annotate doc/manual.tex @ 1422:07ef5771568d

Notice that Basis.now is effectful; smarter JavaScript encoding of initial source values built using server-side expressions that can't be turned into JavaScript
author Adam Chlipala <adam@chlipala.net>
date Tue, 08 Feb 2011 16:54:01 -0500
parents 3dab4696d116
children 8524a1709821
rev   line source
adamc@524 1 \documentclass{article}
adamc@554 2 \usepackage{fullpage,amsmath,amssymb,proof,url}
adamc@524 3
adamc@524 4 \newcommand{\cd}[1]{\texttt{#1}}
adamc@524 5 \newcommand{\mt}[1]{\mathsf{#1}}
adamc@524 6
adamc@524 7 \newcommand{\rc}{+ \hspace{-.075in} + \;}
adamc@527 8 \newcommand{\rcut}{\; \texttt{--} \;}
adamc@527 9 \newcommand{\rcutM}{\; \texttt{---} \;}
adamc@524 10
adamc@524 11 \begin{document}
adamc@524 12
adamc@524 13 \title{The Ur/Web Manual}
adamc@524 14 \author{Adam Chlipala}
adamc@524 15
adamc@524 16 \maketitle
adamc@524 17
adamc@540 18 \tableofcontents
adamc@540 19
adamc@554 20
adamc@554 21 \section{Introduction}
adamc@554 22
adamc@1160 23 \emph{Ur} is a programming language designed to introduce richer type system features into functional programming in the tradition of ML and Haskell. Ur is functional, pure, statically-typed, and strict. Ur supports a powerful kind of \emph{metaprogramming} based on \emph{type-level computation with type-level records}.
adamc@554 24
adamc@554 25 \emph{Ur/Web} is Ur plus a special standard library and associated rules for parsing and optimization. Ur/Web supports construction of dynamic web applications backed by SQL databases. The signature of the standard library is such that well-typed Ur/Web programs ``don't go wrong'' in a very broad sense. Not only do they not crash during particular page generations, but they also may not:
adamc@554 26
adamc@554 27 \begin{itemize}
adamc@554 28 \item Suffer from any kinds of code-injection attacks
adamc@554 29 \item Return invalid HTML
adamc@554 30 \item Contain dead intra-application links
adamc@554 31 \item Have mismatches between HTML forms and the fields expected by their handlers
adamc@652 32 \item Include client-side code that makes incorrect assumptions about the ``AJAX''-style services that the remote web server provides
adamc@554 33 \item Attempt invalid SQL queries
adamc@652 34 \item Use improper marshaling or unmarshaling in communication with SQL databases or between browsers and web servers
adamc@554 35 \end{itemize}
adamc@554 36
adamc@554 37 This type safety is just the foundation of the Ur/Web methodology. It is also possible to use metaprogramming to build significant application pieces by analysis of type structure. For instance, the demo includes an ML-style functor for building an admin interface for an arbitrary SQL table. The type system guarantees that the admin interface sub-application that comes out will always be free of the above-listed bugs, no matter which well-typed table description is given as input.
adamc@554 38
adamc@652 39 The Ur/Web compiler also produces very efficient object code that does not use garbage collection. These compiled programs will often be even more efficient than what most programmers would bother to write in C. The compiler also generates JavaScript versions of client-side code, with no need to write those parts of applications in a different language.
adamc@554 40
adamc@554 41 \medskip
adamc@554 42
adamc@554 43 The official web site for Ur is:
adamc@554 44 \begin{center}
adamc@554 45 \url{http://www.impredicative.com/ur/}
adamc@554 46 \end{center}
adamc@554 47
adamc@555 48
adamc@555 49 \section{Installation}
adamc@555 50
adamc@555 51 If you are lucky, then the following standard command sequence will suffice for installation, in a directory to which you have unpacked the latest distribution tarball.
adamc@555 52
adamc@555 53 \begin{verbatim}
adamc@555 54 ./configure
adamc@555 55 make
adamc@555 56 sudo make install
adamc@555 57 \end{verbatim}
adamc@555 58
adam@1368 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 development files for the OpenSSL C library. As of this writing, in the ``testing'' version of Debian Linux, this command will install the more uncommon of these dependencies:
adamc@896 60 \begin{verbatim}
adam@1368 61 apt-get install mlton libssl-dev
adamc@896 62 \end{verbatim}
adamc@555 63
adamc@896 64 To build programs that access SQL databases, you also need one of these client libraries for supported backends.
adamc@555 65 \begin{verbatim}
adamc@896 66 apt-get install libpq-dev libmysqlclient15-dev libsqlite3-dev
adamc@555 67 \end{verbatim}
adamc@555 68
adamc@555 69 It is also possible to access the modules of the Ur/Web compiler interactively, within Standard ML of New Jersey. To install the prerequisites in Debian testing:
adamc@555 70 \begin{verbatim}
adamc@555 71 apt-get install smlnj libsmlnj-smlnj ml-yacc ml-lpt
adamc@555 72 \end{verbatim}
adamc@555 73
adamc@555 74 To begin an interactive session with the Ur compiler modules, run \texttt{make smlnj}, and then, from within an \texttt{sml} session, run \texttt{CM.make "src/urweb.cm";}. The \texttt{Compiler} module is the main entry point.
adamc@555 75
adamc@896 76 To run an SQL-backed application with a backend besides SQLite, you will probably want to install one of these servers.
adamc@555 77
adamc@555 78 \begin{verbatim}
adam@1400 79 apt-get install postgresql-8.4 mysql-server-5.1
adamc@555 80 \end{verbatim}
adamc@555 81
adamc@555 82 To use the Emacs mode, you must have a modern Emacs installed. We assume that you already know how to do this, if you're in the business of looking for an Emacs mode. The demo generation facility of the compiler will also call out to Emacs to syntax-highlight code, and that process depends on the \texttt{htmlize} module, which can be installed in Debian testing via:
adamc@555 83
adamc@555 84 \begin{verbatim}
adamc@555 85 apt-get install emacs-goodies-el
adamc@555 86 \end{verbatim}
adamc@555 87
adamc@555 88 Even with the right packages installed, configuration and building might fail to work. After you run \texttt{./configure}, you will see the values of some named environment variables printed. You may need to adjust these values to get proper installation for your system. To change a value, store your preferred alternative in the corresponding UNIX environment variable, before running \texttt{./configure}. For instance, here is how to change the list of extra arguments that the Ur/Web compiler will pass to GCC on every invocation.
adamc@555 89
adamc@555 90 \begin{verbatim}
adamc@555 91 GCCARGS=-fnested-functions ./configure
adamc@555 92 \end{verbatim}
adamc@555 93
adamc@1137 94 Some Mac OS X users have reported needing to use this particular GCCARGS value.
adamc@1137 95
adamc@1161 96 Since the author is still getting a handle on the GNU Autotools that provide the build system, you may need to do some further work to get started, especially in environments with significant differences from Linux (where most testing is done). One OS X user reported needing to run \texttt{./configure} with \texttt{CFLAGS=-I/opt/local/include}, since this directory wound up holding a header file associated with a \texttt{libmhash} package installed via DarwinPorts. Further, to get libpq to link, another user reported setting \texttt{GCCARGS="-I/opt/local/include -L/opt/local/lib/postgresql84"}, after creating a symbolic link with \texttt{ln -s /opt/local/include/postgresql84 /opt/local/include/postgresql}.
adamc@555 97
adamc@555 98 The Emacs mode can be set to autoload by adding the following to your \texttt{.emacs} file.
adamc@555 99
adamc@555 100 \begin{verbatim}
adamc@555 101 (add-to-list 'load-path "/usr/local/share/emacs/site-lisp/urweb-mode")
adamc@555 102 (load "urweb-mode-startup")
adamc@555 103 \end{verbatim}
adamc@555 104
adamc@555 105 Change the path in the first line if you chose a different Emacs installation path during configuration.
adamc@555 106
adamc@555 107
adamc@556 108 \section{Command-Line Compiler}
adamc@556 109
adamc@556 110 \subsection{Project Files}
adamc@556 111
adamc@556 112 The basic inputs to the \texttt{urweb} compiler are project files, which have the extension \texttt{.urp}. Here is a sample \texttt{.urp} file.
adamc@556 113
adamc@556 114 \begin{verbatim}
adamc@556 115 database dbname=test
adamc@556 116 sql crud1.sql
adamc@556 117
adamc@556 118 crud
adamc@556 119 crud1
adamc@556 120 \end{verbatim}
adamc@556 121
adamc@556 122 The \texttt{database} line gives the database information string to pass to libpq. In this case, the string only says to connect to a local database named \texttt{test}.
adamc@556 123
adamc@556 124 The \texttt{sql} line asks for an SQL source file to be generated, giving the commands to run to create the tables and sequences that this application expects to find. After building this \texttt{.urp} file, the following commands could be used to initialize the database, assuming that the current UNIX user exists as a Postgres user with database creation privileges:
adamc@556 125
adamc@556 126 \begin{verbatim}
adamc@556 127 createdb test
adamc@556 128 psql -f crud1.sql test
adamc@556 129 \end{verbatim}
adamc@556 130
adam@1331 131 A blank line separates the named directives from a list of modules to include in the project. Any line may contain a shell-script-style comment, where any suffix of a line starting at a hash character \texttt{\#} is ignored.
adamc@556 132
adamc@556 133 For each entry \texttt{M} in the module list, the file \texttt{M.urs} is included in the project if it exists, and the file \texttt{M.ur} must exist and is always included.
adamc@556 134
adamc@783 135 Here is the complete list of directive forms. ``FFI'' stands for ``foreign function interface,'' Ur's facility for interaction between Ur programs and C and JavaScript libraries.
adamc@783 136 \begin{itemize}
adamc@783 137 \item \texttt{[allow|deny] [url|mime] PATTERN} registers a rule governing which URLs or MIME types are allowed in this application. The first such rule to match a URL or MIME type determines the verdict. If \texttt{PATTERN} ends in \texttt{*}, it is interpreted as a prefix rule. Otherwise, a string must match it exactly.
adam@1400 138 \item \texttt{alwaysInline PATH} requests that every call to the referenced function be inlined. Section \ref{structure} explains how functions are assigned path strings.
adamc@1171 139 \item \texttt{benignEffectful Module.ident} registers an FFI function or transaction as having side effects. The optimizer avoids removing, moving, or duplicating calls to such functions. Every effectful FFI function must be registered, or the optimizer may make invalid transformations. This version of the \texttt{effectful} directive registers that this function has only session-local side effects.
adamc@783 140 \item \texttt{clientOnly Module.ident} registers an FFI function or transaction that may only be run in client browsers.
adamc@783 141 \item \texttt{clientToServer Module.ident} adds FFI type \texttt{Module.ident} to the list of types that are OK to marshal from clients to servers. Values like XML trees and SQL queries are hard to marshal without introducing expensive validity checks, so it's easier to ensure that the server never trusts clients to send such values. The file \texttt{include/urweb.h} shows examples of the C support functions that are required of any type that may be marshalled. These include \texttt{attrify}, \texttt{urlify}, and \texttt{unurlify} functions.
adamc@783 142 \item \texttt{database DBSTRING} sets the string to pass to libpq to open a database connection.
adamc@783 143 \item \texttt{debug} saves some intermediate C files, which is mostly useful to help in debugging the compiler itself.
adamc@783 144 \item \texttt{effectful Module.ident} registers an FFI function or transaction as having side effects. The optimizer avoids removing, moving, or duplicating calls to such functions. Every effectful FFI function must be registered, or the optimizer may make invalid transformations.
adamc@783 145 \item \texttt{exe FILENAME} sets the filename to which to write the output executable. The default for file \texttt{P.urp} is \texttt{P.exe}.
adamc@783 146 \item \texttt{ffi FILENAME} reads the file \texttt{FILENAME.urs} to determine the interface to a new FFI module. The name of the module is calculated from \texttt{FILENAME} in the same way as for normal source files. See the files \texttt{include/urweb.h} and \texttt{src/c/urweb.c} for examples of C headers and implementations for FFI modules. In general, every type or value \texttt{Module.ident} becomes \texttt{uw\_Module\_ident} in C.
adamc@1099 147 \item \texttt{include FILENAME} adds \texttt{FILENAME} to the list of files to be \texttt{\#include}d in C sources. This is most useful for interfacing with new FFI modules.
adamc@783 148 \item \texttt{jsFunc Module.ident=name} gives the JavaScript name of an FFI value.
adamc@1089 149 \item \texttt{library FILENAME} parses \texttt{FILENAME.urp} and merges its contents with the rest of the current file's contents. If \texttt{FILENAME.urp} doesn't exist, the compiler also tries \texttt{FILENAME/lib.urp}.
adam@1309 150 \item \texttt{limit class num} sets a resource usage limit for generated applications. The limit \texttt{class} will be set to the non-negative integer \texttt{num}. The classes are:
adam@1309 151 \begin{itemize}
adam@1309 152 \item \texttt{cleanup}: maximum number of cleanup operations (e.g., entries recording the need to deallocate certain temporary objects) that may be active at once per request
adam@1309 153 \item \texttt{database}: maximum size of database files (currently only used by SQLite)
adam@1309 154 \item \texttt{deltas}: maximum number of messages sendable in a single request handler with \texttt{Basis.send}
adam@1309 155 \item \texttt{globals}: maximum number of global variables that FFI libraries may set in a single request context
adam@1309 156 \item \texttt{headers}: maximum size (in bytes) of per-request buffer used to hold HTTP headers for generated pages
adam@1309 157 \item \texttt{heap}: maximum size (in bytes) of per-request heap for dynamically-allocated data
adam@1309 158 \item \texttt{inputs}: maximum number of top-level form fields per request
adam@1309 159 \item \texttt{messages}: maximum size (in bytes) of per-request buffer used to hold a single outgoing message sent with \texttt{Basis.send}
adam@1309 160 \item \texttt{page}: maximum size (in bytes) of per-request buffer used to hold HTML content of generated pages
adam@1309 161 \item \texttt{script}: maximum size (in bytes) of per-request buffer used to hold JavaScript content of generated pages
adam@1309 162 \item \texttt{subinputs}: maximum number of form fields per request, excluding top-level fields
adam@1309 163 \item \texttt{time}: maximum running time of a single page request, in units of approximately 0.1 seconds
adam@1309 164 \item \texttt{transactionals}: maximum number of custom transactional actions (e.g., sending an e-mail) that may be run in a single page generation
adam@1309 165 \end{itemize}
adamc@783 166 \item \texttt{link FILENAME} adds \texttt{FILENAME} to the list of files to be passed to the GCC linker at the end of compilation. This is most useful for importing extra libraries needed by new FFI modules.
adam@1332 167 \item \texttt{minHeap NUMBYTES} sets the initial size for thread-local heaps used in handling requests. These heaps grow automatically as needed (up to any maximum set with \texttt{limit}), but each regrow requires restarting the request handling process.
adam@1297 168 \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@852 169 \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@783 170 \item \texttt{prefix PREFIX} sets the prefix included before every URI within the generated application. The default is \texttt{/}.
adamc@783 171 \item \texttt{profile} generates an executable that may be used with gprof.
adam@1300 172 \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 173 \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@783 174 \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@783 175 \item \texttt{serverOnly Module.ident} registers an FFI function or transaction that may only be run on the server.
adamc@1164 176 \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@783 177 \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@783 178 \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@783 179 \end{itemize}
adamc@701 180
adamc@701 181
adamc@557 182 \subsection{Building an Application}
adamc@557 183
adamc@557 184 To compile project \texttt{P.urp}, simply run
adamc@557 185 \begin{verbatim}
adamc@557 186 urweb P
adamc@557 187 \end{verbatim}
adamc@1198 188 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@557 189
adamc@557 190 To time how long the different compiler phases run, without generating an executable, run
adamc@557 191 \begin{verbatim}
adamc@557 192 urweb -timing P
adamc@557 193 \end{verbatim}
adamc@557 194
adamc@1086 195 To stop the compilation process after type-checking, run
adamc@1086 196 \begin{verbatim}
adamc@1086 197 urweb -tc P
adamc@1086 198 \end{verbatim}
adamc@1086 199
adamc@1170 200 To output information relevant to CSS stylesheets (and not finish regular compilation), run
adamc@1170 201 \begin{verbatim}
adamc@1170 202 urweb -css P
adamc@1170 203 \end{verbatim}
adamc@1170 204 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 205
adamc@896 206 Some other command-line parameters are accepted:
adamc@896 207 \begin{itemize}
adamc@896 208 \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@896 209
adamc@896 210 \item \texttt{-dbms [postgres|mysql|sqlite]}: Sets the database backend to use.
adamc@896 211 \begin{itemize}
adamc@896 212 \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@896 213
adamc@896 214 A command sequence like this can initialize a Postgres database, using a file \texttt{app.sql} generated by the compiler:
adamc@896 215 \begin{verbatim}
adamc@896 216 createdb app
adamc@896 217 psql -f app.sql app
adamc@896 218 \end{verbatim}
adamc@896 219
adamc@896 220 \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@896 221
adamc@896 222 A command sequence like this can initialize a MySQL database:
adamc@896 223 \begin{verbatim}
adamc@896 224 echo "CREATE DATABASE app" | mysql
adamc@896 225 mysql -D app <app.sql
adamc@896 226 \end{verbatim}
adamc@896 227
adamc@896 228 \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@896 229
adamc@896 230 A command like this can initialize an SQLite database:
adamc@896 231 \begin{verbatim}
adamc@896 232 sqlite3 path/to/database/file <app.sql
adamc@896 233 \end{verbatim}
adamc@896 234 \end{itemize}
adamc@896 235
adam@1309 236 \item \texttt{-limit class num}: Equivalent to the \texttt{limit} directive from \texttt{.urp} files
adam@1309 237
adamc@896 238 \item \texttt{-output FILENAME}: Set where the application executable is written.
adamc@896 239
adamc@1127 240 \item \texttt{-path NAME VALUE}: Set the value of path variable \texttt{\$NAME} to \texttt{VALUE}, for use in \texttt{.urp} files.
adamc@1127 241
adam@1335 242 \item \texttt{-prefix PREFIX}: Equivalent to the \texttt{prefix} directive from \texttt{.urp} files
adam@1335 243
adamc@896 244 \item \texttt{-protocol [http|cgi|fastcgi]}: Set the protocol that the generated application speaks.
adamc@896 245 \begin{itemize}
adamc@896 246 \item \texttt{http}: This is the default. It is for building standalone web servers that can be accessed by web browsers directly.
adamc@896 247
adamc@896 248 \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@896 249
adamc@896 250 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@896 251 \begin{verbatim}
adamc@896 252 ScriptAlias /Hello /path/to/hello.exe
adamc@896 253 \end{verbatim}
adamc@896 254
adamc@1163 255 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 256 \begin{verbatim}
adamc@1163 257 Options +ExecCGI
adamc@1163 258 AddHandler cgi-script .exe
adamc@1163 259 \end{verbatim}
adamc@1163 260
adamc@1163 261 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 262 \begin{verbatim}
adamc@1163 263 prefix /dir/script.exe/
adamc@1163 264 \end{verbatim}
adamc@1163 265
adamc@1163 266 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 267
adamc@1164 268 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 269
adamc@896 270 \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@896 271
adamc@896 272 To configure a FastCGI program with Apache, one could combine the above \texttt{ScriptAlias} line with a line like this:
adamc@896 273 \begin{verbatim}
adamc@896 274 FastCgiServer /path/to/hello.exe -idle-timeout 99999
adamc@896 275 \end{verbatim}
adamc@896 276 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@896 277
adamc@896 278 Here is some lighttpd configuration for the same application.
adamc@896 279 \begin{verbatim}
adamc@896 280 fastcgi.server = (
adamc@896 281 "/Hello/" =>
adamc@896 282 (( "bin-path" => "/path/to/hello.exe",
adamc@896 283 "socket" => "/tmp/hello",
adamc@896 284 "check-local" => "disable",
adamc@896 285 "docroot" => "/",
adamc@896 286 "max-procs" => "1"
adamc@896 287 ))
adamc@896 288 )
adamc@896 289 \end{verbatim}
adamc@896 290 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@896 291
adamc@896 292 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@896 293 \end{itemize}
adamc@896 294
adamc@1127 295 \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 296
adamc@1164 297 \item \texttt{-sigfile PATH}: Same as the \texttt{sigfile} directive in \texttt{.urp} files
adamc@1164 298
adamc@896 299 \item \texttt{-sql FILENAME}: Set where a database set-up SQL script is written.
adamc@1095 300
adamc@1095 301 \item \texttt{-static}: Link the runtime system statically. The default is to link against dynamic libraries.
adamc@896 302 \end{itemize}
adamc@896 303
adam@1297 304 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@556 305
adamc@529 306 \section{Ur Syntax}
adamc@529 307
adamc@784 308 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@524 309
adamc@524 310 \subsection{Lexical Conventions}
adamc@524 311
adamc@524 312 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@524 313
adamc@524 314 \begin{center}
adamc@524 315 \begin{tabular}{rl}
adamc@524 316 \textbf{\LaTeX} & \textbf{ASCII} \\
adamc@524 317 $\to$ & \cd{->} \\
adamc@652 318 $\longrightarrow$ & \cd{-->} \\
adamc@524 319 $\times$ & \cd{*} \\
adamc@524 320 $\lambda$ & \cd{fn} \\
adamc@524 321 $\Rightarrow$ & \cd{=>} \\
adamc@652 322 $\Longrightarrow$ & \cd{==>} \\
adamc@529 323 $\neq$ & \cd{<>} \\
adamc@529 324 $\leq$ & \cd{<=} \\
adamc@529 325 $\geq$ & \cd{>=} \\
adamc@524 326 \\
adamc@524 327 $x$ & Normal textual identifier, not beginning with an uppercase letter \\
adamc@525 328 $X$ & Normal textual identifier, beginning with an uppercase letter \\
adamc@524 329 \end{tabular}
adamc@524 330 \end{center}
adamc@524 331
adamc@525 332 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@524 333
adamc@873 334 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@526 335
adamc@527 336 This version of the manual doesn't include operator precedences; see \texttt{src/urweb.grm} for that.
adamc@527 337
adam@1297 338 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 339
adamc@552 340 \subsection{\label{core}Core Syntax}
adamc@524 341
adamc@524 342 \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@524 343 $$\begin{array}{rrcll}
adamc@524 344 \textrm{Kinds} & \kappa &::=& \mt{Type} & \textrm{proper types} \\
adamc@525 345 &&& \mt{Unit} & \textrm{the trivial constructor} \\
adamc@525 346 &&& \mt{Name} & \textrm{field names} \\
adamc@525 347 &&& \kappa \to \kappa & \textrm{type-level functions} \\
adamc@525 348 &&& \{\kappa\} & \textrm{type-level records} \\
adamc@525 349 &&& (\kappa\times^+) & \textrm{type-level tuples} \\
adamc@652 350 &&& X & \textrm{variable} \\
adamc@652 351 &&& X \longrightarrow k & \textrm{kind-polymorphic type-level function} \\
adamc@529 352 &&& \_\_ & \textrm{wildcard} \\
adamc@525 353 &&& (\kappa) & \textrm{explicit precedence} \\
adamc@524 354 \end{array}$$
adamc@524 355
adamc@524 356 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@524 357 $$\begin{array}{rrcll}
adamc@524 358 \textrm{Explicitness} & ? &::=& :: & \textrm{explicit} \\
adamc@558 359 &&& ::: & \textrm{implicit}
adamc@524 360 \end{array}$$
adamc@524 361
adamc@524 362 \emph{Constructors} are the main class of compile-time-only data. They include proper types and are classified by kinds.
adamc@524 363 $$\begin{array}{rrcll}
adamc@524 364 \textrm{Constructors} & c, \tau &::=& (c) :: \kappa & \textrm{kind annotation} \\
adamc@530 365 &&& \hat{x} & \textrm{constructor variable} \\
adamc@524 366 \\
adamc@525 367 &&& \tau \to \tau & \textrm{function type} \\
adamc@525 368 &&& x \; ? \; \kappa \to \tau & \textrm{polymorphic function type} \\
adamc@652 369 &&& X \longrightarrow \tau & \textrm{kind-polymorphic function type} \\
adamc@525 370 &&& \$ c & \textrm{record type} \\
adamc@524 371 \\
adamc@525 372 &&& c \; c & \textrm{type-level function application} \\
adamc@530 373 &&& \lambda x \; :: \; \kappa \Rightarrow c & \textrm{type-level function abstraction} \\
adamc@524 374 \\
adamc@652 375 &&& X \Longrightarrow c & \textrm{type-level kind-polymorphic function abstraction} \\
adamc@655 376 &&& c [\kappa] & \textrm{type-level kind-polymorphic function application} \\
adamc@652 377 \\
adamc@525 378 &&& () & \textrm{type-level unit} \\
adamc@525 379 &&& \#X & \textrm{field name} \\
adamc@524 380 \\
adamc@525 381 &&& [(c = c)^*] & \textrm{known-length type-level record} \\
adamc@525 382 &&& c \rc c & \textrm{type-level record concatenation} \\
adamc@652 383 &&& \mt{map} & \textrm{type-level record map} \\
adamc@524 384 \\
adamc@558 385 &&& (c,^+) & \textrm{type-level tuple} \\
adamc@525 386 &&& c.n & \textrm{type-level tuple projection ($n \in \mathbb N^+$)} \\
adamc@524 387 \\
adamc@652 388 &&& [c \sim c] \Rightarrow \tau & \textrm{guarded type} \\
adamc@524 389 \\
adamc@529 390 &&& \_ :: \kappa & \textrm{wildcard} \\
adamc@525 391 &&& (c) & \textrm{explicit precedence} \\
adamc@530 392 \\
adamc@530 393 \textrm{Qualified uncapitalized variables} & \hat{x} &::=& x & \textrm{not from a module} \\
adamc@530 394 &&& M.x & \textrm{projection from a module} \\
adamc@525 395 \end{array}$$
adamc@525 396
adamc@655 397 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@655 398
adamc@525 399 Modules of the module system are described by \emph{signatures}.
adamc@525 400 $$\begin{array}{rrcll}
adamc@525 401 \textrm{Signatures} & S &::=& \mt{sig} \; s^* \; \mt{end} & \textrm{constant} \\
adamc@525 402 &&& X & \textrm{variable} \\
adamc@525 403 &&& \mt{functor}(X : S) : S & \textrm{functor} \\
adamc@529 404 &&& S \; \mt{where} \; \mt{con} \; x = c & \textrm{concretizing an abstract constructor} \\
adamc@525 405 &&& M.X & \textrm{projection from a module} \\
adamc@525 406 \\
adamc@525 407 \textrm{Signature items} & s &::=& \mt{con} \; x :: \kappa & \textrm{abstract constructor} \\
adamc@525 408 &&& \mt{con} \; x :: \kappa = c & \textrm{concrete constructor} \\
adamc@528 409 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529 410 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@525 411 &&& \mt{val} \; x : \tau & \textrm{value} \\
adamc@525 412 &&& \mt{structure} \; X : S & \textrm{sub-module} \\
adamc@525 413 &&& \mt{signature} \; X = S & \textrm{sub-signature} \\
adamc@525 414 &&& \mt{include} \; S & \textrm{signature inclusion} \\
adamc@525 415 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@654 416 &&& \mt{class} \; x :: \kappa & \textrm{abstract constructor class} \\
adamc@654 417 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@525 418 \\
adamc@525 419 \textrm{Datatype constructors} & dc &::=& X & \textrm{nullary constructor} \\
adamc@525 420 &&& X \; \mt{of} \; \tau & \textrm{unary constructor} \\
adamc@524 421 \end{array}$$
adamc@524 422
adamc@526 423 \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@526 424 $$\begin{array}{rrcll}
adamc@526 425 \textrm{Patterns} & p &::=& \_ & \textrm{wildcard} \\
adamc@526 426 &&& x & \textrm{variable} \\
adamc@526 427 &&& \ell & \textrm{constant} \\
adamc@526 428 &&& \hat{X} & \textrm{nullary constructor} \\
adamc@526 429 &&& \hat{X} \; p & \textrm{unary constructor} \\
adamc@526 430 &&& \{(x = p,)^*\} & \textrm{rigid record pattern} \\
adamc@526 431 &&& \{(x = p,)^+, \ldots\} & \textrm{flexible record pattern} \\
adamc@852 432 &&& p : \tau & \textrm{type annotation} \\
adamc@527 433 &&& (p) & \textrm{explicit precedence} \\
adamc@526 434 \\
adamc@529 435 \textrm{Qualified capitalized variables} & \hat{X} &::=& X & \textrm{not from a module} \\
adamc@526 436 &&& M.X & \textrm{projection from a module} \\
adamc@526 437 \end{array}$$
adamc@526 438
adamc@527 439 \emph{Expressions} are the main run-time entities, corresponding to both ``expressions'' and ``statements'' in mainstream imperative languages.
adamc@527 440 $$\begin{array}{rrcll}
adamc@527 441 \textrm{Expressions} & e &::=& e : \tau & \textrm{type annotation} \\
adamc@529 442 &&& \hat{x} & \textrm{variable} \\
adamc@529 443 &&& \hat{X} & \textrm{datatype constructor} \\
adamc@527 444 &&& \ell & \textrm{constant} \\
adamc@527 445 \\
adamc@527 446 &&& e \; e & \textrm{function application} \\
adamc@527 447 &&& \lambda x : \tau \Rightarrow e & \textrm{function abstraction} \\
adamc@527 448 &&& e [c] & \textrm{polymorphic function application} \\
adamc@852 449 &&& \lambda [x \; ? \; \kappa] \Rightarrow e & \textrm{polymorphic function abstraction} \\
adamc@655 450 &&& e [\kappa] & \textrm{kind-polymorphic function application} \\
adamc@652 451 &&& X \Longrightarrow e & \textrm{kind-polymorphic function abstraction} \\
adamc@527 452 \\
adamc@527 453 &&& \{(c = e,)^*\} & \textrm{known-length record} \\
adamc@527 454 &&& e.c & \textrm{record field projection} \\
adamc@527 455 &&& e \rc e & \textrm{record concatenation} \\
adamc@527 456 &&& e \rcut c & \textrm{removal of a single record field} \\
adamc@527 457 &&& e \rcutM c & \textrm{removal of multiple record fields} \\
adamc@527 458 \\
adamc@527 459 &&& \mt{let} \; ed^* \; \mt{in} \; e \; \mt{end} & \textrm{local definitions} \\
adamc@527 460 \\
adamc@527 461 &&& \mt{case} \; e \; \mt{of} \; (p \Rightarrow e|)^+ & \textrm{pattern matching} \\
adamc@527 462 \\
adamc@654 463 &&& \lambda [c \sim c] \Rightarrow e & \textrm{guarded expression abstraction} \\
adamc@654 464 &&& e \; ! & \textrm{guarded expression application} \\
adamc@527 465 \\
adamc@527 466 &&& \_ & \textrm{wildcard} \\
adamc@527 467 &&& (e) & \textrm{explicit precedence} \\
adamc@527 468 \\
adamc@527 469 \textrm{Local declarations} & ed &::=& \cd{val} \; x : \tau = e & \textrm{non-recursive value} \\
adamc@527 470 &&& \cd{val} \; \cd{rec} \; (x : \tau = e \; \cd{and})^+ & \textrm{mutually-recursive values} \\
adamc@527 471 \end{array}$$
adamc@527 472
adamc@655 473 As with constructors, we include both abstraction and application for kind polymorphism, but applications are only inferred internally.
adamc@655 474
adamc@528 475 \emph{Declarations} primarily bring new symbols into context.
adamc@528 476 $$\begin{array}{rrcll}
adamc@528 477 \textrm{Declarations} & d &::=& \mt{con} \; x :: \kappa = c & \textrm{constructor synonym} \\
adamc@528 478 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529 479 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@528 480 &&& \mt{val} \; x : \tau = e & \textrm{value} \\
adamc@528 481 &&& \mt{val} \; \cd{rec} \; (x : \tau = e \; \mt{and})^+ & \textrm{mutually-recursive values} \\
adamc@528 482 &&& \mt{structure} \; X : S = M & \textrm{module definition} \\
adamc@528 483 &&& \mt{signature} \; X = S & \textrm{signature definition} \\
adamc@528 484 &&& \mt{open} \; M & \textrm{module inclusion} \\
adamc@528 485 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@528 486 &&& \mt{open} \; \mt{constraints} \; M & \textrm{inclusion of just the constraints from a module} \\
adamc@528 487 &&& \mt{table} \; x : c & \textrm{SQL table} \\
adamc@784 488 &&& \mt{view} \; x : c & \textrm{SQL view} \\
adamc@528 489 &&& \mt{sequence} \; x & \textrm{SQL sequence} \\
adamc@535 490 &&& \mt{cookie} \; x : \tau & \textrm{HTTP cookie} \\
adamc@784 491 &&& \mt{style} \; x : \tau & \textrm{CSS class} \\
adamc@654 492 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@1085 493 &&& \mt{task} \; e = e & \textrm{recurring task} \\
adamc@528 494 \\
adamc@529 495 \textrm{Modules} & M &::=& \mt{struct} \; d^* \; \mt{end} & \textrm{constant} \\
adamc@529 496 &&& X & \textrm{variable} \\
adamc@529 497 &&& M.X & \textrm{projection} \\
adamc@529 498 &&& M(M) & \textrm{functor application} \\
adamc@529 499 &&& \mt{functor}(X : S) : S = M & \textrm{functor abstraction} \\
adamc@528 500 \end{array}$$
adamc@528 501
adamc@528 502 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@527 503
adamc@784 504 We omit some extra possibilities in $\mt{table}$ syntax, deferring them to Section \ref{tables}.
adamc@784 505
adamc@529 506 \subsection{Shorthands}
adamc@529 507
adamc@529 508 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@529 509
adamc@529 510 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@529 511
adamc@529 512 A record type may be written $\{(c = c,)^*\}$, which elaborates to $\$[(c = c,)^*]$.
adamc@529 513
adamc@533 514 The notation $[c_1, \ldots, c_n]$ is shorthand for $[c_1 = (), \ldots, c_n = ()]$.
adamc@533 515
adam@1350 516 A tuple type $\tau_1 \times \ldots \times \tau_n$ expands to a record type $\{1 : \tau_1, \ldots, n : \tau_n\}$, with natural numbers as field names. A tuple expression $(e_1, \ldots, e_n)$ expands to a record expression $\{1 = e_1, \ldots, n = e_n\}$. A tuple pattern $(p_1, \ldots, p_n)$ expands to a rigid record pattern $\{1 = p_1, \ldots, n = p_n\}$. Positive natural numbers may be used in most places where field names would be allowed.
adamc@529 517
adamc@852 518 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@529 519
adam@1306 520 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 521
adamc@529 522 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@529 523
adamc@529 524 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@529 525
adamc@654 526 A signature item or declaration $\mt{class} \; x = \lambda y \Rightarrow c$ may be abbreviated $\mt{class} \; x \; y = c$.
adamc@529 527
adam@1354 528 Handling of implicit and explicit constructor arguments may be tweaked with some prefixes to variable references. An expression $@x$ is a version of $x$ where all type class instance and disjointness arguments have been made explicit. An expression $@@x$ achieves the same effect, additionally making explicit all implicit constructor arguments. The default is that implicit arguments are inserted automatically after any reference to a non-local variable, or after any application of a non-local variable to one or more arguments. For such an expression, implicit wildcard arguments are added for the longest prefix of the expression's type consisting only of implicit polymorphism, type class instances, and disjointness obligations. The same syntax works for variables projected out of modules and for capitalized variables (datatype constructors).
adamc@529 529
adamc@852 530 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@529 531
adamc@852 532 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@852 533
adamc@852 534 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@529 535
adamc@529 536 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@529 537
adamc@852 538 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@852 539
adamc@853 540 A declaration $\mt{table} \; x : \{(c = c,)^*\}$ is elaborated into $\mt{table} \; x : [(c = c,)^*]$.
adamc@529 541
adamc@529 542 The syntax $\mt{where} \; \mt{type}$ is an alternate form of $\mt{where} \; \mt{con}$.
adamc@529 543
adamc@529 544 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@529 545
adamc@529 546 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@529 547
adamc@784 548 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@529 549
adamc@530 550
adamc@530 551 \section{Static Semantics}
adamc@530 552
adamc@530 553 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@530 554
adamc@530 555 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@530 556 \begin{itemize}
adamc@655 557 \item $\Gamma \vdash \kappa$ expresses kind well-formedness.
adamc@530 558 \item $\Gamma \vdash c :: \kappa$ assigns a kind to a constructor in a context.
adamc@530 559 \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@531 560 \item $\Gamma \vdash c \hookrightarrow C$ proves that record constructor $c$ decomposes into set $C$ of field names and record constructors.
adamc@530 561 \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@530 562 \item $\Gamma \vdash e : \tau$ is a standard typing judgment.
adamc@534 563 \item $\Gamma \vdash p \leadsto \Gamma; \tau$ combines typing of patterns with calculation of which new variables they bind.
adamc@537 564 \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@537 565 \item $\Gamma \vdash S \equiv S$ is the signature equivalence judgment.
adamc@536 566 \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@530 567 \item $\Gamma \vdash M : S$ is the module signature checking judgment.
adamc@537 568 \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@539 569 \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@530 570 \end{itemize}
adamc@530 571
adamc@655 572
adamc@655 573 \subsection{Kind Well-Formedness}
adamc@655 574
adamc@655 575 $$\infer{\Gamma \vdash \mt{Type}}{}
adamc@655 576 \quad \infer{\Gamma \vdash \mt{Unit}}{}
adamc@655 577 \quad \infer{\Gamma \vdash \mt{Name}}{}
adamc@655 578 \quad \infer{\Gamma \vdash \kappa_1 \to \kappa_2}{
adamc@655 579 \Gamma \vdash \kappa_1
adamc@655 580 & \Gamma \vdash \kappa_2
adamc@655 581 }
adamc@655 582 \quad \infer{\Gamma \vdash \{\kappa\}}{
adamc@655 583 \Gamma \vdash \kappa
adamc@655 584 }
adamc@655 585 \quad \infer{\Gamma \vdash (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@655 586 \forall i: \Gamma \vdash \kappa_i
adamc@655 587 }$$
adamc@655 588
adamc@655 589 $$\infer{\Gamma \vdash X}{
adamc@655 590 X \in \Gamma
adamc@655 591 }
adamc@655 592 \quad \infer{\Gamma \vdash X \longrightarrow \kappa}{
adamc@655 593 \Gamma, X \vdash \kappa
adamc@655 594 }$$
adamc@655 595
adamc@530 596 \subsection{Kinding}
adamc@530 597
adamc@655 598 We write $[X \mapsto \kappa_1]\kappa_2$ for capture-avoiding substitution of $\kappa_1$ for $X$ in $\kappa_2$.
adamc@655 599
adamc@530 600 $$\infer{\Gamma \vdash (c) :: \kappa :: \kappa}{
adamc@530 601 \Gamma \vdash c :: \kappa
adamc@530 602 }
adamc@530 603 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530 604 x :: \kappa \in \Gamma
adamc@530 605 }
adamc@530 606 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530 607 x :: \kappa = c \in \Gamma
adamc@530 608 }$$
adamc@530 609
adamc@530 610 $$\infer{\Gamma \vdash M.x :: \kappa}{
adamc@537 611 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 612 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = \kappa
adamc@530 613 }
adamc@530 614 \quad \infer{\Gamma \vdash M.x :: \kappa}{
adamc@537 615 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 616 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@530 617 }$$
adamc@530 618
adamc@530 619 $$\infer{\Gamma \vdash \tau_1 \to \tau_2 :: \mt{Type}}{
adamc@530 620 \Gamma \vdash \tau_1 :: \mt{Type}
adamc@530 621 & \Gamma \vdash \tau_2 :: \mt{Type}
adamc@530 622 }
adamc@530 623 \quad \infer{\Gamma \vdash x \; ? \: \kappa \to \tau :: \mt{Type}}{
adamc@530 624 \Gamma, x :: \kappa \vdash \tau :: \mt{Type}
adamc@530 625 }
adamc@655 626 \quad \infer{\Gamma \vdash X \longrightarrow \tau :: \mt{Type}}{
adamc@655 627 \Gamma, X \vdash \tau :: \mt{Type}
adamc@655 628 }
adamc@530 629 \quad \infer{\Gamma \vdash \$c :: \mt{Type}}{
adamc@530 630 \Gamma \vdash c :: \{\mt{Type}\}
adamc@530 631 }$$
adamc@530 632
adamc@530 633 $$\infer{\Gamma \vdash c_1 \; c_2 :: \kappa_2}{
adamc@530 634 \Gamma \vdash c_1 :: \kappa_1 \to \kappa_2
adamc@530 635 & \Gamma \vdash c_2 :: \kappa_1
adamc@530 636 }
adamc@530 637 \quad \infer{\Gamma \vdash \lambda x \; :: \; \kappa_1 \Rightarrow c :: \kappa_1 \to \kappa_2}{
adamc@530 638 \Gamma, x :: \kappa_1 \vdash c :: \kappa_2
adamc@530 639 }$$
adamc@530 640
adamc@655 641 $$\infer{\Gamma \vdash c[\kappa'] :: [X \mapsto \kappa']\kappa}{
adamc@655 642 \Gamma \vdash c :: X \to \kappa
adamc@655 643 & \Gamma \vdash \kappa'
adamc@655 644 }
adamc@655 645 \quad \infer{\Gamma \vdash X \Longrightarrow c :: X \to \kappa}{
adamc@655 646 \Gamma, X \vdash c :: \kappa
adamc@655 647 }$$
adamc@655 648
adamc@530 649 $$\infer{\Gamma \vdash () :: \mt{Unit}}{}
adamc@530 650 \quad \infer{\Gamma \vdash \#X :: \mt{Name}}{}$$
adamc@530 651
adamc@530 652 $$\infer{\Gamma \vdash [\overline{c_i = c'_i}] :: \{\kappa\}}{
adamc@530 653 \forall i: \Gamma \vdash c_i : \mt{Name}
adamc@530 654 & \Gamma \vdash c'_i :: \kappa
adamc@530 655 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@530 656 }
adamc@530 657 \quad \infer{\Gamma \vdash c_1 \rc c_2 :: \{\kappa\}}{
adamc@530 658 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530 659 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@530 660 & \Gamma \vdash c_1 \sim c_2
adamc@530 661 }$$
adamc@530 662
adamc@655 663 $$\infer{\Gamma \vdash \mt{map} :: (\kappa_1 \to \kappa_2) \to \{\kappa_1\} \to \{\kappa_2\}}{}$$
adamc@530 664
adamc@573 665 $$\infer{\Gamma \vdash (\overline c) :: (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@573 666 \forall i: \Gamma \vdash c_i :: \kappa_i
adamc@530 667 }
adamc@573 668 \quad \infer{\Gamma \vdash c.i :: \kappa_i}{
adamc@573 669 \Gamma \vdash c :: (\kappa_1 \times \ldots \times \kappa_n)
adamc@530 670 }$$
adamc@530 671
adamc@655 672 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow \tau :: \mt{Type}}{
adamc@655 673 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530 674 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@655 675 & \Gamma, c_1 \sim c_2 \vdash \tau :: \mt{Type}
adamc@530 676 }$$
adamc@530 677
adamc@531 678 \subsection{Record Disjointness}
adamc@531 679
adamc@531 680 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@558 681 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@558 682 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@558 683 & \forall c'_1 \in C_1, c'_2 \in C_2: \Gamma \vdash c'_1 \sim c'_2
adamc@531 684 }
adamc@531 685 \quad \infer{\Gamma \vdash X \sim X'}{
adamc@531 686 X \neq X'
adamc@531 687 }$$
adamc@531 688
adamc@531 689 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@531 690 c'_1 \sim c'_2 \in \Gamma
adamc@558 691 & \Gamma \vdash c'_1 \hookrightarrow C_1
adamc@558 692 & \Gamma \vdash c'_2 \hookrightarrow C_2
adamc@558 693 & c_1 \in C_1
adamc@558 694 & c_2 \in C_2
adamc@531 695 }$$
adamc@531 696
adamc@531 697 $$\infer{\Gamma \vdash c \hookrightarrow \{c\}}{}
adamc@531 698 \quad \infer{\Gamma \vdash [\overline{c = c'}] \hookrightarrow \{\overline{c}\}}{}
adamc@531 699 \quad \infer{\Gamma \vdash c_1 \rc c_2 \hookrightarrow C_1 \cup C_2}{
adamc@531 700 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@531 701 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@531 702 }
adamc@531 703 \quad \infer{\Gamma \vdash c \hookrightarrow C}{
adamc@531 704 \Gamma \vdash c \equiv c'
adamc@531 705 & \Gamma \vdash c' \hookrightarrow C
adamc@531 706 }
adamc@531 707 \quad \infer{\Gamma \vdash \mt{map} \; f \; c \hookrightarrow C}{
adamc@531 708 \Gamma \vdash c \hookrightarrow C
adamc@531 709 }$$
adamc@531 710
adamc@541 711 \subsection{\label{definitional}Definitional Equality}
adamc@532 712
adamc@655 713 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@532 714
adamc@532 715 $$\infer{\Gamma \vdash c \equiv c}{}
adamc@532 716 \quad \infer{\Gamma \vdash c_1 \equiv c_2}{
adamc@532 717 \Gamma \vdash c_2 \equiv c_1
adamc@532 718 }
adamc@532 719 \quad \infer{\Gamma \vdash c_1 \equiv c_3}{
adamc@532 720 \Gamma \vdash c_1 \equiv c_2
adamc@532 721 & \Gamma \vdash c_2 \equiv c_3
adamc@532 722 }
adamc@532 723 \quad \infer{\Gamma \vdash \mathcal C[c_1] \equiv \mathcal C[c_2]}{
adamc@532 724 \Gamma \vdash c_1 \equiv c_2
adamc@532 725 }$$
adamc@532 726
adamc@532 727 $$\infer{\Gamma \vdash x \equiv c}{
adamc@532 728 x :: \kappa = c \in \Gamma
adamc@532 729 }
adamc@532 730 \quad \infer{\Gamma \vdash M.x \equiv c}{
adamc@537 731 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 732 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@532 733 }
adamc@532 734 \quad \infer{\Gamma \vdash (\overline c).i \equiv c_i}{}$$
adamc@532 735
adamc@532 736 $$\infer{\Gamma \vdash (\lambda x :: \kappa \Rightarrow c) \; c' \equiv [x \mapsto c'] c}{}
adamc@655 737 \quad \infer{\Gamma \vdash (X \Longrightarrow c) [\kappa] \equiv [X \mapsto \kappa] c}{}$$
adamc@655 738
adamc@655 739 $$\infer{\Gamma \vdash c_1 \rc c_2 \equiv c_2 \rc c_1}{}
adamc@532 740 \quad \infer{\Gamma \vdash c_1 \rc (c_2 \rc c_3) \equiv (c_1 \rc c_2) \rc c_3}{}$$
adamc@532 741
adamc@532 742 $$\infer{\Gamma \vdash [] \rc c \equiv c}{}
adamc@532 743 \quad \infer{\Gamma \vdash [\overline{c_1 = c'_1}] \rc [\overline{c_2 = c'_2}] \equiv [\overline{c_1 = c'_1}, \overline{c_2 = c'_2}]}{}$$
adamc@532 744
adamc@655 745 $$\infer{\Gamma \vdash \mt{map} \; f \; [] \equiv []}{}
adamc@655 746 \quad \infer{\Gamma \vdash \mt{map} \; f \; ([c_1 = c_2] \rc c) \equiv [c_1 = f \; c_2] \rc \mt{map} \; f \; c}{}$$
adamc@532 747
adamc@532 748 $$\infer{\Gamma \vdash \mt{map} \; (\lambda x \Rightarrow x) \; c \equiv c}{}
adamc@655 749 \quad \infer{\Gamma \vdash \mt{map} \; f \; (\mt{map} \; f' \; c)
adamc@655 750 \equiv \mt{map} \; (\lambda x \Rightarrow f \; (f' \; x)) \; c}{}$$
adamc@532 751
adamc@532 752 $$\infer{\Gamma \vdash \mt{map} \; f \; (c_1 \rc c_2) \equiv \mt{map} \; f \; c_1 \rc \mt{map} \; f \; c_2}{}$$
adamc@531 753
adamc@534 754 \subsection{Expression Typing}
adamc@533 755
adamc@873 756 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@533 757
adamc@533 758 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@533 759
adamc@533 760 $$\infer{\Gamma \vdash e : \tau : \tau}{
adamc@533 761 \Gamma \vdash e : \tau
adamc@533 762 }
adamc@533 763 \quad \infer{\Gamma \vdash e : \tau}{
adamc@533 764 \Gamma \vdash e : \tau'
adamc@533 765 & \Gamma \vdash \tau' \equiv \tau
adamc@533 766 }
adamc@533 767 \quad \infer{\Gamma \vdash \ell : T(\ell)}{}$$
adamc@533 768
adamc@533 769 $$\infer{\Gamma \vdash x : \mathcal I(\tau)}{
adamc@533 770 x : \tau \in \Gamma
adamc@533 771 }
adamc@533 772 \quad \infer{\Gamma \vdash M.x : \mathcal I(\tau)}{
adamc@537 773 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 774 & \mt{proj}(M, \overline{s}, \mt{val} \; x) = \tau
adamc@533 775 }
adamc@533 776 \quad \infer{\Gamma \vdash X : \mathcal I(\tau)}{
adamc@533 777 X : \tau \in \Gamma
adamc@533 778 }
adamc@533 779 \quad \infer{\Gamma \vdash M.X : \mathcal I(\tau)}{
adamc@537 780 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 781 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \tau
adamc@533 782 }$$
adamc@533 783
adamc@533 784 $$\infer{\Gamma \vdash e_1 \; e_2 : \tau_2}{
adamc@533 785 \Gamma \vdash e_1 : \tau_1 \to \tau_2
adamc@533 786 & \Gamma \vdash e_2 : \tau_1
adamc@533 787 }
adamc@533 788 \quad \infer{\Gamma \vdash \lambda x : \tau_1 \Rightarrow e : \tau_1 \to \tau_2}{
adamc@533 789 \Gamma, x : \tau_1 \vdash e : \tau_2
adamc@533 790 }$$
adamc@533 791
adamc@533 792 $$\infer{\Gamma \vdash e [c] : [x \mapsto c]\tau}{
adamc@533 793 \Gamma \vdash e : x :: \kappa \to \tau
adamc@533 794 & \Gamma \vdash c :: \kappa
adamc@533 795 }
adamc@852 796 \quad \infer{\Gamma \vdash \lambda [x \; ? \; \kappa] \Rightarrow e : x \; ? \; \kappa \to \tau}{
adamc@533 797 \Gamma, x :: \kappa \vdash e : \tau
adamc@533 798 }$$
adamc@533 799
adamc@655 800 $$\infer{\Gamma \vdash e [\kappa] : [X \mapsto \kappa]\tau}{
adamc@655 801 \Gamma \vdash e : X \longrightarrow \tau
adamc@655 802 & \Gamma \vdash \kappa
adamc@655 803 }
adamc@655 804 \quad \infer{\Gamma \vdash X \Longrightarrow e : X \longrightarrow \tau}{
adamc@655 805 \Gamma, X \vdash e : \tau
adamc@655 806 }$$
adamc@655 807
adamc@533 808 $$\infer{\Gamma \vdash \{\overline{c = e}\} : \{\overline{c : \tau}\}}{
adamc@533 809 \forall i: \Gamma \vdash c_i :: \mt{Name}
adamc@533 810 & \Gamma \vdash e_i : \tau_i
adamc@533 811 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@533 812 }
adamc@533 813 \quad \infer{\Gamma \vdash e.c : \tau}{
adamc@533 814 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533 815 }
adamc@533 816 \quad \infer{\Gamma \vdash e_1 \rc e_2 : \$(c_1 \rc c_2)}{
adamc@533 817 \Gamma \vdash e_1 : \$c_1
adamc@533 818 & \Gamma \vdash e_2 : \$c_2
adamc@573 819 & \Gamma \vdash c_1 \sim c_2
adamc@533 820 }$$
adamc@533 821
adamc@533 822 $$\infer{\Gamma \vdash e \rcut c : \$c'}{
adamc@533 823 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533 824 }
adamc@533 825 \quad \infer{\Gamma \vdash e \rcutM c : \$c'}{
adamc@533 826 \Gamma \vdash e : \$(c \rc c')
adamc@533 827 }$$
adamc@533 828
adamc@533 829 $$\infer{\Gamma \vdash \mt{let} \; \overline{ed} \; \mt{in} \; e \; \mt{end} : \tau}{
adamc@533 830 \Gamma \vdash \overline{ed} \leadsto \Gamma'
adamc@533 831 & \Gamma' \vdash e : \tau
adamc@533 832 }
adamc@533 833 \quad \infer{\Gamma \vdash \mt{case} \; e \; \mt{of} \; \overline{p \Rightarrow e} : \tau}{
adamc@533 834 \forall i: \Gamma \vdash p_i \leadsto \Gamma_i, \tau'
adamc@533 835 & \Gamma_i \vdash e_i : \tau
adamc@533 836 }$$
adamc@533 837
adamc@573 838 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow e : \lambda [c_1 \sim c_2] \Rightarrow \tau}{
adamc@533 839 \Gamma \vdash c_1 :: \{\kappa\}
adamc@655 840 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@533 841 & \Gamma, c_1 \sim c_2 \vdash e : \tau
adamc@662 842 }
adamc@662 843 \quad \infer{\Gamma \vdash e \; ! : \tau}{
adamc@662 844 \Gamma \vdash e : [c_1 \sim c_2] \Rightarrow \tau
adamc@662 845 & \Gamma \vdash c_1 \sim c_2
adamc@533 846 }$$
adamc@533 847
adamc@534 848 \subsection{Pattern Typing}
adamc@534 849
adamc@534 850 $$\infer{\Gamma \vdash \_ \leadsto \Gamma; \tau}{}
adamc@534 851 \quad \infer{\Gamma \vdash x \leadsto \Gamma, x : \tau; \tau}{}
adamc@534 852 \quad \infer{\Gamma \vdash \ell \leadsto \Gamma; T(\ell)}{}$$
adamc@534 853
adamc@534 854 $$\infer{\Gamma \vdash X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534 855 X : \overline{x ::: \mt{Type}} \to \tau \in \Gamma
adamc@534 856 & \textrm{$\tau$ not a function type}
adamc@534 857 }
adamc@534 858 \quad \infer{\Gamma \vdash X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534 859 X : \overline{x ::: \mt{Type}} \to \tau'' \to \tau \in \Gamma
adamc@534 860 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534 861 }$$
adamc@534 862
adamc@534 863 $$\infer{\Gamma \vdash M.X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537 864 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 865 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau
adamc@534 866 & \textrm{$\tau$ not a function type}
adamc@534 867 }$$
adamc@534 868
adamc@534 869 $$\infer{\Gamma \vdash M.X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537 870 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 871 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau'' \to \tau
adamc@534 872 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534 873 }$$
adamc@534 874
adamc@534 875 $$\infer{\Gamma \vdash \{\overline{x = p}\} \leadsto \Gamma_n; \{\overline{x = \tau}\}}{
adamc@534 876 \Gamma_0 = \Gamma
adamc@534 877 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534 878 }
adamc@534 879 \quad \infer{\Gamma \vdash \{\overline{x = p}, \ldots\} \leadsto \Gamma_n; \$([\overline{x = \tau}] \rc c)}{
adamc@534 880 \Gamma_0 = \Gamma
adamc@534 881 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534 882 }$$
adamc@534 883
adamc@852 884 $$\infer{\Gamma \vdash p : \tau \leadsto \Gamma'; \tau}{
adamc@852 885 \Gamma \vdash p \leadsto \Gamma'; \tau'
adamc@852 886 & \Gamma \vdash \tau' \equiv \tau
adamc@852 887 }$$
adamc@852 888
adamc@535 889 \subsection{Declaration Typing}
adamc@535 890
adamc@535 891 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@535 892
adamc@655 893 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@535 894
adamc@558 895 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@537 896 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@535 897
adamc@535 898 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535 899 \quad \infer{\Gamma \vdash d, \overline{d} \leadsto \Gamma''}{
adamc@535 900 \Gamma \vdash d \leadsto \Gamma'
adamc@535 901 & \Gamma' \vdash \overline{d} \leadsto \Gamma''
adamc@535 902 }$$
adamc@535 903
adamc@535 904 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@535 905 \Gamma \vdash c :: \kappa
adamc@535 906 }
adamc@535 907 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@535 908 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@535 909 }$$
adamc@535 910
adamc@535 911 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537 912 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 913 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@535 914 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@535 915 }$$
adamc@535 916
adamc@535 917 $$\infer{\Gamma \vdash \mt{val} \; x : \tau = e \leadsto \Gamma, x : \tau}{
adamc@535 918 \Gamma \vdash e : \tau
adamc@535 919 }$$
adamc@535 920
adamc@535 921 $$\infer{\Gamma \vdash \mt{val} \; \mt{rec} \; \overline{x : \tau = e} \leadsto \Gamma, \overline{x : \tau}}{
adamc@535 922 \forall i: \Gamma, \overline{x : \tau} \vdash e_i : \tau_i
adamc@535 923 & \textrm{$e_i$ starts with an expression $\lambda$, optionally preceded by constructor and disjointness $\lambda$s}
adamc@535 924 }$$
adamc@535 925
adamc@535 926 $$\infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : S}{
adamc@535 927 \Gamma \vdash M : S
adamc@558 928 & \textrm{ $M$ not a constant or application}
adamc@535 929 }
adamc@558 930 \quad \infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : \mt{selfify}(X, \overline{s})}{
adamc@558 931 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@539 932 }$$
adamc@539 933
adamc@539 934 $$\infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@535 935 \Gamma \vdash S
adamc@535 936 }$$
adamc@535 937
adamc@537 938 $$\infer{\Gamma \vdash \mt{open} \; M \leadsto \Gamma, \mathcal O(M, \overline{s})}{
adamc@537 939 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535 940 }$$
adamc@535 941
adamc@535 942 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma}{
adamc@535 943 \Gamma \vdash c_1 :: \{\kappa\}
adamc@535 944 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@535 945 & \Gamma \vdash c_1 \sim c_2
adamc@535 946 }
adamc@537 947 \quad \infer{\Gamma \vdash \mt{open} \; \mt{constraints} \; M \leadsto \Gamma, \mathcal O_c(M, \overline{s})}{
adamc@537 948 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535 949 }$$
adamc@535 950
adamc@784 951 $$\infer{\Gamma \vdash \mt{table} \; x : c \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_table} \; c \; []}{
adamc@535 952 \Gamma \vdash c :: \{\mt{Type}\}
adamc@535 953 }
adamc@784 954 \quad \infer{\Gamma \vdash \mt{view} \; x : c \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_view} \; c}{
adamc@784 955 \Gamma \vdash c :: \{\mt{Type}\}
adamc@784 956 }$$
adamc@784 957
adamc@784 958 $$\infer{\Gamma \vdash \mt{sequence} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_sequence}}{}$$
adamc@535 959
adamc@535 960 $$\infer{\Gamma \vdash \mt{cookie} \; x : \tau \leadsto \Gamma, x : \mt{Basis}.\mt{http\_cookie} \; \tau}{
adamc@535 961 \Gamma \vdash \tau :: \mt{Type}
adamc@784 962 }
adamc@784 963 \quad \infer{\Gamma \vdash \mt{style} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{css\_class}}{}$$
adamc@535 964
adamc@1085 965 $$\infer{\Gamma \vdash \mt{task} \; e_1 = e_2 \leadsto \Gamma}{
adam@1348 966 \Gamma \vdash e_1 :: \mt{Basis}.\mt{task\_kind} \; \tau
adam@1348 967 & \Gamma \vdash e_2 :: \tau \to \mt{Basis}.\mt{transaction} \; \{\}
adamc@1085 968 }$$
adamc@1085 969
adamc@784 970 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784 971 \Gamma \vdash c :: \kappa
adamc@535 972 }$$
adamc@535 973
adamc@535 974 $$\infer{\overline{y}; x; \Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535 975 \quad \infer{\overline{y}; x; \Gamma \vdash X \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to x \; \overline{y}}{
adamc@535 976 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535 977 }
adamc@535 978 \quad \infer{\overline{y}; x; \Gamma \vdash X \; \mt{of} \; \tau \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to \tau \to x \; \overline{y}}{
adamc@535 979 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535 980 }$$
adamc@535 981
adamc@537 982 \subsection{Signature Item Typing}
adamc@537 983
adamc@537 984 We appeal to a signature item analogue of the $\mathcal O$ function from the last subsection.
adamc@537 985
adamc@537 986 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@537 987 \quad \infer{\Gamma \vdash s, \overline{s} \leadsto \Gamma''}{
adamc@537 988 \Gamma \vdash s \leadsto \Gamma'
adamc@537 989 & \Gamma' \vdash \overline{s} \leadsto \Gamma''
adamc@537 990 }$$
adamc@537 991
adamc@537 992 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}
adamc@537 993 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@537 994 \Gamma \vdash c :: \kappa
adamc@537 995 }
adamc@537 996 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@537 997 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@537 998 }$$
adamc@537 999
adamc@537 1000 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537 1001 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1002 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1003 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@537 1004 }$$
adamc@537 1005
adamc@537 1006 $$\infer{\Gamma \vdash \mt{val} \; x : \tau \leadsto \Gamma, x : \tau}{
adamc@537 1007 \Gamma \vdash \tau :: \mt{Type}
adamc@537 1008 }$$
adamc@537 1009
adamc@537 1010 $$\infer{\Gamma \vdash \mt{structure} \; X : S \leadsto \Gamma, X : S}{
adamc@537 1011 \Gamma \vdash S
adamc@537 1012 }
adamc@537 1013 \quad \infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@537 1014 \Gamma \vdash S
adamc@537 1015 }$$
adamc@537 1016
adamc@537 1017 $$\infer{\Gamma \vdash \mt{include} \; S \leadsto \Gamma, \mathcal O(\overline{s})}{
adamc@537 1018 \Gamma \vdash S
adamc@537 1019 & \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1020 }$$
adamc@537 1021
adamc@537 1022 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma, c_1 \sim c_2}{
adamc@537 1023 \Gamma \vdash c_1 :: \{\kappa\}
adamc@537 1024 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@537 1025 }$$
adamc@537 1026
adamc@784 1027 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784 1028 \Gamma \vdash c :: \kappa
adamc@537 1029 }
adamc@784 1030 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}$$
adamc@537 1031
adamc@536 1032 \subsection{Signature Compatibility}
adamc@536 1033
adamc@558 1034 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 1035
adamc@537 1036 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 1037
adamc@536 1038 $$\infer{\Gamma \vdash S \equiv S}{}
adamc@536 1039 \quad \infer{\Gamma \vdash S_1 \equiv S_2}{
adamc@536 1040 \Gamma \vdash S_2 \equiv S_1
adamc@536 1041 }
adamc@536 1042 \quad \infer{\Gamma \vdash X \equiv S}{
adamc@536 1043 X = S \in \Gamma
adamc@536 1044 }
adamc@536 1045 \quad \infer{\Gamma \vdash M.X \equiv S}{
adamc@537 1046 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1047 & \mt{proj}(M, \overline{s}, \mt{signature} \; X) = S
adamc@536 1048 }$$
adamc@536 1049
adamc@536 1050 $$\infer{\Gamma \vdash S \; \mt{where} \; \mt{con} \; x = c \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa = c \; \overline{s_2} \; \mt{end}}{
adamc@536 1051 \Gamma \vdash S \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa \; \overline{s_2} \; \mt{end}
adamc@536 1052 & \Gamma \vdash c :: \kappa
adamc@537 1053 }
adamc@537 1054 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s^1} \; \mt{include} \; S \; \overline{s^2} \; \mt{end} \equiv \mt{sig} \; \overline{s^1} \; \overline{s} \; \overline{s^2} \; \mt{end}}{
adamc@537 1055 \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@536 1056 }$$
adamc@536 1057
adamc@536 1058 $$\infer{\Gamma \vdash S_1 \leq S_2}{
adamc@536 1059 \Gamma \vdash S_1 \equiv S_2
adamc@536 1060 }
adamc@536 1061 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \mt{end}}{}
adamc@537 1062 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; s' \; \overline{s'} \; \mt{end}}{
adamc@537 1063 \Gamma \vdash \overline{s} \leq s'
adamc@537 1064 & \Gamma \vdash s' \leadsto \Gamma'
adamc@537 1065 & \Gamma' \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \overline{s'} \; \mt{end}
adamc@537 1066 }$$
adamc@537 1067
adamc@537 1068 $$\infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537 1069 \Gamma \vdash s \leq s'
adamc@537 1070 }
adamc@537 1071 \quad \infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537 1072 \Gamma \vdash s \leadsto \Gamma'
adamc@537 1073 & \Gamma' \vdash \overline{s} \leq s'
adamc@536 1074 }$$
adamc@536 1075
adamc@536 1076 $$\infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 \leq \mt{functor} (X : S'_1) : S'_2}{
adamc@536 1077 \Gamma \vdash S'_1 \leq S_1
adamc@536 1078 & \Gamma, X : S'_1 \vdash S_2 \leq S'_2
adamc@536 1079 }$$
adamc@536 1080
adamc@537 1081 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@537 1082 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}
adamc@558 1083 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type}}{}$$
adamc@537 1084
adamc@537 1085 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(y)} \to \mt{Type}}{
adamc@537 1086 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1087 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1088 }$$
adamc@537 1089
adamc@784 1090 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@784 1091 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}$$
adamc@537 1092
adamc@537 1093 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \mt{\kappa} = c_2}{
adamc@537 1094 \Gamma \vdash c_1 \equiv c_2
adamc@537 1095 }
adamc@784 1096 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \kappa = c_2}{
adamc@537 1097 \Gamma \vdash c_1 \equiv c_2
adamc@537 1098 }$$
adamc@537 1099
adamc@537 1100 $$\infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537 1101 \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1102 }$$
adamc@537 1103
adamc@537 1104 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537 1105 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1106 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1107 & \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1108 }$$
adamc@537 1109
adamc@537 1110 $$\infer{\Gamma \vdash \cdot \leq \cdot}{}
adamc@537 1111 \quad \infer{\Gamma \vdash X; \overline{dc} \leq X; \overline{dc'}}{
adamc@537 1112 \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1113 }
adamc@537 1114 \quad \infer{\Gamma \vdash X \; \mt{of} \; \tau_1; \overline{dc} \leq X \; \mt{of} \; \tau_2; \overline{dc'}}{
adamc@537 1115 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537 1116 & \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1117 }$$
adamc@537 1118
adamc@537 1119 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x = \mt{datatype} \; M'.z'}{
adamc@537 1120 \Gamma \vdash M.z \equiv M'.z'
adamc@537 1121 }$$
adamc@537 1122
adamc@537 1123 $$\infer{\Gamma \vdash \mt{val} \; x : \tau_1 \leq \mt{val} \; x : \tau_2}{
adamc@537 1124 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537 1125 }
adamc@537 1126 \quad \infer{\Gamma \vdash \mt{structure} \; X : S_1 \leq \mt{structure} \; X : S_2}{
adamc@537 1127 \Gamma \vdash S_1 \leq S_2
adamc@537 1128 }
adamc@537 1129 \quad \infer{\Gamma \vdash \mt{signature} \; X = S_1 \leq \mt{signature} \; X = S_2}{
adamc@537 1130 \Gamma \vdash S_1 \leq S_2
adamc@537 1131 & \Gamma \vdash S_2 \leq S_1
adamc@537 1132 }$$
adamc@537 1133
adamc@537 1134 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leq \mt{constraint} \; c'_1 \sim c'_2}{
adamc@537 1135 \Gamma \vdash c_1 \equiv c'_1
adamc@537 1136 & \Gamma \vdash c_2 \equiv c'_2
adamc@537 1137 }$$
adamc@537 1138
adamc@655 1139 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{class} \; x :: \kappa}{}
adamc@655 1140 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{class} \; x :: \kappa}{}
adamc@655 1141 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{class} \; x :: \kappa = c_2}{
adamc@537 1142 \Gamma \vdash c_1 \equiv c_2
adamc@537 1143 }$$
adamc@537 1144
adamc@538 1145 \subsection{Module Typing}
adamc@538 1146
adamc@538 1147 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 1148
adamc@538 1149 $$\infer{\Gamma \vdash M : S}{
adamc@538 1150 \Gamma \vdash M : S'
adamc@538 1151 & \Gamma \vdash S' \leq S
adamc@538 1152 }
adamc@538 1153 \quad \infer{\Gamma \vdash \mt{struct} \; \overline{d} \; \mt{end} : \mt{sig} \; \mt{sigOf}(\overline{d}) \; \mt{end}}{
adamc@538 1154 \Gamma \vdash \overline{d} \leadsto \Gamma'
adamc@538 1155 }
adamc@538 1156 \quad \infer{\Gamma \vdash X : S}{
adamc@538 1157 X : S \in \Gamma
adamc@538 1158 }$$
adamc@538 1159
adamc@538 1160 $$\infer{\Gamma \vdash M.X : S}{
adamc@538 1161 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@538 1162 & \mt{proj}(M, \overline{s}, \mt{structure} \; X) = S
adamc@538 1163 }$$
adamc@538 1164
adamc@538 1165 $$\infer{\Gamma \vdash M_1(M_2) : [X \mapsto M_2]S_2}{
adamc@538 1166 \Gamma \vdash M_1 : \mt{functor}(X : S_1) : S_2
adamc@538 1167 & \Gamma \vdash M_2 : S_1
adamc@538 1168 }
adamc@538 1169 \quad \infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 = M : \mt{functor} (X : S_1) : S_2}{
adamc@538 1170 \Gamma \vdash S_1
adamc@538 1171 & \Gamma, X : S_1 \vdash S_2
adamc@538 1172 & \Gamma, X : S_1 \vdash M : S_2
adamc@538 1173 }$$
adamc@538 1174
adamc@538 1175 \begin{eqnarray*}
adamc@538 1176 \mt{sigOf}(\cdot) &=& \cdot \\
adamc@538 1177 \mt{sigOf}(s \; \overline{s'}) &=& \mt{sigOf}(s) \; \mt{sigOf}(\overline{s'}) \\
adamc@538 1178 \\
adamc@538 1179 \mt{sigOf}(\mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@538 1180 \mt{sigOf}(\mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \overline{dc} \\
adamc@538 1181 \mt{sigOf}(\mt{datatype} \; x = \mt{datatype} \; M.z) &=& \mt{datatype} \; x = \mt{datatype} \; M.z \\
adamc@538 1182 \mt{sigOf}(\mt{val} \; x : \tau = e) &=& \mt{val} \; x : \tau \\
adamc@538 1183 \mt{sigOf}(\mt{val} \; \mt{rec} \; \overline{x : \tau = e}) &=& \overline{\mt{val} \; x : \tau} \\
adamc@538 1184 \mt{sigOf}(\mt{structure} \; X : S = M) &=& \mt{structure} \; X : S \\
adamc@538 1185 \mt{sigOf}(\mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@538 1186 \mt{sigOf}(\mt{open} \; M) &=& \mt{include} \; S \textrm{ (where $\Gamma \vdash M : S$)} \\
adamc@538 1187 \mt{sigOf}(\mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@538 1188 \mt{sigOf}(\mt{open} \; \mt{constraints} \; M) &=& \cdot \\
adamc@538 1189 \mt{sigOf}(\mt{table} \; x : c) &=& \mt{table} \; x : c \\
adamc@784 1190 \mt{sigOf}(\mt{view} \; x : c) &=& \mt{view} \; x : c \\
adamc@538 1191 \mt{sigOf}(\mt{sequence} \; x) &=& \mt{sequence} \; x \\
adamc@538 1192 \mt{sigOf}(\mt{cookie} \; x : \tau) &=& \mt{cookie} \; x : \tau \\
adamc@784 1193 \mt{sigOf}(\mt{style} \; x) &=& \mt{style} \; x \\
adamc@655 1194 \mt{sigOf}(\mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@538 1195 \end{eqnarray*}
adamc@539 1196 \begin{eqnarray*}
adamc@539 1197 \mt{selfify}(M, \cdot) &=& \cdot \\
adamc@558 1198 \mt{selfify}(M, s \; \overline{s'}) &=& \mt{selfify}(M, s) \; \mt{selfify}(M, \overline{s'}) \\
adamc@539 1199 \\
adamc@539 1200 \mt{selfify}(M, \mt{con} \; x :: \kappa) &=& \mt{con} \; x :: \kappa = M.x \\
adamc@539 1201 \mt{selfify}(M, \mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@539 1202 \mt{selfify}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \mt{datatype} \; M.x \\
adamc@539 1203 \mt{selfify}(M, \mt{datatype} \; x = \mt{datatype} \; M'.z) &=& \mt{datatype} \; x = \mt{datatype} \; M'.z \\
adamc@539 1204 \mt{selfify}(M, \mt{val} \; x : \tau) &=& \mt{val} \; x : \tau \\
adamc@539 1205 \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 1206 \mt{selfify}(M, \mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@539 1207 \mt{selfify}(M, \mt{include} \; S) &=& \mt{include} \; S \\
adamc@539 1208 \mt{selfify}(M, \mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@655 1209 \mt{selfify}(M, \mt{class} \; x :: \kappa) &=& \mt{class} \; x :: \kappa = M.x \\
adamc@655 1210 \mt{selfify}(M, \mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@539 1211 \end{eqnarray*}
adamc@539 1212
adamc@540 1213 \subsection{Module Projection}
adamc@540 1214
adamc@540 1215 \begin{eqnarray*}
adamc@540 1216 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \\
adamc@540 1217 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa, c) \\
adamc@540 1218 \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 1219 \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 1220 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})$)} \\
adamc@655 1221 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \to \mt{Type} \\
adamc@655 1222 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa \to \mt{Type}, c) \\
adamc@540 1223 \\
adamc@540 1224 \mt{proj}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc} \; \overline{s}, \mt{datatype} \; x) &=& (\overline{y}, \overline{dc}) \\
adamc@540 1225 \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 1226 \\
adamc@540 1227 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, \mt{val} \; x) &=& \tau \\
adamc@540 1228 \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 1229 \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 1230 \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 1231 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \in \overline{dc}$)} \\
adamc@540 1232 \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 1233 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \; \mt{of} \; \tau \in \overline{dc}$)} \\
adamc@540 1234 \\
adamc@540 1235 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, \mt{structure} \; X) &=& S \\
adamc@540 1236 \\
adamc@540 1237 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, \mt{signature} \; X) &=& S \\
adamc@540 1238 \\
adamc@540 1239 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1240 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1241 \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 1242 \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 1243 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@540 1244 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1245 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1246 \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 1247 \mt{proj}(M, \mt{constraint} \; c_1 \sim c_2 \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@655 1248 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@655 1249 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1250 \end{eqnarray*}
adamc@540 1251
adamc@541 1252
adamc@541 1253 \section{Type Inference}
adamc@541 1254
adamc@541 1255 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 1256
adamc@541 1257 \subsection{Basic Unification}
adamc@541 1258
adamc@560 1259 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 1260
adamc@656 1261 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 1262
adamc@541 1263 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 1264
adamc@541 1265 \subsection{Unifying Record Types}
adamc@541 1266
adamc@570 1267 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 1268
adamc@656 1269 \subsection{\label{typeclasses}Constructor Classes}
adamc@541 1270
adamc@784 1271 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 1272
adamc@784 1273 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 1274
adamc@656 1275 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 1276
adamc@656 1277 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 1278
adamc@541 1279 \subsection{Reverse-Engineering Record Types}
adamc@541 1280
adamc@656 1281 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 1282
adamc@541 1283 \subsection{Implicit Arguments in Functor Applications}
adamc@541 1284
adamc@656 1285 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 1286
adamc@541 1287
adamc@542 1288 \section{The Ur Standard Library}
adamc@542 1289
adamc@542 1290 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 1291
adamc@542 1292 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 1293
adamc@542 1294 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 1295 $$\begin{array}{l}
adamc@542 1296 \mt{type} \; \mt{int} \\
adamc@542 1297 \mt{type} \; \mt{float} \\
adamc@873 1298 \mt{type} \; \mt{char} \\
adamc@542 1299 \mt{type} \; \mt{string} \\
adamc@542 1300 \mt{type} \; \mt{time} \\
adamc@785 1301 \mt{type} \; \mt{blob} \\
adamc@542 1302 \\
adamc@542 1303 \mt{type} \; \mt{unit} = \{\} \\
adamc@542 1304 \\
adamc@542 1305 \mt{datatype} \; \mt{bool} = \mt{False} \mid \mt{True} \\
adamc@542 1306 \\
adamc@785 1307 \mt{datatype} \; \mt{option} \; \mt{t} = \mt{None} \mid \mt{Some} \; \mt{of} \; \mt{t} \\
adamc@785 1308 \\
adamc@785 1309 \mt{datatype} \; \mt{list} \; \mt{t} = \mt{Nil} \mid \mt{Cons} \; \mt{of} \; \mt{t} \times \mt{list} \; \mt{t}
adamc@542 1310 \end{array}$$
adamc@542 1311
adamc@1123 1312 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 1313
adam@1297 1314 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 1315 $$\begin{array}{l}
adam@1297 1316 \mt{con} \; \mt{variant} :: \{\mt{Type}\} \to \mt{Type} \\
adam@1297 1317 \mt{val} \; \mt{make} : \mt{nm} :: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{ts} ::: \{\mt{Type}\} \to [[\mt{nm}] \sim \mt{ts}] \Rightarrow \mt{t} \to \mt{variant} \; ([\mt{nm} = \mt{t}] \rc \mt{ts}) \\
adam@1297 1318 \mt{val} \; \mt{match} : \mt{ts} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{variant} \; \mt{ts} \to \$(\mt{map} \; (\lambda \mt{t'} \Rightarrow \mt{t'} \to \mt{t}) \; \mt{ts}) \to \mt{t}
adam@1297 1319 \end{array}$$
adam@1297 1320
adamc@657 1321 Another important generic Ur element comes at the beginning of \texttt{top.urs}.
adamc@657 1322
adamc@657 1323 $$\begin{array}{l}
adamc@657 1324 \mt{con} \; \mt{folder} :: \mt{K} \longrightarrow \{\mt{K}\} \to \mt{Type} \\
adamc@657 1325 \\
adamc@657 1326 \mt{val} \; \mt{fold} : \mt{K} \longrightarrow \mt{tf} :: (\{\mt{K}\} \to \mt{Type}) \\
adamc@657 1327 \hspace{.1in} \to (\mt{nm} :: \mt{Name} \to \mt{v} :: \mt{K} \to \mt{r} :: \{\mt{K}\} \to [[\mt{nm}] \sim \mt{r}] \Rightarrow \\
adamc@657 1328 \hspace{.2in} \mt{tf} \; \mt{r} \to \mt{tf} \; ([\mt{nm} = \mt{v}] \rc \mt{r})) \\
adamc@657 1329 \hspace{.1in} \to \mt{tf} \; [] \\
adamc@657 1330 \hspace{.1in} \to \mt{r} :: \{\mt{K}\} \to \mt{folder} \; \mt{r} \to \mt{tf} \; \mt{r}
adamc@657 1331 \end{array}$$
adamc@657 1332
adamc@657 1333 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 1334
adamc@664 1335 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 1336
adamc@542 1337
adamc@542 1338 \section{The Ur/Web Standard Library}
adamc@542 1339
adam@1400 1340 Some operations are only allowed in server-side code or only in client-side code. The type system does not enforce such restrictions, but the compiler enforces them in the process of whole-program compilation. In the discussion below, we note when a set of operations has a location restriction.
adam@1400 1341
adamc@658 1342 \subsection{Monads}
adamc@658 1343
adamc@658 1344 The Ur Basis defines the monad constructor class from Haskell.
adamc@658 1345
adamc@658 1346 $$\begin{array}{l}
adamc@658 1347 \mt{class} \; \mt{monad} :: \mt{Type} \to \mt{Type} \\
adamc@658 1348 \mt{val} \; \mt{return} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t} ::: \mt{Type} \\
adamc@658 1349 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658 1350 \hspace{.1in} \to \mt{t} \to \mt{m} \; \mt{t} \\
adamc@658 1351 \mt{val} \; \mt{bind} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t1} ::: \mt{Type} \to \mt{t2} ::: \mt{Type} \\
adamc@658 1352 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658 1353 \hspace{.1in} \to \mt{m} \; \mt{t1} \to (\mt{t1} \to \mt{m} \; \mt{t2}) \\
adamc@658 1354 \hspace{.1in} \to \mt{m} \; \mt{t2}
adamc@658 1355 \end{array}$$
adamc@658 1356
adamc@542 1357 \subsection{Transactions}
adamc@542 1358
adamc@542 1359 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 1360 $$\begin{array}{l}
adamc@542 1361 \mt{con} \; \mt{transaction} :: \mt{Type} \to \mt{Type} \\
adamc@658 1362 \mt{val} \; \mt{transaction\_monad} : \mt{monad} \; \mt{transaction}
adamc@542 1363 \end{array}$$
adamc@542 1364
adamc@1123 1365 For debugging purposes, a transactional function is provided for outputting a string on the server process' \texttt{stderr}.
adamc@1123 1366 $$\begin{array}{l}
adamc@1123 1367 \mt{val} \; \mt{debug} : \mt{string} \to \mt{transaction} \; \mt{unit}
adamc@1123 1368 \end{array}$$
adamc@1123 1369
adamc@542 1370 \subsection{HTTP}
adamc@542 1371
adam@1400 1372 There are transactions for reading an HTTP header by name and for getting and setting strongly-typed cookies. Cookies may only be created by the $\mt{cookie}$ declaration form, ensuring that they be named consistently based on module structure. For now, cookie operations are server-side only.
adamc@542 1373 $$\begin{array}{l}
adamc@786 1374 \mt{con} \; \mt{http\_cookie} :: \mt{Type} \to \mt{Type} \\
adamc@786 1375 \mt{val} \; \mt{getCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; (\mt{option} \; \mt{t}) \\
adamc@1050 1376 \mt{val} \; \mt{setCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \{\mt{Value} : \mt{t}, \mt{Expires} : \mt{option} \; \mt{time}, \mt{Secure} : \mt{bool}\} \to \mt{transaction} \; \mt{unit} \\
adamc@1050 1377 \mt{val} \; \mt{clearCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; \mt{unit}
adamc@786 1378 \end{array}$$
adamc@786 1379
adamc@786 1380 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 1381 $$\begin{array}{l}
adamc@786 1382 \mt{type} \; \mt{url} \\
adamc@786 1383 \mt{val} \; \mt{bless} : \mt{string} \to \mt{url} \\
adamc@786 1384 \mt{val} \; \mt{checkUrl} : \mt{string} \to \mt{option} \; \mt{url}
adamc@786 1385 \end{array}$$
adamc@786 1386 $\mt{bless}$ raises a runtime error if the string passed to it fails the URL policy.
adamc@786 1387
adam@1400 1388 It is possible to grab the current page's URL or to build a URL for an arbitrary transaction that would also be an acceptable value of a \texttt{link} attribute of the \texttt{a} tag. These are server-side operations.
adamc@1085 1389 $$\begin{array}{l}
adamc@1085 1390 \mt{val} \; \mt{currentUrl} : \mt{transaction} \; \mt{url} \\
adamc@1085 1391 \mt{val} \; \mt{url} : \mt{transaction} \; \mt{page} \to \mt{url}
adamc@1085 1392 \end{array}$$
adamc@1085 1393
adamc@1085 1394 Page generation may be interrupted at any time with a request to redirect to a particular URL instead.
adamc@1085 1395 $$\begin{array}{l}
adamc@1085 1396 \mt{val} \; \mt{redirect} : \mt{t} ::: \mt{Type} \to \mt{url} \to \mt{transaction} \; \mt{t}
adamc@1085 1397 \end{array}$$
adamc@1085 1398
adam@1400 1399 It's possible for pages to return files of arbitrary MIME types. A file can be input from the user using this data type, along with the $\mt{upload}$ form tag. These functions and those described in the following paragraph are server-side.
adamc@786 1400 $$\begin{array}{l}
adamc@786 1401 \mt{type} \; \mt{file} \\
adamc@786 1402 \mt{val} \; \mt{fileName} : \mt{file} \to \mt{option} \; \mt{string} \\
adamc@786 1403 \mt{val} \; \mt{fileMimeType} : \mt{file} \to \mt{string} \\
adamc@786 1404 \mt{val} \; \mt{fileData} : \mt{file} \to \mt{blob}
adamc@786 1405 \end{array}$$
adamc@786 1406
adamc@786 1407 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 1408 $$\begin{array}{l}
adamc@786 1409 \mt{type} \; \mt{mimeType} \\
adamc@786 1410 \mt{val} \; \mt{blessMime} : \mt{string} \to \mt{mimeType} \\
adamc@786 1411 \mt{val} \; \mt{checkMime} : \mt{string} \to \mt{option} \; \mt{mimeType} \\
adamc@786 1412 \mt{val} \; \mt{returnBlob} : \mt{t} ::: \mt{Type} \to \mt{blob} \to \mt{mimeType} \to \mt{transaction} \; \mt{t}
adamc@542 1413 \end{array}$$
adamc@542 1414
adamc@543 1415 \subsection{SQL}
adamc@543 1416
adam@1400 1417 Everything about SQL database access is restricted to server-side code.
adam@1400 1418
adamc@543 1419 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 1420 $$\begin{array}{l}
adamc@785 1421 \mt{con} \; \mt{sql\_table} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785 1422 \end{array}$$
adamc@785 1423 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 1424
adamc@785 1425 We also have the simpler type family of SQL views, which have no keys.
adamc@785 1426 $$\begin{array}{l}
adamc@785 1427 \mt{con} \; \mt{sql\_view} :: \{\mt{Type}\} \to \mt{Type}
adamc@543 1428 \end{array}$$
adamc@543 1429
adamc@785 1430 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 1431 $$\begin{array}{l}
adamc@785 1432 \mt{class} \; \mt{fieldsOf} :: \mt{Type} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1433 \mt{val} \; \mt{fieldsOf\_table} : \mt{fs} ::: \{\mt{Type}\} \to \mt{keys} ::: \{\{\mt{Unit}\}\} \to \mt{fieldsOf} \; (\mt{sql\_table} \; \mt{fs} \; \mt{keys}) \; \mt{fs} \\
adamc@785 1434 \mt{val} \; \mt{fieldsOf\_view} : \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; (\mt{sql\_view} \; \mt{fs}) \; \mt{fs}
adamc@785 1435 \end{array}$$
adamc@785 1436
adamc@785 1437 \subsubsection{Table Constraints}
adamc@785 1438
adamc@785 1439 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 1440
adamc@785 1441 $$\begin{array}{l}
adamc@785 1442 \mt{con} \; \mt{primary\_key} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type} \\
adamc@785 1443 \mt{val} \; \mt{no\_primary\_key} : \mt{fs} ::: \{\mt{Type}\} \to \mt{primary\_key} \; \mt{fs} \; [] \\
adamc@785 1444 \mt{val} \; \mt{primary\_key} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{key1} :: \mt{Name} \to \mt{keys} :: \{\mt{Type}\} \\
adamc@785 1445 \hspace{.1in} \to [[\mt{key1}] \sim \mt{keys}] \Rightarrow [[\mt{key1} = \mt{t}] \rc \mt{keys} \sim \mt{rest}] \\
adamc@785 1446 \hspace{.1in} \Rightarrow \$([\mt{key1} = \mt{sql\_injectable\_prim} \; \mt{t}] \rc \mt{map} \; \mt{sql\_injectable\_prim} \; \mt{keys}) \\
adamc@785 1447 \hspace{.1in} \to \mt{primary\_key} \; ([\mt{key1} = \mt{t}] \rc \mt{keys} \rc \mt{rest}) \; [\mt{Pkey} = [\mt{key1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{keys}]
adamc@785 1448 \end{array}$$
adamc@785 1449 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 1450
adamc@785 1451 A type family stands for sets of named constraints of the remaining varieties.
adamc@785 1452 $$\begin{array}{l}
adamc@785 1453 \mt{con} \; \mt{sql\_constraints} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785 1454 \end{array}$$
adamc@785 1455 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 1456
adamc@785 1457 There is a type family of individual, unnamed constraints.
adamc@785 1458 $$\begin{array}{l}
adamc@785 1459 \mt{con} \; \mt{sql\_constraint} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \mt{Type}
adamc@785 1460 \end{array}$$
adamc@785 1461 The first argument is the same as above, and the second argument gives the key columns for just this constraint.
adamc@785 1462
adamc@785 1463 We have operations for assembling constraints into constraint sets.
adamc@785 1464 $$\begin{array}{l}
adamc@785 1465 \mt{val} \; \mt{no\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_constraints} \; \mt{fs} \; [] \\
adamc@785 1466 \mt{val} \; \mt{one\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{unique} ::: \{\mt{Unit}\} \to \mt{name} :: \mt{Name} \\
adamc@785 1467 \hspace{.1in} \to \mt{sql\_constraint} \; \mt{fs} \; \mt{unique} \to \mt{sql\_constraints} \; \mt{fs} \; [\mt{name} = \mt{unique}] \\
adamc@785 1468 \mt{val} \; \mt{join\_constraints} : \mt{fs} ::: \{\mt{Type}\} \to \mt{uniques1} ::: \{\{\mt{Unit}\}\} \to \mt{uniques2} ::: \{\{\mt{Unit}\}\} \to [\mt{uniques1} \sim \mt{uniques2}] \\
adamc@785 1469 \hspace{.1in} \Rightarrow \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques1} \to \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques2} \to \mt{sql\_constraints} \; \mt{fs} \; (\mt{uniques1} \rc \mt{uniques2})
adamc@785 1470 \end{array}$$
adamc@785 1471
adamc@785 1472 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 1473 $$\begin{array}{l}
adamc@785 1474 \mt{val} \; \mt{unique} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{unique1} :: \mt{Name} \to \mt{unique} :: \{\mt{Type}\} \\
adamc@785 1475 \hspace{.1in} \to [[\mt{unique1}] \sim \mt{unique}] \Rightarrow [[\mt{unique1} = \mt{t}] \rc \mt{unique} \sim \mt{rest}] \\
adamc@785 1476 \hspace{.1in} \Rightarrow \mt{sql\_constraint} \; ([\mt{unique1} = \mt{t}] \rc \mt{unique} \rc \mt{rest}) \; ([\mt{unique1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{unique})
adamc@785 1477 \end{array}$$
adamc@785 1478
adamc@785 1479 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 1480 $$\begin{array}{l}
adamc@785 1481 \mt{class} \; \mt{linkable} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@785 1482 \mt{val} \; \mt{linkable\_same} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; \mt{t} \\
adamc@785 1483 \mt{val} \; \mt{linkable\_from\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; (\mt{option} \; \mt{t}) \; \mt{t} \\
adamc@785 1484 \mt{val} \; \mt{linkable\_to\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@785 1485 \end{array}$$
adamc@785 1486
adamc@785 1487 The $\mt{matching}$ type family uses $\mt{linkable}$ to define when two keys match up type-wise.
adamc@785 1488 $$\begin{array}{l}
adamc@785 1489 \mt{con} \; \mt{matching} :: \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1490 \mt{val} \; \mt{mat\_nil} : \mt{matching} \; [] \; [] \\
adamc@785 1491 \mt{val} \; \mt{mat\_cons} : \mt{t1} ::: \mt{Type} \to \mt{rest1} ::: \{\mt{Type}\} \to \mt{t2} ::: \mt{Type} \to \mt{rest2} ::: \{\mt{Type}\} \to \mt{nm1} :: \mt{Name} \to \mt{nm2} :: \mt{Name} \\
adamc@785 1492 \hspace{.1in} \to [[\mt{nm1}] \sim \mt{rest1}] \Rightarrow [[\mt{nm2}] \sim \mt{rest2}] \Rightarrow \mt{linkable} \; \mt{t1} \; \mt{t2} \to \mt{matching} \; \mt{rest1} \; \mt{rest2} \\
adamc@785 1493 \hspace{.1in} \to \mt{matching} \; ([\mt{nm1} = \mt{t1}] \rc \mt{rest1}) \; ([\mt{nm2} = \mt{t2}] \rc \mt{rest2})
adamc@785 1494 \end{array}$$
adamc@785 1495
adamc@785 1496 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 1497 $$\begin{array}{l}
adamc@785 1498 \mt{con} \; \mt{propagation\_mode} :: \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1499 \mt{val} \; \mt{restrict} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1500 \mt{val} \; \mt{cascade} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1501 \mt{val} \; \mt{no\_action} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1502 \mt{val} \; \mt{set\_null} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; (\mt{map} \; \mt{option} \; \mt{fs})
adamc@785 1503 \end{array}$$
adamc@785 1504
adamc@785 1505 Finally, we put these ingredient together to define the \texttt{FOREIGN KEY} constraint function.
adamc@785 1506 $$\begin{array}{l}
adamc@785 1507 \mt{val} \; \mt{foreign\_key} : \mt{mine1} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{mine} ::: \{\mt{Type}\} \to \mt{munused} ::: \{\mt{Type}\} \to \mt{foreign} ::: \{\mt{Type}\} \\
adamc@785 1508 \hspace{.1in} \to \mt{funused} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{uniques} ::: \{\{\mt{Unit}\}\} \\
adamc@785 1509 \hspace{.1in} \to [[\mt{mine1}] \sim \mt{mine}] \Rightarrow [[\mt{mine1} = \mt{t}] \rc \mt{mine} \sim \mt{munused}] \Rightarrow [\mt{foreign} \sim \mt{funused}] \Rightarrow [[\mt{nm}] \sim \mt{uniques}] \\
adamc@785 1510 \hspace{.1in} \Rightarrow \mt{matching} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}) \; \mt{foreign} \\
adamc@785 1511 \hspace{.1in} \to \mt{sql\_table} \; (\mt{foreign} \rc \mt{funused}) \; ([\mt{nm} = \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{foreign}] \rc \mt{uniques}) \\
adamc@785 1512 \hspace{.1in} \to \{\mt{OnDelete} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}), \\
adamc@785 1513 \hspace{.2in} \mt{OnUpdate} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine})\} \\
adamc@785 1514 \hspace{.1in} \to \mt{sql\_constraint} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine} \rc \mt{munused}) \; []
adamc@785 1515 \end{array}$$
adamc@785 1516
adamc@785 1517 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 1518 $$\begin{array}{l}
adamc@785 1519 \mt{val} \; \mt{check} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; [] \; [] \; \mt{fs} \; \mt{bool} \to \mt{sql\_constraint} \; \mt{fs} \; []
adamc@785 1520 \end{array}$$
adamc@785 1521
adamc@785 1522 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 1523
adamc@784 1524
adamc@543 1525 \subsubsection{Queries}
adamc@543 1526
adam@1400 1527 A final query is constructed via the $\mt{sql\_query}$ function. Constructor arguments respectively specify the unrestricted free table variables (which will only be available in subqueries), the free table variables that may only be mentioned within arguments to aggregate functions, table fields we select (as records mapping tables to the subsets of their fields that we choose), and the (always named) extra expressions that we select.
adamc@543 1528 $$\begin{array}{l}
adam@1400 1529 \mt{con} \; \mt{sql\_query} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@1193 1530 \mt{val} \; \mt{sql\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400 1531 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1532 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543 1533 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1534 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1193 1535 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adam@1400 1536 \hspace{.1in} \Rightarrow \{\mt{Rows} : \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}, \\
adamc@1193 1537 \hspace{.2in} \mt{OrderBy} : \mt{sql\_order\_by} \; (\mt{free} \rc \mt{tables}) \; \mt{selectedExps}, \\
adamc@543 1538 \hspace{.2in} \mt{Limit} : \mt{sql\_limit}, \\
adamc@543 1539 \hspace{.2in} \mt{Offset} : \mt{sql\_offset}\} \\
adam@1400 1540 \hspace{.1in} \to \mt{sql\_query} \; \mt{free} \; \mt{afree} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1541 \end{array}$$
adamc@543 1542
adamc@545 1543 Queries are used by folding over their results inside transactions.
adamc@545 1544 $$\begin{array}{l}
adam@1400 1545 \mt{val} \; \mt{query} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to [\mt{tables} \sim \mt{exps}] \Rightarrow \mt{state} ::: \mt{Type} \to \mt{sql\_query} \; [] \; [] \; \mt{tables} \; \mt{exps} \\
adamc@658 1546 \hspace{.1in} \to (\$(\mt{exps} \rc \mt{map} \; (\lambda \mt{fields} :: \{\mt{Type}\} \Rightarrow \$\mt{fields}) \; \mt{tables}) \\
adamc@545 1547 \hspace{.2in} \to \mt{state} \to \mt{transaction} \; \mt{state}) \\
adamc@545 1548 \hspace{.1in} \to \mt{state} \to \mt{transaction} \; \mt{state}
adamc@545 1549 \end{array}$$
adamc@545 1550
adam@1400 1551 Most of the complexity of the query encoding is in the type $\mt{sql\_query1}$, which includes simple queries and derived queries based on relational operators. Constructor arguments respectively specify the unrestricted free table veriables, the aggregate-only free table variables, the tables we select from, the subset of fields that we keep from each table for the result rows, and the extra expressions that we select.
adamc@543 1552 $$\begin{array}{l}
adam@1400 1553 \mt{con} \; \mt{sql\_query1} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@543 1554 \\
adamc@543 1555 \mt{type} \; \mt{sql\_relop} \\
adamc@543 1556 \mt{val} \; \mt{sql\_union} : \mt{sql\_relop} \\
adamc@543 1557 \mt{val} \; \mt{sql\_intersect} : \mt{sql\_relop} \\
adamc@543 1558 \mt{val} \; \mt{sql\_except} : \mt{sql\_relop} \\
adam@1400 1559 \mt{val} \; \mt{sql\_relop} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400 1560 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adam@1400 1561 \hspace{.1in} \to \mt{tables1} ::: \{\{\mt{Type}\}\} \\
adamc@543 1562 \hspace{.1in} \to \mt{tables2} ::: \{\{\mt{Type}\}\} \\
adamc@543 1563 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1564 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@543 1565 \hspace{.1in} \to \mt{sql\_relop} \\
adam@1400 1566 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables1} \; \mt{selectedFields} \; \mt{selectedExps} \\
adam@1400 1567 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables2} \; \mt{selectedFields} \; \mt{selectedExps} \\
adam@1400 1568 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{selectedFields} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1569 \end{array}$$
adamc@543 1570
adamc@543 1571 $$\begin{array}{l}
adamc@1193 1572 \mt{val} \; \mt{sql\_query1} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400 1573 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1574 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543 1575 \hspace{.1in} \to \mt{grouped} ::: \{\{\mt{Type}\}\} \\
adamc@543 1576 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1577 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1085 1578 \hspace{.1in} \to \mt{empties} :: \{\mt{Unit}\} \\
adamc@1193 1579 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adamc@1193 1580 \hspace{.1in} \Rightarrow [\mt{free} \sim \mt{grouped}] \\
adam@1400 1581 \hspace{.1in} \Rightarrow [\mt{afree} \sim \mt{tables}] \\
adamc@1193 1582 \hspace{.1in} \Rightarrow [\mt{empties} \sim \mt{selectedFields}] \\
adamc@1085 1583 \hspace{.1in} \Rightarrow \{\mt{Distinct} : \mt{bool}, \\
adamc@1193 1584 \hspace{.2in} \mt{From} : \mt{sql\_from\_items} \; \mt{free} \; \mt{tables}, \\
adam@1400 1585 \hspace{.2in} \mt{Where} : \mt{sql\_exp} \; (\mt{free} \rc \mt{tables}) \; \mt{afree} \; [] \; \mt{bool}, \\
adamc@543 1586 \hspace{.2in} \mt{GroupBy} : \mt{sql\_subset} \; \mt{tables} \; \mt{grouped}, \\
adam@1400 1587 \hspace{.2in} \mt{Having} : \mt{sql\_exp} \; (\mt{free} \rc \mt{grouped}) \; (\mt{afree} \rc \mt{tables}) \; [] \; \mt{bool}, \\
adamc@1085 1588 \hspace{.2in} \mt{SelectFields} : \mt{sql\_subset} \; \mt{grouped} \; (\mt{map} \; (\lambda \_ \Rightarrow []) \; \mt{empties} \rc \mt{selectedFields}), \\
adam@1400 1589 \hspace{.2in} \mt {SelectExps} : \$(\mt{map} \; (\mt{sql\_exp} \; (\mt{free} \rc \mt{grouped}) \; (\mt{afree} \rc \mt{tables}) \; []) \; \mt{selectedExps}) \} \\
adam@1400 1590 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1591 \end{array}$$
adamc@543 1592
adamc@543 1593 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 1594 $$\begin{array}{l}
adamc@543 1595 \mt{con} \; \mt{sql\_subset} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@543 1596 \mt{val} \; \mt{sql\_subset} : \mt{keep\_drop} :: \{(\{\mt{Type}\} \times \{\mt{Type}\})\} \\
adamc@543 1597 \hspace{.1in} \to \mt{sql\_subset} \\
adamc@658 1598 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1 \rc \mt{fields}.2)\; \mt{keep\_drop}) \\
adamc@658 1599 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1) \; \mt{keep\_drop}) \\
adamc@543 1600 \mt{val} \; \mt{sql\_subset\_all} : \mt{tables} :: \{\{\mt{Type}\}\} \to \mt{sql\_subset} \; \mt{tables} \; \mt{tables}
adamc@543 1601 \end{array}$$
adamc@543 1602
adamc@560 1603 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 1604 $$\begin{array}{l}
adamc@543 1605 \mt{con} \; \mt{sql\_exp} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}
adamc@543 1606 \end{array}$$
adamc@543 1607
adamc@543 1608 Any field in scope may be converted to an expression.
adamc@543 1609 $$\begin{array}{l}
adamc@543 1610 \mt{val} \; \mt{sql\_field} : \mt{otherTabs} ::: \{\{\mt{Type}\}\} \to \mt{otherFields} ::: \{\mt{Type}\} \\
adamc@543 1611 \hspace{.1in} \to \mt{fieldType} ::: \mt{Type} \to \mt{agg} ::: \{\{\mt{Type}\}\} \\
adamc@543 1612 \hspace{.1in} \to \mt{exps} ::: \{\mt{Type}\} \\
adamc@543 1613 \hspace{.1in} \to \mt{tab} :: \mt{Name} \to \mt{field} :: \mt{Name} \\
adamc@543 1614 \hspace{.1in} \to \mt{sql\_exp} \; ([\mt{tab} = [\mt{field} = \mt{fieldType}] \rc \mt{otherFields}] \rc \mt{otherTabs}) \; \mt{agg} \; \mt{exps} \; \mt{fieldType}
adamc@543 1615 \end{array}$$
adamc@543 1616
adamc@544 1617 There is an analogous function for referencing named expressions.
adamc@544 1618 $$\begin{array}{l}
adamc@544 1619 \mt{val} \; \mt{sql\_exp} : \mt{tabs} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{t} ::: \mt{Type} \to \mt{rest} ::: \{\mt{Type}\} \to \mt{nm} :: \mt{Name} \\
adamc@544 1620 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tabs} \; \mt{agg} \; ([\mt{nm} = \mt{t}] \rc \mt{rest}) \; \mt{t}
adamc@544 1621 \end{array}$$
adamc@544 1622
adamc@544 1623 Ur values of appropriate types may be injected into SQL expressions.
adamc@544 1624 $$\begin{array}{l}
adamc@786 1625 \mt{class} \; \mt{sql\_injectable\_prim} \\
adamc@786 1626 \mt{val} \; \mt{sql\_bool} : \mt{sql\_injectable\_prim} \; \mt{bool} \\
adamc@786 1627 \mt{val} \; \mt{sql\_int} : \mt{sql\_injectable\_prim} \; \mt{int} \\
adamc@786 1628 \mt{val} \; \mt{sql\_float} : \mt{sql\_injectable\_prim} \; \mt{float} \\
adamc@786 1629 \mt{val} \; \mt{sql\_string} : \mt{sql\_injectable\_prim} \; \mt{string} \\
adamc@786 1630 \mt{val} \; \mt{sql\_time} : \mt{sql\_injectable\_prim} \; \mt{time} \\
adamc@786 1631 \mt{val} \; \mt{sql\_blob} : \mt{sql\_injectable\_prim} \; \mt{blob} \\
adamc@786 1632 \mt{val} \; \mt{sql\_channel} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{channel} \; \mt{t}) \\
adamc@786 1633 \mt{val} \; \mt{sql\_client} : \mt{sql\_injectable\_prim} \; \mt{client} \\
adamc@786 1634 \\
adamc@544 1635 \mt{class} \; \mt{sql\_injectable} \\
adamc@786 1636 \mt{val} \; \mt{sql\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@786 1637 \mt{val} \; \mt{sql\_option\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; (\mt{option} \; \mt{t}) \\
adamc@786 1638 \\
adamc@544 1639 \mt{val} \; \mt{sql\_inject} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@544 1640 \hspace{.1in} \to \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adamc@544 1641 \end{array}$$
adamc@544 1642
adamc@1123 1643 Additionally, most function-free types may be injected safely, via the $\mt{serialized}$ type family.
adamc@1123 1644 $$\begin{array}{l}
adamc@1123 1645 \mt{con} \; \mt{serialized} :: \mt{Type} \to \mt{Type} \\
adamc@1123 1646 \mt{val} \; \mt{serialize} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{serialized} \; \mt{t} \\
adamc@1123 1647 \mt{val} \; \mt{deserialize} : \mt{t} ::: \mt{Type} \to \mt{serialized} \; \mt{t} \to \mt{t} \\
adamc@1123 1648 \mt{val} \; \mt{sql\_serialized} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{serialized} \; \mt{t})
adamc@1123 1649 \end{array}$$
adamc@1123 1650
adamc@544 1651 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 1652 $$\begin{array}{l}
adamc@544 1653 \mt{val} \; \mt{sql\_is\_null} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544 1654 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; (\mt{option} \; \mt{t}) \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{bool}
adamc@544 1655 \end{array}$$
adamc@544 1656
adamc@559 1657 We have generic nullary, unary, and binary operators.
adamc@544 1658 $$\begin{array}{l}
adamc@544 1659 \mt{con} \; \mt{sql\_nfunc} :: \mt{Type} \to \mt{Type} \\
adamc@544 1660 \mt{val} \; \mt{sql\_current\_timestamp} : \mt{sql\_nfunc} \; \mt{time} \\
adamc@544 1661 \mt{val} \; \mt{sql\_nfunc} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544 1662 \hspace{.1in} \to \mt{sql\_nfunc} \; \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\\end{array}$$
adamc@544 1663
adamc@544 1664 $$\begin{array}{l}
adamc@544 1665 \mt{con} \; \mt{sql\_unary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544 1666 \mt{val} \; \mt{sql\_not} : \mt{sql\_unary} \; \mt{bool} \; \mt{bool} \\
adamc@544 1667 \mt{val} \; \mt{sql\_unary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adamc@544 1668 \hspace{.1in} \to \mt{sql\_unary} \; \mt{arg} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res} \\
adamc@544 1669 \end{array}$$
adamc@544 1670
adamc@544 1671 $$\begin{array}{l}
adamc@544 1672 \mt{con} \; \mt{sql\_binary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544 1673 \mt{val} \; \mt{sql\_and} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544 1674 \mt{val} \; \mt{sql\_or} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544 1675 \mt{val} \; \mt{sql\_binary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg_1} ::: \mt{Type} \to \mt{arg_2} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adamc@544 1676 \hspace{.1in} \to \mt{sql\_binary} \; \mt{arg_1} \; \mt{arg_2} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_1} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_2} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res}
adamc@544 1677 \end{array}$$
adamc@544 1678
adamc@544 1679 $$\begin{array}{l}
adamc@559 1680 \mt{class} \; \mt{sql\_arith} \\
adamc@559 1681 \mt{val} \; \mt{sql\_int\_arith} : \mt{sql\_arith} \; \mt{int} \\
adamc@559 1682 \mt{val} \; \mt{sql\_float\_arith} : \mt{sql\_arith} \; \mt{float} \\
adamc@559 1683 \mt{val} \; \mt{sql\_neg} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_unary} \; \mt{t} \; \mt{t} \\
adamc@559 1684 \mt{val} \; \mt{sql\_plus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1685 \mt{val} \; \mt{sql\_minus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1686 \mt{val} \; \mt{sql\_times} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1687 \mt{val} \; \mt{sql\_div} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1688 \mt{val} \; \mt{sql\_mod} : \mt{sql\_binary} \; \mt{int} \; \mt{int} \; \mt{int}
adamc@559 1689 \end{array}$$
adamc@544 1690
adamc@656 1691 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 1692 $$\begin{array}{l}
adamc@544 1693 \mt{val} \; \mt{sql\_count} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int}
adamc@544 1694 \end{array}$$
adamc@544 1695
adamc@544 1696 $$\begin{array}{l}
adamc@1188 1697 \mt{con} \; \mt{sql\_aggregate} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@1188 1698 \mt{val} \; \mt{sql\_aggregate} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{dom} ::: \mt{Type} \to \mt{ran} ::: \mt{Type} \\
adamc@1188 1699 \hspace{.1in} \to \mt{sql\_aggregate} \; \mt{dom} \; \mt{ran} \to \mt{sql\_exp} \; \mt{agg} \; \mt{agg} \; \mt{exps} \; \mt{dom} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{ran}
adamc@1188 1700 \end{array}$$
adamc@1188 1701
adamc@1188 1702 $$\begin{array}{l}
adamc@1188 1703 \mt{val} \; \mt{sql\_count\_col} : \mt{t} ::: \mt{Type} \to \mt{sql\_aggregate} \; (\mt{option} \; \mt{t}) \; \mt{int}
adamc@544 1704 \end{array}$$
adam@1400 1705
adam@1400 1706 Most aggregate functions are typed using a two-parameter constructor class $\mt{nullify}$ which maps $\mt{option}$ types to themselves and adds $\mt{option}$ to others. That is, this constructor class represents the process of making an SQL type ``nullable.''
adamc@544 1707
adamc@544 1708 $$\begin{array}{l}
adamc@544 1709 \mt{class} \; \mt{sql\_summable} \\
adamc@544 1710 \mt{val} \; \mt{sql\_summable\_int} : \mt{sql\_summable} \; \mt{int} \\
adamc@544 1711 \mt{val} \; \mt{sql\_summable\_float} : \mt{sql\_summable} \; \mt{float} \\
adam@1400 1712 \mt{val} \; \mt{sql\_avg} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt} \\
adam@1400 1713 \mt{val} \; \mt{sql\_sum} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt}
adamc@544 1714 \end{array}$$
adamc@544 1715
adamc@544 1716 $$\begin{array}{l}
adamc@544 1717 \mt{class} \; \mt{sql\_maxable} \\
adamc@544 1718 \mt{val} \; \mt{sql\_maxable\_int} : \mt{sql\_maxable} \; \mt{int} \\
adamc@544 1719 \mt{val} \; \mt{sql\_maxable\_float} : \mt{sql\_maxable} \; \mt{float} \\
adamc@544 1720 \mt{val} \; \mt{sql\_maxable\_string} : \mt{sql\_maxable} \; \mt{string} \\
adamc@544 1721 \mt{val} \; \mt{sql\_maxable\_time} : \mt{sql\_maxable} \; \mt{time} \\
adam@1400 1722 \mt{val} \; \mt{sql\_max} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt} \\
adam@1400 1723 \mt{val} \; \mt{sql\_min} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt}
adamc@544 1724 \end{array}$$
adamc@544 1725
adamc@1193 1726 Any SQL query that returns single columns may be turned into a subquery expression.
adamc@1193 1727
adamc@786 1728 $$\begin{array}{l}
adam@1421 1729 \mt{val} \; \mt{sql\_subquery} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \\
adam@1421 1730 \hspace{.1in} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_query} \; \mt{tables} \; \mt{agg} \; [\mt{nm} = \mt{t}] \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{nt}
adamc@1193 1731 \end{array}$$
adamc@1193 1732
adamc@1193 1733 \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 1734 $$\begin{array}{l}
adamc@1193 1735 \mt{con} \; \mt{sql\_from\_items} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@1193 1736 \mt{val} \; \mt{sql\_from\_table} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1737 \hspace{.1in} \to \mt{t} ::: \mt{Type} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; \mt{t} \; \mt{fs} \to \mt{name} :: \mt{Name} \to \mt{t} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193 1738 \mt{val} \; \mt{sql\_from\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{name} :: \mt{Name} \to \mt{sql\_query} \; \mt{free} \; [] \; \mt{fs} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193 1739 \mt{val} \; \mt{sql\_from\_comma} : \mt{free} ::: \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \to [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193 1740 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adamc@1193 1741 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2}) \\
adamc@1193 1742 \mt{val} \; \mt{sql\_inner\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1743 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193 1744 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adamc@1193 1745 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193 1746 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2})
adamc@786 1747 \end{array}$$
adamc@786 1748
adamc@786 1749 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 1750 $$\begin{array}{l}
adamc@786 1751 \mt{class} \; \mt{nullify} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@786 1752 \mt{val} \; \mt{nullify\_option} : \mt{t} ::: \mt{Type} \to \mt{nullify} \; (\mt{option} \; \mt{t}) \; (\mt{option} \; \mt{t}) \\
adamc@786 1753 \mt{val} \; \mt{nullify\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{nullify} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@786 1754 \end{array}$$
adamc@786 1755
adamc@786 1756 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 1757
adamc@786 1758 $$\begin{array}{l}
adamc@1193 1759 \mt{val} \; \mt{sql\_left\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{(\mt{Type} \times \mt{Type})\}\} \\
adamc@1193 1760 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@786 1761 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\lambda \mt{r} \Rightarrow \$(\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{nullify} \; \mt{p}.1 \; \mt{p}.2) \; \mt{r})) \; \mt{tabs2}) \\
adamc@1193 1762 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \\
adamc@1193 1763 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193 1764 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.2)) \; \mt{tabs2})
adamc@786 1765 \end{array}$$
adamc@786 1766
adamc@544 1767 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 1768 $$\begin{array}{l}
adamc@544 1769 \mt{type} \; \mt{sql\_direction} \\
adamc@544 1770 \mt{val} \; \mt{sql\_asc} : \mt{sql\_direction} \\
adamc@544 1771 \mt{val} \; \mt{sql\_desc} : \mt{sql\_direction} \\
adamc@544 1772 \\
adamc@544 1773 \mt{con} \; \mt{sql\_order\_by} :: \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@544 1774 \mt{val} \; \mt{sql\_order\_by\_Nil} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} :: \{\mt{Type}\} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544 1775 \mt{val} \; \mt{sql\_order\_by\_Cons} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544 1776 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; [] \; \mt{exps} \; \mt{t} \to \mt{sql\_direction} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544 1777 \\
adamc@544 1778 \mt{type} \; \mt{sql\_limit} \\
adamc@544 1779 \mt{val} \; \mt{sql\_no\_limit} : \mt{sql\_limit} \\
adamc@544 1780 \mt{val} \; \mt{sql\_limit} : \mt{int} \to \mt{sql\_limit} \\
adamc@544 1781 \\
adamc@544 1782 \mt{type} \; \mt{sql\_offset} \\
adamc@544 1783 \mt{val} \; \mt{sql\_no\_offset} : \mt{sql\_offset} \\
adamc@544 1784 \mt{val} \; \mt{sql\_offset} : \mt{int} \to \mt{sql\_offset}
adamc@544 1785 \end{array}$$
adamc@544 1786
adamc@545 1787
adamc@545 1788 \subsubsection{DML}
adamc@545 1789
adamc@545 1790 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 1791
adamc@545 1792 $$\begin{array}{l}
adamc@545 1793 \mt{type} \; \mt{dml} \\
adamc@545 1794 \mt{val} \; \mt{dml} : \mt{dml} \to \mt{transaction} \; \mt{unit}
adamc@545 1795 \end{array}$$
adamc@545 1796
adam@1297 1797 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 1798
adam@1297 1799 $$\begin{array}{l}
adam@1297 1800 \mt{val} \; \mt{tryDml} : \mt{dml} \to \mt{transaction} \; (\mt{option} \; \mt{string})
adam@1297 1801 \end{array}$$
adam@1297 1802
adamc@545 1803 Properly-typed records may be used to form $\mt{INSERT}$ commands.
adamc@545 1804 $$\begin{array}{l}
adamc@545 1805 \mt{val} \; \mt{insert} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \\
adamc@658 1806 \hspace{.1in} \to \$(\mt{map} \; (\mt{sql\_exp} \; [] \; [] \; []) \; \mt{fields}) \to \mt{dml}
adamc@545 1807 \end{array}$$
adamc@545 1808
adamc@545 1809 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 1810 $$\begin{array}{l}
adam@1380 1811 \mt{val} \; \mt{update} : \mt{unchanged} ::: \{\mt{Type}\} \to \mt{changed} :: \{\mt{Type}\} \to [\mt{changed} \sim \mt{unchanged}] \\
adamc@658 1812 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; []) \; \mt{changed}) \\
adamc@545 1813 \hspace{.1in} \to \mt{sql\_table} \; (\mt{changed} \rc \mt{unchanged}) \to \mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545 1814 \end{array}$$
adamc@545 1815
adamc@545 1816 A $\mt{DELETE}$ command is formed from a table and a $\mt{WHERE}$ clause.
adamc@545 1817 $$\begin{array}{l}
adamc@545 1818 \mt{val} \; \mt{delete} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \to \mt{sql\_exp} \; [\mt{T} = \mt{fields}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545 1819 \end{array}$$
adamc@545 1820
adamc@546 1821 \subsubsection{Sequences}
adamc@546 1822
adamc@546 1823 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 1824
adamc@546 1825 $$\begin{array}{l}
adamc@546 1826 \mt{type} \; \mt{sql\_sequence} \\
adamc@1085 1827 \mt{val} \; \mt{nextval} : \mt{sql\_sequence} \to \mt{transaction} \; \mt{int} \\
adamc@1085 1828 \mt{val} \; \mt{setval} : \mt{sql\_sequence} \to \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@546 1829 \end{array}$$
adamc@546 1830
adamc@546 1831
adamc@547 1832 \subsection{XML}
adamc@547 1833
adam@1333 1834 Ur/Web's library contains an encoding of XML syntax and semantic constraints. We make no effort to follow the standards governing XML schemas. Rather, XML fragments are viewed more as values of ML datatypes, and we only track which tags are allowed inside which other tags. The Ur/Web standard library encodes a very loose version of XHTML, where it is very easy to produce documents which are invalid XHTML, but which still display properly in all major browsers. The main purposes of the invariants that are enforced are first, to provide some documentation about the places where it would make sense to insert XML fragments; and second, to rule out code injection attacks and other abstraction violations related to HTML syntax.
adamc@547 1835
adam@1345 1836 The basic XML type family has arguments respectively indicating the \emph{context} of a fragment, the fields that the fragment expects to be bound on entry (and their types), and the fields that the fragment will bind (and their types). Contexts are a record-based ``poor man's subtyping'' encoding, with each possible set of valid tags corresponding to a different context record. For instance, the context for the \texttt{<td>} tag is $[\mt{Body}, \mt{Tr}]$, to indicate a kind of nesting inside \texttt{<body>} and \texttt{<tr>}. Contexts are maintained in a somewhat ad-hoc way; the only definitive reference for their meanings is the types of the tag values in \texttt{basis.urs}. The arguments dealing with field binding are only relevant to HTML forms.
adamc@547 1837 $$\begin{array}{l}
adamc@547 1838 \mt{con} \; \mt{xml} :: \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547 1839 \end{array}$$
adamc@547 1840
adamc@547 1841 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 1842 $$\begin{array}{l}
adamc@547 1843 \mt{con} \; \mt{tag} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547 1844 \end{array}$$
adamc@547 1845
adamc@547 1846 Literal text may be injected into XML as ``CDATA.''
adamc@547 1847 $$\begin{array}{l}
adamc@547 1848 \mt{val} \; \mt{cdata} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{string} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adamc@547 1849 \end{array}$$
adamc@547 1850
adam@1358 1851 There is also a function to insert the literal value of a character. Since Ur/Web uses the UTF-8 text encoding, the $\mt{cdata}$ function is only sufficient to encode characters with ASCII codes below 128. Higher codes have alternate meanings in UTF-8 than in usual ASCII, so this alternate function should be used with them.
adam@1358 1852 $$\begin{array}{l}
adam@1358 1853 \mt{val} \; \mt{cdataChar} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{char} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adam@1358 1854 \end{array}$$
adam@1358 1855
adamc@547 1856 There is a function for producing an XML tree with a particular tag at its root.
adamc@547 1857 $$\begin{array}{l}
adamc@547 1858 \mt{val} \; \mt{tag} : \mt{attrsGiven} ::: \{\mt{Type}\} \to \mt{attrsAbsent} ::: \{\mt{Type}\} \to \mt{ctxOuter} ::: \{\mt{Unit}\} \to \mt{ctxInner} ::: \{\mt{Unit}\} \\
adamc@547 1859 \hspace{.1in} \to \mt{useOuter} ::: \{\mt{Type}\} \to \mt{useInner} ::: \{\mt{Type}\} \to \mt{bindOuter} ::: \{\mt{Type}\} \to \mt{bindInner} ::: \{\mt{Type}\} \\
adam@1380 1860 \hspace{.1in} \to [\mt{attrsGiven} \sim \mt{attrsAbsent}] \Rightarrow [\mt{useOuter} \sim \mt{useInner}] \Rightarrow [\mt{bindOuter} \sim \mt{bindInner}] \\
adamc@787 1861 \hspace{.1in} \Rightarrow \mt{option} \; \mt{css\_class} \\
adamc@787 1862 \hspace{.1in} \to \$\mt{attrsGiven} \\
adamc@547 1863 \hspace{.1in} \to \mt{tag} \; (\mt{attrsGiven} \rc \mt{attrsAbsent}) \; \mt{ctxOuter} \; \mt{ctxInner} \; \mt{useOuter} \; \mt{bindOuter} \\
adamc@547 1864 \hspace{.1in} \to \mt{xml} \; \mt{ctxInner} \; \mt{useInner} \; \mt{bindInner} \to \mt{xml} \; \mt{ctxOuter} \; (\mt{useOuter} \rc \mt{useInner}) \; (\mt{bindOuter} \rc \mt{bindInner})
adamc@547 1865 \end{array}$$
adam@1297 1866 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 1867
adamc@547 1868 Two XML fragments may be concatenated.
adamc@547 1869 $$\begin{array}{l}
adamc@547 1870 \mt{val} \; \mt{join} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{bind_1} ::: \{\mt{Type}\} \to \mt{bind_2} ::: \{\mt{Type}\} \\
adam@1380 1871 \hspace{.1in} \to [\mt{use_1} \sim \mt{bind_1}] \Rightarrow [\mt{bind_1} \sim \mt{bind_2}] \\
adamc@547 1872 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind_1} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{bind_1}) \; \mt{bind_2} \to \mt{xml} \; \mt{ctx} \; \mt{use_1} \; (\mt{bind_1} \rc \mt{bind_2})
adamc@547 1873 \end{array}$$
adamc@547 1874
adamc@547 1875 Finally, any XML fragment may be updated to ``claim'' to use more form fields than it does.
adamc@547 1876 $$\begin{array}{l}
adam@1380 1877 \mt{val} \; \mt{useMore} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{use_2} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to [\mt{use_1} \sim \mt{use_2}] \\
adamc@547 1878 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{use_2}) \; \mt{bind}
adamc@547 1879 \end{array}$$
adamc@547 1880
adam@1344 1881 We will not list here the different HTML tags and related functions from the standard library. They should be easy enough to understand from the code in \texttt{basis.urs}. The set of tags in the library is not yet claimed to be complete for HTML standards. Also note that there is currently no way for the programmer to add his own tags. It \emph{is} possible to add new tags directly to \texttt{basis.urs}, but this should only be done as a prelude to suggesting a patch to the main distribution.
adamc@547 1882
adamc@547 1883 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 1884 $$\begin{array}{l}
adamc@547 1885 \mt{val} \; \mt{error} : \mt{t} ::: \mt{Type} \to \mt{xml} \; [\mt{Body}] \; [] \; [] \to \mt{t}
adamc@547 1886 \end{array}$$
adamc@547 1887
adamc@549 1888
adamc@701 1889 \subsection{Client-Side Programming}
adamc@659 1890
adamc@701 1891 Ur/Web supports running code on web browsers, via automatic compilation to JavaScript.
adamc@701 1892
adamc@701 1893 \subsubsection{The Basics}
adamc@701 1894
adam@1400 1895 All of the functions in this subsection are client-side only.
adam@1400 1896
adam@1297 1897 Clients can open alert and confirm dialog boxes, in the usual annoying JavaScript way.
adamc@701 1898 $$\begin{array}{l}
adam@1297 1899 \mt{val} \; \mt{alert} : \mt{string} \to \mt{transaction} \; \mt{unit} \\
adam@1297 1900 \mt{val} \; \mt{confirm} : \mt{string} \to \mt{transaction} \; \mt{bool}
adamc@701 1901 \end{array}$$
adamc@701 1902
adamc@701 1903 Any transaction may be run in a new thread with the $\mt{spawn}$ function.
adamc@701 1904 $$\begin{array}{l}
adamc@701 1905 \mt{val} \; \mt{spawn} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit}
adamc@701 1906 \end{array}$$
adamc@701 1907
adamc@701 1908 The current thread can be paused for at least a specified number of milliseconds.
adamc@701 1909 $$\begin{array}{l}
adamc@701 1910 \mt{val} \; \mt{sleep} : \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@701 1911 \end{array}$$
adamc@701 1912
adamc@787 1913 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 1914 $$\begin{array}{l}
adamc@787 1915 \mt{val} \; \mt{onError} : (\mt{xbody} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787 1916 \mt{val} \; \mt{onFail} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787 1917 \mt{val} \; \mt{onConnectFail} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787 1918 \mt{val} \; \mt{onDisconnect} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787 1919 \mt{val} \; \mt{onServerError} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit}
adamc@787 1920 \end{array}$$
adamc@787 1921
adamc@701 1922 \subsubsection{Functional-Reactive Page Generation}
adamc@701 1923
adamc@701 1924 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 1925
adam@1403 1926 More operationally, you can think of a source as a mutable cell with facilities for subscription to change notifications. That level of detail is hidden behind a monadic facility to be described below. First, there are three primitive operations for working with sources just as if they were ML \cd{ref} cells, corresponding to ML's \cd{ref}, \cd{:=}, and \cd{!} operations.
adam@1403 1927
adamc@659 1928 $$\begin{array}{l}
adamc@659 1929 \mt{con} \; \mt{source} :: \mt{Type} \to \mt{Type} \\
adamc@659 1930 \mt{val} \; \mt{source} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{transaction} \; (\mt{source} \; \mt{t}) \\
adamc@659 1931 \mt{val} \; \mt{set} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@659 1932 \mt{val} \; \mt{get} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@659 1933 \end{array}$$
adamc@659 1934
adam@1400 1935 Only source creation and setting are supported server-side, as a convenience to help in setting up a page, where you may wish to allocate many sources that will be referenced through the page. All server-side storage of values inside sources uses string serializations of values, while client-side storage uses normal JavaScript values.
adam@1400 1936
adam@1403 1937 Pure functions over arbitrary numbers of sources are represented in a monad of \emph{signals}, which may only be used in client-side code. This is presented to the programmer in the form of a monad $\mt{signal}$, each of whose values represents (conceptually) some pure function over all sources that may be allocated in the course of program execution. A monad operation $\mt{signal}$ denotes the identity function over a particular source. By using $\mt{signal}$ on a source, you implicitly subscribe to change notifications for that source. That is, your signal will automatically be recomputed as that source changes. The usual monad operators make it possible to build up complex signals that depend on multiple sources; automatic updating upon source-value changes still happens automatically.
adamc@659 1938
adamc@659 1939 $$\begin{array}{l}
adamc@659 1940 \mt{con} \; \mt{signal} :: \mt{Type} \to \mt{Type} \\
adamc@659 1941 \mt{val} \; \mt{signal\_monad} : \mt{monad} \; \mt{signal} \\
adamc@659 1942 \mt{val} \; \mt{signal} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{signal} \; \mt{t}
adamc@659 1943 \end{array}$$
adamc@659 1944
adamc@659 1945 A reactive portion of an HTML page is injected with a $\mt{dyn}$ tag, which has a signal-valued attribute $\mt{Signal}$.
adamc@659 1946
adamc@659 1947 $$\begin{array}{l}
adamc@701 1948 \mt{val} \; \mt{dyn} : \mt{use} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to \mt{unit} \\
adamc@701 1949 \hspace{.1in} \to \mt{tag} \; [\mt{Signal} = \mt{signal} \; (\mt{xml} \; \mt{body} \; \mt{use} \; \mt{bind})] \; \mt{body} \; [] \; \mt{use} \; \mt{bind}
adamc@659 1950 \end{array}$$
adamc@659 1951
adamc@701 1952 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 1953
adamc@914 1954 \subsubsection{Remote Procedure Calls}
adamc@914 1955
adamc@914 1956 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 1957
adamc@914 1958 $$\begin{array}{l}
adamc@914 1959 \mt{val} \; \mt{rpc} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@914 1960 \end{array}$$
adamc@914 1961
adamc@701 1962 \subsubsection{Asynchronous Message-Passing}
adamc@701 1963
adamc@701 1964 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 1965
adamc@701 1966 $$\begin{array}{l}
adamc@701 1967 \mt{type} \; \mt{client} \\
adamc@701 1968 \mt{val} \; \mt{self} : \mt{transaction} \; \mt{client}
adamc@701 1969 \end{array}$$
adamc@701 1970
adamc@701 1971 \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 1972
adamc@701 1973 $$\begin{array}{l}
adamc@701 1974 \mt{con} \; \mt{channel} :: \mt{Type} \to \mt{Type} \\
adamc@701 1975 \mt{val} \; \mt{channel} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; (\mt{channel} \; \mt{t}) \\
adamc@701 1976 \mt{val} \; \mt{send} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@701 1977 \mt{val} \; \mt{recv} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@701 1978 \end{array}$$
adamc@701 1979
adamc@701 1980 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 1981
adamc@701 1982 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 1983
adamc@659 1984
adamc@549 1985 \section{Ur/Web Syntax Extensions}
adamc@549 1986
adamc@549 1987 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 1988
adamc@549 1989 \subsection{SQL}
adamc@549 1990
adamc@786 1991 \subsubsection{\label{tables}Table Declarations}
adamc@786 1992
adamc@788 1993 $\mt{table}$ declarations may include constraints, via these grammar rules.
adamc@788 1994 $$\begin{array}{rrcll}
adamc@788 1995 \textrm{Declarations} & d &::=& \mt{table} \; x : c \; [pk[,]] \; cts \\
adamc@788 1996 \textrm{Primary key constraints} & pk &::=& \mt{PRIMARY} \; \mt{KEY} \; K \\
adamc@788 1997 \textrm{Keys} & K &::=& f \mid (f, (f,)^+) \\
adamc@788 1998 \textrm{Constraint sets} & cts &::=& \mt{CONSTRAINT} f \; ct \mid cts, cts \mid \{\{e\}\} \\
adamc@788 1999 \textrm{Constraints} & ct &::=& \mt{UNIQUE} \; K \mid \mt{CHECK} \; E \\
adamc@788 2000 &&& \mid \mt{FOREIGN} \; \mt{KEY} \; K \; \mt{REFERENCES} \; F \; (K) \; [\mt{ON} \; \mt{DELETE} \; pr] \; [\mt{ON} \; \mt{UPDATE} \; pr] \\
adamc@788 2001 \textrm{Foreign tables} & F &::=& x \mid \{\{e\}\} \\
adamc@788 2002 \textrm{Propagation modes} & pr &::=& \mt{NO} \; \mt{ACTION} \mid \mt{RESTRICT} \mid \mt{CASCADE} \mid \mt{SET} \; \mt{NULL}
adamc@788 2003 \end{array}$$
adamc@788 2004
adamc@788 2005 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 2006
adamc@788 2007
adamc@549 2008 \subsubsection{Queries}
adamc@549 2009
adamc@550 2010 Queries $Q$ are added to the rules for expressions $e$.
adamc@550 2011
adamc@549 2012 $$\begin{array}{rrcll}
adamc@550 2013 \textrm{Queries} & Q &::=& (q \; [\mt{ORDER} \; \mt{BY} \; (E \; [o],)^+] \; [\mt{LIMIT} \; N] \; [\mt{OFFSET} \; N]) \\
adamc@1085 2014 \textrm{Pre-queries} & q &::=& \mt{SELECT} \; [\mt{DISTINCT}] \; P \; \mt{FROM} \; F,^+ \; [\mt{WHERE} \; E] \; [\mt{GROUP} \; \mt{BY} \; p,^+] \; [\mt{HAVING} \; E] \\
adamc@1085 2015 &&& \mid q \; R \; q \mid \{\{\{e\}\}\} \\
adamc@549 2016 \textrm{Relational operators} & R &::=& \mt{UNION} \mid \mt{INTERSECT} \mid \mt{EXCEPT}
adamc@549 2017 \end{array}$$
adamc@549 2018
adamc@549 2019 $$\begin{array}{rrcll}
adamc@549 2020 \textrm{Projections} & P &::=& \ast & \textrm{all columns} \\
adamc@549 2021 &&& p,^+ & \textrm{particular columns} \\
adamc@549 2022 \textrm{Pre-projections} & p &::=& t.f & \textrm{one column from a table} \\
adamc@558 2023 &&& t.\{\{c\}\} & \textrm{a record of columns from a table (of kind $\{\mt{Type}\}$)} \\
adamc@1194 2024 &&& E \; [\mt{AS} \; f] & \textrm{expression column} \\
adamc@549 2025 \textrm{Table names} & t &::=& x & \textrm{constant table name (automatically capitalized)} \\
adamc@549 2026 &&& X & \textrm{constant table name} \\
adamc@549 2027 &&& \{\{c\}\} & \textrm{computed table name (of kind $\mt{Name}$)} \\
adamc@549 2028 \textrm{Column names} & f &::=& X & \textrm{constant column name} \\
adamc@549 2029 &&& \{c\} & \textrm{computed column name (of kind $\mt{Name}$)} \\
adamc@549 2030 \textrm{Tables} & T &::=& x & \textrm{table variable, named locally by its own capitalization} \\
adamc@549 2031 &&& x \; \mt{AS} \; t & \textrm{table variable, with local name} \\
adamc@549 2032 &&& \{\{e\}\} \; \mt{AS} \; t & \textrm{computed table expression, with local name} \\
adamc@1085 2033 \textrm{$\mt{FROM}$ items} & F &::=& T \mid \{\{e\}\} \mid F \; J \; \mt{JOIN} \; F \; \mt{ON} \; E \\
adamc@1085 2034 &&& \mid F \; \mt{CROSS} \; \mt{JOIN} \ F \\
adamc@1193 2035 &&& \mid (Q) \; \mt{AS} \; t \\
adamc@1085 2036 \textrm{Joins} & J &::=& [\mt{INNER}] \\
adamc@1085 2037 &&& \mid [\mt{LEFT} \mid \mt{RIGHT} \mid \mt{FULL}] \; [\mt{OUTER}] \\
adamc@549 2038 \textrm{SQL expressions} & E &::=& p & \textrm{column references} \\
adamc@549 2039 &&& X & \textrm{named expression references} \\
adamc@549 2040 &&& \{\{e\}\} & \textrm{injected native Ur expressions} \\
adamc@549 2041 &&& \{e\} & \textrm{computed expressions, probably using $\mt{sql\_exp}$ directly} \\
adamc@549 2042 &&& \mt{TRUE} \mid \mt{FALSE} & \textrm{boolean constants} \\
adamc@549 2043 &&& \ell & \textrm{primitive type literals} \\
adamc@549 2044 &&& \mt{NULL} & \textrm{null value (injection of $\mt{None}$)} \\
adamc@549 2045 &&& E \; \mt{IS} \; \mt{NULL} & \textrm{nullness test} \\
adamc@549 2046 &&& n & \textrm{nullary operators} \\
adamc@549 2047 &&& u \; E & \textrm{unary operators} \\
adamc@549 2048 &&& E \; b \; E & \textrm{binary operators} \\
adamc@549 2049 &&& \mt{COUNT}(\ast) & \textrm{count number of rows} \\
adamc@549 2050 &&& a(E) & \textrm{other aggregate function} \\
adamc@1193 2051 &&& (Q) & \textrm{subquery (must return a single expression column)} \\
adamc@549 2052 &&& (E) & \textrm{explicit precedence} \\
adamc@549 2053 \textrm{Nullary operators} & n &::=& \mt{CURRENT\_TIMESTAMP} \\
adamc@549 2054 \textrm{Unary operators} & u &::=& \mt{NOT} \\
adamc@549 2055 \textrm{Binary operators} & b &::=& \mt{AND} \mid \mt{OR} \mid \neq \mid < \mid \leq \mid > \mid \geq \\
adamc@1188 2056 \textrm{Aggregate functions} & a &::=& \mt{COUNT} \mid \mt{AVG} \mid \mt{SUM} \mid \mt{MIN} \mid \mt{MAX} \\
adamc@550 2057 \textrm{Directions} & o &::=& \mt{ASC} \mid \mt{DESC} \\
adamc@549 2058 \textrm{SQL integer} & N &::=& n \mid \{e\} \\
adamc@549 2059 \end{array}$$
adamc@549 2060
adamc@1085 2061 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 2062
adamc@1194 2063 Unnamed expression columns in $\mt{SELECT}$ clauses are assigned consecutive natural numbers, starting with 1.
adamc@1194 2064
adamc@550 2065 \subsubsection{DML}
adamc@550 2066
adamc@550 2067 DML commands $D$ are added to the rules for expressions $e$.
adamc@550 2068
adamc@550 2069 $$\begin{array}{rrcll}
adamc@550 2070 \textrm{Commands} & D &::=& (\mt{INSERT} \; \mt{INTO} \; T^E \; (f,^+) \; \mt{VALUES} \; (E,^+)) \\
adamc@550 2071 &&& (\mt{UPDATE} \; T^E \; \mt{SET} \; (f = E,)^+ \; \mt{WHERE} \; E) \\
adamc@550 2072 &&& (\mt{DELETE} \; \mt{FROM} \; T^E \; \mt{WHERE} \; E) \\
adamc@550 2073 \textrm{Table expressions} & T^E &::=& x \mid \{\{e\}\}
adamc@550 2074 \end{array}$$
adamc@550 2075
adamc@550 2076 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 2077
adamc@551 2078 \subsection{XML}
adamc@551 2079
adamc@551 2080 XML fragments $L$ are added to the rules for expressions $e$.
adamc@551 2081
adamc@551 2082 $$\begin{array}{rrcll}
adamc@551 2083 \textrm{XML fragments} & L &::=& \texttt{<xml/>} \mid \texttt{<xml>}l^*\texttt{</xml>} \\
adamc@551 2084 \textrm{XML pieces} & l &::=& \textrm{text} & \textrm{cdata} \\
adamc@551 2085 &&& \texttt{<}g\texttt{/>} & \textrm{tag with no children} \\
adamc@551 2086 &&& \texttt{<}g\texttt{>}l^*\texttt{</}x\texttt{>} & \textrm{tag with children} \\
adamc@559 2087 &&& \{e\} & \textrm{computed XML fragment} \\
adamc@559 2088 &&& \{[e]\} & \textrm{injection of an Ur expression, via the $\mt{Top}.\mt{txt}$ function} \\
adamc@551 2089 \textrm{Tag} & g &::=& h \; (x = v)^* \\
adamc@551 2090 \textrm{Tag head} & h &::=& x & \textrm{tag name} \\
adamc@551 2091 &&& h\{c\} & \textrm{constructor parameter} \\
adamc@551 2092 \textrm{Attribute value} & v &::=& \ell & \textrm{literal value} \\
adamc@551 2093 &&& \{e\} & \textrm{computed value} \\
adamc@551 2094 \end{array}$$
adamc@551 2095
adamc@552 2096
adamc@1198 2097 \section{\label{structure}The Structure of Web Applications}
adamc@553 2098
adamc@1127 2099 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 2100
adam@1347 2101 Normal links are accessible via HTTP \texttt{GET}, which the relevant standard says should never cause side effects. To export a page which may cause side effects, accessible only via HTTP \texttt{POST}, include one argument of the page handler of type $\mt{Basis.postBody}$. When the handler is called, this argument will receive a value that can be deconstructed into a MIME type (with $\mt{Basis.postType}$) and payload (with $\mt{Basis.postData}$). This kind of handler will only work with \texttt{POST} payloads of MIME types besides those associated with HTML forms; for these, use Ur/Web's built-in support, as described below.
adam@1347 2102
adam@1370 2103 Any normal page handler may also include arguments of type $\mt{option \; Basis.queryString}$, which will be handled specially. Rather than being deserialized from the current URI, such an argument is passed the whole query string that the handler received. The string may be analyzed by calling $\mt{Basis.show}$ on it. A handler of this kind may be passed as an argument to $\mt{Basis.effectfulUrl}$ to generate a URL to a page that may be used as a ``callback'' by an external service, such that the handler is allowed to cause side effects.
adam@1370 2104
adamc@553 2105 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 2106
adamc@553 2107 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 2108
adamc@558 2109 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 2110
adamc@660 2111 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 2112
adamc@789 2113 \medskip
adamc@789 2114
adam@1347 2115 The HTTP standard suggests that GET requests only be used in ways that generate no side effects. Side effecting operations should use POST requests instead. The Ur/Web compiler enforces this rule strictly, via a simple conservative program analysis. Any page that may have a side effect must be accessed through a form, all of which use POST requests, or via a direct call to a page handler with some argument of type $\mt{Basis.postBody}$. A page is judged to have a side effect if its code depends syntactically on any of the side-effecting, server-side FFI functions. Links, forms, and most client-side event handlers are not followed during this syntactic traversal, but \texttt{<body onload=\{...\}>} handlers \emph{are} examined, since they run right away and could just as well be considered parts of main page handlers.
adamc@789 2116
adamc@789 2117 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 2118
adam@1348 2119 \subsection{Tasks}
adam@1348 2120
adam@1348 2121 In many web applications, it's useful to run code at points other than requests from browsers. Ur/Web's \emph{task} mechanism facilitates this. A type family of \emph{task kinds} is in the standard library:
adam@1348 2122
adam@1348 2123 $$\begin{array}{l}
adam@1348 2124 \mt{con} \; \mt{task\_kind} :: \mt{Type} \to \mt{Type} \\
adam@1348 2125 \mt{val} \; \mt{initialize} : \mt{task\_kind} \; \mt{unit} \\
adam@1349 2126 \mt{val} \; \mt{clientLeaves} : \mt{task\_kind} \; \mt{client} \\
adam@1349 2127 \mt{val} \; \mt{periodic} : \mt{int} \to \mt{task\_kind} \; \mt{unit}
adam@1348 2128 \end{array}$$
adam@1348 2129
adam@1348 2130 A task kind names a particular extension point of generated applications, where the type parameter of a task kind describes which extra input data is available at that extension point. Add task code with the special declaration form $\mt{task} \; e_1 = e_2$, where $e_1$ is a task kind with data $\tau$, and $e_2$ is a function from $\tau$ to $\mt{transaction} \; \mt{unit}$.
adam@1348 2131
adam@1348 2132 The currently supported task kinds are:
adam@1348 2133 \begin{itemize}
adam@1349 2134 \item $\mt{initialize}$: Code that is run when the application starts up.
adam@1348 2135 \item $\mt{clientLeaves}$: Code that is run for each client that the runtime system decides has surfed away. When a request that generates a new client handle is aborted, that handle will still eventually be passed to $\mt{clientLeaves}$ task code, even though the corresponding browser was never informed of the client handle's existence. In other words, in general, $\mt{clientLeaves}$ handlers will be called more times than there are actual clients.
adam@1349 2136 \item $\mt{periodic} \; n$: Code that is run when the application starts up and then every $n$ seconds thereafter.
adam@1348 2137 \end{itemize}
adam@1348 2138
adamc@553 2139
adamc@897 2140 \section{The Foreign Function Interface}
adamc@897 2141
adamc@897 2142 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 2143
adamc@897 2144 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 2145
adamc@897 2146 \begin{itemize}
adamc@897 2147 \item \texttt{clientOnly Module.ident} registers a value as being allowed only in client-side code.
adamc@897 2148 \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 2149 \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 2150 \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 2151 \item \texttt{include FILE} requests inclusion of a C header file.
adamc@897 2152 \item \texttt{jsFunc Module.ident=name} gives a mapping from an Ur name for a value to a JavaScript name.
adamc@897 2153 \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 2154 \item \texttt{script URL} requests inclusion of a JavaScript source file within application HTML.
adamc@897 2155 \item \texttt{serverOnly Module.ident} registers a value as being allowed only in server-side code.
adamc@897 2156 \end{itemize}
adamc@897 2157
adamc@897 2158 \subsection{Writing C FFI Code}
adamc@897 2159
adamc@897 2160 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 2161
adamc@897 2162 \begin{itemize}
adamc@897 2163 \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 2164 \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 2165 \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 2166 \end{itemize}
adamc@897 2167
adamc@897 2168 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 2169 \begin{itemize}
adamc@897 2170 \item \begin{verbatim}
adamc@897 2171 void uw_error(uw_context, failure_kind, const char *fmt, ...);
adamc@897 2172 \end{verbatim}
adamc@897 2173 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 2174
adam@1329 2175 All pointers to the context-local heap (see description below of \texttt{uw\_malloc()}) become invalid at the start and end of any execution of a main entry point function of an application. For example, if the request handler is restarted because of a \texttt{uw\_error()} call with \texttt{BOUNDED\_RETRY} or for any other reason, it is unsafe to access any local heap pointers that may have been stashed somewhere beforehand.
adam@1329 2176
adamc@897 2177 \item \begin{verbatim}
adamc@897 2178 void uw_push_cleanup(uw_context, void (*func)(void *), void *arg);
adamc@897 2179 void uw_pop_cleanup(uw_context);
adamc@897 2180 \end{verbatim}
adam@1329 2181 Manipulate a stack of actions that should be taken if any kind of error condition arises. Calling the ``pop'' function both removes an action from the stack and executes it. It is a bug to let a page request handler finish successfully with unpopped cleanup actions.
adam@1329 2182
adam@1329 2183 Pending cleanup actions aren't intended to have any complex relationship amongst themselves, so, upon request handler abort, pending actions are executed in first-in-first-out order.
adamc@897 2184
adamc@897 2185 \item \begin{verbatim}
adamc@897 2186 void *uw_malloc(uw_context, size_t);
adamc@897 2187 \end{verbatim}
adam@1329 2188 A version of \texttt{malloc()} that allocates memory inside a context's heap, which is managed with region allocation. Thus, there is no \texttt{uw\_free()}, but you need to be careful not to keep ad-hoc C pointers to this area of memory. In general, \texttt{uw\_malloc()}ed memory should only be used in ways compatible with the computation model of pure Ur. This means it is fine to allocate and return a value that could just as well have been built with core Ur code. In contrast, it is almost never safe to store \texttt{uw\_malloc()}ed pointers in global variables, including when the storage happens implicitly by registering a callback that would take the pointer as an argument.
adam@1329 2189
adam@1329 2190 For performance and correctness reasons, it is usually preferable to use \texttt{uw\_malloc()} instead of \texttt{malloc()}. The former manipulates a local heap that can be kept allocated across page requests, while the latter uses global data structures that may face contention during concurrent execution. However, we emphasize again that \texttt{uw\_malloc()} should never be used to implement some logic that couldn't be implemented trivially by a constant-valued expression in Ur.
adamc@897 2191
adamc@897 2192 \item \begin{verbatim}
adamc@897 2193 typedef void (*uw_callback)(void *);
adam@1328 2194 typedef void (*uw_callback_with_retry)(void *, int will_retry);
adamc@897 2195 void uw_register_transactional(uw_context, void *data, uw_callback commit,
adam@1328 2196 uw_callback rollback, uw_callback_with_retry free);
adamc@897 2197 \end{verbatim}
adam@1328 2198 All side effects in Ur/Web programs need to be compatible with transactions, such that any set of actions can be undone at any time. Thus, you should not perform actions with non-local side effects directly; instead, register handlers to be called when the current transaction is committed or rolled back. The arguments here give an arbitary piece of data to be passed to callbacks, a function to call on commit, a function to call on rollback, and a function to call afterward in either case to clean up any allocated resources. A rollback handler may be called after the associated commit handler has already been called, if some later part of the commit process fails. A free handler is told whether the runtime system expects to retry the current page request after rollback finishes.
adamc@897 2199
adamc@1085 2200 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 2201
adam@1329 2202 When a request handler ends with multiple pending transactional actions, their handlers are run in a first-in-last-out stack-like order, wherever the order would otherwise be ambiguous.
adam@1329 2203
adam@1329 2204 It is not safe for any of these handlers to access a context-local heap through a pointer returned previously by \texttt{uw\_malloc()}, nor should any new calls to that function be made. Think of the context-local heap as meant for use by the Ur/Web code itself, while transactional handlers execute after the Ur/Web code has finished.
adam@1329 2205
adamc@1085 2206 \item \begin{verbatim}
adamc@1085 2207 void *uw_get_global(uw_context, char *name);
adamc@1085 2208 void uw_set_global(uw_context, char *name, void *data, uw_callback free);
adamc@1085 2209 \end{verbatim}
adam@1329 2210 Different FFI-based extensions may want to associate their own pieces of data with contexts. The global interface provides a way of doing that, where each extension must come up with its own unique key. The \texttt{free} argument to \texttt{uw\_set\_global()} explains how to deallocate the saved data. It is never safe to store \texttt{uw\_malloc()}ed pointers in global variable slots.
adamc@1085 2211
adamc@897 2212 \end{itemize}
adamc@897 2213
adamc@897 2214 \subsection{Writing JavaScript FFI Code}
adamc@897 2215
adamc@897 2216 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 2217
adamc@897 2218 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 2219
adamc@897 2220 \begin{itemize}
adamc@897 2221 \item Integers, floats, strings, characters, and booleans are represented in the usual JavaScript way.
adamc@985 2222 \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 2223 \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 2224 \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 2225 \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 2226 \end{itemize}
adamc@897 2227
adamc@897 2228 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 2229
adamc@897 2230
adamc@552 2231 \section{Compiler Phases}
adamc@552 2232
adamc@552 2233 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 2234
adamc@552 2235 In this section, we step through the main phases of compilation, noting what consequences each phase has for effective programming.
adamc@552 2236
adamc@552 2237 \subsection{Parse}
adamc@552 2238
adamc@552 2239 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 2240
adamc@552 2241 \subsection{Elaborate}
adamc@552 2242
adamc@552 2243 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 2244
adam@1378 2245 Those crawling through the compiler source will also want to be aware of another compiler phase, Explify, that occurs immediately afterward. This phase just translates from an AST language that includes unification variables to a very similar language that doesn't; all variables should have been determined by the end of Elaborate, anyway. The new AST language also drops some features that are used only for static checking and that have no influence on runtime behavior, like disjointness constraints.
adam@1378 2246
adamc@552 2247 \subsection{Unnest}
adamc@552 2248
adamc@552 2249 Named local function definitions are moved to the top level, to avoid the need to generate closures.
adamc@552 2250
adamc@552 2251 \subsection{Corify}
adamc@552 2252
adamc@552 2253 Module system features are compiled away, through inlining of functor definitions at application sites. Afterward, most abstraction boundaries are broken, facilitating optimization.
adamc@552 2254
adamc@552 2255 \subsection{Especialize}
adamc@552 2256
adam@1356 2257 Functions are specialized to particular argument patterns. This is an important trick for avoiding the need to maintain any closures at runtime. Currently, specialization only happens for prefixes of a function's full list of parameters, so you may need to take care to put arguments of function types before other arguments. The optimizer will not be effective enough if you use arguments that mix functions and values that must be calculated at run-time. For instance, a tuple of a function and an integer counter would not lead to successful code generation; these should be split into separate arguments via currying.
adamc@552 2258
adamc@552 2259 \subsection{Untangle}
adamc@552 2260
adamc@552 2261 Remove unnecessary mutual recursion, splitting recursive groups into strongly-connected components.
adamc@552 2262
adamc@552 2263 \subsection{Shake}
adamc@552 2264
adamc@552 2265 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 2266
adamc@661 2267 \subsection{Rpcify}
adamc@661 2268
adamc@661 2269 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 2270
adamc@661 2271 \subsection{Untangle, Shake}
adamc@661 2272
adamc@661 2273 Repeat these simplifications.
adamc@661 2274
adamc@553 2275 \subsection{\label{tag}Tag}
adamc@552 2276
adamc@552 2277 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 2278
adamc@552 2279 \subsection{Reduce}
adamc@552 2280
adamc@552 2281 Apply definitional equality rules to simplify the program as much as possible. This effectively includes inlining of every non-recursive definition.
adamc@552 2282
adamc@552 2283 \subsection{Unpoly}
adamc@552 2284
adamc@552 2285 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 2286
adamc@552 2287 \subsection{Specialize}
adamc@552 2288
adamc@558 2289 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 2290
adamc@552 2291 \subsection{Shake}
adamc@552 2292
adamc@558 2293 Here the compiler repeats the earlier Shake phase.
adamc@552 2294
adamc@552 2295 \subsection{Monoize}
adamc@552 2296
adamc@552 2297 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 2298
adamc@552 2299 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 2300
adamc@552 2301 \subsection{MonoOpt}
adamc@552 2302
adamc@552 2303 Simple algebraic laws are applied to simplify the program, focusing especially on efficient imperative generation of HTML pages.
adamc@552 2304
adamc@552 2305 \subsection{MonoUntangle}
adamc@552 2306
adamc@552 2307 Unnecessary mutual recursion is broken up again.
adamc@552 2308
adamc@552 2309 \subsection{MonoReduce}
adamc@552 2310
adamc@552 2311 Equivalents of the definitional equality rules are applied to simplify programs, with inlining again playing a major role.
adamc@552 2312
adamc@552 2313 \subsection{MonoShake, MonoOpt}
adamc@552 2314
adamc@552 2315 Unneeded declarations are removed, and basic optimizations are repeated.
adamc@552 2316
adamc@552 2317 \subsection{Fuse}
adamc@552 2318
adamc@552 2319 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 2320
adamc@552 2321 \subsection{MonoUntangle, MonoShake}
adamc@552 2322
adamc@552 2323 Fuse often creates more opportunities to remove spurious mutual recursion.
adamc@552 2324
adamc@552 2325 \subsection{Pathcheck}
adamc@552 2326
adamc@552 2327 The compiler checks that no link or action name has been used more than once.
adamc@552 2328
adamc@552 2329 \subsection{Cjrize}
adamc@552 2330
adamc@552 2331 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 2332
adamc@552 2333 \subsection{C Compilation and Linking}
adamc@552 2334
adamc@552 2335 The output of the last phase is pretty-printed as C source code and passed to GCC.
adamc@552 2336
adamc@552 2337
adamc@524 2338 \end{document}