adamc@537 1040
adamc@537 1041 $$\infer{\Gamma \vdash \mt{structure} \; X : S \leadsto \Gamma, X : S}{
adamc@537 1042 \Gamma \vdash S
adamc@537 1043 }
adamc@537 1044 \quad \infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@537 1045 \Gamma \vdash S
adamc@537 1046 }$$
adamc@537 1047
adamc@537 1048 $$\infer{\Gamma \vdash \mt{include} \; S \leadsto \Gamma, \mathcal O(\overline{s})}{
adamc@537 1049 \Gamma \vdash S
adamc@537 1050 & \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1051 }$$
adamc@537 1052
adamc@537 1053 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma, c_1 \sim c_2}{
adamc@537 1054 \Gamma \vdash c_1 :: \{\kappa\}
adamc@537 1055 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@537 1056 }$$
adamc@537 1057
adamc@784 1058 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784 1059 \Gamma \vdash c :: \kappa
adamc@537 1060 }
adamc@784 1061 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}$$
adamc@537 1062
adamc@536 1063 \subsection{Signature Compatibility}
adamc@536 1064
adamc@558 1065 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 1066
adamc@537 1067 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 1068
adamc@536 1069 $$\infer{\Gamma \vdash S \equiv S}{}
adamc@536 1070 \quad \infer{\Gamma \vdash S_1 \equiv S_2}{
adamc@536 1071 \Gamma \vdash S_2 \equiv S_1
adamc@536 1072 }
adamc@536 1073 \quad \infer{\Gamma \vdash X \equiv S}{
adamc@536 1074 X = S \in \Gamma
adamc@536 1075 }
adamc@536 1076 \quad \infer{\Gamma \vdash M.X \equiv S}{
adamc@537 1077 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1078 & \mt{proj}(M, \overline{s}, \mt{signature} \; X) = S
adamc@536 1079 }$$
adamc@536 1080
adamc@536 1081 $$\infer{\Gamma \vdash S \; \mt{where} \; \mt{con} \; x = c \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa = c \; \overline{s_2} \; \mt{end}}{
adamc@536 1082 \Gamma \vdash S \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa \; \overline{s_2} \; \mt{end}
adamc@536 1083 & \Gamma \vdash c :: \kappa
adamc@537 1084 }
adamc@537 1085 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s^1} \; \mt{include} \; S \; \overline{s^2} \; \mt{end} \equiv \mt{sig} \; \overline{s^1} \; \overline{s} \; \overline{s^2} \; \mt{end}}{
adamc@537 1086 \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@536 1087 }$$
adamc@536 1088
adamc@536 1089 $$\infer{\Gamma \vdash S_1 \leq S_2}{
adamc@536 1090 \Gamma \vdash S_1 \equiv S_2
adamc@536 1091 }
adamc@536 1092 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \mt{end}}{}
adamc@537 1093 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; s' \; \overline{s'} \; \mt{end}}{
adamc@537 1094 \Gamma \vdash \overline{s} \leq s'
adamc@537 1095 & \Gamma \vdash s' \leadsto \Gamma'
adamc@537 1096 & \Gamma' \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \overline{s'} \; \mt{end}
adamc@537 1097 }$$
adamc@537 1098
adamc@537 1099 $$\infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537 1100 \Gamma \vdash s \leq s'
adamc@537 1101 }
adamc@537 1102 \quad \infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537 1103 \Gamma \vdash s \leadsto \Gamma'
adamc@537 1104 & \Gamma' \vdash \overline{s} \leq s'
adamc@536 1105 }$$
adamc@536 1106
adamc@536 1107 $$\infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 \leq \mt{functor} (X : S'_1) : S'_2}{
adamc@536 1108 \Gamma \vdash S'_1 \leq S_1
adamc@536 1109 & \Gamma, X : S'_1 \vdash S_2 \leq S'_2
adamc@536 1110 }$$
adamc@536 1111
adamc@537 1112 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@537 1113 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}
adamc@558 1114 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type}}{}$$
adamc@537 1115
adamc@537 1116 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(y)} \to \mt{Type}}{
adamc@537 1117 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1118 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1119 }$$
adamc@537 1120
adamc@784 1121 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@784 1122 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}$$
adamc@537 1123
adamc@537 1124 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \mt{\kappa} = c_2}{
adamc@537 1125 \Gamma \vdash c_1 \equiv c_2
adamc@537 1126 }
adamc@784 1127 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \kappa = c_2}{
adamc@537 1128 \Gamma \vdash c_1 \equiv c_2
adamc@537 1129 }$$
adamc@537 1130
adamc@537 1131 $$\infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537 1132 \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1133 }$$
adamc@537 1134
adamc@537 1135 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537 1136 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1137 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1138 & \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1139 }$$
adamc@537 1140
adamc@537 1141 $$\infer{\Gamma \vdash \cdot \leq \cdot}{}
adamc@537 1142 \quad \infer{\Gamma \vdash X; \overline{dc} \leq X; \overline{dc'}}{
adamc@537 1143 \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1144 }
adamc@537 1145 \quad \infer{\Gamma \vdash X \; \mt{of} \; \tau_1; \overline{dc} \leq X \; \mt{of} \; \tau_2; \overline{dc'}}{
adamc@537 1146 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537 1147 & \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1148 }$$
adamc@537 1149
adamc@537 1150 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x = \mt{datatype} \; M'.z'}{
adamc@537 1151 \Gamma \vdash M.z \equiv M'.z'
adamc@537 1152 }$$
adamc@537 1153
adamc@537 1154 $$\infer{\Gamma \vdash \mt{val} \; x : \tau_1 \leq \mt{val} \; x : \tau_2}{
adamc@537 1155 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537 1156 }
adamc@537 1157 \quad \infer{\Gamma \vdash \mt{structure} \; X : S_1 \leq \mt{structure} \; X : S_2}{
adamc@537 1158 \Gamma \vdash S_1 \leq S_2
adamc@537 1159 }
adamc@537 1160 \quad \infer{\Gamma \vdash \mt{signature} \; X = S_1 \leq \mt{signature} \; X = S_2}{
adamc@537 1161 \Gamma \vdash S_1 \leq S_2
adamc@537 1162 & \Gamma \vdash S_2 \leq S_1
adamc@537 1163 }$$
adamc@537 1164
adamc@537 1165 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leq \mt{constraint} \; c'_1 \sim c'_2}{
adamc@537 1166 \Gamma \vdash c_1 \equiv c'_1
adamc@537 1167 & \Gamma \vdash c_2 \equiv c'_2
adamc@537 1168 }$$
adamc@537 1169
adamc@655 1170 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{class} \; x :: \kappa}{}
adamc@655 1171 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{class} \; x :: \kappa}{}
adamc@655 1172 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{class} \; x :: \kappa = c_2}{
adamc@537 1173 \Gamma \vdash c_1 \equiv c_2
adamc@537 1174 }$$
adamc@537 1175
adamc@538 1176 \subsection{Module Typing}
adamc@538 1177
adamc@538 1178 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 1179
adamc@538 1180 $$\infer{\Gamma \vdash M : S}{
adamc@538 1181 \Gamma \vdash M : S'
adamc@538 1182 & \Gamma \vdash S' \leq S
adamc@538 1183 }
adamc@538 1184 \quad \infer{\Gamma \vdash \mt{struct} \; \overline{d} \; \mt{end} : \mt{sig} \; \mt{sigOf}(\overline{d}) \; \mt{end}}{
adamc@538 1185 \Gamma \vdash \overline{d} \leadsto \Gamma'
adamc@538 1186 }
adamc@538 1187 \quad \infer{\Gamma \vdash X : S}{
adamc@538 1188 X : S \in \Gamma
adamc@538 1189 }$$
adamc@538 1190
adamc@538 1191 $$\infer{\Gamma \vdash M.X : S}{
adamc@538 1192 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@538 1193 & \mt{proj}(M, \overline{s}, \mt{structure} \; X) = S
adamc@538 1194 }$$
adamc@538 1195
adamc@538 1196 $$\infer{\Gamma \vdash M_1(M_2) : [X \mapsto M_2]S_2}{
adamc@538 1197 \Gamma \vdash M_1 : \mt{functor}(X : S_1) : S_2
adamc@538 1198 & \Gamma \vdash M_2 : S_1
adamc@538 1199 }
adamc@538 1200 \quad \infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 = M : \mt{functor} (X : S_1) : S_2}{
adamc@538 1201 \Gamma \vdash S_1
adamc@538 1202 & \Gamma, X : S_1 \vdash S_2
adamc@538 1203 & \Gamma, X : S_1 \vdash M : S_2
adamc@538 1204 }$$
adamc@538 1205
adamc@538 1206 \begin{eqnarray*}
adamc@538 1207 \mt{sigOf}(\cdot) &=& \cdot \\
adamc@538 1208 \mt{sigOf}(s \; \overline{s'}) &=& \mt{sigOf}(s) \; \mt{sigOf}(\overline{s'}) \\
adamc@538 1209 \\
adamc@538 1210 \mt{sigOf}(\mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@538 1211 \mt{sigOf}(\mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \overline{dc} \\
adamc@538 1212 \mt{sigOf}(\mt{datatype} \; x = \mt{datatype} \; M.z) &=& \mt{datatype} \; x = \mt{datatype} \; M.z \\
adamc@538 1213 \mt{sigOf}(\mt{val} \; x : \tau = e) &=& \mt{val} \; x : \tau \\
adamc@538 1214 \mt{sigOf}(\mt{val} \; \mt{rec} \; \overline{x : \tau = e}) &=& \overline{\mt{val} \; x : \tau} \\
adamc@538 1215 \mt{sigOf}(\mt{structure} \; X : S = M) &=& \mt{structure} \; X : S \\
adamc@538 1216 \mt{sigOf}(\mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@538 1217 \mt{sigOf}(\mt{open} \; M) &=& \mt{include} \; S \textrm{ (where $\Gamma \vdash M : S$)} \\
adamc@538 1218 \mt{sigOf}(\mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@538 1219 \mt{sigOf}(\mt{open} \; \mt{constraints} \; M) &=& \cdot \\
adamc@538 1220 \mt{sigOf}(\mt{table} \; x : c) &=& \mt{table} \; x : c \\
adamc@784 1221 \mt{sigOf}(\mt{view} \; x : c) &=& \mt{view} \; x : c \\
adamc@538 1222 \mt{sigOf}(\mt{sequence} \; x) &=& \mt{sequence} \; x \\
adamc@538 1223 \mt{sigOf}(\mt{cookie} \; x : \tau) &=& \mt{cookie} \; x : \tau \\
adamc@784 1224 \mt{sigOf}(\mt{style} \; x) &=& \mt{style} \; x \\
adamc@655 1225 \mt{sigOf}(\mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@538 1226 \end{eqnarray*}
adamc@539 1227 \begin{eqnarray*}
adamc@539 1228 \mt{selfify}(M, \cdot) &=& \cdot \\
adamc@558 1229 \mt{selfify}(M, s \; \overline{s'}) &=& \mt{selfify}(M, s) \; \mt{selfify}(M, \overline{s'}) \\
adamc@539 1230 \\
adamc@539 1231 \mt{selfify}(M, \mt{con} \; x :: \kappa) &=& \mt{con} \; x :: \kappa = M.x \\
adamc@539 1232 \mt{selfify}(M, \mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@539 1233 \mt{selfify}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \mt{datatype} \; M.x \\
adamc@539 1234 \mt{selfify}(M, \mt{datatype} \; x = \mt{datatype} \; M'.z) &=& \mt{datatype} \; x = \mt{datatype} \; M'.z \\
adamc@539 1235 \mt{selfify}(M, \mt{val} \; x : \tau) &=& \mt{val} \; x : \tau \\
adamc@539 1236 \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 1237 \mt{selfify}(M, \mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@539 1238 \mt{selfify}(M, \mt{include} \; S) &=& \mt{include} \; S \\
adamc@539 1239 \mt{selfify}(M, \mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@655 1240 \mt{selfify}(M, \mt{class} \; x :: \kappa) &=& \mt{class} \; x :: \kappa = M.x \\
adamc@655 1241 \mt{selfify}(M, \mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@539 1242 \end{eqnarray*}
adamc@539 1243
adamc@540 1244 \subsection{Module Projection}
adamc@540 1245
adamc@540 1246 \begin{eqnarray*}
adamc@540 1247 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \\
adamc@540 1248 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa, c) \\
adamc@540 1249 \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 1250 \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 1251 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})$)} \\
adamc@655 1252 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \to \mt{Type} \\
adamc@655 1253 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa \to \mt{Type}, c) \\
adamc@540 1254 \\
adamc@540 1255 \mt{proj}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc} \; \overline{s}, \mt{datatype} \; x) &=& (\overline{y}, \overline{dc}) \\
adamc@540 1256 \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 1257 \\
adamc@540 1258 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, \mt{val} \; x) &=& \tau \\
adamc@540 1259 \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 1260 \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 1261 \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 1262 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \in \overline{dc}$)} \\
adamc@540 1263 \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 1264 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \; \mt{of} \; \tau \in \overline{dc}$)} \\
adamc@540 1265 \\
adamc@540 1266 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, \mt{structure} \; X) &=& S \\
adamc@540 1267 \\
adamc@540 1268 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, \mt{signature} \; X) &=& S \\
adamc@540 1269 \\
adamc@540 1270 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1271 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1272 \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 1273 \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 1274 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@540 1275 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1276 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1277 \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 1278 \mt{proj}(M, \mt{constraint} \; c_1 \sim c_2 \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@655 1279 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@655 1280 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1281 \end{eqnarray*}
adamc@540 1282
adamc@541 1283
adamc@541 1284 \section{Type Inference}
adamc@541 1285
adamc@541 1286 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 1287
adamc@541 1288 \subsection{Basic Unification}
adamc@541 1289
adamc@560 1290 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 1291
adamc@656 1292 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 1293
adamc@541 1294 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 1295
adamc@541 1296 \subsection{Unifying Record Types}
adamc@541 1297
adamc@570 1298 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 1299
adamc@656 1300 \subsection{\label{typeclasses}Constructor Classes}
adamc@541 1301
adamc@784 1302 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 1303
adamc@784 1304 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.
adamc@541 1305
adamc@656 1306 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.
adamc@541 1307
adamc@656 1308 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. Abstract constructor classes 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.
adamc@541 1309
adamc@541 1310 \subsection{Reverse-Engineering Record Types}
adamc@541 1311
adamc@656 1312 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 1313
adamc@541 1314 \subsection{Implicit Arguments in Functor Applications}
adamc@541 1315
adamc@656 1316 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 1317
adamc@541 1318
adamc@542 1319 \section{The Ur Standard Library}
adamc@542 1320
adamc@542 1321 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 1322
adamc@542 1323 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 1324
adamc@542 1325 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 1326 $$\begin{array}{l}
adamc@542 1327 \mt{type} \; \mt{int} \\
adamc@542 1328 \mt{type} \; \mt{float} \\
adamc@873 1329 \mt{type} \; \mt{char} \\
adamc@542 1330 \mt{type} \; \mt{string} \\
adamc@542 1331 \mt{type} \; \mt{time} \\
adamc@785 1332 \mt{type} \; \mt{blob} \\
adamc@542 1333 \\
adamc@542 1334 \mt{type} \; \mt{unit} = \{\} \\
adamc@542 1335 \\
adamc@542 1336 \mt{datatype} \; \mt{bool} = \mt{False} \mid \mt{True} \\
adamc@542 1337 \\
adamc@785 1338 \mt{datatype} \; \mt{option} \; \mt{t} = \mt{None} \mid \mt{Some} \; \mt{of} \; \mt{t} \\
adamc@785 1339 \\
adamc@785 1340 \mt{datatype} \; \mt{list} \; \mt{t} = \mt{Nil} \mid \mt{Cons} \; \mt{of} \; \mt{t} \times \mt{list} \; \mt{t}
adamc@542 1341 \end{array}$$
adamc@542 1342
adamc@1123 1343 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 1344
adam@1297 1345 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 1346 $$\begin{array}{l}
adam@1297 1347 \mt{con} \; \mt{variant} :: \{\mt{Type}\} \to \mt{Type} \\
adam@1297 1348 \mt{val} \; \mt{make} : \mt{nm} :: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{ts} ::: \{\mt{Type}\} \to [[\mt{nm}] \sim \mt{ts}] \Rightarrow \mt{t} \to \mt{variant} \; ([\mt{nm} = \mt{t}] \rc \mt{ts}) \\
adam@1297 1349 \mt{val} \; \mt{match} : \mt{ts} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{variant} \; \mt{ts} \to \$(\mt{map} \; (\lambda \mt{t'} \Rightarrow \mt{t'} \to \mt{t}) \; \mt{ts}) \to \mt{t}
adam@1297 1350 \end{array}$$
adam@1297 1351
adamc@657 1352 Another important generic Ur element comes at the beginning of \texttt{top.urs}.
adamc@657 1353
adamc@657 1354 $$\begin{array}{l}
adamc@657 1355 \mt{con} \; \mt{folder} :: \mt{K} \longrightarrow \{\mt{K}\} \to \mt{Type} \\
adamc@657 1356 \\
adamc@657 1357 \mt{val} \; \mt{fold} : \mt{K} \longrightarrow \mt{tf} :: (\{\mt{K}\} \to \mt{Type}) \\
adamc@657 1358 \hspace{.1in} \to (\mt{nm} :: \mt{Name} \to \mt{v} :: \mt{K} \to \mt{r} :: \{\mt{K}\} \to [[\mt{nm}] \sim \mt{r}] \Rightarrow \\
adamc@657 1359 \hspace{.2in} \mt{tf} \; \mt{r} \to \mt{tf} \; ([\mt{nm} = \mt{v}] \rc \mt{r})) \\
adamc@657 1360 \hspace{.1in} \to \mt{tf} \; [] \\
adamc@657 1361 \hspace{.1in} \to \mt{r} :: \{\mt{K}\} \to \mt{folder} \; \mt{r} \to \mt{tf} \; \mt{r}
adamc@657 1362 \end{array}$$
adamc@657 1363
adamc@657 1364 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 1365
adamc@664 1366 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 1367
adamc@542 1368
adamc@542 1369 \section{The Ur/Web Standard Library}
adamc@542 1370
adam@1400 1371 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 1372
adamc@658 1373 \subsection{Monads}
adamc@658 1374
adamc@658 1375 The Ur Basis defines the monad constructor class from Haskell.
adamc@658 1376
adamc@658 1377 $$\begin{array}{l}
adamc@658 1378 \mt{class} \; \mt{monad} :: \mt{Type} \to \mt{Type} \\
adamc@658 1379 \mt{val} \; \mt{return} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t} ::: \mt{Type} \\
adamc@658 1380 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658 1381 \hspace{.1in} \to \mt{t} \to \mt{m} \; \mt{t} \\
adamc@658 1382 \mt{val} \; \mt{bind} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t1} ::: \mt{Type} \to \mt{t2} ::: \mt{Type} \\
adamc@658 1383 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658 1384 \hspace{.1in} \to \mt{m} \; \mt{t1} \to (\mt{t1} \to \mt{m} \; \mt{t2}) \\
adamc@658 1385 \hspace{.1in} \to \mt{m} \; \mt{t2}
adamc@658 1386 \end{array}$$
adamc@658 1387
adamc@542 1388 \subsection{Transactions}
adamc@542 1389
adamc@542 1390 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 1391 $$\begin{array}{l}
adamc@542 1392 \mt{con} \; \mt{transaction} :: \mt{Type} \to \mt{Type} \\
adamc@658 1393 \mt{val} \; \mt{transaction\_monad} : \mt{monad} \; \mt{transaction}
adamc@542 1394 \end{array}$$
adamc@542 1395
adamc@1123 1396 For debugging purposes, a transactional function is provided for outputting a string on the server process' \texttt{stderr}.
adamc@1123 1397 $$\begin{array}{l}
adamc@1123 1398 \mt{val} \; \mt{debug} : \mt{string} \to \mt{transaction} \; \mt{unit}
adamc@1123 1399 \end{array}$$
adamc@1123 1400
adamc@542 1401 \subsection{HTTP}
adamc@542 1402
adam@1400 1403 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 1404 $$\begin{array}{l}
adamc@786 1405 \mt{con} \; \mt{http\_cookie} :: \mt{Type} \to \mt{Type} \\
adamc@786 1406 \mt{val} \; \mt{getCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; (\mt{option} \; \mt{t}) \\
adamc@1050 1407 \mt{val} \; \mt{setCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \{\mt{Value} : \mt{t}, \mt{Expires} : \mt{option} \; \mt{time}, \mt{Secure} : \mt{bool}\} \to \mt{transaction} \; \mt{unit} \\
adamc@1050 1408 \mt{val} \; \mt{clearCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; \mt{unit}
adamc@786 1409 \end{array}$$
adamc@786 1410
adamc@786 1411 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 1412 $$\begin{array}{l}
adamc@786 1413 \mt{type} \; \mt{url} \\
adamc@786 1414 \mt{val} \; \mt{bless} : \mt{string} \to \mt{url} \\
adamc@786 1415 \mt{val} \; \mt{checkUrl} : \mt{string} \to \mt{option} \; \mt{url}
adamc@786 1416 \end{array}$$
adamc@786 1417 $\mt{bless}$ raises a runtime error if the string passed to it fails the URL policy.
adamc@786 1418
adam@1400 1419 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 1420 $$\begin{array}{l}
adamc@1085 1421 \mt{val} \; \mt{currentUrl} : \mt{transaction} \; \mt{url} \\
adamc@1085 1422 \mt{val} \; \mt{url} : \mt{transaction} \; \mt{page} \to \mt{url}
adamc@1085 1423 \end{array}$$
adamc@1085 1424
adamc@1085 1425 Page generation may be interrupted at any time with a request to redirect to a particular URL instead.
adamc@1085 1426 $$\begin{array}{l}
adamc@1085 1427 \mt{val} \; \mt{redirect} : \mt{t} ::: \mt{Type} \to \mt{url} \to \mt{transaction} \; \mt{t}
adamc@1085 1428 \end{array}$$
adamc@1085 1429
adam@1400 1430 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 1431 $$\begin{array}{l}
adamc@786 1432 \mt{type} \; \mt{file} \\
adamc@786 1433 \mt{val} \; \mt{fileName} : \mt{file} \to \mt{option} \; \mt{string} \\
adamc@786 1434 \mt{val} \; \mt{fileMimeType} : \mt{file} \to \mt{string} \\
adamc@786 1435 \mt{val} \; \mt{fileData} : \mt{file} \to \mt{blob}
adamc@786 1436 \end{array}$$
adamc@786 1437
adam@1465 1438 It is also possible to get HTTP request headers and set HTTP response headers, using abstract types similar to the one for URLs.
adam@1465 1439
adam@1465 1440 $$\begin{array}{l}
adam@1465 1441 \mt{type} \; \mt{requestHeader} \\
adam@1465 1442 \mt{val} \; \mt{blessRequestHeader} : \mt{string} \to \mt{requestHeader} \\
adam@1465 1443 \mt{val} \; \mt{checkRequestHeader} : \mt{string} \to \mt{option} \; \mt{requestHeader} \\
adam@1465 1444 \mt{val} \; \mt{getHeader} : \mt{requestHeader} \to \mt{transaction} \; (\mt{option} \; \mt{string}) \\
adam@1465 1445 \\
adam@1465 1446 \mt{type} \; \mt{responseHeader} \\
adam@1465 1447 \mt{val} \; \mt{blessResponseHeader} : \mt{string} \to \mt{responseHeader} \\
adam@1465 1448 \mt{val} \; \mt{checkResponseHeader} : \mt{string} \to \mt{option} \; \mt{responseHeader} \\
adam@1465 1449 \mt{val} \; \mt{setHeader} : \mt{responseHeader} \to \mt{string} \to \mt{transaction} \; \mt{unit}
adam@1465 1450 \end{array}$$
adam@1465 1451
adamc@786 1452 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 1453 $$\begin{array}{l}
adamc@786 1454 \mt{type} \; \mt{mimeType} \\
adamc@786 1455 \mt{val} \; \mt{blessMime} : \mt{string} \to \mt{mimeType} \\
adamc@786 1456 \mt{val} \; \mt{checkMime} : \mt{string} \to \mt{option} \; \mt{mimeType} \\
adamc@786 1457 \mt{val} \; \mt{returnBlob} : \mt{t} ::: \mt{Type} \to \mt{blob} \to \mt{mimeType} \to \mt{transaction} \; \mt{t}
adamc@542 1458 \end{array}$$
adamc@542 1459
adamc@543 1460 \subsection{SQL}
adamc@543 1461
adam@1400 1462 Everything about SQL database access is restricted to server-side code.
adam@1400 1463
adamc@543 1464 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 1465 $$\begin{array}{l}
adamc@785 1466 \mt{con} \; \mt{sql\_table} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785 1467 \end{array}$$
adamc@785 1468 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 1469
adamc@785 1470 We also have the simpler type family of SQL views, which have no keys.
adamc@785 1471 $$\begin{array}{l}
adamc@785 1472 \mt{con} \; \mt{sql\_view} :: \{\mt{Type}\} \to \mt{Type}
adamc@543 1473 \end{array}$$
adamc@543 1474
adamc@785 1475 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 1476 $$\begin{array}{l}
adamc@785 1477 \mt{class} \; \mt{fieldsOf} :: \mt{Type} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1478 \mt{val} \; \mt{fieldsOf\_table} : \mt{fs} ::: \{\mt{Type}\} \to \mt{keys} ::: \{\{\mt{Unit}\}\} \to \mt{fieldsOf} \; (\mt{sql\_table} \; \mt{fs} \; \mt{keys}) \; \mt{fs} \\
adamc@785 1479 \mt{val} \; \mt{fieldsOf\_view} : \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; (\mt{sql\_view} \; \mt{fs}) \; \mt{fs}
adamc@785 1480 \end{array}$$
adamc@785 1481
adamc@785 1482 \subsubsection{Table Constraints}
adamc@785 1483
adamc@785 1484 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 1485
adamc@785 1486 $$\begin{array}{l}
adamc@785 1487 \mt{con} \; \mt{primary\_key} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type} \\
adamc@785 1488 \mt{val} \; \mt{no\_primary\_key} : \mt{fs} ::: \{\mt{Type}\} \to \mt{primary\_key} \; \mt{fs} \; [] \\
adamc@785 1489 \mt{val} \; \mt{primary\_key} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{key1} :: \mt{Name} \to \mt{keys} :: \{\mt{Type}\} \\
adamc@785 1490 \hspace{.1in} \to [[\mt{key1}] \sim \mt{keys}] \Rightarrow [[\mt{key1} = \mt{t}] \rc \mt{keys} \sim \mt{rest}] \\
adamc@785 1491 \hspace{.1in} \Rightarrow \$([\mt{key1} = \mt{sql\_injectable\_prim} \; \mt{t}] \rc \mt{map} \; \mt{sql\_injectable\_prim} \; \mt{keys}) \\
adamc@785 1492 \hspace{.1in} \to \mt{primary\_key} \; ([\mt{key1} = \mt{t}] \rc \mt{keys} \rc \mt{rest}) \; [\mt{Pkey} = [\mt{key1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{keys}]
adamc@785 1493 \end{array}$$
adamc@785 1494 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 1495
adamc@785 1496 A type family stands for sets of named constraints of the remaining varieties.
adamc@785 1497 $$\begin{array}{l}
adamc@785 1498 \mt{con} \; \mt{sql\_constraints} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785 1499 \end{array}$$
adamc@785 1500 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 1501
adamc@785 1502 There is a type family of individual, unnamed constraints.
adamc@785 1503 $$\begin{array}{l}
adamc@785 1504 \mt{con} \; \mt{sql\_constraint} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \mt{Type}
adamc@785 1505 \end{array}$$
adamc@785 1506 The first argument is the same as above, and the second argument gives the key columns for just this constraint.
adamc@785 1507
adamc@785 1508 We have operations for assembling constraints into constraint sets.
adamc@785 1509 $$\begin{array}{l}
adamc@785 1510 \mt{val} \; \mt{no\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_constraints} \; \mt{fs} \; [] \\
adamc@785 1511 \mt{val} \; \mt{one\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{unique} ::: \{\mt{Unit}\} \to \mt{name} :: \mt{Name} \\
adamc@785 1512 \hspace{.1in} \to \mt{sql\_constraint} \; \mt{fs} \; \mt{unique} \to \mt{sql\_constraints} \; \mt{fs} \; [\mt{name} = \mt{unique}] \\
adamc@785 1513 \mt{val} \; \mt{join\_constraints} : \mt{fs} ::: \{\mt{Type}\} \to \mt{uniques1} ::: \{\{\mt{Unit}\}\} \to \mt{uniques2} ::: \{\{\mt{Unit}\}\} \to [\mt{uniques1} \sim \mt{uniques2}] \\
adamc@785 1514 \hspace{.1in} \Rightarrow \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques1} \to \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques2} \to \mt{sql\_constraints} \; \mt{fs} \; (\mt{uniques1} \rc \mt{uniques2})
adamc@785 1515 \end{array}$$
adamc@785 1516
adamc@785 1517 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 1518 $$\begin{array}{l}
adamc@785 1519 \mt{val} \; \mt{unique} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{unique1} :: \mt{Name} \to \mt{unique} :: \{\mt{Type}\} \\
adamc@785 1520 \hspace{.1in} \to [[\mt{unique1}] \sim \mt{unique}] \Rightarrow [[\mt{unique1} = \mt{t}] \rc \mt{unique} \sim \mt{rest}] \\
adamc@785 1521 \hspace{.1in} \Rightarrow \mt{sql\_constraint} \; ([\mt{unique1} = \mt{t}] \rc \mt{unique} \rc \mt{rest}) \; ([\mt{unique1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{unique})
adamc@785 1522 \end{array}$$
adamc@785 1523
adamc@785 1524 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 1525 $$\begin{array}{l}
adamc@785 1526 \mt{class} \; \mt{linkable} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@785 1527 \mt{val} \; \mt{linkable\_same} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; \mt{t} \\
adamc@785 1528 \mt{val} \; \mt{linkable\_from\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; (\mt{option} \; \mt{t}) \; \mt{t} \\
adamc@785 1529 \mt{val} \; \mt{linkable\_to\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@785 1530 \end{array}$$
adamc@785 1531
adamc@785 1532 The $\mt{matching}$ type family uses $\mt{linkable}$ to define when two keys match up type-wise.
adamc@785 1533 $$\begin{array}{l}
adamc@785 1534 \mt{con} \; \mt{matching} :: \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1535 \mt{val} \; \mt{mat\_nil} : \mt{matching} \; [] \; [] \\
adamc@785 1536 \mt{val} \; \mt{mat\_cons} : \mt{t1} ::: \mt{Type} \to \mt{rest1} ::: \{\mt{Type}\} \to \mt{t2} ::: \mt{Type} \to \mt{rest2} ::: \{\mt{Type}\} \to \mt{nm1} :: \mt{Name} \to \mt{nm2} :: \mt{Name} \\
adamc@785 1537 \hspace{.1in} \to [[\mt{nm1}] \sim \mt{rest1}] \Rightarrow [[\mt{nm2}] \sim \mt{rest2}] \Rightarrow \mt{linkable} \; \mt{t1} \; \mt{t2} \to \mt{matching} \; \mt{rest1} \; \mt{rest2} \\
adamc@785 1538 \hspace{.1in} \to \mt{matching} \; ([\mt{nm1} = \mt{t1}] \rc \mt{rest1}) \; ([\mt{nm2} = \mt{t2}] \rc \mt{rest2})
adamc@785 1539 \end{array}$$
adamc@785 1540
adamc@785 1541 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 1542 $$\begin{array}{l}
adamc@785 1543 \mt{con} \; \mt{propagation\_mode} :: \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1544 \mt{val} \; \mt{restrict} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1545 \mt{val} \; \mt{cascade} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1546 \mt{val} \; \mt{no\_action} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1547 \mt{val} \; \mt{set\_null} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; (\mt{map} \; \mt{option} \; \mt{fs})
adamc@785 1548 \end{array}$$
adamc@785 1549
adamc@785 1550 Finally, we put these ingredient together to define the \texttt{FOREIGN KEY} constraint function.
adamc@785 1551 $$\begin{array}{l}
adamc@785 1552 \mt{val} \; \mt{foreign\_key} : \mt{mine1} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{mine} ::: \{\mt{Type}\} \to \mt{munused} ::: \{\mt{Type}\} \to \mt{foreign} ::: \{\mt{Type}\} \\
adamc@785 1553 \hspace{.1in} \to \mt{funused} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{uniques} ::: \{\{\mt{Unit}\}\} \\
adamc@785 1554 \hspace{.1in} \to [[\mt{mine1}] \sim \mt{mine}] \Rightarrow [[\mt{mine1} = \mt{t}] \rc \mt{mine} \sim \mt{munused}] \Rightarrow [\mt{foreign} \sim \mt{funused}] \Rightarrow [[\mt{nm}] \sim \mt{uniques}] \\
adamc@785 1555 \hspace{.1in} \Rightarrow \mt{matching} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}) \; \mt{foreign} \\
adamc@785 1556 \hspace{.1in} \to \mt{sql\_table} \; (\mt{foreign} \rc \mt{funused}) \; ([\mt{nm} = \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{foreign}] \rc \mt{uniques}) \\
adamc@785 1557 \hspace{.1in} \to \{\mt{OnDelete} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}), \\
adamc@785 1558 \hspace{.2in} \mt{OnUpdate} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine})\} \\
adamc@785 1559 \hspace{.1in} \to \mt{sql\_constraint} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine} \rc \mt{munused}) \; []
adamc@785 1560 \end{array}$$
adamc@785 1561
adamc@785 1562 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 1563 $$\begin{array}{l}
adamc@785 1564 \mt{val} \; \mt{check} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; [] \; [] \; \mt{fs} \; \mt{bool} \to \mt{sql\_constraint} \; \mt{fs} \; []
adamc@785 1565 \end{array}$$
adamc@785 1566
adamc@785 1567 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 1568
adamc@784 1569
adamc@543 1570 \subsubsection{Queries}
adamc@543 1571
adam@1400 1572 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 1573 $$\begin{array}{l}
adam@1400 1574 \mt{con} \; \mt{sql\_query} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@1193 1575 \mt{val} \; \mt{sql\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400 1576 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1577 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543 1578 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1579 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1193 1580 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adam@1400 1581 \hspace{.1in} \Rightarrow \{\mt{Rows} : \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}, \\
adamc@1193 1582 \hspace{.2in} \mt{OrderBy} : \mt{sql\_order\_by} \; (\mt{free} \rc \mt{tables}) \; \mt{selectedExps}, \\
adamc@543 1583 \hspace{.2in} \mt{Limit} : \mt{sql\_limit}, \\
adamc@543 1584 \hspace{.2in} \mt{Offset} : \mt{sql\_offset}\} \\
adam@1400 1585 \hspace{.1in} \to \mt{sql\_query} \; \mt{free} \; \mt{afree} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1586 \end{array}$$
adamc@543 1587
adamc@545 1588 Queries are used by folding over their results inside transactions.
adamc@545 1589 $$\begin{array}{l}
adam@1400 1590 \mt{val} \; \mt{query} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to [\mt{tables} \sim \mt{exps}] \Rightarrow \mt{state} ::: \mt{Type} \to \mt{sql\_query} \; [] \; [] \; \mt{tables} \; \mt{exps} \\
adamc@658 1591 \hspace{.1in} \to (\$(\mt{exps} \rc \mt{map} \; (\lambda \mt{fields} :: \{\mt{Type}\} \Rightarrow \$\mt{fields}) \; \mt{tables}) \\
adamc@545 1592 \hspace{.2in} \to \mt{state} \to \mt{transaction} \; \mt{state}) \\
adamc@545 1593 \hspace{.1in} \to \mt{state} \to \mt{transaction} \; \mt{state}
adamc@545 1594 \end{array}$$
adamc@545 1595
adam@1400 1596 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 1597 $$\begin{array}{l}
adam@1400 1598 \mt{con} \; \mt{sql\_query1} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@543 1599 \\
adamc@543 1600 \mt{type} \; \mt{sql\_relop} \\
adamc@543 1601 \mt{val} \; \mt{sql\_union} : \mt{sql\_relop} \\
adamc@543 1602 \mt{val} \; \mt{sql\_intersect} : \mt{sql\_relop} \\
adamc@543 1603 \mt{val} \; \mt{sql\_except} : \mt{sql\_relop} \\
adam@1400 1604 \mt{val} \; \mt{sql\_relop} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400 1605 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adam@1400 1606 \hspace{.1in} \to \mt{tables1} ::: \{\{\mt{Type}\}\} \\
adamc@543 1607 \hspace{.1in} \to \mt{tables2} ::: \{\{\mt{Type}\}\} \\
adamc@543 1608 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1609 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@543 1610 \hspace{.1in} \to \mt{sql\_relop} \\
adam@1458 1611 \hspace{.1in} \to \mt{bool} \; (* \; \mt{ALL} \; *) \\
adam@1400 1612 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables1} \; \mt{selectedFields} \; \mt{selectedExps} \\
adam@1400 1613 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables2} \; \mt{selectedFields} \; \mt{selectedExps} \\
adam@1400 1614 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{selectedFields} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1615 \end{array}$$
adamc@543 1616
adamc@543 1617 $$\begin{array}{l}
adamc@1193 1618 \mt{val} \; \mt{sql\_query1} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400 1619 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1620 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543 1621 \hspace{.1in} \to \mt{grouped} ::: \{\{\mt{Type}\}\} \\
adamc@543 1622 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1623 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1085 1624 \hspace{.1in} \to \mt{empties} :: \{\mt{Unit}\} \\
adamc@1193 1625 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adamc@1193 1626 \hspace{.1in} \Rightarrow [\mt{free} \sim \mt{grouped}] \\
adam@1400 1627 \hspace{.1in} \Rightarrow [\mt{afree} \sim \mt{tables}] \\
adamc@1193 1628 \hspace{.1in} \Rightarrow [\mt{empties} \sim \mt{selectedFields}] \\
adamc@1085 1629 \hspace{.1in} \Rightarrow \{\mt{Distinct} : \mt{bool}, \\
adamc@1193 1630 \hspace{.2in} \mt{From} : \mt{sql\_from\_items} \; \mt{free} \; \mt{tables}, \\
adam@1400 1631 \hspace{.2in} \mt{Where} : \mt{sql\_exp} \; (\mt{free} \rc \mt{tables}) \; \mt{afree} \; [] \; \mt{bool}, \\
adamc@543 1632 \hspace{.2in} \mt{GroupBy} : \mt{sql\_subset} \; \mt{tables} \; \mt{grouped}, \\
adam@1400 1633 \hspace{.2in} \mt{Having} : \mt{sql\_exp} \; (\mt{free} \rc \mt{grouped}) \; (\mt{afree} \rc \mt{tables}) \; [] \; \mt{bool}, \\
adamc@1085 1634 \hspace{.2in} \mt{SelectFields} : \mt{sql\_subset} \; \mt{grouped} \; (\mt{map} \; (\lambda \_ \Rightarrow []) \; \mt{empties} \rc \mt{selectedFields}), \\
adam@1400 1635 \hspace{.2in} \mt {SelectExps} : \$(\mt{map} \; (\mt{sql\_exp} \; (\mt{free} \rc \mt{grouped}) \; (\mt{afree} \rc \mt{tables}) \; []) \; \mt{selectedExps}) \} \\
adam@1400 1636 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1637 \end{array}$$
adamc@543 1638
adamc@543 1639 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 1640 $$\begin{array}{l}
adamc@543 1641 \mt{con} \; \mt{sql\_subset} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@543 1642 \mt{val} \; \mt{sql\_subset} : \mt{keep\_drop} :: \{(\{\mt{Type}\} \times \{\mt{Type}\})\} \\
adamc@543 1643 \hspace{.1in} \to \mt{sql\_subset} \\
adamc@658 1644 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1 \rc \mt{fields}.2)\; \mt{keep\_drop}) \\
adamc@658 1645 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1) \; \mt{keep\_drop}) \\
adamc@543 1646 \mt{val} \; \mt{sql\_subset\_all} : \mt{tables} :: \{\{\mt{Type}\}\} \to \mt{sql\_subset} \; \mt{tables} \; \mt{tables}
adamc@543 1647 \end{array}$$
adamc@543 1648
adamc@560 1649 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 1650 $$\begin{array}{l}
adamc@543 1651 \mt{con} \; \mt{sql\_exp} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}
adamc@543 1652 \end{array}$$
adamc@543 1653
adamc@543 1654 Any field in scope may be converted to an expression.
adamc@543 1655 $$\begin{array}{l}
adamc@543 1656 \mt{val} \; \mt{sql\_field} : \mt{otherTabs} ::: \{\{\mt{Type}\}\} \to \mt{otherFields} ::: \{\mt{Type}\} \\
adamc@543 1657 \hspace{.1in} \to \mt{fieldType} ::: \mt{Type} \to \mt{agg} ::: \{\{\mt{Type}\}\} \\
adamc@543 1658 \hspace{.1in} \to \mt{exps} ::: \{\mt{Type}\} \\
adamc@543 1659 \hspace{.1in} \to \mt{tab} :: \mt{Name} \to \mt{field} :: \mt{Name} \\
adamc@543 1660 \hspace{.1in} \to \mt{sql\_exp} \; ([\mt{tab} = [\mt{field} = \mt{fieldType}] \rc \mt{otherFields}] \rc \mt{otherTabs}) \; \mt{agg} \; \mt{exps} \; \mt{fieldType}
adamc@543 1661 \end{array}$$
adamc@543 1662
adamc@544 1663 There is an analogous function for referencing named expressions.
adamc@544 1664 $$\begin{array}{l}
adamc@544 1665 \mt{val} \; \mt{sql\_exp} : \mt{tabs} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{t} ::: \mt{Type} \to \mt{rest} ::: \{\mt{Type}\} \to \mt{nm} :: \mt{Name} \\
adamc@544 1666 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tabs} \; \mt{agg} \; ([\mt{nm} = \mt{t}] \rc \mt{rest}) \; \mt{t}
adamc@544 1667 \end{array}$$
adamc@544 1668
adamc@544 1669 Ur values of appropriate types may be injected into SQL expressions.
adamc@544 1670 $$\begin{array}{l}
adamc@786 1671 \mt{class} \; \mt{sql\_injectable\_prim} \\
adamc@786 1672 \mt{val} \; \mt{sql\_bool} : \mt{sql\_injectable\_prim} \; \mt{bool} \\
adamc@786 1673 \mt{val} \; \mt{sql\_int} : \mt{sql\_injectable\_prim} \; \mt{int} \\
adamc@786 1674 \mt{val} \; \mt{sql\_float} : \mt{sql\_injectable\_prim} \; \mt{float} \\
adamc@786 1675 \mt{val} \; \mt{sql\_string} : \mt{sql\_injectable\_prim} \; \mt{string} \\
adamc@786 1676 \mt{val} \; \mt{sql\_time} : \mt{sql\_injectable\_prim} \; \mt{time} \\
adamc@786 1677 \mt{val} \; \mt{sql\_blob} : \mt{sql\_injectable\_prim} \; \mt{blob} \\
adamc@786 1678 \mt{val} \; \mt{sql\_channel} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{channel} \; \mt{t}) \\
adamc@786 1679 \mt{val} \; \mt{sql\_client} : \mt{sql\_injectable\_prim} \; \mt{client} \\
adamc@786 1680 \\
adamc@544 1681 \mt{class} \; \mt{sql\_injectable} \\
adamc@786 1682 \mt{val} \; \mt{sql\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@786 1683 \mt{val} \; \mt{sql\_option\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; (\mt{option} \; \mt{t}) \\
adamc@786 1684 \\
adamc@544 1685 \mt{val} \; \mt{sql\_inject} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@544 1686 \hspace{.1in} \to \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adamc@544 1687 \end{array}$$
adamc@544 1688
adamc@1123 1689 Additionally, most function-free types may be injected safely, via the $\mt{serialized}$ type family.
adamc@1123 1690 $$\begin{array}{l}
adamc@1123 1691 \mt{con} \; \mt{serialized} :: \mt{Type} \to \mt{Type} \\
adamc@1123 1692 \mt{val} \; \mt{serialize} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{serialized} \; \mt{t} \\
adamc@1123 1693 \mt{val} \; \mt{deserialize} : \mt{t} ::: \mt{Type} \to \mt{serialized} \; \mt{t} \to \mt{t} \\
adamc@1123 1694 \mt{val} \; \mt{sql\_serialized} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{serialized} \; \mt{t})
adamc@1123 1695 \end{array}$$
adamc@1123 1696
adamc@544 1697 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 1698 $$\begin{array}{l}
adamc@544 1699 \mt{val} \; \mt{sql\_is\_null} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544 1700 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; (\mt{option} \; \mt{t}) \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{bool}
adamc@544 1701 \end{array}$$
adamc@544 1702
adamc@559 1703 We have generic nullary, unary, and binary operators.
adamc@544 1704 $$\begin{array}{l}
adamc@544 1705 \mt{con} \; \mt{sql\_nfunc} :: \mt{Type} \to \mt{Type} \\
adamc@544 1706 \mt{val} \; \mt{sql\_current\_timestamp} : \mt{sql\_nfunc} \; \mt{time} \\
adamc@544 1707 \mt{val} \; \mt{sql\_nfunc} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544 1708 \hspace{.1in} \to \mt{sql\_nfunc} \; \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\\end{array}$$
adamc@544 1709
adamc@544 1710 $$\begin{array}{l}
adamc@544 1711 \mt{con} \; \mt{sql\_unary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544 1712 \mt{val} \; \mt{sql\_not} : \mt{sql\_unary} \; \mt{bool} \; \mt{bool} \\
adamc@544 1713 \mt{val} \; \mt{sql\_unary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adamc@544 1714 \hspace{.1in} \to \mt{sql\_unary} \; \mt{arg} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res} \\
adamc@544 1715 \end{array}$$
adamc@544 1716
adamc@544 1717 $$\begin{array}{l}
adamc@544 1718 \mt{con} \; \mt{sql\_binary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544 1719 \mt{val} \; \mt{sql\_and} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544 1720 \mt{val} \; \mt{sql\_or} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544 1721 \mt{val} \; \mt{sql\_binary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg_1} ::: \mt{Type} \to \mt{arg_2} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adamc@544 1722 \hspace{.1in} \to \mt{sql\_binary} \; \mt{arg_1} \; \mt{arg_2} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_1} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_2} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res}
adamc@544 1723 \end{array}$$
adamc@544 1724
adamc@544 1725 $$\begin{array}{l}
adamc@559 1726 \mt{class} \; \mt{sql\_arith} \\
adamc@559 1727 \mt{val} \; \mt{sql\_int\_arith} : \mt{sql\_arith} \; \mt{int} \\
adamc@559 1728 \mt{val} \; \mt{sql\_float\_arith} : \mt{sql\_arith} \; \mt{float} \\
adamc@559 1729 \mt{val} \; \mt{sql\_neg} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_unary} \; \mt{t} \; \mt{t} \\
adamc@559 1730 \mt{val} \; \mt{sql\_plus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1731 \mt{val} \; \mt{sql\_minus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1732 \mt{val} \; \mt{sql\_times} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1733 \mt{val} \; \mt{sql\_div} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1734 \mt{val} \; \mt{sql\_mod} : \mt{sql\_binary} \; \mt{int} \; \mt{int} \; \mt{int}
adamc@559 1735 \end{array}$$
adamc@544 1736
adamc@656 1737 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 1738 $$\begin{array}{l}
adamc@544 1739 \mt{val} \; \mt{sql\_count} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int}
adamc@544 1740 \end{array}$$
adamc@544 1741
adamc@544 1742 $$\begin{array}{l}
adamc@1188 1743 \mt{con} \; \mt{sql\_aggregate} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@1188 1744 \mt{val} \; \mt{sql\_aggregate} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{dom} ::: \mt{Type} \to \mt{ran} ::: \mt{Type} \\
adamc@1188 1745 \hspace{.1in} \to \mt{sql\_aggregate} \; \mt{dom} \; \mt{ran} \to \mt{sql\_exp} \; \mt{agg} \; \mt{agg} \; \mt{exps} \; \mt{dom} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{ran}
adamc@1188 1746 \end{array}$$
adamc@1188 1747
adamc@1188 1748 $$\begin{array}{l}
adamc@1188 1749 \mt{val} \; \mt{sql\_count\_col} : \mt{t} ::: \mt{Type} \to \mt{sql\_aggregate} \; (\mt{option} \; \mt{t}) \; \mt{int}
adamc@544 1750 \end{array}$$
adam@1400 1751
adam@1400 1752 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 1753
adamc@544 1754 $$\begin{array}{l}
adamc@544 1755 \mt{class} \; \mt{sql\_summable} \\
adamc@544 1756 \mt{val} \; \mt{sql\_summable\_int} : \mt{sql\_summable} \; \mt{int} \\
adamc@544 1757 \mt{val} \; \mt{sql\_summable\_float} : \mt{sql\_summable} \; \mt{float} \\
adam@1400 1758 \mt{val} \; \mt{sql\_avg} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt} \\
adam@1400 1759 \mt{val} \; \mt{sql\_sum} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt}
adamc@544 1760 \end{array}$$
adamc@544 1761
adamc@544 1762 $$\begin{array}{l}
adamc@544 1763 \mt{class} \; \mt{sql\_maxable} \\
adamc@544 1764 \mt{val} \; \mt{sql\_maxable\_int} : \mt{sql\_maxable} \; \mt{int} \\
adamc@544 1765 \mt{val} \; \mt{sql\_maxable\_float} : \mt{sql\_maxable} \; \mt{float} \\
adamc@544 1766 \mt{val} \; \mt{sql\_maxable\_string} : \mt{sql\_maxable} \; \mt{string} \\
adamc@544 1767 \mt{val} \; \mt{sql\_maxable\_time} : \mt{sql\_maxable} \; \mt{time} \\
adam@1400 1768 \mt{val} \; \mt{sql\_max} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt} \\
adam@1400 1769 \mt{val} \; \mt{sql\_min} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt}
adamc@544 1770 \end{array}$$
adamc@544 1771
adamc@1193 1772 Any SQL query that returns single columns may be turned into a subquery expression.
adamc@1193 1773
adamc@786 1774 $$\begin{array}{l}
adam@1421 1775 \mt{val} \; \mt{sql\_subquery} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \\
adam@1421 1776 \hspace{.1in} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_query} \; \mt{tables} \; \mt{agg} \; [\mt{nm} = \mt{t}] \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{nt}
adamc@1193 1777 \end{array}$$
adamc@1193 1778
adamc@1193 1779 \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 1780 $$\begin{array}{l}
adamc@1193 1781 \mt{con} \; \mt{sql\_from\_items} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@1193 1782 \mt{val} \; \mt{sql\_from\_table} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1783 \hspace{.1in} \to \mt{t} ::: \mt{Type} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; \mt{t} \; \mt{fs} \to \mt{name} :: \mt{Name} \to \mt{t} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193 1784 \mt{val} \; \mt{sql\_from\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{name} :: \mt{Name} \to \mt{sql\_query} \; \mt{free} \; [] \; \mt{fs} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193 1785 \mt{val} \; \mt{sql\_from\_comma} : \mt{free} ::: \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \to [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193 1786 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adamc@1193 1787 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2}) \\
adamc@1193 1788 \mt{val} \; \mt{sql\_inner\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1789 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193 1790 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adamc@1193 1791 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193 1792 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2})
adamc@786 1793 \end{array}$$
adamc@786 1794
adamc@786 1795 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 1796 $$\begin{array}{l}
adamc@786 1797 \mt{class} \; \mt{nullify} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@786 1798 \mt{val} \; \mt{nullify\_option} : \mt{t} ::: \mt{Type} \to \mt{nullify} \; (\mt{option} \; \mt{t}) \; (\mt{option} \; \mt{t}) \\
adamc@786 1799 \mt{val} \; \mt{nullify\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{nullify} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@786 1800 \end{array}$$
adamc@786 1801
adamc@786 1802 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 1803
adamc@786 1804 $$\begin{array}{l}
adamc@1193 1805 \mt{val} \; \mt{sql\_left\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{(\mt{Type} \times \mt{Type})\}\} \\
adamc@1193 1806 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@786 1807 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\lambda \mt{r} \Rightarrow \$(\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{nullify} \; \mt{p}.1 \; \mt{p}.2) \; \mt{r})) \; \mt{tabs2}) \\
adamc@1193 1808 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \\
adamc@1193 1809 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193 1810 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.2)) \; \mt{tabs2})
adamc@786 1811 \end{array}$$
adamc@786 1812
adamc@544 1813 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 1814 $$\begin{array}{l}
adamc@544 1815 \mt{type} \; \mt{sql\_direction} \\
adamc@544 1816 \mt{val} \; \mt{sql\_asc} : \mt{sql\_direction} \\
adamc@544 1817 \mt{val} \; \mt{sql\_desc} : \mt{sql\_direction} \\
adamc@544 1818 \\
adamc@544 1819 \mt{con} \; \mt{sql\_order\_by} :: \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@544 1820 \mt{val} \; \mt{sql\_order\_by\_Nil} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} :: \{\mt{Type}\} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544 1821 \mt{val} \; \mt{sql\_order\_by\_Cons} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544 1822 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; [] \; \mt{exps} \; \mt{t} \to \mt{sql\_direction} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544 1823 \\
adamc@544 1824 \mt{type} \; \mt{sql\_limit} \\
adamc@544 1825 \mt{val} \; \mt{sql\_no\_limit} : \mt{sql\_limit} \\
adamc@544 1826 \mt{val} \; \mt{sql\_limit} : \mt{int} \to \mt{sql\_limit} \\
adamc@544 1827 \\
adamc@544 1828 \mt{type} \; \mt{sql\_offset} \\
adamc@544 1829 \mt{val} \; \mt{sql\_no\_offset} : \mt{sql\_offset} \\
adamc@544 1830 \mt{val} \; \mt{sql\_offset} : \mt{int} \to \mt{sql\_offset}
adamc@544 1831 \end{array}$$
adamc@544 1832
adamc@545 1833
adamc@545 1834 \subsubsection{DML}
adamc@545 1835
adamc@545 1836 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 1837
adamc@545 1838 $$\begin{array}{l}
adamc@545 1839 \mt{type} \; \mt{dml} \\
adamc@545 1840 \mt{val} \; \mt{dml} : \mt{dml} \to \mt{transaction} \; \mt{unit}
adamc@545 1841 \end{array}$$
adamc@545 1842
adam@1297 1843 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 1844
adam@1297 1845 $$\begin{array}{l}
adam@1297 1846 \mt{val} \; \mt{tryDml} : \mt{dml} \to \mt{transaction} \; (\mt{option} \; \mt{string})
adam@1297 1847 \end{array}$$
adam@1297 1848
adamc@545 1849 Properly-typed records may be used to form $\mt{INSERT}$ commands.
adamc@545 1850 $$\begin{array}{l}
adamc@545 1851 \mt{val} \; \mt{insert} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \\
adamc@658 1852 \hspace{.1in} \to \$(\mt{map} \; (\mt{sql\_exp} \; [] \; [] \; []) \; \mt{fields}) \to \mt{dml}
adamc@545 1853 \end{array}$$
adamc@545 1854
adamc@545 1855 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.
adamc@545 1856 $$\begin{array}{l}
adam@1380 1857 \mt{val} \; \mt{update} : \mt{unchanged} ::: \{\mt{Type}\} \to \mt{changed} :: \{\mt{Type}\} \to [\mt{changed} \sim \mt{unchanged}] \\
adamc@658 1858 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; []) \; \mt{changed}) \\
adamc@545 1859 \hspace{.1in} \to \mt{sql\_table} \; (\mt{changed} \rc \mt{unchanged}) \to \mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545 1860 \end{array}$$
adamc@545 1861
adamc@545 1862 A $\mt{DELETE}$ command is formed from a table and a $\mt{WHERE}$ clause.
adamc@545 1863 $$\begin{array}{l}
adamc@545 1864 \mt{val} \; \mt{delete} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \to \mt{sql\_exp} \; [\mt{T} = \mt{fields}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545 1865 \end{array}$$
adamc@545 1866
adamc@546 1867 \subsubsection{Sequences}
adamc@546 1868
adamc@546 1869 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 1870
adamc@546 1871 $$\begin{array}{l}
adamc@546 1872 \mt{type} \; \mt{sql\_sequence} \\
adamc@1085 1873 \mt{val} \; \mt{nextval} : \mt{sql\_sequence} \to \mt{transaction} \; \mt{int} \\
adamc@1085 1874 \mt{val} \; \mt{setval} : \mt{sql\_sequence} \to \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@546 1875 \end{array}$$
adamc@546 1876
adamc@546 1877
adamc@547 1878 \subsection{XML}
adamc@547 1879
adam@1333 1880 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 1881
adam@1345 1882 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 $[\mt{Body}, \mt{Tr}]$, to indicate a kind of nesting inside \texttt{<body>} and \texttt{<tr>}. 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 1883 $$\begin{array}{l}
adamc@547 1884 \mt{con} \; \mt{xml} :: \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547 1885 \end{array}$$
adamc@547 1886
adamc@547 1887 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 1888 $$\begin{array}{l}
adamc@547 1889 \mt{con} \; \mt{tag} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547 1890 \end{array}$$
adamc@547 1891
adamc@547 1892 Literal text may be injected into XML as ``CDATA.''
adamc@547 1893 $$\begin{array}{l}
adamc@547 1894 \mt{val} \; \mt{cdata} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{string} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adamc@547 1895 \end{array}$$
adamc@547 1896
adam@1358 1897 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 1898 $$\begin{array}{l}
adam@1358 1899 \mt{val} \; \mt{cdataChar} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{char} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adam@1358 1900 \end{array}$$
adam@1358 1901
adamc@547 1902 There is a function for producing an XML tree with a particular tag at its root.
adamc@547 1903 $$\begin{array}{l}
adamc@547 1904 \mt{val} \; \mt{tag} : \mt{attrsGiven} ::: \{\mt{Type}\} \to \mt{attrsAbsent} ::: \{\mt{Type}\} \to \mt{ctxOuter} ::: \{\mt{Unit}\} \to \mt{ctxInner} ::: \{\mt{Unit}\} \\
adamc@547 1905 \hspace{.1in} \to \mt{useOuter} ::: \{\mt{Type}\} \to \mt{useInner} ::: \{\mt{Type}\} \to \mt{bindOuter} ::: \{\mt{Type}\} \to \mt{bindInner} ::: \{\mt{Type}\} \\
adam@1380 1906 \hspace{.1in} \to [\mt{attrsGiven} \sim \mt{attrsAbsent}] \Rightarrow [\mt{useOuter} \sim \mt{useInner}] \Rightarrow [\mt{bindOuter} \sim \mt{bindInner}] \\
adamc@787 1907 \hspace{.1in} \Rightarrow \mt{option} \; \mt{css\_class} \\
adamc@787 1908 \hspace{.1in} \to \$\mt{attrsGiven} \\
adamc@547 1909 \hspace{.1in} \to \mt{tag} \; (\mt{attrsGiven} \rc \mt{attrsAbsent}) \; \mt{ctxOuter} \; \mt{ctxInner} \; \mt{useOuter} \; \mt{bindOuter} \\
adamc@547 1910 \hspace{.1in} \to \mt{xml} \; \mt{ctxInner} \; \mt{useInner} \; \mt{bindInner} \to \mt{xml} \; \mt{ctxOuter} \; (\mt{useOuter} \rc \mt{useInner}) \; (\mt{bindOuter} \rc \mt{bindInner})
adamc@547 1911 \end{array}$$
adam@1297 1912 Note that any tag may be assigned a CSS class. This is the sole way of making use of the values produced by $\mt{style}$ declarations. Ur/Web itself doesn't deal with the syntax or semantics of style sheets; they can be linked via URLs with \texttt{link} tags. However, Ur/Web does make it easy to calculate upper bounds on usage of CSS classes through program analysis. The function $\mt{Basis.classes}$ can be used to specify a list of CSS classes for a single tag.
adamc@547 1913
adamc@547 1914 Two XML fragments may be concatenated.
adamc@547 1915 $$\begin{array}{l}
adamc@547 1916 \mt{val} \; \mt{join} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{bind_1} ::: \{\mt{Type}\} \to \mt{bind_2} ::: \{\mt{Type}\} \\
adam@1380 1917 \hspace{.1in} \to [\mt{use_1} \sim \mt{bind_1}] \Rightarrow [\mt{bind_1} \sim \mt{bind_2}] \\
adamc@547 1918 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind_1} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{bind_1}) \; \mt{bind_2} \to \mt{xml} \; \mt{ctx} \; \mt{use_1} \; (\mt{bind_1} \rc \mt{bind_2})
adamc@547 1919 \end{array}$$
adamc@547 1920
adamc@547 1921 Finally, any XML fragment may be updated to ``claim'' to use more form fields than it does.
adamc@547 1922 $$\begin{array}{l}
adam@1380 1923 \mt{val} \; \mt{useMore} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{use_2} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to [\mt{use_1} \sim \mt{use_2}] \\
adamc@547 1924 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{use_2}) \; \mt{bind}
adamc@547 1925 \end{array}$$
adamc@547 1926
adam@1344 1927 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 1928
adamc@547 1929 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 1930 $$\begin{array}{l}
adamc@547 1931 \mt{val} \; \mt{error} : \mt{t} ::: \mt{Type} \to \mt{xml} \; [\mt{Body}] \; [] \; [] \to \mt{t}
adamc@547 1932 \end{array}$$
adamc@547 1933
adamc@549 1934
adamc@701 1935 \subsection{Client-Side Programming}
adamc@659 1936
adamc@701 1937 Ur/Web supports running code on web browsers, via automatic compilation to JavaScript.
adamc@701 1938
adamc@701 1939 \subsubsection{The Basics}
adamc@701 1940
adam@1400 1941 All of the functions in this subsection are client-side only.
adam@1400 1942
adam@1297 1943 Clients can open alert and confirm dialog boxes, in the usual annoying JavaScript way.
adamc@701 1944 $$\begin{array}{l}
adam@1297 1945 \mt{val} \; \mt{alert} : \mt{string} \to \mt{transaction} \; \mt{unit} \\
adam@1297 1946 \mt{val} \; \mt{confirm} : \mt{string} \to \mt{transaction} \; \mt{bool}
adamc@701 1947 \end{array}$$
adamc@701 1948
adamc@701 1949 Any transaction may be run in a new thread with the $\mt{spawn}$ function.
adamc@701 1950 $$\begin{array}{l}
adamc@701 1951 \mt{val} \; \mt{spawn} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit}
adamc@701 1952 \end{array}$$
adamc@701 1953
adamc@701 1954 The current thread can be paused for at least a specified number of milliseconds.
adamc@701 1955 $$\begin{array}{l}
adamc@701 1956 \mt{val} \; \mt{sleep} : \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@701 1957 \end{array}$$
adamc@701 1958
adamc@787 1959 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 occurrences of that error are ignored silently.
adamc@787 1960 $$\begin{array}{l}
adamc@787 1961 \mt{val} \; \mt{onError} : (\mt{xbody} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787 1962 \mt{val} \; \mt{onFail} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787 1963 \mt{val} \; \mt{onConnectFail} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787 1964 \mt{val} \; \mt{onDisconnect} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787 1965 \mt{val} \; \mt{onServerError} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit}
adamc@787 1966 \end{array}$$
adamc@787 1967
adamc@701 1968 \subsubsection{Functional-Reactive Page Generation}
adamc@701 1969
adamc@701 1970 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 1971
adam@1403 1972 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 1973
adamc@659 1974 $$\begin{array}{l}
adamc@659 1975 \mt{con} \; \mt{source} :: \mt{Type} \to \mt{Type} \\
adamc@659 1976 \mt{val} \; \mt{source} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{transaction} \; (\mt{source} \; \mt{t}) \\
adamc@659 1977 \mt{val} \; \mt{set} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@659 1978 \mt{val} \; \mt{get} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@659 1979 \end{array}$$
adamc@659 1980
adam@1400 1981 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 1982
adam@1403 1983 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.
adamc@659 1984
adamc@659 1985 $$\begin{array}{l}
adamc@659 1986 \mt{con} \; \mt{signal} :: \mt{Type} \to \mt{Type} \\
adamc@659 1987 \mt{val} \; \mt{signal\_monad} : \mt{monad} \; \mt{signal} \\
adamc@659 1988 \mt{val} \; \mt{signal} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{signal} \; \mt{t}
adamc@659 1989 \end{array}$$
adamc@659 1990
adamc@659 1991 A reactive portion of an HTML page is injected with a $\mt{dyn}$ tag, which has a signal-valued attribute $\mt{Signal}$.
adamc@659 1992
adamc@659 1993 $$\begin{array}{l}
adamc@701 1994 \mt{val} \; \mt{dyn} : \mt{use} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to \mt{unit} \\
adamc@701 1995 \hspace{.1in} \to \mt{tag} \; [\mt{Signal} = \mt{signal} \; (\mt{xml} \; \mt{body} \; \mt{use} \; \mt{bind})] \; \mt{body} \; [] \; \mt{use} \; \mt{bind}
adamc@659 1996 \end{array}$$
adamc@659 1997
adamc@701 1998 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.
adamc@701 1999
adamc@914 2000 \subsubsection{Remote Procedure Calls}
adamc@914 2001
adamc@914 2002 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 2003
adamc@914 2004 $$\begin{array}{l}
adamc@914 2005 \mt{val} \; \mt{rpc} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@914 2006 \end{array}$$
adamc@914 2007
adamc@701 2008 \subsubsection{Asynchronous Message-Passing}
adamc@701 2009
adamc@701 2010 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 2011
adamc@701 2012 $$\begin{array}{l}
adamc@701 2013 \mt{type} \; \mt{client} \\
adamc@701 2014 \mt{val} \; \mt{self} : \mt{transaction} \; \mt{client}
adamc@701 2015 \end{array}$$
adamc@701 2016
adamc@701 2017 \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 2018
adamc@701 2019 $$\begin{array}{l}
adamc@701 2020 \mt{con} \; \mt{channel} :: \mt{Type} \to \mt{Type} \\
adamc@701 2021 \mt{val} \; \mt{channel} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; (\mt{channel} \; \mt{t}) \\
adamc@701 2022 \mt{val} \; \mt{send} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@701 2023 \mt{val} \; \mt{recv} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@701 2024 \end{array}$$
adamc@701 2025
adamc@701 2026 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 2027
adamc@701 2028 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 2029
adamc@659 2030
adamc@549 2031 \section{Ur/Web Syntax Extensions}
adamc@549 2032
adamc@549 2033 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 2034
adamc@549 2035 \subsection{SQL}
adamc@549 2036
adamc@786 2037 \subsubsection{\label{tables}Table Declarations}
adamc@786 2038
adamc@788 2039 $\mt{table}$ declarations may include constraints, via these grammar rules.
adamc@788 2040 $$\begin{array}{rrcll}
adamc@788 2041 \textrm{Declarations} & d &::=& \mt{table} \; x : c \; [pk[,]] \; cts \\
adamc@788 2042 \textrm{Primary key constraints} & pk &::=& \mt{PRIMARY} \; \mt{KEY} \; K \\
adamc@788 2043 \textrm{Keys} & K &::=& f \mid (f, (f,)^+) \\
adamc@788 2044 \textrm{Constraint sets} & cts &::=& \mt{CONSTRAINT} f \; ct \mid cts, cts \mid \{\{e\}\} \\
adamc@788 2045 \textrm{Constraints} & ct &::=& \mt{UNIQUE} \; K \mid \mt{CHECK} \; E \\
adamc@788 2046 &&& \mid \mt{FOREIGN} \; \mt{KEY} \; K \; \mt{REFERENCES} \; F \; (K) \; [\mt{ON} \; \mt{DELETE} \; pr] \; [\mt{ON} \; \mt{UPDATE} \; pr] \\
adamc@788 2047 \textrm{Foreign tables} & F &::=& x \mid \{\{e\}\} \\
adamc@788 2048 \textrm{Propagation modes} & pr &::=& \mt{NO} \; \mt{ACTION} \mid \mt{RESTRICT} \mid \mt{CASCADE} \mid \mt{SET} \; \mt{NULL}
adamc@788 2049 \end{array}$$
adamc@788 2050
adamc@788 2051 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 2052
adamc@788 2053
adamc@549 2054 \subsubsection{Queries}
adamc@549 2055
adamc@550 2056 Queries $Q$ are added to the rules for expressions $e$.
adamc@550 2057
adamc@549 2058 $$\begin{array}{rrcll}
adamc@550 2059 \textrm{Queries} & Q &::=& (q \; [\mt{ORDER} \; \mt{BY} \; (E \; [o],)^+] \; [\mt{LIMIT} \; N] \; [\mt{OFFSET} \; N]) \\
adamc@1085 2060 \textrm{Pre-queries} & q &::=& \mt{SELECT} \; [\mt{DISTINCT}] \; P \; \mt{FROM} \; F,^+ \; [\mt{WHERE} \; E] \; [\mt{GROUP} \; \mt{BY} \; p,^+] \; [\mt{HAVING} \; E] \\
adamc@1085 2061 &&& \mid q \; R \; q \mid \{\{\{e\}\}\} \\
adamc@549 2062 \textrm{Relational operators} & R &::=& \mt{UNION} \mid \mt{INTERSECT} \mid \mt{EXCEPT}
adamc@549 2063 \end{array}$$
adamc@549 2064
adamc@549 2065 $$\begin{array}{rrcll}
adamc@549 2066 \textrm{Projections} & P &::=& \ast & \textrm{all columns} \\
adamc@549 2067 &&& p,^+ & \textrm{particular columns} \\
adamc@549 2068 \textrm{Pre-projections} & p &::=& t.f & \textrm{one column from a table} \\
adamc@558 2069 &&& t.\{\{c\}\} & \textrm{a record of columns from a table (of kind $\{\mt{Type}\}$)} \\
adamc@1194 2070 &&& E \; [\mt{AS} \; f] & \textrm{expression column} \\
adamc@549 2071 \textrm{Table names} & t &::=& x & \textrm{constant table name (automatically capitalized)} \\
adamc@549 2072 &&& X & \textrm{constant table name} \\
adamc@549 2073 &&& \{\{c\}\} & \textrm{computed table name (of kind $\mt{Name}$)} \\
adamc@549 2074 \textrm{Column names} & f &::=& X & \textrm{constant column name} \\
adamc@549 2075 &&& \{c\} & \textrm{computed column name (of kind $\mt{Name}$)} \\
adamc@549 2076 \textrm{Tables} & T &::=& x & \textrm{table variable, named locally by its own capitalization} \\
adamc@549 2077 &&& x \; \mt{AS} \; t & \textrm{table variable, with local name} \\
adamc@549 2078 &&& \{\{e\}\} \; \mt{AS} \; t & \textrm{computed table expression, with local name} \\
adamc@1085 2079 \textrm{$\mt{FROM}$ items} & F &::=& T \mid \{\{e\}\} \mid F \; J \; \mt{JOIN} \; F \; \mt{ON} \; E \\
adamc@1085 2080 &&& \mid F \; \mt{CROSS} \; \mt{JOIN} \ F \\
adamc@1193 2081 &&& \mid (Q) \; \mt{AS} \; t \\
adamc@1085 2082 \textrm{Joins} & J &::=& [\mt{INNER}] \\
adamc@1085 2083 &&& \mid [\mt{LEFT} \mid \mt{RIGHT} \mid \mt{FULL}] \; [\mt{OUTER}] \\
adamc@549 2084 \textrm{SQL expressions} & E &::=& p & \textrm{column references} \\
adamc@549 2085 &&& X & \textrm{named expression references} \\
adam@1490 2086 &&& \{[e]\} & \textrm{injected native Ur expressions} \\
adamc@549 2087 &&& \{e\} & \textrm{computed expressions, probably using $\mt{sql\_exp}$ directly} \\
adamc@549 2088 &&& \mt{TRUE} \mid \mt{FALSE} & \textrm{boolean constants} \\
adamc@549 2089 &&& \ell & \textrm{primitive type literals} \\
adamc@549 2090 &&& \mt{NULL} & \textrm{null value (injection of $\mt{None}$)} \\
adamc@549 2091 &&& E \; \mt{IS} \; \mt{NULL} & \textrm{nullness test} \\
adamc@549 2092 &&& n & \textrm{nullary operators} \\
adamc@549 2093 &&& u \; E & \textrm{unary operators} \\
adamc@549 2094 &&& E \; b \; E & \textrm{binary operators} \\
adamc@549 2095 &&& \mt{COUNT}(\ast) & \textrm{count number of rows} \\
adamc@549 2096 &&& a(E) & \textrm{other aggregate function} \\
adamc@1193 2097 &&& (Q) & \textrm{subquery (must return a single expression column)} \\
adamc@549 2098 &&& (E) & \textrm{explicit precedence} \\
adamc@549 2099 \textrm{Nullary operators} & n &::=& \mt{CURRENT\_TIMESTAMP} \\
adamc@549 2100 \textrm{Unary operators} & u &::=& \mt{NOT} \\
adamc@549 2101 \textrm{Binary operators} & b &::=& \mt{AND} \mid \mt{OR} \mid \neq \mid < \mid \leq \mid > \mid \geq \\
adamc@1188 2102 \textrm{Aggregate functions} & a &::=& \mt{COUNT} \mid \mt{AVG} \mid \mt{SUM} \mid \mt{MIN} \mid \mt{MAX} \\
adamc@550 2103 \textrm{Directions} & o &::=& \mt{ASC} \mid \mt{DESC} \\
adamc@549 2104 \textrm{SQL integer} & N &::=& n \mid \{e\} \\
adamc@549 2105 \end{array}$$
adamc@549 2106
adamc@1085 2107 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 2108
adamc@1194 2109 Unnamed expression columns in $\mt{SELECT}$ clauses are assigned consecutive natural numbers, starting with 1.
adamc@1194 2110
adamc@550 2111 \subsubsection{DML}
adamc@550 2112
adamc@550 2113 DML commands $D$ are added to the rules for expressions $e$.
adamc@550 2114
adamc@550 2115 $$\begin{array}{rrcll}
adamc@550 2116 \textrm{Commands} & D &::=& (\mt{INSERT} \; \mt{INTO} \; T^E \; (f,^+) \; \mt{VALUES} \; (E,^+)) \\
adamc@550 2117 &&& (\mt{UPDATE} \; T^E \; \mt{SET} \; (f = E,)^+ \; \mt{WHERE} \; E) \\
adamc@550 2118 &&& (\mt{DELETE} \; \mt{FROM} \; T^E \; \mt{WHERE} \; E) \\
adamc@550 2119 \textrm{Table expressions} & T^E &::=& x \mid \{\{e\}\}
adamc@550 2120 \end{array}$$
adamc@550 2121
adamc@550 2122 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 2123
adamc@551 2124 \subsection{XML}
adamc@551 2125
adamc@551 2126 XML fragments $L$ are added to the rules for expressions $e$.
adamc@551 2127
adamc@551 2128 $$\begin{array}{rrcll}
adamc@551 2129 \textrm{XML fragments} & L &::=& \texttt{<xml/>} \mid \texttt{<xml>}l^*\texttt{</xml>} \\
adamc@551 2130 \textrm{XML pieces} & l &::=& \textrm{text} & \textrm{cdata} \\
adamc@551 2131 &&& \texttt{<}g\texttt{/>} & \textrm{tag with no children} \\
adamc@551 2132 &&& \texttt{<}g\texttt{>}l^*\texttt{</}x\texttt{>} & \textrm{tag with children} \\
adamc@559 2133 &&& \{e\} & \textrm{computed XML fragment} \\
adamc@559 2134 &&& \{[e]\} & \textrm{injection of an Ur expression, via the $\mt{Top}.\mt{txt}$ function} \\
adamc@551 2135 \textrm{Tag} & g &::=& h \; (x = v)^* \\
adamc@551 2136 \textrm{Tag head} & h &::=& x & \textrm{tag name} \\
adamc@551 2137 &&& h\{c\} & \textrm{constructor parameter} \\
adamc@551 2138 \textrm{Attribute value} & v &::=& \ell & \textrm{literal value} \\
adamc@551 2139 &&& \{e\} & \textrm{computed value} \\
adamc@551 2140 \end{array}$$
adamc@551 2141
adamc@552 2142
adamc@1198 2143 \section{\label{structure}The Structure of Web Applications}
adamc@553 2144
adamc@1127 2145 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. Arguments to an entry-point function are deserialized from the part of the URI following \texttt{f}.
adamc@553 2146
adam@1532 2147 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 2148
adam@1347 2149 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 will only work with \texttt{POST} payloads of MIME types besides those associated with HTML forms; for these, use Ur/Web's built-in support, as described below.
adam@1347 2150
adam@1370 2151 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 2152
adamc@553 2153 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 2154
adamc@553 2155 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 2156
adamc@558 2157 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.
adamc@553 2158
adamc@660 2159 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 2160
adamc@789 2161 \medskip
adamc@789 2162
adam@1347 2163 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 2164
adamc@789 2165 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 2166
adam@1348 2167 \subsection{Tasks}
adam@1348 2168
adam@1348 2169 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 2170
adam@1348 2171 $$\begin{array}{l}
adam@1348 2172 \mt{con} \; \mt{task\_kind} :: \mt{Type} \to \mt{Type} \\
adam@1348 2173 \mt{val} \; \mt{initialize} : \mt{task\_kind} \; \mt{unit} \\
adam@1349 2174 \mt{val} \; \mt{clientLeaves} : \mt{task\_kind} \; \mt{client} \\
adam@1349 2175 \mt{val} \; \mt{periodic} : \mt{int} \to \mt{task\_kind} \; \mt{unit}
adam@1348 2176 \end{array}$$
adam@1348 2177
adam@1348 2178 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 2179
adam@1348 2180 The currently supported task kinds are:
adam@1348 2181 \begin{itemize}
adam@1349 2182 \item $\mt{initialize}$: Code that is run when the application starts up.
adam@1348 2183 \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 2184 \item $\mt{periodic} \; n$: Code that is run when the application starts up and then every $n$ seconds thereafter.
adam@1348 2185 \end{itemize}
adam@1348 2186
adamc@553 2187
adamc@897 2188 \section{The Foreign Function Interface}
adamc@897 2189
adamc@897 2190 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 2191
adamc@897 2192 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 2193
adamc@897 2194 \begin{itemize}
adamc@897 2195 \item \texttt{clientOnly Module.ident} registers a value as being allowed only in client-side code.
adamc@897 2196 \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.
adamc@897 2197 \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.
adamc@897 2198 \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 2199 \item \texttt{include FILE} requests inclusion of a C header file.
adamc@897 2200 \item \texttt{jsFunc Module.ident=name} gives a mapping from an Ur name for a value to a JavaScript name.
adamc@897 2201 \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 2202 \item \texttt{script URL} requests inclusion of a JavaScript source file within application HTML.
adamc@897 2203 \item \texttt{serverOnly Module.ident} registers a value as being allowed only in server-side code.
adamc@897 2204 \end{itemize}
adamc@897 2205
adamc@897 2206 \subsection{Writing C FFI Code}
adamc@897 2207
adamc@897 2208 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 2209
adamc@897 2210 \begin{itemize}
adamc@897 2211 \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 2212 \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 2213 \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*}.
adamc@897 2214 \end{itemize}
adamc@897 2215
adamc@897 2216 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 2217 \begin{itemize}
adamc@897 2218 \item \begin{verbatim}
adamc@897 2219 void uw_error(uw_context, failure_kind, const char *fmt, ...);
adamc@897 2220 \end{verbatim}
adamc@897 2221 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 2222
adam@1329 2223 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 2224
adamc@897 2225 \item \begin{verbatim}
adam@1469 2226 void uw_set_error_message(uw_context, const char *fmt, ...);
adam@1469 2227 \end{verbatim}
adam@1469 2228 This simpler form of \texttt{uw\_error()} saves an error message without immediately aborting execution.
adam@1469 2229
adam@1469 2230 \item \begin{verbatim}
adamc@897 2231 void uw_push_cleanup(uw_context, void (*func)(void *), void *arg);
adamc@897 2232 void uw_pop_cleanup(uw_context);
adamc@897 2233 \end{verbatim}
adam@1329 2234 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 2235
adam@1329 2236 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 2237
adamc@897 2238 \item \begin{verbatim}
adamc@897 2239 void *uw_malloc(uw_context, size_t);
adamc@897 2240 \end{verbatim}
adam@1329 2241 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 2242
adam@1329 2243 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 2244
adamc@897 2245 \item \begin{verbatim}
adamc@897 2246 typedef void (*uw_callback)(void *);
adam@1328 2247 typedef void (*uw_callback_with_retry)(void *, int will_retry);
adamc@897 2248 void uw_register_transactional(uw_context, void *data, uw_callback commit,
adam@1328 2249 uw_callback rollback, uw_callback_with_retry free);
adamc@897 2250 \end{verbatim}
adam@1328 2251 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 2252
adamc@1085 2253 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 2254
adam@1329 2255 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 2256
adam@1329 2257 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 2258
adam@1469 2259 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 2260
adamc@1085 2261 \item \begin{verbatim}
adamc@1085 2262 void *uw_get_global(uw_context, char *name);
adamc@1085 2263 void uw_set_global(uw_context, char *name, void *data, uw_callback free);
adamc@1085 2264 \end{verbatim}
adam@1329 2265 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 2266
adamc@897 2267 \end{itemize}
adamc@897 2268
adamc@897 2269 \subsection{Writing JavaScript FFI Code}
adamc@897 2270
adamc@897 2271 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 2272
adamc@897 2273 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 2274
adamc@897 2275 \begin{itemize}
adamc@897 2276 \item Integers, floats, strings, characters, and booleans are represented in the usual JavaScript way.
adamc@985 2277 \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)}.
adamc@897 2278 \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 2279 \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 2280 \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.
adamc@897 2281 \end{itemize}
adamc@897 2282
adamc@897 2283 It is possible to write JavaScript FFI code that interacts with the functional-reactive structure of a document, but this version of the manual doesn't cover the details.
adamc@897 2284
adamc@897 2285
adamc@552 2286 \section{Compiler Phases}
adamc@552 2287
adamc@552 2288 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 2289
adamc@552 2290 In this section, we step through the main phases of compilation, noting what consequences each phase has for effective programming.
adamc@552 2291
adamc@552 2292 \subsection{Parse}
adamc@552 2293
adamc@552 2294 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 2295
adamc@552 2296 \subsection{Elaborate}
adamc@552 2297
adamc@552 2298 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 2299
adam@1378 2300 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 2301
adamc@552 2302 \subsection{Unnest}
adamc@552 2303
adamc@552 2304 Named local function definitions are moved to the top level, to avoid the need to generate closures.
adamc@552 2305
adamc@552 2306 \subsection{Corify}
adamc@552 2307
adamc@552 2308 Module system features are compiled away, through inlining of functor definitions at application sites. Afterward, most abstraction boundaries are broken, facilitating optimization.
adamc@552 2309
adamc@552 2310 \subsection{Especialize}
adamc@552 2311
adam@1356 2312 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 2313
adamc@552 2314 \subsection{Untangle}
adamc@552 2315
adamc@552 2316 Remove unnecessary mutual recursion, splitting recursive groups into strongly-connected components.
adamc@552 2317
adamc@552 2318 \subsection{Shake}
adamc@552 2319
adamc@552 2320 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 2321
adamc@661 2322 \subsection{Rpcify}
adamc@661 2323
adamc@661 2324 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 2325
adamc@661 2326 \subsection{Untangle, Shake}
adamc@661 2327
adamc@661 2328 Repeat these simplifications.
adamc@661 2329
adamc@553 2330 \subsection{\label{tag}Tag}
adamc@552 2331
adamc@552 2332 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 2333
adamc@552 2334 \subsection{Reduce}
adamc@552 2335
adamc@552 2336 Apply definitional equality rules to simplify the program as much as possible. This effectively includes inlining of every non-recursive definition.
adamc@552 2337
adamc@552 2338 \subsection{Unpoly}
adamc@552 2339
adamc@552 2340 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 2341
adamc@552 2342 \subsection{Specialize}
adamc@552 2343
adamc@558 2344 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 2345
adamc@552 2346 \subsection{Shake}
adamc@552 2347
adamc@558 2348 Here the compiler repeats the earlier Shake phase.
adamc@552 2349
adamc@552 2350 \subsection{Monoize}
adamc@552 2351
adamc@552 2352 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 2353
adamc@552 2354 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 2355
adamc@552 2356 \subsection{MonoOpt}
adamc@552 2357
adamc@552 2358 Simple algebraic laws are applied to simplify the program, focusing especially on efficient imperative generation of HTML pages.
adamc@552 2359
adamc@552 2360 \subsection{MonoUntangle}
adamc@552 2361
adamc@552 2362 Unnecessary mutual recursion is broken up again.
adamc@552 2363
adamc@552 2364 \subsection{MonoReduce}
adamc@552 2365
adamc@552 2366 Equivalents of the definitional equality rules are applied to simplify programs, with inlining again playing a major role.
adamc@552 2367
adamc@552 2368 \subsection{MonoShake, MonoOpt}
adamc@552 2369
adamc@552 2370 Unneeded declarations are removed, and basic optimizations are repeated.
adamc@552 2371
adamc@552 2372 \subsection{Fuse}
adamc@552 2373
adamc@552 2374 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 2375
adamc@552 2376 \subsection{MonoUntangle, MonoShake}
adamc@552 2377
adamc@552 2378 Fuse often creates more opportunities to remove spurious mutual recursion.
adamc@552 2379
adamc@552 2380 \subsection{Pathcheck}
adamc@552 2381
adamc@552 2382 The compiler checks that no link or action name has been used more than once.
adamc@552 2383
adamc@552 2384 \subsection{Cjrize}
adamc@552 2385
adamc@552 2386 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 2387
adamc@552 2388 \subsection{C Compilation and Linking}
adamc@552 2389
adam@1523 2390 The output of the last phase is pretty-printed as C source code and passed to the C compiler.
adamc@552 2391
adamc@552 2392
adamc@524 2393 \end{document}