annotate doc/manual.tex @ 1297:41484478a32d

Updating documentation
author Adam Chlipala <adam@chlipala.net>
date Tue, 07 Sep 2010 09:47:06 -0400
parents b52929351402
children e3944a8a128a
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
adamc@1151 131 A blank line separates the named directives from a list of modules to include in the project.
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}.
adamc@783 149 \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@1297 150 \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@852 151 \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@783 152 \item \texttt{prefix PREFIX} sets the prefix included before every URI within the generated application. The default is \texttt{/}.
adamc@783 153 \item \texttt{profile} generates an executable that may be used with gprof.
adamc@783 154 \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}. 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 155 \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@783 156 \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@783 157 \item \texttt{serverOnly Module.ident} registers an FFI function or transaction that may only be run on the server.
adamc@1164 158 \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@783 159 \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@783 160 \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@783 161 \end{itemize}
adamc@701 162
adamc@701 163
adamc@557 164 \subsection{Building an Application}
adamc@557 165
adamc@557 166 To compile project \texttt{P.urp}, simply run
adamc@557 167 \begin{verbatim}
adamc@557 168 urweb P
adamc@557 169 \end{verbatim}
adamc@1198 170 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@557 171
adamc@557 172 To time how long the different compiler phases run, without generating an executable, run
adamc@557 173 \begin{verbatim}
adamc@557 174 urweb -timing P
adamc@557 175 \end{verbatim}
adamc@557 176
adamc@1086 177 To stop the compilation process after type-checking, run
adamc@1086 178 \begin{verbatim}
adamc@1086 179 urweb -tc P
adamc@1086 180 \end{verbatim}
adamc@1086 181
adamc@1170 182 To output information relevant to CSS stylesheets (and not finish regular compilation), run
adamc@1170 183 \begin{verbatim}
adamc@1170 184 urweb -css P
adamc@1170 185 \end{verbatim}
adamc@1170 186 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 187
adamc@896 188 Some other command-line parameters are accepted:
adamc@896 189 \begin{itemize}
adamc@896 190 \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@896 191
adamc@896 192 \item \texttt{-dbms [postgres|mysql|sqlite]}: Sets the database backend to use.
adamc@896 193 \begin{itemize}
adamc@896 194 \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@896 195
adamc@896 196 A command sequence like this can initialize a Postgres database, using a file \texttt{app.sql} generated by the compiler:
adamc@896 197 \begin{verbatim}
adamc@896 198 createdb app
adamc@896 199 psql -f app.sql app
adamc@896 200 \end{verbatim}
adamc@896 201
adamc@896 202 \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@896 203
adamc@896 204 A command sequence like this can initialize a MySQL database:
adamc@896 205 \begin{verbatim}
adamc@896 206 echo "CREATE DATABASE app" | mysql
adamc@896 207 mysql -D app <app.sql
adamc@896 208 \end{verbatim}
adamc@896 209
adamc@896 210 \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@896 211
adamc@896 212 A command like this can initialize an SQLite database:
adamc@896 213 \begin{verbatim}
adamc@896 214 sqlite3 path/to/database/file <app.sql
adamc@896 215 \end{verbatim}
adamc@896 216 \end{itemize}
adamc@896 217
adamc@896 218 \item \texttt{-output FILENAME}: Set where the application executable is written.
adamc@896 219
adamc@1127 220 \item \texttt{-path NAME VALUE}: Set the value of path variable \texttt{\$NAME} to \texttt{VALUE}, for use in \texttt{.urp} files.
adamc@1127 221
adamc@896 222 \item \texttt{-protocol [http|cgi|fastcgi]}: Set the protocol that the generated application speaks.
adamc@896 223 \begin{itemize}
adamc@896 224 \item \texttt{http}: This is the default. It is for building standalone web servers that can be accessed by web browsers directly.
adamc@896 225
adamc@896 226 \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@896 227
adamc@896 228 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@896 229 \begin{verbatim}
adamc@896 230 ScriptAlias /Hello /path/to/hello.exe
adamc@896 231 \end{verbatim}
adamc@896 232
adamc@1163 233 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 234 \begin{verbatim}
adamc@1163 235 Options +ExecCGI
adamc@1163 236 AddHandler cgi-script .exe
adamc@1163 237 \end{verbatim}
adamc@1163 238
adamc@1163 239 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 240 \begin{verbatim}
adamc@1163 241 prefix /dir/script.exe/
adamc@1163 242 \end{verbatim}
adamc@1163 243
adamc@1163 244 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 245
adamc@1164 246 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 247
adamc@896 248 \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@896 249
adamc@896 250 To configure a FastCGI program with Apache, one could combine the above \texttt{ScriptAlias} line with a line like this:
adamc@896 251 \begin{verbatim}
adamc@896 252 FastCgiServer /path/to/hello.exe -idle-timeout 99999
adamc@896 253 \end{verbatim}
adamc@896 254 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@896 255
adamc@896 256 Here is some lighttpd configuration for the same application.
adamc@896 257 \begin{verbatim}
adamc@896 258 fastcgi.server = (
adamc@896 259 "/Hello/" =>
adamc@896 260 (( "bin-path" => "/path/to/hello.exe",
adamc@896 261 "socket" => "/tmp/hello",
adamc@896 262 "check-local" => "disable",
adamc@896 263 "docroot" => "/",
adamc@896 264 "max-procs" => "1"
adamc@896 265 ))
adamc@896 266 )
adamc@896 267 \end{verbatim}
adamc@896 268 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@896 269
adamc@896 270 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@896 271 \end{itemize}
adamc@896 272
adamc@1127 273 \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 274
adamc@1164 275 \item \texttt{-sigfile PATH}: Same as the \texttt{sigfile} directive in \texttt{.urp} files
adamc@1164 276
adamc@896 277 \item \texttt{-sql FILENAME}: Set where a database set-up SQL script is written.
adamc@1095 278
adamc@1095 279 \item \texttt{-static}: Link the runtime system statically. The default is to link against dynamic libraries.
adamc@896 280 \end{itemize}
adamc@896 281
adam@1297 282 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@556 283
adamc@529 284 \section{Ur Syntax}
adamc@529 285
adamc@784 286 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@524 287
adamc@524 288 \subsection{Lexical Conventions}
adamc@524 289
adamc@524 290 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@524 291
adamc@524 292 \begin{center}
adamc@524 293 \begin{tabular}{rl}
adamc@524 294 \textbf{\LaTeX} & \textbf{ASCII} \\
adamc@524 295 $\to$ & \cd{->} \\
adamc@652 296 $\longrightarrow$ & \cd{-->} \\
adamc@524 297 $\times$ & \cd{*} \\
adamc@524 298 $\lambda$ & \cd{fn} \\
adamc@524 299 $\Rightarrow$ & \cd{=>} \\
adamc@652 300 $\Longrightarrow$ & \cd{==>} \\
adamc@529 301 $\neq$ & \cd{<>} \\
adamc@529 302 $\leq$ & \cd{<=} \\
adamc@529 303 $\geq$ & \cd{>=} \\
adamc@524 304 \\
adamc@524 305 $x$ & Normal textual identifier, not beginning with an uppercase letter \\
adamc@525 306 $X$ & Normal textual identifier, beginning with an uppercase letter \\
adamc@524 307 \end{tabular}
adamc@524 308 \end{center}
adamc@524 309
adamc@525 310 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@524 311
adamc@873 312 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@526 313
adamc@527 314 This version of the manual doesn't include operator precedences; see \texttt{src/urweb.grm} for that.
adamc@527 315
adam@1297 316 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 317
adamc@552 318 \subsection{\label{core}Core Syntax}
adamc@524 319
adamc@524 320 \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@524 321 $$\begin{array}{rrcll}
adamc@524 322 \textrm{Kinds} & \kappa &::=& \mt{Type} & \textrm{proper types} \\
adamc@525 323 &&& \mt{Unit} & \textrm{the trivial constructor} \\
adamc@525 324 &&& \mt{Name} & \textrm{field names} \\
adamc@525 325 &&& \kappa \to \kappa & \textrm{type-level functions} \\
adamc@525 326 &&& \{\kappa\} & \textrm{type-level records} \\
adamc@525 327 &&& (\kappa\times^+) & \textrm{type-level tuples} \\
adamc@652 328 &&& X & \textrm{variable} \\
adamc@652 329 &&& X \longrightarrow k & \textrm{kind-polymorphic type-level function} \\
adamc@529 330 &&& \_\_ & \textrm{wildcard} \\
adamc@525 331 &&& (\kappa) & \textrm{explicit precedence} \\
adamc@524 332 \end{array}$$
adamc@524 333
adamc@524 334 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@524 335 $$\begin{array}{rrcll}
adamc@524 336 \textrm{Explicitness} & ? &::=& :: & \textrm{explicit} \\
adamc@558 337 &&& ::: & \textrm{implicit}
adamc@524 338 \end{array}$$
adamc@524 339
adamc@524 340 \emph{Constructors} are the main class of compile-time-only data. They include proper types and are classified by kinds.
adamc@524 341 $$\begin{array}{rrcll}
adamc@524 342 \textrm{Constructors} & c, \tau &::=& (c) :: \kappa & \textrm{kind annotation} \\
adamc@530 343 &&& \hat{x} & \textrm{constructor variable} \\
adamc@524 344 \\
adamc@525 345 &&& \tau \to \tau & \textrm{function type} \\
adamc@525 346 &&& x \; ? \; \kappa \to \tau & \textrm{polymorphic function type} \\
adamc@652 347 &&& X \longrightarrow \tau & \textrm{kind-polymorphic function type} \\
adamc@525 348 &&& \$ c & \textrm{record type} \\
adamc@524 349 \\
adamc@525 350 &&& c \; c & \textrm{type-level function application} \\
adamc@530 351 &&& \lambda x \; :: \; \kappa \Rightarrow c & \textrm{type-level function abstraction} \\
adamc@524 352 \\
adamc@652 353 &&& X \Longrightarrow c & \textrm{type-level kind-polymorphic function abstraction} \\
adamc@655 354 &&& c [\kappa] & \textrm{type-level kind-polymorphic function application} \\
adamc@652 355 \\
adamc@525 356 &&& () & \textrm{type-level unit} \\
adamc@525 357 &&& \#X & \textrm{field name} \\
adamc@524 358 \\
adamc@525 359 &&& [(c = c)^*] & \textrm{known-length type-level record} \\
adamc@525 360 &&& c \rc c & \textrm{type-level record concatenation} \\
adamc@652 361 &&& \mt{map} & \textrm{type-level record map} \\
adamc@524 362 \\
adamc@558 363 &&& (c,^+) & \textrm{type-level tuple} \\
adamc@525 364 &&& c.n & \textrm{type-level tuple projection ($n \in \mathbb N^+$)} \\
adamc@524 365 \\
adamc@652 366 &&& [c \sim c] \Rightarrow \tau & \textrm{guarded type} \\
adamc@524 367 \\
adamc@529 368 &&& \_ :: \kappa & \textrm{wildcard} \\
adamc@525 369 &&& (c) & \textrm{explicit precedence} \\
adamc@530 370 \\
adamc@530 371 \textrm{Qualified uncapitalized variables} & \hat{x} &::=& x & \textrm{not from a module} \\
adamc@530 372 &&& M.x & \textrm{projection from a module} \\
adamc@525 373 \end{array}$$
adamc@525 374
adamc@655 375 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@655 376
adamc@525 377 Modules of the module system are described by \emph{signatures}.
adamc@525 378 $$\begin{array}{rrcll}
adamc@525 379 \textrm{Signatures} & S &::=& \mt{sig} \; s^* \; \mt{end} & \textrm{constant} \\
adamc@525 380 &&& X & \textrm{variable} \\
adamc@525 381 &&& \mt{functor}(X : S) : S & \textrm{functor} \\
adamc@529 382 &&& S \; \mt{where} \; \mt{con} \; x = c & \textrm{concretizing an abstract constructor} \\
adamc@525 383 &&& M.X & \textrm{projection from a module} \\
adamc@525 384 \\
adamc@525 385 \textrm{Signature items} & s &::=& \mt{con} \; x :: \kappa & \textrm{abstract constructor} \\
adamc@525 386 &&& \mt{con} \; x :: \kappa = c & \textrm{concrete constructor} \\
adamc@528 387 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529 388 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@525 389 &&& \mt{val} \; x : \tau & \textrm{value} \\
adamc@525 390 &&& \mt{structure} \; X : S & \textrm{sub-module} \\
adamc@525 391 &&& \mt{signature} \; X = S & \textrm{sub-signature} \\
adamc@525 392 &&& \mt{include} \; S & \textrm{signature inclusion} \\
adamc@525 393 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@654 394 &&& \mt{class} \; x :: \kappa & \textrm{abstract constructor class} \\
adamc@654 395 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@525 396 \\
adamc@525 397 \textrm{Datatype constructors} & dc &::=& X & \textrm{nullary constructor} \\
adamc@525 398 &&& X \; \mt{of} \; \tau & \textrm{unary constructor} \\
adamc@524 399 \end{array}$$
adamc@524 400
adamc@526 401 \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@526 402 $$\begin{array}{rrcll}
adamc@526 403 \textrm{Patterns} & p &::=& \_ & \textrm{wildcard} \\
adamc@526 404 &&& x & \textrm{variable} \\
adamc@526 405 &&& \ell & \textrm{constant} \\
adamc@526 406 &&& \hat{X} & \textrm{nullary constructor} \\
adamc@526 407 &&& \hat{X} \; p & \textrm{unary constructor} \\
adamc@526 408 &&& \{(x = p,)^*\} & \textrm{rigid record pattern} \\
adamc@526 409 &&& \{(x = p,)^+, \ldots\} & \textrm{flexible record pattern} \\
adamc@852 410 &&& p : \tau & \textrm{type annotation} \\
adamc@527 411 &&& (p) & \textrm{explicit precedence} \\
adamc@526 412 \\
adamc@529 413 \textrm{Qualified capitalized variables} & \hat{X} &::=& X & \textrm{not from a module} \\
adamc@526 414 &&& M.X & \textrm{projection from a module} \\
adamc@526 415 \end{array}$$
adamc@526 416
adamc@527 417 \emph{Expressions} are the main run-time entities, corresponding to both ``expressions'' and ``statements'' in mainstream imperative languages.
adamc@527 418 $$\begin{array}{rrcll}
adamc@527 419 \textrm{Expressions} & e &::=& e : \tau & \textrm{type annotation} \\
adamc@529 420 &&& \hat{x} & \textrm{variable} \\
adamc@529 421 &&& \hat{X} & \textrm{datatype constructor} \\
adamc@527 422 &&& \ell & \textrm{constant} \\
adamc@527 423 \\
adamc@527 424 &&& e \; e & \textrm{function application} \\
adamc@527 425 &&& \lambda x : \tau \Rightarrow e & \textrm{function abstraction} \\
adamc@527 426 &&& e [c] & \textrm{polymorphic function application} \\
adamc@852 427 &&& \lambda [x \; ? \; \kappa] \Rightarrow e & \textrm{polymorphic function abstraction} \\
adamc@655 428 &&& e [\kappa] & \textrm{kind-polymorphic function application} \\
adamc@652 429 &&& X \Longrightarrow e & \textrm{kind-polymorphic function abstraction} \\
adamc@527 430 \\
adamc@527 431 &&& \{(c = e,)^*\} & \textrm{known-length record} \\
adamc@527 432 &&& e.c & \textrm{record field projection} \\
adamc@527 433 &&& e \rc e & \textrm{record concatenation} \\
adamc@527 434 &&& e \rcut c & \textrm{removal of a single record field} \\
adamc@527 435 &&& e \rcutM c & \textrm{removal of multiple record fields} \\
adamc@527 436 \\
adamc@527 437 &&& \mt{let} \; ed^* \; \mt{in} \; e \; \mt{end} & \textrm{local definitions} \\
adamc@527 438 \\
adamc@527 439 &&& \mt{case} \; e \; \mt{of} \; (p \Rightarrow e|)^+ & \textrm{pattern matching} \\
adamc@527 440 \\
adamc@654 441 &&& \lambda [c \sim c] \Rightarrow e & \textrm{guarded expression abstraction} \\
adamc@654 442 &&& e \; ! & \textrm{guarded expression application} \\
adamc@527 443 \\
adamc@527 444 &&& \_ & \textrm{wildcard} \\
adamc@527 445 &&& (e) & \textrm{explicit precedence} \\
adamc@527 446 \\
adamc@527 447 \textrm{Local declarations} & ed &::=& \cd{val} \; x : \tau = e & \textrm{non-recursive value} \\
adamc@527 448 &&& \cd{val} \; \cd{rec} \; (x : \tau = e \; \cd{and})^+ & \textrm{mutually-recursive values} \\
adamc@527 449 \end{array}$$
adamc@527 450
adamc@655 451 As with constructors, we include both abstraction and application for kind polymorphism, but applications are only inferred internally.
adamc@655 452
adamc@528 453 \emph{Declarations} primarily bring new symbols into context.
adamc@528 454 $$\begin{array}{rrcll}
adamc@528 455 \textrm{Declarations} & d &::=& \mt{con} \; x :: \kappa = c & \textrm{constructor synonym} \\
adamc@528 456 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529 457 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@528 458 &&& \mt{val} \; x : \tau = e & \textrm{value} \\
adamc@528 459 &&& \mt{val} \; \cd{rec} \; (x : \tau = e \; \mt{and})^+ & \textrm{mutually-recursive values} \\
adamc@528 460 &&& \mt{structure} \; X : S = M & \textrm{module definition} \\
adamc@528 461 &&& \mt{signature} \; X = S & \textrm{signature definition} \\
adamc@528 462 &&& \mt{open} \; M & \textrm{module inclusion} \\
adamc@528 463 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@528 464 &&& \mt{open} \; \mt{constraints} \; M & \textrm{inclusion of just the constraints from a module} \\
adamc@528 465 &&& \mt{table} \; x : c & \textrm{SQL table} \\
adamc@784 466 &&& \mt{view} \; x : c & \textrm{SQL view} \\
adamc@528 467 &&& \mt{sequence} \; x & \textrm{SQL sequence} \\
adamc@535 468 &&& \mt{cookie} \; x : \tau & \textrm{HTTP cookie} \\
adamc@784 469 &&& \mt{style} \; x : \tau & \textrm{CSS class} \\
adamc@654 470 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@1085 471 &&& \mt{task} \; e = e & \textrm{recurring task} \\
adamc@528 472 \\
adamc@529 473 \textrm{Modules} & M &::=& \mt{struct} \; d^* \; \mt{end} & \textrm{constant} \\
adamc@529 474 &&& X & \textrm{variable} \\
adamc@529 475 &&& M.X & \textrm{projection} \\
adamc@529 476 &&& M(M) & \textrm{functor application} \\
adamc@529 477 &&& \mt{functor}(X : S) : S = M & \textrm{functor abstraction} \\
adamc@528 478 \end{array}$$
adamc@528 479
adamc@528 480 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@527 481
adamc@784 482 We omit some extra possibilities in $\mt{table}$ syntax, deferring them to Section \ref{tables}.
adamc@784 483
adamc@529 484 \subsection{Shorthands}
adamc@529 485
adamc@529 486 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@529 487
adamc@529 488 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@529 489
adamc@529 490 A record type may be written $\{(c = c,)^*\}$, which elaborates to $\$[(c = c,)^*]$.
adamc@529 491
adamc@533 492 The notation $[c_1, \ldots, c_n]$ is shorthand for $[c_1 = (), \ldots, c_n = ()]$.
adamc@533 493
adamc@529 494 A tuple type $(\tau_1, \ldots, \tau_n)$ expands to a record type $\{1 = \tau_1, \ldots, n = \tau_n\}$, with natural numbers as field names. 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@529 495
adamc@852 496 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@529 497
adamc@529 498 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@529 499
adamc@529 500 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@529 501
adamc@654 502 A signature item or declaration $\mt{class} \; x = \lambda y \Rightarrow c$ may be abbreviated $\mt{class} \; x \; y = c$.
adamc@529 503
adamc@1102 504 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 implicit constructor arguments have been made explicit. An expression $@@x$ achieves the same effect, additionally halting automatic resolution of type class instances and automatic proving of disjointness constraints. 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@529 505
adamc@852 506 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@529 507
adamc@852 508 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@852 509
adamc@852 510 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@529 511
adamc@529 512 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@529 513
adamc@852 514 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@852 515
adamc@853 516 A declaration $\mt{table} \; x : \{(c = c,)^*\}$ is elaborated into $\mt{table} \; x : [(c = c,)^*]$.
adamc@529 517
adamc@529 518 The syntax $\mt{where} \; \mt{type}$ is an alternate form of $\mt{where} \; \mt{con}$.
adamc@529 519
adamc@529 520 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@529 521
adamc@529 522 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@529 523
adamc@784 524 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@529 525
adamc@530 526
adamc@530 527 \section{Static Semantics}
adamc@530 528
adamc@530 529 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@530 530
adamc@530 531 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@530 532 \begin{itemize}
adamc@655 533 \item $\Gamma \vdash \kappa$ expresses kind well-formedness.
adamc@530 534 \item $\Gamma \vdash c :: \kappa$ assigns a kind to a constructor in a context.
adamc@530 535 \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@531 536 \item $\Gamma \vdash c \hookrightarrow C$ proves that record constructor $c$ decomposes into set $C$ of field names and record constructors.
adamc@530 537 \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@530 538 \item $\Gamma \vdash e : \tau$ is a standard typing judgment.
adamc@534 539 \item $\Gamma \vdash p \leadsto \Gamma; \tau$ combines typing of patterns with calculation of which new variables they bind.
adamc@537 540 \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@537 541 \item $\Gamma \vdash S \equiv S$ is the signature equivalence judgment.
adamc@536 542 \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@530 543 \item $\Gamma \vdash M : S$ is the module signature checking judgment.
adamc@537 544 \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@539 545 \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@530 546 \end{itemize}
adamc@530 547
adamc@655 548
adamc@655 549 \subsection{Kind Well-Formedness}
adamc@655 550
adamc@655 551 $$\infer{\Gamma \vdash \mt{Type}}{}
adamc@655 552 \quad \infer{\Gamma \vdash \mt{Unit}}{}
adamc@655 553 \quad \infer{\Gamma \vdash \mt{Name}}{}
adamc@655 554 \quad \infer{\Gamma \vdash \kappa_1 \to \kappa_2}{
adamc@655 555 \Gamma \vdash \kappa_1
adamc@655 556 & \Gamma \vdash \kappa_2
adamc@655 557 }
adamc@655 558 \quad \infer{\Gamma \vdash \{\kappa\}}{
adamc@655 559 \Gamma \vdash \kappa
adamc@655 560 }
adamc@655 561 \quad \infer{\Gamma \vdash (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@655 562 \forall i: \Gamma \vdash \kappa_i
adamc@655 563 }$$
adamc@655 564
adamc@655 565 $$\infer{\Gamma \vdash X}{
adamc@655 566 X \in \Gamma
adamc@655 567 }
adamc@655 568 \quad \infer{\Gamma \vdash X \longrightarrow \kappa}{
adamc@655 569 \Gamma, X \vdash \kappa
adamc@655 570 }$$
adamc@655 571
adamc@530 572 \subsection{Kinding}
adamc@530 573
adamc@655 574 We write $[X \mapsto \kappa_1]\kappa_2$ for capture-avoiding substitution of $\kappa_1$ for $X$ in $\kappa_2$.
adamc@655 575
adamc@530 576 $$\infer{\Gamma \vdash (c) :: \kappa :: \kappa}{
adamc@530 577 \Gamma \vdash c :: \kappa
adamc@530 578 }
adamc@530 579 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530 580 x :: \kappa \in \Gamma
adamc@530 581 }
adamc@530 582 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530 583 x :: \kappa = c \in \Gamma
adamc@530 584 }$$
adamc@530 585
adamc@530 586 $$\infer{\Gamma \vdash M.x :: \kappa}{
adamc@537 587 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 588 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = \kappa
adamc@530 589 }
adamc@530 590 \quad \infer{\Gamma \vdash M.x :: \kappa}{
adamc@537 591 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 592 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@530 593 }$$
adamc@530 594
adamc@530 595 $$\infer{\Gamma \vdash \tau_1 \to \tau_2 :: \mt{Type}}{
adamc@530 596 \Gamma \vdash \tau_1 :: \mt{Type}
adamc@530 597 & \Gamma \vdash \tau_2 :: \mt{Type}
adamc@530 598 }
adamc@530 599 \quad \infer{\Gamma \vdash x \; ? \: \kappa \to \tau :: \mt{Type}}{
adamc@530 600 \Gamma, x :: \kappa \vdash \tau :: \mt{Type}
adamc@530 601 }
adamc@655 602 \quad \infer{\Gamma \vdash X \longrightarrow \tau :: \mt{Type}}{
adamc@655 603 \Gamma, X \vdash \tau :: \mt{Type}
adamc@655 604 }
adamc@530 605 \quad \infer{\Gamma \vdash \$c :: \mt{Type}}{
adamc@530 606 \Gamma \vdash c :: \{\mt{Type}\}
adamc@530 607 }$$
adamc@530 608
adamc@530 609 $$\infer{\Gamma \vdash c_1 \; c_2 :: \kappa_2}{
adamc@530 610 \Gamma \vdash c_1 :: \kappa_1 \to \kappa_2
adamc@530 611 & \Gamma \vdash c_2 :: \kappa_1
adamc@530 612 }
adamc@530 613 \quad \infer{\Gamma \vdash \lambda x \; :: \; \kappa_1 \Rightarrow c :: \kappa_1 \to \kappa_2}{
adamc@530 614 \Gamma, x :: \kappa_1 \vdash c :: \kappa_2
adamc@530 615 }$$
adamc@530 616
adamc@655 617 $$\infer{\Gamma \vdash c[\kappa'] :: [X \mapsto \kappa']\kappa}{
adamc@655 618 \Gamma \vdash c :: X \to \kappa
adamc@655 619 & \Gamma \vdash \kappa'
adamc@655 620 }
adamc@655 621 \quad \infer{\Gamma \vdash X \Longrightarrow c :: X \to \kappa}{
adamc@655 622 \Gamma, X \vdash c :: \kappa
adamc@655 623 }$$
adamc@655 624
adamc@530 625 $$\infer{\Gamma \vdash () :: \mt{Unit}}{}
adamc@530 626 \quad \infer{\Gamma \vdash \#X :: \mt{Name}}{}$$
adamc@530 627
adamc@530 628 $$\infer{\Gamma \vdash [\overline{c_i = c'_i}] :: \{\kappa\}}{
adamc@530 629 \forall i: \Gamma \vdash c_i : \mt{Name}
adamc@530 630 & \Gamma \vdash c'_i :: \kappa
adamc@530 631 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@530 632 }
adamc@530 633 \quad \infer{\Gamma \vdash c_1 \rc c_2 :: \{\kappa\}}{
adamc@530 634 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530 635 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@530 636 & \Gamma \vdash c_1 \sim c_2
adamc@530 637 }$$
adamc@530 638
adamc@655 639 $$\infer{\Gamma \vdash \mt{map} :: (\kappa_1 \to \kappa_2) \to \{\kappa_1\} \to \{\kappa_2\}}{}$$
adamc@530 640
adamc@573 641 $$\infer{\Gamma \vdash (\overline c) :: (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@573 642 \forall i: \Gamma \vdash c_i :: \kappa_i
adamc@530 643 }
adamc@573 644 \quad \infer{\Gamma \vdash c.i :: \kappa_i}{
adamc@573 645 \Gamma \vdash c :: (\kappa_1 \times \ldots \times \kappa_n)
adamc@530 646 }$$
adamc@530 647
adamc@655 648 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow \tau :: \mt{Type}}{
adamc@655 649 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530 650 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@655 651 & \Gamma, c_1 \sim c_2 \vdash \tau :: \mt{Type}
adamc@530 652 }$$
adamc@530 653
adamc@531 654 \subsection{Record Disjointness}
adamc@531 655
adamc@531 656 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@558 657 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@558 658 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@558 659 & \forall c'_1 \in C_1, c'_2 \in C_2: \Gamma \vdash c'_1 \sim c'_2
adamc@531 660 }
adamc@531 661 \quad \infer{\Gamma \vdash X \sim X'}{
adamc@531 662 X \neq X'
adamc@531 663 }$$
adamc@531 664
adamc@531 665 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@531 666 c'_1 \sim c'_2 \in \Gamma
adamc@558 667 & \Gamma \vdash c'_1 \hookrightarrow C_1
adamc@558 668 & \Gamma \vdash c'_2 \hookrightarrow C_2
adamc@558 669 & c_1 \in C_1
adamc@558 670 & c_2 \in C_2
adamc@531 671 }$$
adamc@531 672
adamc@531 673 $$\infer{\Gamma \vdash c \hookrightarrow \{c\}}{}
adamc@531 674 \quad \infer{\Gamma \vdash [\overline{c = c'}] \hookrightarrow \{\overline{c}\}}{}
adamc@531 675 \quad \infer{\Gamma \vdash c_1 \rc c_2 \hookrightarrow C_1 \cup C_2}{
adamc@531 676 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@531 677 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@531 678 }
adamc@531 679 \quad \infer{\Gamma \vdash c \hookrightarrow C}{
adamc@531 680 \Gamma \vdash c \equiv c'
adamc@531 681 & \Gamma \vdash c' \hookrightarrow C
adamc@531 682 }
adamc@531 683 \quad \infer{\Gamma \vdash \mt{map} \; f \; c \hookrightarrow C}{
adamc@531 684 \Gamma \vdash c \hookrightarrow C
adamc@531 685 }$$
adamc@531 686
adamc@541 687 \subsection{\label{definitional}Definitional Equality}
adamc@532 688
adamc@655 689 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@532 690
adamc@532 691 $$\infer{\Gamma \vdash c \equiv c}{}
adamc@532 692 \quad \infer{\Gamma \vdash c_1 \equiv c_2}{
adamc@532 693 \Gamma \vdash c_2 \equiv c_1
adamc@532 694 }
adamc@532 695 \quad \infer{\Gamma \vdash c_1 \equiv c_3}{
adamc@532 696 \Gamma \vdash c_1 \equiv c_2
adamc@532 697 & \Gamma \vdash c_2 \equiv c_3
adamc@532 698 }
adamc@532 699 \quad \infer{\Gamma \vdash \mathcal C[c_1] \equiv \mathcal C[c_2]}{
adamc@532 700 \Gamma \vdash c_1 \equiv c_2
adamc@532 701 }$$
adamc@532 702
adamc@532 703 $$\infer{\Gamma \vdash x \equiv c}{
adamc@532 704 x :: \kappa = c \in \Gamma
adamc@532 705 }
adamc@532 706 \quad \infer{\Gamma \vdash M.x \equiv c}{
adamc@537 707 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 708 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@532 709 }
adamc@532 710 \quad \infer{\Gamma \vdash (\overline c).i \equiv c_i}{}$$
adamc@532 711
adamc@532 712 $$\infer{\Gamma \vdash (\lambda x :: \kappa \Rightarrow c) \; c' \equiv [x \mapsto c'] c}{}
adamc@655 713 \quad \infer{\Gamma \vdash (X \Longrightarrow c) [\kappa] \equiv [X \mapsto \kappa] c}{}$$
adamc@655 714
adamc@655 715 $$\infer{\Gamma \vdash c_1 \rc c_2 \equiv c_2 \rc c_1}{}
adamc@532 716 \quad \infer{\Gamma \vdash c_1 \rc (c_2 \rc c_3) \equiv (c_1 \rc c_2) \rc c_3}{}$$
adamc@532 717
adamc@532 718 $$\infer{\Gamma \vdash [] \rc c \equiv c}{}
adamc@532 719 \quad \infer{\Gamma \vdash [\overline{c_1 = c'_1}] \rc [\overline{c_2 = c'_2}] \equiv [\overline{c_1 = c'_1}, \overline{c_2 = c'_2}]}{}$$
adamc@532 720
adamc@655 721 $$\infer{\Gamma \vdash \mt{map} \; f \; [] \equiv []}{}
adamc@655 722 \quad \infer{\Gamma \vdash \mt{map} \; f \; ([c_1 = c_2] \rc c) \equiv [c_1 = f \; c_2] \rc \mt{map} \; f \; c}{}$$
adamc@532 723
adamc@532 724 $$\infer{\Gamma \vdash \mt{map} \; (\lambda x \Rightarrow x) \; c \equiv c}{}
adamc@655 725 \quad \infer{\Gamma \vdash \mt{map} \; f \; (\mt{map} \; f' \; c)
adamc@655 726 \equiv \mt{map} \; (\lambda x \Rightarrow f \; (f' \; x)) \; c}{}$$
adamc@532 727
adamc@532 728 $$\infer{\Gamma \vdash \mt{map} \; f \; (c_1 \rc c_2) \equiv \mt{map} \; f \; c_1 \rc \mt{map} \; f \; c_2}{}$$
adamc@531 729
adamc@534 730 \subsection{Expression Typing}
adamc@533 731
adamc@873 732 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@533 733
adamc@533 734 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@533 735
adamc@533 736 $$\infer{\Gamma \vdash e : \tau : \tau}{
adamc@533 737 \Gamma \vdash e : \tau
adamc@533 738 }
adamc@533 739 \quad \infer{\Gamma \vdash e : \tau}{
adamc@533 740 \Gamma \vdash e : \tau'
adamc@533 741 & \Gamma \vdash \tau' \equiv \tau
adamc@533 742 }
adamc@533 743 \quad \infer{\Gamma \vdash \ell : T(\ell)}{}$$
adamc@533 744
adamc@533 745 $$\infer{\Gamma \vdash x : \mathcal I(\tau)}{
adamc@533 746 x : \tau \in \Gamma
adamc@533 747 }
adamc@533 748 \quad \infer{\Gamma \vdash M.x : \mathcal I(\tau)}{
adamc@537 749 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 750 & \mt{proj}(M, \overline{s}, \mt{val} \; x) = \tau
adamc@533 751 }
adamc@533 752 \quad \infer{\Gamma \vdash X : \mathcal I(\tau)}{
adamc@533 753 X : \tau \in \Gamma
adamc@533 754 }
adamc@533 755 \quad \infer{\Gamma \vdash M.X : \mathcal I(\tau)}{
adamc@537 756 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 757 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \tau
adamc@533 758 }$$
adamc@533 759
adamc@533 760 $$\infer{\Gamma \vdash e_1 \; e_2 : \tau_2}{
adamc@533 761 \Gamma \vdash e_1 : \tau_1 \to \tau_2
adamc@533 762 & \Gamma \vdash e_2 : \tau_1
adamc@533 763 }
adamc@533 764 \quad \infer{\Gamma \vdash \lambda x : \tau_1 \Rightarrow e : \tau_1 \to \tau_2}{
adamc@533 765 \Gamma, x : \tau_1 \vdash e : \tau_2
adamc@533 766 }$$
adamc@533 767
adamc@533 768 $$\infer{\Gamma \vdash e [c] : [x \mapsto c]\tau}{
adamc@533 769 \Gamma \vdash e : x :: \kappa \to \tau
adamc@533 770 & \Gamma \vdash c :: \kappa
adamc@533 771 }
adamc@852 772 \quad \infer{\Gamma \vdash \lambda [x \; ? \; \kappa] \Rightarrow e : x \; ? \; \kappa \to \tau}{
adamc@533 773 \Gamma, x :: \kappa \vdash e : \tau
adamc@533 774 }$$
adamc@533 775
adamc@655 776 $$\infer{\Gamma \vdash e [\kappa] : [X \mapsto \kappa]\tau}{
adamc@655 777 \Gamma \vdash e : X \longrightarrow \tau
adamc@655 778 & \Gamma \vdash \kappa
adamc@655 779 }
adamc@655 780 \quad \infer{\Gamma \vdash X \Longrightarrow e : X \longrightarrow \tau}{
adamc@655 781 \Gamma, X \vdash e : \tau
adamc@655 782 }$$
adamc@655 783
adamc@533 784 $$\infer{\Gamma \vdash \{\overline{c = e}\} : \{\overline{c : \tau}\}}{
adamc@533 785 \forall i: \Gamma \vdash c_i :: \mt{Name}
adamc@533 786 & \Gamma \vdash e_i : \tau_i
adamc@533 787 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@533 788 }
adamc@533 789 \quad \infer{\Gamma \vdash e.c : \tau}{
adamc@533 790 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533 791 }
adamc@533 792 \quad \infer{\Gamma \vdash e_1 \rc e_2 : \$(c_1 \rc c_2)}{
adamc@533 793 \Gamma \vdash e_1 : \$c_1
adamc@533 794 & \Gamma \vdash e_2 : \$c_2
adamc@573 795 & \Gamma \vdash c_1 \sim c_2
adamc@533 796 }$$
adamc@533 797
adamc@533 798 $$\infer{\Gamma \vdash e \rcut c : \$c'}{
adamc@533 799 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533 800 }
adamc@533 801 \quad \infer{\Gamma \vdash e \rcutM c : \$c'}{
adamc@533 802 \Gamma \vdash e : \$(c \rc c')
adamc@533 803 }$$
adamc@533 804
adamc@533 805 $$\infer{\Gamma \vdash \mt{let} \; \overline{ed} \; \mt{in} \; e \; \mt{end} : \tau}{
adamc@533 806 \Gamma \vdash \overline{ed} \leadsto \Gamma'
adamc@533 807 & \Gamma' \vdash e : \tau
adamc@533 808 }
adamc@533 809 \quad \infer{\Gamma \vdash \mt{case} \; e \; \mt{of} \; \overline{p \Rightarrow e} : \tau}{
adamc@533 810 \forall i: \Gamma \vdash p_i \leadsto \Gamma_i, \tau'
adamc@533 811 & \Gamma_i \vdash e_i : \tau
adamc@533 812 }$$
adamc@533 813
adamc@573 814 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow e : \lambda [c_1 \sim c_2] \Rightarrow \tau}{
adamc@533 815 \Gamma \vdash c_1 :: \{\kappa\}
adamc@655 816 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@533 817 & \Gamma, c_1 \sim c_2 \vdash e : \tau
adamc@662 818 }
adamc@662 819 \quad \infer{\Gamma \vdash e \; ! : \tau}{
adamc@662 820 \Gamma \vdash e : [c_1 \sim c_2] \Rightarrow \tau
adamc@662 821 & \Gamma \vdash c_1 \sim c_2
adamc@533 822 }$$
adamc@533 823
adamc@534 824 \subsection{Pattern Typing}
adamc@534 825
adamc@534 826 $$\infer{\Gamma \vdash \_ \leadsto \Gamma; \tau}{}
adamc@534 827 \quad \infer{\Gamma \vdash x \leadsto \Gamma, x : \tau; \tau}{}
adamc@534 828 \quad \infer{\Gamma \vdash \ell \leadsto \Gamma; T(\ell)}{}$$
adamc@534 829
adamc@534 830 $$\infer{\Gamma \vdash X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534 831 X : \overline{x ::: \mt{Type}} \to \tau \in \Gamma
adamc@534 832 & \textrm{$\tau$ not a function type}
adamc@534 833 }
adamc@534 834 \quad \infer{\Gamma \vdash X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534 835 X : \overline{x ::: \mt{Type}} \to \tau'' \to \tau \in \Gamma
adamc@534 836 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534 837 }$$
adamc@534 838
adamc@534 839 $$\infer{\Gamma \vdash M.X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537 840 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 841 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau
adamc@534 842 & \textrm{$\tau$ not a function type}
adamc@534 843 }$$
adamc@534 844
adamc@534 845 $$\infer{\Gamma \vdash M.X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537 846 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 847 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau'' \to \tau
adamc@534 848 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534 849 }$$
adamc@534 850
adamc@534 851 $$\infer{\Gamma \vdash \{\overline{x = p}\} \leadsto \Gamma_n; \{\overline{x = \tau}\}}{
adamc@534 852 \Gamma_0 = \Gamma
adamc@534 853 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534 854 }
adamc@534 855 \quad \infer{\Gamma \vdash \{\overline{x = p}, \ldots\} \leadsto \Gamma_n; \$([\overline{x = \tau}] \rc c)}{
adamc@534 856 \Gamma_0 = \Gamma
adamc@534 857 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534 858 }$$
adamc@534 859
adamc@852 860 $$\infer{\Gamma \vdash p : \tau \leadsto \Gamma'; \tau}{
adamc@852 861 \Gamma \vdash p \leadsto \Gamma'; \tau'
adamc@852 862 & \Gamma \vdash \tau' \equiv \tau
adamc@852 863 }$$
adamc@852 864
adamc@535 865 \subsection{Declaration Typing}
adamc@535 866
adamc@535 867 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@535 868
adamc@655 869 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@535 870
adamc@558 871 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@537 872 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@535 873
adamc@535 874 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535 875 \quad \infer{\Gamma \vdash d, \overline{d} \leadsto \Gamma''}{
adamc@535 876 \Gamma \vdash d \leadsto \Gamma'
adamc@535 877 & \Gamma' \vdash \overline{d} \leadsto \Gamma''
adamc@535 878 }$$
adamc@535 879
adamc@535 880 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@535 881 \Gamma \vdash c :: \kappa
adamc@535 882 }
adamc@535 883 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@535 884 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@535 885 }$$
adamc@535 886
adamc@535 887 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537 888 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 889 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@535 890 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@535 891 }$$
adamc@535 892
adamc@535 893 $$\infer{\Gamma \vdash \mt{val} \; x : \tau = e \leadsto \Gamma, x : \tau}{
adamc@535 894 \Gamma \vdash e : \tau
adamc@535 895 }$$
adamc@535 896
adamc@535 897 $$\infer{\Gamma \vdash \mt{val} \; \mt{rec} \; \overline{x : \tau = e} \leadsto \Gamma, \overline{x : \tau}}{
adamc@535 898 \forall i: \Gamma, \overline{x : \tau} \vdash e_i : \tau_i
adamc@535 899 & \textrm{$e_i$ starts with an expression $\lambda$, optionally preceded by constructor and disjointness $\lambda$s}
adamc@535 900 }$$
adamc@535 901
adamc@535 902 $$\infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : S}{
adamc@535 903 \Gamma \vdash M : S
adamc@558 904 & \textrm{ $M$ not a constant or application}
adamc@535 905 }
adamc@558 906 \quad \infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : \mt{selfify}(X, \overline{s})}{
adamc@558 907 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@539 908 }$$
adamc@539 909
adamc@539 910 $$\infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@535 911 \Gamma \vdash S
adamc@535 912 }$$
adamc@535 913
adamc@537 914 $$\infer{\Gamma \vdash \mt{open} \; M \leadsto \Gamma, \mathcal O(M, \overline{s})}{
adamc@537 915 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535 916 }$$
adamc@535 917
adamc@535 918 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma}{
adamc@535 919 \Gamma \vdash c_1 :: \{\kappa\}
adamc@535 920 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@535 921 & \Gamma \vdash c_1 \sim c_2
adamc@535 922 }
adamc@537 923 \quad \infer{\Gamma \vdash \mt{open} \; \mt{constraints} \; M \leadsto \Gamma, \mathcal O_c(M, \overline{s})}{
adamc@537 924 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535 925 }$$
adamc@535 926
adamc@784 927 $$\infer{\Gamma \vdash \mt{table} \; x : c \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_table} \; c \; []}{
adamc@535 928 \Gamma \vdash c :: \{\mt{Type}\}
adamc@535 929 }
adamc@784 930 \quad \infer{\Gamma \vdash \mt{view} \; x : c \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_view} \; c}{
adamc@784 931 \Gamma \vdash c :: \{\mt{Type}\}
adamc@784 932 }$$
adamc@784 933
adamc@784 934 $$\infer{\Gamma \vdash \mt{sequence} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_sequence}}{}$$
adamc@535 935
adamc@535 936 $$\infer{\Gamma \vdash \mt{cookie} \; x : \tau \leadsto \Gamma, x : \mt{Basis}.\mt{http\_cookie} \; \tau}{
adamc@535 937 \Gamma \vdash \tau :: \mt{Type}
adamc@784 938 }
adamc@784 939 \quad \infer{\Gamma \vdash \mt{style} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{css\_class}}{}$$
adamc@535 940
adamc@1085 941 $$\infer{\Gamma \vdash \mt{task} \; e_1 = e_2 \leadsto \Gamma}{
adamc@1085 942 \Gamma \vdash e_1 :: \mt{Basis}.\mt{task\_kind}
adamc@1085 943 & \Gamma \vdash e_2 :: \mt{Basis}.\mt{transaction} \; \{\}
adamc@1085 944 }$$
adamc@1085 945
adamc@784 946 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784 947 \Gamma \vdash c :: \kappa
adamc@535 948 }$$
adamc@535 949
adamc@535 950 $$\infer{\overline{y}; x; \Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535 951 \quad \infer{\overline{y}; x; \Gamma \vdash X \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to x \; \overline{y}}{
adamc@535 952 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535 953 }
adamc@535 954 \quad \infer{\overline{y}; x; \Gamma \vdash X \; \mt{of} \; \tau \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to \tau \to x \; \overline{y}}{
adamc@535 955 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535 956 }$$
adamc@535 957
adamc@537 958 \subsection{Signature Item Typing}
adamc@537 959
adamc@537 960 We appeal to a signature item analogue of the $\mathcal O$ function from the last subsection.
adamc@537 961
adamc@537 962 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@537 963 \quad \infer{\Gamma \vdash s, \overline{s} \leadsto \Gamma''}{
adamc@537 964 \Gamma \vdash s \leadsto \Gamma'
adamc@537 965 & \Gamma' \vdash \overline{s} \leadsto \Gamma''
adamc@537 966 }$$
adamc@537 967
adamc@537 968 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}
adamc@537 969 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@537 970 \Gamma \vdash c :: \kappa
adamc@537 971 }
adamc@537 972 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@537 973 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@537 974 }$$
adamc@537 975
adamc@537 976 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537 977 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 978 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 979 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@537 980 }$$
adamc@537 981
adamc@537 982 $$\infer{\Gamma \vdash \mt{val} \; x : \tau \leadsto \Gamma, x : \tau}{
adamc@537 983 \Gamma \vdash \tau :: \mt{Type}
adamc@537 984 }$$
adamc@537 985
adamc@537 986 $$\infer{\Gamma \vdash \mt{structure} \; X : S \leadsto \Gamma, X : S}{
adamc@537 987 \Gamma \vdash S
adamc@537 988 }
adamc@537 989 \quad \infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@537 990 \Gamma \vdash S
adamc@537 991 }$$
adamc@537 992
adamc@537 993 $$\infer{\Gamma \vdash \mt{include} \; S \leadsto \Gamma, \mathcal O(\overline{s})}{
adamc@537 994 \Gamma \vdash S
adamc@537 995 & \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 996 }$$
adamc@537 997
adamc@537 998 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma, c_1 \sim c_2}{
adamc@537 999 \Gamma \vdash c_1 :: \{\kappa\}
adamc@537 1000 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@537 1001 }$$
adamc@537 1002
adamc@784 1003 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784 1004 \Gamma \vdash c :: \kappa
adamc@537 1005 }
adamc@784 1006 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}$$
adamc@537 1007
adamc@536 1008 \subsection{Signature Compatibility}
adamc@536 1009
adamc@558 1010 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 1011
adamc@537 1012 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 1013
adamc@536 1014 $$\infer{\Gamma \vdash S \equiv S}{}
adamc@536 1015 \quad \infer{\Gamma \vdash S_1 \equiv S_2}{
adamc@536 1016 \Gamma \vdash S_2 \equiv S_1
adamc@536 1017 }
adamc@536 1018 \quad \infer{\Gamma \vdash X \equiv S}{
adamc@536 1019 X = S \in \Gamma
adamc@536 1020 }
adamc@536 1021 \quad \infer{\Gamma \vdash M.X \equiv S}{
adamc@537 1022 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1023 & \mt{proj}(M, \overline{s}, \mt{signature} \; X) = S
adamc@536 1024 }$$
adamc@536 1025
adamc@536 1026 $$\infer{\Gamma \vdash S \; \mt{where} \; \mt{con} \; x = c \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa = c \; \overline{s_2} \; \mt{end}}{
adamc@536 1027 \Gamma \vdash S \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa \; \overline{s_2} \; \mt{end}
adamc@536 1028 & \Gamma \vdash c :: \kappa
adamc@537 1029 }
adamc@537 1030 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s^1} \; \mt{include} \; S \; \overline{s^2} \; \mt{end} \equiv \mt{sig} \; \overline{s^1} \; \overline{s} \; \overline{s^2} \; \mt{end}}{
adamc@537 1031 \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@536 1032 }$$
adamc@536 1033
adamc@536 1034 $$\infer{\Gamma \vdash S_1 \leq S_2}{
adamc@536 1035 \Gamma \vdash S_1 \equiv S_2
adamc@536 1036 }
adamc@536 1037 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \mt{end}}{}
adamc@537 1038 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; s' \; \overline{s'} \; \mt{end}}{
adamc@537 1039 \Gamma \vdash \overline{s} \leq s'
adamc@537 1040 & \Gamma \vdash s' \leadsto \Gamma'
adamc@537 1041 & \Gamma' \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \overline{s'} \; \mt{end}
adamc@537 1042 }$$
adamc@537 1043
adamc@537 1044 $$\infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537 1045 \Gamma \vdash s \leq s'
adamc@537 1046 }
adamc@537 1047 \quad \infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537 1048 \Gamma \vdash s \leadsto \Gamma'
adamc@537 1049 & \Gamma' \vdash \overline{s} \leq s'
adamc@536 1050 }$$
adamc@536 1051
adamc@536 1052 $$\infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 \leq \mt{functor} (X : S'_1) : S'_2}{
adamc@536 1053 \Gamma \vdash S'_1 \leq S_1
adamc@536 1054 & \Gamma, X : S'_1 \vdash S_2 \leq S'_2
adamc@536 1055 }$$
adamc@536 1056
adamc@537 1057 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@537 1058 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}
adamc@558 1059 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type}}{}$$
adamc@537 1060
adamc@537 1061 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(y)} \to \mt{Type}}{
adamc@537 1062 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1063 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1064 }$$
adamc@537 1065
adamc@784 1066 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@784 1067 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}$$
adamc@537 1068
adamc@537 1069 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \mt{\kappa} = c_2}{
adamc@537 1070 \Gamma \vdash c_1 \equiv c_2
adamc@537 1071 }
adamc@784 1072 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \kappa = c_2}{
adamc@537 1073 \Gamma \vdash c_1 \equiv c_2
adamc@537 1074 }$$
adamc@537 1075
adamc@537 1076 $$\infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537 1077 \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1078 }$$
adamc@537 1079
adamc@537 1080 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537 1081 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1082 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1083 & \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1084 }$$
adamc@537 1085
adamc@537 1086 $$\infer{\Gamma \vdash \cdot \leq \cdot}{}
adamc@537 1087 \quad \infer{\Gamma \vdash X; \overline{dc} \leq X; \overline{dc'}}{
adamc@537 1088 \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1089 }
adamc@537 1090 \quad \infer{\Gamma \vdash X \; \mt{of} \; \tau_1; \overline{dc} \leq X \; \mt{of} \; \tau_2; \overline{dc'}}{
adamc@537 1091 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537 1092 & \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1093 }$$
adamc@537 1094
adamc@537 1095 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x = \mt{datatype} \; M'.z'}{
adamc@537 1096 \Gamma \vdash M.z \equiv M'.z'
adamc@537 1097 }$$
adamc@537 1098
adamc@537 1099 $$\infer{\Gamma \vdash \mt{val} \; x : \tau_1 \leq \mt{val} \; x : \tau_2}{
adamc@537 1100 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537 1101 }
adamc@537 1102 \quad \infer{\Gamma \vdash \mt{structure} \; X : S_1 \leq \mt{structure} \; X : S_2}{
adamc@537 1103 \Gamma \vdash S_1 \leq S_2
adamc@537 1104 }
adamc@537 1105 \quad \infer{\Gamma \vdash \mt{signature} \; X = S_1 \leq \mt{signature} \; X = S_2}{
adamc@537 1106 \Gamma \vdash S_1 \leq S_2
adamc@537 1107 & \Gamma \vdash S_2 \leq S_1
adamc@537 1108 }$$
adamc@537 1109
adamc@537 1110 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leq \mt{constraint} \; c'_1 \sim c'_2}{
adamc@537 1111 \Gamma \vdash c_1 \equiv c'_1
adamc@537 1112 & \Gamma \vdash c_2 \equiv c'_2
adamc@537 1113 }$$
adamc@537 1114
adamc@655 1115 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{class} \; x :: \kappa}{}
adamc@655 1116 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{class} \; x :: \kappa}{}
adamc@655 1117 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{class} \; x :: \kappa = c_2}{
adamc@537 1118 \Gamma \vdash c_1 \equiv c_2
adamc@537 1119 }$$
adamc@537 1120
adamc@538 1121 \subsection{Module Typing}
adamc@538 1122
adamc@538 1123 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 1124
adamc@538 1125 $$\infer{\Gamma \vdash M : S}{
adamc@538 1126 \Gamma \vdash M : S'
adamc@538 1127 & \Gamma \vdash S' \leq S
adamc@538 1128 }
adamc@538 1129 \quad \infer{\Gamma \vdash \mt{struct} \; \overline{d} \; \mt{end} : \mt{sig} \; \mt{sigOf}(\overline{d}) \; \mt{end}}{
adamc@538 1130 \Gamma \vdash \overline{d} \leadsto \Gamma'
adamc@538 1131 }
adamc@538 1132 \quad \infer{\Gamma \vdash X : S}{
adamc@538 1133 X : S \in \Gamma
adamc@538 1134 }$$
adamc@538 1135
adamc@538 1136 $$\infer{\Gamma \vdash M.X : S}{
adamc@538 1137 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@538 1138 & \mt{proj}(M, \overline{s}, \mt{structure} \; X) = S
adamc@538 1139 }$$
adamc@538 1140
adamc@538 1141 $$\infer{\Gamma \vdash M_1(M_2) : [X \mapsto M_2]S_2}{
adamc@538 1142 \Gamma \vdash M_1 : \mt{functor}(X : S_1) : S_2
adamc@538 1143 & \Gamma \vdash M_2 : S_1
adamc@538 1144 }
adamc@538 1145 \quad \infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 = M : \mt{functor} (X : S_1) : S_2}{
adamc@538 1146 \Gamma \vdash S_1
adamc@538 1147 & \Gamma, X : S_1 \vdash S_2
adamc@538 1148 & \Gamma, X : S_1 \vdash M : S_2
adamc@538 1149 }$$
adamc@538 1150
adamc@538 1151 \begin{eqnarray*}
adamc@538 1152 \mt{sigOf}(\cdot) &=& \cdot \\
adamc@538 1153 \mt{sigOf}(s \; \overline{s'}) &=& \mt{sigOf}(s) \; \mt{sigOf}(\overline{s'}) \\
adamc@538 1154 \\
adamc@538 1155 \mt{sigOf}(\mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@538 1156 \mt{sigOf}(\mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \overline{dc} \\
adamc@538 1157 \mt{sigOf}(\mt{datatype} \; x = \mt{datatype} \; M.z) &=& \mt{datatype} \; x = \mt{datatype} \; M.z \\
adamc@538 1158 \mt{sigOf}(\mt{val} \; x : \tau = e) &=& \mt{val} \; x : \tau \\
adamc@538 1159 \mt{sigOf}(\mt{val} \; \mt{rec} \; \overline{x : \tau = e}) &=& \overline{\mt{val} \; x : \tau} \\
adamc@538 1160 \mt{sigOf}(\mt{structure} \; X : S = M) &=& \mt{structure} \; X : S \\
adamc@538 1161 \mt{sigOf}(\mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@538 1162 \mt{sigOf}(\mt{open} \; M) &=& \mt{include} \; S \textrm{ (where $\Gamma \vdash M : S$)} \\
adamc@538 1163 \mt{sigOf}(\mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@538 1164 \mt{sigOf}(\mt{open} \; \mt{constraints} \; M) &=& \cdot \\
adamc@538 1165 \mt{sigOf}(\mt{table} \; x : c) &=& \mt{table} \; x : c \\
adamc@784 1166 \mt{sigOf}(\mt{view} \; x : c) &=& \mt{view} \; x : c \\
adamc@538 1167 \mt{sigOf}(\mt{sequence} \; x) &=& \mt{sequence} \; x \\
adamc@538 1168 \mt{sigOf}(\mt{cookie} \; x : \tau) &=& \mt{cookie} \; x : \tau \\
adamc@784 1169 \mt{sigOf}(\mt{style} \; x) &=& \mt{style} \; x \\
adamc@655 1170 \mt{sigOf}(\mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@538 1171 \end{eqnarray*}
adamc@539 1172 \begin{eqnarray*}
adamc@539 1173 \mt{selfify}(M, \cdot) &=& \cdot \\
adamc@558 1174 \mt{selfify}(M, s \; \overline{s'}) &=& \mt{selfify}(M, s) \; \mt{selfify}(M, \overline{s'}) \\
adamc@539 1175 \\
adamc@539 1176 \mt{selfify}(M, \mt{con} \; x :: \kappa) &=& \mt{con} \; x :: \kappa = M.x \\
adamc@539 1177 \mt{selfify}(M, \mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@539 1178 \mt{selfify}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \mt{datatype} \; M.x \\
adamc@539 1179 \mt{selfify}(M, \mt{datatype} \; x = \mt{datatype} \; M'.z) &=& \mt{datatype} \; x = \mt{datatype} \; M'.z \\
adamc@539 1180 \mt{selfify}(M, \mt{val} \; x : \tau) &=& \mt{val} \; x : \tau \\
adamc@539 1181 \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 1182 \mt{selfify}(M, \mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@539 1183 \mt{selfify}(M, \mt{include} \; S) &=& \mt{include} \; S \\
adamc@539 1184 \mt{selfify}(M, \mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@655 1185 \mt{selfify}(M, \mt{class} \; x :: \kappa) &=& \mt{class} \; x :: \kappa = M.x \\
adamc@655 1186 \mt{selfify}(M, \mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@539 1187 \end{eqnarray*}
adamc@539 1188
adamc@540 1189 \subsection{Module Projection}
adamc@540 1190
adamc@540 1191 \begin{eqnarray*}
adamc@540 1192 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \\
adamc@540 1193 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa, c) \\
adamc@540 1194 \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 1195 \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 1196 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})$)} \\
adamc@655 1197 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \to \mt{Type} \\
adamc@655 1198 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa \to \mt{Type}, c) \\
adamc@540 1199 \\
adamc@540 1200 \mt{proj}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc} \; \overline{s}, \mt{datatype} \; x) &=& (\overline{y}, \overline{dc}) \\
adamc@540 1201 \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 1202 \\
adamc@540 1203 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, \mt{val} \; x) &=& \tau \\
adamc@540 1204 \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 1205 \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 1206 \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 1207 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \in \overline{dc}$)} \\
adamc@540 1208 \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 1209 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \; \mt{of} \; \tau \in \overline{dc}$)} \\
adamc@540 1210 \\
adamc@540 1211 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, \mt{structure} \; X) &=& S \\
adamc@540 1212 \\
adamc@540 1213 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, \mt{signature} \; X) &=& S \\
adamc@540 1214 \\
adamc@540 1215 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1216 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1217 \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 1218 \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 1219 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@540 1220 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1221 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1222 \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 1223 \mt{proj}(M, \mt{constraint} \; c_1 \sim c_2 \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@655 1224 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@655 1225 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1226 \end{eqnarray*}
adamc@540 1227
adamc@541 1228
adamc@541 1229 \section{Type Inference}
adamc@541 1230
adamc@541 1231 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 1232
adamc@541 1233 \subsection{Basic Unification}
adamc@541 1234
adamc@560 1235 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 1236
adamc@656 1237 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 1238
adamc@541 1239 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 1240
adamc@541 1241 \subsection{Unifying Record Types}
adamc@541 1242
adamc@570 1243 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 1244
adamc@656 1245 \subsection{\label{typeclasses}Constructor Classes}
adamc@541 1246
adamc@784 1247 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 1248
adamc@784 1249 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 1250
adamc@656 1251 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 1252
adamc@656 1253 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 1254
adamc@541 1255 \subsection{Reverse-Engineering Record Types}
adamc@541 1256
adamc@656 1257 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 1258
adamc@541 1259 \subsection{Implicit Arguments in Functor Applications}
adamc@541 1260
adamc@656 1261 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 1262
adamc@541 1263
adamc@542 1264 \section{The Ur Standard Library}
adamc@542 1265
adamc@542 1266 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 1267
adamc@542 1268 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 1269
adamc@542 1270 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 1271 $$\begin{array}{l}
adamc@542 1272 \mt{type} \; \mt{int} \\
adamc@542 1273 \mt{type} \; \mt{float} \\
adamc@873 1274 \mt{type} \; \mt{char} \\
adamc@542 1275 \mt{type} \; \mt{string} \\
adamc@542 1276 \mt{type} \; \mt{time} \\
adamc@785 1277 \mt{type} \; \mt{blob} \\
adamc@542 1278 \\
adamc@542 1279 \mt{type} \; \mt{unit} = \{\} \\
adamc@542 1280 \\
adamc@542 1281 \mt{datatype} \; \mt{bool} = \mt{False} \mid \mt{True} \\
adamc@542 1282 \\
adamc@785 1283 \mt{datatype} \; \mt{option} \; \mt{t} = \mt{None} \mid \mt{Some} \; \mt{of} \; \mt{t} \\
adamc@785 1284 \\
adamc@785 1285 \mt{datatype} \; \mt{list} \; \mt{t} = \mt{Nil} \mid \mt{Cons} \; \mt{of} \; \mt{t} \times \mt{list} \; \mt{t}
adamc@542 1286 \end{array}$$
adamc@542 1287
adamc@1123 1288 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 1289
adam@1297 1290 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 1291 $$\begin{array}{l}
adam@1297 1292 \mt{con} \; \mt{variant} :: \{\mt{Type}\} \to \mt{Type} \\
adam@1297 1293 \mt{val} \; \mt{make} : \mt{nm} :: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{ts} ::: \{\mt{Type}\} \to [[\mt{nm}] \sim \mt{ts}] \Rightarrow \mt{t} \to \mt{variant} \; ([\mt{nm} = \mt{t}] \rc \mt{ts}) \\
adam@1297 1294 \mt{val} \; \mt{match} : \mt{ts} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{variant} \; \mt{ts} \to \$(\mt{map} \; (\lambda \mt{t'} \Rightarrow \mt{t'} \to \mt{t}) \; \mt{ts}) \to \mt{t}
adam@1297 1295 \end{array}$$
adam@1297 1296
adamc@657 1297 Another important generic Ur element comes at the beginning of \texttt{top.urs}.
adamc@657 1298
adamc@657 1299 $$\begin{array}{l}
adamc@657 1300 \mt{con} \; \mt{folder} :: \mt{K} \longrightarrow \{\mt{K}\} \to \mt{Type} \\
adamc@657 1301 \\
adamc@657 1302 \mt{val} \; \mt{fold} : \mt{K} \longrightarrow \mt{tf} :: (\{\mt{K}\} \to \mt{Type}) \\
adamc@657 1303 \hspace{.1in} \to (\mt{nm} :: \mt{Name} \to \mt{v} :: \mt{K} \to \mt{r} :: \{\mt{K}\} \to [[\mt{nm}] \sim \mt{r}] \Rightarrow \\
adamc@657 1304 \hspace{.2in} \mt{tf} \; \mt{r} \to \mt{tf} \; ([\mt{nm} = \mt{v}] \rc \mt{r})) \\
adamc@657 1305 \hspace{.1in} \to \mt{tf} \; [] \\
adamc@657 1306 \hspace{.1in} \to \mt{r} :: \{\mt{K}\} \to \mt{folder} \; \mt{r} \to \mt{tf} \; \mt{r}
adamc@657 1307 \end{array}$$
adamc@657 1308
adamc@657 1309 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 1310
adamc@664 1311 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 1312
adamc@542 1313
adamc@542 1314 \section{The Ur/Web Standard Library}
adamc@542 1315
adamc@658 1316 \subsection{Monads}
adamc@658 1317
adamc@658 1318 The Ur Basis defines the monad constructor class from Haskell.
adamc@658 1319
adamc@658 1320 $$\begin{array}{l}
adamc@658 1321 \mt{class} \; \mt{monad} :: \mt{Type} \to \mt{Type} \\
adamc@658 1322 \mt{val} \; \mt{return} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t} ::: \mt{Type} \\
adamc@658 1323 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658 1324 \hspace{.1in} \to \mt{t} \to \mt{m} \; \mt{t} \\
adamc@658 1325 \mt{val} \; \mt{bind} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t1} ::: \mt{Type} \to \mt{t2} ::: \mt{Type} \\
adamc@658 1326 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658 1327 \hspace{.1in} \to \mt{m} \; \mt{t1} \to (\mt{t1} \to \mt{m} \; \mt{t2}) \\
adamc@658 1328 \hspace{.1in} \to \mt{m} \; \mt{t2}
adamc@658 1329 \end{array}$$
adamc@658 1330
adamc@542 1331 \subsection{Transactions}
adamc@542 1332
adamc@542 1333 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 1334 $$\begin{array}{l}
adamc@542 1335 \mt{con} \; \mt{transaction} :: \mt{Type} \to \mt{Type} \\
adamc@658 1336 \mt{val} \; \mt{transaction\_monad} : \mt{monad} \; \mt{transaction}
adamc@542 1337 \end{array}$$
adamc@542 1338
adamc@1123 1339 For debugging purposes, a transactional function is provided for outputting a string on the server process' \texttt{stderr}.
adamc@1123 1340 $$\begin{array}{l}
adamc@1123 1341 \mt{val} \; \mt{debug} : \mt{string} \to \mt{transaction} \; \mt{unit}
adamc@1123 1342 \end{array}$$
adamc@1123 1343
adamc@542 1344 \subsection{HTTP}
adamc@542 1345
adamc@542 1346 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 1347 $$\begin{array}{l}
adamc@786 1348 \mt{val} \; \mt{requestHeader} : \mt{string} \to \mt{transaction} \; (\mt{option} \; \mt{string}) \\
adamc@786 1349 \\
adamc@786 1350 \mt{con} \; \mt{http\_cookie} :: \mt{Type} \to \mt{Type} \\
adamc@786 1351 \mt{val} \; \mt{getCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; (\mt{option} \; \mt{t}) \\
adamc@1050 1352 \mt{val} \; \mt{setCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \{\mt{Value} : \mt{t}, \mt{Expires} : \mt{option} \; \mt{time}, \mt{Secure} : \mt{bool}\} \to \mt{transaction} \; \mt{unit} \\
adamc@1050 1353 \mt{val} \; \mt{clearCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; \mt{unit}
adamc@786 1354 \end{array}$$
adamc@786 1355
adamc@786 1356 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 1357 $$\begin{array}{l}
adamc@786 1358 \mt{type} \; \mt{url} \\
adamc@786 1359 \mt{val} \; \mt{bless} : \mt{string} \to \mt{url} \\
adamc@786 1360 \mt{val} \; \mt{checkUrl} : \mt{string} \to \mt{option} \; \mt{url}
adamc@786 1361 \end{array}$$
adamc@786 1362 $\mt{bless}$ raises a runtime error if the string passed to it fails the URL policy.
adamc@786 1363
adamc@1085 1364 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 1365 $$\begin{array}{l}
adamc@1085 1366 \mt{val} \; \mt{currentUrl} : \mt{transaction} \; \mt{url} \\
adamc@1085 1367 \mt{val} \; \mt{url} : \mt{transaction} \; \mt{page} \to \mt{url}
adamc@1085 1368 \end{array}$$
adamc@1085 1369
adamc@1085 1370 Page generation may be interrupted at any time with a request to redirect to a particular URL instead.
adamc@1085 1371 $$\begin{array}{l}
adamc@1085 1372 \mt{val} \; \mt{redirect} : \mt{t} ::: \mt{Type} \to \mt{url} \to \mt{transaction} \; \mt{t}
adamc@1085 1373 \end{array}$$
adamc@1085 1374
adamc@786 1375 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 1376 $$\begin{array}{l}
adamc@786 1377 \mt{type} \; \mt{file} \\
adamc@786 1378 \mt{val} \; \mt{fileName} : \mt{file} \to \mt{option} \; \mt{string} \\
adamc@786 1379 \mt{val} \; \mt{fileMimeType} : \mt{file} \to \mt{string} \\
adamc@786 1380 \mt{val} \; \mt{fileData} : \mt{file} \to \mt{blob}
adamc@786 1381 \end{array}$$
adamc@786 1382
adamc@786 1383 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 1384 $$\begin{array}{l}
adamc@786 1385 \mt{type} \; \mt{mimeType} \\
adamc@786 1386 \mt{val} \; \mt{blessMime} : \mt{string} \to \mt{mimeType} \\
adamc@786 1387 \mt{val} \; \mt{checkMime} : \mt{string} \to \mt{option} \; \mt{mimeType} \\
adamc@786 1388 \mt{val} \; \mt{returnBlob} : \mt{t} ::: \mt{Type} \to \mt{blob} \to \mt{mimeType} \to \mt{transaction} \; \mt{t}
adamc@542 1389 \end{array}$$
adamc@542 1390
adamc@543 1391 \subsection{SQL}
adamc@543 1392
adamc@543 1393 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 1394 $$\begin{array}{l}
adamc@785 1395 \mt{con} \; \mt{sql\_table} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785 1396 \end{array}$$
adamc@785 1397 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 1398
adamc@785 1399 We also have the simpler type family of SQL views, which have no keys.
adamc@785 1400 $$\begin{array}{l}
adamc@785 1401 \mt{con} \; \mt{sql\_view} :: \{\mt{Type}\} \to \mt{Type}
adamc@543 1402 \end{array}$$
adamc@543 1403
adamc@785 1404 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 1405 $$\begin{array}{l}
adamc@785 1406 \mt{class} \; \mt{fieldsOf} :: \mt{Type} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1407 \mt{val} \; \mt{fieldsOf\_table} : \mt{fs} ::: \{\mt{Type}\} \to \mt{keys} ::: \{\{\mt{Unit}\}\} \to \mt{fieldsOf} \; (\mt{sql\_table} \; \mt{fs} \; \mt{keys}) \; \mt{fs} \\
adamc@785 1408 \mt{val} \; \mt{fieldsOf\_view} : \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; (\mt{sql\_view} \; \mt{fs}) \; \mt{fs}
adamc@785 1409 \end{array}$$
adamc@785 1410
adamc@785 1411 \subsubsection{Table Constraints}
adamc@785 1412
adamc@785 1413 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 1414
adamc@785 1415 $$\begin{array}{l}
adamc@785 1416 \mt{con} \; \mt{primary\_key} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type} \\
adamc@785 1417 \mt{val} \; \mt{no\_primary\_key} : \mt{fs} ::: \{\mt{Type}\} \to \mt{primary\_key} \; \mt{fs} \; [] \\
adamc@785 1418 \mt{val} \; \mt{primary\_key} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{key1} :: \mt{Name} \to \mt{keys} :: \{\mt{Type}\} \\
adamc@785 1419 \hspace{.1in} \to [[\mt{key1}] \sim \mt{keys}] \Rightarrow [[\mt{key1} = \mt{t}] \rc \mt{keys} \sim \mt{rest}] \\
adamc@785 1420 \hspace{.1in} \Rightarrow \$([\mt{key1} = \mt{sql\_injectable\_prim} \; \mt{t}] \rc \mt{map} \; \mt{sql\_injectable\_prim} \; \mt{keys}) \\
adamc@785 1421 \hspace{.1in} \to \mt{primary\_key} \; ([\mt{key1} = \mt{t}] \rc \mt{keys} \rc \mt{rest}) \; [\mt{Pkey} = [\mt{key1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{keys}]
adamc@785 1422 \end{array}$$
adamc@785 1423 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 1424
adamc@785 1425 A type family stands for sets of named constraints of the remaining varieties.
adamc@785 1426 $$\begin{array}{l}
adamc@785 1427 \mt{con} \; \mt{sql\_constraints} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785 1428 \end{array}$$
adamc@785 1429 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 1430
adamc@785 1431 There is a type family of individual, unnamed constraints.
adamc@785 1432 $$\begin{array}{l}
adamc@785 1433 \mt{con} \; \mt{sql\_constraint} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \mt{Type}
adamc@785 1434 \end{array}$$
adamc@785 1435 The first argument is the same as above, and the second argument gives the key columns for just this constraint.
adamc@785 1436
adamc@785 1437 We have operations for assembling constraints into constraint sets.
adamc@785 1438 $$\begin{array}{l}
adamc@785 1439 \mt{val} \; \mt{no\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_constraints} \; \mt{fs} \; [] \\
adamc@785 1440 \mt{val} \; \mt{one\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{unique} ::: \{\mt{Unit}\} \to \mt{name} :: \mt{Name} \\
adamc@785 1441 \hspace{.1in} \to \mt{sql\_constraint} \; \mt{fs} \; \mt{unique} \to \mt{sql\_constraints} \; \mt{fs} \; [\mt{name} = \mt{unique}] \\
adamc@785 1442 \mt{val} \; \mt{join\_constraints} : \mt{fs} ::: \{\mt{Type}\} \to \mt{uniques1} ::: \{\{\mt{Unit}\}\} \to \mt{uniques2} ::: \{\{\mt{Unit}\}\} \to [\mt{uniques1} \sim \mt{uniques2}] \\
adamc@785 1443 \hspace{.1in} \Rightarrow \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques1} \to \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques2} \to \mt{sql\_constraints} \; \mt{fs} \; (\mt{uniques1} \rc \mt{uniques2})
adamc@785 1444 \end{array}$$
adamc@785 1445
adamc@785 1446 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 1447 $$\begin{array}{l}
adamc@785 1448 \mt{val} \; \mt{unique} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{unique1} :: \mt{Name} \to \mt{unique} :: \{\mt{Type}\} \\
adamc@785 1449 \hspace{.1in} \to [[\mt{unique1}] \sim \mt{unique}] \Rightarrow [[\mt{unique1} = \mt{t}] \rc \mt{unique} \sim \mt{rest}] \\
adamc@785 1450 \hspace{.1in} \Rightarrow \mt{sql\_constraint} \; ([\mt{unique1} = \mt{t}] \rc \mt{unique} \rc \mt{rest}) \; ([\mt{unique1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{unique})
adamc@785 1451 \end{array}$$
adamc@785 1452
adamc@785 1453 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 1454 $$\begin{array}{l}
adamc@785 1455 \mt{class} \; \mt{linkable} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@785 1456 \mt{val} \; \mt{linkable\_same} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; \mt{t} \\
adamc@785 1457 \mt{val} \; \mt{linkable\_from\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; (\mt{option} \; \mt{t}) \; \mt{t} \\
adamc@785 1458 \mt{val} \; \mt{linkable\_to\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@785 1459 \end{array}$$
adamc@785 1460
adamc@785 1461 The $\mt{matching}$ type family uses $\mt{linkable}$ to define when two keys match up type-wise.
adamc@785 1462 $$\begin{array}{l}
adamc@785 1463 \mt{con} \; \mt{matching} :: \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1464 \mt{val} \; \mt{mat\_nil} : \mt{matching} \; [] \; [] \\
adamc@785 1465 \mt{val} \; \mt{mat\_cons} : \mt{t1} ::: \mt{Type} \to \mt{rest1} ::: \{\mt{Type}\} \to \mt{t2} ::: \mt{Type} \to \mt{rest2} ::: \{\mt{Type}\} \to \mt{nm1} :: \mt{Name} \to \mt{nm2} :: \mt{Name} \\
adamc@785 1466 \hspace{.1in} \to [[\mt{nm1}] \sim \mt{rest1}] \Rightarrow [[\mt{nm2}] \sim \mt{rest2}] \Rightarrow \mt{linkable} \; \mt{t1} \; \mt{t2} \to \mt{matching} \; \mt{rest1} \; \mt{rest2} \\
adamc@785 1467 \hspace{.1in} \to \mt{matching} \; ([\mt{nm1} = \mt{t1}] \rc \mt{rest1}) \; ([\mt{nm2} = \mt{t2}] \rc \mt{rest2})
adamc@785 1468 \end{array}$$
adamc@785 1469
adamc@785 1470 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 1471 $$\begin{array}{l}
adamc@785 1472 \mt{con} \; \mt{propagation\_mode} :: \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1473 \mt{val} \; \mt{restrict} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1474 \mt{val} \; \mt{cascade} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1475 \mt{val} \; \mt{no\_action} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1476 \mt{val} \; \mt{set\_null} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; (\mt{map} \; \mt{option} \; \mt{fs})
adamc@785 1477 \end{array}$$
adamc@785 1478
adamc@785 1479 Finally, we put these ingredient together to define the \texttt{FOREIGN KEY} constraint function.
adamc@785 1480 $$\begin{array}{l}
adamc@785 1481 \mt{val} \; \mt{foreign\_key} : \mt{mine1} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{mine} ::: \{\mt{Type}\} \to \mt{munused} ::: \{\mt{Type}\} \to \mt{foreign} ::: \{\mt{Type}\} \\
adamc@785 1482 \hspace{.1in} \to \mt{funused} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{uniques} ::: \{\{\mt{Unit}\}\} \\
adamc@785 1483 \hspace{.1in} \to [[\mt{mine1}] \sim \mt{mine}] \Rightarrow [[\mt{mine1} = \mt{t}] \rc \mt{mine} \sim \mt{munused}] \Rightarrow [\mt{foreign} \sim \mt{funused}] \Rightarrow [[\mt{nm}] \sim \mt{uniques}] \\
adamc@785 1484 \hspace{.1in} \Rightarrow \mt{matching} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}) \; \mt{foreign} \\
adamc@785 1485 \hspace{.1in} \to \mt{sql\_table} \; (\mt{foreign} \rc \mt{funused}) \; ([\mt{nm} = \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{foreign}] \rc \mt{uniques}) \\
adamc@785 1486 \hspace{.1in} \to \{\mt{OnDelete} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}), \\
adamc@785 1487 \hspace{.2in} \mt{OnUpdate} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine})\} \\
adamc@785 1488 \hspace{.1in} \to \mt{sql\_constraint} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine} \rc \mt{munused}) \; []
adamc@785 1489 \end{array}$$
adamc@785 1490
adamc@785 1491 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 1492 $$\begin{array}{l}
adamc@785 1493 \mt{val} \; \mt{check} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; [] \; [] \; \mt{fs} \; \mt{bool} \to \mt{sql\_constraint} \; \mt{fs} \; []
adamc@785 1494 \end{array}$$
adamc@785 1495
adamc@785 1496 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 1497
adamc@784 1498
adamc@543 1499 \subsubsection{Queries}
adamc@543 1500
adamc@1193 1501 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 1502 $$\begin{array}{l}
adamc@1193 1503 \mt{con} \; \mt{sql\_query} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@1193 1504 \mt{val} \; \mt{sql\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1505 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543 1506 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1507 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1193 1508 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adamc@1193 1509 \hspace{.1in} \Rightarrow \{\mt{Rows} : \mt{sql\_query1} \; \mt{free} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}, \\
adamc@1193 1510 \hspace{.2in} \mt{OrderBy} : \mt{sql\_order\_by} \; (\mt{free} \rc \mt{tables}) \; \mt{selectedExps}, \\
adamc@543 1511 \hspace{.2in} \mt{Limit} : \mt{sql\_limit}, \\
adamc@543 1512 \hspace{.2in} \mt{Offset} : \mt{sql\_offset}\} \\
adamc@1193 1513 \hspace{.1in} \to \mt{sql\_query} \; \mt{free} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1514 \end{array}$$
adamc@543 1515
adamc@545 1516 Queries are used by folding over their results inside transactions.
adamc@545 1517 $$\begin{array}{l}
adamc@1193 1518 \mt{val} \; \mt{query} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \lambda [\mt{tables} \sim \mt{exps}] \Rightarrow \mt{state} ::: \mt{Type} \to \mt{sql\_query} \; [] \; \mt{tables} \; \mt{exps} \\
adamc@658 1519 \hspace{.1in} \to (\$(\mt{exps} \rc \mt{map} \; (\lambda \mt{fields} :: \{\mt{Type}\} \Rightarrow \$\mt{fields}) \; \mt{tables}) \\
adamc@545 1520 \hspace{.2in} \to \mt{state} \to \mt{transaction} \; \mt{state}) \\
adamc@545 1521 \hspace{.1in} \to \mt{state} \to \mt{transaction} \; \mt{state}
adamc@545 1522 \end{array}$$
adamc@545 1523
adamc@1193 1524 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 1525 $$\begin{array}{l}
adamc@1193 1526 \mt{con} \; \mt{sql\_query1} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@543 1527 \\
adamc@543 1528 \mt{type} \; \mt{sql\_relop} \\
adamc@543 1529 \mt{val} \; \mt{sql\_union} : \mt{sql\_relop} \\
adamc@543 1530 \mt{val} \; \mt{sql\_intersect} : \mt{sql\_relop} \\
adamc@543 1531 \mt{val} \; \mt{sql\_except} : \mt{sql\_relop} \\
adamc@543 1532 \mt{val} \; \mt{sql\_relop} : \mt{tables1} ::: \{\{\mt{Type}\}\} \\
adamc@543 1533 \hspace{.1in} \to \mt{tables2} ::: \{\{\mt{Type}\}\} \\
adamc@543 1534 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1535 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@543 1536 \hspace{.1in} \to \mt{sql\_relop} \\
adamc@543 1537 \hspace{.1in} \to \mt{sql\_query1} \; \mt{tables1} \; \mt{selectedFields} \; \mt{selectedExps} \\
adamc@543 1538 \hspace{.1in} \to \mt{sql\_query1} \; \mt{tables2} \; \mt{selectedFields} \; \mt{selectedExps} \\
adamc@543 1539 \hspace{.1in} \to \mt{sql\_query1} \; \mt{selectedFields} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1540 \end{array}$$
adamc@543 1541
adamc@543 1542 $$\begin{array}{l}
adamc@1193 1543 \mt{val} \; \mt{sql\_query1} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1544 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543 1545 \hspace{.1in} \to \mt{grouped} ::: \{\{\mt{Type}\}\} \\
adamc@543 1546 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1547 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1085 1548 \hspace{.1in} \to \mt{empties} :: \{\mt{Unit}\} \\
adamc@1193 1549 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adamc@1193 1550 \hspace{.1in} \Rightarrow [\mt{free} \sim \mt{grouped}] \\
adamc@1193 1551 \hspace{.1in} \Rightarrow [\mt{empties} \sim \mt{selectedFields}] \\
adamc@1085 1552 \hspace{.1in} \Rightarrow \{\mt{Distinct} : \mt{bool}, \\
adamc@1193 1553 \hspace{.2in} \mt{From} : \mt{sql\_from\_items} \; \mt{free} \; \mt{tables}, \\
adamc@1193 1554 \hspace{.2in} \mt{Where} : \mt{sql\_exp} \; (\mt{free} \rc \mt{tables}) \; [] \; [] \; \mt{bool}, \\
adamc@543 1555 \hspace{.2in} \mt{GroupBy} : \mt{sql\_subset} \; \mt{tables} \; \mt{grouped}, \\
adamc@1193 1556 \hspace{.2in} \mt{Having} : \mt{sql\_exp} \; (\mt{free} \rc \mt{grouped}) \; \mt{tables} \; [] \; \mt{bool}, \\
adamc@1085 1557 \hspace{.2in} \mt{SelectFields} : \mt{sql\_subset} \; \mt{grouped} \; (\mt{map} \; (\lambda \_ \Rightarrow []) \; \mt{empties} \rc \mt{selectedFields}), \\
adamc@1193 1558 \hspace{.2in} \mt {SelectExps} : \$(\mt{map} \; (\mt{sql\_exp} \; (\mt{free} \rc \mt{grouped}) \; \mt{tables} \; []) \; \mt{selectedExps}) \} \\
adamc@1193 1559 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1560 \end{array}$$
adamc@543 1561
adamc@543 1562 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 1563 $$\begin{array}{l}
adamc@543 1564 \mt{con} \; \mt{sql\_subset} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@543 1565 \mt{val} \; \mt{sql\_subset} : \mt{keep\_drop} :: \{(\{\mt{Type}\} \times \{\mt{Type}\})\} \\
adamc@543 1566 \hspace{.1in} \to \mt{sql\_subset} \\
adamc@658 1567 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1 \rc \mt{fields}.2)\; \mt{keep\_drop}) \\
adamc@658 1568 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1) \; \mt{keep\_drop}) \\
adamc@543 1569 \mt{val} \; \mt{sql\_subset\_all} : \mt{tables} :: \{\{\mt{Type}\}\} \to \mt{sql\_subset} \; \mt{tables} \; \mt{tables}
adamc@543 1570 \end{array}$$
adamc@543 1571
adamc@560 1572 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 1573 $$\begin{array}{l}
adamc@543 1574 \mt{con} \; \mt{sql\_exp} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}
adamc@543 1575 \end{array}$$
adamc@543 1576
adamc@543 1577 Any field in scope may be converted to an expression.
adamc@543 1578 $$\begin{array}{l}
adamc@543 1579 \mt{val} \; \mt{sql\_field} : \mt{otherTabs} ::: \{\{\mt{Type}\}\} \to \mt{otherFields} ::: \{\mt{Type}\} \\
adamc@543 1580 \hspace{.1in} \to \mt{fieldType} ::: \mt{Type} \to \mt{agg} ::: \{\{\mt{Type}\}\} \\
adamc@543 1581 \hspace{.1in} \to \mt{exps} ::: \{\mt{Type}\} \\
adamc@543 1582 \hspace{.1in} \to \mt{tab} :: \mt{Name} \to \mt{field} :: \mt{Name} \\
adamc@543 1583 \hspace{.1in} \to \mt{sql\_exp} \; ([\mt{tab} = [\mt{field} = \mt{fieldType}] \rc \mt{otherFields}] \rc \mt{otherTabs}) \; \mt{agg} \; \mt{exps} \; \mt{fieldType}
adamc@543 1584 \end{array}$$
adamc@543 1585
adamc@544 1586 There is an analogous function for referencing named expressions.
adamc@544 1587 $$\begin{array}{l}
adamc@544 1588 \mt{val} \; \mt{sql\_exp} : \mt{tabs} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{t} ::: \mt{Type} \to \mt{rest} ::: \{\mt{Type}\} \to \mt{nm} :: \mt{Name} \\
adamc@544 1589 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tabs} \; \mt{agg} \; ([\mt{nm} = \mt{t}] \rc \mt{rest}) \; \mt{t}
adamc@544 1590 \end{array}$$
adamc@544 1591
adamc@544 1592 Ur values of appropriate types may be injected into SQL expressions.
adamc@544 1593 $$\begin{array}{l}
adamc@786 1594 \mt{class} \; \mt{sql\_injectable\_prim} \\
adamc@786 1595 \mt{val} \; \mt{sql\_bool} : \mt{sql\_injectable\_prim} \; \mt{bool} \\
adamc@786 1596 \mt{val} \; \mt{sql\_int} : \mt{sql\_injectable\_prim} \; \mt{int} \\
adamc@786 1597 \mt{val} \; \mt{sql\_float} : \mt{sql\_injectable\_prim} \; \mt{float} \\
adamc@786 1598 \mt{val} \; \mt{sql\_string} : \mt{sql\_injectable\_prim} \; \mt{string} \\
adamc@786 1599 \mt{val} \; \mt{sql\_time} : \mt{sql\_injectable\_prim} \; \mt{time} \\
adamc@786 1600 \mt{val} \; \mt{sql\_blob} : \mt{sql\_injectable\_prim} \; \mt{blob} \\
adamc@786 1601 \mt{val} \; \mt{sql\_channel} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{channel} \; \mt{t}) \\
adamc@786 1602 \mt{val} \; \mt{sql\_client} : \mt{sql\_injectable\_prim} \; \mt{client} \\
adamc@786 1603 \\
adamc@544 1604 \mt{class} \; \mt{sql\_injectable} \\
adamc@786 1605 \mt{val} \; \mt{sql\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@786 1606 \mt{val} \; \mt{sql\_option\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; (\mt{option} \; \mt{t}) \\
adamc@786 1607 \\
adamc@544 1608 \mt{val} \; \mt{sql\_inject} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@544 1609 \hspace{.1in} \to \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adamc@544 1610 \end{array}$$
adamc@544 1611
adamc@1123 1612 Additionally, most function-free types may be injected safely, via the $\mt{serialized}$ type family.
adamc@1123 1613 $$\begin{array}{l}
adamc@1123 1614 \mt{con} \; \mt{serialized} :: \mt{Type} \to \mt{Type} \\
adamc@1123 1615 \mt{val} \; \mt{serialize} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{serialized} \; \mt{t} \\
adamc@1123 1616 \mt{val} \; \mt{deserialize} : \mt{t} ::: \mt{Type} \to \mt{serialized} \; \mt{t} \to \mt{t} \\
adamc@1123 1617 \mt{val} \; \mt{sql\_serialized} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{serialized} \; \mt{t})
adamc@1123 1618 \end{array}$$
adamc@1123 1619
adamc@544 1620 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 1621 $$\begin{array}{l}
adamc@544 1622 \mt{val} \; \mt{sql\_is\_null} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544 1623 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; (\mt{option} \; \mt{t}) \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{bool}
adamc@544 1624 \end{array}$$
adamc@544 1625
adamc@559 1626 We have generic nullary, unary, and binary operators.
adamc@544 1627 $$\begin{array}{l}
adamc@544 1628 \mt{con} \; \mt{sql\_nfunc} :: \mt{Type} \to \mt{Type} \\
adamc@544 1629 \mt{val} \; \mt{sql\_current\_timestamp} : \mt{sql\_nfunc} \; \mt{time} \\
adamc@544 1630 \mt{val} \; \mt{sql\_nfunc} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544 1631 \hspace{.1in} \to \mt{sql\_nfunc} \; \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\\end{array}$$
adamc@544 1632
adamc@544 1633 $$\begin{array}{l}
adamc@544 1634 \mt{con} \; \mt{sql\_unary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544 1635 \mt{val} \; \mt{sql\_not} : \mt{sql\_unary} \; \mt{bool} \; \mt{bool} \\
adamc@544 1636 \mt{val} \; \mt{sql\_unary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adamc@544 1637 \hspace{.1in} \to \mt{sql\_unary} \; \mt{arg} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res} \\
adamc@544 1638 \end{array}$$
adamc@544 1639
adamc@544 1640 $$\begin{array}{l}
adamc@544 1641 \mt{con} \; \mt{sql\_binary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544 1642 \mt{val} \; \mt{sql\_and} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544 1643 \mt{val} \; \mt{sql\_or} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544 1644 \mt{val} \; \mt{sql\_binary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg_1} ::: \mt{Type} \to \mt{arg_2} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adamc@544 1645 \hspace{.1in} \to \mt{sql\_binary} \; \mt{arg_1} \; \mt{arg_2} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_1} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_2} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res}
adamc@544 1646 \end{array}$$
adamc@544 1647
adamc@544 1648 $$\begin{array}{l}
adamc@559 1649 \mt{class} \; \mt{sql\_arith} \\
adamc@559 1650 \mt{val} \; \mt{sql\_int\_arith} : \mt{sql\_arith} \; \mt{int} \\
adamc@559 1651 \mt{val} \; \mt{sql\_float\_arith} : \mt{sql\_arith} \; \mt{float} \\
adamc@559 1652 \mt{val} \; \mt{sql\_neg} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_unary} \; \mt{t} \; \mt{t} \\
adamc@559 1653 \mt{val} \; \mt{sql\_plus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1654 \mt{val} \; \mt{sql\_minus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1655 \mt{val} \; \mt{sql\_times} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1656 \mt{val} \; \mt{sql\_div} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1657 \mt{val} \; \mt{sql\_mod} : \mt{sql\_binary} \; \mt{int} \; \mt{int} \; \mt{int}
adamc@559 1658 \end{array}$$
adamc@544 1659
adamc@656 1660 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 1661 $$\begin{array}{l}
adamc@544 1662 \mt{val} \; \mt{sql\_count} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int}
adamc@544 1663 \end{array}$$
adamc@544 1664
adamc@544 1665 $$\begin{array}{l}
adamc@1188 1666 \mt{con} \; \mt{sql\_aggregate} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@1188 1667 \mt{val} \; \mt{sql\_aggregate} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{dom} ::: \mt{Type} \to \mt{ran} ::: \mt{Type} \\
adamc@1188 1668 \hspace{.1in} \to \mt{sql\_aggregate} \; \mt{dom} \; \mt{ran} \to \mt{sql\_exp} \; \mt{agg} \; \mt{agg} \; \mt{exps} \; \mt{dom} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{ran}
adamc@1188 1669 \end{array}$$
adamc@1188 1670
adamc@1188 1671 $$\begin{array}{l}
adamc@1188 1672 \mt{val} \; \mt{sql\_count\_col} : \mt{t} ::: \mt{Type} \to \mt{sql\_aggregate} \; (\mt{option} \; \mt{t}) \; \mt{int}
adamc@544 1673 \end{array}$$
adamc@544 1674
adamc@544 1675 $$\begin{array}{l}
adamc@544 1676 \mt{class} \; \mt{sql\_summable} \\
adamc@544 1677 \mt{val} \; \mt{sql\_summable\_int} : \mt{sql\_summable} \; \mt{int} \\
adamc@544 1678 \mt{val} \; \mt{sql\_summable\_float} : \mt{sql\_summable} \; \mt{float} \\
adamc@1188 1679 \mt{val} \; \mt{sql\_avg} : \mt{t} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{t} \\
adamc@1188 1680 \mt{val} \; \mt{sql\_sum} : \mt{t} ::: \mt{Type} \to \mt{sql\_summable} \mt{t} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{t}
adamc@544 1681 \end{array}$$
adamc@544 1682
adamc@544 1683 $$\begin{array}{l}
adamc@544 1684 \mt{class} \; \mt{sql\_maxable} \\
adamc@544 1685 \mt{val} \; \mt{sql\_maxable\_int} : \mt{sql\_maxable} \; \mt{int} \\
adamc@544 1686 \mt{val} \; \mt{sql\_maxable\_float} : \mt{sql\_maxable} \; \mt{float} \\
adamc@544 1687 \mt{val} \; \mt{sql\_maxable\_string} : \mt{sql\_maxable} \; \mt{string} \\
adamc@544 1688 \mt{val} \; \mt{sql\_maxable\_time} : \mt{sql\_maxable} \; \mt{time} \\
adamc@1188 1689 \mt{val} \; \mt{sql\_max} : \mt{t} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{t} \\
adamc@1188 1690 \mt{val} \; \mt{sql\_min} : \mt{t} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{t}
adamc@544 1691 \end{array}$$
adamc@544 1692
adamc@1193 1693 Any SQL query that returns single columns may be turned into a subquery expression.
adamc@1193 1694
adamc@786 1695 $$\begin{array}{l}
adamc@1193 1696 \mt{val} \; \mt{sql\_subquery} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \\
adamc@1193 1697 \hspace{.1in} \to \mt{sql\_query} \; \mt{tables} \; [] \; [\mt{nm} = \mt{t}] \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adamc@1193 1698 \end{array}$$
adamc@1193 1699
adamc@1193 1700 \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 1701 $$\begin{array}{l}
adamc@1193 1702 \mt{con} \; \mt{sql\_from\_items} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@1193 1703 \mt{val} \; \mt{sql\_from\_table} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1704 \hspace{.1in} \to \mt{t} ::: \mt{Type} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; \mt{t} \; \mt{fs} \to \mt{name} :: \mt{Name} \to \mt{t} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193 1705 \mt{val} \; \mt{sql\_from\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{name} :: \mt{Name} \to \mt{sql\_query} \; \mt{free} \; [] \; \mt{fs} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193 1706 \mt{val} \; \mt{sql\_from\_comma} : \mt{free} ::: \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \to [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193 1707 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adamc@1193 1708 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2}) \\
adamc@1193 1709 \mt{val} \; \mt{sql\_inner\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1710 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193 1711 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adamc@1193 1712 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193 1713 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2})
adamc@786 1714 \end{array}$$
adamc@786 1715
adamc@786 1716 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 1717 $$\begin{array}{l}
adamc@786 1718 \mt{class} \; \mt{nullify} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@786 1719 \mt{val} \; \mt{nullify\_option} : \mt{t} ::: \mt{Type} \to \mt{nullify} \; (\mt{option} \; \mt{t}) \; (\mt{option} \; \mt{t}) \\
adamc@786 1720 \mt{val} \; \mt{nullify\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{nullify} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@786 1721 \end{array}$$
adamc@786 1722
adamc@786 1723 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 1724
adamc@786 1725 $$\begin{array}{l}
adamc@1193 1726 \mt{val} \; \mt{sql\_left\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{(\mt{Type} \times \mt{Type})\}\} \\
adamc@1193 1727 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@786 1728 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\lambda \mt{r} \Rightarrow \$(\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{nullify} \; \mt{p}.1 \; \mt{p}.2) \; \mt{r})) \; \mt{tabs2}) \\
adamc@1193 1729 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \\
adamc@1193 1730 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193 1731 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.2)) \; \mt{tabs2})
adamc@786 1732 \end{array}$$
adamc@786 1733
adamc@544 1734 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 1735 $$\begin{array}{l}
adamc@544 1736 \mt{type} \; \mt{sql\_direction} \\
adamc@544 1737 \mt{val} \; \mt{sql\_asc} : \mt{sql\_direction} \\
adamc@544 1738 \mt{val} \; \mt{sql\_desc} : \mt{sql\_direction} \\
adamc@544 1739 \\
adamc@544 1740 \mt{con} \; \mt{sql\_order\_by} :: \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@544 1741 \mt{val} \; \mt{sql\_order\_by\_Nil} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} :: \{\mt{Type}\} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544 1742 \mt{val} \; \mt{sql\_order\_by\_Cons} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544 1743 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; [] \; \mt{exps} \; \mt{t} \to \mt{sql\_direction} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544 1744 \\
adamc@544 1745 \mt{type} \; \mt{sql\_limit} \\
adamc@544 1746 \mt{val} \; \mt{sql\_no\_limit} : \mt{sql\_limit} \\
adamc@544 1747 \mt{val} \; \mt{sql\_limit} : \mt{int} \to \mt{sql\_limit} \\
adamc@544 1748 \\
adamc@544 1749 \mt{type} \; \mt{sql\_offset} \\
adamc@544 1750 \mt{val} \; \mt{sql\_no\_offset} : \mt{sql\_offset} \\
adamc@544 1751 \mt{val} \; \mt{sql\_offset} : \mt{int} \to \mt{sql\_offset}
adamc@544 1752 \end{array}$$
adamc@544 1753
adamc@545 1754
adamc@545 1755 \subsubsection{DML}
adamc@545 1756
adamc@545 1757 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 1758
adamc@545 1759 $$\begin{array}{l}
adamc@545 1760 \mt{type} \; \mt{dml} \\
adamc@545 1761 \mt{val} \; \mt{dml} : \mt{dml} \to \mt{transaction} \; \mt{unit}
adamc@545 1762 \end{array}$$
adamc@545 1763
adam@1297 1764 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 1765
adam@1297 1766 $$\begin{array}{l}
adam@1297 1767 \mt{val} \; \mt{tryDml} : \mt{dml} \to \mt{transaction} \; (\mt{option} \; \mt{string})
adam@1297 1768 \end{array}$$
adam@1297 1769
adamc@545 1770 Properly-typed records may be used to form $\mt{INSERT}$ commands.
adamc@545 1771 $$\begin{array}{l}
adamc@545 1772 \mt{val} \; \mt{insert} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \\
adamc@658 1773 \hspace{.1in} \to \$(\mt{map} \; (\mt{sql\_exp} \; [] \; [] \; []) \; \mt{fields}) \to \mt{dml}
adamc@545 1774 \end{array}$$
adamc@545 1775
adamc@545 1776 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 1777 $$\begin{array}{l}
adamc@545 1778 \mt{val} \; \mt{update} : \mt{unchanged} ::: \{\mt{Type}\} \to \mt{changed} :: \{\mt{Type}\} \to \lambda [\mt{changed} \sim \mt{unchanged}] \\
adamc@658 1779 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; []) \; \mt{changed}) \\
adamc@545 1780 \hspace{.1in} \to \mt{sql\_table} \; (\mt{changed} \rc \mt{unchanged}) \to \mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545 1781 \end{array}$$
adamc@545 1782
adamc@545 1783 A $\mt{DELETE}$ command is formed from a table and a $\mt{WHERE}$ clause.
adamc@545 1784 $$\begin{array}{l}
adamc@545 1785 \mt{val} \; \mt{delete} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \to \mt{sql\_exp} \; [\mt{T} = \mt{fields}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545 1786 \end{array}$$
adamc@545 1787
adamc@546 1788 \subsubsection{Sequences}
adamc@546 1789
adamc@546 1790 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 1791
adamc@546 1792 $$\begin{array}{l}
adamc@546 1793 \mt{type} \; \mt{sql\_sequence} \\
adamc@1085 1794 \mt{val} \; \mt{nextval} : \mt{sql\_sequence} \to \mt{transaction} \; \mt{int} \\
adamc@1085 1795 \mt{val} \; \mt{setval} : \mt{sql\_sequence} \to \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@546 1796 \end{array}$$
adamc@546 1797
adamc@546 1798
adamc@547 1799 \subsection{XML}
adamc@547 1800
adamc@547 1801 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.
adamc@547 1802
adamc@547 1803 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. The arguments dealing with field binding are only relevant to HTML forms.
adamc@547 1804 $$\begin{array}{l}
adamc@547 1805 \mt{con} \; \mt{xml} :: \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547 1806 \end{array}$$
adamc@547 1807
adamc@547 1808 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 1809 $$\begin{array}{l}
adamc@547 1810 \mt{con} \; \mt{tag} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547 1811 \end{array}$$
adamc@547 1812
adamc@547 1813 Literal text may be injected into XML as ``CDATA.''
adamc@547 1814 $$\begin{array}{l}
adamc@547 1815 \mt{val} \; \mt{cdata} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{string} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adamc@547 1816 \end{array}$$
adamc@547 1817
adamc@547 1818 There is a function for producing an XML tree with a particular tag at its root.
adamc@547 1819 $$\begin{array}{l}
adamc@547 1820 \mt{val} \; \mt{tag} : \mt{attrsGiven} ::: \{\mt{Type}\} \to \mt{attrsAbsent} ::: \{\mt{Type}\} \to \mt{ctxOuter} ::: \{\mt{Unit}\} \to \mt{ctxInner} ::: \{\mt{Unit}\} \\
adamc@547 1821 \hspace{.1in} \to \mt{useOuter} ::: \{\mt{Type}\} \to \mt{useInner} ::: \{\mt{Type}\} \to \mt{bindOuter} ::: \{\mt{Type}\} \to \mt{bindInner} ::: \{\mt{Type}\} \\
adamc@787 1822 \hspace{.1in} \to \lambda [\mt{attrsGiven} \sim \mt{attrsAbsent}] \; [\mt{useOuter} \sim \mt{useInner}] \; [\mt{bindOuter} \sim \mt{bindInner}] \\
adamc@787 1823 \hspace{.1in} \Rightarrow \mt{option} \; \mt{css\_class} \\
adamc@787 1824 \hspace{.1in} \to \$\mt{attrsGiven} \\
adamc@547 1825 \hspace{.1in} \to \mt{tag} \; (\mt{attrsGiven} \rc \mt{attrsAbsent}) \; \mt{ctxOuter} \; \mt{ctxInner} \; \mt{useOuter} \; \mt{bindOuter} \\
adamc@547 1826 \hspace{.1in} \to \mt{xml} \; \mt{ctxInner} \; \mt{useInner} \; \mt{bindInner} \to \mt{xml} \; \mt{ctxOuter} \; (\mt{useOuter} \rc \mt{useInner}) \; (\mt{bindOuter} \rc \mt{bindInner})
adamc@547 1827 \end{array}$$
adam@1297 1828 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 1829
adamc@547 1830 Two XML fragments may be concatenated.
adamc@547 1831 $$\begin{array}{l}
adamc@547 1832 \mt{val} \; \mt{join} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{bind_1} ::: \{\mt{Type}\} \to \mt{bind_2} ::: \{\mt{Type}\} \\
adamc@547 1833 \hspace{.1in} \to \lambda [\mt{use_1} \sim \mt{bind_1}] \; [\mt{bind_1} \sim \mt{bind_2}] \\
adamc@547 1834 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind_1} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{bind_1}) \; \mt{bind_2} \to \mt{xml} \; \mt{ctx} \; \mt{use_1} \; (\mt{bind_1} \rc \mt{bind_2})
adamc@547 1835 \end{array}$$
adamc@547 1836
adamc@547 1837 Finally, any XML fragment may be updated to ``claim'' to use more form fields than it does.
adamc@547 1838 $$\begin{array}{l}
adamc@547 1839 \mt{val} \; \mt{useMore} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{use_2} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to \lambda [\mt{use_1} \sim \mt{use_2}] \\
adamc@547 1840 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{use_2}) \; \mt{bind}
adamc@547 1841 \end{array}$$
adamc@547 1842
adamc@547 1843 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.
adamc@547 1844
adamc@547 1845 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 1846 $$\begin{array}{l}
adamc@547 1847 \mt{val} \; \mt{error} : \mt{t} ::: \mt{Type} \to \mt{xml} \; [\mt{Body}] \; [] \; [] \to \mt{t}
adamc@547 1848 \end{array}$$
adamc@547 1849
adamc@549 1850
adamc@701 1851 \subsection{Client-Side Programming}
adamc@659 1852
adamc@701 1853 Ur/Web supports running code on web browsers, via automatic compilation to JavaScript.
adamc@701 1854
adamc@701 1855 \subsubsection{The Basics}
adamc@701 1856
adam@1297 1857 Clients can open alert and confirm dialog boxes, in the usual annoying JavaScript way.
adamc@701 1858 $$\begin{array}{l}
adam@1297 1859 \mt{val} \; \mt{alert} : \mt{string} \to \mt{transaction} \; \mt{unit} \\
adam@1297 1860 \mt{val} \; \mt{confirm} : \mt{string} \to \mt{transaction} \; \mt{bool}
adamc@701 1861 \end{array}$$
adamc@701 1862
adamc@701 1863 Any transaction may be run in a new thread with the $\mt{spawn}$ function.
adamc@701 1864 $$\begin{array}{l}
adamc@701 1865 \mt{val} \; \mt{spawn} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit}
adamc@701 1866 \end{array}$$
adamc@701 1867
adamc@701 1868 The current thread can be paused for at least a specified number of milliseconds.
adamc@701 1869 $$\begin{array}{l}
adamc@701 1870 \mt{val} \; \mt{sleep} : \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@701 1871 \end{array}$$
adamc@701 1872
adamc@787 1873 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 1874 $$\begin{array}{l}
adamc@787 1875 \mt{val} \; \mt{onError} : (\mt{xbody} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787 1876 \mt{val} \; \mt{onFail} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787 1877 \mt{val} \; \mt{onConnectFail} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787 1878 \mt{val} \; \mt{onDisconnect} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787 1879 \mt{val} \; \mt{onServerError} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit}
adamc@787 1880 \end{array}$$
adamc@787 1881
adamc@701 1882 \subsubsection{Functional-Reactive Page Generation}
adamc@701 1883
adamc@701 1884 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 1885
adamc@659 1886 $$\begin{array}{l}
adamc@659 1887 \mt{con} \; \mt{source} :: \mt{Type} \to \mt{Type} \\
adamc@659 1888 \mt{val} \; \mt{source} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{transaction} \; (\mt{source} \; \mt{t}) \\
adamc@659 1889 \mt{val} \; \mt{set} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@659 1890 \mt{val} \; \mt{get} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@659 1891 \end{array}$$
adamc@659 1892
adamc@659 1893 Pure functions over sources are represented in a monad of \emph{signals}.
adamc@659 1894
adamc@659 1895 $$\begin{array}{l}
adamc@659 1896 \mt{con} \; \mt{signal} :: \mt{Type} \to \mt{Type} \\
adamc@659 1897 \mt{val} \; \mt{signal\_monad} : \mt{monad} \; \mt{signal} \\
adamc@659 1898 \mt{val} \; \mt{signal} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{signal} \; \mt{t}
adamc@659 1899 \end{array}$$
adamc@659 1900
adamc@659 1901 A reactive portion of an HTML page is injected with a $\mt{dyn}$ tag, which has a signal-valued attribute $\mt{Signal}$.
adamc@659 1902
adamc@659 1903 $$\begin{array}{l}
adamc@701 1904 \mt{val} \; \mt{dyn} : \mt{use} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to \mt{unit} \\
adamc@701 1905 \hspace{.1in} \to \mt{tag} \; [\mt{Signal} = \mt{signal} \; (\mt{xml} \; \mt{body} \; \mt{use} \; \mt{bind})] \; \mt{body} \; [] \; \mt{use} \; \mt{bind}
adamc@659 1906 \end{array}$$
adamc@659 1907
adamc@701 1908 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 1909
adamc@914 1910 \subsubsection{Remote Procedure Calls}
adamc@914 1911
adamc@914 1912 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 1913
adamc@914 1914 $$\begin{array}{l}
adamc@914 1915 \mt{val} \; \mt{rpc} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@914 1916 \end{array}$$
adamc@914 1917
adamc@701 1918 \subsubsection{Asynchronous Message-Passing}
adamc@701 1919
adamc@701 1920 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 1921
adamc@701 1922 $$\begin{array}{l}
adamc@701 1923 \mt{type} \; \mt{client} \\
adamc@701 1924 \mt{val} \; \mt{self} : \mt{transaction} \; \mt{client}
adamc@701 1925 \end{array}$$
adamc@701 1926
adamc@701 1927 \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 1928
adamc@701 1929 $$\begin{array}{l}
adamc@701 1930 \mt{con} \; \mt{channel} :: \mt{Type} \to \mt{Type} \\
adamc@701 1931 \mt{val} \; \mt{channel} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; (\mt{channel} \; \mt{t}) \\
adamc@701 1932 \mt{val} \; \mt{send} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@701 1933 \mt{val} \; \mt{recv} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@701 1934 \end{array}$$
adamc@701 1935
adamc@701 1936 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 1937
adamc@701 1938 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 1939
adamc@659 1940
adamc@549 1941 \section{Ur/Web Syntax Extensions}
adamc@549 1942
adamc@549 1943 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 1944
adamc@549 1945 \subsection{SQL}
adamc@549 1946
adamc@786 1947 \subsubsection{\label{tables}Table Declarations}
adamc@786 1948
adamc@788 1949 $\mt{table}$ declarations may include constraints, via these grammar rules.
adamc@788 1950 $$\begin{array}{rrcll}
adamc@788 1951 \textrm{Declarations} & d &::=& \mt{table} \; x : c \; [pk[,]] \; cts \\
adamc@788 1952 \textrm{Primary key constraints} & pk &::=& \mt{PRIMARY} \; \mt{KEY} \; K \\
adamc@788 1953 \textrm{Keys} & K &::=& f \mid (f, (f,)^+) \\
adamc@788 1954 \textrm{Constraint sets} & cts &::=& \mt{CONSTRAINT} f \; ct \mid cts, cts \mid \{\{e\}\} \\
adamc@788 1955 \textrm{Constraints} & ct &::=& \mt{UNIQUE} \; K \mid \mt{CHECK} \; E \\
adamc@788 1956 &&& \mid \mt{FOREIGN} \; \mt{KEY} \; K \; \mt{REFERENCES} \; F \; (K) \; [\mt{ON} \; \mt{DELETE} \; pr] \; [\mt{ON} \; \mt{UPDATE} \; pr] \\
adamc@788 1957 \textrm{Foreign tables} & F &::=& x \mid \{\{e\}\} \\
adamc@788 1958 \textrm{Propagation modes} & pr &::=& \mt{NO} \; \mt{ACTION} \mid \mt{RESTRICT} \mid \mt{CASCADE} \mid \mt{SET} \; \mt{NULL}
adamc@788 1959 \end{array}$$
adamc@788 1960
adamc@788 1961 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 1962
adamc@788 1963
adamc@549 1964 \subsubsection{Queries}
adamc@549 1965
adamc@550 1966 Queries $Q$ are added to the rules for expressions $e$.
adamc@550 1967
adamc@549 1968 $$\begin{array}{rrcll}
adamc@550 1969 \textrm{Queries} & Q &::=& (q \; [\mt{ORDER} \; \mt{BY} \; (E \; [o],)^+] \; [\mt{LIMIT} \; N] \; [\mt{OFFSET} \; N]) \\
adamc@1085 1970 \textrm{Pre-queries} & q &::=& \mt{SELECT} \; [\mt{DISTINCT}] \; P \; \mt{FROM} \; F,^+ \; [\mt{WHERE} \; E] \; [\mt{GROUP} \; \mt{BY} \; p,^+] \; [\mt{HAVING} \; E] \\
adamc@1085 1971 &&& \mid q \; R \; q \mid \{\{\{e\}\}\} \\
adamc@549 1972 \textrm{Relational operators} & R &::=& \mt{UNION} \mid \mt{INTERSECT} \mid \mt{EXCEPT}
adamc@549 1973 \end{array}$$
adamc@549 1974
adamc@549 1975 $$\begin{array}{rrcll}
adamc@549 1976 \textrm{Projections} & P &::=& \ast & \textrm{all columns} \\
adamc@549 1977 &&& p,^+ & \textrm{particular columns} \\
adamc@549 1978 \textrm{Pre-projections} & p &::=& t.f & \textrm{one column from a table} \\
adamc@558 1979 &&& t.\{\{c\}\} & \textrm{a record of columns from a table (of kind $\{\mt{Type}\}$)} \\
adamc@1194 1980 &&& E \; [\mt{AS} \; f] & \textrm{expression column} \\
adamc@549 1981 \textrm{Table names} & t &::=& x & \textrm{constant table name (automatically capitalized)} \\
adamc@549 1982 &&& X & \textrm{constant table name} \\
adamc@549 1983 &&& \{\{c\}\} & \textrm{computed table name (of kind $\mt{Name}$)} \\
adamc@549 1984 \textrm{Column names} & f &::=& X & \textrm{constant column name} \\
adamc@549 1985 &&& \{c\} & \textrm{computed column name (of kind $\mt{Name}$)} \\
adamc@549 1986 \textrm{Tables} & T &::=& x & \textrm{table variable, named locally by its own capitalization} \\
adamc@549 1987 &&& x \; \mt{AS} \; t & \textrm{table variable, with local name} \\
adamc@549 1988 &&& \{\{e\}\} \; \mt{AS} \; t & \textrm{computed table expression, with local name} \\
adamc@1085 1989 \textrm{$\mt{FROM}$ items} & F &::=& T \mid \{\{e\}\} \mid F \; J \; \mt{JOIN} \; F \; \mt{ON} \; E \\
adamc@1085 1990 &&& \mid F \; \mt{CROSS} \; \mt{JOIN} \ F \\
adamc@1193 1991 &&& \mid (Q) \; \mt{AS} \; t \\
adamc@1085 1992 \textrm{Joins} & J &::=& [\mt{INNER}] \\
adamc@1085 1993 &&& \mid [\mt{LEFT} \mid \mt{RIGHT} \mid \mt{FULL}] \; [\mt{OUTER}] \\
adamc@549 1994 \textrm{SQL expressions} & E &::=& p & \textrm{column references} \\
adamc@549 1995 &&& X & \textrm{named expression references} \\
adamc@549 1996 &&& \{\{e\}\} & \textrm{injected native Ur expressions} \\
adamc@549 1997 &&& \{e\} & \textrm{computed expressions, probably using $\mt{sql\_exp}$ directly} \\
adamc@549 1998 &&& \mt{TRUE} \mid \mt{FALSE} & \textrm{boolean constants} \\
adamc@549 1999 &&& \ell & \textrm{primitive type literals} \\
adamc@549 2000 &&& \mt{NULL} & \textrm{null value (injection of $\mt{None}$)} \\
adamc@549 2001 &&& E \; \mt{IS} \; \mt{NULL} & \textrm{nullness test} \\
adamc@549 2002 &&& n & \textrm{nullary operators} \\
adamc@549 2003 &&& u \; E & \textrm{unary operators} \\
adamc@549 2004 &&& E \; b \; E & \textrm{binary operators} \\
adamc@549 2005 &&& \mt{COUNT}(\ast) & \textrm{count number of rows} \\
adamc@549 2006 &&& a(E) & \textrm{other aggregate function} \\
adamc@1193 2007 &&& (Q) & \textrm{subquery (must return a single expression column)} \\
adamc@549 2008 &&& (E) & \textrm{explicit precedence} \\
adamc@549 2009 \textrm{Nullary operators} & n &::=& \mt{CURRENT\_TIMESTAMP} \\
adamc@549 2010 \textrm{Unary operators} & u &::=& \mt{NOT} \\
adamc@549 2011 \textrm{Binary operators} & b &::=& \mt{AND} \mid \mt{OR} \mid \neq \mid < \mid \leq \mid > \mid \geq \\
adamc@1188 2012 \textrm{Aggregate functions} & a &::=& \mt{COUNT} \mid \mt{AVG} \mid \mt{SUM} \mid \mt{MIN} \mid \mt{MAX} \\
adamc@550 2013 \textrm{Directions} & o &::=& \mt{ASC} \mid \mt{DESC} \\
adamc@549 2014 \textrm{SQL integer} & N &::=& n \mid \{e\} \\
adamc@549 2015 \end{array}$$
adamc@549 2016
adamc@1085 2017 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 2018
adamc@1194 2019 Unnamed expression columns in $\mt{SELECT}$ clauses are assigned consecutive natural numbers, starting with 1.
adamc@1194 2020
adamc@550 2021 \subsubsection{DML}
adamc@550 2022
adamc@550 2023 DML commands $D$ are added to the rules for expressions $e$.
adamc@550 2024
adamc@550 2025 $$\begin{array}{rrcll}
adamc@550 2026 \textrm{Commands} & D &::=& (\mt{INSERT} \; \mt{INTO} \; T^E \; (f,^+) \; \mt{VALUES} \; (E,^+)) \\
adamc@550 2027 &&& (\mt{UPDATE} \; T^E \; \mt{SET} \; (f = E,)^+ \; \mt{WHERE} \; E) \\
adamc@550 2028 &&& (\mt{DELETE} \; \mt{FROM} \; T^E \; \mt{WHERE} \; E) \\
adamc@550 2029 \textrm{Table expressions} & T^E &::=& x \mid \{\{e\}\}
adamc@550 2030 \end{array}$$
adamc@550 2031
adamc@550 2032 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 2033
adamc@551 2034 \subsection{XML}
adamc@551 2035
adamc@551 2036 XML fragments $L$ are added to the rules for expressions $e$.
adamc@551 2037
adamc@551 2038 $$\begin{array}{rrcll}
adamc@551 2039 \textrm{XML fragments} & L &::=& \texttt{<xml/>} \mid \texttt{<xml>}l^*\texttt{</xml>} \\
adamc@551 2040 \textrm{XML pieces} & l &::=& \textrm{text} & \textrm{cdata} \\
adamc@551 2041 &&& \texttt{<}g\texttt{/>} & \textrm{tag with no children} \\
adamc@551 2042 &&& \texttt{<}g\texttt{>}l^*\texttt{</}x\texttt{>} & \textrm{tag with children} \\
adamc@559 2043 &&& \{e\} & \textrm{computed XML fragment} \\
adamc@559 2044 &&& \{[e]\} & \textrm{injection of an Ur expression, via the $\mt{Top}.\mt{txt}$ function} \\
adamc@551 2045 \textrm{Tag} & g &::=& h \; (x = v)^* \\
adamc@551 2046 \textrm{Tag head} & h &::=& x & \textrm{tag name} \\
adamc@551 2047 &&& h\{c\} & \textrm{constructor parameter} \\
adamc@551 2048 \textrm{Attribute value} & v &::=& \ell & \textrm{literal value} \\
adamc@551 2049 &&& \{e\} & \textrm{computed value} \\
adamc@551 2050 \end{array}$$
adamc@551 2051
adamc@552 2052
adamc@1198 2053 \section{\label{structure}The Structure of Web Applications}
adamc@553 2054
adamc@1127 2055 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 2056
adamc@553 2057 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 2058
adamc@553 2059 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 2060
adamc@558 2061 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 2062
adamc@660 2063 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 2064
adamc@789 2065 \medskip
adamc@789 2066
adamc@789 2067 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. 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 2068
adamc@789 2069 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 2070
adamc@553 2071
adamc@897 2072 \section{The Foreign Function Interface}
adamc@897 2073
adamc@897 2074 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 2075
adamc@897 2076 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 2077
adamc@897 2078 \begin{itemize}
adamc@897 2079 \item \texttt{clientOnly Module.ident} registers a value as being allowed only in client-side code.
adamc@897 2080 \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 2081 \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 2082 \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 2083 \item \texttt{include FILE} requests inclusion of a C header file.
adamc@897 2084 \item \texttt{jsFunc Module.ident=name} gives a mapping from an Ur name for a value to a JavaScript name.
adamc@897 2085 \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 2086 \item \texttt{script URL} requests inclusion of a JavaScript source file within application HTML.
adamc@897 2087 \item \texttt{serverOnly Module.ident} registers a value as being allowed only in server-side code.
adamc@897 2088 \end{itemize}
adamc@897 2089
adamc@897 2090 \subsection{Writing C FFI Code}
adamc@897 2091
adamc@897 2092 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 2093
adamc@897 2094 \begin{itemize}
adamc@897 2095 \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 2096 \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 2097 \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 2098 \end{itemize}
adamc@897 2099
adamc@897 2100 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 2101 \begin{itemize}
adamc@897 2102 \item \begin{verbatim}
adamc@897 2103 void uw_error(uw_context, failure_kind, const char *fmt, ...);
adamc@897 2104 \end{verbatim}
adamc@897 2105 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 2106
adamc@897 2107 \item \begin{verbatim}
adamc@897 2108 void uw_push_cleanup(uw_context, void (*func)(void *), void *arg);
adamc@897 2109 void uw_pop_cleanup(uw_context);
adamc@897 2110 \end{verbatim}
adamc@897 2111 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.
adamc@897 2112
adamc@897 2113 \item \begin{verbatim}
adamc@897 2114 void *uw_malloc(uw_context, size_t);
adamc@897 2115 \end{verbatim}
adamc@897 2116 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.
adamc@897 2117
adamc@897 2118 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.
adamc@897 2119
adamc@897 2120 \item \begin{verbatim}
adamc@897 2121 typedef void (*uw_callback)(void *);
adamc@897 2122 void uw_register_transactional(uw_context, void *data, uw_callback commit,
adamc@897 2123 uw_callback rollback, uw_callback free);
adamc@897 2124 \end{verbatim}
adamc@897 2125 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.
adamc@897 2126
adamc@1085 2127 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 2128
adamc@1085 2129 \item \begin{verbatim}
adamc@1085 2130 void *uw_get_global(uw_context, char *name);
adamc@1085 2131 void uw_set_global(uw_context, char *name, void *data, uw_callback free);
adamc@1085 2132 \end{verbatim}
adamc@1085 2133 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.
adamc@1085 2134
adamc@897 2135 \end{itemize}
adamc@897 2136
adamc@897 2137 \subsection{Writing JavaScript FFI Code}
adamc@897 2138
adamc@897 2139 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 2140
adamc@897 2141 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 2142
adamc@897 2143 \begin{itemize}
adamc@897 2144 \item Integers, floats, strings, characters, and booleans are represented in the usual JavaScript way.
adamc@985 2145 \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 2146 \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 2147 \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 2148 \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 2149 \end{itemize}
adamc@897 2150
adamc@897 2151 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 2152
adamc@897 2153
adamc@552 2154 \section{Compiler Phases}
adamc@552 2155
adamc@552 2156 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 2157
adamc@552 2158 In this section, we step through the main phases of compilation, noting what consequences each phase has for effective programming.
adamc@552 2159
adamc@552 2160 \subsection{Parse}
adamc@552 2161
adamc@552 2162 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 2163
adamc@552 2164 \subsection{Elaborate}
adamc@552 2165
adamc@552 2166 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 2167
adamc@552 2168 \subsection{Unnest}
adamc@552 2169
adamc@552 2170 Named local function definitions are moved to the top level, to avoid the need to generate closures.
adamc@552 2171
adamc@552 2172 \subsection{Corify}
adamc@552 2173
adamc@552 2174 Module system features are compiled away, through inlining of functor definitions at application sites. Afterward, most abstraction boundaries are broken, facilitating optimization.
adamc@552 2175
adamc@552 2176 \subsection{Especialize}
adamc@552 2177
adamc@552 2178 Functions are specialized to particular argument patterns. This is an important trick for avoiding the need to maintain any closures at runtime.
adamc@552 2179
adamc@552 2180 \subsection{Untangle}
adamc@552 2181
adamc@552 2182 Remove unnecessary mutual recursion, splitting recursive groups into strongly-connected components.
adamc@552 2183
adamc@552 2184 \subsection{Shake}
adamc@552 2185
adamc@552 2186 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 2187
adamc@661 2188 \subsection{Rpcify}
adamc@661 2189
adamc@661 2190 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 2191
adamc@661 2192 \subsection{Untangle, Shake}
adamc@661 2193
adamc@661 2194 Repeat these simplifications.
adamc@661 2195
adamc@553 2196 \subsection{\label{tag}Tag}
adamc@552 2197
adamc@552 2198 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 2199
adamc@552 2200 \subsection{Reduce}
adamc@552 2201
adamc@552 2202 Apply definitional equality rules to simplify the program as much as possible. This effectively includes inlining of every non-recursive definition.
adamc@552 2203
adamc@552 2204 \subsection{Unpoly}
adamc@552 2205
adamc@552 2206 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 2207
adamc@552 2208 \subsection{Specialize}
adamc@552 2209
adamc@558 2210 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 2211
adamc@552 2212 \subsection{Shake}
adamc@552 2213
adamc@558 2214 Here the compiler repeats the earlier Shake phase.
adamc@552 2215
adamc@552 2216 \subsection{Monoize}
adamc@552 2217
adamc@552 2218 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 2219
adamc@552 2220 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 2221
adamc@552 2222 \subsection{MonoOpt}
adamc@552 2223
adamc@552 2224 Simple algebraic laws are applied to simplify the program, focusing especially on efficient imperative generation of HTML pages.
adamc@552 2225
adamc@552 2226 \subsection{MonoUntangle}
adamc@552 2227
adamc@552 2228 Unnecessary mutual recursion is broken up again.
adamc@552 2229
adamc@552 2230 \subsection{MonoReduce}
adamc@552 2231
adamc@552 2232 Equivalents of the definitional equality rules are applied to simplify programs, with inlining again playing a major role.
adamc@552 2233
adamc@552 2234 \subsection{MonoShake, MonoOpt}
adamc@552 2235
adamc@552 2236 Unneeded declarations are removed, and basic optimizations are repeated.
adamc@552 2237
adamc@552 2238 \subsection{Fuse}
adamc@552 2239
adamc@552 2240 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 2241
adamc@552 2242 \subsection{MonoUntangle, MonoShake}
adamc@552 2243
adamc@552 2244 Fuse often creates more opportunities to remove spurious mutual recursion.
adamc@552 2245
adamc@552 2246 \subsection{Pathcheck}
adamc@552 2247
adamc@552 2248 The compiler checks that no link or action name has been used more than once.
adamc@552 2249
adamc@552 2250 \subsection{Cjrize}
adamc@552 2251
adamc@552 2252 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 2253
adamc@552 2254 \subsection{C Compilation and Linking}
adamc@552 2255
adamc@552 2256 The output of the last phase is pretty-printed as C source code and passed to GCC.
adamc@552 2257
adamc@552 2258
adamc@524 2259 \end{document}