annotate doc/manual.tex @ 1333:dab85a49e0ab

Warn about XHTML looseness
author Adam Chlipala <adam@chlipala.net>
date Sat, 11 Dec 2010 19:57:22 -0500
parents 4dd5d23bace2
children 79557535b843
rev   line source
adamc@524 1 \documentclass{article}
adamc@554 2 \usepackage{fullpage,amsmath,amssymb,proof,url}
adamc@524 3
adamc@524 4 \newcommand{\cd}[1]{\texttt{#1}}
adamc@524 5 \newcommand{\mt}[1]{\mathsf{#1}}
adamc@524 6
adamc@524 7 \newcommand{\rc}{+ \hspace{-.075in} + \;}
adamc@527 8 \newcommand{\rcut}{\; \texttt{--} \;}
adamc@527 9 \newcommand{\rcutM}{\; \texttt{---} \;}
adamc@524 10
adamc@524 11 \begin{document}
adamc@524 12
adamc@524 13 \title{The Ur/Web Manual}
adamc@524 14 \author{Adam Chlipala}
adamc@524 15
adamc@524 16 \maketitle
adamc@524 17
adamc@540 18 \tableofcontents
adamc@540 19
adamc@554 20
adamc@554 21 \section{Introduction}
adamc@554 22
adamc@1160 23 \emph{Ur} is a programming language designed to introduce richer type system features into functional programming in the tradition of ML and Haskell. Ur is functional, pure, statically-typed, and strict. Ur supports a powerful kind of \emph{metaprogramming} based on \emph{type-level computation with type-level records}.
adamc@554 24
adamc@554 25 \emph{Ur/Web} is Ur plus a special standard library and associated rules for parsing and optimization. Ur/Web supports construction of dynamic web applications backed by SQL databases. The signature of the standard library is such that well-typed Ur/Web programs ``don't go wrong'' in a very broad sense. Not only do they not crash during particular page generations, but they also may not:
adamc@554 26
adamc@554 27 \begin{itemize}
adamc@554 28 \item Suffer from any kinds of code-injection attacks
adamc@554 29 \item Return invalid HTML
adamc@554 30 \item Contain dead intra-application links
adamc@554 31 \item Have mismatches between HTML forms and the fields expected by their handlers
adamc@652 32 \item Include client-side code that makes incorrect assumptions about the ``AJAX''-style services that the remote web server provides
adamc@554 33 \item Attempt invalid SQL queries
adamc@652 34 \item Use improper marshaling or unmarshaling in communication with SQL databases or between browsers and web servers
adamc@554 35 \end{itemize}
adamc@554 36
adamc@554 37 This type safety is just the foundation of the Ur/Web methodology. It is also possible to use metaprogramming to build significant application pieces by analysis of type structure. For instance, the demo includes an ML-style functor for building an admin interface for an arbitrary SQL table. The type system guarantees that the admin interface sub-application that comes out will always be free of the above-listed bugs, no matter which well-typed table description is given as input.
adamc@554 38
adamc@652 39 The Ur/Web compiler also produces very efficient object code that does not use garbage collection. These compiled programs will often be even more efficient than what most programmers would bother to write in C. The compiler also generates JavaScript versions of client-side code, with no need to write those parts of applications in a different language.
adamc@554 40
adamc@554 41 \medskip
adamc@554 42
adamc@554 43 The official web site for Ur is:
adamc@554 44 \begin{center}
adamc@554 45 \url{http://www.impredicative.com/ur/}
adamc@554 46 \end{center}
adamc@554 47
adamc@555 48
adamc@555 49 \section{Installation}
adamc@555 50
adamc@555 51 If you are lucky, then the following standard command sequence will suffice for installation, in a directory to which you have unpacked the latest distribution tarball.
adamc@555 52
adamc@555 53 \begin{verbatim}
adamc@555 54 ./configure
adamc@555 55 make
adamc@555 56 sudo make install
adamc@555 57 \end{verbatim}
adamc@555 58
adamc@896 59 Some other packages must be installed for the above to work. At a minimum, you need a standard UNIX shell, with standard UNIX tools like sed and GCC in your execution path; MLton, the whole-program optimizing compiler for Standard ML; and the mhash C library. As of this writing, in the ``testing'' version of Debian Linux, this command will install the more uncommon of these dependencies:
adamc@896 60 \begin{verbatim}
adamc@896 61 apt-get install mlton libmhash-dev
adamc@896 62 \end{verbatim}
adamc@555 63
adamc@896 64 To build programs that access SQL databases, you also need one of these client libraries for supported backends.
adamc@555 65 \begin{verbatim}
adamc@896 66 apt-get install libpq-dev libmysqlclient15-dev libsqlite3-dev
adamc@555 67 \end{verbatim}
adamc@555 68
adamc@555 69 It is also possible to access the modules of the Ur/Web compiler interactively, within Standard ML of New Jersey. To install the prerequisites in Debian testing:
adamc@555 70 \begin{verbatim}
adamc@555 71 apt-get install smlnj libsmlnj-smlnj ml-yacc ml-lpt
adamc@555 72 \end{verbatim}
adamc@555 73
adamc@555 74 To begin an interactive session with the Ur compiler modules, run \texttt{make smlnj}, and then, from within an \texttt{sml} session, run \texttt{CM.make "src/urweb.cm";}. The \texttt{Compiler} module is the main entry point.
adamc@555 75
adamc@896 76 To run an SQL-backed application with a backend besides SQLite, you will probably want to install one of these servers.
adamc@555 77
adamc@555 78 \begin{verbatim}
adamc@896 79 apt-get install postgresql-8.3 mysql-server-5.0
adamc@555 80 \end{verbatim}
adamc@555 81
adamc@555 82 To use the Emacs mode, you must have a modern Emacs installed. We assume that you already know how to do this, if you're in the business of looking for an Emacs mode. The demo generation facility of the compiler will also call out to Emacs to syntax-highlight code, and that process depends on the \texttt{htmlize} module, which can be installed in Debian testing via:
adamc@555 83
adamc@555 84 \begin{verbatim}
adamc@555 85 apt-get install emacs-goodies-el
adamc@555 86 \end{verbatim}
adamc@555 87
adamc@555 88 Even with the right packages installed, configuration and building might fail to work. After you run \texttt{./configure}, you will see the values of some named environment variables printed. You may need to adjust these values to get proper installation for your system. To change a value, store your preferred alternative in the corresponding UNIX environment variable, before running \texttt{./configure}. For instance, here is how to change the list of extra arguments that the Ur/Web compiler will pass to GCC on every invocation.
adamc@555 89
adamc@555 90 \begin{verbatim}
adamc@555 91 GCCARGS=-fnested-functions ./configure
adamc@555 92 \end{verbatim}
adamc@555 93
adamc@1137 94 Some Mac OS X users have reported needing to use this particular GCCARGS value.
adamc@1137 95
adamc@1161 96 Since the author is still getting a handle on the GNU Autotools that provide the build system, you may need to do some further work to get started, especially in environments with significant differences from Linux (where most testing is done). One OS X user reported needing to run \texttt{./configure} with \texttt{CFLAGS=-I/opt/local/include}, since this directory wound up holding a header file associated with a \texttt{libmhash} package installed via DarwinPorts. Further, to get libpq to link, another user reported setting \texttt{GCCARGS="-I/opt/local/include -L/opt/local/lib/postgresql84"}, after creating a symbolic link with \texttt{ln -s /opt/local/include/postgresql84 /opt/local/include/postgresql}.
adamc@555 97
adamc@555 98 The Emacs mode can be set to autoload by adding the following to your \texttt{.emacs} file.
adamc@555 99
adamc@555 100 \begin{verbatim}
adamc@555 101 (add-to-list 'load-path "/usr/local/share/emacs/site-lisp/urweb-mode")
adamc@555 102 (load "urweb-mode-startup")
adamc@555 103 \end{verbatim}
adamc@555 104
adamc@555 105 Change the path in the first line if you chose a different Emacs installation path during configuration.
adamc@555 106
adamc@555 107
adamc@556 108 \section{Command-Line Compiler}
adamc@556 109
adamc@556 110 \subsection{Project Files}
adamc@556 111
adamc@556 112 The basic inputs to the \texttt{urweb} compiler are project files, which have the extension \texttt{.urp}. Here is a sample \texttt{.urp} file.
adamc@556 113
adamc@556 114 \begin{verbatim}
adamc@556 115 database dbname=test
adamc@556 116 sql crud1.sql
adamc@556 117
adamc@556 118 crud
adamc@556 119 crud1
adamc@556 120 \end{verbatim}
adamc@556 121
adamc@556 122 The \texttt{database} line gives the database information string to pass to libpq. In this case, the string only says to connect to a local database named \texttt{test}.
adamc@556 123
adamc@556 124 The \texttt{sql} line asks for an SQL source file to be generated, giving the commands to run to create the tables and sequences that this application expects to find. After building this \texttt{.urp} file, the following commands could be used to initialize the database, assuming that the current UNIX user exists as a Postgres user with database creation privileges:
adamc@556 125
adamc@556 126 \begin{verbatim}
adamc@556 127 createdb test
adamc@556 128 psql -f crud1.sql test
adamc@556 129 \end{verbatim}
adamc@556 130
adam@1331 131 A blank line separates the named directives from a list of modules to include in the project. Any line may contain a shell-script-style comment, where any suffix of a line starting at a hash character \texttt{\#} is ignored.
adamc@556 132
adamc@556 133 For each entry \texttt{M} in the module list, the file \texttt{M.urs} is included in the project if it exists, and the file \texttt{M.ur} must exist and is always included.
adamc@556 134
adamc@783 135 Here is the complete list of directive forms. ``FFI'' stands for ``foreign function interface,'' Ur's facility for interaction between Ur programs and C and JavaScript libraries.
adamc@783 136 \begin{itemize}
adamc@783 137 \item \texttt{[allow|deny] [url|mime] PATTERN} registers a rule governing which URLs or MIME types are allowed in this application. The first such rule to match a URL or MIME type determines the verdict. If \texttt{PATTERN} ends in \texttt{*}, it is interpreted as a prefix rule. Otherwise, a string must match it exactly.
adamc@1171 138 \item \texttt{benignEffectful Module.ident} registers an FFI function or transaction as having side effects. The optimizer avoids removing, moving, or duplicating calls to such functions. Every effectful FFI function must be registered, or the optimizer may make invalid transformations. This version of the \texttt{effectful} directive registers that this function has only session-local side effects.
adamc@783 139 \item \texttt{clientOnly Module.ident} registers an FFI function or transaction that may only be run in client browsers.
adamc@783 140 \item \texttt{clientToServer Module.ident} adds FFI type \texttt{Module.ident} to the list of types that are OK to marshal from clients to servers. Values like XML trees and SQL queries are hard to marshal without introducing expensive validity checks, so it's easier to ensure that the server never trusts clients to send such values. The file \texttt{include/urweb.h} shows examples of the C support functions that are required of any type that may be marshalled. These include \texttt{attrify}, \texttt{urlify}, and \texttt{unurlify} functions.
adamc@783 141 \item \texttt{database DBSTRING} sets the string to pass to libpq to open a database connection.
adamc@783 142 \item \texttt{debug} saves some intermediate C files, which is mostly useful to help in debugging the compiler itself.
adamc@783 143 \item \texttt{effectful Module.ident} registers an FFI function or transaction as having side effects. The optimizer avoids removing, moving, or duplicating calls to such functions. Every effectful FFI function must be registered, or the optimizer may make invalid transformations.
adamc@783 144 \item \texttt{exe FILENAME} sets the filename to which to write the output executable. The default for file \texttt{P.urp} is \texttt{P.exe}.
adamc@783 145 \item \texttt{ffi FILENAME} reads the file \texttt{FILENAME.urs} to determine the interface to a new FFI module. The name of the module is calculated from \texttt{FILENAME} in the same way as for normal source files. See the files \texttt{include/urweb.h} and \texttt{src/c/urweb.c} for examples of C headers and implementations for FFI modules. In general, every type or value \texttt{Module.ident} becomes \texttt{uw\_Module\_ident} in C.
adamc@1099 146 \item \texttt{include FILENAME} adds \texttt{FILENAME} to the list of files to be \texttt{\#include}d in C sources. This is most useful for interfacing with new FFI modules.
adamc@783 147 \item \texttt{jsFunc Module.ident=name} gives the JavaScript name of an FFI value.
adamc@1089 148 \item \texttt{library FILENAME} parses \texttt{FILENAME.urp} and merges its contents with the rest of the current file's contents. If \texttt{FILENAME.urp} doesn't exist, the compiler also tries \texttt{FILENAME/lib.urp}.
adam@1309 149 \item \texttt{limit class num} sets a resource usage limit for generated applications. The limit \texttt{class} will be set to the non-negative integer \texttt{num}. The classes are:
adam@1309 150 \begin{itemize}
adam@1309 151 \item \texttt{cleanup}: maximum number of cleanup operations (e.g., entries recording the need to deallocate certain temporary objects) that may be active at once per request
adam@1309 152 \item \texttt{database}: maximum size of database files (currently only used by SQLite)
adam@1309 153 \item \texttt{deltas}: maximum number of messages sendable in a single request handler with \texttt{Basis.send}
adam@1309 154 \item \texttt{globals}: maximum number of global variables that FFI libraries may set in a single request context
adam@1309 155 \item \texttt{headers}: maximum size (in bytes) of per-request buffer used to hold HTTP headers for generated pages
adam@1309 156 \item \texttt{heap}: maximum size (in bytes) of per-request heap for dynamically-allocated data
adam@1309 157 \item \texttt{inputs}: maximum number of top-level form fields per request
adam@1309 158 \item \texttt{messages}: maximum size (in bytes) of per-request buffer used to hold a single outgoing message sent with \texttt{Basis.send}
adam@1309 159 \item \texttt{page}: maximum size (in bytes) of per-request buffer used to hold HTML content of generated pages
adam@1309 160 \item \texttt{script}: maximum size (in bytes) of per-request buffer used to hold JavaScript content of generated pages
adam@1309 161 \item \texttt{subinputs}: maximum number of form fields per request, excluding top-level fields
adam@1309 162 \item \texttt{time}: maximum running time of a single page request, in units of approximately 0.1 seconds
adam@1309 163 \item \texttt{transactionals}: maximum number of custom transactional actions (e.g., sending an e-mail) that may be run in a single page generation
adam@1309 164 \end{itemize}
adamc@783 165 \item \texttt{link FILENAME} adds \texttt{FILENAME} to the list of files to be passed to the GCC linker at the end of compilation. This is most useful for importing extra libraries needed by new FFI modules.
adam@1332 166 \item \texttt{minHeap NUMBYTES} sets the initial size for thread-local heaps used in handling requests. These heaps grow automatically as needed (up to any maximum set with \texttt{limit}), but each regrow requires restarting the request handling process.
adam@1297 167 \item \texttt{onError Module.var} changes the handling of fatal application errors. Instead of displaying a default, ugly error 500 page, the error page will be generated by calling function \texttt{Module.var} on a piece of XML representing the error message. The error handler should have type $\mt{xbody} \to \mt{transaction} \; \mt{page}$. Note that the error handler \emph{cannot} be in the application's main module, since that would register it as explicitly callable via URLs.
adamc@852 168 \item \texttt{path NAME=VALUE} creates a mapping from \texttt{NAME} to \texttt{VALUE}. This mapping may be used at the beginnings of filesystem paths given to various other configuration directives. A path like \texttt{\$NAME/rest} is expanded to \texttt{VALUE/rest}. There is an initial mapping from the empty name (for paths like \texttt{\$/list}) to the directory where the Ur/Web standard library is installed. If you accept the default \texttt{configure} options, this directory is \texttt{/usr/local/lib/urweb/ur}.
adamc@783 169 \item \texttt{prefix PREFIX} sets the prefix included before every URI within the generated application. The default is \texttt{/}.
adamc@783 170 \item \texttt{profile} generates an executable that may be used with gprof.
adam@1300 171 \item \texttt{rewrite KIND FROM TO} gives a rule for rewriting canonical module paths. For instance, the canonical path of a page may be \texttt{Mod1.Mod2.mypage}, while you would rather the page were accessed via a URL containing only \texttt{page}. The directive \texttt{rewrite url Mod1/Mod2/mypage page} would accomplish that. The possible values of \texttt{KIND} determine which kinds of objects are affected. The kind \texttt{all} matches any object, and \texttt{url} matches page URLs. The kinds \texttt{table}, \texttt{sequence}, and \texttt{view} match those sorts of SQL entities, and \texttt{relation} matches any of those three. \texttt{cookie} matches HTTP cookies, and \texttt{style} matches CSS class names. If \texttt{FROM} ends in \texttt{/*}, it is interpreted as a prefix matching rule, and rewriting occurs by replacing only the appropriate prefix of a path with \texttt{TO}. The \texttt{TO} field may be left empty to express the idea of deleting a prefix. For instance, \texttt{rewrite url Main/*} will strip all \texttt{Main/} prefixes from URLs. While the actual external names of relations and styles have parts separated by underscores instead of slashes, all rewrite rules must be written in terms of slashes.
adamc@1183 172 \item \texttt{safeGet URI} asks to allow the page handler assigned this canonical URI prefix to cause persistent side effects, even if accessed via an HTTP \cd{GET} request.
adamc@783 173 \item \texttt{script URL} adds \texttt{URL} to the list of extra JavaScript files to be included at the beginning of any page that uses JavaScript. This is most useful for importing JavaScript versions of functions found in new FFI modules.
adamc@783 174 \item \texttt{serverOnly Module.ident} registers an FFI function or transaction that may only be run on the server.
adamc@1164 175 \item \texttt{sigfile PATH} sets a path where your application should look for a key to use in cryptographic signing. This is used to prevent cross-site request forgery attacks for any form handler that both reads a cookie and creates side effects. If the referenced file doesn't exist, an application will create it and read its saved data on future invocations. You can also initialize the file manually with any contents at least 16 bytes long; the first 16 bytes will be treated as the key.
adamc@783 176 \item \texttt{sql FILENAME} sets where to write an SQL file with the commands to create the expected database schema. The default is not to create such a file.
adamc@783 177 \item \texttt{timeout N} sets to \texttt{N} seconds the amount of time that the generated server will wait after the last contact from a client before determining that that client has exited the application. Clients that remain active will take the timeout setting into account in determining how often to ping the server, so it only makes sense to set a high timeout to cope with browser and network delays and failures. Higher timeouts can lead to more unnecessary client information taking up memory on the server. The timeout goes unused by any page that doesn't involve the \texttt{recv} function, since the server only needs to store per-client information for clients that receive asynchronous messages.
adamc@783 178 \end{itemize}
adamc@701 179
adamc@701 180
adamc@557 181 \subsection{Building an Application}
adamc@557 182
adamc@557 183 To compile project \texttt{P.urp}, simply run
adamc@557 184 \begin{verbatim}
adamc@557 185 urweb P
adamc@557 186 \end{verbatim}
adamc@1198 187 The output executable is a standalone web server. Run it with the command-line argument \texttt{-h} to see which options it takes. If the project file lists a database, the web server will attempt to connect to that database on startup. See Section \ref{structure} for an explanation of the URI mapping convention, which determines how each page of your application may be accessed via URLs.
adamc@557 188
adamc@557 189 To time how long the different compiler phases run, without generating an executable, run
adamc@557 190 \begin{verbatim}
adamc@557 191 urweb -timing P
adamc@557 192 \end{verbatim}
adamc@557 193
adamc@1086 194 To stop the compilation process after type-checking, run
adamc@1086 195 \begin{verbatim}
adamc@1086 196 urweb -tc P
adamc@1086 197 \end{verbatim}
adamc@1086 198
adamc@1170 199 To output information relevant to CSS stylesheets (and not finish regular compilation), run
adamc@1170 200 \begin{verbatim}
adamc@1170 201 urweb -css P
adamc@1170 202 \end{verbatim}
adamc@1170 203 The first output line is a list of categories of CSS properties that would be worth setting on the document body. The remaining lines are space-separated pairs of CSS class names and categories of properties that would be worth setting for that class. The category codes are divided into two varieties. Codes that reveal properties of a tag or its (recursive) children are \cd{B} for block-level elements, \cd{C} for table captions, \cd{D} for table cells, \cd{L} for lists, and \cd{T} for tables. Codes that reveal properties of the precise tag that uses a class are \cd{b} for block-level elements, \cd{t} for tables, \cd{d} for table cells, \cd{-} for table rows, \cd{H} for the possibility to set a height, \cd{N} for non-replaced inline-level elements, \cd{R} for replaced inline elements, and \cd{W} for the possibility to set a width.
adamc@1170 204
adamc@896 205 Some other command-line parameters are accepted:
adamc@896 206 \begin{itemize}
adamc@896 207 \item \texttt{-db <DBSTRING>}: Set database connection information, using the format expected by Postgres's \texttt{PQconnectdb()}, which is \texttt{name1=value1 ... nameN=valueN}. The same format is also parsed and used to discover connection parameters for MySQL and SQLite. The only significant settings for MySQL are \texttt{host}, \texttt{hostaddr}, \texttt{port}, \texttt{dbname}, \texttt{user}, and \texttt{password}. The only significant setting for SQLite is \texttt{dbname}, which is interpreted as the filesystem path to the database. Additionally, when using SQLite, a database string may be just a file path.
adamc@896 208
adamc@896 209 \item \texttt{-dbms [postgres|mysql|sqlite]}: Sets the database backend to use.
adamc@896 210 \begin{itemize}
adamc@896 211 \item \texttt{postgres}: This is PostgreSQL, the default. Among the supported engines, Postgres best matches the design philosophy behind Ur, with a focus on consistent views of data, even in the face of much concurrency. Different database engines have different quirks of SQL syntax. Ur/Web tends to use Postgres idioms where there are choices to be made, though the compiler translates SQL as needed to support other backends.
adamc@896 212
adamc@896 213 A command sequence like this can initialize a Postgres database, using a file \texttt{app.sql} generated by the compiler:
adamc@896 214 \begin{verbatim}
adamc@896 215 createdb app
adamc@896 216 psql -f app.sql app
adamc@896 217 \end{verbatim}
adamc@896 218
adamc@896 219 \item \texttt{mysql}: This is MySQL, another popular relational database engine that uses persistent server processes. Ur/Web needs transactions to function properly. Many installations of MySQL use non-transactional storage engines by default. Ur/Web generates table definitions that try to use MySQL's InnoDB engine, which supports transactions. You can edit the first line of a generated \texttt{.sql} file to change this behavior, but it really is true that Ur/Web applications will exhibit bizarre behavior if you choose an engine that ignores transaction commands.
adamc@896 220
adamc@896 221 A command sequence like this can initialize a MySQL database:
adamc@896 222 \begin{verbatim}
adamc@896 223 echo "CREATE DATABASE app" | mysql
adamc@896 224 mysql -D app <app.sql
adamc@896 225 \end{verbatim}
adamc@896 226
adamc@896 227 \item \texttt{sqlite}: This is SQLite, a simple filesystem-based transactional database engine. With this backend, Ur/Web applications can run without any additional server processes. The other engines are generally preferred for large-workload performance and full admin feature sets, while SQLite is popular for its low resource footprint and ease of set-up.
adamc@896 228
adamc@896 229 A command like this can initialize an SQLite database:
adamc@896 230 \begin{verbatim}
adamc@896 231 sqlite3 path/to/database/file <app.sql
adamc@896 232 \end{verbatim}
adamc@896 233 \end{itemize}
adamc@896 234
adam@1309 235 \item \texttt{-limit class num}: Equivalent to the \texttt{limit} directive from \texttt{.urp} files
adam@1309 236
adamc@896 237 \item \texttt{-output FILENAME}: Set where the application executable is written.
adamc@896 238
adamc@1127 239 \item \texttt{-path NAME VALUE}: Set the value of path variable \texttt{\$NAME} to \texttt{VALUE}, for use in \texttt{.urp} files.
adamc@1127 240
adamc@896 241 \item \texttt{-protocol [http|cgi|fastcgi]}: Set the protocol that the generated application speaks.
adamc@896 242 \begin{itemize}
adamc@896 243 \item \texttt{http}: This is the default. It is for building standalone web servers that can be accessed by web browsers directly.
adamc@896 244
adamc@896 245 \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@896 246
adamc@896 247 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@896 248 \begin{verbatim}
adamc@896 249 ScriptAlias /Hello /path/to/hello.exe
adamc@896 250 \end{verbatim}
adamc@896 251
adamc@1163 252 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 253 \begin{verbatim}
adamc@1163 254 Options +ExecCGI
adamc@1163 255 AddHandler cgi-script .exe
adamc@1163 256 \end{verbatim}
adamc@1163 257
adamc@1163 258 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 259 \begin{verbatim}
adamc@1163 260 prefix /dir/script.exe/
adamc@1163 261 \end{verbatim}
adamc@1163 262
adamc@1163 263 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 264
adamc@1164 265 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 266
adamc@896 267 \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@896 268
adamc@896 269 To configure a FastCGI program with Apache, one could combine the above \texttt{ScriptAlias} line with a line like this:
adamc@896 270 \begin{verbatim}
adamc@896 271 FastCgiServer /path/to/hello.exe -idle-timeout 99999
adamc@896 272 \end{verbatim}
adamc@896 273 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@896 274
adamc@896 275 Here is some lighttpd configuration for the same application.
adamc@896 276 \begin{verbatim}
adamc@896 277 fastcgi.server = (
adamc@896 278 "/Hello/" =>
adamc@896 279 (( "bin-path" => "/path/to/hello.exe",
adamc@896 280 "socket" => "/tmp/hello",
adamc@896 281 "check-local" => "disable",
adamc@896 282 "docroot" => "/",
adamc@896 283 "max-procs" => "1"
adamc@896 284 ))
adamc@896 285 )
adamc@896 286 \end{verbatim}
adamc@896 287 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@896 288
adamc@896 289 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@896 290 \end{itemize}
adamc@896 291
adamc@1127 292 \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 293
adamc@1164 294 \item \texttt{-sigfile PATH}: Same as the \texttt{sigfile} directive in \texttt{.urp} files
adamc@1164 295
adamc@896 296 \item \texttt{-sql FILENAME}: Set where a database set-up SQL script is written.
adamc@1095 297
adamc@1095 298 \item \texttt{-static}: Link the runtime system statically. The default is to link against dynamic libraries.
adamc@896 299 \end{itemize}
adamc@896 300
adam@1297 301 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@556 302
adamc@529 303 \section{Ur Syntax}
adamc@529 304
adamc@784 305 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@524 306
adamc@524 307 \subsection{Lexical Conventions}
adamc@524 308
adamc@524 309 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@524 310
adamc@524 311 \begin{center}
adamc@524 312 \begin{tabular}{rl}
adamc@524 313 \textbf{\LaTeX} & \textbf{ASCII} \\
adamc@524 314 $\to$ & \cd{->} \\
adamc@652 315 $\longrightarrow$ & \cd{-->} \\
adamc@524 316 $\times$ & \cd{*} \\
adamc@524 317 $\lambda$ & \cd{fn} \\
adamc@524 318 $\Rightarrow$ & \cd{=>} \\
adamc@652 319 $\Longrightarrow$ & \cd{==>} \\
adamc@529 320 $\neq$ & \cd{<>} \\
adamc@529 321 $\leq$ & \cd{<=} \\
adamc@529 322 $\geq$ & \cd{>=} \\
adamc@524 323 \\
adamc@524 324 $x$ & Normal textual identifier, not beginning with an uppercase letter \\
adamc@525 325 $X$ & Normal textual identifier, beginning with an uppercase letter \\
adamc@524 326 \end{tabular}
adamc@524 327 \end{center}
adamc@524 328
adamc@525 329 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@524 330
adamc@873 331 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@526 332
adamc@527 333 This version of the manual doesn't include operator precedences; see \texttt{src/urweb.grm} for that.
adamc@527 334
adam@1297 335 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 336
adamc@552 337 \subsection{\label{core}Core Syntax}
adamc@524 338
adamc@524 339 \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@524 340 $$\begin{array}{rrcll}
adamc@524 341 \textrm{Kinds} & \kappa &::=& \mt{Type} & \textrm{proper types} \\
adamc@525 342 &&& \mt{Unit} & \textrm{the trivial constructor} \\
adamc@525 343 &&& \mt{Name} & \textrm{field names} \\
adamc@525 344 &&& \kappa \to \kappa & \textrm{type-level functions} \\
adamc@525 345 &&& \{\kappa\} & \textrm{type-level records} \\
adamc@525 346 &&& (\kappa\times^+) & \textrm{type-level tuples} \\
adamc@652 347 &&& X & \textrm{variable} \\
adamc@652 348 &&& X \longrightarrow k & \textrm{kind-polymorphic type-level function} \\
adamc@529 349 &&& \_\_ & \textrm{wildcard} \\
adamc@525 350 &&& (\kappa) & \textrm{explicit precedence} \\
adamc@524 351 \end{array}$$
adamc@524 352
adamc@524 353 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@524 354 $$\begin{array}{rrcll}
adamc@524 355 \textrm{Explicitness} & ? &::=& :: & \textrm{explicit} \\
adamc@558 356 &&& ::: & \textrm{implicit}
adamc@524 357 \end{array}$$
adamc@524 358
adamc@524 359 \emph{Constructors} are the main class of compile-time-only data. They include proper types and are classified by kinds.
adamc@524 360 $$\begin{array}{rrcll}
adamc@524 361 \textrm{Constructors} & c, \tau &::=& (c) :: \kappa & \textrm{kind annotation} \\
adamc@530 362 &&& \hat{x} & \textrm{constructor variable} \\
adamc@524 363 \\
adamc@525 364 &&& \tau \to \tau & \textrm{function type} \\
adamc@525 365 &&& x \; ? \; \kappa \to \tau & \textrm{polymorphic function type} \\
adamc@652 366 &&& X \longrightarrow \tau & \textrm{kind-polymorphic function type} \\
adamc@525 367 &&& \$ c & \textrm{record type} \\
adamc@524 368 \\
adamc@525 369 &&& c \; c & \textrm{type-level function application} \\
adamc@530 370 &&& \lambda x \; :: \; \kappa \Rightarrow c & \textrm{type-level function abstraction} \\
adamc@524 371 \\
adamc@652 372 &&& X \Longrightarrow c & \textrm{type-level kind-polymorphic function abstraction} \\
adamc@655 373 &&& c [\kappa] & \textrm{type-level kind-polymorphic function application} \\
adamc@652 374 \\
adamc@525 375 &&& () & \textrm{type-level unit} \\
adamc@525 376 &&& \#X & \textrm{field name} \\
adamc@524 377 \\
adamc@525 378 &&& [(c = c)^*] & \textrm{known-length type-level record} \\
adamc@525 379 &&& c \rc c & \textrm{type-level record concatenation} \\
adamc@652 380 &&& \mt{map} & \textrm{type-level record map} \\
adamc@524 381 \\
adamc@558 382 &&& (c,^+) & \textrm{type-level tuple} \\
adamc@525 383 &&& c.n & \textrm{type-level tuple projection ($n \in \mathbb N^+$)} \\
adamc@524 384 \\
adamc@652 385 &&& [c \sim c] \Rightarrow \tau & \textrm{guarded type} \\
adamc@524 386 \\
adamc@529 387 &&& \_ :: \kappa & \textrm{wildcard} \\
adamc@525 388 &&& (c) & \textrm{explicit precedence} \\
adamc@530 389 \\
adamc@530 390 \textrm{Qualified uncapitalized variables} & \hat{x} &::=& x & \textrm{not from a module} \\
adamc@530 391 &&& M.x & \textrm{projection from a module} \\
adamc@525 392 \end{array}$$
adamc@525 393
adamc@655 394 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@655 395
adamc@525 396 Modules of the module system are described by \emph{signatures}.
adamc@525 397 $$\begin{array}{rrcll}
adamc@525 398 \textrm{Signatures} & S &::=& \mt{sig} \; s^* \; \mt{end} & \textrm{constant} \\
adamc@525 399 &&& X & \textrm{variable} \\
adamc@525 400 &&& \mt{functor}(X : S) : S & \textrm{functor} \\
adamc@529 401 &&& S \; \mt{where} \; \mt{con} \; x = c & \textrm{concretizing an abstract constructor} \\
adamc@525 402 &&& M.X & \textrm{projection from a module} \\
adamc@525 403 \\
adamc@525 404 \textrm{Signature items} & s &::=& \mt{con} \; x :: \kappa & \textrm{abstract constructor} \\
adamc@525 405 &&& \mt{con} \; x :: \kappa = c & \textrm{concrete constructor} \\
adamc@528 406 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529 407 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@525 408 &&& \mt{val} \; x : \tau & \textrm{value} \\
adamc@525 409 &&& \mt{structure} \; X : S & \textrm{sub-module} \\
adamc@525 410 &&& \mt{signature} \; X = S & \textrm{sub-signature} \\
adamc@525 411 &&& \mt{include} \; S & \textrm{signature inclusion} \\
adamc@525 412 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@654 413 &&& \mt{class} \; x :: \kappa & \textrm{abstract constructor class} \\
adamc@654 414 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@525 415 \\
adamc@525 416 \textrm{Datatype constructors} & dc &::=& X & \textrm{nullary constructor} \\
adamc@525 417 &&& X \; \mt{of} \; \tau & \textrm{unary constructor} \\
adamc@524 418 \end{array}$$
adamc@524 419
adamc@526 420 \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@526 421 $$\begin{array}{rrcll}
adamc@526 422 \textrm{Patterns} & p &::=& \_ & \textrm{wildcard} \\
adamc@526 423 &&& x & \textrm{variable} \\
adamc@526 424 &&& \ell & \textrm{constant} \\
adamc@526 425 &&& \hat{X} & \textrm{nullary constructor} \\
adamc@526 426 &&& \hat{X} \; p & \textrm{unary constructor} \\
adamc@526 427 &&& \{(x = p,)^*\} & \textrm{rigid record pattern} \\
adamc@526 428 &&& \{(x = p,)^+, \ldots\} & \textrm{flexible record pattern} \\
adamc@852 429 &&& p : \tau & \textrm{type annotation} \\
adamc@527 430 &&& (p) & \textrm{explicit precedence} \\
adamc@526 431 \\
adamc@529 432 \textrm{Qualified capitalized variables} & \hat{X} &::=& X & \textrm{not from a module} \\
adamc@526 433 &&& M.X & \textrm{projection from a module} \\
adamc@526 434 \end{array}$$
adamc@526 435
adamc@527 436 \emph{Expressions} are the main run-time entities, corresponding to both ``expressions'' and ``statements'' in mainstream imperative languages.
adamc@527 437 $$\begin{array}{rrcll}
adamc@527 438 \textrm{Expressions} & e &::=& e : \tau & \textrm{type annotation} \\
adamc@529 439 &&& \hat{x} & \textrm{variable} \\
adamc@529 440 &&& \hat{X} & \textrm{datatype constructor} \\
adamc@527 441 &&& \ell & \textrm{constant} \\
adamc@527 442 \\
adamc@527 443 &&& e \; e & \textrm{function application} \\
adamc@527 444 &&& \lambda x : \tau \Rightarrow e & \textrm{function abstraction} \\
adamc@527 445 &&& e [c] & \textrm{polymorphic function application} \\
adamc@852 446 &&& \lambda [x \; ? \; \kappa] \Rightarrow e & \textrm{polymorphic function abstraction} \\
adamc@655 447 &&& e [\kappa] & \textrm{kind-polymorphic function application} \\
adamc@652 448 &&& X \Longrightarrow e & \textrm{kind-polymorphic function abstraction} \\
adamc@527 449 \\
adamc@527 450 &&& \{(c = e,)^*\} & \textrm{known-length record} \\
adamc@527 451 &&& e.c & \textrm{record field projection} \\
adamc@527 452 &&& e \rc e & \textrm{record concatenation} \\
adamc@527 453 &&& e \rcut c & \textrm{removal of a single record field} \\
adamc@527 454 &&& e \rcutM c & \textrm{removal of multiple record fields} \\
adamc@527 455 \\
adamc@527 456 &&& \mt{let} \; ed^* \; \mt{in} \; e \; \mt{end} & \textrm{local definitions} \\
adamc@527 457 \\
adamc@527 458 &&& \mt{case} \; e \; \mt{of} \; (p \Rightarrow e|)^+ & \textrm{pattern matching} \\
adamc@527 459 \\
adamc@654 460 &&& \lambda [c \sim c] \Rightarrow e & \textrm{guarded expression abstraction} \\
adamc@654 461 &&& e \; ! & \textrm{guarded expression application} \\
adamc@527 462 \\
adamc@527 463 &&& \_ & \textrm{wildcard} \\
adamc@527 464 &&& (e) & \textrm{explicit precedence} \\
adamc@527 465 \\
adamc@527 466 \textrm{Local declarations} & ed &::=& \cd{val} \; x : \tau = e & \textrm{non-recursive value} \\
adamc@527 467 &&& \cd{val} \; \cd{rec} \; (x : \tau = e \; \cd{and})^+ & \textrm{mutually-recursive values} \\
adamc@527 468 \end{array}$$
adamc@527 469
adamc@655 470 As with constructors, we include both abstraction and application for kind polymorphism, but applications are only inferred internally.
adamc@655 471
adamc@528 472 \emph{Declarations} primarily bring new symbols into context.
adamc@528 473 $$\begin{array}{rrcll}
adamc@528 474 \textrm{Declarations} & d &::=& \mt{con} \; x :: \kappa = c & \textrm{constructor synonym} \\
adamc@528 475 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529 476 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@528 477 &&& \mt{val} \; x : \tau = e & \textrm{value} \\
adamc@528 478 &&& \mt{val} \; \cd{rec} \; (x : \tau = e \; \mt{and})^+ & \textrm{mutually-recursive values} \\
adamc@528 479 &&& \mt{structure} \; X : S = M & \textrm{module definition} \\
adamc@528 480 &&& \mt{signature} \; X = S & \textrm{signature definition} \\
adamc@528 481 &&& \mt{open} \; M & \textrm{module inclusion} \\
adamc@528 482 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@528 483 &&& \mt{open} \; \mt{constraints} \; M & \textrm{inclusion of just the constraints from a module} \\
adamc@528 484 &&& \mt{table} \; x : c & \textrm{SQL table} \\
adamc@784 485 &&& \mt{view} \; x : c & \textrm{SQL view} \\
adamc@528 486 &&& \mt{sequence} \; x & \textrm{SQL sequence} \\
adamc@535 487 &&& \mt{cookie} \; x : \tau & \textrm{HTTP cookie} \\
adamc@784 488 &&& \mt{style} \; x : \tau & \textrm{CSS class} \\
adamc@654 489 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@1085 490 &&& \mt{task} \; e = e & \textrm{recurring task} \\
adamc@528 491 \\
adamc@529 492 \textrm{Modules} & M &::=& \mt{struct} \; d^* \; \mt{end} & \textrm{constant} \\
adamc@529 493 &&& X & \textrm{variable} \\
adamc@529 494 &&& M.X & \textrm{projection} \\
adamc@529 495 &&& M(M) & \textrm{functor application} \\
adamc@529 496 &&& \mt{functor}(X : S) : S = M & \textrm{functor abstraction} \\
adamc@528 497 \end{array}$$
adamc@528 498
adamc@528 499 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@527 500
adamc@784 501 We omit some extra possibilities in $\mt{table}$ syntax, deferring them to Section \ref{tables}.
adamc@784 502
adamc@529 503 \subsection{Shorthands}
adamc@529 504
adamc@529 505 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@529 506
adamc@529 507 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@529 508
adamc@529 509 A record type may be written $\{(c = c,)^*\}$, which elaborates to $\$[(c = c,)^*]$.
adamc@529 510
adamc@533 511 The notation $[c_1, \ldots, c_n]$ is shorthand for $[c_1 = (), \ldots, c_n = ()]$.
adamc@533 512
adamc@529 513 A tuple type $(\tau_1, \ldots, \tau_n)$ expands to a record type $\{1 = \tau_1, \ldots, n = \tau_n\}$, with natural numbers as field names. A tuple pattern $(p_1, \ldots, p_n)$ expands to a rigid record pattern $\{1 = p_1, \ldots, n = p_n\}$. Positive natural numbers may be used in most places where field names would be allowed.
adamc@529 514
adamc@852 515 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@529 516
adam@1306 517 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 518
adamc@529 519 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@529 520
adamc@529 521 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@529 522
adamc@654 523 A signature item or declaration $\mt{class} \; x = \lambda y \Rightarrow c$ may be abbreviated $\mt{class} \; x \; y = c$.
adamc@529 524
adamc@1102 525 Handling of implicit and explicit constructor arguments may be tweaked with some prefixes to variable references. An expression $@x$ is a version of $x$ where all implicit constructor arguments have been made explicit. An expression $@@x$ achieves the same effect, additionally halting automatic resolution of type class instances and automatic proving of disjointness constraints. The default is that implicit arguments are inserted automatically after any reference to a non-local variable, or after any application of a non-local variable to one or more arguments. For such an expression, implicit wildcard arguments are added for the longest prefix of the expression's type consisting only of implicit polymorphism, type class instances, and disjointness obligations. The same syntax works for variables projected out of modules and for capitalized variables (datatype constructors).
adamc@529 526
adamc@852 527 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@529 528
adamc@852 529 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@852 530
adamc@852 531 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@529 532
adamc@529 533 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@529 534
adamc@852 535 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@852 536
adamc@853 537 A declaration $\mt{table} \; x : \{(c = c,)^*\}$ is elaborated into $\mt{table} \; x : [(c = c,)^*]$.
adamc@529 538
adamc@529 539 The syntax $\mt{where} \; \mt{type}$ is an alternate form of $\mt{where} \; \mt{con}$.
adamc@529 540
adamc@529 541 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@529 542
adamc@529 543 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@529 544
adamc@784 545 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@529 546
adamc@530 547
adamc@530 548 \section{Static Semantics}
adamc@530 549
adamc@530 550 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@530 551
adamc@530 552 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@530 553 \begin{itemize}
adamc@655 554 \item $\Gamma \vdash \kappa$ expresses kind well-formedness.
adamc@530 555 \item $\Gamma \vdash c :: \kappa$ assigns a kind to a constructor in a context.
adamc@530 556 \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@531 557 \item $\Gamma \vdash c \hookrightarrow C$ proves that record constructor $c$ decomposes into set $C$ of field names and record constructors.
adamc@530 558 \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@530 559 \item $\Gamma \vdash e : \tau$ is a standard typing judgment.
adamc@534 560 \item $\Gamma \vdash p \leadsto \Gamma; \tau$ combines typing of patterns with calculation of which new variables they bind.
adamc@537 561 \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@537 562 \item $\Gamma \vdash S \equiv S$ is the signature equivalence judgment.
adamc@536 563 \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@530 564 \item $\Gamma \vdash M : S$ is the module signature checking judgment.
adamc@537 565 \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@539 566 \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@530 567 \end{itemize}
adamc@530 568
adamc@655 569
adamc@655 570 \subsection{Kind Well-Formedness}
adamc@655 571
adamc@655 572 $$\infer{\Gamma \vdash \mt{Type}}{}
adamc@655 573 \quad \infer{\Gamma \vdash \mt{Unit}}{}
adamc@655 574 \quad \infer{\Gamma \vdash \mt{Name}}{}
adamc@655 575 \quad \infer{\Gamma \vdash \kappa_1 \to \kappa_2}{
adamc@655 576 \Gamma \vdash \kappa_1
adamc@655 577 & \Gamma \vdash \kappa_2
adamc@655 578 }
adamc@655 579 \quad \infer{\Gamma \vdash \{\kappa\}}{
adamc@655 580 \Gamma \vdash \kappa
adamc@655 581 }
adamc@655 582 \quad \infer{\Gamma \vdash (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@655 583 \forall i: \Gamma \vdash \kappa_i
adamc@655 584 }$$
adamc@655 585
adamc@655 586 $$\infer{\Gamma \vdash X}{
adamc@655 587 X \in \Gamma
adamc@655 588 }
adamc@655 589 \quad \infer{\Gamma \vdash X \longrightarrow \kappa}{
adamc@655 590 \Gamma, X \vdash \kappa
adamc@655 591 }$$
adamc@655 592
adamc@530 593 \subsection{Kinding}
adamc@530 594
adamc@655 595 We write $[X \mapsto \kappa_1]\kappa_2$ for capture-avoiding substitution of $\kappa_1$ for $X$ in $\kappa_2$.
adamc@655 596
adamc@530 597 $$\infer{\Gamma \vdash (c) :: \kappa :: \kappa}{
adamc@530 598 \Gamma \vdash c :: \kappa
adamc@530 599 }
adamc@530 600 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530 601 x :: \kappa \in \Gamma
adamc@530 602 }
adamc@530 603 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530 604 x :: \kappa = c \in \Gamma
adamc@530 605 }$$
adamc@530 606
adamc@530 607 $$\infer{\Gamma \vdash M.x :: \kappa}{
adamc@537 608 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 609 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = \kappa
adamc@530 610 }
adamc@530 611 \quad \infer{\Gamma \vdash M.x :: \kappa}{
adamc@537 612 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 613 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@530 614 }$$
adamc@530 615
adamc@530 616 $$\infer{\Gamma \vdash \tau_1 \to \tau_2 :: \mt{Type}}{
adamc@530 617 \Gamma \vdash \tau_1 :: \mt{Type}
adamc@530 618 & \Gamma \vdash \tau_2 :: \mt{Type}
adamc@530 619 }
adamc@530 620 \quad \infer{\Gamma \vdash x \; ? \: \kappa \to \tau :: \mt{Type}}{
adamc@530 621 \Gamma, x :: \kappa \vdash \tau :: \mt{Type}
adamc@530 622 }
adamc@655 623 \quad \infer{\Gamma \vdash X \longrightarrow \tau :: \mt{Type}}{
adamc@655 624 \Gamma, X \vdash \tau :: \mt{Type}
adamc@655 625 }
adamc@530 626 \quad \infer{\Gamma \vdash \$c :: \mt{Type}}{
adamc@530 627 \Gamma \vdash c :: \{\mt{Type}\}
adamc@530 628 }$$
adamc@530 629
adamc@530 630 $$\infer{\Gamma \vdash c_1 \; c_2 :: \kappa_2}{
adamc@530 631 \Gamma \vdash c_1 :: \kappa_1 \to \kappa_2
adamc@530 632 & \Gamma \vdash c_2 :: \kappa_1
adamc@530 633 }
adamc@530 634 \quad \infer{\Gamma \vdash \lambda x \; :: \; \kappa_1 \Rightarrow c :: \kappa_1 \to \kappa_2}{
adamc@530 635 \Gamma, x :: \kappa_1 \vdash c :: \kappa_2
adamc@530 636 }$$
adamc@530 637
adamc@655 638 $$\infer{\Gamma \vdash c[\kappa'] :: [X \mapsto \kappa']\kappa}{
adamc@655 639 \Gamma \vdash c :: X \to \kappa
adamc@655 640 & \Gamma \vdash \kappa'
adamc@655 641 }
adamc@655 642 \quad \infer{\Gamma \vdash X \Longrightarrow c :: X \to \kappa}{
adamc@655 643 \Gamma, X \vdash c :: \kappa
adamc@655 644 }$$
adamc@655 645
adamc@530 646 $$\infer{\Gamma \vdash () :: \mt{Unit}}{}
adamc@530 647 \quad \infer{\Gamma \vdash \#X :: \mt{Name}}{}$$
adamc@530 648
adamc@530 649 $$\infer{\Gamma \vdash [\overline{c_i = c'_i}] :: \{\kappa\}}{
adamc@530 650 \forall i: \Gamma \vdash c_i : \mt{Name}
adamc@530 651 & \Gamma \vdash c'_i :: \kappa
adamc@530 652 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@530 653 }
adamc@530 654 \quad \infer{\Gamma \vdash c_1 \rc c_2 :: \{\kappa\}}{
adamc@530 655 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530 656 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@530 657 & \Gamma \vdash c_1 \sim c_2
adamc@530 658 }$$
adamc@530 659
adamc@655 660 $$\infer{\Gamma \vdash \mt{map} :: (\kappa_1 \to \kappa_2) \to \{\kappa_1\} \to \{\kappa_2\}}{}$$
adamc@530 661
adamc@573 662 $$\infer{\Gamma \vdash (\overline c) :: (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@573 663 \forall i: \Gamma \vdash c_i :: \kappa_i
adamc@530 664 }
adamc@573 665 \quad \infer{\Gamma \vdash c.i :: \kappa_i}{
adamc@573 666 \Gamma \vdash c :: (\kappa_1 \times \ldots \times \kappa_n)
adamc@530 667 }$$
adamc@530 668
adamc@655 669 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow \tau :: \mt{Type}}{
adamc@655 670 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530 671 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@655 672 & \Gamma, c_1 \sim c_2 \vdash \tau :: \mt{Type}
adamc@530 673 }$$
adamc@530 674
adamc@531 675 \subsection{Record Disjointness}
adamc@531 676
adamc@531 677 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@558 678 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@558 679 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@558 680 & \forall c'_1 \in C_1, c'_2 \in C_2: \Gamma \vdash c'_1 \sim c'_2
adamc@531 681 }
adamc@531 682 \quad \infer{\Gamma \vdash X \sim X'}{
adamc@531 683 X \neq X'
adamc@531 684 }$$
adamc@531 685
adamc@531 686 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@531 687 c'_1 \sim c'_2 \in \Gamma
adamc@558 688 & \Gamma \vdash c'_1 \hookrightarrow C_1
adamc@558 689 & \Gamma \vdash c'_2 \hookrightarrow C_2
adamc@558 690 & c_1 \in C_1
adamc@558 691 & c_2 \in C_2
adamc@531 692 }$$
adamc@531 693
adamc@531 694 $$\infer{\Gamma \vdash c \hookrightarrow \{c\}}{}
adamc@531 695 \quad \infer{\Gamma \vdash [\overline{c = c'}] \hookrightarrow \{\overline{c}\}}{}
adamc@531 696 \quad \infer{\Gamma \vdash c_1 \rc c_2 \hookrightarrow C_1 \cup C_2}{
adamc@531 697 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@531 698 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@531 699 }
adamc@531 700 \quad \infer{\Gamma \vdash c \hookrightarrow C}{
adamc@531 701 \Gamma \vdash c \equiv c'
adamc@531 702 & \Gamma \vdash c' \hookrightarrow C
adamc@531 703 }
adamc@531 704 \quad \infer{\Gamma \vdash \mt{map} \; f \; c \hookrightarrow C}{
adamc@531 705 \Gamma \vdash c \hookrightarrow C
adamc@531 706 }$$
adamc@531 707
adamc@541 708 \subsection{\label{definitional}Definitional Equality}
adamc@532 709
adamc@655 710 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@532 711
adamc@532 712 $$\infer{\Gamma \vdash c \equiv c}{}
adamc@532 713 \quad \infer{\Gamma \vdash c_1 \equiv c_2}{
adamc@532 714 \Gamma \vdash c_2 \equiv c_1
adamc@532 715 }
adamc@532 716 \quad \infer{\Gamma \vdash c_1 \equiv c_3}{
adamc@532 717 \Gamma \vdash c_1 \equiv c_2
adamc@532 718 & \Gamma \vdash c_2 \equiv c_3
adamc@532 719 }
adamc@532 720 \quad \infer{\Gamma \vdash \mathcal C[c_1] \equiv \mathcal C[c_2]}{
adamc@532 721 \Gamma \vdash c_1 \equiv c_2
adamc@532 722 }$$
adamc@532 723
adamc@532 724 $$\infer{\Gamma \vdash x \equiv c}{
adamc@532 725 x :: \kappa = c \in \Gamma
adamc@532 726 }
adamc@532 727 \quad \infer{\Gamma \vdash M.x \equiv c}{
adamc@537 728 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 729 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@532 730 }
adamc@532 731 \quad \infer{\Gamma \vdash (\overline c).i \equiv c_i}{}$$
adamc@532 732
adamc@532 733 $$\infer{\Gamma \vdash (\lambda x :: \kappa \Rightarrow c) \; c' \equiv [x \mapsto c'] c}{}
adamc@655 734 \quad \infer{\Gamma \vdash (X \Longrightarrow c) [\kappa] \equiv [X \mapsto \kappa] c}{}$$
adamc@655 735
adamc@655 736 $$\infer{\Gamma \vdash c_1 \rc c_2 \equiv c_2 \rc c_1}{}
adamc@532 737 \quad \infer{\Gamma \vdash c_1 \rc (c_2 \rc c_3) \equiv (c_1 \rc c_2) \rc c_3}{}$$
adamc@532 738
adamc@532 739 $$\infer{\Gamma \vdash [] \rc c \equiv c}{}
adamc@532 740 \quad \infer{\Gamma \vdash [\overline{c_1 = c'_1}] \rc [\overline{c_2 = c'_2}] \equiv [\overline{c_1 = c'_1}, \overline{c_2 = c'_2}]}{}$$
adamc@532 741
adamc@655 742 $$\infer{\Gamma \vdash \mt{map} \; f \; [] \equiv []}{}
adamc@655 743 \quad \infer{\Gamma \vdash \mt{map} \; f \; ([c_1 = c_2] \rc c) \equiv [c_1 = f \; c_2] \rc \mt{map} \; f \; c}{}$$
adamc@532 744
adamc@532 745 $$\infer{\Gamma \vdash \mt{map} \; (\lambda x \Rightarrow x) \; c \equiv c}{}
adamc@655 746 \quad \infer{\Gamma \vdash \mt{map} \; f \; (\mt{map} \; f' \; c)
adamc@655 747 \equiv \mt{map} \; (\lambda x \Rightarrow f \; (f' \; x)) \; c}{}$$
adamc@532 748
adamc@532 749 $$\infer{\Gamma \vdash \mt{map} \; f \; (c_1 \rc c_2) \equiv \mt{map} \; f \; c_1 \rc \mt{map} \; f \; c_2}{}$$
adamc@531 750
adamc@534 751 \subsection{Expression Typing}
adamc@533 752
adamc@873 753 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@533 754
adamc@533 755 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@533 756
adamc@533 757 $$\infer{\Gamma \vdash e : \tau : \tau}{
adamc@533 758 \Gamma \vdash e : \tau
adamc@533 759 }
adamc@533 760 \quad \infer{\Gamma \vdash e : \tau}{
adamc@533 761 \Gamma \vdash e : \tau'
adamc@533 762 & \Gamma \vdash \tau' \equiv \tau
adamc@533 763 }
adamc@533 764 \quad \infer{\Gamma \vdash \ell : T(\ell)}{}$$
adamc@533 765
adamc@533 766 $$\infer{\Gamma \vdash x : \mathcal I(\tau)}{
adamc@533 767 x : \tau \in \Gamma
adamc@533 768 }
adamc@533 769 \quad \infer{\Gamma \vdash M.x : \mathcal I(\tau)}{
adamc@537 770 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 771 & \mt{proj}(M, \overline{s}, \mt{val} \; x) = \tau
adamc@533 772 }
adamc@533 773 \quad \infer{\Gamma \vdash X : \mathcal I(\tau)}{
adamc@533 774 X : \tau \in \Gamma
adamc@533 775 }
adamc@533 776 \quad \infer{\Gamma \vdash M.X : \mathcal I(\tau)}{
adamc@537 777 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 778 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \tau
adamc@533 779 }$$
adamc@533 780
adamc@533 781 $$\infer{\Gamma \vdash e_1 \; e_2 : \tau_2}{
adamc@533 782 \Gamma \vdash e_1 : \tau_1 \to \tau_2
adamc@533 783 & \Gamma \vdash e_2 : \tau_1
adamc@533 784 }
adamc@533 785 \quad \infer{\Gamma \vdash \lambda x : \tau_1 \Rightarrow e : \tau_1 \to \tau_2}{
adamc@533 786 \Gamma, x : \tau_1 \vdash e : \tau_2
adamc@533 787 }$$
adamc@533 788
adamc@533 789 $$\infer{\Gamma \vdash e [c] : [x \mapsto c]\tau}{
adamc@533 790 \Gamma \vdash e : x :: \kappa \to \tau
adamc@533 791 & \Gamma \vdash c :: \kappa
adamc@533 792 }
adamc@852 793 \quad \infer{\Gamma \vdash \lambda [x \; ? \; \kappa] \Rightarrow e : x \; ? \; \kappa \to \tau}{
adamc@533 794 \Gamma, x :: \kappa \vdash e : \tau
adamc@533 795 }$$
adamc@533 796
adamc@655 797 $$\infer{\Gamma \vdash e [\kappa] : [X \mapsto \kappa]\tau}{
adamc@655 798 \Gamma \vdash e : X \longrightarrow \tau
adamc@655 799 & \Gamma \vdash \kappa
adamc@655 800 }
adamc@655 801 \quad \infer{\Gamma \vdash X \Longrightarrow e : X \longrightarrow \tau}{
adamc@655 802 \Gamma, X \vdash e : \tau
adamc@655 803 }$$
adamc@655 804
adamc@533 805 $$\infer{\Gamma \vdash \{\overline{c = e}\} : \{\overline{c : \tau}\}}{
adamc@533 806 \forall i: \Gamma \vdash c_i :: \mt{Name}
adamc@533 807 & \Gamma \vdash e_i : \tau_i
adamc@533 808 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@533 809 }
adamc@533 810 \quad \infer{\Gamma \vdash e.c : \tau}{
adamc@533 811 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533 812 }
adamc@533 813 \quad \infer{\Gamma \vdash e_1 \rc e_2 : \$(c_1 \rc c_2)}{
adamc@533 814 \Gamma \vdash e_1 : \$c_1
adamc@533 815 & \Gamma \vdash e_2 : \$c_2
adamc@573 816 & \Gamma \vdash c_1 \sim c_2
adamc@533 817 }$$
adamc@533 818
adamc@533 819 $$\infer{\Gamma \vdash e \rcut c : \$c'}{
adamc@533 820 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533 821 }
adamc@533 822 \quad \infer{\Gamma \vdash e \rcutM c : \$c'}{
adamc@533 823 \Gamma \vdash e : \$(c \rc c')
adamc@533 824 }$$
adamc@533 825
adamc@533 826 $$\infer{\Gamma \vdash \mt{let} \; \overline{ed} \; \mt{in} \; e \; \mt{end} : \tau}{
adamc@533 827 \Gamma \vdash \overline{ed} \leadsto \Gamma'
adamc@533 828 & \Gamma' \vdash e : \tau
adamc@533 829 }
adamc@533 830 \quad \infer{\Gamma \vdash \mt{case} \; e \; \mt{of} \; \overline{p \Rightarrow e} : \tau}{
adamc@533 831 \forall i: \Gamma \vdash p_i \leadsto \Gamma_i, \tau'
adamc@533 832 & \Gamma_i \vdash e_i : \tau
adamc@533 833 }$$
adamc@533 834
adamc@573 835 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow e : \lambda [c_1 \sim c_2] \Rightarrow \tau}{
adamc@533 836 \Gamma \vdash c_1 :: \{\kappa\}
adamc@655 837 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@533 838 & \Gamma, c_1 \sim c_2 \vdash e : \tau
adamc@662 839 }
adamc@662 840 \quad \infer{\Gamma \vdash e \; ! : \tau}{
adamc@662 841 \Gamma \vdash e : [c_1 \sim c_2] \Rightarrow \tau
adamc@662 842 & \Gamma \vdash c_1 \sim c_2
adamc@533 843 }$$
adamc@533 844
adamc@534 845 \subsection{Pattern Typing}
adamc@534 846
adamc@534 847 $$\infer{\Gamma \vdash \_ \leadsto \Gamma; \tau}{}
adamc@534 848 \quad \infer{\Gamma \vdash x \leadsto \Gamma, x : \tau; \tau}{}
adamc@534 849 \quad \infer{\Gamma \vdash \ell \leadsto \Gamma; T(\ell)}{}$$
adamc@534 850
adamc@534 851 $$\infer{\Gamma \vdash X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534 852 X : \overline{x ::: \mt{Type}} \to \tau \in \Gamma
adamc@534 853 & \textrm{$\tau$ not a function type}
adamc@534 854 }
adamc@534 855 \quad \infer{\Gamma \vdash X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534 856 X : \overline{x ::: \mt{Type}} \to \tau'' \to \tau \in \Gamma
adamc@534 857 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534 858 }$$
adamc@534 859
adamc@534 860 $$\infer{\Gamma \vdash M.X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537 861 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 862 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau
adamc@534 863 & \textrm{$\tau$ not a function type}
adamc@534 864 }$$
adamc@534 865
adamc@534 866 $$\infer{\Gamma \vdash M.X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537 867 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 868 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau'' \to \tau
adamc@534 869 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534 870 }$$
adamc@534 871
adamc@534 872 $$\infer{\Gamma \vdash \{\overline{x = p}\} \leadsto \Gamma_n; \{\overline{x = \tau}\}}{
adamc@534 873 \Gamma_0 = \Gamma
adamc@534 874 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534 875 }
adamc@534 876 \quad \infer{\Gamma \vdash \{\overline{x = p}, \ldots\} \leadsto \Gamma_n; \$([\overline{x = \tau}] \rc c)}{
adamc@534 877 \Gamma_0 = \Gamma
adamc@534 878 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534 879 }$$
adamc@534 880
adamc@852 881 $$\infer{\Gamma \vdash p : \tau \leadsto \Gamma'; \tau}{
adamc@852 882 \Gamma \vdash p \leadsto \Gamma'; \tau'
adamc@852 883 & \Gamma \vdash \tau' \equiv \tau
adamc@852 884 }$$
adamc@852 885
adamc@535 886 \subsection{Declaration Typing}
adamc@535 887
adamc@535 888 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@535 889
adamc@655 890 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@535 891
adamc@558 892 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@537 893 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@535 894
adamc@535 895 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535 896 \quad \infer{\Gamma \vdash d, \overline{d} \leadsto \Gamma''}{
adamc@535 897 \Gamma \vdash d \leadsto \Gamma'
adamc@535 898 & \Gamma' \vdash \overline{d} \leadsto \Gamma''
adamc@535 899 }$$
adamc@535 900
adamc@535 901 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@535 902 \Gamma \vdash c :: \kappa
adamc@535 903 }
adamc@535 904 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@535 905 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@535 906 }$$
adamc@535 907
adamc@535 908 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537 909 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 910 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@535 911 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@535 912 }$$
adamc@535 913
adamc@535 914 $$\infer{\Gamma \vdash \mt{val} \; x : \tau = e \leadsto \Gamma, x : \tau}{
adamc@535 915 \Gamma \vdash e : \tau
adamc@535 916 }$$
adamc@535 917
adamc@535 918 $$\infer{\Gamma \vdash \mt{val} \; \mt{rec} \; \overline{x : \tau = e} \leadsto \Gamma, \overline{x : \tau}}{
adamc@535 919 \forall i: \Gamma, \overline{x : \tau} \vdash e_i : \tau_i
adamc@535 920 & \textrm{$e_i$ starts with an expression $\lambda$, optionally preceded by constructor and disjointness $\lambda$s}
adamc@535 921 }$$
adamc@535 922
adamc@535 923 $$\infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : S}{
adamc@535 924 \Gamma \vdash M : S
adamc@558 925 & \textrm{ $M$ not a constant or application}
adamc@535 926 }
adamc@558 927 \quad \infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : \mt{selfify}(X, \overline{s})}{
adamc@558 928 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@539 929 }$$
adamc@539 930
adamc@539 931 $$\infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@535 932 \Gamma \vdash S
adamc@535 933 }$$
adamc@535 934
adamc@537 935 $$\infer{\Gamma \vdash \mt{open} \; M \leadsto \Gamma, \mathcal O(M, \overline{s})}{
adamc@537 936 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535 937 }$$
adamc@535 938
adamc@535 939 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma}{
adamc@535 940 \Gamma \vdash c_1 :: \{\kappa\}
adamc@535 941 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@535 942 & \Gamma \vdash c_1 \sim c_2
adamc@535 943 }
adamc@537 944 \quad \infer{\Gamma \vdash \mt{open} \; \mt{constraints} \; M \leadsto \Gamma, \mathcal O_c(M, \overline{s})}{
adamc@537 945 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535 946 }$$
adamc@535 947
adamc@784 948 $$\infer{\Gamma \vdash \mt{table} \; x : c \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_table} \; c \; []}{
adamc@535 949 \Gamma \vdash c :: \{\mt{Type}\}
adamc@535 950 }
adamc@784 951 \quad \infer{\Gamma \vdash \mt{view} \; x : c \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_view} \; c}{
adamc@784 952 \Gamma \vdash c :: \{\mt{Type}\}
adamc@784 953 }$$
adamc@784 954
adamc@784 955 $$\infer{\Gamma \vdash \mt{sequence} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_sequence}}{}$$
adamc@535 956
adamc@535 957 $$\infer{\Gamma \vdash \mt{cookie} \; x : \tau \leadsto \Gamma, x : \mt{Basis}.\mt{http\_cookie} \; \tau}{
adamc@535 958 \Gamma \vdash \tau :: \mt{Type}
adamc@784 959 }
adamc@784 960 \quad \infer{\Gamma \vdash \mt{style} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{css\_class}}{}$$
adamc@535 961
adamc@1085 962 $$\infer{\Gamma \vdash \mt{task} \; e_1 = e_2 \leadsto \Gamma}{
adamc@1085 963 \Gamma \vdash e_1 :: \mt{Basis}.\mt{task\_kind}
adamc@1085 964 & \Gamma \vdash e_2 :: \mt{Basis}.\mt{transaction} \; \{\}
adamc@1085 965 }$$
adamc@1085 966
adamc@784 967 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784 968 \Gamma \vdash c :: \kappa
adamc@535 969 }$$
adamc@535 970
adamc@535 971 $$\infer{\overline{y}; x; \Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535 972 \quad \infer{\overline{y}; x; \Gamma \vdash X \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to x \; \overline{y}}{
adamc@535 973 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535 974 }
adamc@535 975 \quad \infer{\overline{y}; x; \Gamma \vdash X \; \mt{of} \; \tau \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to \tau \to x \; \overline{y}}{
adamc@535 976 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535 977 }$$
adamc@535 978
adamc@537 979 \subsection{Signature Item Typing}
adamc@537 980
adamc@537 981 We appeal to a signature item analogue of the $\mathcal O$ function from the last subsection.
adamc@537 982
adamc@537 983 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@537 984 \quad \infer{\Gamma \vdash s, \overline{s} \leadsto \Gamma''}{
adamc@537 985 \Gamma \vdash s \leadsto \Gamma'
adamc@537 986 & \Gamma' \vdash \overline{s} \leadsto \Gamma''
adamc@537 987 }$$
adamc@537 988
adamc@537 989 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}
adamc@537 990 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@537 991 \Gamma \vdash c :: \kappa
adamc@537 992 }
adamc@537 993 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@537 994 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@537 995 }$$
adamc@537 996
adamc@537 997 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537 998 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 999 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1000 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@537 1001 }$$
adamc@537 1002
adamc@537 1003 $$\infer{\Gamma \vdash \mt{val} \; x : \tau \leadsto \Gamma, x : \tau}{
adamc@537 1004 \Gamma \vdash \tau :: \mt{Type}
adamc@537 1005 }$$
adamc@537 1006
adamc@537 1007 $$\infer{\Gamma \vdash \mt{structure} \; X : S \leadsto \Gamma, X : S}{
adamc@537 1008 \Gamma \vdash S
adamc@537 1009 }
adamc@537 1010 \quad \infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@537 1011 \Gamma \vdash S
adamc@537 1012 }$$
adamc@537 1013
adamc@537 1014 $$\infer{\Gamma \vdash \mt{include} \; S \leadsto \Gamma, \mathcal O(\overline{s})}{
adamc@537 1015 \Gamma \vdash S
adamc@537 1016 & \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1017 }$$
adamc@537 1018
adamc@537 1019 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma, c_1 \sim c_2}{
adamc@537 1020 \Gamma \vdash c_1 :: \{\kappa\}
adamc@537 1021 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@537 1022 }$$
adamc@537 1023
adamc@784 1024 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784 1025 \Gamma \vdash c :: \kappa
adamc@537 1026 }
adamc@784 1027 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}$$
adamc@537 1028
adamc@536 1029 \subsection{Signature Compatibility}
adamc@536 1030
adamc@558 1031 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 1032
adamc@537 1033 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 1034
adamc@536 1035 $$\infer{\Gamma \vdash S \equiv S}{}
adamc@536 1036 \quad \infer{\Gamma \vdash S_1 \equiv S_2}{
adamc@536 1037 \Gamma \vdash S_2 \equiv S_1
adamc@536 1038 }
adamc@536 1039 \quad \infer{\Gamma \vdash X \equiv S}{
adamc@536 1040 X = S \in \Gamma
adamc@536 1041 }
adamc@536 1042 \quad \infer{\Gamma \vdash M.X \equiv S}{
adamc@537 1043 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1044 & \mt{proj}(M, \overline{s}, \mt{signature} \; X) = S
adamc@536 1045 }$$
adamc@536 1046
adamc@536 1047 $$\infer{\Gamma \vdash S \; \mt{where} \; \mt{con} \; x = c \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa = c \; \overline{s_2} \; \mt{end}}{
adamc@536 1048 \Gamma \vdash S \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa \; \overline{s_2} \; \mt{end}
adamc@536 1049 & \Gamma \vdash c :: \kappa
adamc@537 1050 }
adamc@537 1051 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s^1} \; \mt{include} \; S \; \overline{s^2} \; \mt{end} \equiv \mt{sig} \; \overline{s^1} \; \overline{s} \; \overline{s^2} \; \mt{end}}{
adamc@537 1052 \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@536 1053 }$$
adamc@536 1054
adamc@536 1055 $$\infer{\Gamma \vdash S_1 \leq S_2}{
adamc@536 1056 \Gamma \vdash S_1 \equiv S_2
adamc@536 1057 }
adamc@536 1058 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \mt{end}}{}
adamc@537 1059 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; s' \; \overline{s'} \; \mt{end}}{
adamc@537 1060 \Gamma \vdash \overline{s} \leq s'
adamc@537 1061 & \Gamma \vdash s' \leadsto \Gamma'
adamc@537 1062 & \Gamma' \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \overline{s'} \; \mt{end}
adamc@537 1063 }$$
adamc@537 1064
adamc@537 1065 $$\infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537 1066 \Gamma \vdash s \leq s'
adamc@537 1067 }
adamc@537 1068 \quad \infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537 1069 \Gamma \vdash s \leadsto \Gamma'
adamc@537 1070 & \Gamma' \vdash \overline{s} \leq s'
adamc@536 1071 }$$
adamc@536 1072
adamc@536 1073 $$\infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 \leq \mt{functor} (X : S'_1) : S'_2}{
adamc@536 1074 \Gamma \vdash S'_1 \leq S_1
adamc@536 1075 & \Gamma, X : S'_1 \vdash S_2 \leq S'_2
adamc@536 1076 }$$
adamc@536 1077
adamc@537 1078 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@537 1079 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}
adamc@558 1080 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type}}{}$$
adamc@537 1081
adamc@537 1082 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(y)} \to \mt{Type}}{
adamc@537 1083 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1084 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1085 }$$
adamc@537 1086
adamc@784 1087 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@784 1088 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}$$
adamc@537 1089
adamc@537 1090 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \mt{\kappa} = c_2}{
adamc@537 1091 \Gamma \vdash c_1 \equiv c_2
adamc@537 1092 }
adamc@784 1093 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \kappa = c_2}{
adamc@537 1094 \Gamma \vdash c_1 \equiv c_2
adamc@537 1095 }$$
adamc@537 1096
adamc@537 1097 $$\infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537 1098 \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1099 }$$
adamc@537 1100
adamc@537 1101 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537 1102 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1103 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1104 & \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1105 }$$
adamc@537 1106
adamc@537 1107 $$\infer{\Gamma \vdash \cdot \leq \cdot}{}
adamc@537 1108 \quad \infer{\Gamma \vdash X; \overline{dc} \leq X; \overline{dc'}}{
adamc@537 1109 \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1110 }
adamc@537 1111 \quad \infer{\Gamma \vdash X \; \mt{of} \; \tau_1; \overline{dc} \leq X \; \mt{of} \; \tau_2; \overline{dc'}}{
adamc@537 1112 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537 1113 & \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1114 }$$
adamc@537 1115
adamc@537 1116 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x = \mt{datatype} \; M'.z'}{
adamc@537 1117 \Gamma \vdash M.z \equiv M'.z'
adamc@537 1118 }$$
adamc@537 1119
adamc@537 1120 $$\infer{\Gamma \vdash \mt{val} \; x : \tau_1 \leq \mt{val} \; x : \tau_2}{
adamc@537 1121 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537 1122 }
adamc@537 1123 \quad \infer{\Gamma \vdash \mt{structure} \; X : S_1 \leq \mt{structure} \; X : S_2}{
adamc@537 1124 \Gamma \vdash S_1 \leq S_2
adamc@537 1125 }
adamc@537 1126 \quad \infer{\Gamma \vdash \mt{signature} \; X = S_1 \leq \mt{signature} \; X = S_2}{
adamc@537 1127 \Gamma \vdash S_1 \leq S_2
adamc@537 1128 & \Gamma \vdash S_2 \leq S_1
adamc@537 1129 }$$
adamc@537 1130
adamc@537 1131 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leq \mt{constraint} \; c'_1 \sim c'_2}{
adamc@537 1132 \Gamma \vdash c_1 \equiv c'_1
adamc@537 1133 & \Gamma \vdash c_2 \equiv c'_2
adamc@537 1134 }$$
adamc@537 1135
adamc@655 1136 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{class} \; x :: \kappa}{}
adamc@655 1137 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{class} \; x :: \kappa}{}
adamc@655 1138 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{class} \; x :: \kappa = c_2}{
adamc@537 1139 \Gamma \vdash c_1 \equiv c_2
adamc@537 1140 }$$
adamc@537 1141
adamc@538 1142 \subsection{Module Typing}
adamc@538 1143
adamc@538 1144 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 1145
adamc@538 1146 $$\infer{\Gamma \vdash M : S}{
adamc@538 1147 \Gamma \vdash M : S'
adamc@538 1148 & \Gamma \vdash S' \leq S
adamc@538 1149 }
adamc@538 1150 \quad \infer{\Gamma \vdash \mt{struct} \; \overline{d} \; \mt{end} : \mt{sig} \; \mt{sigOf}(\overline{d}) \; \mt{end}}{
adamc@538 1151 \Gamma \vdash \overline{d} \leadsto \Gamma'
adamc@538 1152 }
adamc@538 1153 \quad \infer{\Gamma \vdash X : S}{
adamc@538 1154 X : S \in \Gamma
adamc@538 1155 }$$
adamc@538 1156
adamc@538 1157 $$\infer{\Gamma \vdash M.X : S}{
adamc@538 1158 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@538 1159 & \mt{proj}(M, \overline{s}, \mt{structure} \; X) = S
adamc@538 1160 }$$
adamc@538 1161
adamc@538 1162 $$\infer{\Gamma \vdash M_1(M_2) : [X \mapsto M_2]S_2}{
adamc@538 1163 \Gamma \vdash M_1 : \mt{functor}(X : S_1) : S_2
adamc@538 1164 & \Gamma \vdash M_2 : S_1
adamc@538 1165 }
adamc@538 1166 \quad \infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 = M : \mt{functor} (X : S_1) : S_2}{
adamc@538 1167 \Gamma \vdash S_1
adamc@538 1168 & \Gamma, X : S_1 \vdash S_2
adamc@538 1169 & \Gamma, X : S_1 \vdash M : S_2
adamc@538 1170 }$$
adamc@538 1171
adamc@538 1172 \begin{eqnarray*}
adamc@538 1173 \mt{sigOf}(\cdot) &=& \cdot \\
adamc@538 1174 \mt{sigOf}(s \; \overline{s'}) &=& \mt{sigOf}(s) \; \mt{sigOf}(\overline{s'}) \\
adamc@538 1175 \\
adamc@538 1176 \mt{sigOf}(\mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@538 1177 \mt{sigOf}(\mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \overline{dc} \\
adamc@538 1178 \mt{sigOf}(\mt{datatype} \; x = \mt{datatype} \; M.z) &=& \mt{datatype} \; x = \mt{datatype} \; M.z \\
adamc@538 1179 \mt{sigOf}(\mt{val} \; x : \tau = e) &=& \mt{val} \; x : \tau \\
adamc@538 1180 \mt{sigOf}(\mt{val} \; \mt{rec} \; \overline{x : \tau = e}) &=& \overline{\mt{val} \; x : \tau} \\
adamc@538 1181 \mt{sigOf}(\mt{structure} \; X : S = M) &=& \mt{structure} \; X : S \\
adamc@538 1182 \mt{sigOf}(\mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@538 1183 \mt{sigOf}(\mt{open} \; M) &=& \mt{include} \; S \textrm{ (where $\Gamma \vdash M : S$)} \\
adamc@538 1184 \mt{sigOf}(\mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@538 1185 \mt{sigOf}(\mt{open} \; \mt{constraints} \; M) &=& \cdot \\
adamc@538 1186 \mt{sigOf}(\mt{table} \; x : c) &=& \mt{table} \; x : c \\
adamc@784 1187 \mt{sigOf}(\mt{view} \; x : c) &=& \mt{view} \; x : c \\
adamc@538 1188 \mt{sigOf}(\mt{sequence} \; x) &=& \mt{sequence} \; x \\
adamc@538 1189 \mt{sigOf}(\mt{cookie} \; x : \tau) &=& \mt{cookie} \; x : \tau \\
adamc@784 1190 \mt{sigOf}(\mt{style} \; x) &=& \mt{style} \; x \\
adamc@655 1191 \mt{sigOf}(\mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@538 1192 \end{eqnarray*}
adamc@539 1193 \begin{eqnarray*}
adamc@539 1194 \mt{selfify}(M, \cdot) &=& \cdot \\
adamc@558 1195 \mt{selfify}(M, s \; \overline{s'}) &=& \mt{selfify}(M, s) \; \mt{selfify}(M, \overline{s'}) \\
adamc@539 1196 \\
adamc@539 1197 \mt{selfify}(M, \mt{con} \; x :: \kappa) &=& \mt{con} \; x :: \kappa = M.x \\
adamc@539 1198 \mt{selfify}(M, \mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@539 1199 \mt{selfify}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \mt{datatype} \; M.x \\
adamc@539 1200 \mt{selfify}(M, \mt{datatype} \; x = \mt{datatype} \; M'.z) &=& \mt{datatype} \; x = \mt{datatype} \; M'.z \\
adamc@539 1201 \mt{selfify}(M, \mt{val} \; x : \tau) &=& \mt{val} \; x : \tau \\
adamc@539 1202 \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 1203 \mt{selfify}(M, \mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@539 1204 \mt{selfify}(M, \mt{include} \; S) &=& \mt{include} \; S \\
adamc@539 1205 \mt{selfify}(M, \mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@655 1206 \mt{selfify}(M, \mt{class} \; x :: \kappa) &=& \mt{class} \; x :: \kappa = M.x \\
adamc@655 1207 \mt{selfify}(M, \mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@539 1208 \end{eqnarray*}
adamc@539 1209
adamc@540 1210 \subsection{Module Projection}
adamc@540 1211
adamc@540 1212 \begin{eqnarray*}
adamc@540 1213 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \\
adamc@540 1214 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa, c) \\
adamc@540 1215 \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 1216 \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 1217 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})$)} \\
adamc@655 1218 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \to \mt{Type} \\
adamc@655 1219 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa \to \mt{Type}, c) \\
adamc@540 1220 \\
adamc@540 1221 \mt{proj}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc} \; \overline{s}, \mt{datatype} \; x) &=& (\overline{y}, \overline{dc}) \\
adamc@540 1222 \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 1223 \\
adamc@540 1224 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, \mt{val} \; x) &=& \tau \\
adamc@540 1225 \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 1226 \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 1227 \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 1228 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \in \overline{dc}$)} \\
adamc@540 1229 \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 1230 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \; \mt{of} \; \tau \in \overline{dc}$)} \\
adamc@540 1231 \\
adamc@540 1232 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, \mt{structure} \; X) &=& S \\
adamc@540 1233 \\
adamc@540 1234 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, \mt{signature} \; X) &=& S \\
adamc@540 1235 \\
adamc@540 1236 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1237 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1238 \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 1239 \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 1240 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@540 1241 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1242 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1243 \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 1244 \mt{proj}(M, \mt{constraint} \; c_1 \sim c_2 \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@655 1245 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@655 1246 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1247 \end{eqnarray*}
adamc@540 1248
adamc@541 1249
adamc@541 1250 \section{Type Inference}
adamc@541 1251
adamc@541 1252 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 1253
adamc@541 1254 \subsection{Basic Unification}
adamc@541 1255
adamc@560 1256 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 1257
adamc@656 1258 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 1259
adamc@541 1260 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 1261
adamc@541 1262 \subsection{Unifying Record Types}
adamc@541 1263
adamc@570 1264 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 1265
adamc@656 1266 \subsection{\label{typeclasses}Constructor Classes}
adamc@541 1267
adamc@784 1268 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 1269
adamc@784 1270 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 1271
adamc@656 1272 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 1273
adamc@656 1274 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 1275
adamc@541 1276 \subsection{Reverse-Engineering Record Types}
adamc@541 1277
adamc@656 1278 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 1279
adamc@541 1280 \subsection{Implicit Arguments in Functor Applications}
adamc@541 1281
adamc@656 1282 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 1283
adamc@541 1284
adamc@542 1285 \section{The Ur Standard Library}
adamc@542 1286
adamc@542 1287 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 1288
adamc@542 1289 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 1290
adamc@542 1291 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 1292 $$\begin{array}{l}
adamc@542 1293 \mt{type} \; \mt{int} \\
adamc@542 1294 \mt{type} \; \mt{float} \\
adamc@873 1295 \mt{type} \; \mt{char} \\
adamc@542 1296 \mt{type} \; \mt{string} \\
adamc@542 1297 \mt{type} \; \mt{time} \\
adamc@785 1298 \mt{type} \; \mt{blob} \\
adamc@542 1299 \\
adamc@542 1300 \mt{type} \; \mt{unit} = \{\} \\
adamc@542 1301 \\
adamc@542 1302 \mt{datatype} \; \mt{bool} = \mt{False} \mid \mt{True} \\
adamc@542 1303 \\
adamc@785 1304 \mt{datatype} \; \mt{option} \; \mt{t} = \mt{None} \mid \mt{Some} \; \mt{of} \; \mt{t} \\
adamc@785 1305 \\
adamc@785 1306 \mt{datatype} \; \mt{list} \; \mt{t} = \mt{Nil} \mid \mt{Cons} \; \mt{of} \; \mt{t} \times \mt{list} \; \mt{t}
adamc@542 1307 \end{array}$$
adamc@542 1308
adamc@1123 1309 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 1310
adam@1297 1311 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 1312 $$\begin{array}{l}
adam@1297 1313 \mt{con} \; \mt{variant} :: \{\mt{Type}\} \to \mt{Type} \\
adam@1297 1314 \mt{val} \; \mt{make} : \mt{nm} :: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{ts} ::: \{\mt{Type}\} \to [[\mt{nm}] \sim \mt{ts}] \Rightarrow \mt{t} \to \mt{variant} \; ([\mt{nm} = \mt{t}] \rc \mt{ts}) \\
adam@1297 1315 \mt{val} \; \mt{match} : \mt{ts} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{variant} \; \mt{ts} \to \$(\mt{map} \; (\lambda \mt{t'} \Rightarrow \mt{t'} \to \mt{t}) \; \mt{ts}) \to \mt{t}
adam@1297 1316 \end{array}$$
adam@1297 1317
adamc@657 1318 Another important generic Ur element comes at the beginning of \texttt{top.urs}.
adamc@657 1319
adamc@657 1320 $$\begin{array}{l}
adamc@657 1321 \mt{con} \; \mt{folder} :: \mt{K} \longrightarrow \{\mt{K}\} \to \mt{Type} \\
adamc@657 1322 \\
adamc@657 1323 \mt{val} \; \mt{fold} : \mt{K} \longrightarrow \mt{tf} :: (\{\mt{K}\} \to \mt{Type}) \\
adamc@657 1324 \hspace{.1in} \to (\mt{nm} :: \mt{Name} \to \mt{v} :: \mt{K} \to \mt{r} :: \{\mt{K}\} \to [[\mt{nm}] \sim \mt{r}] \Rightarrow \\
adamc@657 1325 \hspace{.2in} \mt{tf} \; \mt{r} \to \mt{tf} \; ([\mt{nm} = \mt{v}] \rc \mt{r})) \\
adamc@657 1326 \hspace{.1in} \to \mt{tf} \; [] \\
adamc@657 1327 \hspace{.1in} \to \mt{r} :: \{\mt{K}\} \to \mt{folder} \; \mt{r} \to \mt{tf} \; \mt{r}
adamc@657 1328 \end{array}$$
adamc@657 1329
adamc@657 1330 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 1331
adamc@664 1332 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 1333
adamc@542 1334
adamc@542 1335 \section{The Ur/Web Standard Library}
adamc@542 1336
adamc@658 1337 \subsection{Monads}
adamc@658 1338
adamc@658 1339 The Ur Basis defines the monad constructor class from Haskell.
adamc@658 1340
adamc@658 1341 $$\begin{array}{l}
adamc@658 1342 \mt{class} \; \mt{monad} :: \mt{Type} \to \mt{Type} \\
adamc@658 1343 \mt{val} \; \mt{return} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t} ::: \mt{Type} \\
adamc@658 1344 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658 1345 \hspace{.1in} \to \mt{t} \to \mt{m} \; \mt{t} \\
adamc@658 1346 \mt{val} \; \mt{bind} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t1} ::: \mt{Type} \to \mt{t2} ::: \mt{Type} \\
adamc@658 1347 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658 1348 \hspace{.1in} \to \mt{m} \; \mt{t1} \to (\mt{t1} \to \mt{m} \; \mt{t2}) \\
adamc@658 1349 \hspace{.1in} \to \mt{m} \; \mt{t2}
adamc@658 1350 \end{array}$$
adamc@658 1351
adamc@542 1352 \subsection{Transactions}
adamc@542 1353
adamc@542 1354 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 1355 $$\begin{array}{l}
adamc@542 1356 \mt{con} \; \mt{transaction} :: \mt{Type} \to \mt{Type} \\
adamc@658 1357 \mt{val} \; \mt{transaction\_monad} : \mt{monad} \; \mt{transaction}
adamc@542 1358 \end{array}$$
adamc@542 1359
adamc@1123 1360 For debugging purposes, a transactional function is provided for outputting a string on the server process' \texttt{stderr}.
adamc@1123 1361 $$\begin{array}{l}
adamc@1123 1362 \mt{val} \; \mt{debug} : \mt{string} \to \mt{transaction} \; \mt{unit}
adamc@1123 1363 \end{array}$$
adamc@1123 1364
adamc@542 1365 \subsection{HTTP}
adamc@542 1366
adamc@542 1367 There are transactions for reading an HTTP header by name and for getting and setting strongly-typed cookies. Cookies may only be created by the $\mt{cookie}$ declaration form, ensuring that they be named consistently based on module structure.
adamc@542 1368 $$\begin{array}{l}
adamc@786 1369 \mt{val} \; \mt{requestHeader} : \mt{string} \to \mt{transaction} \; (\mt{option} \; \mt{string}) \\
adamc@786 1370 \\
adamc@786 1371 \mt{con} \; \mt{http\_cookie} :: \mt{Type} \to \mt{Type} \\
adamc@786 1372 \mt{val} \; \mt{getCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; (\mt{option} \; \mt{t}) \\
adamc@1050 1373 \mt{val} \; \mt{setCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \{\mt{Value} : \mt{t}, \mt{Expires} : \mt{option} \; \mt{time}, \mt{Secure} : \mt{bool}\} \to \mt{transaction} \; \mt{unit} \\
adamc@1050 1374 \mt{val} \; \mt{clearCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; \mt{unit}
adamc@786 1375 \end{array}$$
adamc@786 1376
adamc@786 1377 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 1378 $$\begin{array}{l}
adamc@786 1379 \mt{type} \; \mt{url} \\
adamc@786 1380 \mt{val} \; \mt{bless} : \mt{string} \to \mt{url} \\
adamc@786 1381 \mt{val} \; \mt{checkUrl} : \mt{string} \to \mt{option} \; \mt{url}
adamc@786 1382 \end{array}$$
adamc@786 1383 $\mt{bless}$ raises a runtime error if the string passed to it fails the URL policy.
adamc@786 1384
adamc@1085 1385 It is possible to grab the current page's URL or to build a URL for an arbitrary transaction that would also be an acceptable value of a \texttt{link} attribute of the \texttt{a} tag.
adamc@1085 1386 $$\begin{array}{l}
adamc@1085 1387 \mt{val} \; \mt{currentUrl} : \mt{transaction} \; \mt{url} \\
adamc@1085 1388 \mt{val} \; \mt{url} : \mt{transaction} \; \mt{page} \to \mt{url}
adamc@1085 1389 \end{array}$$
adamc@1085 1390
adamc@1085 1391 Page generation may be interrupted at any time with a request to redirect to a particular URL instead.
adamc@1085 1392 $$\begin{array}{l}
adamc@1085 1393 \mt{val} \; \mt{redirect} : \mt{t} ::: \mt{Type} \to \mt{url} \to \mt{transaction} \; \mt{t}
adamc@1085 1394 \end{array}$$
adamc@1085 1395
adamc@786 1396 It's possible for pages to return files of arbitrary MIME types. A file can be input from the user using this data type, along with the $\mt{upload}$ form tag.
adamc@786 1397 $$\begin{array}{l}
adamc@786 1398 \mt{type} \; \mt{file} \\
adamc@786 1399 \mt{val} \; \mt{fileName} : \mt{file} \to \mt{option} \; \mt{string} \\
adamc@786 1400 \mt{val} \; \mt{fileMimeType} : \mt{file} \to \mt{string} \\
adamc@786 1401 \mt{val} \; \mt{fileData} : \mt{file} \to \mt{blob}
adamc@786 1402 \end{array}$$
adamc@786 1403
adamc@786 1404 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 1405 $$\begin{array}{l}
adamc@786 1406 \mt{type} \; \mt{mimeType} \\
adamc@786 1407 \mt{val} \; \mt{blessMime} : \mt{string} \to \mt{mimeType} \\
adamc@786 1408 \mt{val} \; \mt{checkMime} : \mt{string} \to \mt{option} \; \mt{mimeType} \\
adamc@786 1409 \mt{val} \; \mt{returnBlob} : \mt{t} ::: \mt{Type} \to \mt{blob} \to \mt{mimeType} \to \mt{transaction} \; \mt{t}
adamc@542 1410 \end{array}$$
adamc@542 1411
adamc@543 1412 \subsection{SQL}
adamc@543 1413
adamc@543 1414 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 1415 $$\begin{array}{l}
adamc@785 1416 \mt{con} \; \mt{sql\_table} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785 1417 \end{array}$$
adamc@785 1418 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 1419
adamc@785 1420 We also have the simpler type family of SQL views, which have no keys.
adamc@785 1421 $$\begin{array}{l}
adamc@785 1422 \mt{con} \; \mt{sql\_view} :: \{\mt{Type}\} \to \mt{Type}
adamc@543 1423 \end{array}$$
adamc@543 1424
adamc@785 1425 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 1426 $$\begin{array}{l}
adamc@785 1427 \mt{class} \; \mt{fieldsOf} :: \mt{Type} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1428 \mt{val} \; \mt{fieldsOf\_table} : \mt{fs} ::: \{\mt{Type}\} \to \mt{keys} ::: \{\{\mt{Unit}\}\} \to \mt{fieldsOf} \; (\mt{sql\_table} \; \mt{fs} \; \mt{keys}) \; \mt{fs} \\
adamc@785 1429 \mt{val} \; \mt{fieldsOf\_view} : \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; (\mt{sql\_view} \; \mt{fs}) \; \mt{fs}
adamc@785 1430 \end{array}$$
adamc@785 1431
adamc@785 1432 \subsubsection{Table Constraints}
adamc@785 1433
adamc@785 1434 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 1435
adamc@785 1436 $$\begin{array}{l}
adamc@785 1437 \mt{con} \; \mt{primary\_key} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type} \\
adamc@785 1438 \mt{val} \; \mt{no\_primary\_key} : \mt{fs} ::: \{\mt{Type}\} \to \mt{primary\_key} \; \mt{fs} \; [] \\
adamc@785 1439 \mt{val} \; \mt{primary\_key} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{key1} :: \mt{Name} \to \mt{keys} :: \{\mt{Type}\} \\
adamc@785 1440 \hspace{.1in} \to [[\mt{key1}] \sim \mt{keys}] \Rightarrow [[\mt{key1} = \mt{t}] \rc \mt{keys} \sim \mt{rest}] \\
adamc@785 1441 \hspace{.1in} \Rightarrow \$([\mt{key1} = \mt{sql\_injectable\_prim} \; \mt{t}] \rc \mt{map} \; \mt{sql\_injectable\_prim} \; \mt{keys}) \\
adamc@785 1442 \hspace{.1in} \to \mt{primary\_key} \; ([\mt{key1} = \mt{t}] \rc \mt{keys} \rc \mt{rest}) \; [\mt{Pkey} = [\mt{key1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{keys}]
adamc@785 1443 \end{array}$$
adamc@785 1444 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 1445
adamc@785 1446 A type family stands for sets of named constraints of the remaining varieties.
adamc@785 1447 $$\begin{array}{l}
adamc@785 1448 \mt{con} \; \mt{sql\_constraints} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785 1449 \end{array}$$
adamc@785 1450 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 1451
adamc@785 1452 There is a type family of individual, unnamed constraints.
adamc@785 1453 $$\begin{array}{l}
adamc@785 1454 \mt{con} \; \mt{sql\_constraint} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \mt{Type}
adamc@785 1455 \end{array}$$
adamc@785 1456 The first argument is the same as above, and the second argument gives the key columns for just this constraint.
adamc@785 1457
adamc@785 1458 We have operations for assembling constraints into constraint sets.
adamc@785 1459 $$\begin{array}{l}
adamc@785 1460 \mt{val} \; \mt{no\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_constraints} \; \mt{fs} \; [] \\
adamc@785 1461 \mt{val} \; \mt{one\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{unique} ::: \{\mt{Unit}\} \to \mt{name} :: \mt{Name} \\
adamc@785 1462 \hspace{.1in} \to \mt{sql\_constraint} \; \mt{fs} \; \mt{unique} \to \mt{sql\_constraints} \; \mt{fs} \; [\mt{name} = \mt{unique}] \\
adamc@785 1463 \mt{val} \; \mt{join\_constraints} : \mt{fs} ::: \{\mt{Type}\} \to \mt{uniques1} ::: \{\{\mt{Unit}\}\} \to \mt{uniques2} ::: \{\{\mt{Unit}\}\} \to [\mt{uniques1} \sim \mt{uniques2}] \\
adamc@785 1464 \hspace{.1in} \Rightarrow \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques1} \to \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques2} \to \mt{sql\_constraints} \; \mt{fs} \; (\mt{uniques1} \rc \mt{uniques2})
adamc@785 1465 \end{array}$$
adamc@785 1466
adamc@785 1467 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 1468 $$\begin{array}{l}
adamc@785 1469 \mt{val} \; \mt{unique} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{unique1} :: \mt{Name} \to \mt{unique} :: \{\mt{Type}\} \\
adamc@785 1470 \hspace{.1in} \to [[\mt{unique1}] \sim \mt{unique}] \Rightarrow [[\mt{unique1} = \mt{t}] \rc \mt{unique} \sim \mt{rest}] \\
adamc@785 1471 \hspace{.1in} \Rightarrow \mt{sql\_constraint} \; ([\mt{unique1} = \mt{t}] \rc \mt{unique} \rc \mt{rest}) \; ([\mt{unique1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{unique})
adamc@785 1472 \end{array}$$
adamc@785 1473
adamc@785 1474 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 1475 $$\begin{array}{l}
adamc@785 1476 \mt{class} \; \mt{linkable} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@785 1477 \mt{val} \; \mt{linkable\_same} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; \mt{t} \\
adamc@785 1478 \mt{val} \; \mt{linkable\_from\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; (\mt{option} \; \mt{t}) \; \mt{t} \\
adamc@785 1479 \mt{val} \; \mt{linkable\_to\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@785 1480 \end{array}$$
adamc@785 1481
adamc@785 1482 The $\mt{matching}$ type family uses $\mt{linkable}$ to define when two keys match up type-wise.
adamc@785 1483 $$\begin{array}{l}
adamc@785 1484 \mt{con} \; \mt{matching} :: \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1485 \mt{val} \; \mt{mat\_nil} : \mt{matching} \; [] \; [] \\
adamc@785 1486 \mt{val} \; \mt{mat\_cons} : \mt{t1} ::: \mt{Type} \to \mt{rest1} ::: \{\mt{Type}\} \to \mt{t2} ::: \mt{Type} \to \mt{rest2} ::: \{\mt{Type}\} \to \mt{nm1} :: \mt{Name} \to \mt{nm2} :: \mt{Name} \\
adamc@785 1487 \hspace{.1in} \to [[\mt{nm1}] \sim \mt{rest1}] \Rightarrow [[\mt{nm2}] \sim \mt{rest2}] \Rightarrow \mt{linkable} \; \mt{t1} \; \mt{t2} \to \mt{matching} \; \mt{rest1} \; \mt{rest2} \\
adamc@785 1488 \hspace{.1in} \to \mt{matching} \; ([\mt{nm1} = \mt{t1}] \rc \mt{rest1}) \; ([\mt{nm2} = \mt{t2}] \rc \mt{rest2})
adamc@785 1489 \end{array}$$
adamc@785 1490
adamc@785 1491 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 1492 $$\begin{array}{l}
adamc@785 1493 \mt{con} \; \mt{propagation\_mode} :: \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1494 \mt{val} \; \mt{restrict} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1495 \mt{val} \; \mt{cascade} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1496 \mt{val} \; \mt{no\_action} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1497 \mt{val} \; \mt{set\_null} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; (\mt{map} \; \mt{option} \; \mt{fs})
adamc@785 1498 \end{array}$$
adamc@785 1499
adamc@785 1500 Finally, we put these ingredient together to define the \texttt{FOREIGN KEY} constraint function.
adamc@785 1501 $$\begin{array}{l}
adamc@785 1502 \mt{val} \; \mt{foreign\_key} : \mt{mine1} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{mine} ::: \{\mt{Type}\} \to \mt{munused} ::: \{\mt{Type}\} \to \mt{foreign} ::: \{\mt{Type}\} \\
adamc@785 1503 \hspace{.1in} \to \mt{funused} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{uniques} ::: \{\{\mt{Unit}\}\} \\
adamc@785 1504 \hspace{.1in} \to [[\mt{mine1}] \sim \mt{mine}] \Rightarrow [[\mt{mine1} = \mt{t}] \rc \mt{mine} \sim \mt{munused}] \Rightarrow [\mt{foreign} \sim \mt{funused}] \Rightarrow [[\mt{nm}] \sim \mt{uniques}] \\
adamc@785 1505 \hspace{.1in} \Rightarrow \mt{matching} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}) \; \mt{foreign} \\
adamc@785 1506 \hspace{.1in} \to \mt{sql\_table} \; (\mt{foreign} \rc \mt{funused}) \; ([\mt{nm} = \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{foreign}] \rc \mt{uniques}) \\
adamc@785 1507 \hspace{.1in} \to \{\mt{OnDelete} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}), \\
adamc@785 1508 \hspace{.2in} \mt{OnUpdate} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine})\} \\
adamc@785 1509 \hspace{.1in} \to \mt{sql\_constraint} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine} \rc \mt{munused}) \; []
adamc@785 1510 \end{array}$$
adamc@785 1511
adamc@785 1512 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 1513 $$\begin{array}{l}
adamc@785 1514 \mt{val} \; \mt{check} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; [] \; [] \; \mt{fs} \; \mt{bool} \to \mt{sql\_constraint} \; \mt{fs} \; []
adamc@785 1515 \end{array}$$
adamc@785 1516
adamc@785 1517 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 1518
adamc@784 1519
adamc@543 1520 \subsubsection{Queries}
adamc@543 1521
adamc@1193 1522 A final query is constructed via the $\mt{sql\_query}$ function. Constructor arguments respectively specify the free table variables (which will only be available in subqueries), table fields we select (as records mapping tables to the subsets of their fields that we choose) and the (always named) extra expressions that we select.
adamc@543 1523 $$\begin{array}{l}
adamc@1193 1524 \mt{con} \; \mt{sql\_query} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@1193 1525 \mt{val} \; \mt{sql\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1526 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543 1527 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1528 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1193 1529 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adamc@1193 1530 \hspace{.1in} \Rightarrow \{\mt{Rows} : \mt{sql\_query1} \; \mt{free} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}, \\
adamc@1193 1531 \hspace{.2in} \mt{OrderBy} : \mt{sql\_order\_by} \; (\mt{free} \rc \mt{tables}) \; \mt{selectedExps}, \\
adamc@543 1532 \hspace{.2in} \mt{Limit} : \mt{sql\_limit}, \\
adamc@543 1533 \hspace{.2in} \mt{Offset} : \mt{sql\_offset}\} \\
adamc@1193 1534 \hspace{.1in} \to \mt{sql\_query} \; \mt{free} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1535 \end{array}$$
adamc@543 1536
adamc@545 1537 Queries are used by folding over their results inside transactions.
adamc@545 1538 $$\begin{array}{l}
adamc@1193 1539 \mt{val} \; \mt{query} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \lambda [\mt{tables} \sim \mt{exps}] \Rightarrow \mt{state} ::: \mt{Type} \to \mt{sql\_query} \; [] \; \mt{tables} \; \mt{exps} \\
adamc@658 1540 \hspace{.1in} \to (\$(\mt{exps} \rc \mt{map} \; (\lambda \mt{fields} :: \{\mt{Type}\} \Rightarrow \$\mt{fields}) \; \mt{tables}) \\
adamc@545 1541 \hspace{.2in} \to \mt{state} \to \mt{transaction} \; \mt{state}) \\
adamc@545 1542 \hspace{.1in} \to \mt{state} \to \mt{transaction} \; \mt{state}
adamc@545 1543 \end{array}$$
adamc@545 1544
adamc@1193 1545 Most of the complexity of the query encoding is in the type $\mt{sql\_query1}$, which includes simple queries and derived queries based on relational operators. Constructor arguments respectively specify the free table veriables, the tables we select from, the subset of fields that we keep from each table for the result rows, and the extra expressions that we select.
adamc@543 1546 $$\begin{array}{l}
adamc@1193 1547 \mt{con} \; \mt{sql\_query1} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@543 1548 \\
adamc@543 1549 \mt{type} \; \mt{sql\_relop} \\
adamc@543 1550 \mt{val} \; \mt{sql\_union} : \mt{sql\_relop} \\
adamc@543 1551 \mt{val} \; \mt{sql\_intersect} : \mt{sql\_relop} \\
adamc@543 1552 \mt{val} \; \mt{sql\_except} : \mt{sql\_relop} \\
adamc@543 1553 \mt{val} \; \mt{sql\_relop} : \mt{tables1} ::: \{\{\mt{Type}\}\} \\
adamc@543 1554 \hspace{.1in} \to \mt{tables2} ::: \{\{\mt{Type}\}\} \\
adamc@543 1555 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1556 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@543 1557 \hspace{.1in} \to \mt{sql\_relop} \\
adamc@543 1558 \hspace{.1in} \to \mt{sql\_query1} \; \mt{tables1} \; \mt{selectedFields} \; \mt{selectedExps} \\
adamc@543 1559 \hspace{.1in} \to \mt{sql\_query1} \; \mt{tables2} \; \mt{selectedFields} \; \mt{selectedExps} \\
adamc@543 1560 \hspace{.1in} \to \mt{sql\_query1} \; \mt{selectedFields} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1561 \end{array}$$
adamc@543 1562
adamc@543 1563 $$\begin{array}{l}
adamc@1193 1564 \mt{val} \; \mt{sql\_query1} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1565 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543 1566 \hspace{.1in} \to \mt{grouped} ::: \{\{\mt{Type}\}\} \\
adamc@543 1567 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1568 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1085 1569 \hspace{.1in} \to \mt{empties} :: \{\mt{Unit}\} \\
adamc@1193 1570 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adamc@1193 1571 \hspace{.1in} \Rightarrow [\mt{free} \sim \mt{grouped}] \\
adamc@1193 1572 \hspace{.1in} \Rightarrow [\mt{empties} \sim \mt{selectedFields}] \\
adamc@1085 1573 \hspace{.1in} \Rightarrow \{\mt{Distinct} : \mt{bool}, \\
adamc@1193 1574 \hspace{.2in} \mt{From} : \mt{sql\_from\_items} \; \mt{free} \; \mt{tables}, \\
adamc@1193 1575 \hspace{.2in} \mt{Where} : \mt{sql\_exp} \; (\mt{free} \rc \mt{tables}) \; [] \; [] \; \mt{bool}, \\
adamc@543 1576 \hspace{.2in} \mt{GroupBy} : \mt{sql\_subset} \; \mt{tables} \; \mt{grouped}, \\
adamc@1193 1577 \hspace{.2in} \mt{Having} : \mt{sql\_exp} \; (\mt{free} \rc \mt{grouped}) \; \mt{tables} \; [] \; \mt{bool}, \\
adamc@1085 1578 \hspace{.2in} \mt{SelectFields} : \mt{sql\_subset} \; \mt{grouped} \; (\mt{map} \; (\lambda \_ \Rightarrow []) \; \mt{empties} \rc \mt{selectedFields}), \\
adamc@1193 1579 \hspace{.2in} \mt {SelectExps} : \$(\mt{map} \; (\mt{sql\_exp} \; (\mt{free} \rc \mt{grouped}) \; \mt{tables} \; []) \; \mt{selectedExps}) \} \\
adamc@1193 1580 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1581 \end{array}$$
adamc@543 1582
adamc@543 1583 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 1584 $$\begin{array}{l}
adamc@543 1585 \mt{con} \; \mt{sql\_subset} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@543 1586 \mt{val} \; \mt{sql\_subset} : \mt{keep\_drop} :: \{(\{\mt{Type}\} \times \{\mt{Type}\})\} \\
adamc@543 1587 \hspace{.1in} \to \mt{sql\_subset} \\
adamc@658 1588 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1 \rc \mt{fields}.2)\; \mt{keep\_drop}) \\
adamc@658 1589 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1) \; \mt{keep\_drop}) \\
adamc@543 1590 \mt{val} \; \mt{sql\_subset\_all} : \mt{tables} :: \{\{\mt{Type}\}\} \to \mt{sql\_subset} \; \mt{tables} \; \mt{tables}
adamc@543 1591 \end{array}$$
adamc@543 1592
adamc@560 1593 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 1594 $$\begin{array}{l}
adamc@543 1595 \mt{con} \; \mt{sql\_exp} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}
adamc@543 1596 \end{array}$$
adamc@543 1597
adamc@543 1598 Any field in scope may be converted to an expression.
adamc@543 1599 $$\begin{array}{l}
adamc@543 1600 \mt{val} \; \mt{sql\_field} : \mt{otherTabs} ::: \{\{\mt{Type}\}\} \to \mt{otherFields} ::: \{\mt{Type}\} \\
adamc@543 1601 \hspace{.1in} \to \mt{fieldType} ::: \mt{Type} \to \mt{agg} ::: \{\{\mt{Type}\}\} \\
adamc@543 1602 \hspace{.1in} \to \mt{exps} ::: \{\mt{Type}\} \\
adamc@543 1603 \hspace{.1in} \to \mt{tab} :: \mt{Name} \to \mt{field} :: \mt{Name} \\
adamc@543 1604 \hspace{.1in} \to \mt{sql\_exp} \; ([\mt{tab} = [\mt{field} = \mt{fieldType}] \rc \mt{otherFields}] \rc \mt{otherTabs}) \; \mt{agg} \; \mt{exps} \; \mt{fieldType}
adamc@543 1605 \end{array}$$
adamc@543 1606
adamc@544 1607 There is an analogous function for referencing named expressions.
adamc@544 1608 $$\begin{array}{l}
adamc@544 1609 \mt{val} \; \mt{sql\_exp} : \mt{tabs} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{t} ::: \mt{Type} \to \mt{rest} ::: \{\mt{Type}\} \to \mt{nm} :: \mt{Name} \\
adamc@544 1610 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tabs} \; \mt{agg} \; ([\mt{nm} = \mt{t}] \rc \mt{rest}) \; \mt{t}
adamc@544 1611 \end{array}$$
adamc@544 1612
adamc@544 1613 Ur values of appropriate types may be injected into SQL expressions.
adamc@544 1614 $$\begin{array}{l}
adamc@786 1615 \mt{class} \; \mt{sql\_injectable\_prim} \\
adamc@786 1616 \mt{val} \; \mt{sql\_bool} : \mt{sql\_injectable\_prim} \; \mt{bool} \\
adamc@786 1617 \mt{val} \; \mt{sql\_int} : \mt{sql\_injectable\_prim} \; \mt{int} \\
adamc@786 1618 \mt{val} \; \mt{sql\_float} : \mt{sql\_injectable\_prim} \; \mt{float} \\
adamc@786 1619 \mt{val} \; \mt{sql\_string} : \mt{sql\_injectable\_prim} \; \mt{string} \\
adamc@786 1620 \mt{val} \; \mt{sql\_time} : \mt{sql\_injectable\_prim} \; \mt{time} \\
adamc@786 1621 \mt{val} \; \mt{sql\_blob} : \mt{sql\_injectable\_prim} \; \mt{blob} \\
adamc@786 1622 \mt{val} \; \mt{sql\_channel} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{channel} \; \mt{t}) \\
adamc@786 1623 \mt{val} \; \mt{sql\_client} : \mt{sql\_injectable\_prim} \; \mt{client} \\
adamc@786 1624 \\
adamc@544 1625 \mt{class} \; \mt{sql\_injectable} \\
adamc@786 1626 \mt{val} \; \mt{sql\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@786 1627 \mt{val} \; \mt{sql\_option\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; (\mt{option} \; \mt{t}) \\
adamc@786 1628 \\
adamc@544 1629 \mt{val} \; \mt{sql\_inject} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@544 1630 \hspace{.1in} \to \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adamc@544 1631 \end{array}$$
adamc@544 1632
adamc@1123 1633 Additionally, most function-free types may be injected safely, via the $\mt{serialized}$ type family.
adamc@1123 1634 $$\begin{array}{l}
adamc@1123 1635 \mt{con} \; \mt{serialized} :: \mt{Type} \to \mt{Type} \\
adamc@1123 1636 \mt{val} \; \mt{serialize} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{serialized} \; \mt{t} \\
adamc@1123 1637 \mt{val} \; \mt{deserialize} : \mt{t} ::: \mt{Type} \to \mt{serialized} \; \mt{t} \to \mt{t} \\
adamc@1123 1638 \mt{val} \; \mt{sql\_serialized} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{serialized} \; \mt{t})
adamc@1123 1639 \end{array}$$
adamc@1123 1640
adamc@544 1641 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 1642 $$\begin{array}{l}
adamc@544 1643 \mt{val} \; \mt{sql\_is\_null} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544 1644 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; (\mt{option} \; \mt{t}) \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{bool}
adamc@544 1645 \end{array}$$
adamc@544 1646
adamc@559 1647 We have generic nullary, unary, and binary operators.
adamc@544 1648 $$\begin{array}{l}
adamc@544 1649 \mt{con} \; \mt{sql\_nfunc} :: \mt{Type} \to \mt{Type} \\
adamc@544 1650 \mt{val} \; \mt{sql\_current\_timestamp} : \mt{sql\_nfunc} \; \mt{time} \\
adamc@544 1651 \mt{val} \; \mt{sql\_nfunc} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544 1652 \hspace{.1in} \to \mt{sql\_nfunc} \; \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\\end{array}$$
adamc@544 1653
adamc@544 1654 $$\begin{array}{l}
adamc@544 1655 \mt{con} \; \mt{sql\_unary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544 1656 \mt{val} \; \mt{sql\_not} : \mt{sql\_unary} \; \mt{bool} \; \mt{bool} \\
adamc@544 1657 \mt{val} \; \mt{sql\_unary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adamc@544 1658 \hspace{.1in} \to \mt{sql\_unary} \; \mt{arg} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res} \\
adamc@544 1659 \end{array}$$
adamc@544 1660
adamc@544 1661 $$\begin{array}{l}
adamc@544 1662 \mt{con} \; \mt{sql\_binary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544 1663 \mt{val} \; \mt{sql\_and} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544 1664 \mt{val} \; \mt{sql\_or} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544 1665 \mt{val} \; \mt{sql\_binary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg_1} ::: \mt{Type} \to \mt{arg_2} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adamc@544 1666 \hspace{.1in} \to \mt{sql\_binary} \; \mt{arg_1} \; \mt{arg_2} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_1} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_2} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res}
adamc@544 1667 \end{array}$$
adamc@544 1668
adamc@544 1669 $$\begin{array}{l}
adamc@559 1670 \mt{class} \; \mt{sql\_arith} \\
adamc@559 1671 \mt{val} \; \mt{sql\_int\_arith} : \mt{sql\_arith} \; \mt{int} \\
adamc@559 1672 \mt{val} \; \mt{sql\_float\_arith} : \mt{sql\_arith} \; \mt{float} \\
adamc@559 1673 \mt{val} \; \mt{sql\_neg} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_unary} \; \mt{t} \; \mt{t} \\
adamc@559 1674 \mt{val} \; \mt{sql\_plus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1675 \mt{val} \; \mt{sql\_minus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1676 \mt{val} \; \mt{sql\_times} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1677 \mt{val} \; \mt{sql\_div} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1678 \mt{val} \; \mt{sql\_mod} : \mt{sql\_binary} \; \mt{int} \; \mt{int} \; \mt{int}
adamc@559 1679 \end{array}$$
adamc@544 1680
adamc@656 1681 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 1682 $$\begin{array}{l}
adamc@544 1683 \mt{val} \; \mt{sql\_count} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int}
adamc@544 1684 \end{array}$$
adamc@544 1685
adamc@544 1686 $$\begin{array}{l}
adamc@1188 1687 \mt{con} \; \mt{sql\_aggregate} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@1188 1688 \mt{val} \; \mt{sql\_aggregate} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{dom} ::: \mt{Type} \to \mt{ran} ::: \mt{Type} \\
adamc@1188 1689 \hspace{.1in} \to \mt{sql\_aggregate} \; \mt{dom} \; \mt{ran} \to \mt{sql\_exp} \; \mt{agg} \; \mt{agg} \; \mt{exps} \; \mt{dom} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{ran}
adamc@1188 1690 \end{array}$$
adamc@1188 1691
adamc@1188 1692 $$\begin{array}{l}
adamc@1188 1693 \mt{val} \; \mt{sql\_count\_col} : \mt{t} ::: \mt{Type} \to \mt{sql\_aggregate} \; (\mt{option} \; \mt{t}) \; \mt{int}
adamc@544 1694 \end{array}$$
adamc@544 1695
adamc@544 1696 $$\begin{array}{l}
adamc@544 1697 \mt{class} \; \mt{sql\_summable} \\
adamc@544 1698 \mt{val} \; \mt{sql\_summable\_int} : \mt{sql\_summable} \; \mt{int} \\
adamc@544 1699 \mt{val} \; \mt{sql\_summable\_float} : \mt{sql\_summable} \; \mt{float} \\
adamc@1188 1700 \mt{val} \; \mt{sql\_avg} : \mt{t} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{t} \\
adamc@1188 1701 \mt{val} \; \mt{sql\_sum} : \mt{t} ::: \mt{Type} \to \mt{sql\_summable} \mt{t} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{t}
adamc@544 1702 \end{array}$$
adamc@544 1703
adamc@544 1704 $$\begin{array}{l}
adamc@544 1705 \mt{class} \; \mt{sql\_maxable} \\
adamc@544 1706 \mt{val} \; \mt{sql\_maxable\_int} : \mt{sql\_maxable} \; \mt{int} \\
adamc@544 1707 \mt{val} \; \mt{sql\_maxable\_float} : \mt{sql\_maxable} \; \mt{float} \\
adamc@544 1708 \mt{val} \; \mt{sql\_maxable\_string} : \mt{sql\_maxable} \; \mt{string} \\
adamc@544 1709 \mt{val} \; \mt{sql\_maxable\_time} : \mt{sql\_maxable} \; \mt{time} \\
adamc@1188 1710 \mt{val} \; \mt{sql\_max} : \mt{t} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{t} \\
adamc@1188 1711 \mt{val} \; \mt{sql\_min} : \mt{t} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{t}
adamc@544 1712 \end{array}$$
adamc@544 1713
adamc@1193 1714 Any SQL query that returns single columns may be turned into a subquery expression.
adamc@1193 1715
adamc@786 1716 $$\begin{array}{l}
adamc@1193 1717 \mt{val} \; \mt{sql\_subquery} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \\
adamc@1193 1718 \hspace{.1in} \to \mt{sql\_query} \; \mt{tables} \; [] \; [\mt{nm} = \mt{t}] \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adamc@1193 1719 \end{array}$$
adamc@1193 1720
adamc@1193 1721 \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 1722 $$\begin{array}{l}
adamc@1193 1723 \mt{con} \; \mt{sql\_from\_items} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@1193 1724 \mt{val} \; \mt{sql\_from\_table} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1725 \hspace{.1in} \to \mt{t} ::: \mt{Type} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; \mt{t} \; \mt{fs} \to \mt{name} :: \mt{Name} \to \mt{t} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193 1726 \mt{val} \; \mt{sql\_from\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{name} :: \mt{Name} \to \mt{sql\_query} \; \mt{free} \; [] \; \mt{fs} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193 1727 \mt{val} \; \mt{sql\_from\_comma} : \mt{free} ::: \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \to [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193 1728 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adamc@1193 1729 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2}) \\
adamc@1193 1730 \mt{val} \; \mt{sql\_inner\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1731 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193 1732 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adamc@1193 1733 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193 1734 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2})
adamc@786 1735 \end{array}$$
adamc@786 1736
adamc@786 1737 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 1738 $$\begin{array}{l}
adamc@786 1739 \mt{class} \; \mt{nullify} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@786 1740 \mt{val} \; \mt{nullify\_option} : \mt{t} ::: \mt{Type} \to \mt{nullify} \; (\mt{option} \; \mt{t}) \; (\mt{option} \; \mt{t}) \\
adamc@786 1741 \mt{val} \; \mt{nullify\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{nullify} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@786 1742 \end{array}$$
adamc@786 1743
adamc@786 1744 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 1745
adamc@786 1746 $$\begin{array}{l}
adamc@1193 1747 \mt{val} \; \mt{sql\_left\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{(\mt{Type} \times \mt{Type})\}\} \\
adamc@1193 1748 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@786 1749 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\lambda \mt{r} \Rightarrow \$(\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{nullify} \; \mt{p}.1 \; \mt{p}.2) \; \mt{r})) \; \mt{tabs2}) \\
adamc@1193 1750 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \\
adamc@1193 1751 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193 1752 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.2)) \; \mt{tabs2})
adamc@786 1753 \end{array}$$
adamc@786 1754
adamc@544 1755 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 1756 $$\begin{array}{l}
adamc@544 1757 \mt{type} \; \mt{sql\_direction} \\
adamc@544 1758 \mt{val} \; \mt{sql\_asc} : \mt{sql\_direction} \\
adamc@544 1759 \mt{val} \; \mt{sql\_desc} : \mt{sql\_direction} \\
adamc@544 1760 \\
adamc@544 1761 \mt{con} \; \mt{sql\_order\_by} :: \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@544 1762 \mt{val} \; \mt{sql\_order\_by\_Nil} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} :: \{\mt{Type}\} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544 1763 \mt{val} \; \mt{sql\_order\_by\_Cons} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544 1764 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; [] \; \mt{exps} \; \mt{t} \to \mt{sql\_direction} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544 1765 \\
adamc@544 1766 \mt{type} \; \mt{sql\_limit} \\
adamc@544 1767 \mt{val} \; \mt{sql\_no\_limit} : \mt{sql\_limit} \\
adamc@544 1768 \mt{val} \; \mt{sql\_limit} : \mt{int} \to \mt{sql\_limit} \\
adamc@544 1769 \\
adamc@544 1770 \mt{type} \; \mt{sql\_offset} \\
adamc@544 1771 \mt{val} \; \mt{sql\_no\_offset} : \mt{sql\_offset} \\
adamc@544 1772 \mt{val} \; \mt{sql\_offset} : \mt{int} \to \mt{sql\_offset}
adamc@544 1773 \end{array}$$
adamc@544 1774
adamc@545 1775
adamc@545 1776 \subsubsection{DML}
adamc@545 1777
adamc@545 1778 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 1779
adamc@545 1780 $$\begin{array}{l}
adamc@545 1781 \mt{type} \; \mt{dml} \\
adamc@545 1782 \mt{val} \; \mt{dml} : \mt{dml} \to \mt{transaction} \; \mt{unit}
adamc@545 1783 \end{array}$$
adamc@545 1784
adam@1297 1785 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 1786
adam@1297 1787 $$\begin{array}{l}
adam@1297 1788 \mt{val} \; \mt{tryDml} : \mt{dml} \to \mt{transaction} \; (\mt{option} \; \mt{string})
adam@1297 1789 \end{array}$$
adam@1297 1790
adamc@545 1791 Properly-typed records may be used to form $\mt{INSERT}$ commands.
adamc@545 1792 $$\begin{array}{l}
adamc@545 1793 \mt{val} \; \mt{insert} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \\
adamc@658 1794 \hspace{.1in} \to \$(\mt{map} \; (\mt{sql\_exp} \; [] \; [] \; []) \; \mt{fields}) \to \mt{dml}
adamc@545 1795 \end{array}$$
adamc@545 1796
adamc@545 1797 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 1798 $$\begin{array}{l}
adamc@545 1799 \mt{val} \; \mt{update} : \mt{unchanged} ::: \{\mt{Type}\} \to \mt{changed} :: \{\mt{Type}\} \to \lambda [\mt{changed} \sim \mt{unchanged}] \\
adamc@658 1800 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; []) \; \mt{changed}) \\
adamc@545 1801 \hspace{.1in} \to \mt{sql\_table} \; (\mt{changed} \rc \mt{unchanged}) \to \mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545 1802 \end{array}$$
adamc@545 1803
adamc@545 1804 A $\mt{DELETE}$ command is formed from a table and a $\mt{WHERE}$ clause.
adamc@545 1805 $$\begin{array}{l}
adamc@545 1806 \mt{val} \; \mt{delete} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \to \mt{sql\_exp} \; [\mt{T} = \mt{fields}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545 1807 \end{array}$$
adamc@545 1808
adamc@546 1809 \subsubsection{Sequences}
adamc@546 1810
adamc@546 1811 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 1812
adamc@546 1813 $$\begin{array}{l}
adamc@546 1814 \mt{type} \; \mt{sql\_sequence} \\
adamc@1085 1815 \mt{val} \; \mt{nextval} : \mt{sql\_sequence} \to \mt{transaction} \; \mt{int} \\
adamc@1085 1816 \mt{val} \; \mt{setval} : \mt{sql\_sequence} \to \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@546 1817 \end{array}$$
adamc@546 1818
adamc@546 1819
adamc@547 1820 \subsection{XML}
adamc@547 1821
adam@1333 1822 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 1823
adamc@547 1824 The basic XML type family has arguments respectively indicating the \emph{context} of a fragment, the fields that the fragment expects to be bound on entry (and their types), and the fields that the fragment will bind (and their types). Contexts are a record-based ``poor man's subtyping'' encoding, with each possible set of valid tags corresponding to a different context record. The arguments dealing with field binding are only relevant to HTML forms.
adamc@547 1825 $$\begin{array}{l}
adamc@547 1826 \mt{con} \; \mt{xml} :: \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547 1827 \end{array}$$
adamc@547 1828
adamc@547 1829 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 1830 $$\begin{array}{l}
adamc@547 1831 \mt{con} \; \mt{tag} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547 1832 \end{array}$$
adamc@547 1833
adamc@547 1834 Literal text may be injected into XML as ``CDATA.''
adamc@547 1835 $$\begin{array}{l}
adamc@547 1836 \mt{val} \; \mt{cdata} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{string} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adamc@547 1837 \end{array}$$
adamc@547 1838
adamc@547 1839 There is a function for producing an XML tree with a particular tag at its root.
adamc@547 1840 $$\begin{array}{l}
adamc@547 1841 \mt{val} \; \mt{tag} : \mt{attrsGiven} ::: \{\mt{Type}\} \to \mt{attrsAbsent} ::: \{\mt{Type}\} \to \mt{ctxOuter} ::: \{\mt{Unit}\} \to \mt{ctxInner} ::: \{\mt{Unit}\} \\
adamc@547 1842 \hspace{.1in} \to \mt{useOuter} ::: \{\mt{Type}\} \to \mt{useInner} ::: \{\mt{Type}\} \to \mt{bindOuter} ::: \{\mt{Type}\} \to \mt{bindInner} ::: \{\mt{Type}\} \\
adamc@787 1843 \hspace{.1in} \to \lambda [\mt{attrsGiven} \sim \mt{attrsAbsent}] \; [\mt{useOuter} \sim \mt{useInner}] \; [\mt{bindOuter} \sim \mt{bindInner}] \\
adamc@787 1844 \hspace{.1in} \Rightarrow \mt{option} \; \mt{css\_class} \\
adamc@787 1845 \hspace{.1in} \to \$\mt{attrsGiven} \\
adamc@547 1846 \hspace{.1in} \to \mt{tag} \; (\mt{attrsGiven} \rc \mt{attrsAbsent}) \; \mt{ctxOuter} \; \mt{ctxInner} \; \mt{useOuter} \; \mt{bindOuter} \\
adamc@547 1847 \hspace{.1in} \to \mt{xml} \; \mt{ctxInner} \; \mt{useInner} \; \mt{bindInner} \to \mt{xml} \; \mt{ctxOuter} \; (\mt{useOuter} \rc \mt{useInner}) \; (\mt{bindOuter} \rc \mt{bindInner})
adamc@547 1848 \end{array}$$
adam@1297 1849 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 1850
adamc@547 1851 Two XML fragments may be concatenated.
adamc@547 1852 $$\begin{array}{l}
adamc@547 1853 \mt{val} \; \mt{join} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{bind_1} ::: \{\mt{Type}\} \to \mt{bind_2} ::: \{\mt{Type}\} \\
adamc@547 1854 \hspace{.1in} \to \lambda [\mt{use_1} \sim \mt{bind_1}] \; [\mt{bind_1} \sim \mt{bind_2}] \\
adamc@547 1855 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind_1} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{bind_1}) \; \mt{bind_2} \to \mt{xml} \; \mt{ctx} \; \mt{use_1} \; (\mt{bind_1} \rc \mt{bind_2})
adamc@547 1856 \end{array}$$
adamc@547 1857
adamc@547 1858 Finally, any XML fragment may be updated to ``claim'' to use more form fields than it does.
adamc@547 1859 $$\begin{array}{l}
adamc@547 1860 \mt{val} \; \mt{useMore} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{use_2} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to \lambda [\mt{use_1} \sim \mt{use_2}] \\
adamc@547 1861 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{use_2}) \; \mt{bind}
adamc@547 1862 \end{array}$$
adamc@547 1863
adamc@547 1864 We will not list here the different HTML tags and related functions from the standard library. They should be easy enough to understand from the code in \texttt{basis.urs}. The set of tags in the library is not yet claimed to be complete for HTML standards.
adamc@547 1865
adamc@547 1866 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 1867 $$\begin{array}{l}
adamc@547 1868 \mt{val} \; \mt{error} : \mt{t} ::: \mt{Type} \to \mt{xml} \; [\mt{Body}] \; [] \; [] \to \mt{t}
adamc@547 1869 \end{array}$$
adamc@547 1870
adamc@549 1871
adamc@701 1872 \subsection{Client-Side Programming}
adamc@659 1873
adamc@701 1874 Ur/Web supports running code on web browsers, via automatic compilation to JavaScript.
adamc@701 1875
adamc@701 1876 \subsubsection{The Basics}
adamc@701 1877
adam@1297 1878 Clients can open alert and confirm dialog boxes, in the usual annoying JavaScript way.
adamc@701 1879 $$\begin{array}{l}
adam@1297 1880 \mt{val} \; \mt{alert} : \mt{string} \to \mt{transaction} \; \mt{unit} \\
adam@1297 1881 \mt{val} \; \mt{confirm} : \mt{string} \to \mt{transaction} \; \mt{bool}
adamc@701 1882 \end{array}$$
adamc@701 1883
adamc@701 1884 Any transaction may be run in a new thread with the $\mt{spawn}$ function.
adamc@701 1885 $$\begin{array}{l}
adamc@701 1886 \mt{val} \; \mt{spawn} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit}
adamc@701 1887 \end{array}$$
adamc@701 1888
adamc@701 1889 The current thread can be paused for at least a specified number of milliseconds.
adamc@701 1890 $$\begin{array}{l}
adamc@701 1891 \mt{val} \; \mt{sleep} : \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@701 1892 \end{array}$$
adamc@701 1893
adamc@787 1894 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 1895 $$\begin{array}{l}
adamc@787 1896 \mt{val} \; \mt{onError} : (\mt{xbody} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787 1897 \mt{val} \; \mt{onFail} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787 1898 \mt{val} \; \mt{onConnectFail} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787 1899 \mt{val} \; \mt{onDisconnect} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787 1900 \mt{val} \; \mt{onServerError} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit}
adamc@787 1901 \end{array}$$
adamc@787 1902
adamc@701 1903 \subsubsection{Functional-Reactive Page Generation}
adamc@701 1904
adamc@701 1905 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 1906
adamc@659 1907 $$\begin{array}{l}
adamc@659 1908 \mt{con} \; \mt{source} :: \mt{Type} \to \mt{Type} \\
adamc@659 1909 \mt{val} \; \mt{source} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{transaction} \; (\mt{source} \; \mt{t}) \\
adamc@659 1910 \mt{val} \; \mt{set} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@659 1911 \mt{val} \; \mt{get} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@659 1912 \end{array}$$
adamc@659 1913
adamc@659 1914 Pure functions over sources are represented in a monad of \emph{signals}.
adamc@659 1915
adamc@659 1916 $$\begin{array}{l}
adamc@659 1917 \mt{con} \; \mt{signal} :: \mt{Type} \to \mt{Type} \\
adamc@659 1918 \mt{val} \; \mt{signal\_monad} : \mt{monad} \; \mt{signal} \\
adamc@659 1919 \mt{val} \; \mt{signal} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{signal} \; \mt{t}
adamc@659 1920 \end{array}$$
adamc@659 1921
adamc@659 1922 A reactive portion of an HTML page is injected with a $\mt{dyn}$ tag, which has a signal-valued attribute $\mt{Signal}$.
adamc@659 1923
adamc@659 1924 $$\begin{array}{l}
adamc@701 1925 \mt{val} \; \mt{dyn} : \mt{use} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to \mt{unit} \\
adamc@701 1926 \hspace{.1in} \to \mt{tag} \; [\mt{Signal} = \mt{signal} \; (\mt{xml} \; \mt{body} \; \mt{use} \; \mt{bind})] \; \mt{body} \; [] \; \mt{use} \; \mt{bind}
adamc@659 1927 \end{array}$$
adamc@659 1928
adamc@701 1929 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 1930
adamc@914 1931 \subsubsection{Remote Procedure Calls}
adamc@914 1932
adamc@914 1933 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 1934
adamc@914 1935 $$\begin{array}{l}
adamc@914 1936 \mt{val} \; \mt{rpc} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@914 1937 \end{array}$$
adamc@914 1938
adamc@701 1939 \subsubsection{Asynchronous Message-Passing}
adamc@701 1940
adamc@701 1941 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 1942
adamc@701 1943 $$\begin{array}{l}
adamc@701 1944 \mt{type} \; \mt{client} \\
adamc@701 1945 \mt{val} \; \mt{self} : \mt{transaction} \; \mt{client}
adamc@701 1946 \end{array}$$
adamc@701 1947
adamc@701 1948 \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 1949
adamc@701 1950 $$\begin{array}{l}
adamc@701 1951 \mt{con} \; \mt{channel} :: \mt{Type} \to \mt{Type} \\
adamc@701 1952 \mt{val} \; \mt{channel} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; (\mt{channel} \; \mt{t}) \\
adamc@701 1953 \mt{val} \; \mt{send} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@701 1954 \mt{val} \; \mt{recv} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@701 1955 \end{array}$$
adamc@701 1956
adamc@701 1957 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 1958
adamc@701 1959 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 1960
adamc@659 1961
adamc@549 1962 \section{Ur/Web Syntax Extensions}
adamc@549 1963
adamc@549 1964 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 1965
adamc@549 1966 \subsection{SQL}
adamc@549 1967
adamc@786 1968 \subsubsection{\label{tables}Table Declarations}
adamc@786 1969
adamc@788 1970 $\mt{table}$ declarations may include constraints, via these grammar rules.
adamc@788 1971 $$\begin{array}{rrcll}
adamc@788 1972 \textrm{Declarations} & d &::=& \mt{table} \; x : c \; [pk[,]] \; cts \\
adamc@788 1973 \textrm{Primary key constraints} & pk &::=& \mt{PRIMARY} \; \mt{KEY} \; K \\
adamc@788 1974 \textrm{Keys} & K &::=& f \mid (f, (f,)^+) \\
adamc@788 1975 \textrm{Constraint sets} & cts &::=& \mt{CONSTRAINT} f \; ct \mid cts, cts \mid \{\{e\}\} \\
adamc@788 1976 \textrm{Constraints} & ct &::=& \mt{UNIQUE} \; K \mid \mt{CHECK} \; E \\
adamc@788 1977 &&& \mid \mt{FOREIGN} \; \mt{KEY} \; K \; \mt{REFERENCES} \; F \; (K) \; [\mt{ON} \; \mt{DELETE} \; pr] \; [\mt{ON} \; \mt{UPDATE} \; pr] \\
adamc@788 1978 \textrm{Foreign tables} & F &::=& x \mid \{\{e\}\} \\
adamc@788 1979 \textrm{Propagation modes} & pr &::=& \mt{NO} \; \mt{ACTION} \mid \mt{RESTRICT} \mid \mt{CASCADE} \mid \mt{SET} \; \mt{NULL}
adamc@788 1980 \end{array}$$
adamc@788 1981
adamc@788 1982 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 1983
adamc@788 1984
adamc@549 1985 \subsubsection{Queries}
adamc@549 1986
adamc@550 1987 Queries $Q$ are added to the rules for expressions $e$.
adamc@550 1988
adamc@549 1989 $$\begin{array}{rrcll}
adamc@550 1990 \textrm{Queries} & Q &::=& (q \; [\mt{ORDER} \; \mt{BY} \; (E \; [o],)^+] \; [\mt{LIMIT} \; N] \; [\mt{OFFSET} \; N]) \\
adamc@1085 1991 \textrm{Pre-queries} & q &::=& \mt{SELECT} \; [\mt{DISTINCT}] \; P \; \mt{FROM} \; F,^+ \; [\mt{WHERE} \; E] \; [\mt{GROUP} \; \mt{BY} \; p,^+] \; [\mt{HAVING} \; E] \\
adamc@1085 1992 &&& \mid q \; R \; q \mid \{\{\{e\}\}\} \\
adamc@549 1993 \textrm{Relational operators} & R &::=& \mt{UNION} \mid \mt{INTERSECT} \mid \mt{EXCEPT}
adamc@549 1994 \end{array}$$
adamc@549 1995
adamc@549 1996 $$\begin{array}{rrcll}
adamc@549 1997 \textrm{Projections} & P &::=& \ast & \textrm{all columns} \\
adamc@549 1998 &&& p,^+ & \textrm{particular columns} \\
adamc@549 1999 \textrm{Pre-projections} & p &::=& t.f & \textrm{one column from a table} \\
adamc@558 2000 &&& t.\{\{c\}\} & \textrm{a record of columns from a table (of kind $\{\mt{Type}\}$)} \\
adamc@1194 2001 &&& E \; [\mt{AS} \; f] & \textrm{expression column} \\
adamc@549 2002 \textrm{Table names} & t &::=& x & \textrm{constant table name (automatically capitalized)} \\
adamc@549 2003 &&& X & \textrm{constant table name} \\
adamc@549 2004 &&& \{\{c\}\} & \textrm{computed table name (of kind $\mt{Name}$)} \\
adamc@549 2005 \textrm{Column names} & f &::=& X & \textrm{constant column name} \\
adamc@549 2006 &&& \{c\} & \textrm{computed column name (of kind $\mt{Name}$)} \\
adamc@549 2007 \textrm{Tables} & T &::=& x & \textrm{table variable, named locally by its own capitalization} \\
adamc@549 2008 &&& x \; \mt{AS} \; t & \textrm{table variable, with local name} \\
adamc@549 2009 &&& \{\{e\}\} \; \mt{AS} \; t & \textrm{computed table expression, with local name} \\
adamc@1085 2010 \textrm{$\mt{FROM}$ items} & F &::=& T \mid \{\{e\}\} \mid F \; J \; \mt{JOIN} \; F \; \mt{ON} \; E \\
adamc@1085 2011 &&& \mid F \; \mt{CROSS} \; \mt{JOIN} \ F \\
adamc@1193 2012 &&& \mid (Q) \; \mt{AS} \; t \\
adamc@1085 2013 \textrm{Joins} & J &::=& [\mt{INNER}] \\
adamc@1085 2014 &&& \mid [\mt{LEFT} \mid \mt{RIGHT} \mid \mt{FULL}] \; [\mt{OUTER}] \\
adamc@549 2015 \textrm{SQL expressions} & E &::=& p & \textrm{column references} \\
adamc@549 2016 &&& X & \textrm{named expression references} \\
adamc@549 2017 &&& \{\{e\}\} & \textrm{injected native Ur expressions} \\
adamc@549 2018 &&& \{e\} & \textrm{computed expressions, probably using $\mt{sql\_exp}$ directly} \\
adamc@549 2019 &&& \mt{TRUE} \mid \mt{FALSE} & \textrm{boolean constants} \\
adamc@549 2020 &&& \ell & \textrm{primitive type literals} \\
adamc@549 2021 &&& \mt{NULL} & \textrm{null value (injection of $\mt{None}$)} \\
adamc@549 2022 &&& E \; \mt{IS} \; \mt{NULL} & \textrm{nullness test} \\
adamc@549 2023 &&& n & \textrm{nullary operators} \\
adamc@549 2024 &&& u \; E & \textrm{unary operators} \\
adamc@549 2025 &&& E \; b \; E & \textrm{binary operators} \\
adamc@549 2026 &&& \mt{COUNT}(\ast) & \textrm{count number of rows} \\
adamc@549 2027 &&& a(E) & \textrm{other aggregate function} \\
adamc@1193 2028 &&& (Q) & \textrm{subquery (must return a single expression column)} \\
adamc@549 2029 &&& (E) & \textrm{explicit precedence} \\
adamc@549 2030 \textrm{Nullary operators} & n &::=& \mt{CURRENT\_TIMESTAMP} \\
adamc@549 2031 \textrm{Unary operators} & u &::=& \mt{NOT} \\
adamc@549 2032 \textrm{Binary operators} & b &::=& \mt{AND} \mid \mt{OR} \mid \neq \mid < \mid \leq \mid > \mid \geq \\
adamc@1188 2033 \textrm{Aggregate functions} & a &::=& \mt{COUNT} \mid \mt{AVG} \mid \mt{SUM} \mid \mt{MIN} \mid \mt{MAX} \\
adamc@550 2034 \textrm{Directions} & o &::=& \mt{ASC} \mid \mt{DESC} \\
adamc@549 2035 \textrm{SQL integer} & N &::=& n \mid \{e\} \\
adamc@549 2036 \end{array}$$
adamc@549 2037
adamc@1085 2038 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 2039
adamc@1194 2040 Unnamed expression columns in $\mt{SELECT}$ clauses are assigned consecutive natural numbers, starting with 1.
adamc@1194 2041
adamc@550 2042 \subsubsection{DML}
adamc@550 2043
adamc@550 2044 DML commands $D$ are added to the rules for expressions $e$.
adamc@550 2045
adamc@550 2046 $$\begin{array}{rrcll}
adamc@550 2047 \textrm{Commands} & D &::=& (\mt{INSERT} \; \mt{INTO} \; T^E \; (f,^+) \; \mt{VALUES} \; (E,^+)) \\
adamc@550 2048 &&& (\mt{UPDATE} \; T^E \; \mt{SET} \; (f = E,)^+ \; \mt{WHERE} \; E) \\
adamc@550 2049 &&& (\mt{DELETE} \; \mt{FROM} \; T^E \; \mt{WHERE} \; E) \\
adamc@550 2050 \textrm{Table expressions} & T^E &::=& x \mid \{\{e\}\}
adamc@550 2051 \end{array}$$
adamc@550 2052
adamc@550 2053 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 2054
adamc@551 2055 \subsection{XML}
adamc@551 2056
adamc@551 2057 XML fragments $L$ are added to the rules for expressions $e$.
adamc@551 2058
adamc@551 2059 $$\begin{array}{rrcll}
adamc@551 2060 \textrm{XML fragments} & L &::=& \texttt{<xml/>} \mid \texttt{<xml>}l^*\texttt{</xml>} \\
adamc@551 2061 \textrm{XML pieces} & l &::=& \textrm{text} & \textrm{cdata} \\
adamc@551 2062 &&& \texttt{<}g\texttt{/>} & \textrm{tag with no children} \\
adamc@551 2063 &&& \texttt{<}g\texttt{>}l^*\texttt{</}x\texttt{>} & \textrm{tag with children} \\
adamc@559 2064 &&& \{e\} & \textrm{computed XML fragment} \\
adamc@559 2065 &&& \{[e]\} & \textrm{injection of an Ur expression, via the $\mt{Top}.\mt{txt}$ function} \\
adamc@551 2066 \textrm{Tag} & g &::=& h \; (x = v)^* \\
adamc@551 2067 \textrm{Tag head} & h &::=& x & \textrm{tag name} \\
adamc@551 2068 &&& h\{c\} & \textrm{constructor parameter} \\
adamc@551 2069 \textrm{Attribute value} & v &::=& \ell & \textrm{literal value} \\
adamc@551 2070 &&& \{e\} & \textrm{computed value} \\
adamc@551 2071 \end{array}$$
adamc@551 2072
adamc@552 2073
adamc@1198 2074 \section{\label{structure}The Structure of Web Applications}
adamc@553 2075
adamc@1127 2076 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 2077
adamc@553 2078 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 2079
adamc@553 2080 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 2081
adamc@558 2082 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 2083
adamc@660 2084 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 2085
adamc@789 2086 \medskip
adamc@789 2087
adamc@789 2088 The HTTP standard suggests that GET requests only be used in ways that generate no side effects. Side effecting operations should use POST requests instead. The Ur/Web compiler enforces this rule strictly, via a simple conservative program analysis. Any page that may have a side effect must be accessed through a form, all of which use POST requests. A page is judged to have a side effect if its code depends syntactically on any of the side-effecting, server-side FFI functions. Links, forms, and most client-side event handlers are not followed during this syntactic traversal, but \texttt{<body onload=\{...\}>} handlers \emph{are} examined, since they run right away and could just as well be considered parts of main page handlers.
adamc@789 2089
adamc@789 2090 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 2091
adamc@553 2092
adamc@897 2093 \section{The Foreign Function Interface}
adamc@897 2094
adamc@897 2095 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 2096
adamc@897 2097 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 2098
adamc@897 2099 \begin{itemize}
adamc@897 2100 \item \texttt{clientOnly Module.ident} registers a value as being allowed only in client-side code.
adamc@897 2101 \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 2102 \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 2103 \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 2104 \item \texttt{include FILE} requests inclusion of a C header file.
adamc@897 2105 \item \texttt{jsFunc Module.ident=name} gives a mapping from an Ur name for a value to a JavaScript name.
adamc@897 2106 \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 2107 \item \texttt{script URL} requests inclusion of a JavaScript source file within application HTML.
adamc@897 2108 \item \texttt{serverOnly Module.ident} registers a value as being allowed only in server-side code.
adamc@897 2109 \end{itemize}
adamc@897 2110
adamc@897 2111 \subsection{Writing C FFI Code}
adamc@897 2112
adamc@897 2113 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 2114
adamc@897 2115 \begin{itemize}
adamc@897 2116 \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 2117 \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 2118 \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 2119 \end{itemize}
adamc@897 2120
adamc@897 2121 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 2122 \begin{itemize}
adamc@897 2123 \item \begin{verbatim}
adamc@897 2124 void uw_error(uw_context, failure_kind, const char *fmt, ...);
adamc@897 2125 \end{verbatim}
adamc@897 2126 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 2127
adam@1329 2128 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 2129
adamc@897 2130 \item \begin{verbatim}
adamc@897 2131 void uw_push_cleanup(uw_context, void (*func)(void *), void *arg);
adamc@897 2132 void uw_pop_cleanup(uw_context);
adamc@897 2133 \end{verbatim}
adam@1329 2134 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 2135
adam@1329 2136 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 2137
adamc@897 2138 \item \begin{verbatim}
adamc@897 2139 void *uw_malloc(uw_context, size_t);
adamc@897 2140 \end{verbatim}
adam@1329 2141 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 2142
adam@1329 2143 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 2144
adamc@897 2145 \item \begin{verbatim}
adamc@897 2146 typedef void (*uw_callback)(void *);
adam@1328 2147 typedef void (*uw_callback_with_retry)(void *, int will_retry);
adamc@897 2148 void uw_register_transactional(uw_context, void *data, uw_callback commit,
adam@1328 2149 uw_callback rollback, uw_callback_with_retry free);
adamc@897 2150 \end{verbatim}
adam@1328 2151 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 2152
adamc@1085 2153 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 2154
adam@1329 2155 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 2156
adam@1329 2157 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 2158
adamc@1085 2159 \item \begin{verbatim}
adamc@1085 2160 void *uw_get_global(uw_context, char *name);
adamc@1085 2161 void uw_set_global(uw_context, char *name, void *data, uw_callback free);
adamc@1085 2162 \end{verbatim}
adam@1329 2163 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 2164
adamc@897 2165 \end{itemize}
adamc@897 2166
adamc@897 2167 \subsection{Writing JavaScript FFI Code}
adamc@897 2168
adamc@897 2169 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 2170
adamc@897 2171 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 2172
adamc@897 2173 \begin{itemize}
adamc@897 2174 \item Integers, floats, strings, characters, and booleans are represented in the usual JavaScript way.
adamc@985 2175 \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 2176 \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 2177 \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 2178 \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 2179 \end{itemize}
adamc@897 2180
adamc@897 2181 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 2182
adamc@897 2183
adamc@552 2184 \section{Compiler Phases}
adamc@552 2185
adamc@552 2186 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 2187
adamc@552 2188 In this section, we step through the main phases of compilation, noting what consequences each phase has for effective programming.
adamc@552 2189
adamc@552 2190 \subsection{Parse}
adamc@552 2191
adamc@552 2192 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 2193
adamc@552 2194 \subsection{Elaborate}
adamc@552 2195
adamc@552 2196 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 2197
adamc@552 2198 \subsection{Unnest}
adamc@552 2199
adamc@552 2200 Named local function definitions are moved to the top level, to avoid the need to generate closures.
adamc@552 2201
adamc@552 2202 \subsection{Corify}
adamc@552 2203
adamc@552 2204 Module system features are compiled away, through inlining of functor definitions at application sites. Afterward, most abstraction boundaries are broken, facilitating optimization.
adamc@552 2205
adamc@552 2206 \subsection{Especialize}
adamc@552 2207
adamc@552 2208 Functions are specialized to particular argument patterns. This is an important trick for avoiding the need to maintain any closures at runtime.
adamc@552 2209
adamc@552 2210 \subsection{Untangle}
adamc@552 2211
adamc@552 2212 Remove unnecessary mutual recursion, splitting recursive groups into strongly-connected components.
adamc@552 2213
adamc@552 2214 \subsection{Shake}
adamc@552 2215
adamc@552 2216 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 2217
adamc@661 2218 \subsection{Rpcify}
adamc@661 2219
adamc@661 2220 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 2221
adamc@661 2222 \subsection{Untangle, Shake}
adamc@661 2223
adamc@661 2224 Repeat these simplifications.
adamc@661 2225
adamc@553 2226 \subsection{\label{tag}Tag}
adamc@552 2227
adamc@552 2228 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 2229
adamc@552 2230 \subsection{Reduce}
adamc@552 2231
adamc@552 2232 Apply definitional equality rules to simplify the program as much as possible. This effectively includes inlining of every non-recursive definition.
adamc@552 2233
adamc@552 2234 \subsection{Unpoly}
adamc@552 2235
adamc@552 2236 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 2237
adamc@552 2238 \subsection{Specialize}
adamc@552 2239
adamc@558 2240 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 2241
adamc@552 2242 \subsection{Shake}
adamc@552 2243
adamc@558 2244 Here the compiler repeats the earlier Shake phase.
adamc@552 2245
adamc@552 2246 \subsection{Monoize}
adamc@552 2247
adamc@552 2248 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 2249
adamc@552 2250 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 2251
adamc@552 2252 \subsection{MonoOpt}
adamc@552 2253
adamc@552 2254 Simple algebraic laws are applied to simplify the program, focusing especially on efficient imperative generation of HTML pages.
adamc@552 2255
adamc@552 2256 \subsection{MonoUntangle}
adamc@552 2257
adamc@552 2258 Unnecessary mutual recursion is broken up again.
adamc@552 2259
adamc@552 2260 \subsection{MonoReduce}
adamc@552 2261
adamc@552 2262 Equivalents of the definitional equality rules are applied to simplify programs, with inlining again playing a major role.
adamc@552 2263
adamc@552 2264 \subsection{MonoShake, MonoOpt}
adamc@552 2265
adamc@552 2266 Unneeded declarations are removed, and basic optimizations are repeated.
adamc@552 2267
adamc@552 2268 \subsection{Fuse}
adamc@552 2269
adamc@552 2270 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 2271
adamc@552 2272 \subsection{MonoUntangle, MonoShake}
adamc@552 2273
adamc@552 2274 Fuse often creates more opportunities to remove spurious mutual recursion.
adamc@552 2275
adamc@552 2276 \subsection{Pathcheck}
adamc@552 2277
adamc@552 2278 The compiler checks that no link or action name has been used more than once.
adamc@552 2279
adamc@552 2280 \subsection{Cjrize}
adamc@552 2281
adamc@552 2282 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 2283
adamc@552 2284 \subsection{C Compilation and Linking}
adamc@552 2285
adamc@552 2286 The output of the last phase is pretty-printed as C source code and passed to GCC.
adamc@552 2287
adamc@552 2288
adamc@524 2289 \end{document}