annotate doc/manual.tex @ 1172:ad15700272f6

Changing foldRX to mapX
author Adam Chlipala <adamc@hcoop.net>
date Sun, 28 Feb 2010 13:06:10 -0500
parents 7a2a7a8f9cab
children 9d3ccb8b39ac
rev   line source
adamc@524 1 \documentclass{article}
adamc@554 2 \usepackage{fullpage,amsmath,amssymb,proof,url}
adamc@524 3
adamc@524 4 \newcommand{\cd}[1]{\texttt{#1}}
adamc@524 5 \newcommand{\mt}[1]{\mathsf{#1}}
adamc@524 6
adamc@524 7 \newcommand{\rc}{+ \hspace{-.075in} + \;}
adamc@527 8 \newcommand{\rcut}{\; \texttt{--} \;}
adamc@527 9 \newcommand{\rcutM}{\; \texttt{---} \;}
adamc@524 10
adamc@524 11 \begin{document}
adamc@524 12
adamc@524 13 \title{The Ur/Web Manual}
adamc@524 14 \author{Adam Chlipala}
adamc@524 15
adamc@524 16 \maketitle
adamc@524 17
adamc@540 18 \tableofcontents
adamc@540 19
adamc@554 20
adamc@554 21 \section{Introduction}
adamc@554 22
adamc@1160 23 \emph{Ur} is a programming language designed to introduce richer type system features into functional programming in the tradition of ML and Haskell. Ur is functional, pure, statically-typed, and strict. Ur supports a powerful kind of \emph{metaprogramming} based on \emph{type-level computation with type-level records}.
adamc@554 24
adamc@554 25 \emph{Ur/Web} is Ur plus a special standard library and associated rules for parsing and optimization. Ur/Web supports construction of dynamic web applications backed by SQL databases. The signature of the standard library is such that well-typed Ur/Web programs ``don't go wrong'' in a very broad sense. Not only do they not crash during particular page generations, but they also may not:
adamc@554 26
adamc@554 27 \begin{itemize}
adamc@554 28 \item Suffer from any kinds of code-injection attacks
adamc@554 29 \item Return invalid HTML
adamc@554 30 \item Contain dead intra-application links
adamc@554 31 \item Have mismatches between HTML forms and the fields expected by their handlers
adamc@652 32 \item Include client-side code that makes incorrect assumptions about the ``AJAX''-style services that the remote web server provides
adamc@554 33 \item Attempt invalid SQL queries
adamc@652 34 \item Use improper marshaling or unmarshaling in communication with SQL databases or between browsers and web servers
adamc@554 35 \end{itemize}
adamc@554 36
adamc@554 37 This type safety is just the foundation of the Ur/Web methodology. It is also possible to use metaprogramming to build significant application pieces by analysis of type structure. For instance, the demo includes an ML-style functor for building an admin interface for an arbitrary SQL table. The type system guarantees that the admin interface sub-application that comes out will always be free of the above-listed bugs, no matter which well-typed table description is given as input.
adamc@554 38
adamc@652 39 The Ur/Web compiler also produces very efficient object code that does not use garbage collection. These compiled programs will often be even more efficient than what most programmers would bother to write in C. The compiler also generates JavaScript versions of client-side code, with no need to write those parts of applications in a different language.
adamc@554 40
adamc@554 41 \medskip
adamc@554 42
adamc@554 43 The official web site for Ur is:
adamc@554 44 \begin{center}
adamc@554 45 \url{http://www.impredicative.com/ur/}
adamc@554 46 \end{center}
adamc@554 47
adamc@555 48
adamc@555 49 \section{Installation}
adamc@555 50
adamc@555 51 If you are lucky, then the following standard command sequence will suffice for installation, in a directory to which you have unpacked the latest distribution tarball.
adamc@555 52
adamc@555 53 \begin{verbatim}
adamc@555 54 ./configure
adamc@555 55 make
adamc@555 56 sudo make install
adamc@555 57 \end{verbatim}
adamc@555 58
adamc@896 59 Some other packages must be installed for the above to work. At a minimum, you need a standard UNIX shell, with standard UNIX tools like sed and GCC in your execution path; MLton, the whole-program optimizing compiler for Standard ML; and the mhash C library. As of this writing, in the ``testing'' version of Debian Linux, this command will install the more uncommon of these dependencies:
adamc@896 60 \begin{verbatim}
adamc@896 61 apt-get install mlton libmhash-dev
adamc@896 62 \end{verbatim}
adamc@555 63
adamc@896 64 To build programs that access SQL databases, you also need one of these client libraries for supported backends.
adamc@555 65 \begin{verbatim}
adamc@896 66 apt-get install libpq-dev libmysqlclient15-dev libsqlite3-dev
adamc@555 67 \end{verbatim}
adamc@555 68
adamc@555 69 It is also possible to access the modules of the Ur/Web compiler interactively, within Standard ML of New Jersey. To install the prerequisites in Debian testing:
adamc@555 70 \begin{verbatim}
adamc@555 71 apt-get install smlnj libsmlnj-smlnj ml-yacc ml-lpt
adamc@555 72 \end{verbatim}
adamc@555 73
adamc@555 74 To begin an interactive session with the Ur compiler modules, run \texttt{make smlnj}, and then, from within an \texttt{sml} session, run \texttt{CM.make "src/urweb.cm";}. The \texttt{Compiler} module is the main entry point.
adamc@555 75
adamc@896 76 To run an SQL-backed application with a backend besides SQLite, you will probably want to install one of these servers.
adamc@555 77
adamc@555 78 \begin{verbatim}
adamc@896 79 apt-get install postgresql-8.3 mysql-server-5.0
adamc@555 80 \end{verbatim}
adamc@555 81
adamc@555 82 To use the Emacs mode, you must have a modern Emacs installed. We assume that you already know how to do this, if you're in the business of looking for an Emacs mode. The demo generation facility of the compiler will also call out to Emacs to syntax-highlight code, and that process depends on the \texttt{htmlize} module, which can be installed in Debian testing via:
adamc@555 83
adamc@555 84 \begin{verbatim}
adamc@555 85 apt-get install emacs-goodies-el
adamc@555 86 \end{verbatim}
adamc@555 87
adamc@555 88 Even with the right packages installed, configuration and building might fail to work. After you run \texttt{./configure}, you will see the values of some named environment variables printed. You may need to adjust these values to get proper installation for your system. To change a value, store your preferred alternative in the corresponding UNIX environment variable, before running \texttt{./configure}. For instance, here is how to change the list of extra arguments that the Ur/Web compiler will pass to GCC on every invocation.
adamc@555 89
adamc@555 90 \begin{verbatim}
adamc@555 91 GCCARGS=-fnested-functions ./configure
adamc@555 92 \end{verbatim}
adamc@555 93
adamc@1137 94 Some Mac OS X users have reported needing to use this particular GCCARGS value.
adamc@1137 95
adamc@1161 96 Since the author is still getting a handle on the GNU Autotools that provide the build system, you may need to do some further work to get started, especially in environments with significant differences from Linux (where most testing is done). One OS X user reported needing to run \texttt{./configure} with \texttt{CFLAGS=-I/opt/local/include}, since this directory wound up holding a header file associated with a \texttt{libmhash} package installed via DarwinPorts. Further, to get libpq to link, another user reported setting \texttt{GCCARGS="-I/opt/local/include -L/opt/local/lib/postgresql84"}, after creating a symbolic link with \texttt{ln -s /opt/local/include/postgresql84 /opt/local/include/postgresql}.
adamc@555 97
adamc@555 98 The Emacs mode can be set to autoload by adding the following to your \texttt{.emacs} file.
adamc@555 99
adamc@555 100 \begin{verbatim}
adamc@555 101 (add-to-list 'load-path "/usr/local/share/emacs/site-lisp/urweb-mode")
adamc@555 102 (load "urweb-mode-startup")
adamc@555 103 \end{verbatim}
adamc@555 104
adamc@555 105 Change the path in the first line if you chose a different Emacs installation path during configuration.
adamc@555 106
adamc@555 107
adamc@556 108 \section{Command-Line Compiler}
adamc@556 109
adamc@556 110 \subsection{Project Files}
adamc@556 111
adamc@556 112 The basic inputs to the \texttt{urweb} compiler are project files, which have the extension \texttt{.urp}. Here is a sample \texttt{.urp} file.
adamc@556 113
adamc@556 114 \begin{verbatim}
adamc@556 115 database dbname=test
adamc@556 116 sql crud1.sql
adamc@556 117
adamc@556 118 crud
adamc@556 119 crud1
adamc@556 120 \end{verbatim}
adamc@556 121
adamc@556 122 The \texttt{database} line gives the database information string to pass to libpq. In this case, the string only says to connect to a local database named \texttt{test}.
adamc@556 123
adamc@556 124 The \texttt{sql} line asks for an SQL source file to be generated, giving the commands to run to create the tables and sequences that this application expects to find. After building this \texttt{.urp} file, the following commands could be used to initialize the database, assuming that the current UNIX user exists as a Postgres user with database creation privileges:
adamc@556 125
adamc@556 126 \begin{verbatim}
adamc@556 127 createdb test
adamc@556 128 psql -f crud1.sql test
adamc@556 129 \end{verbatim}
adamc@556 130
adamc@1151 131 A blank line separates the named directives from a list of modules to include in the project.
adamc@556 132
adamc@556 133 For each entry \texttt{M} in the module list, the file \texttt{M.urs} is included in the project if it exists, and the file \texttt{M.ur} must exist and is always included.
adamc@556 134
adamc@783 135 Here is the complete list of directive forms. ``FFI'' stands for ``foreign function interface,'' Ur's facility for interaction between Ur programs and C and JavaScript libraries.
adamc@783 136 \begin{itemize}
adamc@783 137 \item \texttt{[allow|deny] [url|mime] PATTERN} registers a rule governing which URLs or MIME types are allowed in this application. The first such rule to match a URL or MIME type determines the verdict. If \texttt{PATTERN} ends in \texttt{*}, it is interpreted as a prefix rule. Otherwise, a string must match it exactly.
adamc@1171 138 \item \texttt{benignEffectful Module.ident} registers an FFI function or transaction as having side effects. The optimizer avoids removing, moving, or duplicating calls to such functions. Every effectful FFI function must be registered, or the optimizer may make invalid transformations. This version of the \texttt{effectful} directive registers that this function has only session-local side effects.
adamc@783 139 \item \texttt{clientOnly Module.ident} registers an FFI function or transaction that may only be run in client browsers.
adamc@783 140 \item \texttt{clientToServer Module.ident} adds FFI type \texttt{Module.ident} to the list of types that are OK to marshal from clients to servers. Values like XML trees and SQL queries are hard to marshal without introducing expensive validity checks, so it's easier to ensure that the server never trusts clients to send such values. The file \texttt{include/urweb.h} shows examples of the C support functions that are required of any type that may be marshalled. These include \texttt{attrify}, \texttt{urlify}, and \texttt{unurlify} functions.
adamc@783 141 \item \texttt{database DBSTRING} sets the string to pass to libpq to open a database connection.
adamc@783 142 \item \texttt{debug} saves some intermediate C files, which is mostly useful to help in debugging the compiler itself.
adamc@783 143 \item \texttt{effectful Module.ident} registers an FFI function or transaction as having side effects. The optimizer avoids removing, moving, or duplicating calls to such functions. Every effectful FFI function must be registered, or the optimizer may make invalid transformations.
adamc@783 144 \item \texttt{exe FILENAME} sets the filename to which to write the output executable. The default for file \texttt{P.urp} is \texttt{P.exe}.
adamc@783 145 \item \texttt{ffi FILENAME} reads the file \texttt{FILENAME.urs} to determine the interface to a new FFI module. The name of the module is calculated from \texttt{FILENAME} in the same way as for normal source files. See the files \texttt{include/urweb.h} and \texttt{src/c/urweb.c} for examples of C headers and implementations for FFI modules. In general, every type or value \texttt{Module.ident} becomes \texttt{uw\_Module\_ident} in C.
adamc@1099 146 \item \texttt{include FILENAME} adds \texttt{FILENAME} to the list of files to be \texttt{\#include}d in C sources. This is most useful for interfacing with new FFI modules.
adamc@783 147 \item \texttt{jsFunc Module.ident=name} gives the JavaScript name of an FFI value.
adamc@1089 148 \item \texttt{library FILENAME} parses \texttt{FILENAME.urp} and merges its contents with the rest of the current file's contents. If \texttt{FILENAME.urp} doesn't exist, the compiler also tries \texttt{FILENAME/lib.urp}.
adamc@783 149 \item \texttt{link FILENAME} adds \texttt{FILENAME} to the list of files to be passed to the GCC linker at the end of compilation. This is most useful for importing extra libraries needed by new FFI modules.
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@783 154 \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@783 155 \item \texttt{serverOnly Module.ident} registers an FFI function or transaction that may only be run on the server.
adamc@1164 156 \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@783 157 \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@783 158 \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@783 159 \end{itemize}
adamc@701 160
adamc@701 161
adamc@557 162 \subsection{Building an Application}
adamc@557 163
adamc@557 164 To compile project \texttt{P.urp}, simply run
adamc@557 165 \begin{verbatim}
adamc@557 166 urweb P
adamc@557 167 \end{verbatim}
adamc@558 168 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@557 169
adamc@557 170 To time how long the different compiler phases run, without generating an executable, run
adamc@557 171 \begin{verbatim}
adamc@557 172 urweb -timing P
adamc@557 173 \end{verbatim}
adamc@557 174
adamc@1086 175 To stop the compilation process after type-checking, run
adamc@1086 176 \begin{verbatim}
adamc@1086 177 urweb -tc P
adamc@1086 178 \end{verbatim}
adamc@1086 179
adamc@1170 180 To output information relevant to CSS stylesheets (and not finish regular compilation), run
adamc@1170 181 \begin{verbatim}
adamc@1170 182 urweb -css P
adamc@1170 183 \end{verbatim}
adamc@1170 184 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 185
adamc@896 186 Some other command-line parameters are accepted:
adamc@896 187 \begin{itemize}
adamc@896 188 \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@896 189
adamc@896 190 \item \texttt{-dbms [postgres|mysql|sqlite]}: Sets the database backend to use.
adamc@896 191 \begin{itemize}
adamc@896 192 \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@896 193
adamc@896 194 A command sequence like this can initialize a Postgres database, using a file \texttt{app.sql} generated by the compiler:
adamc@896 195 \begin{verbatim}
adamc@896 196 createdb app
adamc@896 197 psql -f app.sql app
adamc@896 198 \end{verbatim}
adamc@896 199
adamc@896 200 \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@896 201
adamc@896 202 A command sequence like this can initialize a MySQL database:
adamc@896 203 \begin{verbatim}
adamc@896 204 echo "CREATE DATABASE app" | mysql
adamc@896 205 mysql -D app <app.sql
adamc@896 206 \end{verbatim}
adamc@896 207
adamc@896 208 \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@896 209
adamc@896 210 A command like this can initialize an SQLite database:
adamc@896 211 \begin{verbatim}
adamc@896 212 sqlite3 path/to/database/file <app.sql
adamc@896 213 \end{verbatim}
adamc@896 214 \end{itemize}
adamc@896 215
adamc@896 216 \item \texttt{-output FILENAME}: Set where the application executable is written.
adamc@896 217
adamc@1127 218 \item \texttt{-path NAME VALUE}: Set the value of path variable \texttt{\$NAME} to \texttt{VALUE}, for use in \texttt{.urp} files.
adamc@1127 219
adamc@896 220 \item \texttt{-protocol [http|cgi|fastcgi]}: Set the protocol that the generated application speaks.
adamc@896 221 \begin{itemize}
adamc@896 222 \item \texttt{http}: This is the default. It is for building standalone web servers that can be accessed by web browsers directly.
adamc@896 223
adamc@896 224 \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@896 225
adamc@896 226 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@896 227 \begin{verbatim}
adamc@896 228 ScriptAlias /Hello /path/to/hello.exe
adamc@896 229 \end{verbatim}
adamc@896 230
adamc@1163 231 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 232 \begin{verbatim}
adamc@1163 233 Options +ExecCGI
adamc@1163 234 AddHandler cgi-script .exe
adamc@1163 235 \end{verbatim}
adamc@1163 236
adamc@1163 237 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 238 \begin{verbatim}
adamc@1163 239 prefix /dir/script.exe/
adamc@1163 240 \end{verbatim}
adamc@1163 241
adamc@1163 242 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 243
adamc@1164 244 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 245
adamc@896 246 \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@896 247
adamc@896 248 To configure a FastCGI program with Apache, one could combine the above \texttt{ScriptAlias} line with a line like this:
adamc@896 249 \begin{verbatim}
adamc@896 250 FastCgiServer /path/to/hello.exe -idle-timeout 99999
adamc@896 251 \end{verbatim}
adamc@896 252 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@896 253
adamc@896 254 Here is some lighttpd configuration for the same application.
adamc@896 255 \begin{verbatim}
adamc@896 256 fastcgi.server = (
adamc@896 257 "/Hello/" =>
adamc@896 258 (( "bin-path" => "/path/to/hello.exe",
adamc@896 259 "socket" => "/tmp/hello",
adamc@896 260 "check-local" => "disable",
adamc@896 261 "docroot" => "/",
adamc@896 262 "max-procs" => "1"
adamc@896 263 ))
adamc@896 264 )
adamc@896 265 \end{verbatim}
adamc@896 266 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@896 267
adamc@896 268 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@896 269 \end{itemize}
adamc@896 270
adamc@1127 271 \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 272
adamc@1164 273 \item \texttt{-sigfile PATH}: Same as the \texttt{sigfile} directive in \texttt{.urp} files
adamc@1164 274
adamc@896 275 \item \texttt{-sql FILENAME}: Set where a database set-up SQL script is written.
adamc@1095 276
adamc@1095 277 \item \texttt{-static}: Link the runtime system statically. The default is to link against dynamic libraries.
adamc@896 278 \end{itemize}
adamc@896 279
adamc@556 280
adamc@529 281 \section{Ur Syntax}
adamc@529 282
adamc@784 283 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@524 284
adamc@524 285 \subsection{Lexical Conventions}
adamc@524 286
adamc@524 287 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@524 288
adamc@524 289 \begin{center}
adamc@524 290 \begin{tabular}{rl}
adamc@524 291 \textbf{\LaTeX} & \textbf{ASCII} \\
adamc@524 292 $\to$ & \cd{->} \\
adamc@652 293 $\longrightarrow$ & \cd{-->} \\
adamc@524 294 $\times$ & \cd{*} \\
adamc@524 295 $\lambda$ & \cd{fn} \\
adamc@524 296 $\Rightarrow$ & \cd{=>} \\
adamc@652 297 $\Longrightarrow$ & \cd{==>} \\
adamc@529 298 $\neq$ & \cd{<>} \\
adamc@529 299 $\leq$ & \cd{<=} \\
adamc@529 300 $\geq$ & \cd{>=} \\
adamc@524 301 \\
adamc@524 302 $x$ & Normal textual identifier, not beginning with an uppercase letter \\
adamc@525 303 $X$ & Normal textual identifier, beginning with an uppercase letter \\
adamc@524 304 \end{tabular}
adamc@524 305 \end{center}
adamc@524 306
adamc@525 307 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@524 308
adamc@873 309 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@526 310
adamc@527 311 This version of the manual doesn't include operator precedences; see \texttt{src/urweb.grm} for that.
adamc@527 312
adamc@552 313 \subsection{\label{core}Core Syntax}
adamc@524 314
adamc@524 315 \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@524 316 $$\begin{array}{rrcll}
adamc@524 317 \textrm{Kinds} & \kappa &::=& \mt{Type} & \textrm{proper types} \\
adamc@525 318 &&& \mt{Unit} & \textrm{the trivial constructor} \\
adamc@525 319 &&& \mt{Name} & \textrm{field names} \\
adamc@525 320 &&& \kappa \to \kappa & \textrm{type-level functions} \\
adamc@525 321 &&& \{\kappa\} & \textrm{type-level records} \\
adamc@525 322 &&& (\kappa\times^+) & \textrm{type-level tuples} \\
adamc@652 323 &&& X & \textrm{variable} \\
adamc@652 324 &&& X \longrightarrow k & \textrm{kind-polymorphic type-level function} \\
adamc@529 325 &&& \_\_ & \textrm{wildcard} \\
adamc@525 326 &&& (\kappa) & \textrm{explicit precedence} \\
adamc@524 327 \end{array}$$
adamc@524 328
adamc@524 329 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@524 330 $$\begin{array}{rrcll}
adamc@524 331 \textrm{Explicitness} & ? &::=& :: & \textrm{explicit} \\
adamc@558 332 &&& ::: & \textrm{implicit}
adamc@524 333 \end{array}$$
adamc@524 334
adamc@524 335 \emph{Constructors} are the main class of compile-time-only data. They include proper types and are classified by kinds.
adamc@524 336 $$\begin{array}{rrcll}
adamc@524 337 \textrm{Constructors} & c, \tau &::=& (c) :: \kappa & \textrm{kind annotation} \\
adamc@530 338 &&& \hat{x} & \textrm{constructor variable} \\
adamc@524 339 \\
adamc@525 340 &&& \tau \to \tau & \textrm{function type} \\
adamc@525 341 &&& x \; ? \; \kappa \to \tau & \textrm{polymorphic function type} \\
adamc@652 342 &&& X \longrightarrow \tau & \textrm{kind-polymorphic function type} \\
adamc@525 343 &&& \$ c & \textrm{record type} \\
adamc@524 344 \\
adamc@525 345 &&& c \; c & \textrm{type-level function application} \\
adamc@530 346 &&& \lambda x \; :: \; \kappa \Rightarrow c & \textrm{type-level function abstraction} \\
adamc@524 347 \\
adamc@652 348 &&& X \Longrightarrow c & \textrm{type-level kind-polymorphic function abstraction} \\
adamc@655 349 &&& c [\kappa] & \textrm{type-level kind-polymorphic function application} \\
adamc@652 350 \\
adamc@525 351 &&& () & \textrm{type-level unit} \\
adamc@525 352 &&& \#X & \textrm{field name} \\
adamc@524 353 \\
adamc@525 354 &&& [(c = c)^*] & \textrm{known-length type-level record} \\
adamc@525 355 &&& c \rc c & \textrm{type-level record concatenation} \\
adamc@652 356 &&& \mt{map} & \textrm{type-level record map} \\
adamc@524 357 \\
adamc@558 358 &&& (c,^+) & \textrm{type-level tuple} \\
adamc@525 359 &&& c.n & \textrm{type-level tuple projection ($n \in \mathbb N^+$)} \\
adamc@524 360 \\
adamc@652 361 &&& [c \sim c] \Rightarrow \tau & \textrm{guarded type} \\
adamc@524 362 \\
adamc@529 363 &&& \_ :: \kappa & \textrm{wildcard} \\
adamc@525 364 &&& (c) & \textrm{explicit precedence} \\
adamc@530 365 \\
adamc@530 366 \textrm{Qualified uncapitalized variables} & \hat{x} &::=& x & \textrm{not from a module} \\
adamc@530 367 &&& M.x & \textrm{projection from a module} \\
adamc@525 368 \end{array}$$
adamc@525 369
adamc@655 370 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@655 371
adamc@525 372 Modules of the module system are described by \emph{signatures}.
adamc@525 373 $$\begin{array}{rrcll}
adamc@525 374 \textrm{Signatures} & S &::=& \mt{sig} \; s^* \; \mt{end} & \textrm{constant} \\
adamc@525 375 &&& X & \textrm{variable} \\
adamc@525 376 &&& \mt{functor}(X : S) : S & \textrm{functor} \\
adamc@529 377 &&& S \; \mt{where} \; \mt{con} \; x = c & \textrm{concretizing an abstract constructor} \\
adamc@525 378 &&& M.X & \textrm{projection from a module} \\
adamc@525 379 \\
adamc@525 380 \textrm{Signature items} & s &::=& \mt{con} \; x :: \kappa & \textrm{abstract constructor} \\
adamc@525 381 &&& \mt{con} \; x :: \kappa = c & \textrm{concrete constructor} \\
adamc@528 382 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529 383 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@525 384 &&& \mt{val} \; x : \tau & \textrm{value} \\
adamc@525 385 &&& \mt{structure} \; X : S & \textrm{sub-module} \\
adamc@525 386 &&& \mt{signature} \; X = S & \textrm{sub-signature} \\
adamc@525 387 &&& \mt{include} \; S & \textrm{signature inclusion} \\
adamc@525 388 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@654 389 &&& \mt{class} \; x :: \kappa & \textrm{abstract constructor class} \\
adamc@654 390 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@525 391 \\
adamc@525 392 \textrm{Datatype constructors} & dc &::=& X & \textrm{nullary constructor} \\
adamc@525 393 &&& X \; \mt{of} \; \tau & \textrm{unary constructor} \\
adamc@524 394 \end{array}$$
adamc@524 395
adamc@526 396 \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@526 397 $$\begin{array}{rrcll}
adamc@526 398 \textrm{Patterns} & p &::=& \_ & \textrm{wildcard} \\
adamc@526 399 &&& x & \textrm{variable} \\
adamc@526 400 &&& \ell & \textrm{constant} \\
adamc@526 401 &&& \hat{X} & \textrm{nullary constructor} \\
adamc@526 402 &&& \hat{X} \; p & \textrm{unary constructor} \\
adamc@526 403 &&& \{(x = p,)^*\} & \textrm{rigid record pattern} \\
adamc@526 404 &&& \{(x = p,)^+, \ldots\} & \textrm{flexible record pattern} \\
adamc@852 405 &&& p : \tau & \textrm{type annotation} \\
adamc@527 406 &&& (p) & \textrm{explicit precedence} \\
adamc@526 407 \\
adamc@529 408 \textrm{Qualified capitalized variables} & \hat{X} &::=& X & \textrm{not from a module} \\
adamc@526 409 &&& M.X & \textrm{projection from a module} \\
adamc@526 410 \end{array}$$
adamc@526 411
adamc@527 412 \emph{Expressions} are the main run-time entities, corresponding to both ``expressions'' and ``statements'' in mainstream imperative languages.
adamc@527 413 $$\begin{array}{rrcll}
adamc@527 414 \textrm{Expressions} & e &::=& e : \tau & \textrm{type annotation} \\
adamc@529 415 &&& \hat{x} & \textrm{variable} \\
adamc@529 416 &&& \hat{X} & \textrm{datatype constructor} \\
adamc@527 417 &&& \ell & \textrm{constant} \\
adamc@527 418 \\
adamc@527 419 &&& e \; e & \textrm{function application} \\
adamc@527 420 &&& \lambda x : \tau \Rightarrow e & \textrm{function abstraction} \\
adamc@527 421 &&& e [c] & \textrm{polymorphic function application} \\
adamc@852 422 &&& \lambda [x \; ? \; \kappa] \Rightarrow e & \textrm{polymorphic function abstraction} \\
adamc@655 423 &&& e [\kappa] & \textrm{kind-polymorphic function application} \\
adamc@652 424 &&& X \Longrightarrow e & \textrm{kind-polymorphic function abstraction} \\
adamc@527 425 \\
adamc@527 426 &&& \{(c = e,)^*\} & \textrm{known-length record} \\
adamc@527 427 &&& e.c & \textrm{record field projection} \\
adamc@527 428 &&& e \rc e & \textrm{record concatenation} \\
adamc@527 429 &&& e \rcut c & \textrm{removal of a single record field} \\
adamc@527 430 &&& e \rcutM c & \textrm{removal of multiple record fields} \\
adamc@527 431 \\
adamc@527 432 &&& \mt{let} \; ed^* \; \mt{in} \; e \; \mt{end} & \textrm{local definitions} \\
adamc@527 433 \\
adamc@527 434 &&& \mt{case} \; e \; \mt{of} \; (p \Rightarrow e|)^+ & \textrm{pattern matching} \\
adamc@527 435 \\
adamc@654 436 &&& \lambda [c \sim c] \Rightarrow e & \textrm{guarded expression abstraction} \\
adamc@654 437 &&& e \; ! & \textrm{guarded expression application} \\
adamc@527 438 \\
adamc@527 439 &&& \_ & \textrm{wildcard} \\
adamc@527 440 &&& (e) & \textrm{explicit precedence} \\
adamc@527 441 \\
adamc@527 442 \textrm{Local declarations} & ed &::=& \cd{val} \; x : \tau = e & \textrm{non-recursive value} \\
adamc@527 443 &&& \cd{val} \; \cd{rec} \; (x : \tau = e \; \cd{and})^+ & \textrm{mutually-recursive values} \\
adamc@527 444 \end{array}$$
adamc@527 445
adamc@655 446 As with constructors, we include both abstraction and application for kind polymorphism, but applications are only inferred internally.
adamc@655 447
adamc@528 448 \emph{Declarations} primarily bring new symbols into context.
adamc@528 449 $$\begin{array}{rrcll}
adamc@528 450 \textrm{Declarations} & d &::=& \mt{con} \; x :: \kappa = c & \textrm{constructor synonym} \\
adamc@528 451 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529 452 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@528 453 &&& \mt{val} \; x : \tau = e & \textrm{value} \\
adamc@528 454 &&& \mt{val} \; \cd{rec} \; (x : \tau = e \; \mt{and})^+ & \textrm{mutually-recursive values} \\
adamc@528 455 &&& \mt{structure} \; X : S = M & \textrm{module definition} \\
adamc@528 456 &&& \mt{signature} \; X = S & \textrm{signature definition} \\
adamc@528 457 &&& \mt{open} \; M & \textrm{module inclusion} \\
adamc@528 458 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@528 459 &&& \mt{open} \; \mt{constraints} \; M & \textrm{inclusion of just the constraints from a module} \\
adamc@528 460 &&& \mt{table} \; x : c & \textrm{SQL table} \\
adamc@784 461 &&& \mt{view} \; x : c & \textrm{SQL view} \\
adamc@528 462 &&& \mt{sequence} \; x & \textrm{SQL sequence} \\
adamc@535 463 &&& \mt{cookie} \; x : \tau & \textrm{HTTP cookie} \\
adamc@784 464 &&& \mt{style} \; x : \tau & \textrm{CSS class} \\
adamc@654 465 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@1085 466 &&& \mt{task} \; e = e & \textrm{recurring task} \\
adamc@528 467 \\
adamc@529 468 \textrm{Modules} & M &::=& \mt{struct} \; d^* \; \mt{end} & \textrm{constant} \\
adamc@529 469 &&& X & \textrm{variable} \\
adamc@529 470 &&& M.X & \textrm{projection} \\
adamc@529 471 &&& M(M) & \textrm{functor application} \\
adamc@529 472 &&& \mt{functor}(X : S) : S = M & \textrm{functor abstraction} \\
adamc@528 473 \end{array}$$
adamc@528 474
adamc@528 475 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@527 476
adamc@784 477 We omit some extra possibilities in $\mt{table}$ syntax, deferring them to Section \ref{tables}.
adamc@784 478
adamc@529 479 \subsection{Shorthands}
adamc@529 480
adamc@529 481 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@529 482
adamc@529 483 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@529 484
adamc@529 485 A record type may be written $\{(c = c,)^*\}$, which elaborates to $\$[(c = c,)^*]$.
adamc@529 486
adamc@533 487 The notation $[c_1, \ldots, c_n]$ is shorthand for $[c_1 = (), \ldots, c_n = ()]$.
adamc@533 488
adamc@529 489 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@529 490
adamc@852 491 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@529 492
adamc@529 493 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@529 494
adamc@529 495 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@529 496
adamc@654 497 A signature item or declaration $\mt{class} \; x = \lambda y \Rightarrow c$ may be abbreviated $\mt{class} \; x \; y = c$.
adamc@529 498
adamc@1102 499 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@529 500
adamc@852 501 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@529 502
adamc@852 503 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@852 504
adamc@852 505 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@529 506
adamc@529 507 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@529 508
adamc@852 509 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@852 510
adamc@853 511 A declaration $\mt{table} \; x : \{(c = c,)^*\}$ is elaborated into $\mt{table} \; x : [(c = c,)^*]$.
adamc@529 512
adamc@529 513 The syntax $\mt{where} \; \mt{type}$ is an alternate form of $\mt{where} \; \mt{con}$.
adamc@529 514
adamc@529 515 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@529 516
adamc@529 517 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@529 518
adamc@784 519 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@529 520
adamc@530 521
adamc@530 522 \section{Static Semantics}
adamc@530 523
adamc@530 524 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@530 525
adamc@530 526 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@530 527 \begin{itemize}
adamc@655 528 \item $\Gamma \vdash \kappa$ expresses kind well-formedness.
adamc@530 529 \item $\Gamma \vdash c :: \kappa$ assigns a kind to a constructor in a context.
adamc@530 530 \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@531 531 \item $\Gamma \vdash c \hookrightarrow C$ proves that record constructor $c$ decomposes into set $C$ of field names and record constructors.
adamc@530 532 \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@530 533 \item $\Gamma \vdash e : \tau$ is a standard typing judgment.
adamc@534 534 \item $\Gamma \vdash p \leadsto \Gamma; \tau$ combines typing of patterns with calculation of which new variables they bind.
adamc@537 535 \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@537 536 \item $\Gamma \vdash S \equiv S$ is the signature equivalence judgment.
adamc@536 537 \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@530 538 \item $\Gamma \vdash M : S$ is the module signature checking judgment.
adamc@537 539 \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@539 540 \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@530 541 \end{itemize}
adamc@530 542
adamc@655 543
adamc@655 544 \subsection{Kind Well-Formedness}
adamc@655 545
adamc@655 546 $$\infer{\Gamma \vdash \mt{Type}}{}
adamc@655 547 \quad \infer{\Gamma \vdash \mt{Unit}}{}
adamc@655 548 \quad \infer{\Gamma \vdash \mt{Name}}{}
adamc@655 549 \quad \infer{\Gamma \vdash \kappa_1 \to \kappa_2}{
adamc@655 550 \Gamma \vdash \kappa_1
adamc@655 551 & \Gamma \vdash \kappa_2
adamc@655 552 }
adamc@655 553 \quad \infer{\Gamma \vdash \{\kappa\}}{
adamc@655 554 \Gamma \vdash \kappa
adamc@655 555 }
adamc@655 556 \quad \infer{\Gamma \vdash (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@655 557 \forall i: \Gamma \vdash \kappa_i
adamc@655 558 }$$
adamc@655 559
adamc@655 560 $$\infer{\Gamma \vdash X}{
adamc@655 561 X \in \Gamma
adamc@655 562 }
adamc@655 563 \quad \infer{\Gamma \vdash X \longrightarrow \kappa}{
adamc@655 564 \Gamma, X \vdash \kappa
adamc@655 565 }$$
adamc@655 566
adamc@530 567 \subsection{Kinding}
adamc@530 568
adamc@655 569 We write $[X \mapsto \kappa_1]\kappa_2$ for capture-avoiding substitution of $\kappa_1$ for $X$ in $\kappa_2$.
adamc@655 570
adamc@530 571 $$\infer{\Gamma \vdash (c) :: \kappa :: \kappa}{
adamc@530 572 \Gamma \vdash c :: \kappa
adamc@530 573 }
adamc@530 574 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530 575 x :: \kappa \in \Gamma
adamc@530 576 }
adamc@530 577 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530 578 x :: \kappa = c \in \Gamma
adamc@530 579 }$$
adamc@530 580
adamc@530 581 $$\infer{\Gamma \vdash M.x :: \kappa}{
adamc@537 582 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 583 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = \kappa
adamc@530 584 }
adamc@530 585 \quad \infer{\Gamma \vdash M.x :: \kappa}{
adamc@537 586 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 587 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@530 588 }$$
adamc@530 589
adamc@530 590 $$\infer{\Gamma \vdash \tau_1 \to \tau_2 :: \mt{Type}}{
adamc@530 591 \Gamma \vdash \tau_1 :: \mt{Type}
adamc@530 592 & \Gamma \vdash \tau_2 :: \mt{Type}
adamc@530 593 }
adamc@530 594 \quad \infer{\Gamma \vdash x \; ? \: \kappa \to \tau :: \mt{Type}}{
adamc@530 595 \Gamma, x :: \kappa \vdash \tau :: \mt{Type}
adamc@530 596 }
adamc@655 597 \quad \infer{\Gamma \vdash X \longrightarrow \tau :: \mt{Type}}{
adamc@655 598 \Gamma, X \vdash \tau :: \mt{Type}
adamc@655 599 }
adamc@530 600 \quad \infer{\Gamma \vdash \$c :: \mt{Type}}{
adamc@530 601 \Gamma \vdash c :: \{\mt{Type}\}
adamc@530 602 }$$
adamc@530 603
adamc@530 604 $$\infer{\Gamma \vdash c_1 \; c_2 :: \kappa_2}{
adamc@530 605 \Gamma \vdash c_1 :: \kappa_1 \to \kappa_2
adamc@530 606 & \Gamma \vdash c_2 :: \kappa_1
adamc@530 607 }
adamc@530 608 \quad \infer{\Gamma \vdash \lambda x \; :: \; \kappa_1 \Rightarrow c :: \kappa_1 \to \kappa_2}{
adamc@530 609 \Gamma, x :: \kappa_1 \vdash c :: \kappa_2
adamc@530 610 }$$
adamc@530 611
adamc@655 612 $$\infer{\Gamma \vdash c[\kappa'] :: [X \mapsto \kappa']\kappa}{
adamc@655 613 \Gamma \vdash c :: X \to \kappa
adamc@655 614 & \Gamma \vdash \kappa'
adamc@655 615 }
adamc@655 616 \quad \infer{\Gamma \vdash X \Longrightarrow c :: X \to \kappa}{
adamc@655 617 \Gamma, X \vdash c :: \kappa
adamc@655 618 }$$
adamc@655 619
adamc@530 620 $$\infer{\Gamma \vdash () :: \mt{Unit}}{}
adamc@530 621 \quad \infer{\Gamma \vdash \#X :: \mt{Name}}{}$$
adamc@530 622
adamc@530 623 $$\infer{\Gamma \vdash [\overline{c_i = c'_i}] :: \{\kappa\}}{
adamc@530 624 \forall i: \Gamma \vdash c_i : \mt{Name}
adamc@530 625 & \Gamma \vdash c'_i :: \kappa
adamc@530 626 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@530 627 }
adamc@530 628 \quad \infer{\Gamma \vdash c_1 \rc c_2 :: \{\kappa\}}{
adamc@530 629 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530 630 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@530 631 & \Gamma \vdash c_1 \sim c_2
adamc@530 632 }$$
adamc@530 633
adamc@655 634 $$\infer{\Gamma \vdash \mt{map} :: (\kappa_1 \to \kappa_2) \to \{\kappa_1\} \to \{\kappa_2\}}{}$$
adamc@530 635
adamc@573 636 $$\infer{\Gamma \vdash (\overline c) :: (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@573 637 \forall i: \Gamma \vdash c_i :: \kappa_i
adamc@530 638 }
adamc@573 639 \quad \infer{\Gamma \vdash c.i :: \kappa_i}{
adamc@573 640 \Gamma \vdash c :: (\kappa_1 \times \ldots \times \kappa_n)
adamc@530 641 }$$
adamc@530 642
adamc@655 643 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow \tau :: \mt{Type}}{
adamc@655 644 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530 645 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@655 646 & \Gamma, c_1 \sim c_2 \vdash \tau :: \mt{Type}
adamc@530 647 }$$
adamc@530 648
adamc@531 649 \subsection{Record Disjointness}
adamc@531 650
adamc@531 651 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@558 652 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@558 653 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@558 654 & \forall c'_1 \in C_1, c'_2 \in C_2: \Gamma \vdash c'_1 \sim c'_2
adamc@531 655 }
adamc@531 656 \quad \infer{\Gamma \vdash X \sim X'}{
adamc@531 657 X \neq X'
adamc@531 658 }$$
adamc@531 659
adamc@531 660 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@531 661 c'_1 \sim c'_2 \in \Gamma
adamc@558 662 & \Gamma \vdash c'_1 \hookrightarrow C_1
adamc@558 663 & \Gamma \vdash c'_2 \hookrightarrow C_2
adamc@558 664 & c_1 \in C_1
adamc@558 665 & c_2 \in C_2
adamc@531 666 }$$
adamc@531 667
adamc@531 668 $$\infer{\Gamma \vdash c \hookrightarrow \{c\}}{}
adamc@531 669 \quad \infer{\Gamma \vdash [\overline{c = c'}] \hookrightarrow \{\overline{c}\}}{}
adamc@531 670 \quad \infer{\Gamma \vdash c_1 \rc c_2 \hookrightarrow C_1 \cup C_2}{
adamc@531 671 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@531 672 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@531 673 }
adamc@531 674 \quad \infer{\Gamma \vdash c \hookrightarrow C}{
adamc@531 675 \Gamma \vdash c \equiv c'
adamc@531 676 & \Gamma \vdash c' \hookrightarrow C
adamc@531 677 }
adamc@531 678 \quad \infer{\Gamma \vdash \mt{map} \; f \; c \hookrightarrow C}{
adamc@531 679 \Gamma \vdash c \hookrightarrow C
adamc@531 680 }$$
adamc@531 681
adamc@541 682 \subsection{\label{definitional}Definitional Equality}
adamc@532 683
adamc@655 684 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@532 685
adamc@532 686 $$\infer{\Gamma \vdash c \equiv c}{}
adamc@532 687 \quad \infer{\Gamma \vdash c_1 \equiv c_2}{
adamc@532 688 \Gamma \vdash c_2 \equiv c_1
adamc@532 689 }
adamc@532 690 \quad \infer{\Gamma \vdash c_1 \equiv c_3}{
adamc@532 691 \Gamma \vdash c_1 \equiv c_2
adamc@532 692 & \Gamma \vdash c_2 \equiv c_3
adamc@532 693 }
adamc@532 694 \quad \infer{\Gamma \vdash \mathcal C[c_1] \equiv \mathcal C[c_2]}{
adamc@532 695 \Gamma \vdash c_1 \equiv c_2
adamc@532 696 }$$
adamc@532 697
adamc@532 698 $$\infer{\Gamma \vdash x \equiv c}{
adamc@532 699 x :: \kappa = c \in \Gamma
adamc@532 700 }
adamc@532 701 \quad \infer{\Gamma \vdash M.x \equiv c}{
adamc@537 702 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 703 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@532 704 }
adamc@532 705 \quad \infer{\Gamma \vdash (\overline c).i \equiv c_i}{}$$
adamc@532 706
adamc@532 707 $$\infer{\Gamma \vdash (\lambda x :: \kappa \Rightarrow c) \; c' \equiv [x \mapsto c'] c}{}
adamc@655 708 \quad \infer{\Gamma \vdash (X \Longrightarrow c) [\kappa] \equiv [X \mapsto \kappa] c}{}$$
adamc@655 709
adamc@655 710 $$\infer{\Gamma \vdash c_1 \rc c_2 \equiv c_2 \rc c_1}{}
adamc@532 711 \quad \infer{\Gamma \vdash c_1 \rc (c_2 \rc c_3) \equiv (c_1 \rc c_2) \rc c_3}{}$$
adamc@532 712
adamc@532 713 $$\infer{\Gamma \vdash [] \rc c \equiv c}{}
adamc@532 714 \quad \infer{\Gamma \vdash [\overline{c_1 = c'_1}] \rc [\overline{c_2 = c'_2}] \equiv [\overline{c_1 = c'_1}, \overline{c_2 = c'_2}]}{}$$
adamc@532 715
adamc@655 716 $$\infer{\Gamma \vdash \mt{map} \; f \; [] \equiv []}{}
adamc@655 717 \quad \infer{\Gamma \vdash \mt{map} \; f \; ([c_1 = c_2] \rc c) \equiv [c_1 = f \; c_2] \rc \mt{map} \; f \; c}{}$$
adamc@532 718
adamc@532 719 $$\infer{\Gamma \vdash \mt{map} \; (\lambda x \Rightarrow x) \; c \equiv c}{}
adamc@655 720 \quad \infer{\Gamma \vdash \mt{map} \; f \; (\mt{map} \; f' \; c)
adamc@655 721 \equiv \mt{map} \; (\lambda x \Rightarrow f \; (f' \; x)) \; c}{}$$
adamc@532 722
adamc@532 723 $$\infer{\Gamma \vdash \mt{map} \; f \; (c_1 \rc c_2) \equiv \mt{map} \; f \; c_1 \rc \mt{map} \; f \; c_2}{}$$
adamc@531 724
adamc@534 725 \subsection{Expression Typing}
adamc@533 726
adamc@873 727 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@533 728
adamc@533 729 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@533 730
adamc@533 731 $$\infer{\Gamma \vdash e : \tau : \tau}{
adamc@533 732 \Gamma \vdash e : \tau
adamc@533 733 }
adamc@533 734 \quad \infer{\Gamma \vdash e : \tau}{
adamc@533 735 \Gamma \vdash e : \tau'
adamc@533 736 & \Gamma \vdash \tau' \equiv \tau
adamc@533 737 }
adamc@533 738 \quad \infer{\Gamma \vdash \ell : T(\ell)}{}$$
adamc@533 739
adamc@533 740 $$\infer{\Gamma \vdash x : \mathcal I(\tau)}{
adamc@533 741 x : \tau \in \Gamma
adamc@533 742 }
adamc@533 743 \quad \infer{\Gamma \vdash M.x : \mathcal I(\tau)}{
adamc@537 744 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 745 & \mt{proj}(M, \overline{s}, \mt{val} \; x) = \tau
adamc@533 746 }
adamc@533 747 \quad \infer{\Gamma \vdash X : \mathcal I(\tau)}{
adamc@533 748 X : \tau \in \Gamma
adamc@533 749 }
adamc@533 750 \quad \infer{\Gamma \vdash M.X : \mathcal I(\tau)}{
adamc@537 751 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 752 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \tau
adamc@533 753 }$$
adamc@533 754
adamc@533 755 $$\infer{\Gamma \vdash e_1 \; e_2 : \tau_2}{
adamc@533 756 \Gamma \vdash e_1 : \tau_1 \to \tau_2
adamc@533 757 & \Gamma \vdash e_2 : \tau_1
adamc@533 758 }
adamc@533 759 \quad \infer{\Gamma \vdash \lambda x : \tau_1 \Rightarrow e : \tau_1 \to \tau_2}{
adamc@533 760 \Gamma, x : \tau_1 \vdash e : \tau_2
adamc@533 761 }$$
adamc@533 762
adamc@533 763 $$\infer{\Gamma \vdash e [c] : [x \mapsto c]\tau}{
adamc@533 764 \Gamma \vdash e : x :: \kappa \to \tau
adamc@533 765 & \Gamma \vdash c :: \kappa
adamc@533 766 }
adamc@852 767 \quad \infer{\Gamma \vdash \lambda [x \; ? \; \kappa] \Rightarrow e : x \; ? \; \kappa \to \tau}{
adamc@533 768 \Gamma, x :: \kappa \vdash e : \tau
adamc@533 769 }$$
adamc@533 770
adamc@655 771 $$\infer{\Gamma \vdash e [\kappa] : [X \mapsto \kappa]\tau}{
adamc@655 772 \Gamma \vdash e : X \longrightarrow \tau
adamc@655 773 & \Gamma \vdash \kappa
adamc@655 774 }
adamc@655 775 \quad \infer{\Gamma \vdash X \Longrightarrow e : X \longrightarrow \tau}{
adamc@655 776 \Gamma, X \vdash e : \tau
adamc@655 777 }$$
adamc@655 778
adamc@533 779 $$\infer{\Gamma \vdash \{\overline{c = e}\} : \{\overline{c : \tau}\}}{
adamc@533 780 \forall i: \Gamma \vdash c_i :: \mt{Name}
adamc@533 781 & \Gamma \vdash e_i : \tau_i
adamc@533 782 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@533 783 }
adamc@533 784 \quad \infer{\Gamma \vdash e.c : \tau}{
adamc@533 785 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533 786 }
adamc@533 787 \quad \infer{\Gamma \vdash e_1 \rc e_2 : \$(c_1 \rc c_2)}{
adamc@533 788 \Gamma \vdash e_1 : \$c_1
adamc@533 789 & \Gamma \vdash e_2 : \$c_2
adamc@573 790 & \Gamma \vdash c_1 \sim c_2
adamc@533 791 }$$
adamc@533 792
adamc@533 793 $$\infer{\Gamma \vdash e \rcut c : \$c'}{
adamc@533 794 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533 795 }
adamc@533 796 \quad \infer{\Gamma \vdash e \rcutM c : \$c'}{
adamc@533 797 \Gamma \vdash e : \$(c \rc c')
adamc@533 798 }$$
adamc@533 799
adamc@533 800 $$\infer{\Gamma \vdash \mt{let} \; \overline{ed} \; \mt{in} \; e \; \mt{end} : \tau}{
adamc@533 801 \Gamma \vdash \overline{ed} \leadsto \Gamma'
adamc@533 802 & \Gamma' \vdash e : \tau
adamc@533 803 }
adamc@533 804 \quad \infer{\Gamma \vdash \mt{case} \; e \; \mt{of} \; \overline{p \Rightarrow e} : \tau}{
adamc@533 805 \forall i: \Gamma \vdash p_i \leadsto \Gamma_i, \tau'
adamc@533 806 & \Gamma_i \vdash e_i : \tau
adamc@533 807 }$$
adamc@533 808
adamc@573 809 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow e : \lambda [c_1 \sim c_2] \Rightarrow \tau}{
adamc@533 810 \Gamma \vdash c_1 :: \{\kappa\}
adamc@655 811 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@533 812 & \Gamma, c_1 \sim c_2 \vdash e : \tau
adamc@662 813 }
adamc@662 814 \quad \infer{\Gamma \vdash e \; ! : \tau}{
adamc@662 815 \Gamma \vdash e : [c_1 \sim c_2] \Rightarrow \tau
adamc@662 816 & \Gamma \vdash c_1 \sim c_2
adamc@533 817 }$$
adamc@533 818
adamc@534 819 \subsection{Pattern Typing}
adamc@534 820
adamc@534 821 $$\infer{\Gamma \vdash \_ \leadsto \Gamma; \tau}{}
adamc@534 822 \quad \infer{\Gamma \vdash x \leadsto \Gamma, x : \tau; \tau}{}
adamc@534 823 \quad \infer{\Gamma \vdash \ell \leadsto \Gamma; T(\ell)}{}$$
adamc@534 824
adamc@534 825 $$\infer{\Gamma \vdash X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534 826 X : \overline{x ::: \mt{Type}} \to \tau \in \Gamma
adamc@534 827 & \textrm{$\tau$ not a function type}
adamc@534 828 }
adamc@534 829 \quad \infer{\Gamma \vdash X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534 830 X : \overline{x ::: \mt{Type}} \to \tau'' \to \tau \in \Gamma
adamc@534 831 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534 832 }$$
adamc@534 833
adamc@534 834 $$\infer{\Gamma \vdash M.X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537 835 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 836 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau
adamc@534 837 & \textrm{$\tau$ not a function type}
adamc@534 838 }$$
adamc@534 839
adamc@534 840 $$\infer{\Gamma \vdash M.X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537 841 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 842 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau'' \to \tau
adamc@534 843 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534 844 }$$
adamc@534 845
adamc@534 846 $$\infer{\Gamma \vdash \{\overline{x = p}\} \leadsto \Gamma_n; \{\overline{x = \tau}\}}{
adamc@534 847 \Gamma_0 = \Gamma
adamc@534 848 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534 849 }
adamc@534 850 \quad \infer{\Gamma \vdash \{\overline{x = p}, \ldots\} \leadsto \Gamma_n; \$([\overline{x = \tau}] \rc c)}{
adamc@534 851 \Gamma_0 = \Gamma
adamc@534 852 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534 853 }$$
adamc@534 854
adamc@852 855 $$\infer{\Gamma \vdash p : \tau \leadsto \Gamma'; \tau}{
adamc@852 856 \Gamma \vdash p \leadsto \Gamma'; \tau'
adamc@852 857 & \Gamma \vdash \tau' \equiv \tau
adamc@852 858 }$$
adamc@852 859
adamc@535 860 \subsection{Declaration Typing}
adamc@535 861
adamc@535 862 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@535 863
adamc@655 864 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@535 865
adamc@558 866 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@537 867 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@535 868
adamc@535 869 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535 870 \quad \infer{\Gamma \vdash d, \overline{d} \leadsto \Gamma''}{
adamc@535 871 \Gamma \vdash d \leadsto \Gamma'
adamc@535 872 & \Gamma' \vdash \overline{d} \leadsto \Gamma''
adamc@535 873 }$$
adamc@535 874
adamc@535 875 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@535 876 \Gamma \vdash c :: \kappa
adamc@535 877 }
adamc@535 878 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@535 879 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@535 880 }$$
adamc@535 881
adamc@535 882 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537 883 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 884 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@535 885 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@535 886 }$$
adamc@535 887
adamc@535 888 $$\infer{\Gamma \vdash \mt{val} \; x : \tau = e \leadsto \Gamma, x : \tau}{
adamc@535 889 \Gamma \vdash e : \tau
adamc@535 890 }$$
adamc@535 891
adamc@535 892 $$\infer{\Gamma \vdash \mt{val} \; \mt{rec} \; \overline{x : \tau = e} \leadsto \Gamma, \overline{x : \tau}}{
adamc@535 893 \forall i: \Gamma, \overline{x : \tau} \vdash e_i : \tau_i
adamc@535 894 & \textrm{$e_i$ starts with an expression $\lambda$, optionally preceded by constructor and disjointness $\lambda$s}
adamc@535 895 }$$
adamc@535 896
adamc@535 897 $$\infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : S}{
adamc@535 898 \Gamma \vdash M : S
adamc@558 899 & \textrm{ $M$ not a constant or application}
adamc@535 900 }
adamc@558 901 \quad \infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : \mt{selfify}(X, \overline{s})}{
adamc@558 902 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@539 903 }$$
adamc@539 904
adamc@539 905 $$\infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@535 906 \Gamma \vdash S
adamc@535 907 }$$
adamc@535 908
adamc@537 909 $$\infer{\Gamma \vdash \mt{open} \; M \leadsto \Gamma, \mathcal O(M, \overline{s})}{
adamc@537 910 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535 911 }$$
adamc@535 912
adamc@535 913 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma}{
adamc@535 914 \Gamma \vdash c_1 :: \{\kappa\}
adamc@535 915 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@535 916 & \Gamma \vdash c_1 \sim c_2
adamc@535 917 }
adamc@537 918 \quad \infer{\Gamma \vdash \mt{open} \; \mt{constraints} \; M \leadsto \Gamma, \mathcal O_c(M, \overline{s})}{
adamc@537 919 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535 920 }$$
adamc@535 921
adamc@784 922 $$\infer{\Gamma \vdash \mt{table} \; x : c \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_table} \; c \; []}{
adamc@535 923 \Gamma \vdash c :: \{\mt{Type}\}
adamc@535 924 }
adamc@784 925 \quad \infer{\Gamma \vdash \mt{view} \; x : c \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_view} \; c}{
adamc@784 926 \Gamma \vdash c :: \{\mt{Type}\}
adamc@784 927 }$$
adamc@784 928
adamc@784 929 $$\infer{\Gamma \vdash \mt{sequence} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_sequence}}{}$$
adamc@535 930
adamc@535 931 $$\infer{\Gamma \vdash \mt{cookie} \; x : \tau \leadsto \Gamma, x : \mt{Basis}.\mt{http\_cookie} \; \tau}{
adamc@535 932 \Gamma \vdash \tau :: \mt{Type}
adamc@784 933 }
adamc@784 934 \quad \infer{\Gamma \vdash \mt{style} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{css\_class}}{}$$
adamc@535 935
adamc@1085 936 $$\infer{\Gamma \vdash \mt{task} \; e_1 = e_2 \leadsto \Gamma}{
adamc@1085 937 \Gamma \vdash e_1 :: \mt{Basis}.\mt{task\_kind}
adamc@1085 938 & \Gamma \vdash e_2 :: \mt{Basis}.\mt{transaction} \; \{\}
adamc@1085 939 }$$
adamc@1085 940
adamc@784 941 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784 942 \Gamma \vdash c :: \kappa
adamc@535 943 }$$
adamc@535 944
adamc@535 945 $$\infer{\overline{y}; x; \Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535 946 \quad \infer{\overline{y}; x; \Gamma \vdash X \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to x \; \overline{y}}{
adamc@535 947 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535 948 }
adamc@535 949 \quad \infer{\overline{y}; x; \Gamma \vdash X \; \mt{of} \; \tau \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to \tau \to x \; \overline{y}}{
adamc@535 950 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535 951 }$$
adamc@535 952
adamc@537 953 \subsection{Signature Item Typing}
adamc@537 954
adamc@537 955 We appeal to a signature item analogue of the $\mathcal O$ function from the last subsection.
adamc@537 956
adamc@537 957 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@537 958 \quad \infer{\Gamma \vdash s, \overline{s} \leadsto \Gamma''}{
adamc@537 959 \Gamma \vdash s \leadsto \Gamma'
adamc@537 960 & \Gamma' \vdash \overline{s} \leadsto \Gamma''
adamc@537 961 }$$
adamc@537 962
adamc@537 963 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}
adamc@537 964 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@537 965 \Gamma \vdash c :: \kappa
adamc@537 966 }
adamc@537 967 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@537 968 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@537 969 }$$
adamc@537 970
adamc@537 971 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537 972 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 973 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 974 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@537 975 }$$
adamc@537 976
adamc@537 977 $$\infer{\Gamma \vdash \mt{val} \; x : \tau \leadsto \Gamma, x : \tau}{
adamc@537 978 \Gamma \vdash \tau :: \mt{Type}
adamc@537 979 }$$
adamc@537 980
adamc@537 981 $$\infer{\Gamma \vdash \mt{structure} \; X : S \leadsto \Gamma, X : S}{
adamc@537 982 \Gamma \vdash S
adamc@537 983 }
adamc@537 984 \quad \infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@537 985 \Gamma \vdash S
adamc@537 986 }$$
adamc@537 987
adamc@537 988 $$\infer{\Gamma \vdash \mt{include} \; S \leadsto \Gamma, \mathcal O(\overline{s})}{
adamc@537 989 \Gamma \vdash S
adamc@537 990 & \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 991 }$$
adamc@537 992
adamc@537 993 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma, c_1 \sim c_2}{
adamc@537 994 \Gamma \vdash c_1 :: \{\kappa\}
adamc@537 995 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@537 996 }$$
adamc@537 997
adamc@784 998 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784 999 \Gamma \vdash c :: \kappa
adamc@537 1000 }
adamc@784 1001 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}$$
adamc@537 1002
adamc@536 1003 \subsection{Signature Compatibility}
adamc@536 1004
adamc@558 1005 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 1006
adamc@537 1007 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 1008
adamc@536 1009 $$\infer{\Gamma \vdash S \equiv S}{}
adamc@536 1010 \quad \infer{\Gamma \vdash S_1 \equiv S_2}{
adamc@536 1011 \Gamma \vdash S_2 \equiv S_1
adamc@536 1012 }
adamc@536 1013 \quad \infer{\Gamma \vdash X \equiv S}{
adamc@536 1014 X = S \in \Gamma
adamc@536 1015 }
adamc@536 1016 \quad \infer{\Gamma \vdash M.X \equiv S}{
adamc@537 1017 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1018 & \mt{proj}(M, \overline{s}, \mt{signature} \; X) = S
adamc@536 1019 }$$
adamc@536 1020
adamc@536 1021 $$\infer{\Gamma \vdash S \; \mt{where} \; \mt{con} \; x = c \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa = c \; \overline{s_2} \; \mt{end}}{
adamc@536 1022 \Gamma \vdash S \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa \; \overline{s_2} \; \mt{end}
adamc@536 1023 & \Gamma \vdash c :: \kappa
adamc@537 1024 }
adamc@537 1025 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s^1} \; \mt{include} \; S \; \overline{s^2} \; \mt{end} \equiv \mt{sig} \; \overline{s^1} \; \overline{s} \; \overline{s^2} \; \mt{end}}{
adamc@537 1026 \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@536 1027 }$$
adamc@536 1028
adamc@536 1029 $$\infer{\Gamma \vdash S_1 \leq S_2}{
adamc@536 1030 \Gamma \vdash S_1 \equiv S_2
adamc@536 1031 }
adamc@536 1032 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \mt{end}}{}
adamc@537 1033 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; s' \; \overline{s'} \; \mt{end}}{
adamc@537 1034 \Gamma \vdash \overline{s} \leq s'
adamc@537 1035 & \Gamma \vdash s' \leadsto \Gamma'
adamc@537 1036 & \Gamma' \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \overline{s'} \; \mt{end}
adamc@537 1037 }$$
adamc@537 1038
adamc@537 1039 $$\infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537 1040 \Gamma \vdash s \leq s'
adamc@537 1041 }
adamc@537 1042 \quad \infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537 1043 \Gamma \vdash s \leadsto \Gamma'
adamc@537 1044 & \Gamma' \vdash \overline{s} \leq s'
adamc@536 1045 }$$
adamc@536 1046
adamc@536 1047 $$\infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 \leq \mt{functor} (X : S'_1) : S'_2}{
adamc@536 1048 \Gamma \vdash S'_1 \leq S_1
adamc@536 1049 & \Gamma, X : S'_1 \vdash S_2 \leq S'_2
adamc@536 1050 }$$
adamc@536 1051
adamc@537 1052 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@537 1053 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}
adamc@558 1054 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type}}{}$$
adamc@537 1055
adamc@537 1056 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(y)} \to \mt{Type}}{
adamc@537 1057 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1058 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1059 }$$
adamc@537 1060
adamc@784 1061 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@784 1062 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}$$
adamc@537 1063
adamc@537 1064 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \mt{\kappa} = c_2}{
adamc@537 1065 \Gamma \vdash c_1 \equiv c_2
adamc@537 1066 }
adamc@784 1067 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \kappa = c_2}{
adamc@537 1068 \Gamma \vdash c_1 \equiv c_2
adamc@537 1069 }$$
adamc@537 1070
adamc@537 1071 $$\infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537 1072 \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1073 }$$
adamc@537 1074
adamc@537 1075 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537 1076 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1077 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1078 & \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1079 }$$
adamc@537 1080
adamc@537 1081 $$\infer{\Gamma \vdash \cdot \leq \cdot}{}
adamc@537 1082 \quad \infer{\Gamma \vdash X; \overline{dc} \leq X; \overline{dc'}}{
adamc@537 1083 \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1084 }
adamc@537 1085 \quad \infer{\Gamma \vdash X \; \mt{of} \; \tau_1; \overline{dc} \leq X \; \mt{of} \; \tau_2; \overline{dc'}}{
adamc@537 1086 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537 1087 & \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1088 }$$
adamc@537 1089
adamc@537 1090 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x = \mt{datatype} \; M'.z'}{
adamc@537 1091 \Gamma \vdash M.z \equiv M'.z'
adamc@537 1092 }$$
adamc@537 1093
adamc@537 1094 $$\infer{\Gamma \vdash \mt{val} \; x : \tau_1 \leq \mt{val} \; x : \tau_2}{
adamc@537 1095 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537 1096 }
adamc@537 1097 \quad \infer{\Gamma \vdash \mt{structure} \; X : S_1 \leq \mt{structure} \; X : S_2}{
adamc@537 1098 \Gamma \vdash S_1 \leq S_2
adamc@537 1099 }
adamc@537 1100 \quad \infer{\Gamma \vdash \mt{signature} \; X = S_1 \leq \mt{signature} \; X = S_2}{
adamc@537 1101 \Gamma \vdash S_1 \leq S_2
adamc@537 1102 & \Gamma \vdash S_2 \leq S_1
adamc@537 1103 }$$
adamc@537 1104
adamc@537 1105 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leq \mt{constraint} \; c'_1 \sim c'_2}{
adamc@537 1106 \Gamma \vdash c_1 \equiv c'_1
adamc@537 1107 & \Gamma \vdash c_2 \equiv c'_2
adamc@537 1108 }$$
adamc@537 1109
adamc@655 1110 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{class} \; x :: \kappa}{}
adamc@655 1111 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{class} \; x :: \kappa}{}
adamc@655 1112 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{class} \; x :: \kappa = c_2}{
adamc@537 1113 \Gamma \vdash c_1 \equiv c_2
adamc@537 1114 }$$
adamc@537 1115
adamc@538 1116 \subsection{Module Typing}
adamc@538 1117
adamc@538 1118 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 1119
adamc@538 1120 $$\infer{\Gamma \vdash M : S}{
adamc@538 1121 \Gamma \vdash M : S'
adamc@538 1122 & \Gamma \vdash S' \leq S
adamc@538 1123 }
adamc@538 1124 \quad \infer{\Gamma \vdash \mt{struct} \; \overline{d} \; \mt{end} : \mt{sig} \; \mt{sigOf}(\overline{d}) \; \mt{end}}{
adamc@538 1125 \Gamma \vdash \overline{d} \leadsto \Gamma'
adamc@538 1126 }
adamc@538 1127 \quad \infer{\Gamma \vdash X : S}{
adamc@538 1128 X : S \in \Gamma
adamc@538 1129 }$$
adamc@538 1130
adamc@538 1131 $$\infer{\Gamma \vdash M.X : S}{
adamc@538 1132 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@538 1133 & \mt{proj}(M, \overline{s}, \mt{structure} \; X) = S
adamc@538 1134 }$$
adamc@538 1135
adamc@538 1136 $$\infer{\Gamma \vdash M_1(M_2) : [X \mapsto M_2]S_2}{
adamc@538 1137 \Gamma \vdash M_1 : \mt{functor}(X : S_1) : S_2
adamc@538 1138 & \Gamma \vdash M_2 : S_1
adamc@538 1139 }
adamc@538 1140 \quad \infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 = M : \mt{functor} (X : S_1) : S_2}{
adamc@538 1141 \Gamma \vdash S_1
adamc@538 1142 & \Gamma, X : S_1 \vdash S_2
adamc@538 1143 & \Gamma, X : S_1 \vdash M : S_2
adamc@538 1144 }$$
adamc@538 1145
adamc@538 1146 \begin{eqnarray*}
adamc@538 1147 \mt{sigOf}(\cdot) &=& \cdot \\
adamc@538 1148 \mt{sigOf}(s \; \overline{s'}) &=& \mt{sigOf}(s) \; \mt{sigOf}(\overline{s'}) \\
adamc@538 1149 \\
adamc@538 1150 \mt{sigOf}(\mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@538 1151 \mt{sigOf}(\mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \overline{dc} \\
adamc@538 1152 \mt{sigOf}(\mt{datatype} \; x = \mt{datatype} \; M.z) &=& \mt{datatype} \; x = \mt{datatype} \; M.z \\
adamc@538 1153 \mt{sigOf}(\mt{val} \; x : \tau = e) &=& \mt{val} \; x : \tau \\
adamc@538 1154 \mt{sigOf}(\mt{val} \; \mt{rec} \; \overline{x : \tau = e}) &=& \overline{\mt{val} \; x : \tau} \\
adamc@538 1155 \mt{sigOf}(\mt{structure} \; X : S = M) &=& \mt{structure} \; X : S \\
adamc@538 1156 \mt{sigOf}(\mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@538 1157 \mt{sigOf}(\mt{open} \; M) &=& \mt{include} \; S \textrm{ (where $\Gamma \vdash M : S$)} \\
adamc@538 1158 \mt{sigOf}(\mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@538 1159 \mt{sigOf}(\mt{open} \; \mt{constraints} \; M) &=& \cdot \\
adamc@538 1160 \mt{sigOf}(\mt{table} \; x : c) &=& \mt{table} \; x : c \\
adamc@784 1161 \mt{sigOf}(\mt{view} \; x : c) &=& \mt{view} \; x : c \\
adamc@538 1162 \mt{sigOf}(\mt{sequence} \; x) &=& \mt{sequence} \; x \\
adamc@538 1163 \mt{sigOf}(\mt{cookie} \; x : \tau) &=& \mt{cookie} \; x : \tau \\
adamc@784 1164 \mt{sigOf}(\mt{style} \; x) &=& \mt{style} \; x \\
adamc@655 1165 \mt{sigOf}(\mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@538 1166 \end{eqnarray*}
adamc@539 1167 \begin{eqnarray*}
adamc@539 1168 \mt{selfify}(M, \cdot) &=& \cdot \\
adamc@558 1169 \mt{selfify}(M, s \; \overline{s'}) &=& \mt{selfify}(M, s) \; \mt{selfify}(M, \overline{s'}) \\
adamc@539 1170 \\
adamc@539 1171 \mt{selfify}(M, \mt{con} \; x :: \kappa) &=& \mt{con} \; x :: \kappa = M.x \\
adamc@539 1172 \mt{selfify}(M, \mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@539 1173 \mt{selfify}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \mt{datatype} \; M.x \\
adamc@539 1174 \mt{selfify}(M, \mt{datatype} \; x = \mt{datatype} \; M'.z) &=& \mt{datatype} \; x = \mt{datatype} \; M'.z \\
adamc@539 1175 \mt{selfify}(M, \mt{val} \; x : \tau) &=& \mt{val} \; x : \tau \\
adamc@539 1176 \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 1177 \mt{selfify}(M, \mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@539 1178 \mt{selfify}(M, \mt{include} \; S) &=& \mt{include} \; S \\
adamc@539 1179 \mt{selfify}(M, \mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@655 1180 \mt{selfify}(M, \mt{class} \; x :: \kappa) &=& \mt{class} \; x :: \kappa = M.x \\
adamc@655 1181 \mt{selfify}(M, \mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@539 1182 \end{eqnarray*}
adamc@539 1183
adamc@540 1184 \subsection{Module Projection}
adamc@540 1185
adamc@540 1186 \begin{eqnarray*}
adamc@540 1187 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \\
adamc@540 1188 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa, c) \\
adamc@540 1189 \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 1190 \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 1191 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})$)} \\
adamc@655 1192 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \to \mt{Type} \\
adamc@655 1193 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa \to \mt{Type}, c) \\
adamc@540 1194 \\
adamc@540 1195 \mt{proj}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc} \; \overline{s}, \mt{datatype} \; x) &=& (\overline{y}, \overline{dc}) \\
adamc@540 1196 \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 1197 \\
adamc@540 1198 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, \mt{val} \; x) &=& \tau \\
adamc@540 1199 \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 1200 \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 1201 \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 1202 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \in \overline{dc}$)} \\
adamc@540 1203 \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 1204 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \; \mt{of} \; \tau \in \overline{dc}$)} \\
adamc@540 1205 \\
adamc@540 1206 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, \mt{structure} \; X) &=& S \\
adamc@540 1207 \\
adamc@540 1208 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, \mt{signature} \; X) &=& S \\
adamc@540 1209 \\
adamc@540 1210 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1211 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1212 \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 1213 \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 1214 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@540 1215 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1216 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1217 \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 1218 \mt{proj}(M, \mt{constraint} \; c_1 \sim c_2 \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@655 1219 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@655 1220 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1221 \end{eqnarray*}
adamc@540 1222
adamc@541 1223
adamc@541 1224 \section{Type Inference}
adamc@541 1225
adamc@541 1226 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 1227
adamc@541 1228 \subsection{Basic Unification}
adamc@541 1229
adamc@560 1230 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 1231
adamc@656 1232 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 1233
adamc@541 1234 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 1235
adamc@541 1236 \subsection{Unifying Record Types}
adamc@541 1237
adamc@570 1238 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 1239
adamc@656 1240 \subsection{\label{typeclasses}Constructor Classes}
adamc@541 1241
adamc@784 1242 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 1243
adamc@784 1244 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 1245
adamc@656 1246 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 1247
adamc@656 1248 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 1249
adamc@541 1250 \subsection{Reverse-Engineering Record Types}
adamc@541 1251
adamc@656 1252 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 1253
adamc@541 1254 \subsection{Implicit Arguments in Functor Applications}
adamc@541 1255
adamc@656 1256 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 1257
adamc@541 1258
adamc@542 1259 \section{The Ur Standard Library}
adamc@542 1260
adamc@542 1261 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 1262
adamc@542 1263 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 1264
adamc@542 1265 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 1266 $$\begin{array}{l}
adamc@542 1267 \mt{type} \; \mt{int} \\
adamc@542 1268 \mt{type} \; \mt{float} \\
adamc@873 1269 \mt{type} \; \mt{char} \\
adamc@542 1270 \mt{type} \; \mt{string} \\
adamc@542 1271 \mt{type} \; \mt{time} \\
adamc@785 1272 \mt{type} \; \mt{blob} \\
adamc@542 1273 \\
adamc@542 1274 \mt{type} \; \mt{unit} = \{\} \\
adamc@542 1275 \\
adamc@542 1276 \mt{datatype} \; \mt{bool} = \mt{False} \mid \mt{True} \\
adamc@542 1277 \\
adamc@785 1278 \mt{datatype} \; \mt{option} \; \mt{t} = \mt{None} \mid \mt{Some} \; \mt{of} \; \mt{t} \\
adamc@785 1279 \\
adamc@785 1280 \mt{datatype} \; \mt{list} \; \mt{t} = \mt{Nil} \mid \mt{Cons} \; \mt{of} \; \mt{t} \times \mt{list} \; \mt{t}
adamc@542 1281 \end{array}$$
adamc@542 1282
adamc@1123 1283 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 1284
adamc@657 1285 Another important generic Ur element comes at the beginning of \texttt{top.urs}.
adamc@657 1286
adamc@657 1287 $$\begin{array}{l}
adamc@657 1288 \mt{con} \; \mt{folder} :: \mt{K} \longrightarrow \{\mt{K}\} \to \mt{Type} \\
adamc@657 1289 \\
adamc@657 1290 \mt{val} \; \mt{fold} : \mt{K} \longrightarrow \mt{tf} :: (\{\mt{K}\} \to \mt{Type}) \\
adamc@657 1291 \hspace{.1in} \to (\mt{nm} :: \mt{Name} \to \mt{v} :: \mt{K} \to \mt{r} :: \{\mt{K}\} \to [[\mt{nm}] \sim \mt{r}] \Rightarrow \\
adamc@657 1292 \hspace{.2in} \mt{tf} \; \mt{r} \to \mt{tf} \; ([\mt{nm} = \mt{v}] \rc \mt{r})) \\
adamc@657 1293 \hspace{.1in} \to \mt{tf} \; [] \\
adamc@657 1294 \hspace{.1in} \to \mt{r} :: \{\mt{K}\} \to \mt{folder} \; \mt{r} \to \mt{tf} \; \mt{r}
adamc@657 1295 \end{array}$$
adamc@657 1296
adamc@657 1297 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 1298
adamc@664 1299 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 1300
adamc@542 1301
adamc@542 1302 \section{The Ur/Web Standard Library}
adamc@542 1303
adamc@658 1304 \subsection{Monads}
adamc@658 1305
adamc@658 1306 The Ur Basis defines the monad constructor class from Haskell.
adamc@658 1307
adamc@658 1308 $$\begin{array}{l}
adamc@658 1309 \mt{class} \; \mt{monad} :: \mt{Type} \to \mt{Type} \\
adamc@658 1310 \mt{val} \; \mt{return} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t} ::: \mt{Type} \\
adamc@658 1311 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658 1312 \hspace{.1in} \to \mt{t} \to \mt{m} \; \mt{t} \\
adamc@658 1313 \mt{val} \; \mt{bind} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t1} ::: \mt{Type} \to \mt{t2} ::: \mt{Type} \\
adamc@658 1314 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658 1315 \hspace{.1in} \to \mt{m} \; \mt{t1} \to (\mt{t1} \to \mt{m} \; \mt{t2}) \\
adamc@658 1316 \hspace{.1in} \to \mt{m} \; \mt{t2}
adamc@658 1317 \end{array}$$
adamc@658 1318
adamc@542 1319 \subsection{Transactions}
adamc@542 1320
adamc@542 1321 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 1322 $$\begin{array}{l}
adamc@542 1323 \mt{con} \; \mt{transaction} :: \mt{Type} \to \mt{Type} \\
adamc@658 1324 \mt{val} \; \mt{transaction\_monad} : \mt{monad} \; \mt{transaction}
adamc@542 1325 \end{array}$$
adamc@542 1326
adamc@1123 1327 For debugging purposes, a transactional function is provided for outputting a string on the server process' \texttt{stderr}.
adamc@1123 1328 $$\begin{array}{l}
adamc@1123 1329 \mt{val} \; \mt{debug} : \mt{string} \to \mt{transaction} \; \mt{unit}
adamc@1123 1330 \end{array}$$
adamc@1123 1331
adamc@542 1332 \subsection{HTTP}
adamc@542 1333
adamc@542 1334 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 1335 $$\begin{array}{l}
adamc@786 1336 \mt{val} \; \mt{requestHeader} : \mt{string} \to \mt{transaction} \; (\mt{option} \; \mt{string}) \\
adamc@786 1337 \\
adamc@786 1338 \mt{con} \; \mt{http\_cookie} :: \mt{Type} \to \mt{Type} \\
adamc@786 1339 \mt{val} \; \mt{getCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; (\mt{option} \; \mt{t}) \\
adamc@1050 1340 \mt{val} \; \mt{setCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \{\mt{Value} : \mt{t}, \mt{Expires} : \mt{option} \; \mt{time}, \mt{Secure} : \mt{bool}\} \to \mt{transaction} \; \mt{unit} \\
adamc@1050 1341 \mt{val} \; \mt{clearCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; \mt{unit}
adamc@786 1342 \end{array}$$
adamc@786 1343
adamc@786 1344 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 1345 $$\begin{array}{l}
adamc@786 1346 \mt{type} \; \mt{url} \\
adamc@786 1347 \mt{val} \; \mt{bless} : \mt{string} \to \mt{url} \\
adamc@786 1348 \mt{val} \; \mt{checkUrl} : \mt{string} \to \mt{option} \; \mt{url}
adamc@786 1349 \end{array}$$
adamc@786 1350 $\mt{bless}$ raises a runtime error if the string passed to it fails the URL policy.
adamc@786 1351
adamc@1085 1352 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 1353 $$\begin{array}{l}
adamc@1085 1354 \mt{val} \; \mt{currentUrl} : \mt{transaction} \; \mt{url} \\
adamc@1085 1355 \mt{val} \; \mt{url} : \mt{transaction} \; \mt{page} \to \mt{url}
adamc@1085 1356 \end{array}$$
adamc@1085 1357
adamc@1085 1358 Page generation may be interrupted at any time with a request to redirect to a particular URL instead.
adamc@1085 1359 $$\begin{array}{l}
adamc@1085 1360 \mt{val} \; \mt{redirect} : \mt{t} ::: \mt{Type} \to \mt{url} \to \mt{transaction} \; \mt{t}
adamc@1085 1361 \end{array}$$
adamc@1085 1362
adamc@786 1363 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 1364 $$\begin{array}{l}
adamc@786 1365 \mt{type} \; \mt{file} \\
adamc@786 1366 \mt{val} \; \mt{fileName} : \mt{file} \to \mt{option} \; \mt{string} \\
adamc@786 1367 \mt{val} \; \mt{fileMimeType} : \mt{file} \to \mt{string} \\
adamc@786 1368 \mt{val} \; \mt{fileData} : \mt{file} \to \mt{blob}
adamc@786 1369 \end{array}$$
adamc@786 1370
adamc@786 1371 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 1372 $$\begin{array}{l}
adamc@786 1373 \mt{type} \; \mt{mimeType} \\
adamc@786 1374 \mt{val} \; \mt{blessMime} : \mt{string} \to \mt{mimeType} \\
adamc@786 1375 \mt{val} \; \mt{checkMime} : \mt{string} \to \mt{option} \; \mt{mimeType} \\
adamc@786 1376 \mt{val} \; \mt{returnBlob} : \mt{t} ::: \mt{Type} \to \mt{blob} \to \mt{mimeType} \to \mt{transaction} \; \mt{t}
adamc@542 1377 \end{array}$$
adamc@542 1378
adamc@543 1379 \subsection{SQL}
adamc@543 1380
adamc@543 1381 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 1382 $$\begin{array}{l}
adamc@785 1383 \mt{con} \; \mt{sql\_table} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785 1384 \end{array}$$
adamc@785 1385 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 1386
adamc@785 1387 We also have the simpler type family of SQL views, which have no keys.
adamc@785 1388 $$\begin{array}{l}
adamc@785 1389 \mt{con} \; \mt{sql\_view} :: \{\mt{Type}\} \to \mt{Type}
adamc@543 1390 \end{array}$$
adamc@543 1391
adamc@785 1392 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 1393 $$\begin{array}{l}
adamc@785 1394 \mt{class} \; \mt{fieldsOf} :: \mt{Type} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1395 \mt{val} \; \mt{fieldsOf\_table} : \mt{fs} ::: \{\mt{Type}\} \to \mt{keys} ::: \{\{\mt{Unit}\}\} \to \mt{fieldsOf} \; (\mt{sql\_table} \; \mt{fs} \; \mt{keys}) \; \mt{fs} \\
adamc@785 1396 \mt{val} \; \mt{fieldsOf\_view} : \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; (\mt{sql\_view} \; \mt{fs}) \; \mt{fs}
adamc@785 1397 \end{array}$$
adamc@785 1398
adamc@785 1399 \subsubsection{Table Constraints}
adamc@785 1400
adamc@785 1401 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 1402
adamc@785 1403 $$\begin{array}{l}
adamc@785 1404 \mt{con} \; \mt{primary\_key} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type} \\
adamc@785 1405 \mt{val} \; \mt{no\_primary\_key} : \mt{fs} ::: \{\mt{Type}\} \to \mt{primary\_key} \; \mt{fs} \; [] \\
adamc@785 1406 \mt{val} \; \mt{primary\_key} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{key1} :: \mt{Name} \to \mt{keys} :: \{\mt{Type}\} \\
adamc@785 1407 \hspace{.1in} \to [[\mt{key1}] \sim \mt{keys}] \Rightarrow [[\mt{key1} = \mt{t}] \rc \mt{keys} \sim \mt{rest}] \\
adamc@785 1408 \hspace{.1in} \Rightarrow \$([\mt{key1} = \mt{sql\_injectable\_prim} \; \mt{t}] \rc \mt{map} \; \mt{sql\_injectable\_prim} \; \mt{keys}) \\
adamc@785 1409 \hspace{.1in} \to \mt{primary\_key} \; ([\mt{key1} = \mt{t}] \rc \mt{keys} \rc \mt{rest}) \; [\mt{Pkey} = [\mt{key1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{keys}]
adamc@785 1410 \end{array}$$
adamc@785 1411 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 1412
adamc@785 1413 A type family stands for sets of named constraints of the remaining varieties.
adamc@785 1414 $$\begin{array}{l}
adamc@785 1415 \mt{con} \; \mt{sql\_constraints} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785 1416 \end{array}$$
adamc@785 1417 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 1418
adamc@785 1419 There is a type family of individual, unnamed constraints.
adamc@785 1420 $$\begin{array}{l}
adamc@785 1421 \mt{con} \; \mt{sql\_constraint} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \mt{Type}
adamc@785 1422 \end{array}$$
adamc@785 1423 The first argument is the same as above, and the second argument gives the key columns for just this constraint.
adamc@785 1424
adamc@785 1425 We have operations for assembling constraints into constraint sets.
adamc@785 1426 $$\begin{array}{l}
adamc@785 1427 \mt{val} \; \mt{no\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_constraints} \; \mt{fs} \; [] \\
adamc@785 1428 \mt{val} \; \mt{one\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{unique} ::: \{\mt{Unit}\} \to \mt{name} :: \mt{Name} \\
adamc@785 1429 \hspace{.1in} \to \mt{sql\_constraint} \; \mt{fs} \; \mt{unique} \to \mt{sql\_constraints} \; \mt{fs} \; [\mt{name} = \mt{unique}] \\
adamc@785 1430 \mt{val} \; \mt{join\_constraints} : \mt{fs} ::: \{\mt{Type}\} \to \mt{uniques1} ::: \{\{\mt{Unit}\}\} \to \mt{uniques2} ::: \{\{\mt{Unit}\}\} \to [\mt{uniques1} \sim \mt{uniques2}] \\
adamc@785 1431 \hspace{.1in} \Rightarrow \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques1} \to \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques2} \to \mt{sql\_constraints} \; \mt{fs} \; (\mt{uniques1} \rc \mt{uniques2})
adamc@785 1432 \end{array}$$
adamc@785 1433
adamc@785 1434 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 1435 $$\begin{array}{l}
adamc@785 1436 \mt{val} \; \mt{unique} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{unique1} :: \mt{Name} \to \mt{unique} :: \{\mt{Type}\} \\
adamc@785 1437 \hspace{.1in} \to [[\mt{unique1}] \sim \mt{unique}] \Rightarrow [[\mt{unique1} = \mt{t}] \rc \mt{unique} \sim \mt{rest}] \\
adamc@785 1438 \hspace{.1in} \Rightarrow \mt{sql\_constraint} \; ([\mt{unique1} = \mt{t}] \rc \mt{unique} \rc \mt{rest}) \; ([\mt{unique1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{unique})
adamc@785 1439 \end{array}$$
adamc@785 1440
adamc@785 1441 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 1442 $$\begin{array}{l}
adamc@785 1443 \mt{class} \; \mt{linkable} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@785 1444 \mt{val} \; \mt{linkable\_same} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; \mt{t} \\
adamc@785 1445 \mt{val} \; \mt{linkable\_from\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; (\mt{option} \; \mt{t}) \; \mt{t} \\
adamc@785 1446 \mt{val} \; \mt{linkable\_to\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@785 1447 \end{array}$$
adamc@785 1448
adamc@785 1449 The $\mt{matching}$ type family uses $\mt{linkable}$ to define when two keys match up type-wise.
adamc@785 1450 $$\begin{array}{l}
adamc@785 1451 \mt{con} \; \mt{matching} :: \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1452 \mt{val} \; \mt{mat\_nil} : \mt{matching} \; [] \; [] \\
adamc@785 1453 \mt{val} \; \mt{mat\_cons} : \mt{t1} ::: \mt{Type} \to \mt{rest1} ::: \{\mt{Type}\} \to \mt{t2} ::: \mt{Type} \to \mt{rest2} ::: \{\mt{Type}\} \to \mt{nm1} :: \mt{Name} \to \mt{nm2} :: \mt{Name} \\
adamc@785 1454 \hspace{.1in} \to [[\mt{nm1}] \sim \mt{rest1}] \Rightarrow [[\mt{nm2}] \sim \mt{rest2}] \Rightarrow \mt{linkable} \; \mt{t1} \; \mt{t2} \to \mt{matching} \; \mt{rest1} \; \mt{rest2} \\
adamc@785 1455 \hspace{.1in} \to \mt{matching} \; ([\mt{nm1} = \mt{t1}] \rc \mt{rest1}) \; ([\mt{nm2} = \mt{t2}] \rc \mt{rest2})
adamc@785 1456 \end{array}$$
adamc@785 1457
adamc@785 1458 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 1459 $$\begin{array}{l}
adamc@785 1460 \mt{con} \; \mt{propagation\_mode} :: \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1461 \mt{val} \; \mt{restrict} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1462 \mt{val} \; \mt{cascade} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1463 \mt{val} \; \mt{no\_action} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1464 \mt{val} \; \mt{set\_null} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; (\mt{map} \; \mt{option} \; \mt{fs})
adamc@785 1465 \end{array}$$
adamc@785 1466
adamc@785 1467 Finally, we put these ingredient together to define the \texttt{FOREIGN KEY} constraint function.
adamc@785 1468 $$\begin{array}{l}
adamc@785 1469 \mt{val} \; \mt{foreign\_key} : \mt{mine1} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{mine} ::: \{\mt{Type}\} \to \mt{munused} ::: \{\mt{Type}\} \to \mt{foreign} ::: \{\mt{Type}\} \\
adamc@785 1470 \hspace{.1in} \to \mt{funused} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{uniques} ::: \{\{\mt{Unit}\}\} \\
adamc@785 1471 \hspace{.1in} \to [[\mt{mine1}] \sim \mt{mine}] \Rightarrow [[\mt{mine1} = \mt{t}] \rc \mt{mine} \sim \mt{munused}] \Rightarrow [\mt{foreign} \sim \mt{funused}] \Rightarrow [[\mt{nm}] \sim \mt{uniques}] \\
adamc@785 1472 \hspace{.1in} \Rightarrow \mt{matching} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}) \; \mt{foreign} \\
adamc@785 1473 \hspace{.1in} \to \mt{sql\_table} \; (\mt{foreign} \rc \mt{funused}) \; ([\mt{nm} = \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{foreign}] \rc \mt{uniques}) \\
adamc@785 1474 \hspace{.1in} \to \{\mt{OnDelete} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}), \\
adamc@785 1475 \hspace{.2in} \mt{OnUpdate} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine})\} \\
adamc@785 1476 \hspace{.1in} \to \mt{sql\_constraint} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine} \rc \mt{munused}) \; []
adamc@785 1477 \end{array}$$
adamc@785 1478
adamc@785 1479 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 1480 $$\begin{array}{l}
adamc@785 1481 \mt{val} \; \mt{check} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; [] \; [] \; \mt{fs} \; \mt{bool} \to \mt{sql\_constraint} \; \mt{fs} \; []
adamc@785 1482 \end{array}$$
adamc@785 1483
adamc@785 1484 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 1485
adamc@784 1486
adamc@543 1487 \subsubsection{Queries}
adamc@543 1488
adamc@543 1489 A final query is constructed via the $\mt{sql\_query}$ function. Constructor arguments respectively specify the 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 1490 $$\begin{array}{l}
adamc@543 1491 \mt{con} \; \mt{sql\_query} :: \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@543 1492 \mt{val} \; \mt{sql\_query} : \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543 1493 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1494 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@543 1495 \hspace{.1in} \to \{\mt{Rows} : \mt{sql\_query1} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}, \\
adamc@543 1496 \hspace{.2in} \mt{OrderBy} : \mt{sql\_order\_by} \; \mt{tables} \; \mt{selectedExps}, \\
adamc@543 1497 \hspace{.2in} \mt{Limit} : \mt{sql\_limit}, \\
adamc@543 1498 \hspace{.2in} \mt{Offset} : \mt{sql\_offset}\} \\
adamc@543 1499 \hspace{.1in} \to \mt{sql\_query} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1500 \end{array}$$
adamc@543 1501
adamc@545 1502 Queries are used by folding over their results inside transactions.
adamc@545 1503 $$\begin{array}{l}
adamc@545 1504 \mt{val} \; \mt{query} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \lambda [\mt{tables} \sim \mt{exps}] \Rightarrow \mt{state} ::: \mt{Type} \to \mt{sql\_query} \; \mt{tables} \; \mt{exps} \\
adamc@658 1505 \hspace{.1in} \to (\$(\mt{exps} \rc \mt{map} \; (\lambda \mt{fields} :: \{\mt{Type}\} \Rightarrow \$\mt{fields}) \; \mt{tables}) \\
adamc@545 1506 \hspace{.2in} \to \mt{state} \to \mt{transaction} \; \mt{state}) \\
adamc@545 1507 \hspace{.1in} \to \mt{state} \to \mt{transaction} \; \mt{state}
adamc@545 1508 \end{array}$$
adamc@545 1509
adamc@543 1510 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 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 1511 $$\begin{array}{l}
adamc@543 1512 \mt{con} \; \mt{sql\_query1} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@543 1513 \\
adamc@543 1514 \mt{type} \; \mt{sql\_relop} \\
adamc@543 1515 \mt{val} \; \mt{sql\_union} : \mt{sql\_relop} \\
adamc@543 1516 \mt{val} \; \mt{sql\_intersect} : \mt{sql\_relop} \\
adamc@543 1517 \mt{val} \; \mt{sql\_except} : \mt{sql\_relop} \\
adamc@543 1518 \mt{val} \; \mt{sql\_relop} : \mt{tables1} ::: \{\{\mt{Type}\}\} \\
adamc@543 1519 \hspace{.1in} \to \mt{tables2} ::: \{\{\mt{Type}\}\} \\
adamc@543 1520 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1521 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@543 1522 \hspace{.1in} \to \mt{sql\_relop} \\
adamc@543 1523 \hspace{.1in} \to \mt{sql\_query1} \; \mt{tables1} \; \mt{selectedFields} \; \mt{selectedExps} \\
adamc@543 1524 \hspace{.1in} \to \mt{sql\_query1} \; \mt{tables2} \; \mt{selectedFields} \; \mt{selectedExps} \\
adamc@543 1525 \hspace{.1in} \to \mt{sql\_query1} \; \mt{selectedFields} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1526 \end{array}$$
adamc@543 1527
adamc@543 1528 $$\begin{array}{l}
adamc@543 1529 \mt{val} \; \mt{sql\_query1} : \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543 1530 \hspace{.1in} \to \mt{grouped} ::: \{\{\mt{Type}\}\} \\
adamc@543 1531 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1532 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1085 1533 \hspace{.1in} \to \mt{empties} :: \{\mt{Unit}\} \\
adamc@1085 1534 \hspace{.1in} \to [\mt{empties} \sim \mt{selectedFields}] \\
adamc@1085 1535 \hspace{.1in} \Rightarrow \{\mt{Distinct} : \mt{bool}, \\
adamc@994 1536 \hspace{.2in} \mt{From} : \mt{sql\_from\_items} \; \mt{tables}, \\
adamc@543 1537 \hspace{.2in} \mt{Where} : \mt{sql\_exp} \; \mt{tables} \; [] \; [] \; \mt{bool}, \\
adamc@543 1538 \hspace{.2in} \mt{GroupBy} : \mt{sql\_subset} \; \mt{tables} \; \mt{grouped}, \\
adamc@543 1539 \hspace{.2in} \mt{Having} : \mt{sql\_exp} \; \mt{grouped} \; \mt{tables} \; [] \; \mt{bool}, \\
adamc@1085 1540 \hspace{.2in} \mt{SelectFields} : \mt{sql\_subset} \; \mt{grouped} \; (\mt{map} \; (\lambda \_ \Rightarrow []) \; \mt{empties} \rc \mt{selectedFields}), \\
adamc@658 1541 \hspace{.2in} \mt {SelectExps} : \$(\mt{map} \; (\mt{sql\_exp} \; \mt{grouped} \; \mt{tables} \; []) \; \mt{selectedExps}) \} \\
adamc@543 1542 \hspace{.1in} \to \mt{sql\_query1} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1543 \end{array}$$
adamc@543 1544
adamc@543 1545 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 1546 $$\begin{array}{l}
adamc@543 1547 \mt{con} \; \mt{sql\_subset} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@543 1548 \mt{val} \; \mt{sql\_subset} : \mt{keep\_drop} :: \{(\{\mt{Type}\} \times \{\mt{Type}\})\} \\
adamc@543 1549 \hspace{.1in} \to \mt{sql\_subset} \\
adamc@658 1550 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1 \rc \mt{fields}.2)\; \mt{keep\_drop}) \\
adamc@658 1551 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1) \; \mt{keep\_drop}) \\
adamc@543 1552 \mt{val} \; \mt{sql\_subset\_all} : \mt{tables} :: \{\{\mt{Type}\}\} \to \mt{sql\_subset} \; \mt{tables} \; \mt{tables}
adamc@543 1553 \end{array}$$
adamc@543 1554
adamc@560 1555 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 1556 $$\begin{array}{l}
adamc@543 1557 \mt{con} \; \mt{sql\_exp} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}
adamc@543 1558 \end{array}$$
adamc@543 1559
adamc@543 1560 Any field in scope may be converted to an expression.
adamc@543 1561 $$\begin{array}{l}
adamc@543 1562 \mt{val} \; \mt{sql\_field} : \mt{otherTabs} ::: \{\{\mt{Type}\}\} \to \mt{otherFields} ::: \{\mt{Type}\} \\
adamc@543 1563 \hspace{.1in} \to \mt{fieldType} ::: \mt{Type} \to \mt{agg} ::: \{\{\mt{Type}\}\} \\
adamc@543 1564 \hspace{.1in} \to \mt{exps} ::: \{\mt{Type}\} \\
adamc@543 1565 \hspace{.1in} \to \mt{tab} :: \mt{Name} \to \mt{field} :: \mt{Name} \\
adamc@543 1566 \hspace{.1in} \to \mt{sql\_exp} \; ([\mt{tab} = [\mt{field} = \mt{fieldType}] \rc \mt{otherFields}] \rc \mt{otherTabs}) \; \mt{agg} \; \mt{exps} \; \mt{fieldType}
adamc@543 1567 \end{array}$$
adamc@543 1568
adamc@544 1569 There is an analogous function for referencing named expressions.
adamc@544 1570 $$\begin{array}{l}
adamc@544 1571 \mt{val} \; \mt{sql\_exp} : \mt{tabs} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{t} ::: \mt{Type} \to \mt{rest} ::: \{\mt{Type}\} \to \mt{nm} :: \mt{Name} \\
adamc@544 1572 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tabs} \; \mt{agg} \; ([\mt{nm} = \mt{t}] \rc \mt{rest}) \; \mt{t}
adamc@544 1573 \end{array}$$
adamc@544 1574
adamc@544 1575 Ur values of appropriate types may be injected into SQL expressions.
adamc@544 1576 $$\begin{array}{l}
adamc@786 1577 \mt{class} \; \mt{sql\_injectable\_prim} \\
adamc@786 1578 \mt{val} \; \mt{sql\_bool} : \mt{sql\_injectable\_prim} \; \mt{bool} \\
adamc@786 1579 \mt{val} \; \mt{sql\_int} : \mt{sql\_injectable\_prim} \; \mt{int} \\
adamc@786 1580 \mt{val} \; \mt{sql\_float} : \mt{sql\_injectable\_prim} \; \mt{float} \\
adamc@786 1581 \mt{val} \; \mt{sql\_string} : \mt{sql\_injectable\_prim} \; \mt{string} \\
adamc@786 1582 \mt{val} \; \mt{sql\_time} : \mt{sql\_injectable\_prim} \; \mt{time} \\
adamc@786 1583 \mt{val} \; \mt{sql\_blob} : \mt{sql\_injectable\_prim} \; \mt{blob} \\
adamc@786 1584 \mt{val} \; \mt{sql\_channel} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{channel} \; \mt{t}) \\
adamc@786 1585 \mt{val} \; \mt{sql\_client} : \mt{sql\_injectable\_prim} \; \mt{client} \\
adamc@786 1586 \\
adamc@544 1587 \mt{class} \; \mt{sql\_injectable} \\
adamc@786 1588 \mt{val} \; \mt{sql\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@786 1589 \mt{val} \; \mt{sql\_option\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; (\mt{option} \; \mt{t}) \\
adamc@786 1590 \\
adamc@544 1591 \mt{val} \; \mt{sql\_inject} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@544 1592 \hspace{.1in} \to \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adamc@544 1593 \end{array}$$
adamc@544 1594
adamc@1123 1595 Additionally, most function-free types may be injected safely, via the $\mt{serialized}$ type family.
adamc@1123 1596 $$\begin{array}{l}
adamc@1123 1597 \mt{con} \; \mt{serialized} :: \mt{Type} \to \mt{Type} \\
adamc@1123 1598 \mt{val} \; \mt{serialize} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{serialized} \; \mt{t} \\
adamc@1123 1599 \mt{val} \; \mt{deserialize} : \mt{t} ::: \mt{Type} \to \mt{serialized} \; \mt{t} \to \mt{t} \\
adamc@1123 1600 \mt{val} \; \mt{sql\_serialized} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{serialized} \; \mt{t})
adamc@1123 1601 \end{array}$$
adamc@1123 1602
adamc@544 1603 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 1604 $$\begin{array}{l}
adamc@544 1605 \mt{val} \; \mt{sql\_is\_null} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544 1606 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; (\mt{option} \; \mt{t}) \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{bool}
adamc@544 1607 \end{array}$$
adamc@544 1608
adamc@559 1609 We have generic nullary, unary, and binary operators.
adamc@544 1610 $$\begin{array}{l}
adamc@544 1611 \mt{con} \; \mt{sql\_nfunc} :: \mt{Type} \to \mt{Type} \\
adamc@544 1612 \mt{val} \; \mt{sql\_current\_timestamp} : \mt{sql\_nfunc} \; \mt{time} \\
adamc@544 1613 \mt{val} \; \mt{sql\_nfunc} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544 1614 \hspace{.1in} \to \mt{sql\_nfunc} \; \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\\end{array}$$
adamc@544 1615
adamc@544 1616 $$\begin{array}{l}
adamc@544 1617 \mt{con} \; \mt{sql\_unary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544 1618 \mt{val} \; \mt{sql\_not} : \mt{sql\_unary} \; \mt{bool} \; \mt{bool} \\
adamc@544 1619 \mt{val} \; \mt{sql\_unary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adamc@544 1620 \hspace{.1in} \to \mt{sql\_unary} \; \mt{arg} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res} \\
adamc@544 1621 \end{array}$$
adamc@544 1622
adamc@544 1623 $$\begin{array}{l}
adamc@544 1624 \mt{con} \; \mt{sql\_binary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544 1625 \mt{val} \; \mt{sql\_and} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544 1626 \mt{val} \; \mt{sql\_or} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544 1627 \mt{val} \; \mt{sql\_binary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg_1} ::: \mt{Type} \to \mt{arg_2} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adamc@544 1628 \hspace{.1in} \to \mt{sql\_binary} \; \mt{arg_1} \; \mt{arg_2} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_1} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_2} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res}
adamc@544 1629 \end{array}$$
adamc@544 1630
adamc@544 1631 $$\begin{array}{l}
adamc@559 1632 \mt{class} \; \mt{sql\_arith} \\
adamc@559 1633 \mt{val} \; \mt{sql\_int\_arith} : \mt{sql\_arith} \; \mt{int} \\
adamc@559 1634 \mt{val} \; \mt{sql\_float\_arith} : \mt{sql\_arith} \; \mt{float} \\
adamc@559 1635 \mt{val} \; \mt{sql\_neg} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_unary} \; \mt{t} \; \mt{t} \\
adamc@559 1636 \mt{val} \; \mt{sql\_plus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1637 \mt{val} \; \mt{sql\_minus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1638 \mt{val} \; \mt{sql\_times} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1639 \mt{val} \; \mt{sql\_div} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1640 \mt{val} \; \mt{sql\_mod} : \mt{sql\_binary} \; \mt{int} \; \mt{int} \; \mt{int}
adamc@559 1641 \end{array}$$
adamc@544 1642
adamc@656 1643 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 1644 $$\begin{array}{l}
adamc@544 1645 \mt{val} \; \mt{sql\_count} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int}
adamc@544 1646 \end{array}$$
adamc@544 1647
adamc@544 1648 $$\begin{array}{l}
adamc@544 1649 \mt{con} \; \mt{sql\_aggregate} :: \mt{Type} \to \mt{Type} \\
adamc@544 1650 \mt{val} \; \mt{sql\_aggregate} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544 1651 \hspace{.1in} \to \mt{sql\_aggregate} \; \mt{t} \to \mt{sql\_exp} \; \mt{agg} \; \mt{agg} \; \mt{exps} \; \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adamc@544 1652 \end{array}$$
adamc@544 1653
adamc@544 1654 $$\begin{array}{l}
adamc@544 1655 \mt{class} \; \mt{sql\_summable} \\
adamc@544 1656 \mt{val} \; \mt{sql\_summable\_int} : \mt{sql\_summable} \; \mt{int} \\
adamc@544 1657 \mt{val} \; \mt{sql\_summable\_float} : \mt{sql\_summable} \; \mt{float} \\
adamc@544 1658 \mt{val} \; \mt{sql\_avg} : \mt{t} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{sql\_aggregate} \; \mt{t} \\
adamc@544 1659 \mt{val} \; \mt{sql\_sum} : \mt{t} ::: \mt{Type} \to \mt{sql\_summable} \mt{t} \to \mt{sql\_aggregate} \; \mt{t}
adamc@544 1660 \end{array}$$
adamc@544 1661
adamc@544 1662 $$\begin{array}{l}
adamc@544 1663 \mt{class} \; \mt{sql\_maxable} \\
adamc@544 1664 \mt{val} \; \mt{sql\_maxable\_int} : \mt{sql\_maxable} \; \mt{int} \\
adamc@544 1665 \mt{val} \; \mt{sql\_maxable\_float} : \mt{sql\_maxable} \; \mt{float} \\
adamc@544 1666 \mt{val} \; \mt{sql\_maxable\_string} : \mt{sql\_maxable} \; \mt{string} \\
adamc@544 1667 \mt{val} \; \mt{sql\_maxable\_time} : \mt{sql\_maxable} \; \mt{time} \\
adamc@544 1668 \mt{val} \; \mt{sql\_max} : \mt{t} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{sql\_aggregate} \; \mt{t} \\
adamc@544 1669 \mt{val} \; \mt{sql\_min} : \mt{t} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{sql\_aggregate} \; \mt{t}
adamc@544 1670 \end{array}$$
adamc@544 1671
adamc@786 1672 \texttt{FROM} clauses are specified using a type family.
adamc@786 1673 $$\begin{array}{l}
adamc@786 1674 \mt{con} \; \mt{sql\_from\_items} :: \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@786 1675 \mt{val} \; \mt{sql\_from\_table} : \mt{t} ::: \mt{Type} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; \mt{t} \; \mt{fs} \to \mt{name} :: \mt{Name} \to \mt{t} \to \mt{sql\_from\_items} \; [\mt{name} = \mt{fs}] \\
adamc@786 1676 \mt{val} \; \mt{sql\_from\_comma} : \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \to [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@786 1677 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{tabs2} \\
adamc@786 1678 \hspace{.1in} \to \mt{sql\_from\_items} \; (\mt{tabs1} \rc \mt{tabs2}) \\
adamc@786 1679 \mt{val} \; \mt{sql\_inner\_join} : \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \to [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@786 1680 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{tabs2} \\
adamc@786 1681 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{tabs1} \rc \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@786 1682 \hspace{.1in} \to \mt{sql\_from\_items} \; (\mt{tabs1} \rc \mt{tabs2})
adamc@786 1683 \end{array}$$
adamc@786 1684
adamc@786 1685 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 1686 $$\begin{array}{l}
adamc@786 1687 \mt{class} \; \mt{nullify} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@786 1688 \mt{val} \; \mt{nullify\_option} : \mt{t} ::: \mt{Type} \to \mt{nullify} \; (\mt{option} \; \mt{t}) \; (\mt{option} \; \mt{t}) \\
adamc@786 1689 \mt{val} \; \mt{nullify\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{nullify} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@786 1690 \end{array}$$
adamc@786 1691
adamc@786 1692 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 1693
adamc@786 1694 $$\begin{array}{l}
adamc@786 1695 \mt{val} \; \mt{sql\_left\_join} : \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{(\mt{Type} \times \mt{Type})\}\} \to [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@786 1696 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\lambda \mt{r} \Rightarrow \$(\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{nullify} \; \mt{p}.1 \; \mt{p}.2) \; \mt{r})) \; \mt{tabs2}) \\
adamc@786 1697 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{tabs1} \to \mt{sql\_from\_items} \; (\mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \\
adamc@786 1698 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@786 1699 \hspace{.1in} \to \mt{sql\_from\_items} \; (\mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.2)) \; \mt{tabs2})
adamc@786 1700 \end{array}$$
adamc@786 1701
adamc@544 1702 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 1703 $$\begin{array}{l}
adamc@544 1704 \mt{type} \; \mt{sql\_direction} \\
adamc@544 1705 \mt{val} \; \mt{sql\_asc} : \mt{sql\_direction} \\
adamc@544 1706 \mt{val} \; \mt{sql\_desc} : \mt{sql\_direction} \\
adamc@544 1707 \\
adamc@544 1708 \mt{con} \; \mt{sql\_order\_by} :: \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@544 1709 \mt{val} \; \mt{sql\_order\_by\_Nil} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} :: \{\mt{Type}\} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544 1710 \mt{val} \; \mt{sql\_order\_by\_Cons} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544 1711 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; [] \; \mt{exps} \; \mt{t} \to \mt{sql\_direction} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544 1712 \\
adamc@544 1713 \mt{type} \; \mt{sql\_limit} \\
adamc@544 1714 \mt{val} \; \mt{sql\_no\_limit} : \mt{sql\_limit} \\
adamc@544 1715 \mt{val} \; \mt{sql\_limit} : \mt{int} \to \mt{sql\_limit} \\
adamc@544 1716 \\
adamc@544 1717 \mt{type} \; \mt{sql\_offset} \\
adamc@544 1718 \mt{val} \; \mt{sql\_no\_offset} : \mt{sql\_offset} \\
adamc@544 1719 \mt{val} \; \mt{sql\_offset} : \mt{int} \to \mt{sql\_offset}
adamc@544 1720 \end{array}$$
adamc@544 1721
adamc@545 1722
adamc@545 1723 \subsubsection{DML}
adamc@545 1724
adamc@545 1725 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 1726
adamc@545 1727 $$\begin{array}{l}
adamc@545 1728 \mt{type} \; \mt{dml} \\
adamc@545 1729 \mt{val} \; \mt{dml} : \mt{dml} \to \mt{transaction} \; \mt{unit}
adamc@545 1730 \end{array}$$
adamc@545 1731
adamc@545 1732 Properly-typed records may be used to form $\mt{INSERT}$ commands.
adamc@545 1733 $$\begin{array}{l}
adamc@545 1734 \mt{val} \; \mt{insert} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \\
adamc@658 1735 \hspace{.1in} \to \$(\mt{map} \; (\mt{sql\_exp} \; [] \; [] \; []) \; \mt{fields}) \to \mt{dml}
adamc@545 1736 \end{array}$$
adamc@545 1737
adamc@545 1738 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 1739 $$\begin{array}{l}
adamc@545 1740 \mt{val} \; \mt{update} : \mt{unchanged} ::: \{\mt{Type}\} \to \mt{changed} :: \{\mt{Type}\} \to \lambda [\mt{changed} \sim \mt{unchanged}] \\
adamc@658 1741 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; []) \; \mt{changed}) \\
adamc@545 1742 \hspace{.1in} \to \mt{sql\_table} \; (\mt{changed} \rc \mt{unchanged}) \to \mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545 1743 \end{array}$$
adamc@545 1744
adamc@545 1745 A $\mt{DELETE}$ command is formed from a table and a $\mt{WHERE}$ clause.
adamc@545 1746 $$\begin{array}{l}
adamc@545 1747 \mt{val} \; \mt{delete} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \to \mt{sql\_exp} \; [\mt{T} = \mt{fields}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545 1748 \end{array}$$
adamc@545 1749
adamc@546 1750 \subsubsection{Sequences}
adamc@546 1751
adamc@546 1752 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 1753
adamc@546 1754 $$\begin{array}{l}
adamc@546 1755 \mt{type} \; \mt{sql\_sequence} \\
adamc@1085 1756 \mt{val} \; \mt{nextval} : \mt{sql\_sequence} \to \mt{transaction} \; \mt{int} \\
adamc@1085 1757 \mt{val} \; \mt{setval} : \mt{sql\_sequence} \to \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@546 1758 \end{array}$$
adamc@546 1759
adamc@546 1760
adamc@547 1761 \subsection{XML}
adamc@547 1762
adamc@547 1763 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 1764
adamc@547 1765 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 1766 $$\begin{array}{l}
adamc@547 1767 \mt{con} \; \mt{xml} :: \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547 1768 \end{array}$$
adamc@547 1769
adamc@547 1770 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 1771 $$\begin{array}{l}
adamc@547 1772 \mt{con} \; \mt{tag} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547 1773 \end{array}$$
adamc@547 1774
adamc@547 1775 Literal text may be injected into XML as ``CDATA.''
adamc@547 1776 $$\begin{array}{l}
adamc@547 1777 \mt{val} \; \mt{cdata} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{string} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adamc@547 1778 \end{array}$$
adamc@547 1779
adamc@547 1780 There is a function for producing an XML tree with a particular tag at its root.
adamc@547 1781 $$\begin{array}{l}
adamc@547 1782 \mt{val} \; \mt{tag} : \mt{attrsGiven} ::: \{\mt{Type}\} \to \mt{attrsAbsent} ::: \{\mt{Type}\} \to \mt{ctxOuter} ::: \{\mt{Unit}\} \to \mt{ctxInner} ::: \{\mt{Unit}\} \\
adamc@547 1783 \hspace{.1in} \to \mt{useOuter} ::: \{\mt{Type}\} \to \mt{useInner} ::: \{\mt{Type}\} \to \mt{bindOuter} ::: \{\mt{Type}\} \to \mt{bindInner} ::: \{\mt{Type}\} \\
adamc@787 1784 \hspace{.1in} \to \lambda [\mt{attrsGiven} \sim \mt{attrsAbsent}] \; [\mt{useOuter} \sim \mt{useInner}] \; [\mt{bindOuter} \sim \mt{bindInner}] \\
adamc@787 1785 \hspace{.1in} \Rightarrow \mt{option} \; \mt{css\_class} \\
adamc@787 1786 \hspace{.1in} \to \$\mt{attrsGiven} \\
adamc@547 1787 \hspace{.1in} \to \mt{tag} \; (\mt{attrsGiven} \rc \mt{attrsAbsent}) \; \mt{ctxOuter} \; \mt{ctxInner} \; \mt{useOuter} \; \mt{bindOuter} \\
adamc@547 1788 \hspace{.1in} \to \mt{xml} \; \mt{ctxInner} \; \mt{useInner} \; \mt{bindInner} \to \mt{xml} \; \mt{ctxOuter} \; (\mt{useOuter} \rc \mt{useInner}) \; (\mt{bindOuter} \rc \mt{bindInner})
adamc@547 1789 \end{array}$$
adamc@787 1790 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 1791
adamc@547 1792 Two XML fragments may be concatenated.
adamc@547 1793 $$\begin{array}{l}
adamc@547 1794 \mt{val} \; \mt{join} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{bind_1} ::: \{\mt{Type}\} \to \mt{bind_2} ::: \{\mt{Type}\} \\
adamc@547 1795 \hspace{.1in} \to \lambda [\mt{use_1} \sim \mt{bind_1}] \; [\mt{bind_1} \sim \mt{bind_2}] \\
adamc@547 1796 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind_1} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{bind_1}) \; \mt{bind_2} \to \mt{xml} \; \mt{ctx} \; \mt{use_1} \; (\mt{bind_1} \rc \mt{bind_2})
adamc@547 1797 \end{array}$$
adamc@547 1798
adamc@547 1799 Finally, any XML fragment may be updated to ``claim'' to use more form fields than it does.
adamc@547 1800 $$\begin{array}{l}
adamc@547 1801 \mt{val} \; \mt{useMore} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{use_2} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to \lambda [\mt{use_1} \sim \mt{use_2}] \\
adamc@547 1802 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{use_2}) \; \mt{bind}
adamc@547 1803 \end{array}$$
adamc@547 1804
adamc@547 1805 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 1806
adamc@547 1807 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 1808 $$\begin{array}{l}
adamc@547 1809 \mt{val} \; \mt{error} : \mt{t} ::: \mt{Type} \to \mt{xml} \; [\mt{Body}] \; [] \; [] \to \mt{t}
adamc@547 1810 \end{array}$$
adamc@547 1811
adamc@549 1812
adamc@701 1813 \subsection{Client-Side Programming}
adamc@659 1814
adamc@701 1815 Ur/Web supports running code on web browsers, via automatic compilation to JavaScript.
adamc@701 1816
adamc@701 1817 \subsubsection{The Basics}
adamc@701 1818
adamc@701 1819 Clients can open alert dialog boxes, in the usual annoying JavaScript way.
adamc@701 1820 $$\begin{array}{l}
adamc@701 1821 \mt{val} \; \mt{alert} : \mt{string} \to \mt{transaction} \; \mt{unit}
adamc@701 1822 \end{array}$$
adamc@701 1823
adamc@701 1824 Any transaction may be run in a new thread with the $\mt{spawn}$ function.
adamc@701 1825 $$\begin{array}{l}
adamc@701 1826 \mt{val} \; \mt{spawn} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit}
adamc@701 1827 \end{array}$$
adamc@701 1828
adamc@701 1829 The current thread can be paused for at least a specified number of milliseconds.
adamc@701 1830 $$\begin{array}{l}
adamc@701 1831 \mt{val} \; \mt{sleep} : \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@701 1832 \end{array}$$
adamc@701 1833
adamc@787 1834 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 1835 $$\begin{array}{l}
adamc@787 1836 \mt{val} \; \mt{onError} : (\mt{xbody} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787 1837 \mt{val} \; \mt{onFail} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787 1838 \mt{val} \; \mt{onConnectFail} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787 1839 \mt{val} \; \mt{onDisconnect} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787 1840 \mt{val} \; \mt{onServerError} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit}
adamc@787 1841 \end{array}$$
adamc@787 1842
adamc@701 1843 \subsubsection{Functional-Reactive Page Generation}
adamc@701 1844
adamc@701 1845 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 1846
adamc@659 1847 $$\begin{array}{l}
adamc@659 1848 \mt{con} \; \mt{source} :: \mt{Type} \to \mt{Type} \\
adamc@659 1849 \mt{val} \; \mt{source} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{transaction} \; (\mt{source} \; \mt{t}) \\
adamc@659 1850 \mt{val} \; \mt{set} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@659 1851 \mt{val} \; \mt{get} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@659 1852 \end{array}$$
adamc@659 1853
adamc@659 1854 Pure functions over sources are represented in a monad of \emph{signals}.
adamc@659 1855
adamc@659 1856 $$\begin{array}{l}
adamc@659 1857 \mt{con} \; \mt{signal} :: \mt{Type} \to \mt{Type} \\
adamc@659 1858 \mt{val} \; \mt{signal\_monad} : \mt{monad} \; \mt{signal} \\
adamc@659 1859 \mt{val} \; \mt{signal} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{signal} \; \mt{t}
adamc@659 1860 \end{array}$$
adamc@659 1861
adamc@659 1862 A reactive portion of an HTML page is injected with a $\mt{dyn}$ tag, which has a signal-valued attribute $\mt{Signal}$.
adamc@659 1863
adamc@659 1864 $$\begin{array}{l}
adamc@701 1865 \mt{val} \; \mt{dyn} : \mt{use} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to \mt{unit} \\
adamc@701 1866 \hspace{.1in} \to \mt{tag} \; [\mt{Signal} = \mt{signal} \; (\mt{xml} \; \mt{body} \; \mt{use} \; \mt{bind})] \; \mt{body} \; [] \; \mt{use} \; \mt{bind}
adamc@659 1867 \end{array}$$
adamc@659 1868
adamc@701 1869 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 1870
adamc@914 1871 \subsubsection{Remote Procedure Calls}
adamc@914 1872
adamc@914 1873 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 1874
adamc@914 1875 $$\begin{array}{l}
adamc@914 1876 \mt{val} \; \mt{rpc} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@914 1877 \end{array}$$
adamc@914 1878
adamc@701 1879 \subsubsection{Asynchronous Message-Passing}
adamc@701 1880
adamc@701 1881 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 1882
adamc@701 1883 $$\begin{array}{l}
adamc@701 1884 \mt{type} \; \mt{client} \\
adamc@701 1885 \mt{val} \; \mt{self} : \mt{transaction} \; \mt{client}
adamc@701 1886 \end{array}$$
adamc@701 1887
adamc@701 1888 \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 1889
adamc@701 1890 $$\begin{array}{l}
adamc@701 1891 \mt{con} \; \mt{channel} :: \mt{Type} \to \mt{Type} \\
adamc@701 1892 \mt{val} \; \mt{channel} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; (\mt{channel} \; \mt{t}) \\
adamc@701 1893 \mt{val} \; \mt{send} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@701 1894 \mt{val} \; \mt{recv} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@701 1895 \end{array}$$
adamc@701 1896
adamc@701 1897 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 1898
adamc@701 1899 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 1900
adamc@659 1901
adamc@549 1902 \section{Ur/Web Syntax Extensions}
adamc@549 1903
adamc@549 1904 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 1905
adamc@549 1906 \subsection{SQL}
adamc@549 1907
adamc@786 1908 \subsubsection{\label{tables}Table Declarations}
adamc@786 1909
adamc@788 1910 $\mt{table}$ declarations may include constraints, via these grammar rules.
adamc@788 1911 $$\begin{array}{rrcll}
adamc@788 1912 \textrm{Declarations} & d &::=& \mt{table} \; x : c \; [pk[,]] \; cts \\
adamc@788 1913 \textrm{Primary key constraints} & pk &::=& \mt{PRIMARY} \; \mt{KEY} \; K \\
adamc@788 1914 \textrm{Keys} & K &::=& f \mid (f, (f,)^+) \\
adamc@788 1915 \textrm{Constraint sets} & cts &::=& \mt{CONSTRAINT} f \; ct \mid cts, cts \mid \{\{e\}\} \\
adamc@788 1916 \textrm{Constraints} & ct &::=& \mt{UNIQUE} \; K \mid \mt{CHECK} \; E \\
adamc@788 1917 &&& \mid \mt{FOREIGN} \; \mt{KEY} \; K \; \mt{REFERENCES} \; F \; (K) \; [\mt{ON} \; \mt{DELETE} \; pr] \; [\mt{ON} \; \mt{UPDATE} \; pr] \\
adamc@788 1918 \textrm{Foreign tables} & F &::=& x \mid \{\{e\}\} \\
adamc@788 1919 \textrm{Propagation modes} & pr &::=& \mt{NO} \; \mt{ACTION} \mid \mt{RESTRICT} \mid \mt{CASCADE} \mid \mt{SET} \; \mt{NULL}
adamc@788 1920 \end{array}$$
adamc@788 1921
adamc@788 1922 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 1923
adamc@788 1924
adamc@549 1925 \subsubsection{Queries}
adamc@549 1926
adamc@550 1927 Queries $Q$ are added to the rules for expressions $e$.
adamc@550 1928
adamc@549 1929 $$\begin{array}{rrcll}
adamc@550 1930 \textrm{Queries} & Q &::=& (q \; [\mt{ORDER} \; \mt{BY} \; (E \; [o],)^+] \; [\mt{LIMIT} \; N] \; [\mt{OFFSET} \; N]) \\
adamc@1085 1931 \textrm{Pre-queries} & q &::=& \mt{SELECT} \; [\mt{DISTINCT}] \; P \; \mt{FROM} \; F,^+ \; [\mt{WHERE} \; E] \; [\mt{GROUP} \; \mt{BY} \; p,^+] \; [\mt{HAVING} \; E] \\
adamc@1085 1932 &&& \mid q \; R \; q \mid \{\{\{e\}\}\} \\
adamc@549 1933 \textrm{Relational operators} & R &::=& \mt{UNION} \mid \mt{INTERSECT} \mid \mt{EXCEPT}
adamc@549 1934 \end{array}$$
adamc@549 1935
adamc@549 1936 $$\begin{array}{rrcll}
adamc@549 1937 \textrm{Projections} & P &::=& \ast & \textrm{all columns} \\
adamc@549 1938 &&& p,^+ & \textrm{particular columns} \\
adamc@549 1939 \textrm{Pre-projections} & p &::=& t.f & \textrm{one column from a table} \\
adamc@558 1940 &&& t.\{\{c\}\} & \textrm{a record of columns from a table (of kind $\{\mt{Type}\}$)} \\
adamc@549 1941 \textrm{Table names} & t &::=& x & \textrm{constant table name (automatically capitalized)} \\
adamc@549 1942 &&& X & \textrm{constant table name} \\
adamc@549 1943 &&& \{\{c\}\} & \textrm{computed table name (of kind $\mt{Name}$)} \\
adamc@549 1944 \textrm{Column names} & f &::=& X & \textrm{constant column name} \\
adamc@549 1945 &&& \{c\} & \textrm{computed column name (of kind $\mt{Name}$)} \\
adamc@549 1946 \textrm{Tables} & T &::=& x & \textrm{table variable, named locally by its own capitalization} \\
adamc@549 1947 &&& x \; \mt{AS} \; t & \textrm{table variable, with local name} \\
adamc@549 1948 &&& \{\{e\}\} \; \mt{AS} \; t & \textrm{computed table expression, with local name} \\
adamc@1085 1949 \textrm{$\mt{FROM}$ items} & F &::=& T \mid \{\{e\}\} \mid F \; J \; \mt{JOIN} \; F \; \mt{ON} \; E \\
adamc@1085 1950 &&& \mid F \; \mt{CROSS} \; \mt{JOIN} \ F \\
adamc@1085 1951 \textrm{Joins} & J &::=& [\mt{INNER}] \\
adamc@1085 1952 &&& \mid [\mt{LEFT} \mid \mt{RIGHT} \mid \mt{FULL}] \; [\mt{OUTER}] \\
adamc@549 1953 \textrm{SQL expressions} & E &::=& p & \textrm{column references} \\
adamc@549 1954 &&& X & \textrm{named expression references} \\
adamc@549 1955 &&& \{\{e\}\} & \textrm{injected native Ur expressions} \\
adamc@549 1956 &&& \{e\} & \textrm{computed expressions, probably using $\mt{sql\_exp}$ directly} \\
adamc@549 1957 &&& \mt{TRUE} \mid \mt{FALSE} & \textrm{boolean constants} \\
adamc@549 1958 &&& \ell & \textrm{primitive type literals} \\
adamc@549 1959 &&& \mt{NULL} & \textrm{null value (injection of $\mt{None}$)} \\
adamc@549 1960 &&& E \; \mt{IS} \; \mt{NULL} & \textrm{nullness test} \\
adamc@549 1961 &&& n & \textrm{nullary operators} \\
adamc@549 1962 &&& u \; E & \textrm{unary operators} \\
adamc@549 1963 &&& E \; b \; E & \textrm{binary operators} \\
adamc@549 1964 &&& \mt{COUNT}(\ast) & \textrm{count number of rows} \\
adamc@549 1965 &&& a(E) & \textrm{other aggregate function} \\
adamc@549 1966 &&& (E) & \textrm{explicit precedence} \\
adamc@549 1967 \textrm{Nullary operators} & n &::=& \mt{CURRENT\_TIMESTAMP} \\
adamc@549 1968 \textrm{Unary operators} & u &::=& \mt{NOT} \\
adamc@549 1969 \textrm{Binary operators} & b &::=& \mt{AND} \mid \mt{OR} \mid \neq \mid < \mid \leq \mid > \mid \geq \\
adamc@549 1970 \textrm{Aggregate functions} & a &::=& \mt{AVG} \mid \mt{SUM} \mid \mt{MIN} \mid \mt{MAX} \\
adamc@550 1971 \textrm{Directions} & o &::=& \mt{ASC} \mid \mt{DESC} \\
adamc@549 1972 \textrm{SQL integer} & N &::=& n \mid \{e\} \\
adamc@549 1973 \end{array}$$
adamc@549 1974
adamc@1085 1975 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 1976
adamc@550 1977 \subsubsection{DML}
adamc@550 1978
adamc@550 1979 DML commands $D$ are added to the rules for expressions $e$.
adamc@550 1980
adamc@550 1981 $$\begin{array}{rrcll}
adamc@550 1982 \textrm{Commands} & D &::=& (\mt{INSERT} \; \mt{INTO} \; T^E \; (f,^+) \; \mt{VALUES} \; (E,^+)) \\
adamc@550 1983 &&& (\mt{UPDATE} \; T^E \; \mt{SET} \; (f = E,)^+ \; \mt{WHERE} \; E) \\
adamc@550 1984 &&& (\mt{DELETE} \; \mt{FROM} \; T^E \; \mt{WHERE} \; E) \\
adamc@550 1985 \textrm{Table expressions} & T^E &::=& x \mid \{\{e\}\}
adamc@550 1986 \end{array}$$
adamc@550 1987
adamc@550 1988 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 1989
adamc@551 1990 \subsection{XML}
adamc@551 1991
adamc@551 1992 XML fragments $L$ are added to the rules for expressions $e$.
adamc@551 1993
adamc@551 1994 $$\begin{array}{rrcll}
adamc@551 1995 \textrm{XML fragments} & L &::=& \texttt{<xml/>} \mid \texttt{<xml>}l^*\texttt{</xml>} \\
adamc@551 1996 \textrm{XML pieces} & l &::=& \textrm{text} & \textrm{cdata} \\
adamc@551 1997 &&& \texttt{<}g\texttt{/>} & \textrm{tag with no children} \\
adamc@551 1998 &&& \texttt{<}g\texttt{>}l^*\texttt{</}x\texttt{>} & \textrm{tag with children} \\
adamc@559 1999 &&& \{e\} & \textrm{computed XML fragment} \\
adamc@559 2000 &&& \{[e]\} & \textrm{injection of an Ur expression, via the $\mt{Top}.\mt{txt}$ function} \\
adamc@551 2001 \textrm{Tag} & g &::=& h \; (x = v)^* \\
adamc@551 2002 \textrm{Tag head} & h &::=& x & \textrm{tag name} \\
adamc@551 2003 &&& h\{c\} & \textrm{constructor parameter} \\
adamc@551 2004 \textrm{Attribute value} & v &::=& \ell & \textrm{literal value} \\
adamc@551 2005 &&& \{e\} & \textrm{computed value} \\
adamc@551 2006 \end{array}$$
adamc@551 2007
adamc@552 2008
adamc@553 2009 \section{The Structure of Web Applications}
adamc@553 2010
adamc@1127 2011 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 2012
adamc@553 2013 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 2014
adamc@553 2015 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 2016
adamc@558 2017 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 2018
adamc@660 2019 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 2020
adamc@789 2021 \medskip
adamc@789 2022
adamc@789 2023 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 2024
adamc@789 2025 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 2026
adamc@553 2027
adamc@897 2028 \section{The Foreign Function Interface}
adamc@897 2029
adamc@897 2030 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 2031
adamc@897 2032 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 2033
adamc@897 2034 \begin{itemize}
adamc@897 2035 \item \texttt{clientOnly Module.ident} registers a value as being allowed only in client-side code.
adamc@897 2036 \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 2037 \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 2038 \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 2039 \item \texttt{include FILE} requests inclusion of a C header file.
adamc@897 2040 \item \texttt{jsFunc Module.ident=name} gives a mapping from an Ur name for a value to a JavaScript name.
adamc@897 2041 \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 2042 \item \texttt{script URL} requests inclusion of a JavaScript source file within application HTML.
adamc@897 2043 \item \texttt{serverOnly Module.ident} registers a value as being allowed only in server-side code.
adamc@897 2044 \end{itemize}
adamc@897 2045
adamc@897 2046 \subsection{Writing C FFI Code}
adamc@897 2047
adamc@897 2048 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 2049
adamc@897 2050 \begin{itemize}
adamc@897 2051 \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 2052 \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 2053 \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 2054 \end{itemize}
adamc@897 2055
adamc@897 2056 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 2057 \begin{itemize}
adamc@897 2058 \item \begin{verbatim}
adamc@897 2059 void uw_error(uw_context, failure_kind, const char *fmt, ...);
adamc@897 2060 \end{verbatim}
adamc@897 2061 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 2062
adamc@897 2063 \item \begin{verbatim}
adamc@897 2064 void uw_push_cleanup(uw_context, void (*func)(void *), void *arg);
adamc@897 2065 void uw_pop_cleanup(uw_context);
adamc@897 2066 \end{verbatim}
adamc@897 2067 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 2068
adamc@897 2069 \item \begin{verbatim}
adamc@897 2070 void *uw_malloc(uw_context, size_t);
adamc@897 2071 \end{verbatim}
adamc@897 2072 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 2073
adamc@897 2074 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 2075
adamc@897 2076 \item \begin{verbatim}
adamc@897 2077 typedef void (*uw_callback)(void *);
adamc@897 2078 void uw_register_transactional(uw_context, void *data, uw_callback commit,
adamc@897 2079 uw_callback rollback, uw_callback free);
adamc@897 2080 \end{verbatim}
adamc@897 2081 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 2082
adamc@1085 2083 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 2084
adamc@1085 2085 \item \begin{verbatim}
adamc@1085 2086 void *uw_get_global(uw_context, char *name);
adamc@1085 2087 void uw_set_global(uw_context, char *name, void *data, uw_callback free);
adamc@1085 2088 \end{verbatim}
adamc@1085 2089 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 2090
adamc@897 2091 \end{itemize}
adamc@897 2092
adamc@897 2093 \subsection{Writing JavaScript FFI Code}
adamc@897 2094
adamc@897 2095 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 2096
adamc@897 2097 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 2098
adamc@897 2099 \begin{itemize}
adamc@897 2100 \item Integers, floats, strings, characters, and booleans are represented in the usual JavaScript way.
adamc@985 2101 \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 2102 \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 2103 \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 2104 \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 2105 \end{itemize}
adamc@897 2106
adamc@897 2107 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 2108
adamc@897 2109
adamc@552 2110 \section{Compiler Phases}
adamc@552 2111
adamc@552 2112 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 2113
adamc@552 2114 In this section, we step through the main phases of compilation, noting what consequences each phase has for effective programming.
adamc@552 2115
adamc@552 2116 \subsection{Parse}
adamc@552 2117
adamc@552 2118 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 2119
adamc@552 2120 \subsection{Elaborate}
adamc@552 2121
adamc@552 2122 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 2123
adamc@552 2124 \subsection{Unnest}
adamc@552 2125
adamc@552 2126 Named local function definitions are moved to the top level, to avoid the need to generate closures.
adamc@552 2127
adamc@552 2128 \subsection{Corify}
adamc@552 2129
adamc@552 2130 Module system features are compiled away, through inlining of functor definitions at application sites. Afterward, most abstraction boundaries are broken, facilitating optimization.
adamc@552 2131
adamc@552 2132 \subsection{Especialize}
adamc@552 2133
adamc@552 2134 Functions are specialized to particular argument patterns. This is an important trick for avoiding the need to maintain any closures at runtime.
adamc@552 2135
adamc@552 2136 \subsection{Untangle}
adamc@552 2137
adamc@552 2138 Remove unnecessary mutual recursion, splitting recursive groups into strongly-connected components.
adamc@552 2139
adamc@552 2140 \subsection{Shake}
adamc@552 2141
adamc@552 2142 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 2143
adamc@661 2144 \subsection{Rpcify}
adamc@661 2145
adamc@661 2146 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 2147
adamc@661 2148 \subsection{Untangle, Shake}
adamc@661 2149
adamc@661 2150 Repeat these simplifications.
adamc@661 2151
adamc@553 2152 \subsection{\label{tag}Tag}
adamc@552 2153
adamc@552 2154 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 2155
adamc@552 2156 \subsection{Reduce}
adamc@552 2157
adamc@552 2158 Apply definitional equality rules to simplify the program as much as possible. This effectively includes inlining of every non-recursive definition.
adamc@552 2159
adamc@552 2160 \subsection{Unpoly}
adamc@552 2161
adamc@552 2162 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 2163
adamc@552 2164 \subsection{Specialize}
adamc@552 2165
adamc@558 2166 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 2167
adamc@552 2168 \subsection{Shake}
adamc@552 2169
adamc@558 2170 Here the compiler repeats the earlier Shake phase.
adamc@552 2171
adamc@552 2172 \subsection{Monoize}
adamc@552 2173
adamc@552 2174 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 2175
adamc@552 2176 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 2177
adamc@552 2178 \subsection{MonoOpt}
adamc@552 2179
adamc@552 2180 Simple algebraic laws are applied to simplify the program, focusing especially on efficient imperative generation of HTML pages.
adamc@552 2181
adamc@552 2182 \subsection{MonoUntangle}
adamc@552 2183
adamc@552 2184 Unnecessary mutual recursion is broken up again.
adamc@552 2185
adamc@552 2186 \subsection{MonoReduce}
adamc@552 2187
adamc@552 2188 Equivalents of the definitional equality rules are applied to simplify programs, with inlining again playing a major role.
adamc@552 2189
adamc@552 2190 \subsection{MonoShake, MonoOpt}
adamc@552 2191
adamc@552 2192 Unneeded declarations are removed, and basic optimizations are repeated.
adamc@552 2193
adamc@552 2194 \subsection{Fuse}
adamc@552 2195
adamc@552 2196 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 2197
adamc@552 2198 \subsection{MonoUntangle, MonoShake}
adamc@552 2199
adamc@552 2200 Fuse often creates more opportunities to remove spurious mutual recursion.
adamc@552 2201
adamc@552 2202 \subsection{Pathcheck}
adamc@552 2203
adamc@552 2204 The compiler checks that no link or action name has been used more than once.
adamc@552 2205
adamc@552 2206 \subsection{Cjrize}
adamc@552 2207
adamc@552 2208 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 2209
adamc@552 2210 \subsection{C Compilation and Linking}
adamc@552 2211
adamc@552 2212 The output of the last phase is pretty-printed as C source code and passed to GCC.
adamc@552 2213
adamc@552 2214
adamc@524 2215 \end{document}