annotate doc/manual.tex @ 1310:f0909fb3848f

Simplify type of Monad.appR2
author Adam Chlipala <adam@chlipala.net>
date Sun, 17 Oct 2010 13:26:11 -0400
parents 127561e4aef1
children c5799b1e4c58
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}.
adam@1309 149 \item \texttt{limit class num} sets a resource usage limit for generated applications. The limit \texttt{class} will be set to the non-negative integer \texttt{num}. The classes are:
adam@1309 150 \begin{itemize}
adam@1309 151 \item \texttt{cleanup}: maximum number of cleanup operations (e.g., entries recording the need to deallocate certain temporary objects) that may be active at once per request
adam@1309 152 \item \texttt{database}: maximum size of database files (currently only used by SQLite)
adam@1309 153 \item \texttt{deltas}: maximum number of messages sendable in a single request handler with \texttt{Basis.send}
adam@1309 154 \item \texttt{globals}: maximum number of global variables that FFI libraries may set in a single request context
adam@1309 155 \item \texttt{headers}: maximum size (in bytes) of per-request buffer used to hold HTTP headers for generated pages
adam@1309 156 \item \texttt{heap}: maximum size (in bytes) of per-request heap for dynamically-allocated data
adam@1309 157 \item \texttt{inputs}: maximum number of top-level form fields per request
adam@1309 158 \item \texttt{messages}: maximum size (in bytes) of per-request buffer used to hold a single outgoing message sent with \texttt{Basis.send}
adam@1309 159 \item \texttt{page}: maximum size (in bytes) of per-request buffer used to hold HTML content of generated pages
adam@1309 160 \item \texttt{script}: maximum size (in bytes) of per-request buffer used to hold JavaScript content of generated pages
adam@1309 161 \item \texttt{subinputs}: maximum number of form fields per request, excluding top-level fields
adam@1309 162 \item \texttt{time}: maximum running time of a single page request, in units of approximately 0.1 seconds
adam@1309 163 \item \texttt{transactionals}: maximum number of custom transactional actions (e.g., sending an e-mail) that may be run in a single page generation
adam@1309 164 \end{itemize}
adamc@783 165 \item \texttt{link FILENAME} adds \texttt{FILENAME} to the list of files to be passed to the GCC linker at the end of compilation. This is most useful for importing extra libraries needed by new FFI modules.
adam@1297 166 \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@852 167 \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@783 168 \item \texttt{prefix PREFIX} sets the prefix included before every URI within the generated application. The default is \texttt{/}.
adamc@783 169 \item \texttt{profile} generates an executable that may be used with gprof.
adam@1300 170 \item \texttt{rewrite KIND FROM TO} gives a rule for rewriting canonical module paths. For instance, the canonical path of a page may be \texttt{Mod1.Mod2.mypage}, while you would rather the page were accessed via a URL containing only \texttt{page}. The directive \texttt{rewrite url Mod1/Mod2/mypage page} would accomplish that. The possible values of \texttt{KIND} determine which kinds of objects are affected. The kind \texttt{all} matches any object, and \texttt{url} matches page URLs. The kinds \texttt{table}, \texttt{sequence}, and \texttt{view} match those sorts of SQL entities, and \texttt{relation} matches any of those three. \texttt{cookie} matches HTTP cookies, and \texttt{style} matches CSS class names. If \texttt{FROM} ends in \texttt{/*}, it is interpreted as a prefix matching rule, and rewriting occurs by replacing only the appropriate prefix of a path with \texttt{TO}. The \texttt{TO} field may be left empty to express the idea of deleting a prefix. For instance, \texttt{rewrite url Main/*} will strip all \texttt{Main/} prefixes from URLs. While the actual external names of relations and styles have parts separated by underscores instead of slashes, all rewrite rules must be written in terms of slashes.
adamc@1183 171 \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@783 172 \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@783 173 \item \texttt{serverOnly Module.ident} registers an FFI function or transaction that may only be run on the server.
adamc@1164 174 \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@783 175 \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@783 176 \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@783 177 \end{itemize}
adamc@701 178
adamc@701 179
adamc@557 180 \subsection{Building an Application}
adamc@557 181
adamc@557 182 To compile project \texttt{P.urp}, simply run
adamc@557 183 \begin{verbatim}
adamc@557 184 urweb P
adamc@557 185 \end{verbatim}
adamc@1198 186 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@557 187
adamc@557 188 To time how long the different compiler phases run, without generating an executable, run
adamc@557 189 \begin{verbatim}
adamc@557 190 urweb -timing P
adamc@557 191 \end{verbatim}
adamc@557 192
adamc@1086 193 To stop the compilation process after type-checking, run
adamc@1086 194 \begin{verbatim}
adamc@1086 195 urweb -tc P
adamc@1086 196 \end{verbatim}
adamc@1086 197
adamc@1170 198 To output information relevant to CSS stylesheets (and not finish regular compilation), run
adamc@1170 199 \begin{verbatim}
adamc@1170 200 urweb -css P
adamc@1170 201 \end{verbatim}
adamc@1170 202 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 203
adamc@896 204 Some other command-line parameters are accepted:
adamc@896 205 \begin{itemize}
adamc@896 206 \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@896 207
adamc@896 208 \item \texttt{-dbms [postgres|mysql|sqlite]}: Sets the database backend to use.
adamc@896 209 \begin{itemize}
adamc@896 210 \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@896 211
adamc@896 212 A command sequence like this can initialize a Postgres database, using a file \texttt{app.sql} generated by the compiler:
adamc@896 213 \begin{verbatim}
adamc@896 214 createdb app
adamc@896 215 psql -f app.sql app
adamc@896 216 \end{verbatim}
adamc@896 217
adamc@896 218 \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@896 219
adamc@896 220 A command sequence like this can initialize a MySQL database:
adamc@896 221 \begin{verbatim}
adamc@896 222 echo "CREATE DATABASE app" | mysql
adamc@896 223 mysql -D app <app.sql
adamc@896 224 \end{verbatim}
adamc@896 225
adamc@896 226 \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@896 227
adamc@896 228 A command like this can initialize an SQLite database:
adamc@896 229 \begin{verbatim}
adamc@896 230 sqlite3 path/to/database/file <app.sql
adamc@896 231 \end{verbatim}
adamc@896 232 \end{itemize}
adamc@896 233
adam@1309 234 \item \texttt{-limit class num}: Equivalent to the \texttt{limit} directive from \texttt{.urp} files
adam@1309 235
adamc@896 236 \item \texttt{-output FILENAME}: Set where the application executable is written.
adamc@896 237
adamc@1127 238 \item \texttt{-path NAME VALUE}: Set the value of path variable \texttt{\$NAME} to \texttt{VALUE}, for use in \texttt{.urp} files.
adamc@1127 239
adamc@896 240 \item \texttt{-protocol [http|cgi|fastcgi]}: Set the protocol that the generated application speaks.
adamc@896 241 \begin{itemize}
adamc@896 242 \item \texttt{http}: This is the default. It is for building standalone web servers that can be accessed by web browsers directly.
adamc@896 243
adamc@896 244 \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@896 245
adamc@896 246 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@896 247 \begin{verbatim}
adamc@896 248 ScriptAlias /Hello /path/to/hello.exe
adamc@896 249 \end{verbatim}
adamc@896 250
adamc@1163 251 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 252 \begin{verbatim}
adamc@1163 253 Options +ExecCGI
adamc@1163 254 AddHandler cgi-script .exe
adamc@1163 255 \end{verbatim}
adamc@1163 256
adamc@1163 257 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 258 \begin{verbatim}
adamc@1163 259 prefix /dir/script.exe/
adamc@1163 260 \end{verbatim}
adamc@1163 261
adamc@1163 262 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 263
adamc@1164 264 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 265
adamc@896 266 \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@896 267
adamc@896 268 To configure a FastCGI program with Apache, one could combine the above \texttt{ScriptAlias} line with a line like this:
adamc@896 269 \begin{verbatim}
adamc@896 270 FastCgiServer /path/to/hello.exe -idle-timeout 99999
adamc@896 271 \end{verbatim}
adamc@896 272 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@896 273
adamc@896 274 Here is some lighttpd configuration for the same application.
adamc@896 275 \begin{verbatim}
adamc@896 276 fastcgi.server = (
adamc@896 277 "/Hello/" =>
adamc@896 278 (( "bin-path" => "/path/to/hello.exe",
adamc@896 279 "socket" => "/tmp/hello",
adamc@896 280 "check-local" => "disable",
adamc@896 281 "docroot" => "/",
adamc@896 282 "max-procs" => "1"
adamc@896 283 ))
adamc@896 284 )
adamc@896 285 \end{verbatim}
adamc@896 286 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@896 287
adamc@896 288 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@896 289 \end{itemize}
adamc@896 290
adamc@1127 291 \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 292
adamc@1164 293 \item \texttt{-sigfile PATH}: Same as the \texttt{sigfile} directive in \texttt{.urp} files
adamc@1164 294
adamc@896 295 \item \texttt{-sql FILENAME}: Set where a database set-up SQL script is written.
adamc@1095 296
adamc@1095 297 \item \texttt{-static}: Link the runtime system statically. The default is to link against dynamic libraries.
adamc@896 298 \end{itemize}
adamc@896 299
adam@1297 300 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@556 301
adamc@529 302 \section{Ur Syntax}
adamc@529 303
adamc@784 304 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@524 305
adamc@524 306 \subsection{Lexical Conventions}
adamc@524 307
adamc@524 308 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@524 309
adamc@524 310 \begin{center}
adamc@524 311 \begin{tabular}{rl}
adamc@524 312 \textbf{\LaTeX} & \textbf{ASCII} \\
adamc@524 313 $\to$ & \cd{->} \\
adamc@652 314 $\longrightarrow$ & \cd{-->} \\
adamc@524 315 $\times$ & \cd{*} \\
adamc@524 316 $\lambda$ & \cd{fn} \\
adamc@524 317 $\Rightarrow$ & \cd{=>} \\
adamc@652 318 $\Longrightarrow$ & \cd{==>} \\
adamc@529 319 $\neq$ & \cd{<>} \\
adamc@529 320 $\leq$ & \cd{<=} \\
adamc@529 321 $\geq$ & \cd{>=} \\
adamc@524 322 \\
adamc@524 323 $x$ & Normal textual identifier, not beginning with an uppercase letter \\
adamc@525 324 $X$ & Normal textual identifier, beginning with an uppercase letter \\
adamc@524 325 \end{tabular}
adamc@524 326 \end{center}
adamc@524 327
adamc@525 328 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@524 329
adamc@873 330 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@526 331
adamc@527 332 This version of the manual doesn't include operator precedences; see \texttt{src/urweb.grm} for that.
adamc@527 333
adam@1297 334 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 335
adamc@552 336 \subsection{\label{core}Core Syntax}
adamc@524 337
adamc@524 338 \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@524 339 $$\begin{array}{rrcll}
adamc@524 340 \textrm{Kinds} & \kappa &::=& \mt{Type} & \textrm{proper types} \\
adamc@525 341 &&& \mt{Unit} & \textrm{the trivial constructor} \\
adamc@525 342 &&& \mt{Name} & \textrm{field names} \\
adamc@525 343 &&& \kappa \to \kappa & \textrm{type-level functions} \\
adamc@525 344 &&& \{\kappa\} & \textrm{type-level records} \\
adamc@525 345 &&& (\kappa\times^+) & \textrm{type-level tuples} \\
adamc@652 346 &&& X & \textrm{variable} \\
adamc@652 347 &&& X \longrightarrow k & \textrm{kind-polymorphic type-level function} \\
adamc@529 348 &&& \_\_ & \textrm{wildcard} \\
adamc@525 349 &&& (\kappa) & \textrm{explicit precedence} \\
adamc@524 350 \end{array}$$
adamc@524 351
adamc@524 352 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@524 353 $$\begin{array}{rrcll}
adamc@524 354 \textrm{Explicitness} & ? &::=& :: & \textrm{explicit} \\
adamc@558 355 &&& ::: & \textrm{implicit}
adamc@524 356 \end{array}$$
adamc@524 357
adamc@524 358 \emph{Constructors} are the main class of compile-time-only data. They include proper types and are classified by kinds.
adamc@524 359 $$\begin{array}{rrcll}
adamc@524 360 \textrm{Constructors} & c, \tau &::=& (c) :: \kappa & \textrm{kind annotation} \\
adamc@530 361 &&& \hat{x} & \textrm{constructor variable} \\
adamc@524 362 \\
adamc@525 363 &&& \tau \to \tau & \textrm{function type} \\
adamc@525 364 &&& x \; ? \; \kappa \to \tau & \textrm{polymorphic function type} \\
adamc@652 365 &&& X \longrightarrow \tau & \textrm{kind-polymorphic function type} \\
adamc@525 366 &&& \$ c & \textrm{record type} \\
adamc@524 367 \\
adamc@525 368 &&& c \; c & \textrm{type-level function application} \\
adamc@530 369 &&& \lambda x \; :: \; \kappa \Rightarrow c & \textrm{type-level function abstraction} \\
adamc@524 370 \\
adamc@652 371 &&& X \Longrightarrow c & \textrm{type-level kind-polymorphic function abstraction} \\
adamc@655 372 &&& c [\kappa] & \textrm{type-level kind-polymorphic function application} \\
adamc@652 373 \\
adamc@525 374 &&& () & \textrm{type-level unit} \\
adamc@525 375 &&& \#X & \textrm{field name} \\
adamc@524 376 \\
adamc@525 377 &&& [(c = c)^*] & \textrm{known-length type-level record} \\
adamc@525 378 &&& c \rc c & \textrm{type-level record concatenation} \\
adamc@652 379 &&& \mt{map} & \textrm{type-level record map} \\
adamc@524 380 \\
adamc@558 381 &&& (c,^+) & \textrm{type-level tuple} \\
adamc@525 382 &&& c.n & \textrm{type-level tuple projection ($n \in \mathbb N^+$)} \\
adamc@524 383 \\
adamc@652 384 &&& [c \sim c] \Rightarrow \tau & \textrm{guarded type} \\
adamc@524 385 \\
adamc@529 386 &&& \_ :: \kappa & \textrm{wildcard} \\
adamc@525 387 &&& (c) & \textrm{explicit precedence} \\
adamc@530 388 \\
adamc@530 389 \textrm{Qualified uncapitalized variables} & \hat{x} &::=& x & \textrm{not from a module} \\
adamc@530 390 &&& M.x & \textrm{projection from a module} \\
adamc@525 391 \end{array}$$
adamc@525 392
adamc@655 393 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@655 394
adamc@525 395 Modules of the module system are described by \emph{signatures}.
adamc@525 396 $$\begin{array}{rrcll}
adamc@525 397 \textrm{Signatures} & S &::=& \mt{sig} \; s^* \; \mt{end} & \textrm{constant} \\
adamc@525 398 &&& X & \textrm{variable} \\
adamc@525 399 &&& \mt{functor}(X : S) : S & \textrm{functor} \\
adamc@529 400 &&& S \; \mt{where} \; \mt{con} \; x = c & \textrm{concretizing an abstract constructor} \\
adamc@525 401 &&& M.X & \textrm{projection from a module} \\
adamc@525 402 \\
adamc@525 403 \textrm{Signature items} & s &::=& \mt{con} \; x :: \kappa & \textrm{abstract constructor} \\
adamc@525 404 &&& \mt{con} \; x :: \kappa = c & \textrm{concrete constructor} \\
adamc@528 405 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529 406 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@525 407 &&& \mt{val} \; x : \tau & \textrm{value} \\
adamc@525 408 &&& \mt{structure} \; X : S & \textrm{sub-module} \\
adamc@525 409 &&& \mt{signature} \; X = S & \textrm{sub-signature} \\
adamc@525 410 &&& \mt{include} \; S & \textrm{signature inclusion} \\
adamc@525 411 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@654 412 &&& \mt{class} \; x :: \kappa & \textrm{abstract constructor class} \\
adamc@654 413 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@525 414 \\
adamc@525 415 \textrm{Datatype constructors} & dc &::=& X & \textrm{nullary constructor} \\
adamc@525 416 &&& X \; \mt{of} \; \tau & \textrm{unary constructor} \\
adamc@524 417 \end{array}$$
adamc@524 418
adamc@526 419 \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@526 420 $$\begin{array}{rrcll}
adamc@526 421 \textrm{Patterns} & p &::=& \_ & \textrm{wildcard} \\
adamc@526 422 &&& x & \textrm{variable} \\
adamc@526 423 &&& \ell & \textrm{constant} \\
adamc@526 424 &&& \hat{X} & \textrm{nullary constructor} \\
adamc@526 425 &&& \hat{X} \; p & \textrm{unary constructor} \\
adamc@526 426 &&& \{(x = p,)^*\} & \textrm{rigid record pattern} \\
adamc@526 427 &&& \{(x = p,)^+, \ldots\} & \textrm{flexible record pattern} \\
adamc@852 428 &&& p : \tau & \textrm{type annotation} \\
adamc@527 429 &&& (p) & \textrm{explicit precedence} \\
adamc@526 430 \\
adamc@529 431 \textrm{Qualified capitalized variables} & \hat{X} &::=& X & \textrm{not from a module} \\
adamc@526 432 &&& M.X & \textrm{projection from a module} \\
adamc@526 433 \end{array}$$
adamc@526 434
adamc@527 435 \emph{Expressions} are the main run-time entities, corresponding to both ``expressions'' and ``statements'' in mainstream imperative languages.
adamc@527 436 $$\begin{array}{rrcll}
adamc@527 437 \textrm{Expressions} & e &::=& e : \tau & \textrm{type annotation} \\
adamc@529 438 &&& \hat{x} & \textrm{variable} \\
adamc@529 439 &&& \hat{X} & \textrm{datatype constructor} \\
adamc@527 440 &&& \ell & \textrm{constant} \\
adamc@527 441 \\
adamc@527 442 &&& e \; e & \textrm{function application} \\
adamc@527 443 &&& \lambda x : \tau \Rightarrow e & \textrm{function abstraction} \\
adamc@527 444 &&& e [c] & \textrm{polymorphic function application} \\
adamc@852 445 &&& \lambda [x \; ? \; \kappa] \Rightarrow e & \textrm{polymorphic function abstraction} \\
adamc@655 446 &&& e [\kappa] & \textrm{kind-polymorphic function application} \\
adamc@652 447 &&& X \Longrightarrow e & \textrm{kind-polymorphic function abstraction} \\
adamc@527 448 \\
adamc@527 449 &&& \{(c = e,)^*\} & \textrm{known-length record} \\
adamc@527 450 &&& e.c & \textrm{record field projection} \\
adamc@527 451 &&& e \rc e & \textrm{record concatenation} \\
adamc@527 452 &&& e \rcut c & \textrm{removal of a single record field} \\
adamc@527 453 &&& e \rcutM c & \textrm{removal of multiple record fields} \\
adamc@527 454 \\
adamc@527 455 &&& \mt{let} \; ed^* \; \mt{in} \; e \; \mt{end} & \textrm{local definitions} \\
adamc@527 456 \\
adamc@527 457 &&& \mt{case} \; e \; \mt{of} \; (p \Rightarrow e|)^+ & \textrm{pattern matching} \\
adamc@527 458 \\
adamc@654 459 &&& \lambda [c \sim c] \Rightarrow e & \textrm{guarded expression abstraction} \\
adamc@654 460 &&& e \; ! & \textrm{guarded expression application} \\
adamc@527 461 \\
adamc@527 462 &&& \_ & \textrm{wildcard} \\
adamc@527 463 &&& (e) & \textrm{explicit precedence} \\
adamc@527 464 \\
adamc@527 465 \textrm{Local declarations} & ed &::=& \cd{val} \; x : \tau = e & \textrm{non-recursive value} \\
adamc@527 466 &&& \cd{val} \; \cd{rec} \; (x : \tau = e \; \cd{and})^+ & \textrm{mutually-recursive values} \\
adamc@527 467 \end{array}$$
adamc@527 468
adamc@655 469 As with constructors, we include both abstraction and application for kind polymorphism, but applications are only inferred internally.
adamc@655 470
adamc@528 471 \emph{Declarations} primarily bring new symbols into context.
adamc@528 472 $$\begin{array}{rrcll}
adamc@528 473 \textrm{Declarations} & d &::=& \mt{con} \; x :: \kappa = c & \textrm{constructor synonym} \\
adamc@528 474 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529 475 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@528 476 &&& \mt{val} \; x : \tau = e & \textrm{value} \\
adamc@528 477 &&& \mt{val} \; \cd{rec} \; (x : \tau = e \; \mt{and})^+ & \textrm{mutually-recursive values} \\
adamc@528 478 &&& \mt{structure} \; X : S = M & \textrm{module definition} \\
adamc@528 479 &&& \mt{signature} \; X = S & \textrm{signature definition} \\
adamc@528 480 &&& \mt{open} \; M & \textrm{module inclusion} \\
adamc@528 481 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@528 482 &&& \mt{open} \; \mt{constraints} \; M & \textrm{inclusion of just the constraints from a module} \\
adamc@528 483 &&& \mt{table} \; x : c & \textrm{SQL table} \\
adamc@784 484 &&& \mt{view} \; x : c & \textrm{SQL view} \\
adamc@528 485 &&& \mt{sequence} \; x & \textrm{SQL sequence} \\
adamc@535 486 &&& \mt{cookie} \; x : \tau & \textrm{HTTP cookie} \\
adamc@784 487 &&& \mt{style} \; x : \tau & \textrm{CSS class} \\
adamc@654 488 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@1085 489 &&& \mt{task} \; e = e & \textrm{recurring task} \\
adamc@528 490 \\
adamc@529 491 \textrm{Modules} & M &::=& \mt{struct} \; d^* \; \mt{end} & \textrm{constant} \\
adamc@529 492 &&& X & \textrm{variable} \\
adamc@529 493 &&& M.X & \textrm{projection} \\
adamc@529 494 &&& M(M) & \textrm{functor application} \\
adamc@529 495 &&& \mt{functor}(X : S) : S = M & \textrm{functor abstraction} \\
adamc@528 496 \end{array}$$
adamc@528 497
adamc@528 498 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@527 499
adamc@784 500 We omit some extra possibilities in $\mt{table}$ syntax, deferring them to Section \ref{tables}.
adamc@784 501
adamc@529 502 \subsection{Shorthands}
adamc@529 503
adamc@529 504 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@529 505
adamc@529 506 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@529 507
adamc@529 508 A record type may be written $\{(c = c,)^*\}$, which elaborates to $\$[(c = c,)^*]$.
adamc@529 509
adamc@533 510 The notation $[c_1, \ldots, c_n]$ is shorthand for $[c_1 = (), \ldots, c_n = ()]$.
adamc@533 511
adamc@529 512 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@529 513
adamc@852 514 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@529 515
adam@1306 516 In some contexts, the parser isn't happy with token sequences like $x :: \_$, to indicate a constructor variable of wildcard kind. In such cases, write the second two tokens as $::\hspace{-.05in}\_$, with no intervening spaces. Analogous syntax $:::\hspace{-.05in}\_$ is available for implicit constructor arguments.
adam@1302 517
adamc@529 518 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@529 519
adamc@529 520 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@529 521
adamc@654 522 A signature item or declaration $\mt{class} \; x = \lambda y \Rightarrow c$ may be abbreviated $\mt{class} \; x \; y = c$.
adamc@529 523
adamc@1102 524 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@529 525
adamc@852 526 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@529 527
adamc@852 528 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@852 529
adamc@852 530 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@529 531
adamc@529 532 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@529 533
adamc@852 534 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@852 535
adamc@853 536 A declaration $\mt{table} \; x : \{(c = c,)^*\}$ is elaborated into $\mt{table} \; x : [(c = c,)^*]$.
adamc@529 537
adamc@529 538 The syntax $\mt{where} \; \mt{type}$ is an alternate form of $\mt{where} \; \mt{con}$.
adamc@529 539
adamc@529 540 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@529 541
adamc@529 542 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@529 543
adamc@784 544 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@529 545
adamc@530 546
adamc@530 547 \section{Static Semantics}
adamc@530 548
adamc@530 549 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@530 550
adamc@530 551 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@530 552 \begin{itemize}
adamc@655 553 \item $\Gamma \vdash \kappa$ expresses kind well-formedness.
adamc@530 554 \item $\Gamma \vdash c :: \kappa$ assigns a kind to a constructor in a context.
adamc@530 555 \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@531 556 \item $\Gamma \vdash c \hookrightarrow C$ proves that record constructor $c$ decomposes into set $C$ of field names and record constructors.
adamc@530 557 \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@530 558 \item $\Gamma \vdash e : \tau$ is a standard typing judgment.
adamc@534 559 \item $\Gamma \vdash p \leadsto \Gamma; \tau$ combines typing of patterns with calculation of which new variables they bind.
adamc@537 560 \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@537 561 \item $\Gamma \vdash S \equiv S$ is the signature equivalence judgment.
adamc@536 562 \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@530 563 \item $\Gamma \vdash M : S$ is the module signature checking judgment.
adamc@537 564 \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@539 565 \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@530 566 \end{itemize}
adamc@530 567
adamc@655 568
adamc@655 569 \subsection{Kind Well-Formedness}
adamc@655 570
adamc@655 571 $$\infer{\Gamma \vdash \mt{Type}}{}
adamc@655 572 \quad \infer{\Gamma \vdash \mt{Unit}}{}
adamc@655 573 \quad \infer{\Gamma \vdash \mt{Name}}{}
adamc@655 574 \quad \infer{\Gamma \vdash \kappa_1 \to \kappa_2}{
adamc@655 575 \Gamma \vdash \kappa_1
adamc@655 576 & \Gamma \vdash \kappa_2
adamc@655 577 }
adamc@655 578 \quad \infer{\Gamma \vdash \{\kappa\}}{
adamc@655 579 \Gamma \vdash \kappa
adamc@655 580 }
adamc@655 581 \quad \infer{\Gamma \vdash (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@655 582 \forall i: \Gamma \vdash \kappa_i
adamc@655 583 }$$
adamc@655 584
adamc@655 585 $$\infer{\Gamma \vdash X}{
adamc@655 586 X \in \Gamma
adamc@655 587 }
adamc@655 588 \quad \infer{\Gamma \vdash X \longrightarrow \kappa}{
adamc@655 589 \Gamma, X \vdash \kappa
adamc@655 590 }$$
adamc@655 591
adamc@530 592 \subsection{Kinding}
adamc@530 593
adamc@655 594 We write $[X \mapsto \kappa_1]\kappa_2$ for capture-avoiding substitution of $\kappa_1$ for $X$ in $\kappa_2$.
adamc@655 595
adamc@530 596 $$\infer{\Gamma \vdash (c) :: \kappa :: \kappa}{
adamc@530 597 \Gamma \vdash c :: \kappa
adamc@530 598 }
adamc@530 599 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530 600 x :: \kappa \in \Gamma
adamc@530 601 }
adamc@530 602 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530 603 x :: \kappa = c \in \Gamma
adamc@530 604 }$$
adamc@530 605
adamc@530 606 $$\infer{\Gamma \vdash M.x :: \kappa}{
adamc@537 607 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 608 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = \kappa
adamc@530 609 }
adamc@530 610 \quad \infer{\Gamma \vdash M.x :: \kappa}{
adamc@537 611 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 612 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@530 613 }$$
adamc@530 614
adamc@530 615 $$\infer{\Gamma \vdash \tau_1 \to \tau_2 :: \mt{Type}}{
adamc@530 616 \Gamma \vdash \tau_1 :: \mt{Type}
adamc@530 617 & \Gamma \vdash \tau_2 :: \mt{Type}
adamc@530 618 }
adamc@530 619 \quad \infer{\Gamma \vdash x \; ? \: \kappa \to \tau :: \mt{Type}}{
adamc@530 620 \Gamma, x :: \kappa \vdash \tau :: \mt{Type}
adamc@530 621 }
adamc@655 622 \quad \infer{\Gamma \vdash X \longrightarrow \tau :: \mt{Type}}{
adamc@655 623 \Gamma, X \vdash \tau :: \mt{Type}
adamc@655 624 }
adamc@530 625 \quad \infer{\Gamma \vdash \$c :: \mt{Type}}{
adamc@530 626 \Gamma \vdash c :: \{\mt{Type}\}
adamc@530 627 }$$
adamc@530 628
adamc@530 629 $$\infer{\Gamma \vdash c_1 \; c_2 :: \kappa_2}{
adamc@530 630 \Gamma \vdash c_1 :: \kappa_1 \to \kappa_2
adamc@530 631 & \Gamma \vdash c_2 :: \kappa_1
adamc@530 632 }
adamc@530 633 \quad \infer{\Gamma \vdash \lambda x \; :: \; \kappa_1 \Rightarrow c :: \kappa_1 \to \kappa_2}{
adamc@530 634 \Gamma, x :: \kappa_1 \vdash c :: \kappa_2
adamc@530 635 }$$
adamc@530 636
adamc@655 637 $$\infer{\Gamma \vdash c[\kappa'] :: [X \mapsto \kappa']\kappa}{
adamc@655 638 \Gamma \vdash c :: X \to \kappa
adamc@655 639 & \Gamma \vdash \kappa'
adamc@655 640 }
adamc@655 641 \quad \infer{\Gamma \vdash X \Longrightarrow c :: X \to \kappa}{
adamc@655 642 \Gamma, X \vdash c :: \kappa
adamc@655 643 }$$
adamc@655 644
adamc@530 645 $$\infer{\Gamma \vdash () :: \mt{Unit}}{}
adamc@530 646 \quad \infer{\Gamma \vdash \#X :: \mt{Name}}{}$$
adamc@530 647
adamc@530 648 $$\infer{\Gamma \vdash [\overline{c_i = c'_i}] :: \{\kappa\}}{
adamc@530 649 \forall i: \Gamma \vdash c_i : \mt{Name}
adamc@530 650 & \Gamma \vdash c'_i :: \kappa
adamc@530 651 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@530 652 }
adamc@530 653 \quad \infer{\Gamma \vdash c_1 \rc c_2 :: \{\kappa\}}{
adamc@530 654 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530 655 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@530 656 & \Gamma \vdash c_1 \sim c_2
adamc@530 657 }$$
adamc@530 658
adamc@655 659 $$\infer{\Gamma \vdash \mt{map} :: (\kappa_1 \to \kappa_2) \to \{\kappa_1\} \to \{\kappa_2\}}{}$$
adamc@530 660
adamc@573 661 $$\infer{\Gamma \vdash (\overline c) :: (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@573 662 \forall i: \Gamma \vdash c_i :: \kappa_i
adamc@530 663 }
adamc@573 664 \quad \infer{\Gamma \vdash c.i :: \kappa_i}{
adamc@573 665 \Gamma \vdash c :: (\kappa_1 \times \ldots \times \kappa_n)
adamc@530 666 }$$
adamc@530 667
adamc@655 668 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow \tau :: \mt{Type}}{
adamc@655 669 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530 670 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@655 671 & \Gamma, c_1 \sim c_2 \vdash \tau :: \mt{Type}
adamc@530 672 }$$
adamc@530 673
adamc@531 674 \subsection{Record Disjointness}
adamc@531 675
adamc@531 676 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@558 677 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@558 678 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@558 679 & \forall c'_1 \in C_1, c'_2 \in C_2: \Gamma \vdash c'_1 \sim c'_2
adamc@531 680 }
adamc@531 681 \quad \infer{\Gamma \vdash X \sim X'}{
adamc@531 682 X \neq X'
adamc@531 683 }$$
adamc@531 684
adamc@531 685 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@531 686 c'_1 \sim c'_2 \in \Gamma
adamc@558 687 & \Gamma \vdash c'_1 \hookrightarrow C_1
adamc@558 688 & \Gamma \vdash c'_2 \hookrightarrow C_2
adamc@558 689 & c_1 \in C_1
adamc@558 690 & c_2 \in C_2
adamc@531 691 }$$
adamc@531 692
adamc@531 693 $$\infer{\Gamma \vdash c \hookrightarrow \{c\}}{}
adamc@531 694 \quad \infer{\Gamma \vdash [\overline{c = c'}] \hookrightarrow \{\overline{c}\}}{}
adamc@531 695 \quad \infer{\Gamma \vdash c_1 \rc c_2 \hookrightarrow C_1 \cup C_2}{
adamc@531 696 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@531 697 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@531 698 }
adamc@531 699 \quad \infer{\Gamma \vdash c \hookrightarrow C}{
adamc@531 700 \Gamma \vdash c \equiv c'
adamc@531 701 & \Gamma \vdash c' \hookrightarrow C
adamc@531 702 }
adamc@531 703 \quad \infer{\Gamma \vdash \mt{map} \; f \; c \hookrightarrow C}{
adamc@531 704 \Gamma \vdash c \hookrightarrow C
adamc@531 705 }$$
adamc@531 706
adamc@541 707 \subsection{\label{definitional}Definitional Equality}
adamc@532 708
adamc@655 709 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@532 710
adamc@532 711 $$\infer{\Gamma \vdash c \equiv c}{}
adamc@532 712 \quad \infer{\Gamma \vdash c_1 \equiv c_2}{
adamc@532 713 \Gamma \vdash c_2 \equiv c_1
adamc@532 714 }
adamc@532 715 \quad \infer{\Gamma \vdash c_1 \equiv c_3}{
adamc@532 716 \Gamma \vdash c_1 \equiv c_2
adamc@532 717 & \Gamma \vdash c_2 \equiv c_3
adamc@532 718 }
adamc@532 719 \quad \infer{\Gamma \vdash \mathcal C[c_1] \equiv \mathcal C[c_2]}{
adamc@532 720 \Gamma \vdash c_1 \equiv c_2
adamc@532 721 }$$
adamc@532 722
adamc@532 723 $$\infer{\Gamma \vdash x \equiv c}{
adamc@532 724 x :: \kappa = c \in \Gamma
adamc@532 725 }
adamc@532 726 \quad \infer{\Gamma \vdash M.x \equiv c}{
adamc@537 727 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 728 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@532 729 }
adamc@532 730 \quad \infer{\Gamma \vdash (\overline c).i \equiv c_i}{}$$
adamc@532 731
adamc@532 732 $$\infer{\Gamma \vdash (\lambda x :: \kappa \Rightarrow c) \; c' \equiv [x \mapsto c'] c}{}
adamc@655 733 \quad \infer{\Gamma \vdash (X \Longrightarrow c) [\kappa] \equiv [X \mapsto \kappa] c}{}$$
adamc@655 734
adamc@655 735 $$\infer{\Gamma \vdash c_1 \rc c_2 \equiv c_2 \rc c_1}{}
adamc@532 736 \quad \infer{\Gamma \vdash c_1 \rc (c_2 \rc c_3) \equiv (c_1 \rc c_2) \rc c_3}{}$$
adamc@532 737
adamc@532 738 $$\infer{\Gamma \vdash [] \rc c \equiv c}{}
adamc@532 739 \quad \infer{\Gamma \vdash [\overline{c_1 = c'_1}] \rc [\overline{c_2 = c'_2}] \equiv [\overline{c_1 = c'_1}, \overline{c_2 = c'_2}]}{}$$
adamc@532 740
adamc@655 741 $$\infer{\Gamma \vdash \mt{map} \; f \; [] \equiv []}{}
adamc@655 742 \quad \infer{\Gamma \vdash \mt{map} \; f \; ([c_1 = c_2] \rc c) \equiv [c_1 = f \; c_2] \rc \mt{map} \; f \; c}{}$$
adamc@532 743
adamc@532 744 $$\infer{\Gamma \vdash \mt{map} \; (\lambda x \Rightarrow x) \; c \equiv c}{}
adamc@655 745 \quad \infer{\Gamma \vdash \mt{map} \; f \; (\mt{map} \; f' \; c)
adamc@655 746 \equiv \mt{map} \; (\lambda x \Rightarrow f \; (f' \; x)) \; c}{}$$
adamc@532 747
adamc@532 748 $$\infer{\Gamma \vdash \mt{map} \; f \; (c_1 \rc c_2) \equiv \mt{map} \; f \; c_1 \rc \mt{map} \; f \; c_2}{}$$
adamc@531 749
adamc@534 750 \subsection{Expression Typing}
adamc@533 751
adamc@873 752 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@533 753
adamc@533 754 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@533 755
adamc@533 756 $$\infer{\Gamma \vdash e : \tau : \tau}{
adamc@533 757 \Gamma \vdash e : \tau
adamc@533 758 }
adamc@533 759 \quad \infer{\Gamma \vdash e : \tau}{
adamc@533 760 \Gamma \vdash e : \tau'
adamc@533 761 & \Gamma \vdash \tau' \equiv \tau
adamc@533 762 }
adamc@533 763 \quad \infer{\Gamma \vdash \ell : T(\ell)}{}$$
adamc@533 764
adamc@533 765 $$\infer{\Gamma \vdash x : \mathcal I(\tau)}{
adamc@533 766 x : \tau \in \Gamma
adamc@533 767 }
adamc@533 768 \quad \infer{\Gamma \vdash M.x : \mathcal I(\tau)}{
adamc@537 769 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 770 & \mt{proj}(M, \overline{s}, \mt{val} \; x) = \tau
adamc@533 771 }
adamc@533 772 \quad \infer{\Gamma \vdash X : \mathcal I(\tau)}{
adamc@533 773 X : \tau \in \Gamma
adamc@533 774 }
adamc@533 775 \quad \infer{\Gamma \vdash M.X : \mathcal I(\tau)}{
adamc@537 776 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 777 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \tau
adamc@533 778 }$$
adamc@533 779
adamc@533 780 $$\infer{\Gamma \vdash e_1 \; e_2 : \tau_2}{
adamc@533 781 \Gamma \vdash e_1 : \tau_1 \to \tau_2
adamc@533 782 & \Gamma \vdash e_2 : \tau_1
adamc@533 783 }
adamc@533 784 \quad \infer{\Gamma \vdash \lambda x : \tau_1 \Rightarrow e : \tau_1 \to \tau_2}{
adamc@533 785 \Gamma, x : \tau_1 \vdash e : \tau_2
adamc@533 786 }$$
adamc@533 787
adamc@533 788 $$\infer{\Gamma \vdash e [c] : [x \mapsto c]\tau}{
adamc@533 789 \Gamma \vdash e : x :: \kappa \to \tau
adamc@533 790 & \Gamma \vdash c :: \kappa
adamc@533 791 }
adamc@852 792 \quad \infer{\Gamma \vdash \lambda [x \; ? \; \kappa] \Rightarrow e : x \; ? \; \kappa \to \tau}{
adamc@533 793 \Gamma, x :: \kappa \vdash e : \tau
adamc@533 794 }$$
adamc@533 795
adamc@655 796 $$\infer{\Gamma \vdash e [\kappa] : [X \mapsto \kappa]\tau}{
adamc@655 797 \Gamma \vdash e : X \longrightarrow \tau
adamc@655 798 & \Gamma \vdash \kappa
adamc@655 799 }
adamc@655 800 \quad \infer{\Gamma \vdash X \Longrightarrow e : X \longrightarrow \tau}{
adamc@655 801 \Gamma, X \vdash e : \tau
adamc@655 802 }$$
adamc@655 803
adamc@533 804 $$\infer{\Gamma \vdash \{\overline{c = e}\} : \{\overline{c : \tau}\}}{
adamc@533 805 \forall i: \Gamma \vdash c_i :: \mt{Name}
adamc@533 806 & \Gamma \vdash e_i : \tau_i
adamc@533 807 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@533 808 }
adamc@533 809 \quad \infer{\Gamma \vdash e.c : \tau}{
adamc@533 810 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533 811 }
adamc@533 812 \quad \infer{\Gamma \vdash e_1 \rc e_2 : \$(c_1 \rc c_2)}{
adamc@533 813 \Gamma \vdash e_1 : \$c_1
adamc@533 814 & \Gamma \vdash e_2 : \$c_2
adamc@573 815 & \Gamma \vdash c_1 \sim c_2
adamc@533 816 }$$
adamc@533 817
adamc@533 818 $$\infer{\Gamma \vdash e \rcut c : \$c'}{
adamc@533 819 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533 820 }
adamc@533 821 \quad \infer{\Gamma \vdash e \rcutM c : \$c'}{
adamc@533 822 \Gamma \vdash e : \$(c \rc c')
adamc@533 823 }$$
adamc@533 824
adamc@533 825 $$\infer{\Gamma \vdash \mt{let} \; \overline{ed} \; \mt{in} \; e \; \mt{end} : \tau}{
adamc@533 826 \Gamma \vdash \overline{ed} \leadsto \Gamma'
adamc@533 827 & \Gamma' \vdash e : \tau
adamc@533 828 }
adamc@533 829 \quad \infer{\Gamma \vdash \mt{case} \; e \; \mt{of} \; \overline{p \Rightarrow e} : \tau}{
adamc@533 830 \forall i: \Gamma \vdash p_i \leadsto \Gamma_i, \tau'
adamc@533 831 & \Gamma_i \vdash e_i : \tau
adamc@533 832 }$$
adamc@533 833
adamc@573 834 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow e : \lambda [c_1 \sim c_2] \Rightarrow \tau}{
adamc@533 835 \Gamma \vdash c_1 :: \{\kappa\}
adamc@655 836 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@533 837 & \Gamma, c_1 \sim c_2 \vdash e : \tau
adamc@662 838 }
adamc@662 839 \quad \infer{\Gamma \vdash e \; ! : \tau}{
adamc@662 840 \Gamma \vdash e : [c_1 \sim c_2] \Rightarrow \tau
adamc@662 841 & \Gamma \vdash c_1 \sim c_2
adamc@533 842 }$$
adamc@533 843
adamc@534 844 \subsection{Pattern Typing}
adamc@534 845
adamc@534 846 $$\infer{\Gamma \vdash \_ \leadsto \Gamma; \tau}{}
adamc@534 847 \quad \infer{\Gamma \vdash x \leadsto \Gamma, x : \tau; \tau}{}
adamc@534 848 \quad \infer{\Gamma \vdash \ell \leadsto \Gamma; T(\ell)}{}$$
adamc@534 849
adamc@534 850 $$\infer{\Gamma \vdash X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534 851 X : \overline{x ::: \mt{Type}} \to \tau \in \Gamma
adamc@534 852 & \textrm{$\tau$ not a function type}
adamc@534 853 }
adamc@534 854 \quad \infer{\Gamma \vdash X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534 855 X : \overline{x ::: \mt{Type}} \to \tau'' \to \tau \in \Gamma
adamc@534 856 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534 857 }$$
adamc@534 858
adamc@534 859 $$\infer{\Gamma \vdash M.X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537 860 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 861 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau
adamc@534 862 & \textrm{$\tau$ not a function type}
adamc@534 863 }$$
adamc@534 864
adamc@534 865 $$\infer{\Gamma \vdash M.X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537 866 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 867 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau'' \to \tau
adamc@534 868 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534 869 }$$
adamc@534 870
adamc@534 871 $$\infer{\Gamma \vdash \{\overline{x = p}\} \leadsto \Gamma_n; \{\overline{x = \tau}\}}{
adamc@534 872 \Gamma_0 = \Gamma
adamc@534 873 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534 874 }
adamc@534 875 \quad \infer{\Gamma \vdash \{\overline{x = p}, \ldots\} \leadsto \Gamma_n; \$([\overline{x = \tau}] \rc c)}{
adamc@534 876 \Gamma_0 = \Gamma
adamc@534 877 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534 878 }$$
adamc@534 879
adamc@852 880 $$\infer{\Gamma \vdash p : \tau \leadsto \Gamma'; \tau}{
adamc@852 881 \Gamma \vdash p \leadsto \Gamma'; \tau'
adamc@852 882 & \Gamma \vdash \tau' \equiv \tau
adamc@852 883 }$$
adamc@852 884
adamc@535 885 \subsection{Declaration Typing}
adamc@535 886
adamc@535 887 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@535 888
adamc@655 889 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@535 890
adamc@558 891 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@537 892 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@535 893
adamc@535 894 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535 895 \quad \infer{\Gamma \vdash d, \overline{d} \leadsto \Gamma''}{
adamc@535 896 \Gamma \vdash d \leadsto \Gamma'
adamc@535 897 & \Gamma' \vdash \overline{d} \leadsto \Gamma''
adamc@535 898 }$$
adamc@535 899
adamc@535 900 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@535 901 \Gamma \vdash c :: \kappa
adamc@535 902 }
adamc@535 903 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@535 904 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@535 905 }$$
adamc@535 906
adamc@535 907 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537 908 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 909 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@535 910 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@535 911 }$$
adamc@535 912
adamc@535 913 $$\infer{\Gamma \vdash \mt{val} \; x : \tau = e \leadsto \Gamma, x : \tau}{
adamc@535 914 \Gamma \vdash e : \tau
adamc@535 915 }$$
adamc@535 916
adamc@535 917 $$\infer{\Gamma \vdash \mt{val} \; \mt{rec} \; \overline{x : \tau = e} \leadsto \Gamma, \overline{x : \tau}}{
adamc@535 918 \forall i: \Gamma, \overline{x : \tau} \vdash e_i : \tau_i
adamc@535 919 & \textrm{$e_i$ starts with an expression $\lambda$, optionally preceded by constructor and disjointness $\lambda$s}
adamc@535 920 }$$
adamc@535 921
adamc@535 922 $$\infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : S}{
adamc@535 923 \Gamma \vdash M : S
adamc@558 924 & \textrm{ $M$ not a constant or application}
adamc@535 925 }
adamc@558 926 \quad \infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : \mt{selfify}(X, \overline{s})}{
adamc@558 927 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@539 928 }$$
adamc@539 929
adamc@539 930 $$\infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@535 931 \Gamma \vdash S
adamc@535 932 }$$
adamc@535 933
adamc@537 934 $$\infer{\Gamma \vdash \mt{open} \; M \leadsto \Gamma, \mathcal O(M, \overline{s})}{
adamc@537 935 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535 936 }$$
adamc@535 937
adamc@535 938 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma}{
adamc@535 939 \Gamma \vdash c_1 :: \{\kappa\}
adamc@535 940 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@535 941 & \Gamma \vdash c_1 \sim c_2
adamc@535 942 }
adamc@537 943 \quad \infer{\Gamma \vdash \mt{open} \; \mt{constraints} \; M \leadsto \Gamma, \mathcal O_c(M, \overline{s})}{
adamc@537 944 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535 945 }$$
adamc@535 946
adamc@784 947 $$\infer{\Gamma \vdash \mt{table} \; x : c \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_table} \; c \; []}{
adamc@535 948 \Gamma \vdash c :: \{\mt{Type}\}
adamc@535 949 }
adamc@784 950 \quad \infer{\Gamma \vdash \mt{view} \; x : c \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_view} \; c}{
adamc@784 951 \Gamma \vdash c :: \{\mt{Type}\}
adamc@784 952 }$$
adamc@784 953
adamc@784 954 $$\infer{\Gamma \vdash \mt{sequence} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_sequence}}{}$$
adamc@535 955
adamc@535 956 $$\infer{\Gamma \vdash \mt{cookie} \; x : \tau \leadsto \Gamma, x : \mt{Basis}.\mt{http\_cookie} \; \tau}{
adamc@535 957 \Gamma \vdash \tau :: \mt{Type}
adamc@784 958 }
adamc@784 959 \quad \infer{\Gamma \vdash \mt{style} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{css\_class}}{}$$
adamc@535 960
adamc@1085 961 $$\infer{\Gamma \vdash \mt{task} \; e_1 = e_2 \leadsto \Gamma}{
adamc@1085 962 \Gamma \vdash e_1 :: \mt{Basis}.\mt{task\_kind}
adamc@1085 963 & \Gamma \vdash e_2 :: \mt{Basis}.\mt{transaction} \; \{\}
adamc@1085 964 }$$
adamc@1085 965
adamc@784 966 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784 967 \Gamma \vdash c :: \kappa
adamc@535 968 }$$
adamc@535 969
adamc@535 970 $$\infer{\overline{y}; x; \Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535 971 \quad \infer{\overline{y}; x; \Gamma \vdash X \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to x \; \overline{y}}{
adamc@535 972 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535 973 }
adamc@535 974 \quad \infer{\overline{y}; x; \Gamma \vdash X \; \mt{of} \; \tau \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to \tau \to x \; \overline{y}}{
adamc@535 975 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535 976 }$$
adamc@535 977
adamc@537 978 \subsection{Signature Item Typing}
adamc@537 979
adamc@537 980 We appeal to a signature item analogue of the $\mathcal O$ function from the last subsection.
adamc@537 981
adamc@537 982 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@537 983 \quad \infer{\Gamma \vdash s, \overline{s} \leadsto \Gamma''}{
adamc@537 984 \Gamma \vdash s \leadsto \Gamma'
adamc@537 985 & \Gamma' \vdash \overline{s} \leadsto \Gamma''
adamc@537 986 }$$
adamc@537 987
adamc@537 988 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}
adamc@537 989 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@537 990 \Gamma \vdash c :: \kappa
adamc@537 991 }
adamc@537 992 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@537 993 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@537 994 }$$
adamc@537 995
adamc@537 996 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537 997 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 998 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 999 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@537 1000 }$$
adamc@537 1001
adamc@537 1002 $$\infer{\Gamma \vdash \mt{val} \; x : \tau \leadsto \Gamma, x : \tau}{
adamc@537 1003 \Gamma \vdash \tau :: \mt{Type}
adamc@537 1004 }$$
adamc@537 1005
adamc@537 1006 $$\infer{\Gamma \vdash \mt{structure} \; X : S \leadsto \Gamma, X : S}{
adamc@537 1007 \Gamma \vdash S
adamc@537 1008 }
adamc@537 1009 \quad \infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@537 1010 \Gamma \vdash S
adamc@537 1011 }$$
adamc@537 1012
adamc@537 1013 $$\infer{\Gamma \vdash \mt{include} \; S \leadsto \Gamma, \mathcal O(\overline{s})}{
adamc@537 1014 \Gamma \vdash S
adamc@537 1015 & \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1016 }$$
adamc@537 1017
adamc@537 1018 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma, c_1 \sim c_2}{
adamc@537 1019 \Gamma \vdash c_1 :: \{\kappa\}
adamc@537 1020 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@537 1021 }$$
adamc@537 1022
adamc@784 1023 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784 1024 \Gamma \vdash c :: \kappa
adamc@537 1025 }
adamc@784 1026 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}$$
adamc@537 1027
adamc@536 1028 \subsection{Signature Compatibility}
adamc@536 1029
adamc@558 1030 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 1031
adamc@537 1032 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 1033
adamc@536 1034 $$\infer{\Gamma \vdash S \equiv S}{}
adamc@536 1035 \quad \infer{\Gamma \vdash S_1 \equiv S_2}{
adamc@536 1036 \Gamma \vdash S_2 \equiv S_1
adamc@536 1037 }
adamc@536 1038 \quad \infer{\Gamma \vdash X \equiv S}{
adamc@536 1039 X = S \in \Gamma
adamc@536 1040 }
adamc@536 1041 \quad \infer{\Gamma \vdash M.X \equiv S}{
adamc@537 1042 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1043 & \mt{proj}(M, \overline{s}, \mt{signature} \; X) = S
adamc@536 1044 }$$
adamc@536 1045
adamc@536 1046 $$\infer{\Gamma \vdash S \; \mt{where} \; \mt{con} \; x = c \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa = c \; \overline{s_2} \; \mt{end}}{
adamc@536 1047 \Gamma \vdash S \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa \; \overline{s_2} \; \mt{end}
adamc@536 1048 & \Gamma \vdash c :: \kappa
adamc@537 1049 }
adamc@537 1050 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s^1} \; \mt{include} \; S \; \overline{s^2} \; \mt{end} \equiv \mt{sig} \; \overline{s^1} \; \overline{s} \; \overline{s^2} \; \mt{end}}{
adamc@537 1051 \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@536 1052 }$$
adamc@536 1053
adamc@536 1054 $$\infer{\Gamma \vdash S_1 \leq S_2}{
adamc@536 1055 \Gamma \vdash S_1 \equiv S_2
adamc@536 1056 }
adamc@536 1057 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \mt{end}}{}
adamc@537 1058 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; s' \; \overline{s'} \; \mt{end}}{
adamc@537 1059 \Gamma \vdash \overline{s} \leq s'
adamc@537 1060 & \Gamma \vdash s' \leadsto \Gamma'
adamc@537 1061 & \Gamma' \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \overline{s'} \; \mt{end}
adamc@537 1062 }$$
adamc@537 1063
adamc@537 1064 $$\infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537 1065 \Gamma \vdash s \leq s'
adamc@537 1066 }
adamc@537 1067 \quad \infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537 1068 \Gamma \vdash s \leadsto \Gamma'
adamc@537 1069 & \Gamma' \vdash \overline{s} \leq s'
adamc@536 1070 }$$
adamc@536 1071
adamc@536 1072 $$\infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 \leq \mt{functor} (X : S'_1) : S'_2}{
adamc@536 1073 \Gamma \vdash S'_1 \leq S_1
adamc@536 1074 & \Gamma, X : S'_1 \vdash S_2 \leq S'_2
adamc@536 1075 }$$
adamc@536 1076
adamc@537 1077 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@537 1078 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}
adamc@558 1079 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type}}{}$$
adamc@537 1080
adamc@537 1081 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(y)} \to \mt{Type}}{
adamc@537 1082 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1083 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1084 }$$
adamc@537 1085
adamc@784 1086 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@784 1087 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}$$
adamc@537 1088
adamc@537 1089 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \mt{\kappa} = c_2}{
adamc@537 1090 \Gamma \vdash c_1 \equiv c_2
adamc@537 1091 }
adamc@784 1092 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \kappa = c_2}{
adamc@537 1093 \Gamma \vdash c_1 \equiv c_2
adamc@537 1094 }$$
adamc@537 1095
adamc@537 1096 $$\infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537 1097 \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1098 }$$
adamc@537 1099
adamc@537 1100 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537 1101 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1102 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1103 & \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1104 }$$
adamc@537 1105
adamc@537 1106 $$\infer{\Gamma \vdash \cdot \leq \cdot}{}
adamc@537 1107 \quad \infer{\Gamma \vdash X; \overline{dc} \leq X; \overline{dc'}}{
adamc@537 1108 \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1109 }
adamc@537 1110 \quad \infer{\Gamma \vdash X \; \mt{of} \; \tau_1; \overline{dc} \leq X \; \mt{of} \; \tau_2; \overline{dc'}}{
adamc@537 1111 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537 1112 & \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1113 }$$
adamc@537 1114
adamc@537 1115 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x = \mt{datatype} \; M'.z'}{
adamc@537 1116 \Gamma \vdash M.z \equiv M'.z'
adamc@537 1117 }$$
adamc@537 1118
adamc@537 1119 $$\infer{\Gamma \vdash \mt{val} \; x : \tau_1 \leq \mt{val} \; x : \tau_2}{
adamc@537 1120 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537 1121 }
adamc@537 1122 \quad \infer{\Gamma \vdash \mt{structure} \; X : S_1 \leq \mt{structure} \; X : S_2}{
adamc@537 1123 \Gamma \vdash S_1 \leq S_2
adamc@537 1124 }
adamc@537 1125 \quad \infer{\Gamma \vdash \mt{signature} \; X = S_1 \leq \mt{signature} \; X = S_2}{
adamc@537 1126 \Gamma \vdash S_1 \leq S_2
adamc@537 1127 & \Gamma \vdash S_2 \leq S_1
adamc@537 1128 }$$
adamc@537 1129
adamc@537 1130 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leq \mt{constraint} \; c'_1 \sim c'_2}{
adamc@537 1131 \Gamma \vdash c_1 \equiv c'_1
adamc@537 1132 & \Gamma \vdash c_2 \equiv c'_2
adamc@537 1133 }$$
adamc@537 1134
adamc@655 1135 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{class} \; x :: \kappa}{}
adamc@655 1136 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{class} \; x :: \kappa}{}
adamc@655 1137 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{class} \; x :: \kappa = c_2}{
adamc@537 1138 \Gamma \vdash c_1 \equiv c_2
adamc@537 1139 }$$
adamc@537 1140
adamc@538 1141 \subsection{Module Typing}
adamc@538 1142
adamc@538 1143 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 1144
adamc@538 1145 $$\infer{\Gamma \vdash M : S}{
adamc@538 1146 \Gamma \vdash M : S'
adamc@538 1147 & \Gamma \vdash S' \leq S
adamc@538 1148 }
adamc@538 1149 \quad \infer{\Gamma \vdash \mt{struct} \; \overline{d} \; \mt{end} : \mt{sig} \; \mt{sigOf}(\overline{d}) \; \mt{end}}{
adamc@538 1150 \Gamma \vdash \overline{d} \leadsto \Gamma'
adamc@538 1151 }
adamc@538 1152 \quad \infer{\Gamma \vdash X : S}{
adamc@538 1153 X : S \in \Gamma
adamc@538 1154 }$$
adamc@538 1155
adamc@538 1156 $$\infer{\Gamma \vdash M.X : S}{
adamc@538 1157 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@538 1158 & \mt{proj}(M, \overline{s}, \mt{structure} \; X) = S
adamc@538 1159 }$$
adamc@538 1160
adamc@538 1161 $$\infer{\Gamma \vdash M_1(M_2) : [X \mapsto M_2]S_2}{
adamc@538 1162 \Gamma \vdash M_1 : \mt{functor}(X : S_1) : S_2
adamc@538 1163 & \Gamma \vdash M_2 : S_1
adamc@538 1164 }
adamc@538 1165 \quad \infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 = M : \mt{functor} (X : S_1) : S_2}{
adamc@538 1166 \Gamma \vdash S_1
adamc@538 1167 & \Gamma, X : S_1 \vdash S_2
adamc@538 1168 & \Gamma, X : S_1 \vdash M : S_2
adamc@538 1169 }$$
adamc@538 1170
adamc@538 1171 \begin{eqnarray*}
adamc@538 1172 \mt{sigOf}(\cdot) &=& \cdot \\
adamc@538 1173 \mt{sigOf}(s \; \overline{s'}) &=& \mt{sigOf}(s) \; \mt{sigOf}(\overline{s'}) \\
adamc@538 1174 \\
adamc@538 1175 \mt{sigOf}(\mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@538 1176 \mt{sigOf}(\mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \overline{dc} \\
adamc@538 1177 \mt{sigOf}(\mt{datatype} \; x = \mt{datatype} \; M.z) &=& \mt{datatype} \; x = \mt{datatype} \; M.z \\
adamc@538 1178 \mt{sigOf}(\mt{val} \; x : \tau = e) &=& \mt{val} \; x : \tau \\
adamc@538 1179 \mt{sigOf}(\mt{val} \; \mt{rec} \; \overline{x : \tau = e}) &=& \overline{\mt{val} \; x : \tau} \\
adamc@538 1180 \mt{sigOf}(\mt{structure} \; X : S = M) &=& \mt{structure} \; X : S \\
adamc@538 1181 \mt{sigOf}(\mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@538 1182 \mt{sigOf}(\mt{open} \; M) &=& \mt{include} \; S \textrm{ (where $\Gamma \vdash M : S$)} \\
adamc@538 1183 \mt{sigOf}(\mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@538 1184 \mt{sigOf}(\mt{open} \; \mt{constraints} \; M) &=& \cdot \\
adamc@538 1185 \mt{sigOf}(\mt{table} \; x : c) &=& \mt{table} \; x : c \\
adamc@784 1186 \mt{sigOf}(\mt{view} \; x : c) &=& \mt{view} \; x : c \\
adamc@538 1187 \mt{sigOf}(\mt{sequence} \; x) &=& \mt{sequence} \; x \\
adamc@538 1188 \mt{sigOf}(\mt{cookie} \; x : \tau) &=& \mt{cookie} \; x : \tau \\
adamc@784 1189 \mt{sigOf}(\mt{style} \; x) &=& \mt{style} \; x \\
adamc@655 1190 \mt{sigOf}(\mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@538 1191 \end{eqnarray*}
adamc@539 1192 \begin{eqnarray*}
adamc@539 1193 \mt{selfify}(M, \cdot) &=& \cdot \\
adamc@558 1194 \mt{selfify}(M, s \; \overline{s'}) &=& \mt{selfify}(M, s) \; \mt{selfify}(M, \overline{s'}) \\
adamc@539 1195 \\
adamc@539 1196 \mt{selfify}(M, \mt{con} \; x :: \kappa) &=& \mt{con} \; x :: \kappa = M.x \\
adamc@539 1197 \mt{selfify}(M, \mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@539 1198 \mt{selfify}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \mt{datatype} \; M.x \\
adamc@539 1199 \mt{selfify}(M, \mt{datatype} \; x = \mt{datatype} \; M'.z) &=& \mt{datatype} \; x = \mt{datatype} \; M'.z \\
adamc@539 1200 \mt{selfify}(M, \mt{val} \; x : \tau) &=& \mt{val} \; x : \tau \\
adamc@539 1201 \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 1202 \mt{selfify}(M, \mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@539 1203 \mt{selfify}(M, \mt{include} \; S) &=& \mt{include} \; S \\
adamc@539 1204 \mt{selfify}(M, \mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@655 1205 \mt{selfify}(M, \mt{class} \; x :: \kappa) &=& \mt{class} \; x :: \kappa = M.x \\
adamc@655 1206 \mt{selfify}(M, \mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@539 1207 \end{eqnarray*}
adamc@539 1208
adamc@540 1209 \subsection{Module Projection}
adamc@540 1210
adamc@540 1211 \begin{eqnarray*}
adamc@540 1212 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \\
adamc@540 1213 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa, c) \\
adamc@540 1214 \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 1215 \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 1216 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})$)} \\
adamc@655 1217 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \to \mt{Type} \\
adamc@655 1218 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa \to \mt{Type}, c) \\
adamc@540 1219 \\
adamc@540 1220 \mt{proj}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc} \; \overline{s}, \mt{datatype} \; x) &=& (\overline{y}, \overline{dc}) \\
adamc@540 1221 \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 1222 \\
adamc@540 1223 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, \mt{val} \; x) &=& \tau \\
adamc@540 1224 \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 1225 \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 1226 \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 1227 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \in \overline{dc}$)} \\
adamc@540 1228 \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 1229 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \; \mt{of} \; \tau \in \overline{dc}$)} \\
adamc@540 1230 \\
adamc@540 1231 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, \mt{structure} \; X) &=& S \\
adamc@540 1232 \\
adamc@540 1233 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, \mt{signature} \; X) &=& S \\
adamc@540 1234 \\
adamc@540 1235 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1236 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1237 \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 1238 \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 1239 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@540 1240 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1241 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1242 \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 1243 \mt{proj}(M, \mt{constraint} \; c_1 \sim c_2 \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@655 1244 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@655 1245 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1246 \end{eqnarray*}
adamc@540 1247
adamc@541 1248
adamc@541 1249 \section{Type Inference}
adamc@541 1250
adamc@541 1251 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 1252
adamc@541 1253 \subsection{Basic Unification}
adamc@541 1254
adamc@560 1255 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 1256
adamc@656 1257 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 1258
adamc@541 1259 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 1260
adamc@541 1261 \subsection{Unifying Record Types}
adamc@541 1262
adamc@570 1263 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 1264
adamc@656 1265 \subsection{\label{typeclasses}Constructor Classes}
adamc@541 1266
adamc@784 1267 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 1268
adamc@784 1269 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 1270
adamc@656 1271 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 1272
adamc@656 1273 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 1274
adamc@541 1275 \subsection{Reverse-Engineering Record Types}
adamc@541 1276
adamc@656 1277 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 1278
adamc@541 1279 \subsection{Implicit Arguments in Functor Applications}
adamc@541 1280
adamc@656 1281 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 1282
adamc@541 1283
adamc@542 1284 \section{The Ur Standard Library}
adamc@542 1285
adamc@542 1286 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 1287
adamc@542 1288 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 1289
adamc@542 1290 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 1291 $$\begin{array}{l}
adamc@542 1292 \mt{type} \; \mt{int} \\
adamc@542 1293 \mt{type} \; \mt{float} \\
adamc@873 1294 \mt{type} \; \mt{char} \\
adamc@542 1295 \mt{type} \; \mt{string} \\
adamc@542 1296 \mt{type} \; \mt{time} \\
adamc@785 1297 \mt{type} \; \mt{blob} \\
adamc@542 1298 \\
adamc@542 1299 \mt{type} \; \mt{unit} = \{\} \\
adamc@542 1300 \\
adamc@542 1301 \mt{datatype} \; \mt{bool} = \mt{False} \mid \mt{True} \\
adamc@542 1302 \\
adamc@785 1303 \mt{datatype} \; \mt{option} \; \mt{t} = \mt{None} \mid \mt{Some} \; \mt{of} \; \mt{t} \\
adamc@785 1304 \\
adamc@785 1305 \mt{datatype} \; \mt{list} \; \mt{t} = \mt{Nil} \mid \mt{Cons} \; \mt{of} \; \mt{t} \times \mt{list} \; \mt{t}
adamc@542 1306 \end{array}$$
adamc@542 1307
adamc@1123 1308 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 1309
adam@1297 1310 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 1311 $$\begin{array}{l}
adam@1297 1312 \mt{con} \; \mt{variant} :: \{\mt{Type}\} \to \mt{Type} \\
adam@1297 1313 \mt{val} \; \mt{make} : \mt{nm} :: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{ts} ::: \{\mt{Type}\} \to [[\mt{nm}] \sim \mt{ts}] \Rightarrow \mt{t} \to \mt{variant} \; ([\mt{nm} = \mt{t}] \rc \mt{ts}) \\
adam@1297 1314 \mt{val} \; \mt{match} : \mt{ts} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{variant} \; \mt{ts} \to \$(\mt{map} \; (\lambda \mt{t'} \Rightarrow \mt{t'} \to \mt{t}) \; \mt{ts}) \to \mt{t}
adam@1297 1315 \end{array}$$
adam@1297 1316
adamc@657 1317 Another important generic Ur element comes at the beginning of \texttt{top.urs}.
adamc@657 1318
adamc@657 1319 $$\begin{array}{l}
adamc@657 1320 \mt{con} \; \mt{folder} :: \mt{K} \longrightarrow \{\mt{K}\} \to \mt{Type} \\
adamc@657 1321 \\
adamc@657 1322 \mt{val} \; \mt{fold} : \mt{K} \longrightarrow \mt{tf} :: (\{\mt{K}\} \to \mt{Type}) \\
adamc@657 1323 \hspace{.1in} \to (\mt{nm} :: \mt{Name} \to \mt{v} :: \mt{K} \to \mt{r} :: \{\mt{K}\} \to [[\mt{nm}] \sim \mt{r}] \Rightarrow \\
adamc@657 1324 \hspace{.2in} \mt{tf} \; \mt{r} \to \mt{tf} \; ([\mt{nm} = \mt{v}] \rc \mt{r})) \\
adamc@657 1325 \hspace{.1in} \to \mt{tf} \; [] \\
adamc@657 1326 \hspace{.1in} \to \mt{r} :: \{\mt{K}\} \to \mt{folder} \; \mt{r} \to \mt{tf} \; \mt{r}
adamc@657 1327 \end{array}$$
adamc@657 1328
adamc@657 1329 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 1330
adamc@664 1331 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 1332
adamc@542 1333
adamc@542 1334 \section{The Ur/Web Standard Library}
adamc@542 1335
adamc@658 1336 \subsection{Monads}
adamc@658 1337
adamc@658 1338 The Ur Basis defines the monad constructor class from Haskell.
adamc@658 1339
adamc@658 1340 $$\begin{array}{l}
adamc@658 1341 \mt{class} \; \mt{monad} :: \mt{Type} \to \mt{Type} \\
adamc@658 1342 \mt{val} \; \mt{return} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t} ::: \mt{Type} \\
adamc@658 1343 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658 1344 \hspace{.1in} \to \mt{t} \to \mt{m} \; \mt{t} \\
adamc@658 1345 \mt{val} \; \mt{bind} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t1} ::: \mt{Type} \to \mt{t2} ::: \mt{Type} \\
adamc@658 1346 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658 1347 \hspace{.1in} \to \mt{m} \; \mt{t1} \to (\mt{t1} \to \mt{m} \; \mt{t2}) \\
adamc@658 1348 \hspace{.1in} \to \mt{m} \; \mt{t2}
adamc@658 1349 \end{array}$$
adamc@658 1350
adamc@542 1351 \subsection{Transactions}
adamc@542 1352
adamc@542 1353 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 1354 $$\begin{array}{l}
adamc@542 1355 \mt{con} \; \mt{transaction} :: \mt{Type} \to \mt{Type} \\
adamc@658 1356 \mt{val} \; \mt{transaction\_monad} : \mt{monad} \; \mt{transaction}
adamc@542 1357 \end{array}$$
adamc@542 1358
adamc@1123 1359 For debugging purposes, a transactional function is provided for outputting a string on the server process' \texttt{stderr}.
adamc@1123 1360 $$\begin{array}{l}
adamc@1123 1361 \mt{val} \; \mt{debug} : \mt{string} \to \mt{transaction} \; \mt{unit}
adamc@1123 1362 \end{array}$$
adamc@1123 1363
adamc@542 1364 \subsection{HTTP}
adamc@542 1365
adamc@542 1366 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 1367 $$\begin{array}{l}
adamc@786 1368 \mt{val} \; \mt{requestHeader} : \mt{string} \to \mt{transaction} \; (\mt{option} \; \mt{string}) \\
adamc@786 1369 \\
adamc@786 1370 \mt{con} \; \mt{http\_cookie} :: \mt{Type} \to \mt{Type} \\
adamc@786 1371 \mt{val} \; \mt{getCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; (\mt{option} \; \mt{t}) \\
adamc@1050 1372 \mt{val} \; \mt{setCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \{\mt{Value} : \mt{t}, \mt{Expires} : \mt{option} \; \mt{time}, \mt{Secure} : \mt{bool}\} \to \mt{transaction} \; \mt{unit} \\
adamc@1050 1373 \mt{val} \; \mt{clearCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; \mt{unit}
adamc@786 1374 \end{array}$$
adamc@786 1375
adamc@786 1376 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 1377 $$\begin{array}{l}
adamc@786 1378 \mt{type} \; \mt{url} \\
adamc@786 1379 \mt{val} \; \mt{bless} : \mt{string} \to \mt{url} \\
adamc@786 1380 \mt{val} \; \mt{checkUrl} : \mt{string} \to \mt{option} \; \mt{url}
adamc@786 1381 \end{array}$$
adamc@786 1382 $\mt{bless}$ raises a runtime error if the string passed to it fails the URL policy.
adamc@786 1383
adamc@1085 1384 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 1385 $$\begin{array}{l}
adamc@1085 1386 \mt{val} \; \mt{currentUrl} : \mt{transaction} \; \mt{url} \\
adamc@1085 1387 \mt{val} \; \mt{url} : \mt{transaction} \; \mt{page} \to \mt{url}
adamc@1085 1388 \end{array}$$
adamc@1085 1389
adamc@1085 1390 Page generation may be interrupted at any time with a request to redirect to a particular URL instead.
adamc@1085 1391 $$\begin{array}{l}
adamc@1085 1392 \mt{val} \; \mt{redirect} : \mt{t} ::: \mt{Type} \to \mt{url} \to \mt{transaction} \; \mt{t}
adamc@1085 1393 \end{array}$$
adamc@1085 1394
adamc@786 1395 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 1396 $$\begin{array}{l}
adamc@786 1397 \mt{type} \; \mt{file} \\
adamc@786 1398 \mt{val} \; \mt{fileName} : \mt{file} \to \mt{option} \; \mt{string} \\
adamc@786 1399 \mt{val} \; \mt{fileMimeType} : \mt{file} \to \mt{string} \\
adamc@786 1400 \mt{val} \; \mt{fileData} : \mt{file} \to \mt{blob}
adamc@786 1401 \end{array}$$
adamc@786 1402
adamc@786 1403 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 1404 $$\begin{array}{l}
adamc@786 1405 \mt{type} \; \mt{mimeType} \\
adamc@786 1406 \mt{val} \; \mt{blessMime} : \mt{string} \to \mt{mimeType} \\
adamc@786 1407 \mt{val} \; \mt{checkMime} : \mt{string} \to \mt{option} \; \mt{mimeType} \\
adamc@786 1408 \mt{val} \; \mt{returnBlob} : \mt{t} ::: \mt{Type} \to \mt{blob} \to \mt{mimeType} \to \mt{transaction} \; \mt{t}
adamc@542 1409 \end{array}$$
adamc@542 1410
adamc@543 1411 \subsection{SQL}
adamc@543 1412
adamc@543 1413 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 1414 $$\begin{array}{l}
adamc@785 1415 \mt{con} \; \mt{sql\_table} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785 1416 \end{array}$$
adamc@785 1417 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 1418
adamc@785 1419 We also have the simpler type family of SQL views, which have no keys.
adamc@785 1420 $$\begin{array}{l}
adamc@785 1421 \mt{con} \; \mt{sql\_view} :: \{\mt{Type}\} \to \mt{Type}
adamc@543 1422 \end{array}$$
adamc@543 1423
adamc@785 1424 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 1425 $$\begin{array}{l}
adamc@785 1426 \mt{class} \; \mt{fieldsOf} :: \mt{Type} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1427 \mt{val} \; \mt{fieldsOf\_table} : \mt{fs} ::: \{\mt{Type}\} \to \mt{keys} ::: \{\{\mt{Unit}\}\} \to \mt{fieldsOf} \; (\mt{sql\_table} \; \mt{fs} \; \mt{keys}) \; \mt{fs} \\
adamc@785 1428 \mt{val} \; \mt{fieldsOf\_view} : \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; (\mt{sql\_view} \; \mt{fs}) \; \mt{fs}
adamc@785 1429 \end{array}$$
adamc@785 1430
adamc@785 1431 \subsubsection{Table Constraints}
adamc@785 1432
adamc@785 1433 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 1434
adamc@785 1435 $$\begin{array}{l}
adamc@785 1436 \mt{con} \; \mt{primary\_key} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type} \\
adamc@785 1437 \mt{val} \; \mt{no\_primary\_key} : \mt{fs} ::: \{\mt{Type}\} \to \mt{primary\_key} \; \mt{fs} \; [] \\
adamc@785 1438 \mt{val} \; \mt{primary\_key} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{key1} :: \mt{Name} \to \mt{keys} :: \{\mt{Type}\} \\
adamc@785 1439 \hspace{.1in} \to [[\mt{key1}] \sim \mt{keys}] \Rightarrow [[\mt{key1} = \mt{t}] \rc \mt{keys} \sim \mt{rest}] \\
adamc@785 1440 \hspace{.1in} \Rightarrow \$([\mt{key1} = \mt{sql\_injectable\_prim} \; \mt{t}] \rc \mt{map} \; \mt{sql\_injectable\_prim} \; \mt{keys}) \\
adamc@785 1441 \hspace{.1in} \to \mt{primary\_key} \; ([\mt{key1} = \mt{t}] \rc \mt{keys} \rc \mt{rest}) \; [\mt{Pkey} = [\mt{key1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{keys}]
adamc@785 1442 \end{array}$$
adamc@785 1443 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 1444
adamc@785 1445 A type family stands for sets of named constraints of the remaining varieties.
adamc@785 1446 $$\begin{array}{l}
adamc@785 1447 \mt{con} \; \mt{sql\_constraints} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785 1448 \end{array}$$
adamc@785 1449 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 1450
adamc@785 1451 There is a type family of individual, unnamed constraints.
adamc@785 1452 $$\begin{array}{l}
adamc@785 1453 \mt{con} \; \mt{sql\_constraint} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \mt{Type}
adamc@785 1454 \end{array}$$
adamc@785 1455 The first argument is the same as above, and the second argument gives the key columns for just this constraint.
adamc@785 1456
adamc@785 1457 We have operations for assembling constraints into constraint sets.
adamc@785 1458 $$\begin{array}{l}
adamc@785 1459 \mt{val} \; \mt{no\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_constraints} \; \mt{fs} \; [] \\
adamc@785 1460 \mt{val} \; \mt{one\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{unique} ::: \{\mt{Unit}\} \to \mt{name} :: \mt{Name} \\
adamc@785 1461 \hspace{.1in} \to \mt{sql\_constraint} \; \mt{fs} \; \mt{unique} \to \mt{sql\_constraints} \; \mt{fs} \; [\mt{name} = \mt{unique}] \\
adamc@785 1462 \mt{val} \; \mt{join\_constraints} : \mt{fs} ::: \{\mt{Type}\} \to \mt{uniques1} ::: \{\{\mt{Unit}\}\} \to \mt{uniques2} ::: \{\{\mt{Unit}\}\} \to [\mt{uniques1} \sim \mt{uniques2}] \\
adamc@785 1463 \hspace{.1in} \Rightarrow \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques1} \to \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques2} \to \mt{sql\_constraints} \; \mt{fs} \; (\mt{uniques1} \rc \mt{uniques2})
adamc@785 1464 \end{array}$$
adamc@785 1465
adamc@785 1466 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 1467 $$\begin{array}{l}
adamc@785 1468 \mt{val} \; \mt{unique} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{unique1} :: \mt{Name} \to \mt{unique} :: \{\mt{Type}\} \\
adamc@785 1469 \hspace{.1in} \to [[\mt{unique1}] \sim \mt{unique}] \Rightarrow [[\mt{unique1} = \mt{t}] \rc \mt{unique} \sim \mt{rest}] \\
adamc@785 1470 \hspace{.1in} \Rightarrow \mt{sql\_constraint} \; ([\mt{unique1} = \mt{t}] \rc \mt{unique} \rc \mt{rest}) \; ([\mt{unique1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{unique})
adamc@785 1471 \end{array}$$
adamc@785 1472
adamc@785 1473 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 1474 $$\begin{array}{l}
adamc@785 1475 \mt{class} \; \mt{linkable} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@785 1476 \mt{val} \; \mt{linkable\_same} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; \mt{t} \\
adamc@785 1477 \mt{val} \; \mt{linkable\_from\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; (\mt{option} \; \mt{t}) \; \mt{t} \\
adamc@785 1478 \mt{val} \; \mt{linkable\_to\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@785 1479 \end{array}$$
adamc@785 1480
adamc@785 1481 The $\mt{matching}$ type family uses $\mt{linkable}$ to define when two keys match up type-wise.
adamc@785 1482 $$\begin{array}{l}
adamc@785 1483 \mt{con} \; \mt{matching} :: \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1484 \mt{val} \; \mt{mat\_nil} : \mt{matching} \; [] \; [] \\
adamc@785 1485 \mt{val} \; \mt{mat\_cons} : \mt{t1} ::: \mt{Type} \to \mt{rest1} ::: \{\mt{Type}\} \to \mt{t2} ::: \mt{Type} \to \mt{rest2} ::: \{\mt{Type}\} \to \mt{nm1} :: \mt{Name} \to \mt{nm2} :: \mt{Name} \\
adamc@785 1486 \hspace{.1in} \to [[\mt{nm1}] \sim \mt{rest1}] \Rightarrow [[\mt{nm2}] \sim \mt{rest2}] \Rightarrow \mt{linkable} \; \mt{t1} \; \mt{t2} \to \mt{matching} \; \mt{rest1} \; \mt{rest2} \\
adamc@785 1487 \hspace{.1in} \to \mt{matching} \; ([\mt{nm1} = \mt{t1}] \rc \mt{rest1}) \; ([\mt{nm2} = \mt{t2}] \rc \mt{rest2})
adamc@785 1488 \end{array}$$
adamc@785 1489
adamc@785 1490 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 1491 $$\begin{array}{l}
adamc@785 1492 \mt{con} \; \mt{propagation\_mode} :: \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1493 \mt{val} \; \mt{restrict} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1494 \mt{val} \; \mt{cascade} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1495 \mt{val} \; \mt{no\_action} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1496 \mt{val} \; \mt{set\_null} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; (\mt{map} \; \mt{option} \; \mt{fs})
adamc@785 1497 \end{array}$$
adamc@785 1498
adamc@785 1499 Finally, we put these ingredient together to define the \texttt{FOREIGN KEY} constraint function.
adamc@785 1500 $$\begin{array}{l}
adamc@785 1501 \mt{val} \; \mt{foreign\_key} : \mt{mine1} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{mine} ::: \{\mt{Type}\} \to \mt{munused} ::: \{\mt{Type}\} \to \mt{foreign} ::: \{\mt{Type}\} \\
adamc@785 1502 \hspace{.1in} \to \mt{funused} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{uniques} ::: \{\{\mt{Unit}\}\} \\
adamc@785 1503 \hspace{.1in} \to [[\mt{mine1}] \sim \mt{mine}] \Rightarrow [[\mt{mine1} = \mt{t}] \rc \mt{mine} \sim \mt{munused}] \Rightarrow [\mt{foreign} \sim \mt{funused}] \Rightarrow [[\mt{nm}] \sim \mt{uniques}] \\
adamc@785 1504 \hspace{.1in} \Rightarrow \mt{matching} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}) \; \mt{foreign} \\
adamc@785 1505 \hspace{.1in} \to \mt{sql\_table} \; (\mt{foreign} \rc \mt{funused}) \; ([\mt{nm} = \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{foreign}] \rc \mt{uniques}) \\
adamc@785 1506 \hspace{.1in} \to \{\mt{OnDelete} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}), \\
adamc@785 1507 \hspace{.2in} \mt{OnUpdate} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine})\} \\
adamc@785 1508 \hspace{.1in} \to \mt{sql\_constraint} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine} \rc \mt{munused}) \; []
adamc@785 1509 \end{array}$$
adamc@785 1510
adamc@785 1511 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 1512 $$\begin{array}{l}
adamc@785 1513 \mt{val} \; \mt{check} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; [] \; [] \; \mt{fs} \; \mt{bool} \to \mt{sql\_constraint} \; \mt{fs} \; []
adamc@785 1514 \end{array}$$
adamc@785 1515
adamc@785 1516 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 1517
adamc@784 1518
adamc@543 1519 \subsubsection{Queries}
adamc@543 1520
adamc@1193 1521 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 1522 $$\begin{array}{l}
adamc@1193 1523 \mt{con} \; \mt{sql\_query} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@1193 1524 \mt{val} \; \mt{sql\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1525 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543 1526 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1527 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1193 1528 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adamc@1193 1529 \hspace{.1in} \Rightarrow \{\mt{Rows} : \mt{sql\_query1} \; \mt{free} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}, \\
adamc@1193 1530 \hspace{.2in} \mt{OrderBy} : \mt{sql\_order\_by} \; (\mt{free} \rc \mt{tables}) \; \mt{selectedExps}, \\
adamc@543 1531 \hspace{.2in} \mt{Limit} : \mt{sql\_limit}, \\
adamc@543 1532 \hspace{.2in} \mt{Offset} : \mt{sql\_offset}\} \\
adamc@1193 1533 \hspace{.1in} \to \mt{sql\_query} \; \mt{free} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1534 \end{array}$$
adamc@543 1535
adamc@545 1536 Queries are used by folding over their results inside transactions.
adamc@545 1537 $$\begin{array}{l}
adamc@1193 1538 \mt{val} \; \mt{query} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \lambda [\mt{tables} \sim \mt{exps}] \Rightarrow \mt{state} ::: \mt{Type} \to \mt{sql\_query} \; [] \; \mt{tables} \; \mt{exps} \\
adamc@658 1539 \hspace{.1in} \to (\$(\mt{exps} \rc \mt{map} \; (\lambda \mt{fields} :: \{\mt{Type}\} \Rightarrow \$\mt{fields}) \; \mt{tables}) \\
adamc@545 1540 \hspace{.2in} \to \mt{state} \to \mt{transaction} \; \mt{state}) \\
adamc@545 1541 \hspace{.1in} \to \mt{state} \to \mt{transaction} \; \mt{state}
adamc@545 1542 \end{array}$$
adamc@545 1543
adamc@1193 1544 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 1545 $$\begin{array}{l}
adamc@1193 1546 \mt{con} \; \mt{sql\_query1} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@543 1547 \\
adamc@543 1548 \mt{type} \; \mt{sql\_relop} \\
adamc@543 1549 \mt{val} \; \mt{sql\_union} : \mt{sql\_relop} \\
adamc@543 1550 \mt{val} \; \mt{sql\_intersect} : \mt{sql\_relop} \\
adamc@543 1551 \mt{val} \; \mt{sql\_except} : \mt{sql\_relop} \\
adamc@543 1552 \mt{val} \; \mt{sql\_relop} : \mt{tables1} ::: \{\{\mt{Type}\}\} \\
adamc@543 1553 \hspace{.1in} \to \mt{tables2} ::: \{\{\mt{Type}\}\} \\
adamc@543 1554 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1555 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@543 1556 \hspace{.1in} \to \mt{sql\_relop} \\
adamc@543 1557 \hspace{.1in} \to \mt{sql\_query1} \; \mt{tables1} \; \mt{selectedFields} \; \mt{selectedExps} \\
adamc@543 1558 \hspace{.1in} \to \mt{sql\_query1} \; \mt{tables2} \; \mt{selectedFields} \; \mt{selectedExps} \\
adamc@543 1559 \hspace{.1in} \to \mt{sql\_query1} \; \mt{selectedFields} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1560 \end{array}$$
adamc@543 1561
adamc@543 1562 $$\begin{array}{l}
adamc@1193 1563 \mt{val} \; \mt{sql\_query1} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1564 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543 1565 \hspace{.1in} \to \mt{grouped} ::: \{\{\mt{Type}\}\} \\
adamc@543 1566 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1567 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1085 1568 \hspace{.1in} \to \mt{empties} :: \{\mt{Unit}\} \\
adamc@1193 1569 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adamc@1193 1570 \hspace{.1in} \Rightarrow [\mt{free} \sim \mt{grouped}] \\
adamc@1193 1571 \hspace{.1in} \Rightarrow [\mt{empties} \sim \mt{selectedFields}] \\
adamc@1085 1572 \hspace{.1in} \Rightarrow \{\mt{Distinct} : \mt{bool}, \\
adamc@1193 1573 \hspace{.2in} \mt{From} : \mt{sql\_from\_items} \; \mt{free} \; \mt{tables}, \\
adamc@1193 1574 \hspace{.2in} \mt{Where} : \mt{sql\_exp} \; (\mt{free} \rc \mt{tables}) \; [] \; [] \; \mt{bool}, \\
adamc@543 1575 \hspace{.2in} \mt{GroupBy} : \mt{sql\_subset} \; \mt{tables} \; \mt{grouped}, \\
adamc@1193 1576 \hspace{.2in} \mt{Having} : \mt{sql\_exp} \; (\mt{free} \rc \mt{grouped}) \; \mt{tables} \; [] \; \mt{bool}, \\
adamc@1085 1577 \hspace{.2in} \mt{SelectFields} : \mt{sql\_subset} \; \mt{grouped} \; (\mt{map} \; (\lambda \_ \Rightarrow []) \; \mt{empties} \rc \mt{selectedFields}), \\
adamc@1193 1578 \hspace{.2in} \mt {SelectExps} : \$(\mt{map} \; (\mt{sql\_exp} \; (\mt{free} \rc \mt{grouped}) \; \mt{tables} \; []) \; \mt{selectedExps}) \} \\
adamc@1193 1579 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1580 \end{array}$$
adamc@543 1581
adamc@543 1582 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 1583 $$\begin{array}{l}
adamc@543 1584 \mt{con} \; \mt{sql\_subset} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@543 1585 \mt{val} \; \mt{sql\_subset} : \mt{keep\_drop} :: \{(\{\mt{Type}\} \times \{\mt{Type}\})\} \\
adamc@543 1586 \hspace{.1in} \to \mt{sql\_subset} \\
adamc@658 1587 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1 \rc \mt{fields}.2)\; \mt{keep\_drop}) \\
adamc@658 1588 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1) \; \mt{keep\_drop}) \\
adamc@543 1589 \mt{val} \; \mt{sql\_subset\_all} : \mt{tables} :: \{\{\mt{Type}\}\} \to \mt{sql\_subset} \; \mt{tables} \; \mt{tables}
adamc@543 1590 \end{array}$$
adamc@543 1591
adamc@560 1592 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 1593 $$\begin{array}{l}
adamc@543 1594 \mt{con} \; \mt{sql\_exp} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}
adamc@543 1595 \end{array}$$
adamc@543 1596
adamc@543 1597 Any field in scope may be converted to an expression.
adamc@543 1598 $$\begin{array}{l}
adamc@543 1599 \mt{val} \; \mt{sql\_field} : \mt{otherTabs} ::: \{\{\mt{Type}\}\} \to \mt{otherFields} ::: \{\mt{Type}\} \\
adamc@543 1600 \hspace{.1in} \to \mt{fieldType} ::: \mt{Type} \to \mt{agg} ::: \{\{\mt{Type}\}\} \\
adamc@543 1601 \hspace{.1in} \to \mt{exps} ::: \{\mt{Type}\} \\
adamc@543 1602 \hspace{.1in} \to \mt{tab} :: \mt{Name} \to \mt{field} :: \mt{Name} \\
adamc@543 1603 \hspace{.1in} \to \mt{sql\_exp} \; ([\mt{tab} = [\mt{field} = \mt{fieldType}] \rc \mt{otherFields}] \rc \mt{otherTabs}) \; \mt{agg} \; \mt{exps} \; \mt{fieldType}
adamc@543 1604 \end{array}$$
adamc@543 1605
adamc@544 1606 There is an analogous function for referencing named expressions.
adamc@544 1607 $$\begin{array}{l}
adamc@544 1608 \mt{val} \; \mt{sql\_exp} : \mt{tabs} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{t} ::: \mt{Type} \to \mt{rest} ::: \{\mt{Type}\} \to \mt{nm} :: \mt{Name} \\
adamc@544 1609 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tabs} \; \mt{agg} \; ([\mt{nm} = \mt{t}] \rc \mt{rest}) \; \mt{t}
adamc@544 1610 \end{array}$$
adamc@544 1611
adamc@544 1612 Ur values of appropriate types may be injected into SQL expressions.
adamc@544 1613 $$\begin{array}{l}
adamc@786 1614 \mt{class} \; \mt{sql\_injectable\_prim} \\
adamc@786 1615 \mt{val} \; \mt{sql\_bool} : \mt{sql\_injectable\_prim} \; \mt{bool} \\
adamc@786 1616 \mt{val} \; \mt{sql\_int} : \mt{sql\_injectable\_prim} \; \mt{int} \\
adamc@786 1617 \mt{val} \; \mt{sql\_float} : \mt{sql\_injectable\_prim} \; \mt{float} \\
adamc@786 1618 \mt{val} \; \mt{sql\_string} : \mt{sql\_injectable\_prim} \; \mt{string} \\
adamc@786 1619 \mt{val} \; \mt{sql\_time} : \mt{sql\_injectable\_prim} \; \mt{time} \\
adamc@786 1620 \mt{val} \; \mt{sql\_blob} : \mt{sql\_injectable\_prim} \; \mt{blob} \\
adamc@786 1621 \mt{val} \; \mt{sql\_channel} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{channel} \; \mt{t}) \\
adamc@786 1622 \mt{val} \; \mt{sql\_client} : \mt{sql\_injectable\_prim} \; \mt{client} \\
adamc@786 1623 \\
adamc@544 1624 \mt{class} \; \mt{sql\_injectable} \\
adamc@786 1625 \mt{val} \; \mt{sql\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@786 1626 \mt{val} \; \mt{sql\_option\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; (\mt{option} \; \mt{t}) \\
adamc@786 1627 \\
adamc@544 1628 \mt{val} \; \mt{sql\_inject} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@544 1629 \hspace{.1in} \to \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adamc@544 1630 \end{array}$$
adamc@544 1631
adamc@1123 1632 Additionally, most function-free types may be injected safely, via the $\mt{serialized}$ type family.
adamc@1123 1633 $$\begin{array}{l}
adamc@1123 1634 \mt{con} \; \mt{serialized} :: \mt{Type} \to \mt{Type} \\
adamc@1123 1635 \mt{val} \; \mt{serialize} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{serialized} \; \mt{t} \\
adamc@1123 1636 \mt{val} \; \mt{deserialize} : \mt{t} ::: \mt{Type} \to \mt{serialized} \; \mt{t} \to \mt{t} \\
adamc@1123 1637 \mt{val} \; \mt{sql\_serialized} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{serialized} \; \mt{t})
adamc@1123 1638 \end{array}$$
adamc@1123 1639
adamc@544 1640 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 1641 $$\begin{array}{l}
adamc@544 1642 \mt{val} \; \mt{sql\_is\_null} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544 1643 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; (\mt{option} \; \mt{t}) \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{bool}
adamc@544 1644 \end{array}$$
adamc@544 1645
adamc@559 1646 We have generic nullary, unary, and binary operators.
adamc@544 1647 $$\begin{array}{l}
adamc@544 1648 \mt{con} \; \mt{sql\_nfunc} :: \mt{Type} \to \mt{Type} \\
adamc@544 1649 \mt{val} \; \mt{sql\_current\_timestamp} : \mt{sql\_nfunc} \; \mt{time} \\
adamc@544 1650 \mt{val} \; \mt{sql\_nfunc} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544 1651 \hspace{.1in} \to \mt{sql\_nfunc} \; \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\\end{array}$$
adamc@544 1652
adamc@544 1653 $$\begin{array}{l}
adamc@544 1654 \mt{con} \; \mt{sql\_unary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544 1655 \mt{val} \; \mt{sql\_not} : \mt{sql\_unary} \; \mt{bool} \; \mt{bool} \\
adamc@544 1656 \mt{val} \; \mt{sql\_unary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adamc@544 1657 \hspace{.1in} \to \mt{sql\_unary} \; \mt{arg} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res} \\
adamc@544 1658 \end{array}$$
adamc@544 1659
adamc@544 1660 $$\begin{array}{l}
adamc@544 1661 \mt{con} \; \mt{sql\_binary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544 1662 \mt{val} \; \mt{sql\_and} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544 1663 \mt{val} \; \mt{sql\_or} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544 1664 \mt{val} \; \mt{sql\_binary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg_1} ::: \mt{Type} \to \mt{arg_2} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adamc@544 1665 \hspace{.1in} \to \mt{sql\_binary} \; \mt{arg_1} \; \mt{arg_2} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_1} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_2} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res}
adamc@544 1666 \end{array}$$
adamc@544 1667
adamc@544 1668 $$\begin{array}{l}
adamc@559 1669 \mt{class} \; \mt{sql\_arith} \\
adamc@559 1670 \mt{val} \; \mt{sql\_int\_arith} : \mt{sql\_arith} \; \mt{int} \\
adamc@559 1671 \mt{val} \; \mt{sql\_float\_arith} : \mt{sql\_arith} \; \mt{float} \\
adamc@559 1672 \mt{val} \; \mt{sql\_neg} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_unary} \; \mt{t} \; \mt{t} \\
adamc@559 1673 \mt{val} \; \mt{sql\_plus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1674 \mt{val} \; \mt{sql\_minus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1675 \mt{val} \; \mt{sql\_times} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1676 \mt{val} \; \mt{sql\_div} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1677 \mt{val} \; \mt{sql\_mod} : \mt{sql\_binary} \; \mt{int} \; \mt{int} \; \mt{int}
adamc@559 1678 \end{array}$$
adamc@544 1679
adamc@656 1680 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 1681 $$\begin{array}{l}
adamc@544 1682 \mt{val} \; \mt{sql\_count} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int}
adamc@544 1683 \end{array}$$
adamc@544 1684
adamc@544 1685 $$\begin{array}{l}
adamc@1188 1686 \mt{con} \; \mt{sql\_aggregate} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@1188 1687 \mt{val} \; \mt{sql\_aggregate} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{dom} ::: \mt{Type} \to \mt{ran} ::: \mt{Type} \\
adamc@1188 1688 \hspace{.1in} \to \mt{sql\_aggregate} \; \mt{dom} \; \mt{ran} \to \mt{sql\_exp} \; \mt{agg} \; \mt{agg} \; \mt{exps} \; \mt{dom} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{ran}
adamc@1188 1689 \end{array}$$
adamc@1188 1690
adamc@1188 1691 $$\begin{array}{l}
adamc@1188 1692 \mt{val} \; \mt{sql\_count\_col} : \mt{t} ::: \mt{Type} \to \mt{sql\_aggregate} \; (\mt{option} \; \mt{t}) \; \mt{int}
adamc@544 1693 \end{array}$$
adamc@544 1694
adamc@544 1695 $$\begin{array}{l}
adamc@544 1696 \mt{class} \; \mt{sql\_summable} \\
adamc@544 1697 \mt{val} \; \mt{sql\_summable\_int} : \mt{sql\_summable} \; \mt{int} \\
adamc@544 1698 \mt{val} \; \mt{sql\_summable\_float} : \mt{sql\_summable} \; \mt{float} \\
adamc@1188 1699 \mt{val} \; \mt{sql\_avg} : \mt{t} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{t} \\
adamc@1188 1700 \mt{val} \; \mt{sql\_sum} : \mt{t} ::: \mt{Type} \to \mt{sql\_summable} \mt{t} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{t}
adamc@544 1701 \end{array}$$
adamc@544 1702
adamc@544 1703 $$\begin{array}{l}
adamc@544 1704 \mt{class} \; \mt{sql\_maxable} \\
adamc@544 1705 \mt{val} \; \mt{sql\_maxable\_int} : \mt{sql\_maxable} \; \mt{int} \\
adamc@544 1706 \mt{val} \; \mt{sql\_maxable\_float} : \mt{sql\_maxable} \; \mt{float} \\
adamc@544 1707 \mt{val} \; \mt{sql\_maxable\_string} : \mt{sql\_maxable} \; \mt{string} \\
adamc@544 1708 \mt{val} \; \mt{sql\_maxable\_time} : \mt{sql\_maxable} \; \mt{time} \\
adamc@1188 1709 \mt{val} \; \mt{sql\_max} : \mt{t} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{t} \\
adamc@1188 1710 \mt{val} \; \mt{sql\_min} : \mt{t} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{t}
adamc@544 1711 \end{array}$$
adamc@544 1712
adamc@1193 1713 Any SQL query that returns single columns may be turned into a subquery expression.
adamc@1193 1714
adamc@786 1715 $$\begin{array}{l}
adamc@1193 1716 \mt{val} \; \mt{sql\_subquery} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \\
adamc@1193 1717 \hspace{.1in} \to \mt{sql\_query} \; \mt{tables} \; [] \; [\mt{nm} = \mt{t}] \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adamc@1193 1718 \end{array}$$
adamc@1193 1719
adamc@1193 1720 \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 1721 $$\begin{array}{l}
adamc@1193 1722 \mt{con} \; \mt{sql\_from\_items} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@1193 1723 \mt{val} \; \mt{sql\_from\_table} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1724 \hspace{.1in} \to \mt{t} ::: \mt{Type} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; \mt{t} \; \mt{fs} \to \mt{name} :: \mt{Name} \to \mt{t} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193 1725 \mt{val} \; \mt{sql\_from\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{name} :: \mt{Name} \to \mt{sql\_query} \; \mt{free} \; [] \; \mt{fs} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193 1726 \mt{val} \; \mt{sql\_from\_comma} : \mt{free} ::: \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \to [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193 1727 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adamc@1193 1728 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2}) \\
adamc@1193 1729 \mt{val} \; \mt{sql\_inner\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1730 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193 1731 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adamc@1193 1732 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193 1733 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2})
adamc@786 1734 \end{array}$$
adamc@786 1735
adamc@786 1736 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 1737 $$\begin{array}{l}
adamc@786 1738 \mt{class} \; \mt{nullify} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@786 1739 \mt{val} \; \mt{nullify\_option} : \mt{t} ::: \mt{Type} \to \mt{nullify} \; (\mt{option} \; \mt{t}) \; (\mt{option} \; \mt{t}) \\
adamc@786 1740 \mt{val} \; \mt{nullify\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{nullify} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@786 1741 \end{array}$$
adamc@786 1742
adamc@786 1743 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 1744
adamc@786 1745 $$\begin{array}{l}
adamc@1193 1746 \mt{val} \; \mt{sql\_left\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{(\mt{Type} \times \mt{Type})\}\} \\
adamc@1193 1747 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@786 1748 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\lambda \mt{r} \Rightarrow \$(\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{nullify} \; \mt{p}.1 \; \mt{p}.2) \; \mt{r})) \; \mt{tabs2}) \\
adamc@1193 1749 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \\
adamc@1193 1750 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193 1751 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.2)) \; \mt{tabs2})
adamc@786 1752 \end{array}$$
adamc@786 1753
adamc@544 1754 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 1755 $$\begin{array}{l}
adamc@544 1756 \mt{type} \; \mt{sql\_direction} \\
adamc@544 1757 \mt{val} \; \mt{sql\_asc} : \mt{sql\_direction} \\
adamc@544 1758 \mt{val} \; \mt{sql\_desc} : \mt{sql\_direction} \\
adamc@544 1759 \\
adamc@544 1760 \mt{con} \; \mt{sql\_order\_by} :: \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@544 1761 \mt{val} \; \mt{sql\_order\_by\_Nil} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} :: \{\mt{Type}\} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544 1762 \mt{val} \; \mt{sql\_order\_by\_Cons} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544 1763 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; [] \; \mt{exps} \; \mt{t} \to \mt{sql\_direction} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544 1764 \\
adamc@544 1765 \mt{type} \; \mt{sql\_limit} \\
adamc@544 1766 \mt{val} \; \mt{sql\_no\_limit} : \mt{sql\_limit} \\
adamc@544 1767 \mt{val} \; \mt{sql\_limit} : \mt{int} \to \mt{sql\_limit} \\
adamc@544 1768 \\
adamc@544 1769 \mt{type} \; \mt{sql\_offset} \\
adamc@544 1770 \mt{val} \; \mt{sql\_no\_offset} : \mt{sql\_offset} \\
adamc@544 1771 \mt{val} \; \mt{sql\_offset} : \mt{int} \to \mt{sql\_offset}
adamc@544 1772 \end{array}$$
adamc@544 1773
adamc@545 1774
adamc@545 1775 \subsubsection{DML}
adamc@545 1776
adamc@545 1777 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 1778
adamc@545 1779 $$\begin{array}{l}
adamc@545 1780 \mt{type} \; \mt{dml} \\
adamc@545 1781 \mt{val} \; \mt{dml} : \mt{dml} \to \mt{transaction} \; \mt{unit}
adamc@545 1782 \end{array}$$
adamc@545 1783
adam@1297 1784 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 1785
adam@1297 1786 $$\begin{array}{l}
adam@1297 1787 \mt{val} \; \mt{tryDml} : \mt{dml} \to \mt{transaction} \; (\mt{option} \; \mt{string})
adam@1297 1788 \end{array}$$
adam@1297 1789
adamc@545 1790 Properly-typed records may be used to form $\mt{INSERT}$ commands.
adamc@545 1791 $$\begin{array}{l}
adamc@545 1792 \mt{val} \; \mt{insert} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \\
adamc@658 1793 \hspace{.1in} \to \$(\mt{map} \; (\mt{sql\_exp} \; [] \; [] \; []) \; \mt{fields}) \to \mt{dml}
adamc@545 1794 \end{array}$$
adamc@545 1795
adamc@545 1796 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 1797 $$\begin{array}{l}
adamc@545 1798 \mt{val} \; \mt{update} : \mt{unchanged} ::: \{\mt{Type}\} \to \mt{changed} :: \{\mt{Type}\} \to \lambda [\mt{changed} \sim \mt{unchanged}] \\
adamc@658 1799 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; []) \; \mt{changed}) \\
adamc@545 1800 \hspace{.1in} \to \mt{sql\_table} \; (\mt{changed} \rc \mt{unchanged}) \to \mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545 1801 \end{array}$$
adamc@545 1802
adamc@545 1803 A $\mt{DELETE}$ command is formed from a table and a $\mt{WHERE}$ clause.
adamc@545 1804 $$\begin{array}{l}
adamc@545 1805 \mt{val} \; \mt{delete} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \to \mt{sql\_exp} \; [\mt{T} = \mt{fields}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545 1806 \end{array}$$
adamc@545 1807
adamc@546 1808 \subsubsection{Sequences}
adamc@546 1809
adamc@546 1810 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 1811
adamc@546 1812 $$\begin{array}{l}
adamc@546 1813 \mt{type} \; \mt{sql\_sequence} \\
adamc@1085 1814 \mt{val} \; \mt{nextval} : \mt{sql\_sequence} \to \mt{transaction} \; \mt{int} \\
adamc@1085 1815 \mt{val} \; \mt{setval} : \mt{sql\_sequence} \to \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@546 1816 \end{array}$$
adamc@546 1817
adamc@546 1818
adamc@547 1819 \subsection{XML}
adamc@547 1820
adamc@547 1821 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 1822
adamc@547 1823 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 1824 $$\begin{array}{l}
adamc@547 1825 \mt{con} \; \mt{xml} :: \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547 1826 \end{array}$$
adamc@547 1827
adamc@547 1828 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 1829 $$\begin{array}{l}
adamc@547 1830 \mt{con} \; \mt{tag} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547 1831 \end{array}$$
adamc@547 1832
adamc@547 1833 Literal text may be injected into XML as ``CDATA.''
adamc@547 1834 $$\begin{array}{l}
adamc@547 1835 \mt{val} \; \mt{cdata} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{string} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adamc@547 1836 \end{array}$$
adamc@547 1837
adamc@547 1838 There is a function for producing an XML tree with a particular tag at its root.
adamc@547 1839 $$\begin{array}{l}
adamc@547 1840 \mt{val} \; \mt{tag} : \mt{attrsGiven} ::: \{\mt{Type}\} \to \mt{attrsAbsent} ::: \{\mt{Type}\} \to \mt{ctxOuter} ::: \{\mt{Unit}\} \to \mt{ctxInner} ::: \{\mt{Unit}\} \\
adamc@547 1841 \hspace{.1in} \to \mt{useOuter} ::: \{\mt{Type}\} \to \mt{useInner} ::: \{\mt{Type}\} \to \mt{bindOuter} ::: \{\mt{Type}\} \to \mt{bindInner} ::: \{\mt{Type}\} \\
adamc@787 1842 \hspace{.1in} \to \lambda [\mt{attrsGiven} \sim \mt{attrsAbsent}] \; [\mt{useOuter} \sim \mt{useInner}] \; [\mt{bindOuter} \sim \mt{bindInner}] \\
adamc@787 1843 \hspace{.1in} \Rightarrow \mt{option} \; \mt{css\_class} \\
adamc@787 1844 \hspace{.1in} \to \$\mt{attrsGiven} \\
adamc@547 1845 \hspace{.1in} \to \mt{tag} \; (\mt{attrsGiven} \rc \mt{attrsAbsent}) \; \mt{ctxOuter} \; \mt{ctxInner} \; \mt{useOuter} \; \mt{bindOuter} \\
adamc@547 1846 \hspace{.1in} \to \mt{xml} \; \mt{ctxInner} \; \mt{useInner} \; \mt{bindInner} \to \mt{xml} \; \mt{ctxOuter} \; (\mt{useOuter} \rc \mt{useInner}) \; (\mt{bindOuter} \rc \mt{bindInner})
adamc@547 1847 \end{array}$$
adam@1297 1848 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 1849
adamc@547 1850 Two XML fragments may be concatenated.
adamc@547 1851 $$\begin{array}{l}
adamc@547 1852 \mt{val} \; \mt{join} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{bind_1} ::: \{\mt{Type}\} \to \mt{bind_2} ::: \{\mt{Type}\} \\
adamc@547 1853 \hspace{.1in} \to \lambda [\mt{use_1} \sim \mt{bind_1}] \; [\mt{bind_1} \sim \mt{bind_2}] \\
adamc@547 1854 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind_1} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{bind_1}) \; \mt{bind_2} \to \mt{xml} \; \mt{ctx} \; \mt{use_1} \; (\mt{bind_1} \rc \mt{bind_2})
adamc@547 1855 \end{array}$$
adamc@547 1856
adamc@547 1857 Finally, any XML fragment may be updated to ``claim'' to use more form fields than it does.
adamc@547 1858 $$\begin{array}{l}
adamc@547 1859 \mt{val} \; \mt{useMore} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{use_2} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to \lambda [\mt{use_1} \sim \mt{use_2}] \\
adamc@547 1860 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{use_2}) \; \mt{bind}
adamc@547 1861 \end{array}$$
adamc@547 1862
adamc@547 1863 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 1864
adamc@547 1865 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 1866 $$\begin{array}{l}
adamc@547 1867 \mt{val} \; \mt{error} : \mt{t} ::: \mt{Type} \to \mt{xml} \; [\mt{Body}] \; [] \; [] \to \mt{t}
adamc@547 1868 \end{array}$$
adamc@547 1869
adamc@549 1870
adamc@701 1871 \subsection{Client-Side Programming}
adamc@659 1872
adamc@701 1873 Ur/Web supports running code on web browsers, via automatic compilation to JavaScript.
adamc@701 1874
adamc@701 1875 \subsubsection{The Basics}
adamc@701 1876
adam@1297 1877 Clients can open alert and confirm dialog boxes, in the usual annoying JavaScript way.
adamc@701 1878 $$\begin{array}{l}
adam@1297 1879 \mt{val} \; \mt{alert} : \mt{string} \to \mt{transaction} \; \mt{unit} \\
adam@1297 1880 \mt{val} \; \mt{confirm} : \mt{string} \to \mt{transaction} \; \mt{bool}
adamc@701 1881 \end{array}$$
adamc@701 1882
adamc@701 1883 Any transaction may be run in a new thread with the $\mt{spawn}$ function.
adamc@701 1884 $$\begin{array}{l}
adamc@701 1885 \mt{val} \; \mt{spawn} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit}
adamc@701 1886 \end{array}$$
adamc@701 1887
adamc@701 1888 The current thread can be paused for at least a specified number of milliseconds.
adamc@701 1889 $$\begin{array}{l}
adamc@701 1890 \mt{val} \; \mt{sleep} : \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@701 1891 \end{array}$$
adamc@701 1892
adamc@787 1893 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 1894 $$\begin{array}{l}
adamc@787 1895 \mt{val} \; \mt{onError} : (\mt{xbody} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787 1896 \mt{val} \; \mt{onFail} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787 1897 \mt{val} \; \mt{onConnectFail} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787 1898 \mt{val} \; \mt{onDisconnect} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787 1899 \mt{val} \; \mt{onServerError} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit}
adamc@787 1900 \end{array}$$
adamc@787 1901
adamc@701 1902 \subsubsection{Functional-Reactive Page Generation}
adamc@701 1903
adamc@701 1904 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 1905
adamc@659 1906 $$\begin{array}{l}
adamc@659 1907 \mt{con} \; \mt{source} :: \mt{Type} \to \mt{Type} \\
adamc@659 1908 \mt{val} \; \mt{source} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{transaction} \; (\mt{source} \; \mt{t}) \\
adamc@659 1909 \mt{val} \; \mt{set} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@659 1910 \mt{val} \; \mt{get} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@659 1911 \end{array}$$
adamc@659 1912
adamc@659 1913 Pure functions over sources are represented in a monad of \emph{signals}.
adamc@659 1914
adamc@659 1915 $$\begin{array}{l}
adamc@659 1916 \mt{con} \; \mt{signal} :: \mt{Type} \to \mt{Type} \\
adamc@659 1917 \mt{val} \; \mt{signal\_monad} : \mt{monad} \; \mt{signal} \\
adamc@659 1918 \mt{val} \; \mt{signal} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{signal} \; \mt{t}
adamc@659 1919 \end{array}$$
adamc@659 1920
adamc@659 1921 A reactive portion of an HTML page is injected with a $\mt{dyn}$ tag, which has a signal-valued attribute $\mt{Signal}$.
adamc@659 1922
adamc@659 1923 $$\begin{array}{l}
adamc@701 1924 \mt{val} \; \mt{dyn} : \mt{use} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to \mt{unit} \\
adamc@701 1925 \hspace{.1in} \to \mt{tag} \; [\mt{Signal} = \mt{signal} \; (\mt{xml} \; \mt{body} \; \mt{use} \; \mt{bind})] \; \mt{body} \; [] \; \mt{use} \; \mt{bind}
adamc@659 1926 \end{array}$$
adamc@659 1927
adamc@701 1928 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 1929
adamc@914 1930 \subsubsection{Remote Procedure Calls}
adamc@914 1931
adamc@914 1932 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 1933
adamc@914 1934 $$\begin{array}{l}
adamc@914 1935 \mt{val} \; \mt{rpc} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@914 1936 \end{array}$$
adamc@914 1937
adamc@701 1938 \subsubsection{Asynchronous Message-Passing}
adamc@701 1939
adamc@701 1940 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 1941
adamc@701 1942 $$\begin{array}{l}
adamc@701 1943 \mt{type} \; \mt{client} \\
adamc@701 1944 \mt{val} \; \mt{self} : \mt{transaction} \; \mt{client}
adamc@701 1945 \end{array}$$
adamc@701 1946
adamc@701 1947 \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 1948
adamc@701 1949 $$\begin{array}{l}
adamc@701 1950 \mt{con} \; \mt{channel} :: \mt{Type} \to \mt{Type} \\
adamc@701 1951 \mt{val} \; \mt{channel} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; (\mt{channel} \; \mt{t}) \\
adamc@701 1952 \mt{val} \; \mt{send} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@701 1953 \mt{val} \; \mt{recv} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@701 1954 \end{array}$$
adamc@701 1955
adamc@701 1956 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 1957
adamc@701 1958 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 1959
adamc@659 1960
adamc@549 1961 \section{Ur/Web Syntax Extensions}
adamc@549 1962
adamc@549 1963 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 1964
adamc@549 1965 \subsection{SQL}
adamc@549 1966
adamc@786 1967 \subsubsection{\label{tables}Table Declarations}
adamc@786 1968
adamc@788 1969 $\mt{table}$ declarations may include constraints, via these grammar rules.
adamc@788 1970 $$\begin{array}{rrcll}
adamc@788 1971 \textrm{Declarations} & d &::=& \mt{table} \; x : c \; [pk[,]] \; cts \\
adamc@788 1972 \textrm{Primary key constraints} & pk &::=& \mt{PRIMARY} \; \mt{KEY} \; K \\
adamc@788 1973 \textrm{Keys} & K &::=& f \mid (f, (f,)^+) \\
adamc@788 1974 \textrm{Constraint sets} & cts &::=& \mt{CONSTRAINT} f \; ct \mid cts, cts \mid \{\{e\}\} \\
adamc@788 1975 \textrm{Constraints} & ct &::=& \mt{UNIQUE} \; K \mid \mt{CHECK} \; E \\
adamc@788 1976 &&& \mid \mt{FOREIGN} \; \mt{KEY} \; K \; \mt{REFERENCES} \; F \; (K) \; [\mt{ON} \; \mt{DELETE} \; pr] \; [\mt{ON} \; \mt{UPDATE} \; pr] \\
adamc@788 1977 \textrm{Foreign tables} & F &::=& x \mid \{\{e\}\} \\
adamc@788 1978 \textrm{Propagation modes} & pr &::=& \mt{NO} \; \mt{ACTION} \mid \mt{RESTRICT} \mid \mt{CASCADE} \mid \mt{SET} \; \mt{NULL}
adamc@788 1979 \end{array}$$
adamc@788 1980
adamc@788 1981 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 1982
adamc@788 1983
adamc@549 1984 \subsubsection{Queries}
adamc@549 1985
adamc@550 1986 Queries $Q$ are added to the rules for expressions $e$.
adamc@550 1987
adamc@549 1988 $$\begin{array}{rrcll}
adamc@550 1989 \textrm{Queries} & Q &::=& (q \; [\mt{ORDER} \; \mt{BY} \; (E \; [o],)^+] \; [\mt{LIMIT} \; N] \; [\mt{OFFSET} \; N]) \\
adamc@1085 1990 \textrm{Pre-queries} & q &::=& \mt{SELECT} \; [\mt{DISTINCT}] \; P \; \mt{FROM} \; F,^+ \; [\mt{WHERE} \; E] \; [\mt{GROUP} \; \mt{BY} \; p,^+] \; [\mt{HAVING} \; E] \\
adamc@1085 1991 &&& \mid q \; R \; q \mid \{\{\{e\}\}\} \\
adamc@549 1992 \textrm{Relational operators} & R &::=& \mt{UNION} \mid \mt{INTERSECT} \mid \mt{EXCEPT}
adamc@549 1993 \end{array}$$
adamc@549 1994
adamc@549 1995 $$\begin{array}{rrcll}
adamc@549 1996 \textrm{Projections} & P &::=& \ast & \textrm{all columns} \\
adamc@549 1997 &&& p,^+ & \textrm{particular columns} \\
adamc@549 1998 \textrm{Pre-projections} & p &::=& t.f & \textrm{one column from a table} \\
adamc@558 1999 &&& t.\{\{c\}\} & \textrm{a record of columns from a table (of kind $\{\mt{Type}\}$)} \\
adamc@1194 2000 &&& E \; [\mt{AS} \; f] & \textrm{expression column} \\
adamc@549 2001 \textrm{Table names} & t &::=& x & \textrm{constant table name (automatically capitalized)} \\
adamc@549 2002 &&& X & \textrm{constant table name} \\
adamc@549 2003 &&& \{\{c\}\} & \textrm{computed table name (of kind $\mt{Name}$)} \\
adamc@549 2004 \textrm{Column names} & f &::=& X & \textrm{constant column name} \\
adamc@549 2005 &&& \{c\} & \textrm{computed column name (of kind $\mt{Name}$)} \\
adamc@549 2006 \textrm{Tables} & T &::=& x & \textrm{table variable, named locally by its own capitalization} \\
adamc@549 2007 &&& x \; \mt{AS} \; t & \textrm{table variable, with local name} \\
adamc@549 2008 &&& \{\{e\}\} \; \mt{AS} \; t & \textrm{computed table expression, with local name} \\
adamc@1085 2009 \textrm{$\mt{FROM}$ items} & F &::=& T \mid \{\{e\}\} \mid F \; J \; \mt{JOIN} \; F \; \mt{ON} \; E \\
adamc@1085 2010 &&& \mid F \; \mt{CROSS} \; \mt{JOIN} \ F \\
adamc@1193 2011 &&& \mid (Q) \; \mt{AS} \; t \\
adamc@1085 2012 \textrm{Joins} & J &::=& [\mt{INNER}] \\
adamc@1085 2013 &&& \mid [\mt{LEFT} \mid \mt{RIGHT} \mid \mt{FULL}] \; [\mt{OUTER}] \\
adamc@549 2014 \textrm{SQL expressions} & E &::=& p & \textrm{column references} \\
adamc@549 2015 &&& X & \textrm{named expression references} \\
adamc@549 2016 &&& \{\{e\}\} & \textrm{injected native Ur expressions} \\
adamc@549 2017 &&& \{e\} & \textrm{computed expressions, probably using $\mt{sql\_exp}$ directly} \\
adamc@549 2018 &&& \mt{TRUE} \mid \mt{FALSE} & \textrm{boolean constants} \\
adamc@549 2019 &&& \ell & \textrm{primitive type literals} \\
adamc@549 2020 &&& \mt{NULL} & \textrm{null value (injection of $\mt{None}$)} \\
adamc@549 2021 &&& E \; \mt{IS} \; \mt{NULL} & \textrm{nullness test} \\
adamc@549 2022 &&& n & \textrm{nullary operators} \\
adamc@549 2023 &&& u \; E & \textrm{unary operators} \\
adamc@549 2024 &&& E \; b \; E & \textrm{binary operators} \\
adamc@549 2025 &&& \mt{COUNT}(\ast) & \textrm{count number of rows} \\
adamc@549 2026 &&& a(E) & \textrm{other aggregate function} \\
adamc@1193 2027 &&& (Q) & \textrm{subquery (must return a single expression column)} \\
adamc@549 2028 &&& (E) & \textrm{explicit precedence} \\
adamc@549 2029 \textrm{Nullary operators} & n &::=& \mt{CURRENT\_TIMESTAMP} \\
adamc@549 2030 \textrm{Unary operators} & u &::=& \mt{NOT} \\
adamc@549 2031 \textrm{Binary operators} & b &::=& \mt{AND} \mid \mt{OR} \mid \neq \mid < \mid \leq \mid > \mid \geq \\
adamc@1188 2032 \textrm{Aggregate functions} & a &::=& \mt{COUNT} \mid \mt{AVG} \mid \mt{SUM} \mid \mt{MIN} \mid \mt{MAX} \\
adamc@550 2033 \textrm{Directions} & o &::=& \mt{ASC} \mid \mt{DESC} \\
adamc@549 2034 \textrm{SQL integer} & N &::=& n \mid \{e\} \\
adamc@549 2035 \end{array}$$
adamc@549 2036
adamc@1085 2037 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 2038
adamc@1194 2039 Unnamed expression columns in $\mt{SELECT}$ clauses are assigned consecutive natural numbers, starting with 1.
adamc@1194 2040
adamc@550 2041 \subsubsection{DML}
adamc@550 2042
adamc@550 2043 DML commands $D$ are added to the rules for expressions $e$.
adamc@550 2044
adamc@550 2045 $$\begin{array}{rrcll}
adamc@550 2046 \textrm{Commands} & D &::=& (\mt{INSERT} \; \mt{INTO} \; T^E \; (f,^+) \; \mt{VALUES} \; (E,^+)) \\
adamc@550 2047 &&& (\mt{UPDATE} \; T^E \; \mt{SET} \; (f = E,)^+ \; \mt{WHERE} \; E) \\
adamc@550 2048 &&& (\mt{DELETE} \; \mt{FROM} \; T^E \; \mt{WHERE} \; E) \\
adamc@550 2049 \textrm{Table expressions} & T^E &::=& x \mid \{\{e\}\}
adamc@550 2050 \end{array}$$
adamc@550 2051
adamc@550 2052 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 2053
adamc@551 2054 \subsection{XML}
adamc@551 2055
adamc@551 2056 XML fragments $L$ are added to the rules for expressions $e$.
adamc@551 2057
adamc@551 2058 $$\begin{array}{rrcll}
adamc@551 2059 \textrm{XML fragments} & L &::=& \texttt{<xml/>} \mid \texttt{<xml>}l^*\texttt{</xml>} \\
adamc@551 2060 \textrm{XML pieces} & l &::=& \textrm{text} & \textrm{cdata} \\
adamc@551 2061 &&& \texttt{<}g\texttt{/>} & \textrm{tag with no children} \\
adamc@551 2062 &&& \texttt{<}g\texttt{>}l^*\texttt{</}x\texttt{>} & \textrm{tag with children} \\
adamc@559 2063 &&& \{e\} & \textrm{computed XML fragment} \\
adamc@559 2064 &&& \{[e]\} & \textrm{injection of an Ur expression, via the $\mt{Top}.\mt{txt}$ function} \\
adamc@551 2065 \textrm{Tag} & g &::=& h \; (x = v)^* \\
adamc@551 2066 \textrm{Tag head} & h &::=& x & \textrm{tag name} \\
adamc@551 2067 &&& h\{c\} & \textrm{constructor parameter} \\
adamc@551 2068 \textrm{Attribute value} & v &::=& \ell & \textrm{literal value} \\
adamc@551 2069 &&& \{e\} & \textrm{computed value} \\
adamc@551 2070 \end{array}$$
adamc@551 2071
adamc@552 2072
adamc@1198 2073 \section{\label{structure}The Structure of Web Applications}
adamc@553 2074
adamc@1127 2075 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 2076
adamc@553 2077 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 2078
adamc@553 2079 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 2080
adamc@558 2081 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 2082
adamc@660 2083 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 2084
adamc@789 2085 \medskip
adamc@789 2086
adamc@789 2087 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 2088
adamc@789 2089 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 2090
adamc@553 2091
adamc@897 2092 \section{The Foreign Function Interface}
adamc@897 2093
adamc@897 2094 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 2095
adamc@897 2096 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 2097
adamc@897 2098 \begin{itemize}
adamc@897 2099 \item \texttt{clientOnly Module.ident} registers a value as being allowed only in client-side code.
adamc@897 2100 \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 2101 \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 2102 \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 2103 \item \texttt{include FILE} requests inclusion of a C header file.
adamc@897 2104 \item \texttt{jsFunc Module.ident=name} gives a mapping from an Ur name for a value to a JavaScript name.
adamc@897 2105 \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 2106 \item \texttt{script URL} requests inclusion of a JavaScript source file within application HTML.
adamc@897 2107 \item \texttt{serverOnly Module.ident} registers a value as being allowed only in server-side code.
adamc@897 2108 \end{itemize}
adamc@897 2109
adamc@897 2110 \subsection{Writing C FFI Code}
adamc@897 2111
adamc@897 2112 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 2113
adamc@897 2114 \begin{itemize}
adamc@897 2115 \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 2116 \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 2117 \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 2118 \end{itemize}
adamc@897 2119
adamc@897 2120 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 2121 \begin{itemize}
adamc@897 2122 \item \begin{verbatim}
adamc@897 2123 void uw_error(uw_context, failure_kind, const char *fmt, ...);
adamc@897 2124 \end{verbatim}
adamc@897 2125 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 2126
adamc@897 2127 \item \begin{verbatim}
adamc@897 2128 void uw_push_cleanup(uw_context, void (*func)(void *), void *arg);
adamc@897 2129 void uw_pop_cleanup(uw_context);
adamc@897 2130 \end{verbatim}
adamc@897 2131 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 2132
adamc@897 2133 \item \begin{verbatim}
adamc@897 2134 void *uw_malloc(uw_context, size_t);
adamc@897 2135 \end{verbatim}
adamc@897 2136 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 2137
adamc@897 2138 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 2139
adamc@897 2140 \item \begin{verbatim}
adamc@897 2141 typedef void (*uw_callback)(void *);
adamc@897 2142 void uw_register_transactional(uw_context, void *data, uw_callback commit,
adamc@897 2143 uw_callback rollback, uw_callback free);
adamc@897 2144 \end{verbatim}
adamc@897 2145 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 2146
adamc@1085 2147 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 2148
adamc@1085 2149 \item \begin{verbatim}
adamc@1085 2150 void *uw_get_global(uw_context, char *name);
adamc@1085 2151 void uw_set_global(uw_context, char *name, void *data, uw_callback free);
adamc@1085 2152 \end{verbatim}
adamc@1085 2153 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 2154
adamc@897 2155 \end{itemize}
adamc@897 2156
adamc@897 2157 \subsection{Writing JavaScript FFI Code}
adamc@897 2158
adamc@897 2159 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 2160
adamc@897 2161 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 2162
adamc@897 2163 \begin{itemize}
adamc@897 2164 \item Integers, floats, strings, characters, and booleans are represented in the usual JavaScript way.
adamc@985 2165 \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 2166 \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 2167 \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 2168 \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 2169 \end{itemize}
adamc@897 2170
adamc@897 2171 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 2172
adamc@897 2173
adamc@552 2174 \section{Compiler Phases}
adamc@552 2175
adamc@552 2176 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 2177
adamc@552 2178 In this section, we step through the main phases of compilation, noting what consequences each phase has for effective programming.
adamc@552 2179
adamc@552 2180 \subsection{Parse}
adamc@552 2181
adamc@552 2182 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 2183
adamc@552 2184 \subsection{Elaborate}
adamc@552 2185
adamc@552 2186 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 2187
adamc@552 2188 \subsection{Unnest}
adamc@552 2189
adamc@552 2190 Named local function definitions are moved to the top level, to avoid the need to generate closures.
adamc@552 2191
adamc@552 2192 \subsection{Corify}
adamc@552 2193
adamc@552 2194 Module system features are compiled away, through inlining of functor definitions at application sites. Afterward, most abstraction boundaries are broken, facilitating optimization.
adamc@552 2195
adamc@552 2196 \subsection{Especialize}
adamc@552 2197
adamc@552 2198 Functions are specialized to particular argument patterns. This is an important trick for avoiding the need to maintain any closures at runtime.
adamc@552 2199
adamc@552 2200 \subsection{Untangle}
adamc@552 2201
adamc@552 2202 Remove unnecessary mutual recursion, splitting recursive groups into strongly-connected components.
adamc@552 2203
adamc@552 2204 \subsection{Shake}
adamc@552 2205
adamc@552 2206 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 2207
adamc@661 2208 \subsection{Rpcify}
adamc@661 2209
adamc@661 2210 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 2211
adamc@661 2212 \subsection{Untangle, Shake}
adamc@661 2213
adamc@661 2214 Repeat these simplifications.
adamc@661 2215
adamc@553 2216 \subsection{\label{tag}Tag}
adamc@552 2217
adamc@552 2218 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 2219
adamc@552 2220 \subsection{Reduce}
adamc@552 2221
adamc@552 2222 Apply definitional equality rules to simplify the program as much as possible. This effectively includes inlining of every non-recursive definition.
adamc@552 2223
adamc@552 2224 \subsection{Unpoly}
adamc@552 2225
adamc@552 2226 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 2227
adamc@552 2228 \subsection{Specialize}
adamc@552 2229
adamc@558 2230 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 2231
adamc@552 2232 \subsection{Shake}
adamc@552 2233
adamc@558 2234 Here the compiler repeats the earlier Shake phase.
adamc@552 2235
adamc@552 2236 \subsection{Monoize}
adamc@552 2237
adamc@552 2238 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 2239
adamc@552 2240 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 2241
adamc@552 2242 \subsection{MonoOpt}
adamc@552 2243
adamc@552 2244 Simple algebraic laws are applied to simplify the program, focusing especially on efficient imperative generation of HTML pages.
adamc@552 2245
adamc@552 2246 \subsection{MonoUntangle}
adamc@552 2247
adamc@552 2248 Unnecessary mutual recursion is broken up again.
adamc@552 2249
adamc@552 2250 \subsection{MonoReduce}
adamc@552 2251
adamc@552 2252 Equivalents of the definitional equality rules are applied to simplify programs, with inlining again playing a major role.
adamc@552 2253
adamc@552 2254 \subsection{MonoShake, MonoOpt}
adamc@552 2255
adamc@552 2256 Unneeded declarations are removed, and basic optimizations are repeated.
adamc@552 2257
adamc@552 2258 \subsection{Fuse}
adamc@552 2259
adamc@552 2260 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 2261
adamc@552 2262 \subsection{MonoUntangle, MonoShake}
adamc@552 2263
adamc@552 2264 Fuse often creates more opportunities to remove spurious mutual recursion.
adamc@552 2265
adamc@552 2266 \subsection{Pathcheck}
adamc@552 2267
adamc@552 2268 The compiler checks that no link or action name has been used more than once.
adamc@552 2269
adamc@552 2270 \subsection{Cjrize}
adamc@552 2271
adamc@552 2272 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 2273
adamc@552 2274 \subsection{C Compilation and Linking}
adamc@552 2275
adamc@552 2276 The output of the last phase is pretty-printed as C source code and passed to GCC.
adamc@552 2277
adamc@552 2278
adamc@524 2279 \end{document}