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author Adam Chlipala <adamc@hcoop.net>
date Sun, 18 Apr 2010 13:00:36 -0400
parents 601a77af0477
children b52929351402
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adamc@524 1 \documentclass{article}
adamc@554 2 \usepackage{fullpage,amsmath,amssymb,proof,url}
adamc@524 3
adamc@524 4 \newcommand{\cd}[1]{\texttt{#1}}
adamc@524 5 \newcommand{\mt}[1]{\mathsf{#1}}
adamc@524 6
adamc@524 7 \newcommand{\rc}{+ \hspace{-.075in} + \;}
adamc@527 8 \newcommand{\rcut}{\; \texttt{--} \;}
adamc@527 9 \newcommand{\rcutM}{\; \texttt{---} \;}
adamc@524 10
adamc@524 11 \begin{document}
adamc@524 12
adamc@524 13 \title{The Ur/Web Manual}
adamc@524 14 \author{Adam Chlipala}
adamc@524 15
adamc@524 16 \maketitle
adamc@524 17
adamc@540 18 \tableofcontents
adamc@540 19
adamc@554 20
adamc@554 21 \section{Introduction}
adamc@554 22
adamc@1160 23 \emph{Ur} is a programming language designed to introduce richer type system features into functional programming in the tradition of ML and Haskell. Ur is functional, pure, statically-typed, and strict. Ur supports a powerful kind of \emph{metaprogramming} based on \emph{type-level computation with type-level records}.
adamc@554 24
adamc@554 25 \emph{Ur/Web} is Ur plus a special standard library and associated rules for parsing and optimization. Ur/Web supports construction of dynamic web applications backed by SQL databases. The signature of the standard library is such that well-typed Ur/Web programs ``don't go wrong'' in a very broad sense. Not only do they not crash during particular page generations, but they also may not:
adamc@554 26
adamc@554 27 \begin{itemize}
adamc@554 28 \item Suffer from any kinds of code-injection attacks
adamc@554 29 \item Return invalid HTML
adamc@554 30 \item Contain dead intra-application links
adamc@554 31 \item Have mismatches between HTML forms and the fields expected by their handlers
adamc@652 32 \item Include client-side code that makes incorrect assumptions about the ``AJAX''-style services that the remote web server provides
adamc@554 33 \item Attempt invalid SQL queries
adamc@652 34 \item Use improper marshaling or unmarshaling in communication with SQL databases or between browsers and web servers
adamc@554 35 \end{itemize}
adamc@554 36
adamc@554 37 This type safety is just the foundation of the Ur/Web methodology. It is also possible to use metaprogramming to build significant application pieces by analysis of type structure. For instance, the demo includes an ML-style functor for building an admin interface for an arbitrary SQL table. The type system guarantees that the admin interface sub-application that comes out will always be free of the above-listed bugs, no matter which well-typed table description is given as input.
adamc@554 38
adamc@652 39 The Ur/Web compiler also produces very efficient object code that does not use garbage collection. These compiled programs will often be even more efficient than what most programmers would bother to write in C. The compiler also generates JavaScript versions of client-side code, with no need to write those parts of applications in a different language.
adamc@554 40
adamc@554 41 \medskip
adamc@554 42
adamc@554 43 The official web site for Ur is:
adamc@554 44 \begin{center}
adamc@554 45 \url{http://www.impredicative.com/ur/}
adamc@554 46 \end{center}
adamc@554 47
adamc@555 48
adamc@555 49 \section{Installation}
adamc@555 50
adamc@555 51 If you are lucky, then the following standard command sequence will suffice for installation, in a directory to which you have unpacked the latest distribution tarball.
adamc@555 52
adamc@555 53 \begin{verbatim}
adamc@555 54 ./configure
adamc@555 55 make
adamc@555 56 sudo make install
adamc@555 57 \end{verbatim}
adamc@555 58
adamc@896 59 Some other packages must be installed for the above to work. At a minimum, you need a standard UNIX shell, with standard UNIX tools like sed and GCC in your execution path; MLton, the whole-program optimizing compiler for Standard ML; and the mhash C library. As of this writing, in the ``testing'' version of Debian Linux, this command will install the more uncommon of these dependencies:
adamc@896 60 \begin{verbatim}
adamc@896 61 apt-get install mlton libmhash-dev
adamc@896 62 \end{verbatim}
adamc@555 63
adamc@896 64 To build programs that access SQL databases, you also need one of these client libraries for supported backends.
adamc@555 65 \begin{verbatim}
adamc@896 66 apt-get install libpq-dev libmysqlclient15-dev libsqlite3-dev
adamc@555 67 \end{verbatim}
adamc@555 68
adamc@555 69 It is also possible to access the modules of the Ur/Web compiler interactively, within Standard ML of New Jersey. To install the prerequisites in Debian testing:
adamc@555 70 \begin{verbatim}
adamc@555 71 apt-get install smlnj libsmlnj-smlnj ml-yacc ml-lpt
adamc@555 72 \end{verbatim}
adamc@555 73
adamc@555 74 To begin an interactive session with the Ur compiler modules, run \texttt{make smlnj}, and then, from within an \texttt{sml} session, run \texttt{CM.make "src/urweb.cm";}. The \texttt{Compiler} module is the main entry point.
adamc@555 75
adamc@896 76 To run an SQL-backed application with a backend besides SQLite, you will probably want to install one of these servers.
adamc@555 77
adamc@555 78 \begin{verbatim}
adamc@896 79 apt-get install postgresql-8.3 mysql-server-5.0
adamc@555 80 \end{verbatim}
adamc@555 81
adamc@555 82 To use the Emacs mode, you must have a modern Emacs installed. We assume that you already know how to do this, if you're in the business of looking for an Emacs mode. The demo generation facility of the compiler will also call out to Emacs to syntax-highlight code, and that process depends on the \texttt{htmlize} module, which can be installed in Debian testing via:
adamc@555 83
adamc@555 84 \begin{verbatim}
adamc@555 85 apt-get install emacs-goodies-el
adamc@555 86 \end{verbatim}
adamc@555 87
adamc@555 88 Even with the right packages installed, configuration and building might fail to work. After you run \texttt{./configure}, you will see the values of some named environment variables printed. You may need to adjust these values to get proper installation for your system. To change a value, store your preferred alternative in the corresponding UNIX environment variable, before running \texttt{./configure}. For instance, here is how to change the list of extra arguments that the Ur/Web compiler will pass to GCC on every invocation.
adamc@555 89
adamc@555 90 \begin{verbatim}
adamc@555 91 GCCARGS=-fnested-functions ./configure
adamc@555 92 \end{verbatim}
adamc@555 93
adamc@1137 94 Some Mac OS X users have reported needing to use this particular GCCARGS value.
adamc@1137 95
adamc@1161 96 Since the author is still getting a handle on the GNU Autotools that provide the build system, you may need to do some further work to get started, especially in environments with significant differences from Linux (where most testing is done). One OS X user reported needing to run \texttt{./configure} with \texttt{CFLAGS=-I/opt/local/include}, since this directory wound up holding a header file associated with a \texttt{libmhash} package installed via DarwinPorts. Further, to get libpq to link, another user reported setting \texttt{GCCARGS="-I/opt/local/include -L/opt/local/lib/postgresql84"}, after creating a symbolic link with \texttt{ln -s /opt/local/include/postgresql84 /opt/local/include/postgresql}.
adamc@555 97
adamc@555 98 The Emacs mode can be set to autoload by adding the following to your \texttt{.emacs} file.
adamc@555 99
adamc@555 100 \begin{verbatim}
adamc@555 101 (add-to-list 'load-path "/usr/local/share/emacs/site-lisp/urweb-mode")
adamc@555 102 (load "urweb-mode-startup")
adamc@555 103 \end{verbatim}
adamc@555 104
adamc@555 105 Change the path in the first line if you chose a different Emacs installation path during configuration.
adamc@555 106
adamc@555 107
adamc@556 108 \section{Command-Line Compiler}
adamc@556 109
adamc@556 110 \subsection{Project Files}
adamc@556 111
adamc@556 112 The basic inputs to the \texttt{urweb} compiler are project files, which have the extension \texttt{.urp}. Here is a sample \texttt{.urp} file.
adamc@556 113
adamc@556 114 \begin{verbatim}
adamc@556 115 database dbname=test
adamc@556 116 sql crud1.sql
adamc@556 117
adamc@556 118 crud
adamc@556 119 crud1
adamc@556 120 \end{verbatim}
adamc@556 121
adamc@556 122 The \texttt{database} line gives the database information string to pass to libpq. In this case, the string only says to connect to a local database named \texttt{test}.
adamc@556 123
adamc@556 124 The \texttt{sql} line asks for an SQL source file to be generated, giving the commands to run to create the tables and sequences that this application expects to find. After building this \texttt{.urp} file, the following commands could be used to initialize the database, assuming that the current UNIX user exists as a Postgres user with database creation privileges:
adamc@556 125
adamc@556 126 \begin{verbatim}
adamc@556 127 createdb test
adamc@556 128 psql -f crud1.sql test
adamc@556 129 \end{verbatim}
adamc@556 130
adamc@1151 131 A blank line separates the named directives from a list of modules to include in the project.
adamc@556 132
adamc@556 133 For each entry \texttt{M} in the module list, the file \texttt{M.urs} is included in the project if it exists, and the file \texttt{M.ur} must exist and is always included.
adamc@556 134
adamc@783 135 Here is the complete list of directive forms. ``FFI'' stands for ``foreign function interface,'' Ur's facility for interaction between Ur programs and C and JavaScript libraries.
adamc@783 136 \begin{itemize}
adamc@783 137 \item \texttt{[allow|deny] [url|mime] PATTERN} registers a rule governing which URLs or MIME types are allowed in this application. The first such rule to match a URL or MIME type determines the verdict. If \texttt{PATTERN} ends in \texttt{*}, it is interpreted as a prefix rule. Otherwise, a string must match it exactly.
adamc@1171 138 \item \texttt{benignEffectful Module.ident} registers an FFI function or transaction as having side effects. The optimizer avoids removing, moving, or duplicating calls to such functions. Every effectful FFI function must be registered, or the optimizer may make invalid transformations. This version of the \texttt{effectful} directive registers that this function has only session-local side effects.
adamc@783 139 \item \texttt{clientOnly Module.ident} registers an FFI function or transaction that may only be run in client browsers.
adamc@783 140 \item \texttt{clientToServer Module.ident} adds FFI type \texttt{Module.ident} to the list of types that are OK to marshal from clients to servers. Values like XML trees and SQL queries are hard to marshal without introducing expensive validity checks, so it's easier to ensure that the server never trusts clients to send such values. The file \texttt{include/urweb.h} shows examples of the C support functions that are required of any type that may be marshalled. These include \texttt{attrify}, \texttt{urlify}, and \texttt{unurlify} functions.
adamc@783 141 \item \texttt{database DBSTRING} sets the string to pass to libpq to open a database connection.
adamc@783 142 \item \texttt{debug} saves some intermediate C files, which is mostly useful to help in debugging the compiler itself.
adamc@783 143 \item \texttt{effectful Module.ident} registers an FFI function or transaction as having side effects. The optimizer avoids removing, moving, or duplicating calls to such functions. Every effectful FFI function must be registered, or the optimizer may make invalid transformations.
adamc@783 144 \item \texttt{exe FILENAME} sets the filename to which to write the output executable. The default for file \texttt{P.urp} is \texttt{P.exe}.
adamc@783 145 \item \texttt{ffi FILENAME} reads the file \texttt{FILENAME.urs} to determine the interface to a new FFI module. The name of the module is calculated from \texttt{FILENAME} in the same way as for normal source files. See the files \texttt{include/urweb.h} and \texttt{src/c/urweb.c} for examples of C headers and implementations for FFI modules. In general, every type or value \texttt{Module.ident} becomes \texttt{uw\_Module\_ident} in C.
adamc@1099 146 \item \texttt{include FILENAME} adds \texttt{FILENAME} to the list of files to be \texttt{\#include}d in C sources. This is most useful for interfacing with new FFI modules.
adamc@783 147 \item \texttt{jsFunc Module.ident=name} gives the JavaScript name of an FFI value.
adamc@1089 148 \item \texttt{library FILENAME} parses \texttt{FILENAME.urp} and merges its contents with the rest of the current file's contents. If \texttt{FILENAME.urp} doesn't exist, the compiler also tries \texttt{FILENAME/lib.urp}.
adamc@783 149 \item \texttt{link FILENAME} adds \texttt{FILENAME} to the list of files to be passed to the GCC linker at the end of compilation. This is most useful for importing extra libraries needed by new FFI modules.
adamc@852 150 \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@783 151 \item \texttt{prefix PREFIX} sets the prefix included before every URI within the generated application. The default is \texttt{/}.
adamc@783 152 \item \texttt{profile} generates an executable that may be used with gprof.
adamc@783 153 \item \texttt{rewrite KIND FROM TO} gives a rule for rewriting canonical module paths. For instance, the canonical path of a page may be \texttt{Mod1.Mod2.mypage}, while you would rather the page were accessed via a URL containing only \texttt{page}. The directive \texttt{rewrite url Mod1/Mod2/mypage page} would accomplish that. The possible values of \texttt{KIND} determine which kinds of objects are affected. The kind \texttt{all} matches any object, and \texttt{url} matches page URLs. The kinds \texttt{table}, \texttt{sequence}, and \texttt{view} match those sorts of SQL entities, and \texttt{relation} matches any of those three. \texttt{cookie} matches HTTP cookies, and \texttt{style} matches CSS class names. If \texttt{FROM} ends in \texttt{/*}, it is interpreted as a prefix matching rule, and rewriting occurs by replacing only the appropriate prefix of a path with \texttt{TO}. While the actual external names of relations and styles have parts separated by underscores instead of slashes, all rewrite rules must be written in terms of slashes.
adamc@1183 154 \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@783 155 \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@783 156 \item \texttt{serverOnly Module.ident} registers an FFI function or transaction that may only be run on the server.
adamc@1164 157 \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@783 158 \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@783 159 \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@783 160 \end{itemize}
adamc@701 161
adamc@701 162
adamc@557 163 \subsection{Building an Application}
adamc@557 164
adamc@557 165 To compile project \texttt{P.urp}, simply run
adamc@557 166 \begin{verbatim}
adamc@557 167 urweb P
adamc@557 168 \end{verbatim}
adamc@558 169 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.
adamc@557 170
adamc@557 171 To time how long the different compiler phases run, without generating an executable, run
adamc@557 172 \begin{verbatim}
adamc@557 173 urweb -timing P
adamc@557 174 \end{verbatim}
adamc@557 175
adamc@1086 176 To stop the compilation process after type-checking, run
adamc@1086 177 \begin{verbatim}
adamc@1086 178 urweb -tc P
adamc@1086 179 \end{verbatim}
adamc@1086 180
adamc@1170 181 To output information relevant to CSS stylesheets (and not finish regular compilation), run
adamc@1170 182 \begin{verbatim}
adamc@1170 183 urweb -css P
adamc@1170 184 \end{verbatim}
adamc@1170 185 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 186
adamc@896 187 Some other command-line parameters are accepted:
adamc@896 188 \begin{itemize}
adamc@896 189 \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@896 190
adamc@896 191 \item \texttt{-dbms [postgres|mysql|sqlite]}: Sets the database backend to use.
adamc@896 192 \begin{itemize}
adamc@896 193 \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@896 194
adamc@896 195 A command sequence like this can initialize a Postgres database, using a file \texttt{app.sql} generated by the compiler:
adamc@896 196 \begin{verbatim}
adamc@896 197 createdb app
adamc@896 198 psql -f app.sql app
adamc@896 199 \end{verbatim}
adamc@896 200
adamc@896 201 \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@896 202
adamc@896 203 A command sequence like this can initialize a MySQL database:
adamc@896 204 \begin{verbatim}
adamc@896 205 echo "CREATE DATABASE app" | mysql
adamc@896 206 mysql -D app <app.sql
adamc@896 207 \end{verbatim}
adamc@896 208
adamc@896 209 \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@896 210
adamc@896 211 A command like this can initialize an SQLite database:
adamc@896 212 \begin{verbatim}
adamc@896 213 sqlite3 path/to/database/file <app.sql
adamc@896 214 \end{verbatim}
adamc@896 215 \end{itemize}
adamc@896 216
adamc@896 217 \item \texttt{-output FILENAME}: Set where the application executable is written.
adamc@896 218
adamc@1127 219 \item \texttt{-path NAME VALUE}: Set the value of path variable \texttt{\$NAME} to \texttt{VALUE}, for use in \texttt{.urp} files.
adamc@1127 220
adamc@896 221 \item \texttt{-protocol [http|cgi|fastcgi]}: Set the protocol that the generated application speaks.
adamc@896 222 \begin{itemize}
adamc@896 223 \item \texttt{http}: This is the default. It is for building standalone web servers that can be accessed by web browsers directly.
adamc@896 224
adamc@896 225 \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@896 226
adamc@896 227 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@896 228 \begin{verbatim}
adamc@896 229 ScriptAlias /Hello /path/to/hello.exe
adamc@896 230 \end{verbatim}
adamc@896 231
adamc@1163 232 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 233 \begin{verbatim}
adamc@1163 234 Options +ExecCGI
adamc@1163 235 AddHandler cgi-script .exe
adamc@1163 236 \end{verbatim}
adamc@1163 237
adamc@1163 238 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 239 \begin{verbatim}
adamc@1163 240 prefix /dir/script.exe/
adamc@1163 241 \end{verbatim}
adamc@1163 242
adamc@1163 243 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 244
adamc@1164 245 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 246
adamc@896 247 \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@896 248
adamc@896 249 To configure a FastCGI program with Apache, one could combine the above \texttt{ScriptAlias} line with a line like this:
adamc@896 250 \begin{verbatim}
adamc@896 251 FastCgiServer /path/to/hello.exe -idle-timeout 99999
adamc@896 252 \end{verbatim}
adamc@896 253 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@896 254
adamc@896 255 Here is some lighttpd configuration for the same application.
adamc@896 256 \begin{verbatim}
adamc@896 257 fastcgi.server = (
adamc@896 258 "/Hello/" =>
adamc@896 259 (( "bin-path" => "/path/to/hello.exe",
adamc@896 260 "socket" => "/tmp/hello",
adamc@896 261 "check-local" => "disable",
adamc@896 262 "docroot" => "/",
adamc@896 263 "max-procs" => "1"
adamc@896 264 ))
adamc@896 265 )
adamc@896 266 \end{verbatim}
adamc@896 267 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@896 268
adamc@896 269 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@896 270 \end{itemize}
adamc@896 271
adamc@1127 272 \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 273
adamc@1164 274 \item \texttt{-sigfile PATH}: Same as the \texttt{sigfile} directive in \texttt{.urp} files
adamc@1164 275
adamc@896 276 \item \texttt{-sql FILENAME}: Set where a database set-up SQL script is written.
adamc@1095 277
adamc@1095 278 \item \texttt{-static}: Link the runtime system statically. The default is to link against dynamic libraries.
adamc@896 279 \end{itemize}
adamc@896 280
adamc@556 281
adamc@529 282 \section{Ur Syntax}
adamc@529 283
adamc@784 284 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@524 285
adamc@524 286 \subsection{Lexical Conventions}
adamc@524 287
adamc@524 288 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@524 289
adamc@524 290 \begin{center}
adamc@524 291 \begin{tabular}{rl}
adamc@524 292 \textbf{\LaTeX} & \textbf{ASCII} \\
adamc@524 293 $\to$ & \cd{->} \\
adamc@652 294 $\longrightarrow$ & \cd{-->} \\
adamc@524 295 $\times$ & \cd{*} \\
adamc@524 296 $\lambda$ & \cd{fn} \\
adamc@524 297 $\Rightarrow$ & \cd{=>} \\
adamc@652 298 $\Longrightarrow$ & \cd{==>} \\
adamc@529 299 $\neq$ & \cd{<>} \\
adamc@529 300 $\leq$ & \cd{<=} \\
adamc@529 301 $\geq$ & \cd{>=} \\
adamc@524 302 \\
adamc@524 303 $x$ & Normal textual identifier, not beginning with an uppercase letter \\
adamc@525 304 $X$ & Normal textual identifier, beginning with an uppercase letter \\
adamc@524 305 \end{tabular}
adamc@524 306 \end{center}
adamc@524 307
adamc@525 308 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@524 309
adamc@873 310 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@526 311
adamc@527 312 This version of the manual doesn't include operator precedences; see \texttt{src/urweb.grm} for that.
adamc@527 313
adamc@552 314 \subsection{\label{core}Core Syntax}
adamc@524 315
adamc@524 316 \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@524 317 $$\begin{array}{rrcll}
adamc@524 318 \textrm{Kinds} & \kappa &::=& \mt{Type} & \textrm{proper types} \\
adamc@525 319 &&& \mt{Unit} & \textrm{the trivial constructor} \\
adamc@525 320 &&& \mt{Name} & \textrm{field names} \\
adamc@525 321 &&& \kappa \to \kappa & \textrm{type-level functions} \\
adamc@525 322 &&& \{\kappa\} & \textrm{type-level records} \\
adamc@525 323 &&& (\kappa\times^+) & \textrm{type-level tuples} \\
adamc@652 324 &&& X & \textrm{variable} \\
adamc@652 325 &&& X \longrightarrow k & \textrm{kind-polymorphic type-level function} \\
adamc@529 326 &&& \_\_ & \textrm{wildcard} \\
adamc@525 327 &&& (\kappa) & \textrm{explicit precedence} \\
adamc@524 328 \end{array}$$
adamc@524 329
adamc@524 330 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@524 331 $$\begin{array}{rrcll}
adamc@524 332 \textrm{Explicitness} & ? &::=& :: & \textrm{explicit} \\
adamc@558 333 &&& ::: & \textrm{implicit}
adamc@524 334 \end{array}$$
adamc@524 335
adamc@524 336 \emph{Constructors} are the main class of compile-time-only data. They include proper types and are classified by kinds.
adamc@524 337 $$\begin{array}{rrcll}
adamc@524 338 \textrm{Constructors} & c, \tau &::=& (c) :: \kappa & \textrm{kind annotation} \\
adamc@530 339 &&& \hat{x} & \textrm{constructor variable} \\
adamc@524 340 \\
adamc@525 341 &&& \tau \to \tau & \textrm{function type} \\
adamc@525 342 &&& x \; ? \; \kappa \to \tau & \textrm{polymorphic function type} \\
adamc@652 343 &&& X \longrightarrow \tau & \textrm{kind-polymorphic function type} \\
adamc@525 344 &&& \$ c & \textrm{record type} \\
adamc@524 345 \\
adamc@525 346 &&& c \; c & \textrm{type-level function application} \\
adamc@530 347 &&& \lambda x \; :: \; \kappa \Rightarrow c & \textrm{type-level function abstraction} \\
adamc@524 348 \\
adamc@652 349 &&& X \Longrightarrow c & \textrm{type-level kind-polymorphic function abstraction} \\
adamc@655 350 &&& c [\kappa] & \textrm{type-level kind-polymorphic function application} \\
adamc@652 351 \\
adamc@525 352 &&& () & \textrm{type-level unit} \\
adamc@525 353 &&& \#X & \textrm{field name} \\
adamc@524 354 \\
adamc@525 355 &&& [(c = c)^*] & \textrm{known-length type-level record} \\
adamc@525 356 &&& c \rc c & \textrm{type-level record concatenation} \\
adamc@652 357 &&& \mt{map} & \textrm{type-level record map} \\
adamc@524 358 \\
adamc@558 359 &&& (c,^+) & \textrm{type-level tuple} \\
adamc@525 360 &&& c.n & \textrm{type-level tuple projection ($n \in \mathbb N^+$)} \\
adamc@524 361 \\
adamc@652 362 &&& [c \sim c] \Rightarrow \tau & \textrm{guarded type} \\
adamc@524 363 \\
adamc@529 364 &&& \_ :: \kappa & \textrm{wildcard} \\
adamc@525 365 &&& (c) & \textrm{explicit precedence} \\
adamc@530 366 \\
adamc@530 367 \textrm{Qualified uncapitalized variables} & \hat{x} &::=& x & \textrm{not from a module} \\
adamc@530 368 &&& M.x & \textrm{projection from a module} \\
adamc@525 369 \end{array}$$
adamc@525 370
adamc@655 371 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@655 372
adamc@525 373 Modules of the module system are described by \emph{signatures}.
adamc@525 374 $$\begin{array}{rrcll}
adamc@525 375 \textrm{Signatures} & S &::=& \mt{sig} \; s^* \; \mt{end} & \textrm{constant} \\
adamc@525 376 &&& X & \textrm{variable} \\
adamc@525 377 &&& \mt{functor}(X : S) : S & \textrm{functor} \\
adamc@529 378 &&& S \; \mt{where} \; \mt{con} \; x = c & \textrm{concretizing an abstract constructor} \\
adamc@525 379 &&& M.X & \textrm{projection from a module} \\
adamc@525 380 \\
adamc@525 381 \textrm{Signature items} & s &::=& \mt{con} \; x :: \kappa & \textrm{abstract constructor} \\
adamc@525 382 &&& \mt{con} \; x :: \kappa = c & \textrm{concrete constructor} \\
adamc@528 383 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529 384 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@525 385 &&& \mt{val} \; x : \tau & \textrm{value} \\
adamc@525 386 &&& \mt{structure} \; X : S & \textrm{sub-module} \\
adamc@525 387 &&& \mt{signature} \; X = S & \textrm{sub-signature} \\
adamc@525 388 &&& \mt{include} \; S & \textrm{signature inclusion} \\
adamc@525 389 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@654 390 &&& \mt{class} \; x :: \kappa & \textrm{abstract constructor class} \\
adamc@654 391 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@525 392 \\
adamc@525 393 \textrm{Datatype constructors} & dc &::=& X & \textrm{nullary constructor} \\
adamc@525 394 &&& X \; \mt{of} \; \tau & \textrm{unary constructor} \\
adamc@524 395 \end{array}$$
adamc@524 396
adamc@526 397 \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@526 398 $$\begin{array}{rrcll}
adamc@526 399 \textrm{Patterns} & p &::=& \_ & \textrm{wildcard} \\
adamc@526 400 &&& x & \textrm{variable} \\
adamc@526 401 &&& \ell & \textrm{constant} \\
adamc@526 402 &&& \hat{X} & \textrm{nullary constructor} \\
adamc@526 403 &&& \hat{X} \; p & \textrm{unary constructor} \\
adamc@526 404 &&& \{(x = p,)^*\} & \textrm{rigid record pattern} \\
adamc@526 405 &&& \{(x = p,)^+, \ldots\} & \textrm{flexible record pattern} \\
adamc@852 406 &&& p : \tau & \textrm{type annotation} \\
adamc@527 407 &&& (p) & \textrm{explicit precedence} \\
adamc@526 408 \\
adamc@529 409 \textrm{Qualified capitalized variables} & \hat{X} &::=& X & \textrm{not from a module} \\
adamc@526 410 &&& M.X & \textrm{projection from a module} \\
adamc@526 411 \end{array}$$
adamc@526 412
adamc@527 413 \emph{Expressions} are the main run-time entities, corresponding to both ``expressions'' and ``statements'' in mainstream imperative languages.
adamc@527 414 $$\begin{array}{rrcll}
adamc@527 415 \textrm{Expressions} & e &::=& e : \tau & \textrm{type annotation} \\
adamc@529 416 &&& \hat{x} & \textrm{variable} \\
adamc@529 417 &&& \hat{X} & \textrm{datatype constructor} \\
adamc@527 418 &&& \ell & \textrm{constant} \\
adamc@527 419 \\
adamc@527 420 &&& e \; e & \textrm{function application} \\
adamc@527 421 &&& \lambda x : \tau \Rightarrow e & \textrm{function abstraction} \\
adamc@527 422 &&& e [c] & \textrm{polymorphic function application} \\
adamc@852 423 &&& \lambda [x \; ? \; \kappa] \Rightarrow e & \textrm{polymorphic function abstraction} \\
adamc@655 424 &&& e [\kappa] & \textrm{kind-polymorphic function application} \\
adamc@652 425 &&& X \Longrightarrow e & \textrm{kind-polymorphic function abstraction} \\
adamc@527 426 \\
adamc@527 427 &&& \{(c = e,)^*\} & \textrm{known-length record} \\
adamc@527 428 &&& e.c & \textrm{record field projection} \\
adamc@527 429 &&& e \rc e & \textrm{record concatenation} \\
adamc@527 430 &&& e \rcut c & \textrm{removal of a single record field} \\
adamc@527 431 &&& e \rcutM c & \textrm{removal of multiple record fields} \\
adamc@527 432 \\
adamc@527 433 &&& \mt{let} \; ed^* \; \mt{in} \; e \; \mt{end} & \textrm{local definitions} \\
adamc@527 434 \\
adamc@527 435 &&& \mt{case} \; e \; \mt{of} \; (p \Rightarrow e|)^+ & \textrm{pattern matching} \\
adamc@527 436 \\
adamc@654 437 &&& \lambda [c \sim c] \Rightarrow e & \textrm{guarded expression abstraction} \\
adamc@654 438 &&& e \; ! & \textrm{guarded expression application} \\
adamc@527 439 \\
adamc@527 440 &&& \_ & \textrm{wildcard} \\
adamc@527 441 &&& (e) & \textrm{explicit precedence} \\
adamc@527 442 \\
adamc@527 443 \textrm{Local declarations} & ed &::=& \cd{val} \; x : \tau = e & \textrm{non-recursive value} \\
adamc@527 444 &&& \cd{val} \; \cd{rec} \; (x : \tau = e \; \cd{and})^+ & \textrm{mutually-recursive values} \\
adamc@527 445 \end{array}$$
adamc@527 446
adamc@655 447 As with constructors, we include both abstraction and application for kind polymorphism, but applications are only inferred internally.
adamc@655 448
adamc@528 449 \emph{Declarations} primarily bring new symbols into context.
adamc@528 450 $$\begin{array}{rrcll}
adamc@528 451 \textrm{Declarations} & d &::=& \mt{con} \; x :: \kappa = c & \textrm{constructor synonym} \\
adamc@528 452 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529 453 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@528 454 &&& \mt{val} \; x : \tau = e & \textrm{value} \\
adamc@528 455 &&& \mt{val} \; \cd{rec} \; (x : \tau = e \; \mt{and})^+ & \textrm{mutually-recursive values} \\
adamc@528 456 &&& \mt{structure} \; X : S = M & \textrm{module definition} \\
adamc@528 457 &&& \mt{signature} \; X = S & \textrm{signature definition} \\
adamc@528 458 &&& \mt{open} \; M & \textrm{module inclusion} \\
adamc@528 459 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@528 460 &&& \mt{open} \; \mt{constraints} \; M & \textrm{inclusion of just the constraints from a module} \\
adamc@528 461 &&& \mt{table} \; x : c & \textrm{SQL table} \\
adamc@784 462 &&& \mt{view} \; x : c & \textrm{SQL view} \\
adamc@528 463 &&& \mt{sequence} \; x & \textrm{SQL sequence} \\
adamc@535 464 &&& \mt{cookie} \; x : \tau & \textrm{HTTP cookie} \\
adamc@784 465 &&& \mt{style} \; x : \tau & \textrm{CSS class} \\
adamc@654 466 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@1085 467 &&& \mt{task} \; e = e & \textrm{recurring task} \\
adamc@528 468 \\
adamc@529 469 \textrm{Modules} & M &::=& \mt{struct} \; d^* \; \mt{end} & \textrm{constant} \\
adamc@529 470 &&& X & \textrm{variable} \\
adamc@529 471 &&& M.X & \textrm{projection} \\
adamc@529 472 &&& M(M) & \textrm{functor application} \\
adamc@529 473 &&& \mt{functor}(X : S) : S = M & \textrm{functor abstraction} \\
adamc@528 474 \end{array}$$
adamc@528 475
adamc@528 476 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@527 477
adamc@784 478 We omit some extra possibilities in $\mt{table}$ syntax, deferring them to Section \ref{tables}.
adamc@784 479
adamc@529 480 \subsection{Shorthands}
adamc@529 481
adamc@529 482 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@529 483
adamc@529 484 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@529 485
adamc@529 486 A record type may be written $\{(c = c,)^*\}$, which elaborates to $\$[(c = c,)^*]$.
adamc@529 487
adamc@533 488 The notation $[c_1, \ldots, c_n]$ is shorthand for $[c_1 = (), \ldots, c_n = ()]$.
adamc@533 489
adamc@529 490 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@529 491
adamc@852 492 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@529 493
adamc@529 494 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@529 495
adamc@529 496 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@529 497
adamc@654 498 A signature item or declaration $\mt{class} \; x = \lambda y \Rightarrow c$ may be abbreviated $\mt{class} \; x \; y = c$.
adamc@529 499
adamc@1102 500 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@529 501
adamc@852 502 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@529 503
adamc@852 504 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@852 505
adamc@852 506 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@529 507
adamc@529 508 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@529 509
adamc@852 510 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@852 511
adamc@853 512 A declaration $\mt{table} \; x : \{(c = c,)^*\}$ is elaborated into $\mt{table} \; x : [(c = c,)^*]$.
adamc@529 513
adamc@529 514 The syntax $\mt{where} \; \mt{type}$ is an alternate form of $\mt{where} \; \mt{con}$.
adamc@529 515
adamc@529 516 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@529 517
adamc@529 518 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@529 519
adamc@784 520 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@529 521
adamc@530 522
adamc@530 523 \section{Static Semantics}
adamc@530 524
adamc@530 525 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@530 526
adamc@530 527 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@530 528 \begin{itemize}
adamc@655 529 \item $\Gamma \vdash \kappa$ expresses kind well-formedness.
adamc@530 530 \item $\Gamma \vdash c :: \kappa$ assigns a kind to a constructor in a context.
adamc@530 531 \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@531 532 \item $\Gamma \vdash c \hookrightarrow C$ proves that record constructor $c$ decomposes into set $C$ of field names and record constructors.
adamc@530 533 \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@530 534 \item $\Gamma \vdash e : \tau$ is a standard typing judgment.
adamc@534 535 \item $\Gamma \vdash p \leadsto \Gamma; \tau$ combines typing of patterns with calculation of which new variables they bind.
adamc@537 536 \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@537 537 \item $\Gamma \vdash S \equiv S$ is the signature equivalence judgment.
adamc@536 538 \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@530 539 \item $\Gamma \vdash M : S$ is the module signature checking judgment.
adamc@537 540 \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@539 541 \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@530 542 \end{itemize}
adamc@530 543
adamc@655 544
adamc@655 545 \subsection{Kind Well-Formedness}
adamc@655 546
adamc@655 547 $$\infer{\Gamma \vdash \mt{Type}}{}
adamc@655 548 \quad \infer{\Gamma \vdash \mt{Unit}}{}
adamc@655 549 \quad \infer{\Gamma \vdash \mt{Name}}{}
adamc@655 550 \quad \infer{\Gamma \vdash \kappa_1 \to \kappa_2}{
adamc@655 551 \Gamma \vdash \kappa_1
adamc@655 552 & \Gamma \vdash \kappa_2
adamc@655 553 }
adamc@655 554 \quad \infer{\Gamma \vdash \{\kappa\}}{
adamc@655 555 \Gamma \vdash \kappa
adamc@655 556 }
adamc@655 557 \quad \infer{\Gamma \vdash (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@655 558 \forall i: \Gamma \vdash \kappa_i
adamc@655 559 }$$
adamc@655 560
adamc@655 561 $$\infer{\Gamma \vdash X}{
adamc@655 562 X \in \Gamma
adamc@655 563 }
adamc@655 564 \quad \infer{\Gamma \vdash X \longrightarrow \kappa}{
adamc@655 565 \Gamma, X \vdash \kappa
adamc@655 566 }$$
adamc@655 567
adamc@530 568 \subsection{Kinding}
adamc@530 569
adamc@655 570 We write $[X \mapsto \kappa_1]\kappa_2$ for capture-avoiding substitution of $\kappa_1$ for $X$ in $\kappa_2$.
adamc@655 571
adamc@530 572 $$\infer{\Gamma \vdash (c) :: \kappa :: \kappa}{
adamc@530 573 \Gamma \vdash c :: \kappa
adamc@530 574 }
adamc@530 575 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530 576 x :: \kappa \in \Gamma
adamc@530 577 }
adamc@530 578 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530 579 x :: \kappa = c \in \Gamma
adamc@530 580 }$$
adamc@530 581
adamc@530 582 $$\infer{\Gamma \vdash M.x :: \kappa}{
adamc@537 583 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 584 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = \kappa
adamc@530 585 }
adamc@530 586 \quad \infer{\Gamma \vdash M.x :: \kappa}{
adamc@537 587 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 588 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@530 589 }$$
adamc@530 590
adamc@530 591 $$\infer{\Gamma \vdash \tau_1 \to \tau_2 :: \mt{Type}}{
adamc@530 592 \Gamma \vdash \tau_1 :: \mt{Type}
adamc@530 593 & \Gamma \vdash \tau_2 :: \mt{Type}
adamc@530 594 }
adamc@530 595 \quad \infer{\Gamma \vdash x \; ? \: \kappa \to \tau :: \mt{Type}}{
adamc@530 596 \Gamma, x :: \kappa \vdash \tau :: \mt{Type}
adamc@530 597 }
adamc@655 598 \quad \infer{\Gamma \vdash X \longrightarrow \tau :: \mt{Type}}{
adamc@655 599 \Gamma, X \vdash \tau :: \mt{Type}
adamc@655 600 }
adamc@530 601 \quad \infer{\Gamma \vdash \$c :: \mt{Type}}{
adamc@530 602 \Gamma \vdash c :: \{\mt{Type}\}
adamc@530 603 }$$
adamc@530 604
adamc@530 605 $$\infer{\Gamma \vdash c_1 \; c_2 :: \kappa_2}{
adamc@530 606 \Gamma \vdash c_1 :: \kappa_1 \to \kappa_2
adamc@530 607 & \Gamma \vdash c_2 :: \kappa_1
adamc@530 608 }
adamc@530 609 \quad \infer{\Gamma \vdash \lambda x \; :: \; \kappa_1 \Rightarrow c :: \kappa_1 \to \kappa_2}{
adamc@530 610 \Gamma, x :: \kappa_1 \vdash c :: \kappa_2
adamc@530 611 }$$
adamc@530 612
adamc@655 613 $$\infer{\Gamma \vdash c[\kappa'] :: [X \mapsto \kappa']\kappa}{
adamc@655 614 \Gamma \vdash c :: X \to \kappa
adamc@655 615 & \Gamma \vdash \kappa'
adamc@655 616 }
adamc@655 617 \quad \infer{\Gamma \vdash X \Longrightarrow c :: X \to \kappa}{
adamc@655 618 \Gamma, X \vdash c :: \kappa
adamc@655 619 }$$
adamc@655 620
adamc@530 621 $$\infer{\Gamma \vdash () :: \mt{Unit}}{}
adamc@530 622 \quad \infer{\Gamma \vdash \#X :: \mt{Name}}{}$$
adamc@530 623
adamc@530 624 $$\infer{\Gamma \vdash [\overline{c_i = c'_i}] :: \{\kappa\}}{
adamc@530 625 \forall i: \Gamma \vdash c_i : \mt{Name}
adamc@530 626 & \Gamma \vdash c'_i :: \kappa
adamc@530 627 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@530 628 }
adamc@530 629 \quad \infer{\Gamma \vdash c_1 \rc c_2 :: \{\kappa\}}{
adamc@530 630 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530 631 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@530 632 & \Gamma \vdash c_1 \sim c_2
adamc@530 633 }$$
adamc@530 634
adamc@655 635 $$\infer{\Gamma \vdash \mt{map} :: (\kappa_1 \to \kappa_2) \to \{\kappa_1\} \to \{\kappa_2\}}{}$$
adamc@530 636
adamc@573 637 $$\infer{\Gamma \vdash (\overline c) :: (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@573 638 \forall i: \Gamma \vdash c_i :: \kappa_i
adamc@530 639 }
adamc@573 640 \quad \infer{\Gamma \vdash c.i :: \kappa_i}{
adamc@573 641 \Gamma \vdash c :: (\kappa_1 \times \ldots \times \kappa_n)
adamc@530 642 }$$
adamc@530 643
adamc@655 644 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow \tau :: \mt{Type}}{
adamc@655 645 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530 646 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@655 647 & \Gamma, c_1 \sim c_2 \vdash \tau :: \mt{Type}
adamc@530 648 }$$
adamc@530 649
adamc@531 650 \subsection{Record Disjointness}
adamc@531 651
adamc@531 652 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@558 653 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@558 654 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@558 655 & \forall c'_1 \in C_1, c'_2 \in C_2: \Gamma \vdash c'_1 \sim c'_2
adamc@531 656 }
adamc@531 657 \quad \infer{\Gamma \vdash X \sim X'}{
adamc@531 658 X \neq X'
adamc@531 659 }$$
adamc@531 660
adamc@531 661 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@531 662 c'_1 \sim c'_2 \in \Gamma
adamc@558 663 & \Gamma \vdash c'_1 \hookrightarrow C_1
adamc@558 664 & \Gamma \vdash c'_2 \hookrightarrow C_2
adamc@558 665 & c_1 \in C_1
adamc@558 666 & c_2 \in C_2
adamc@531 667 }$$
adamc@531 668
adamc@531 669 $$\infer{\Gamma \vdash c \hookrightarrow \{c\}}{}
adamc@531 670 \quad \infer{\Gamma \vdash [\overline{c = c'}] \hookrightarrow \{\overline{c}\}}{}
adamc@531 671 \quad \infer{\Gamma \vdash c_1 \rc c_2 \hookrightarrow C_1 \cup C_2}{
adamc@531 672 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@531 673 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@531 674 }
adamc@531 675 \quad \infer{\Gamma \vdash c \hookrightarrow C}{
adamc@531 676 \Gamma \vdash c \equiv c'
adamc@531 677 & \Gamma \vdash c' \hookrightarrow C
adamc@531 678 }
adamc@531 679 \quad \infer{\Gamma \vdash \mt{map} \; f \; c \hookrightarrow C}{
adamc@531 680 \Gamma \vdash c \hookrightarrow C
adamc@531 681 }$$
adamc@531 682
adamc@541 683 \subsection{\label{definitional}Definitional Equality}
adamc@532 684
adamc@655 685 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@532 686
adamc@532 687 $$\infer{\Gamma \vdash c \equiv c}{}
adamc@532 688 \quad \infer{\Gamma \vdash c_1 \equiv c_2}{
adamc@532 689 \Gamma \vdash c_2 \equiv c_1
adamc@532 690 }
adamc@532 691 \quad \infer{\Gamma \vdash c_1 \equiv c_3}{
adamc@532 692 \Gamma \vdash c_1 \equiv c_2
adamc@532 693 & \Gamma \vdash c_2 \equiv c_3
adamc@532 694 }
adamc@532 695 \quad \infer{\Gamma \vdash \mathcal C[c_1] \equiv \mathcal C[c_2]}{
adamc@532 696 \Gamma \vdash c_1 \equiv c_2
adamc@532 697 }$$
adamc@532 698
adamc@532 699 $$\infer{\Gamma \vdash x \equiv c}{
adamc@532 700 x :: \kappa = c \in \Gamma
adamc@532 701 }
adamc@532 702 \quad \infer{\Gamma \vdash M.x \equiv c}{
adamc@537 703 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 704 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@532 705 }
adamc@532 706 \quad \infer{\Gamma \vdash (\overline c).i \equiv c_i}{}$$
adamc@532 707
adamc@532 708 $$\infer{\Gamma \vdash (\lambda x :: \kappa \Rightarrow c) \; c' \equiv [x \mapsto c'] c}{}
adamc@655 709 \quad \infer{\Gamma \vdash (X \Longrightarrow c) [\kappa] \equiv [X \mapsto \kappa] c}{}$$
adamc@655 710
adamc@655 711 $$\infer{\Gamma \vdash c_1 \rc c_2 \equiv c_2 \rc c_1}{}
adamc@532 712 \quad \infer{\Gamma \vdash c_1 \rc (c_2 \rc c_3) \equiv (c_1 \rc c_2) \rc c_3}{}$$
adamc@532 713
adamc@532 714 $$\infer{\Gamma \vdash [] \rc c \equiv c}{}
adamc@532 715 \quad \infer{\Gamma \vdash [\overline{c_1 = c'_1}] \rc [\overline{c_2 = c'_2}] \equiv [\overline{c_1 = c'_1}, \overline{c_2 = c'_2}]}{}$$
adamc@532 716
adamc@655 717 $$\infer{\Gamma \vdash \mt{map} \; f \; [] \equiv []}{}
adamc@655 718 \quad \infer{\Gamma \vdash \mt{map} \; f \; ([c_1 = c_2] \rc c) \equiv [c_1 = f \; c_2] \rc \mt{map} \; f \; c}{}$$
adamc@532 719
adamc@532 720 $$\infer{\Gamma \vdash \mt{map} \; (\lambda x \Rightarrow x) \; c \equiv c}{}
adamc@655 721 \quad \infer{\Gamma \vdash \mt{map} \; f \; (\mt{map} \; f' \; c)
adamc@655 722 \equiv \mt{map} \; (\lambda x \Rightarrow f \; (f' \; x)) \; c}{}$$
adamc@532 723
adamc@532 724 $$\infer{\Gamma \vdash \mt{map} \; f \; (c_1 \rc c_2) \equiv \mt{map} \; f \; c_1 \rc \mt{map} \; f \; c_2}{}$$
adamc@531 725
adamc@534 726 \subsection{Expression Typing}
adamc@533 727
adamc@873 728 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@533 729
adamc@533 730 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@533 731
adamc@533 732 $$\infer{\Gamma \vdash e : \tau : \tau}{
adamc@533 733 \Gamma \vdash e : \tau
adamc@533 734 }
adamc@533 735 \quad \infer{\Gamma \vdash e : \tau}{
adamc@533 736 \Gamma \vdash e : \tau'
adamc@533 737 & \Gamma \vdash \tau' \equiv \tau
adamc@533 738 }
adamc@533 739 \quad \infer{\Gamma \vdash \ell : T(\ell)}{}$$
adamc@533 740
adamc@533 741 $$\infer{\Gamma \vdash x : \mathcal I(\tau)}{
adamc@533 742 x : \tau \in \Gamma
adamc@533 743 }
adamc@533 744 \quad \infer{\Gamma \vdash M.x : \mathcal I(\tau)}{
adamc@537 745 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 746 & \mt{proj}(M, \overline{s}, \mt{val} \; x) = \tau
adamc@533 747 }
adamc@533 748 \quad \infer{\Gamma \vdash X : \mathcal I(\tau)}{
adamc@533 749 X : \tau \in \Gamma
adamc@533 750 }
adamc@533 751 \quad \infer{\Gamma \vdash M.X : \mathcal I(\tau)}{
adamc@537 752 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 753 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \tau
adamc@533 754 }$$
adamc@533 755
adamc@533 756 $$\infer{\Gamma \vdash e_1 \; e_2 : \tau_2}{
adamc@533 757 \Gamma \vdash e_1 : \tau_1 \to \tau_2
adamc@533 758 & \Gamma \vdash e_2 : \tau_1
adamc@533 759 }
adamc@533 760 \quad \infer{\Gamma \vdash \lambda x : \tau_1 \Rightarrow e : \tau_1 \to \tau_2}{
adamc@533 761 \Gamma, x : \tau_1 \vdash e : \tau_2
adamc@533 762 }$$
adamc@533 763
adamc@533 764 $$\infer{\Gamma \vdash e [c] : [x \mapsto c]\tau}{
adamc@533 765 \Gamma \vdash e : x :: \kappa \to \tau
adamc@533 766 & \Gamma \vdash c :: \kappa
adamc@533 767 }
adamc@852 768 \quad \infer{\Gamma \vdash \lambda [x \; ? \; \kappa] \Rightarrow e : x \; ? \; \kappa \to \tau}{
adamc@533 769 \Gamma, x :: \kappa \vdash e : \tau
adamc@533 770 }$$
adamc@533 771
adamc@655 772 $$\infer{\Gamma \vdash e [\kappa] : [X \mapsto \kappa]\tau}{
adamc@655 773 \Gamma \vdash e : X \longrightarrow \tau
adamc@655 774 & \Gamma \vdash \kappa
adamc@655 775 }
adamc@655 776 \quad \infer{\Gamma \vdash X \Longrightarrow e : X \longrightarrow \tau}{
adamc@655 777 \Gamma, X \vdash e : \tau
adamc@655 778 }$$
adamc@655 779
adamc@533 780 $$\infer{\Gamma \vdash \{\overline{c = e}\} : \{\overline{c : \tau}\}}{
adamc@533 781 \forall i: \Gamma \vdash c_i :: \mt{Name}
adamc@533 782 & \Gamma \vdash e_i : \tau_i
adamc@533 783 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@533 784 }
adamc@533 785 \quad \infer{\Gamma \vdash e.c : \tau}{
adamc@533 786 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533 787 }
adamc@533 788 \quad \infer{\Gamma \vdash e_1 \rc e_2 : \$(c_1 \rc c_2)}{
adamc@533 789 \Gamma \vdash e_1 : \$c_1
adamc@533 790 & \Gamma \vdash e_2 : \$c_2
adamc@573 791 & \Gamma \vdash c_1 \sim c_2
adamc@533 792 }$$
adamc@533 793
adamc@533 794 $$\infer{\Gamma \vdash e \rcut c : \$c'}{
adamc@533 795 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533 796 }
adamc@533 797 \quad \infer{\Gamma \vdash e \rcutM c : \$c'}{
adamc@533 798 \Gamma \vdash e : \$(c \rc c')
adamc@533 799 }$$
adamc@533 800
adamc@533 801 $$\infer{\Gamma \vdash \mt{let} \; \overline{ed} \; \mt{in} \; e \; \mt{end} : \tau}{
adamc@533 802 \Gamma \vdash \overline{ed} \leadsto \Gamma'
adamc@533 803 & \Gamma' \vdash e : \tau
adamc@533 804 }
adamc@533 805 \quad \infer{\Gamma \vdash \mt{case} \; e \; \mt{of} \; \overline{p \Rightarrow e} : \tau}{
adamc@533 806 \forall i: \Gamma \vdash p_i \leadsto \Gamma_i, \tau'
adamc@533 807 & \Gamma_i \vdash e_i : \tau
adamc@533 808 }$$
adamc@533 809
adamc@573 810 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow e : \lambda [c_1 \sim c_2] \Rightarrow \tau}{
adamc@533 811 \Gamma \vdash c_1 :: \{\kappa\}
adamc@655 812 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@533 813 & \Gamma, c_1 \sim c_2 \vdash e : \tau
adamc@662 814 }
adamc@662 815 \quad \infer{\Gamma \vdash e \; ! : \tau}{
adamc@662 816 \Gamma \vdash e : [c_1 \sim c_2] \Rightarrow \tau
adamc@662 817 & \Gamma \vdash c_1 \sim c_2
adamc@533 818 }$$
adamc@533 819
adamc@534 820 \subsection{Pattern Typing}
adamc@534 821
adamc@534 822 $$\infer{\Gamma \vdash \_ \leadsto \Gamma; \tau}{}
adamc@534 823 \quad \infer{\Gamma \vdash x \leadsto \Gamma, x : \tau; \tau}{}
adamc@534 824 \quad \infer{\Gamma \vdash \ell \leadsto \Gamma; T(\ell)}{}$$
adamc@534 825
adamc@534 826 $$\infer{\Gamma \vdash X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534 827 X : \overline{x ::: \mt{Type}} \to \tau \in \Gamma
adamc@534 828 & \textrm{$\tau$ not a function type}
adamc@534 829 }
adamc@534 830 \quad \infer{\Gamma \vdash X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534 831 X : \overline{x ::: \mt{Type}} \to \tau'' \to \tau \in \Gamma
adamc@534 832 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534 833 }$$
adamc@534 834
adamc@534 835 $$\infer{\Gamma \vdash M.X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537 836 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 837 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau
adamc@534 838 & \textrm{$\tau$ not a function type}
adamc@534 839 }$$
adamc@534 840
adamc@534 841 $$\infer{\Gamma \vdash M.X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537 842 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 843 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau'' \to \tau
adamc@534 844 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534 845 }$$
adamc@534 846
adamc@534 847 $$\infer{\Gamma \vdash \{\overline{x = p}\} \leadsto \Gamma_n; \{\overline{x = \tau}\}}{
adamc@534 848 \Gamma_0 = \Gamma
adamc@534 849 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534 850 }
adamc@534 851 \quad \infer{\Gamma \vdash \{\overline{x = p}, \ldots\} \leadsto \Gamma_n; \$([\overline{x = \tau}] \rc c)}{
adamc@534 852 \Gamma_0 = \Gamma
adamc@534 853 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534 854 }$$
adamc@534 855
adamc@852 856 $$\infer{\Gamma \vdash p : \tau \leadsto \Gamma'; \tau}{
adamc@852 857 \Gamma \vdash p \leadsto \Gamma'; \tau'
adamc@852 858 & \Gamma \vdash \tau' \equiv \tau
adamc@852 859 }$$
adamc@852 860
adamc@535 861 \subsection{Declaration Typing}
adamc@535 862
adamc@535 863 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@535 864
adamc@655 865 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@535 866
adamc@558 867 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@537 868 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@535 869
adamc@535 870 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535 871 \quad \infer{\Gamma \vdash d, \overline{d} \leadsto \Gamma''}{
adamc@535 872 \Gamma \vdash d \leadsto \Gamma'
adamc@535 873 & \Gamma' \vdash \overline{d} \leadsto \Gamma''
adamc@535 874 }$$
adamc@535 875
adamc@535 876 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@535 877 \Gamma \vdash c :: \kappa
adamc@535 878 }
adamc@535 879 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@535 880 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@535 881 }$$
adamc@535 882
adamc@535 883 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537 884 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 885 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@535 886 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@535 887 }$$
adamc@535 888
adamc@535 889 $$\infer{\Gamma \vdash \mt{val} \; x : \tau = e \leadsto \Gamma, x : \tau}{
adamc@535 890 \Gamma \vdash e : \tau
adamc@535 891 }$$
adamc@535 892
adamc@535 893 $$\infer{\Gamma \vdash \mt{val} \; \mt{rec} \; \overline{x : \tau = e} \leadsto \Gamma, \overline{x : \tau}}{
adamc@535 894 \forall i: \Gamma, \overline{x : \tau} \vdash e_i : \tau_i
adamc@535 895 & \textrm{$e_i$ starts with an expression $\lambda$, optionally preceded by constructor and disjointness $\lambda$s}
adamc@535 896 }$$
adamc@535 897
adamc@535 898 $$\infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : S}{
adamc@535 899 \Gamma \vdash M : S
adamc@558 900 & \textrm{ $M$ not a constant or application}
adamc@535 901 }
adamc@558 902 \quad \infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : \mt{selfify}(X, \overline{s})}{
adamc@558 903 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@539 904 }$$
adamc@539 905
adamc@539 906 $$\infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@535 907 \Gamma \vdash S
adamc@535 908 }$$
adamc@535 909
adamc@537 910 $$\infer{\Gamma \vdash \mt{open} \; M \leadsto \Gamma, \mathcal O(M, \overline{s})}{
adamc@537 911 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535 912 }$$
adamc@535 913
adamc@535 914 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma}{
adamc@535 915 \Gamma \vdash c_1 :: \{\kappa\}
adamc@535 916 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@535 917 & \Gamma \vdash c_1 \sim c_2
adamc@535 918 }
adamc@537 919 \quad \infer{\Gamma \vdash \mt{open} \; \mt{constraints} \; M \leadsto \Gamma, \mathcal O_c(M, \overline{s})}{
adamc@537 920 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535 921 }$$
adamc@535 922
adamc@784 923 $$\infer{\Gamma \vdash \mt{table} \; x : c \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_table} \; c \; []}{
adamc@535 924 \Gamma \vdash c :: \{\mt{Type}\}
adamc@535 925 }
adamc@784 926 \quad \infer{\Gamma \vdash \mt{view} \; x : c \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_view} \; c}{
adamc@784 927 \Gamma \vdash c :: \{\mt{Type}\}
adamc@784 928 }$$
adamc@784 929
adamc@784 930 $$\infer{\Gamma \vdash \mt{sequence} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_sequence}}{}$$
adamc@535 931
adamc@535 932 $$\infer{\Gamma \vdash \mt{cookie} \; x : \tau \leadsto \Gamma, x : \mt{Basis}.\mt{http\_cookie} \; \tau}{
adamc@535 933 \Gamma \vdash \tau :: \mt{Type}
adamc@784 934 }
adamc@784 935 \quad \infer{\Gamma \vdash \mt{style} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{css\_class}}{}$$
adamc@535 936
adamc@1085 937 $$\infer{\Gamma \vdash \mt{task} \; e_1 = e_2 \leadsto \Gamma}{
adamc@1085 938 \Gamma \vdash e_1 :: \mt{Basis}.\mt{task\_kind}
adamc@1085 939 & \Gamma \vdash e_2 :: \mt{Basis}.\mt{transaction} \; \{\}
adamc@1085 940 }$$
adamc@1085 941
adamc@784 942 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784 943 \Gamma \vdash c :: \kappa
adamc@535 944 }$$
adamc@535 945
adamc@535 946 $$\infer{\overline{y}; x; \Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535 947 \quad \infer{\overline{y}; x; \Gamma \vdash X \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to x \; \overline{y}}{
adamc@535 948 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535 949 }
adamc@535 950 \quad \infer{\overline{y}; x; \Gamma \vdash X \; \mt{of} \; \tau \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to \tau \to x \; \overline{y}}{
adamc@535 951 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535 952 }$$
adamc@535 953
adamc@537 954 \subsection{Signature Item Typing}
adamc@537 955
adamc@537 956 We appeal to a signature item analogue of the $\mathcal O$ function from the last subsection.
adamc@537 957
adamc@537 958 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@537 959 \quad \infer{\Gamma \vdash s, \overline{s} \leadsto \Gamma''}{
adamc@537 960 \Gamma \vdash s \leadsto \Gamma'
adamc@537 961 & \Gamma' \vdash \overline{s} \leadsto \Gamma''
adamc@537 962 }$$
adamc@537 963
adamc@537 964 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}
adamc@537 965 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@537 966 \Gamma \vdash c :: \kappa
adamc@537 967 }
adamc@537 968 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@537 969 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@537 970 }$$
adamc@537 971
adamc@537 972 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537 973 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 974 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 975 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@537 976 }$$
adamc@537 977
adamc@537 978 $$\infer{\Gamma \vdash \mt{val} \; x : \tau \leadsto \Gamma, x : \tau}{
adamc@537 979 \Gamma \vdash \tau :: \mt{Type}
adamc@537 980 }$$
adamc@537 981
adamc@537 982 $$\infer{\Gamma \vdash \mt{structure} \; X : S \leadsto \Gamma, X : S}{
adamc@537 983 \Gamma \vdash S
adamc@537 984 }
adamc@537 985 \quad \infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@537 986 \Gamma \vdash S
adamc@537 987 }$$
adamc@537 988
adamc@537 989 $$\infer{\Gamma \vdash \mt{include} \; S \leadsto \Gamma, \mathcal O(\overline{s})}{
adamc@537 990 \Gamma \vdash S
adamc@537 991 & \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 992 }$$
adamc@537 993
adamc@537 994 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma, c_1 \sim c_2}{
adamc@537 995 \Gamma \vdash c_1 :: \{\kappa\}
adamc@537 996 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@537 997 }$$
adamc@537 998
adamc@784 999 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784 1000 \Gamma \vdash c :: \kappa
adamc@537 1001 }
adamc@784 1002 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}$$
adamc@537 1003
adamc@536 1004 \subsection{Signature Compatibility}
adamc@536 1005
adamc@558 1006 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 1007
adamc@537 1008 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 1009
adamc@536 1010 $$\infer{\Gamma \vdash S \equiv S}{}
adamc@536 1011 \quad \infer{\Gamma \vdash S_1 \equiv S_2}{
adamc@536 1012 \Gamma \vdash S_2 \equiv S_1
adamc@536 1013 }
adamc@536 1014 \quad \infer{\Gamma \vdash X \equiv S}{
adamc@536 1015 X = S \in \Gamma
adamc@536 1016 }
adamc@536 1017 \quad \infer{\Gamma \vdash M.X \equiv S}{
adamc@537 1018 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1019 & \mt{proj}(M, \overline{s}, \mt{signature} \; X) = S
adamc@536 1020 }$$
adamc@536 1021
adamc@536 1022 $$\infer{\Gamma \vdash S \; \mt{where} \; \mt{con} \; x = c \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa = c \; \overline{s_2} \; \mt{end}}{
adamc@536 1023 \Gamma \vdash S \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa \; \overline{s_2} \; \mt{end}
adamc@536 1024 & \Gamma \vdash c :: \kappa
adamc@537 1025 }
adamc@537 1026 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s^1} \; \mt{include} \; S \; \overline{s^2} \; \mt{end} \equiv \mt{sig} \; \overline{s^1} \; \overline{s} \; \overline{s^2} \; \mt{end}}{
adamc@537 1027 \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@536 1028 }$$
adamc@536 1029
adamc@536 1030 $$\infer{\Gamma \vdash S_1 \leq S_2}{
adamc@536 1031 \Gamma \vdash S_1 \equiv S_2
adamc@536 1032 }
adamc@536 1033 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \mt{end}}{}
adamc@537 1034 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; s' \; \overline{s'} \; \mt{end}}{
adamc@537 1035 \Gamma \vdash \overline{s} \leq s'
adamc@537 1036 & \Gamma \vdash s' \leadsto \Gamma'
adamc@537 1037 & \Gamma' \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \overline{s'} \; \mt{end}
adamc@537 1038 }$$
adamc@537 1039
adamc@537 1040 $$\infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537 1041 \Gamma \vdash s \leq s'
adamc@537 1042 }
adamc@537 1043 \quad \infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537 1044 \Gamma \vdash s \leadsto \Gamma'
adamc@537 1045 & \Gamma' \vdash \overline{s} \leq s'
adamc@536 1046 }$$
adamc@536 1047
adamc@536 1048 $$\infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 \leq \mt{functor} (X : S'_1) : S'_2}{
adamc@536 1049 \Gamma \vdash S'_1 \leq S_1
adamc@536 1050 & \Gamma, X : S'_1 \vdash S_2 \leq S'_2
adamc@536 1051 }$$
adamc@536 1052
adamc@537 1053 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@537 1054 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}
adamc@558 1055 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type}}{}$$
adamc@537 1056
adamc@537 1057 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(y)} \to \mt{Type}}{
adamc@537 1058 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1059 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1060 }$$
adamc@537 1061
adamc@784 1062 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@784 1063 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}$$
adamc@537 1064
adamc@537 1065 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \mt{\kappa} = c_2}{
adamc@537 1066 \Gamma \vdash c_1 \equiv c_2
adamc@537 1067 }
adamc@784 1068 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \kappa = c_2}{
adamc@537 1069 \Gamma \vdash c_1 \equiv c_2
adamc@537 1070 }$$
adamc@537 1071
adamc@537 1072 $$\infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537 1073 \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1074 }$$
adamc@537 1075
adamc@537 1076 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537 1077 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1078 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1079 & \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1080 }$$
adamc@537 1081
adamc@537 1082 $$\infer{\Gamma \vdash \cdot \leq \cdot}{}
adamc@537 1083 \quad \infer{\Gamma \vdash X; \overline{dc} \leq X; \overline{dc'}}{
adamc@537 1084 \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1085 }
adamc@537 1086 \quad \infer{\Gamma \vdash X \; \mt{of} \; \tau_1; \overline{dc} \leq X \; \mt{of} \; \tau_2; \overline{dc'}}{
adamc@537 1087 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537 1088 & \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1089 }$$
adamc@537 1090
adamc@537 1091 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x = \mt{datatype} \; M'.z'}{
adamc@537 1092 \Gamma \vdash M.z \equiv M'.z'
adamc@537 1093 }$$
adamc@537 1094
adamc@537 1095 $$\infer{\Gamma \vdash \mt{val} \; x : \tau_1 \leq \mt{val} \; x : \tau_2}{
adamc@537 1096 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537 1097 }
adamc@537 1098 \quad \infer{\Gamma \vdash \mt{structure} \; X : S_1 \leq \mt{structure} \; X : S_2}{
adamc@537 1099 \Gamma \vdash S_1 \leq S_2
adamc@537 1100 }
adamc@537 1101 \quad \infer{\Gamma \vdash \mt{signature} \; X = S_1 \leq \mt{signature} \; X = S_2}{
adamc@537 1102 \Gamma \vdash S_1 \leq S_2
adamc@537 1103 & \Gamma \vdash S_2 \leq S_1
adamc@537 1104 }$$
adamc@537 1105
adamc@537 1106 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leq \mt{constraint} \; c'_1 \sim c'_2}{
adamc@537 1107 \Gamma \vdash c_1 \equiv c'_1
adamc@537 1108 & \Gamma \vdash c_2 \equiv c'_2
adamc@537 1109 }$$
adamc@537 1110
adamc@655 1111 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{class} \; x :: \kappa}{}
adamc@655 1112 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{class} \; x :: \kappa}{}
adamc@655 1113 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{class} \; x :: \kappa = c_2}{
adamc@537 1114 \Gamma \vdash c_1 \equiv c_2
adamc@537 1115 }$$
adamc@537 1116
adamc@538 1117 \subsection{Module Typing}
adamc@538 1118
adamc@538 1119 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 1120
adamc@538 1121 $$\infer{\Gamma \vdash M : S}{
adamc@538 1122 \Gamma \vdash M : S'
adamc@538 1123 & \Gamma \vdash S' \leq S
adamc@538 1124 }
adamc@538 1125 \quad \infer{\Gamma \vdash \mt{struct} \; \overline{d} \; \mt{end} : \mt{sig} \; \mt{sigOf}(\overline{d}) \; \mt{end}}{
adamc@538 1126 \Gamma \vdash \overline{d} \leadsto \Gamma'
adamc@538 1127 }
adamc@538 1128 \quad \infer{\Gamma \vdash X : S}{
adamc@538 1129 X : S \in \Gamma
adamc@538 1130 }$$
adamc@538 1131
adamc@538 1132 $$\infer{\Gamma \vdash M.X : S}{
adamc@538 1133 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@538 1134 & \mt{proj}(M, \overline{s}, \mt{structure} \; X) = S
adamc@538 1135 }$$
adamc@538 1136
adamc@538 1137 $$\infer{\Gamma \vdash M_1(M_2) : [X \mapsto M_2]S_2}{
adamc@538 1138 \Gamma \vdash M_1 : \mt{functor}(X : S_1) : S_2
adamc@538 1139 & \Gamma \vdash M_2 : S_1
adamc@538 1140 }
adamc@538 1141 \quad \infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 = M : \mt{functor} (X : S_1) : S_2}{
adamc@538 1142 \Gamma \vdash S_1
adamc@538 1143 & \Gamma, X : S_1 \vdash S_2
adamc@538 1144 & \Gamma, X : S_1 \vdash M : S_2
adamc@538 1145 }$$
adamc@538 1146
adamc@538 1147 \begin{eqnarray*}
adamc@538 1148 \mt{sigOf}(\cdot) &=& \cdot \\
adamc@538 1149 \mt{sigOf}(s \; \overline{s'}) &=& \mt{sigOf}(s) \; \mt{sigOf}(\overline{s'}) \\
adamc@538 1150 \\
adamc@538 1151 \mt{sigOf}(\mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@538 1152 \mt{sigOf}(\mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \overline{dc} \\
adamc@538 1153 \mt{sigOf}(\mt{datatype} \; x = \mt{datatype} \; M.z) &=& \mt{datatype} \; x = \mt{datatype} \; M.z \\
adamc@538 1154 \mt{sigOf}(\mt{val} \; x : \tau = e) &=& \mt{val} \; x : \tau \\
adamc@538 1155 \mt{sigOf}(\mt{val} \; \mt{rec} \; \overline{x : \tau = e}) &=& \overline{\mt{val} \; x : \tau} \\
adamc@538 1156 \mt{sigOf}(\mt{structure} \; X : S = M) &=& \mt{structure} \; X : S \\
adamc@538 1157 \mt{sigOf}(\mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@538 1158 \mt{sigOf}(\mt{open} \; M) &=& \mt{include} \; S \textrm{ (where $\Gamma \vdash M : S$)} \\
adamc@538 1159 \mt{sigOf}(\mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@538 1160 \mt{sigOf}(\mt{open} \; \mt{constraints} \; M) &=& \cdot \\
adamc@538 1161 \mt{sigOf}(\mt{table} \; x : c) &=& \mt{table} \; x : c \\
adamc@784 1162 \mt{sigOf}(\mt{view} \; x : c) &=& \mt{view} \; x : c \\
adamc@538 1163 \mt{sigOf}(\mt{sequence} \; x) &=& \mt{sequence} \; x \\
adamc@538 1164 \mt{sigOf}(\mt{cookie} \; x : \tau) &=& \mt{cookie} \; x : \tau \\
adamc@784 1165 \mt{sigOf}(\mt{style} \; x) &=& \mt{style} \; x \\
adamc@655 1166 \mt{sigOf}(\mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@538 1167 \end{eqnarray*}
adamc@539 1168 \begin{eqnarray*}
adamc@539 1169 \mt{selfify}(M, \cdot) &=& \cdot \\
adamc@558 1170 \mt{selfify}(M, s \; \overline{s'}) &=& \mt{selfify}(M, s) \; \mt{selfify}(M, \overline{s'}) \\
adamc@539 1171 \\
adamc@539 1172 \mt{selfify}(M, \mt{con} \; x :: \kappa) &=& \mt{con} \; x :: \kappa = M.x \\
adamc@539 1173 \mt{selfify}(M, \mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@539 1174 \mt{selfify}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \mt{datatype} \; M.x \\
adamc@539 1175 \mt{selfify}(M, \mt{datatype} \; x = \mt{datatype} \; M'.z) &=& \mt{datatype} \; x = \mt{datatype} \; M'.z \\
adamc@539 1176 \mt{selfify}(M, \mt{val} \; x : \tau) &=& \mt{val} \; x : \tau \\
adamc@539 1177 \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 1178 \mt{selfify}(M, \mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@539 1179 \mt{selfify}(M, \mt{include} \; S) &=& \mt{include} \; S \\
adamc@539 1180 \mt{selfify}(M, \mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@655 1181 \mt{selfify}(M, \mt{class} \; x :: \kappa) &=& \mt{class} \; x :: \kappa = M.x \\
adamc@655 1182 \mt{selfify}(M, \mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@539 1183 \end{eqnarray*}
adamc@539 1184
adamc@540 1185 \subsection{Module Projection}
adamc@540 1186
adamc@540 1187 \begin{eqnarray*}
adamc@540 1188 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \\
adamc@540 1189 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa, c) \\
adamc@540 1190 \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 1191 \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 1192 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})$)} \\
adamc@655 1193 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \to \mt{Type} \\
adamc@655 1194 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa \to \mt{Type}, c) \\
adamc@540 1195 \\
adamc@540 1196 \mt{proj}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc} \; \overline{s}, \mt{datatype} \; x) &=& (\overline{y}, \overline{dc}) \\
adamc@540 1197 \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 1198 \\
adamc@540 1199 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, \mt{val} \; x) &=& \tau \\
adamc@540 1200 \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 1201 \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 1202 \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 1203 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \in \overline{dc}$)} \\
adamc@540 1204 \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 1205 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \; \mt{of} \; \tau \in \overline{dc}$)} \\
adamc@540 1206 \\
adamc@540 1207 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, \mt{structure} \; X) &=& S \\
adamc@540 1208 \\
adamc@540 1209 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, \mt{signature} \; X) &=& S \\
adamc@540 1210 \\
adamc@540 1211 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1212 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1213 \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 1214 \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 1215 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@540 1216 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1217 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1218 \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 1219 \mt{proj}(M, \mt{constraint} \; c_1 \sim c_2 \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@655 1220 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@655 1221 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1222 \end{eqnarray*}
adamc@540 1223
adamc@541 1224
adamc@541 1225 \section{Type Inference}
adamc@541 1226
adamc@541 1227 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 1228
adamc@541 1229 \subsection{Basic Unification}
adamc@541 1230
adamc@560 1231 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 1232
adamc@656 1233 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 1234
adamc@541 1235 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 1236
adamc@541 1237 \subsection{Unifying Record Types}
adamc@541 1238
adamc@570 1239 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 1240
adamc@656 1241 \subsection{\label{typeclasses}Constructor Classes}
adamc@541 1242
adamc@784 1243 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 1244
adamc@784 1245 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 1246
adamc@656 1247 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 1248
adamc@656 1249 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 1250
adamc@541 1251 \subsection{Reverse-Engineering Record Types}
adamc@541 1252
adamc@656 1253 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 1254
adamc@541 1255 \subsection{Implicit Arguments in Functor Applications}
adamc@541 1256
adamc@656 1257 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 1258
adamc@541 1259
adamc@542 1260 \section{The Ur Standard Library}
adamc@542 1261
adamc@542 1262 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 1263
adamc@542 1264 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 1265
adamc@542 1266 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 1267 $$\begin{array}{l}
adamc@542 1268 \mt{type} \; \mt{int} \\
adamc@542 1269 \mt{type} \; \mt{float} \\
adamc@873 1270 \mt{type} \; \mt{char} \\
adamc@542 1271 \mt{type} \; \mt{string} \\
adamc@542 1272 \mt{type} \; \mt{time} \\
adamc@785 1273 \mt{type} \; \mt{blob} \\
adamc@542 1274 \\
adamc@542 1275 \mt{type} \; \mt{unit} = \{\} \\
adamc@542 1276 \\
adamc@542 1277 \mt{datatype} \; \mt{bool} = \mt{False} \mid \mt{True} \\
adamc@542 1278 \\
adamc@785 1279 \mt{datatype} \; \mt{option} \; \mt{t} = \mt{None} \mid \mt{Some} \; \mt{of} \; \mt{t} \\
adamc@785 1280 \\
adamc@785 1281 \mt{datatype} \; \mt{list} \; \mt{t} = \mt{Nil} \mid \mt{Cons} \; \mt{of} \; \mt{t} \times \mt{list} \; \mt{t}
adamc@542 1282 \end{array}$$
adamc@542 1283
adamc@1123 1284 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 1285
adamc@657 1286 Another important generic Ur element comes at the beginning of \texttt{top.urs}.
adamc@657 1287
adamc@657 1288 $$\begin{array}{l}
adamc@657 1289 \mt{con} \; \mt{folder} :: \mt{K} \longrightarrow \{\mt{K}\} \to \mt{Type} \\
adamc@657 1290 \\
adamc@657 1291 \mt{val} \; \mt{fold} : \mt{K} \longrightarrow \mt{tf} :: (\{\mt{K}\} \to \mt{Type}) \\
adamc@657 1292 \hspace{.1in} \to (\mt{nm} :: \mt{Name} \to \mt{v} :: \mt{K} \to \mt{r} :: \{\mt{K}\} \to [[\mt{nm}] \sim \mt{r}] \Rightarrow \\
adamc@657 1293 \hspace{.2in} \mt{tf} \; \mt{r} \to \mt{tf} \; ([\mt{nm} = \mt{v}] \rc \mt{r})) \\
adamc@657 1294 \hspace{.1in} \to \mt{tf} \; [] \\
adamc@657 1295 \hspace{.1in} \to \mt{r} :: \{\mt{K}\} \to \mt{folder} \; \mt{r} \to \mt{tf} \; \mt{r}
adamc@657 1296 \end{array}$$
adamc@657 1297
adamc@657 1298 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 1299
adamc@664 1300 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 1301
adamc@542 1302
adamc@542 1303 \section{The Ur/Web Standard Library}
adamc@542 1304
adamc@658 1305 \subsection{Monads}
adamc@658 1306
adamc@658 1307 The Ur Basis defines the monad constructor class from Haskell.
adamc@658 1308
adamc@658 1309 $$\begin{array}{l}
adamc@658 1310 \mt{class} \; \mt{monad} :: \mt{Type} \to \mt{Type} \\
adamc@658 1311 \mt{val} \; \mt{return} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t} ::: \mt{Type} \\
adamc@658 1312 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658 1313 \hspace{.1in} \to \mt{t} \to \mt{m} \; \mt{t} \\
adamc@658 1314 \mt{val} \; \mt{bind} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t1} ::: \mt{Type} \to \mt{t2} ::: \mt{Type} \\
adamc@658 1315 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658 1316 \hspace{.1in} \to \mt{m} \; \mt{t1} \to (\mt{t1} \to \mt{m} \; \mt{t2}) \\
adamc@658 1317 \hspace{.1in} \to \mt{m} \; \mt{t2}
adamc@658 1318 \end{array}$$
adamc@658 1319
adamc@542 1320 \subsection{Transactions}
adamc@542 1321
adamc@542 1322 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 1323 $$\begin{array}{l}
adamc@542 1324 \mt{con} \; \mt{transaction} :: \mt{Type} \to \mt{Type} \\
adamc@658 1325 \mt{val} \; \mt{transaction\_monad} : \mt{monad} \; \mt{transaction}
adamc@542 1326 \end{array}$$
adamc@542 1327
adamc@1123 1328 For debugging purposes, a transactional function is provided for outputting a string on the server process' \texttt{stderr}.
adamc@1123 1329 $$\begin{array}{l}
adamc@1123 1330 \mt{val} \; \mt{debug} : \mt{string} \to \mt{transaction} \; \mt{unit}
adamc@1123 1331 \end{array}$$
adamc@1123 1332
adamc@542 1333 \subsection{HTTP}
adamc@542 1334
adamc@542 1335 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 1336 $$\begin{array}{l}
adamc@786 1337 \mt{val} \; \mt{requestHeader} : \mt{string} \to \mt{transaction} \; (\mt{option} \; \mt{string}) \\
adamc@786 1338 \\
adamc@786 1339 \mt{con} \; \mt{http\_cookie} :: \mt{Type} \to \mt{Type} \\
adamc@786 1340 \mt{val} \; \mt{getCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; (\mt{option} \; \mt{t}) \\
adamc@1050 1341 \mt{val} \; \mt{setCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \{\mt{Value} : \mt{t}, \mt{Expires} : \mt{option} \; \mt{time}, \mt{Secure} : \mt{bool}\} \to \mt{transaction} \; \mt{unit} \\
adamc@1050 1342 \mt{val} \; \mt{clearCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; \mt{unit}
adamc@786 1343 \end{array}$$
adamc@786 1344
adamc@786 1345 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 1346 $$\begin{array}{l}
adamc@786 1347 \mt{type} \; \mt{url} \\
adamc@786 1348 \mt{val} \; \mt{bless} : \mt{string} \to \mt{url} \\
adamc@786 1349 \mt{val} \; \mt{checkUrl} : \mt{string} \to \mt{option} \; \mt{url}
adamc@786 1350 \end{array}$$
adamc@786 1351 $\mt{bless}$ raises a runtime error if the string passed to it fails the URL policy.
adamc@786 1352
adamc@1085 1353 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 1354 $$\begin{array}{l}
adamc@1085 1355 \mt{val} \; \mt{currentUrl} : \mt{transaction} \; \mt{url} \\
adamc@1085 1356 \mt{val} \; \mt{url} : \mt{transaction} \; \mt{page} \to \mt{url}
adamc@1085 1357 \end{array}$$
adamc@1085 1358
adamc@1085 1359 Page generation may be interrupted at any time with a request to redirect to a particular URL instead.
adamc@1085 1360 $$\begin{array}{l}
adamc@1085 1361 \mt{val} \; \mt{redirect} : \mt{t} ::: \mt{Type} \to \mt{url} \to \mt{transaction} \; \mt{t}
adamc@1085 1362 \end{array}$$
adamc@1085 1363
adamc@786 1364 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 1365 $$\begin{array}{l}
adamc@786 1366 \mt{type} \; \mt{file} \\
adamc@786 1367 \mt{val} \; \mt{fileName} : \mt{file} \to \mt{option} \; \mt{string} \\
adamc@786 1368 \mt{val} \; \mt{fileMimeType} : \mt{file} \to \mt{string} \\
adamc@786 1369 \mt{val} \; \mt{fileData} : \mt{file} \to \mt{blob}
adamc@786 1370 \end{array}$$
adamc@786 1371
adamc@786 1372 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 1373 $$\begin{array}{l}
adamc@786 1374 \mt{type} \; \mt{mimeType} \\
adamc@786 1375 \mt{val} \; \mt{blessMime} : \mt{string} \to \mt{mimeType} \\
adamc@786 1376 \mt{val} \; \mt{checkMime} : \mt{string} \to \mt{option} \; \mt{mimeType} \\
adamc@786 1377 \mt{val} \; \mt{returnBlob} : \mt{t} ::: \mt{Type} \to \mt{blob} \to \mt{mimeType} \to \mt{transaction} \; \mt{t}
adamc@542 1378 \end{array}$$
adamc@542 1379
adamc@543 1380 \subsection{SQL}
adamc@543 1381
adamc@543 1382 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 1383 $$\begin{array}{l}
adamc@785 1384 \mt{con} \; \mt{sql\_table} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785 1385 \end{array}$$
adamc@785 1386 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 1387
adamc@785 1388 We also have the simpler type family of SQL views, which have no keys.
adamc@785 1389 $$\begin{array}{l}
adamc@785 1390 \mt{con} \; \mt{sql\_view} :: \{\mt{Type}\} \to \mt{Type}
adamc@543 1391 \end{array}$$
adamc@543 1392
adamc@785 1393 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 1394 $$\begin{array}{l}
adamc@785 1395 \mt{class} \; \mt{fieldsOf} :: \mt{Type} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1396 \mt{val} \; \mt{fieldsOf\_table} : \mt{fs} ::: \{\mt{Type}\} \to \mt{keys} ::: \{\{\mt{Unit}\}\} \to \mt{fieldsOf} \; (\mt{sql\_table} \; \mt{fs} \; \mt{keys}) \; \mt{fs} \\
adamc@785 1397 \mt{val} \; \mt{fieldsOf\_view} : \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; (\mt{sql\_view} \; \mt{fs}) \; \mt{fs}
adamc@785 1398 \end{array}$$
adamc@785 1399
adamc@785 1400 \subsubsection{Table Constraints}
adamc@785 1401
adamc@785 1402 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 1403
adamc@785 1404 $$\begin{array}{l}
adamc@785 1405 \mt{con} \; \mt{primary\_key} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type} \\
adamc@785 1406 \mt{val} \; \mt{no\_primary\_key} : \mt{fs} ::: \{\mt{Type}\} \to \mt{primary\_key} \; \mt{fs} \; [] \\
adamc@785 1407 \mt{val} \; \mt{primary\_key} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{key1} :: \mt{Name} \to \mt{keys} :: \{\mt{Type}\} \\
adamc@785 1408 \hspace{.1in} \to [[\mt{key1}] \sim \mt{keys}] \Rightarrow [[\mt{key1} = \mt{t}] \rc \mt{keys} \sim \mt{rest}] \\
adamc@785 1409 \hspace{.1in} \Rightarrow \$([\mt{key1} = \mt{sql\_injectable\_prim} \; \mt{t}] \rc \mt{map} \; \mt{sql\_injectable\_prim} \; \mt{keys}) \\
adamc@785 1410 \hspace{.1in} \to \mt{primary\_key} \; ([\mt{key1} = \mt{t}] \rc \mt{keys} \rc \mt{rest}) \; [\mt{Pkey} = [\mt{key1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{keys}]
adamc@785 1411 \end{array}$$
adamc@785 1412 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 1413
adamc@785 1414 A type family stands for sets of named constraints of the remaining varieties.
adamc@785 1415 $$\begin{array}{l}
adamc@785 1416 \mt{con} \; \mt{sql\_constraints} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785 1417 \end{array}$$
adamc@785 1418 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 1419
adamc@785 1420 There is a type family of individual, unnamed constraints.
adamc@785 1421 $$\begin{array}{l}
adamc@785 1422 \mt{con} \; \mt{sql\_constraint} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \mt{Type}
adamc@785 1423 \end{array}$$
adamc@785 1424 The first argument is the same as above, and the second argument gives the key columns for just this constraint.
adamc@785 1425
adamc@785 1426 We have operations for assembling constraints into constraint sets.
adamc@785 1427 $$\begin{array}{l}
adamc@785 1428 \mt{val} \; \mt{no\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_constraints} \; \mt{fs} \; [] \\
adamc@785 1429 \mt{val} \; \mt{one\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{unique} ::: \{\mt{Unit}\} \to \mt{name} :: \mt{Name} \\
adamc@785 1430 \hspace{.1in} \to \mt{sql\_constraint} \; \mt{fs} \; \mt{unique} \to \mt{sql\_constraints} \; \mt{fs} \; [\mt{name} = \mt{unique}] \\
adamc@785 1431 \mt{val} \; \mt{join\_constraints} : \mt{fs} ::: \{\mt{Type}\} \to \mt{uniques1} ::: \{\{\mt{Unit}\}\} \to \mt{uniques2} ::: \{\{\mt{Unit}\}\} \to [\mt{uniques1} \sim \mt{uniques2}] \\
adamc@785 1432 \hspace{.1in} \Rightarrow \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques1} \to \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques2} \to \mt{sql\_constraints} \; \mt{fs} \; (\mt{uniques1} \rc \mt{uniques2})
adamc@785 1433 \end{array}$$
adamc@785 1434
adamc@785 1435 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 1436 $$\begin{array}{l}
adamc@785 1437 \mt{val} \; \mt{unique} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{unique1} :: \mt{Name} \to \mt{unique} :: \{\mt{Type}\} \\
adamc@785 1438 \hspace{.1in} \to [[\mt{unique1}] \sim \mt{unique}] \Rightarrow [[\mt{unique1} = \mt{t}] \rc \mt{unique} \sim \mt{rest}] \\
adamc@785 1439 \hspace{.1in} \Rightarrow \mt{sql\_constraint} \; ([\mt{unique1} = \mt{t}] \rc \mt{unique} \rc \mt{rest}) \; ([\mt{unique1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{unique})
adamc@785 1440 \end{array}$$
adamc@785 1441
adamc@785 1442 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 1443 $$\begin{array}{l}
adamc@785 1444 \mt{class} \; \mt{linkable} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@785 1445 \mt{val} \; \mt{linkable\_same} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; \mt{t} \\
adamc@785 1446 \mt{val} \; \mt{linkable\_from\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; (\mt{option} \; \mt{t}) \; \mt{t} \\
adamc@785 1447 \mt{val} \; \mt{linkable\_to\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@785 1448 \end{array}$$
adamc@785 1449
adamc@785 1450 The $\mt{matching}$ type family uses $\mt{linkable}$ to define when two keys match up type-wise.
adamc@785 1451 $$\begin{array}{l}
adamc@785 1452 \mt{con} \; \mt{matching} :: \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1453 \mt{val} \; \mt{mat\_nil} : \mt{matching} \; [] \; [] \\
adamc@785 1454 \mt{val} \; \mt{mat\_cons} : \mt{t1} ::: \mt{Type} \to \mt{rest1} ::: \{\mt{Type}\} \to \mt{t2} ::: \mt{Type} \to \mt{rest2} ::: \{\mt{Type}\} \to \mt{nm1} :: \mt{Name} \to \mt{nm2} :: \mt{Name} \\
adamc@785 1455 \hspace{.1in} \to [[\mt{nm1}] \sim \mt{rest1}] \Rightarrow [[\mt{nm2}] \sim \mt{rest2}] \Rightarrow \mt{linkable} \; \mt{t1} \; \mt{t2} \to \mt{matching} \; \mt{rest1} \; \mt{rest2} \\
adamc@785 1456 \hspace{.1in} \to \mt{matching} \; ([\mt{nm1} = \mt{t1}] \rc \mt{rest1}) \; ([\mt{nm2} = \mt{t2}] \rc \mt{rest2})
adamc@785 1457 \end{array}$$
adamc@785 1458
adamc@785 1459 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 1460 $$\begin{array}{l}
adamc@785 1461 \mt{con} \; \mt{propagation\_mode} :: \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1462 \mt{val} \; \mt{restrict} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1463 \mt{val} \; \mt{cascade} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1464 \mt{val} \; \mt{no\_action} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1465 \mt{val} \; \mt{set\_null} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; (\mt{map} \; \mt{option} \; \mt{fs})
adamc@785 1466 \end{array}$$
adamc@785 1467
adamc@785 1468 Finally, we put these ingredient together to define the \texttt{FOREIGN KEY} constraint function.
adamc@785 1469 $$\begin{array}{l}
adamc@785 1470 \mt{val} \; \mt{foreign\_key} : \mt{mine1} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{mine} ::: \{\mt{Type}\} \to \mt{munused} ::: \{\mt{Type}\} \to \mt{foreign} ::: \{\mt{Type}\} \\
adamc@785 1471 \hspace{.1in} \to \mt{funused} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{uniques} ::: \{\{\mt{Unit}\}\} \\
adamc@785 1472 \hspace{.1in} \to [[\mt{mine1}] \sim \mt{mine}] \Rightarrow [[\mt{mine1} = \mt{t}] \rc \mt{mine} \sim \mt{munused}] \Rightarrow [\mt{foreign} \sim \mt{funused}] \Rightarrow [[\mt{nm}] \sim \mt{uniques}] \\
adamc@785 1473 \hspace{.1in} \Rightarrow \mt{matching} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}) \; \mt{foreign} \\
adamc@785 1474 \hspace{.1in} \to \mt{sql\_table} \; (\mt{foreign} \rc \mt{funused}) \; ([\mt{nm} = \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{foreign}] \rc \mt{uniques}) \\
adamc@785 1475 \hspace{.1in} \to \{\mt{OnDelete} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}), \\
adamc@785 1476 \hspace{.2in} \mt{OnUpdate} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine})\} \\
adamc@785 1477 \hspace{.1in} \to \mt{sql\_constraint} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine} \rc \mt{munused}) \; []
adamc@785 1478 \end{array}$$
adamc@785 1479
adamc@785 1480 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 1481 $$\begin{array}{l}
adamc@785 1482 \mt{val} \; \mt{check} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; [] \; [] \; \mt{fs} \; \mt{bool} \to \mt{sql\_constraint} \; \mt{fs} \; []
adamc@785 1483 \end{array}$$
adamc@785 1484
adamc@785 1485 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 1486
adamc@784 1487
adamc@543 1488 \subsubsection{Queries}
adamc@543 1489
adamc@1193 1490 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 1491 $$\begin{array}{l}
adamc@1193 1492 \mt{con} \; \mt{sql\_query} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@1193 1493 \mt{val} \; \mt{sql\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1494 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543 1495 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1496 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1193 1497 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adamc@1193 1498 \hspace{.1in} \Rightarrow \{\mt{Rows} : \mt{sql\_query1} \; \mt{free} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}, \\
adamc@1193 1499 \hspace{.2in} \mt{OrderBy} : \mt{sql\_order\_by} \; (\mt{free} \rc \mt{tables}) \; \mt{selectedExps}, \\
adamc@543 1500 \hspace{.2in} \mt{Limit} : \mt{sql\_limit}, \\
adamc@543 1501 \hspace{.2in} \mt{Offset} : \mt{sql\_offset}\} \\
adamc@1193 1502 \hspace{.1in} \to \mt{sql\_query} \; \mt{free} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1503 \end{array}$$
adamc@543 1504
adamc@545 1505 Queries are used by folding over their results inside transactions.
adamc@545 1506 $$\begin{array}{l}
adamc@1193 1507 \mt{val} \; \mt{query} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \lambda [\mt{tables} \sim \mt{exps}] \Rightarrow \mt{state} ::: \mt{Type} \to \mt{sql\_query} \; [] \; \mt{tables} \; \mt{exps} \\
adamc@658 1508 \hspace{.1in} \to (\$(\mt{exps} \rc \mt{map} \; (\lambda \mt{fields} :: \{\mt{Type}\} \Rightarrow \$\mt{fields}) \; \mt{tables}) \\
adamc@545 1509 \hspace{.2in} \to \mt{state} \to \mt{transaction} \; \mt{state}) \\
adamc@545 1510 \hspace{.1in} \to \mt{state} \to \mt{transaction} \; \mt{state}
adamc@545 1511 \end{array}$$
adamc@545 1512
adamc@1193 1513 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 1514 $$\begin{array}{l}
adamc@1193 1515 \mt{con} \; \mt{sql\_query1} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@543 1516 \\
adamc@543 1517 \mt{type} \; \mt{sql\_relop} \\
adamc@543 1518 \mt{val} \; \mt{sql\_union} : \mt{sql\_relop} \\
adamc@543 1519 \mt{val} \; \mt{sql\_intersect} : \mt{sql\_relop} \\
adamc@543 1520 \mt{val} \; \mt{sql\_except} : \mt{sql\_relop} \\
adamc@543 1521 \mt{val} \; \mt{sql\_relop} : \mt{tables1} ::: \{\{\mt{Type}\}\} \\
adamc@543 1522 \hspace{.1in} \to \mt{tables2} ::: \{\{\mt{Type}\}\} \\
adamc@543 1523 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1524 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@543 1525 \hspace{.1in} \to \mt{sql\_relop} \\
adamc@543 1526 \hspace{.1in} \to \mt{sql\_query1} \; \mt{tables1} \; \mt{selectedFields} \; \mt{selectedExps} \\
adamc@543 1527 \hspace{.1in} \to \mt{sql\_query1} \; \mt{tables2} \; \mt{selectedFields} \; \mt{selectedExps} \\
adamc@543 1528 \hspace{.1in} \to \mt{sql\_query1} \; \mt{selectedFields} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1529 \end{array}$$
adamc@543 1530
adamc@543 1531 $$\begin{array}{l}
adamc@1193 1532 \mt{val} \; \mt{sql\_query1} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1533 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543 1534 \hspace{.1in} \to \mt{grouped} ::: \{\{\mt{Type}\}\} \\
adamc@543 1535 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1536 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1085 1537 \hspace{.1in} \to \mt{empties} :: \{\mt{Unit}\} \\
adamc@1193 1538 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adamc@1193 1539 \hspace{.1in} \Rightarrow [\mt{free} \sim \mt{grouped}] \\
adamc@1193 1540 \hspace{.1in} \Rightarrow [\mt{empties} \sim \mt{selectedFields}] \\
adamc@1085 1541 \hspace{.1in} \Rightarrow \{\mt{Distinct} : \mt{bool}, \\
adamc@1193 1542 \hspace{.2in} \mt{From} : \mt{sql\_from\_items} \; \mt{free} \; \mt{tables}, \\
adamc@1193 1543 \hspace{.2in} \mt{Where} : \mt{sql\_exp} \; (\mt{free} \rc \mt{tables}) \; [] \; [] \; \mt{bool}, \\
adamc@543 1544 \hspace{.2in} \mt{GroupBy} : \mt{sql\_subset} \; \mt{tables} \; \mt{grouped}, \\
adamc@1193 1545 \hspace{.2in} \mt{Having} : \mt{sql\_exp} \; (\mt{free} \rc \mt{grouped}) \; \mt{tables} \; [] \; \mt{bool}, \\
adamc@1085 1546 \hspace{.2in} \mt{SelectFields} : \mt{sql\_subset} \; \mt{grouped} \; (\mt{map} \; (\lambda \_ \Rightarrow []) \; \mt{empties} \rc \mt{selectedFields}), \\
adamc@1193 1547 \hspace{.2in} \mt {SelectExps} : \$(\mt{map} \; (\mt{sql\_exp} \; (\mt{free} \rc \mt{grouped}) \; \mt{tables} \; []) \; \mt{selectedExps}) \} \\
adamc@1193 1548 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1549 \end{array}$$
adamc@543 1550
adamc@543 1551 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 1552 $$\begin{array}{l}
adamc@543 1553 \mt{con} \; \mt{sql\_subset} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@543 1554 \mt{val} \; \mt{sql\_subset} : \mt{keep\_drop} :: \{(\{\mt{Type}\} \times \{\mt{Type}\})\} \\
adamc@543 1555 \hspace{.1in} \to \mt{sql\_subset} \\
adamc@658 1556 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1 \rc \mt{fields}.2)\; \mt{keep\_drop}) \\
adamc@658 1557 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1) \; \mt{keep\_drop}) \\
adamc@543 1558 \mt{val} \; \mt{sql\_subset\_all} : \mt{tables} :: \{\{\mt{Type}\}\} \to \mt{sql\_subset} \; \mt{tables} \; \mt{tables}
adamc@543 1559 \end{array}$$
adamc@543 1560
adamc@560 1561 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 1562 $$\begin{array}{l}
adamc@543 1563 \mt{con} \; \mt{sql\_exp} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}
adamc@543 1564 \end{array}$$
adamc@543 1565
adamc@543 1566 Any field in scope may be converted to an expression.
adamc@543 1567 $$\begin{array}{l}
adamc@543 1568 \mt{val} \; \mt{sql\_field} : \mt{otherTabs} ::: \{\{\mt{Type}\}\} \to \mt{otherFields} ::: \{\mt{Type}\} \\
adamc@543 1569 \hspace{.1in} \to \mt{fieldType} ::: \mt{Type} \to \mt{agg} ::: \{\{\mt{Type}\}\} \\
adamc@543 1570 \hspace{.1in} \to \mt{exps} ::: \{\mt{Type}\} \\
adamc@543 1571 \hspace{.1in} \to \mt{tab} :: \mt{Name} \to \mt{field} :: \mt{Name} \\
adamc@543 1572 \hspace{.1in} \to \mt{sql\_exp} \; ([\mt{tab} = [\mt{field} = \mt{fieldType}] \rc \mt{otherFields}] \rc \mt{otherTabs}) \; \mt{agg} \; \mt{exps} \; \mt{fieldType}
adamc@543 1573 \end{array}$$
adamc@543 1574
adamc@544 1575 There is an analogous function for referencing named expressions.
adamc@544 1576 $$\begin{array}{l}
adamc@544 1577 \mt{val} \; \mt{sql\_exp} : \mt{tabs} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{t} ::: \mt{Type} \to \mt{rest} ::: \{\mt{Type}\} \to \mt{nm} :: \mt{Name} \\
adamc@544 1578 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tabs} \; \mt{agg} \; ([\mt{nm} = \mt{t}] \rc \mt{rest}) \; \mt{t}
adamc@544 1579 \end{array}$$
adamc@544 1580
adamc@544 1581 Ur values of appropriate types may be injected into SQL expressions.
adamc@544 1582 $$\begin{array}{l}
adamc@786 1583 \mt{class} \; \mt{sql\_injectable\_prim} \\
adamc@786 1584 \mt{val} \; \mt{sql\_bool} : \mt{sql\_injectable\_prim} \; \mt{bool} \\
adamc@786 1585 \mt{val} \; \mt{sql\_int} : \mt{sql\_injectable\_prim} \; \mt{int} \\
adamc@786 1586 \mt{val} \; \mt{sql\_float} : \mt{sql\_injectable\_prim} \; \mt{float} \\
adamc@786 1587 \mt{val} \; \mt{sql\_string} : \mt{sql\_injectable\_prim} \; \mt{string} \\
adamc@786 1588 \mt{val} \; \mt{sql\_time} : \mt{sql\_injectable\_prim} \; \mt{time} \\
adamc@786 1589 \mt{val} \; \mt{sql\_blob} : \mt{sql\_injectable\_prim} \; \mt{blob} \\
adamc@786 1590 \mt{val} \; \mt{sql\_channel} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{channel} \; \mt{t}) \\
adamc@786 1591 \mt{val} \; \mt{sql\_client} : \mt{sql\_injectable\_prim} \; \mt{client} \\
adamc@786 1592 \\
adamc@544 1593 \mt{class} \; \mt{sql\_injectable} \\
adamc@786 1594 \mt{val} \; \mt{sql\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@786 1595 \mt{val} \; \mt{sql\_option\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; (\mt{option} \; \mt{t}) \\
adamc@786 1596 \\
adamc@544 1597 \mt{val} \; \mt{sql\_inject} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@544 1598 \hspace{.1in} \to \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adamc@544 1599 \end{array}$$
adamc@544 1600
adamc@1123 1601 Additionally, most function-free types may be injected safely, via the $\mt{serialized}$ type family.
adamc@1123 1602 $$\begin{array}{l}
adamc@1123 1603 \mt{con} \; \mt{serialized} :: \mt{Type} \to \mt{Type} \\
adamc@1123 1604 \mt{val} \; \mt{serialize} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{serialized} \; \mt{t} \\
adamc@1123 1605 \mt{val} \; \mt{deserialize} : \mt{t} ::: \mt{Type} \to \mt{serialized} \; \mt{t} \to \mt{t} \\
adamc@1123 1606 \mt{val} \; \mt{sql\_serialized} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{serialized} \; \mt{t})
adamc@1123 1607 \end{array}$$
adamc@1123 1608
adamc@544 1609 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 1610 $$\begin{array}{l}
adamc@544 1611 \mt{val} \; \mt{sql\_is\_null} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544 1612 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; (\mt{option} \; \mt{t}) \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{bool}
adamc@544 1613 \end{array}$$
adamc@544 1614
adamc@559 1615 We have generic nullary, unary, and binary operators.
adamc@544 1616 $$\begin{array}{l}
adamc@544 1617 \mt{con} \; \mt{sql\_nfunc} :: \mt{Type} \to \mt{Type} \\
adamc@544 1618 \mt{val} \; \mt{sql\_current\_timestamp} : \mt{sql\_nfunc} \; \mt{time} \\
adamc@544 1619 \mt{val} \; \mt{sql\_nfunc} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544 1620 \hspace{.1in} \to \mt{sql\_nfunc} \; \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\\end{array}$$
adamc@544 1621
adamc@544 1622 $$\begin{array}{l}
adamc@544 1623 \mt{con} \; \mt{sql\_unary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544 1624 \mt{val} \; \mt{sql\_not} : \mt{sql\_unary} \; \mt{bool} \; \mt{bool} \\
adamc@544 1625 \mt{val} \; \mt{sql\_unary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adamc@544 1626 \hspace{.1in} \to \mt{sql\_unary} \; \mt{arg} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res} \\
adamc@544 1627 \end{array}$$
adamc@544 1628
adamc@544 1629 $$\begin{array}{l}
adamc@544 1630 \mt{con} \; \mt{sql\_binary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544 1631 \mt{val} \; \mt{sql\_and} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544 1632 \mt{val} \; \mt{sql\_or} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544 1633 \mt{val} \; \mt{sql\_binary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg_1} ::: \mt{Type} \to \mt{arg_2} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adamc@544 1634 \hspace{.1in} \to \mt{sql\_binary} \; \mt{arg_1} \; \mt{arg_2} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_1} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_2} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res}
adamc@544 1635 \end{array}$$
adamc@544 1636
adamc@544 1637 $$\begin{array}{l}
adamc@559 1638 \mt{class} \; \mt{sql\_arith} \\
adamc@559 1639 \mt{val} \; \mt{sql\_int\_arith} : \mt{sql\_arith} \; \mt{int} \\
adamc@559 1640 \mt{val} \; \mt{sql\_float\_arith} : \mt{sql\_arith} \; \mt{float} \\
adamc@559 1641 \mt{val} \; \mt{sql\_neg} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_unary} \; \mt{t} \; \mt{t} \\
adamc@559 1642 \mt{val} \; \mt{sql\_plus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1643 \mt{val} \; \mt{sql\_minus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1644 \mt{val} \; \mt{sql\_times} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1645 \mt{val} \; \mt{sql\_div} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1646 \mt{val} \; \mt{sql\_mod} : \mt{sql\_binary} \; \mt{int} \; \mt{int} \; \mt{int}
adamc@559 1647 \end{array}$$
adamc@544 1648
adamc@656 1649 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 1650 $$\begin{array}{l}
adamc@544 1651 \mt{val} \; \mt{sql\_count} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int}
adamc@544 1652 \end{array}$$
adamc@544 1653
adamc@544 1654 $$\begin{array}{l}
adamc@1188 1655 \mt{con} \; \mt{sql\_aggregate} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@1188 1656 \mt{val} \; \mt{sql\_aggregate} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{dom} ::: \mt{Type} \to \mt{ran} ::: \mt{Type} \\
adamc@1188 1657 \hspace{.1in} \to \mt{sql\_aggregate} \; \mt{dom} \; \mt{ran} \to \mt{sql\_exp} \; \mt{agg} \; \mt{agg} \; \mt{exps} \; \mt{dom} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{ran}
adamc@1188 1658 \end{array}$$
adamc@1188 1659
adamc@1188 1660 $$\begin{array}{l}
adamc@1188 1661 \mt{val} \; \mt{sql\_count\_col} : \mt{t} ::: \mt{Type} \to \mt{sql\_aggregate} \; (\mt{option} \; \mt{t}) \; \mt{int}
adamc@544 1662 \end{array}$$
adamc@544 1663
adamc@544 1664 $$\begin{array}{l}
adamc@544 1665 \mt{class} \; \mt{sql\_summable} \\
adamc@544 1666 \mt{val} \; \mt{sql\_summable\_int} : \mt{sql\_summable} \; \mt{int} \\
adamc@544 1667 \mt{val} \; \mt{sql\_summable\_float} : \mt{sql\_summable} \; \mt{float} \\
adamc@1188 1668 \mt{val} \; \mt{sql\_avg} : \mt{t} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{t} \\
adamc@1188 1669 \mt{val} \; \mt{sql\_sum} : \mt{t} ::: \mt{Type} \to \mt{sql\_summable} \mt{t} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{t}
adamc@544 1670 \end{array}$$
adamc@544 1671
adamc@544 1672 $$\begin{array}{l}
adamc@544 1673 \mt{class} \; \mt{sql\_maxable} \\
adamc@544 1674 \mt{val} \; \mt{sql\_maxable\_int} : \mt{sql\_maxable} \; \mt{int} \\
adamc@544 1675 \mt{val} \; \mt{sql\_maxable\_float} : \mt{sql\_maxable} \; \mt{float} \\
adamc@544 1676 \mt{val} \; \mt{sql\_maxable\_string} : \mt{sql\_maxable} \; \mt{string} \\
adamc@544 1677 \mt{val} \; \mt{sql\_maxable\_time} : \mt{sql\_maxable} \; \mt{time} \\
adamc@1188 1678 \mt{val} \; \mt{sql\_max} : \mt{t} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{t} \\
adamc@1188 1679 \mt{val} \; \mt{sql\_min} : \mt{t} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{t}
adamc@544 1680 \end{array}$$
adamc@544 1681
adamc@1193 1682 Any SQL query that returns single columns may be turned into a subquery expression.
adamc@1193 1683
adamc@786 1684 $$\begin{array}{l}
adamc@1193 1685 \mt{val} \; \mt{sql\_subquery} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \\
adamc@1193 1686 \hspace{.1in} \to \mt{sql\_query} \; \mt{tables} \; [] \; [\mt{nm} = \mt{t}] \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adamc@1193 1687 \end{array}$$
adamc@1193 1688
adamc@1193 1689 \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 1690 $$\begin{array}{l}
adamc@1193 1691 \mt{con} \; \mt{sql\_from\_items} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@1193 1692 \mt{val} \; \mt{sql\_from\_table} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1693 \hspace{.1in} \to \mt{t} ::: \mt{Type} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; \mt{t} \; \mt{fs} \to \mt{name} :: \mt{Name} \to \mt{t} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193 1694 \mt{val} \; \mt{sql\_from\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{name} :: \mt{Name} \to \mt{sql\_query} \; \mt{free} \; [] \; \mt{fs} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193 1695 \mt{val} \; \mt{sql\_from\_comma} : \mt{free} ::: \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \to [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193 1696 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adamc@1193 1697 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2}) \\
adamc@1193 1698 \mt{val} \; \mt{sql\_inner\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1699 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193 1700 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adamc@1193 1701 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193 1702 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2})
adamc@786 1703 \end{array}$$
adamc@786 1704
adamc@786 1705 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 1706 $$\begin{array}{l}
adamc@786 1707 \mt{class} \; \mt{nullify} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@786 1708 \mt{val} \; \mt{nullify\_option} : \mt{t} ::: \mt{Type} \to \mt{nullify} \; (\mt{option} \; \mt{t}) \; (\mt{option} \; \mt{t}) \\
adamc@786 1709 \mt{val} \; \mt{nullify\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{nullify} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@786 1710 \end{array}$$
adamc@786 1711
adamc@786 1712 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 1713
adamc@786 1714 $$\begin{array}{l}
adamc@1193 1715 \mt{val} \; \mt{sql\_left\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{(\mt{Type} \times \mt{Type})\}\} \\
adamc@1193 1716 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@786 1717 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\lambda \mt{r} \Rightarrow \$(\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{nullify} \; \mt{p}.1 \; \mt{p}.2) \; \mt{r})) \; \mt{tabs2}) \\
adamc@1193 1718 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \\
adamc@1193 1719 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193 1720 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.2)) \; \mt{tabs2})
adamc@786 1721 \end{array}$$
adamc@786 1722
adamc@544 1723 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 1724 $$\begin{array}{l}
adamc@544 1725 \mt{type} \; \mt{sql\_direction} \\
adamc@544 1726 \mt{val} \; \mt{sql\_asc} : \mt{sql\_direction} \\
adamc@544 1727 \mt{val} \; \mt{sql\_desc} : \mt{sql\_direction} \\
adamc@544 1728 \\
adamc@544 1729 \mt{con} \; \mt{sql\_order\_by} :: \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@544 1730 \mt{val} \; \mt{sql\_order\_by\_Nil} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} :: \{\mt{Type}\} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544 1731 \mt{val} \; \mt{sql\_order\_by\_Cons} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544 1732 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; [] \; \mt{exps} \; \mt{t} \to \mt{sql\_direction} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544 1733 \\
adamc@544 1734 \mt{type} \; \mt{sql\_limit} \\
adamc@544 1735 \mt{val} \; \mt{sql\_no\_limit} : \mt{sql\_limit} \\
adamc@544 1736 \mt{val} \; \mt{sql\_limit} : \mt{int} \to \mt{sql\_limit} \\
adamc@544 1737 \\
adamc@544 1738 \mt{type} \; \mt{sql\_offset} \\
adamc@544 1739 \mt{val} \; \mt{sql\_no\_offset} : \mt{sql\_offset} \\
adamc@544 1740 \mt{val} \; \mt{sql\_offset} : \mt{int} \to \mt{sql\_offset}
adamc@544 1741 \end{array}$$
adamc@544 1742
adamc@545 1743
adamc@545 1744 \subsubsection{DML}
adamc@545 1745
adamc@545 1746 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 1747
adamc@545 1748 $$\begin{array}{l}
adamc@545 1749 \mt{type} \; \mt{dml} \\
adamc@545 1750 \mt{val} \; \mt{dml} : \mt{dml} \to \mt{transaction} \; \mt{unit}
adamc@545 1751 \end{array}$$
adamc@545 1752
adamc@545 1753 Properly-typed records may be used to form $\mt{INSERT}$ commands.
adamc@545 1754 $$\begin{array}{l}
adamc@545 1755 \mt{val} \; \mt{insert} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \\
adamc@658 1756 \hspace{.1in} \to \$(\mt{map} \; (\mt{sql\_exp} \; [] \; [] \; []) \; \mt{fields}) \to \mt{dml}
adamc@545 1757 \end{array}$$
adamc@545 1758
adamc@545 1759 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 1760 $$\begin{array}{l}
adamc@545 1761 \mt{val} \; \mt{update} : \mt{unchanged} ::: \{\mt{Type}\} \to \mt{changed} :: \{\mt{Type}\} \to \lambda [\mt{changed} \sim \mt{unchanged}] \\
adamc@658 1762 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; []) \; \mt{changed}) \\
adamc@545 1763 \hspace{.1in} \to \mt{sql\_table} \; (\mt{changed} \rc \mt{unchanged}) \to \mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545 1764 \end{array}$$
adamc@545 1765
adamc@545 1766 A $\mt{DELETE}$ command is formed from a table and a $\mt{WHERE}$ clause.
adamc@545 1767 $$\begin{array}{l}
adamc@545 1768 \mt{val} \; \mt{delete} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \to \mt{sql\_exp} \; [\mt{T} = \mt{fields}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545 1769 \end{array}$$
adamc@545 1770
adamc@546 1771 \subsubsection{Sequences}
adamc@546 1772
adamc@546 1773 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 1774
adamc@546 1775 $$\begin{array}{l}
adamc@546 1776 \mt{type} \; \mt{sql\_sequence} \\
adamc@1085 1777 \mt{val} \; \mt{nextval} : \mt{sql\_sequence} \to \mt{transaction} \; \mt{int} \\
adamc@1085 1778 \mt{val} \; \mt{setval} : \mt{sql\_sequence} \to \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@546 1779 \end{array}$$
adamc@546 1780
adamc@546 1781
adamc@547 1782 \subsection{XML}
adamc@547 1783
adamc@547 1784 Ur/Web's library contains an encoding of XML syntax and semantic constraints. We make no effort to follow the standards governing XML schemas. Rather, XML fragments are viewed more as values of ML datatypes, and we only track which tags are allowed inside which other tags.
adamc@547 1785
adamc@547 1786 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 1787 $$\begin{array}{l}
adamc@547 1788 \mt{con} \; \mt{xml} :: \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547 1789 \end{array}$$
adamc@547 1790
adamc@547 1791 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 1792 $$\begin{array}{l}
adamc@547 1793 \mt{con} \; \mt{tag} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547 1794 \end{array}$$
adamc@547 1795
adamc@547 1796 Literal text may be injected into XML as ``CDATA.''
adamc@547 1797 $$\begin{array}{l}
adamc@547 1798 \mt{val} \; \mt{cdata} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{string} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adamc@547 1799 \end{array}$$
adamc@547 1800
adamc@547 1801 There is a function for producing an XML tree with a particular tag at its root.
adamc@547 1802 $$\begin{array}{l}
adamc@547 1803 \mt{val} \; \mt{tag} : \mt{attrsGiven} ::: \{\mt{Type}\} \to \mt{attrsAbsent} ::: \{\mt{Type}\} \to \mt{ctxOuter} ::: \{\mt{Unit}\} \to \mt{ctxInner} ::: \{\mt{Unit}\} \\
adamc@547 1804 \hspace{.1in} \to \mt{useOuter} ::: \{\mt{Type}\} \to \mt{useInner} ::: \{\mt{Type}\} \to \mt{bindOuter} ::: \{\mt{Type}\} \to \mt{bindInner} ::: \{\mt{Type}\} \\
adamc@787 1805 \hspace{.1in} \to \lambda [\mt{attrsGiven} \sim \mt{attrsAbsent}] \; [\mt{useOuter} \sim \mt{useInner}] \; [\mt{bindOuter} \sim \mt{bindInner}] \\
adamc@787 1806 \hspace{.1in} \Rightarrow \mt{option} \; \mt{css\_class} \\
adamc@787 1807 \hspace{.1in} \to \$\mt{attrsGiven} \\
adamc@547 1808 \hspace{.1in} \to \mt{tag} \; (\mt{attrsGiven} \rc \mt{attrsAbsent}) \; \mt{ctxOuter} \; \mt{ctxInner} \; \mt{useOuter} \; \mt{bindOuter} \\
adamc@547 1809 \hspace{.1in} \to \mt{xml} \; \mt{ctxInner} \; \mt{useInner} \; \mt{bindInner} \to \mt{xml} \; \mt{ctxOuter} \; (\mt{useOuter} \rc \mt{useInner}) \; (\mt{bindOuter} \rc \mt{bindInner})
adamc@547 1810 \end{array}$$
adamc@787 1811 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.
adamc@547 1812
adamc@547 1813 Two XML fragments may be concatenated.
adamc@547 1814 $$\begin{array}{l}
adamc@547 1815 \mt{val} \; \mt{join} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{bind_1} ::: \{\mt{Type}\} \to \mt{bind_2} ::: \{\mt{Type}\} \\
adamc@547 1816 \hspace{.1in} \to \lambda [\mt{use_1} \sim \mt{bind_1}] \; [\mt{bind_1} \sim \mt{bind_2}] \\
adamc@547 1817 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind_1} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{bind_1}) \; \mt{bind_2} \to \mt{xml} \; \mt{ctx} \; \mt{use_1} \; (\mt{bind_1} \rc \mt{bind_2})
adamc@547 1818 \end{array}$$
adamc@547 1819
adamc@547 1820 Finally, any XML fragment may be updated to ``claim'' to use more form fields than it does.
adamc@547 1821 $$\begin{array}{l}
adamc@547 1822 \mt{val} \; \mt{useMore} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{use_2} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to \lambda [\mt{use_1} \sim \mt{use_2}] \\
adamc@547 1823 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{use_2}) \; \mt{bind}
adamc@547 1824 \end{array}$$
adamc@547 1825
adamc@547 1826 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 1827
adamc@547 1828 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 1829 $$\begin{array}{l}
adamc@547 1830 \mt{val} \; \mt{error} : \mt{t} ::: \mt{Type} \to \mt{xml} \; [\mt{Body}] \; [] \; [] \to \mt{t}
adamc@547 1831 \end{array}$$
adamc@547 1832
adamc@549 1833
adamc@701 1834 \subsection{Client-Side Programming}
adamc@659 1835
adamc@701 1836 Ur/Web supports running code on web browsers, via automatic compilation to JavaScript.
adamc@701 1837
adamc@701 1838 \subsubsection{The Basics}
adamc@701 1839
adamc@701 1840 Clients can open alert dialog boxes, in the usual annoying JavaScript way.
adamc@701 1841 $$\begin{array}{l}
adamc@701 1842 \mt{val} \; \mt{alert} : \mt{string} \to \mt{transaction} \; \mt{unit}
adamc@701 1843 \end{array}$$
adamc@701 1844
adamc@701 1845 Any transaction may be run in a new thread with the $\mt{spawn}$ function.
adamc@701 1846 $$\begin{array}{l}
adamc@701 1847 \mt{val} \; \mt{spawn} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit}
adamc@701 1848 \end{array}$$
adamc@701 1849
adamc@701 1850 The current thread can be paused for at least a specified number of milliseconds.
adamc@701 1851 $$\begin{array}{l}
adamc@701 1852 \mt{val} \; \mt{sleep} : \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@701 1853 \end{array}$$
adamc@701 1854
adamc@787 1855 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 1856 $$\begin{array}{l}
adamc@787 1857 \mt{val} \; \mt{onError} : (\mt{xbody} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787 1858 \mt{val} \; \mt{onFail} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787 1859 \mt{val} \; \mt{onConnectFail} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787 1860 \mt{val} \; \mt{onDisconnect} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787 1861 \mt{val} \; \mt{onServerError} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit}
adamc@787 1862 \end{array}$$
adamc@787 1863
adamc@701 1864 \subsubsection{Functional-Reactive Page Generation}
adamc@701 1865
adamc@701 1866 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 1867
adamc@659 1868 $$\begin{array}{l}
adamc@659 1869 \mt{con} \; \mt{source} :: \mt{Type} \to \mt{Type} \\
adamc@659 1870 \mt{val} \; \mt{source} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{transaction} \; (\mt{source} \; \mt{t}) \\
adamc@659 1871 \mt{val} \; \mt{set} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@659 1872 \mt{val} \; \mt{get} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@659 1873 \end{array}$$
adamc@659 1874
adamc@659 1875 Pure functions over sources are represented in a monad of \emph{signals}.
adamc@659 1876
adamc@659 1877 $$\begin{array}{l}
adamc@659 1878 \mt{con} \; \mt{signal} :: \mt{Type} \to \mt{Type} \\
adamc@659 1879 \mt{val} \; \mt{signal\_monad} : \mt{monad} \; \mt{signal} \\
adamc@659 1880 \mt{val} \; \mt{signal} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{signal} \; \mt{t}
adamc@659 1881 \end{array}$$
adamc@659 1882
adamc@659 1883 A reactive portion of an HTML page is injected with a $\mt{dyn}$ tag, which has a signal-valued attribute $\mt{Signal}$.
adamc@659 1884
adamc@659 1885 $$\begin{array}{l}
adamc@701 1886 \mt{val} \; \mt{dyn} : \mt{use} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to \mt{unit} \\
adamc@701 1887 \hspace{.1in} \to \mt{tag} \; [\mt{Signal} = \mt{signal} \; (\mt{xml} \; \mt{body} \; \mt{use} \; \mt{bind})] \; \mt{body} \; [] \; \mt{use} \; \mt{bind}
adamc@659 1888 \end{array}$$
adamc@659 1889
adamc@701 1890 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 1891
adamc@914 1892 \subsubsection{Remote Procedure Calls}
adamc@914 1893
adamc@914 1894 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 1895
adamc@914 1896 $$\begin{array}{l}
adamc@914 1897 \mt{val} \; \mt{rpc} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@914 1898 \end{array}$$
adamc@914 1899
adamc@701 1900 \subsubsection{Asynchronous Message-Passing}
adamc@701 1901
adamc@701 1902 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 1903
adamc@701 1904 $$\begin{array}{l}
adamc@701 1905 \mt{type} \; \mt{client} \\
adamc@701 1906 \mt{val} \; \mt{self} : \mt{transaction} \; \mt{client}
adamc@701 1907 \end{array}$$
adamc@701 1908
adamc@701 1909 \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 1910
adamc@701 1911 $$\begin{array}{l}
adamc@701 1912 \mt{con} \; \mt{channel} :: \mt{Type} \to \mt{Type} \\
adamc@701 1913 \mt{val} \; \mt{channel} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; (\mt{channel} \; \mt{t}) \\
adamc@701 1914 \mt{val} \; \mt{send} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@701 1915 \mt{val} \; \mt{recv} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@701 1916 \end{array}$$
adamc@701 1917
adamc@701 1918 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 1919
adamc@701 1920 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 1921
adamc@659 1922
adamc@549 1923 \section{Ur/Web Syntax Extensions}
adamc@549 1924
adamc@549 1925 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 1926
adamc@549 1927 \subsection{SQL}
adamc@549 1928
adamc@786 1929 \subsubsection{\label{tables}Table Declarations}
adamc@786 1930
adamc@788 1931 $\mt{table}$ declarations may include constraints, via these grammar rules.
adamc@788 1932 $$\begin{array}{rrcll}
adamc@788 1933 \textrm{Declarations} & d &::=& \mt{table} \; x : c \; [pk[,]] \; cts \\
adamc@788 1934 \textrm{Primary key constraints} & pk &::=& \mt{PRIMARY} \; \mt{KEY} \; K \\
adamc@788 1935 \textrm{Keys} & K &::=& f \mid (f, (f,)^+) \\
adamc@788 1936 \textrm{Constraint sets} & cts &::=& \mt{CONSTRAINT} f \; ct \mid cts, cts \mid \{\{e\}\} \\
adamc@788 1937 \textrm{Constraints} & ct &::=& \mt{UNIQUE} \; K \mid \mt{CHECK} \; E \\
adamc@788 1938 &&& \mid \mt{FOREIGN} \; \mt{KEY} \; K \; \mt{REFERENCES} \; F \; (K) \; [\mt{ON} \; \mt{DELETE} \; pr] \; [\mt{ON} \; \mt{UPDATE} \; pr] \\
adamc@788 1939 \textrm{Foreign tables} & F &::=& x \mid \{\{e\}\} \\
adamc@788 1940 \textrm{Propagation modes} & pr &::=& \mt{NO} \; \mt{ACTION} \mid \mt{RESTRICT} \mid \mt{CASCADE} \mid \mt{SET} \; \mt{NULL}
adamc@788 1941 \end{array}$$
adamc@788 1942
adamc@788 1943 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 1944
adamc@788 1945
adamc@549 1946 \subsubsection{Queries}
adamc@549 1947
adamc@550 1948 Queries $Q$ are added to the rules for expressions $e$.
adamc@550 1949
adamc@549 1950 $$\begin{array}{rrcll}
adamc@550 1951 \textrm{Queries} & Q &::=& (q \; [\mt{ORDER} \; \mt{BY} \; (E \; [o],)^+] \; [\mt{LIMIT} \; N] \; [\mt{OFFSET} \; N]) \\
adamc@1085 1952 \textrm{Pre-queries} & q &::=& \mt{SELECT} \; [\mt{DISTINCT}] \; P \; \mt{FROM} \; F,^+ \; [\mt{WHERE} \; E] \; [\mt{GROUP} \; \mt{BY} \; p,^+] \; [\mt{HAVING} \; E] \\
adamc@1085 1953 &&& \mid q \; R \; q \mid \{\{\{e\}\}\} \\
adamc@549 1954 \textrm{Relational operators} & R &::=& \mt{UNION} \mid \mt{INTERSECT} \mid \mt{EXCEPT}
adamc@549 1955 \end{array}$$
adamc@549 1956
adamc@549 1957 $$\begin{array}{rrcll}
adamc@549 1958 \textrm{Projections} & P &::=& \ast & \textrm{all columns} \\
adamc@549 1959 &&& p,^+ & \textrm{particular columns} \\
adamc@549 1960 \textrm{Pre-projections} & p &::=& t.f & \textrm{one column from a table} \\
adamc@558 1961 &&& t.\{\{c\}\} & \textrm{a record of columns from a table (of kind $\{\mt{Type}\}$)} \\
adamc@1194 1962 &&& E \; [\mt{AS} \; f] & \textrm{expression column} \\
adamc@549 1963 \textrm{Table names} & t &::=& x & \textrm{constant table name (automatically capitalized)} \\
adamc@549 1964 &&& X & \textrm{constant table name} \\
adamc@549 1965 &&& \{\{c\}\} & \textrm{computed table name (of kind $\mt{Name}$)} \\
adamc@549 1966 \textrm{Column names} & f &::=& X & \textrm{constant column name} \\
adamc@549 1967 &&& \{c\} & \textrm{computed column name (of kind $\mt{Name}$)} \\
adamc@549 1968 \textrm{Tables} & T &::=& x & \textrm{table variable, named locally by its own capitalization} \\
adamc@549 1969 &&& x \; \mt{AS} \; t & \textrm{table variable, with local name} \\
adamc@549 1970 &&& \{\{e\}\} \; \mt{AS} \; t & \textrm{computed table expression, with local name} \\
adamc@1085 1971 \textrm{$\mt{FROM}$ items} & F &::=& T \mid \{\{e\}\} \mid F \; J \; \mt{JOIN} \; F \; \mt{ON} \; E \\
adamc@1085 1972 &&& \mid F \; \mt{CROSS} \; \mt{JOIN} \ F \\
adamc@1193 1973 &&& \mid (Q) \; \mt{AS} \; t \\
adamc@1085 1974 \textrm{Joins} & J &::=& [\mt{INNER}] \\
adamc@1085 1975 &&& \mid [\mt{LEFT} \mid \mt{RIGHT} \mid \mt{FULL}] \; [\mt{OUTER}] \\
adamc@549 1976 \textrm{SQL expressions} & E &::=& p & \textrm{column references} \\
adamc@549 1977 &&& X & \textrm{named expression references} \\
adamc@549 1978 &&& \{\{e\}\} & \textrm{injected native Ur expressions} \\
adamc@549 1979 &&& \{e\} & \textrm{computed expressions, probably using $\mt{sql\_exp}$ directly} \\
adamc@549 1980 &&& \mt{TRUE} \mid \mt{FALSE} & \textrm{boolean constants} \\
adamc@549 1981 &&& \ell & \textrm{primitive type literals} \\
adamc@549 1982 &&& \mt{NULL} & \textrm{null value (injection of $\mt{None}$)} \\
adamc@549 1983 &&& E \; \mt{IS} \; \mt{NULL} & \textrm{nullness test} \\
adamc@549 1984 &&& n & \textrm{nullary operators} \\
adamc@549 1985 &&& u \; E & \textrm{unary operators} \\
adamc@549 1986 &&& E \; b \; E & \textrm{binary operators} \\
adamc@549 1987 &&& \mt{COUNT}(\ast) & \textrm{count number of rows} \\
adamc@549 1988 &&& a(E) & \textrm{other aggregate function} \\
adamc@1193 1989 &&& (Q) & \textrm{subquery (must return a single expression column)} \\
adamc@549 1990 &&& (E) & \textrm{explicit precedence} \\
adamc@549 1991 \textrm{Nullary operators} & n &::=& \mt{CURRENT\_TIMESTAMP} \\
adamc@549 1992 \textrm{Unary operators} & u &::=& \mt{NOT} \\
adamc@549 1993 \textrm{Binary operators} & b &::=& \mt{AND} \mid \mt{OR} \mid \neq \mid < \mid \leq \mid > \mid \geq \\
adamc@1188 1994 \textrm{Aggregate functions} & a &::=& \mt{COUNT} \mid \mt{AVG} \mid \mt{SUM} \mid \mt{MIN} \mid \mt{MAX} \\
adamc@550 1995 \textrm{Directions} & o &::=& \mt{ASC} \mid \mt{DESC} \\
adamc@549 1996 \textrm{SQL integer} & N &::=& n \mid \{e\} \\
adamc@549 1997 \end{array}$$
adamc@549 1998
adamc@1085 1999 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 2000
adamc@1194 2001 Unnamed expression columns in $\mt{SELECT}$ clauses are assigned consecutive natural numbers, starting with 1.
adamc@1194 2002
adamc@550 2003 \subsubsection{DML}
adamc@550 2004
adamc@550 2005 DML commands $D$ are added to the rules for expressions $e$.
adamc@550 2006
adamc@550 2007 $$\begin{array}{rrcll}
adamc@550 2008 \textrm{Commands} & D &::=& (\mt{INSERT} \; \mt{INTO} \; T^E \; (f,^+) \; \mt{VALUES} \; (E,^+)) \\
adamc@550 2009 &&& (\mt{UPDATE} \; T^E \; \mt{SET} \; (f = E,)^+ \; \mt{WHERE} \; E) \\
adamc@550 2010 &&& (\mt{DELETE} \; \mt{FROM} \; T^E \; \mt{WHERE} \; E) \\
adamc@550 2011 \textrm{Table expressions} & T^E &::=& x \mid \{\{e\}\}
adamc@550 2012 \end{array}$$
adamc@550 2013
adamc@550 2014 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 2015
adamc@551 2016 \subsection{XML}
adamc@551 2017
adamc@551 2018 XML fragments $L$ are added to the rules for expressions $e$.
adamc@551 2019
adamc@551 2020 $$\begin{array}{rrcll}
adamc@551 2021 \textrm{XML fragments} & L &::=& \texttt{<xml/>} \mid \texttt{<xml>}l^*\texttt{</xml>} \\
adamc@551 2022 \textrm{XML pieces} & l &::=& \textrm{text} & \textrm{cdata} \\
adamc@551 2023 &&& \texttt{<}g\texttt{/>} & \textrm{tag with no children} \\
adamc@551 2024 &&& \texttt{<}g\texttt{>}l^*\texttt{</}x\texttt{>} & \textrm{tag with children} \\
adamc@559 2025 &&& \{e\} & \textrm{computed XML fragment} \\
adamc@559 2026 &&& \{[e]\} & \textrm{injection of an Ur expression, via the $\mt{Top}.\mt{txt}$ function} \\
adamc@551 2027 \textrm{Tag} & g &::=& h \; (x = v)^* \\
adamc@551 2028 \textrm{Tag head} & h &::=& x & \textrm{tag name} \\
adamc@551 2029 &&& h\{c\} & \textrm{constructor parameter} \\
adamc@551 2030 \textrm{Attribute value} & v &::=& \ell & \textrm{literal value} \\
adamc@551 2031 &&& \{e\} & \textrm{computed value} \\
adamc@551 2032 \end{array}$$
adamc@551 2033
adamc@552 2034
adamc@553 2035 \section{The Structure of Web Applications}
adamc@553 2036
adamc@1127 2037 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 2038
adamc@553 2039 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 2040
adamc@553 2041 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 2042
adamc@558 2043 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 2044
adamc@660 2045 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 2046
adamc@789 2047 \medskip
adamc@789 2048
adamc@789 2049 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 2050
adamc@789 2051 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 2052
adamc@553 2053
adamc@897 2054 \section{The Foreign Function Interface}
adamc@897 2055
adamc@897 2056 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 2057
adamc@897 2058 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 2059
adamc@897 2060 \begin{itemize}
adamc@897 2061 \item \texttt{clientOnly Module.ident} registers a value as being allowed only in client-side code.
adamc@897 2062 \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 2063 \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 2064 \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 2065 \item \texttt{include FILE} requests inclusion of a C header file.
adamc@897 2066 \item \texttt{jsFunc Module.ident=name} gives a mapping from an Ur name for a value to a JavaScript name.
adamc@897 2067 \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 2068 \item \texttt{script URL} requests inclusion of a JavaScript source file within application HTML.
adamc@897 2069 \item \texttt{serverOnly Module.ident} registers a value as being allowed only in server-side code.
adamc@897 2070 \end{itemize}
adamc@897 2071
adamc@897 2072 \subsection{Writing C FFI Code}
adamc@897 2073
adamc@897 2074 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 2075
adamc@897 2076 \begin{itemize}
adamc@897 2077 \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 2078 \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 2079 \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 2080 \end{itemize}
adamc@897 2081
adamc@897 2082 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 2083 \begin{itemize}
adamc@897 2084 \item \begin{verbatim}
adamc@897 2085 void uw_error(uw_context, failure_kind, const char *fmt, ...);
adamc@897 2086 \end{verbatim}
adamc@897 2087 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 2088
adamc@897 2089 \item \begin{verbatim}
adamc@897 2090 void uw_push_cleanup(uw_context, void (*func)(void *), void *arg);
adamc@897 2091 void uw_pop_cleanup(uw_context);
adamc@897 2092 \end{verbatim}
adamc@897 2093 Manipulate a stack of actions that should be taken if any kind of error condition arises. Calling the ``pop'' function both removes an action from the stack and executes it.
adamc@897 2094
adamc@897 2095 \item \begin{verbatim}
adamc@897 2096 void *uw_malloc(uw_context, size_t);
adamc@897 2097 \end{verbatim}
adamc@897 2098 A version of \texttt{malloc()} that allocates memory inside a context's heap, which is managed with region allocation. Thus, there is no \texttt{uw\_free()}, but you need to be careful not to keep ad-hoc C pointers to this area of memory.
adamc@897 2099
adamc@897 2100 For performance and correctness reasons, it is usually preferable to use \texttt{uw\_malloc()} instead of \texttt{malloc()}. The former manipulates a local heap that can be kept allocated across page requests, while the latter uses global data structures that may face contention during concurrent execution.
adamc@897 2101
adamc@897 2102 \item \begin{verbatim}
adamc@897 2103 typedef void (*uw_callback)(void *);
adamc@897 2104 void uw_register_transactional(uw_context, void *data, uw_callback commit,
adamc@897 2105 uw_callback rollback, uw_callback free);
adamc@897 2106 \end{verbatim}
adamc@897 2107 All side effects in Ur/Web programs need to be compatible with transactions, such that any set of actions can be undone at any time. Thus, you should not perform actions with non-local side effects directly; instead, register handlers to be called when the current transaction is committed or rolled back. The arguments here give an arbitary piece of data to be passed to callbacks, a function to call on commit, a function to call on rollback, and a function to call afterward in either case to clean up any allocated resources. A rollback handler may be called after the associated commit handler has already been called, if some later part of the commit process fails.
adamc@897 2108
adamc@1085 2109 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 2110
adamc@1085 2111 \item \begin{verbatim}
adamc@1085 2112 void *uw_get_global(uw_context, char *name);
adamc@1085 2113 void uw_set_global(uw_context, char *name, void *data, uw_callback free);
adamc@1085 2114 \end{verbatim}
adamc@1085 2115 Different FFI-based extensions may want to associate their own pieces of data with contexts. The global interface provides a way of doing that, where each extension must come up with its own unique key. The \texttt{free} argument to \texttt{uw\_set\_global()} explains how to deallocate the saved data.
adamc@1085 2116
adamc@897 2117 \end{itemize}
adamc@897 2118
adamc@897 2119 \subsection{Writing JavaScript FFI Code}
adamc@897 2120
adamc@897 2121 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 2122
adamc@897 2123 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 2124
adamc@897 2125 \begin{itemize}
adamc@897 2126 \item Integers, floats, strings, characters, and booleans are represented in the usual JavaScript way.
adamc@985 2127 \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 2128 \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 2129 \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 2130 \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 2131 \end{itemize}
adamc@897 2132
adamc@897 2133 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 2134
adamc@897 2135
adamc@552 2136 \section{Compiler Phases}
adamc@552 2137
adamc@552 2138 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 2139
adamc@552 2140 In this section, we step through the main phases of compilation, noting what consequences each phase has for effective programming.
adamc@552 2141
adamc@552 2142 \subsection{Parse}
adamc@552 2143
adamc@552 2144 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 2145
adamc@552 2146 \subsection{Elaborate}
adamc@552 2147
adamc@552 2148 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 2149
adamc@552 2150 \subsection{Unnest}
adamc@552 2151
adamc@552 2152 Named local function definitions are moved to the top level, to avoid the need to generate closures.
adamc@552 2153
adamc@552 2154 \subsection{Corify}
adamc@552 2155
adamc@552 2156 Module system features are compiled away, through inlining of functor definitions at application sites. Afterward, most abstraction boundaries are broken, facilitating optimization.
adamc@552 2157
adamc@552 2158 \subsection{Especialize}
adamc@552 2159
adamc@552 2160 Functions are specialized to particular argument patterns. This is an important trick for avoiding the need to maintain any closures at runtime.
adamc@552 2161
adamc@552 2162 \subsection{Untangle}
adamc@552 2163
adamc@552 2164 Remove unnecessary mutual recursion, splitting recursive groups into strongly-connected components.
adamc@552 2165
adamc@552 2166 \subsection{Shake}
adamc@552 2167
adamc@552 2168 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 2169
adamc@661 2170 \subsection{Rpcify}
adamc@661 2171
adamc@661 2172 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 2173
adamc@661 2174 \subsection{Untangle, Shake}
adamc@661 2175
adamc@661 2176 Repeat these simplifications.
adamc@661 2177
adamc@553 2178 \subsection{\label{tag}Tag}
adamc@552 2179
adamc@552 2180 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 2181
adamc@552 2182 \subsection{Reduce}
adamc@552 2183
adamc@552 2184 Apply definitional equality rules to simplify the program as much as possible. This effectively includes inlining of every non-recursive definition.
adamc@552 2185
adamc@552 2186 \subsection{Unpoly}
adamc@552 2187
adamc@552 2188 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 2189
adamc@552 2190 \subsection{Specialize}
adamc@552 2191
adamc@558 2192 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 2193
adamc@552 2194 \subsection{Shake}
adamc@552 2195
adamc@558 2196 Here the compiler repeats the earlier Shake phase.
adamc@552 2197
adamc@552 2198 \subsection{Monoize}
adamc@552 2199
adamc@552 2200 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 2201
adamc@552 2202 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 2203
adamc@552 2204 \subsection{MonoOpt}
adamc@552 2205
adamc@552 2206 Simple algebraic laws are applied to simplify the program, focusing especially on efficient imperative generation of HTML pages.
adamc@552 2207
adamc@552 2208 \subsection{MonoUntangle}
adamc@552 2209
adamc@552 2210 Unnecessary mutual recursion is broken up again.
adamc@552 2211
adamc@552 2212 \subsection{MonoReduce}
adamc@552 2213
adamc@552 2214 Equivalents of the definitional equality rules are applied to simplify programs, with inlining again playing a major role.
adamc@552 2215
adamc@552 2216 \subsection{MonoShake, MonoOpt}
adamc@552 2217
adamc@552 2218 Unneeded declarations are removed, and basic optimizations are repeated.
adamc@552 2219
adamc@552 2220 \subsection{Fuse}
adamc@552 2221
adamc@552 2222 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 2223
adamc@552 2224 \subsection{MonoUntangle, MonoShake}
adamc@552 2225
adamc@552 2226 Fuse often creates more opportunities to remove spurious mutual recursion.
adamc@552 2227
adamc@552 2228 \subsection{Pathcheck}
adamc@552 2229
adamc@552 2230 The compiler checks that no link or action name has been used more than once.
adamc@552 2231
adamc@552 2232 \subsection{Cjrize}
adamc@552 2233
adamc@552 2234 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 2235
adamc@552 2236 \subsection{C Compilation and Linking}
adamc@552 2237
adamc@552 2238 The output of the last phase is pretty-printed as C source code and passed to GCC.
adamc@552 2239
adamc@552 2240
adamc@524 2241 \end{document}