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New release
author Adam Chlipala <adamc@hcoop.net>
date Sat, 30 Jan 2010 08:45:31 -0500
parents f93dc2ea30c1
children a9ba22d551f0
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@554 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{row types}.
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@1137 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. While that user built Ur/Web successfully with no further tweaks, another OS X user reported that he needed to install Autoconf and Automake from MacPorts and run the following before \texttt{./configure}:
adamc@1137 97
adamc@1137 98 \begin{verbatim}
adamc@1137 99 aclocal
adamc@1137 100 autoconf
adamc@1137 101 \end{verbatim}
adamc@1137 102
adamc@1137 103 He also reported needing to add \texttt{/opt/local/bin/} to his \texttt{\$PATH}, because of an unusual set-up where Autotools files were installed in that directory.
adamc@555 104
adamc@555 105 The Emacs mode can be set to autoload by adding the following to your \texttt{.emacs} file.
adamc@555 106
adamc@555 107 \begin{verbatim}
adamc@555 108 (add-to-list 'load-path "/usr/local/share/emacs/site-lisp/urweb-mode")
adamc@555 109 (load "urweb-mode-startup")
adamc@555 110 \end{verbatim}
adamc@555 111
adamc@555 112 Change the path in the first line if you chose a different Emacs installation path during configuration.
adamc@555 113
adamc@555 114
adamc@556 115 \section{Command-Line Compiler}
adamc@556 116
adamc@556 117 \subsection{Project Files}
adamc@556 118
adamc@556 119 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@556 120
adamc@556 121 \begin{verbatim}
adamc@556 122 database dbname=test
adamc@556 123 sql crud1.sql
adamc@556 124
adamc@556 125 crud
adamc@556 126 crud1
adamc@556 127 \end{verbatim}
adamc@556 128
adamc@556 129 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@556 130
adamc@556 131 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@556 132
adamc@556 133 \begin{verbatim}
adamc@556 134 createdb test
adamc@556 135 psql -f crud1.sql test
adamc@556 136 \end{verbatim}
adamc@556 137
adamc@556 138 A blank line always separates the named directives from a list of modules to include in the project; if there are no named directives, a blank line must begin the file.
adamc@556 139
adamc@556 140 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@556 141
adamc@783 142 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@783 143 \begin{itemize}
adamc@783 144 \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@783 145 \item \texttt{clientOnly Module.ident} registers an FFI function or transaction that may only be run in client browsers.
adamc@783 146 \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@783 147 \item \texttt{database DBSTRING} sets the string to pass to libpq to open a database connection.
adamc@783 148 \item \texttt{debug} saves some intermediate C files, which is mostly useful to help in debugging the compiler itself.
adamc@783 149 \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@783 150 \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@783 151 \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 152 \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@783 153 \item \texttt{jsFunc Module.ident=name} gives the JavaScript name of an FFI value.
adamc@1089 154 \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@783 155 \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@852 156 \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@783 157 \item \texttt{prefix PREFIX} sets the prefix included before every URI within the generated application. The default is \texttt{/}.
adamc@783 158 \item \texttt{profile} generates an executable that may be used with gprof.
adamc@783 159 \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@783 160 \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@783 161 \item \texttt{serverOnly Module.ident} registers an FFI function or transaction that may only be run on the server.
adamc@783 162 \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@783 163 \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@783 164 \end{itemize}
adamc@701 165
adamc@701 166
adamc@557 167 \subsection{Building an Application}
adamc@557 168
adamc@557 169 To compile project \texttt{P.urp}, simply run
adamc@557 170 \begin{verbatim}
adamc@557 171 urweb P
adamc@557 172 \end{verbatim}
adamc@558 173 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@557 174
adamc@557 175 To time how long the different compiler phases run, without generating an executable, run
adamc@557 176 \begin{verbatim}
adamc@557 177 urweb -timing P
adamc@557 178 \end{verbatim}
adamc@557 179
adamc@1086 180 To stop the compilation process after type-checking, run
adamc@1086 181 \begin{verbatim}
adamc@1086 182 urweb -tc P
adamc@1086 183 \end{verbatim}
adamc@1086 184
adamc@896 185 Some other command-line parameters are accepted:
adamc@896 186 \begin{itemize}
adamc@896 187 \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@896 188
adamc@896 189 \item \texttt{-dbms [postgres|mysql|sqlite]}: Sets the database backend to use.
adamc@896 190 \begin{itemize}
adamc@896 191 \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@896 192
adamc@896 193 A command sequence like this can initialize a Postgres database, using a file \texttt{app.sql} generated by the compiler:
adamc@896 194 \begin{verbatim}
adamc@896 195 createdb app
adamc@896 196 psql -f app.sql app
adamc@896 197 \end{verbatim}
adamc@896 198
adamc@896 199 \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@896 200
adamc@896 201 A command sequence like this can initialize a MySQL database:
adamc@896 202 \begin{verbatim}
adamc@896 203 echo "CREATE DATABASE app" | mysql
adamc@896 204 mysql -D app <app.sql
adamc@896 205 \end{verbatim}
adamc@896 206
adamc@896 207 \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@896 208
adamc@896 209 A command like this can initialize an SQLite database:
adamc@896 210 \begin{verbatim}
adamc@896 211 sqlite3 path/to/database/file <app.sql
adamc@896 212 \end{verbatim}
adamc@896 213 \end{itemize}
adamc@896 214
adamc@896 215 \item \texttt{-output FILENAME}: Set where the application executable is written.
adamc@896 216
adamc@1127 217 \item \texttt{-path NAME VALUE}: Set the value of path variable \texttt{\$NAME} to \texttt{VALUE}, for use in \texttt{.urp} files.
adamc@1127 218
adamc@896 219 \item \texttt{-protocol [http|cgi|fastcgi]}: Set the protocol that the generated application speaks.
adamc@896 220 \begin{itemize}
adamc@896 221 \item \texttt{http}: This is the default. It is for building standalone web servers that can be accessed by web browsers directly.
adamc@896 222
adamc@896 223 \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@896 224
adamc@896 225 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@896 226 \begin{verbatim}
adamc@896 227 ScriptAlias /Hello /path/to/hello.exe
adamc@896 228 \end{verbatim}
adamc@896 229
adamc@896 230 \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@896 231
adamc@896 232 To configure a FastCGI program with Apache, one could combine the above \texttt{ScriptAlias} line with a line like this:
adamc@896 233 \begin{verbatim}
adamc@896 234 FastCgiServer /path/to/hello.exe -idle-timeout 99999
adamc@896 235 \end{verbatim}
adamc@896 236 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@896 237
adamc@896 238 Here is some lighttpd configuration for the same application.
adamc@896 239 \begin{verbatim}
adamc@896 240 fastcgi.server = (
adamc@896 241 "/Hello/" =>
adamc@896 242 (( "bin-path" => "/path/to/hello.exe",
adamc@896 243 "socket" => "/tmp/hello",
adamc@896 244 "check-local" => "disable",
adamc@896 245 "docroot" => "/",
adamc@896 246 "max-procs" => "1"
adamc@896 247 ))
adamc@896 248 )
adamc@896 249 \end{verbatim}
adamc@896 250 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@896 251
adamc@896 252 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@896 253 \end{itemize}
adamc@896 254
adamc@1127 255 \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 256
adamc@896 257 \item \texttt{-sql FILENAME}: Set where a database set-up SQL script is written.
adamc@1095 258
adamc@1095 259 \item \texttt{-static}: Link the runtime system statically. The default is to link against dynamic libraries.
adamc@896 260 \end{itemize}
adamc@896 261
adamc@556 262
adamc@529 263 \section{Ur Syntax}
adamc@529 264
adamc@784 265 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@524 266
adamc@524 267 \subsection{Lexical Conventions}
adamc@524 268
adamc@524 269 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@524 270
adamc@524 271 \begin{center}
adamc@524 272 \begin{tabular}{rl}
adamc@524 273 \textbf{\LaTeX} & \textbf{ASCII} \\
adamc@524 274 $\to$ & \cd{->} \\
adamc@652 275 $\longrightarrow$ & \cd{-->} \\
adamc@524 276 $\times$ & \cd{*} \\
adamc@524 277 $\lambda$ & \cd{fn} \\
adamc@524 278 $\Rightarrow$ & \cd{=>} \\
adamc@652 279 $\Longrightarrow$ & \cd{==>} \\
adamc@529 280 $\neq$ & \cd{<>} \\
adamc@529 281 $\leq$ & \cd{<=} \\
adamc@529 282 $\geq$ & \cd{>=} \\
adamc@524 283 \\
adamc@524 284 $x$ & Normal textual identifier, not beginning with an uppercase letter \\
adamc@525 285 $X$ & Normal textual identifier, beginning with an uppercase letter \\
adamc@524 286 \end{tabular}
adamc@524 287 \end{center}
adamc@524 288
adamc@525 289 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@524 290
adamc@873 291 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@526 292
adamc@527 293 This version of the manual doesn't include operator precedences; see \texttt{src/urweb.grm} for that.
adamc@527 294
adamc@552 295 \subsection{\label{core}Core Syntax}
adamc@524 296
adamc@524 297 \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@524 298 $$\begin{array}{rrcll}
adamc@524 299 \textrm{Kinds} & \kappa &::=& \mt{Type} & \textrm{proper types} \\
adamc@525 300 &&& \mt{Unit} & \textrm{the trivial constructor} \\
adamc@525 301 &&& \mt{Name} & \textrm{field names} \\
adamc@525 302 &&& \kappa \to \kappa & \textrm{type-level functions} \\
adamc@525 303 &&& \{\kappa\} & \textrm{type-level records} \\
adamc@525 304 &&& (\kappa\times^+) & \textrm{type-level tuples} \\
adamc@652 305 &&& X & \textrm{variable} \\
adamc@652 306 &&& X \longrightarrow k & \textrm{kind-polymorphic type-level function} \\
adamc@529 307 &&& \_\_ & \textrm{wildcard} \\
adamc@525 308 &&& (\kappa) & \textrm{explicit precedence} \\
adamc@524 309 \end{array}$$
adamc@524 310
adamc@524 311 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@524 312 $$\begin{array}{rrcll}
adamc@524 313 \textrm{Explicitness} & ? &::=& :: & \textrm{explicit} \\
adamc@558 314 &&& ::: & \textrm{implicit}
adamc@524 315 \end{array}$$
adamc@524 316
adamc@524 317 \emph{Constructors} are the main class of compile-time-only data. They include proper types and are classified by kinds.
adamc@524 318 $$\begin{array}{rrcll}
adamc@524 319 \textrm{Constructors} & c, \tau &::=& (c) :: \kappa & \textrm{kind annotation} \\
adamc@530 320 &&& \hat{x} & \textrm{constructor variable} \\
adamc@524 321 \\
adamc@525 322 &&& \tau \to \tau & \textrm{function type} \\
adamc@525 323 &&& x \; ? \; \kappa \to \tau & \textrm{polymorphic function type} \\
adamc@652 324 &&& X \longrightarrow \tau & \textrm{kind-polymorphic function type} \\
adamc@525 325 &&& \$ c & \textrm{record type} \\
adamc@524 326 \\
adamc@525 327 &&& c \; c & \textrm{type-level function application} \\
adamc@530 328 &&& \lambda x \; :: \; \kappa \Rightarrow c & \textrm{type-level function abstraction} \\
adamc@524 329 \\
adamc@652 330 &&& X \Longrightarrow c & \textrm{type-level kind-polymorphic function abstraction} \\
adamc@655 331 &&& c [\kappa] & \textrm{type-level kind-polymorphic function application} \\
adamc@652 332 \\
adamc@525 333 &&& () & \textrm{type-level unit} \\
adamc@525 334 &&& \#X & \textrm{field name} \\
adamc@524 335 \\
adamc@525 336 &&& [(c = c)^*] & \textrm{known-length type-level record} \\
adamc@525 337 &&& c \rc c & \textrm{type-level record concatenation} \\
adamc@652 338 &&& \mt{map} & \textrm{type-level record map} \\
adamc@524 339 \\
adamc@558 340 &&& (c,^+) & \textrm{type-level tuple} \\
adamc@525 341 &&& c.n & \textrm{type-level tuple projection ($n \in \mathbb N^+$)} \\
adamc@524 342 \\
adamc@652 343 &&& [c \sim c] \Rightarrow \tau & \textrm{guarded type} \\
adamc@524 344 \\
adamc@529 345 &&& \_ :: \kappa & \textrm{wildcard} \\
adamc@525 346 &&& (c) & \textrm{explicit precedence} \\
adamc@530 347 \\
adamc@530 348 \textrm{Qualified uncapitalized variables} & \hat{x} &::=& x & \textrm{not from a module} \\
adamc@530 349 &&& M.x & \textrm{projection from a module} \\
adamc@525 350 \end{array}$$
adamc@525 351
adamc@655 352 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@655 353
adamc@525 354 Modules of the module system are described by \emph{signatures}.
adamc@525 355 $$\begin{array}{rrcll}
adamc@525 356 \textrm{Signatures} & S &::=& \mt{sig} \; s^* \; \mt{end} & \textrm{constant} \\
adamc@525 357 &&& X & \textrm{variable} \\
adamc@525 358 &&& \mt{functor}(X : S) : S & \textrm{functor} \\
adamc@529 359 &&& S \; \mt{where} \; \mt{con} \; x = c & \textrm{concretizing an abstract constructor} \\
adamc@525 360 &&& M.X & \textrm{projection from a module} \\
adamc@525 361 \\
adamc@525 362 \textrm{Signature items} & s &::=& \mt{con} \; x :: \kappa & \textrm{abstract constructor} \\
adamc@525 363 &&& \mt{con} \; x :: \kappa = c & \textrm{concrete constructor} \\
adamc@528 364 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529 365 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@525 366 &&& \mt{val} \; x : \tau & \textrm{value} \\
adamc@525 367 &&& \mt{structure} \; X : S & \textrm{sub-module} \\
adamc@525 368 &&& \mt{signature} \; X = S & \textrm{sub-signature} \\
adamc@525 369 &&& \mt{include} \; S & \textrm{signature inclusion} \\
adamc@525 370 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@654 371 &&& \mt{class} \; x :: \kappa & \textrm{abstract constructor class} \\
adamc@654 372 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@525 373 \\
adamc@525 374 \textrm{Datatype constructors} & dc &::=& X & \textrm{nullary constructor} \\
adamc@525 375 &&& X \; \mt{of} \; \tau & \textrm{unary constructor} \\
adamc@524 376 \end{array}$$
adamc@524 377
adamc@526 378 \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@526 379 $$\begin{array}{rrcll}
adamc@526 380 \textrm{Patterns} & p &::=& \_ & \textrm{wildcard} \\
adamc@526 381 &&& x & \textrm{variable} \\
adamc@526 382 &&& \ell & \textrm{constant} \\
adamc@526 383 &&& \hat{X} & \textrm{nullary constructor} \\
adamc@526 384 &&& \hat{X} \; p & \textrm{unary constructor} \\
adamc@526 385 &&& \{(x = p,)^*\} & \textrm{rigid record pattern} \\
adamc@526 386 &&& \{(x = p,)^+, \ldots\} & \textrm{flexible record pattern} \\
adamc@852 387 &&& p : \tau & \textrm{type annotation} \\
adamc@527 388 &&& (p) & \textrm{explicit precedence} \\
adamc@526 389 \\
adamc@529 390 \textrm{Qualified capitalized variables} & \hat{X} &::=& X & \textrm{not from a module} \\
adamc@526 391 &&& M.X & \textrm{projection from a module} \\
adamc@526 392 \end{array}$$
adamc@526 393
adamc@527 394 \emph{Expressions} are the main run-time entities, corresponding to both ``expressions'' and ``statements'' in mainstream imperative languages.
adamc@527 395 $$\begin{array}{rrcll}
adamc@527 396 \textrm{Expressions} & e &::=& e : \tau & \textrm{type annotation} \\
adamc@529 397 &&& \hat{x} & \textrm{variable} \\
adamc@529 398 &&& \hat{X} & \textrm{datatype constructor} \\
adamc@527 399 &&& \ell & \textrm{constant} \\
adamc@527 400 \\
adamc@527 401 &&& e \; e & \textrm{function application} \\
adamc@527 402 &&& \lambda x : \tau \Rightarrow e & \textrm{function abstraction} \\
adamc@527 403 &&& e [c] & \textrm{polymorphic function application} \\
adamc@852 404 &&& \lambda [x \; ? \; \kappa] \Rightarrow e & \textrm{polymorphic function abstraction} \\
adamc@655 405 &&& e [\kappa] & \textrm{kind-polymorphic function application} \\
adamc@652 406 &&& X \Longrightarrow e & \textrm{kind-polymorphic function abstraction} \\
adamc@527 407 \\
adamc@527 408 &&& \{(c = e,)^*\} & \textrm{known-length record} \\
adamc@527 409 &&& e.c & \textrm{record field projection} \\
adamc@527 410 &&& e \rc e & \textrm{record concatenation} \\
adamc@527 411 &&& e \rcut c & \textrm{removal of a single record field} \\
adamc@527 412 &&& e \rcutM c & \textrm{removal of multiple record fields} \\
adamc@527 413 \\
adamc@527 414 &&& \mt{let} \; ed^* \; \mt{in} \; e \; \mt{end} & \textrm{local definitions} \\
adamc@527 415 \\
adamc@527 416 &&& \mt{case} \; e \; \mt{of} \; (p \Rightarrow e|)^+ & \textrm{pattern matching} \\
adamc@527 417 \\
adamc@654 418 &&& \lambda [c \sim c] \Rightarrow e & \textrm{guarded expression abstraction} \\
adamc@654 419 &&& e \; ! & \textrm{guarded expression application} \\
adamc@527 420 \\
adamc@527 421 &&& \_ & \textrm{wildcard} \\
adamc@527 422 &&& (e) & \textrm{explicit precedence} \\
adamc@527 423 \\
adamc@527 424 \textrm{Local declarations} & ed &::=& \cd{val} \; x : \tau = e & \textrm{non-recursive value} \\
adamc@527 425 &&& \cd{val} \; \cd{rec} \; (x : \tau = e \; \cd{and})^+ & \textrm{mutually-recursive values} \\
adamc@527 426 \end{array}$$
adamc@527 427
adamc@655 428 As with constructors, we include both abstraction and application for kind polymorphism, but applications are only inferred internally.
adamc@655 429
adamc@528 430 \emph{Declarations} primarily bring new symbols into context.
adamc@528 431 $$\begin{array}{rrcll}
adamc@528 432 \textrm{Declarations} & d &::=& \mt{con} \; x :: \kappa = c & \textrm{constructor synonym} \\
adamc@528 433 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529 434 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@528 435 &&& \mt{val} \; x : \tau = e & \textrm{value} \\
adamc@528 436 &&& \mt{val} \; \cd{rec} \; (x : \tau = e \; \mt{and})^+ & \textrm{mutually-recursive values} \\
adamc@528 437 &&& \mt{structure} \; X : S = M & \textrm{module definition} \\
adamc@528 438 &&& \mt{signature} \; X = S & \textrm{signature definition} \\
adamc@528 439 &&& \mt{open} \; M & \textrm{module inclusion} \\
adamc@528 440 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@528 441 &&& \mt{open} \; \mt{constraints} \; M & \textrm{inclusion of just the constraints from a module} \\
adamc@528 442 &&& \mt{table} \; x : c & \textrm{SQL table} \\
adamc@784 443 &&& \mt{view} \; x : c & \textrm{SQL view} \\
adamc@528 444 &&& \mt{sequence} \; x & \textrm{SQL sequence} \\
adamc@535 445 &&& \mt{cookie} \; x : \tau & \textrm{HTTP cookie} \\
adamc@784 446 &&& \mt{style} \; x : \tau & \textrm{CSS class} \\
adamc@654 447 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@1085 448 &&& \mt{task} \; e = e & \textrm{recurring task} \\
adamc@528 449 \\
adamc@529 450 \textrm{Modules} & M &::=& \mt{struct} \; d^* \; \mt{end} & \textrm{constant} \\
adamc@529 451 &&& X & \textrm{variable} \\
adamc@529 452 &&& M.X & \textrm{projection} \\
adamc@529 453 &&& M(M) & \textrm{functor application} \\
adamc@529 454 &&& \mt{functor}(X : S) : S = M & \textrm{functor abstraction} \\
adamc@528 455 \end{array}$$
adamc@528 456
adamc@528 457 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@527 458
adamc@784 459 We omit some extra possibilities in $\mt{table}$ syntax, deferring them to Section \ref{tables}.
adamc@784 460
adamc@529 461 \subsection{Shorthands}
adamc@529 462
adamc@529 463 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@529 464
adamc@529 465 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@529 466
adamc@529 467 A record type may be written $\{(c = c,)^*\}$, which elaborates to $\$[(c = c,)^*]$.
adamc@529 468
adamc@533 469 The notation $[c_1, \ldots, c_n]$ is shorthand for $[c_1 = (), \ldots, c_n = ()]$.
adamc@533 470
adamc@529 471 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@529 472
adamc@852 473 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@529 474
adamc@529 475 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@529 476
adamc@529 477 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@529 478
adamc@654 479 A signature item or declaration $\mt{class} \; x = \lambda y \Rightarrow c$ may be abbreviated $\mt{class} \; x \; y = c$.
adamc@529 480
adamc@1102 481 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@529 482
adamc@852 483 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@529 484
adamc@852 485 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@852 486
adamc@852 487 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@529 488
adamc@529 489 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@529 490
adamc@852 491 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@852 492
adamc@853 493 A declaration $\mt{table} \; x : \{(c = c,)^*\}$ is elaborated into $\mt{table} \; x : [(c = c,)^*]$.
adamc@529 494
adamc@529 495 The syntax $\mt{where} \; \mt{type}$ is an alternate form of $\mt{where} \; \mt{con}$.
adamc@529 496
adamc@529 497 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@529 498
adamc@529 499 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@529 500
adamc@784 501 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@529 502
adamc@530 503
adamc@530 504 \section{Static Semantics}
adamc@530 505
adamc@530 506 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@530 507
adamc@530 508 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@530 509 \begin{itemize}
adamc@655 510 \item $\Gamma \vdash \kappa$ expresses kind well-formedness.
adamc@530 511 \item $\Gamma \vdash c :: \kappa$ assigns a kind to a constructor in a context.
adamc@530 512 \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@531 513 \item $\Gamma \vdash c \hookrightarrow C$ proves that record constructor $c$ decomposes into set $C$ of field names and record constructors.
adamc@530 514 \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@530 515 \item $\Gamma \vdash e : \tau$ is a standard typing judgment.
adamc@534 516 \item $\Gamma \vdash p \leadsto \Gamma; \tau$ combines typing of patterns with calculation of which new variables they bind.
adamc@537 517 \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@537 518 \item $\Gamma \vdash S \equiv S$ is the signature equivalence judgment.
adamc@536 519 \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@530 520 \item $\Gamma \vdash M : S$ is the module signature checking judgment.
adamc@537 521 \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@539 522 \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@530 523 \end{itemize}
adamc@530 524
adamc@655 525
adamc@655 526 \subsection{Kind Well-Formedness}
adamc@655 527
adamc@655 528 $$\infer{\Gamma \vdash \mt{Type}}{}
adamc@655 529 \quad \infer{\Gamma \vdash \mt{Unit}}{}
adamc@655 530 \quad \infer{\Gamma \vdash \mt{Name}}{}
adamc@655 531 \quad \infer{\Gamma \vdash \kappa_1 \to \kappa_2}{
adamc@655 532 \Gamma \vdash \kappa_1
adamc@655 533 & \Gamma \vdash \kappa_2
adamc@655 534 }
adamc@655 535 \quad \infer{\Gamma \vdash \{\kappa\}}{
adamc@655 536 \Gamma \vdash \kappa
adamc@655 537 }
adamc@655 538 \quad \infer{\Gamma \vdash (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@655 539 \forall i: \Gamma \vdash \kappa_i
adamc@655 540 }$$
adamc@655 541
adamc@655 542 $$\infer{\Gamma \vdash X}{
adamc@655 543 X \in \Gamma
adamc@655 544 }
adamc@655 545 \quad \infer{\Gamma \vdash X \longrightarrow \kappa}{
adamc@655 546 \Gamma, X \vdash \kappa
adamc@655 547 }$$
adamc@655 548
adamc@530 549 \subsection{Kinding}
adamc@530 550
adamc@655 551 We write $[X \mapsto \kappa_1]\kappa_2$ for capture-avoiding substitution of $\kappa_1$ for $X$ in $\kappa_2$.
adamc@655 552
adamc@530 553 $$\infer{\Gamma \vdash (c) :: \kappa :: \kappa}{
adamc@530 554 \Gamma \vdash c :: \kappa
adamc@530 555 }
adamc@530 556 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530 557 x :: \kappa \in \Gamma
adamc@530 558 }
adamc@530 559 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530 560 x :: \kappa = c \in \Gamma
adamc@530 561 }$$
adamc@530 562
adamc@530 563 $$\infer{\Gamma \vdash M.x :: \kappa}{
adamc@537 564 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 565 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = \kappa
adamc@530 566 }
adamc@530 567 \quad \infer{\Gamma \vdash M.x :: \kappa}{
adamc@537 568 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 569 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@530 570 }$$
adamc@530 571
adamc@530 572 $$\infer{\Gamma \vdash \tau_1 \to \tau_2 :: \mt{Type}}{
adamc@530 573 \Gamma \vdash \tau_1 :: \mt{Type}
adamc@530 574 & \Gamma \vdash \tau_2 :: \mt{Type}
adamc@530 575 }
adamc@530 576 \quad \infer{\Gamma \vdash x \; ? \: \kappa \to \tau :: \mt{Type}}{
adamc@530 577 \Gamma, x :: \kappa \vdash \tau :: \mt{Type}
adamc@530 578 }
adamc@655 579 \quad \infer{\Gamma \vdash X \longrightarrow \tau :: \mt{Type}}{
adamc@655 580 \Gamma, X \vdash \tau :: \mt{Type}
adamc@655 581 }
adamc@530 582 \quad \infer{\Gamma \vdash \$c :: \mt{Type}}{
adamc@530 583 \Gamma \vdash c :: \{\mt{Type}\}
adamc@530 584 }$$
adamc@530 585
adamc@530 586 $$\infer{\Gamma \vdash c_1 \; c_2 :: \kappa_2}{
adamc@530 587 \Gamma \vdash c_1 :: \kappa_1 \to \kappa_2
adamc@530 588 & \Gamma \vdash c_2 :: \kappa_1
adamc@530 589 }
adamc@530 590 \quad \infer{\Gamma \vdash \lambda x \; :: \; \kappa_1 \Rightarrow c :: \kappa_1 \to \kappa_2}{
adamc@530 591 \Gamma, x :: \kappa_1 \vdash c :: \kappa_2
adamc@530 592 }$$
adamc@530 593
adamc@655 594 $$\infer{\Gamma \vdash c[\kappa'] :: [X \mapsto \kappa']\kappa}{
adamc@655 595 \Gamma \vdash c :: X \to \kappa
adamc@655 596 & \Gamma \vdash \kappa'
adamc@655 597 }
adamc@655 598 \quad \infer{\Gamma \vdash X \Longrightarrow c :: X \to \kappa}{
adamc@655 599 \Gamma, X \vdash c :: \kappa
adamc@655 600 }$$
adamc@655 601
adamc@530 602 $$\infer{\Gamma \vdash () :: \mt{Unit}}{}
adamc@530 603 \quad \infer{\Gamma \vdash \#X :: \mt{Name}}{}$$
adamc@530 604
adamc@530 605 $$\infer{\Gamma \vdash [\overline{c_i = c'_i}] :: \{\kappa\}}{
adamc@530 606 \forall i: \Gamma \vdash c_i : \mt{Name}
adamc@530 607 & \Gamma \vdash c'_i :: \kappa
adamc@530 608 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@530 609 }
adamc@530 610 \quad \infer{\Gamma \vdash c_1 \rc c_2 :: \{\kappa\}}{
adamc@530 611 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530 612 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@530 613 & \Gamma \vdash c_1 \sim c_2
adamc@530 614 }$$
adamc@530 615
adamc@655 616 $$\infer{\Gamma \vdash \mt{map} :: (\kappa_1 \to \kappa_2) \to \{\kappa_1\} \to \{\kappa_2\}}{}$$
adamc@530 617
adamc@573 618 $$\infer{\Gamma \vdash (\overline c) :: (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@573 619 \forall i: \Gamma \vdash c_i :: \kappa_i
adamc@530 620 }
adamc@573 621 \quad \infer{\Gamma \vdash c.i :: \kappa_i}{
adamc@573 622 \Gamma \vdash c :: (\kappa_1 \times \ldots \times \kappa_n)
adamc@530 623 }$$
adamc@530 624
adamc@655 625 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow \tau :: \mt{Type}}{
adamc@655 626 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530 627 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@655 628 & \Gamma, c_1 \sim c_2 \vdash \tau :: \mt{Type}
adamc@530 629 }$$
adamc@530 630
adamc@531 631 \subsection{Record Disjointness}
adamc@531 632
adamc@531 633 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@558 634 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@558 635 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@558 636 & \forall c'_1 \in C_1, c'_2 \in C_2: \Gamma \vdash c'_1 \sim c'_2
adamc@531 637 }
adamc@531 638 \quad \infer{\Gamma \vdash X \sim X'}{
adamc@531 639 X \neq X'
adamc@531 640 }$$
adamc@531 641
adamc@531 642 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@531 643 c'_1 \sim c'_2 \in \Gamma
adamc@558 644 & \Gamma \vdash c'_1 \hookrightarrow C_1
adamc@558 645 & \Gamma \vdash c'_2 \hookrightarrow C_2
adamc@558 646 & c_1 \in C_1
adamc@558 647 & c_2 \in C_2
adamc@531 648 }$$
adamc@531 649
adamc@531 650 $$\infer{\Gamma \vdash c \hookrightarrow \{c\}}{}
adamc@531 651 \quad \infer{\Gamma \vdash [\overline{c = c'}] \hookrightarrow \{\overline{c}\}}{}
adamc@531 652 \quad \infer{\Gamma \vdash c_1 \rc c_2 \hookrightarrow C_1 \cup C_2}{
adamc@531 653 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@531 654 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@531 655 }
adamc@531 656 \quad \infer{\Gamma \vdash c \hookrightarrow C}{
adamc@531 657 \Gamma \vdash c \equiv c'
adamc@531 658 & \Gamma \vdash c' \hookrightarrow C
adamc@531 659 }
adamc@531 660 \quad \infer{\Gamma \vdash \mt{map} \; f \; c \hookrightarrow C}{
adamc@531 661 \Gamma \vdash c \hookrightarrow C
adamc@531 662 }$$
adamc@531 663
adamc@541 664 \subsection{\label{definitional}Definitional Equality}
adamc@532 665
adamc@655 666 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@532 667
adamc@532 668 $$\infer{\Gamma \vdash c \equiv c}{}
adamc@532 669 \quad \infer{\Gamma \vdash c_1 \equiv c_2}{
adamc@532 670 \Gamma \vdash c_2 \equiv c_1
adamc@532 671 }
adamc@532 672 \quad \infer{\Gamma \vdash c_1 \equiv c_3}{
adamc@532 673 \Gamma \vdash c_1 \equiv c_2
adamc@532 674 & \Gamma \vdash c_2 \equiv c_3
adamc@532 675 }
adamc@532 676 \quad \infer{\Gamma \vdash \mathcal C[c_1] \equiv \mathcal C[c_2]}{
adamc@532 677 \Gamma \vdash c_1 \equiv c_2
adamc@532 678 }$$
adamc@532 679
adamc@532 680 $$\infer{\Gamma \vdash x \equiv c}{
adamc@532 681 x :: \kappa = c \in \Gamma
adamc@532 682 }
adamc@532 683 \quad \infer{\Gamma \vdash M.x \equiv c}{
adamc@537 684 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 685 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@532 686 }
adamc@532 687 \quad \infer{\Gamma \vdash (\overline c).i \equiv c_i}{}$$
adamc@532 688
adamc@532 689 $$\infer{\Gamma \vdash (\lambda x :: \kappa \Rightarrow c) \; c' \equiv [x \mapsto c'] c}{}
adamc@655 690 \quad \infer{\Gamma \vdash (X \Longrightarrow c) [\kappa] \equiv [X \mapsto \kappa] c}{}$$
adamc@655 691
adamc@655 692 $$\infer{\Gamma \vdash c_1 \rc c_2 \equiv c_2 \rc c_1}{}
adamc@532 693 \quad \infer{\Gamma \vdash c_1 \rc (c_2 \rc c_3) \equiv (c_1 \rc c_2) \rc c_3}{}$$
adamc@532 694
adamc@532 695 $$\infer{\Gamma \vdash [] \rc c \equiv c}{}
adamc@532 696 \quad \infer{\Gamma \vdash [\overline{c_1 = c'_1}] \rc [\overline{c_2 = c'_2}] \equiv [\overline{c_1 = c'_1}, \overline{c_2 = c'_2}]}{}$$
adamc@532 697
adamc@655 698 $$\infer{\Gamma \vdash \mt{map} \; f \; [] \equiv []}{}
adamc@655 699 \quad \infer{\Gamma \vdash \mt{map} \; f \; ([c_1 = c_2] \rc c) \equiv [c_1 = f \; c_2] \rc \mt{map} \; f \; c}{}$$
adamc@532 700
adamc@532 701 $$\infer{\Gamma \vdash \mt{map} \; (\lambda x \Rightarrow x) \; c \equiv c}{}
adamc@655 702 \quad \infer{\Gamma \vdash \mt{map} \; f \; (\mt{map} \; f' \; c)
adamc@655 703 \equiv \mt{map} \; (\lambda x \Rightarrow f \; (f' \; x)) \; c}{}$$
adamc@532 704
adamc@532 705 $$\infer{\Gamma \vdash \mt{map} \; f \; (c_1 \rc c_2) \equiv \mt{map} \; f \; c_1 \rc \mt{map} \; f \; c_2}{}$$
adamc@531 706
adamc@534 707 \subsection{Expression Typing}
adamc@533 708
adamc@873 709 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@533 710
adamc@533 711 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@533 712
adamc@533 713 $$\infer{\Gamma \vdash e : \tau : \tau}{
adamc@533 714 \Gamma \vdash e : \tau
adamc@533 715 }
adamc@533 716 \quad \infer{\Gamma \vdash e : \tau}{
adamc@533 717 \Gamma \vdash e : \tau'
adamc@533 718 & \Gamma \vdash \tau' \equiv \tau
adamc@533 719 }
adamc@533 720 \quad \infer{\Gamma \vdash \ell : T(\ell)}{}$$
adamc@533 721
adamc@533 722 $$\infer{\Gamma \vdash x : \mathcal I(\tau)}{
adamc@533 723 x : \tau \in \Gamma
adamc@533 724 }
adamc@533 725 \quad \infer{\Gamma \vdash M.x : \mathcal I(\tau)}{
adamc@537 726 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 727 & \mt{proj}(M, \overline{s}, \mt{val} \; x) = \tau
adamc@533 728 }
adamc@533 729 \quad \infer{\Gamma \vdash X : \mathcal I(\tau)}{
adamc@533 730 X : \tau \in \Gamma
adamc@533 731 }
adamc@533 732 \quad \infer{\Gamma \vdash M.X : \mathcal I(\tau)}{
adamc@537 733 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 734 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \tau
adamc@533 735 }$$
adamc@533 736
adamc@533 737 $$\infer{\Gamma \vdash e_1 \; e_2 : \tau_2}{
adamc@533 738 \Gamma \vdash e_1 : \tau_1 \to \tau_2
adamc@533 739 & \Gamma \vdash e_2 : \tau_1
adamc@533 740 }
adamc@533 741 \quad \infer{\Gamma \vdash \lambda x : \tau_1 \Rightarrow e : \tau_1 \to \tau_2}{
adamc@533 742 \Gamma, x : \tau_1 \vdash e : \tau_2
adamc@533 743 }$$
adamc@533 744
adamc@533 745 $$\infer{\Gamma \vdash e [c] : [x \mapsto c]\tau}{
adamc@533 746 \Gamma \vdash e : x :: \kappa \to \tau
adamc@533 747 & \Gamma \vdash c :: \kappa
adamc@533 748 }
adamc@852 749 \quad \infer{\Gamma \vdash \lambda [x \; ? \; \kappa] \Rightarrow e : x \; ? \; \kappa \to \tau}{
adamc@533 750 \Gamma, x :: \kappa \vdash e : \tau
adamc@533 751 }$$
adamc@533 752
adamc@655 753 $$\infer{\Gamma \vdash e [\kappa] : [X \mapsto \kappa]\tau}{
adamc@655 754 \Gamma \vdash e : X \longrightarrow \tau
adamc@655 755 & \Gamma \vdash \kappa
adamc@655 756 }
adamc@655 757 \quad \infer{\Gamma \vdash X \Longrightarrow e : X \longrightarrow \tau}{
adamc@655 758 \Gamma, X \vdash e : \tau
adamc@655 759 }$$
adamc@655 760
adamc@533 761 $$\infer{\Gamma \vdash \{\overline{c = e}\} : \{\overline{c : \tau}\}}{
adamc@533 762 \forall i: \Gamma \vdash c_i :: \mt{Name}
adamc@533 763 & \Gamma \vdash e_i : \tau_i
adamc@533 764 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@533 765 }
adamc@533 766 \quad \infer{\Gamma \vdash e.c : \tau}{
adamc@533 767 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533 768 }
adamc@533 769 \quad \infer{\Gamma \vdash e_1 \rc e_2 : \$(c_1 \rc c_2)}{
adamc@533 770 \Gamma \vdash e_1 : \$c_1
adamc@533 771 & \Gamma \vdash e_2 : \$c_2
adamc@573 772 & \Gamma \vdash c_1 \sim c_2
adamc@533 773 }$$
adamc@533 774
adamc@533 775 $$\infer{\Gamma \vdash e \rcut c : \$c'}{
adamc@533 776 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533 777 }
adamc@533 778 \quad \infer{\Gamma \vdash e \rcutM c : \$c'}{
adamc@533 779 \Gamma \vdash e : \$(c \rc c')
adamc@533 780 }$$
adamc@533 781
adamc@533 782 $$\infer{\Gamma \vdash \mt{let} \; \overline{ed} \; \mt{in} \; e \; \mt{end} : \tau}{
adamc@533 783 \Gamma \vdash \overline{ed} \leadsto \Gamma'
adamc@533 784 & \Gamma' \vdash e : \tau
adamc@533 785 }
adamc@533 786 \quad \infer{\Gamma \vdash \mt{case} \; e \; \mt{of} \; \overline{p \Rightarrow e} : \tau}{
adamc@533 787 \forall i: \Gamma \vdash p_i \leadsto \Gamma_i, \tau'
adamc@533 788 & \Gamma_i \vdash e_i : \tau
adamc@533 789 }$$
adamc@533 790
adamc@573 791 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow e : \lambda [c_1 \sim c_2] \Rightarrow \tau}{
adamc@533 792 \Gamma \vdash c_1 :: \{\kappa\}
adamc@655 793 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@533 794 & \Gamma, c_1 \sim c_2 \vdash e : \tau
adamc@662 795 }
adamc@662 796 \quad \infer{\Gamma \vdash e \; ! : \tau}{
adamc@662 797 \Gamma \vdash e : [c_1 \sim c_2] \Rightarrow \tau
adamc@662 798 & \Gamma \vdash c_1 \sim c_2
adamc@533 799 }$$
adamc@533 800
adamc@534 801 \subsection{Pattern Typing}
adamc@534 802
adamc@534 803 $$\infer{\Gamma \vdash \_ \leadsto \Gamma; \tau}{}
adamc@534 804 \quad \infer{\Gamma \vdash x \leadsto \Gamma, x : \tau; \tau}{}
adamc@534 805 \quad \infer{\Gamma \vdash \ell \leadsto \Gamma; T(\ell)}{}$$
adamc@534 806
adamc@534 807 $$\infer{\Gamma \vdash X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534 808 X : \overline{x ::: \mt{Type}} \to \tau \in \Gamma
adamc@534 809 & \textrm{$\tau$ not a function type}
adamc@534 810 }
adamc@534 811 \quad \infer{\Gamma \vdash X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534 812 X : \overline{x ::: \mt{Type}} \to \tau'' \to \tau \in \Gamma
adamc@534 813 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534 814 }$$
adamc@534 815
adamc@534 816 $$\infer{\Gamma \vdash M.X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537 817 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 818 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau
adamc@534 819 & \textrm{$\tau$ not a function type}
adamc@534 820 }$$
adamc@534 821
adamc@534 822 $$\infer{\Gamma \vdash M.X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537 823 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 824 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau'' \to \tau
adamc@534 825 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534 826 }$$
adamc@534 827
adamc@534 828 $$\infer{\Gamma \vdash \{\overline{x = p}\} \leadsto \Gamma_n; \{\overline{x = \tau}\}}{
adamc@534 829 \Gamma_0 = \Gamma
adamc@534 830 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534 831 }
adamc@534 832 \quad \infer{\Gamma \vdash \{\overline{x = p}, \ldots\} \leadsto \Gamma_n; \$([\overline{x = \tau}] \rc c)}{
adamc@534 833 \Gamma_0 = \Gamma
adamc@534 834 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534 835 }$$
adamc@534 836
adamc@852 837 $$\infer{\Gamma \vdash p : \tau \leadsto \Gamma'; \tau}{
adamc@852 838 \Gamma \vdash p \leadsto \Gamma'; \tau'
adamc@852 839 & \Gamma \vdash \tau' \equiv \tau
adamc@852 840 }$$
adamc@852 841
adamc@535 842 \subsection{Declaration Typing}
adamc@535 843
adamc@535 844 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@535 845
adamc@655 846 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@535 847
adamc@558 848 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@537 849 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@535 850
adamc@535 851 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535 852 \quad \infer{\Gamma \vdash d, \overline{d} \leadsto \Gamma''}{
adamc@535 853 \Gamma \vdash d \leadsto \Gamma'
adamc@535 854 & \Gamma' \vdash \overline{d} \leadsto \Gamma''
adamc@535 855 }$$
adamc@535 856
adamc@535 857 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@535 858 \Gamma \vdash c :: \kappa
adamc@535 859 }
adamc@535 860 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@535 861 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@535 862 }$$
adamc@535 863
adamc@535 864 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537 865 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 866 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@535 867 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@535 868 }$$
adamc@535 869
adamc@535 870 $$\infer{\Gamma \vdash \mt{val} \; x : \tau = e \leadsto \Gamma, x : \tau}{
adamc@535 871 \Gamma \vdash e : \tau
adamc@535 872 }$$
adamc@535 873
adamc@535 874 $$\infer{\Gamma \vdash \mt{val} \; \mt{rec} \; \overline{x : \tau = e} \leadsto \Gamma, \overline{x : \tau}}{
adamc@535 875 \forall i: \Gamma, \overline{x : \tau} \vdash e_i : \tau_i
adamc@535 876 & \textrm{$e_i$ starts with an expression $\lambda$, optionally preceded by constructor and disjointness $\lambda$s}
adamc@535 877 }$$
adamc@535 878
adamc@535 879 $$\infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : S}{
adamc@535 880 \Gamma \vdash M : S
adamc@558 881 & \textrm{ $M$ not a constant or application}
adamc@535 882 }
adamc@558 883 \quad \infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : \mt{selfify}(X, \overline{s})}{
adamc@558 884 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@539 885 }$$
adamc@539 886
adamc@539 887 $$\infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@535 888 \Gamma \vdash S
adamc@535 889 }$$
adamc@535 890
adamc@537 891 $$\infer{\Gamma \vdash \mt{open} \; M \leadsto \Gamma, \mathcal O(M, \overline{s})}{
adamc@537 892 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535 893 }$$
adamc@535 894
adamc@535 895 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma}{
adamc@535 896 \Gamma \vdash c_1 :: \{\kappa\}
adamc@535 897 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@535 898 & \Gamma \vdash c_1 \sim c_2
adamc@535 899 }
adamc@537 900 \quad \infer{\Gamma \vdash \mt{open} \; \mt{constraints} \; M \leadsto \Gamma, \mathcal O_c(M, \overline{s})}{
adamc@537 901 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535 902 }$$
adamc@535 903
adamc@784 904 $$\infer{\Gamma \vdash \mt{table} \; x : c \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_table} \; c \; []}{
adamc@535 905 \Gamma \vdash c :: \{\mt{Type}\}
adamc@535 906 }
adamc@784 907 \quad \infer{\Gamma \vdash \mt{view} \; x : c \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_view} \; c}{
adamc@784 908 \Gamma \vdash c :: \{\mt{Type}\}
adamc@784 909 }$$
adamc@784 910
adamc@784 911 $$\infer{\Gamma \vdash \mt{sequence} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_sequence}}{}$$
adamc@535 912
adamc@535 913 $$\infer{\Gamma \vdash \mt{cookie} \; x : \tau \leadsto \Gamma, x : \mt{Basis}.\mt{http\_cookie} \; \tau}{
adamc@535 914 \Gamma \vdash \tau :: \mt{Type}
adamc@784 915 }
adamc@784 916 \quad \infer{\Gamma \vdash \mt{style} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{css\_class}}{}$$
adamc@535 917
adamc@1085 918 $$\infer{\Gamma \vdash \mt{task} \; e_1 = e_2 \leadsto \Gamma}{
adamc@1085 919 \Gamma \vdash e_1 :: \mt{Basis}.\mt{task\_kind}
adamc@1085 920 & \Gamma \vdash e_2 :: \mt{Basis}.\mt{transaction} \; \{\}
adamc@1085 921 }$$
adamc@1085 922
adamc@784 923 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784 924 \Gamma \vdash c :: \kappa
adamc@535 925 }$$
adamc@535 926
adamc@535 927 $$\infer{\overline{y}; x; \Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535 928 \quad \infer{\overline{y}; x; \Gamma \vdash X \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to x \; \overline{y}}{
adamc@535 929 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535 930 }
adamc@535 931 \quad \infer{\overline{y}; x; \Gamma \vdash X \; \mt{of} \; \tau \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to \tau \to x \; \overline{y}}{
adamc@535 932 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535 933 }$$
adamc@535 934
adamc@537 935 \subsection{Signature Item Typing}
adamc@537 936
adamc@537 937 We appeal to a signature item analogue of the $\mathcal O$ function from the last subsection.
adamc@537 938
adamc@537 939 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@537 940 \quad \infer{\Gamma \vdash s, \overline{s} \leadsto \Gamma''}{
adamc@537 941 \Gamma \vdash s \leadsto \Gamma'
adamc@537 942 & \Gamma' \vdash \overline{s} \leadsto \Gamma''
adamc@537 943 }$$
adamc@537 944
adamc@537 945 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}
adamc@537 946 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@537 947 \Gamma \vdash c :: \kappa
adamc@537 948 }
adamc@537 949 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@537 950 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@537 951 }$$
adamc@537 952
adamc@537 953 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537 954 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 955 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 956 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@537 957 }$$
adamc@537 958
adamc@537 959 $$\infer{\Gamma \vdash \mt{val} \; x : \tau \leadsto \Gamma, x : \tau}{
adamc@537 960 \Gamma \vdash \tau :: \mt{Type}
adamc@537 961 }$$
adamc@537 962
adamc@537 963 $$\infer{\Gamma \vdash \mt{structure} \; X : S \leadsto \Gamma, X : S}{
adamc@537 964 \Gamma \vdash S
adamc@537 965 }
adamc@537 966 \quad \infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@537 967 \Gamma \vdash S
adamc@537 968 }$$
adamc@537 969
adamc@537 970 $$\infer{\Gamma \vdash \mt{include} \; S \leadsto \Gamma, \mathcal O(\overline{s})}{
adamc@537 971 \Gamma \vdash S
adamc@537 972 & \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 973 }$$
adamc@537 974
adamc@537 975 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma, c_1 \sim c_2}{
adamc@537 976 \Gamma \vdash c_1 :: \{\kappa\}
adamc@537 977 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@537 978 }$$
adamc@537 979
adamc@784 980 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784 981 \Gamma \vdash c :: \kappa
adamc@537 982 }
adamc@784 983 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}$$
adamc@537 984
adamc@536 985 \subsection{Signature Compatibility}
adamc@536 986
adamc@558 987 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@537 988
adamc@537 989 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@537 990
adamc@536 991 $$\infer{\Gamma \vdash S \equiv S}{}
adamc@536 992 \quad \infer{\Gamma \vdash S_1 \equiv S_2}{
adamc@536 993 \Gamma \vdash S_2 \equiv S_1
adamc@536 994 }
adamc@536 995 \quad \infer{\Gamma \vdash X \equiv S}{
adamc@536 996 X = S \in \Gamma
adamc@536 997 }
adamc@536 998 \quad \infer{\Gamma \vdash M.X \equiv S}{
adamc@537 999 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1000 & \mt{proj}(M, \overline{s}, \mt{signature} \; X) = S
adamc@536 1001 }$$
adamc@536 1002
adamc@536 1003 $$\infer{\Gamma \vdash S \; \mt{where} \; \mt{con} \; x = c \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa = c \; \overline{s_2} \; \mt{end}}{
adamc@536 1004 \Gamma \vdash S \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa \; \overline{s_2} \; \mt{end}
adamc@536 1005 & \Gamma \vdash c :: \kappa
adamc@537 1006 }
adamc@537 1007 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s^1} \; \mt{include} \; S \; \overline{s^2} \; \mt{end} \equiv \mt{sig} \; \overline{s^1} \; \overline{s} \; \overline{s^2} \; \mt{end}}{
adamc@537 1008 \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@536 1009 }$$
adamc@536 1010
adamc@536 1011 $$\infer{\Gamma \vdash S_1 \leq S_2}{
adamc@536 1012 \Gamma \vdash S_1 \equiv S_2
adamc@536 1013 }
adamc@536 1014 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \mt{end}}{}
adamc@537 1015 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; s' \; \overline{s'} \; \mt{end}}{
adamc@537 1016 \Gamma \vdash \overline{s} \leq s'
adamc@537 1017 & \Gamma \vdash s' \leadsto \Gamma'
adamc@537 1018 & \Gamma' \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \overline{s'} \; \mt{end}
adamc@537 1019 }$$
adamc@537 1020
adamc@537 1021 $$\infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537 1022 \Gamma \vdash s \leq s'
adamc@537 1023 }
adamc@537 1024 \quad \infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537 1025 \Gamma \vdash s \leadsto \Gamma'
adamc@537 1026 & \Gamma' \vdash \overline{s} \leq s'
adamc@536 1027 }$$
adamc@536 1028
adamc@536 1029 $$\infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 \leq \mt{functor} (X : S'_1) : S'_2}{
adamc@536 1030 \Gamma \vdash S'_1 \leq S_1
adamc@536 1031 & \Gamma, X : S'_1 \vdash S_2 \leq S'_2
adamc@536 1032 }$$
adamc@536 1033
adamc@537 1034 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@537 1035 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}
adamc@558 1036 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type}}{}$$
adamc@537 1037
adamc@537 1038 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(y)} \to \mt{Type}}{
adamc@537 1039 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1040 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1041 }$$
adamc@537 1042
adamc@784 1043 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@784 1044 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}$$
adamc@537 1045
adamc@537 1046 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \mt{\kappa} = c_2}{
adamc@537 1047 \Gamma \vdash c_1 \equiv c_2
adamc@537 1048 }
adamc@784 1049 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \kappa = c_2}{
adamc@537 1050 \Gamma \vdash c_1 \equiv c_2
adamc@537 1051 }$$
adamc@537 1052
adamc@537 1053 $$\infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537 1054 \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1055 }$$
adamc@537 1056
adamc@537 1057 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537 1058 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1059 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1060 & \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1061 }$$
adamc@537 1062
adamc@537 1063 $$\infer{\Gamma \vdash \cdot \leq \cdot}{}
adamc@537 1064 \quad \infer{\Gamma \vdash X; \overline{dc} \leq X; \overline{dc'}}{
adamc@537 1065 \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1066 }
adamc@537 1067 \quad \infer{\Gamma \vdash X \; \mt{of} \; \tau_1; \overline{dc} \leq X \; \mt{of} \; \tau_2; \overline{dc'}}{
adamc@537 1068 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537 1069 & \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1070 }$$
adamc@537 1071
adamc@537 1072 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x = \mt{datatype} \; M'.z'}{
adamc@537 1073 \Gamma \vdash M.z \equiv M'.z'
adamc@537 1074 }$$
adamc@537 1075
adamc@537 1076 $$\infer{\Gamma \vdash \mt{val} \; x : \tau_1 \leq \mt{val} \; x : \tau_2}{
adamc@537 1077 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537 1078 }
adamc@537 1079 \quad \infer{\Gamma \vdash \mt{structure} \; X : S_1 \leq \mt{structure} \; X : S_2}{
adamc@537 1080 \Gamma \vdash S_1 \leq S_2
adamc@537 1081 }
adamc@537 1082 \quad \infer{\Gamma \vdash \mt{signature} \; X = S_1 \leq \mt{signature} \; X = S_2}{
adamc@537 1083 \Gamma \vdash S_1 \leq S_2
adamc@537 1084 & \Gamma \vdash S_2 \leq S_1
adamc@537 1085 }$$
adamc@537 1086
adamc@537 1087 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leq \mt{constraint} \; c'_1 \sim c'_2}{
adamc@537 1088 \Gamma \vdash c_1 \equiv c'_1
adamc@537 1089 & \Gamma \vdash c_2 \equiv c'_2
adamc@537 1090 }$$
adamc@537 1091
adamc@655 1092 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{class} \; x :: \kappa}{}
adamc@655 1093 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{class} \; x :: \kappa}{}
adamc@655 1094 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{class} \; x :: \kappa = c_2}{
adamc@537 1095 \Gamma \vdash c_1 \equiv c_2
adamc@537 1096 }$$
adamc@537 1097
adamc@538 1098 \subsection{Module Typing}
adamc@538 1099
adamc@538 1100 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 1101
adamc@538 1102 $$\infer{\Gamma \vdash M : S}{
adamc@538 1103 \Gamma \vdash M : S'
adamc@538 1104 & \Gamma \vdash S' \leq S
adamc@538 1105 }
adamc@538 1106 \quad \infer{\Gamma \vdash \mt{struct} \; \overline{d} \; \mt{end} : \mt{sig} \; \mt{sigOf}(\overline{d}) \; \mt{end}}{
adamc@538 1107 \Gamma \vdash \overline{d} \leadsto \Gamma'
adamc@538 1108 }
adamc@538 1109 \quad \infer{\Gamma \vdash X : S}{
adamc@538 1110 X : S \in \Gamma
adamc@538 1111 }$$
adamc@538 1112
adamc@538 1113 $$\infer{\Gamma \vdash M.X : S}{
adamc@538 1114 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@538 1115 & \mt{proj}(M, \overline{s}, \mt{structure} \; X) = S
adamc@538 1116 }$$
adamc@538 1117
adamc@538 1118 $$\infer{\Gamma \vdash M_1(M_2) : [X \mapsto M_2]S_2}{
adamc@538 1119 \Gamma \vdash M_1 : \mt{functor}(X : S_1) : S_2
adamc@538 1120 & \Gamma \vdash M_2 : S_1
adamc@538 1121 }
adamc@538 1122 \quad \infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 = M : \mt{functor} (X : S_1) : S_2}{
adamc@538 1123 \Gamma \vdash S_1
adamc@538 1124 & \Gamma, X : S_1 \vdash S_2
adamc@538 1125 & \Gamma, X : S_1 \vdash M : S_2
adamc@538 1126 }$$
adamc@538 1127
adamc@538 1128 \begin{eqnarray*}
adamc@538 1129 \mt{sigOf}(\cdot) &=& \cdot \\
adamc@538 1130 \mt{sigOf}(s \; \overline{s'}) &=& \mt{sigOf}(s) \; \mt{sigOf}(\overline{s'}) \\
adamc@538 1131 \\
adamc@538 1132 \mt{sigOf}(\mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@538 1133 \mt{sigOf}(\mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \overline{dc} \\
adamc@538 1134 \mt{sigOf}(\mt{datatype} \; x = \mt{datatype} \; M.z) &=& \mt{datatype} \; x = \mt{datatype} \; M.z \\
adamc@538 1135 \mt{sigOf}(\mt{val} \; x : \tau = e) &=& \mt{val} \; x : \tau \\
adamc@538 1136 \mt{sigOf}(\mt{val} \; \mt{rec} \; \overline{x : \tau = e}) &=& \overline{\mt{val} \; x : \tau} \\
adamc@538 1137 \mt{sigOf}(\mt{structure} \; X : S = M) &=& \mt{structure} \; X : S \\
adamc@538 1138 \mt{sigOf}(\mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@538 1139 \mt{sigOf}(\mt{open} \; M) &=& \mt{include} \; S \textrm{ (where $\Gamma \vdash M : S$)} \\
adamc@538 1140 \mt{sigOf}(\mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@538 1141 \mt{sigOf}(\mt{open} \; \mt{constraints} \; M) &=& \cdot \\
adamc@538 1142 \mt{sigOf}(\mt{table} \; x : c) &=& \mt{table} \; x : c \\
adamc@784 1143 \mt{sigOf}(\mt{view} \; x : c) &=& \mt{view} \; x : c \\
adamc@538 1144 \mt{sigOf}(\mt{sequence} \; x) &=& \mt{sequence} \; x \\
adamc@538 1145 \mt{sigOf}(\mt{cookie} \; x : \tau) &=& \mt{cookie} \; x : \tau \\
adamc@784 1146 \mt{sigOf}(\mt{style} \; x) &=& \mt{style} \; x \\
adamc@655 1147 \mt{sigOf}(\mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@538 1148 \end{eqnarray*}
adamc@539 1149 \begin{eqnarray*}
adamc@539 1150 \mt{selfify}(M, \cdot) &=& \cdot \\
adamc@558 1151 \mt{selfify}(M, s \; \overline{s'}) &=& \mt{selfify}(M, s) \; \mt{selfify}(M, \overline{s'}) \\
adamc@539 1152 \\
adamc@539 1153 \mt{selfify}(M, \mt{con} \; x :: \kappa) &=& \mt{con} \; x :: \kappa = M.x \\
adamc@539 1154 \mt{selfify}(M, \mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@539 1155 \mt{selfify}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \mt{datatype} \; M.x \\
adamc@539 1156 \mt{selfify}(M, \mt{datatype} \; x = \mt{datatype} \; M'.z) &=& \mt{datatype} \; x = \mt{datatype} \; M'.z \\
adamc@539 1157 \mt{selfify}(M, \mt{val} \; x : \tau) &=& \mt{val} \; x : \tau \\
adamc@539 1158 \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 1159 \mt{selfify}(M, \mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@539 1160 \mt{selfify}(M, \mt{include} \; S) &=& \mt{include} \; S \\
adamc@539 1161 \mt{selfify}(M, \mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@655 1162 \mt{selfify}(M, \mt{class} \; x :: \kappa) &=& \mt{class} \; x :: \kappa = M.x \\
adamc@655 1163 \mt{selfify}(M, \mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@539 1164 \end{eqnarray*}
adamc@539 1165
adamc@540 1166 \subsection{Module Projection}
adamc@540 1167
adamc@540 1168 \begin{eqnarray*}
adamc@540 1169 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \\
adamc@540 1170 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa, c) \\
adamc@540 1171 \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 1172 \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 1173 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})$)} \\
adamc@655 1174 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \to \mt{Type} \\
adamc@655 1175 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa \to \mt{Type}, c) \\
adamc@540 1176 \\
adamc@540 1177 \mt{proj}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc} \; \overline{s}, \mt{datatype} \; x) &=& (\overline{y}, \overline{dc}) \\
adamc@540 1178 \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 1179 \\
adamc@540 1180 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, \mt{val} \; x) &=& \tau \\
adamc@540 1181 \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 1182 \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 1183 \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 1184 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \in \overline{dc}$)} \\
adamc@540 1185 \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 1186 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \; \mt{of} \; \tau \in \overline{dc}$)} \\
adamc@540 1187 \\
adamc@540 1188 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, \mt{structure} \; X) &=& S \\
adamc@540 1189 \\
adamc@540 1190 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, \mt{signature} \; X) &=& S \\
adamc@540 1191 \\
adamc@540 1192 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1193 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1194 \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 1195 \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 1196 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@540 1197 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1198 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1199 \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 1200 \mt{proj}(M, \mt{constraint} \; c_1 \sim c_2 \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@655 1201 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@655 1202 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1203 \end{eqnarray*}
adamc@540 1204
adamc@541 1205
adamc@541 1206 \section{Type Inference}
adamc@541 1207
adamc@541 1208 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 1209
adamc@541 1210 \subsection{Basic Unification}
adamc@541 1211
adamc@560 1212 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 1213
adamc@656 1214 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 1215
adamc@541 1216 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 1217
adamc@541 1218 \subsection{Unifying Record Types}
adamc@541 1219
adamc@570 1220 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 1221
adamc@656 1222 \subsection{\label{typeclasses}Constructor Classes}
adamc@541 1223
adamc@784 1224 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 1225
adamc@784 1226 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 1227
adamc@656 1228 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 1229
adamc@656 1230 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 1231
adamc@541 1232 \subsection{Reverse-Engineering Record Types}
adamc@541 1233
adamc@656 1234 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 1235
adamc@541 1236 \subsection{Implicit Arguments in Functor Applications}
adamc@541 1237
adamc@656 1238 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 1239
adamc@541 1240
adamc@542 1241 \section{The Ur Standard Library}
adamc@542 1242
adamc@542 1243 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 1244
adamc@542 1245 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 1246
adamc@542 1247 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 1248 $$\begin{array}{l}
adamc@542 1249 \mt{type} \; \mt{int} \\
adamc@542 1250 \mt{type} \; \mt{float} \\
adamc@873 1251 \mt{type} \; \mt{char} \\
adamc@542 1252 \mt{type} \; \mt{string} \\
adamc@542 1253 \mt{type} \; \mt{time} \\
adamc@785 1254 \mt{type} \; \mt{blob} \\
adamc@542 1255 \\
adamc@542 1256 \mt{type} \; \mt{unit} = \{\} \\
adamc@542 1257 \\
adamc@542 1258 \mt{datatype} \; \mt{bool} = \mt{False} \mid \mt{True} \\
adamc@542 1259 \\
adamc@785 1260 \mt{datatype} \; \mt{option} \; \mt{t} = \mt{None} \mid \mt{Some} \; \mt{of} \; \mt{t} \\
adamc@785 1261 \\
adamc@785 1262 \mt{datatype} \; \mt{list} \; \mt{t} = \mt{Nil} \mid \mt{Cons} \; \mt{of} \; \mt{t} \times \mt{list} \; \mt{t}
adamc@542 1263 \end{array}$$
adamc@542 1264
adamc@1123 1265 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 1266
adamc@657 1267 Another important generic Ur element comes at the beginning of \texttt{top.urs}.
adamc@657 1268
adamc@657 1269 $$\begin{array}{l}
adamc@657 1270 \mt{con} \; \mt{folder} :: \mt{K} \longrightarrow \{\mt{K}\} \to \mt{Type} \\
adamc@657 1271 \\
adamc@657 1272 \mt{val} \; \mt{fold} : \mt{K} \longrightarrow \mt{tf} :: (\{\mt{K}\} \to \mt{Type}) \\
adamc@657 1273 \hspace{.1in} \to (\mt{nm} :: \mt{Name} \to \mt{v} :: \mt{K} \to \mt{r} :: \{\mt{K}\} \to [[\mt{nm}] \sim \mt{r}] \Rightarrow \\
adamc@657 1274 \hspace{.2in} \mt{tf} \; \mt{r} \to \mt{tf} \; ([\mt{nm} = \mt{v}] \rc \mt{r})) \\
adamc@657 1275 \hspace{.1in} \to \mt{tf} \; [] \\
adamc@657 1276 \hspace{.1in} \to \mt{r} :: \{\mt{K}\} \to \mt{folder} \; \mt{r} \to \mt{tf} \; \mt{r}
adamc@657 1277 \end{array}$$
adamc@657 1278
adamc@657 1279 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 1280
adamc@664 1281 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 1282
adamc@542 1283
adamc@542 1284 \section{The Ur/Web Standard Library}
adamc@542 1285
adamc@658 1286 \subsection{Monads}
adamc@658 1287
adamc@658 1288 The Ur Basis defines the monad constructor class from Haskell.
adamc@658 1289
adamc@658 1290 $$\begin{array}{l}
adamc@658 1291 \mt{class} \; \mt{monad} :: \mt{Type} \to \mt{Type} \\
adamc@658 1292 \mt{val} \; \mt{return} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t} ::: \mt{Type} \\
adamc@658 1293 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658 1294 \hspace{.1in} \to \mt{t} \to \mt{m} \; \mt{t} \\
adamc@658 1295 \mt{val} \; \mt{bind} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t1} ::: \mt{Type} \to \mt{t2} ::: \mt{Type} \\
adamc@658 1296 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658 1297 \hspace{.1in} \to \mt{m} \; \mt{t1} \to (\mt{t1} \to \mt{m} \; \mt{t2}) \\
adamc@658 1298 \hspace{.1in} \to \mt{m} \; \mt{t2}
adamc@658 1299 \end{array}$$
adamc@658 1300
adamc@542 1301 \subsection{Transactions}
adamc@542 1302
adamc@542 1303 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 1304 $$\begin{array}{l}
adamc@542 1305 \mt{con} \; \mt{transaction} :: \mt{Type} \to \mt{Type} \\
adamc@658 1306 \mt{val} \; \mt{transaction\_monad} : \mt{monad} \; \mt{transaction}
adamc@542 1307 \end{array}$$
adamc@542 1308
adamc@1123 1309 For debugging purposes, a transactional function is provided for outputting a string on the server process' \texttt{stderr}.
adamc@1123 1310 $$\begin{array}{l}
adamc@1123 1311 \mt{val} \; \mt{debug} : \mt{string} \to \mt{transaction} \; \mt{unit}
adamc@1123 1312 \end{array}$$
adamc@1123 1313
adamc@542 1314 \subsection{HTTP}
adamc@542 1315
adamc@542 1316 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 1317 $$\begin{array}{l}
adamc@786 1318 \mt{val} \; \mt{requestHeader} : \mt{string} \to \mt{transaction} \; (\mt{option} \; \mt{string}) \\
adamc@786 1319 \\
adamc@786 1320 \mt{con} \; \mt{http\_cookie} :: \mt{Type} \to \mt{Type} \\
adamc@786 1321 \mt{val} \; \mt{getCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; (\mt{option} \; \mt{t}) \\
adamc@1050 1322 \mt{val} \; \mt{setCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \{\mt{Value} : \mt{t}, \mt{Expires} : \mt{option} \; \mt{time}, \mt{Secure} : \mt{bool}\} \to \mt{transaction} \; \mt{unit} \\
adamc@1050 1323 \mt{val} \; \mt{clearCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; \mt{unit}
adamc@786 1324 \end{array}$$
adamc@786 1325
adamc@786 1326 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 1327 $$\begin{array}{l}
adamc@786 1328 \mt{type} \; \mt{url} \\
adamc@786 1329 \mt{val} \; \mt{bless} : \mt{string} \to \mt{url} \\
adamc@786 1330 \mt{val} \; \mt{checkUrl} : \mt{string} \to \mt{option} \; \mt{url}
adamc@786 1331 \end{array}$$
adamc@786 1332 $\mt{bless}$ raises a runtime error if the string passed to it fails the URL policy.
adamc@786 1333
adamc@1085 1334 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 1335 $$\begin{array}{l}
adamc@1085 1336 \mt{val} \; \mt{currentUrl} : \mt{transaction} \; \mt{url} \\
adamc@1085 1337 \mt{val} \; \mt{url} : \mt{transaction} \; \mt{page} \to \mt{url}
adamc@1085 1338 \end{array}$$
adamc@1085 1339
adamc@1085 1340 Page generation may be interrupted at any time with a request to redirect to a particular URL instead.
adamc@1085 1341 $$\begin{array}{l}
adamc@1085 1342 \mt{val} \; \mt{redirect} : \mt{t} ::: \mt{Type} \to \mt{url} \to \mt{transaction} \; \mt{t}
adamc@1085 1343 \end{array}$$
adamc@1085 1344
adamc@786 1345 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 1346 $$\begin{array}{l}
adamc@786 1347 \mt{type} \; \mt{file} \\
adamc@786 1348 \mt{val} \; \mt{fileName} : \mt{file} \to \mt{option} \; \mt{string} \\
adamc@786 1349 \mt{val} \; \mt{fileMimeType} : \mt{file} \to \mt{string} \\
adamc@786 1350 \mt{val} \; \mt{fileData} : \mt{file} \to \mt{blob}
adamc@786 1351 \end{array}$$
adamc@786 1352
adamc@786 1353 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 1354 $$\begin{array}{l}
adamc@786 1355 \mt{type} \; \mt{mimeType} \\
adamc@786 1356 \mt{val} \; \mt{blessMime} : \mt{string} \to \mt{mimeType} \\
adamc@786 1357 \mt{val} \; \mt{checkMime} : \mt{string} \to \mt{option} \; \mt{mimeType} \\
adamc@786 1358 \mt{val} \; \mt{returnBlob} : \mt{t} ::: \mt{Type} \to \mt{blob} \to \mt{mimeType} \to \mt{transaction} \; \mt{t}
adamc@542 1359 \end{array}$$
adamc@542 1360
adamc@543 1361 \subsection{SQL}
adamc@543 1362
adamc@543 1363 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 1364 $$\begin{array}{l}
adamc@785 1365 \mt{con} \; \mt{sql\_table} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785 1366 \end{array}$$
adamc@785 1367 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 1368
adamc@785 1369 We also have the simpler type family of SQL views, which have no keys.
adamc@785 1370 $$\begin{array}{l}
adamc@785 1371 \mt{con} \; \mt{sql\_view} :: \{\mt{Type}\} \to \mt{Type}
adamc@543 1372 \end{array}$$
adamc@543 1373
adamc@785 1374 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 1375 $$\begin{array}{l}
adamc@785 1376 \mt{class} \; \mt{fieldsOf} :: \mt{Type} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1377 \mt{val} \; \mt{fieldsOf\_table} : \mt{fs} ::: \{\mt{Type}\} \to \mt{keys} ::: \{\{\mt{Unit}\}\} \to \mt{fieldsOf} \; (\mt{sql\_table} \; \mt{fs} \; \mt{keys}) \; \mt{fs} \\
adamc@785 1378 \mt{val} \; \mt{fieldsOf\_view} : \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; (\mt{sql\_view} \; \mt{fs}) \; \mt{fs}
adamc@785 1379 \end{array}$$
adamc@785 1380
adamc@785 1381 \subsubsection{Table Constraints}
adamc@785 1382
adamc@785 1383 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 1384
adamc@785 1385 $$\begin{array}{l}
adamc@785 1386 \mt{con} \; \mt{primary\_key} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type} \\
adamc@785 1387 \mt{val} \; \mt{no\_primary\_key} : \mt{fs} ::: \{\mt{Type}\} \to \mt{primary\_key} \; \mt{fs} \; [] \\
adamc@785 1388 \mt{val} \; \mt{primary\_key} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{key1} :: \mt{Name} \to \mt{keys} :: \{\mt{Type}\} \\
adamc@785 1389 \hspace{.1in} \to [[\mt{key1}] \sim \mt{keys}] \Rightarrow [[\mt{key1} = \mt{t}] \rc \mt{keys} \sim \mt{rest}] \\
adamc@785 1390 \hspace{.1in} \Rightarrow \$([\mt{key1} = \mt{sql\_injectable\_prim} \; \mt{t}] \rc \mt{map} \; \mt{sql\_injectable\_prim} \; \mt{keys}) \\
adamc@785 1391 \hspace{.1in} \to \mt{primary\_key} \; ([\mt{key1} = \mt{t}] \rc \mt{keys} \rc \mt{rest}) \; [\mt{Pkey} = [\mt{key1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{keys}]
adamc@785 1392 \end{array}$$
adamc@785 1393 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 1394
adamc@785 1395 A type family stands for sets of named constraints of the remaining varieties.
adamc@785 1396 $$\begin{array}{l}
adamc@785 1397 \mt{con} \; \mt{sql\_constraints} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785 1398 \end{array}$$
adamc@785 1399 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 1400
adamc@785 1401 There is a type family of individual, unnamed constraints.
adamc@785 1402 $$\begin{array}{l}
adamc@785 1403 \mt{con} \; \mt{sql\_constraint} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \mt{Type}
adamc@785 1404 \end{array}$$
adamc@785 1405 The first argument is the same as above, and the second argument gives the key columns for just this constraint.
adamc@785 1406
adamc@785 1407 We have operations for assembling constraints into constraint sets.
adamc@785 1408 $$\begin{array}{l}
adamc@785 1409 \mt{val} \; \mt{no\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_constraints} \; \mt{fs} \; [] \\
adamc@785 1410 \mt{val} \; \mt{one\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{unique} ::: \{\mt{Unit}\} \to \mt{name} :: \mt{Name} \\
adamc@785 1411 \hspace{.1in} \to \mt{sql\_constraint} \; \mt{fs} \; \mt{unique} \to \mt{sql\_constraints} \; \mt{fs} \; [\mt{name} = \mt{unique}] \\
adamc@785 1412 \mt{val} \; \mt{join\_constraints} : \mt{fs} ::: \{\mt{Type}\} \to \mt{uniques1} ::: \{\{\mt{Unit}\}\} \to \mt{uniques2} ::: \{\{\mt{Unit}\}\} \to [\mt{uniques1} \sim \mt{uniques2}] \\
adamc@785 1413 \hspace{.1in} \Rightarrow \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques1} \to \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques2} \to \mt{sql\_constraints} \; \mt{fs} \; (\mt{uniques1} \rc \mt{uniques2})
adamc@785 1414 \end{array}$$
adamc@785 1415
adamc@785 1416 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 1417 $$\begin{array}{l}
adamc@785 1418 \mt{val} \; \mt{unique} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{unique1} :: \mt{Name} \to \mt{unique} :: \{\mt{Type}\} \\
adamc@785 1419 \hspace{.1in} \to [[\mt{unique1}] \sim \mt{unique}] \Rightarrow [[\mt{unique1} = \mt{t}] \rc \mt{unique} \sim \mt{rest}] \\
adamc@785 1420 \hspace{.1in} \Rightarrow \mt{sql\_constraint} \; ([\mt{unique1} = \mt{t}] \rc \mt{unique} \rc \mt{rest}) \; ([\mt{unique1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{unique})
adamc@785 1421 \end{array}$$
adamc@785 1422
adamc@785 1423 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 1424 $$\begin{array}{l}
adamc@785 1425 \mt{class} \; \mt{linkable} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@785 1426 \mt{val} \; \mt{linkable\_same} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; \mt{t} \\
adamc@785 1427 \mt{val} \; \mt{linkable\_from\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; (\mt{option} \; \mt{t}) \; \mt{t} \\
adamc@785 1428 \mt{val} \; \mt{linkable\_to\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@785 1429 \end{array}$$
adamc@785 1430
adamc@785 1431 The $\mt{matching}$ type family uses $\mt{linkable}$ to define when two keys match up type-wise.
adamc@785 1432 $$\begin{array}{l}
adamc@785 1433 \mt{con} \; \mt{matching} :: \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1434 \mt{val} \; \mt{mat\_nil} : \mt{matching} \; [] \; [] \\
adamc@785 1435 \mt{val} \; \mt{mat\_cons} : \mt{t1} ::: \mt{Type} \to \mt{rest1} ::: \{\mt{Type}\} \to \mt{t2} ::: \mt{Type} \to \mt{rest2} ::: \{\mt{Type}\} \to \mt{nm1} :: \mt{Name} \to \mt{nm2} :: \mt{Name} \\
adamc@785 1436 \hspace{.1in} \to [[\mt{nm1}] \sim \mt{rest1}] \Rightarrow [[\mt{nm2}] \sim \mt{rest2}] \Rightarrow \mt{linkable} \; \mt{t1} \; \mt{t2} \to \mt{matching} \; \mt{rest1} \; \mt{rest2} \\
adamc@785 1437 \hspace{.1in} \to \mt{matching} \; ([\mt{nm1} = \mt{t1}] \rc \mt{rest1}) \; ([\mt{nm2} = \mt{t2}] \rc \mt{rest2})
adamc@785 1438 \end{array}$$
adamc@785 1439
adamc@785 1440 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 1441 $$\begin{array}{l}
adamc@785 1442 \mt{con} \; \mt{propagation\_mode} :: \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1443 \mt{val} \; \mt{restrict} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1444 \mt{val} \; \mt{cascade} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1445 \mt{val} \; \mt{no\_action} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1446 \mt{val} \; \mt{set\_null} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; (\mt{map} \; \mt{option} \; \mt{fs})
adamc@785 1447 \end{array}$$
adamc@785 1448
adamc@785 1449 Finally, we put these ingredient together to define the \texttt{FOREIGN KEY} constraint function.
adamc@785 1450 $$\begin{array}{l}
adamc@785 1451 \mt{val} \; \mt{foreign\_key} : \mt{mine1} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{mine} ::: \{\mt{Type}\} \to \mt{munused} ::: \{\mt{Type}\} \to \mt{foreign} ::: \{\mt{Type}\} \\
adamc@785 1452 \hspace{.1in} \to \mt{funused} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{uniques} ::: \{\{\mt{Unit}\}\} \\
adamc@785 1453 \hspace{.1in} \to [[\mt{mine1}] \sim \mt{mine}] \Rightarrow [[\mt{mine1} = \mt{t}] \rc \mt{mine} \sim \mt{munused}] \Rightarrow [\mt{foreign} \sim \mt{funused}] \Rightarrow [[\mt{nm}] \sim \mt{uniques}] \\
adamc@785 1454 \hspace{.1in} \Rightarrow \mt{matching} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}) \; \mt{foreign} \\
adamc@785 1455 \hspace{.1in} \to \mt{sql\_table} \; (\mt{foreign} \rc \mt{funused}) \; ([\mt{nm} = \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{foreign}] \rc \mt{uniques}) \\
adamc@785 1456 \hspace{.1in} \to \{\mt{OnDelete} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}), \\
adamc@785 1457 \hspace{.2in} \mt{OnUpdate} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine})\} \\
adamc@785 1458 \hspace{.1in} \to \mt{sql\_constraint} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine} \rc \mt{munused}) \; []
adamc@785 1459 \end{array}$$
adamc@785 1460
adamc@785 1461 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 1462 $$\begin{array}{l}
adamc@785 1463 \mt{val} \; \mt{check} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; [] \; [] \; \mt{fs} \; \mt{bool} \to \mt{sql\_constraint} \; \mt{fs} \; []
adamc@785 1464 \end{array}$$
adamc@785 1465
adamc@785 1466 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 1467
adamc@784 1468
adamc@543 1469 \subsubsection{Queries}
adamc@543 1470
adamc@543 1471 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 1472 $$\begin{array}{l}
adamc@543 1473 \mt{con} \; \mt{sql\_query} :: \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@543 1474 \mt{val} \; \mt{sql\_query} : \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543 1475 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1476 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@543 1477 \hspace{.1in} \to \{\mt{Rows} : \mt{sql\_query1} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}, \\
adamc@543 1478 \hspace{.2in} \mt{OrderBy} : \mt{sql\_order\_by} \; \mt{tables} \; \mt{selectedExps}, \\
adamc@543 1479 \hspace{.2in} \mt{Limit} : \mt{sql\_limit}, \\
adamc@543 1480 \hspace{.2in} \mt{Offset} : \mt{sql\_offset}\} \\
adamc@543 1481 \hspace{.1in} \to \mt{sql\_query} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1482 \end{array}$$
adamc@543 1483
adamc@545 1484 Queries are used by folding over their results inside transactions.
adamc@545 1485 $$\begin{array}{l}
adamc@545 1486 \mt{val} \; \mt{query} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \lambda [\mt{tables} \sim \mt{exps}] \Rightarrow \mt{state} ::: \mt{Type} \to \mt{sql\_query} \; \mt{tables} \; \mt{exps} \\
adamc@658 1487 \hspace{.1in} \to (\$(\mt{exps} \rc \mt{map} \; (\lambda \mt{fields} :: \{\mt{Type}\} \Rightarrow \$\mt{fields}) \; \mt{tables}) \\
adamc@545 1488 \hspace{.2in} \to \mt{state} \to \mt{transaction} \; \mt{state}) \\
adamc@545 1489 \hspace{.1in} \to \mt{state} \to \mt{transaction} \; \mt{state}
adamc@545 1490 \end{array}$$
adamc@545 1491
adamc@543 1492 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 1493 $$\begin{array}{l}
adamc@543 1494 \mt{con} \; \mt{sql\_query1} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@543 1495 \\
adamc@543 1496 \mt{type} \; \mt{sql\_relop} \\
adamc@543 1497 \mt{val} \; \mt{sql\_union} : \mt{sql\_relop} \\
adamc@543 1498 \mt{val} \; \mt{sql\_intersect} : \mt{sql\_relop} \\
adamc@543 1499 \mt{val} \; \mt{sql\_except} : \mt{sql\_relop} \\
adamc@543 1500 \mt{val} \; \mt{sql\_relop} : \mt{tables1} ::: \{\{\mt{Type}\}\} \\
adamc@543 1501 \hspace{.1in} \to \mt{tables2} ::: \{\{\mt{Type}\}\} \\
adamc@543 1502 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1503 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@543 1504 \hspace{.1in} \to \mt{sql\_relop} \\
adamc@543 1505 \hspace{.1in} \to \mt{sql\_query1} \; \mt{tables1} \; \mt{selectedFields} \; \mt{selectedExps} \\
adamc@543 1506 \hspace{.1in} \to \mt{sql\_query1} \; \mt{tables2} \; \mt{selectedFields} \; \mt{selectedExps} \\
adamc@543 1507 \hspace{.1in} \to \mt{sql\_query1} \; \mt{selectedFields} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1508 \end{array}$$
adamc@543 1509
adamc@543 1510 $$\begin{array}{l}
adamc@543 1511 \mt{val} \; \mt{sql\_query1} : \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543 1512 \hspace{.1in} \to \mt{grouped} ::: \{\{\mt{Type}\}\} \\
adamc@543 1513 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1514 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1085 1515 \hspace{.1in} \to \mt{empties} :: \{\mt{Unit}\} \\
adamc@1085 1516 \hspace{.1in} \to [\mt{empties} \sim \mt{selectedFields}] \\
adamc@1085 1517 \hspace{.1in} \Rightarrow \{\mt{Distinct} : \mt{bool}, \\
adamc@994 1518 \hspace{.2in} \mt{From} : \mt{sql\_from\_items} \; \mt{tables}, \\
adamc@543 1519 \hspace{.2in} \mt{Where} : \mt{sql\_exp} \; \mt{tables} \; [] \; [] \; \mt{bool}, \\
adamc@543 1520 \hspace{.2in} \mt{GroupBy} : \mt{sql\_subset} \; \mt{tables} \; \mt{grouped}, \\
adamc@543 1521 \hspace{.2in} \mt{Having} : \mt{sql\_exp} \; \mt{grouped} \; \mt{tables} \; [] \; \mt{bool}, \\
adamc@1085 1522 \hspace{.2in} \mt{SelectFields} : \mt{sql\_subset} \; \mt{grouped} \; (\mt{map} \; (\lambda \_ \Rightarrow []) \; \mt{empties} \rc \mt{selectedFields}), \\
adamc@658 1523 \hspace{.2in} \mt {SelectExps} : \$(\mt{map} \; (\mt{sql\_exp} \; \mt{grouped} \; \mt{tables} \; []) \; \mt{selectedExps}) \} \\
adamc@543 1524 \hspace{.1in} \to \mt{sql\_query1} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1525 \end{array}$$
adamc@543 1526
adamc@543 1527 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 1528 $$\begin{array}{l}
adamc@543 1529 \mt{con} \; \mt{sql\_subset} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@543 1530 \mt{val} \; \mt{sql\_subset} : \mt{keep\_drop} :: \{(\{\mt{Type}\} \times \{\mt{Type}\})\} \\
adamc@543 1531 \hspace{.1in} \to \mt{sql\_subset} \\
adamc@658 1532 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1 \rc \mt{fields}.2)\; \mt{keep\_drop}) \\
adamc@658 1533 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1) \; \mt{keep\_drop}) \\
adamc@543 1534 \mt{val} \; \mt{sql\_subset\_all} : \mt{tables} :: \{\{\mt{Type}\}\} \to \mt{sql\_subset} \; \mt{tables} \; \mt{tables}
adamc@543 1535 \end{array}$$
adamc@543 1536
adamc@560 1537 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 1538 $$\begin{array}{l}
adamc@543 1539 \mt{con} \; \mt{sql\_exp} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}
adamc@543 1540 \end{array}$$
adamc@543 1541
adamc@543 1542 Any field in scope may be converted to an expression.
adamc@543 1543 $$\begin{array}{l}
adamc@543 1544 \mt{val} \; \mt{sql\_field} : \mt{otherTabs} ::: \{\{\mt{Type}\}\} \to \mt{otherFields} ::: \{\mt{Type}\} \\
adamc@543 1545 \hspace{.1in} \to \mt{fieldType} ::: \mt{Type} \to \mt{agg} ::: \{\{\mt{Type}\}\} \\
adamc@543 1546 \hspace{.1in} \to \mt{exps} ::: \{\mt{Type}\} \\
adamc@543 1547 \hspace{.1in} \to \mt{tab} :: \mt{Name} \to \mt{field} :: \mt{Name} \\
adamc@543 1548 \hspace{.1in} \to \mt{sql\_exp} \; ([\mt{tab} = [\mt{field} = \mt{fieldType}] \rc \mt{otherFields}] \rc \mt{otherTabs}) \; \mt{agg} \; \mt{exps} \; \mt{fieldType}
adamc@543 1549 \end{array}$$
adamc@543 1550
adamc@544 1551 There is an analogous function for referencing named expressions.
adamc@544 1552 $$\begin{array}{l}
adamc@544 1553 \mt{val} \; \mt{sql\_exp} : \mt{tabs} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{t} ::: \mt{Type} \to \mt{rest} ::: \{\mt{Type}\} \to \mt{nm} :: \mt{Name} \\
adamc@544 1554 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tabs} \; \mt{agg} \; ([\mt{nm} = \mt{t}] \rc \mt{rest}) \; \mt{t}
adamc@544 1555 \end{array}$$
adamc@544 1556
adamc@544 1557 Ur values of appropriate types may be injected into SQL expressions.
adamc@544 1558 $$\begin{array}{l}
adamc@786 1559 \mt{class} \; \mt{sql\_injectable\_prim} \\
adamc@786 1560 \mt{val} \; \mt{sql\_bool} : \mt{sql\_injectable\_prim} \; \mt{bool} \\
adamc@786 1561 \mt{val} \; \mt{sql\_int} : \mt{sql\_injectable\_prim} \; \mt{int} \\
adamc@786 1562 \mt{val} \; \mt{sql\_float} : \mt{sql\_injectable\_prim} \; \mt{float} \\
adamc@786 1563 \mt{val} \; \mt{sql\_string} : \mt{sql\_injectable\_prim} \; \mt{string} \\
adamc@786 1564 \mt{val} \; \mt{sql\_time} : \mt{sql\_injectable\_prim} \; \mt{time} \\
adamc@786 1565 \mt{val} \; \mt{sql\_blob} : \mt{sql\_injectable\_prim} \; \mt{blob} \\
adamc@786 1566 \mt{val} \; \mt{sql\_channel} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{channel} \; \mt{t}) \\
adamc@786 1567 \mt{val} \; \mt{sql\_client} : \mt{sql\_injectable\_prim} \; \mt{client} \\
adamc@786 1568 \\
adamc@544 1569 \mt{class} \; \mt{sql\_injectable} \\
adamc@786 1570 \mt{val} \; \mt{sql\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@786 1571 \mt{val} \; \mt{sql\_option\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; (\mt{option} \; \mt{t}) \\
adamc@786 1572 \\
adamc@544 1573 \mt{val} \; \mt{sql\_inject} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@544 1574 \hspace{.1in} \to \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adamc@544 1575 \end{array}$$
adamc@544 1576
adamc@1123 1577 Additionally, most function-free types may be injected safely, via the $\mt{serialized}$ type family.
adamc@1123 1578 $$\begin{array}{l}
adamc@1123 1579 \mt{con} \; \mt{serialized} :: \mt{Type} \to \mt{Type} \\
adamc@1123 1580 \mt{val} \; \mt{serialize} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{serialized} \; \mt{t} \\
adamc@1123 1581 \mt{val} \; \mt{deserialize} : \mt{t} ::: \mt{Type} \to \mt{serialized} \; \mt{t} \to \mt{t} \\
adamc@1123 1582 \mt{val} \; \mt{sql\_serialized} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{serialized} \; \mt{t})
adamc@1123 1583 \end{array}$$
adamc@1123 1584
adamc@544 1585 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 1586 $$\begin{array}{l}
adamc@544 1587 \mt{val} \; \mt{sql\_is\_null} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544 1588 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; (\mt{option} \; \mt{t}) \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{bool}
adamc@544 1589 \end{array}$$
adamc@544 1590
adamc@559 1591 We have generic nullary, unary, and binary operators.
adamc@544 1592 $$\begin{array}{l}
adamc@544 1593 \mt{con} \; \mt{sql\_nfunc} :: \mt{Type} \to \mt{Type} \\
adamc@544 1594 \mt{val} \; \mt{sql\_current\_timestamp} : \mt{sql\_nfunc} \; \mt{time} \\
adamc@544 1595 \mt{val} \; \mt{sql\_nfunc} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544 1596 \hspace{.1in} \to \mt{sql\_nfunc} \; \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\\end{array}$$
adamc@544 1597
adamc@544 1598 $$\begin{array}{l}
adamc@544 1599 \mt{con} \; \mt{sql\_unary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544 1600 \mt{val} \; \mt{sql\_not} : \mt{sql\_unary} \; \mt{bool} \; \mt{bool} \\
adamc@544 1601 \mt{val} \; \mt{sql\_unary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adamc@544 1602 \hspace{.1in} \to \mt{sql\_unary} \; \mt{arg} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res} \\
adamc@544 1603 \end{array}$$
adamc@544 1604
adamc@544 1605 $$\begin{array}{l}
adamc@544 1606 \mt{con} \; \mt{sql\_binary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544 1607 \mt{val} \; \mt{sql\_and} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544 1608 \mt{val} \; \mt{sql\_or} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544 1609 \mt{val} \; \mt{sql\_binary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg_1} ::: \mt{Type} \to \mt{arg_2} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adamc@544 1610 \hspace{.1in} \to \mt{sql\_binary} \; \mt{arg_1} \; \mt{arg_2} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_1} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_2} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res}
adamc@544 1611 \end{array}$$
adamc@544 1612
adamc@544 1613 $$\begin{array}{l}
adamc@559 1614 \mt{class} \; \mt{sql\_arith} \\
adamc@559 1615 \mt{val} \; \mt{sql\_int\_arith} : \mt{sql\_arith} \; \mt{int} \\
adamc@559 1616 \mt{val} \; \mt{sql\_float\_arith} : \mt{sql\_arith} \; \mt{float} \\
adamc@559 1617 \mt{val} \; \mt{sql\_neg} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_unary} \; \mt{t} \; \mt{t} \\
adamc@559 1618 \mt{val} \; \mt{sql\_plus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1619 \mt{val} \; \mt{sql\_minus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1620 \mt{val} \; \mt{sql\_times} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1621 \mt{val} \; \mt{sql\_div} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1622 \mt{val} \; \mt{sql\_mod} : \mt{sql\_binary} \; \mt{int} \; \mt{int} \; \mt{int}
adamc@559 1623 \end{array}$$
adamc@544 1624
adamc@656 1625 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 1626 $$\begin{array}{l}
adamc@544 1627 \mt{val} \; \mt{sql\_count} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int}
adamc@544 1628 \end{array}$$
adamc@544 1629
adamc@544 1630 $$\begin{array}{l}
adamc@544 1631 \mt{con} \; \mt{sql\_aggregate} :: \mt{Type} \to \mt{Type} \\
adamc@544 1632 \mt{val} \; \mt{sql\_aggregate} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544 1633 \hspace{.1in} \to \mt{sql\_aggregate} \; \mt{t} \to \mt{sql\_exp} \; \mt{agg} \; \mt{agg} \; \mt{exps} \; \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adamc@544 1634 \end{array}$$
adamc@544 1635
adamc@544 1636 $$\begin{array}{l}
adamc@544 1637 \mt{class} \; \mt{sql\_summable} \\
adamc@544 1638 \mt{val} \; \mt{sql\_summable\_int} : \mt{sql\_summable} \; \mt{int} \\
adamc@544 1639 \mt{val} \; \mt{sql\_summable\_float} : \mt{sql\_summable} \; \mt{float} \\
adamc@544 1640 \mt{val} \; \mt{sql\_avg} : \mt{t} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{sql\_aggregate} \; \mt{t} \\
adamc@544 1641 \mt{val} \; \mt{sql\_sum} : \mt{t} ::: \mt{Type} \to \mt{sql\_summable} \mt{t} \to \mt{sql\_aggregate} \; \mt{t}
adamc@544 1642 \end{array}$$
adamc@544 1643
adamc@544 1644 $$\begin{array}{l}
adamc@544 1645 \mt{class} \; \mt{sql\_maxable} \\
adamc@544 1646 \mt{val} \; \mt{sql\_maxable\_int} : \mt{sql\_maxable} \; \mt{int} \\
adamc@544 1647 \mt{val} \; \mt{sql\_maxable\_float} : \mt{sql\_maxable} \; \mt{float} \\
adamc@544 1648 \mt{val} \; \mt{sql\_maxable\_string} : \mt{sql\_maxable} \; \mt{string} \\
adamc@544 1649 \mt{val} \; \mt{sql\_maxable\_time} : \mt{sql\_maxable} \; \mt{time} \\
adamc@544 1650 \mt{val} \; \mt{sql\_max} : \mt{t} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{sql\_aggregate} \; \mt{t} \\
adamc@544 1651 \mt{val} \; \mt{sql\_min} : \mt{t} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{sql\_aggregate} \; \mt{t}
adamc@544 1652 \end{array}$$
adamc@544 1653
adamc@786 1654 \texttt{FROM} clauses are specified using a type family.
adamc@786 1655 $$\begin{array}{l}
adamc@786 1656 \mt{con} \; \mt{sql\_from\_items} :: \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@786 1657 \mt{val} \; \mt{sql\_from\_table} : \mt{t} ::: \mt{Type} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; \mt{t} \; \mt{fs} \to \mt{name} :: \mt{Name} \to \mt{t} \to \mt{sql\_from\_items} \; [\mt{name} = \mt{fs}] \\
adamc@786 1658 \mt{val} \; \mt{sql\_from\_comma} : \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \to [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@786 1659 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{tabs2} \\
adamc@786 1660 \hspace{.1in} \to \mt{sql\_from\_items} \; (\mt{tabs1} \rc \mt{tabs2}) \\
adamc@786 1661 \mt{val} \; \mt{sql\_inner\_join} : \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \to [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@786 1662 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{tabs2} \\
adamc@786 1663 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{tabs1} \rc \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@786 1664 \hspace{.1in} \to \mt{sql\_from\_items} \; (\mt{tabs1} \rc \mt{tabs2})
adamc@786 1665 \end{array}$$
adamc@786 1666
adamc@786 1667 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 1668 $$\begin{array}{l}
adamc@786 1669 \mt{class} \; \mt{nullify} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@786 1670 \mt{val} \; \mt{nullify\_option} : \mt{t} ::: \mt{Type} \to \mt{nullify} \; (\mt{option} \; \mt{t}) \; (\mt{option} \; \mt{t}) \\
adamc@786 1671 \mt{val} \; \mt{nullify\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{nullify} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@786 1672 \end{array}$$
adamc@786 1673
adamc@786 1674 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 1675
adamc@786 1676 $$\begin{array}{l}
adamc@786 1677 \mt{val} \; \mt{sql\_left\_join} : \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{(\mt{Type} \times \mt{Type})\}\} \to [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@786 1678 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\lambda \mt{r} \Rightarrow \$(\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{nullify} \; \mt{p}.1 \; \mt{p}.2) \; \mt{r})) \; \mt{tabs2}) \\
adamc@786 1679 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{tabs1} \to \mt{sql\_from\_items} \; (\mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \\
adamc@786 1680 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@786 1681 \hspace{.1in} \to \mt{sql\_from\_items} \; (\mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.2)) \; \mt{tabs2})
adamc@786 1682 \end{array}$$
adamc@786 1683
adamc@544 1684 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 1685 $$\begin{array}{l}
adamc@544 1686 \mt{type} \; \mt{sql\_direction} \\
adamc@544 1687 \mt{val} \; \mt{sql\_asc} : \mt{sql\_direction} \\
adamc@544 1688 \mt{val} \; \mt{sql\_desc} : \mt{sql\_direction} \\
adamc@544 1689 \\
adamc@544 1690 \mt{con} \; \mt{sql\_order\_by} :: \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@544 1691 \mt{val} \; \mt{sql\_order\_by\_Nil} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} :: \{\mt{Type}\} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544 1692 \mt{val} \; \mt{sql\_order\_by\_Cons} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544 1693 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; [] \; \mt{exps} \; \mt{t} \to \mt{sql\_direction} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544 1694 \\
adamc@544 1695 \mt{type} \; \mt{sql\_limit} \\
adamc@544 1696 \mt{val} \; \mt{sql\_no\_limit} : \mt{sql\_limit} \\
adamc@544 1697 \mt{val} \; \mt{sql\_limit} : \mt{int} \to \mt{sql\_limit} \\
adamc@544 1698 \\
adamc@544 1699 \mt{type} \; \mt{sql\_offset} \\
adamc@544 1700 \mt{val} \; \mt{sql\_no\_offset} : \mt{sql\_offset} \\
adamc@544 1701 \mt{val} \; \mt{sql\_offset} : \mt{int} \to \mt{sql\_offset}
adamc@544 1702 \end{array}$$
adamc@544 1703
adamc@545 1704
adamc@545 1705 \subsubsection{DML}
adamc@545 1706
adamc@545 1707 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 1708
adamc@545 1709 $$\begin{array}{l}
adamc@545 1710 \mt{type} \; \mt{dml} \\
adamc@545 1711 \mt{val} \; \mt{dml} : \mt{dml} \to \mt{transaction} \; \mt{unit}
adamc@545 1712 \end{array}$$
adamc@545 1713
adamc@545 1714 Properly-typed records may be used to form $\mt{INSERT}$ commands.
adamc@545 1715 $$\begin{array}{l}
adamc@545 1716 \mt{val} \; \mt{insert} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \\
adamc@658 1717 \hspace{.1in} \to \$(\mt{map} \; (\mt{sql\_exp} \; [] \; [] \; []) \; \mt{fields}) \to \mt{dml}
adamc@545 1718 \end{array}$$
adamc@545 1719
adamc@545 1720 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 1721 $$\begin{array}{l}
adamc@545 1722 \mt{val} \; \mt{update} : \mt{unchanged} ::: \{\mt{Type}\} \to \mt{changed} :: \{\mt{Type}\} \to \lambda [\mt{changed} \sim \mt{unchanged}] \\
adamc@658 1723 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; []) \; \mt{changed}) \\
adamc@545 1724 \hspace{.1in} \to \mt{sql\_table} \; (\mt{changed} \rc \mt{unchanged}) \to \mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545 1725 \end{array}$$
adamc@545 1726
adamc@545 1727 A $\mt{DELETE}$ command is formed from a table and a $\mt{WHERE}$ clause.
adamc@545 1728 $$\begin{array}{l}
adamc@545 1729 \mt{val} \; \mt{delete} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \to \mt{sql\_exp} \; [\mt{T} = \mt{fields}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545 1730 \end{array}$$
adamc@545 1731
adamc@546 1732 \subsubsection{Sequences}
adamc@546 1733
adamc@546 1734 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 1735
adamc@546 1736 $$\begin{array}{l}
adamc@546 1737 \mt{type} \; \mt{sql\_sequence} \\
adamc@1085 1738 \mt{val} \; \mt{nextval} : \mt{sql\_sequence} \to \mt{transaction} \; \mt{int} \\
adamc@1085 1739 \mt{val} \; \mt{setval} : \mt{sql\_sequence} \to \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@546 1740 \end{array}$$
adamc@546 1741
adamc@546 1742
adamc@547 1743 \subsection{XML}
adamc@547 1744
adamc@547 1745 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 1746
adamc@547 1747 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 1748 $$\begin{array}{l}
adamc@547 1749 \mt{con} \; \mt{xml} :: \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547 1750 \end{array}$$
adamc@547 1751
adamc@547 1752 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 1753 $$\begin{array}{l}
adamc@547 1754 \mt{con} \; \mt{tag} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547 1755 \end{array}$$
adamc@547 1756
adamc@547 1757 Literal text may be injected into XML as ``CDATA.''
adamc@547 1758 $$\begin{array}{l}
adamc@547 1759 \mt{val} \; \mt{cdata} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{string} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adamc@547 1760 \end{array}$$
adamc@547 1761
adamc@547 1762 There is a function for producing an XML tree with a particular tag at its root.
adamc@547 1763 $$\begin{array}{l}
adamc@547 1764 \mt{val} \; \mt{tag} : \mt{attrsGiven} ::: \{\mt{Type}\} \to \mt{attrsAbsent} ::: \{\mt{Type}\} \to \mt{ctxOuter} ::: \{\mt{Unit}\} \to \mt{ctxInner} ::: \{\mt{Unit}\} \\
adamc@547 1765 \hspace{.1in} \to \mt{useOuter} ::: \{\mt{Type}\} \to \mt{useInner} ::: \{\mt{Type}\} \to \mt{bindOuter} ::: \{\mt{Type}\} \to \mt{bindInner} ::: \{\mt{Type}\} \\
adamc@787 1766 \hspace{.1in} \to \lambda [\mt{attrsGiven} \sim \mt{attrsAbsent}] \; [\mt{useOuter} \sim \mt{useInner}] \; [\mt{bindOuter} \sim \mt{bindInner}] \\
adamc@787 1767 \hspace{.1in} \Rightarrow \mt{option} \; \mt{css\_class} \\
adamc@787 1768 \hspace{.1in} \to \$\mt{attrsGiven} \\
adamc@547 1769 \hspace{.1in} \to \mt{tag} \; (\mt{attrsGiven} \rc \mt{attrsAbsent}) \; \mt{ctxOuter} \; \mt{ctxInner} \; \mt{useOuter} \; \mt{bindOuter} \\
adamc@547 1770 \hspace{.1in} \to \mt{xml} \; \mt{ctxInner} \; \mt{useInner} \; \mt{bindInner} \to \mt{xml} \; \mt{ctxOuter} \; (\mt{useOuter} \rc \mt{useInner}) \; (\mt{bindOuter} \rc \mt{bindInner})
adamc@547 1771 \end{array}$$
adamc@787 1772 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 1773
adamc@547 1774 Two XML fragments may be concatenated.
adamc@547 1775 $$\begin{array}{l}
adamc@547 1776 \mt{val} \; \mt{join} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{bind_1} ::: \{\mt{Type}\} \to \mt{bind_2} ::: \{\mt{Type}\} \\
adamc@547 1777 \hspace{.1in} \to \lambda [\mt{use_1} \sim \mt{bind_1}] \; [\mt{bind_1} \sim \mt{bind_2}] \\
adamc@547 1778 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind_1} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{bind_1}) \; \mt{bind_2} \to \mt{xml} \; \mt{ctx} \; \mt{use_1} \; (\mt{bind_1} \rc \mt{bind_2})
adamc@547 1779 \end{array}$$
adamc@547 1780
adamc@547 1781 Finally, any XML fragment may be updated to ``claim'' to use more form fields than it does.
adamc@547 1782 $$\begin{array}{l}
adamc@547 1783 \mt{val} \; \mt{useMore} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{use_2} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to \lambda [\mt{use_1} \sim \mt{use_2}] \\
adamc@547 1784 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{use_2}) \; \mt{bind}
adamc@547 1785 \end{array}$$
adamc@547 1786
adamc@547 1787 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 1788
adamc@547 1789 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 1790 $$\begin{array}{l}
adamc@547 1791 \mt{val} \; \mt{error} : \mt{t} ::: \mt{Type} \to \mt{xml} \; [\mt{Body}] \; [] \; [] \to \mt{t}
adamc@547 1792 \end{array}$$
adamc@547 1793
adamc@549 1794
adamc@701 1795 \subsection{Client-Side Programming}
adamc@659 1796
adamc@701 1797 Ur/Web supports running code on web browsers, via automatic compilation to JavaScript.
adamc@701 1798
adamc@701 1799 \subsubsection{The Basics}
adamc@701 1800
adamc@701 1801 Clients can open alert dialog boxes, in the usual annoying JavaScript way.
adamc@701 1802 $$\begin{array}{l}
adamc@701 1803 \mt{val} \; \mt{alert} : \mt{string} \to \mt{transaction} \; \mt{unit}
adamc@701 1804 \end{array}$$
adamc@701 1805
adamc@701 1806 Any transaction may be run in a new thread with the $\mt{spawn}$ function.
adamc@701 1807 $$\begin{array}{l}
adamc@701 1808 \mt{val} \; \mt{spawn} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit}
adamc@701 1809 \end{array}$$
adamc@701 1810
adamc@701 1811 The current thread can be paused for at least a specified number of milliseconds.
adamc@701 1812 $$\begin{array}{l}
adamc@701 1813 \mt{val} \; \mt{sleep} : \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@701 1814 \end{array}$$
adamc@701 1815
adamc@787 1816 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 1817 $$\begin{array}{l}
adamc@787 1818 \mt{val} \; \mt{onError} : (\mt{xbody} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787 1819 \mt{val} \; \mt{onFail} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787 1820 \mt{val} \; \mt{onConnectFail} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787 1821 \mt{val} \; \mt{onDisconnect} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787 1822 \mt{val} \; \mt{onServerError} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit}
adamc@787 1823 \end{array}$$
adamc@787 1824
adamc@701 1825 \subsubsection{Functional-Reactive Page Generation}
adamc@701 1826
adamc@701 1827 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 1828
adamc@659 1829 $$\begin{array}{l}
adamc@659 1830 \mt{con} \; \mt{source} :: \mt{Type} \to \mt{Type} \\
adamc@659 1831 \mt{val} \; \mt{source} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{transaction} \; (\mt{source} \; \mt{t}) \\
adamc@659 1832 \mt{val} \; \mt{set} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@659 1833 \mt{val} \; \mt{get} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@659 1834 \end{array}$$
adamc@659 1835
adamc@659 1836 Pure functions over sources are represented in a monad of \emph{signals}.
adamc@659 1837
adamc@659 1838 $$\begin{array}{l}
adamc@659 1839 \mt{con} \; \mt{signal} :: \mt{Type} \to \mt{Type} \\
adamc@659 1840 \mt{val} \; \mt{signal\_monad} : \mt{monad} \; \mt{signal} \\
adamc@659 1841 \mt{val} \; \mt{signal} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{signal} \; \mt{t}
adamc@659 1842 \end{array}$$
adamc@659 1843
adamc@659 1844 A reactive portion of an HTML page is injected with a $\mt{dyn}$ tag, which has a signal-valued attribute $\mt{Signal}$.
adamc@659 1845
adamc@659 1846 $$\begin{array}{l}
adamc@701 1847 \mt{val} \; \mt{dyn} : \mt{use} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to \mt{unit} \\
adamc@701 1848 \hspace{.1in} \to \mt{tag} \; [\mt{Signal} = \mt{signal} \; (\mt{xml} \; \mt{body} \; \mt{use} \; \mt{bind})] \; \mt{body} \; [] \; \mt{use} \; \mt{bind}
adamc@659 1849 \end{array}$$
adamc@659 1850
adamc@701 1851 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 1852
adamc@914 1853 \subsubsection{Remote Procedure Calls}
adamc@914 1854
adamc@914 1855 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 1856
adamc@914 1857 $$\begin{array}{l}
adamc@914 1858 \mt{val} \; \mt{rpc} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@914 1859 \end{array}$$
adamc@914 1860
adamc@701 1861 \subsubsection{Asynchronous Message-Passing}
adamc@701 1862
adamc@701 1863 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 1864
adamc@701 1865 $$\begin{array}{l}
adamc@701 1866 \mt{type} \; \mt{client} \\
adamc@701 1867 \mt{val} \; \mt{self} : \mt{transaction} \; \mt{client}
adamc@701 1868 \end{array}$$
adamc@701 1869
adamc@701 1870 \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 1871
adamc@701 1872 $$\begin{array}{l}
adamc@701 1873 \mt{con} \; \mt{channel} :: \mt{Type} \to \mt{Type} \\
adamc@701 1874 \mt{val} \; \mt{channel} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; (\mt{channel} \; \mt{t}) \\
adamc@701 1875 \mt{val} \; \mt{send} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@701 1876 \mt{val} \; \mt{recv} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@701 1877 \end{array}$$
adamc@701 1878
adamc@701 1879 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 1880
adamc@701 1881 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 1882
adamc@659 1883
adamc@549 1884 \section{Ur/Web Syntax Extensions}
adamc@549 1885
adamc@549 1886 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 1887
adamc@549 1888 \subsection{SQL}
adamc@549 1889
adamc@786 1890 \subsubsection{\label{tables}Table Declarations}
adamc@786 1891
adamc@788 1892 $\mt{table}$ declarations may include constraints, via these grammar rules.
adamc@788 1893 $$\begin{array}{rrcll}
adamc@788 1894 \textrm{Declarations} & d &::=& \mt{table} \; x : c \; [pk[,]] \; cts \\
adamc@788 1895 \textrm{Primary key constraints} & pk &::=& \mt{PRIMARY} \; \mt{KEY} \; K \\
adamc@788 1896 \textrm{Keys} & K &::=& f \mid (f, (f,)^+) \\
adamc@788 1897 \textrm{Constraint sets} & cts &::=& \mt{CONSTRAINT} f \; ct \mid cts, cts \mid \{\{e\}\} \\
adamc@788 1898 \textrm{Constraints} & ct &::=& \mt{UNIQUE} \; K \mid \mt{CHECK} \; E \\
adamc@788 1899 &&& \mid \mt{FOREIGN} \; \mt{KEY} \; K \; \mt{REFERENCES} \; F \; (K) \; [\mt{ON} \; \mt{DELETE} \; pr] \; [\mt{ON} \; \mt{UPDATE} \; pr] \\
adamc@788 1900 \textrm{Foreign tables} & F &::=& x \mid \{\{e\}\} \\
adamc@788 1901 \textrm{Propagation modes} & pr &::=& \mt{NO} \; \mt{ACTION} \mid \mt{RESTRICT} \mid \mt{CASCADE} \mid \mt{SET} \; \mt{NULL}
adamc@788 1902 \end{array}$$
adamc@788 1903
adamc@788 1904 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 1905
adamc@788 1906
adamc@549 1907 \subsubsection{Queries}
adamc@549 1908
adamc@550 1909 Queries $Q$ are added to the rules for expressions $e$.
adamc@550 1910
adamc@549 1911 $$\begin{array}{rrcll}
adamc@550 1912 \textrm{Queries} & Q &::=& (q \; [\mt{ORDER} \; \mt{BY} \; (E \; [o],)^+] \; [\mt{LIMIT} \; N] \; [\mt{OFFSET} \; N]) \\
adamc@1085 1913 \textrm{Pre-queries} & q &::=& \mt{SELECT} \; [\mt{DISTINCT}] \; P \; \mt{FROM} \; F,^+ \; [\mt{WHERE} \; E] \; [\mt{GROUP} \; \mt{BY} \; p,^+] \; [\mt{HAVING} \; E] \\
adamc@1085 1914 &&& \mid q \; R \; q \mid \{\{\{e\}\}\} \\
adamc@549 1915 \textrm{Relational operators} & R &::=& \mt{UNION} \mid \mt{INTERSECT} \mid \mt{EXCEPT}
adamc@549 1916 \end{array}$$
adamc@549 1917
adamc@549 1918 $$\begin{array}{rrcll}
adamc@549 1919 \textrm{Projections} & P &::=& \ast & \textrm{all columns} \\
adamc@549 1920 &&& p,^+ & \textrm{particular columns} \\
adamc@549 1921 \textrm{Pre-projections} & p &::=& t.f & \textrm{one column from a table} \\
adamc@558 1922 &&& t.\{\{c\}\} & \textrm{a record of columns from a table (of kind $\{\mt{Type}\}$)} \\
adamc@549 1923 \textrm{Table names} & t &::=& x & \textrm{constant table name (automatically capitalized)} \\
adamc@549 1924 &&& X & \textrm{constant table name} \\
adamc@549 1925 &&& \{\{c\}\} & \textrm{computed table name (of kind $\mt{Name}$)} \\
adamc@549 1926 \textrm{Column names} & f &::=& X & \textrm{constant column name} \\
adamc@549 1927 &&& \{c\} & \textrm{computed column name (of kind $\mt{Name}$)} \\
adamc@549 1928 \textrm{Tables} & T &::=& x & \textrm{table variable, named locally by its own capitalization} \\
adamc@549 1929 &&& x \; \mt{AS} \; t & \textrm{table variable, with local name} \\
adamc@549 1930 &&& \{\{e\}\} \; \mt{AS} \; t & \textrm{computed table expression, with local name} \\
adamc@1085 1931 \textrm{$\mt{FROM}$ items} & F &::=& T \mid \{\{e\}\} \mid F \; J \; \mt{JOIN} \; F \; \mt{ON} \; E \\
adamc@1085 1932 &&& \mid F \; \mt{CROSS} \; \mt{JOIN} \ F \\
adamc@1085 1933 \textrm{Joins} & J &::=& [\mt{INNER}] \\
adamc@1085 1934 &&& \mid [\mt{LEFT} \mid \mt{RIGHT} \mid \mt{FULL}] \; [\mt{OUTER}] \\
adamc@549 1935 \textrm{SQL expressions} & E &::=& p & \textrm{column references} \\
adamc@549 1936 &&& X & \textrm{named expression references} \\
adamc@549 1937 &&& \{\{e\}\} & \textrm{injected native Ur expressions} \\
adamc@549 1938 &&& \{e\} & \textrm{computed expressions, probably using $\mt{sql\_exp}$ directly} \\
adamc@549 1939 &&& \mt{TRUE} \mid \mt{FALSE} & \textrm{boolean constants} \\
adamc@549 1940 &&& \ell & \textrm{primitive type literals} \\
adamc@549 1941 &&& \mt{NULL} & \textrm{null value (injection of $\mt{None}$)} \\
adamc@549 1942 &&& E \; \mt{IS} \; \mt{NULL} & \textrm{nullness test} \\
adamc@549 1943 &&& n & \textrm{nullary operators} \\
adamc@549 1944 &&& u \; E & \textrm{unary operators} \\
adamc@549 1945 &&& E \; b \; E & \textrm{binary operators} \\
adamc@549 1946 &&& \mt{COUNT}(\ast) & \textrm{count number of rows} \\
adamc@549 1947 &&& a(E) & \textrm{other aggregate function} \\
adamc@549 1948 &&& (E) & \textrm{explicit precedence} \\
adamc@549 1949 \textrm{Nullary operators} & n &::=& \mt{CURRENT\_TIMESTAMP} \\
adamc@549 1950 \textrm{Unary operators} & u &::=& \mt{NOT} \\
adamc@549 1951 \textrm{Binary operators} & b &::=& \mt{AND} \mid \mt{OR} \mid \neq \mid < \mid \leq \mid > \mid \geq \\
adamc@549 1952 \textrm{Aggregate functions} & a &::=& \mt{AVG} \mid \mt{SUM} \mid \mt{MIN} \mid \mt{MAX} \\
adamc@550 1953 \textrm{Directions} & o &::=& \mt{ASC} \mid \mt{DESC} \\
adamc@549 1954 \textrm{SQL integer} & N &::=& n \mid \{e\} \\
adamc@549 1955 \end{array}$$
adamc@549 1956
adamc@1085 1957 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 1958
adamc@550 1959 \subsubsection{DML}
adamc@550 1960
adamc@550 1961 DML commands $D$ are added to the rules for expressions $e$.
adamc@550 1962
adamc@550 1963 $$\begin{array}{rrcll}
adamc@550 1964 \textrm{Commands} & D &::=& (\mt{INSERT} \; \mt{INTO} \; T^E \; (f,^+) \; \mt{VALUES} \; (E,^+)) \\
adamc@550 1965 &&& (\mt{UPDATE} \; T^E \; \mt{SET} \; (f = E,)^+ \; \mt{WHERE} \; E) \\
adamc@550 1966 &&& (\mt{DELETE} \; \mt{FROM} \; T^E \; \mt{WHERE} \; E) \\
adamc@550 1967 \textrm{Table expressions} & T^E &::=& x \mid \{\{e\}\}
adamc@550 1968 \end{array}$$
adamc@550 1969
adamc@550 1970 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 1971
adamc@551 1972 \subsection{XML}
adamc@551 1973
adamc@551 1974 XML fragments $L$ are added to the rules for expressions $e$.
adamc@551 1975
adamc@551 1976 $$\begin{array}{rrcll}
adamc@551 1977 \textrm{XML fragments} & L &::=& \texttt{<xml/>} \mid \texttt{<xml>}l^*\texttt{</xml>} \\
adamc@551 1978 \textrm{XML pieces} & l &::=& \textrm{text} & \textrm{cdata} \\
adamc@551 1979 &&& \texttt{<}g\texttt{/>} & \textrm{tag with no children} \\
adamc@551 1980 &&& \texttt{<}g\texttt{>}l^*\texttt{</}x\texttt{>} & \textrm{tag with children} \\
adamc@559 1981 &&& \{e\} & \textrm{computed XML fragment} \\
adamc@559 1982 &&& \{[e]\} & \textrm{injection of an Ur expression, via the $\mt{Top}.\mt{txt}$ function} \\
adamc@551 1983 \textrm{Tag} & g &::=& h \; (x = v)^* \\
adamc@551 1984 \textrm{Tag head} & h &::=& x & \textrm{tag name} \\
adamc@551 1985 &&& h\{c\} & \textrm{constructor parameter} \\
adamc@551 1986 \textrm{Attribute value} & v &::=& \ell & \textrm{literal value} \\
adamc@551 1987 &&& \{e\} & \textrm{computed value} \\
adamc@551 1988 \end{array}$$
adamc@551 1989
adamc@552 1990
adamc@553 1991 \section{The Structure of Web Applications}
adamc@553 1992
adamc@1127 1993 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 1994
adamc@553 1995 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 1996
adamc@553 1997 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 1998
adamc@558 1999 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 2000
adamc@660 2001 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 2002
adamc@789 2003 \medskip
adamc@789 2004
adamc@789 2005 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 2006
adamc@789 2007 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 2008
adamc@553 2009
adamc@897 2010 \section{The Foreign Function Interface}
adamc@897 2011
adamc@897 2012 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 2013
adamc@897 2014 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 2015
adamc@897 2016 \begin{itemize}
adamc@897 2017 \item \texttt{clientOnly Module.ident} registers a value as being allowed only in client-side code.
adamc@897 2018 \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 2019 \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 2020 \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 2021 \item \texttt{include FILE} requests inclusion of a C header file.
adamc@897 2022 \item \texttt{jsFunc Module.ident=name} gives a mapping from an Ur name for a value to a JavaScript name.
adamc@897 2023 \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 2024 \item \texttt{script URL} requests inclusion of a JavaScript source file within application HTML.
adamc@897 2025 \item \texttt{serverOnly Module.ident} registers a value as being allowed only in server-side code.
adamc@897 2026 \end{itemize}
adamc@897 2027
adamc@897 2028 \subsection{Writing C FFI Code}
adamc@897 2029
adamc@897 2030 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 2031
adamc@897 2032 \begin{itemize}
adamc@897 2033 \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 2034 \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 2035 \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 2036 \end{itemize}
adamc@897 2037
adamc@897 2038 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 2039 \begin{itemize}
adamc@897 2040 \item \begin{verbatim}
adamc@897 2041 void uw_error(uw_context, failure_kind, const char *fmt, ...);
adamc@897 2042 \end{verbatim}
adamc@897 2043 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 2044
adamc@897 2045 \item \begin{verbatim}
adamc@897 2046 void uw_push_cleanup(uw_context, void (*func)(void *), void *arg);
adamc@897 2047 void uw_pop_cleanup(uw_context);
adamc@897 2048 \end{verbatim}
adamc@897 2049 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 2050
adamc@897 2051 \item \begin{verbatim}
adamc@897 2052 void *uw_malloc(uw_context, size_t);
adamc@897 2053 \end{verbatim}
adamc@897 2054 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 2055
adamc@897 2056 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 2057
adamc@897 2058 \item \begin{verbatim}
adamc@897 2059 typedef void (*uw_callback)(void *);
adamc@897 2060 void uw_register_transactional(uw_context, void *data, uw_callback commit,
adamc@897 2061 uw_callback rollback, uw_callback free);
adamc@897 2062 \end{verbatim}
adamc@897 2063 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 2064
adamc@1085 2065 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 2066
adamc@1085 2067 \item \begin{verbatim}
adamc@1085 2068 void *uw_get_global(uw_context, char *name);
adamc@1085 2069 void uw_set_global(uw_context, char *name, void *data, uw_callback free);
adamc@1085 2070 \end{verbatim}
adamc@1085 2071 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 2072
adamc@897 2073 \end{itemize}
adamc@897 2074
adamc@897 2075 \subsection{Writing JavaScript FFI Code}
adamc@897 2076
adamc@897 2077 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 2078
adamc@897 2079 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 2080
adamc@897 2081 \begin{itemize}
adamc@897 2082 \item Integers, floats, strings, characters, and booleans are represented in the usual JavaScript way.
adamc@985 2083 \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 2084 \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 2085 \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 2086 \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 2087 \end{itemize}
adamc@897 2088
adamc@897 2089 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 2090
adamc@897 2091
adamc@552 2092 \section{Compiler Phases}
adamc@552 2093
adamc@552 2094 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 2095
adamc@552 2096 In this section, we step through the main phases of compilation, noting what consequences each phase has for effective programming.
adamc@552 2097
adamc@552 2098 \subsection{Parse}
adamc@552 2099
adamc@552 2100 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 2101
adamc@552 2102 \subsection{Elaborate}
adamc@552 2103
adamc@552 2104 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 2105
adamc@552 2106 \subsection{Unnest}
adamc@552 2107
adamc@552 2108 Named local function definitions are moved to the top level, to avoid the need to generate closures.
adamc@552 2109
adamc@552 2110 \subsection{Corify}
adamc@552 2111
adamc@552 2112 Module system features are compiled away, through inlining of functor definitions at application sites. Afterward, most abstraction boundaries are broken, facilitating optimization.
adamc@552 2113
adamc@552 2114 \subsection{Especialize}
adamc@552 2115
adamc@552 2116 Functions are specialized to particular argument patterns. This is an important trick for avoiding the need to maintain any closures at runtime.
adamc@552 2117
adamc@552 2118 \subsection{Untangle}
adamc@552 2119
adamc@552 2120 Remove unnecessary mutual recursion, splitting recursive groups into strongly-connected components.
adamc@552 2121
adamc@552 2122 \subsection{Shake}
adamc@552 2123
adamc@552 2124 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 2125
adamc@661 2126 \subsection{Rpcify}
adamc@661 2127
adamc@661 2128 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 2129
adamc@661 2130 \subsection{Untangle, Shake}
adamc@661 2131
adamc@661 2132 Repeat these simplifications.
adamc@661 2133
adamc@553 2134 \subsection{\label{tag}Tag}
adamc@552 2135
adamc@552 2136 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 2137
adamc@552 2138 \subsection{Reduce}
adamc@552 2139
adamc@552 2140 Apply definitional equality rules to simplify the program as much as possible. This effectively includes inlining of every non-recursive definition.
adamc@552 2141
adamc@552 2142 \subsection{Unpoly}
adamc@552 2143
adamc@552 2144 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 2145
adamc@552 2146 \subsection{Specialize}
adamc@552 2147
adamc@558 2148 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 2149
adamc@552 2150 \subsection{Shake}
adamc@552 2151
adamc@558 2152 Here the compiler repeats the earlier Shake phase.
adamc@552 2153
adamc@552 2154 \subsection{Monoize}
adamc@552 2155
adamc@552 2156 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 2157
adamc@552 2158 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 2159
adamc@552 2160 \subsection{MonoOpt}
adamc@552 2161
adamc@552 2162 Simple algebraic laws are applied to simplify the program, focusing especially on efficient imperative generation of HTML pages.
adamc@552 2163
adamc@552 2164 \subsection{MonoUntangle}
adamc@552 2165
adamc@552 2166 Unnecessary mutual recursion is broken up again.
adamc@552 2167
adamc@552 2168 \subsection{MonoReduce}
adamc@552 2169
adamc@552 2170 Equivalents of the definitional equality rules are applied to simplify programs, with inlining again playing a major role.
adamc@552 2171
adamc@552 2172 \subsection{MonoShake, MonoOpt}
adamc@552 2173
adamc@552 2174 Unneeded declarations are removed, and basic optimizations are repeated.
adamc@552 2175
adamc@552 2176 \subsection{Fuse}
adamc@552 2177
adamc@552 2178 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 2179
adamc@552 2180 \subsection{MonoUntangle, MonoShake}
adamc@552 2181
adamc@552 2182 Fuse often creates more opportunities to remove spurious mutual recursion.
adamc@552 2183
adamc@552 2184 \subsection{Pathcheck}
adamc@552 2185
adamc@552 2186 The compiler checks that no link or action name has been used more than once.
adamc@552 2187
adamc@552 2188 \subsection{Cjrize}
adamc@552 2189
adamc@552 2190 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 2191
adamc@552 2192 \subsection{C Compilation and Linking}
adamc@552 2193
adamc@552 2194 The output of the last phase is pretty-printed as C source code and passed to GCC.
adamc@552 2195
adamc@552 2196
adamc@524 2197 \end{document}