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Fix .urp parsing for real
author Adam Chlipala <adamc@hcoop.net>
date Sun, 07 Feb 2010 09:51:41 -0500
parents de48dc2c9ee8
children 277a5db17aa1
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@1143 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.
adamc@555 97
adamc@555 98 The Emacs mode can be set to autoload by adding the following to your \texttt{.emacs} file.
adamc@555 99
adamc@555 100 \begin{verbatim}
adamc@555 101 (add-to-list 'load-path "/usr/local/share/emacs/site-lisp/urweb-mode")
adamc@555 102 (load "urweb-mode-startup")
adamc@555 103 \end{verbatim}
adamc@555 104
adamc@555 105 Change the path in the first line if you chose a different Emacs installation path during configuration.
adamc@555 106
adamc@555 107
adamc@556 108 \section{Command-Line Compiler}
adamc@556 109
adamc@556 110 \subsection{Project Files}
adamc@556 111
adamc@556 112 The basic inputs to the \texttt{urweb} compiler are project files, which have the extension \texttt{.urp}. Here is a sample \texttt{.urp} file.
adamc@556 113
adamc@556 114 \begin{verbatim}
adamc@556 115 database dbname=test
adamc@556 116 sql crud1.sql
adamc@556 117
adamc@556 118 crud
adamc@556 119 crud1
adamc@556 120 \end{verbatim}
adamc@556 121
adamc@556 122 The \texttt{database} line gives the database information string to pass to libpq. In this case, the string only says to connect to a local database named \texttt{test}.
adamc@556 123
adamc@556 124 The \texttt{sql} line asks for an SQL source file to be generated, giving the commands to run to create the tables and sequences that this application expects to find. After building this \texttt{.urp} file, the following commands could be used to initialize the database, assuming that the current UNIX user exists as a Postgres user with database creation privileges:
adamc@556 125
adamc@556 126 \begin{verbatim}
adamc@556 127 createdb test
adamc@556 128 psql -f crud1.sql test
adamc@556 129 \end{verbatim}
adamc@556 130
adamc@1151 131 A blank line separates the named directives from a list of modules to include in the project.
adamc@556 132
adamc@556 133 For each entry \texttt{M} in the module list, the file \texttt{M.urs} is included in the project if it exists, and the file \texttt{M.ur} must exist and is always included.
adamc@556 134
adamc@783 135 Here is the complete list of directive forms. ``FFI'' stands for ``foreign function interface,'' Ur's facility for interaction between Ur programs and C and JavaScript libraries.
adamc@783 136 \begin{itemize}
adamc@783 137 \item \texttt{[allow|deny] [url|mime] PATTERN} registers a rule governing which URLs or MIME types are allowed in this application. The first such rule to match a URL or MIME type determines the verdict. If \texttt{PATTERN} ends in \texttt{*}, it is interpreted as a prefix rule. Otherwise, a string must match it exactly.
adamc@783 138 \item \texttt{clientOnly Module.ident} registers an FFI function or transaction that may only be run in client browsers.
adamc@783 139 \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@783 140 \item \texttt{database DBSTRING} sets the string to pass to libpq to open a database connection.
adamc@783 141 \item \texttt{debug} saves some intermediate C files, which is mostly useful to help in debugging the compiler itself.
adamc@783 142 \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@783 143 \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@783 144 \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 145 \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@783 146 \item \texttt{jsFunc Module.ident=name} gives the JavaScript name of an FFI value.
adamc@1089 147 \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@783 148 \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@852 149 \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@783 150 \item \texttt{prefix PREFIX} sets the prefix included before every URI within the generated application. The default is \texttt{/}.
adamc@783 151 \item \texttt{profile} generates an executable that may be used with gprof.
adamc@783 152 \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@783 153 \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@783 154 \item \texttt{serverOnly Module.ident} registers an FFI function or transaction that may only be run on the server.
adamc@783 155 \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@783 156 \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@783 157 \end{itemize}
adamc@701 158
adamc@701 159
adamc@557 160 \subsection{Building an Application}
adamc@557 161
adamc@557 162 To compile project \texttt{P.urp}, simply run
adamc@557 163 \begin{verbatim}
adamc@557 164 urweb P
adamc@557 165 \end{verbatim}
adamc@558 166 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@557 167
adamc@557 168 To time how long the different compiler phases run, without generating an executable, run
adamc@557 169 \begin{verbatim}
adamc@557 170 urweb -timing P
adamc@557 171 \end{verbatim}
adamc@557 172
adamc@1086 173 To stop the compilation process after type-checking, run
adamc@1086 174 \begin{verbatim}
adamc@1086 175 urweb -tc P
adamc@1086 176 \end{verbatim}
adamc@1086 177
adamc@896 178 Some other command-line parameters are accepted:
adamc@896 179 \begin{itemize}
adamc@896 180 \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@896 181
adamc@896 182 \item \texttt{-dbms [postgres|mysql|sqlite]}: Sets the database backend to use.
adamc@896 183 \begin{itemize}
adamc@896 184 \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@896 185
adamc@896 186 A command sequence like this can initialize a Postgres database, using a file \texttt{app.sql} generated by the compiler:
adamc@896 187 \begin{verbatim}
adamc@896 188 createdb app
adamc@896 189 psql -f app.sql app
adamc@896 190 \end{verbatim}
adamc@896 191
adamc@896 192 \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@896 193
adamc@896 194 A command sequence like this can initialize a MySQL database:
adamc@896 195 \begin{verbatim}
adamc@896 196 echo "CREATE DATABASE app" | mysql
adamc@896 197 mysql -D app <app.sql
adamc@896 198 \end{verbatim}
adamc@896 199
adamc@896 200 \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@896 201
adamc@896 202 A command like this can initialize an SQLite database:
adamc@896 203 \begin{verbatim}
adamc@896 204 sqlite3 path/to/database/file <app.sql
adamc@896 205 \end{verbatim}
adamc@896 206 \end{itemize}
adamc@896 207
adamc@896 208 \item \texttt{-output FILENAME}: Set where the application executable is written.
adamc@896 209
adamc@1127 210 \item \texttt{-path NAME VALUE}: Set the value of path variable \texttt{\$NAME} to \texttt{VALUE}, for use in \texttt{.urp} files.
adamc@1127 211
adamc@896 212 \item \texttt{-protocol [http|cgi|fastcgi]}: Set the protocol that the generated application speaks.
adamc@896 213 \begin{itemize}
adamc@896 214 \item \texttt{http}: This is the default. It is for building standalone web servers that can be accessed by web browsers directly.
adamc@896 215
adamc@896 216 \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@896 217
adamc@896 218 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@896 219 \begin{verbatim}
adamc@896 220 ScriptAlias /Hello /path/to/hello.exe
adamc@896 221 \end{verbatim}
adamc@896 222
adamc@896 223 \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@896 224
adamc@896 225 To configure a FastCGI program with Apache, one could combine the above \texttt{ScriptAlias} line with a line like this:
adamc@896 226 \begin{verbatim}
adamc@896 227 FastCgiServer /path/to/hello.exe -idle-timeout 99999
adamc@896 228 \end{verbatim}
adamc@896 229 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@896 230
adamc@896 231 Here is some lighttpd configuration for the same application.
adamc@896 232 \begin{verbatim}
adamc@896 233 fastcgi.server = (
adamc@896 234 "/Hello/" =>
adamc@896 235 (( "bin-path" => "/path/to/hello.exe",
adamc@896 236 "socket" => "/tmp/hello",
adamc@896 237 "check-local" => "disable",
adamc@896 238 "docroot" => "/",
adamc@896 239 "max-procs" => "1"
adamc@896 240 ))
adamc@896 241 )
adamc@896 242 \end{verbatim}
adamc@896 243 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@896 244
adamc@896 245 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@896 246 \end{itemize}
adamc@896 247
adamc@1127 248 \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 249
adamc@896 250 \item \texttt{-sql FILENAME}: Set where a database set-up SQL script is written.
adamc@1095 251
adamc@1095 252 \item \texttt{-static}: Link the runtime system statically. The default is to link against dynamic libraries.
adamc@896 253 \end{itemize}
adamc@896 254
adamc@556 255
adamc@529 256 \section{Ur Syntax}
adamc@529 257
adamc@784 258 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@524 259
adamc@524 260 \subsection{Lexical Conventions}
adamc@524 261
adamc@524 262 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@524 263
adamc@524 264 \begin{center}
adamc@524 265 \begin{tabular}{rl}
adamc@524 266 \textbf{\LaTeX} & \textbf{ASCII} \\
adamc@524 267 $\to$ & \cd{->} \\
adamc@652 268 $\longrightarrow$ & \cd{-->} \\
adamc@524 269 $\times$ & \cd{*} \\
adamc@524 270 $\lambda$ & \cd{fn} \\
adamc@524 271 $\Rightarrow$ & \cd{=>} \\
adamc@652 272 $\Longrightarrow$ & \cd{==>} \\
adamc@529 273 $\neq$ & \cd{<>} \\
adamc@529 274 $\leq$ & \cd{<=} \\
adamc@529 275 $\geq$ & \cd{>=} \\
adamc@524 276 \\
adamc@524 277 $x$ & Normal textual identifier, not beginning with an uppercase letter \\
adamc@525 278 $X$ & Normal textual identifier, beginning with an uppercase letter \\
adamc@524 279 \end{tabular}
adamc@524 280 \end{center}
adamc@524 281
adamc@525 282 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@524 283
adamc@873 284 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@526 285
adamc@527 286 This version of the manual doesn't include operator precedences; see \texttt{src/urweb.grm} for that.
adamc@527 287
adamc@552 288 \subsection{\label{core}Core Syntax}
adamc@524 289
adamc@524 290 \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@524 291 $$\begin{array}{rrcll}
adamc@524 292 \textrm{Kinds} & \kappa &::=& \mt{Type} & \textrm{proper types} \\
adamc@525 293 &&& \mt{Unit} & \textrm{the trivial constructor} \\
adamc@525 294 &&& \mt{Name} & \textrm{field names} \\
adamc@525 295 &&& \kappa \to \kappa & \textrm{type-level functions} \\
adamc@525 296 &&& \{\kappa\} & \textrm{type-level records} \\
adamc@525 297 &&& (\kappa\times^+) & \textrm{type-level tuples} \\
adamc@652 298 &&& X & \textrm{variable} \\
adamc@652 299 &&& X \longrightarrow k & \textrm{kind-polymorphic type-level function} \\
adamc@529 300 &&& \_\_ & \textrm{wildcard} \\
adamc@525 301 &&& (\kappa) & \textrm{explicit precedence} \\
adamc@524 302 \end{array}$$
adamc@524 303
adamc@524 304 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@524 305 $$\begin{array}{rrcll}
adamc@524 306 \textrm{Explicitness} & ? &::=& :: & \textrm{explicit} \\
adamc@558 307 &&& ::: & \textrm{implicit}
adamc@524 308 \end{array}$$
adamc@524 309
adamc@524 310 \emph{Constructors} are the main class of compile-time-only data. They include proper types and are classified by kinds.
adamc@524 311 $$\begin{array}{rrcll}
adamc@524 312 \textrm{Constructors} & c, \tau &::=& (c) :: \kappa & \textrm{kind annotation} \\
adamc@530 313 &&& \hat{x} & \textrm{constructor variable} \\
adamc@524 314 \\
adamc@525 315 &&& \tau \to \tau & \textrm{function type} \\
adamc@525 316 &&& x \; ? \; \kappa \to \tau & \textrm{polymorphic function type} \\
adamc@652 317 &&& X \longrightarrow \tau & \textrm{kind-polymorphic function type} \\
adamc@525 318 &&& \$ c & \textrm{record type} \\
adamc@524 319 \\
adamc@525 320 &&& c \; c & \textrm{type-level function application} \\
adamc@530 321 &&& \lambda x \; :: \; \kappa \Rightarrow c & \textrm{type-level function abstraction} \\
adamc@524 322 \\
adamc@652 323 &&& X \Longrightarrow c & \textrm{type-level kind-polymorphic function abstraction} \\
adamc@655 324 &&& c [\kappa] & \textrm{type-level kind-polymorphic function application} \\
adamc@652 325 \\
adamc@525 326 &&& () & \textrm{type-level unit} \\
adamc@525 327 &&& \#X & \textrm{field name} \\
adamc@524 328 \\
adamc@525 329 &&& [(c = c)^*] & \textrm{known-length type-level record} \\
adamc@525 330 &&& c \rc c & \textrm{type-level record concatenation} \\
adamc@652 331 &&& \mt{map} & \textrm{type-level record map} \\
adamc@524 332 \\
adamc@558 333 &&& (c,^+) & \textrm{type-level tuple} \\
adamc@525 334 &&& c.n & \textrm{type-level tuple projection ($n \in \mathbb N^+$)} \\
adamc@524 335 \\
adamc@652 336 &&& [c \sim c] \Rightarrow \tau & \textrm{guarded type} \\
adamc@524 337 \\
adamc@529 338 &&& \_ :: \kappa & \textrm{wildcard} \\
adamc@525 339 &&& (c) & \textrm{explicit precedence} \\
adamc@530 340 \\
adamc@530 341 \textrm{Qualified uncapitalized variables} & \hat{x} &::=& x & \textrm{not from a module} \\
adamc@530 342 &&& M.x & \textrm{projection from a module} \\
adamc@525 343 \end{array}$$
adamc@525 344
adamc@655 345 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@655 346
adamc@525 347 Modules of the module system are described by \emph{signatures}.
adamc@525 348 $$\begin{array}{rrcll}
adamc@525 349 \textrm{Signatures} & S &::=& \mt{sig} \; s^* \; \mt{end} & \textrm{constant} \\
adamc@525 350 &&& X & \textrm{variable} \\
adamc@525 351 &&& \mt{functor}(X : S) : S & \textrm{functor} \\
adamc@529 352 &&& S \; \mt{where} \; \mt{con} \; x = c & \textrm{concretizing an abstract constructor} \\
adamc@525 353 &&& M.X & \textrm{projection from a module} \\
adamc@525 354 \\
adamc@525 355 \textrm{Signature items} & s &::=& \mt{con} \; x :: \kappa & \textrm{abstract constructor} \\
adamc@525 356 &&& \mt{con} \; x :: \kappa = c & \textrm{concrete constructor} \\
adamc@528 357 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529 358 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@525 359 &&& \mt{val} \; x : \tau & \textrm{value} \\
adamc@525 360 &&& \mt{structure} \; X : S & \textrm{sub-module} \\
adamc@525 361 &&& \mt{signature} \; X = S & \textrm{sub-signature} \\
adamc@525 362 &&& \mt{include} \; S & \textrm{signature inclusion} \\
adamc@525 363 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@654 364 &&& \mt{class} \; x :: \kappa & \textrm{abstract constructor class} \\
adamc@654 365 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@525 366 \\
adamc@525 367 \textrm{Datatype constructors} & dc &::=& X & \textrm{nullary constructor} \\
adamc@525 368 &&& X \; \mt{of} \; \tau & \textrm{unary constructor} \\
adamc@524 369 \end{array}$$
adamc@524 370
adamc@526 371 \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@526 372 $$\begin{array}{rrcll}
adamc@526 373 \textrm{Patterns} & p &::=& \_ & \textrm{wildcard} \\
adamc@526 374 &&& x & \textrm{variable} \\
adamc@526 375 &&& \ell & \textrm{constant} \\
adamc@526 376 &&& \hat{X} & \textrm{nullary constructor} \\
adamc@526 377 &&& \hat{X} \; p & \textrm{unary constructor} \\
adamc@526 378 &&& \{(x = p,)^*\} & \textrm{rigid record pattern} \\
adamc@526 379 &&& \{(x = p,)^+, \ldots\} & \textrm{flexible record pattern} \\
adamc@852 380 &&& p : \tau & \textrm{type annotation} \\
adamc@527 381 &&& (p) & \textrm{explicit precedence} \\
adamc@526 382 \\
adamc@529 383 \textrm{Qualified capitalized variables} & \hat{X} &::=& X & \textrm{not from a module} \\
adamc@526 384 &&& M.X & \textrm{projection from a module} \\
adamc@526 385 \end{array}$$
adamc@526 386
adamc@527 387 \emph{Expressions} are the main run-time entities, corresponding to both ``expressions'' and ``statements'' in mainstream imperative languages.
adamc@527 388 $$\begin{array}{rrcll}
adamc@527 389 \textrm{Expressions} & e &::=& e : \tau & \textrm{type annotation} \\
adamc@529 390 &&& \hat{x} & \textrm{variable} \\
adamc@529 391 &&& \hat{X} & \textrm{datatype constructor} \\
adamc@527 392 &&& \ell & \textrm{constant} \\
adamc@527 393 \\
adamc@527 394 &&& e \; e & \textrm{function application} \\
adamc@527 395 &&& \lambda x : \tau \Rightarrow e & \textrm{function abstraction} \\
adamc@527 396 &&& e [c] & \textrm{polymorphic function application} \\
adamc@852 397 &&& \lambda [x \; ? \; \kappa] \Rightarrow e & \textrm{polymorphic function abstraction} \\
adamc@655 398 &&& e [\kappa] & \textrm{kind-polymorphic function application} \\
adamc@652 399 &&& X \Longrightarrow e & \textrm{kind-polymorphic function abstraction} \\
adamc@527 400 \\
adamc@527 401 &&& \{(c = e,)^*\} & \textrm{known-length record} \\
adamc@527 402 &&& e.c & \textrm{record field projection} \\
adamc@527 403 &&& e \rc e & \textrm{record concatenation} \\
adamc@527 404 &&& e \rcut c & \textrm{removal of a single record field} \\
adamc@527 405 &&& e \rcutM c & \textrm{removal of multiple record fields} \\
adamc@527 406 \\
adamc@527 407 &&& \mt{let} \; ed^* \; \mt{in} \; e \; \mt{end} & \textrm{local definitions} \\
adamc@527 408 \\
adamc@527 409 &&& \mt{case} \; e \; \mt{of} \; (p \Rightarrow e|)^+ & \textrm{pattern matching} \\
adamc@527 410 \\
adamc@654 411 &&& \lambda [c \sim c] \Rightarrow e & \textrm{guarded expression abstraction} \\
adamc@654 412 &&& e \; ! & \textrm{guarded expression application} \\
adamc@527 413 \\
adamc@527 414 &&& \_ & \textrm{wildcard} \\
adamc@527 415 &&& (e) & \textrm{explicit precedence} \\
adamc@527 416 \\
adamc@527 417 \textrm{Local declarations} & ed &::=& \cd{val} \; x : \tau = e & \textrm{non-recursive value} \\
adamc@527 418 &&& \cd{val} \; \cd{rec} \; (x : \tau = e \; \cd{and})^+ & \textrm{mutually-recursive values} \\
adamc@527 419 \end{array}$$
adamc@527 420
adamc@655 421 As with constructors, we include both abstraction and application for kind polymorphism, but applications are only inferred internally.
adamc@655 422
adamc@528 423 \emph{Declarations} primarily bring new symbols into context.
adamc@528 424 $$\begin{array}{rrcll}
adamc@528 425 \textrm{Declarations} & d &::=& \mt{con} \; x :: \kappa = c & \textrm{constructor synonym} \\
adamc@528 426 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529 427 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@528 428 &&& \mt{val} \; x : \tau = e & \textrm{value} \\
adamc@528 429 &&& \mt{val} \; \cd{rec} \; (x : \tau = e \; \mt{and})^+ & \textrm{mutually-recursive values} \\
adamc@528 430 &&& \mt{structure} \; X : S = M & \textrm{module definition} \\
adamc@528 431 &&& \mt{signature} \; X = S & \textrm{signature definition} \\
adamc@528 432 &&& \mt{open} \; M & \textrm{module inclusion} \\
adamc@528 433 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@528 434 &&& \mt{open} \; \mt{constraints} \; M & \textrm{inclusion of just the constraints from a module} \\
adamc@528 435 &&& \mt{table} \; x : c & \textrm{SQL table} \\
adamc@784 436 &&& \mt{view} \; x : c & \textrm{SQL view} \\
adamc@528 437 &&& \mt{sequence} \; x & \textrm{SQL sequence} \\
adamc@535 438 &&& \mt{cookie} \; x : \tau & \textrm{HTTP cookie} \\
adamc@784 439 &&& \mt{style} \; x : \tau & \textrm{CSS class} \\
adamc@654 440 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@1085 441 &&& \mt{task} \; e = e & \textrm{recurring task} \\
adamc@528 442 \\
adamc@529 443 \textrm{Modules} & M &::=& \mt{struct} \; d^* \; \mt{end} & \textrm{constant} \\
adamc@529 444 &&& X & \textrm{variable} \\
adamc@529 445 &&& M.X & \textrm{projection} \\
adamc@529 446 &&& M(M) & \textrm{functor application} \\
adamc@529 447 &&& \mt{functor}(X : S) : S = M & \textrm{functor abstraction} \\
adamc@528 448 \end{array}$$
adamc@528 449
adamc@528 450 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@527 451
adamc@784 452 We omit some extra possibilities in $\mt{table}$ syntax, deferring them to Section \ref{tables}.
adamc@784 453
adamc@529 454 \subsection{Shorthands}
adamc@529 455
adamc@529 456 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@529 457
adamc@529 458 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@529 459
adamc@529 460 A record type may be written $\{(c = c,)^*\}$, which elaborates to $\$[(c = c,)^*]$.
adamc@529 461
adamc@533 462 The notation $[c_1, \ldots, c_n]$ is shorthand for $[c_1 = (), \ldots, c_n = ()]$.
adamc@533 463
adamc@529 464 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@529 465
adamc@852 466 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@529 467
adamc@529 468 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@529 469
adamc@529 470 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@529 471
adamc@654 472 A signature item or declaration $\mt{class} \; x = \lambda y \Rightarrow c$ may be abbreviated $\mt{class} \; x \; y = c$.
adamc@529 473
adamc@1102 474 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@529 475
adamc@852 476 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@529 477
adamc@852 478 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@852 479
adamc@852 480 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@529 481
adamc@529 482 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@529 483
adamc@852 484 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@852 485
adamc@853 486 A declaration $\mt{table} \; x : \{(c = c,)^*\}$ is elaborated into $\mt{table} \; x : [(c = c,)^*]$.
adamc@529 487
adamc@529 488 The syntax $\mt{where} \; \mt{type}$ is an alternate form of $\mt{where} \; \mt{con}$.
adamc@529 489
adamc@529 490 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@529 491
adamc@529 492 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@529 493
adamc@784 494 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@529 495
adamc@530 496
adamc@530 497 \section{Static Semantics}
adamc@530 498
adamc@530 499 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@530 500
adamc@530 501 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@530 502 \begin{itemize}
adamc@655 503 \item $\Gamma \vdash \kappa$ expresses kind well-formedness.
adamc@530 504 \item $\Gamma \vdash c :: \kappa$ assigns a kind to a constructor in a context.
adamc@530 505 \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@531 506 \item $\Gamma \vdash c \hookrightarrow C$ proves that record constructor $c$ decomposes into set $C$ of field names and record constructors.
adamc@530 507 \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@530 508 \item $\Gamma \vdash e : \tau$ is a standard typing judgment.
adamc@534 509 \item $\Gamma \vdash p \leadsto \Gamma; \tau$ combines typing of patterns with calculation of which new variables they bind.
adamc@537 510 \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@537 511 \item $\Gamma \vdash S \equiv S$ is the signature equivalence judgment.
adamc@536 512 \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@530 513 \item $\Gamma \vdash M : S$ is the module signature checking judgment.
adamc@537 514 \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@539 515 \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@530 516 \end{itemize}
adamc@530 517
adamc@655 518
adamc@655 519 \subsection{Kind Well-Formedness}
adamc@655 520
adamc@655 521 $$\infer{\Gamma \vdash \mt{Type}}{}
adamc@655 522 \quad \infer{\Gamma \vdash \mt{Unit}}{}
adamc@655 523 \quad \infer{\Gamma \vdash \mt{Name}}{}
adamc@655 524 \quad \infer{\Gamma \vdash \kappa_1 \to \kappa_2}{
adamc@655 525 \Gamma \vdash \kappa_1
adamc@655 526 & \Gamma \vdash \kappa_2
adamc@655 527 }
adamc@655 528 \quad \infer{\Gamma \vdash \{\kappa\}}{
adamc@655 529 \Gamma \vdash \kappa
adamc@655 530 }
adamc@655 531 \quad \infer{\Gamma \vdash (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@655 532 \forall i: \Gamma \vdash \kappa_i
adamc@655 533 }$$
adamc@655 534
adamc@655 535 $$\infer{\Gamma \vdash X}{
adamc@655 536 X \in \Gamma
adamc@655 537 }
adamc@655 538 \quad \infer{\Gamma \vdash X \longrightarrow \kappa}{
adamc@655 539 \Gamma, X \vdash \kappa
adamc@655 540 }$$
adamc@655 541
adamc@530 542 \subsection{Kinding}
adamc@530 543
adamc@655 544 We write $[X \mapsto \kappa_1]\kappa_2$ for capture-avoiding substitution of $\kappa_1$ for $X$ in $\kappa_2$.
adamc@655 545
adamc@530 546 $$\infer{\Gamma \vdash (c) :: \kappa :: \kappa}{
adamc@530 547 \Gamma \vdash c :: \kappa
adamc@530 548 }
adamc@530 549 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530 550 x :: \kappa \in \Gamma
adamc@530 551 }
adamc@530 552 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530 553 x :: \kappa = c \in \Gamma
adamc@530 554 }$$
adamc@530 555
adamc@530 556 $$\infer{\Gamma \vdash M.x :: \kappa}{
adamc@537 557 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 558 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = \kappa
adamc@530 559 }
adamc@530 560 \quad \infer{\Gamma \vdash M.x :: \kappa}{
adamc@537 561 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 562 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@530 563 }$$
adamc@530 564
adamc@530 565 $$\infer{\Gamma \vdash \tau_1 \to \tau_2 :: \mt{Type}}{
adamc@530 566 \Gamma \vdash \tau_1 :: \mt{Type}
adamc@530 567 & \Gamma \vdash \tau_2 :: \mt{Type}
adamc@530 568 }
adamc@530 569 \quad \infer{\Gamma \vdash x \; ? \: \kappa \to \tau :: \mt{Type}}{
adamc@530 570 \Gamma, x :: \kappa \vdash \tau :: \mt{Type}
adamc@530 571 }
adamc@655 572 \quad \infer{\Gamma \vdash X \longrightarrow \tau :: \mt{Type}}{
adamc@655 573 \Gamma, X \vdash \tau :: \mt{Type}
adamc@655 574 }
adamc@530 575 \quad \infer{\Gamma \vdash \$c :: \mt{Type}}{
adamc@530 576 \Gamma \vdash c :: \{\mt{Type}\}
adamc@530 577 }$$
adamc@530 578
adamc@530 579 $$\infer{\Gamma \vdash c_1 \; c_2 :: \kappa_2}{
adamc@530 580 \Gamma \vdash c_1 :: \kappa_1 \to \kappa_2
adamc@530 581 & \Gamma \vdash c_2 :: \kappa_1
adamc@530 582 }
adamc@530 583 \quad \infer{\Gamma \vdash \lambda x \; :: \; \kappa_1 \Rightarrow c :: \kappa_1 \to \kappa_2}{
adamc@530 584 \Gamma, x :: \kappa_1 \vdash c :: \kappa_2
adamc@530 585 }$$
adamc@530 586
adamc@655 587 $$\infer{\Gamma \vdash c[\kappa'] :: [X \mapsto \kappa']\kappa}{
adamc@655 588 \Gamma \vdash c :: X \to \kappa
adamc@655 589 & \Gamma \vdash \kappa'
adamc@655 590 }
adamc@655 591 \quad \infer{\Gamma \vdash X \Longrightarrow c :: X \to \kappa}{
adamc@655 592 \Gamma, X \vdash c :: \kappa
adamc@655 593 }$$
adamc@655 594
adamc@530 595 $$\infer{\Gamma \vdash () :: \mt{Unit}}{}
adamc@530 596 \quad \infer{\Gamma \vdash \#X :: \mt{Name}}{}$$
adamc@530 597
adamc@530 598 $$\infer{\Gamma \vdash [\overline{c_i = c'_i}] :: \{\kappa\}}{
adamc@530 599 \forall i: \Gamma \vdash c_i : \mt{Name}
adamc@530 600 & \Gamma \vdash c'_i :: \kappa
adamc@530 601 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@530 602 }
adamc@530 603 \quad \infer{\Gamma \vdash c_1 \rc c_2 :: \{\kappa\}}{
adamc@530 604 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530 605 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@530 606 & \Gamma \vdash c_1 \sim c_2
adamc@530 607 }$$
adamc@530 608
adamc@655 609 $$\infer{\Gamma \vdash \mt{map} :: (\kappa_1 \to \kappa_2) \to \{\kappa_1\} \to \{\kappa_2\}}{}$$
adamc@530 610
adamc@573 611 $$\infer{\Gamma \vdash (\overline c) :: (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@573 612 \forall i: \Gamma \vdash c_i :: \kappa_i
adamc@530 613 }
adamc@573 614 \quad \infer{\Gamma \vdash c.i :: \kappa_i}{
adamc@573 615 \Gamma \vdash c :: (\kappa_1 \times \ldots \times \kappa_n)
adamc@530 616 }$$
adamc@530 617
adamc@655 618 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow \tau :: \mt{Type}}{
adamc@655 619 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530 620 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@655 621 & \Gamma, c_1 \sim c_2 \vdash \tau :: \mt{Type}
adamc@530 622 }$$
adamc@530 623
adamc@531 624 \subsection{Record Disjointness}
adamc@531 625
adamc@531 626 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@558 627 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@558 628 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@558 629 & \forall c'_1 \in C_1, c'_2 \in C_2: \Gamma \vdash c'_1 \sim c'_2
adamc@531 630 }
adamc@531 631 \quad \infer{\Gamma \vdash X \sim X'}{
adamc@531 632 X \neq X'
adamc@531 633 }$$
adamc@531 634
adamc@531 635 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@531 636 c'_1 \sim c'_2 \in \Gamma
adamc@558 637 & \Gamma \vdash c'_1 \hookrightarrow C_1
adamc@558 638 & \Gamma \vdash c'_2 \hookrightarrow C_2
adamc@558 639 & c_1 \in C_1
adamc@558 640 & c_2 \in C_2
adamc@531 641 }$$
adamc@531 642
adamc@531 643 $$\infer{\Gamma \vdash c \hookrightarrow \{c\}}{}
adamc@531 644 \quad \infer{\Gamma \vdash [\overline{c = c'}] \hookrightarrow \{\overline{c}\}}{}
adamc@531 645 \quad \infer{\Gamma \vdash c_1 \rc c_2 \hookrightarrow C_1 \cup C_2}{
adamc@531 646 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@531 647 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@531 648 }
adamc@531 649 \quad \infer{\Gamma \vdash c \hookrightarrow C}{
adamc@531 650 \Gamma \vdash c \equiv c'
adamc@531 651 & \Gamma \vdash c' \hookrightarrow C
adamc@531 652 }
adamc@531 653 \quad \infer{\Gamma \vdash \mt{map} \; f \; c \hookrightarrow C}{
adamc@531 654 \Gamma \vdash c \hookrightarrow C
adamc@531 655 }$$
adamc@531 656
adamc@541 657 \subsection{\label{definitional}Definitional Equality}
adamc@532 658
adamc@655 659 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@532 660
adamc@532 661 $$\infer{\Gamma \vdash c \equiv c}{}
adamc@532 662 \quad \infer{\Gamma \vdash c_1 \equiv c_2}{
adamc@532 663 \Gamma \vdash c_2 \equiv c_1
adamc@532 664 }
adamc@532 665 \quad \infer{\Gamma \vdash c_1 \equiv c_3}{
adamc@532 666 \Gamma \vdash c_1 \equiv c_2
adamc@532 667 & \Gamma \vdash c_2 \equiv c_3
adamc@532 668 }
adamc@532 669 \quad \infer{\Gamma \vdash \mathcal C[c_1] \equiv \mathcal C[c_2]}{
adamc@532 670 \Gamma \vdash c_1 \equiv c_2
adamc@532 671 }$$
adamc@532 672
adamc@532 673 $$\infer{\Gamma \vdash x \equiv c}{
adamc@532 674 x :: \kappa = c \in \Gamma
adamc@532 675 }
adamc@532 676 \quad \infer{\Gamma \vdash M.x \equiv c}{
adamc@537 677 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 678 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@532 679 }
adamc@532 680 \quad \infer{\Gamma \vdash (\overline c).i \equiv c_i}{}$$
adamc@532 681
adamc@532 682 $$\infer{\Gamma \vdash (\lambda x :: \kappa \Rightarrow c) \; c' \equiv [x \mapsto c'] c}{}
adamc@655 683 \quad \infer{\Gamma \vdash (X \Longrightarrow c) [\kappa] \equiv [X \mapsto \kappa] c}{}$$
adamc@655 684
adamc@655 685 $$\infer{\Gamma \vdash c_1 \rc c_2 \equiv c_2 \rc c_1}{}
adamc@532 686 \quad \infer{\Gamma \vdash c_1 \rc (c_2 \rc c_3) \equiv (c_1 \rc c_2) \rc c_3}{}$$
adamc@532 687
adamc@532 688 $$\infer{\Gamma \vdash [] \rc c \equiv c}{}
adamc@532 689 \quad \infer{\Gamma \vdash [\overline{c_1 = c'_1}] \rc [\overline{c_2 = c'_2}] \equiv [\overline{c_1 = c'_1}, \overline{c_2 = c'_2}]}{}$$
adamc@532 690
adamc@655 691 $$\infer{\Gamma \vdash \mt{map} \; f \; [] \equiv []}{}
adamc@655 692 \quad \infer{\Gamma \vdash \mt{map} \; f \; ([c_1 = c_2] \rc c) \equiv [c_1 = f \; c_2] \rc \mt{map} \; f \; c}{}$$
adamc@532 693
adamc@532 694 $$\infer{\Gamma \vdash \mt{map} \; (\lambda x \Rightarrow x) \; c \equiv c}{}
adamc@655 695 \quad \infer{\Gamma \vdash \mt{map} \; f \; (\mt{map} \; f' \; c)
adamc@655 696 \equiv \mt{map} \; (\lambda x \Rightarrow f \; (f' \; x)) \; c}{}$$
adamc@532 697
adamc@532 698 $$\infer{\Gamma \vdash \mt{map} \; f \; (c_1 \rc c_2) \equiv \mt{map} \; f \; c_1 \rc \mt{map} \; f \; c_2}{}$$
adamc@531 699
adamc@534 700 \subsection{Expression Typing}
adamc@533 701
adamc@873 702 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@533 703
adamc@533 704 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@533 705
adamc@533 706 $$\infer{\Gamma \vdash e : \tau : \tau}{
adamc@533 707 \Gamma \vdash e : \tau
adamc@533 708 }
adamc@533 709 \quad \infer{\Gamma \vdash e : \tau}{
adamc@533 710 \Gamma \vdash e : \tau'
adamc@533 711 & \Gamma \vdash \tau' \equiv \tau
adamc@533 712 }
adamc@533 713 \quad \infer{\Gamma \vdash \ell : T(\ell)}{}$$
adamc@533 714
adamc@533 715 $$\infer{\Gamma \vdash x : \mathcal I(\tau)}{
adamc@533 716 x : \tau \in \Gamma
adamc@533 717 }
adamc@533 718 \quad \infer{\Gamma \vdash M.x : \mathcal I(\tau)}{
adamc@537 719 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 720 & \mt{proj}(M, \overline{s}, \mt{val} \; x) = \tau
adamc@533 721 }
adamc@533 722 \quad \infer{\Gamma \vdash X : \mathcal I(\tau)}{
adamc@533 723 X : \tau \in \Gamma
adamc@533 724 }
adamc@533 725 \quad \infer{\Gamma \vdash M.X : \mathcal I(\tau)}{
adamc@537 726 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 727 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \tau
adamc@533 728 }$$
adamc@533 729
adamc@533 730 $$\infer{\Gamma \vdash e_1 \; e_2 : \tau_2}{
adamc@533 731 \Gamma \vdash e_1 : \tau_1 \to \tau_2
adamc@533 732 & \Gamma \vdash e_2 : \tau_1
adamc@533 733 }
adamc@533 734 \quad \infer{\Gamma \vdash \lambda x : \tau_1 \Rightarrow e : \tau_1 \to \tau_2}{
adamc@533 735 \Gamma, x : \tau_1 \vdash e : \tau_2
adamc@533 736 }$$
adamc@533 737
adamc@533 738 $$\infer{\Gamma \vdash e [c] : [x \mapsto c]\tau}{
adamc@533 739 \Gamma \vdash e : x :: \kappa \to \tau
adamc@533 740 & \Gamma \vdash c :: \kappa
adamc@533 741 }
adamc@852 742 \quad \infer{\Gamma \vdash \lambda [x \; ? \; \kappa] \Rightarrow e : x \; ? \; \kappa \to \tau}{
adamc@533 743 \Gamma, x :: \kappa \vdash e : \tau
adamc@533 744 }$$
adamc@533 745
adamc@655 746 $$\infer{\Gamma \vdash e [\kappa] : [X \mapsto \kappa]\tau}{
adamc@655 747 \Gamma \vdash e : X \longrightarrow \tau
adamc@655 748 & \Gamma \vdash \kappa
adamc@655 749 }
adamc@655 750 \quad \infer{\Gamma \vdash X \Longrightarrow e : X \longrightarrow \tau}{
adamc@655 751 \Gamma, X \vdash e : \tau
adamc@655 752 }$$
adamc@655 753
adamc@533 754 $$\infer{\Gamma \vdash \{\overline{c = e}\} : \{\overline{c : \tau}\}}{
adamc@533 755 \forall i: \Gamma \vdash c_i :: \mt{Name}
adamc@533 756 & \Gamma \vdash e_i : \tau_i
adamc@533 757 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@533 758 }
adamc@533 759 \quad \infer{\Gamma \vdash e.c : \tau}{
adamc@533 760 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533 761 }
adamc@533 762 \quad \infer{\Gamma \vdash e_1 \rc e_2 : \$(c_1 \rc c_2)}{
adamc@533 763 \Gamma \vdash e_1 : \$c_1
adamc@533 764 & \Gamma \vdash e_2 : \$c_2
adamc@573 765 & \Gamma \vdash c_1 \sim c_2
adamc@533 766 }$$
adamc@533 767
adamc@533 768 $$\infer{\Gamma \vdash e \rcut c : \$c'}{
adamc@533 769 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533 770 }
adamc@533 771 \quad \infer{\Gamma \vdash e \rcutM c : \$c'}{
adamc@533 772 \Gamma \vdash e : \$(c \rc c')
adamc@533 773 }$$
adamc@533 774
adamc@533 775 $$\infer{\Gamma \vdash \mt{let} \; \overline{ed} \; \mt{in} \; e \; \mt{end} : \tau}{
adamc@533 776 \Gamma \vdash \overline{ed} \leadsto \Gamma'
adamc@533 777 & \Gamma' \vdash e : \tau
adamc@533 778 }
adamc@533 779 \quad \infer{\Gamma \vdash \mt{case} \; e \; \mt{of} \; \overline{p \Rightarrow e} : \tau}{
adamc@533 780 \forall i: \Gamma \vdash p_i \leadsto \Gamma_i, \tau'
adamc@533 781 & \Gamma_i \vdash e_i : \tau
adamc@533 782 }$$
adamc@533 783
adamc@573 784 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow e : \lambda [c_1 \sim c_2] \Rightarrow \tau}{
adamc@533 785 \Gamma \vdash c_1 :: \{\kappa\}
adamc@655 786 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@533 787 & \Gamma, c_1 \sim c_2 \vdash e : \tau
adamc@662 788 }
adamc@662 789 \quad \infer{\Gamma \vdash e \; ! : \tau}{
adamc@662 790 \Gamma \vdash e : [c_1 \sim c_2] \Rightarrow \tau
adamc@662 791 & \Gamma \vdash c_1 \sim c_2
adamc@533 792 }$$
adamc@533 793
adamc@534 794 \subsection{Pattern Typing}
adamc@534 795
adamc@534 796 $$\infer{\Gamma \vdash \_ \leadsto \Gamma; \tau}{}
adamc@534 797 \quad \infer{\Gamma \vdash x \leadsto \Gamma, x : \tau; \tau}{}
adamc@534 798 \quad \infer{\Gamma \vdash \ell \leadsto \Gamma; T(\ell)}{}$$
adamc@534 799
adamc@534 800 $$\infer{\Gamma \vdash X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534 801 X : \overline{x ::: \mt{Type}} \to \tau \in \Gamma
adamc@534 802 & \textrm{$\tau$ not a function type}
adamc@534 803 }
adamc@534 804 \quad \infer{\Gamma \vdash X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534 805 X : \overline{x ::: \mt{Type}} \to \tau'' \to \tau \in \Gamma
adamc@534 806 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534 807 }$$
adamc@534 808
adamc@534 809 $$\infer{\Gamma \vdash M.X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537 810 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 811 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau
adamc@534 812 & \textrm{$\tau$ not a function type}
adamc@534 813 }$$
adamc@534 814
adamc@534 815 $$\infer{\Gamma \vdash M.X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537 816 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 817 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau'' \to \tau
adamc@534 818 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534 819 }$$
adamc@534 820
adamc@534 821 $$\infer{\Gamma \vdash \{\overline{x = p}\} \leadsto \Gamma_n; \{\overline{x = \tau}\}}{
adamc@534 822 \Gamma_0 = \Gamma
adamc@534 823 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534 824 }
adamc@534 825 \quad \infer{\Gamma \vdash \{\overline{x = p}, \ldots\} \leadsto \Gamma_n; \$([\overline{x = \tau}] \rc c)}{
adamc@534 826 \Gamma_0 = \Gamma
adamc@534 827 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534 828 }$$
adamc@534 829
adamc@852 830 $$\infer{\Gamma \vdash p : \tau \leadsto \Gamma'; \tau}{
adamc@852 831 \Gamma \vdash p \leadsto \Gamma'; \tau'
adamc@852 832 & \Gamma \vdash \tau' \equiv \tau
adamc@852 833 }$$
adamc@852 834
adamc@535 835 \subsection{Declaration Typing}
adamc@535 836
adamc@535 837 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@535 838
adamc@655 839 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@535 840
adamc@558 841 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@537 842 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@535 843
adamc@535 844 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535 845 \quad \infer{\Gamma \vdash d, \overline{d} \leadsto \Gamma''}{
adamc@535 846 \Gamma \vdash d \leadsto \Gamma'
adamc@535 847 & \Gamma' \vdash \overline{d} \leadsto \Gamma''
adamc@535 848 }$$
adamc@535 849
adamc@535 850 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@535 851 \Gamma \vdash c :: \kappa
adamc@535 852 }
adamc@535 853 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@535 854 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@535 855 }$$
adamc@535 856
adamc@535 857 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537 858 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 859 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@535 860 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@535 861 }$$
adamc@535 862
adamc@535 863 $$\infer{\Gamma \vdash \mt{val} \; x : \tau = e \leadsto \Gamma, x : \tau}{
adamc@535 864 \Gamma \vdash e : \tau
adamc@535 865 }$$
adamc@535 866
adamc@535 867 $$\infer{\Gamma \vdash \mt{val} \; \mt{rec} \; \overline{x : \tau = e} \leadsto \Gamma, \overline{x : \tau}}{
adamc@535 868 \forall i: \Gamma, \overline{x : \tau} \vdash e_i : \tau_i
adamc@535 869 & \textrm{$e_i$ starts with an expression $\lambda$, optionally preceded by constructor and disjointness $\lambda$s}
adamc@535 870 }$$
adamc@535 871
adamc@535 872 $$\infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : S}{
adamc@535 873 \Gamma \vdash M : S
adamc@558 874 & \textrm{ $M$ not a constant or application}
adamc@535 875 }
adamc@558 876 \quad \infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : \mt{selfify}(X, \overline{s})}{
adamc@558 877 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@539 878 }$$
adamc@539 879
adamc@539 880 $$\infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@535 881 \Gamma \vdash S
adamc@535 882 }$$
adamc@535 883
adamc@537 884 $$\infer{\Gamma \vdash \mt{open} \; M \leadsto \Gamma, \mathcal O(M, \overline{s})}{
adamc@537 885 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535 886 }$$
adamc@535 887
adamc@535 888 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma}{
adamc@535 889 \Gamma \vdash c_1 :: \{\kappa\}
adamc@535 890 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@535 891 & \Gamma \vdash c_1 \sim c_2
adamc@535 892 }
adamc@537 893 \quad \infer{\Gamma \vdash \mt{open} \; \mt{constraints} \; M \leadsto \Gamma, \mathcal O_c(M, \overline{s})}{
adamc@537 894 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535 895 }$$
adamc@535 896
adamc@784 897 $$\infer{\Gamma \vdash \mt{table} \; x : c \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_table} \; c \; []}{
adamc@535 898 \Gamma \vdash c :: \{\mt{Type}\}
adamc@535 899 }
adamc@784 900 \quad \infer{\Gamma \vdash \mt{view} \; x : c \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_view} \; c}{
adamc@784 901 \Gamma \vdash c :: \{\mt{Type}\}
adamc@784 902 }$$
adamc@784 903
adamc@784 904 $$\infer{\Gamma \vdash \mt{sequence} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_sequence}}{}$$
adamc@535 905
adamc@535 906 $$\infer{\Gamma \vdash \mt{cookie} \; x : \tau \leadsto \Gamma, x : \mt{Basis}.\mt{http\_cookie} \; \tau}{
adamc@535 907 \Gamma \vdash \tau :: \mt{Type}
adamc@784 908 }
adamc@784 909 \quad \infer{\Gamma \vdash \mt{style} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{css\_class}}{}$$
adamc@535 910
adamc@1085 911 $$\infer{\Gamma \vdash \mt{task} \; e_1 = e_2 \leadsto \Gamma}{
adamc@1085 912 \Gamma \vdash e_1 :: \mt{Basis}.\mt{task\_kind}
adamc@1085 913 & \Gamma \vdash e_2 :: \mt{Basis}.\mt{transaction} \; \{\}
adamc@1085 914 }$$
adamc@1085 915
adamc@784 916 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784 917 \Gamma \vdash c :: \kappa
adamc@535 918 }$$
adamc@535 919
adamc@535 920 $$\infer{\overline{y}; x; \Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535 921 \quad \infer{\overline{y}; x; \Gamma \vdash X \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to x \; \overline{y}}{
adamc@535 922 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535 923 }
adamc@535 924 \quad \infer{\overline{y}; x; \Gamma \vdash X \; \mt{of} \; \tau \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to \tau \to x \; \overline{y}}{
adamc@535 925 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535 926 }$$
adamc@535 927
adamc@537 928 \subsection{Signature Item Typing}
adamc@537 929
adamc@537 930 We appeal to a signature item analogue of the $\mathcal O$ function from the last subsection.
adamc@537 931
adamc@537 932 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@537 933 \quad \infer{\Gamma \vdash s, \overline{s} \leadsto \Gamma''}{
adamc@537 934 \Gamma \vdash s \leadsto \Gamma'
adamc@537 935 & \Gamma' \vdash \overline{s} \leadsto \Gamma''
adamc@537 936 }$$
adamc@537 937
adamc@537 938 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}
adamc@537 939 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@537 940 \Gamma \vdash c :: \kappa
adamc@537 941 }
adamc@537 942 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@537 943 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@537 944 }$$
adamc@537 945
adamc@537 946 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537 947 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 948 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 949 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@537 950 }$$
adamc@537 951
adamc@537 952 $$\infer{\Gamma \vdash \mt{val} \; x : \tau \leadsto \Gamma, x : \tau}{
adamc@537 953 \Gamma \vdash \tau :: \mt{Type}
adamc@537 954 }$$
adamc@537 955
adamc@537 956 $$\infer{\Gamma \vdash \mt{structure} \; X : S \leadsto \Gamma, X : S}{
adamc@537 957 \Gamma \vdash S
adamc@537 958 }
adamc@537 959 \quad \infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@537 960 \Gamma \vdash S
adamc@537 961 }$$
adamc@537 962
adamc@537 963 $$\infer{\Gamma \vdash \mt{include} \; S \leadsto \Gamma, \mathcal O(\overline{s})}{
adamc@537 964 \Gamma \vdash S
adamc@537 965 & \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 966 }$$
adamc@537 967
adamc@537 968 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma, c_1 \sim c_2}{
adamc@537 969 \Gamma \vdash c_1 :: \{\kappa\}
adamc@537 970 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@537 971 }$$
adamc@537 972
adamc@784 973 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784 974 \Gamma \vdash c :: \kappa
adamc@537 975 }
adamc@784 976 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}$$
adamc@537 977
adamc@536 978 \subsection{Signature Compatibility}
adamc@536 979
adamc@558 980 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@537 981
adamc@537 982 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@537 983
adamc@536 984 $$\infer{\Gamma \vdash S \equiv S}{}
adamc@536 985 \quad \infer{\Gamma \vdash S_1 \equiv S_2}{
adamc@536 986 \Gamma \vdash S_2 \equiv S_1
adamc@536 987 }
adamc@536 988 \quad \infer{\Gamma \vdash X \equiv S}{
adamc@536 989 X = S \in \Gamma
adamc@536 990 }
adamc@536 991 \quad \infer{\Gamma \vdash M.X \equiv S}{
adamc@537 992 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 993 & \mt{proj}(M, \overline{s}, \mt{signature} \; X) = S
adamc@536 994 }$$
adamc@536 995
adamc@536 996 $$\infer{\Gamma \vdash S \; \mt{where} \; \mt{con} \; x = c \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa = c \; \overline{s_2} \; \mt{end}}{
adamc@536 997 \Gamma \vdash S \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa \; \overline{s_2} \; \mt{end}
adamc@536 998 & \Gamma \vdash c :: \kappa
adamc@537 999 }
adamc@537 1000 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s^1} \; \mt{include} \; S \; \overline{s^2} \; \mt{end} \equiv \mt{sig} \; \overline{s^1} \; \overline{s} \; \overline{s^2} \; \mt{end}}{
adamc@537 1001 \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@536 1002 }$$
adamc@536 1003
adamc@536 1004 $$\infer{\Gamma \vdash S_1 \leq S_2}{
adamc@536 1005 \Gamma \vdash S_1 \equiv S_2
adamc@536 1006 }
adamc@536 1007 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \mt{end}}{}
adamc@537 1008 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; s' \; \overline{s'} \; \mt{end}}{
adamc@537 1009 \Gamma \vdash \overline{s} \leq s'
adamc@537 1010 & \Gamma \vdash s' \leadsto \Gamma'
adamc@537 1011 & \Gamma' \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \overline{s'} \; \mt{end}
adamc@537 1012 }$$
adamc@537 1013
adamc@537 1014 $$\infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537 1015 \Gamma \vdash s \leq s'
adamc@537 1016 }
adamc@537 1017 \quad \infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537 1018 \Gamma \vdash s \leadsto \Gamma'
adamc@537 1019 & \Gamma' \vdash \overline{s} \leq s'
adamc@536 1020 }$$
adamc@536 1021
adamc@536 1022 $$\infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 \leq \mt{functor} (X : S'_1) : S'_2}{
adamc@536 1023 \Gamma \vdash S'_1 \leq S_1
adamc@536 1024 & \Gamma, X : S'_1 \vdash S_2 \leq S'_2
adamc@536 1025 }$$
adamc@536 1026
adamc@537 1027 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@537 1028 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}
adamc@558 1029 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type}}{}$$
adamc@537 1030
adamc@537 1031 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(y)} \to \mt{Type}}{
adamc@537 1032 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1033 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1034 }$$
adamc@537 1035
adamc@784 1036 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@784 1037 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}$$
adamc@537 1038
adamc@537 1039 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \mt{\kappa} = c_2}{
adamc@537 1040 \Gamma \vdash c_1 \equiv c_2
adamc@537 1041 }
adamc@784 1042 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \kappa = c_2}{
adamc@537 1043 \Gamma \vdash c_1 \equiv c_2
adamc@537 1044 }$$
adamc@537 1045
adamc@537 1046 $$\infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537 1047 \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1048 }$$
adamc@537 1049
adamc@537 1050 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537 1051 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1052 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1053 & \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1054 }$$
adamc@537 1055
adamc@537 1056 $$\infer{\Gamma \vdash \cdot \leq \cdot}{}
adamc@537 1057 \quad \infer{\Gamma \vdash X; \overline{dc} \leq X; \overline{dc'}}{
adamc@537 1058 \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1059 }
adamc@537 1060 \quad \infer{\Gamma \vdash X \; \mt{of} \; \tau_1; \overline{dc} \leq X \; \mt{of} \; \tau_2; \overline{dc'}}{
adamc@537 1061 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537 1062 & \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1063 }$$
adamc@537 1064
adamc@537 1065 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x = \mt{datatype} \; M'.z'}{
adamc@537 1066 \Gamma \vdash M.z \equiv M'.z'
adamc@537 1067 }$$
adamc@537 1068
adamc@537 1069 $$\infer{\Gamma \vdash \mt{val} \; x : \tau_1 \leq \mt{val} \; x : \tau_2}{
adamc@537 1070 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537 1071 }
adamc@537 1072 \quad \infer{\Gamma \vdash \mt{structure} \; X : S_1 \leq \mt{structure} \; X : S_2}{
adamc@537 1073 \Gamma \vdash S_1 \leq S_2
adamc@537 1074 }
adamc@537 1075 \quad \infer{\Gamma \vdash \mt{signature} \; X = S_1 \leq \mt{signature} \; X = S_2}{
adamc@537 1076 \Gamma \vdash S_1 \leq S_2
adamc@537 1077 & \Gamma \vdash S_2 \leq S_1
adamc@537 1078 }$$
adamc@537 1079
adamc@537 1080 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leq \mt{constraint} \; c'_1 \sim c'_2}{
adamc@537 1081 \Gamma \vdash c_1 \equiv c'_1
adamc@537 1082 & \Gamma \vdash c_2 \equiv c'_2
adamc@537 1083 }$$
adamc@537 1084
adamc@655 1085 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{class} \; x :: \kappa}{}
adamc@655 1086 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{class} \; x :: \kappa}{}
adamc@655 1087 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{class} \; x :: \kappa = c_2}{
adamc@537 1088 \Gamma \vdash c_1 \equiv c_2
adamc@537 1089 }$$
adamc@537 1090
adamc@538 1091 \subsection{Module Typing}
adamc@538 1092
adamc@538 1093 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 1094
adamc@538 1095 $$\infer{\Gamma \vdash M : S}{
adamc@538 1096 \Gamma \vdash M : S'
adamc@538 1097 & \Gamma \vdash S' \leq S
adamc@538 1098 }
adamc@538 1099 \quad \infer{\Gamma \vdash \mt{struct} \; \overline{d} \; \mt{end} : \mt{sig} \; \mt{sigOf}(\overline{d}) \; \mt{end}}{
adamc@538 1100 \Gamma \vdash \overline{d} \leadsto \Gamma'
adamc@538 1101 }
adamc@538 1102 \quad \infer{\Gamma \vdash X : S}{
adamc@538 1103 X : S \in \Gamma
adamc@538 1104 }$$
adamc@538 1105
adamc@538 1106 $$\infer{\Gamma \vdash M.X : S}{
adamc@538 1107 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@538 1108 & \mt{proj}(M, \overline{s}, \mt{structure} \; X) = S
adamc@538 1109 }$$
adamc@538 1110
adamc@538 1111 $$\infer{\Gamma \vdash M_1(M_2) : [X \mapsto M_2]S_2}{
adamc@538 1112 \Gamma \vdash M_1 : \mt{functor}(X : S_1) : S_2
adamc@538 1113 & \Gamma \vdash M_2 : S_1
adamc@538 1114 }
adamc@538 1115 \quad \infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 = M : \mt{functor} (X : S_1) : S_2}{
adamc@538 1116 \Gamma \vdash S_1
adamc@538 1117 & \Gamma, X : S_1 \vdash S_2
adamc@538 1118 & \Gamma, X : S_1 \vdash M : S_2
adamc@538 1119 }$$
adamc@538 1120
adamc@538 1121 \begin{eqnarray*}
adamc@538 1122 \mt{sigOf}(\cdot) &=& \cdot \\
adamc@538 1123 \mt{sigOf}(s \; \overline{s'}) &=& \mt{sigOf}(s) \; \mt{sigOf}(\overline{s'}) \\
adamc@538 1124 \\
adamc@538 1125 \mt{sigOf}(\mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@538 1126 \mt{sigOf}(\mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \overline{dc} \\
adamc@538 1127 \mt{sigOf}(\mt{datatype} \; x = \mt{datatype} \; M.z) &=& \mt{datatype} \; x = \mt{datatype} \; M.z \\
adamc@538 1128 \mt{sigOf}(\mt{val} \; x : \tau = e) &=& \mt{val} \; x : \tau \\
adamc@538 1129 \mt{sigOf}(\mt{val} \; \mt{rec} \; \overline{x : \tau = e}) &=& \overline{\mt{val} \; x : \tau} \\
adamc@538 1130 \mt{sigOf}(\mt{structure} \; X : S = M) &=& \mt{structure} \; X : S \\
adamc@538 1131 \mt{sigOf}(\mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@538 1132 \mt{sigOf}(\mt{open} \; M) &=& \mt{include} \; S \textrm{ (where $\Gamma \vdash M : S$)} \\
adamc@538 1133 \mt{sigOf}(\mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@538 1134 \mt{sigOf}(\mt{open} \; \mt{constraints} \; M) &=& \cdot \\
adamc@538 1135 \mt{sigOf}(\mt{table} \; x : c) &=& \mt{table} \; x : c \\
adamc@784 1136 \mt{sigOf}(\mt{view} \; x : c) &=& \mt{view} \; x : c \\
adamc@538 1137 \mt{sigOf}(\mt{sequence} \; x) &=& \mt{sequence} \; x \\
adamc@538 1138 \mt{sigOf}(\mt{cookie} \; x : \tau) &=& \mt{cookie} \; x : \tau \\
adamc@784 1139 \mt{sigOf}(\mt{style} \; x) &=& \mt{style} \; x \\
adamc@655 1140 \mt{sigOf}(\mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@538 1141 \end{eqnarray*}
adamc@539 1142 \begin{eqnarray*}
adamc@539 1143 \mt{selfify}(M, \cdot) &=& \cdot \\
adamc@558 1144 \mt{selfify}(M, s \; \overline{s'}) &=& \mt{selfify}(M, s) \; \mt{selfify}(M, \overline{s'}) \\
adamc@539 1145 \\
adamc@539 1146 \mt{selfify}(M, \mt{con} \; x :: \kappa) &=& \mt{con} \; x :: \kappa = M.x \\
adamc@539 1147 \mt{selfify}(M, \mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@539 1148 \mt{selfify}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \mt{datatype} \; M.x \\
adamc@539 1149 \mt{selfify}(M, \mt{datatype} \; x = \mt{datatype} \; M'.z) &=& \mt{datatype} \; x = \mt{datatype} \; M'.z \\
adamc@539 1150 \mt{selfify}(M, \mt{val} \; x : \tau) &=& \mt{val} \; x : \tau \\
adamc@539 1151 \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 1152 \mt{selfify}(M, \mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@539 1153 \mt{selfify}(M, \mt{include} \; S) &=& \mt{include} \; S \\
adamc@539 1154 \mt{selfify}(M, \mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@655 1155 \mt{selfify}(M, \mt{class} \; x :: \kappa) &=& \mt{class} \; x :: \kappa = M.x \\
adamc@655 1156 \mt{selfify}(M, \mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@539 1157 \end{eqnarray*}
adamc@539 1158
adamc@540 1159 \subsection{Module Projection}
adamc@540 1160
adamc@540 1161 \begin{eqnarray*}
adamc@540 1162 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \\
adamc@540 1163 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa, c) \\
adamc@540 1164 \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 1165 \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 1166 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})$)} \\
adamc@655 1167 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \to \mt{Type} \\
adamc@655 1168 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa \to \mt{Type}, c) \\
adamc@540 1169 \\
adamc@540 1170 \mt{proj}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc} \; \overline{s}, \mt{datatype} \; x) &=& (\overline{y}, \overline{dc}) \\
adamc@540 1171 \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 1172 \\
adamc@540 1173 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, \mt{val} \; x) &=& \tau \\
adamc@540 1174 \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 1175 \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 1176 \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 1177 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \in \overline{dc}$)} \\
adamc@540 1178 \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 1179 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \; \mt{of} \; \tau \in \overline{dc}$)} \\
adamc@540 1180 \\
adamc@540 1181 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, \mt{structure} \; X) &=& S \\
adamc@540 1182 \\
adamc@540 1183 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, \mt{signature} \; X) &=& S \\
adamc@540 1184 \\
adamc@540 1185 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1186 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1187 \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 1188 \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 1189 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@540 1190 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1191 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1192 \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 1193 \mt{proj}(M, \mt{constraint} \; c_1 \sim c_2 \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@655 1194 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@655 1195 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1196 \end{eqnarray*}
adamc@540 1197
adamc@541 1198
adamc@541 1199 \section{Type Inference}
adamc@541 1200
adamc@541 1201 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 1202
adamc@541 1203 \subsection{Basic Unification}
adamc@541 1204
adamc@560 1205 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 1206
adamc@656 1207 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 1208
adamc@541 1209 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 1210
adamc@541 1211 \subsection{Unifying Record Types}
adamc@541 1212
adamc@570 1213 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 1214
adamc@656 1215 \subsection{\label{typeclasses}Constructor Classes}
adamc@541 1216
adamc@784 1217 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 1218
adamc@784 1219 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 1220
adamc@656 1221 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 1222
adamc@656 1223 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 1224
adamc@541 1225 \subsection{Reverse-Engineering Record Types}
adamc@541 1226
adamc@656 1227 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 1228
adamc@541 1229 \subsection{Implicit Arguments in Functor Applications}
adamc@541 1230
adamc@656 1231 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 1232
adamc@541 1233
adamc@542 1234 \section{The Ur Standard Library}
adamc@542 1235
adamc@542 1236 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 1237
adamc@542 1238 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 1239
adamc@542 1240 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 1241 $$\begin{array}{l}
adamc@542 1242 \mt{type} \; \mt{int} \\
adamc@542 1243 \mt{type} \; \mt{float} \\
adamc@873 1244 \mt{type} \; \mt{char} \\
adamc@542 1245 \mt{type} \; \mt{string} \\
adamc@542 1246 \mt{type} \; \mt{time} \\
adamc@785 1247 \mt{type} \; \mt{blob} \\
adamc@542 1248 \\
adamc@542 1249 \mt{type} \; \mt{unit} = \{\} \\
adamc@542 1250 \\
adamc@542 1251 \mt{datatype} \; \mt{bool} = \mt{False} \mid \mt{True} \\
adamc@542 1252 \\
adamc@785 1253 \mt{datatype} \; \mt{option} \; \mt{t} = \mt{None} \mid \mt{Some} \; \mt{of} \; \mt{t} \\
adamc@785 1254 \\
adamc@785 1255 \mt{datatype} \; \mt{list} \; \mt{t} = \mt{Nil} \mid \mt{Cons} \; \mt{of} \; \mt{t} \times \mt{list} \; \mt{t}
adamc@542 1256 \end{array}$$
adamc@542 1257
adamc@1123 1258 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 1259
adamc@657 1260 Another important generic Ur element comes at the beginning of \texttt{top.urs}.
adamc@657 1261
adamc@657 1262 $$\begin{array}{l}
adamc@657 1263 \mt{con} \; \mt{folder} :: \mt{K} \longrightarrow \{\mt{K}\} \to \mt{Type} \\
adamc@657 1264 \\
adamc@657 1265 \mt{val} \; \mt{fold} : \mt{K} \longrightarrow \mt{tf} :: (\{\mt{K}\} \to \mt{Type}) \\
adamc@657 1266 \hspace{.1in} \to (\mt{nm} :: \mt{Name} \to \mt{v} :: \mt{K} \to \mt{r} :: \{\mt{K}\} \to [[\mt{nm}] \sim \mt{r}] \Rightarrow \\
adamc@657 1267 \hspace{.2in} \mt{tf} \; \mt{r} \to \mt{tf} \; ([\mt{nm} = \mt{v}] \rc \mt{r})) \\
adamc@657 1268 \hspace{.1in} \to \mt{tf} \; [] \\
adamc@657 1269 \hspace{.1in} \to \mt{r} :: \{\mt{K}\} \to \mt{folder} \; \mt{r} \to \mt{tf} \; \mt{r}
adamc@657 1270 \end{array}$$
adamc@657 1271
adamc@657 1272 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 1273
adamc@664 1274 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 1275
adamc@542 1276
adamc@542 1277 \section{The Ur/Web Standard Library}
adamc@542 1278
adamc@658 1279 \subsection{Monads}
adamc@658 1280
adamc@658 1281 The Ur Basis defines the monad constructor class from Haskell.
adamc@658 1282
adamc@658 1283 $$\begin{array}{l}
adamc@658 1284 \mt{class} \; \mt{monad} :: \mt{Type} \to \mt{Type} \\
adamc@658 1285 \mt{val} \; \mt{return} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t} ::: \mt{Type} \\
adamc@658 1286 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658 1287 \hspace{.1in} \to \mt{t} \to \mt{m} \; \mt{t} \\
adamc@658 1288 \mt{val} \; \mt{bind} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t1} ::: \mt{Type} \to \mt{t2} ::: \mt{Type} \\
adamc@658 1289 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658 1290 \hspace{.1in} \to \mt{m} \; \mt{t1} \to (\mt{t1} \to \mt{m} \; \mt{t2}) \\
adamc@658 1291 \hspace{.1in} \to \mt{m} \; \mt{t2}
adamc@658 1292 \end{array}$$
adamc@658 1293
adamc@542 1294 \subsection{Transactions}
adamc@542 1295
adamc@542 1296 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 1297 $$\begin{array}{l}
adamc@542 1298 \mt{con} \; \mt{transaction} :: \mt{Type} \to \mt{Type} \\
adamc@658 1299 \mt{val} \; \mt{transaction\_monad} : \mt{monad} \; \mt{transaction}
adamc@542 1300 \end{array}$$
adamc@542 1301
adamc@1123 1302 For debugging purposes, a transactional function is provided for outputting a string on the server process' \texttt{stderr}.
adamc@1123 1303 $$\begin{array}{l}
adamc@1123 1304 \mt{val} \; \mt{debug} : \mt{string} \to \mt{transaction} \; \mt{unit}
adamc@1123 1305 \end{array}$$
adamc@1123 1306
adamc@542 1307 \subsection{HTTP}
adamc@542 1308
adamc@542 1309 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 1310 $$\begin{array}{l}
adamc@786 1311 \mt{val} \; \mt{requestHeader} : \mt{string} \to \mt{transaction} \; (\mt{option} \; \mt{string}) \\
adamc@786 1312 \\
adamc@786 1313 \mt{con} \; \mt{http\_cookie} :: \mt{Type} \to \mt{Type} \\
adamc@786 1314 \mt{val} \; \mt{getCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; (\mt{option} \; \mt{t}) \\
adamc@1050 1315 \mt{val} \; \mt{setCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \{\mt{Value} : \mt{t}, \mt{Expires} : \mt{option} \; \mt{time}, \mt{Secure} : \mt{bool}\} \to \mt{transaction} \; \mt{unit} \\
adamc@1050 1316 \mt{val} \; \mt{clearCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; \mt{unit}
adamc@786 1317 \end{array}$$
adamc@786 1318
adamc@786 1319 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 1320 $$\begin{array}{l}
adamc@786 1321 \mt{type} \; \mt{url} \\
adamc@786 1322 \mt{val} \; \mt{bless} : \mt{string} \to \mt{url} \\
adamc@786 1323 \mt{val} \; \mt{checkUrl} : \mt{string} \to \mt{option} \; \mt{url}
adamc@786 1324 \end{array}$$
adamc@786 1325 $\mt{bless}$ raises a runtime error if the string passed to it fails the URL policy.
adamc@786 1326
adamc@1085 1327 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 1328 $$\begin{array}{l}
adamc@1085 1329 \mt{val} \; \mt{currentUrl} : \mt{transaction} \; \mt{url} \\
adamc@1085 1330 \mt{val} \; \mt{url} : \mt{transaction} \; \mt{page} \to \mt{url}
adamc@1085 1331 \end{array}$$
adamc@1085 1332
adamc@1085 1333 Page generation may be interrupted at any time with a request to redirect to a particular URL instead.
adamc@1085 1334 $$\begin{array}{l}
adamc@1085 1335 \mt{val} \; \mt{redirect} : \mt{t} ::: \mt{Type} \to \mt{url} \to \mt{transaction} \; \mt{t}
adamc@1085 1336 \end{array}$$
adamc@1085 1337
adamc@786 1338 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 1339 $$\begin{array}{l}
adamc@786 1340 \mt{type} \; \mt{file} \\
adamc@786 1341 \mt{val} \; \mt{fileName} : \mt{file} \to \mt{option} \; \mt{string} \\
adamc@786 1342 \mt{val} \; \mt{fileMimeType} : \mt{file} \to \mt{string} \\
adamc@786 1343 \mt{val} \; \mt{fileData} : \mt{file} \to \mt{blob}
adamc@786 1344 \end{array}$$
adamc@786 1345
adamc@786 1346 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 1347 $$\begin{array}{l}
adamc@786 1348 \mt{type} \; \mt{mimeType} \\
adamc@786 1349 \mt{val} \; \mt{blessMime} : \mt{string} \to \mt{mimeType} \\
adamc@786 1350 \mt{val} \; \mt{checkMime} : \mt{string} \to \mt{option} \; \mt{mimeType} \\
adamc@786 1351 \mt{val} \; \mt{returnBlob} : \mt{t} ::: \mt{Type} \to \mt{blob} \to \mt{mimeType} \to \mt{transaction} \; \mt{t}
adamc@542 1352 \end{array}$$
adamc@542 1353
adamc@543 1354 \subsection{SQL}
adamc@543 1355
adamc@543 1356 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 1357 $$\begin{array}{l}
adamc@785 1358 \mt{con} \; \mt{sql\_table} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785 1359 \end{array}$$
adamc@785 1360 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 1361
adamc@785 1362 We also have the simpler type family of SQL views, which have no keys.
adamc@785 1363 $$\begin{array}{l}
adamc@785 1364 \mt{con} \; \mt{sql\_view} :: \{\mt{Type}\} \to \mt{Type}
adamc@543 1365 \end{array}$$
adamc@543 1366
adamc@785 1367 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 1368 $$\begin{array}{l}
adamc@785 1369 \mt{class} \; \mt{fieldsOf} :: \mt{Type} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1370 \mt{val} \; \mt{fieldsOf\_table} : \mt{fs} ::: \{\mt{Type}\} \to \mt{keys} ::: \{\{\mt{Unit}\}\} \to \mt{fieldsOf} \; (\mt{sql\_table} \; \mt{fs} \; \mt{keys}) \; \mt{fs} \\
adamc@785 1371 \mt{val} \; \mt{fieldsOf\_view} : \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; (\mt{sql\_view} \; \mt{fs}) \; \mt{fs}
adamc@785 1372 \end{array}$$
adamc@785 1373
adamc@785 1374 \subsubsection{Table Constraints}
adamc@785 1375
adamc@785 1376 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 1377
adamc@785 1378 $$\begin{array}{l}
adamc@785 1379 \mt{con} \; \mt{primary\_key} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type} \\
adamc@785 1380 \mt{val} \; \mt{no\_primary\_key} : \mt{fs} ::: \{\mt{Type}\} \to \mt{primary\_key} \; \mt{fs} \; [] \\
adamc@785 1381 \mt{val} \; \mt{primary\_key} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{key1} :: \mt{Name} \to \mt{keys} :: \{\mt{Type}\} \\
adamc@785 1382 \hspace{.1in} \to [[\mt{key1}] \sim \mt{keys}] \Rightarrow [[\mt{key1} = \mt{t}] \rc \mt{keys} \sim \mt{rest}] \\
adamc@785 1383 \hspace{.1in} \Rightarrow \$([\mt{key1} = \mt{sql\_injectable\_prim} \; \mt{t}] \rc \mt{map} \; \mt{sql\_injectable\_prim} \; \mt{keys}) \\
adamc@785 1384 \hspace{.1in} \to \mt{primary\_key} \; ([\mt{key1} = \mt{t}] \rc \mt{keys} \rc \mt{rest}) \; [\mt{Pkey} = [\mt{key1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{keys}]
adamc@785 1385 \end{array}$$
adamc@785 1386 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 1387
adamc@785 1388 A type family stands for sets of named constraints of the remaining varieties.
adamc@785 1389 $$\begin{array}{l}
adamc@785 1390 \mt{con} \; \mt{sql\_constraints} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785 1391 \end{array}$$
adamc@785 1392 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 1393
adamc@785 1394 There is a type family of individual, unnamed constraints.
adamc@785 1395 $$\begin{array}{l}
adamc@785 1396 \mt{con} \; \mt{sql\_constraint} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \mt{Type}
adamc@785 1397 \end{array}$$
adamc@785 1398 The first argument is the same as above, and the second argument gives the key columns for just this constraint.
adamc@785 1399
adamc@785 1400 We have operations for assembling constraints into constraint sets.
adamc@785 1401 $$\begin{array}{l}
adamc@785 1402 \mt{val} \; \mt{no\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_constraints} \; \mt{fs} \; [] \\
adamc@785 1403 \mt{val} \; \mt{one\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{unique} ::: \{\mt{Unit}\} \to \mt{name} :: \mt{Name} \\
adamc@785 1404 \hspace{.1in} \to \mt{sql\_constraint} \; \mt{fs} \; \mt{unique} \to \mt{sql\_constraints} \; \mt{fs} \; [\mt{name} = \mt{unique}] \\
adamc@785 1405 \mt{val} \; \mt{join\_constraints} : \mt{fs} ::: \{\mt{Type}\} \to \mt{uniques1} ::: \{\{\mt{Unit}\}\} \to \mt{uniques2} ::: \{\{\mt{Unit}\}\} \to [\mt{uniques1} \sim \mt{uniques2}] \\
adamc@785 1406 \hspace{.1in} \Rightarrow \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques1} \to \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques2} \to \mt{sql\_constraints} \; \mt{fs} \; (\mt{uniques1} \rc \mt{uniques2})
adamc@785 1407 \end{array}$$
adamc@785 1408
adamc@785 1409 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 1410 $$\begin{array}{l}
adamc@785 1411 \mt{val} \; \mt{unique} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{unique1} :: \mt{Name} \to \mt{unique} :: \{\mt{Type}\} \\
adamc@785 1412 \hspace{.1in} \to [[\mt{unique1}] \sim \mt{unique}] \Rightarrow [[\mt{unique1} = \mt{t}] \rc \mt{unique} \sim \mt{rest}] \\
adamc@785 1413 \hspace{.1in} \Rightarrow \mt{sql\_constraint} \; ([\mt{unique1} = \mt{t}] \rc \mt{unique} \rc \mt{rest}) \; ([\mt{unique1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{unique})
adamc@785 1414 \end{array}$$
adamc@785 1415
adamc@785 1416 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 1417 $$\begin{array}{l}
adamc@785 1418 \mt{class} \; \mt{linkable} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@785 1419 \mt{val} \; \mt{linkable\_same} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; \mt{t} \\
adamc@785 1420 \mt{val} \; \mt{linkable\_from\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; (\mt{option} \; \mt{t}) \; \mt{t} \\
adamc@785 1421 \mt{val} \; \mt{linkable\_to\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@785 1422 \end{array}$$
adamc@785 1423
adamc@785 1424 The $\mt{matching}$ type family uses $\mt{linkable}$ to define when two keys match up type-wise.
adamc@785 1425 $$\begin{array}{l}
adamc@785 1426 \mt{con} \; \mt{matching} :: \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1427 \mt{val} \; \mt{mat\_nil} : \mt{matching} \; [] \; [] \\
adamc@785 1428 \mt{val} \; \mt{mat\_cons} : \mt{t1} ::: \mt{Type} \to \mt{rest1} ::: \{\mt{Type}\} \to \mt{t2} ::: \mt{Type} \to \mt{rest2} ::: \{\mt{Type}\} \to \mt{nm1} :: \mt{Name} \to \mt{nm2} :: \mt{Name} \\
adamc@785 1429 \hspace{.1in} \to [[\mt{nm1}] \sim \mt{rest1}] \Rightarrow [[\mt{nm2}] \sim \mt{rest2}] \Rightarrow \mt{linkable} \; \mt{t1} \; \mt{t2} \to \mt{matching} \; \mt{rest1} \; \mt{rest2} \\
adamc@785 1430 \hspace{.1in} \to \mt{matching} \; ([\mt{nm1} = \mt{t1}] \rc \mt{rest1}) \; ([\mt{nm2} = \mt{t2}] \rc \mt{rest2})
adamc@785 1431 \end{array}$$
adamc@785 1432
adamc@785 1433 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 1434 $$\begin{array}{l}
adamc@785 1435 \mt{con} \; \mt{propagation\_mode} :: \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1436 \mt{val} \; \mt{restrict} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1437 \mt{val} \; \mt{cascade} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1438 \mt{val} \; \mt{no\_action} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1439 \mt{val} \; \mt{set\_null} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; (\mt{map} \; \mt{option} \; \mt{fs})
adamc@785 1440 \end{array}$$
adamc@785 1441
adamc@785 1442 Finally, we put these ingredient together to define the \texttt{FOREIGN KEY} constraint function.
adamc@785 1443 $$\begin{array}{l}
adamc@785 1444 \mt{val} \; \mt{foreign\_key} : \mt{mine1} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{mine} ::: \{\mt{Type}\} \to \mt{munused} ::: \{\mt{Type}\} \to \mt{foreign} ::: \{\mt{Type}\} \\
adamc@785 1445 \hspace{.1in} \to \mt{funused} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{uniques} ::: \{\{\mt{Unit}\}\} \\
adamc@785 1446 \hspace{.1in} \to [[\mt{mine1}] \sim \mt{mine}] \Rightarrow [[\mt{mine1} = \mt{t}] \rc \mt{mine} \sim \mt{munused}] \Rightarrow [\mt{foreign} \sim \mt{funused}] \Rightarrow [[\mt{nm}] \sim \mt{uniques}] \\
adamc@785 1447 \hspace{.1in} \Rightarrow \mt{matching} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}) \; \mt{foreign} \\
adamc@785 1448 \hspace{.1in} \to \mt{sql\_table} \; (\mt{foreign} \rc \mt{funused}) \; ([\mt{nm} = \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{foreign}] \rc \mt{uniques}) \\
adamc@785 1449 \hspace{.1in} \to \{\mt{OnDelete} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}), \\
adamc@785 1450 \hspace{.2in} \mt{OnUpdate} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine})\} \\
adamc@785 1451 \hspace{.1in} \to \mt{sql\_constraint} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine} \rc \mt{munused}) \; []
adamc@785 1452 \end{array}$$
adamc@785 1453
adamc@785 1454 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 1455 $$\begin{array}{l}
adamc@785 1456 \mt{val} \; \mt{check} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; [] \; [] \; \mt{fs} \; \mt{bool} \to \mt{sql\_constraint} \; \mt{fs} \; []
adamc@785 1457 \end{array}$$
adamc@785 1458
adamc@785 1459 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 1460
adamc@784 1461
adamc@543 1462 \subsubsection{Queries}
adamc@543 1463
adamc@543 1464 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 1465 $$\begin{array}{l}
adamc@543 1466 \mt{con} \; \mt{sql\_query} :: \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@543 1467 \mt{val} \; \mt{sql\_query} : \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543 1468 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1469 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@543 1470 \hspace{.1in} \to \{\mt{Rows} : \mt{sql\_query1} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}, \\
adamc@543 1471 \hspace{.2in} \mt{OrderBy} : \mt{sql\_order\_by} \; \mt{tables} \; \mt{selectedExps}, \\
adamc@543 1472 \hspace{.2in} \mt{Limit} : \mt{sql\_limit}, \\
adamc@543 1473 \hspace{.2in} \mt{Offset} : \mt{sql\_offset}\} \\
adamc@543 1474 \hspace{.1in} \to \mt{sql\_query} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1475 \end{array}$$
adamc@543 1476
adamc@545 1477 Queries are used by folding over their results inside transactions.
adamc@545 1478 $$\begin{array}{l}
adamc@545 1479 \mt{val} \; \mt{query} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \lambda [\mt{tables} \sim \mt{exps}] \Rightarrow \mt{state} ::: \mt{Type} \to \mt{sql\_query} \; \mt{tables} \; \mt{exps} \\
adamc@658 1480 \hspace{.1in} \to (\$(\mt{exps} \rc \mt{map} \; (\lambda \mt{fields} :: \{\mt{Type}\} \Rightarrow \$\mt{fields}) \; \mt{tables}) \\
adamc@545 1481 \hspace{.2in} \to \mt{state} \to \mt{transaction} \; \mt{state}) \\
adamc@545 1482 \hspace{.1in} \to \mt{state} \to \mt{transaction} \; \mt{state}
adamc@545 1483 \end{array}$$
adamc@545 1484
adamc@543 1485 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 1486 $$\begin{array}{l}
adamc@543 1487 \mt{con} \; \mt{sql\_query1} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@543 1488 \\
adamc@543 1489 \mt{type} \; \mt{sql\_relop} \\
adamc@543 1490 \mt{val} \; \mt{sql\_union} : \mt{sql\_relop} \\
adamc@543 1491 \mt{val} \; \mt{sql\_intersect} : \mt{sql\_relop} \\
adamc@543 1492 \mt{val} \; \mt{sql\_except} : \mt{sql\_relop} \\
adamc@543 1493 \mt{val} \; \mt{sql\_relop} : \mt{tables1} ::: \{\{\mt{Type}\}\} \\
adamc@543 1494 \hspace{.1in} \to \mt{tables2} ::: \{\{\mt{Type}\}\} \\
adamc@543 1495 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1496 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@543 1497 \hspace{.1in} \to \mt{sql\_relop} \\
adamc@543 1498 \hspace{.1in} \to \mt{sql\_query1} \; \mt{tables1} \; \mt{selectedFields} \; \mt{selectedExps} \\
adamc@543 1499 \hspace{.1in} \to \mt{sql\_query1} \; \mt{tables2} \; \mt{selectedFields} \; \mt{selectedExps} \\
adamc@543 1500 \hspace{.1in} \to \mt{sql\_query1} \; \mt{selectedFields} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1501 \end{array}$$
adamc@543 1502
adamc@543 1503 $$\begin{array}{l}
adamc@543 1504 \mt{val} \; \mt{sql\_query1} : \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543 1505 \hspace{.1in} \to \mt{grouped} ::: \{\{\mt{Type}\}\} \\
adamc@543 1506 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1507 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1085 1508 \hspace{.1in} \to \mt{empties} :: \{\mt{Unit}\} \\
adamc@1085 1509 \hspace{.1in} \to [\mt{empties} \sim \mt{selectedFields}] \\
adamc@1085 1510 \hspace{.1in} \Rightarrow \{\mt{Distinct} : \mt{bool}, \\
adamc@994 1511 \hspace{.2in} \mt{From} : \mt{sql\_from\_items} \; \mt{tables}, \\
adamc@543 1512 \hspace{.2in} \mt{Where} : \mt{sql\_exp} \; \mt{tables} \; [] \; [] \; \mt{bool}, \\
adamc@543 1513 \hspace{.2in} \mt{GroupBy} : \mt{sql\_subset} \; \mt{tables} \; \mt{grouped}, \\
adamc@543 1514 \hspace{.2in} \mt{Having} : \mt{sql\_exp} \; \mt{grouped} \; \mt{tables} \; [] \; \mt{bool}, \\
adamc@1085 1515 \hspace{.2in} \mt{SelectFields} : \mt{sql\_subset} \; \mt{grouped} \; (\mt{map} \; (\lambda \_ \Rightarrow []) \; \mt{empties} \rc \mt{selectedFields}), \\
adamc@658 1516 \hspace{.2in} \mt {SelectExps} : \$(\mt{map} \; (\mt{sql\_exp} \; \mt{grouped} \; \mt{tables} \; []) \; \mt{selectedExps}) \} \\
adamc@543 1517 \hspace{.1in} \to \mt{sql\_query1} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1518 \end{array}$$
adamc@543 1519
adamc@543 1520 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 1521 $$\begin{array}{l}
adamc@543 1522 \mt{con} \; \mt{sql\_subset} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@543 1523 \mt{val} \; \mt{sql\_subset} : \mt{keep\_drop} :: \{(\{\mt{Type}\} \times \{\mt{Type}\})\} \\
adamc@543 1524 \hspace{.1in} \to \mt{sql\_subset} \\
adamc@658 1525 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1 \rc \mt{fields}.2)\; \mt{keep\_drop}) \\
adamc@658 1526 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1) \; \mt{keep\_drop}) \\
adamc@543 1527 \mt{val} \; \mt{sql\_subset\_all} : \mt{tables} :: \{\{\mt{Type}\}\} \to \mt{sql\_subset} \; \mt{tables} \; \mt{tables}
adamc@543 1528 \end{array}$$
adamc@543 1529
adamc@560 1530 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 1531 $$\begin{array}{l}
adamc@543 1532 \mt{con} \; \mt{sql\_exp} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}
adamc@543 1533 \end{array}$$
adamc@543 1534
adamc@543 1535 Any field in scope may be converted to an expression.
adamc@543 1536 $$\begin{array}{l}
adamc@543 1537 \mt{val} \; \mt{sql\_field} : \mt{otherTabs} ::: \{\{\mt{Type}\}\} \to \mt{otherFields} ::: \{\mt{Type}\} \\
adamc@543 1538 \hspace{.1in} \to \mt{fieldType} ::: \mt{Type} \to \mt{agg} ::: \{\{\mt{Type}\}\} \\
adamc@543 1539 \hspace{.1in} \to \mt{exps} ::: \{\mt{Type}\} \\
adamc@543 1540 \hspace{.1in} \to \mt{tab} :: \mt{Name} \to \mt{field} :: \mt{Name} \\
adamc@543 1541 \hspace{.1in} \to \mt{sql\_exp} \; ([\mt{tab} = [\mt{field} = \mt{fieldType}] \rc \mt{otherFields}] \rc \mt{otherTabs}) \; \mt{agg} \; \mt{exps} \; \mt{fieldType}
adamc@543 1542 \end{array}$$
adamc@543 1543
adamc@544 1544 There is an analogous function for referencing named expressions.
adamc@544 1545 $$\begin{array}{l}
adamc@544 1546 \mt{val} \; \mt{sql\_exp} : \mt{tabs} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{t} ::: \mt{Type} \to \mt{rest} ::: \{\mt{Type}\} \to \mt{nm} :: \mt{Name} \\
adamc@544 1547 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tabs} \; \mt{agg} \; ([\mt{nm} = \mt{t}] \rc \mt{rest}) \; \mt{t}
adamc@544 1548 \end{array}$$
adamc@544 1549
adamc@544 1550 Ur values of appropriate types may be injected into SQL expressions.
adamc@544 1551 $$\begin{array}{l}
adamc@786 1552 \mt{class} \; \mt{sql\_injectable\_prim} \\
adamc@786 1553 \mt{val} \; \mt{sql\_bool} : \mt{sql\_injectable\_prim} \; \mt{bool} \\
adamc@786 1554 \mt{val} \; \mt{sql\_int} : \mt{sql\_injectable\_prim} \; \mt{int} \\
adamc@786 1555 \mt{val} \; \mt{sql\_float} : \mt{sql\_injectable\_prim} \; \mt{float} \\
adamc@786 1556 \mt{val} \; \mt{sql\_string} : \mt{sql\_injectable\_prim} \; \mt{string} \\
adamc@786 1557 \mt{val} \; \mt{sql\_time} : \mt{sql\_injectable\_prim} \; \mt{time} \\
adamc@786 1558 \mt{val} \; \mt{sql\_blob} : \mt{sql\_injectable\_prim} \; \mt{blob} \\
adamc@786 1559 \mt{val} \; \mt{sql\_channel} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{channel} \; \mt{t}) \\
adamc@786 1560 \mt{val} \; \mt{sql\_client} : \mt{sql\_injectable\_prim} \; \mt{client} \\
adamc@786 1561 \\
adamc@544 1562 \mt{class} \; \mt{sql\_injectable} \\
adamc@786 1563 \mt{val} \; \mt{sql\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@786 1564 \mt{val} \; \mt{sql\_option\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; (\mt{option} \; \mt{t}) \\
adamc@786 1565 \\
adamc@544 1566 \mt{val} \; \mt{sql\_inject} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@544 1567 \hspace{.1in} \to \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adamc@544 1568 \end{array}$$
adamc@544 1569
adamc@1123 1570 Additionally, most function-free types may be injected safely, via the $\mt{serialized}$ type family.
adamc@1123 1571 $$\begin{array}{l}
adamc@1123 1572 \mt{con} \; \mt{serialized} :: \mt{Type} \to \mt{Type} \\
adamc@1123 1573 \mt{val} \; \mt{serialize} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{serialized} \; \mt{t} \\
adamc@1123 1574 \mt{val} \; \mt{deserialize} : \mt{t} ::: \mt{Type} \to \mt{serialized} \; \mt{t} \to \mt{t} \\
adamc@1123 1575 \mt{val} \; \mt{sql\_serialized} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{serialized} \; \mt{t})
adamc@1123 1576 \end{array}$$
adamc@1123 1577
adamc@544 1578 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 1579 $$\begin{array}{l}
adamc@544 1580 \mt{val} \; \mt{sql\_is\_null} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544 1581 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; (\mt{option} \; \mt{t}) \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{bool}
adamc@544 1582 \end{array}$$
adamc@544 1583
adamc@559 1584 We have generic nullary, unary, and binary operators.
adamc@544 1585 $$\begin{array}{l}
adamc@544 1586 \mt{con} \; \mt{sql\_nfunc} :: \mt{Type} \to \mt{Type} \\
adamc@544 1587 \mt{val} \; \mt{sql\_current\_timestamp} : \mt{sql\_nfunc} \; \mt{time} \\
adamc@544 1588 \mt{val} \; \mt{sql\_nfunc} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544 1589 \hspace{.1in} \to \mt{sql\_nfunc} \; \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\\end{array}$$
adamc@544 1590
adamc@544 1591 $$\begin{array}{l}
adamc@544 1592 \mt{con} \; \mt{sql\_unary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544 1593 \mt{val} \; \mt{sql\_not} : \mt{sql\_unary} \; \mt{bool} \; \mt{bool} \\
adamc@544 1594 \mt{val} \; \mt{sql\_unary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adamc@544 1595 \hspace{.1in} \to \mt{sql\_unary} \; \mt{arg} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res} \\
adamc@544 1596 \end{array}$$
adamc@544 1597
adamc@544 1598 $$\begin{array}{l}
adamc@544 1599 \mt{con} \; \mt{sql\_binary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544 1600 \mt{val} \; \mt{sql\_and} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544 1601 \mt{val} \; \mt{sql\_or} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544 1602 \mt{val} \; \mt{sql\_binary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg_1} ::: \mt{Type} \to \mt{arg_2} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adamc@544 1603 \hspace{.1in} \to \mt{sql\_binary} \; \mt{arg_1} \; \mt{arg_2} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_1} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_2} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res}
adamc@544 1604 \end{array}$$
adamc@544 1605
adamc@544 1606 $$\begin{array}{l}
adamc@559 1607 \mt{class} \; \mt{sql\_arith} \\
adamc@559 1608 \mt{val} \; \mt{sql\_int\_arith} : \mt{sql\_arith} \; \mt{int} \\
adamc@559 1609 \mt{val} \; \mt{sql\_float\_arith} : \mt{sql\_arith} \; \mt{float} \\
adamc@559 1610 \mt{val} \; \mt{sql\_neg} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_unary} \; \mt{t} \; \mt{t} \\
adamc@559 1611 \mt{val} \; \mt{sql\_plus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1612 \mt{val} \; \mt{sql\_minus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1613 \mt{val} \; \mt{sql\_times} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1614 \mt{val} \; \mt{sql\_div} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1615 \mt{val} \; \mt{sql\_mod} : \mt{sql\_binary} \; \mt{int} \; \mt{int} \; \mt{int}
adamc@559 1616 \end{array}$$
adamc@544 1617
adamc@656 1618 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 1619 $$\begin{array}{l}
adamc@544 1620 \mt{val} \; \mt{sql\_count} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int}
adamc@544 1621 \end{array}$$
adamc@544 1622
adamc@544 1623 $$\begin{array}{l}
adamc@544 1624 \mt{con} \; \mt{sql\_aggregate} :: \mt{Type} \to \mt{Type} \\
adamc@544 1625 \mt{val} \; \mt{sql\_aggregate} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544 1626 \hspace{.1in} \to \mt{sql\_aggregate} \; \mt{t} \to \mt{sql\_exp} \; \mt{agg} \; \mt{agg} \; \mt{exps} \; \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adamc@544 1627 \end{array}$$
adamc@544 1628
adamc@544 1629 $$\begin{array}{l}
adamc@544 1630 \mt{class} \; \mt{sql\_summable} \\
adamc@544 1631 \mt{val} \; \mt{sql\_summable\_int} : \mt{sql\_summable} \; \mt{int} \\
adamc@544 1632 \mt{val} \; \mt{sql\_summable\_float} : \mt{sql\_summable} \; \mt{float} \\
adamc@544 1633 \mt{val} \; \mt{sql\_avg} : \mt{t} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{sql\_aggregate} \; \mt{t} \\
adamc@544 1634 \mt{val} \; \mt{sql\_sum} : \mt{t} ::: \mt{Type} \to \mt{sql\_summable} \mt{t} \to \mt{sql\_aggregate} \; \mt{t}
adamc@544 1635 \end{array}$$
adamc@544 1636
adamc@544 1637 $$\begin{array}{l}
adamc@544 1638 \mt{class} \; \mt{sql\_maxable} \\
adamc@544 1639 \mt{val} \; \mt{sql\_maxable\_int} : \mt{sql\_maxable} \; \mt{int} \\
adamc@544 1640 \mt{val} \; \mt{sql\_maxable\_float} : \mt{sql\_maxable} \; \mt{float} \\
adamc@544 1641 \mt{val} \; \mt{sql\_maxable\_string} : \mt{sql\_maxable} \; \mt{string} \\
adamc@544 1642 \mt{val} \; \mt{sql\_maxable\_time} : \mt{sql\_maxable} \; \mt{time} \\
adamc@544 1643 \mt{val} \; \mt{sql\_max} : \mt{t} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{sql\_aggregate} \; \mt{t} \\
adamc@544 1644 \mt{val} \; \mt{sql\_min} : \mt{t} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{sql\_aggregate} \; \mt{t}
adamc@544 1645 \end{array}$$
adamc@544 1646
adamc@786 1647 \texttt{FROM} clauses are specified using a type family.
adamc@786 1648 $$\begin{array}{l}
adamc@786 1649 \mt{con} \; \mt{sql\_from\_items} :: \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@786 1650 \mt{val} \; \mt{sql\_from\_table} : \mt{t} ::: \mt{Type} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; \mt{t} \; \mt{fs} \to \mt{name} :: \mt{Name} \to \mt{t} \to \mt{sql\_from\_items} \; [\mt{name} = \mt{fs}] \\
adamc@786 1651 \mt{val} \; \mt{sql\_from\_comma} : \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \to [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@786 1652 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{tabs2} \\
adamc@786 1653 \hspace{.1in} \to \mt{sql\_from\_items} \; (\mt{tabs1} \rc \mt{tabs2}) \\
adamc@786 1654 \mt{val} \; \mt{sql\_inner\_join} : \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \to [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@786 1655 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{tabs2} \\
adamc@786 1656 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{tabs1} \rc \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@786 1657 \hspace{.1in} \to \mt{sql\_from\_items} \; (\mt{tabs1} \rc \mt{tabs2})
adamc@786 1658 \end{array}$$
adamc@786 1659
adamc@786 1660 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 1661 $$\begin{array}{l}
adamc@786 1662 \mt{class} \; \mt{nullify} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@786 1663 \mt{val} \; \mt{nullify\_option} : \mt{t} ::: \mt{Type} \to \mt{nullify} \; (\mt{option} \; \mt{t}) \; (\mt{option} \; \mt{t}) \\
adamc@786 1664 \mt{val} \; \mt{nullify\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{nullify} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@786 1665 \end{array}$$
adamc@786 1666
adamc@786 1667 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 1668
adamc@786 1669 $$\begin{array}{l}
adamc@786 1670 \mt{val} \; \mt{sql\_left\_join} : \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{(\mt{Type} \times \mt{Type})\}\} \to [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@786 1671 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\lambda \mt{r} \Rightarrow \$(\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{nullify} \; \mt{p}.1 \; \mt{p}.2) \; \mt{r})) \; \mt{tabs2}) \\
adamc@786 1672 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{tabs1} \to \mt{sql\_from\_items} \; (\mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \\
adamc@786 1673 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@786 1674 \hspace{.1in} \to \mt{sql\_from\_items} \; (\mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.2)) \; \mt{tabs2})
adamc@786 1675 \end{array}$$
adamc@786 1676
adamc@544 1677 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 1678 $$\begin{array}{l}
adamc@544 1679 \mt{type} \; \mt{sql\_direction} \\
adamc@544 1680 \mt{val} \; \mt{sql\_asc} : \mt{sql\_direction} \\
adamc@544 1681 \mt{val} \; \mt{sql\_desc} : \mt{sql\_direction} \\
adamc@544 1682 \\
adamc@544 1683 \mt{con} \; \mt{sql\_order\_by} :: \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@544 1684 \mt{val} \; \mt{sql\_order\_by\_Nil} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} :: \{\mt{Type}\} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544 1685 \mt{val} \; \mt{sql\_order\_by\_Cons} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544 1686 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; [] \; \mt{exps} \; \mt{t} \to \mt{sql\_direction} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544 1687 \\
adamc@544 1688 \mt{type} \; \mt{sql\_limit} \\
adamc@544 1689 \mt{val} \; \mt{sql\_no\_limit} : \mt{sql\_limit} \\
adamc@544 1690 \mt{val} \; \mt{sql\_limit} : \mt{int} \to \mt{sql\_limit} \\
adamc@544 1691 \\
adamc@544 1692 \mt{type} \; \mt{sql\_offset} \\
adamc@544 1693 \mt{val} \; \mt{sql\_no\_offset} : \mt{sql\_offset} \\
adamc@544 1694 \mt{val} \; \mt{sql\_offset} : \mt{int} \to \mt{sql\_offset}
adamc@544 1695 \end{array}$$
adamc@544 1696
adamc@545 1697
adamc@545 1698 \subsubsection{DML}
adamc@545 1699
adamc@545 1700 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 1701
adamc@545 1702 $$\begin{array}{l}
adamc@545 1703 \mt{type} \; \mt{dml} \\
adamc@545 1704 \mt{val} \; \mt{dml} : \mt{dml} \to \mt{transaction} \; \mt{unit}
adamc@545 1705 \end{array}$$
adamc@545 1706
adamc@545 1707 Properly-typed records may be used to form $\mt{INSERT}$ commands.
adamc@545 1708 $$\begin{array}{l}
adamc@545 1709 \mt{val} \; \mt{insert} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \\
adamc@658 1710 \hspace{.1in} \to \$(\mt{map} \; (\mt{sql\_exp} \; [] \; [] \; []) \; \mt{fields}) \to \mt{dml}
adamc@545 1711 \end{array}$$
adamc@545 1712
adamc@545 1713 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 1714 $$\begin{array}{l}
adamc@545 1715 \mt{val} \; \mt{update} : \mt{unchanged} ::: \{\mt{Type}\} \to \mt{changed} :: \{\mt{Type}\} \to \lambda [\mt{changed} \sim \mt{unchanged}] \\
adamc@658 1716 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; []) \; \mt{changed}) \\
adamc@545 1717 \hspace{.1in} \to \mt{sql\_table} \; (\mt{changed} \rc \mt{unchanged}) \to \mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545 1718 \end{array}$$
adamc@545 1719
adamc@545 1720 A $\mt{DELETE}$ command is formed from a table and a $\mt{WHERE}$ clause.
adamc@545 1721 $$\begin{array}{l}
adamc@545 1722 \mt{val} \; \mt{delete} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \to \mt{sql\_exp} \; [\mt{T} = \mt{fields}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545 1723 \end{array}$$
adamc@545 1724
adamc@546 1725 \subsubsection{Sequences}
adamc@546 1726
adamc@546 1727 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 1728
adamc@546 1729 $$\begin{array}{l}
adamc@546 1730 \mt{type} \; \mt{sql\_sequence} \\
adamc@1085 1731 \mt{val} \; \mt{nextval} : \mt{sql\_sequence} \to \mt{transaction} \; \mt{int} \\
adamc@1085 1732 \mt{val} \; \mt{setval} : \mt{sql\_sequence} \to \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@546 1733 \end{array}$$
adamc@546 1734
adamc@546 1735
adamc@547 1736 \subsection{XML}
adamc@547 1737
adamc@547 1738 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 1739
adamc@547 1740 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 1741 $$\begin{array}{l}
adamc@547 1742 \mt{con} \; \mt{xml} :: \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547 1743 \end{array}$$
adamc@547 1744
adamc@547 1745 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 1746 $$\begin{array}{l}
adamc@547 1747 \mt{con} \; \mt{tag} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547 1748 \end{array}$$
adamc@547 1749
adamc@547 1750 Literal text may be injected into XML as ``CDATA.''
adamc@547 1751 $$\begin{array}{l}
adamc@547 1752 \mt{val} \; \mt{cdata} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{string} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adamc@547 1753 \end{array}$$
adamc@547 1754
adamc@547 1755 There is a function for producing an XML tree with a particular tag at its root.
adamc@547 1756 $$\begin{array}{l}
adamc@547 1757 \mt{val} \; \mt{tag} : \mt{attrsGiven} ::: \{\mt{Type}\} \to \mt{attrsAbsent} ::: \{\mt{Type}\} \to \mt{ctxOuter} ::: \{\mt{Unit}\} \to \mt{ctxInner} ::: \{\mt{Unit}\} \\
adamc@547 1758 \hspace{.1in} \to \mt{useOuter} ::: \{\mt{Type}\} \to \mt{useInner} ::: \{\mt{Type}\} \to \mt{bindOuter} ::: \{\mt{Type}\} \to \mt{bindInner} ::: \{\mt{Type}\} \\
adamc@787 1759 \hspace{.1in} \to \lambda [\mt{attrsGiven} \sim \mt{attrsAbsent}] \; [\mt{useOuter} \sim \mt{useInner}] \; [\mt{bindOuter} \sim \mt{bindInner}] \\
adamc@787 1760 \hspace{.1in} \Rightarrow \mt{option} \; \mt{css\_class} \\
adamc@787 1761 \hspace{.1in} \to \$\mt{attrsGiven} \\
adamc@547 1762 \hspace{.1in} \to \mt{tag} \; (\mt{attrsGiven} \rc \mt{attrsAbsent}) \; \mt{ctxOuter} \; \mt{ctxInner} \; \mt{useOuter} \; \mt{bindOuter} \\
adamc@547 1763 \hspace{.1in} \to \mt{xml} \; \mt{ctxInner} \; \mt{useInner} \; \mt{bindInner} \to \mt{xml} \; \mt{ctxOuter} \; (\mt{useOuter} \rc \mt{useInner}) \; (\mt{bindOuter} \rc \mt{bindInner})
adamc@547 1764 \end{array}$$
adamc@787 1765 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 1766
adamc@547 1767 Two XML fragments may be concatenated.
adamc@547 1768 $$\begin{array}{l}
adamc@547 1769 \mt{val} \; \mt{join} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{bind_1} ::: \{\mt{Type}\} \to \mt{bind_2} ::: \{\mt{Type}\} \\
adamc@547 1770 \hspace{.1in} \to \lambda [\mt{use_1} \sim \mt{bind_1}] \; [\mt{bind_1} \sim \mt{bind_2}] \\
adamc@547 1771 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind_1} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{bind_1}) \; \mt{bind_2} \to \mt{xml} \; \mt{ctx} \; \mt{use_1} \; (\mt{bind_1} \rc \mt{bind_2})
adamc@547 1772 \end{array}$$
adamc@547 1773
adamc@547 1774 Finally, any XML fragment may be updated to ``claim'' to use more form fields than it does.
adamc@547 1775 $$\begin{array}{l}
adamc@547 1776 \mt{val} \; \mt{useMore} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{use_2} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to \lambda [\mt{use_1} \sim \mt{use_2}] \\
adamc@547 1777 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{use_2}) \; \mt{bind}
adamc@547 1778 \end{array}$$
adamc@547 1779
adamc@547 1780 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 1781
adamc@547 1782 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 1783 $$\begin{array}{l}
adamc@547 1784 \mt{val} \; \mt{error} : \mt{t} ::: \mt{Type} \to \mt{xml} \; [\mt{Body}] \; [] \; [] \to \mt{t}
adamc@547 1785 \end{array}$$
adamc@547 1786
adamc@549 1787
adamc@701 1788 \subsection{Client-Side Programming}
adamc@659 1789
adamc@701 1790 Ur/Web supports running code on web browsers, via automatic compilation to JavaScript.
adamc@701 1791
adamc@701 1792 \subsubsection{The Basics}
adamc@701 1793
adamc@701 1794 Clients can open alert dialog boxes, in the usual annoying JavaScript way.
adamc@701 1795 $$\begin{array}{l}
adamc@701 1796 \mt{val} \; \mt{alert} : \mt{string} \to \mt{transaction} \; \mt{unit}
adamc@701 1797 \end{array}$$
adamc@701 1798
adamc@701 1799 Any transaction may be run in a new thread with the $\mt{spawn}$ function.
adamc@701 1800 $$\begin{array}{l}
adamc@701 1801 \mt{val} \; \mt{spawn} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit}
adamc@701 1802 \end{array}$$
adamc@701 1803
adamc@701 1804 The current thread can be paused for at least a specified number of milliseconds.
adamc@701 1805 $$\begin{array}{l}
adamc@701 1806 \mt{val} \; \mt{sleep} : \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@701 1807 \end{array}$$
adamc@701 1808
adamc@787 1809 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 1810 $$\begin{array}{l}
adamc@787 1811 \mt{val} \; \mt{onError} : (\mt{xbody} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787 1812 \mt{val} \; \mt{onFail} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787 1813 \mt{val} \; \mt{onConnectFail} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787 1814 \mt{val} \; \mt{onDisconnect} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787 1815 \mt{val} \; \mt{onServerError} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit}
adamc@787 1816 \end{array}$$
adamc@787 1817
adamc@701 1818 \subsubsection{Functional-Reactive Page Generation}
adamc@701 1819
adamc@701 1820 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 1821
adamc@659 1822 $$\begin{array}{l}
adamc@659 1823 \mt{con} \; \mt{source} :: \mt{Type} \to \mt{Type} \\
adamc@659 1824 \mt{val} \; \mt{source} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{transaction} \; (\mt{source} \; \mt{t}) \\
adamc@659 1825 \mt{val} \; \mt{set} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@659 1826 \mt{val} \; \mt{get} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@659 1827 \end{array}$$
adamc@659 1828
adamc@659 1829 Pure functions over sources are represented in a monad of \emph{signals}.
adamc@659 1830
adamc@659 1831 $$\begin{array}{l}
adamc@659 1832 \mt{con} \; \mt{signal} :: \mt{Type} \to \mt{Type} \\
adamc@659 1833 \mt{val} \; \mt{signal\_monad} : \mt{monad} \; \mt{signal} \\
adamc@659 1834 \mt{val} \; \mt{signal} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{signal} \; \mt{t}
adamc@659 1835 \end{array}$$
adamc@659 1836
adamc@659 1837 A reactive portion of an HTML page is injected with a $\mt{dyn}$ tag, which has a signal-valued attribute $\mt{Signal}$.
adamc@659 1838
adamc@659 1839 $$\begin{array}{l}
adamc@701 1840 \mt{val} \; \mt{dyn} : \mt{use} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to \mt{unit} \\
adamc@701 1841 \hspace{.1in} \to \mt{tag} \; [\mt{Signal} = \mt{signal} \; (\mt{xml} \; \mt{body} \; \mt{use} \; \mt{bind})] \; \mt{body} \; [] \; \mt{use} \; \mt{bind}
adamc@659 1842 \end{array}$$
adamc@659 1843
adamc@701 1844 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 1845
adamc@914 1846 \subsubsection{Remote Procedure Calls}
adamc@914 1847
adamc@914 1848 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 1849
adamc@914 1850 $$\begin{array}{l}
adamc@914 1851 \mt{val} \; \mt{rpc} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@914 1852 \end{array}$$
adamc@914 1853
adamc@701 1854 \subsubsection{Asynchronous Message-Passing}
adamc@701 1855
adamc@701 1856 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 1857
adamc@701 1858 $$\begin{array}{l}
adamc@701 1859 \mt{type} \; \mt{client} \\
adamc@701 1860 \mt{val} \; \mt{self} : \mt{transaction} \; \mt{client}
adamc@701 1861 \end{array}$$
adamc@701 1862
adamc@701 1863 \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 1864
adamc@701 1865 $$\begin{array}{l}
adamc@701 1866 \mt{con} \; \mt{channel} :: \mt{Type} \to \mt{Type} \\
adamc@701 1867 \mt{val} \; \mt{channel} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; (\mt{channel} \; \mt{t}) \\
adamc@701 1868 \mt{val} \; \mt{send} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@701 1869 \mt{val} \; \mt{recv} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@701 1870 \end{array}$$
adamc@701 1871
adamc@701 1872 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 1873
adamc@701 1874 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 1875
adamc@659 1876
adamc@549 1877 \section{Ur/Web Syntax Extensions}
adamc@549 1878
adamc@549 1879 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 1880
adamc@549 1881 \subsection{SQL}
adamc@549 1882
adamc@786 1883 \subsubsection{\label{tables}Table Declarations}
adamc@786 1884
adamc@788 1885 $\mt{table}$ declarations may include constraints, via these grammar rules.
adamc@788 1886 $$\begin{array}{rrcll}
adamc@788 1887 \textrm{Declarations} & d &::=& \mt{table} \; x : c \; [pk[,]] \; cts \\
adamc@788 1888 \textrm{Primary key constraints} & pk &::=& \mt{PRIMARY} \; \mt{KEY} \; K \\
adamc@788 1889 \textrm{Keys} & K &::=& f \mid (f, (f,)^+) \\
adamc@788 1890 \textrm{Constraint sets} & cts &::=& \mt{CONSTRAINT} f \; ct \mid cts, cts \mid \{\{e\}\} \\
adamc@788 1891 \textrm{Constraints} & ct &::=& \mt{UNIQUE} \; K \mid \mt{CHECK} \; E \\
adamc@788 1892 &&& \mid \mt{FOREIGN} \; \mt{KEY} \; K \; \mt{REFERENCES} \; F \; (K) \; [\mt{ON} \; \mt{DELETE} \; pr] \; [\mt{ON} \; \mt{UPDATE} \; pr] \\
adamc@788 1893 \textrm{Foreign tables} & F &::=& x \mid \{\{e\}\} \\
adamc@788 1894 \textrm{Propagation modes} & pr &::=& \mt{NO} \; \mt{ACTION} \mid \mt{RESTRICT} \mid \mt{CASCADE} \mid \mt{SET} \; \mt{NULL}
adamc@788 1895 \end{array}$$
adamc@788 1896
adamc@788 1897 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 1898
adamc@788 1899
adamc@549 1900 \subsubsection{Queries}
adamc@549 1901
adamc@550 1902 Queries $Q$ are added to the rules for expressions $e$.
adamc@550 1903
adamc@549 1904 $$\begin{array}{rrcll}
adamc@550 1905 \textrm{Queries} & Q &::=& (q \; [\mt{ORDER} \; \mt{BY} \; (E \; [o],)^+] \; [\mt{LIMIT} \; N] \; [\mt{OFFSET} \; N]) \\
adamc@1085 1906 \textrm{Pre-queries} & q &::=& \mt{SELECT} \; [\mt{DISTINCT}] \; P \; \mt{FROM} \; F,^+ \; [\mt{WHERE} \; E] \; [\mt{GROUP} \; \mt{BY} \; p,^+] \; [\mt{HAVING} \; E] \\
adamc@1085 1907 &&& \mid q \; R \; q \mid \{\{\{e\}\}\} \\
adamc@549 1908 \textrm{Relational operators} & R &::=& \mt{UNION} \mid \mt{INTERSECT} \mid \mt{EXCEPT}
adamc@549 1909 \end{array}$$
adamc@549 1910
adamc@549 1911 $$\begin{array}{rrcll}
adamc@549 1912 \textrm{Projections} & P &::=& \ast & \textrm{all columns} \\
adamc@549 1913 &&& p,^+ & \textrm{particular columns} \\
adamc@549 1914 \textrm{Pre-projections} & p &::=& t.f & \textrm{one column from a table} \\
adamc@558 1915 &&& t.\{\{c\}\} & \textrm{a record of columns from a table (of kind $\{\mt{Type}\}$)} \\
adamc@549 1916 \textrm{Table names} & t &::=& x & \textrm{constant table name (automatically capitalized)} \\
adamc@549 1917 &&& X & \textrm{constant table name} \\
adamc@549 1918 &&& \{\{c\}\} & \textrm{computed table name (of kind $\mt{Name}$)} \\
adamc@549 1919 \textrm{Column names} & f &::=& X & \textrm{constant column name} \\
adamc@549 1920 &&& \{c\} & \textrm{computed column name (of kind $\mt{Name}$)} \\
adamc@549 1921 \textrm{Tables} & T &::=& x & \textrm{table variable, named locally by its own capitalization} \\
adamc@549 1922 &&& x \; \mt{AS} \; t & \textrm{table variable, with local name} \\
adamc@549 1923 &&& \{\{e\}\} \; \mt{AS} \; t & \textrm{computed table expression, with local name} \\
adamc@1085 1924 \textrm{$\mt{FROM}$ items} & F &::=& T \mid \{\{e\}\} \mid F \; J \; \mt{JOIN} \; F \; \mt{ON} \; E \\
adamc@1085 1925 &&& \mid F \; \mt{CROSS} \; \mt{JOIN} \ F \\
adamc@1085 1926 \textrm{Joins} & J &::=& [\mt{INNER}] \\
adamc@1085 1927 &&& \mid [\mt{LEFT} \mid \mt{RIGHT} \mid \mt{FULL}] \; [\mt{OUTER}] \\
adamc@549 1928 \textrm{SQL expressions} & E &::=& p & \textrm{column references} \\
adamc@549 1929 &&& X & \textrm{named expression references} \\
adamc@549 1930 &&& \{\{e\}\} & \textrm{injected native Ur expressions} \\
adamc@549 1931 &&& \{e\} & \textrm{computed expressions, probably using $\mt{sql\_exp}$ directly} \\
adamc@549 1932 &&& \mt{TRUE} \mid \mt{FALSE} & \textrm{boolean constants} \\
adamc@549 1933 &&& \ell & \textrm{primitive type literals} \\
adamc@549 1934 &&& \mt{NULL} & \textrm{null value (injection of $\mt{None}$)} \\
adamc@549 1935 &&& E \; \mt{IS} \; \mt{NULL} & \textrm{nullness test} \\
adamc@549 1936 &&& n & \textrm{nullary operators} \\
adamc@549 1937 &&& u \; E & \textrm{unary operators} \\
adamc@549 1938 &&& E \; b \; E & \textrm{binary operators} \\
adamc@549 1939 &&& \mt{COUNT}(\ast) & \textrm{count number of rows} \\
adamc@549 1940 &&& a(E) & \textrm{other aggregate function} \\
adamc@549 1941 &&& (E) & \textrm{explicit precedence} \\
adamc@549 1942 \textrm{Nullary operators} & n &::=& \mt{CURRENT\_TIMESTAMP} \\
adamc@549 1943 \textrm{Unary operators} & u &::=& \mt{NOT} \\
adamc@549 1944 \textrm{Binary operators} & b &::=& \mt{AND} \mid \mt{OR} \mid \neq \mid < \mid \leq \mid > \mid \geq \\
adamc@549 1945 \textrm{Aggregate functions} & a &::=& \mt{AVG} \mid \mt{SUM} \mid \mt{MIN} \mid \mt{MAX} \\
adamc@550 1946 \textrm{Directions} & o &::=& \mt{ASC} \mid \mt{DESC} \\
adamc@549 1947 \textrm{SQL integer} & N &::=& n \mid \{e\} \\
adamc@549 1948 \end{array}$$
adamc@549 1949
adamc@1085 1950 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 1951
adamc@550 1952 \subsubsection{DML}
adamc@550 1953
adamc@550 1954 DML commands $D$ are added to the rules for expressions $e$.
adamc@550 1955
adamc@550 1956 $$\begin{array}{rrcll}
adamc@550 1957 \textrm{Commands} & D &::=& (\mt{INSERT} \; \mt{INTO} \; T^E \; (f,^+) \; \mt{VALUES} \; (E,^+)) \\
adamc@550 1958 &&& (\mt{UPDATE} \; T^E \; \mt{SET} \; (f = E,)^+ \; \mt{WHERE} \; E) \\
adamc@550 1959 &&& (\mt{DELETE} \; \mt{FROM} \; T^E \; \mt{WHERE} \; E) \\
adamc@550 1960 \textrm{Table expressions} & T^E &::=& x \mid \{\{e\}\}
adamc@550 1961 \end{array}$$
adamc@550 1962
adamc@550 1963 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 1964
adamc@551 1965 \subsection{XML}
adamc@551 1966
adamc@551 1967 XML fragments $L$ are added to the rules for expressions $e$.
adamc@551 1968
adamc@551 1969 $$\begin{array}{rrcll}
adamc@551 1970 \textrm{XML fragments} & L &::=& \texttt{<xml/>} \mid \texttt{<xml>}l^*\texttt{</xml>} \\
adamc@551 1971 \textrm{XML pieces} & l &::=& \textrm{text} & \textrm{cdata} \\
adamc@551 1972 &&& \texttt{<}g\texttt{/>} & \textrm{tag with no children} \\
adamc@551 1973 &&& \texttt{<}g\texttt{>}l^*\texttt{</}x\texttt{>} & \textrm{tag with children} \\
adamc@559 1974 &&& \{e\} & \textrm{computed XML fragment} \\
adamc@559 1975 &&& \{[e]\} & \textrm{injection of an Ur expression, via the $\mt{Top}.\mt{txt}$ function} \\
adamc@551 1976 \textrm{Tag} & g &::=& h \; (x = v)^* \\
adamc@551 1977 \textrm{Tag head} & h &::=& x & \textrm{tag name} \\
adamc@551 1978 &&& h\{c\} & \textrm{constructor parameter} \\
adamc@551 1979 \textrm{Attribute value} & v &::=& \ell & \textrm{literal value} \\
adamc@551 1980 &&& \{e\} & \textrm{computed value} \\
adamc@551 1981 \end{array}$$
adamc@551 1982
adamc@552 1983
adamc@553 1984 \section{The Structure of Web Applications}
adamc@553 1985
adamc@1127 1986 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 1987
adamc@553 1988 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 1989
adamc@553 1990 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 1991
adamc@558 1992 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 1993
adamc@660 1994 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 1995
adamc@789 1996 \medskip
adamc@789 1997
adamc@789 1998 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 1999
adamc@789 2000 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 2001
adamc@553 2002
adamc@897 2003 \section{The Foreign Function Interface}
adamc@897 2004
adamc@897 2005 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 2006
adamc@897 2007 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 2008
adamc@897 2009 \begin{itemize}
adamc@897 2010 \item \texttt{clientOnly Module.ident} registers a value as being allowed only in client-side code.
adamc@897 2011 \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 2012 \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 2013 \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 2014 \item \texttt{include FILE} requests inclusion of a C header file.
adamc@897 2015 \item \texttt{jsFunc Module.ident=name} gives a mapping from an Ur name for a value to a JavaScript name.
adamc@897 2016 \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 2017 \item \texttt{script URL} requests inclusion of a JavaScript source file within application HTML.
adamc@897 2018 \item \texttt{serverOnly Module.ident} registers a value as being allowed only in server-side code.
adamc@897 2019 \end{itemize}
adamc@897 2020
adamc@897 2021 \subsection{Writing C FFI Code}
adamc@897 2022
adamc@897 2023 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 2024
adamc@897 2025 \begin{itemize}
adamc@897 2026 \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 2027 \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 2028 \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 2029 \end{itemize}
adamc@897 2030
adamc@897 2031 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 2032 \begin{itemize}
adamc@897 2033 \item \begin{verbatim}
adamc@897 2034 void uw_error(uw_context, failure_kind, const char *fmt, ...);
adamc@897 2035 \end{verbatim}
adamc@897 2036 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 2037
adamc@897 2038 \item \begin{verbatim}
adamc@897 2039 void uw_push_cleanup(uw_context, void (*func)(void *), void *arg);
adamc@897 2040 void uw_pop_cleanup(uw_context);
adamc@897 2041 \end{verbatim}
adamc@897 2042 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 2043
adamc@897 2044 \item \begin{verbatim}
adamc@897 2045 void *uw_malloc(uw_context, size_t);
adamc@897 2046 \end{verbatim}
adamc@897 2047 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 2048
adamc@897 2049 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 2050
adamc@897 2051 \item \begin{verbatim}
adamc@897 2052 typedef void (*uw_callback)(void *);
adamc@897 2053 void uw_register_transactional(uw_context, void *data, uw_callback commit,
adamc@897 2054 uw_callback rollback, uw_callback free);
adamc@897 2055 \end{verbatim}
adamc@897 2056 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 2057
adamc@1085 2058 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 2059
adamc@1085 2060 \item \begin{verbatim}
adamc@1085 2061 void *uw_get_global(uw_context, char *name);
adamc@1085 2062 void uw_set_global(uw_context, char *name, void *data, uw_callback free);
adamc@1085 2063 \end{verbatim}
adamc@1085 2064 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 2065
adamc@897 2066 \end{itemize}
adamc@897 2067
adamc@897 2068 \subsection{Writing JavaScript FFI Code}
adamc@897 2069
adamc@897 2070 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 2071
adamc@897 2072 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 2073
adamc@897 2074 \begin{itemize}
adamc@897 2075 \item Integers, floats, strings, characters, and booleans are represented in the usual JavaScript way.
adamc@985 2076 \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 2077 \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 2078 \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 2079 \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 2080 \end{itemize}
adamc@897 2081
adamc@897 2082 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 2083
adamc@897 2084
adamc@552 2085 \section{Compiler Phases}
adamc@552 2086
adamc@552 2087 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 2088
adamc@552 2089 In this section, we step through the main phases of compilation, noting what consequences each phase has for effective programming.
adamc@552 2090
adamc@552 2091 \subsection{Parse}
adamc@552 2092
adamc@552 2093 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 2094
adamc@552 2095 \subsection{Elaborate}
adamc@552 2096
adamc@552 2097 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 2098
adamc@552 2099 \subsection{Unnest}
adamc@552 2100
adamc@552 2101 Named local function definitions are moved to the top level, to avoid the need to generate closures.
adamc@552 2102
adamc@552 2103 \subsection{Corify}
adamc@552 2104
adamc@552 2105 Module system features are compiled away, through inlining of functor definitions at application sites. Afterward, most abstraction boundaries are broken, facilitating optimization.
adamc@552 2106
adamc@552 2107 \subsection{Especialize}
adamc@552 2108
adamc@552 2109 Functions are specialized to particular argument patterns. This is an important trick for avoiding the need to maintain any closures at runtime.
adamc@552 2110
adamc@552 2111 \subsection{Untangle}
adamc@552 2112
adamc@552 2113 Remove unnecessary mutual recursion, splitting recursive groups into strongly-connected components.
adamc@552 2114
adamc@552 2115 \subsection{Shake}
adamc@552 2116
adamc@552 2117 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 2118
adamc@661 2119 \subsection{Rpcify}
adamc@661 2120
adamc@661 2121 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 2122
adamc@661 2123 \subsection{Untangle, Shake}
adamc@661 2124
adamc@661 2125 Repeat these simplifications.
adamc@661 2126
adamc@553 2127 \subsection{\label{tag}Tag}
adamc@552 2128
adamc@552 2129 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 2130
adamc@552 2131 \subsection{Reduce}
adamc@552 2132
adamc@552 2133 Apply definitional equality rules to simplify the program as much as possible. This effectively includes inlining of every non-recursive definition.
adamc@552 2134
adamc@552 2135 \subsection{Unpoly}
adamc@552 2136
adamc@552 2137 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 2138
adamc@552 2139 \subsection{Specialize}
adamc@552 2140
adamc@558 2141 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 2142
adamc@552 2143 \subsection{Shake}
adamc@552 2144
adamc@558 2145 Here the compiler repeats the earlier Shake phase.
adamc@552 2146
adamc@552 2147 \subsection{Monoize}
adamc@552 2148
adamc@552 2149 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 2150
adamc@552 2151 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 2152
adamc@552 2153 \subsection{MonoOpt}
adamc@552 2154
adamc@552 2155 Simple algebraic laws are applied to simplify the program, focusing especially on efficient imperative generation of HTML pages.
adamc@552 2156
adamc@552 2157 \subsection{MonoUntangle}
adamc@552 2158
adamc@552 2159 Unnecessary mutual recursion is broken up again.
adamc@552 2160
adamc@552 2161 \subsection{MonoReduce}
adamc@552 2162
adamc@552 2163 Equivalents of the definitional equality rules are applied to simplify programs, with inlining again playing a major role.
adamc@552 2164
adamc@552 2165 \subsection{MonoShake, MonoOpt}
adamc@552 2166
adamc@552 2167 Unneeded declarations are removed, and basic optimizations are repeated.
adamc@552 2168
adamc@552 2169 \subsection{Fuse}
adamc@552 2170
adamc@552 2171 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 2172
adamc@552 2173 \subsection{MonoUntangle, MonoShake}
adamc@552 2174
adamc@552 2175 Fuse often creates more opportunities to remove spurious mutual recursion.
adamc@552 2176
adamc@552 2177 \subsection{Pathcheck}
adamc@552 2178
adamc@552 2179 The compiler checks that no link or action name has been used more than once.
adamc@552 2180
adamc@552 2181 \subsection{Cjrize}
adamc@552 2182
adamc@552 2183 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 2184
adamc@552 2185 \subsection{C Compilation and Linking}
adamc@552 2186
adamc@552 2187 The output of the last phase is pretty-printed as C source code and passed to GCC.
adamc@552 2188
adamc@552 2189
adamc@524 2190 \end{document}