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author Adam Chlipala <adamc@hcoop.net>
date Tue, 12 Jan 2010 11:19:02 -0500
parents 81ddb010751e
children a8921f5ef6bd
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adamc@524 1 \documentclass{article}
adamc@554 2 \usepackage{fullpage,amsmath,amssymb,proof,url}
adamc@524 3
adamc@524 4 \newcommand{\cd}[1]{\texttt{#1}}
adamc@524 5 \newcommand{\mt}[1]{\mathsf{#1}}
adamc@524 6
adamc@524 7 \newcommand{\rc}{+ \hspace{-.075in} + \;}
adamc@527 8 \newcommand{\rcut}{\; \texttt{--} \;}
adamc@527 9 \newcommand{\rcutM}{\; \texttt{---} \;}
adamc@524 10
adamc@524 11 \begin{document}
adamc@524 12
adamc@524 13 \title{The Ur/Web Manual}
adamc@524 14 \author{Adam Chlipala}
adamc@524 15
adamc@524 16 \maketitle
adamc@524 17
adamc@540 18 \tableofcontents
adamc@540 19
adamc@554 20
adamc@554 21 \section{Introduction}
adamc@554 22
adamc@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@555 94 Some OSX users have reported needing to use this particular GCCARGS value.
adamc@555 95
adamc@555 96 The Emacs mode can be set to autoload by adding the following to your \texttt{.emacs} file.
adamc@555 97
adamc@555 98 \begin{verbatim}
adamc@555 99 (add-to-list 'load-path "/usr/local/share/emacs/site-lisp/urweb-mode")
adamc@555 100 (load "urweb-mode-startup")
adamc@555 101 \end{verbatim}
adamc@555 102
adamc@555 103 Change the path in the first line if you chose a different Emacs installation path during configuration.
adamc@555 104
adamc@555 105
adamc@556 106 \section{Command-Line Compiler}
adamc@556 107
adamc@556 108 \subsection{Project Files}
adamc@556 109
adamc@556 110 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@556 111
adamc@556 112 \begin{verbatim}
adamc@556 113 database dbname=test
adamc@556 114 sql crud1.sql
adamc@556 115
adamc@556 116 crud
adamc@556 117 crud1
adamc@556 118 \end{verbatim}
adamc@556 119
adamc@556 120 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@556 121
adamc@556 122 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@556 123
adamc@556 124 \begin{verbatim}
adamc@556 125 createdb test
adamc@556 126 psql -f crud1.sql test
adamc@556 127 \end{verbatim}
adamc@556 128
adamc@556 129 A blank line always separates the named directives from a list of modules to include in the project; if there are no named directives, a blank line must begin the file.
adamc@556 130
adamc@556 131 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@556 132
adamc@783 133 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@783 134 \begin{itemize}
adamc@783 135 \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@783 136 \item \texttt{clientOnly Module.ident} registers an FFI function or transaction that may only be run in client browsers.
adamc@783 137 \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@783 138 \item \texttt{database DBSTRING} sets the string to pass to libpq to open a database connection.
adamc@783 139 \item \texttt{debug} saves some intermediate C files, which is mostly useful to help in debugging the compiler itself.
adamc@783 140 \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@783 141 \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@783 142 \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 143 \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@783 144 \item \texttt{jsFunc Module.ident=name} gives the JavaScript name of an FFI value.
adamc@1089 145 \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@783 146 \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@852 147 \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@783 148 \item \texttt{prefix PREFIX} sets the prefix included before every URI within the generated application. The default is \texttt{/}.
adamc@783 149 \item \texttt{profile} generates an executable that may be used with gprof.
adamc@783 150 \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@783 151 \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@783 152 \item \texttt{serverOnly Module.ident} registers an FFI function or transaction that may only be run on the server.
adamc@783 153 \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@783 154 \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@783 155 \end{itemize}
adamc@701 156
adamc@701 157
adamc@557 158 \subsection{Building an Application}
adamc@557 159
adamc@557 160 To compile project \texttt{P.urp}, simply run
adamc@557 161 \begin{verbatim}
adamc@557 162 urweb P
adamc@557 163 \end{verbatim}
adamc@558 164 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@557 165
adamc@557 166 To time how long the different compiler phases run, without generating an executable, run
adamc@557 167 \begin{verbatim}
adamc@557 168 urweb -timing P
adamc@557 169 \end{verbatim}
adamc@557 170
adamc@1086 171 To stop the compilation process after type-checking, run
adamc@1086 172 \begin{verbatim}
adamc@1086 173 urweb -tc P
adamc@1086 174 \end{verbatim}
adamc@1086 175
adamc@896 176 Some other command-line parameters are accepted:
adamc@896 177 \begin{itemize}
adamc@896 178 \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@896 179
adamc@896 180 \item \texttt{-dbms [postgres|mysql|sqlite]}: Sets the database backend to use.
adamc@896 181 \begin{itemize}
adamc@896 182 \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@896 183
adamc@896 184 A command sequence like this can initialize a Postgres database, using a file \texttt{app.sql} generated by the compiler:
adamc@896 185 \begin{verbatim}
adamc@896 186 createdb app
adamc@896 187 psql -f app.sql app
adamc@896 188 \end{verbatim}
adamc@896 189
adamc@896 190 \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@896 191
adamc@896 192 A command sequence like this can initialize a MySQL database:
adamc@896 193 \begin{verbatim}
adamc@896 194 echo "CREATE DATABASE app" | mysql
adamc@896 195 mysql -D app <app.sql
adamc@896 196 \end{verbatim}
adamc@896 197
adamc@896 198 \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@896 199
adamc@896 200 A command like this can initialize an SQLite database:
adamc@896 201 \begin{verbatim}
adamc@896 202 sqlite3 path/to/database/file <app.sql
adamc@896 203 \end{verbatim}
adamc@896 204 \end{itemize}
adamc@896 205
adamc@896 206 \item \texttt{-output FILENAME}: Set where the application executable is written.
adamc@896 207
adamc@1127 208 \item \texttt{-path NAME VALUE}: Set the value of path variable \texttt{\$NAME} to \texttt{VALUE}, for use in \texttt{.urp} files.
adamc@1127 209
adamc@896 210 \item \texttt{-protocol [http|cgi|fastcgi]}: Set the protocol that the generated application speaks.
adamc@896 211 \begin{itemize}
adamc@896 212 \item \texttt{http}: This is the default. It is for building standalone web servers that can be accessed by web browsers directly.
adamc@896 213
adamc@896 214 \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@896 215
adamc@896 216 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@896 217 \begin{verbatim}
adamc@896 218 ScriptAlias /Hello /path/to/hello.exe
adamc@896 219 \end{verbatim}
adamc@896 220
adamc@896 221 \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@896 222
adamc@896 223 To configure a FastCGI program with Apache, one could combine the above \texttt{ScriptAlias} line with a line like this:
adamc@896 224 \begin{verbatim}
adamc@896 225 FastCgiServer /path/to/hello.exe -idle-timeout 99999
adamc@896 226 \end{verbatim}
adamc@896 227 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@896 228
adamc@896 229 Here is some lighttpd configuration for the same application.
adamc@896 230 \begin{verbatim}
adamc@896 231 fastcgi.server = (
adamc@896 232 "/Hello/" =>
adamc@896 233 (( "bin-path" => "/path/to/hello.exe",
adamc@896 234 "socket" => "/tmp/hello",
adamc@896 235 "check-local" => "disable",
adamc@896 236 "docroot" => "/",
adamc@896 237 "max-procs" => "1"
adamc@896 238 ))
adamc@896 239 )
adamc@896 240 \end{verbatim}
adamc@896 241 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@896 242
adamc@896 243 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@896 244 \end{itemize}
adamc@896 245
adamc@1127 246 \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 247
adamc@896 248 \item \texttt{-sql FILENAME}: Set where a database set-up SQL script is written.
adamc@1095 249
adamc@1095 250 \item \texttt{-static}: Link the runtime system statically. The default is to link against dynamic libraries.
adamc@896 251 \end{itemize}
adamc@896 252
adamc@556 253
adamc@529 254 \section{Ur Syntax}
adamc@529 255
adamc@784 256 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@524 257
adamc@524 258 \subsection{Lexical Conventions}
adamc@524 259
adamc@524 260 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@524 261
adamc@524 262 \begin{center}
adamc@524 263 \begin{tabular}{rl}
adamc@524 264 \textbf{\LaTeX} & \textbf{ASCII} \\
adamc@524 265 $\to$ & \cd{->} \\
adamc@652 266 $\longrightarrow$ & \cd{-->} \\
adamc@524 267 $\times$ & \cd{*} \\
adamc@524 268 $\lambda$ & \cd{fn} \\
adamc@524 269 $\Rightarrow$ & \cd{=>} \\
adamc@652 270 $\Longrightarrow$ & \cd{==>} \\
adamc@529 271 $\neq$ & \cd{<>} \\
adamc@529 272 $\leq$ & \cd{<=} \\
adamc@529 273 $\geq$ & \cd{>=} \\
adamc@524 274 \\
adamc@524 275 $x$ & Normal textual identifier, not beginning with an uppercase letter \\
adamc@525 276 $X$ & Normal textual identifier, beginning with an uppercase letter \\
adamc@524 277 \end{tabular}
adamc@524 278 \end{center}
adamc@524 279
adamc@525 280 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@524 281
adamc@873 282 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@526 283
adamc@527 284 This version of the manual doesn't include operator precedences; see \texttt{src/urweb.grm} for that.
adamc@527 285
adamc@552 286 \subsection{\label{core}Core Syntax}
adamc@524 287
adamc@524 288 \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@524 289 $$\begin{array}{rrcll}
adamc@524 290 \textrm{Kinds} & \kappa &::=& \mt{Type} & \textrm{proper types} \\
adamc@525 291 &&& \mt{Unit} & \textrm{the trivial constructor} \\
adamc@525 292 &&& \mt{Name} & \textrm{field names} \\
adamc@525 293 &&& \kappa \to \kappa & \textrm{type-level functions} \\
adamc@525 294 &&& \{\kappa\} & \textrm{type-level records} \\
adamc@525 295 &&& (\kappa\times^+) & \textrm{type-level tuples} \\
adamc@652 296 &&& X & \textrm{variable} \\
adamc@652 297 &&& X \longrightarrow k & \textrm{kind-polymorphic type-level function} \\
adamc@529 298 &&& \_\_ & \textrm{wildcard} \\
adamc@525 299 &&& (\kappa) & \textrm{explicit precedence} \\
adamc@524 300 \end{array}$$
adamc@524 301
adamc@524 302 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@524 303 $$\begin{array}{rrcll}
adamc@524 304 \textrm{Explicitness} & ? &::=& :: & \textrm{explicit} \\
adamc@558 305 &&& ::: & \textrm{implicit}
adamc@524 306 \end{array}$$
adamc@524 307
adamc@524 308 \emph{Constructors} are the main class of compile-time-only data. They include proper types and are classified by kinds.
adamc@524 309 $$\begin{array}{rrcll}
adamc@524 310 \textrm{Constructors} & c, \tau &::=& (c) :: \kappa & \textrm{kind annotation} \\
adamc@530 311 &&& \hat{x} & \textrm{constructor variable} \\
adamc@524 312 \\
adamc@525 313 &&& \tau \to \tau & \textrm{function type} \\
adamc@525 314 &&& x \; ? \; \kappa \to \tau & \textrm{polymorphic function type} \\
adamc@652 315 &&& X \longrightarrow \tau & \textrm{kind-polymorphic function type} \\
adamc@525 316 &&& \$ c & \textrm{record type} \\
adamc@524 317 \\
adamc@525 318 &&& c \; c & \textrm{type-level function application} \\
adamc@530 319 &&& \lambda x \; :: \; \kappa \Rightarrow c & \textrm{type-level function abstraction} \\
adamc@524 320 \\
adamc@652 321 &&& X \Longrightarrow c & \textrm{type-level kind-polymorphic function abstraction} \\
adamc@655 322 &&& c [\kappa] & \textrm{type-level kind-polymorphic function application} \\
adamc@652 323 \\
adamc@525 324 &&& () & \textrm{type-level unit} \\
adamc@525 325 &&& \#X & \textrm{field name} \\
adamc@524 326 \\
adamc@525 327 &&& [(c = c)^*] & \textrm{known-length type-level record} \\
adamc@525 328 &&& c \rc c & \textrm{type-level record concatenation} \\
adamc@652 329 &&& \mt{map} & \textrm{type-level record map} \\
adamc@524 330 \\
adamc@558 331 &&& (c,^+) & \textrm{type-level tuple} \\
adamc@525 332 &&& c.n & \textrm{type-level tuple projection ($n \in \mathbb N^+$)} \\
adamc@524 333 \\
adamc@652 334 &&& [c \sim c] \Rightarrow \tau & \textrm{guarded type} \\
adamc@524 335 \\
adamc@529 336 &&& \_ :: \kappa & \textrm{wildcard} \\
adamc@525 337 &&& (c) & \textrm{explicit precedence} \\
adamc@530 338 \\
adamc@530 339 \textrm{Qualified uncapitalized variables} & \hat{x} &::=& x & \textrm{not from a module} \\
adamc@530 340 &&& M.x & \textrm{projection from a module} \\
adamc@525 341 \end{array}$$
adamc@525 342
adamc@655 343 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@655 344
adamc@525 345 Modules of the module system are described by \emph{signatures}.
adamc@525 346 $$\begin{array}{rrcll}
adamc@525 347 \textrm{Signatures} & S &::=& \mt{sig} \; s^* \; \mt{end} & \textrm{constant} \\
adamc@525 348 &&& X & \textrm{variable} \\
adamc@525 349 &&& \mt{functor}(X : S) : S & \textrm{functor} \\
adamc@529 350 &&& S \; \mt{where} \; \mt{con} \; x = c & \textrm{concretizing an abstract constructor} \\
adamc@525 351 &&& M.X & \textrm{projection from a module} \\
adamc@525 352 \\
adamc@525 353 \textrm{Signature items} & s &::=& \mt{con} \; x :: \kappa & \textrm{abstract constructor} \\
adamc@525 354 &&& \mt{con} \; x :: \kappa = c & \textrm{concrete constructor} \\
adamc@528 355 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529 356 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@525 357 &&& \mt{val} \; x : \tau & \textrm{value} \\
adamc@525 358 &&& \mt{structure} \; X : S & \textrm{sub-module} \\
adamc@525 359 &&& \mt{signature} \; X = S & \textrm{sub-signature} \\
adamc@525 360 &&& \mt{include} \; S & \textrm{signature inclusion} \\
adamc@525 361 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@654 362 &&& \mt{class} \; x :: \kappa & \textrm{abstract constructor class} \\
adamc@654 363 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@525 364 \\
adamc@525 365 \textrm{Datatype constructors} & dc &::=& X & \textrm{nullary constructor} \\
adamc@525 366 &&& X \; \mt{of} \; \tau & \textrm{unary constructor} \\
adamc@524 367 \end{array}$$
adamc@524 368
adamc@526 369 \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@526 370 $$\begin{array}{rrcll}
adamc@526 371 \textrm{Patterns} & p &::=& \_ & \textrm{wildcard} \\
adamc@526 372 &&& x & \textrm{variable} \\
adamc@526 373 &&& \ell & \textrm{constant} \\
adamc@526 374 &&& \hat{X} & \textrm{nullary constructor} \\
adamc@526 375 &&& \hat{X} \; p & \textrm{unary constructor} \\
adamc@526 376 &&& \{(x = p,)^*\} & \textrm{rigid record pattern} \\
adamc@526 377 &&& \{(x = p,)^+, \ldots\} & \textrm{flexible record pattern} \\
adamc@852 378 &&& p : \tau & \textrm{type annotation} \\
adamc@527 379 &&& (p) & \textrm{explicit precedence} \\
adamc@526 380 \\
adamc@529 381 \textrm{Qualified capitalized variables} & \hat{X} &::=& X & \textrm{not from a module} \\
adamc@526 382 &&& M.X & \textrm{projection from a module} \\
adamc@526 383 \end{array}$$
adamc@526 384
adamc@527 385 \emph{Expressions} are the main run-time entities, corresponding to both ``expressions'' and ``statements'' in mainstream imperative languages.
adamc@527 386 $$\begin{array}{rrcll}
adamc@527 387 \textrm{Expressions} & e &::=& e : \tau & \textrm{type annotation} \\
adamc@529 388 &&& \hat{x} & \textrm{variable} \\
adamc@529 389 &&& \hat{X} & \textrm{datatype constructor} \\
adamc@527 390 &&& \ell & \textrm{constant} \\
adamc@527 391 \\
adamc@527 392 &&& e \; e & \textrm{function application} \\
adamc@527 393 &&& \lambda x : \tau \Rightarrow e & \textrm{function abstraction} \\
adamc@527 394 &&& e [c] & \textrm{polymorphic function application} \\
adamc@852 395 &&& \lambda [x \; ? \; \kappa] \Rightarrow e & \textrm{polymorphic function abstraction} \\
adamc@655 396 &&& e [\kappa] & \textrm{kind-polymorphic function application} \\
adamc@652 397 &&& X \Longrightarrow e & \textrm{kind-polymorphic function abstraction} \\
adamc@527 398 \\
adamc@527 399 &&& \{(c = e,)^*\} & \textrm{known-length record} \\
adamc@527 400 &&& e.c & \textrm{record field projection} \\
adamc@527 401 &&& e \rc e & \textrm{record concatenation} \\
adamc@527 402 &&& e \rcut c & \textrm{removal of a single record field} \\
adamc@527 403 &&& e \rcutM c & \textrm{removal of multiple record fields} \\
adamc@527 404 \\
adamc@527 405 &&& \mt{let} \; ed^* \; \mt{in} \; e \; \mt{end} & \textrm{local definitions} \\
adamc@527 406 \\
adamc@527 407 &&& \mt{case} \; e \; \mt{of} \; (p \Rightarrow e|)^+ & \textrm{pattern matching} \\
adamc@527 408 \\
adamc@654 409 &&& \lambda [c \sim c] \Rightarrow e & \textrm{guarded expression abstraction} \\
adamc@654 410 &&& e \; ! & \textrm{guarded expression application} \\
adamc@527 411 \\
adamc@527 412 &&& \_ & \textrm{wildcard} \\
adamc@527 413 &&& (e) & \textrm{explicit precedence} \\
adamc@527 414 \\
adamc@527 415 \textrm{Local declarations} & ed &::=& \cd{val} \; x : \tau = e & \textrm{non-recursive value} \\
adamc@527 416 &&& \cd{val} \; \cd{rec} \; (x : \tau = e \; \cd{and})^+ & \textrm{mutually-recursive values} \\
adamc@527 417 \end{array}$$
adamc@527 418
adamc@655 419 As with constructors, we include both abstraction and application for kind polymorphism, but applications are only inferred internally.
adamc@655 420
adamc@528 421 \emph{Declarations} primarily bring new symbols into context.
adamc@528 422 $$\begin{array}{rrcll}
adamc@528 423 \textrm{Declarations} & d &::=& \mt{con} \; x :: \kappa = c & \textrm{constructor synonym} \\
adamc@528 424 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529 425 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@528 426 &&& \mt{val} \; x : \tau = e & \textrm{value} \\
adamc@528 427 &&& \mt{val} \; \cd{rec} \; (x : \tau = e \; \mt{and})^+ & \textrm{mutually-recursive values} \\
adamc@528 428 &&& \mt{structure} \; X : S = M & \textrm{module definition} \\
adamc@528 429 &&& \mt{signature} \; X = S & \textrm{signature definition} \\
adamc@528 430 &&& \mt{open} \; M & \textrm{module inclusion} \\
adamc@528 431 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@528 432 &&& \mt{open} \; \mt{constraints} \; M & \textrm{inclusion of just the constraints from a module} \\
adamc@528 433 &&& \mt{table} \; x : c & \textrm{SQL table} \\
adamc@784 434 &&& \mt{view} \; x : c & \textrm{SQL view} \\
adamc@528 435 &&& \mt{sequence} \; x & \textrm{SQL sequence} \\
adamc@535 436 &&& \mt{cookie} \; x : \tau & \textrm{HTTP cookie} \\
adamc@784 437 &&& \mt{style} \; x : \tau & \textrm{CSS class} \\
adamc@654 438 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@1085 439 &&& \mt{task} \; e = e & \textrm{recurring task} \\
adamc@528 440 \\
adamc@529 441 \textrm{Modules} & M &::=& \mt{struct} \; d^* \; \mt{end} & \textrm{constant} \\
adamc@529 442 &&& X & \textrm{variable} \\
adamc@529 443 &&& M.X & \textrm{projection} \\
adamc@529 444 &&& M(M) & \textrm{functor application} \\
adamc@529 445 &&& \mt{functor}(X : S) : S = M & \textrm{functor abstraction} \\
adamc@528 446 \end{array}$$
adamc@528 447
adamc@528 448 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@527 449
adamc@784 450 We omit some extra possibilities in $\mt{table}$ syntax, deferring them to Section \ref{tables}.
adamc@784 451
adamc@529 452 \subsection{Shorthands}
adamc@529 453
adamc@529 454 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@529 455
adamc@529 456 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@529 457
adamc@529 458 A record type may be written $\{(c = c,)^*\}$, which elaborates to $\$[(c = c,)^*]$.
adamc@529 459
adamc@533 460 The notation $[c_1, \ldots, c_n]$ is shorthand for $[c_1 = (), \ldots, c_n = ()]$.
adamc@533 461
adamc@529 462 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@529 463
adamc@852 464 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@529 465
adamc@529 466 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@529 467
adamc@529 468 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@529 469
adamc@654 470 A signature item or declaration $\mt{class} \; x = \lambda y \Rightarrow c$ may be abbreviated $\mt{class} \; x \; y = c$.
adamc@529 471
adamc@1102 472 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@529 473
adamc@852 474 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@529 475
adamc@852 476 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@852 477
adamc@852 478 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@529 479
adamc@529 480 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@529 481
adamc@852 482 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@852 483
adamc@853 484 A declaration $\mt{table} \; x : \{(c = c,)^*\}$ is elaborated into $\mt{table} \; x : [(c = c,)^*]$.
adamc@529 485
adamc@529 486 The syntax $\mt{where} \; \mt{type}$ is an alternate form of $\mt{where} \; \mt{con}$.
adamc@529 487
adamc@529 488 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@529 489
adamc@529 490 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@529 491
adamc@784 492 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@529 493
adamc@530 494
adamc@530 495 \section{Static Semantics}
adamc@530 496
adamc@530 497 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@530 498
adamc@530 499 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@530 500 \begin{itemize}
adamc@655 501 \item $\Gamma \vdash \kappa$ expresses kind well-formedness.
adamc@530 502 \item $\Gamma \vdash c :: \kappa$ assigns a kind to a constructor in a context.
adamc@530 503 \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@531 504 \item $\Gamma \vdash c \hookrightarrow C$ proves that record constructor $c$ decomposes into set $C$ of field names and record constructors.
adamc@530 505 \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@530 506 \item $\Gamma \vdash e : \tau$ is a standard typing judgment.
adamc@534 507 \item $\Gamma \vdash p \leadsto \Gamma; \tau$ combines typing of patterns with calculation of which new variables they bind.
adamc@537 508 \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@537 509 \item $\Gamma \vdash S \equiv S$ is the signature equivalence judgment.
adamc@536 510 \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@530 511 \item $\Gamma \vdash M : S$ is the module signature checking judgment.
adamc@537 512 \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@539 513 \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@530 514 \end{itemize}
adamc@530 515
adamc@655 516
adamc@655 517 \subsection{Kind Well-Formedness}
adamc@655 518
adamc@655 519 $$\infer{\Gamma \vdash \mt{Type}}{}
adamc@655 520 \quad \infer{\Gamma \vdash \mt{Unit}}{}
adamc@655 521 \quad \infer{\Gamma \vdash \mt{Name}}{}
adamc@655 522 \quad \infer{\Gamma \vdash \kappa_1 \to \kappa_2}{
adamc@655 523 \Gamma \vdash \kappa_1
adamc@655 524 & \Gamma \vdash \kappa_2
adamc@655 525 }
adamc@655 526 \quad \infer{\Gamma \vdash \{\kappa\}}{
adamc@655 527 \Gamma \vdash \kappa
adamc@655 528 }
adamc@655 529 \quad \infer{\Gamma \vdash (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@655 530 \forall i: \Gamma \vdash \kappa_i
adamc@655 531 }$$
adamc@655 532
adamc@655 533 $$\infer{\Gamma \vdash X}{
adamc@655 534 X \in \Gamma
adamc@655 535 }
adamc@655 536 \quad \infer{\Gamma \vdash X \longrightarrow \kappa}{
adamc@655 537 \Gamma, X \vdash \kappa
adamc@655 538 }$$
adamc@655 539
adamc@530 540 \subsection{Kinding}
adamc@530 541
adamc@655 542 We write $[X \mapsto \kappa_1]\kappa_2$ for capture-avoiding substitution of $\kappa_1$ for $X$ in $\kappa_2$.
adamc@655 543
adamc@530 544 $$\infer{\Gamma \vdash (c) :: \kappa :: \kappa}{
adamc@530 545 \Gamma \vdash c :: \kappa
adamc@530 546 }
adamc@530 547 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530 548 x :: \kappa \in \Gamma
adamc@530 549 }
adamc@530 550 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530 551 x :: \kappa = c \in \Gamma
adamc@530 552 }$$
adamc@530 553
adamc@530 554 $$\infer{\Gamma \vdash M.x :: \kappa}{
adamc@537 555 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 556 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = \kappa
adamc@530 557 }
adamc@530 558 \quad \infer{\Gamma \vdash M.x :: \kappa}{
adamc@537 559 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 560 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@530 561 }$$
adamc@530 562
adamc@530 563 $$\infer{\Gamma \vdash \tau_1 \to \tau_2 :: \mt{Type}}{
adamc@530 564 \Gamma \vdash \tau_1 :: \mt{Type}
adamc@530 565 & \Gamma \vdash \tau_2 :: \mt{Type}
adamc@530 566 }
adamc@530 567 \quad \infer{\Gamma \vdash x \; ? \: \kappa \to \tau :: \mt{Type}}{
adamc@530 568 \Gamma, x :: \kappa \vdash \tau :: \mt{Type}
adamc@530 569 }
adamc@655 570 \quad \infer{\Gamma \vdash X \longrightarrow \tau :: \mt{Type}}{
adamc@655 571 \Gamma, X \vdash \tau :: \mt{Type}
adamc@655 572 }
adamc@530 573 \quad \infer{\Gamma \vdash \$c :: \mt{Type}}{
adamc@530 574 \Gamma \vdash c :: \{\mt{Type}\}
adamc@530 575 }$$
adamc@530 576
adamc@530 577 $$\infer{\Gamma \vdash c_1 \; c_2 :: \kappa_2}{
adamc@530 578 \Gamma \vdash c_1 :: \kappa_1 \to \kappa_2
adamc@530 579 & \Gamma \vdash c_2 :: \kappa_1
adamc@530 580 }
adamc@530 581 \quad \infer{\Gamma \vdash \lambda x \; :: \; \kappa_1 \Rightarrow c :: \kappa_1 \to \kappa_2}{
adamc@530 582 \Gamma, x :: \kappa_1 \vdash c :: \kappa_2
adamc@530 583 }$$
adamc@530 584
adamc@655 585 $$\infer{\Gamma \vdash c[\kappa'] :: [X \mapsto \kappa']\kappa}{
adamc@655 586 \Gamma \vdash c :: X \to \kappa
adamc@655 587 & \Gamma \vdash \kappa'
adamc@655 588 }
adamc@655 589 \quad \infer{\Gamma \vdash X \Longrightarrow c :: X \to \kappa}{
adamc@655 590 \Gamma, X \vdash c :: \kappa
adamc@655 591 }$$
adamc@655 592
adamc@530 593 $$\infer{\Gamma \vdash () :: \mt{Unit}}{}
adamc@530 594 \quad \infer{\Gamma \vdash \#X :: \mt{Name}}{}$$
adamc@530 595
adamc@530 596 $$\infer{\Gamma \vdash [\overline{c_i = c'_i}] :: \{\kappa\}}{
adamc@530 597 \forall i: \Gamma \vdash c_i : \mt{Name}
adamc@530 598 & \Gamma \vdash c'_i :: \kappa
adamc@530 599 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@530 600 }
adamc@530 601 \quad \infer{\Gamma \vdash c_1 \rc c_2 :: \{\kappa\}}{
adamc@530 602 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530 603 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@530 604 & \Gamma \vdash c_1 \sim c_2
adamc@530 605 }$$
adamc@530 606
adamc@655 607 $$\infer{\Gamma \vdash \mt{map} :: (\kappa_1 \to \kappa_2) \to \{\kappa_1\} \to \{\kappa_2\}}{}$$
adamc@530 608
adamc@573 609 $$\infer{\Gamma \vdash (\overline c) :: (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@573 610 \forall i: \Gamma \vdash c_i :: \kappa_i
adamc@530 611 }
adamc@573 612 \quad \infer{\Gamma \vdash c.i :: \kappa_i}{
adamc@573 613 \Gamma \vdash c :: (\kappa_1 \times \ldots \times \kappa_n)
adamc@530 614 }$$
adamc@530 615
adamc@655 616 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow \tau :: \mt{Type}}{
adamc@655 617 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530 618 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@655 619 & \Gamma, c_1 \sim c_2 \vdash \tau :: \mt{Type}
adamc@530 620 }$$
adamc@530 621
adamc@531 622 \subsection{Record Disjointness}
adamc@531 623
adamc@531 624 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@558 625 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@558 626 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@558 627 & \forall c'_1 \in C_1, c'_2 \in C_2: \Gamma \vdash c'_1 \sim c'_2
adamc@531 628 }
adamc@531 629 \quad \infer{\Gamma \vdash X \sim X'}{
adamc@531 630 X \neq X'
adamc@531 631 }$$
adamc@531 632
adamc@531 633 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@531 634 c'_1 \sim c'_2 \in \Gamma
adamc@558 635 & \Gamma \vdash c'_1 \hookrightarrow C_1
adamc@558 636 & \Gamma \vdash c'_2 \hookrightarrow C_2
adamc@558 637 & c_1 \in C_1
adamc@558 638 & c_2 \in C_2
adamc@531 639 }$$
adamc@531 640
adamc@531 641 $$\infer{\Gamma \vdash c \hookrightarrow \{c\}}{}
adamc@531 642 \quad \infer{\Gamma \vdash [\overline{c = c'}] \hookrightarrow \{\overline{c}\}}{}
adamc@531 643 \quad \infer{\Gamma \vdash c_1 \rc c_2 \hookrightarrow C_1 \cup C_2}{
adamc@531 644 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@531 645 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@531 646 }
adamc@531 647 \quad \infer{\Gamma \vdash c \hookrightarrow C}{
adamc@531 648 \Gamma \vdash c \equiv c'
adamc@531 649 & \Gamma \vdash c' \hookrightarrow C
adamc@531 650 }
adamc@531 651 \quad \infer{\Gamma \vdash \mt{map} \; f \; c \hookrightarrow C}{
adamc@531 652 \Gamma \vdash c \hookrightarrow C
adamc@531 653 }$$
adamc@531 654
adamc@541 655 \subsection{\label{definitional}Definitional Equality}
adamc@532 656
adamc@655 657 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@532 658
adamc@532 659 $$\infer{\Gamma \vdash c \equiv c}{}
adamc@532 660 \quad \infer{\Gamma \vdash c_1 \equiv c_2}{
adamc@532 661 \Gamma \vdash c_2 \equiv c_1
adamc@532 662 }
adamc@532 663 \quad \infer{\Gamma \vdash c_1 \equiv c_3}{
adamc@532 664 \Gamma \vdash c_1 \equiv c_2
adamc@532 665 & \Gamma \vdash c_2 \equiv c_3
adamc@532 666 }
adamc@532 667 \quad \infer{\Gamma \vdash \mathcal C[c_1] \equiv \mathcal C[c_2]}{
adamc@532 668 \Gamma \vdash c_1 \equiv c_2
adamc@532 669 }$$
adamc@532 670
adamc@532 671 $$\infer{\Gamma \vdash x \equiv c}{
adamc@532 672 x :: \kappa = c \in \Gamma
adamc@532 673 }
adamc@532 674 \quad \infer{\Gamma \vdash M.x \equiv c}{
adamc@537 675 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 676 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@532 677 }
adamc@532 678 \quad \infer{\Gamma \vdash (\overline c).i \equiv c_i}{}$$
adamc@532 679
adamc@532 680 $$\infer{\Gamma \vdash (\lambda x :: \kappa \Rightarrow c) \; c' \equiv [x \mapsto c'] c}{}
adamc@655 681 \quad \infer{\Gamma \vdash (X \Longrightarrow c) [\kappa] \equiv [X \mapsto \kappa] c}{}$$
adamc@655 682
adamc@655 683 $$\infer{\Gamma \vdash c_1 \rc c_2 \equiv c_2 \rc c_1}{}
adamc@532 684 \quad \infer{\Gamma \vdash c_1 \rc (c_2 \rc c_3) \equiv (c_1 \rc c_2) \rc c_3}{}$$
adamc@532 685
adamc@532 686 $$\infer{\Gamma \vdash [] \rc c \equiv c}{}
adamc@532 687 \quad \infer{\Gamma \vdash [\overline{c_1 = c'_1}] \rc [\overline{c_2 = c'_2}] \equiv [\overline{c_1 = c'_1}, \overline{c_2 = c'_2}]}{}$$
adamc@532 688
adamc@655 689 $$\infer{\Gamma \vdash \mt{map} \; f \; [] \equiv []}{}
adamc@655 690 \quad \infer{\Gamma \vdash \mt{map} \; f \; ([c_1 = c_2] \rc c) \equiv [c_1 = f \; c_2] \rc \mt{map} \; f \; c}{}$$
adamc@532 691
adamc@532 692 $$\infer{\Gamma \vdash \mt{map} \; (\lambda x \Rightarrow x) \; c \equiv c}{}
adamc@655 693 \quad \infer{\Gamma \vdash \mt{map} \; f \; (\mt{map} \; f' \; c)
adamc@655 694 \equiv \mt{map} \; (\lambda x \Rightarrow f \; (f' \; x)) \; c}{}$$
adamc@532 695
adamc@532 696 $$\infer{\Gamma \vdash \mt{map} \; f \; (c_1 \rc c_2) \equiv \mt{map} \; f \; c_1 \rc \mt{map} \; f \; c_2}{}$$
adamc@531 697
adamc@534 698 \subsection{Expression Typing}
adamc@533 699
adamc@873 700 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@533 701
adamc@533 702 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@533 703
adamc@533 704 $$\infer{\Gamma \vdash e : \tau : \tau}{
adamc@533 705 \Gamma \vdash e : \tau
adamc@533 706 }
adamc@533 707 \quad \infer{\Gamma \vdash e : \tau}{
adamc@533 708 \Gamma \vdash e : \tau'
adamc@533 709 & \Gamma \vdash \tau' \equiv \tau
adamc@533 710 }
adamc@533 711 \quad \infer{\Gamma \vdash \ell : T(\ell)}{}$$
adamc@533 712
adamc@533 713 $$\infer{\Gamma \vdash x : \mathcal I(\tau)}{
adamc@533 714 x : \tau \in \Gamma
adamc@533 715 }
adamc@533 716 \quad \infer{\Gamma \vdash M.x : \mathcal I(\tau)}{
adamc@537 717 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 718 & \mt{proj}(M, \overline{s}, \mt{val} \; x) = \tau
adamc@533 719 }
adamc@533 720 \quad \infer{\Gamma \vdash X : \mathcal I(\tau)}{
adamc@533 721 X : \tau \in \Gamma
adamc@533 722 }
adamc@533 723 \quad \infer{\Gamma \vdash M.X : \mathcal I(\tau)}{
adamc@537 724 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 725 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \tau
adamc@533 726 }$$
adamc@533 727
adamc@533 728 $$\infer{\Gamma \vdash e_1 \; e_2 : \tau_2}{
adamc@533 729 \Gamma \vdash e_1 : \tau_1 \to \tau_2
adamc@533 730 & \Gamma \vdash e_2 : \tau_1
adamc@533 731 }
adamc@533 732 \quad \infer{\Gamma \vdash \lambda x : \tau_1 \Rightarrow e : \tau_1 \to \tau_2}{
adamc@533 733 \Gamma, x : \tau_1 \vdash e : \tau_2
adamc@533 734 }$$
adamc@533 735
adamc@533 736 $$\infer{\Gamma \vdash e [c] : [x \mapsto c]\tau}{
adamc@533 737 \Gamma \vdash e : x :: \kappa \to \tau
adamc@533 738 & \Gamma \vdash c :: \kappa
adamc@533 739 }
adamc@852 740 \quad \infer{\Gamma \vdash \lambda [x \; ? \; \kappa] \Rightarrow e : x \; ? \; \kappa \to \tau}{
adamc@533 741 \Gamma, x :: \kappa \vdash e : \tau
adamc@533 742 }$$
adamc@533 743
adamc@655 744 $$\infer{\Gamma \vdash e [\kappa] : [X \mapsto \kappa]\tau}{
adamc@655 745 \Gamma \vdash e : X \longrightarrow \tau
adamc@655 746 & \Gamma \vdash \kappa
adamc@655 747 }
adamc@655 748 \quad \infer{\Gamma \vdash X \Longrightarrow e : X \longrightarrow \tau}{
adamc@655 749 \Gamma, X \vdash e : \tau
adamc@655 750 }$$
adamc@655 751
adamc@533 752 $$\infer{\Gamma \vdash \{\overline{c = e}\} : \{\overline{c : \tau}\}}{
adamc@533 753 \forall i: \Gamma \vdash c_i :: \mt{Name}
adamc@533 754 & \Gamma \vdash e_i : \tau_i
adamc@533 755 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@533 756 }
adamc@533 757 \quad \infer{\Gamma \vdash e.c : \tau}{
adamc@533 758 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533 759 }
adamc@533 760 \quad \infer{\Gamma \vdash e_1 \rc e_2 : \$(c_1 \rc c_2)}{
adamc@533 761 \Gamma \vdash e_1 : \$c_1
adamc@533 762 & \Gamma \vdash e_2 : \$c_2
adamc@573 763 & \Gamma \vdash c_1 \sim c_2
adamc@533 764 }$$
adamc@533 765
adamc@533 766 $$\infer{\Gamma \vdash e \rcut c : \$c'}{
adamc@533 767 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533 768 }
adamc@533 769 \quad \infer{\Gamma \vdash e \rcutM c : \$c'}{
adamc@533 770 \Gamma \vdash e : \$(c \rc c')
adamc@533 771 }$$
adamc@533 772
adamc@533 773 $$\infer{\Gamma \vdash \mt{let} \; \overline{ed} \; \mt{in} \; e \; \mt{end} : \tau}{
adamc@533 774 \Gamma \vdash \overline{ed} \leadsto \Gamma'
adamc@533 775 & \Gamma' \vdash e : \tau
adamc@533 776 }
adamc@533 777 \quad \infer{\Gamma \vdash \mt{case} \; e \; \mt{of} \; \overline{p \Rightarrow e} : \tau}{
adamc@533 778 \forall i: \Gamma \vdash p_i \leadsto \Gamma_i, \tau'
adamc@533 779 & \Gamma_i \vdash e_i : \tau
adamc@533 780 }$$
adamc@533 781
adamc@573 782 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow e : \lambda [c_1 \sim c_2] \Rightarrow \tau}{
adamc@533 783 \Gamma \vdash c_1 :: \{\kappa\}
adamc@655 784 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@533 785 & \Gamma, c_1 \sim c_2 \vdash e : \tau
adamc@662 786 }
adamc@662 787 \quad \infer{\Gamma \vdash e \; ! : \tau}{
adamc@662 788 \Gamma \vdash e : [c_1 \sim c_2] \Rightarrow \tau
adamc@662 789 & \Gamma \vdash c_1 \sim c_2
adamc@533 790 }$$
adamc@533 791
adamc@534 792 \subsection{Pattern Typing}
adamc@534 793
adamc@534 794 $$\infer{\Gamma \vdash \_ \leadsto \Gamma; \tau}{}
adamc@534 795 \quad \infer{\Gamma \vdash x \leadsto \Gamma, x : \tau; \tau}{}
adamc@534 796 \quad \infer{\Gamma \vdash \ell \leadsto \Gamma; T(\ell)}{}$$
adamc@534 797
adamc@534 798 $$\infer{\Gamma \vdash X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534 799 X : \overline{x ::: \mt{Type}} \to \tau \in \Gamma
adamc@534 800 & \textrm{$\tau$ not a function type}
adamc@534 801 }
adamc@534 802 \quad \infer{\Gamma \vdash X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534 803 X : \overline{x ::: \mt{Type}} \to \tau'' \to \tau \in \Gamma
adamc@534 804 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534 805 }$$
adamc@534 806
adamc@534 807 $$\infer{\Gamma \vdash M.X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537 808 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 809 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau
adamc@534 810 & \textrm{$\tau$ not a function type}
adamc@534 811 }$$
adamc@534 812
adamc@534 813 $$\infer{\Gamma \vdash M.X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537 814 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 815 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau'' \to \tau
adamc@534 816 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534 817 }$$
adamc@534 818
adamc@534 819 $$\infer{\Gamma \vdash \{\overline{x = p}\} \leadsto \Gamma_n; \{\overline{x = \tau}\}}{
adamc@534 820 \Gamma_0 = \Gamma
adamc@534 821 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534 822 }
adamc@534 823 \quad \infer{\Gamma \vdash \{\overline{x = p}, \ldots\} \leadsto \Gamma_n; \$([\overline{x = \tau}] \rc c)}{
adamc@534 824 \Gamma_0 = \Gamma
adamc@534 825 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534 826 }$$
adamc@534 827
adamc@852 828 $$\infer{\Gamma \vdash p : \tau \leadsto \Gamma'; \tau}{
adamc@852 829 \Gamma \vdash p \leadsto \Gamma'; \tau'
adamc@852 830 & \Gamma \vdash \tau' \equiv \tau
adamc@852 831 }$$
adamc@852 832
adamc@535 833 \subsection{Declaration Typing}
adamc@535 834
adamc@535 835 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@535 836
adamc@655 837 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@535 838
adamc@558 839 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@537 840 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@535 841
adamc@535 842 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535 843 \quad \infer{\Gamma \vdash d, \overline{d} \leadsto \Gamma''}{
adamc@535 844 \Gamma \vdash d \leadsto \Gamma'
adamc@535 845 & \Gamma' \vdash \overline{d} \leadsto \Gamma''
adamc@535 846 }$$
adamc@535 847
adamc@535 848 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@535 849 \Gamma \vdash c :: \kappa
adamc@535 850 }
adamc@535 851 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@535 852 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@535 853 }$$
adamc@535 854
adamc@535 855 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537 856 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 857 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@535 858 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@535 859 }$$
adamc@535 860
adamc@535 861 $$\infer{\Gamma \vdash \mt{val} \; x : \tau = e \leadsto \Gamma, x : \tau}{
adamc@535 862 \Gamma \vdash e : \tau
adamc@535 863 }$$
adamc@535 864
adamc@535 865 $$\infer{\Gamma \vdash \mt{val} \; \mt{rec} \; \overline{x : \tau = e} \leadsto \Gamma, \overline{x : \tau}}{
adamc@535 866 \forall i: \Gamma, \overline{x : \tau} \vdash e_i : \tau_i
adamc@535 867 & \textrm{$e_i$ starts with an expression $\lambda$, optionally preceded by constructor and disjointness $\lambda$s}
adamc@535 868 }$$
adamc@535 869
adamc@535 870 $$\infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : S}{
adamc@535 871 \Gamma \vdash M : S
adamc@558 872 & \textrm{ $M$ not a constant or application}
adamc@535 873 }
adamc@558 874 \quad \infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : \mt{selfify}(X, \overline{s})}{
adamc@558 875 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@539 876 }$$
adamc@539 877
adamc@539 878 $$\infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@535 879 \Gamma \vdash S
adamc@535 880 }$$
adamc@535 881
adamc@537 882 $$\infer{\Gamma \vdash \mt{open} \; M \leadsto \Gamma, \mathcal O(M, \overline{s})}{
adamc@537 883 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535 884 }$$
adamc@535 885
adamc@535 886 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma}{
adamc@535 887 \Gamma \vdash c_1 :: \{\kappa\}
adamc@535 888 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@535 889 & \Gamma \vdash c_1 \sim c_2
adamc@535 890 }
adamc@537 891 \quad \infer{\Gamma \vdash \mt{open} \; \mt{constraints} \; M \leadsto \Gamma, \mathcal O_c(M, \overline{s})}{
adamc@537 892 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535 893 }$$
adamc@535 894
adamc@784 895 $$\infer{\Gamma \vdash \mt{table} \; x : c \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_table} \; c \; []}{
adamc@535 896 \Gamma \vdash c :: \{\mt{Type}\}
adamc@535 897 }
adamc@784 898 \quad \infer{\Gamma \vdash \mt{view} \; x : c \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_view} \; c}{
adamc@784 899 \Gamma \vdash c :: \{\mt{Type}\}
adamc@784 900 }$$
adamc@784 901
adamc@784 902 $$\infer{\Gamma \vdash \mt{sequence} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_sequence}}{}$$
adamc@535 903
adamc@535 904 $$\infer{\Gamma \vdash \mt{cookie} \; x : \tau \leadsto \Gamma, x : \mt{Basis}.\mt{http\_cookie} \; \tau}{
adamc@535 905 \Gamma \vdash \tau :: \mt{Type}
adamc@784 906 }
adamc@784 907 \quad \infer{\Gamma \vdash \mt{style} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{css\_class}}{}$$
adamc@535 908
adamc@1085 909 $$\infer{\Gamma \vdash \mt{task} \; e_1 = e_2 \leadsto \Gamma}{
adamc@1085 910 \Gamma \vdash e_1 :: \mt{Basis}.\mt{task\_kind}
adamc@1085 911 & \Gamma \vdash e_2 :: \mt{Basis}.\mt{transaction} \; \{\}
adamc@1085 912 }$$
adamc@1085 913
adamc@784 914 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784 915 \Gamma \vdash c :: \kappa
adamc@535 916 }$$
adamc@535 917
adamc@535 918 $$\infer{\overline{y}; x; \Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535 919 \quad \infer{\overline{y}; x; \Gamma \vdash X \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to x \; \overline{y}}{
adamc@535 920 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535 921 }
adamc@535 922 \quad \infer{\overline{y}; x; \Gamma \vdash X \; \mt{of} \; \tau \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to \tau \to x \; \overline{y}}{
adamc@535 923 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535 924 }$$
adamc@535 925
adamc@537 926 \subsection{Signature Item Typing}
adamc@537 927
adamc@537 928 We appeal to a signature item analogue of the $\mathcal O$ function from the last subsection.
adamc@537 929
adamc@537 930 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@537 931 \quad \infer{\Gamma \vdash s, \overline{s} \leadsto \Gamma''}{
adamc@537 932 \Gamma \vdash s \leadsto \Gamma'
adamc@537 933 & \Gamma' \vdash \overline{s} \leadsto \Gamma''
adamc@537 934 }$$
adamc@537 935
adamc@537 936 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}
adamc@537 937 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@537 938 \Gamma \vdash c :: \kappa
adamc@537 939 }
adamc@537 940 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@537 941 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@537 942 }$$
adamc@537 943
adamc@537 944 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537 945 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 946 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 947 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@537 948 }$$
adamc@537 949
adamc@537 950 $$\infer{\Gamma \vdash \mt{val} \; x : \tau \leadsto \Gamma, x : \tau}{
adamc@537 951 \Gamma \vdash \tau :: \mt{Type}
adamc@537 952 }$$
adamc@537 953
adamc@537 954 $$\infer{\Gamma \vdash \mt{structure} \; X : S \leadsto \Gamma, X : S}{
adamc@537 955 \Gamma \vdash S
adamc@537 956 }
adamc@537 957 \quad \infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@537 958 \Gamma \vdash S
adamc@537 959 }$$
adamc@537 960
adamc@537 961 $$\infer{\Gamma \vdash \mt{include} \; S \leadsto \Gamma, \mathcal O(\overline{s})}{
adamc@537 962 \Gamma \vdash S
adamc@537 963 & \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 964 }$$
adamc@537 965
adamc@537 966 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma, c_1 \sim c_2}{
adamc@537 967 \Gamma \vdash c_1 :: \{\kappa\}
adamc@537 968 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@537 969 }$$
adamc@537 970
adamc@784 971 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784 972 \Gamma \vdash c :: \kappa
adamc@537 973 }
adamc@784 974 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}$$
adamc@537 975
adamc@536 976 \subsection{Signature Compatibility}
adamc@536 977
adamc@558 978 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@537 979
adamc@537 980 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@537 981
adamc@536 982 $$\infer{\Gamma \vdash S \equiv S}{}
adamc@536 983 \quad \infer{\Gamma \vdash S_1 \equiv S_2}{
adamc@536 984 \Gamma \vdash S_2 \equiv S_1
adamc@536 985 }
adamc@536 986 \quad \infer{\Gamma \vdash X \equiv S}{
adamc@536 987 X = S \in \Gamma
adamc@536 988 }
adamc@536 989 \quad \infer{\Gamma \vdash M.X \equiv S}{
adamc@537 990 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 991 & \mt{proj}(M, \overline{s}, \mt{signature} \; X) = S
adamc@536 992 }$$
adamc@536 993
adamc@536 994 $$\infer{\Gamma \vdash S \; \mt{where} \; \mt{con} \; x = c \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa = c \; \overline{s_2} \; \mt{end}}{
adamc@536 995 \Gamma \vdash S \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa \; \overline{s_2} \; \mt{end}
adamc@536 996 & \Gamma \vdash c :: \kappa
adamc@537 997 }
adamc@537 998 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s^1} \; \mt{include} \; S \; \overline{s^2} \; \mt{end} \equiv \mt{sig} \; \overline{s^1} \; \overline{s} \; \overline{s^2} \; \mt{end}}{
adamc@537 999 \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@536 1000 }$$
adamc@536 1001
adamc@536 1002 $$\infer{\Gamma \vdash S_1 \leq S_2}{
adamc@536 1003 \Gamma \vdash S_1 \equiv S_2
adamc@536 1004 }
adamc@536 1005 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \mt{end}}{}
adamc@537 1006 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; s' \; \overline{s'} \; \mt{end}}{
adamc@537 1007 \Gamma \vdash \overline{s} \leq s'
adamc@537 1008 & \Gamma \vdash s' \leadsto \Gamma'
adamc@537 1009 & \Gamma' \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \overline{s'} \; \mt{end}
adamc@537 1010 }$$
adamc@537 1011
adamc@537 1012 $$\infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537 1013 \Gamma \vdash s \leq s'
adamc@537 1014 }
adamc@537 1015 \quad \infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537 1016 \Gamma \vdash s \leadsto \Gamma'
adamc@537 1017 & \Gamma' \vdash \overline{s} \leq s'
adamc@536 1018 }$$
adamc@536 1019
adamc@536 1020 $$\infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 \leq \mt{functor} (X : S'_1) : S'_2}{
adamc@536 1021 \Gamma \vdash S'_1 \leq S_1
adamc@536 1022 & \Gamma, X : S'_1 \vdash S_2 \leq S'_2
adamc@536 1023 }$$
adamc@536 1024
adamc@537 1025 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@537 1026 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}
adamc@558 1027 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type}}{}$$
adamc@537 1028
adamc@537 1029 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(y)} \to \mt{Type}}{
adamc@537 1030 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1031 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1032 }$$
adamc@537 1033
adamc@784 1034 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@784 1035 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}$$
adamc@537 1036
adamc@537 1037 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \mt{\kappa} = c_2}{
adamc@537 1038 \Gamma \vdash c_1 \equiv c_2
adamc@537 1039 }
adamc@784 1040 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \kappa = c_2}{
adamc@537 1041 \Gamma \vdash c_1 \equiv c_2
adamc@537 1042 }$$
adamc@537 1043
adamc@537 1044 $$\infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537 1045 \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1046 }$$
adamc@537 1047
adamc@537 1048 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537 1049 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1050 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1051 & \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1052 }$$
adamc@537 1053
adamc@537 1054 $$\infer{\Gamma \vdash \cdot \leq \cdot}{}
adamc@537 1055 \quad \infer{\Gamma \vdash X; \overline{dc} \leq X; \overline{dc'}}{
adamc@537 1056 \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1057 }
adamc@537 1058 \quad \infer{\Gamma \vdash X \; \mt{of} \; \tau_1; \overline{dc} \leq X \; \mt{of} \; \tau_2; \overline{dc'}}{
adamc@537 1059 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537 1060 & \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1061 }$$
adamc@537 1062
adamc@537 1063 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x = \mt{datatype} \; M'.z'}{
adamc@537 1064 \Gamma \vdash M.z \equiv M'.z'
adamc@537 1065 }$$
adamc@537 1066
adamc@537 1067 $$\infer{\Gamma \vdash \mt{val} \; x : \tau_1 \leq \mt{val} \; x : \tau_2}{
adamc@537 1068 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537 1069 }
adamc@537 1070 \quad \infer{\Gamma \vdash \mt{structure} \; X : S_1 \leq \mt{structure} \; X : S_2}{
adamc@537 1071 \Gamma \vdash S_1 \leq S_2
adamc@537 1072 }
adamc@537 1073 \quad \infer{\Gamma \vdash \mt{signature} \; X = S_1 \leq \mt{signature} \; X = S_2}{
adamc@537 1074 \Gamma \vdash S_1 \leq S_2
adamc@537 1075 & \Gamma \vdash S_2 \leq S_1
adamc@537 1076 }$$
adamc@537 1077
adamc@537 1078 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leq \mt{constraint} \; c'_1 \sim c'_2}{
adamc@537 1079 \Gamma \vdash c_1 \equiv c'_1
adamc@537 1080 & \Gamma \vdash c_2 \equiv c'_2
adamc@537 1081 }$$
adamc@537 1082
adamc@655 1083 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{class} \; x :: \kappa}{}
adamc@655 1084 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{class} \; x :: \kappa}{}
adamc@655 1085 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{class} \; x :: \kappa = c_2}{
adamc@537 1086 \Gamma \vdash c_1 \equiv c_2
adamc@537 1087 }$$
adamc@537 1088
adamc@538 1089 \subsection{Module Typing}
adamc@538 1090
adamc@538 1091 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 1092
adamc@538 1093 $$\infer{\Gamma \vdash M : S}{
adamc@538 1094 \Gamma \vdash M : S'
adamc@538 1095 & \Gamma \vdash S' \leq S
adamc@538 1096 }
adamc@538 1097 \quad \infer{\Gamma \vdash \mt{struct} \; \overline{d} \; \mt{end} : \mt{sig} \; \mt{sigOf}(\overline{d}) \; \mt{end}}{
adamc@538 1098 \Gamma \vdash \overline{d} \leadsto \Gamma'
adamc@538 1099 }
adamc@538 1100 \quad \infer{\Gamma \vdash X : S}{
adamc@538 1101 X : S \in \Gamma
adamc@538 1102 }$$
adamc@538 1103
adamc@538 1104 $$\infer{\Gamma \vdash M.X : S}{
adamc@538 1105 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@538 1106 & \mt{proj}(M, \overline{s}, \mt{structure} \; X) = S
adamc@538 1107 }$$
adamc@538 1108
adamc@538 1109 $$\infer{\Gamma \vdash M_1(M_2) : [X \mapsto M_2]S_2}{
adamc@538 1110 \Gamma \vdash M_1 : \mt{functor}(X : S_1) : S_2
adamc@538 1111 & \Gamma \vdash M_2 : S_1
adamc@538 1112 }
adamc@538 1113 \quad \infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 = M : \mt{functor} (X : S_1) : S_2}{
adamc@538 1114 \Gamma \vdash S_1
adamc@538 1115 & \Gamma, X : S_1 \vdash S_2
adamc@538 1116 & \Gamma, X : S_1 \vdash M : S_2
adamc@538 1117 }$$
adamc@538 1118
adamc@538 1119 \begin{eqnarray*}
adamc@538 1120 \mt{sigOf}(\cdot) &=& \cdot \\
adamc@538 1121 \mt{sigOf}(s \; \overline{s'}) &=& \mt{sigOf}(s) \; \mt{sigOf}(\overline{s'}) \\
adamc@538 1122 \\
adamc@538 1123 \mt{sigOf}(\mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@538 1124 \mt{sigOf}(\mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \overline{dc} \\
adamc@538 1125 \mt{sigOf}(\mt{datatype} \; x = \mt{datatype} \; M.z) &=& \mt{datatype} \; x = \mt{datatype} \; M.z \\
adamc@538 1126 \mt{sigOf}(\mt{val} \; x : \tau = e) &=& \mt{val} \; x : \tau \\
adamc@538 1127 \mt{sigOf}(\mt{val} \; \mt{rec} \; \overline{x : \tau = e}) &=& \overline{\mt{val} \; x : \tau} \\
adamc@538 1128 \mt{sigOf}(\mt{structure} \; X : S = M) &=& \mt{structure} \; X : S \\
adamc@538 1129 \mt{sigOf}(\mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@538 1130 \mt{sigOf}(\mt{open} \; M) &=& \mt{include} \; S \textrm{ (where $\Gamma \vdash M : S$)} \\
adamc@538 1131 \mt{sigOf}(\mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@538 1132 \mt{sigOf}(\mt{open} \; \mt{constraints} \; M) &=& \cdot \\
adamc@538 1133 \mt{sigOf}(\mt{table} \; x : c) &=& \mt{table} \; x : c \\
adamc@784 1134 \mt{sigOf}(\mt{view} \; x : c) &=& \mt{view} \; x : c \\
adamc@538 1135 \mt{sigOf}(\mt{sequence} \; x) &=& \mt{sequence} \; x \\
adamc@538 1136 \mt{sigOf}(\mt{cookie} \; x : \tau) &=& \mt{cookie} \; x : \tau \\
adamc@784 1137 \mt{sigOf}(\mt{style} \; x) &=& \mt{style} \; x \\
adamc@655 1138 \mt{sigOf}(\mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@538 1139 \end{eqnarray*}
adamc@539 1140 \begin{eqnarray*}
adamc@539 1141 \mt{selfify}(M, \cdot) &=& \cdot \\
adamc@558 1142 \mt{selfify}(M, s \; \overline{s'}) &=& \mt{selfify}(M, s) \; \mt{selfify}(M, \overline{s'}) \\
adamc@539 1143 \\
adamc@539 1144 \mt{selfify}(M, \mt{con} \; x :: \kappa) &=& \mt{con} \; x :: \kappa = M.x \\
adamc@539 1145 \mt{selfify}(M, \mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@539 1146 \mt{selfify}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \mt{datatype} \; M.x \\
adamc@539 1147 \mt{selfify}(M, \mt{datatype} \; x = \mt{datatype} \; M'.z) &=& \mt{datatype} \; x = \mt{datatype} \; M'.z \\
adamc@539 1148 \mt{selfify}(M, \mt{val} \; x : \tau) &=& \mt{val} \; x : \tau \\
adamc@539 1149 \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 1150 \mt{selfify}(M, \mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@539 1151 \mt{selfify}(M, \mt{include} \; S) &=& \mt{include} \; S \\
adamc@539 1152 \mt{selfify}(M, \mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@655 1153 \mt{selfify}(M, \mt{class} \; x :: \kappa) &=& \mt{class} \; x :: \kappa = M.x \\
adamc@655 1154 \mt{selfify}(M, \mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@539 1155 \end{eqnarray*}
adamc@539 1156
adamc@540 1157 \subsection{Module Projection}
adamc@540 1158
adamc@540 1159 \begin{eqnarray*}
adamc@540 1160 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \\
adamc@540 1161 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa, c) \\
adamc@540 1162 \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 1163 \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 1164 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})$)} \\
adamc@655 1165 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \to \mt{Type} \\
adamc@655 1166 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa \to \mt{Type}, c) \\
adamc@540 1167 \\
adamc@540 1168 \mt{proj}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc} \; \overline{s}, \mt{datatype} \; x) &=& (\overline{y}, \overline{dc}) \\
adamc@540 1169 \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 1170 \\
adamc@540 1171 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, \mt{val} \; x) &=& \tau \\
adamc@540 1172 \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 1173 \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 1174 \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 1175 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \in \overline{dc}$)} \\
adamc@540 1176 \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 1177 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \; \mt{of} \; \tau \in \overline{dc}$)} \\
adamc@540 1178 \\
adamc@540 1179 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, \mt{structure} \; X) &=& S \\
adamc@540 1180 \\
adamc@540 1181 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, \mt{signature} \; X) &=& S \\
adamc@540 1182 \\
adamc@540 1183 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1184 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1185 \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 1186 \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 1187 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@540 1188 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1189 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1190 \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 1191 \mt{proj}(M, \mt{constraint} \; c_1 \sim c_2 \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@655 1192 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@655 1193 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1194 \end{eqnarray*}
adamc@540 1195
adamc@541 1196
adamc@541 1197 \section{Type Inference}
adamc@541 1198
adamc@541 1199 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 1200
adamc@541 1201 \subsection{Basic Unification}
adamc@541 1202
adamc@560 1203 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 1204
adamc@656 1205 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 1206
adamc@541 1207 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 1208
adamc@541 1209 \subsection{Unifying Record Types}
adamc@541 1210
adamc@570 1211 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 1212
adamc@656 1213 \subsection{\label{typeclasses}Constructor Classes}
adamc@541 1214
adamc@784 1215 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 1216
adamc@784 1217 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 1218
adamc@656 1219 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 1220
adamc@656 1221 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 1222
adamc@541 1223 \subsection{Reverse-Engineering Record Types}
adamc@541 1224
adamc@656 1225 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 1226
adamc@541 1227 \subsection{Implicit Arguments in Functor Applications}
adamc@541 1228
adamc@656 1229 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 1230
adamc@541 1231
adamc@542 1232 \section{The Ur Standard Library}
adamc@542 1233
adamc@542 1234 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 1235
adamc@542 1236 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 1237
adamc@542 1238 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 1239 $$\begin{array}{l}
adamc@542 1240 \mt{type} \; \mt{int} \\
adamc@542 1241 \mt{type} \; \mt{float} \\
adamc@873 1242 \mt{type} \; \mt{char} \\
adamc@542 1243 \mt{type} \; \mt{string} \\
adamc@542 1244 \mt{type} \; \mt{time} \\
adamc@785 1245 \mt{type} \; \mt{blob} \\
adamc@542 1246 \\
adamc@542 1247 \mt{type} \; \mt{unit} = \{\} \\
adamc@542 1248 \\
adamc@542 1249 \mt{datatype} \; \mt{bool} = \mt{False} \mid \mt{True} \\
adamc@542 1250 \\
adamc@785 1251 \mt{datatype} \; \mt{option} \; \mt{t} = \mt{None} \mid \mt{Some} \; \mt{of} \; \mt{t} \\
adamc@785 1252 \\
adamc@785 1253 \mt{datatype} \; \mt{list} \; \mt{t} = \mt{Nil} \mid \mt{Cons} \; \mt{of} \; \mt{t} \times \mt{list} \; \mt{t}
adamc@542 1254 \end{array}$$
adamc@542 1255
adamc@1123 1256 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 1257
adamc@657 1258 Another important generic Ur element comes at the beginning of \texttt{top.urs}.
adamc@657 1259
adamc@657 1260 $$\begin{array}{l}
adamc@657 1261 \mt{con} \; \mt{folder} :: \mt{K} \longrightarrow \{\mt{K}\} \to \mt{Type} \\
adamc@657 1262 \\
adamc@657 1263 \mt{val} \; \mt{fold} : \mt{K} \longrightarrow \mt{tf} :: (\{\mt{K}\} \to \mt{Type}) \\
adamc@657 1264 \hspace{.1in} \to (\mt{nm} :: \mt{Name} \to \mt{v} :: \mt{K} \to \mt{r} :: \{\mt{K}\} \to [[\mt{nm}] \sim \mt{r}] \Rightarrow \\
adamc@657 1265 \hspace{.2in} \mt{tf} \; \mt{r} \to \mt{tf} \; ([\mt{nm} = \mt{v}] \rc \mt{r})) \\
adamc@657 1266 \hspace{.1in} \to \mt{tf} \; [] \\
adamc@657 1267 \hspace{.1in} \to \mt{r} :: \{\mt{K}\} \to \mt{folder} \; \mt{r} \to \mt{tf} \; \mt{r}
adamc@657 1268 \end{array}$$
adamc@657 1269
adamc@657 1270 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 1271
adamc@664 1272 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 1273
adamc@542 1274
adamc@542 1275 \section{The Ur/Web Standard Library}
adamc@542 1276
adamc@658 1277 \subsection{Monads}
adamc@658 1278
adamc@658 1279 The Ur Basis defines the monad constructor class from Haskell.
adamc@658 1280
adamc@658 1281 $$\begin{array}{l}
adamc@658 1282 \mt{class} \; \mt{monad} :: \mt{Type} \to \mt{Type} \\
adamc@658 1283 \mt{val} \; \mt{return} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t} ::: \mt{Type} \\
adamc@658 1284 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658 1285 \hspace{.1in} \to \mt{t} \to \mt{m} \; \mt{t} \\
adamc@658 1286 \mt{val} \; \mt{bind} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t1} ::: \mt{Type} \to \mt{t2} ::: \mt{Type} \\
adamc@658 1287 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658 1288 \hspace{.1in} \to \mt{m} \; \mt{t1} \to (\mt{t1} \to \mt{m} \; \mt{t2}) \\
adamc@658 1289 \hspace{.1in} \to \mt{m} \; \mt{t2}
adamc@658 1290 \end{array}$$
adamc@658 1291
adamc@542 1292 \subsection{Transactions}
adamc@542 1293
adamc@542 1294 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 1295 $$\begin{array}{l}
adamc@542 1296 \mt{con} \; \mt{transaction} :: \mt{Type} \to \mt{Type} \\
adamc@658 1297 \mt{val} \; \mt{transaction\_monad} : \mt{monad} \; \mt{transaction}
adamc@542 1298 \end{array}$$
adamc@542 1299
adamc@1123 1300 For debugging purposes, a transactional function is provided for outputting a string on the server process' \texttt{stderr}.
adamc@1123 1301 $$\begin{array}{l}
adamc@1123 1302 \mt{val} \; \mt{debug} : \mt{string} \to \mt{transaction} \; \mt{unit}
adamc@1123 1303 \end{array}$$
adamc@1123 1304
adamc@542 1305 \subsection{HTTP}
adamc@542 1306
adamc@542 1307 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 1308 $$\begin{array}{l}
adamc@786 1309 \mt{val} \; \mt{requestHeader} : \mt{string} \to \mt{transaction} \; (\mt{option} \; \mt{string}) \\
adamc@786 1310 \\
adamc@786 1311 \mt{con} \; \mt{http\_cookie} :: \mt{Type} \to \mt{Type} \\
adamc@786 1312 \mt{val} \; \mt{getCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; (\mt{option} \; \mt{t}) \\
adamc@1050 1313 \mt{val} \; \mt{setCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \{\mt{Value} : \mt{t}, \mt{Expires} : \mt{option} \; \mt{time}, \mt{Secure} : \mt{bool}\} \to \mt{transaction} \; \mt{unit} \\
adamc@1050 1314 \mt{val} \; \mt{clearCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; \mt{unit}
adamc@786 1315 \end{array}$$
adamc@786 1316
adamc@786 1317 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 1318 $$\begin{array}{l}
adamc@786 1319 \mt{type} \; \mt{url} \\
adamc@786 1320 \mt{val} \; \mt{bless} : \mt{string} \to \mt{url} \\
adamc@786 1321 \mt{val} \; \mt{checkUrl} : \mt{string} \to \mt{option} \; \mt{url}
adamc@786 1322 \end{array}$$
adamc@786 1323 $\mt{bless}$ raises a runtime error if the string passed to it fails the URL policy.
adamc@786 1324
adamc@1085 1325 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 1326 $$\begin{array}{l}
adamc@1085 1327 \mt{val} \; \mt{currentUrl} : \mt{transaction} \; \mt{url} \\
adamc@1085 1328 \mt{val} \; \mt{url} : \mt{transaction} \; \mt{page} \to \mt{url}
adamc@1085 1329 \end{array}$$
adamc@1085 1330
adamc@1085 1331 Page generation may be interrupted at any time with a request to redirect to a particular URL instead.
adamc@1085 1332 $$\begin{array}{l}
adamc@1085 1333 \mt{val} \; \mt{redirect} : \mt{t} ::: \mt{Type} \to \mt{url} \to \mt{transaction} \; \mt{t}
adamc@1085 1334 \end{array}$$
adamc@1085 1335
adamc@786 1336 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 1337 $$\begin{array}{l}
adamc@786 1338 \mt{type} \; \mt{file} \\
adamc@786 1339 \mt{val} \; \mt{fileName} : \mt{file} \to \mt{option} \; \mt{string} \\
adamc@786 1340 \mt{val} \; \mt{fileMimeType} : \mt{file} \to \mt{string} \\
adamc@786 1341 \mt{val} \; \mt{fileData} : \mt{file} \to \mt{blob}
adamc@786 1342 \end{array}$$
adamc@786 1343
adamc@786 1344 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 1345 $$\begin{array}{l}
adamc@786 1346 \mt{type} \; \mt{mimeType} \\
adamc@786 1347 \mt{val} \; \mt{blessMime} : \mt{string} \to \mt{mimeType} \\
adamc@786 1348 \mt{val} \; \mt{checkMime} : \mt{string} \to \mt{option} \; \mt{mimeType} \\
adamc@786 1349 \mt{val} \; \mt{returnBlob} : \mt{t} ::: \mt{Type} \to \mt{blob} \to \mt{mimeType} \to \mt{transaction} \; \mt{t}
adamc@542 1350 \end{array}$$
adamc@542 1351
adamc@543 1352 \subsection{SQL}
adamc@543 1353
adamc@543 1354 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 1355 $$\begin{array}{l}
adamc@785 1356 \mt{con} \; \mt{sql\_table} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785 1357 \end{array}$$
adamc@785 1358 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 1359
adamc@785 1360 We also have the simpler type family of SQL views, which have no keys.
adamc@785 1361 $$\begin{array}{l}
adamc@785 1362 \mt{con} \; \mt{sql\_view} :: \{\mt{Type}\} \to \mt{Type}
adamc@543 1363 \end{array}$$
adamc@543 1364
adamc@785 1365 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 1366 $$\begin{array}{l}
adamc@785 1367 \mt{class} \; \mt{fieldsOf} :: \mt{Type} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1368 \mt{val} \; \mt{fieldsOf\_table} : \mt{fs} ::: \{\mt{Type}\} \to \mt{keys} ::: \{\{\mt{Unit}\}\} \to \mt{fieldsOf} \; (\mt{sql\_table} \; \mt{fs} \; \mt{keys}) \; \mt{fs} \\
adamc@785 1369 \mt{val} \; \mt{fieldsOf\_view} : \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; (\mt{sql\_view} \; \mt{fs}) \; \mt{fs}
adamc@785 1370 \end{array}$$
adamc@785 1371
adamc@785 1372 \subsubsection{Table Constraints}
adamc@785 1373
adamc@785 1374 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 1375
adamc@785 1376 $$\begin{array}{l}
adamc@785 1377 \mt{con} \; \mt{primary\_key} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type} \\
adamc@785 1378 \mt{val} \; \mt{no\_primary\_key} : \mt{fs} ::: \{\mt{Type}\} \to \mt{primary\_key} \; \mt{fs} \; [] \\
adamc@785 1379 \mt{val} \; \mt{primary\_key} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{key1} :: \mt{Name} \to \mt{keys} :: \{\mt{Type}\} \\
adamc@785 1380 \hspace{.1in} \to [[\mt{key1}] \sim \mt{keys}] \Rightarrow [[\mt{key1} = \mt{t}] \rc \mt{keys} \sim \mt{rest}] \\
adamc@785 1381 \hspace{.1in} \Rightarrow \$([\mt{key1} = \mt{sql\_injectable\_prim} \; \mt{t}] \rc \mt{map} \; \mt{sql\_injectable\_prim} \; \mt{keys}) \\
adamc@785 1382 \hspace{.1in} \to \mt{primary\_key} \; ([\mt{key1} = \mt{t}] \rc \mt{keys} \rc \mt{rest}) \; [\mt{Pkey} = [\mt{key1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{keys}]
adamc@785 1383 \end{array}$$
adamc@785 1384 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 1385
adamc@785 1386 A type family stands for sets of named constraints of the remaining varieties.
adamc@785 1387 $$\begin{array}{l}
adamc@785 1388 \mt{con} \; \mt{sql\_constraints} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785 1389 \end{array}$$
adamc@785 1390 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 1391
adamc@785 1392 There is a type family of individual, unnamed constraints.
adamc@785 1393 $$\begin{array}{l}
adamc@785 1394 \mt{con} \; \mt{sql\_constraint} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \mt{Type}
adamc@785 1395 \end{array}$$
adamc@785 1396 The first argument is the same as above, and the second argument gives the key columns for just this constraint.
adamc@785 1397
adamc@785 1398 We have operations for assembling constraints into constraint sets.
adamc@785 1399 $$\begin{array}{l}
adamc@785 1400 \mt{val} \; \mt{no\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_constraints} \; \mt{fs} \; [] \\
adamc@785 1401 \mt{val} \; \mt{one\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{unique} ::: \{\mt{Unit}\} \to \mt{name} :: \mt{Name} \\
adamc@785 1402 \hspace{.1in} \to \mt{sql\_constraint} \; \mt{fs} \; \mt{unique} \to \mt{sql\_constraints} \; \mt{fs} \; [\mt{name} = \mt{unique}] \\
adamc@785 1403 \mt{val} \; \mt{join\_constraints} : \mt{fs} ::: \{\mt{Type}\} \to \mt{uniques1} ::: \{\{\mt{Unit}\}\} \to \mt{uniques2} ::: \{\{\mt{Unit}\}\} \to [\mt{uniques1} \sim \mt{uniques2}] \\
adamc@785 1404 \hspace{.1in} \Rightarrow \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques1} \to \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques2} \to \mt{sql\_constraints} \; \mt{fs} \; (\mt{uniques1} \rc \mt{uniques2})
adamc@785 1405 \end{array}$$
adamc@785 1406
adamc@785 1407 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 1408 $$\begin{array}{l}
adamc@785 1409 \mt{val} \; \mt{unique} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{unique1} :: \mt{Name} \to \mt{unique} :: \{\mt{Type}\} \\
adamc@785 1410 \hspace{.1in} \to [[\mt{unique1}] \sim \mt{unique}] \Rightarrow [[\mt{unique1} = \mt{t}] \rc \mt{unique} \sim \mt{rest}] \\
adamc@785 1411 \hspace{.1in} \Rightarrow \mt{sql\_constraint} \; ([\mt{unique1} = \mt{t}] \rc \mt{unique} \rc \mt{rest}) \; ([\mt{unique1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{unique})
adamc@785 1412 \end{array}$$
adamc@785 1413
adamc@785 1414 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 1415 $$\begin{array}{l}
adamc@785 1416 \mt{class} \; \mt{linkable} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@785 1417 \mt{val} \; \mt{linkable\_same} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; \mt{t} \\
adamc@785 1418 \mt{val} \; \mt{linkable\_from\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; (\mt{option} \; \mt{t}) \; \mt{t} \\
adamc@785 1419 \mt{val} \; \mt{linkable\_to\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@785 1420 \end{array}$$
adamc@785 1421
adamc@785 1422 The $\mt{matching}$ type family uses $\mt{linkable}$ to define when two keys match up type-wise.
adamc@785 1423 $$\begin{array}{l}
adamc@785 1424 \mt{con} \; \mt{matching} :: \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1425 \mt{val} \; \mt{mat\_nil} : \mt{matching} \; [] \; [] \\
adamc@785 1426 \mt{val} \; \mt{mat\_cons} : \mt{t1} ::: \mt{Type} \to \mt{rest1} ::: \{\mt{Type}\} \to \mt{t2} ::: \mt{Type} \to \mt{rest2} ::: \{\mt{Type}\} \to \mt{nm1} :: \mt{Name} \to \mt{nm2} :: \mt{Name} \\
adamc@785 1427 \hspace{.1in} \to [[\mt{nm1}] \sim \mt{rest1}] \Rightarrow [[\mt{nm2}] \sim \mt{rest2}] \Rightarrow \mt{linkable} \; \mt{t1} \; \mt{t2} \to \mt{matching} \; \mt{rest1} \; \mt{rest2} \\
adamc@785 1428 \hspace{.1in} \to \mt{matching} \; ([\mt{nm1} = \mt{t1}] \rc \mt{rest1}) \; ([\mt{nm2} = \mt{t2}] \rc \mt{rest2})
adamc@785 1429 \end{array}$$
adamc@785 1430
adamc@785 1431 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 1432 $$\begin{array}{l}
adamc@785 1433 \mt{con} \; \mt{propagation\_mode} :: \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1434 \mt{val} \; \mt{restrict} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1435 \mt{val} \; \mt{cascade} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1436 \mt{val} \; \mt{no\_action} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1437 \mt{val} \; \mt{set\_null} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; (\mt{map} \; \mt{option} \; \mt{fs})
adamc@785 1438 \end{array}$$
adamc@785 1439
adamc@785 1440 Finally, we put these ingredient together to define the \texttt{FOREIGN KEY} constraint function.
adamc@785 1441 $$\begin{array}{l}
adamc@785 1442 \mt{val} \; \mt{foreign\_key} : \mt{mine1} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{mine} ::: \{\mt{Type}\} \to \mt{munused} ::: \{\mt{Type}\} \to \mt{foreign} ::: \{\mt{Type}\} \\
adamc@785 1443 \hspace{.1in} \to \mt{funused} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{uniques} ::: \{\{\mt{Unit}\}\} \\
adamc@785 1444 \hspace{.1in} \to [[\mt{mine1}] \sim \mt{mine}] \Rightarrow [[\mt{mine1} = \mt{t}] \rc \mt{mine} \sim \mt{munused}] \Rightarrow [\mt{foreign} \sim \mt{funused}] \Rightarrow [[\mt{nm}] \sim \mt{uniques}] \\
adamc@785 1445 \hspace{.1in} \Rightarrow \mt{matching} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}) \; \mt{foreign} \\
adamc@785 1446 \hspace{.1in} \to \mt{sql\_table} \; (\mt{foreign} \rc \mt{funused}) \; ([\mt{nm} = \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{foreign}] \rc \mt{uniques}) \\
adamc@785 1447 \hspace{.1in} \to \{\mt{OnDelete} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}), \\
adamc@785 1448 \hspace{.2in} \mt{OnUpdate} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine})\} \\
adamc@785 1449 \hspace{.1in} \to \mt{sql\_constraint} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine} \rc \mt{munused}) \; []
adamc@785 1450 \end{array}$$
adamc@785 1451
adamc@785 1452 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 1453 $$\begin{array}{l}
adamc@785 1454 \mt{val} \; \mt{check} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; [] \; [] \; \mt{fs} \; \mt{bool} \to \mt{sql\_constraint} \; \mt{fs} \; []
adamc@785 1455 \end{array}$$
adamc@785 1456
adamc@785 1457 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 1458
adamc@784 1459
adamc@543 1460 \subsubsection{Queries}
adamc@543 1461
adamc@543 1462 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 1463 $$\begin{array}{l}
adamc@543 1464 \mt{con} \; \mt{sql\_query} :: \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@543 1465 \mt{val} \; \mt{sql\_query} : \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543 1466 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1467 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@543 1468 \hspace{.1in} \to \{\mt{Rows} : \mt{sql\_query1} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}, \\
adamc@543 1469 \hspace{.2in} \mt{OrderBy} : \mt{sql\_order\_by} \; \mt{tables} \; \mt{selectedExps}, \\
adamc@543 1470 \hspace{.2in} \mt{Limit} : \mt{sql\_limit}, \\
adamc@543 1471 \hspace{.2in} \mt{Offset} : \mt{sql\_offset}\} \\
adamc@543 1472 \hspace{.1in} \to \mt{sql\_query} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1473 \end{array}$$
adamc@543 1474
adamc@545 1475 Queries are used by folding over their results inside transactions.
adamc@545 1476 $$\begin{array}{l}
adamc@545 1477 \mt{val} \; \mt{query} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \lambda [\mt{tables} \sim \mt{exps}] \Rightarrow \mt{state} ::: \mt{Type} \to \mt{sql\_query} \; \mt{tables} \; \mt{exps} \\
adamc@658 1478 \hspace{.1in} \to (\$(\mt{exps} \rc \mt{map} \; (\lambda \mt{fields} :: \{\mt{Type}\} \Rightarrow \$\mt{fields}) \; \mt{tables}) \\
adamc@545 1479 \hspace{.2in} \to \mt{state} \to \mt{transaction} \; \mt{state}) \\
adamc@545 1480 \hspace{.1in} \to \mt{state} \to \mt{transaction} \; \mt{state}
adamc@545 1481 \end{array}$$
adamc@545 1482
adamc@543 1483 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 1484 $$\begin{array}{l}
adamc@543 1485 \mt{con} \; \mt{sql\_query1} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@543 1486 \\
adamc@543 1487 \mt{type} \; \mt{sql\_relop} \\
adamc@543 1488 \mt{val} \; \mt{sql\_union} : \mt{sql\_relop} \\
adamc@543 1489 \mt{val} \; \mt{sql\_intersect} : \mt{sql\_relop} \\
adamc@543 1490 \mt{val} \; \mt{sql\_except} : \mt{sql\_relop} \\
adamc@543 1491 \mt{val} \; \mt{sql\_relop} : \mt{tables1} ::: \{\{\mt{Type}\}\} \\
adamc@543 1492 \hspace{.1in} \to \mt{tables2} ::: \{\{\mt{Type}\}\} \\
adamc@543 1493 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1494 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@543 1495 \hspace{.1in} \to \mt{sql\_relop} \\
adamc@543 1496 \hspace{.1in} \to \mt{sql\_query1} \; \mt{tables1} \; \mt{selectedFields} \; \mt{selectedExps} \\
adamc@543 1497 \hspace{.1in} \to \mt{sql\_query1} \; \mt{tables2} \; \mt{selectedFields} \; \mt{selectedExps} \\
adamc@543 1498 \hspace{.1in} \to \mt{sql\_query1} \; \mt{selectedFields} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1499 \end{array}$$
adamc@543 1500
adamc@543 1501 $$\begin{array}{l}
adamc@543 1502 \mt{val} \; \mt{sql\_query1} : \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543 1503 \hspace{.1in} \to \mt{grouped} ::: \{\{\mt{Type}\}\} \\
adamc@543 1504 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1505 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1085 1506 \hspace{.1in} \to \mt{empties} :: \{\mt{Unit}\} \\
adamc@1085 1507 \hspace{.1in} \to [\mt{empties} \sim \mt{selectedFields}] \\
adamc@1085 1508 \hspace{.1in} \Rightarrow \{\mt{Distinct} : \mt{bool}, \\
adamc@994 1509 \hspace{.2in} \mt{From} : \mt{sql\_from\_items} \; \mt{tables}, \\
adamc@543 1510 \hspace{.2in} \mt{Where} : \mt{sql\_exp} \; \mt{tables} \; [] \; [] \; \mt{bool}, \\
adamc@543 1511 \hspace{.2in} \mt{GroupBy} : \mt{sql\_subset} \; \mt{tables} \; \mt{grouped}, \\
adamc@543 1512 \hspace{.2in} \mt{Having} : \mt{sql\_exp} \; \mt{grouped} \; \mt{tables} \; [] \; \mt{bool}, \\
adamc@1085 1513 \hspace{.2in} \mt{SelectFields} : \mt{sql\_subset} \; \mt{grouped} \; (\mt{map} \; (\lambda \_ \Rightarrow []) \; \mt{empties} \rc \mt{selectedFields}), \\
adamc@658 1514 \hspace{.2in} \mt {SelectExps} : \$(\mt{map} \; (\mt{sql\_exp} \; \mt{grouped} \; \mt{tables} \; []) \; \mt{selectedExps}) \} \\
adamc@543 1515 \hspace{.1in} \to \mt{sql\_query1} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1516 \end{array}$$
adamc@543 1517
adamc@543 1518 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 1519 $$\begin{array}{l}
adamc@543 1520 \mt{con} \; \mt{sql\_subset} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@543 1521 \mt{val} \; \mt{sql\_subset} : \mt{keep\_drop} :: \{(\{\mt{Type}\} \times \{\mt{Type}\})\} \\
adamc@543 1522 \hspace{.1in} \to \mt{sql\_subset} \\
adamc@658 1523 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1 \rc \mt{fields}.2)\; \mt{keep\_drop}) \\
adamc@658 1524 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1) \; \mt{keep\_drop}) \\
adamc@543 1525 \mt{val} \; \mt{sql\_subset\_all} : \mt{tables} :: \{\{\mt{Type}\}\} \to \mt{sql\_subset} \; \mt{tables} \; \mt{tables}
adamc@543 1526 \end{array}$$
adamc@543 1527
adamc@560 1528 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 1529 $$\begin{array}{l}
adamc@543 1530 \mt{con} \; \mt{sql\_exp} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}
adamc@543 1531 \end{array}$$
adamc@543 1532
adamc@543 1533 Any field in scope may be converted to an expression.
adamc@543 1534 $$\begin{array}{l}
adamc@543 1535 \mt{val} \; \mt{sql\_field} : \mt{otherTabs} ::: \{\{\mt{Type}\}\} \to \mt{otherFields} ::: \{\mt{Type}\} \\
adamc@543 1536 \hspace{.1in} \to \mt{fieldType} ::: \mt{Type} \to \mt{agg} ::: \{\{\mt{Type}\}\} \\
adamc@543 1537 \hspace{.1in} \to \mt{exps} ::: \{\mt{Type}\} \\
adamc@543 1538 \hspace{.1in} \to \mt{tab} :: \mt{Name} \to \mt{field} :: \mt{Name} \\
adamc@543 1539 \hspace{.1in} \to \mt{sql\_exp} \; ([\mt{tab} = [\mt{field} = \mt{fieldType}] \rc \mt{otherFields}] \rc \mt{otherTabs}) \; \mt{agg} \; \mt{exps} \; \mt{fieldType}
adamc@543 1540 \end{array}$$
adamc@543 1541
adamc@544 1542 There is an analogous function for referencing named expressions.
adamc@544 1543 $$\begin{array}{l}
adamc@544 1544 \mt{val} \; \mt{sql\_exp} : \mt{tabs} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{t} ::: \mt{Type} \to \mt{rest} ::: \{\mt{Type}\} \to \mt{nm} :: \mt{Name} \\
adamc@544 1545 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tabs} \; \mt{agg} \; ([\mt{nm} = \mt{t}] \rc \mt{rest}) \; \mt{t}
adamc@544 1546 \end{array}$$
adamc@544 1547
adamc@544 1548 Ur values of appropriate types may be injected into SQL expressions.
adamc@544 1549 $$\begin{array}{l}
adamc@786 1550 \mt{class} \; \mt{sql\_injectable\_prim} \\
adamc@786 1551 \mt{val} \; \mt{sql\_bool} : \mt{sql\_injectable\_prim} \; \mt{bool} \\
adamc@786 1552 \mt{val} \; \mt{sql\_int} : \mt{sql\_injectable\_prim} \; \mt{int} \\
adamc@786 1553 \mt{val} \; \mt{sql\_float} : \mt{sql\_injectable\_prim} \; \mt{float} \\
adamc@786 1554 \mt{val} \; \mt{sql\_string} : \mt{sql\_injectable\_prim} \; \mt{string} \\
adamc@786 1555 \mt{val} \; \mt{sql\_time} : \mt{sql\_injectable\_prim} \; \mt{time} \\
adamc@786 1556 \mt{val} \; \mt{sql\_blob} : \mt{sql\_injectable\_prim} \; \mt{blob} \\
adamc@786 1557 \mt{val} \; \mt{sql\_channel} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{channel} \; \mt{t}) \\
adamc@786 1558 \mt{val} \; \mt{sql\_client} : \mt{sql\_injectable\_prim} \; \mt{client} \\
adamc@786 1559 \\
adamc@544 1560 \mt{class} \; \mt{sql\_injectable} \\
adamc@786 1561 \mt{val} \; \mt{sql\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@786 1562 \mt{val} \; \mt{sql\_option\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; (\mt{option} \; \mt{t}) \\
adamc@786 1563 \\
adamc@544 1564 \mt{val} \; \mt{sql\_inject} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@544 1565 \hspace{.1in} \to \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adamc@544 1566 \end{array}$$
adamc@544 1567
adamc@1123 1568 Additionally, most function-free types may be injected safely, via the $\mt{serialized}$ type family.
adamc@1123 1569 $$\begin{array}{l}
adamc@1123 1570 \mt{con} \; \mt{serialized} :: \mt{Type} \to \mt{Type} \\
adamc@1123 1571 \mt{val} \; \mt{serialize} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{serialized} \; \mt{t} \\
adamc@1123 1572 \mt{val} \; \mt{deserialize} : \mt{t} ::: \mt{Type} \to \mt{serialized} \; \mt{t} \to \mt{t} \\
adamc@1123 1573 \mt{val} \; \mt{sql\_serialized} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{serialized} \; \mt{t})
adamc@1123 1574 \end{array}$$
adamc@1123 1575
adamc@544 1576 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 1577 $$\begin{array}{l}
adamc@544 1578 \mt{val} \; \mt{sql\_is\_null} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544 1579 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; (\mt{option} \; \mt{t}) \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{bool}
adamc@544 1580 \end{array}$$
adamc@544 1581
adamc@559 1582 We have generic nullary, unary, and binary operators.
adamc@544 1583 $$\begin{array}{l}
adamc@544 1584 \mt{con} \; \mt{sql\_nfunc} :: \mt{Type} \to \mt{Type} \\
adamc@544 1585 \mt{val} \; \mt{sql\_current\_timestamp} : \mt{sql\_nfunc} \; \mt{time} \\
adamc@544 1586 \mt{val} \; \mt{sql\_nfunc} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544 1587 \hspace{.1in} \to \mt{sql\_nfunc} \; \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\\end{array}$$
adamc@544 1588
adamc@544 1589 $$\begin{array}{l}
adamc@544 1590 \mt{con} \; \mt{sql\_unary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544 1591 \mt{val} \; \mt{sql\_not} : \mt{sql\_unary} \; \mt{bool} \; \mt{bool} \\
adamc@544 1592 \mt{val} \; \mt{sql\_unary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adamc@544 1593 \hspace{.1in} \to \mt{sql\_unary} \; \mt{arg} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res} \\
adamc@544 1594 \end{array}$$
adamc@544 1595
adamc@544 1596 $$\begin{array}{l}
adamc@544 1597 \mt{con} \; \mt{sql\_binary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544 1598 \mt{val} \; \mt{sql\_and} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544 1599 \mt{val} \; \mt{sql\_or} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544 1600 \mt{val} \; \mt{sql\_binary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg_1} ::: \mt{Type} \to \mt{arg_2} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adamc@544 1601 \hspace{.1in} \to \mt{sql\_binary} \; \mt{arg_1} \; \mt{arg_2} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_1} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_2} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res}
adamc@544 1602 \end{array}$$
adamc@544 1603
adamc@544 1604 $$\begin{array}{l}
adamc@559 1605 \mt{class} \; \mt{sql\_arith} \\
adamc@559 1606 \mt{val} \; \mt{sql\_int\_arith} : \mt{sql\_arith} \; \mt{int} \\
adamc@559 1607 \mt{val} \; \mt{sql\_float\_arith} : \mt{sql\_arith} \; \mt{float} \\
adamc@559 1608 \mt{val} \; \mt{sql\_neg} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_unary} \; \mt{t} \; \mt{t} \\
adamc@559 1609 \mt{val} \; \mt{sql\_plus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1610 \mt{val} \; \mt{sql\_minus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1611 \mt{val} \; \mt{sql\_times} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1612 \mt{val} \; \mt{sql\_div} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1613 \mt{val} \; \mt{sql\_mod} : \mt{sql\_binary} \; \mt{int} \; \mt{int} \; \mt{int}
adamc@559 1614 \end{array}$$
adamc@544 1615
adamc@656 1616 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 1617 $$\begin{array}{l}
adamc@544 1618 \mt{val} \; \mt{sql\_count} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int}
adamc@544 1619 \end{array}$$
adamc@544 1620
adamc@544 1621 $$\begin{array}{l}
adamc@544 1622 \mt{con} \; \mt{sql\_aggregate} :: \mt{Type} \to \mt{Type} \\
adamc@544 1623 \mt{val} \; \mt{sql\_aggregate} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544 1624 \hspace{.1in} \to \mt{sql\_aggregate} \; \mt{t} \to \mt{sql\_exp} \; \mt{agg} \; \mt{agg} \; \mt{exps} \; \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adamc@544 1625 \end{array}$$
adamc@544 1626
adamc@544 1627 $$\begin{array}{l}
adamc@544 1628 \mt{class} \; \mt{sql\_summable} \\
adamc@544 1629 \mt{val} \; \mt{sql\_summable\_int} : \mt{sql\_summable} \; \mt{int} \\
adamc@544 1630 \mt{val} \; \mt{sql\_summable\_float} : \mt{sql\_summable} \; \mt{float} \\
adamc@544 1631 \mt{val} \; \mt{sql\_avg} : \mt{t} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{sql\_aggregate} \; \mt{t} \\
adamc@544 1632 \mt{val} \; \mt{sql\_sum} : \mt{t} ::: \mt{Type} \to \mt{sql\_summable} \mt{t} \to \mt{sql\_aggregate} \; \mt{t}
adamc@544 1633 \end{array}$$
adamc@544 1634
adamc@544 1635 $$\begin{array}{l}
adamc@544 1636 \mt{class} \; \mt{sql\_maxable} \\
adamc@544 1637 \mt{val} \; \mt{sql\_maxable\_int} : \mt{sql\_maxable} \; \mt{int} \\
adamc@544 1638 \mt{val} \; \mt{sql\_maxable\_float} : \mt{sql\_maxable} \; \mt{float} \\
adamc@544 1639 \mt{val} \; \mt{sql\_maxable\_string} : \mt{sql\_maxable} \; \mt{string} \\
adamc@544 1640 \mt{val} \; \mt{sql\_maxable\_time} : \mt{sql\_maxable} \; \mt{time} \\
adamc@544 1641 \mt{val} \; \mt{sql\_max} : \mt{t} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{sql\_aggregate} \; \mt{t} \\
adamc@544 1642 \mt{val} \; \mt{sql\_min} : \mt{t} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{sql\_aggregate} \; \mt{t}
adamc@544 1643 \end{array}$$
adamc@544 1644
adamc@786 1645 \texttt{FROM} clauses are specified using a type family.
adamc@786 1646 $$\begin{array}{l}
adamc@786 1647 \mt{con} \; \mt{sql\_from\_items} :: \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@786 1648 \mt{val} \; \mt{sql\_from\_table} : \mt{t} ::: \mt{Type} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; \mt{t} \; \mt{fs} \to \mt{name} :: \mt{Name} \to \mt{t} \to \mt{sql\_from\_items} \; [\mt{name} = \mt{fs}] \\
adamc@786 1649 \mt{val} \; \mt{sql\_from\_comma} : \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \to [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@786 1650 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{tabs2} \\
adamc@786 1651 \hspace{.1in} \to \mt{sql\_from\_items} \; (\mt{tabs1} \rc \mt{tabs2}) \\
adamc@786 1652 \mt{val} \; \mt{sql\_inner\_join} : \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \to [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@786 1653 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{tabs2} \\
adamc@786 1654 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{tabs1} \rc \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@786 1655 \hspace{.1in} \to \mt{sql\_from\_items} \; (\mt{tabs1} \rc \mt{tabs2})
adamc@786 1656 \end{array}$$
adamc@786 1657
adamc@786 1658 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 1659 $$\begin{array}{l}
adamc@786 1660 \mt{class} \; \mt{nullify} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@786 1661 \mt{val} \; \mt{nullify\_option} : \mt{t} ::: \mt{Type} \to \mt{nullify} \; (\mt{option} \; \mt{t}) \; (\mt{option} \; \mt{t}) \\
adamc@786 1662 \mt{val} \; \mt{nullify\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{nullify} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@786 1663 \end{array}$$
adamc@786 1664
adamc@786 1665 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 1666
adamc@786 1667 $$\begin{array}{l}
adamc@786 1668 \mt{val} \; \mt{sql\_left\_join} : \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{(\mt{Type} \times \mt{Type})\}\} \to [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@786 1669 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\lambda \mt{r} \Rightarrow \$(\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{nullify} \; \mt{p}.1 \; \mt{p}.2) \; \mt{r})) \; \mt{tabs2}) \\
adamc@786 1670 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{tabs1} \to \mt{sql\_from\_items} \; (\mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \\
adamc@786 1671 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@786 1672 \hspace{.1in} \to \mt{sql\_from\_items} \; (\mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.2)) \; \mt{tabs2})
adamc@786 1673 \end{array}$$
adamc@786 1674
adamc@544 1675 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 1676 $$\begin{array}{l}
adamc@544 1677 \mt{type} \; \mt{sql\_direction} \\
adamc@544 1678 \mt{val} \; \mt{sql\_asc} : \mt{sql\_direction} \\
adamc@544 1679 \mt{val} \; \mt{sql\_desc} : \mt{sql\_direction} \\
adamc@544 1680 \\
adamc@544 1681 \mt{con} \; \mt{sql\_order\_by} :: \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@544 1682 \mt{val} \; \mt{sql\_order\_by\_Nil} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} :: \{\mt{Type}\} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544 1683 \mt{val} \; \mt{sql\_order\_by\_Cons} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544 1684 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; [] \; \mt{exps} \; \mt{t} \to \mt{sql\_direction} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544 1685 \\
adamc@544 1686 \mt{type} \; \mt{sql\_limit} \\
adamc@544 1687 \mt{val} \; \mt{sql\_no\_limit} : \mt{sql\_limit} \\
adamc@544 1688 \mt{val} \; \mt{sql\_limit} : \mt{int} \to \mt{sql\_limit} \\
adamc@544 1689 \\
adamc@544 1690 \mt{type} \; \mt{sql\_offset} \\
adamc@544 1691 \mt{val} \; \mt{sql\_no\_offset} : \mt{sql\_offset} \\
adamc@544 1692 \mt{val} \; \mt{sql\_offset} : \mt{int} \to \mt{sql\_offset}
adamc@544 1693 \end{array}$$
adamc@544 1694
adamc@545 1695
adamc@545 1696 \subsubsection{DML}
adamc@545 1697
adamc@545 1698 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 1699
adamc@545 1700 $$\begin{array}{l}
adamc@545 1701 \mt{type} \; \mt{dml} \\
adamc@545 1702 \mt{val} \; \mt{dml} : \mt{dml} \to \mt{transaction} \; \mt{unit}
adamc@545 1703 \end{array}$$
adamc@545 1704
adamc@545 1705 Properly-typed records may be used to form $\mt{INSERT}$ commands.
adamc@545 1706 $$\begin{array}{l}
adamc@545 1707 \mt{val} \; \mt{insert} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \\
adamc@658 1708 \hspace{.1in} \to \$(\mt{map} \; (\mt{sql\_exp} \; [] \; [] \; []) \; \mt{fields}) \to \mt{dml}
adamc@545 1709 \end{array}$$
adamc@545 1710
adamc@545 1711 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 1712 $$\begin{array}{l}
adamc@545 1713 \mt{val} \; \mt{update} : \mt{unchanged} ::: \{\mt{Type}\} \to \mt{changed} :: \{\mt{Type}\} \to \lambda [\mt{changed} \sim \mt{unchanged}] \\
adamc@658 1714 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; []) \; \mt{changed}) \\
adamc@545 1715 \hspace{.1in} \to \mt{sql\_table} \; (\mt{changed} \rc \mt{unchanged}) \to \mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545 1716 \end{array}$$
adamc@545 1717
adamc@545 1718 A $\mt{DELETE}$ command is formed from a table and a $\mt{WHERE}$ clause.
adamc@545 1719 $$\begin{array}{l}
adamc@545 1720 \mt{val} \; \mt{delete} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \to \mt{sql\_exp} \; [\mt{T} = \mt{fields}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545 1721 \end{array}$$
adamc@545 1722
adamc@546 1723 \subsubsection{Sequences}
adamc@546 1724
adamc@546 1725 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 1726
adamc@546 1727 $$\begin{array}{l}
adamc@546 1728 \mt{type} \; \mt{sql\_sequence} \\
adamc@1085 1729 \mt{val} \; \mt{nextval} : \mt{sql\_sequence} \to \mt{transaction} \; \mt{int} \\
adamc@1085 1730 \mt{val} \; \mt{setval} : \mt{sql\_sequence} \to \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@546 1731 \end{array}$$
adamc@546 1732
adamc@546 1733
adamc@547 1734 \subsection{XML}
adamc@547 1735
adamc@547 1736 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 1737
adamc@547 1738 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 1739 $$\begin{array}{l}
adamc@547 1740 \mt{con} \; \mt{xml} :: \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547 1741 \end{array}$$
adamc@547 1742
adamc@547 1743 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 1744 $$\begin{array}{l}
adamc@547 1745 \mt{con} \; \mt{tag} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547 1746 \end{array}$$
adamc@547 1747
adamc@547 1748 Literal text may be injected into XML as ``CDATA.''
adamc@547 1749 $$\begin{array}{l}
adamc@547 1750 \mt{val} \; \mt{cdata} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{string} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adamc@547 1751 \end{array}$$
adamc@547 1752
adamc@547 1753 There is a function for producing an XML tree with a particular tag at its root.
adamc@547 1754 $$\begin{array}{l}
adamc@547 1755 \mt{val} \; \mt{tag} : \mt{attrsGiven} ::: \{\mt{Type}\} \to \mt{attrsAbsent} ::: \{\mt{Type}\} \to \mt{ctxOuter} ::: \{\mt{Unit}\} \to \mt{ctxInner} ::: \{\mt{Unit}\} \\
adamc@547 1756 \hspace{.1in} \to \mt{useOuter} ::: \{\mt{Type}\} \to \mt{useInner} ::: \{\mt{Type}\} \to \mt{bindOuter} ::: \{\mt{Type}\} \to \mt{bindInner} ::: \{\mt{Type}\} \\
adamc@787 1757 \hspace{.1in} \to \lambda [\mt{attrsGiven} \sim \mt{attrsAbsent}] \; [\mt{useOuter} \sim \mt{useInner}] \; [\mt{bindOuter} \sim \mt{bindInner}] \\
adamc@787 1758 \hspace{.1in} \Rightarrow \mt{option} \; \mt{css\_class} \\
adamc@787 1759 \hspace{.1in} \to \$\mt{attrsGiven} \\
adamc@547 1760 \hspace{.1in} \to \mt{tag} \; (\mt{attrsGiven} \rc \mt{attrsAbsent}) \; \mt{ctxOuter} \; \mt{ctxInner} \; \mt{useOuter} \; \mt{bindOuter} \\
adamc@547 1761 \hspace{.1in} \to \mt{xml} \; \mt{ctxInner} \; \mt{useInner} \; \mt{bindInner} \to \mt{xml} \; \mt{ctxOuter} \; (\mt{useOuter} \rc \mt{useInner}) \; (\mt{bindOuter} \rc \mt{bindInner})
adamc@547 1762 \end{array}$$
adamc@787 1763 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 1764
adamc@547 1765 Two XML fragments may be concatenated.
adamc@547 1766 $$\begin{array}{l}
adamc@547 1767 \mt{val} \; \mt{join} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{bind_1} ::: \{\mt{Type}\} \to \mt{bind_2} ::: \{\mt{Type}\} \\
adamc@547 1768 \hspace{.1in} \to \lambda [\mt{use_1} \sim \mt{bind_1}] \; [\mt{bind_1} \sim \mt{bind_2}] \\
adamc@547 1769 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind_1} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{bind_1}) \; \mt{bind_2} \to \mt{xml} \; \mt{ctx} \; \mt{use_1} \; (\mt{bind_1} \rc \mt{bind_2})
adamc@547 1770 \end{array}$$
adamc@547 1771
adamc@547 1772 Finally, any XML fragment may be updated to ``claim'' to use more form fields than it does.
adamc@547 1773 $$\begin{array}{l}
adamc@547 1774 \mt{val} \; \mt{useMore} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{use_2} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to \lambda [\mt{use_1} \sim \mt{use_2}] \\
adamc@547 1775 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{use_2}) \; \mt{bind}
adamc@547 1776 \end{array}$$
adamc@547 1777
adamc@547 1778 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 1779
adamc@547 1780 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 1781 $$\begin{array}{l}
adamc@547 1782 \mt{val} \; \mt{error} : \mt{t} ::: \mt{Type} \to \mt{xml} \; [\mt{Body}] \; [] \; [] \to \mt{t}
adamc@547 1783 \end{array}$$
adamc@547 1784
adamc@549 1785
adamc@701 1786 \subsection{Client-Side Programming}
adamc@659 1787
adamc@701 1788 Ur/Web supports running code on web browsers, via automatic compilation to JavaScript.
adamc@701 1789
adamc@701 1790 \subsubsection{The Basics}
adamc@701 1791
adamc@701 1792 Clients can open alert dialog boxes, in the usual annoying JavaScript way.
adamc@701 1793 $$\begin{array}{l}
adamc@701 1794 \mt{val} \; \mt{alert} : \mt{string} \to \mt{transaction} \; \mt{unit}
adamc@701 1795 \end{array}$$
adamc@701 1796
adamc@701 1797 Any transaction may be run in a new thread with the $\mt{spawn}$ function.
adamc@701 1798 $$\begin{array}{l}
adamc@701 1799 \mt{val} \; \mt{spawn} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit}
adamc@701 1800 \end{array}$$
adamc@701 1801
adamc@701 1802 The current thread can be paused for at least a specified number of milliseconds.
adamc@701 1803 $$\begin{array}{l}
adamc@701 1804 \mt{val} \; \mt{sleep} : \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@701 1805 \end{array}$$
adamc@701 1806
adamc@787 1807 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 1808 $$\begin{array}{l}
adamc@787 1809 \mt{val} \; \mt{onError} : (\mt{xbody} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787 1810 \mt{val} \; \mt{onFail} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787 1811 \mt{val} \; \mt{onConnectFail} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787 1812 \mt{val} \; \mt{onDisconnect} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787 1813 \mt{val} \; \mt{onServerError} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit}
adamc@787 1814 \end{array}$$
adamc@787 1815
adamc@701 1816 \subsubsection{Functional-Reactive Page Generation}
adamc@701 1817
adamc@701 1818 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 1819
adamc@659 1820 $$\begin{array}{l}
adamc@659 1821 \mt{con} \; \mt{source} :: \mt{Type} \to \mt{Type} \\
adamc@659 1822 \mt{val} \; \mt{source} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{transaction} \; (\mt{source} \; \mt{t}) \\
adamc@659 1823 \mt{val} \; \mt{set} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@659 1824 \mt{val} \; \mt{get} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@659 1825 \end{array}$$
adamc@659 1826
adamc@659 1827 Pure functions over sources are represented in a monad of \emph{signals}.
adamc@659 1828
adamc@659 1829 $$\begin{array}{l}
adamc@659 1830 \mt{con} \; \mt{signal} :: \mt{Type} \to \mt{Type} \\
adamc@659 1831 \mt{val} \; \mt{signal\_monad} : \mt{monad} \; \mt{signal} \\
adamc@659 1832 \mt{val} \; \mt{signal} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{signal} \; \mt{t}
adamc@659 1833 \end{array}$$
adamc@659 1834
adamc@659 1835 A reactive portion of an HTML page is injected with a $\mt{dyn}$ tag, which has a signal-valued attribute $\mt{Signal}$.
adamc@659 1836
adamc@659 1837 $$\begin{array}{l}
adamc@701 1838 \mt{val} \; \mt{dyn} : \mt{use} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to \mt{unit} \\
adamc@701 1839 \hspace{.1in} \to \mt{tag} \; [\mt{Signal} = \mt{signal} \; (\mt{xml} \; \mt{body} \; \mt{use} \; \mt{bind})] \; \mt{body} \; [] \; \mt{use} \; \mt{bind}
adamc@659 1840 \end{array}$$
adamc@659 1841
adamc@701 1842 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 1843
adamc@914 1844 \subsubsection{Remote Procedure Calls}
adamc@914 1845
adamc@914 1846 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 1847
adamc@914 1848 $$\begin{array}{l}
adamc@914 1849 \mt{val} \; \mt{rpc} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@914 1850 \end{array}$$
adamc@914 1851
adamc@701 1852 \subsubsection{Asynchronous Message-Passing}
adamc@701 1853
adamc@701 1854 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 1855
adamc@701 1856 $$\begin{array}{l}
adamc@701 1857 \mt{type} \; \mt{client} \\
adamc@701 1858 \mt{val} \; \mt{self} : \mt{transaction} \; \mt{client}
adamc@701 1859 \end{array}$$
adamc@701 1860
adamc@701 1861 \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 1862
adamc@701 1863 $$\begin{array}{l}
adamc@701 1864 \mt{con} \; \mt{channel} :: \mt{Type} \to \mt{Type} \\
adamc@701 1865 \mt{val} \; \mt{channel} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; (\mt{channel} \; \mt{t}) \\
adamc@701 1866 \mt{val} \; \mt{send} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@701 1867 \mt{val} \; \mt{recv} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@701 1868 \end{array}$$
adamc@701 1869
adamc@701 1870 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 1871
adamc@701 1872 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 1873
adamc@659 1874
adamc@549 1875 \section{Ur/Web Syntax Extensions}
adamc@549 1876
adamc@549 1877 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 1878
adamc@549 1879 \subsection{SQL}
adamc@549 1880
adamc@786 1881 \subsubsection{\label{tables}Table Declarations}
adamc@786 1882
adamc@788 1883 $\mt{table}$ declarations may include constraints, via these grammar rules.
adamc@788 1884 $$\begin{array}{rrcll}
adamc@788 1885 \textrm{Declarations} & d &::=& \mt{table} \; x : c \; [pk[,]] \; cts \\
adamc@788 1886 \textrm{Primary key constraints} & pk &::=& \mt{PRIMARY} \; \mt{KEY} \; K \\
adamc@788 1887 \textrm{Keys} & K &::=& f \mid (f, (f,)^+) \\
adamc@788 1888 \textrm{Constraint sets} & cts &::=& \mt{CONSTRAINT} f \; ct \mid cts, cts \mid \{\{e\}\} \\
adamc@788 1889 \textrm{Constraints} & ct &::=& \mt{UNIQUE} \; K \mid \mt{CHECK} \; E \\
adamc@788 1890 &&& \mid \mt{FOREIGN} \; \mt{KEY} \; K \; \mt{REFERENCES} \; F \; (K) \; [\mt{ON} \; \mt{DELETE} \; pr] \; [\mt{ON} \; \mt{UPDATE} \; pr] \\
adamc@788 1891 \textrm{Foreign tables} & F &::=& x \mid \{\{e\}\} \\
adamc@788 1892 \textrm{Propagation modes} & pr &::=& \mt{NO} \; \mt{ACTION} \mid \mt{RESTRICT} \mid \mt{CASCADE} \mid \mt{SET} \; \mt{NULL}
adamc@788 1893 \end{array}$$
adamc@788 1894
adamc@788 1895 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 1896
adamc@788 1897
adamc@549 1898 \subsubsection{Queries}
adamc@549 1899
adamc@550 1900 Queries $Q$ are added to the rules for expressions $e$.
adamc@550 1901
adamc@549 1902 $$\begin{array}{rrcll}
adamc@550 1903 \textrm{Queries} & Q &::=& (q \; [\mt{ORDER} \; \mt{BY} \; (E \; [o],)^+] \; [\mt{LIMIT} \; N] \; [\mt{OFFSET} \; N]) \\
adamc@1085 1904 \textrm{Pre-queries} & q &::=& \mt{SELECT} \; [\mt{DISTINCT}] \; P \; \mt{FROM} \; F,^+ \; [\mt{WHERE} \; E] \; [\mt{GROUP} \; \mt{BY} \; p,^+] \; [\mt{HAVING} \; E] \\
adamc@1085 1905 &&& \mid q \; R \; q \mid \{\{\{e\}\}\} \\
adamc@549 1906 \textrm{Relational operators} & R &::=& \mt{UNION} \mid \mt{INTERSECT} \mid \mt{EXCEPT}
adamc@549 1907 \end{array}$$
adamc@549 1908
adamc@549 1909 $$\begin{array}{rrcll}
adamc@549 1910 \textrm{Projections} & P &::=& \ast & \textrm{all columns} \\
adamc@549 1911 &&& p,^+ & \textrm{particular columns} \\
adamc@549 1912 \textrm{Pre-projections} & p &::=& t.f & \textrm{one column from a table} \\
adamc@558 1913 &&& t.\{\{c\}\} & \textrm{a record of columns from a table (of kind $\{\mt{Type}\}$)} \\
adamc@549 1914 \textrm{Table names} & t &::=& x & \textrm{constant table name (automatically capitalized)} \\
adamc@549 1915 &&& X & \textrm{constant table name} \\
adamc@549 1916 &&& \{\{c\}\} & \textrm{computed table name (of kind $\mt{Name}$)} \\
adamc@549 1917 \textrm{Column names} & f &::=& X & \textrm{constant column name} \\
adamc@549 1918 &&& \{c\} & \textrm{computed column name (of kind $\mt{Name}$)} \\
adamc@549 1919 \textrm{Tables} & T &::=& x & \textrm{table variable, named locally by its own capitalization} \\
adamc@549 1920 &&& x \; \mt{AS} \; t & \textrm{table variable, with local name} \\
adamc@549 1921 &&& \{\{e\}\} \; \mt{AS} \; t & \textrm{computed table expression, with local name} \\
adamc@1085 1922 \textrm{$\mt{FROM}$ items} & F &::=& T \mid \{\{e\}\} \mid F \; J \; \mt{JOIN} \; F \; \mt{ON} \; E \\
adamc@1085 1923 &&& \mid F \; \mt{CROSS} \; \mt{JOIN} \ F \\
adamc@1085 1924 \textrm{Joins} & J &::=& [\mt{INNER}] \\
adamc@1085 1925 &&& \mid [\mt{LEFT} \mid \mt{RIGHT} \mid \mt{FULL}] \; [\mt{OUTER}] \\
adamc@549 1926 \textrm{SQL expressions} & E &::=& p & \textrm{column references} \\
adamc@549 1927 &&& X & \textrm{named expression references} \\
adamc@549 1928 &&& \{\{e\}\} & \textrm{injected native Ur expressions} \\
adamc@549 1929 &&& \{e\} & \textrm{computed expressions, probably using $\mt{sql\_exp}$ directly} \\
adamc@549 1930 &&& \mt{TRUE} \mid \mt{FALSE} & \textrm{boolean constants} \\
adamc@549 1931 &&& \ell & \textrm{primitive type literals} \\
adamc@549 1932 &&& \mt{NULL} & \textrm{null value (injection of $\mt{None}$)} \\
adamc@549 1933 &&& E \; \mt{IS} \; \mt{NULL} & \textrm{nullness test} \\
adamc@549 1934 &&& n & \textrm{nullary operators} \\
adamc@549 1935 &&& u \; E & \textrm{unary operators} \\
adamc@549 1936 &&& E \; b \; E & \textrm{binary operators} \\
adamc@549 1937 &&& \mt{COUNT}(\ast) & \textrm{count number of rows} \\
adamc@549 1938 &&& a(E) & \textrm{other aggregate function} \\
adamc@549 1939 &&& (E) & \textrm{explicit precedence} \\
adamc@549 1940 \textrm{Nullary operators} & n &::=& \mt{CURRENT\_TIMESTAMP} \\
adamc@549 1941 \textrm{Unary operators} & u &::=& \mt{NOT} \\
adamc@549 1942 \textrm{Binary operators} & b &::=& \mt{AND} \mid \mt{OR} \mid \neq \mid < \mid \leq \mid > \mid \geq \\
adamc@549 1943 \textrm{Aggregate functions} & a &::=& \mt{AVG} \mid \mt{SUM} \mid \mt{MIN} \mid \mt{MAX} \\
adamc@550 1944 \textrm{Directions} & o &::=& \mt{ASC} \mid \mt{DESC} \\
adamc@549 1945 \textrm{SQL integer} & N &::=& n \mid \{e\} \\
adamc@549 1946 \end{array}$$
adamc@549 1947
adamc@1085 1948 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 1949
adamc@550 1950 \subsubsection{DML}
adamc@550 1951
adamc@550 1952 DML commands $D$ are added to the rules for expressions $e$.
adamc@550 1953
adamc@550 1954 $$\begin{array}{rrcll}
adamc@550 1955 \textrm{Commands} & D &::=& (\mt{INSERT} \; \mt{INTO} \; T^E \; (f,^+) \; \mt{VALUES} \; (E,^+)) \\
adamc@550 1956 &&& (\mt{UPDATE} \; T^E \; \mt{SET} \; (f = E,)^+ \; \mt{WHERE} \; E) \\
adamc@550 1957 &&& (\mt{DELETE} \; \mt{FROM} \; T^E \; \mt{WHERE} \; E) \\
adamc@550 1958 \textrm{Table expressions} & T^E &::=& x \mid \{\{e\}\}
adamc@550 1959 \end{array}$$
adamc@550 1960
adamc@550 1961 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 1962
adamc@551 1963 \subsection{XML}
adamc@551 1964
adamc@551 1965 XML fragments $L$ are added to the rules for expressions $e$.
adamc@551 1966
adamc@551 1967 $$\begin{array}{rrcll}
adamc@551 1968 \textrm{XML fragments} & L &::=& \texttt{<xml/>} \mid \texttt{<xml>}l^*\texttt{</xml>} \\
adamc@551 1969 \textrm{XML pieces} & l &::=& \textrm{text} & \textrm{cdata} \\
adamc@551 1970 &&& \texttt{<}g\texttt{/>} & \textrm{tag with no children} \\
adamc@551 1971 &&& \texttt{<}g\texttt{>}l^*\texttt{</}x\texttt{>} & \textrm{tag with children} \\
adamc@559 1972 &&& \{e\} & \textrm{computed XML fragment} \\
adamc@559 1973 &&& \{[e]\} & \textrm{injection of an Ur expression, via the $\mt{Top}.\mt{txt}$ function} \\
adamc@551 1974 \textrm{Tag} & g &::=& h \; (x = v)^* \\
adamc@551 1975 \textrm{Tag head} & h &::=& x & \textrm{tag name} \\
adamc@551 1976 &&& h\{c\} & \textrm{constructor parameter} \\
adamc@551 1977 \textrm{Attribute value} & v &::=& \ell & \textrm{literal value} \\
adamc@551 1978 &&& \{e\} & \textrm{computed value} \\
adamc@551 1979 \end{array}$$
adamc@551 1980
adamc@552 1981
adamc@553 1982 \section{The Structure of Web Applications}
adamc@553 1983
adamc@1127 1984 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 1985
adamc@553 1986 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 1987
adamc@553 1988 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 1989
adamc@558 1990 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 1991
adamc@660 1992 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 1993
adamc@789 1994 \medskip
adamc@789 1995
adamc@789 1996 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 1997
adamc@789 1998 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 1999
adamc@553 2000
adamc@897 2001 \section{The Foreign Function Interface}
adamc@897 2002
adamc@897 2003 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 2004
adamc@897 2005 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 2006
adamc@897 2007 \begin{itemize}
adamc@897 2008 \item \texttt{clientOnly Module.ident} registers a value as being allowed only in client-side code.
adamc@897 2009 \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 2010 \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 2011 \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 2012 \item \texttt{include FILE} requests inclusion of a C header file.
adamc@897 2013 \item \texttt{jsFunc Module.ident=name} gives a mapping from an Ur name for a value to a JavaScript name.
adamc@897 2014 \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 2015 \item \texttt{script URL} requests inclusion of a JavaScript source file within application HTML.
adamc@897 2016 \item \texttt{serverOnly Module.ident} registers a value as being allowed only in server-side code.
adamc@897 2017 \end{itemize}
adamc@897 2018
adamc@897 2019 \subsection{Writing C FFI Code}
adamc@897 2020
adamc@897 2021 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 2022
adamc@897 2023 \begin{itemize}
adamc@897 2024 \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 2025 \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 2026 \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 2027 \end{itemize}
adamc@897 2028
adamc@897 2029 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 2030 \begin{itemize}
adamc@897 2031 \item \begin{verbatim}
adamc@897 2032 void uw_error(uw_context, failure_kind, const char *fmt, ...);
adamc@897 2033 \end{verbatim}
adamc@897 2034 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 2035
adamc@897 2036 \item \begin{verbatim}
adamc@897 2037 void uw_push_cleanup(uw_context, void (*func)(void *), void *arg);
adamc@897 2038 void uw_pop_cleanup(uw_context);
adamc@897 2039 \end{verbatim}
adamc@897 2040 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 2041
adamc@897 2042 \item \begin{verbatim}
adamc@897 2043 void *uw_malloc(uw_context, size_t);
adamc@897 2044 \end{verbatim}
adamc@897 2045 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 2046
adamc@897 2047 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 2048
adamc@897 2049 \item \begin{verbatim}
adamc@897 2050 typedef void (*uw_callback)(void *);
adamc@897 2051 void uw_register_transactional(uw_context, void *data, uw_callback commit,
adamc@897 2052 uw_callback rollback, uw_callback free);
adamc@897 2053 \end{verbatim}
adamc@897 2054 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 2055
adamc@1085 2056 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 2057
adamc@1085 2058 \item \begin{verbatim}
adamc@1085 2059 void *uw_get_global(uw_context, char *name);
adamc@1085 2060 void uw_set_global(uw_context, char *name, void *data, uw_callback free);
adamc@1085 2061 \end{verbatim}
adamc@1085 2062 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 2063
adamc@897 2064 \end{itemize}
adamc@897 2065
adamc@897 2066 \subsection{Writing JavaScript FFI Code}
adamc@897 2067
adamc@897 2068 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 2069
adamc@897 2070 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 2071
adamc@897 2072 \begin{itemize}
adamc@897 2073 \item Integers, floats, strings, characters, and booleans are represented in the usual JavaScript way.
adamc@985 2074 \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 2075 \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 2076 \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 2077 \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 2078 \end{itemize}
adamc@897 2079
adamc@897 2080 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 2081
adamc@897 2082
adamc@552 2083 \section{Compiler Phases}
adamc@552 2084
adamc@552 2085 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 2086
adamc@552 2087 In this section, we step through the main phases of compilation, noting what consequences each phase has for effective programming.
adamc@552 2088
adamc@552 2089 \subsection{Parse}
adamc@552 2090
adamc@552 2091 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 2092
adamc@552 2093 \subsection{Elaborate}
adamc@552 2094
adamc@552 2095 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 2096
adamc@552 2097 \subsection{Unnest}
adamc@552 2098
adamc@552 2099 Named local function definitions are moved to the top level, to avoid the need to generate closures.
adamc@552 2100
adamc@552 2101 \subsection{Corify}
adamc@552 2102
adamc@552 2103 Module system features are compiled away, through inlining of functor definitions at application sites. Afterward, most abstraction boundaries are broken, facilitating optimization.
adamc@552 2104
adamc@552 2105 \subsection{Especialize}
adamc@552 2106
adamc@552 2107 Functions are specialized to particular argument patterns. This is an important trick for avoiding the need to maintain any closures at runtime.
adamc@552 2108
adamc@552 2109 \subsection{Untangle}
adamc@552 2110
adamc@552 2111 Remove unnecessary mutual recursion, splitting recursive groups into strongly-connected components.
adamc@552 2112
adamc@552 2113 \subsection{Shake}
adamc@552 2114
adamc@552 2115 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 2116
adamc@661 2117 \subsection{Rpcify}
adamc@661 2118
adamc@661 2119 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 2120
adamc@661 2121 \subsection{Untangle, Shake}
adamc@661 2122
adamc@661 2123 Repeat these simplifications.
adamc@661 2124
adamc@553 2125 \subsection{\label{tag}Tag}
adamc@552 2126
adamc@552 2127 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 2128
adamc@552 2129 \subsection{Reduce}
adamc@552 2130
adamc@552 2131 Apply definitional equality rules to simplify the program as much as possible. This effectively includes inlining of every non-recursive definition.
adamc@552 2132
adamc@552 2133 \subsection{Unpoly}
adamc@552 2134
adamc@552 2135 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 2136
adamc@552 2137 \subsection{Specialize}
adamc@552 2138
adamc@558 2139 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 2140
adamc@552 2141 \subsection{Shake}
adamc@552 2142
adamc@558 2143 Here the compiler repeats the earlier Shake phase.
adamc@552 2144
adamc@552 2145 \subsection{Monoize}
adamc@552 2146
adamc@552 2147 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 2148
adamc@552 2149 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 2150
adamc@552 2151 \subsection{MonoOpt}
adamc@552 2152
adamc@552 2153 Simple algebraic laws are applied to simplify the program, focusing especially on efficient imperative generation of HTML pages.
adamc@552 2154
adamc@552 2155 \subsection{MonoUntangle}
adamc@552 2156
adamc@552 2157 Unnecessary mutual recursion is broken up again.
adamc@552 2158
adamc@552 2159 \subsection{MonoReduce}
adamc@552 2160
adamc@552 2161 Equivalents of the definitional equality rules are applied to simplify programs, with inlining again playing a major role.
adamc@552 2162
adamc@552 2163 \subsection{MonoShake, MonoOpt}
adamc@552 2164
adamc@552 2165 Unneeded declarations are removed, and basic optimizations are repeated.
adamc@552 2166
adamc@552 2167 \subsection{Fuse}
adamc@552 2168
adamc@552 2169 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 2170
adamc@552 2171 \subsection{MonoUntangle, MonoShake}
adamc@552 2172
adamc@552 2173 Fuse often creates more opportunities to remove spurious mutual recursion.
adamc@552 2174
adamc@552 2175 \subsection{Pathcheck}
adamc@552 2176
adamc@552 2177 The compiler checks that no link or action name has been used more than once.
adamc@552 2178
adamc@552 2179 \subsection{Cjrize}
adamc@552 2180
adamc@552 2181 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 2182
adamc@552 2183 \subsection{C Compilation and Linking}
adamc@552 2184
adamc@552 2185 The output of the last phase is pretty-printed as C source code and passed to GCC.
adamc@552 2186
adamc@552 2187
adamc@524 2188 \end{document}