annotate doc/manual.tex @ 1355:ccf1d445b794

Hopeful fix to stop Especialize infinite looping
author Adam Chlipala <adam@chlipala.net>
date Tue, 21 Dec 2010 13:57:12 -0500
parents 1b286f2309bc
children 977901cb52cc
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
adamc@896 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 in your execution path; MLton, the whole-program optimizing compiler for Standard ML; and the mhash 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}
adamc@896 61 apt-get install mlton libmhash-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}
adamc@896 79 apt-get install postgresql-8.3 mysql-server-5.0
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
adamc@555 88 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 GCC on every invocation.
adamc@555 89
adamc@555 90 \begin{verbatim}
adamc@555 91 GCCARGS=-fnested-functions ./configure
adamc@555 92 \end{verbatim}
adamc@555 93
adamc@1137 94 Some Mac OS X users have reported needing to use this particular GCCARGS value.
adamc@1137 95
adamc@1161 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). One OS X user reported needing to run \texttt{./configure} with \texttt{CFLAGS=-I/opt/local/include}, since this directory wound up holding a header file associated with a \texttt{libmhash} package installed via DarwinPorts. Further, to get libpq to link, another user reported setting \texttt{GCCARGS="-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}
adamc@783 137 \item \texttt{[allow|deny] [url|mime] PATTERN} registers a rule governing which URLs or MIME types are allowed in this application. The first such rule to match a URL or MIME type determines the verdict. If \texttt{PATTERN} ends in \texttt{*}, it is interpreted as a prefix rule. Otherwise, a string must match it exactly.
adamc@1171 138 \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 has only session-local side effects.
adamc@783 139 \item \texttt{clientOnly Module.ident} registers an FFI function or transaction that may only be run in client browsers.
adamc@783 140 \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@783 141 \item \texttt{database DBSTRING} sets the string to pass to libpq to open a database connection.
adamc@783 142 \item \texttt{debug} saves some intermediate C files, which is mostly useful to help in debugging the compiler itself.
adamc@783 143 \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@783 144 \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@783 145 \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 146 \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@783 147 \item \texttt{jsFunc Module.ident=name} gives the JavaScript name of an FFI value.
adamc@1089 148 \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 149 \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 150 \begin{itemize}
adam@1309 151 \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 152 \item \texttt{database}: maximum size of database files (currently only used by SQLite)
adam@1309 153 \item \texttt{deltas}: maximum number of messages sendable in a single request handler with \texttt{Basis.send}
adam@1309 154 \item \texttt{globals}: maximum number of global variables that FFI libraries may set in a single request context
adam@1309 155 \item \texttt{headers}: maximum size (in bytes) of per-request buffer used to hold HTTP headers for generated pages
adam@1309 156 \item \texttt{heap}: maximum size (in bytes) of per-request heap for dynamically-allocated data
adam@1309 157 \item \texttt{inputs}: maximum number of top-level form fields per request
adam@1309 158 \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 159 \item \texttt{page}: maximum size (in bytes) of per-request buffer used to hold HTML content of generated pages
adam@1309 160 \item \texttt{script}: maximum size (in bytes) of per-request buffer used to hold JavaScript content of generated pages
adam@1309 161 \item \texttt{subinputs}: maximum number of form fields per request, excluding top-level fields
adam@1309 162 \item \texttt{time}: maximum running time of a single page request, in units of approximately 0.1 seconds
adam@1309 163 \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 164 \end{itemize}
adamc@783 165 \item \texttt{link FILENAME} adds \texttt{FILENAME} to the list of files to be passed to the GCC linker at the end of compilation. This is most useful for importing extra libraries needed by new FFI modules.
adam@1332 166 \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@1297 167 \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@852 168 \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@783 169 \item \texttt{prefix PREFIX} sets the prefix included before every URI within the generated application. The default is \texttt{/}.
adamc@783 170 \item \texttt{profile} generates an executable that may be used with gprof.
adam@1300 171 \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 172 \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@783 173 \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@783 174 \item \texttt{serverOnly Module.ident} registers an FFI function or transaction that may only be run on the server.
adamc@1164 175 \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@783 176 \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@783 177 \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@783 178 \end{itemize}
adamc@701 179
adamc@701 180
adamc@557 181 \subsection{Building an Application}
adamc@557 182
adamc@557 183 To compile project \texttt{P.urp}, simply run
adamc@557 184 \begin{verbatim}
adamc@557 185 urweb P
adamc@557 186 \end{verbatim}
adamc@1198 187 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@557 188
adamc@557 189 To time how long the different compiler phases run, without generating an executable, run
adamc@557 190 \begin{verbatim}
adamc@557 191 urweb -timing P
adamc@557 192 \end{verbatim}
adamc@557 193
adamc@1086 194 To stop the compilation process after type-checking, run
adamc@1086 195 \begin{verbatim}
adamc@1086 196 urweb -tc P
adamc@1086 197 \end{verbatim}
adamc@1086 198
adamc@1170 199 To output information relevant to CSS stylesheets (and not finish regular compilation), run
adamc@1170 200 \begin{verbatim}
adamc@1170 201 urweb -css P
adamc@1170 202 \end{verbatim}
adamc@1170 203 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 204
adamc@896 205 Some other command-line parameters are accepted:
adamc@896 206 \begin{itemize}
adamc@896 207 \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@896 208
adamc@896 209 \item \texttt{-dbms [postgres|mysql|sqlite]}: Sets the database backend to use.
adamc@896 210 \begin{itemize}
adamc@896 211 \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@896 212
adamc@896 213 A command sequence like this can initialize a Postgres database, using a file \texttt{app.sql} generated by the compiler:
adamc@896 214 \begin{verbatim}
adamc@896 215 createdb app
adamc@896 216 psql -f app.sql app
adamc@896 217 \end{verbatim}
adamc@896 218
adamc@896 219 \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@896 220
adamc@896 221 A command sequence like this can initialize a MySQL database:
adamc@896 222 \begin{verbatim}
adamc@896 223 echo "CREATE DATABASE app" | mysql
adamc@896 224 mysql -D app <app.sql
adamc@896 225 \end{verbatim}
adamc@896 226
adamc@896 227 \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@896 228
adamc@896 229 A command like this can initialize an SQLite database:
adamc@896 230 \begin{verbatim}
adamc@896 231 sqlite3 path/to/database/file <app.sql
adamc@896 232 \end{verbatim}
adamc@896 233 \end{itemize}
adamc@896 234
adam@1309 235 \item \texttt{-limit class num}: Equivalent to the \texttt{limit} directive from \texttt{.urp} files
adam@1309 236
adamc@896 237 \item \texttt{-output FILENAME}: Set where the application executable is written.
adamc@896 238
adamc@1127 239 \item \texttt{-path NAME VALUE}: Set the value of path variable \texttt{\$NAME} to \texttt{VALUE}, for use in \texttt{.urp} files.
adamc@1127 240
adam@1335 241 \item \texttt{-prefix PREFIX}: Equivalent to the \texttt{prefix} directive from \texttt{.urp} files
adam@1335 242
adamc@896 243 \item \texttt{-protocol [http|cgi|fastcgi]}: Set the protocol that the generated application speaks.
adamc@896 244 \begin{itemize}
adamc@896 245 \item \texttt{http}: This is the default. It is for building standalone web servers that can be accessed by web browsers directly.
adamc@896 246
adamc@896 247 \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@896 248
adamc@896 249 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@896 250 \begin{verbatim}
adamc@896 251 ScriptAlias /Hello /path/to/hello.exe
adamc@896 252 \end{verbatim}
adamc@896 253
adamc@1163 254 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 255 \begin{verbatim}
adamc@1163 256 Options +ExecCGI
adamc@1163 257 AddHandler cgi-script .exe
adamc@1163 258 \end{verbatim}
adamc@1163 259
adamc@1163 260 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 261 \begin{verbatim}
adamc@1163 262 prefix /dir/script.exe/
adamc@1163 263 \end{verbatim}
adamc@1163 264
adamc@1163 265 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 266
adamc@1164 267 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 268
adamc@896 269 \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@896 270
adamc@896 271 To configure a FastCGI program with Apache, one could combine the above \texttt{ScriptAlias} line with a line like this:
adamc@896 272 \begin{verbatim}
adamc@896 273 FastCgiServer /path/to/hello.exe -idle-timeout 99999
adamc@896 274 \end{verbatim}
adamc@896 275 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@896 276
adamc@896 277 Here is some lighttpd configuration for the same application.
adamc@896 278 \begin{verbatim}
adamc@896 279 fastcgi.server = (
adamc@896 280 "/Hello/" =>
adamc@896 281 (( "bin-path" => "/path/to/hello.exe",
adamc@896 282 "socket" => "/tmp/hello",
adamc@896 283 "check-local" => "disable",
adamc@896 284 "docroot" => "/",
adamc@896 285 "max-procs" => "1"
adamc@896 286 ))
adamc@896 287 )
adamc@896 288 \end{verbatim}
adamc@896 289 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@896 290
adamc@896 291 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.
adamc@896 292 \end{itemize}
adamc@896 293
adamc@1127 294 \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 295
adamc@1164 296 \item \texttt{-sigfile PATH}: Same as the \texttt{sigfile} directive in \texttt{.urp} files
adamc@1164 297
adamc@896 298 \item \texttt{-sql FILENAME}: Set where a database set-up SQL script is written.
adamc@1095 299
adamc@1095 300 \item \texttt{-static}: Link the runtime system statically. The default is to link against dynamic libraries.
adamc@896 301 \end{itemize}
adamc@896 302
adam@1297 303 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@556 304
adamc@529 305 \section{Ur Syntax}
adamc@529 306
adamc@784 307 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@524 308
adamc@524 309 \subsection{Lexical Conventions}
adamc@524 310
adamc@524 311 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@524 312
adamc@524 313 \begin{center}
adamc@524 314 \begin{tabular}{rl}
adamc@524 315 \textbf{\LaTeX} & \textbf{ASCII} \\
adamc@524 316 $\to$ & \cd{->} \\
adamc@652 317 $\longrightarrow$ & \cd{-->} \\
adamc@524 318 $\times$ & \cd{*} \\
adamc@524 319 $\lambda$ & \cd{fn} \\
adamc@524 320 $\Rightarrow$ & \cd{=>} \\
adamc@652 321 $\Longrightarrow$ & \cd{==>} \\
adamc@529 322 $\neq$ & \cd{<>} \\
adamc@529 323 $\leq$ & \cd{<=} \\
adamc@529 324 $\geq$ & \cd{>=} \\
adamc@524 325 \\
adamc@524 326 $x$ & Normal textual identifier, not beginning with an uppercase letter \\
adamc@525 327 $X$ & Normal textual identifier, beginning with an uppercase letter \\
adamc@524 328 \end{tabular}
adamc@524 329 \end{center}
adamc@524 330
adamc@525 331 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@524 332
adamc@873 333 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@526 334
adamc@527 335 This version of the manual doesn't include operator precedences; see \texttt{src/urweb.grm} for that.
adamc@527 336
adam@1297 337 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 338
adamc@552 339 \subsection{\label{core}Core Syntax}
adamc@524 340
adamc@524 341 \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@524 342 $$\begin{array}{rrcll}
adamc@524 343 \textrm{Kinds} & \kappa &::=& \mt{Type} & \textrm{proper types} \\
adamc@525 344 &&& \mt{Unit} & \textrm{the trivial constructor} \\
adamc@525 345 &&& \mt{Name} & \textrm{field names} \\
adamc@525 346 &&& \kappa \to \kappa & \textrm{type-level functions} \\
adamc@525 347 &&& \{\kappa\} & \textrm{type-level records} \\
adamc@525 348 &&& (\kappa\times^+) & \textrm{type-level tuples} \\
adamc@652 349 &&& X & \textrm{variable} \\
adamc@652 350 &&& X \longrightarrow k & \textrm{kind-polymorphic type-level function} \\
adamc@529 351 &&& \_\_ & \textrm{wildcard} \\
adamc@525 352 &&& (\kappa) & \textrm{explicit precedence} \\
adamc@524 353 \end{array}$$
adamc@524 354
adamc@524 355 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@524 356 $$\begin{array}{rrcll}
adamc@524 357 \textrm{Explicitness} & ? &::=& :: & \textrm{explicit} \\
adamc@558 358 &&& ::: & \textrm{implicit}
adamc@524 359 \end{array}$$
adamc@524 360
adamc@524 361 \emph{Constructors} are the main class of compile-time-only data. They include proper types and are classified by kinds.
adamc@524 362 $$\begin{array}{rrcll}
adamc@524 363 \textrm{Constructors} & c, \tau &::=& (c) :: \kappa & \textrm{kind annotation} \\
adamc@530 364 &&& \hat{x} & \textrm{constructor variable} \\
adamc@524 365 \\
adamc@525 366 &&& \tau \to \tau & \textrm{function type} \\
adamc@525 367 &&& x \; ? \; \kappa \to \tau & \textrm{polymorphic function type} \\
adamc@652 368 &&& X \longrightarrow \tau & \textrm{kind-polymorphic function type} \\
adamc@525 369 &&& \$ c & \textrm{record type} \\
adamc@524 370 \\
adamc@525 371 &&& c \; c & \textrm{type-level function application} \\
adamc@530 372 &&& \lambda x \; :: \; \kappa \Rightarrow c & \textrm{type-level function abstraction} \\
adamc@524 373 \\
adamc@652 374 &&& X \Longrightarrow c & \textrm{type-level kind-polymorphic function abstraction} \\
adamc@655 375 &&& c [\kappa] & \textrm{type-level kind-polymorphic function application} \\
adamc@652 376 \\
adamc@525 377 &&& () & \textrm{type-level unit} \\
adamc@525 378 &&& \#X & \textrm{field name} \\
adamc@524 379 \\
adamc@525 380 &&& [(c = c)^*] & \textrm{known-length type-level record} \\
adamc@525 381 &&& c \rc c & \textrm{type-level record concatenation} \\
adamc@652 382 &&& \mt{map} & \textrm{type-level record map} \\
adamc@524 383 \\
adamc@558 384 &&& (c,^+) & \textrm{type-level tuple} \\
adamc@525 385 &&& c.n & \textrm{type-level tuple projection ($n \in \mathbb N^+$)} \\
adamc@524 386 \\
adamc@652 387 &&& [c \sim c] \Rightarrow \tau & \textrm{guarded type} \\
adamc@524 388 \\
adamc@529 389 &&& \_ :: \kappa & \textrm{wildcard} \\
adamc@525 390 &&& (c) & \textrm{explicit precedence} \\
adamc@530 391 \\
adamc@530 392 \textrm{Qualified uncapitalized variables} & \hat{x} &::=& x & \textrm{not from a module} \\
adamc@530 393 &&& M.x & \textrm{projection from a module} \\
adamc@525 394 \end{array}$$
adamc@525 395
adamc@655 396 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@655 397
adamc@525 398 Modules of the module system are described by \emph{signatures}.
adamc@525 399 $$\begin{array}{rrcll}
adamc@525 400 \textrm{Signatures} & S &::=& \mt{sig} \; s^* \; \mt{end} & \textrm{constant} \\
adamc@525 401 &&& X & \textrm{variable} \\
adamc@525 402 &&& \mt{functor}(X : S) : S & \textrm{functor} \\
adamc@529 403 &&& S \; \mt{where} \; \mt{con} \; x = c & \textrm{concretizing an abstract constructor} \\
adamc@525 404 &&& M.X & \textrm{projection from a module} \\
adamc@525 405 \\
adamc@525 406 \textrm{Signature items} & s &::=& \mt{con} \; x :: \kappa & \textrm{abstract constructor} \\
adamc@525 407 &&& \mt{con} \; x :: \kappa = c & \textrm{concrete constructor} \\
adamc@528 408 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529 409 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@525 410 &&& \mt{val} \; x : \tau & \textrm{value} \\
adamc@525 411 &&& \mt{structure} \; X : S & \textrm{sub-module} \\
adamc@525 412 &&& \mt{signature} \; X = S & \textrm{sub-signature} \\
adamc@525 413 &&& \mt{include} \; S & \textrm{signature inclusion} \\
adamc@525 414 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@654 415 &&& \mt{class} \; x :: \kappa & \textrm{abstract constructor class} \\
adamc@654 416 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@525 417 \\
adamc@525 418 \textrm{Datatype constructors} & dc &::=& X & \textrm{nullary constructor} \\
adamc@525 419 &&& X \; \mt{of} \; \tau & \textrm{unary constructor} \\
adamc@524 420 \end{array}$$
adamc@524 421
adamc@526 422 \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@526 423 $$\begin{array}{rrcll}
adamc@526 424 \textrm{Patterns} & p &::=& \_ & \textrm{wildcard} \\
adamc@526 425 &&& x & \textrm{variable} \\
adamc@526 426 &&& \ell & \textrm{constant} \\
adamc@526 427 &&& \hat{X} & \textrm{nullary constructor} \\
adamc@526 428 &&& \hat{X} \; p & \textrm{unary constructor} \\
adamc@526 429 &&& \{(x = p,)^*\} & \textrm{rigid record pattern} \\
adamc@526 430 &&& \{(x = p,)^+, \ldots\} & \textrm{flexible record pattern} \\
adamc@852 431 &&& p : \tau & \textrm{type annotation} \\
adamc@527 432 &&& (p) & \textrm{explicit precedence} \\
adamc@526 433 \\
adamc@529 434 \textrm{Qualified capitalized variables} & \hat{X} &::=& X & \textrm{not from a module} \\
adamc@526 435 &&& M.X & \textrm{projection from a module} \\
adamc@526 436 \end{array}$$
adamc@526 437
adamc@527 438 \emph{Expressions} are the main run-time entities, corresponding to both ``expressions'' and ``statements'' in mainstream imperative languages.
adamc@527 439 $$\begin{array}{rrcll}
adamc@527 440 \textrm{Expressions} & e &::=& e : \tau & \textrm{type annotation} \\
adamc@529 441 &&& \hat{x} & \textrm{variable} \\
adamc@529 442 &&& \hat{X} & \textrm{datatype constructor} \\
adamc@527 443 &&& \ell & \textrm{constant} \\
adamc@527 444 \\
adamc@527 445 &&& e \; e & \textrm{function application} \\
adamc@527 446 &&& \lambda x : \tau \Rightarrow e & \textrm{function abstraction} \\
adamc@527 447 &&& e [c] & \textrm{polymorphic function application} \\
adamc@852 448 &&& \lambda [x \; ? \; \kappa] \Rightarrow e & \textrm{polymorphic function abstraction} \\
adamc@655 449 &&& e [\kappa] & \textrm{kind-polymorphic function application} \\
adamc@652 450 &&& X \Longrightarrow e & \textrm{kind-polymorphic function abstraction} \\
adamc@527 451 \\
adamc@527 452 &&& \{(c = e,)^*\} & \textrm{known-length record} \\
adamc@527 453 &&& e.c & \textrm{record field projection} \\
adamc@527 454 &&& e \rc e & \textrm{record concatenation} \\
adamc@527 455 &&& e \rcut c & \textrm{removal of a single record field} \\
adamc@527 456 &&& e \rcutM c & \textrm{removal of multiple record fields} \\
adamc@527 457 \\
adamc@527 458 &&& \mt{let} \; ed^* \; \mt{in} \; e \; \mt{end} & \textrm{local definitions} \\
adamc@527 459 \\
adamc@527 460 &&& \mt{case} \; e \; \mt{of} \; (p \Rightarrow e|)^+ & \textrm{pattern matching} \\
adamc@527 461 \\
adamc@654 462 &&& \lambda [c \sim c] \Rightarrow e & \textrm{guarded expression abstraction} \\
adamc@654 463 &&& e \; ! & \textrm{guarded expression application} \\
adamc@527 464 \\
adamc@527 465 &&& \_ & \textrm{wildcard} \\
adamc@527 466 &&& (e) & \textrm{explicit precedence} \\
adamc@527 467 \\
adamc@527 468 \textrm{Local declarations} & ed &::=& \cd{val} \; x : \tau = e & \textrm{non-recursive value} \\
adamc@527 469 &&& \cd{val} \; \cd{rec} \; (x : \tau = e \; \cd{and})^+ & \textrm{mutually-recursive values} \\
adamc@527 470 \end{array}$$
adamc@527 471
adamc@655 472 As with constructors, we include both abstraction and application for kind polymorphism, but applications are only inferred internally.
adamc@655 473
adamc@528 474 \emph{Declarations} primarily bring new symbols into context.
adamc@528 475 $$\begin{array}{rrcll}
adamc@528 476 \textrm{Declarations} & d &::=& \mt{con} \; x :: \kappa = c & \textrm{constructor synonym} \\
adamc@528 477 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529 478 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@528 479 &&& \mt{val} \; x : \tau = e & \textrm{value} \\
adamc@528 480 &&& \mt{val} \; \cd{rec} \; (x : \tau = e \; \mt{and})^+ & \textrm{mutually-recursive values} \\
adamc@528 481 &&& \mt{structure} \; X : S = M & \textrm{module definition} \\
adamc@528 482 &&& \mt{signature} \; X = S & \textrm{signature definition} \\
adamc@528 483 &&& \mt{open} \; M & \textrm{module inclusion} \\
adamc@528 484 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@528 485 &&& \mt{open} \; \mt{constraints} \; M & \textrm{inclusion of just the constraints from a module} \\
adamc@528 486 &&& \mt{table} \; x : c & \textrm{SQL table} \\
adamc@784 487 &&& \mt{view} \; x : c & \textrm{SQL view} \\
adamc@528 488 &&& \mt{sequence} \; x & \textrm{SQL sequence} \\
adamc@535 489 &&& \mt{cookie} \; x : \tau & \textrm{HTTP cookie} \\
adamc@784 490 &&& \mt{style} \; x : \tau & \textrm{CSS class} \\
adamc@654 491 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@1085 492 &&& \mt{task} \; e = e & \textrm{recurring task} \\
adamc@528 493 \\
adamc@529 494 \textrm{Modules} & M &::=& \mt{struct} \; d^* \; \mt{end} & \textrm{constant} \\
adamc@529 495 &&& X & \textrm{variable} \\
adamc@529 496 &&& M.X & \textrm{projection} \\
adamc@529 497 &&& M(M) & \textrm{functor application} \\
adamc@529 498 &&& \mt{functor}(X : S) : S = M & \textrm{functor abstraction} \\
adamc@528 499 \end{array}$$
adamc@528 500
adamc@528 501 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@527 502
adamc@784 503 We omit some extra possibilities in $\mt{table}$ syntax, deferring them to Section \ref{tables}.
adamc@784 504
adamc@529 505 \subsection{Shorthands}
adamc@529 506
adamc@529 507 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@529 508
adamc@529 509 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@529 510
adamc@529 511 A record type may be written $\{(c = c,)^*\}$, which elaborates to $\$[(c = c,)^*]$.
adamc@529 512
adamc@533 513 The notation $[c_1, \ldots, c_n]$ is shorthand for $[c_1 = (), \ldots, c_n = ()]$.
adamc@533 514
adam@1350 515 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@529 516
adamc@852 517 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@529 518
adam@1306 519 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 520
adamc@529 521 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@529 522
adamc@529 523 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@529 524
adamc@654 525 A signature item or declaration $\mt{class} \; x = \lambda y \Rightarrow c$ may be abbreviated $\mt{class} \; x \; y = c$.
adamc@529 526
adam@1354 527 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. 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 non-local variable, or after any application of a non-local 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@529 528
adamc@852 529 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@529 530
adamc@852 531 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@852 532
adamc@852 533 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@529 534
adamc@529 535 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@529 536
adamc@852 537 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@852 538
adamc@853 539 A declaration $\mt{table} \; x : \{(c = c,)^*\}$ is elaborated into $\mt{table} \; x : [(c = c,)^*]$.
adamc@529 540
adamc@529 541 The syntax $\mt{where} \; \mt{type}$ is an alternate form of $\mt{where} \; \mt{con}$.
adamc@529 542
adamc@529 543 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@529 544
adamc@529 545 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@529 546
adamc@784 547 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@529 548
adamc@530 549
adamc@530 550 \section{Static Semantics}
adamc@530 551
adamc@530 552 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@530 553
adamc@530 554 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@530 555 \begin{itemize}
adamc@655 556 \item $\Gamma \vdash \kappa$ expresses kind well-formedness.
adamc@530 557 \item $\Gamma \vdash c :: \kappa$ assigns a kind to a constructor in a context.
adamc@530 558 \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@531 559 \item $\Gamma \vdash c \hookrightarrow C$ proves that record constructor $c$ decomposes into set $C$ of field names and record constructors.
adamc@530 560 \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@530 561 \item $\Gamma \vdash e : \tau$ is a standard typing judgment.
adamc@534 562 \item $\Gamma \vdash p \leadsto \Gamma; \tau$ combines typing of patterns with calculation of which new variables they bind.
adamc@537 563 \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@537 564 \item $\Gamma \vdash S \equiv S$ is the signature equivalence judgment.
adamc@536 565 \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@530 566 \item $\Gamma \vdash M : S$ is the module signature checking judgment.
adamc@537 567 \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@539 568 \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@530 569 \end{itemize}
adamc@530 570
adamc@655 571
adamc@655 572 \subsection{Kind Well-Formedness}
adamc@655 573
adamc@655 574 $$\infer{\Gamma \vdash \mt{Type}}{}
adamc@655 575 \quad \infer{\Gamma \vdash \mt{Unit}}{}
adamc@655 576 \quad \infer{\Gamma \vdash \mt{Name}}{}
adamc@655 577 \quad \infer{\Gamma \vdash \kappa_1 \to \kappa_2}{
adamc@655 578 \Gamma \vdash \kappa_1
adamc@655 579 & \Gamma \vdash \kappa_2
adamc@655 580 }
adamc@655 581 \quad \infer{\Gamma \vdash \{\kappa\}}{
adamc@655 582 \Gamma \vdash \kappa
adamc@655 583 }
adamc@655 584 \quad \infer{\Gamma \vdash (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@655 585 \forall i: \Gamma \vdash \kappa_i
adamc@655 586 }$$
adamc@655 587
adamc@655 588 $$\infer{\Gamma \vdash X}{
adamc@655 589 X \in \Gamma
adamc@655 590 }
adamc@655 591 \quad \infer{\Gamma \vdash X \longrightarrow \kappa}{
adamc@655 592 \Gamma, X \vdash \kappa
adamc@655 593 }$$
adamc@655 594
adamc@530 595 \subsection{Kinding}
adamc@530 596
adamc@655 597 We write $[X \mapsto \kappa_1]\kappa_2$ for capture-avoiding substitution of $\kappa_1$ for $X$ in $\kappa_2$.
adamc@655 598
adamc@530 599 $$\infer{\Gamma \vdash (c) :: \kappa :: \kappa}{
adamc@530 600 \Gamma \vdash c :: \kappa
adamc@530 601 }
adamc@530 602 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530 603 x :: \kappa \in \Gamma
adamc@530 604 }
adamc@530 605 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530 606 x :: \kappa = c \in \Gamma
adamc@530 607 }$$
adamc@530 608
adamc@530 609 $$\infer{\Gamma \vdash M.x :: \kappa}{
adamc@537 610 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 611 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = \kappa
adamc@530 612 }
adamc@530 613 \quad \infer{\Gamma \vdash M.x :: \kappa}{
adamc@537 614 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 615 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@530 616 }$$
adamc@530 617
adamc@530 618 $$\infer{\Gamma \vdash \tau_1 \to \tau_2 :: \mt{Type}}{
adamc@530 619 \Gamma \vdash \tau_1 :: \mt{Type}
adamc@530 620 & \Gamma \vdash \tau_2 :: \mt{Type}
adamc@530 621 }
adamc@530 622 \quad \infer{\Gamma \vdash x \; ? \: \kappa \to \tau :: \mt{Type}}{
adamc@530 623 \Gamma, x :: \kappa \vdash \tau :: \mt{Type}
adamc@530 624 }
adamc@655 625 \quad \infer{\Gamma \vdash X \longrightarrow \tau :: \mt{Type}}{
adamc@655 626 \Gamma, X \vdash \tau :: \mt{Type}
adamc@655 627 }
adamc@530 628 \quad \infer{\Gamma \vdash \$c :: \mt{Type}}{
adamc@530 629 \Gamma \vdash c :: \{\mt{Type}\}
adamc@530 630 }$$
adamc@530 631
adamc@530 632 $$\infer{\Gamma \vdash c_1 \; c_2 :: \kappa_2}{
adamc@530 633 \Gamma \vdash c_1 :: \kappa_1 \to \kappa_2
adamc@530 634 & \Gamma \vdash c_2 :: \kappa_1
adamc@530 635 }
adamc@530 636 \quad \infer{\Gamma \vdash \lambda x \; :: \; \kappa_1 \Rightarrow c :: \kappa_1 \to \kappa_2}{
adamc@530 637 \Gamma, x :: \kappa_1 \vdash c :: \kappa_2
adamc@530 638 }$$
adamc@530 639
adamc@655 640 $$\infer{\Gamma \vdash c[\kappa'] :: [X \mapsto \kappa']\kappa}{
adamc@655 641 \Gamma \vdash c :: X \to \kappa
adamc@655 642 & \Gamma \vdash \kappa'
adamc@655 643 }
adamc@655 644 \quad \infer{\Gamma \vdash X \Longrightarrow c :: X \to \kappa}{
adamc@655 645 \Gamma, X \vdash c :: \kappa
adamc@655 646 }$$
adamc@655 647
adamc@530 648 $$\infer{\Gamma \vdash () :: \mt{Unit}}{}
adamc@530 649 \quad \infer{\Gamma \vdash \#X :: \mt{Name}}{}$$
adamc@530 650
adamc@530 651 $$\infer{\Gamma \vdash [\overline{c_i = c'_i}] :: \{\kappa\}}{
adamc@530 652 \forall i: \Gamma \vdash c_i : \mt{Name}
adamc@530 653 & \Gamma \vdash c'_i :: \kappa
adamc@530 654 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@530 655 }
adamc@530 656 \quad \infer{\Gamma \vdash c_1 \rc c_2 :: \{\kappa\}}{
adamc@530 657 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530 658 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@530 659 & \Gamma \vdash c_1 \sim c_2
adamc@530 660 }$$
adamc@530 661
adamc@655 662 $$\infer{\Gamma \vdash \mt{map} :: (\kappa_1 \to \kappa_2) \to \{\kappa_1\} \to \{\kappa_2\}}{}$$
adamc@530 663
adamc@573 664 $$\infer{\Gamma \vdash (\overline c) :: (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@573 665 \forall i: \Gamma \vdash c_i :: \kappa_i
adamc@530 666 }
adamc@573 667 \quad \infer{\Gamma \vdash c.i :: \kappa_i}{
adamc@573 668 \Gamma \vdash c :: (\kappa_1 \times \ldots \times \kappa_n)
adamc@530 669 }$$
adamc@530 670
adamc@655 671 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow \tau :: \mt{Type}}{
adamc@655 672 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530 673 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@655 674 & \Gamma, c_1 \sim c_2 \vdash \tau :: \mt{Type}
adamc@530 675 }$$
adamc@530 676
adamc@531 677 \subsection{Record Disjointness}
adamc@531 678
adamc@531 679 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@558 680 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@558 681 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@558 682 & \forall c'_1 \in C_1, c'_2 \in C_2: \Gamma \vdash c'_1 \sim c'_2
adamc@531 683 }
adamc@531 684 \quad \infer{\Gamma \vdash X \sim X'}{
adamc@531 685 X \neq X'
adamc@531 686 }$$
adamc@531 687
adamc@531 688 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@531 689 c'_1 \sim c'_2 \in \Gamma
adamc@558 690 & \Gamma \vdash c'_1 \hookrightarrow C_1
adamc@558 691 & \Gamma \vdash c'_2 \hookrightarrow C_2
adamc@558 692 & c_1 \in C_1
adamc@558 693 & c_2 \in C_2
adamc@531 694 }$$
adamc@531 695
adamc@531 696 $$\infer{\Gamma \vdash c \hookrightarrow \{c\}}{}
adamc@531 697 \quad \infer{\Gamma \vdash [\overline{c = c'}] \hookrightarrow \{\overline{c}\}}{}
adamc@531 698 \quad \infer{\Gamma \vdash c_1 \rc c_2 \hookrightarrow C_1 \cup C_2}{
adamc@531 699 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@531 700 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@531 701 }
adamc@531 702 \quad \infer{\Gamma \vdash c \hookrightarrow C}{
adamc@531 703 \Gamma \vdash c \equiv c'
adamc@531 704 & \Gamma \vdash c' \hookrightarrow C
adamc@531 705 }
adamc@531 706 \quad \infer{\Gamma \vdash \mt{map} \; f \; c \hookrightarrow C}{
adamc@531 707 \Gamma \vdash c \hookrightarrow C
adamc@531 708 }$$
adamc@531 709
adamc@541 710 \subsection{\label{definitional}Definitional Equality}
adamc@532 711
adamc@655 712 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@532 713
adamc@532 714 $$\infer{\Gamma \vdash c \equiv c}{}
adamc@532 715 \quad \infer{\Gamma \vdash c_1 \equiv c_2}{
adamc@532 716 \Gamma \vdash c_2 \equiv c_1
adamc@532 717 }
adamc@532 718 \quad \infer{\Gamma \vdash c_1 \equiv c_3}{
adamc@532 719 \Gamma \vdash c_1 \equiv c_2
adamc@532 720 & \Gamma \vdash c_2 \equiv c_3
adamc@532 721 }
adamc@532 722 \quad \infer{\Gamma \vdash \mathcal C[c_1] \equiv \mathcal C[c_2]}{
adamc@532 723 \Gamma \vdash c_1 \equiv c_2
adamc@532 724 }$$
adamc@532 725
adamc@532 726 $$\infer{\Gamma \vdash x \equiv c}{
adamc@532 727 x :: \kappa = c \in \Gamma
adamc@532 728 }
adamc@532 729 \quad \infer{\Gamma \vdash M.x \equiv c}{
adamc@537 730 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 731 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@532 732 }
adamc@532 733 \quad \infer{\Gamma \vdash (\overline c).i \equiv c_i}{}$$
adamc@532 734
adamc@532 735 $$\infer{\Gamma \vdash (\lambda x :: \kappa \Rightarrow c) \; c' \equiv [x \mapsto c'] c}{}
adamc@655 736 \quad \infer{\Gamma \vdash (X \Longrightarrow c) [\kappa] \equiv [X \mapsto \kappa] c}{}$$
adamc@655 737
adamc@655 738 $$\infer{\Gamma \vdash c_1 \rc c_2 \equiv c_2 \rc c_1}{}
adamc@532 739 \quad \infer{\Gamma \vdash c_1 \rc (c_2 \rc c_3) \equiv (c_1 \rc c_2) \rc c_3}{}$$
adamc@532 740
adamc@532 741 $$\infer{\Gamma \vdash [] \rc c \equiv c}{}
adamc@532 742 \quad \infer{\Gamma \vdash [\overline{c_1 = c'_1}] \rc [\overline{c_2 = c'_2}] \equiv [\overline{c_1 = c'_1}, \overline{c_2 = c'_2}]}{}$$
adamc@532 743
adamc@655 744 $$\infer{\Gamma \vdash \mt{map} \; f \; [] \equiv []}{}
adamc@655 745 \quad \infer{\Gamma \vdash \mt{map} \; f \; ([c_1 = c_2] \rc c) \equiv [c_1 = f \; c_2] \rc \mt{map} \; f \; c}{}$$
adamc@532 746
adamc@532 747 $$\infer{\Gamma \vdash \mt{map} \; (\lambda x \Rightarrow x) \; c \equiv c}{}
adamc@655 748 \quad \infer{\Gamma \vdash \mt{map} \; f \; (\mt{map} \; f' \; c)
adamc@655 749 \equiv \mt{map} \; (\lambda x \Rightarrow f \; (f' \; x)) \; c}{}$$
adamc@532 750
adamc@532 751 $$\infer{\Gamma \vdash \mt{map} \; f \; (c_1 \rc c_2) \equiv \mt{map} \; f \; c_1 \rc \mt{map} \; f \; c_2}{}$$
adamc@531 752
adamc@534 753 \subsection{Expression Typing}
adamc@533 754
adamc@873 755 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@533 756
adamc@533 757 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@533 758
adamc@533 759 $$\infer{\Gamma \vdash e : \tau : \tau}{
adamc@533 760 \Gamma \vdash e : \tau
adamc@533 761 }
adamc@533 762 \quad \infer{\Gamma \vdash e : \tau}{
adamc@533 763 \Gamma \vdash e : \tau'
adamc@533 764 & \Gamma \vdash \tau' \equiv \tau
adamc@533 765 }
adamc@533 766 \quad \infer{\Gamma \vdash \ell : T(\ell)}{}$$
adamc@533 767
adamc@533 768 $$\infer{\Gamma \vdash x : \mathcal I(\tau)}{
adamc@533 769 x : \tau \in \Gamma
adamc@533 770 }
adamc@533 771 \quad \infer{\Gamma \vdash M.x : \mathcal I(\tau)}{
adamc@537 772 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 773 & \mt{proj}(M, \overline{s}, \mt{val} \; x) = \tau
adamc@533 774 }
adamc@533 775 \quad \infer{\Gamma \vdash X : \mathcal I(\tau)}{
adamc@533 776 X : \tau \in \Gamma
adamc@533 777 }
adamc@533 778 \quad \infer{\Gamma \vdash M.X : \mathcal I(\tau)}{
adamc@537 779 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 780 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \tau
adamc@533 781 }$$
adamc@533 782
adamc@533 783 $$\infer{\Gamma \vdash e_1 \; e_2 : \tau_2}{
adamc@533 784 \Gamma \vdash e_1 : \tau_1 \to \tau_2
adamc@533 785 & \Gamma \vdash e_2 : \tau_1
adamc@533 786 }
adamc@533 787 \quad \infer{\Gamma \vdash \lambda x : \tau_1 \Rightarrow e : \tau_1 \to \tau_2}{
adamc@533 788 \Gamma, x : \tau_1 \vdash e : \tau_2
adamc@533 789 }$$
adamc@533 790
adamc@533 791 $$\infer{\Gamma \vdash e [c] : [x \mapsto c]\tau}{
adamc@533 792 \Gamma \vdash e : x :: \kappa \to \tau
adamc@533 793 & \Gamma \vdash c :: \kappa
adamc@533 794 }
adamc@852 795 \quad \infer{\Gamma \vdash \lambda [x \; ? \; \kappa] \Rightarrow e : x \; ? \; \kappa \to \tau}{
adamc@533 796 \Gamma, x :: \kappa \vdash e : \tau
adamc@533 797 }$$
adamc@533 798
adamc@655 799 $$\infer{\Gamma \vdash e [\kappa] : [X \mapsto \kappa]\tau}{
adamc@655 800 \Gamma \vdash e : X \longrightarrow \tau
adamc@655 801 & \Gamma \vdash \kappa
adamc@655 802 }
adamc@655 803 \quad \infer{\Gamma \vdash X \Longrightarrow e : X \longrightarrow \tau}{
adamc@655 804 \Gamma, X \vdash e : \tau
adamc@655 805 }$$
adamc@655 806
adamc@533 807 $$\infer{\Gamma \vdash \{\overline{c = e}\} : \{\overline{c : \tau}\}}{
adamc@533 808 \forall i: \Gamma \vdash c_i :: \mt{Name}
adamc@533 809 & \Gamma \vdash e_i : \tau_i
adamc@533 810 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@533 811 }
adamc@533 812 \quad \infer{\Gamma \vdash e.c : \tau}{
adamc@533 813 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533 814 }
adamc@533 815 \quad \infer{\Gamma \vdash e_1 \rc e_2 : \$(c_1 \rc c_2)}{
adamc@533 816 \Gamma \vdash e_1 : \$c_1
adamc@533 817 & \Gamma \vdash e_2 : \$c_2
adamc@573 818 & \Gamma \vdash c_1 \sim c_2
adamc@533 819 }$$
adamc@533 820
adamc@533 821 $$\infer{\Gamma \vdash e \rcut c : \$c'}{
adamc@533 822 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533 823 }
adamc@533 824 \quad \infer{\Gamma \vdash e \rcutM c : \$c'}{
adamc@533 825 \Gamma \vdash e : \$(c \rc c')
adamc@533 826 }$$
adamc@533 827
adamc@533 828 $$\infer{\Gamma \vdash \mt{let} \; \overline{ed} \; \mt{in} \; e \; \mt{end} : \tau}{
adamc@533 829 \Gamma \vdash \overline{ed} \leadsto \Gamma'
adamc@533 830 & \Gamma' \vdash e : \tau
adamc@533 831 }
adamc@533 832 \quad \infer{\Gamma \vdash \mt{case} \; e \; \mt{of} \; \overline{p \Rightarrow e} : \tau}{
adamc@533 833 \forall i: \Gamma \vdash p_i \leadsto \Gamma_i, \tau'
adamc@533 834 & \Gamma_i \vdash e_i : \tau
adamc@533 835 }$$
adamc@533 836
adamc@573 837 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow e : \lambda [c_1 \sim c_2] \Rightarrow \tau}{
adamc@533 838 \Gamma \vdash c_1 :: \{\kappa\}
adamc@655 839 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@533 840 & \Gamma, c_1 \sim c_2 \vdash e : \tau
adamc@662 841 }
adamc@662 842 \quad \infer{\Gamma \vdash e \; ! : \tau}{
adamc@662 843 \Gamma \vdash e : [c_1 \sim c_2] \Rightarrow \tau
adamc@662 844 & \Gamma \vdash c_1 \sim c_2
adamc@533 845 }$$
adamc@533 846
adamc@534 847 \subsection{Pattern Typing}
adamc@534 848
adamc@534 849 $$\infer{\Gamma \vdash \_ \leadsto \Gamma; \tau}{}
adamc@534 850 \quad \infer{\Gamma \vdash x \leadsto \Gamma, x : \tau; \tau}{}
adamc@534 851 \quad \infer{\Gamma \vdash \ell \leadsto \Gamma; T(\ell)}{}$$
adamc@534 852
adamc@534 853 $$\infer{\Gamma \vdash X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534 854 X : \overline{x ::: \mt{Type}} \to \tau \in \Gamma
adamc@534 855 & \textrm{$\tau$ not a function type}
adamc@534 856 }
adamc@534 857 \quad \infer{\Gamma \vdash X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534 858 X : \overline{x ::: \mt{Type}} \to \tau'' \to \tau \in \Gamma
adamc@534 859 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534 860 }$$
adamc@534 861
adamc@534 862 $$\infer{\Gamma \vdash M.X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537 863 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 864 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau
adamc@534 865 & \textrm{$\tau$ not a function type}
adamc@534 866 }$$
adamc@534 867
adamc@534 868 $$\infer{\Gamma \vdash M.X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537 869 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 870 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau'' \to \tau
adamc@534 871 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534 872 }$$
adamc@534 873
adamc@534 874 $$\infer{\Gamma \vdash \{\overline{x = p}\} \leadsto \Gamma_n; \{\overline{x = \tau}\}}{
adamc@534 875 \Gamma_0 = \Gamma
adamc@534 876 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534 877 }
adamc@534 878 \quad \infer{\Gamma \vdash \{\overline{x = p}, \ldots\} \leadsto \Gamma_n; \$([\overline{x = \tau}] \rc c)}{
adamc@534 879 \Gamma_0 = \Gamma
adamc@534 880 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534 881 }$$
adamc@534 882
adamc@852 883 $$\infer{\Gamma \vdash p : \tau \leadsto \Gamma'; \tau}{
adamc@852 884 \Gamma \vdash p \leadsto \Gamma'; \tau'
adamc@852 885 & \Gamma \vdash \tau' \equiv \tau
adamc@852 886 }$$
adamc@852 887
adamc@535 888 \subsection{Declaration Typing}
adamc@535 889
adamc@535 890 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@535 891
adamc@655 892 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@535 893
adamc@558 894 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@537 895 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@535 896
adamc@535 897 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535 898 \quad \infer{\Gamma \vdash d, \overline{d} \leadsto \Gamma''}{
adamc@535 899 \Gamma \vdash d \leadsto \Gamma'
adamc@535 900 & \Gamma' \vdash \overline{d} \leadsto \Gamma''
adamc@535 901 }$$
adamc@535 902
adamc@535 903 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@535 904 \Gamma \vdash c :: \kappa
adamc@535 905 }
adamc@535 906 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@535 907 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@535 908 }$$
adamc@535 909
adamc@535 910 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537 911 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 912 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@535 913 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@535 914 }$$
adamc@535 915
adamc@535 916 $$\infer{\Gamma \vdash \mt{val} \; x : \tau = e \leadsto \Gamma, x : \tau}{
adamc@535 917 \Gamma \vdash e : \tau
adamc@535 918 }$$
adamc@535 919
adamc@535 920 $$\infer{\Gamma \vdash \mt{val} \; \mt{rec} \; \overline{x : \tau = e} \leadsto \Gamma, \overline{x : \tau}}{
adamc@535 921 \forall i: \Gamma, \overline{x : \tau} \vdash e_i : \tau_i
adamc@535 922 & \textrm{$e_i$ starts with an expression $\lambda$, optionally preceded by constructor and disjointness $\lambda$s}
adamc@535 923 }$$
adamc@535 924
adamc@535 925 $$\infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : S}{
adamc@535 926 \Gamma \vdash M : S
adamc@558 927 & \textrm{ $M$ not a constant or application}
adamc@535 928 }
adamc@558 929 \quad \infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : \mt{selfify}(X, \overline{s})}{
adamc@558 930 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@539 931 }$$
adamc@539 932
adamc@539 933 $$\infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@535 934 \Gamma \vdash S
adamc@535 935 }$$
adamc@535 936
adamc@537 937 $$\infer{\Gamma \vdash \mt{open} \; M \leadsto \Gamma, \mathcal O(M, \overline{s})}{
adamc@537 938 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535 939 }$$
adamc@535 940
adamc@535 941 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma}{
adamc@535 942 \Gamma \vdash c_1 :: \{\kappa\}
adamc@535 943 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@535 944 & \Gamma \vdash c_1 \sim c_2
adamc@535 945 }
adamc@537 946 \quad \infer{\Gamma \vdash \mt{open} \; \mt{constraints} \; M \leadsto \Gamma, \mathcal O_c(M, \overline{s})}{
adamc@537 947 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535 948 }$$
adamc@535 949
adamc@784 950 $$\infer{\Gamma \vdash \mt{table} \; x : c \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_table} \; c \; []}{
adamc@535 951 \Gamma \vdash c :: \{\mt{Type}\}
adamc@535 952 }
adamc@784 953 \quad \infer{\Gamma \vdash \mt{view} \; x : c \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_view} \; c}{
adamc@784 954 \Gamma \vdash c :: \{\mt{Type}\}
adamc@784 955 }$$
adamc@784 956
adamc@784 957 $$\infer{\Gamma \vdash \mt{sequence} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_sequence}}{}$$
adamc@535 958
adamc@535 959 $$\infer{\Gamma \vdash \mt{cookie} \; x : \tau \leadsto \Gamma, x : \mt{Basis}.\mt{http\_cookie} \; \tau}{
adamc@535 960 \Gamma \vdash \tau :: \mt{Type}
adamc@784 961 }
adamc@784 962 \quad \infer{\Gamma \vdash \mt{style} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{css\_class}}{}$$
adamc@535 963
adamc@1085 964 $$\infer{\Gamma \vdash \mt{task} \; e_1 = e_2 \leadsto \Gamma}{
adam@1348 965 \Gamma \vdash e_1 :: \mt{Basis}.\mt{task\_kind} \; \tau
adam@1348 966 & \Gamma \vdash e_2 :: \tau \to \mt{Basis}.\mt{transaction} \; \{\}
adamc@1085 967 }$$
adamc@1085 968
adamc@784 969 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784 970 \Gamma \vdash c :: \kappa
adamc@535 971 }$$
adamc@535 972
adamc@535 973 $$\infer{\overline{y}; x; \Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535 974 \quad \infer{\overline{y}; x; \Gamma \vdash X \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to x \; \overline{y}}{
adamc@535 975 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535 976 }
adamc@535 977 \quad \infer{\overline{y}; x; \Gamma \vdash X \; \mt{of} \; \tau \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to \tau \to x \; \overline{y}}{
adamc@535 978 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535 979 }$$
adamc@535 980
adamc@537 981 \subsection{Signature Item Typing}
adamc@537 982
adamc@537 983 We appeal to a signature item analogue of the $\mathcal O$ function from the last subsection.
adamc@537 984
adamc@537 985 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@537 986 \quad \infer{\Gamma \vdash s, \overline{s} \leadsto \Gamma''}{
adamc@537 987 \Gamma \vdash s \leadsto \Gamma'
adamc@537 988 & \Gamma' \vdash \overline{s} \leadsto \Gamma''
adamc@537 989 }$$
adamc@537 990
adamc@537 991 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}
adamc@537 992 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@537 993 \Gamma \vdash c :: \kappa
adamc@537 994 }
adamc@537 995 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@537 996 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@537 997 }$$
adamc@537 998
adamc@537 999 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537 1000 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1001 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1002 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@537 1003 }$$
adamc@537 1004
adamc@537 1005 $$\infer{\Gamma \vdash \mt{val} \; x : \tau \leadsto \Gamma, x : \tau}{
adamc@537 1006 \Gamma \vdash \tau :: \mt{Type}
adamc@537 1007 }$$
adamc@537 1008
adamc@537 1009 $$\infer{\Gamma \vdash \mt{structure} \; X : S \leadsto \Gamma, X : S}{
adamc@537 1010 \Gamma \vdash S
adamc@537 1011 }
adamc@537 1012 \quad \infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@537 1013 \Gamma \vdash S
adamc@537 1014 }$$
adamc@537 1015
adamc@537 1016 $$\infer{\Gamma \vdash \mt{include} \; S \leadsto \Gamma, \mathcal O(\overline{s})}{
adamc@537 1017 \Gamma \vdash S
adamc@537 1018 & \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1019 }$$
adamc@537 1020
adamc@537 1021 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma, c_1 \sim c_2}{
adamc@537 1022 \Gamma \vdash c_1 :: \{\kappa\}
adamc@537 1023 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@537 1024 }$$
adamc@537 1025
adamc@784 1026 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784 1027 \Gamma \vdash c :: \kappa
adamc@537 1028 }
adamc@784 1029 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}$$
adamc@537 1030
adamc@536 1031 \subsection{Signature Compatibility}
adamc@536 1032
adamc@558 1033 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 1034
adamc@537 1035 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 1036
adamc@536 1037 $$\infer{\Gamma \vdash S \equiv S}{}
adamc@536 1038 \quad \infer{\Gamma \vdash S_1 \equiv S_2}{
adamc@536 1039 \Gamma \vdash S_2 \equiv S_1
adamc@536 1040 }
adamc@536 1041 \quad \infer{\Gamma \vdash X \equiv S}{
adamc@536 1042 X = S \in \Gamma
adamc@536 1043 }
adamc@536 1044 \quad \infer{\Gamma \vdash M.X \equiv S}{
adamc@537 1045 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1046 & \mt{proj}(M, \overline{s}, \mt{signature} \; X) = S
adamc@536 1047 }$$
adamc@536 1048
adamc@536 1049 $$\infer{\Gamma \vdash S \; \mt{where} \; \mt{con} \; x = c \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa = c \; \overline{s_2} \; \mt{end}}{
adamc@536 1050 \Gamma \vdash S \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa \; \overline{s_2} \; \mt{end}
adamc@536 1051 & \Gamma \vdash c :: \kappa
adamc@537 1052 }
adamc@537 1053 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s^1} \; \mt{include} \; S \; \overline{s^2} \; \mt{end} \equiv \mt{sig} \; \overline{s^1} \; \overline{s} \; \overline{s^2} \; \mt{end}}{
adamc@537 1054 \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@536 1055 }$$
adamc@536 1056
adamc@536 1057 $$\infer{\Gamma \vdash S_1 \leq S_2}{
adamc@536 1058 \Gamma \vdash S_1 \equiv S_2
adamc@536 1059 }
adamc@536 1060 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \mt{end}}{}
adamc@537 1061 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; s' \; \overline{s'} \; \mt{end}}{
adamc@537 1062 \Gamma \vdash \overline{s} \leq s'
adamc@537 1063 & \Gamma \vdash s' \leadsto \Gamma'
adamc@537 1064 & \Gamma' \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \overline{s'} \; \mt{end}
adamc@537 1065 }$$
adamc@537 1066
adamc@537 1067 $$\infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537 1068 \Gamma \vdash s \leq s'
adamc@537 1069 }
adamc@537 1070 \quad \infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537 1071 \Gamma \vdash s \leadsto \Gamma'
adamc@537 1072 & \Gamma' \vdash \overline{s} \leq s'
adamc@536 1073 }$$
adamc@536 1074
adamc@536 1075 $$\infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 \leq \mt{functor} (X : S'_1) : S'_2}{
adamc@536 1076 \Gamma \vdash S'_1 \leq S_1
adamc@536 1077 & \Gamma, X : S'_1 \vdash S_2 \leq S'_2
adamc@536 1078 }$$
adamc@536 1079
adamc@537 1080 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@537 1081 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}
adamc@558 1082 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type}}{}$$
adamc@537 1083
adamc@537 1084 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(y)} \to \mt{Type}}{
adamc@537 1085 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1086 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1087 }$$
adamc@537 1088
adamc@784 1089 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@784 1090 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}$$
adamc@537 1091
adamc@537 1092 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \mt{\kappa} = c_2}{
adamc@537 1093 \Gamma \vdash c_1 \equiv c_2
adamc@537 1094 }
adamc@784 1095 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \kappa = c_2}{
adamc@537 1096 \Gamma \vdash c_1 \equiv c_2
adamc@537 1097 }$$
adamc@537 1098
adamc@537 1099 $$\infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537 1100 \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1101 }$$
adamc@537 1102
adamc@537 1103 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537 1104 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1105 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1106 & \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1107 }$$
adamc@537 1108
adamc@537 1109 $$\infer{\Gamma \vdash \cdot \leq \cdot}{}
adamc@537 1110 \quad \infer{\Gamma \vdash X; \overline{dc} \leq X; \overline{dc'}}{
adamc@537 1111 \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1112 }
adamc@537 1113 \quad \infer{\Gamma \vdash X \; \mt{of} \; \tau_1; \overline{dc} \leq X \; \mt{of} \; \tau_2; \overline{dc'}}{
adamc@537 1114 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537 1115 & \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1116 }$$
adamc@537 1117
adamc@537 1118 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x = \mt{datatype} \; M'.z'}{
adamc@537 1119 \Gamma \vdash M.z \equiv M'.z'
adamc@537 1120 }$$
adamc@537 1121
adamc@537 1122 $$\infer{\Gamma \vdash \mt{val} \; x : \tau_1 \leq \mt{val} \; x : \tau_2}{
adamc@537 1123 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537 1124 }
adamc@537 1125 \quad \infer{\Gamma \vdash \mt{structure} \; X : S_1 \leq \mt{structure} \; X : S_2}{
adamc@537 1126 \Gamma \vdash S_1 \leq S_2
adamc@537 1127 }
adamc@537 1128 \quad \infer{\Gamma \vdash \mt{signature} \; X = S_1 \leq \mt{signature} \; X = S_2}{
adamc@537 1129 \Gamma \vdash S_1 \leq S_2
adamc@537 1130 & \Gamma \vdash S_2 \leq S_1
adamc@537 1131 }$$
adamc@537 1132
adamc@537 1133 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leq \mt{constraint} \; c'_1 \sim c'_2}{
adamc@537 1134 \Gamma \vdash c_1 \equiv c'_1
adamc@537 1135 & \Gamma \vdash c_2 \equiv c'_2
adamc@537 1136 }$$
adamc@537 1137
adamc@655 1138 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{class} \; x :: \kappa}{}
adamc@655 1139 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{class} \; x :: \kappa}{}
adamc@655 1140 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{class} \; x :: \kappa = c_2}{
adamc@537 1141 \Gamma \vdash c_1 \equiv c_2
adamc@537 1142 }$$
adamc@537 1143
adamc@538 1144 \subsection{Module Typing}
adamc@538 1145
adamc@538 1146 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 1147
adamc@538 1148 $$\infer{\Gamma \vdash M : S}{
adamc@538 1149 \Gamma \vdash M : S'
adamc@538 1150 & \Gamma \vdash S' \leq S
adamc@538 1151 }
adamc@538 1152 \quad \infer{\Gamma \vdash \mt{struct} \; \overline{d} \; \mt{end} : \mt{sig} \; \mt{sigOf}(\overline{d}) \; \mt{end}}{
adamc@538 1153 \Gamma \vdash \overline{d} \leadsto \Gamma'
adamc@538 1154 }
adamc@538 1155 \quad \infer{\Gamma \vdash X : S}{
adamc@538 1156 X : S \in \Gamma
adamc@538 1157 }$$
adamc@538 1158
adamc@538 1159 $$\infer{\Gamma \vdash M.X : S}{
adamc@538 1160 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@538 1161 & \mt{proj}(M, \overline{s}, \mt{structure} \; X) = S
adamc@538 1162 }$$
adamc@538 1163
adamc@538 1164 $$\infer{\Gamma \vdash M_1(M_2) : [X \mapsto M_2]S_2}{
adamc@538 1165 \Gamma \vdash M_1 : \mt{functor}(X : S_1) : S_2
adamc@538 1166 & \Gamma \vdash M_2 : S_1
adamc@538 1167 }
adamc@538 1168 \quad \infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 = M : \mt{functor} (X : S_1) : S_2}{
adamc@538 1169 \Gamma \vdash S_1
adamc@538 1170 & \Gamma, X : S_1 \vdash S_2
adamc@538 1171 & \Gamma, X : S_1 \vdash M : S_2
adamc@538 1172 }$$
adamc@538 1173
adamc@538 1174 \begin{eqnarray*}
adamc@538 1175 \mt{sigOf}(\cdot) &=& \cdot \\
adamc@538 1176 \mt{sigOf}(s \; \overline{s'}) &=& \mt{sigOf}(s) \; \mt{sigOf}(\overline{s'}) \\
adamc@538 1177 \\
adamc@538 1178 \mt{sigOf}(\mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@538 1179 \mt{sigOf}(\mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \overline{dc} \\
adamc@538 1180 \mt{sigOf}(\mt{datatype} \; x = \mt{datatype} \; M.z) &=& \mt{datatype} \; x = \mt{datatype} \; M.z \\
adamc@538 1181 \mt{sigOf}(\mt{val} \; x : \tau = e) &=& \mt{val} \; x : \tau \\
adamc@538 1182 \mt{sigOf}(\mt{val} \; \mt{rec} \; \overline{x : \tau = e}) &=& \overline{\mt{val} \; x : \tau} \\
adamc@538 1183 \mt{sigOf}(\mt{structure} \; X : S = M) &=& \mt{structure} \; X : S \\
adamc@538 1184 \mt{sigOf}(\mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@538 1185 \mt{sigOf}(\mt{open} \; M) &=& \mt{include} \; S \textrm{ (where $\Gamma \vdash M : S$)} \\
adamc@538 1186 \mt{sigOf}(\mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@538 1187 \mt{sigOf}(\mt{open} \; \mt{constraints} \; M) &=& \cdot \\
adamc@538 1188 \mt{sigOf}(\mt{table} \; x : c) &=& \mt{table} \; x : c \\
adamc@784 1189 \mt{sigOf}(\mt{view} \; x : c) &=& \mt{view} \; x : c \\
adamc@538 1190 \mt{sigOf}(\mt{sequence} \; x) &=& \mt{sequence} \; x \\
adamc@538 1191 \mt{sigOf}(\mt{cookie} \; x : \tau) &=& \mt{cookie} \; x : \tau \\
adamc@784 1192 \mt{sigOf}(\mt{style} \; x) &=& \mt{style} \; x \\
adamc@655 1193 \mt{sigOf}(\mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@538 1194 \end{eqnarray*}
adamc@539 1195 \begin{eqnarray*}
adamc@539 1196 \mt{selfify}(M, \cdot) &=& \cdot \\
adamc@558 1197 \mt{selfify}(M, s \; \overline{s'}) &=& \mt{selfify}(M, s) \; \mt{selfify}(M, \overline{s'}) \\
adamc@539 1198 \\
adamc@539 1199 \mt{selfify}(M, \mt{con} \; x :: \kappa) &=& \mt{con} \; x :: \kappa = M.x \\
adamc@539 1200 \mt{selfify}(M, \mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@539 1201 \mt{selfify}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \mt{datatype} \; M.x \\
adamc@539 1202 \mt{selfify}(M, \mt{datatype} \; x = \mt{datatype} \; M'.z) &=& \mt{datatype} \; x = \mt{datatype} \; M'.z \\
adamc@539 1203 \mt{selfify}(M, \mt{val} \; x : \tau) &=& \mt{val} \; x : \tau \\
adamc@539 1204 \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 1205 \mt{selfify}(M, \mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@539 1206 \mt{selfify}(M, \mt{include} \; S) &=& \mt{include} \; S \\
adamc@539 1207 \mt{selfify}(M, \mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@655 1208 \mt{selfify}(M, \mt{class} \; x :: \kappa) &=& \mt{class} \; x :: \kappa = M.x \\
adamc@655 1209 \mt{selfify}(M, \mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@539 1210 \end{eqnarray*}
adamc@539 1211
adamc@540 1212 \subsection{Module Projection}
adamc@540 1213
adamc@540 1214 \begin{eqnarray*}
adamc@540 1215 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \\
adamc@540 1216 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa, c) \\
adamc@540 1217 \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 1218 \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 1219 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})$)} \\
adamc@655 1220 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \to \mt{Type} \\
adamc@655 1221 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa \to \mt{Type}, c) \\
adamc@540 1222 \\
adamc@540 1223 \mt{proj}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc} \; \overline{s}, \mt{datatype} \; x) &=& (\overline{y}, \overline{dc}) \\
adamc@540 1224 \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 1225 \\
adamc@540 1226 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, \mt{val} \; x) &=& \tau \\
adamc@540 1227 \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 1228 \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 1229 \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 1230 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \in \overline{dc}$)} \\
adamc@540 1231 \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 1232 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \; \mt{of} \; \tau \in \overline{dc}$)} \\
adamc@540 1233 \\
adamc@540 1234 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, \mt{structure} \; X) &=& S \\
adamc@540 1235 \\
adamc@540 1236 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, \mt{signature} \; X) &=& S \\
adamc@540 1237 \\
adamc@540 1238 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1239 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1240 \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 1241 \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 1242 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@540 1243 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1244 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1245 \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 1246 \mt{proj}(M, \mt{constraint} \; c_1 \sim c_2 \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@655 1247 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@655 1248 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1249 \end{eqnarray*}
adamc@540 1250
adamc@541 1251
adamc@541 1252 \section{Type Inference}
adamc@541 1253
adamc@541 1254 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 1255
adamc@541 1256 \subsection{Basic Unification}
adamc@541 1257
adamc@560 1258 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 1259
adamc@656 1260 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 1261
adamc@541 1262 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 1263
adamc@541 1264 \subsection{Unifying Record Types}
adamc@541 1265
adamc@570 1266 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 1267
adamc@656 1268 \subsection{\label{typeclasses}Constructor Classes}
adamc@541 1269
adamc@784 1270 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 1271
adamc@784 1272 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 1273
adamc@656 1274 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 1275
adamc@656 1276 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 1277
adamc@541 1278 \subsection{Reverse-Engineering Record Types}
adamc@541 1279
adamc@656 1280 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 1281
adamc@541 1282 \subsection{Implicit Arguments in Functor Applications}
adamc@541 1283
adamc@656 1284 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 1285
adamc@541 1286
adamc@542 1287 \section{The Ur Standard Library}
adamc@542 1288
adamc@542 1289 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 1290
adamc@542 1291 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 1292
adamc@542 1293 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 1294 $$\begin{array}{l}
adamc@542 1295 \mt{type} \; \mt{int} \\
adamc@542 1296 \mt{type} \; \mt{float} \\
adamc@873 1297 \mt{type} \; \mt{char} \\
adamc@542 1298 \mt{type} \; \mt{string} \\
adamc@542 1299 \mt{type} \; \mt{time} \\
adamc@785 1300 \mt{type} \; \mt{blob} \\
adamc@542 1301 \\
adamc@542 1302 \mt{type} \; \mt{unit} = \{\} \\
adamc@542 1303 \\
adamc@542 1304 \mt{datatype} \; \mt{bool} = \mt{False} \mid \mt{True} \\
adamc@542 1305 \\
adamc@785 1306 \mt{datatype} \; \mt{option} \; \mt{t} = \mt{None} \mid \mt{Some} \; \mt{of} \; \mt{t} \\
adamc@785 1307 \\
adamc@785 1308 \mt{datatype} \; \mt{list} \; \mt{t} = \mt{Nil} \mid \mt{Cons} \; \mt{of} \; \mt{t} \times \mt{list} \; \mt{t}
adamc@542 1309 \end{array}$$
adamc@542 1310
adamc@1123 1311 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 1312
adam@1297 1313 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 1314 $$\begin{array}{l}
adam@1297 1315 \mt{con} \; \mt{variant} :: \{\mt{Type}\} \to \mt{Type} \\
adam@1297 1316 \mt{val} \; \mt{make} : \mt{nm} :: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{ts} ::: \{\mt{Type}\} \to [[\mt{nm}] \sim \mt{ts}] \Rightarrow \mt{t} \to \mt{variant} \; ([\mt{nm} = \mt{t}] \rc \mt{ts}) \\
adam@1297 1317 \mt{val} \; \mt{match} : \mt{ts} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{variant} \; \mt{ts} \to \$(\mt{map} \; (\lambda \mt{t'} \Rightarrow \mt{t'} \to \mt{t}) \; \mt{ts}) \to \mt{t}
adam@1297 1318 \end{array}$$
adam@1297 1319
adamc@657 1320 Another important generic Ur element comes at the beginning of \texttt{top.urs}.
adamc@657 1321
adamc@657 1322 $$\begin{array}{l}
adamc@657 1323 \mt{con} \; \mt{folder} :: \mt{K} \longrightarrow \{\mt{K}\} \to \mt{Type} \\
adamc@657 1324 \\
adamc@657 1325 \mt{val} \; \mt{fold} : \mt{K} \longrightarrow \mt{tf} :: (\{\mt{K}\} \to \mt{Type}) \\
adamc@657 1326 \hspace{.1in} \to (\mt{nm} :: \mt{Name} \to \mt{v} :: \mt{K} \to \mt{r} :: \{\mt{K}\} \to [[\mt{nm}] \sim \mt{r}] \Rightarrow \\
adamc@657 1327 \hspace{.2in} \mt{tf} \; \mt{r} \to \mt{tf} \; ([\mt{nm} = \mt{v}] \rc \mt{r})) \\
adamc@657 1328 \hspace{.1in} \to \mt{tf} \; [] \\
adamc@657 1329 \hspace{.1in} \to \mt{r} :: \{\mt{K}\} \to \mt{folder} \; \mt{r} \to \mt{tf} \; \mt{r}
adamc@657 1330 \end{array}$$
adamc@657 1331
adamc@657 1332 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 1333
adamc@664 1334 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 1335
adamc@542 1336
adamc@542 1337 \section{The Ur/Web Standard Library}
adamc@542 1338
adamc@658 1339 \subsection{Monads}
adamc@658 1340
adamc@658 1341 The Ur Basis defines the monad constructor class from Haskell.
adamc@658 1342
adamc@658 1343 $$\begin{array}{l}
adamc@658 1344 \mt{class} \; \mt{monad} :: \mt{Type} \to \mt{Type} \\
adamc@658 1345 \mt{val} \; \mt{return} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t} ::: \mt{Type} \\
adamc@658 1346 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658 1347 \hspace{.1in} \to \mt{t} \to \mt{m} \; \mt{t} \\
adamc@658 1348 \mt{val} \; \mt{bind} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t1} ::: \mt{Type} \to \mt{t2} ::: \mt{Type} \\
adamc@658 1349 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658 1350 \hspace{.1in} \to \mt{m} \; \mt{t1} \to (\mt{t1} \to \mt{m} \; \mt{t2}) \\
adamc@658 1351 \hspace{.1in} \to \mt{m} \; \mt{t2}
adamc@658 1352 \end{array}$$
adamc@658 1353
adamc@542 1354 \subsection{Transactions}
adamc@542 1355
adamc@542 1356 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 1357 $$\begin{array}{l}
adamc@542 1358 \mt{con} \; \mt{transaction} :: \mt{Type} \to \mt{Type} \\
adamc@658 1359 \mt{val} \; \mt{transaction\_monad} : \mt{monad} \; \mt{transaction}
adamc@542 1360 \end{array}$$
adamc@542 1361
adamc@1123 1362 For debugging purposes, a transactional function is provided for outputting a string on the server process' \texttt{stderr}.
adamc@1123 1363 $$\begin{array}{l}
adamc@1123 1364 \mt{val} \; \mt{debug} : \mt{string} \to \mt{transaction} \; \mt{unit}
adamc@1123 1365 \end{array}$$
adamc@1123 1366
adamc@542 1367 \subsection{HTTP}
adamc@542 1368
adamc@542 1369 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.
adamc@542 1370 $$\begin{array}{l}
adamc@786 1371 \mt{val} \; \mt{requestHeader} : \mt{string} \to \mt{transaction} \; (\mt{option} \; \mt{string}) \\
adamc@786 1372 \\
adamc@786 1373 \mt{con} \; \mt{http\_cookie} :: \mt{Type} \to \mt{Type} \\
adamc@786 1374 \mt{val} \; \mt{getCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; (\mt{option} \; \mt{t}) \\
adamc@1050 1375 \mt{val} \; \mt{setCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \{\mt{Value} : \mt{t}, \mt{Expires} : \mt{option} \; \mt{time}, \mt{Secure} : \mt{bool}\} \to \mt{transaction} \; \mt{unit} \\
adamc@1050 1376 \mt{val} \; \mt{clearCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; \mt{unit}
adamc@786 1377 \end{array}$$
adamc@786 1378
adamc@786 1379 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 1380 $$\begin{array}{l}
adamc@786 1381 \mt{type} \; \mt{url} \\
adamc@786 1382 \mt{val} \; \mt{bless} : \mt{string} \to \mt{url} \\
adamc@786 1383 \mt{val} \; \mt{checkUrl} : \mt{string} \to \mt{option} \; \mt{url}
adamc@786 1384 \end{array}$$
adamc@786 1385 $\mt{bless}$ raises a runtime error if the string passed to it fails the URL policy.
adamc@786 1386
adamc@1085 1387 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.
adamc@1085 1388 $$\begin{array}{l}
adamc@1085 1389 \mt{val} \; \mt{currentUrl} : \mt{transaction} \; \mt{url} \\
adamc@1085 1390 \mt{val} \; \mt{url} : \mt{transaction} \; \mt{page} \to \mt{url}
adamc@1085 1391 \end{array}$$
adamc@1085 1392
adamc@1085 1393 Page generation may be interrupted at any time with a request to redirect to a particular URL instead.
adamc@1085 1394 $$\begin{array}{l}
adamc@1085 1395 \mt{val} \; \mt{redirect} : \mt{t} ::: \mt{Type} \to \mt{url} \to \mt{transaction} \; \mt{t}
adamc@1085 1396 \end{array}$$
adamc@1085 1397
adamc@786 1398 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.
adamc@786 1399 $$\begin{array}{l}
adamc@786 1400 \mt{type} \; \mt{file} \\
adamc@786 1401 \mt{val} \; \mt{fileName} : \mt{file} \to \mt{option} \; \mt{string} \\
adamc@786 1402 \mt{val} \; \mt{fileMimeType} : \mt{file} \to \mt{string} \\
adamc@786 1403 \mt{val} \; \mt{fileData} : \mt{file} \to \mt{blob}
adamc@786 1404 \end{array}$$
adamc@786 1405
adamc@786 1406 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 1407 $$\begin{array}{l}
adamc@786 1408 \mt{type} \; \mt{mimeType} \\
adamc@786 1409 \mt{val} \; \mt{blessMime} : \mt{string} \to \mt{mimeType} \\
adamc@786 1410 \mt{val} \; \mt{checkMime} : \mt{string} \to \mt{option} \; \mt{mimeType} \\
adamc@786 1411 \mt{val} \; \mt{returnBlob} : \mt{t} ::: \mt{Type} \to \mt{blob} \to \mt{mimeType} \to \mt{transaction} \; \mt{t}
adamc@542 1412 \end{array}$$
adamc@542 1413
adamc@543 1414 \subsection{SQL}
adamc@543 1415
adamc@543 1416 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 1417 $$\begin{array}{l}
adamc@785 1418 \mt{con} \; \mt{sql\_table} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785 1419 \end{array}$$
adamc@785 1420 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 1421
adamc@785 1422 We also have the simpler type family of SQL views, which have no keys.
adamc@785 1423 $$\begin{array}{l}
adamc@785 1424 \mt{con} \; \mt{sql\_view} :: \{\mt{Type}\} \to \mt{Type}
adamc@543 1425 \end{array}$$
adamc@543 1426
adamc@785 1427 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 1428 $$\begin{array}{l}
adamc@785 1429 \mt{class} \; \mt{fieldsOf} :: \mt{Type} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1430 \mt{val} \; \mt{fieldsOf\_table} : \mt{fs} ::: \{\mt{Type}\} \to \mt{keys} ::: \{\{\mt{Unit}\}\} \to \mt{fieldsOf} \; (\mt{sql\_table} \; \mt{fs} \; \mt{keys}) \; \mt{fs} \\
adamc@785 1431 \mt{val} \; \mt{fieldsOf\_view} : \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; (\mt{sql\_view} \; \mt{fs}) \; \mt{fs}
adamc@785 1432 \end{array}$$
adamc@785 1433
adamc@785 1434 \subsubsection{Table Constraints}
adamc@785 1435
adamc@785 1436 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 1437
adamc@785 1438 $$\begin{array}{l}
adamc@785 1439 \mt{con} \; \mt{primary\_key} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type} \\
adamc@785 1440 \mt{val} \; \mt{no\_primary\_key} : \mt{fs} ::: \{\mt{Type}\} \to \mt{primary\_key} \; \mt{fs} \; [] \\
adamc@785 1441 \mt{val} \; \mt{primary\_key} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{key1} :: \mt{Name} \to \mt{keys} :: \{\mt{Type}\} \\
adamc@785 1442 \hspace{.1in} \to [[\mt{key1}] \sim \mt{keys}] \Rightarrow [[\mt{key1} = \mt{t}] \rc \mt{keys} \sim \mt{rest}] \\
adamc@785 1443 \hspace{.1in} \Rightarrow \$([\mt{key1} = \mt{sql\_injectable\_prim} \; \mt{t}] \rc \mt{map} \; \mt{sql\_injectable\_prim} \; \mt{keys}) \\
adamc@785 1444 \hspace{.1in} \to \mt{primary\_key} \; ([\mt{key1} = \mt{t}] \rc \mt{keys} \rc \mt{rest}) \; [\mt{Pkey} = [\mt{key1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{keys}]
adamc@785 1445 \end{array}$$
adamc@785 1446 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 1447
adamc@785 1448 A type family stands for sets of named constraints of the remaining varieties.
adamc@785 1449 $$\begin{array}{l}
adamc@785 1450 \mt{con} \; \mt{sql\_constraints} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785 1451 \end{array}$$
adamc@785 1452 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 1453
adamc@785 1454 There is a type family of individual, unnamed constraints.
adamc@785 1455 $$\begin{array}{l}
adamc@785 1456 \mt{con} \; \mt{sql\_constraint} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \mt{Type}
adamc@785 1457 \end{array}$$
adamc@785 1458 The first argument is the same as above, and the second argument gives the key columns for just this constraint.
adamc@785 1459
adamc@785 1460 We have operations for assembling constraints into constraint sets.
adamc@785 1461 $$\begin{array}{l}
adamc@785 1462 \mt{val} \; \mt{no\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_constraints} \; \mt{fs} \; [] \\
adamc@785 1463 \mt{val} \; \mt{one\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{unique} ::: \{\mt{Unit}\} \to \mt{name} :: \mt{Name} \\
adamc@785 1464 \hspace{.1in} \to \mt{sql\_constraint} \; \mt{fs} \; \mt{unique} \to \mt{sql\_constraints} \; \mt{fs} \; [\mt{name} = \mt{unique}] \\
adamc@785 1465 \mt{val} \; \mt{join\_constraints} : \mt{fs} ::: \{\mt{Type}\} \to \mt{uniques1} ::: \{\{\mt{Unit}\}\} \to \mt{uniques2} ::: \{\{\mt{Unit}\}\} \to [\mt{uniques1} \sim \mt{uniques2}] \\
adamc@785 1466 \hspace{.1in} \Rightarrow \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques1} \to \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques2} \to \mt{sql\_constraints} \; \mt{fs} \; (\mt{uniques1} \rc \mt{uniques2})
adamc@785 1467 \end{array}$$
adamc@785 1468
adamc@785 1469 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 1470 $$\begin{array}{l}
adamc@785 1471 \mt{val} \; \mt{unique} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{unique1} :: \mt{Name} \to \mt{unique} :: \{\mt{Type}\} \\
adamc@785 1472 \hspace{.1in} \to [[\mt{unique1}] \sim \mt{unique}] \Rightarrow [[\mt{unique1} = \mt{t}] \rc \mt{unique} \sim \mt{rest}] \\
adamc@785 1473 \hspace{.1in} \Rightarrow \mt{sql\_constraint} \; ([\mt{unique1} = \mt{t}] \rc \mt{unique} \rc \mt{rest}) \; ([\mt{unique1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{unique})
adamc@785 1474 \end{array}$$
adamc@785 1475
adamc@785 1476 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 1477 $$\begin{array}{l}
adamc@785 1478 \mt{class} \; \mt{linkable} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@785 1479 \mt{val} \; \mt{linkable\_same} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; \mt{t} \\
adamc@785 1480 \mt{val} \; \mt{linkable\_from\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; (\mt{option} \; \mt{t}) \; \mt{t} \\
adamc@785 1481 \mt{val} \; \mt{linkable\_to\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@785 1482 \end{array}$$
adamc@785 1483
adamc@785 1484 The $\mt{matching}$ type family uses $\mt{linkable}$ to define when two keys match up type-wise.
adamc@785 1485 $$\begin{array}{l}
adamc@785 1486 \mt{con} \; \mt{matching} :: \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1487 \mt{val} \; \mt{mat\_nil} : \mt{matching} \; [] \; [] \\
adamc@785 1488 \mt{val} \; \mt{mat\_cons} : \mt{t1} ::: \mt{Type} \to \mt{rest1} ::: \{\mt{Type}\} \to \mt{t2} ::: \mt{Type} \to \mt{rest2} ::: \{\mt{Type}\} \to \mt{nm1} :: \mt{Name} \to \mt{nm2} :: \mt{Name} \\
adamc@785 1489 \hspace{.1in} \to [[\mt{nm1}] \sim \mt{rest1}] \Rightarrow [[\mt{nm2}] \sim \mt{rest2}] \Rightarrow \mt{linkable} \; \mt{t1} \; \mt{t2} \to \mt{matching} \; \mt{rest1} \; \mt{rest2} \\
adamc@785 1490 \hspace{.1in} \to \mt{matching} \; ([\mt{nm1} = \mt{t1}] \rc \mt{rest1}) \; ([\mt{nm2} = \mt{t2}] \rc \mt{rest2})
adamc@785 1491 \end{array}$$
adamc@785 1492
adamc@785 1493 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 1494 $$\begin{array}{l}
adamc@785 1495 \mt{con} \; \mt{propagation\_mode} :: \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1496 \mt{val} \; \mt{restrict} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1497 \mt{val} \; \mt{cascade} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1498 \mt{val} \; \mt{no\_action} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1499 \mt{val} \; \mt{set\_null} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; (\mt{map} \; \mt{option} \; \mt{fs})
adamc@785 1500 \end{array}$$
adamc@785 1501
adamc@785 1502 Finally, we put these ingredient together to define the \texttt{FOREIGN KEY} constraint function.
adamc@785 1503 $$\begin{array}{l}
adamc@785 1504 \mt{val} \; \mt{foreign\_key} : \mt{mine1} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{mine} ::: \{\mt{Type}\} \to \mt{munused} ::: \{\mt{Type}\} \to \mt{foreign} ::: \{\mt{Type}\} \\
adamc@785 1505 \hspace{.1in} \to \mt{funused} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{uniques} ::: \{\{\mt{Unit}\}\} \\
adamc@785 1506 \hspace{.1in} \to [[\mt{mine1}] \sim \mt{mine}] \Rightarrow [[\mt{mine1} = \mt{t}] \rc \mt{mine} \sim \mt{munused}] \Rightarrow [\mt{foreign} \sim \mt{funused}] \Rightarrow [[\mt{nm}] \sim \mt{uniques}] \\
adamc@785 1507 \hspace{.1in} \Rightarrow \mt{matching} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}) \; \mt{foreign} \\
adamc@785 1508 \hspace{.1in} \to \mt{sql\_table} \; (\mt{foreign} \rc \mt{funused}) \; ([\mt{nm} = \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{foreign}] \rc \mt{uniques}) \\
adamc@785 1509 \hspace{.1in} \to \{\mt{OnDelete} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}), \\
adamc@785 1510 \hspace{.2in} \mt{OnUpdate} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine})\} \\
adamc@785 1511 \hspace{.1in} \to \mt{sql\_constraint} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine} \rc \mt{munused}) \; []
adamc@785 1512 \end{array}$$
adamc@785 1513
adamc@785 1514 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 1515 $$\begin{array}{l}
adamc@785 1516 \mt{val} \; \mt{check} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; [] \; [] \; \mt{fs} \; \mt{bool} \to \mt{sql\_constraint} \; \mt{fs} \; []
adamc@785 1517 \end{array}$$
adamc@785 1518
adamc@785 1519 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 1520
adamc@784 1521
adamc@543 1522 \subsubsection{Queries}
adamc@543 1523
adamc@1193 1524 A final query is constructed via the $\mt{sql\_query}$ function. Constructor arguments respectively specify the free table variables (which will only be available in subqueries), 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 1525 $$\begin{array}{l}
adamc@1193 1526 \mt{con} \; \mt{sql\_query} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@1193 1527 \mt{val} \; \mt{sql\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1528 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543 1529 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1530 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1193 1531 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adamc@1193 1532 \hspace{.1in} \Rightarrow \{\mt{Rows} : \mt{sql\_query1} \; \mt{free} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}, \\
adamc@1193 1533 \hspace{.2in} \mt{OrderBy} : \mt{sql\_order\_by} \; (\mt{free} \rc \mt{tables}) \; \mt{selectedExps}, \\
adamc@543 1534 \hspace{.2in} \mt{Limit} : \mt{sql\_limit}, \\
adamc@543 1535 \hspace{.2in} \mt{Offset} : \mt{sql\_offset}\} \\
adamc@1193 1536 \hspace{.1in} \to \mt{sql\_query} \; \mt{free} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1537 \end{array}$$
adamc@543 1538
adamc@545 1539 Queries are used by folding over their results inside transactions.
adamc@545 1540 $$\begin{array}{l}
adamc@1193 1541 \mt{val} \; \mt{query} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \lambda [\mt{tables} \sim \mt{exps}] \Rightarrow \mt{state} ::: \mt{Type} \to \mt{sql\_query} \; [] \; \mt{tables} \; \mt{exps} \\
adamc@658 1542 \hspace{.1in} \to (\$(\mt{exps} \rc \mt{map} \; (\lambda \mt{fields} :: \{\mt{Type}\} \Rightarrow \$\mt{fields}) \; \mt{tables}) \\
adamc@545 1543 \hspace{.2in} \to \mt{state} \to \mt{transaction} \; \mt{state}) \\
adamc@545 1544 \hspace{.1in} \to \mt{state} \to \mt{transaction} \; \mt{state}
adamc@545 1545 \end{array}$$
adamc@545 1546
adamc@1193 1547 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 free table veriables, 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 1548 $$\begin{array}{l}
adamc@1193 1549 \mt{con} \; \mt{sql\_query1} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@543 1550 \\
adamc@543 1551 \mt{type} \; \mt{sql\_relop} \\
adamc@543 1552 \mt{val} \; \mt{sql\_union} : \mt{sql\_relop} \\
adamc@543 1553 \mt{val} \; \mt{sql\_intersect} : \mt{sql\_relop} \\
adamc@543 1554 \mt{val} \; \mt{sql\_except} : \mt{sql\_relop} \\
adamc@543 1555 \mt{val} \; \mt{sql\_relop} : \mt{tables1} ::: \{\{\mt{Type}\}\} \\
adamc@543 1556 \hspace{.1in} \to \mt{tables2} ::: \{\{\mt{Type}\}\} \\
adamc@543 1557 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1558 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@543 1559 \hspace{.1in} \to \mt{sql\_relop} \\
adamc@543 1560 \hspace{.1in} \to \mt{sql\_query1} \; \mt{tables1} \; \mt{selectedFields} \; \mt{selectedExps} \\
adamc@543 1561 \hspace{.1in} \to \mt{sql\_query1} \; \mt{tables2} \; \mt{selectedFields} \; \mt{selectedExps} \\
adamc@543 1562 \hspace{.1in} \to \mt{sql\_query1} \; \mt{selectedFields} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1563 \end{array}$$
adamc@543 1564
adamc@543 1565 $$\begin{array}{l}
adamc@1193 1566 \mt{val} \; \mt{sql\_query1} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1567 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543 1568 \hspace{.1in} \to \mt{grouped} ::: \{\{\mt{Type}\}\} \\
adamc@543 1569 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1570 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1085 1571 \hspace{.1in} \to \mt{empties} :: \{\mt{Unit}\} \\
adamc@1193 1572 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adamc@1193 1573 \hspace{.1in} \Rightarrow [\mt{free} \sim \mt{grouped}] \\
adamc@1193 1574 \hspace{.1in} \Rightarrow [\mt{empties} \sim \mt{selectedFields}] \\
adamc@1085 1575 \hspace{.1in} \Rightarrow \{\mt{Distinct} : \mt{bool}, \\
adamc@1193 1576 \hspace{.2in} \mt{From} : \mt{sql\_from\_items} \; \mt{free} \; \mt{tables}, \\
adamc@1193 1577 \hspace{.2in} \mt{Where} : \mt{sql\_exp} \; (\mt{free} \rc \mt{tables}) \; [] \; [] \; \mt{bool}, \\
adamc@543 1578 \hspace{.2in} \mt{GroupBy} : \mt{sql\_subset} \; \mt{tables} \; \mt{grouped}, \\
adamc@1193 1579 \hspace{.2in} \mt{Having} : \mt{sql\_exp} \; (\mt{free} \rc \mt{grouped}) \; \mt{tables} \; [] \; \mt{bool}, \\
adamc@1085 1580 \hspace{.2in} \mt{SelectFields} : \mt{sql\_subset} \; \mt{grouped} \; (\mt{map} \; (\lambda \_ \Rightarrow []) \; \mt{empties} \rc \mt{selectedFields}), \\
adamc@1193 1581 \hspace{.2in} \mt {SelectExps} : \$(\mt{map} \; (\mt{sql\_exp} \; (\mt{free} \rc \mt{grouped}) \; \mt{tables} \; []) \; \mt{selectedExps}) \} \\
adamc@1193 1582 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1583 \end{array}$$
adamc@543 1584
adamc@543 1585 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 1586 $$\begin{array}{l}
adamc@543 1587 \mt{con} \; \mt{sql\_subset} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@543 1588 \mt{val} \; \mt{sql\_subset} : \mt{keep\_drop} :: \{(\{\mt{Type}\} \times \{\mt{Type}\})\} \\
adamc@543 1589 \hspace{.1in} \to \mt{sql\_subset} \\
adamc@658 1590 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1 \rc \mt{fields}.2)\; \mt{keep\_drop}) \\
adamc@658 1591 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1) \; \mt{keep\_drop}) \\
adamc@543 1592 \mt{val} \; \mt{sql\_subset\_all} : \mt{tables} :: \{\{\mt{Type}\}\} \to \mt{sql\_subset} \; \mt{tables} \; \mt{tables}
adamc@543 1593 \end{array}$$
adamc@543 1594
adamc@560 1595 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 1596 $$\begin{array}{l}
adamc@543 1597 \mt{con} \; \mt{sql\_exp} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}
adamc@543 1598 \end{array}$$
adamc@543 1599
adamc@543 1600 Any field in scope may be converted to an expression.
adamc@543 1601 $$\begin{array}{l}
adamc@543 1602 \mt{val} \; \mt{sql\_field} : \mt{otherTabs} ::: \{\{\mt{Type}\}\} \to \mt{otherFields} ::: \{\mt{Type}\} \\
adamc@543 1603 \hspace{.1in} \to \mt{fieldType} ::: \mt{Type} \to \mt{agg} ::: \{\{\mt{Type}\}\} \\
adamc@543 1604 \hspace{.1in} \to \mt{exps} ::: \{\mt{Type}\} \\
adamc@543 1605 \hspace{.1in} \to \mt{tab} :: \mt{Name} \to \mt{field} :: \mt{Name} \\
adamc@543 1606 \hspace{.1in} \to \mt{sql\_exp} \; ([\mt{tab} = [\mt{field} = \mt{fieldType}] \rc \mt{otherFields}] \rc \mt{otherTabs}) \; \mt{agg} \; \mt{exps} \; \mt{fieldType}
adamc@543 1607 \end{array}$$
adamc@543 1608
adamc@544 1609 There is an analogous function for referencing named expressions.
adamc@544 1610 $$\begin{array}{l}
adamc@544 1611 \mt{val} \; \mt{sql\_exp} : \mt{tabs} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{t} ::: \mt{Type} \to \mt{rest} ::: \{\mt{Type}\} \to \mt{nm} :: \mt{Name} \\
adamc@544 1612 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tabs} \; \mt{agg} \; ([\mt{nm} = \mt{t}] \rc \mt{rest}) \; \mt{t}
adamc@544 1613 \end{array}$$
adamc@544 1614
adamc@544 1615 Ur values of appropriate types may be injected into SQL expressions.
adamc@544 1616 $$\begin{array}{l}
adamc@786 1617 \mt{class} \; \mt{sql\_injectable\_prim} \\
adamc@786 1618 \mt{val} \; \mt{sql\_bool} : \mt{sql\_injectable\_prim} \; \mt{bool} \\
adamc@786 1619 \mt{val} \; \mt{sql\_int} : \mt{sql\_injectable\_prim} \; \mt{int} \\
adamc@786 1620 \mt{val} \; \mt{sql\_float} : \mt{sql\_injectable\_prim} \; \mt{float} \\
adamc@786 1621 \mt{val} \; \mt{sql\_string} : \mt{sql\_injectable\_prim} \; \mt{string} \\
adamc@786 1622 \mt{val} \; \mt{sql\_time} : \mt{sql\_injectable\_prim} \; \mt{time} \\
adamc@786 1623 \mt{val} \; \mt{sql\_blob} : \mt{sql\_injectable\_prim} \; \mt{blob} \\
adamc@786 1624 \mt{val} \; \mt{sql\_channel} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{channel} \; \mt{t}) \\
adamc@786 1625 \mt{val} \; \mt{sql\_client} : \mt{sql\_injectable\_prim} \; \mt{client} \\
adamc@786 1626 \\
adamc@544 1627 \mt{class} \; \mt{sql\_injectable} \\
adamc@786 1628 \mt{val} \; \mt{sql\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@786 1629 \mt{val} \; \mt{sql\_option\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; (\mt{option} \; \mt{t}) \\
adamc@786 1630 \\
adamc@544 1631 \mt{val} \; \mt{sql\_inject} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@544 1632 \hspace{.1in} \to \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adamc@544 1633 \end{array}$$
adamc@544 1634
adamc@1123 1635 Additionally, most function-free types may be injected safely, via the $\mt{serialized}$ type family.
adamc@1123 1636 $$\begin{array}{l}
adamc@1123 1637 \mt{con} \; \mt{serialized} :: \mt{Type} \to \mt{Type} \\
adamc@1123 1638 \mt{val} \; \mt{serialize} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{serialized} \; \mt{t} \\
adamc@1123 1639 \mt{val} \; \mt{deserialize} : \mt{t} ::: \mt{Type} \to \mt{serialized} \; \mt{t} \to \mt{t} \\
adamc@1123 1640 \mt{val} \; \mt{sql\_serialized} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{serialized} \; \mt{t})
adamc@1123 1641 \end{array}$$
adamc@1123 1642
adamc@544 1643 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 1644 $$\begin{array}{l}
adamc@544 1645 \mt{val} \; \mt{sql\_is\_null} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544 1646 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; (\mt{option} \; \mt{t}) \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{bool}
adamc@544 1647 \end{array}$$
adamc@544 1648
adamc@559 1649 We have generic nullary, unary, and binary operators.
adamc@544 1650 $$\begin{array}{l}
adamc@544 1651 \mt{con} \; \mt{sql\_nfunc} :: \mt{Type} \to \mt{Type} \\
adamc@544 1652 \mt{val} \; \mt{sql\_current\_timestamp} : \mt{sql\_nfunc} \; \mt{time} \\
adamc@544 1653 \mt{val} \; \mt{sql\_nfunc} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544 1654 \hspace{.1in} \to \mt{sql\_nfunc} \; \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\\end{array}$$
adamc@544 1655
adamc@544 1656 $$\begin{array}{l}
adamc@544 1657 \mt{con} \; \mt{sql\_unary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544 1658 \mt{val} \; \mt{sql\_not} : \mt{sql\_unary} \; \mt{bool} \; \mt{bool} \\
adamc@544 1659 \mt{val} \; \mt{sql\_unary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adamc@544 1660 \hspace{.1in} \to \mt{sql\_unary} \; \mt{arg} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res} \\
adamc@544 1661 \end{array}$$
adamc@544 1662
adamc@544 1663 $$\begin{array}{l}
adamc@544 1664 \mt{con} \; \mt{sql\_binary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544 1665 \mt{val} \; \mt{sql\_and} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544 1666 \mt{val} \; \mt{sql\_or} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544 1667 \mt{val} \; \mt{sql\_binary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg_1} ::: \mt{Type} \to \mt{arg_2} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adamc@544 1668 \hspace{.1in} \to \mt{sql\_binary} \; \mt{arg_1} \; \mt{arg_2} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_1} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_2} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res}
adamc@544 1669 \end{array}$$
adamc@544 1670
adamc@544 1671 $$\begin{array}{l}
adamc@559 1672 \mt{class} \; \mt{sql\_arith} \\
adamc@559 1673 \mt{val} \; \mt{sql\_int\_arith} : \mt{sql\_arith} \; \mt{int} \\
adamc@559 1674 \mt{val} \; \mt{sql\_float\_arith} : \mt{sql\_arith} \; \mt{float} \\
adamc@559 1675 \mt{val} \; \mt{sql\_neg} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_unary} \; \mt{t} \; \mt{t} \\
adamc@559 1676 \mt{val} \; \mt{sql\_plus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1677 \mt{val} \; \mt{sql\_minus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1678 \mt{val} \; \mt{sql\_times} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1679 \mt{val} \; \mt{sql\_div} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1680 \mt{val} \; \mt{sql\_mod} : \mt{sql\_binary} \; \mt{int} \; \mt{int} \; \mt{int}
adamc@559 1681 \end{array}$$
adamc@544 1682
adamc@656 1683 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 1684 $$\begin{array}{l}
adamc@544 1685 \mt{val} \; \mt{sql\_count} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int}
adamc@544 1686 \end{array}$$
adamc@544 1687
adamc@544 1688 $$\begin{array}{l}
adamc@1188 1689 \mt{con} \; \mt{sql\_aggregate} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@1188 1690 \mt{val} \; \mt{sql\_aggregate} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{dom} ::: \mt{Type} \to \mt{ran} ::: \mt{Type} \\
adamc@1188 1691 \hspace{.1in} \to \mt{sql\_aggregate} \; \mt{dom} \; \mt{ran} \to \mt{sql\_exp} \; \mt{agg} \; \mt{agg} \; \mt{exps} \; \mt{dom} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{ran}
adamc@1188 1692 \end{array}$$
adamc@1188 1693
adamc@1188 1694 $$\begin{array}{l}
adamc@1188 1695 \mt{val} \; \mt{sql\_count\_col} : \mt{t} ::: \mt{Type} \to \mt{sql\_aggregate} \; (\mt{option} \; \mt{t}) \; \mt{int}
adamc@544 1696 \end{array}$$
adamc@544 1697
adamc@544 1698 $$\begin{array}{l}
adamc@544 1699 \mt{class} \; \mt{sql\_summable} \\
adamc@544 1700 \mt{val} \; \mt{sql\_summable\_int} : \mt{sql\_summable} \; \mt{int} \\
adamc@544 1701 \mt{val} \; \mt{sql\_summable\_float} : \mt{sql\_summable} \; \mt{float} \\
adamc@1188 1702 \mt{val} \; \mt{sql\_avg} : \mt{t} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{t} \\
adamc@1188 1703 \mt{val} \; \mt{sql\_sum} : \mt{t} ::: \mt{Type} \to \mt{sql\_summable} \mt{t} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{t}
adamc@544 1704 \end{array}$$
adamc@544 1705
adamc@544 1706 $$\begin{array}{l}
adamc@544 1707 \mt{class} \; \mt{sql\_maxable} \\
adamc@544 1708 \mt{val} \; \mt{sql\_maxable\_int} : \mt{sql\_maxable} \; \mt{int} \\
adamc@544 1709 \mt{val} \; \mt{sql\_maxable\_float} : \mt{sql\_maxable} \; \mt{float} \\
adamc@544 1710 \mt{val} \; \mt{sql\_maxable\_string} : \mt{sql\_maxable} \; \mt{string} \\
adamc@544 1711 \mt{val} \; \mt{sql\_maxable\_time} : \mt{sql\_maxable} \; \mt{time} \\
adamc@1188 1712 \mt{val} \; \mt{sql\_max} : \mt{t} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{t} \\
adamc@1188 1713 \mt{val} \; \mt{sql\_min} : \mt{t} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{t}
adamc@544 1714 \end{array}$$
adamc@544 1715
adamc@1193 1716 Any SQL query that returns single columns may be turned into a subquery expression.
adamc@1193 1717
adamc@786 1718 $$\begin{array}{l}
adamc@1193 1719 \mt{val} \; \mt{sql\_subquery} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \\
adamc@1193 1720 \hspace{.1in} \to \mt{sql\_query} \; \mt{tables} \; [] \; [\mt{nm} = \mt{t}] \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adamc@1193 1721 \end{array}$$
adamc@1193 1722
adamc@1193 1723 \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 1724 $$\begin{array}{l}
adamc@1193 1725 \mt{con} \; \mt{sql\_from\_items} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@1193 1726 \mt{val} \; \mt{sql\_from\_table} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1727 \hspace{.1in} \to \mt{t} ::: \mt{Type} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; \mt{t} \; \mt{fs} \to \mt{name} :: \mt{Name} \to \mt{t} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193 1728 \mt{val} \; \mt{sql\_from\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{name} :: \mt{Name} \to \mt{sql\_query} \; \mt{free} \; [] \; \mt{fs} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193 1729 \mt{val} \; \mt{sql\_from\_comma} : \mt{free} ::: \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \to [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193 1730 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adamc@1193 1731 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2}) \\
adamc@1193 1732 \mt{val} \; \mt{sql\_inner\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1733 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193 1734 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adamc@1193 1735 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193 1736 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2})
adamc@786 1737 \end{array}$$
adamc@786 1738
adamc@786 1739 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 1740 $$\begin{array}{l}
adamc@786 1741 \mt{class} \; \mt{nullify} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@786 1742 \mt{val} \; \mt{nullify\_option} : \mt{t} ::: \mt{Type} \to \mt{nullify} \; (\mt{option} \; \mt{t}) \; (\mt{option} \; \mt{t}) \\
adamc@786 1743 \mt{val} \; \mt{nullify\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{nullify} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@786 1744 \end{array}$$
adamc@786 1745
adamc@786 1746 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 1747
adamc@786 1748 $$\begin{array}{l}
adamc@1193 1749 \mt{val} \; \mt{sql\_left\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{(\mt{Type} \times \mt{Type})\}\} \\
adamc@1193 1750 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@786 1751 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\lambda \mt{r} \Rightarrow \$(\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{nullify} \; \mt{p}.1 \; \mt{p}.2) \; \mt{r})) \; \mt{tabs2}) \\
adamc@1193 1752 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \\
adamc@1193 1753 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193 1754 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.2)) \; \mt{tabs2})
adamc@786 1755 \end{array}$$
adamc@786 1756
adamc@544 1757 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 1758 $$\begin{array}{l}
adamc@544 1759 \mt{type} \; \mt{sql\_direction} \\
adamc@544 1760 \mt{val} \; \mt{sql\_asc} : \mt{sql\_direction} \\
adamc@544 1761 \mt{val} \; \mt{sql\_desc} : \mt{sql\_direction} \\
adamc@544 1762 \\
adamc@544 1763 \mt{con} \; \mt{sql\_order\_by} :: \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@544 1764 \mt{val} \; \mt{sql\_order\_by\_Nil} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} :: \{\mt{Type}\} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544 1765 \mt{val} \; \mt{sql\_order\_by\_Cons} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544 1766 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; [] \; \mt{exps} \; \mt{t} \to \mt{sql\_direction} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544 1767 \\
adamc@544 1768 \mt{type} \; \mt{sql\_limit} \\
adamc@544 1769 \mt{val} \; \mt{sql\_no\_limit} : \mt{sql\_limit} \\
adamc@544 1770 \mt{val} \; \mt{sql\_limit} : \mt{int} \to \mt{sql\_limit} \\
adamc@544 1771 \\
adamc@544 1772 \mt{type} \; \mt{sql\_offset} \\
adamc@544 1773 \mt{val} \; \mt{sql\_no\_offset} : \mt{sql\_offset} \\
adamc@544 1774 \mt{val} \; \mt{sql\_offset} : \mt{int} \to \mt{sql\_offset}
adamc@544 1775 \end{array}$$
adamc@544 1776
adamc@545 1777
adamc@545 1778 \subsubsection{DML}
adamc@545 1779
adamc@545 1780 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 1781
adamc@545 1782 $$\begin{array}{l}
adamc@545 1783 \mt{type} \; \mt{dml} \\
adamc@545 1784 \mt{val} \; \mt{dml} : \mt{dml} \to \mt{transaction} \; \mt{unit}
adamc@545 1785 \end{array}$$
adamc@545 1786
adam@1297 1787 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 1788
adam@1297 1789 $$\begin{array}{l}
adam@1297 1790 \mt{val} \; \mt{tryDml} : \mt{dml} \to \mt{transaction} \; (\mt{option} \; \mt{string})
adam@1297 1791 \end{array}$$
adam@1297 1792
adamc@545 1793 Properly-typed records may be used to form $\mt{INSERT}$ commands.
adamc@545 1794 $$\begin{array}{l}
adamc@545 1795 \mt{val} \; \mt{insert} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \\
adamc@658 1796 \hspace{.1in} \to \$(\mt{map} \; (\mt{sql\_exp} \; [] \; [] \; []) \; \mt{fields}) \to \mt{dml}
adamc@545 1797 \end{array}$$
adamc@545 1798
adamc@545 1799 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 1800 $$\begin{array}{l}
adamc@545 1801 \mt{val} \; \mt{update} : \mt{unchanged} ::: \{\mt{Type}\} \to \mt{changed} :: \{\mt{Type}\} \to \lambda [\mt{changed} \sim \mt{unchanged}] \\
adamc@658 1802 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; []) \; \mt{changed}) \\
adamc@545 1803 \hspace{.1in} \to \mt{sql\_table} \; (\mt{changed} \rc \mt{unchanged}) \to \mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545 1804 \end{array}$$
adamc@545 1805
adamc@545 1806 A $\mt{DELETE}$ command is formed from a table and a $\mt{WHERE}$ clause.
adamc@545 1807 $$\begin{array}{l}
adamc@545 1808 \mt{val} \; \mt{delete} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \to \mt{sql\_exp} \; [\mt{T} = \mt{fields}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545 1809 \end{array}$$
adamc@545 1810
adamc@546 1811 \subsubsection{Sequences}
adamc@546 1812
adamc@546 1813 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 1814
adamc@546 1815 $$\begin{array}{l}
adamc@546 1816 \mt{type} \; \mt{sql\_sequence} \\
adamc@1085 1817 \mt{val} \; \mt{nextval} : \mt{sql\_sequence} \to \mt{transaction} \; \mt{int} \\
adamc@1085 1818 \mt{val} \; \mt{setval} : \mt{sql\_sequence} \to \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@546 1819 \end{array}$$
adamc@546 1820
adamc@546 1821
adamc@547 1822 \subsection{XML}
adamc@547 1823
adam@1333 1824 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 1825
adam@1345 1826 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 1827 $$\begin{array}{l}
adamc@547 1828 \mt{con} \; \mt{xml} :: \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547 1829 \end{array}$$
adamc@547 1830
adamc@547 1831 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 1832 $$\begin{array}{l}
adamc@547 1833 \mt{con} \; \mt{tag} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547 1834 \end{array}$$
adamc@547 1835
adamc@547 1836 Literal text may be injected into XML as ``CDATA.''
adamc@547 1837 $$\begin{array}{l}
adamc@547 1838 \mt{val} \; \mt{cdata} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{string} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adamc@547 1839 \end{array}$$
adamc@547 1840
adamc@547 1841 There is a function for producing an XML tree with a particular tag at its root.
adamc@547 1842 $$\begin{array}{l}
adamc@547 1843 \mt{val} \; \mt{tag} : \mt{attrsGiven} ::: \{\mt{Type}\} \to \mt{attrsAbsent} ::: \{\mt{Type}\} \to \mt{ctxOuter} ::: \{\mt{Unit}\} \to \mt{ctxInner} ::: \{\mt{Unit}\} \\
adamc@547 1844 \hspace{.1in} \to \mt{useOuter} ::: \{\mt{Type}\} \to \mt{useInner} ::: \{\mt{Type}\} \to \mt{bindOuter} ::: \{\mt{Type}\} \to \mt{bindInner} ::: \{\mt{Type}\} \\
adamc@787 1845 \hspace{.1in} \to \lambda [\mt{attrsGiven} \sim \mt{attrsAbsent}] \; [\mt{useOuter} \sim \mt{useInner}] \; [\mt{bindOuter} \sim \mt{bindInner}] \\
adamc@787 1846 \hspace{.1in} \Rightarrow \mt{option} \; \mt{css\_class} \\
adamc@787 1847 \hspace{.1in} \to \$\mt{attrsGiven} \\
adamc@547 1848 \hspace{.1in} \to \mt{tag} \; (\mt{attrsGiven} \rc \mt{attrsAbsent}) \; \mt{ctxOuter} \; \mt{ctxInner} \; \mt{useOuter} \; \mt{bindOuter} \\
adamc@547 1849 \hspace{.1in} \to \mt{xml} \; \mt{ctxInner} \; \mt{useInner} \; \mt{bindInner} \to \mt{xml} \; \mt{ctxOuter} \; (\mt{useOuter} \rc \mt{useInner}) \; (\mt{bindOuter} \rc \mt{bindInner})
adamc@547 1850 \end{array}$$
adam@1297 1851 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 1852
adamc@547 1853 Two XML fragments may be concatenated.
adamc@547 1854 $$\begin{array}{l}
adamc@547 1855 \mt{val} \; \mt{join} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{bind_1} ::: \{\mt{Type}\} \to \mt{bind_2} ::: \{\mt{Type}\} \\
adamc@547 1856 \hspace{.1in} \to \lambda [\mt{use_1} \sim \mt{bind_1}] \; [\mt{bind_1} \sim \mt{bind_2}] \\
adamc@547 1857 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind_1} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{bind_1}) \; \mt{bind_2} \to \mt{xml} \; \mt{ctx} \; \mt{use_1} \; (\mt{bind_1} \rc \mt{bind_2})
adamc@547 1858 \end{array}$$
adamc@547 1859
adamc@547 1860 Finally, any XML fragment may be updated to ``claim'' to use more form fields than it does.
adamc@547 1861 $$\begin{array}{l}
adamc@547 1862 \mt{val} \; \mt{useMore} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{use_2} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to \lambda [\mt{use_1} \sim \mt{use_2}] \\
adamc@547 1863 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{use_2}) \; \mt{bind}
adamc@547 1864 \end{array}$$
adamc@547 1865
adam@1344 1866 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 1867
adamc@547 1868 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 1869 $$\begin{array}{l}
adamc@547 1870 \mt{val} \; \mt{error} : \mt{t} ::: \mt{Type} \to \mt{xml} \; [\mt{Body}] \; [] \; [] \to \mt{t}
adamc@547 1871 \end{array}$$
adamc@547 1872
adamc@549 1873
adamc@701 1874 \subsection{Client-Side Programming}
adamc@659 1875
adamc@701 1876 Ur/Web supports running code on web browsers, via automatic compilation to JavaScript.
adamc@701 1877
adamc@701 1878 \subsubsection{The Basics}
adamc@701 1879
adam@1297 1880 Clients can open alert and confirm dialog boxes, in the usual annoying JavaScript way.
adamc@701 1881 $$\begin{array}{l}
adam@1297 1882 \mt{val} \; \mt{alert} : \mt{string} \to \mt{transaction} \; \mt{unit} \\
adam@1297 1883 \mt{val} \; \mt{confirm} : \mt{string} \to \mt{transaction} \; \mt{bool}
adamc@701 1884 \end{array}$$
adamc@701 1885
adamc@701 1886 Any transaction may be run in a new thread with the $\mt{spawn}$ function.
adamc@701 1887 $$\begin{array}{l}
adamc@701 1888 \mt{val} \; \mt{spawn} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit}
adamc@701 1889 \end{array}$$
adamc@701 1890
adamc@701 1891 The current thread can be paused for at least a specified number of milliseconds.
adamc@701 1892 $$\begin{array}{l}
adamc@701 1893 \mt{val} \; \mt{sleep} : \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@701 1894 \end{array}$$
adamc@701 1895
adamc@787 1896 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 1897 $$\begin{array}{l}
adamc@787 1898 \mt{val} \; \mt{onError} : (\mt{xbody} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787 1899 \mt{val} \; \mt{onFail} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787 1900 \mt{val} \; \mt{onConnectFail} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787 1901 \mt{val} \; \mt{onDisconnect} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787 1902 \mt{val} \; \mt{onServerError} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit}
adamc@787 1903 \end{array}$$
adamc@787 1904
adamc@701 1905 \subsubsection{Functional-Reactive Page Generation}
adamc@701 1906
adamc@701 1907 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 1908
adamc@659 1909 $$\begin{array}{l}
adamc@659 1910 \mt{con} \; \mt{source} :: \mt{Type} \to \mt{Type} \\
adamc@659 1911 \mt{val} \; \mt{source} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{transaction} \; (\mt{source} \; \mt{t}) \\
adamc@659 1912 \mt{val} \; \mt{set} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@659 1913 \mt{val} \; \mt{get} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@659 1914 \end{array}$$
adamc@659 1915
adamc@659 1916 Pure functions over sources are represented in a monad of \emph{signals}.
adamc@659 1917
adamc@659 1918 $$\begin{array}{l}
adamc@659 1919 \mt{con} \; \mt{signal} :: \mt{Type} \to \mt{Type} \\
adamc@659 1920 \mt{val} \; \mt{signal\_monad} : \mt{monad} \; \mt{signal} \\
adamc@659 1921 \mt{val} \; \mt{signal} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{signal} \; \mt{t}
adamc@659 1922 \end{array}$$
adamc@659 1923
adamc@659 1924 A reactive portion of an HTML page is injected with a $\mt{dyn}$ tag, which has a signal-valued attribute $\mt{Signal}$.
adamc@659 1925
adamc@659 1926 $$\begin{array}{l}
adamc@701 1927 \mt{val} \; \mt{dyn} : \mt{use} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to \mt{unit} \\
adamc@701 1928 \hspace{.1in} \to \mt{tag} \; [\mt{Signal} = \mt{signal} \; (\mt{xml} \; \mt{body} \; \mt{use} \; \mt{bind})] \; \mt{body} \; [] \; \mt{use} \; \mt{bind}
adamc@659 1929 \end{array}$$
adamc@659 1930
adamc@701 1931 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 1932
adamc@914 1933 \subsubsection{Remote Procedure Calls}
adamc@914 1934
adamc@914 1935 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 1936
adamc@914 1937 $$\begin{array}{l}
adamc@914 1938 \mt{val} \; \mt{rpc} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@914 1939 \end{array}$$
adamc@914 1940
adamc@701 1941 \subsubsection{Asynchronous Message-Passing}
adamc@701 1942
adamc@701 1943 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 1944
adamc@701 1945 $$\begin{array}{l}
adamc@701 1946 \mt{type} \; \mt{client} \\
adamc@701 1947 \mt{val} \; \mt{self} : \mt{transaction} \; \mt{client}
adamc@701 1948 \end{array}$$
adamc@701 1949
adamc@701 1950 \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 1951
adamc@701 1952 $$\begin{array}{l}
adamc@701 1953 \mt{con} \; \mt{channel} :: \mt{Type} \to \mt{Type} \\
adamc@701 1954 \mt{val} \; \mt{channel} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; (\mt{channel} \; \mt{t}) \\
adamc@701 1955 \mt{val} \; \mt{send} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@701 1956 \mt{val} \; \mt{recv} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@701 1957 \end{array}$$
adamc@701 1958
adamc@701 1959 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 1960
adamc@701 1961 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 1962
adamc@659 1963
adamc@549 1964 \section{Ur/Web Syntax Extensions}
adamc@549 1965
adamc@549 1966 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 1967
adamc@549 1968 \subsection{SQL}
adamc@549 1969
adamc@786 1970 \subsubsection{\label{tables}Table Declarations}
adamc@786 1971
adamc@788 1972 $\mt{table}$ declarations may include constraints, via these grammar rules.
adamc@788 1973 $$\begin{array}{rrcll}
adamc@788 1974 \textrm{Declarations} & d &::=& \mt{table} \; x : c \; [pk[,]] \; cts \\
adamc@788 1975 \textrm{Primary key constraints} & pk &::=& \mt{PRIMARY} \; \mt{KEY} \; K \\
adamc@788 1976 \textrm{Keys} & K &::=& f \mid (f, (f,)^+) \\
adamc@788 1977 \textrm{Constraint sets} & cts &::=& \mt{CONSTRAINT} f \; ct \mid cts, cts \mid \{\{e\}\} \\
adamc@788 1978 \textrm{Constraints} & ct &::=& \mt{UNIQUE} \; K \mid \mt{CHECK} \; E \\
adamc@788 1979 &&& \mid \mt{FOREIGN} \; \mt{KEY} \; K \; \mt{REFERENCES} \; F \; (K) \; [\mt{ON} \; \mt{DELETE} \; pr] \; [\mt{ON} \; \mt{UPDATE} \; pr] \\
adamc@788 1980 \textrm{Foreign tables} & F &::=& x \mid \{\{e\}\} \\
adamc@788 1981 \textrm{Propagation modes} & pr &::=& \mt{NO} \; \mt{ACTION} \mid \mt{RESTRICT} \mid \mt{CASCADE} \mid \mt{SET} \; \mt{NULL}
adamc@788 1982 \end{array}$$
adamc@788 1983
adamc@788 1984 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 1985
adamc@788 1986
adamc@549 1987 \subsubsection{Queries}
adamc@549 1988
adamc@550 1989 Queries $Q$ are added to the rules for expressions $e$.
adamc@550 1990
adamc@549 1991 $$\begin{array}{rrcll}
adamc@550 1992 \textrm{Queries} & Q &::=& (q \; [\mt{ORDER} \; \mt{BY} \; (E \; [o],)^+] \; [\mt{LIMIT} \; N] \; [\mt{OFFSET} \; N]) \\
adamc@1085 1993 \textrm{Pre-queries} & q &::=& \mt{SELECT} \; [\mt{DISTINCT}] \; P \; \mt{FROM} \; F,^+ \; [\mt{WHERE} \; E] \; [\mt{GROUP} \; \mt{BY} \; p,^+] \; [\mt{HAVING} \; E] \\
adamc@1085 1994 &&& \mid q \; R \; q \mid \{\{\{e\}\}\} \\
adamc@549 1995 \textrm{Relational operators} & R &::=& \mt{UNION} \mid \mt{INTERSECT} \mid \mt{EXCEPT}
adamc@549 1996 \end{array}$$
adamc@549 1997
adamc@549 1998 $$\begin{array}{rrcll}
adamc@549 1999 \textrm{Projections} & P &::=& \ast & \textrm{all columns} \\
adamc@549 2000 &&& p,^+ & \textrm{particular columns} \\
adamc@549 2001 \textrm{Pre-projections} & p &::=& t.f & \textrm{one column from a table} \\
adamc@558 2002 &&& t.\{\{c\}\} & \textrm{a record of columns from a table (of kind $\{\mt{Type}\}$)} \\
adamc@1194 2003 &&& E \; [\mt{AS} \; f] & \textrm{expression column} \\
adamc@549 2004 \textrm{Table names} & t &::=& x & \textrm{constant table name (automatically capitalized)} \\
adamc@549 2005 &&& X & \textrm{constant table name} \\
adamc@549 2006 &&& \{\{c\}\} & \textrm{computed table name (of kind $\mt{Name}$)} \\
adamc@549 2007 \textrm{Column names} & f &::=& X & \textrm{constant column name} \\
adamc@549 2008 &&& \{c\} & \textrm{computed column name (of kind $\mt{Name}$)} \\
adamc@549 2009 \textrm{Tables} & T &::=& x & \textrm{table variable, named locally by its own capitalization} \\
adamc@549 2010 &&& x \; \mt{AS} \; t & \textrm{table variable, with local name} \\
adamc@549 2011 &&& \{\{e\}\} \; \mt{AS} \; t & \textrm{computed table expression, with local name} \\
adamc@1085 2012 \textrm{$\mt{FROM}$ items} & F &::=& T \mid \{\{e\}\} \mid F \; J \; \mt{JOIN} \; F \; \mt{ON} \; E \\
adamc@1085 2013 &&& \mid F \; \mt{CROSS} \; \mt{JOIN} \ F \\
adamc@1193 2014 &&& \mid (Q) \; \mt{AS} \; t \\
adamc@1085 2015 \textrm{Joins} & J &::=& [\mt{INNER}] \\
adamc@1085 2016 &&& \mid [\mt{LEFT} \mid \mt{RIGHT} \mid \mt{FULL}] \; [\mt{OUTER}] \\
adamc@549 2017 \textrm{SQL expressions} & E &::=& p & \textrm{column references} \\
adamc@549 2018 &&& X & \textrm{named expression references} \\
adamc@549 2019 &&& \{\{e\}\} & \textrm{injected native Ur expressions} \\
adamc@549 2020 &&& \{e\} & \textrm{computed expressions, probably using $\mt{sql\_exp}$ directly} \\
adamc@549 2021 &&& \mt{TRUE} \mid \mt{FALSE} & \textrm{boolean constants} \\
adamc@549 2022 &&& \ell & \textrm{primitive type literals} \\
adamc@549 2023 &&& \mt{NULL} & \textrm{null value (injection of $\mt{None}$)} \\
adamc@549 2024 &&& E \; \mt{IS} \; \mt{NULL} & \textrm{nullness test} \\
adamc@549 2025 &&& n & \textrm{nullary operators} \\
adamc@549 2026 &&& u \; E & \textrm{unary operators} \\
adamc@549 2027 &&& E \; b \; E & \textrm{binary operators} \\
adamc@549 2028 &&& \mt{COUNT}(\ast) & \textrm{count number of rows} \\
adamc@549 2029 &&& a(E) & \textrm{other aggregate function} \\
adamc@1193 2030 &&& (Q) & \textrm{subquery (must return a single expression column)} \\
adamc@549 2031 &&& (E) & \textrm{explicit precedence} \\
adamc@549 2032 \textrm{Nullary operators} & n &::=& \mt{CURRENT\_TIMESTAMP} \\
adamc@549 2033 \textrm{Unary operators} & u &::=& \mt{NOT} \\
adamc@549 2034 \textrm{Binary operators} & b &::=& \mt{AND} \mid \mt{OR} \mid \neq \mid < \mid \leq \mid > \mid \geq \\
adamc@1188 2035 \textrm{Aggregate functions} & a &::=& \mt{COUNT} \mid \mt{AVG} \mid \mt{SUM} \mid \mt{MIN} \mid \mt{MAX} \\
adamc@550 2036 \textrm{Directions} & o &::=& \mt{ASC} \mid \mt{DESC} \\
adamc@549 2037 \textrm{SQL integer} & N &::=& n \mid \{e\} \\
adamc@549 2038 \end{array}$$
adamc@549 2039
adamc@1085 2040 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 2041
adamc@1194 2042 Unnamed expression columns in $\mt{SELECT}$ clauses are assigned consecutive natural numbers, starting with 1.
adamc@1194 2043
adamc@550 2044 \subsubsection{DML}
adamc@550 2045
adamc@550 2046 DML commands $D$ are added to the rules for expressions $e$.
adamc@550 2047
adamc@550 2048 $$\begin{array}{rrcll}
adamc@550 2049 \textrm{Commands} & D &::=& (\mt{INSERT} \; \mt{INTO} \; T^E \; (f,^+) \; \mt{VALUES} \; (E,^+)) \\
adamc@550 2050 &&& (\mt{UPDATE} \; T^E \; \mt{SET} \; (f = E,)^+ \; \mt{WHERE} \; E) \\
adamc@550 2051 &&& (\mt{DELETE} \; \mt{FROM} \; T^E \; \mt{WHERE} \; E) \\
adamc@550 2052 \textrm{Table expressions} & T^E &::=& x \mid \{\{e\}\}
adamc@550 2053 \end{array}$$
adamc@550 2054
adamc@550 2055 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 2056
adamc@551 2057 \subsection{XML}
adamc@551 2058
adamc@551 2059 XML fragments $L$ are added to the rules for expressions $e$.
adamc@551 2060
adamc@551 2061 $$\begin{array}{rrcll}
adamc@551 2062 \textrm{XML fragments} & L &::=& \texttt{<xml/>} \mid \texttt{<xml>}l^*\texttt{</xml>} \\
adamc@551 2063 \textrm{XML pieces} & l &::=& \textrm{text} & \textrm{cdata} \\
adamc@551 2064 &&& \texttt{<}g\texttt{/>} & \textrm{tag with no children} \\
adamc@551 2065 &&& \texttt{<}g\texttt{>}l^*\texttt{</}x\texttt{>} & \textrm{tag with children} \\
adamc@559 2066 &&& \{e\} & \textrm{computed XML fragment} \\
adamc@559 2067 &&& \{[e]\} & \textrm{injection of an Ur expression, via the $\mt{Top}.\mt{txt}$ function} \\
adamc@551 2068 \textrm{Tag} & g &::=& h \; (x = v)^* \\
adamc@551 2069 \textrm{Tag head} & h &::=& x & \textrm{tag name} \\
adamc@551 2070 &&& h\{c\} & \textrm{constructor parameter} \\
adamc@551 2071 \textrm{Attribute value} & v &::=& \ell & \textrm{literal value} \\
adamc@551 2072 &&& \{e\} & \textrm{computed value} \\
adamc@551 2073 \end{array}$$
adamc@551 2074
adamc@552 2075
adamc@1198 2076 \section{\label{structure}The Structure of Web Applications}
adamc@553 2077
adamc@1127 2078 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 2079
adam@1347 2080 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 2081
adamc@553 2082 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 2083
adamc@553 2084 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 2085
adamc@558 2086 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 2087
adamc@660 2088 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 2089
adamc@789 2090 \medskip
adamc@789 2091
adam@1347 2092 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 2093
adamc@789 2094 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 2095
adam@1348 2096 \subsection{Tasks}
adam@1348 2097
adam@1348 2098 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 2099
adam@1348 2100 $$\begin{array}{l}
adam@1348 2101 \mt{con} \; \mt{task\_kind} :: \mt{Type} \to \mt{Type} \\
adam@1348 2102 \mt{val} \; \mt{initialize} : \mt{task\_kind} \; \mt{unit} \\
adam@1349 2103 \mt{val} \; \mt{clientLeaves} : \mt{task\_kind} \; \mt{client} \\
adam@1349 2104 \mt{val} \; \mt{periodic} : \mt{int} \to \mt{task\_kind} \; \mt{unit}
adam@1348 2105 \end{array}$$
adam@1348 2106
adam@1348 2107 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 2108
adam@1348 2109 The currently supported task kinds are:
adam@1348 2110 \begin{itemize}
adam@1349 2111 \item $\mt{initialize}$: Code that is run when the application starts up.
adam@1348 2112 \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 2113 \item $\mt{periodic} \; n$: Code that is run when the application starts up and then every $n$ seconds thereafter.
adam@1348 2114 \end{itemize}
adam@1348 2115
adamc@553 2116
adamc@897 2117 \section{The Foreign Function Interface}
adamc@897 2118
adamc@897 2119 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 2120
adamc@897 2121 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 2122
adamc@897 2123 \begin{itemize}
adamc@897 2124 \item \texttt{clientOnly Module.ident} registers a value as being allowed only in client-side code.
adamc@897 2125 \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 2126 \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 2127 \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 2128 \item \texttt{include FILE} requests inclusion of a C header file.
adamc@897 2129 \item \texttt{jsFunc Module.ident=name} gives a mapping from an Ur name for a value to a JavaScript name.
adamc@897 2130 \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 2131 \item \texttt{script URL} requests inclusion of a JavaScript source file within application HTML.
adamc@897 2132 \item \texttt{serverOnly Module.ident} registers a value as being allowed only in server-side code.
adamc@897 2133 \end{itemize}
adamc@897 2134
adamc@897 2135 \subsection{Writing C FFI Code}
adamc@897 2136
adamc@897 2137 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 2138
adamc@897 2139 \begin{itemize}
adamc@897 2140 \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 2141 \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 2142 \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 2143 \end{itemize}
adamc@897 2144
adamc@897 2145 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 2146 \begin{itemize}
adamc@897 2147 \item \begin{verbatim}
adamc@897 2148 void uw_error(uw_context, failure_kind, const char *fmt, ...);
adamc@897 2149 \end{verbatim}
adamc@897 2150 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 2151
adam@1329 2152 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 2153
adamc@897 2154 \item \begin{verbatim}
adamc@897 2155 void uw_push_cleanup(uw_context, void (*func)(void *), void *arg);
adamc@897 2156 void uw_pop_cleanup(uw_context);
adamc@897 2157 \end{verbatim}
adam@1329 2158 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 2159
adam@1329 2160 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 2161
adamc@897 2162 \item \begin{verbatim}
adamc@897 2163 void *uw_malloc(uw_context, size_t);
adamc@897 2164 \end{verbatim}
adam@1329 2165 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 2166
adam@1329 2167 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 2168
adamc@897 2169 \item \begin{verbatim}
adamc@897 2170 typedef void (*uw_callback)(void *);
adam@1328 2171 typedef void (*uw_callback_with_retry)(void *, int will_retry);
adamc@897 2172 void uw_register_transactional(uw_context, void *data, uw_callback commit,
adam@1328 2173 uw_callback rollback, uw_callback_with_retry free);
adamc@897 2174 \end{verbatim}
adam@1328 2175 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 2176
adamc@1085 2177 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 2178
adam@1329 2179 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 2180
adam@1329 2181 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 2182
adamc@1085 2183 \item \begin{verbatim}
adamc@1085 2184 void *uw_get_global(uw_context, char *name);
adamc@1085 2185 void uw_set_global(uw_context, char *name, void *data, uw_callback free);
adamc@1085 2186 \end{verbatim}
adam@1329 2187 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 2188
adamc@897 2189 \end{itemize}
adamc@897 2190
adamc@897 2191 \subsection{Writing JavaScript FFI Code}
adamc@897 2192
adamc@897 2193 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 2194
adamc@897 2195 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 2196
adamc@897 2197 \begin{itemize}
adamc@897 2198 \item Integers, floats, strings, characters, and booleans are represented in the usual JavaScript way.
adamc@985 2199 \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 2200 \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 2201 \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 2202 \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 2203 \end{itemize}
adamc@897 2204
adamc@897 2205 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 2206
adamc@897 2207
adamc@552 2208 \section{Compiler Phases}
adamc@552 2209
adamc@552 2210 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 2211
adamc@552 2212 In this section, we step through the main phases of compilation, noting what consequences each phase has for effective programming.
adamc@552 2213
adamc@552 2214 \subsection{Parse}
adamc@552 2215
adamc@552 2216 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 2217
adamc@552 2218 \subsection{Elaborate}
adamc@552 2219
adamc@552 2220 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 2221
adamc@552 2222 \subsection{Unnest}
adamc@552 2223
adamc@552 2224 Named local function definitions are moved to the top level, to avoid the need to generate closures.
adamc@552 2225
adamc@552 2226 \subsection{Corify}
adamc@552 2227
adamc@552 2228 Module system features are compiled away, through inlining of functor definitions at application sites. Afterward, most abstraction boundaries are broken, facilitating optimization.
adamc@552 2229
adamc@552 2230 \subsection{Especialize}
adamc@552 2231
adamc@552 2232 Functions are specialized to particular argument patterns. This is an important trick for avoiding the need to maintain any closures at runtime.
adamc@552 2233
adamc@552 2234 \subsection{Untangle}
adamc@552 2235
adamc@552 2236 Remove unnecessary mutual recursion, splitting recursive groups into strongly-connected components.
adamc@552 2237
adamc@552 2238 \subsection{Shake}
adamc@552 2239
adamc@552 2240 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 2241
adamc@661 2242 \subsection{Rpcify}
adamc@661 2243
adamc@661 2244 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 2245
adamc@661 2246 \subsection{Untangle, Shake}
adamc@661 2247
adamc@661 2248 Repeat these simplifications.
adamc@661 2249
adamc@553 2250 \subsection{\label{tag}Tag}
adamc@552 2251
adamc@552 2252 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 2253
adamc@552 2254 \subsection{Reduce}
adamc@552 2255
adamc@552 2256 Apply definitional equality rules to simplify the program as much as possible. This effectively includes inlining of every non-recursive definition.
adamc@552 2257
adamc@552 2258 \subsection{Unpoly}
adamc@552 2259
adamc@552 2260 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 2261
adamc@552 2262 \subsection{Specialize}
adamc@552 2263
adamc@558 2264 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 2265
adamc@552 2266 \subsection{Shake}
adamc@552 2267
adamc@558 2268 Here the compiler repeats the earlier Shake phase.
adamc@552 2269
adamc@552 2270 \subsection{Monoize}
adamc@552 2271
adamc@552 2272 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 2273
adamc@552 2274 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 2275
adamc@552 2276 \subsection{MonoOpt}
adamc@552 2277
adamc@552 2278 Simple algebraic laws are applied to simplify the program, focusing especially on efficient imperative generation of HTML pages.
adamc@552 2279
adamc@552 2280 \subsection{MonoUntangle}
adamc@552 2281
adamc@552 2282 Unnecessary mutual recursion is broken up again.
adamc@552 2283
adamc@552 2284 \subsection{MonoReduce}
adamc@552 2285
adamc@552 2286 Equivalents of the definitional equality rules are applied to simplify programs, with inlining again playing a major role.
adamc@552 2287
adamc@552 2288 \subsection{MonoShake, MonoOpt}
adamc@552 2289
adamc@552 2290 Unneeded declarations are removed, and basic optimizations are repeated.
adamc@552 2291
adamc@552 2292 \subsection{Fuse}
adamc@552 2293
adamc@552 2294 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 2295
adamc@552 2296 \subsection{MonoUntangle, MonoShake}
adamc@552 2297
adamc@552 2298 Fuse often creates more opportunities to remove spurious mutual recursion.
adamc@552 2299
adamc@552 2300 \subsection{Pathcheck}
adamc@552 2301
adamc@552 2302 The compiler checks that no link or action name has been used more than once.
adamc@552 2303
adamc@552 2304 \subsection{Cjrize}
adamc@552 2305
adamc@552 2306 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 2307
adamc@552 2308 \subsection{C Compilation and Linking}
adamc@552 2309
adamc@552 2310 The output of the last phase is pretty-printed as C source code and passed to GCC.
adamc@552 2311
adamc@552 2312
adamc@524 2313 \end{document}