annotate doc/manual.tex @ 1872:6507e973af84

Add -print-ccompiler command line option
author Sergey Mironov <grrwlf@gmail.com>
date Wed, 18 Sep 2013 15:45:18 +0400
parents 30c56e3bcf47
children c44bfaa69dd8
rev   line source
adamc@524 1 \documentclass{article}
adamc@554 2 \usepackage{fullpage,amsmath,amssymb,proof,url}
rmbruijn@1568 3 \usepackage[T1]{fontenc}
vshabanoff@1765 4 \usepackage{ae,aecompl}
adamc@524 5 \newcommand{\cd}[1]{\texttt{#1}}
adamc@524 6 \newcommand{\mt}[1]{\mathsf{#1}}
adamc@524 7
adamc@524 8 \newcommand{\rc}{+ \hspace{-.075in} + \;}
adamc@527 9 \newcommand{\rcut}{\; \texttt{--} \;}
adamc@527 10 \newcommand{\rcutM}{\; \texttt{---} \;}
adamc@524 11
adamc@524 12 \begin{document}
adamc@524 13
adamc@524 14 \title{The Ur/Web Manual}
adamc@524 15 \author{Adam Chlipala}
adamc@524 16
adamc@524 17 \maketitle
adamc@524 18
adamc@540 19 \tableofcontents
adamc@540 20
adamc@554 21
adamc@554 22 \section{Introduction}
adamc@554 23
adam@1797 24 \emph{Ur} is a programming language designed to introduce richer type system features into functional programming in the tradition of ML and Haskell. Ur is functional, pure, statically typed, and strict. Ur supports a powerful kind of \emph{metaprogramming} based on \emph{type-level computation with type-level records}.
adamc@554 25
adamc@554 26 \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 27
adamc@554 28 \begin{itemize}
adamc@554 29 \item Suffer from any kinds of code-injection attacks
adamc@554 30 \item Return invalid HTML
adamc@554 31 \item Contain dead intra-application links
adamc@554 32 \item Have mismatches between HTML forms and the fields expected by their handlers
adamc@652 33 \item Include client-side code that makes incorrect assumptions about the ``AJAX''-style services that the remote web server provides
adamc@554 34 \item Attempt invalid SQL queries
adamc@652 35 \item Use improper marshaling or unmarshaling in communication with SQL databases or between browsers and web servers
adamc@554 36 \end{itemize}
adamc@554 37
adamc@554 38 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 39
adamc@652 40 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 41
adamc@554 42 \medskip
adamc@554 43
adamc@554 44 The official web site for Ur is:
adamc@554 45 \begin{center}
adamc@554 46 \url{http://www.impredicative.com/ur/}
adamc@554 47 \end{center}
adamc@554 48
adamc@555 49
adamc@555 50 \section{Installation}
adamc@555 51
adamc@555 52 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 53
adamc@555 54 \begin{verbatim}
adamc@555 55 ./configure
adamc@555 56 make
adamc@555 57 sudo make install
adamc@555 58 \end{verbatim}
adamc@555 59
adam@1523 60 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 (or an alternate C compiler) in your execution path; MLton, the whole-program optimizing compiler for Standard ML; and the development files for the OpenSSL 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 61 \begin{verbatim}
adam@1368 62 apt-get install mlton libssl-dev
adamc@896 63 \end{verbatim}
adamc@555 64
adamc@896 65 To build programs that access SQL databases, you also need one of these client libraries for supported backends.
adamc@555 66 \begin{verbatim}
adamc@896 67 apt-get install libpq-dev libmysqlclient15-dev libsqlite3-dev
adamc@555 68 \end{verbatim}
adamc@555 69
adamc@555 70 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 71 \begin{verbatim}
adamc@555 72 apt-get install smlnj libsmlnj-smlnj ml-yacc ml-lpt
adamc@555 73 \end{verbatim}
adamc@555 74
adamc@555 75 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 76
adamc@896 77 To run an SQL-backed application with a backend besides SQLite, you will probably want to install one of these servers.
adamc@555 78
adamc@555 79 \begin{verbatim}
adam@1400 80 apt-get install postgresql-8.4 mysql-server-5.1
adamc@555 81 \end{verbatim}
adamc@555 82
adamc@555 83 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 84
adamc@555 85 \begin{verbatim}
adamc@555 86 apt-get install emacs-goodies-el
adamc@555 87 \end{verbatim}
adamc@555 88
adam@1441 89 If you don't want to install the Emacs mode, run \texttt{./configure} with the argument \texttt{--without-emacs}.
adam@1441 90
adam@1523 91 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 the C compiler and linker on every invocation. Some older GCC versions need this setting to mask a bug in function inlining.
adamc@555 92
adamc@555 93 \begin{verbatim}
adam@1523 94 CCARGS=-fno-inline ./configure
adamc@555 95 \end{verbatim}
adamc@555 96
adam@1523 97 Since the author is still getting a handle on the GNU Autotools that provide the build system, you may need to do some further work to get started, especially in environments with significant differences from Linux (where most testing is done). The variables \texttt{PGHEADER}, \texttt{MSHEADER}, and \texttt{SQHEADER} may be used to set the proper C header files to include for the development libraries of PostgreSQL, MySQL, and SQLite, respectively. To get libpq to link, one OS X user reported setting \texttt{CCARGS="-I/opt/local/include -L/opt/local/lib/postgresql84"}, after creating a symbolic link with \texttt{ln -s /opt/local/include/postgresql84 /opt/local/include/postgresql}.
adamc@555 98
adamc@555 99 The Emacs mode can be set to autoload by adding the following to your \texttt{.emacs} file.
adamc@555 100
adamc@555 101 \begin{verbatim}
adamc@555 102 (add-to-list 'load-path "/usr/local/share/emacs/site-lisp/urweb-mode")
adamc@555 103 (load "urweb-mode-startup")
adamc@555 104 \end{verbatim}
adamc@555 105
adamc@555 106 Change the path in the first line if you chose a different Emacs installation path during configuration.
adamc@555 107
adamc@555 108
adamc@556 109 \section{Command-Line Compiler}
adamc@556 110
adam@1604 111 \subsection{\label{cl}Project Files}
adamc@556 112
adamc@556 113 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@556 114
adamc@556 115 \begin{verbatim}
adamc@556 116 database dbname=test
adamc@556 117 sql crud1.sql
adamc@556 118
adamc@556 119 crud
adamc@556 120 crud1
adamc@556 121 \end{verbatim}
adamc@556 122
adamc@556 123 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@556 124
adamc@556 125 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@556 126
adamc@556 127 \begin{verbatim}
adamc@556 128 createdb test
adamc@556 129 psql -f crud1.sql test
adamc@556 130 \end{verbatim}
adamc@556 131
adam@1331 132 A blank line separates the named directives from a list of modules to include in the project. Any line may contain a shell-script-style comment, where any suffix of a line starting at a hash character \texttt{\#} is ignored.
adamc@556 133
adamc@556 134 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@556 135
adamc@783 136 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@783 137 \begin{itemize}
adam@1799 138 \item \texttt{[allow|deny] [url|mime|requestHeader|responseHeader|env] PATTERN} registers a rule governing which URLs, MIME types, HTTP request headers, HTTP response headers, or environment variable names are allowed to appear explicitly in this application. The first such rule to match a name determines the verdict. If \texttt{PATTERN} ends in \texttt{*}, it is interpreted as a prefix rule. Otherwise, a string must match it exactly.
adam@1400 139 \item \texttt{alwaysInline PATH} requests that every call to the referenced function be inlined. Section \ref{structure} explains how functions are assigned path strings.
adam@1462 140 \item \texttt{benignEffectful Module.ident} registers an FFI function or transaction as having side effects. The optimizer avoids removing, moving, or duplicating calls to such functions. Every effectful FFI function must be registered, or the optimizer may make invalid transformations. This version of the \texttt{effectful} directive registers that this function only has side effects that remain local to a single page generation.
adamc@783 141 \item \texttt{clientOnly Module.ident} registers an FFI function or transaction that may only be run in client browsers.
adamc@783 142 \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.
adam@1816 143 \item \texttt{coreInline TREESIZE} sets how many nodes the AST of a function definition may have before the optimizer stops trying hard to inline calls to that function. (This is one of two options for one of two intermediate languages within the compiler.)
adamc@783 144 \item \texttt{database DBSTRING} sets the string to pass to libpq to open a database connection.
adamc@783 145 \item \texttt{debug} saves some intermediate C files, which is mostly useful to help in debugging the compiler itself.
adam@1699 146 \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. (Note that merely assigning a function a \texttt{transaction}-based type does not mark it as effectful in this way!)
adamc@783 147 \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@783 148 \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 149 \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@783 150 \item \texttt{jsFunc Module.ident=name} gives the JavaScript name of an FFI value.
adamc@1089 151 \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}.
adam@1309 152 \item \texttt{limit class num} sets a resource usage limit for generated applications. The limit \texttt{class} will be set to the non-negative integer \texttt{num}. The classes are:
adam@1309 153 \begin{itemize}
adam@1309 154 \item \texttt{cleanup}: maximum number of cleanup operations (e.g., entries recording the need to deallocate certain temporary objects) that may be active at once per request
adam@1850 155 \item \texttt{clients}: maximum number of simultaneous connections to one application by web clients waiting for new asynchronous messages sent with \texttt{Basis.send}
adam@1850 156 \item \texttt{database}: maximum size of a database file (currently only used by SQLite, which interprets the parameter as a number of pages, where page size is itself a quantity configurable in SQLite)
adam@1309 157 \item \texttt{deltas}: maximum number of messages sendable in a single request handler with \texttt{Basis.send}
adam@1309 158 \item \texttt{globals}: maximum number of global variables that FFI libraries may set in a single request context
adam@1309 159 \item \texttt{headers}: maximum size (in bytes) of per-request buffer used to hold HTTP headers for generated pages
adam@1797 160 \item \texttt{heap}: maximum size (in bytes) of per-request heap for dynamically allocated data
adam@1309 161 \item \texttt{inputs}: maximum number of top-level form fields per request
adam@1309 162 \item \texttt{messages}: maximum size (in bytes) of per-request buffer used to hold a single outgoing message sent with \texttt{Basis.send}
adam@1309 163 \item \texttt{page}: maximum size (in bytes) of per-request buffer used to hold HTML content of generated pages
adam@1309 164 \item \texttt{script}: maximum size (in bytes) of per-request buffer used to hold JavaScript content of generated pages
adam@1309 165 \item \texttt{subinputs}: maximum number of form fields per request, excluding top-level fields
adam@1309 166 \item \texttt{time}: maximum running time of a single page request, in units of approximately 0.1 seconds
adam@1309 167 \item \texttt{transactionals}: maximum number of custom transactional actions (e.g., sending an e-mail) that may be run in a single page generation
adam@1309 168 \end{itemize}
adam@1523 169 \item \texttt{link FILENAME} adds \texttt{FILENAME} to the list of files to be passed to the linker at the end of compilation. This is most useful for importing extra libraries needed by new FFI modules.
adam@1725 170 \item \texttt{linker CMD} sets \texttt{CMD} as the command line prefix to use for linking C object files. The command line will be completed with a space-separated list of \texttt{.o} and \texttt{.a} files, \texttt{-L} and \texttt{-l} flags, and finally with a \texttt{-o} flag to set the location where the executable should be written.
adam@1332 171 \item \texttt{minHeap NUMBYTES} sets the initial size for thread-local heaps used in handling requests. These heaps grow automatically as needed (up to any maximum set with \texttt{limit}), but each regrow requires restarting the request handling process.
adam@1816 172 \item \texttt{monoInline TREESIZE} sets how many nodes the AST of a function definition may have before the optimizer stops trying hard to inline calls to that function. (This is one of two options for one of two intermediate languages within the compiler.)
adam@1478 173 \item \texttt{noXsrfProtection URIPREFIX} turns off automatic cross-site request forgery protection for the page handler identified by the given URI prefix. This will avoid checking cryptographic signatures on cookies, which is generally a reasonable idea for some pages, such as login pages that are going to discard all old cookie values, anyway.
adam@1297 174 \item \texttt{onError Module.var} changes the handling of fatal application errors. Instead of displaying a default, ugly error 500 page, the error page will be generated by calling function \texttt{Module.var} on a piece of XML representing the error message. The error handler should have type $\mt{xbody} \to \mt{transaction} \; \mt{page}$. Note that the error handler \emph{cannot} be in the application's main module, since that would register it as explicitly callable via URLs.
adamc@852 175 \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@783 176 \item \texttt{prefix PREFIX} sets the prefix included before every URI within the generated application. The default is \texttt{/}.
adamc@783 177 \item \texttt{profile} generates an executable that may be used with gprof.
adam@1752 178 \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}. The \texttt{TO} field may be left empty to express the idea of deleting a prefix. For instance, \texttt{rewrite url Main/*} will strip all \texttt{Main/} prefixes from URLs. 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. An optional suffix of \cd{[-]} for a \cd{rewrite} directive asks to additionally replace all \cd{\_} characters with \cd{-} characters, which can be handy for, e.g., interfacing with an off-the-shelf CSS library that prefers hyphens over underscores.
adamc@1183 179 \item \texttt{safeGet URI} asks to allow the page handler assigned this canonical URI prefix to cause persistent side effects, even if accessed via an HTTP \cd{GET} request.
adamc@783 180 \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@783 181 \item \texttt{serverOnly Module.ident} registers an FFI function or transaction that may only be run on the server.
adamc@1164 182 \item \texttt{sigfile PATH} sets a path where your application should look for a key to use in cryptographic signing. This is used to prevent cross-site request forgery attacks for any form handler that both reads a cookie and creates side effects. If the referenced file doesn't exist, an application will create it and read its saved data on future invocations. You can also initialize the file manually with any contents at least 16 bytes long; the first 16 bytes will be treated as the key.
adamc@783 183 \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.
adam@1629 184 \item \texttt{timeFormat FMT} accepts a time format string, as processed by the POSIX C function \texttt{strftime()}. This controls the default rendering of $\mt{time}$ values, via the $\mt{show}$ instance for $\mt{time}$.
adamc@783 185 \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@783 186 \end{itemize}
adamc@701 187
adamc@701 188
adamc@557 189 \subsection{Building an Application}
adamc@557 190
adamc@557 191 To compile project \texttt{P.urp}, simply run
adamc@557 192 \begin{verbatim}
adamc@557 193 urweb P
adamc@557 194 \end{verbatim}
adamc@1198 195 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. See Section \ref{structure} for an explanation of the URI mapping convention, which determines how each page of your application may be accessed via URLs.
adamc@557 196
adamc@557 197 To time how long the different compiler phases run, without generating an executable, run
adamc@557 198 \begin{verbatim}
adamc@557 199 urweb -timing P
adamc@557 200 \end{verbatim}
adamc@557 201
adamc@1086 202 To stop the compilation process after type-checking, run
adamc@1086 203 \begin{verbatim}
adamc@1086 204 urweb -tc P
adamc@1086 205 \end{verbatim}
adam@1530 206 It is often worthwhile to run \cd{urweb} in this mode, because later phases of compilation can take significantly longer than type-checking alone, and the type checker catches many errors that would traditionally be found through debugging a running application.
adamc@1086 207
adam@1745 208 A related option is \cd{-dumpTypes}, which, as long as parsing succeeds, outputs to stdout a summary of the kinds of all identifiers declared with \cd{con} and the types of all identifiers declared with \cd{val} or \cd{val rec}. This information is dumped even if there are errors during type inference. Compiler error messages go to stderr, not stdout, so it is easy to distinguish the two kinds of output programmatically. A refined version of this option is \cd{-dumpTypesOnError}, which only has an effect when there are compilation errors.
adam@1531 209
adam@1723 210 It may be useful to combine another option \cd{-unifyMore} with \cd{-dumpTypes}. Ur/Web type inference proceeds in a series of stages, where the first is standard Hindley-Milner type inference as in ML, and the later phases add more complex aspects. By default, an error detected in one phase cuts off the execution of later phases. However, the later phases might still determine more values of unification variables. These value choices might be ``misguided,'' since earlier phases have not come up with reasonable types at a coarser detail level; but the unification decisions may still be useful for debugging and program understanding. So, if a run with \cd{-dumpTypes} leaves unification variables undetermined in positions where you would like to see best-effort guesses instead, consider \cd{-unifyMore}. Note that \cd{-unifyMore} has no effect when type inference succeeds fully, but it may lead to many more error messages when inference fails.
adam@1723 211
adamc@1170 212 To output information relevant to CSS stylesheets (and not finish regular compilation), run
adamc@1170 213 \begin{verbatim}
adamc@1170 214 urweb -css P
adamc@1170 215 \end{verbatim}
adamc@1170 216 The first output line is a list of categories of CSS properties that would be worth setting on the document body. The remaining lines are space-separated pairs of CSS class names and categories of properties that would be worth setting for that class. The category codes are divided into two varieties. Codes that reveal properties of a tag or its (recursive) children are \cd{B} for block-level elements, \cd{C} for table captions, \cd{D} for table cells, \cd{L} for lists, and \cd{T} for tables. Codes that reveal properties of the precise tag that uses a class are \cd{b} for block-level elements, \cd{t} for tables, \cd{d} for table cells, \cd{-} for table rows, \cd{H} for the possibility to set a height, \cd{N} for non-replaced inline-level elements, \cd{R} for replaced inline elements, and \cd{W} for the possibility to set a width.
adamc@1170 217
adam@1733 218 Ur/Web type inference can take a significant amount of time, so it can be helpful to cache type-inferred versions of source files. This mode can be activated by running
adam@1733 219 \begin{verbatim}
adam@1733 220 urweb daemon start
adam@1733 221 \end{verbatim}
adam@1733 222 Further \cd{urweb} invocations in the same working directory will send requests to a background daemon process that reuses type inference results whenever possible, tracking source file dependencies and modification times. To stop the background daemon, run
adam@1733 223 \begin{verbatim}
adam@1733 224 urweb daemon stop
adam@1733 225 \end{verbatim}
adam@1733 226 Communication happens via a UNIX domain socket in file \cd{.urweb\_daemon} in the working directory.
adam@1733 227
adam@1733 228 \medskip
adam@1733 229
adamc@896 230 Some other command-line parameters are accepted:
adamc@896 231 \begin{itemize}
ezyang@1739 232 \item \texttt{-boot}: Run Ur/Web from a build tree (and not from a system install). This is useful if you're testing the compiler and don't want to install it. It forces generation of statically linked executables.
ezyang@1739 233
adamc@896 234 \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@896 235
adamc@896 236 \item \texttt{-dbms [postgres|mysql|sqlite]}: Sets the database backend to use.
adamc@896 237 \begin{itemize}
adamc@896 238 \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@896 239
adamc@896 240 A command sequence like this can initialize a Postgres database, using a file \texttt{app.sql} generated by the compiler:
adamc@896 241 \begin{verbatim}
adamc@896 242 createdb app
adamc@896 243 psql -f app.sql app
adamc@896 244 \end{verbatim}
adamc@896 245
adamc@896 246 \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@896 247
adamc@896 248 A command sequence like this can initialize a MySQL database:
adamc@896 249 \begin{verbatim}
adamc@896 250 echo "CREATE DATABASE app" | mysql
adamc@896 251 mysql -D app <app.sql
adamc@896 252 \end{verbatim}
adamc@896 253
adamc@896 254 \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@896 255
adamc@896 256 A command like this can initialize an SQLite database:
adamc@896 257 \begin{verbatim}
adamc@896 258 sqlite3 path/to/database/file <app.sql
adamc@896 259 \end{verbatim}
adamc@896 260 \end{itemize}
adamc@896 261
adam@1693 262 \item \texttt{-dumpSource}: When compilation fails, output to stderr the complete source code of the last intermediate program before the compilation phase that signaled the error. (Warning: these outputs can be very long and aren't especially optimized for readability!)
adam@1693 263
adam@1309 264 \item \texttt{-limit class num}: Equivalent to the \texttt{limit} directive from \texttt{.urp} files
adam@1309 265
adam@1850 266 \item \texttt{-moduleOf FILENAME}: Prints the Ur/Web module name corresponding to source file \texttt{FILENAME}, exiting immediately afterward.
adam@1850 267
adamc@896 268 \item \texttt{-output FILENAME}: Set where the application executable is written.
adamc@896 269
adamc@1127 270 \item \texttt{-path NAME VALUE}: Set the value of path variable \texttt{\$NAME} to \texttt{VALUE}, for use in \texttt{.urp} files.
adamc@1127 271
adam@1335 272 \item \texttt{-prefix PREFIX}: Equivalent to the \texttt{prefix} directive from \texttt{.urp} files
adam@1335 273
adam@1753 274 \item \texttt{-protocol [http|cgi|fastcgi|static]}: Set the protocol that the generated application speaks.
adamc@896 275 \begin{itemize}
adamc@896 276 \item \texttt{http}: This is the default. It is for building standalone web servers that can be accessed by web browsers directly.
adamc@896 277
adamc@896 278 \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@896 279
adamc@896 280 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@896 281 \begin{verbatim}
adamc@896 282 ScriptAlias /Hello /path/to/hello.exe
adamc@896 283 \end{verbatim}
adamc@896 284
adamc@1163 285 A different method can be used for, e.g., a shared host, where you can only configure Apache via \texttt{.htaccess} files. Drop the generated executable into your web space and mark it as CGI somehow. For instance, if the script ends in \texttt{.exe}, you might put this in \texttt{.htaccess} in the directory containing the script:
adamc@1163 286 \begin{verbatim}
adamc@1163 287 Options +ExecCGI
adamc@1163 288 AddHandler cgi-script .exe
adamc@1163 289 \end{verbatim}
adamc@1163 290
adamc@1163 291 Additionally, make sure that Ur/Web knows the proper URI prefix for your script. For instance, if the script is accessed via \texttt{http://somewhere/dir/script.exe}, then include this line in your \texttt{.urp} file:
adamc@1163 292 \begin{verbatim}
adamc@1163 293 prefix /dir/script.exe/
adamc@1163 294 \end{verbatim}
adamc@1163 295
adamc@1163 296 To access the \texttt{foo} function in the \texttt{Bar} module, you would then hit \texttt{http://somewhere/dir/script.exe/Bar/foo}.
adamc@1163 297
adamc@1164 298 If your application contains form handlers that read cookies before causing side effects, then you will need to use the \texttt{sigfile} \texttt{.urp} directive, too.
adamc@1164 299
adamc@896 300 \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@896 301
adamc@896 302 To configure a FastCGI program with Apache, one could combine the above \texttt{ScriptAlias} line with a line like this:
adamc@896 303 \begin{verbatim}
adamc@896 304 FastCgiServer /path/to/hello.exe -idle-timeout 99999
adamc@896 305 \end{verbatim}
adamc@896 306 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@896 307
adam@1753 308 Also see the discussion of the \cd{prefix} directive for CGI above; similar configuration is likely to be necessary for FastCGI. An Ur/Web application won't generally run correctly if it doesn't have a unique URI prefix assigned to it and configured with \cd{prefix}.
adam@1753 309
adamc@896 310 Here is some lighttpd configuration for the same application.
adamc@896 311 \begin{verbatim}
adamc@896 312 fastcgi.server = (
adamc@896 313 "/Hello/" =>
adamc@896 314 (( "bin-path" => "/path/to/hello.exe",
adamc@896 315 "socket" => "/tmp/hello",
adamc@896 316 "check-local" => "disable",
adamc@896 317 "docroot" => "/",
adamc@896 318 "max-procs" => "1"
adamc@896 319 ))
adamc@896 320 )
adamc@896 321 \end{verbatim}
adamc@896 322 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@896 323
adamc@896 324 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.
adam@1509 325
adam@1509 326 \item \texttt{static}: This protocol may be used to generate static web pages from Ur/Web code. The output executable expects a single command-line argument, giving the URI of a page to generate. For instance, this argument might be \cd{/main}, in which case a static HTTP response for that page will be written to stdout.
adamc@896 327 \end{itemize}
adamc@896 328
adamc@1127 329 \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 330
adamc@1164 331 \item \texttt{-sigfile PATH}: Same as the \texttt{sigfile} directive in \texttt{.urp} files
adamc@1164 332
adamc@896 333 \item \texttt{-sql FILENAME}: Set where a database set-up SQL script is written.
adamc@1095 334
adamc@1095 335 \item \texttt{-static}: Link the runtime system statically. The default is to link against dynamic libraries.
adamc@896 336 \end{itemize}
adamc@896 337
adam@1297 338 There is an additional convenience method for invoking \texttt{urweb}. If the main argument is \texttt{FOO}, and \texttt{FOO.ur} exists but \texttt{FOO.urp} doesn't, then the invocation is interpreted as if called on a \texttt{.urp} file containing \texttt{FOO} as its only main entry, with an additional \texttt{rewrite all FOO/*} directive.
adamc@556 339
adam@1509 340 \subsection{Tutorial Formatting}
adam@1509 341
adam@1509 342 The Ur/Web compiler also supports rendering of nice HTML tutorials from Ur source files, when invoked like \cd{urweb -tutorial DIR}. The directory \cd{DIR} is examined for files whose names end in \cd{.ur}. Every such file is translated into a \cd{.html} version.
adam@1509 343
adam@1509 344 These input files follow normal Ur syntax, with a few exceptions:
adam@1509 345 \begin{itemize}
adam@1509 346 \item The first line must be a comment like \cd{(* TITLE *)}, where \cd{TITLE} is a string of your choice that will be used as the title of the output page.
adam@1509 347 \item While most code in the output HTML will be formatted as a monospaced code listing, text in regular Ur comments is formatted as normal English text.
adam@1509 348 \item A comment like \cd{(* * HEADING *)} introduces a section heading, with text \cd{HEADING} of your choice.
adam@1509 349 \item To include both a rendering of an Ur expression and a pretty-printed version of its value, bracket the expression with \cd{(* begin eval *)} and \cd{(* end *)}. The result of expression evaluation is pretty-printed with \cd{show}, so the expression type must belong to that type class.
adam@1509 350 \item To include code that should not be shown in the tutorial (e.g., to add a \cd{show} instance to use with \cd{eval}), bracket the code with \cd{(* begin hide *)} and \cd{(* end *)}.
adam@1509 351 \end{itemize}
adam@1509 352
adam@1509 353 A word of warning: as for demo generation, tutorial generation calls Emacs to syntax-highlight Ur code.
adam@1509 354
adam@1522 355 \subsection{Run-Time Options}
adam@1522 356
adam@1522 357 Compiled applications consult a few environment variables to modify their behavior:
adam@1522 358
adam@1522 359 \begin{itemize}
adam@1522 360 \item \cd{URWEB\_NUM\_THREADS}: alternative to the \cd{-t} command-line argument (currently used only by FastCGI)
adam@1522 361 \item \cd{URWEB\_STACK\_SIZE}: size of per-thread stacks, in bytes
as@1564 362 \item \cd{URWEB\_PQ\_CON}: when using PostgreSQL, overrides the compiled-in connection string
adam@1522 363 \end{itemize}
adam@1522 364
adam@1509 365
adamc@529 366 \section{Ur Syntax}
adamc@529 367
adamc@784 368 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@524 369
adamc@524 370 \subsection{Lexical Conventions}
adamc@524 371
adamc@524 372 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@524 373
adamc@524 374 \begin{center}
adamc@524 375 \begin{tabular}{rl}
adamc@524 376 \textbf{\LaTeX} & \textbf{ASCII} \\
adamc@524 377 $\to$ & \cd{->} \\
adam@1687 378 $\longrightarrow$ & \cd{-{}->} \\
adamc@524 379 $\times$ & \cd{*} \\
adamc@524 380 $\lambda$ & \cd{fn} \\
adamc@524 381 $\Rightarrow$ & \cd{=>} \\
adamc@652 382 $\Longrightarrow$ & \cd{==>} \\
adamc@529 383 $\neq$ & \cd{<>} \\
adamc@529 384 $\leq$ & \cd{<=} \\
adamc@529 385 $\geq$ & \cd{>=} \\
adamc@524 386 \\
adamc@524 387 $x$ & Normal textual identifier, not beginning with an uppercase letter \\
adamc@525 388 $X$ & Normal textual identifier, beginning with an uppercase letter \\
adamc@524 389 \end{tabular}
adamc@524 390 \end{center}
adamc@524 391
adamc@525 392 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@524 393
adamc@873 394 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@526 395
adamc@527 396 This version of the manual doesn't include operator precedences; see \texttt{src/urweb.grm} for that.
adamc@527 397
adam@1297 398 As in the ML language family, the syntax \texttt{(* ... *)} is used for (nestable) comments. Within XML literals, Ur/Web also supports the usual \texttt{<!-- ... -->} XML comments.
adam@1297 399
adamc@552 400 \subsection{\label{core}Core Syntax}
adamc@524 401
adamc@524 402 \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@524 403 $$\begin{array}{rrcll}
adamc@524 404 \textrm{Kinds} & \kappa &::=& \mt{Type} & \textrm{proper types} \\
adamc@525 405 &&& \mt{Unit} & \textrm{the trivial constructor} \\
adamc@525 406 &&& \mt{Name} & \textrm{field names} \\
adamc@525 407 &&& \kappa \to \kappa & \textrm{type-level functions} \\
adamc@525 408 &&& \{\kappa\} & \textrm{type-level records} \\
adamc@525 409 &&& (\kappa\times^+) & \textrm{type-level tuples} \\
adamc@652 410 &&& X & \textrm{variable} \\
adam@1574 411 &&& X \longrightarrow \kappa & \textrm{kind-polymorphic type-level function} \\
adamc@529 412 &&& \_\_ & \textrm{wildcard} \\
adamc@525 413 &&& (\kappa) & \textrm{explicit precedence} \\
adamc@524 414 \end{array}$$
adamc@524 415
adamc@524 416 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@524 417 $$\begin{array}{rrcll}
adamc@524 418 \textrm{Explicitness} & ? &::=& :: & \textrm{explicit} \\
adamc@558 419 &&& ::: & \textrm{implicit}
adamc@524 420 \end{array}$$
adamc@524 421
adamc@524 422 \emph{Constructors} are the main class of compile-time-only data. They include proper types and are classified by kinds.
adamc@524 423 $$\begin{array}{rrcll}
adamc@524 424 \textrm{Constructors} & c, \tau &::=& (c) :: \kappa & \textrm{kind annotation} \\
adamc@530 425 &&& \hat{x} & \textrm{constructor variable} \\
adamc@524 426 \\
adamc@525 427 &&& \tau \to \tau & \textrm{function type} \\
adamc@525 428 &&& x \; ? \; \kappa \to \tau & \textrm{polymorphic function type} \\
adamc@652 429 &&& X \longrightarrow \tau & \textrm{kind-polymorphic function type} \\
adamc@525 430 &&& \$ c & \textrm{record type} \\
adamc@524 431 \\
adamc@525 432 &&& c \; c & \textrm{type-level function application} \\
adamc@530 433 &&& \lambda x \; :: \; \kappa \Rightarrow c & \textrm{type-level function abstraction} \\
adamc@524 434 \\
adamc@652 435 &&& X \Longrightarrow c & \textrm{type-level kind-polymorphic function abstraction} \\
adamc@655 436 &&& c [\kappa] & \textrm{type-level kind-polymorphic function application} \\
adamc@652 437 \\
adamc@525 438 &&& () & \textrm{type-level unit} \\
adamc@525 439 &&& \#X & \textrm{field name} \\
adamc@524 440 \\
adamc@525 441 &&& [(c = c)^*] & \textrm{known-length type-level record} \\
adamc@525 442 &&& c \rc c & \textrm{type-level record concatenation} \\
adamc@652 443 &&& \mt{map} & \textrm{type-level record map} \\
adamc@524 444 \\
adamc@558 445 &&& (c,^+) & \textrm{type-level tuple} \\
adamc@525 446 &&& c.n & \textrm{type-level tuple projection ($n \in \mathbb N^+$)} \\
adamc@524 447 \\
adamc@652 448 &&& [c \sim c] \Rightarrow \tau & \textrm{guarded type} \\
adamc@524 449 \\
adamc@529 450 &&& \_ :: \kappa & \textrm{wildcard} \\
adamc@525 451 &&& (c) & \textrm{explicit precedence} \\
adamc@530 452 \\
adamc@530 453 \textrm{Qualified uncapitalized variables} & \hat{x} &::=& x & \textrm{not from a module} \\
adamc@530 454 &&& M.x & \textrm{projection from a module} \\
adamc@525 455 \end{array}$$
adamc@525 456
adam@1579 457 We include both abstraction and application for kind polymorphism, but applications are only inferred internally; they may not be written explicitly in source programs. Also, in the ``known-length type-level record'' form, in $c_1 = c_2$ terms, the parser currently only allows $c_1$ to be of the forms $X$ (as a shorthand for $\#X$) or $x$, or a natural number to stand for the corresponding field name (e.g., for tuples).
adamc@655 458
adamc@525 459 Modules of the module system are described by \emph{signatures}.
adamc@525 460 $$\begin{array}{rrcll}
adamc@525 461 \textrm{Signatures} & S &::=& \mt{sig} \; s^* \; \mt{end} & \textrm{constant} \\
adamc@525 462 &&& X & \textrm{variable} \\
adamc@525 463 &&& \mt{functor}(X : S) : S & \textrm{functor} \\
adamc@529 464 &&& S \; \mt{where} \; \mt{con} \; x = c & \textrm{concretizing an abstract constructor} \\
adamc@525 465 &&& M.X & \textrm{projection from a module} \\
adamc@525 466 \\
adamc@525 467 \textrm{Signature items} & s &::=& \mt{con} \; x :: \kappa & \textrm{abstract constructor} \\
adamc@525 468 &&& \mt{con} \; x :: \kappa = c & \textrm{concrete constructor} \\
adamc@528 469 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529 470 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@525 471 &&& \mt{val} \; x : \tau & \textrm{value} \\
adamc@525 472 &&& \mt{structure} \; X : S & \textrm{sub-module} \\
adamc@525 473 &&& \mt{signature} \; X = S & \textrm{sub-signature} \\
adamc@525 474 &&& \mt{include} \; S & \textrm{signature inclusion} \\
adamc@525 475 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@654 476 &&& \mt{class} \; x :: \kappa & \textrm{abstract constructor class} \\
adamc@654 477 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@525 478 \\
adamc@525 479 \textrm{Datatype constructors} & dc &::=& X & \textrm{nullary constructor} \\
adamc@525 480 &&& X \; \mt{of} \; \tau & \textrm{unary constructor} \\
adamc@524 481 \end{array}$$
adamc@524 482
adamc@526 483 \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@526 484 $$\begin{array}{rrcll}
adamc@526 485 \textrm{Patterns} & p &::=& \_ & \textrm{wildcard} \\
adamc@526 486 &&& x & \textrm{variable} \\
adamc@526 487 &&& \ell & \textrm{constant} \\
adamc@526 488 &&& \hat{X} & \textrm{nullary constructor} \\
adamc@526 489 &&& \hat{X} \; p & \textrm{unary constructor} \\
adamc@526 490 &&& \{(x = p,)^*\} & \textrm{rigid record pattern} \\
adamc@526 491 &&& \{(x = p,)^+, \ldots\} & \textrm{flexible record pattern} \\
adamc@852 492 &&& p : \tau & \textrm{type annotation} \\
adamc@527 493 &&& (p) & \textrm{explicit precedence} \\
adamc@526 494 \\
adamc@529 495 \textrm{Qualified capitalized variables} & \hat{X} &::=& X & \textrm{not from a module} \\
adamc@526 496 &&& M.X & \textrm{projection from a module} \\
adamc@526 497 \end{array}$$
adamc@526 498
adamc@527 499 \emph{Expressions} are the main run-time entities, corresponding to both ``expressions'' and ``statements'' in mainstream imperative languages.
adamc@527 500 $$\begin{array}{rrcll}
adamc@527 501 \textrm{Expressions} & e &::=& e : \tau & \textrm{type annotation} \\
adamc@529 502 &&& \hat{x} & \textrm{variable} \\
adamc@529 503 &&& \hat{X} & \textrm{datatype constructor} \\
adamc@527 504 &&& \ell & \textrm{constant} \\
adamc@527 505 \\
adamc@527 506 &&& e \; e & \textrm{function application} \\
adamc@527 507 &&& \lambda x : \tau \Rightarrow e & \textrm{function abstraction} \\
adamc@527 508 &&& e [c] & \textrm{polymorphic function application} \\
adamc@852 509 &&& \lambda [x \; ? \; \kappa] \Rightarrow e & \textrm{polymorphic function abstraction} \\
adamc@655 510 &&& e [\kappa] & \textrm{kind-polymorphic function application} \\
adamc@652 511 &&& X \Longrightarrow e & \textrm{kind-polymorphic function abstraction} \\
adamc@527 512 \\
adamc@527 513 &&& \{(c = e,)^*\} & \textrm{known-length record} \\
adamc@527 514 &&& e.c & \textrm{record field projection} \\
adamc@527 515 &&& e \rc e & \textrm{record concatenation} \\
adamc@527 516 &&& e \rcut c & \textrm{removal of a single record field} \\
adamc@527 517 &&& e \rcutM c & \textrm{removal of multiple record fields} \\
adamc@527 518 \\
adamc@527 519 &&& \mt{let} \; ed^* \; \mt{in} \; e \; \mt{end} & \textrm{local definitions} \\
adamc@527 520 \\
adamc@527 521 &&& \mt{case} \; e \; \mt{of} \; (p \Rightarrow e|)^+ & \textrm{pattern matching} \\
adamc@527 522 \\
adamc@654 523 &&& \lambda [c \sim c] \Rightarrow e & \textrm{guarded expression abstraction} \\
adamc@654 524 &&& e \; ! & \textrm{guarded expression application} \\
adamc@527 525 \\
adamc@527 526 &&& \_ & \textrm{wildcard} \\
adamc@527 527 &&& (e) & \textrm{explicit precedence} \\
adamc@527 528 \\
adamc@527 529 \textrm{Local declarations} & ed &::=& \cd{val} \; x : \tau = e & \textrm{non-recursive value} \\
adam@1797 530 &&& \cd{val} \; \cd{rec} \; (x : \tau = e \; \cd{and})^+ & \textrm{mutually recursive values} \\
adamc@527 531 \end{array}$$
adamc@527 532
adamc@655 533 As with constructors, we include both abstraction and application for kind polymorphism, but applications are only inferred internally.
adamc@655 534
adamc@528 535 \emph{Declarations} primarily bring new symbols into context.
adamc@528 536 $$\begin{array}{rrcll}
adamc@528 537 \textrm{Declarations} & d &::=& \mt{con} \; x :: \kappa = c & \textrm{constructor synonym} \\
adamc@528 538 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529 539 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@528 540 &&& \mt{val} \; x : \tau = e & \textrm{value} \\
adam@1797 541 &&& \mt{val} \; \cd{rec} \; (x : \tau = e \; \mt{and})^+ & \textrm{mutually recursive values} \\
adamc@528 542 &&& \mt{structure} \; X : S = M & \textrm{module definition} \\
adamc@528 543 &&& \mt{signature} \; X = S & \textrm{signature definition} \\
adamc@528 544 &&& \mt{open} \; M & \textrm{module inclusion} \\
adamc@528 545 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@528 546 &&& \mt{open} \; \mt{constraints} \; M & \textrm{inclusion of just the constraints from a module} \\
adamc@528 547 &&& \mt{table} \; x : c & \textrm{SQL table} \\
adam@1594 548 &&& \mt{view} \; x = e & \textrm{SQL view} \\
adamc@528 549 &&& \mt{sequence} \; x & \textrm{SQL sequence} \\
adamc@535 550 &&& \mt{cookie} \; x : \tau & \textrm{HTTP cookie} \\
adamc@784 551 &&& \mt{style} \; x : \tau & \textrm{CSS class} \\
adamc@1085 552 &&& \mt{task} \; e = e & \textrm{recurring task} \\
adamc@528 553 \\
adamc@529 554 \textrm{Modules} & M &::=& \mt{struct} \; d^* \; \mt{end} & \textrm{constant} \\
adamc@529 555 &&& X & \textrm{variable} \\
adamc@529 556 &&& M.X & \textrm{projection} \\
adamc@529 557 &&& M(M) & \textrm{functor application} \\
adamc@529 558 &&& \mt{functor}(X : S) : S = M & \textrm{functor abstraction} \\
adamc@528 559 \end{array}$$
adamc@528 560
adamc@528 561 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@527 562
adam@1594 563 We omit some extra possibilities in $\mt{table}$ syntax, deferring them to Section \ref{tables}. The concrete syntax of $\mt{view}$ declarations is also more complex than shown in the table above, with details deferred to Section \ref{tables}.
adamc@784 564
adamc@529 565 \subsection{Shorthands}
adamc@529 566
adamc@529 567 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@529 568
adamc@529 569 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@529 570
adamc@529 571 A record type may be written $\{(c = c,)^*\}$, which elaborates to $\$[(c = c,)^*]$.
adamc@529 572
adamc@533 573 The notation $[c_1, \ldots, c_n]$ is shorthand for $[c_1 = (), \ldots, c_n = ()]$.
adamc@533 574
adam@1350 575 A tuple type $\tau_1 \times \ldots \times \tau_n$ expands to a record type $\{1 : \tau_1, \ldots, n : \tau_n\}$, with natural numbers as field names. A tuple expression $(e_1, \ldots, e_n)$ expands to a record expression $\{1 = e_1, \ldots, n = e_n\}$. 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@529 576
adam@1687 577 The syntax $()$ expands to $\{\}$ as a pattern or expression.
adam@1687 578
adamc@852 579 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@529 580
adam@1574 581 Further, the signature item or declaration syntax $\mt{con} \; x \; b^+ = c$ is shorthand for wrapping of the appropriate $\lambda$s around the righthand side $c$. The $b$ elements may not include $X$, and there may also be an optional $:: \kappa$ before the $=$.
adam@1574 582
adam@1306 583 In some contexts, the parser isn't happy with token sequences like $x :: \_$, to indicate a constructor variable of wildcard kind. In such cases, write the second two tokens as $::\hspace{-.05in}\_$, with no intervening spaces. Analogous syntax $:::\hspace{-.05in}\_$ is available for implicit constructor arguments.
adam@1302 584
adamc@529 585 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@529 586
adamc@529 587 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@529 588
adamc@654 589 A signature item or declaration $\mt{class} \; x = \lambda y \Rightarrow c$ may be abbreviated $\mt{class} \; x \; y = c$.
adamc@529 590
adam@1738 591 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 type class instance and disjointness arguments have been made explicit. (For the purposes of this paragraph, the type family $\mt{Top.folder}$ is a type class, though it isn't marked as one by the usual means; and any record type is considered to be a type class instance type when every field's type is a type class instance type.) An expression $@@x$ achieves the same effect, additionally making explicit all implicit constructor arguments. The default is that implicit arguments are inserted automatically after any reference to a variable, or after any application of a 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@529 592
adamc@852 593 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@529 594
adamc@852 595 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@852 596
adam@1797 597 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@529 598
adamc@529 599 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@529 600
adamc@852 601 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@852 602
adamc@853 603 A declaration $\mt{table} \; x : \{(c = c,)^*\}$ is elaborated into $\mt{table} \; x : [(c = c,)^*]$.
adamc@529 604
adamc@529 605 The syntax $\mt{where} \; \mt{type}$ is an alternate form of $\mt{where} \; \mt{con}$.
adamc@529 606
adamc@529 607 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@529 608
adamc@529 609 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@529 610
adamc@784 611 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@529 612
adamc@530 613
adamc@530 614 \section{Static Semantics}
adamc@530 615
adamc@530 616 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@530 617
adamc@530 618 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@530 619 \begin{itemize}
adamc@655 620 \item $\Gamma \vdash \kappa$ expresses kind well-formedness.
adamc@530 621 \item $\Gamma \vdash c :: \kappa$ assigns a kind to a constructor in a context.
adamc@530 622 \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@531 623 \item $\Gamma \vdash c \hookrightarrow C$ proves that record constructor $c$ decomposes into set $C$ of field names and record constructors.
adamc@530 624 \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@530 625 \item $\Gamma \vdash e : \tau$ is a standard typing judgment.
adamc@534 626 \item $\Gamma \vdash p \leadsto \Gamma; \tau$ combines typing of patterns with calculation of which new variables they bind.
adamc@537 627 \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@537 628 \item $\Gamma \vdash S \equiv S$ is the signature equivalence judgment.
adamc@536 629 \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@530 630 \item $\Gamma \vdash M : S$ is the module signature checking judgment.
adamc@537 631 \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@539 632 \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@530 633 \end{itemize}
adamc@530 634
adamc@655 635
adamc@655 636 \subsection{Kind Well-Formedness}
adamc@655 637
adamc@655 638 $$\infer{\Gamma \vdash \mt{Type}}{}
adamc@655 639 \quad \infer{\Gamma \vdash \mt{Unit}}{}
adamc@655 640 \quad \infer{\Gamma \vdash \mt{Name}}{}
adamc@655 641 \quad \infer{\Gamma \vdash \kappa_1 \to \kappa_2}{
adamc@655 642 \Gamma \vdash \kappa_1
adamc@655 643 & \Gamma \vdash \kappa_2
adamc@655 644 }
adamc@655 645 \quad \infer{\Gamma \vdash \{\kappa\}}{
adamc@655 646 \Gamma \vdash \kappa
adamc@655 647 }
adamc@655 648 \quad \infer{\Gamma \vdash (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@655 649 \forall i: \Gamma \vdash \kappa_i
adamc@655 650 }$$
adamc@655 651
adamc@655 652 $$\infer{\Gamma \vdash X}{
adamc@655 653 X \in \Gamma
adamc@655 654 }
adamc@655 655 \quad \infer{\Gamma \vdash X \longrightarrow \kappa}{
adamc@655 656 \Gamma, X \vdash \kappa
adamc@655 657 }$$
adamc@655 658
adamc@530 659 \subsection{Kinding}
adamc@530 660
adamc@655 661 We write $[X \mapsto \kappa_1]\kappa_2$ for capture-avoiding substitution of $\kappa_1$ for $X$ in $\kappa_2$.
adamc@655 662
adamc@530 663 $$\infer{\Gamma \vdash (c) :: \kappa :: \kappa}{
adamc@530 664 \Gamma \vdash c :: \kappa
adamc@530 665 }
adamc@530 666 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530 667 x :: \kappa \in \Gamma
adamc@530 668 }
adamc@530 669 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530 670 x :: \kappa = c \in \Gamma
adamc@530 671 }$$
adamc@530 672
adamc@530 673 $$\infer{\Gamma \vdash M.x :: \kappa}{
adamc@537 674 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 675 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = \kappa
adamc@530 676 }
adamc@530 677 \quad \infer{\Gamma \vdash M.x :: \kappa}{
adamc@537 678 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 679 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@530 680 }$$
adamc@530 681
adamc@530 682 $$\infer{\Gamma \vdash \tau_1 \to \tau_2 :: \mt{Type}}{
adamc@530 683 \Gamma \vdash \tau_1 :: \mt{Type}
adamc@530 684 & \Gamma \vdash \tau_2 :: \mt{Type}
adamc@530 685 }
adamc@530 686 \quad \infer{\Gamma \vdash x \; ? \: \kappa \to \tau :: \mt{Type}}{
adamc@530 687 \Gamma, x :: \kappa \vdash \tau :: \mt{Type}
adamc@530 688 }
adamc@655 689 \quad \infer{\Gamma \vdash X \longrightarrow \tau :: \mt{Type}}{
adamc@655 690 \Gamma, X \vdash \tau :: \mt{Type}
adamc@655 691 }
adamc@530 692 \quad \infer{\Gamma \vdash \$c :: \mt{Type}}{
adamc@530 693 \Gamma \vdash c :: \{\mt{Type}\}
adamc@530 694 }$$
adamc@530 695
adamc@530 696 $$\infer{\Gamma \vdash c_1 \; c_2 :: \kappa_2}{
adamc@530 697 \Gamma \vdash c_1 :: \kappa_1 \to \kappa_2
adamc@530 698 & \Gamma \vdash c_2 :: \kappa_1
adamc@530 699 }
adamc@530 700 \quad \infer{\Gamma \vdash \lambda x \; :: \; \kappa_1 \Rightarrow c :: \kappa_1 \to \kappa_2}{
adamc@530 701 \Gamma, x :: \kappa_1 \vdash c :: \kappa_2
adamc@530 702 }$$
adamc@530 703
adamc@655 704 $$\infer{\Gamma \vdash c[\kappa'] :: [X \mapsto \kappa']\kappa}{
adamc@655 705 \Gamma \vdash c :: X \to \kappa
adamc@655 706 & \Gamma \vdash \kappa'
adamc@655 707 }
adamc@655 708 \quad \infer{\Gamma \vdash X \Longrightarrow c :: X \to \kappa}{
adamc@655 709 \Gamma, X \vdash c :: \kappa
adamc@655 710 }$$
adamc@655 711
adamc@530 712 $$\infer{\Gamma \vdash () :: \mt{Unit}}{}
adamc@530 713 \quad \infer{\Gamma \vdash \#X :: \mt{Name}}{}$$
adamc@530 714
adamc@530 715 $$\infer{\Gamma \vdash [\overline{c_i = c'_i}] :: \{\kappa\}}{
adamc@530 716 \forall i: \Gamma \vdash c_i : \mt{Name}
adamc@530 717 & \Gamma \vdash c'_i :: \kappa
adamc@530 718 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@530 719 }
adamc@530 720 \quad \infer{\Gamma \vdash c_1 \rc c_2 :: \{\kappa\}}{
adamc@530 721 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530 722 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@530 723 & \Gamma \vdash c_1 \sim c_2
adamc@530 724 }$$
adamc@530 725
adamc@655 726 $$\infer{\Gamma \vdash \mt{map} :: (\kappa_1 \to \kappa_2) \to \{\kappa_1\} \to \{\kappa_2\}}{}$$
adamc@530 727
adamc@573 728 $$\infer{\Gamma \vdash (\overline c) :: (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@573 729 \forall i: \Gamma \vdash c_i :: \kappa_i
adamc@530 730 }
adamc@573 731 \quad \infer{\Gamma \vdash c.i :: \kappa_i}{
adamc@573 732 \Gamma \vdash c :: (\kappa_1 \times \ldots \times \kappa_n)
adamc@530 733 }$$
adamc@530 734
adamc@655 735 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow \tau :: \mt{Type}}{
adamc@655 736 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530 737 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@655 738 & \Gamma, c_1 \sim c_2 \vdash \tau :: \mt{Type}
adamc@530 739 }$$
adamc@530 740
adamc@531 741 \subsection{Record Disjointness}
adamc@531 742
adamc@531 743 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@558 744 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@558 745 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@558 746 & \forall c'_1 \in C_1, c'_2 \in C_2: \Gamma \vdash c'_1 \sim c'_2
adamc@531 747 }
adamc@531 748 \quad \infer{\Gamma \vdash X \sim X'}{
adamc@531 749 X \neq X'
adamc@531 750 }$$
adamc@531 751
adamc@531 752 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@531 753 c'_1 \sim c'_2 \in \Gamma
adamc@558 754 & \Gamma \vdash c'_1 \hookrightarrow C_1
adamc@558 755 & \Gamma \vdash c'_2 \hookrightarrow C_2
adamc@558 756 & c_1 \in C_1
adamc@558 757 & c_2 \in C_2
adamc@531 758 }$$
adamc@531 759
adamc@531 760 $$\infer{\Gamma \vdash c \hookrightarrow \{c\}}{}
adamc@531 761 \quad \infer{\Gamma \vdash [\overline{c = c'}] \hookrightarrow \{\overline{c}\}}{}
adamc@531 762 \quad \infer{\Gamma \vdash c_1 \rc c_2 \hookrightarrow C_1 \cup C_2}{
adamc@531 763 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@531 764 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@531 765 }
adamc@531 766 \quad \infer{\Gamma \vdash c \hookrightarrow C}{
adamc@531 767 \Gamma \vdash c \equiv c'
adamc@531 768 & \Gamma \vdash c' \hookrightarrow C
adamc@531 769 }
adamc@531 770 \quad \infer{\Gamma \vdash \mt{map} \; f \; c \hookrightarrow C}{
adamc@531 771 \Gamma \vdash c \hookrightarrow C
adamc@531 772 }$$
adamc@531 773
adamc@541 774 \subsection{\label{definitional}Definitional Equality}
adamc@532 775
adamc@655 776 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@532 777
adamc@532 778 $$\infer{\Gamma \vdash c \equiv c}{}
adamc@532 779 \quad \infer{\Gamma \vdash c_1 \equiv c_2}{
adamc@532 780 \Gamma \vdash c_2 \equiv c_1
adamc@532 781 }
adamc@532 782 \quad \infer{\Gamma \vdash c_1 \equiv c_3}{
adamc@532 783 \Gamma \vdash c_1 \equiv c_2
adamc@532 784 & \Gamma \vdash c_2 \equiv c_3
adamc@532 785 }
adamc@532 786 \quad \infer{\Gamma \vdash \mathcal C[c_1] \equiv \mathcal C[c_2]}{
adamc@532 787 \Gamma \vdash c_1 \equiv c_2
adamc@532 788 }$$
adamc@532 789
adamc@532 790 $$\infer{\Gamma \vdash x \equiv c}{
adamc@532 791 x :: \kappa = c \in \Gamma
adamc@532 792 }
adamc@532 793 \quad \infer{\Gamma \vdash M.x \equiv c}{
adamc@537 794 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 795 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@532 796 }
adamc@532 797 \quad \infer{\Gamma \vdash (\overline c).i \equiv c_i}{}$$
adamc@532 798
adamc@532 799 $$\infer{\Gamma \vdash (\lambda x :: \kappa \Rightarrow c) \; c' \equiv [x \mapsto c'] c}{}
adamc@655 800 \quad \infer{\Gamma \vdash (X \Longrightarrow c) [\kappa] \equiv [X \mapsto \kappa] c}{}$$
adamc@655 801
adamc@655 802 $$\infer{\Gamma \vdash c_1 \rc c_2 \equiv c_2 \rc c_1}{}
adamc@532 803 \quad \infer{\Gamma \vdash c_1 \rc (c_2 \rc c_3) \equiv (c_1 \rc c_2) \rc c_3}{}$$
adamc@532 804
adamc@532 805 $$\infer{\Gamma \vdash [] \rc c \equiv c}{}
adamc@532 806 \quad \infer{\Gamma \vdash [\overline{c_1 = c'_1}] \rc [\overline{c_2 = c'_2}] \equiv [\overline{c_1 = c'_1}, \overline{c_2 = c'_2}]}{}$$
adamc@532 807
adamc@655 808 $$\infer{\Gamma \vdash \mt{map} \; f \; [] \equiv []}{}
adamc@655 809 \quad \infer{\Gamma \vdash \mt{map} \; f \; ([c_1 = c_2] \rc c) \equiv [c_1 = f \; c_2] \rc \mt{map} \; f \; c}{}$$
adamc@532 810
adamc@532 811 $$\infer{\Gamma \vdash \mt{map} \; (\lambda x \Rightarrow x) \; c \equiv c}{}
adamc@655 812 \quad \infer{\Gamma \vdash \mt{map} \; f \; (\mt{map} \; f' \; c)
adamc@655 813 \equiv \mt{map} \; (\lambda x \Rightarrow f \; (f' \; x)) \; c}{}$$
adamc@532 814
adamc@532 815 $$\infer{\Gamma \vdash \mt{map} \; f \; (c_1 \rc c_2) \equiv \mt{map} \; f \; c_1 \rc \mt{map} \; f \; c_2}{}$$
adamc@531 816
adamc@534 817 \subsection{Expression Typing}
adamc@533 818
adamc@873 819 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@533 820
adamc@533 821 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@533 822
adamc@533 823 $$\infer{\Gamma \vdash e : \tau : \tau}{
adamc@533 824 \Gamma \vdash e : \tau
adamc@533 825 }
adamc@533 826 \quad \infer{\Gamma \vdash e : \tau}{
adamc@533 827 \Gamma \vdash e : \tau'
adamc@533 828 & \Gamma \vdash \tau' \equiv \tau
adamc@533 829 }
adamc@533 830 \quad \infer{\Gamma \vdash \ell : T(\ell)}{}$$
adamc@533 831
adamc@533 832 $$\infer{\Gamma \vdash x : \mathcal I(\tau)}{
adamc@533 833 x : \tau \in \Gamma
adamc@533 834 }
adamc@533 835 \quad \infer{\Gamma \vdash M.x : \mathcal I(\tau)}{
adamc@537 836 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 837 & \mt{proj}(M, \overline{s}, \mt{val} \; x) = \tau
adamc@533 838 }
adamc@533 839 \quad \infer{\Gamma \vdash X : \mathcal I(\tau)}{
adamc@533 840 X : \tau \in \Gamma
adamc@533 841 }
adamc@533 842 \quad \infer{\Gamma \vdash M.X : \mathcal I(\tau)}{
adamc@537 843 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 844 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \tau
adamc@533 845 }$$
adamc@533 846
adamc@533 847 $$\infer{\Gamma \vdash e_1 \; e_2 : \tau_2}{
adamc@533 848 \Gamma \vdash e_1 : \tau_1 \to \tau_2
adamc@533 849 & \Gamma \vdash e_2 : \tau_1
adamc@533 850 }
adamc@533 851 \quad \infer{\Gamma \vdash \lambda x : \tau_1 \Rightarrow e : \tau_1 \to \tau_2}{
adamc@533 852 \Gamma, x : \tau_1 \vdash e : \tau_2
adamc@533 853 }$$
adamc@533 854
adamc@533 855 $$\infer{\Gamma \vdash e [c] : [x \mapsto c]\tau}{
adamc@533 856 \Gamma \vdash e : x :: \kappa \to \tau
adamc@533 857 & \Gamma \vdash c :: \kappa
adamc@533 858 }
adamc@852 859 \quad \infer{\Gamma \vdash \lambda [x \; ? \; \kappa] \Rightarrow e : x \; ? \; \kappa \to \tau}{
adamc@533 860 \Gamma, x :: \kappa \vdash e : \tau
adamc@533 861 }$$
adamc@533 862
adamc@655 863 $$\infer{\Gamma \vdash e [\kappa] : [X \mapsto \kappa]\tau}{
adamc@655 864 \Gamma \vdash e : X \longrightarrow \tau
adamc@655 865 & \Gamma \vdash \kappa
adamc@655 866 }
adamc@655 867 \quad \infer{\Gamma \vdash X \Longrightarrow e : X \longrightarrow \tau}{
adamc@655 868 \Gamma, X \vdash e : \tau
adamc@655 869 }$$
adamc@655 870
adamc@533 871 $$\infer{\Gamma \vdash \{\overline{c = e}\} : \{\overline{c : \tau}\}}{
adamc@533 872 \forall i: \Gamma \vdash c_i :: \mt{Name}
adamc@533 873 & \Gamma \vdash e_i : \tau_i
adamc@533 874 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@533 875 }
adamc@533 876 \quad \infer{\Gamma \vdash e.c : \tau}{
adamc@533 877 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533 878 }
adamc@533 879 \quad \infer{\Gamma \vdash e_1 \rc e_2 : \$(c_1 \rc c_2)}{
adamc@533 880 \Gamma \vdash e_1 : \$c_1
adamc@533 881 & \Gamma \vdash e_2 : \$c_2
adamc@573 882 & \Gamma \vdash c_1 \sim c_2
adamc@533 883 }$$
adamc@533 884
adamc@533 885 $$\infer{\Gamma \vdash e \rcut c : \$c'}{
adamc@533 886 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533 887 }
adamc@533 888 \quad \infer{\Gamma \vdash e \rcutM c : \$c'}{
adamc@533 889 \Gamma \vdash e : \$(c \rc c')
adamc@533 890 }$$
adamc@533 891
adamc@533 892 $$\infer{\Gamma \vdash \mt{let} \; \overline{ed} \; \mt{in} \; e \; \mt{end} : \tau}{
adamc@533 893 \Gamma \vdash \overline{ed} \leadsto \Gamma'
adamc@533 894 & \Gamma' \vdash e : \tau
adamc@533 895 }
adamc@533 896 \quad \infer{\Gamma \vdash \mt{case} \; e \; \mt{of} \; \overline{p \Rightarrow e} : \tau}{
adamc@533 897 \forall i: \Gamma \vdash p_i \leadsto \Gamma_i, \tau'
adamc@533 898 & \Gamma_i \vdash e_i : \tau
adamc@533 899 }$$
adamc@533 900
adamc@573 901 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow e : \lambda [c_1 \sim c_2] \Rightarrow \tau}{
adamc@533 902 \Gamma \vdash c_1 :: \{\kappa\}
adamc@655 903 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@533 904 & \Gamma, c_1 \sim c_2 \vdash e : \tau
adamc@662 905 }
adamc@662 906 \quad \infer{\Gamma \vdash e \; ! : \tau}{
adamc@662 907 \Gamma \vdash e : [c_1 \sim c_2] \Rightarrow \tau
adamc@662 908 & \Gamma \vdash c_1 \sim c_2
adamc@533 909 }$$
adamc@533 910
adamc@534 911 \subsection{Pattern Typing}
adamc@534 912
adamc@534 913 $$\infer{\Gamma \vdash \_ \leadsto \Gamma; \tau}{}
adamc@534 914 \quad \infer{\Gamma \vdash x \leadsto \Gamma, x : \tau; \tau}{}
adamc@534 915 \quad \infer{\Gamma \vdash \ell \leadsto \Gamma; T(\ell)}{}$$
adamc@534 916
adamc@534 917 $$\infer{\Gamma \vdash X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534 918 X : \overline{x ::: \mt{Type}} \to \tau \in \Gamma
adamc@534 919 & \textrm{$\tau$ not a function type}
adamc@534 920 }
adamc@534 921 \quad \infer{\Gamma \vdash X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534 922 X : \overline{x ::: \mt{Type}} \to \tau'' \to \tau \in \Gamma
adamc@534 923 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534 924 }$$
adamc@534 925
adamc@534 926 $$\infer{\Gamma \vdash M.X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537 927 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 928 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau
adamc@534 929 & \textrm{$\tau$ not a function type}
adamc@534 930 }$$
adamc@534 931
adamc@534 932 $$\infer{\Gamma \vdash M.X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537 933 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 934 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau'' \to \tau
adamc@534 935 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534 936 }$$
adamc@534 937
adamc@534 938 $$\infer{\Gamma \vdash \{\overline{x = p}\} \leadsto \Gamma_n; \{\overline{x = \tau}\}}{
adamc@534 939 \Gamma_0 = \Gamma
adamc@534 940 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534 941 }
adamc@534 942 \quad \infer{\Gamma \vdash \{\overline{x = p}, \ldots\} \leadsto \Gamma_n; \$([\overline{x = \tau}] \rc c)}{
adamc@534 943 \Gamma_0 = \Gamma
adamc@534 944 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534 945 }$$
adamc@534 946
adamc@852 947 $$\infer{\Gamma \vdash p : \tau \leadsto \Gamma'; \tau}{
adamc@852 948 \Gamma \vdash p \leadsto \Gamma'; \tau'
adamc@852 949 & \Gamma \vdash \tau' \equiv \tau
adamc@852 950 }$$
adamc@852 951
adamc@535 952 \subsection{Declaration Typing}
adamc@535 953
adamc@535 954 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@535 955
adamc@558 956 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@537 957 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@535 958
adamc@535 959 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535 960 \quad \infer{\Gamma \vdash d, \overline{d} \leadsto \Gamma''}{
adamc@535 961 \Gamma \vdash d \leadsto \Gamma'
adamc@535 962 & \Gamma' \vdash \overline{d} \leadsto \Gamma''
adamc@535 963 }$$
adamc@535 964
adamc@535 965 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@535 966 \Gamma \vdash c :: \kappa
adamc@535 967 }
adamc@535 968 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@535 969 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@535 970 }$$
adamc@535 971
adamc@535 972 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537 973 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 974 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@535 975 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@535 976 }$$
adamc@535 977
adamc@535 978 $$\infer{\Gamma \vdash \mt{val} \; x : \tau = e \leadsto \Gamma, x : \tau}{
adamc@535 979 \Gamma \vdash e : \tau
adamc@535 980 }$$
adamc@535 981
adamc@535 982 $$\infer{\Gamma \vdash \mt{val} \; \mt{rec} \; \overline{x : \tau = e} \leadsto \Gamma, \overline{x : \tau}}{
adamc@535 983 \forall i: \Gamma, \overline{x : \tau} \vdash e_i : \tau_i
adamc@535 984 & \textrm{$e_i$ starts with an expression $\lambda$, optionally preceded by constructor and disjointness $\lambda$s}
adamc@535 985 }$$
adamc@535 986
adamc@535 987 $$\infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : S}{
adamc@535 988 \Gamma \vdash M : S
adamc@558 989 & \textrm{ $M$ not a constant or application}
adamc@535 990 }
adamc@558 991 \quad \infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : \mt{selfify}(X, \overline{s})}{
adamc@558 992 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@539 993 }$$
adamc@539 994
adamc@539 995 $$\infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@535 996 \Gamma \vdash S
adamc@535 997 }$$
adamc@535 998
adamc@537 999 $$\infer{\Gamma \vdash \mt{open} \; M \leadsto \Gamma, \mathcal O(M, \overline{s})}{
adamc@537 1000 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535 1001 }$$
adamc@535 1002
adamc@535 1003 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma}{
adamc@535 1004 \Gamma \vdash c_1 :: \{\kappa\}
adamc@535 1005 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@535 1006 & \Gamma \vdash c_1 \sim c_2
adamc@535 1007 }
adamc@537 1008 \quad \infer{\Gamma \vdash \mt{open} \; \mt{constraints} \; M \leadsto \Gamma, \mathcal O_c(M, \overline{s})}{
adamc@537 1009 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535 1010 }$$
adamc@535 1011
adamc@784 1012 $$\infer{\Gamma \vdash \mt{table} \; x : c \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_table} \; c \; []}{
adamc@535 1013 \Gamma \vdash c :: \{\mt{Type}\}
adamc@535 1014 }
adam@1594 1015 \quad \infer{\Gamma \vdash \mt{view} \; x = e \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_view} \; c}{
adam@1594 1016 \Gamma \vdash e :: \mt{Basis}.\mt{sql\_query} \; [] \; [] \; (\mt{map} \; (\lambda \_ \Rightarrow []) \; c') \; c
adamc@784 1017 }$$
adamc@784 1018
adamc@784 1019 $$\infer{\Gamma \vdash \mt{sequence} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_sequence}}{}$$
adamc@535 1020
adamc@535 1021 $$\infer{\Gamma \vdash \mt{cookie} \; x : \tau \leadsto \Gamma, x : \mt{Basis}.\mt{http\_cookie} \; \tau}{
adamc@535 1022 \Gamma \vdash \tau :: \mt{Type}
adamc@784 1023 }
adamc@784 1024 \quad \infer{\Gamma \vdash \mt{style} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{css\_class}}{}$$
adamc@535 1025
adamc@1085 1026 $$\infer{\Gamma \vdash \mt{task} \; e_1 = e_2 \leadsto \Gamma}{
adam@1348 1027 \Gamma \vdash e_1 :: \mt{Basis}.\mt{task\_kind} \; \tau
adam@1348 1028 & \Gamma \vdash e_2 :: \tau \to \mt{Basis}.\mt{transaction} \; \{\}
adamc@1085 1029 }$$
adamc@1085 1030
adamc@535 1031 $$\infer{\overline{y}; x; \Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535 1032 \quad \infer{\overline{y}; x; \Gamma \vdash X \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to x \; \overline{y}}{
adamc@535 1033 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535 1034 }
adamc@535 1035 \quad \infer{\overline{y}; x; \Gamma \vdash X \; \mt{of} \; \tau \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to \tau \to x \; \overline{y}}{
adamc@535 1036 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535 1037 }$$
adamc@535 1038
adamc@537 1039 \subsection{Signature Item Typing}
adamc@537 1040
adamc@537 1041 We appeal to a signature item analogue of the $\mathcal O$ function from the last subsection.
adamc@537 1042
adam@1797 1043 This is the first judgment where we deal with constructor classes, for the $\mt{class}$ forms. We will omit their special handling in this formal specification. Section \ref{typeclasses} gives an informal description of how constructor classes influence type inference.
adam@1797 1044
adamc@537 1045 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@537 1046 \quad \infer{\Gamma \vdash s, \overline{s} \leadsto \Gamma''}{
adamc@537 1047 \Gamma \vdash s \leadsto \Gamma'
adamc@537 1048 & \Gamma' \vdash \overline{s} \leadsto \Gamma''
adamc@537 1049 }$$
adamc@537 1050
adamc@537 1051 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}
adamc@537 1052 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@537 1053 \Gamma \vdash c :: \kappa
adamc@537 1054 }
adamc@537 1055 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@537 1056 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@537 1057 }$$
adamc@537 1058
adamc@537 1059 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537 1060 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1061 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1062 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@537 1063 }$$
adamc@537 1064
adamc@537 1065 $$\infer{\Gamma \vdash \mt{val} \; x : \tau \leadsto \Gamma, x : \tau}{
adamc@537 1066 \Gamma \vdash \tau :: \mt{Type}
adamc@537 1067 }$$
adamc@537 1068
adamc@537 1069 $$\infer{\Gamma \vdash \mt{structure} \; X : S \leadsto \Gamma, X : S}{
adamc@537 1070 \Gamma \vdash S
adamc@537 1071 }
adamc@537 1072 \quad \infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@537 1073 \Gamma \vdash S
adamc@537 1074 }$$
adamc@537 1075
adamc@537 1076 $$\infer{\Gamma \vdash \mt{include} \; S \leadsto \Gamma, \mathcal O(\overline{s})}{
adamc@537 1077 \Gamma \vdash S
adamc@537 1078 & \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1079 }$$
adamc@537 1080
adamc@537 1081 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma, c_1 \sim c_2}{
adamc@537 1082 \Gamma \vdash c_1 :: \{\kappa\}
adamc@537 1083 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@537 1084 }$$
adamc@537 1085
adamc@784 1086 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784 1087 \Gamma \vdash c :: \kappa
adamc@537 1088 }
adamc@784 1089 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}$$
adamc@537 1090
adamc@536 1091 \subsection{Signature Compatibility}
adamc@536 1092
adam@1797 1093 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 1094
adamc@537 1095 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 1096
adamc@536 1097 $$\infer{\Gamma \vdash S \equiv S}{}
adamc@536 1098 \quad \infer{\Gamma \vdash S_1 \equiv S_2}{
adamc@536 1099 \Gamma \vdash S_2 \equiv S_1
adamc@536 1100 }
adamc@536 1101 \quad \infer{\Gamma \vdash X \equiv S}{
adamc@536 1102 X = S \in \Gamma
adamc@536 1103 }
adamc@536 1104 \quad \infer{\Gamma \vdash M.X \equiv S}{
adamc@537 1105 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1106 & \mt{proj}(M, \overline{s}, \mt{signature} \; X) = S
adamc@536 1107 }$$
adamc@536 1108
adamc@536 1109 $$\infer{\Gamma \vdash S \; \mt{where} \; \mt{con} \; x = c \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa = c \; \overline{s_2} \; \mt{end}}{
adamc@536 1110 \Gamma \vdash S \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa \; \overline{s_2} \; \mt{end}
adamc@536 1111 & \Gamma \vdash c :: \kappa
adamc@537 1112 }
adamc@537 1113 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s^1} \; \mt{include} \; S \; \overline{s^2} \; \mt{end} \equiv \mt{sig} \; \overline{s^1} \; \overline{s} \; \overline{s^2} \; \mt{end}}{
adamc@537 1114 \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@536 1115 }$$
adamc@536 1116
adamc@536 1117 $$\infer{\Gamma \vdash S_1 \leq S_2}{
adamc@536 1118 \Gamma \vdash S_1 \equiv S_2
adamc@536 1119 }
adamc@536 1120 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \mt{end}}{}
adamc@537 1121 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; s' \; \overline{s'} \; \mt{end}}{
adamc@537 1122 \Gamma \vdash \overline{s} \leq s'
adamc@537 1123 & \Gamma \vdash s' \leadsto \Gamma'
adamc@537 1124 & \Gamma' \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \overline{s'} \; \mt{end}
adamc@537 1125 }$$
adamc@537 1126
adamc@537 1127 $$\infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537 1128 \Gamma \vdash s \leq s'
adamc@537 1129 }
adamc@537 1130 \quad \infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537 1131 \Gamma \vdash s \leadsto \Gamma'
adamc@537 1132 & \Gamma' \vdash \overline{s} \leq s'
adamc@536 1133 }$$
adamc@536 1134
adamc@536 1135 $$\infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 \leq \mt{functor} (X : S'_1) : S'_2}{
adamc@536 1136 \Gamma \vdash S'_1 \leq S_1
adamc@536 1137 & \Gamma, X : S'_1 \vdash S_2 \leq S'_2
adamc@536 1138 }$$
adamc@536 1139
adamc@537 1140 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@537 1141 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}
adamc@558 1142 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type}}{}$$
adamc@537 1143
adamc@537 1144 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(y)} \to \mt{Type}}{
adamc@537 1145 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1146 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1147 }$$
adamc@537 1148
adamc@784 1149 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@784 1150 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}$$
adamc@537 1151
adamc@537 1152 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \mt{\kappa} = c_2}{
adamc@537 1153 \Gamma \vdash c_1 \equiv c_2
adamc@537 1154 }
adamc@784 1155 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \kappa = c_2}{
adamc@537 1156 \Gamma \vdash c_1 \equiv c_2
adamc@537 1157 }$$
adamc@537 1158
adamc@537 1159 $$\infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537 1160 \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1161 }$$
adamc@537 1162
adamc@537 1163 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537 1164 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1165 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1166 & \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1167 }$$
adamc@537 1168
adamc@537 1169 $$\infer{\Gamma \vdash \cdot \leq \cdot}{}
adamc@537 1170 \quad \infer{\Gamma \vdash X; \overline{dc} \leq X; \overline{dc'}}{
adamc@537 1171 \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1172 }
adamc@537 1173 \quad \infer{\Gamma \vdash X \; \mt{of} \; \tau_1; \overline{dc} \leq X \; \mt{of} \; \tau_2; \overline{dc'}}{
adamc@537 1174 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537 1175 & \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1176 }$$
adamc@537 1177
adamc@537 1178 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x = \mt{datatype} \; M'.z'}{
adamc@537 1179 \Gamma \vdash M.z \equiv M'.z'
adamc@537 1180 }$$
adamc@537 1181
adamc@537 1182 $$\infer{\Gamma \vdash \mt{val} \; x : \tau_1 \leq \mt{val} \; x : \tau_2}{
adamc@537 1183 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537 1184 }
adamc@537 1185 \quad \infer{\Gamma \vdash \mt{structure} \; X : S_1 \leq \mt{structure} \; X : S_2}{
adamc@537 1186 \Gamma \vdash S_1 \leq S_2
adamc@537 1187 }
adamc@537 1188 \quad \infer{\Gamma \vdash \mt{signature} \; X = S_1 \leq \mt{signature} \; X = S_2}{
adamc@537 1189 \Gamma \vdash S_1 \leq S_2
adamc@537 1190 & \Gamma \vdash S_2 \leq S_1
adamc@537 1191 }$$
adamc@537 1192
adamc@537 1193 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leq \mt{constraint} \; c'_1 \sim c'_2}{
adamc@537 1194 \Gamma \vdash c_1 \equiv c'_1
adamc@537 1195 & \Gamma \vdash c_2 \equiv c'_2
adamc@537 1196 }$$
adamc@537 1197
adamc@655 1198 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{class} \; x :: \kappa}{}
adamc@655 1199 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{class} \; x :: \kappa}{}
adamc@655 1200 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{class} \; x :: \kappa = c_2}{
adamc@537 1201 \Gamma \vdash c_1 \equiv c_2
adamc@537 1202 }$$
adamc@537 1203
adam@1797 1204 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leq \mt{class} \; x :: \kappa}{}
adam@1797 1205 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leq \mt{class} \; x :: \kappa}{}
adam@1797 1206 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c_1 \leq \mt{class} \; x :: \kappa = c_2}{
adam@1797 1207 \Gamma \vdash c_1 \equiv c_2
adam@1797 1208 }$$
adam@1797 1209
adamc@538 1210 \subsection{Module Typing}
adamc@538 1211
adamc@538 1212 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 1213
adamc@538 1214 $$\infer{\Gamma \vdash M : S}{
adamc@538 1215 \Gamma \vdash M : S'
adamc@538 1216 & \Gamma \vdash S' \leq S
adamc@538 1217 }
adamc@538 1218 \quad \infer{\Gamma \vdash \mt{struct} \; \overline{d} \; \mt{end} : \mt{sig} \; \mt{sigOf}(\overline{d}) \; \mt{end}}{
adamc@538 1219 \Gamma \vdash \overline{d} \leadsto \Gamma'
adamc@538 1220 }
adamc@538 1221 \quad \infer{\Gamma \vdash X : S}{
adamc@538 1222 X : S \in \Gamma
adamc@538 1223 }$$
adamc@538 1224
adamc@538 1225 $$\infer{\Gamma \vdash M.X : S}{
adamc@538 1226 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@538 1227 & \mt{proj}(M, \overline{s}, \mt{structure} \; X) = S
adamc@538 1228 }$$
adamc@538 1229
adamc@538 1230 $$\infer{\Gamma \vdash M_1(M_2) : [X \mapsto M_2]S_2}{
adamc@538 1231 \Gamma \vdash M_1 : \mt{functor}(X : S_1) : S_2
adamc@538 1232 & \Gamma \vdash M_2 : S_1
adamc@538 1233 }
adamc@538 1234 \quad \infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 = M : \mt{functor} (X : S_1) : S_2}{
adamc@538 1235 \Gamma \vdash S_1
adamc@538 1236 & \Gamma, X : S_1 \vdash S_2
adamc@538 1237 & \Gamma, X : S_1 \vdash M : S_2
adamc@538 1238 }$$
adamc@538 1239
adamc@538 1240 \begin{eqnarray*}
adamc@538 1241 \mt{sigOf}(\cdot) &=& \cdot \\
adamc@538 1242 \mt{sigOf}(s \; \overline{s'}) &=& \mt{sigOf}(s) \; \mt{sigOf}(\overline{s'}) \\
adamc@538 1243 \\
adamc@538 1244 \mt{sigOf}(\mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@538 1245 \mt{sigOf}(\mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \overline{dc} \\
adamc@538 1246 \mt{sigOf}(\mt{datatype} \; x = \mt{datatype} \; M.z) &=& \mt{datatype} \; x = \mt{datatype} \; M.z \\
adamc@538 1247 \mt{sigOf}(\mt{val} \; x : \tau = e) &=& \mt{val} \; x : \tau \\
adamc@538 1248 \mt{sigOf}(\mt{val} \; \mt{rec} \; \overline{x : \tau = e}) &=& \overline{\mt{val} \; x : \tau} \\
adamc@538 1249 \mt{sigOf}(\mt{structure} \; X : S = M) &=& \mt{structure} \; X : S \\
adamc@538 1250 \mt{sigOf}(\mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@538 1251 \mt{sigOf}(\mt{open} \; M) &=& \mt{include} \; S \textrm{ (where $\Gamma \vdash M : S$)} \\
adamc@538 1252 \mt{sigOf}(\mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@538 1253 \mt{sigOf}(\mt{open} \; \mt{constraints} \; M) &=& \cdot \\
adamc@538 1254 \mt{sigOf}(\mt{table} \; x : c) &=& \mt{table} \; x : c \\
adam@1594 1255 \mt{sigOf}(\mt{view} \; x = e) &=& \mt{view} \; x : c \textrm{ (where $\Gamma \vdash e : \mt{Basis}.\mt{sql\_query} \; [] \; [] \; (\mt{map} \; (\lambda \_ \Rightarrow []) \; c') \; c$)} \\
adamc@538 1256 \mt{sigOf}(\mt{sequence} \; x) &=& \mt{sequence} \; x \\
adamc@538 1257 \mt{sigOf}(\mt{cookie} \; x : \tau) &=& \mt{cookie} \; x : \tau \\
adam@1797 1258 \mt{sigOf}(\mt{style} \; x) &=& \mt{style} \; x
adamc@538 1259 \end{eqnarray*}
adamc@539 1260 \begin{eqnarray*}
adamc@539 1261 \mt{selfify}(M, \cdot) &=& \cdot \\
adamc@558 1262 \mt{selfify}(M, s \; \overline{s'}) &=& \mt{selfify}(M, s) \; \mt{selfify}(M, \overline{s'}) \\
adamc@539 1263 \\
adamc@539 1264 \mt{selfify}(M, \mt{con} \; x :: \kappa) &=& \mt{con} \; x :: \kappa = M.x \\
adamc@539 1265 \mt{selfify}(M, \mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@539 1266 \mt{selfify}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \mt{datatype} \; M.x \\
adamc@539 1267 \mt{selfify}(M, \mt{datatype} \; x = \mt{datatype} \; M'.z) &=& \mt{datatype} \; x = \mt{datatype} \; M'.z \\
adamc@539 1268 \mt{selfify}(M, \mt{val} \; x : \tau) &=& \mt{val} \; x : \tau \\
adamc@539 1269 \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 1270 \mt{selfify}(M, \mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@539 1271 \mt{selfify}(M, \mt{include} \; S) &=& \mt{include} \; S \\
adamc@539 1272 \mt{selfify}(M, \mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@655 1273 \mt{selfify}(M, \mt{class} \; x :: \kappa) &=& \mt{class} \; x :: \kappa = M.x \\
adamc@655 1274 \mt{selfify}(M, \mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@539 1275 \end{eqnarray*}
adamc@539 1276
adamc@540 1277 \subsection{Module Projection}
adamc@540 1278
adamc@540 1279 \begin{eqnarray*}
adamc@540 1280 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \\
adamc@540 1281 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa, c) \\
adamc@540 1282 \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 1283 \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 1284 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})$)} \\
adamc@655 1285 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \to \mt{Type} \\
adamc@655 1286 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa \to \mt{Type}, c) \\
adamc@540 1287 \\
adamc@540 1288 \mt{proj}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc} \; \overline{s}, \mt{datatype} \; x) &=& (\overline{y}, \overline{dc}) \\
adamc@540 1289 \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 1290 \\
adamc@540 1291 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, \mt{val} \; x) &=& \tau \\
adamc@540 1292 \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 1293 \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 1294 \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 1295 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \in \overline{dc}$)} \\
adamc@540 1296 \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 1297 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \; \mt{of} \; \tau \in \overline{dc}$)} \\
adamc@540 1298 \\
adamc@540 1299 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, \mt{structure} \; X) &=& S \\
adamc@540 1300 \\
adamc@540 1301 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, \mt{signature} \; X) &=& S \\
adamc@540 1302 \\
adamc@540 1303 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1304 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1305 \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 1306 \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 1307 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@540 1308 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1309 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1310 \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 1311 \mt{proj}(M, \mt{constraint} \; c_1 \sim c_2 \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@655 1312 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@655 1313 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1314 \end{eqnarray*}
adamc@540 1315
adamc@541 1316
adamc@541 1317 \section{Type Inference}
adamc@541 1318
adamc@541 1319 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 1320
adamc@541 1321 \subsection{Basic Unification}
adamc@541 1322
adamc@560 1323 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 1324
adamc@656 1325 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 1326
adamc@541 1327 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 1328
adamc@541 1329 \subsection{Unifying Record Types}
adamc@541 1330
adamc@570 1331 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 1332
adamc@656 1333 \subsection{\label{typeclasses}Constructor Classes}
adamc@541 1334
adamc@784 1335 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 1336
adam@1797 1337 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. Any suitably kinded constructor within a module may be exposed as a constructor class from outside the module, simply by using a $\mt{class}$ signature item instead of a $\mt{con}$ signature item in the module's signature.
adam@1797 1338
adam@1797 1339 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.
adam@1797 1340
adam@1797 1341 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. Automatic inference of concrete class instances will not generally work, so abstract classes are almost always the right choice. They 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. Free extension of a concrete class is easily supported by exporting a constructor function from a module, since the class implementation will be concrete within the module.
adamc@541 1342
adamc@541 1343 \subsection{Reverse-Engineering Record Types}
adamc@541 1344
adamc@656 1345 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 1346
adamc@541 1347 \subsection{Implicit Arguments in Functor Applications}
adamc@541 1348
adamc@656 1349 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 1350
adamc@541 1351
adamc@542 1352 \section{The Ur Standard Library}
adamc@542 1353
adamc@542 1354 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 1355
adamc@542 1356 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 1357
adamc@542 1358 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 1359 $$\begin{array}{l}
adamc@542 1360 \mt{type} \; \mt{int} \\
adamc@542 1361 \mt{type} \; \mt{float} \\
adamc@873 1362 \mt{type} \; \mt{char} \\
adamc@542 1363 \mt{type} \; \mt{string} \\
adamc@542 1364 \mt{type} \; \mt{time} \\
adamc@785 1365 \mt{type} \; \mt{blob} \\
adamc@542 1366 \\
adamc@542 1367 \mt{type} \; \mt{unit} = \{\} \\
adamc@542 1368 \\
adamc@542 1369 \mt{datatype} \; \mt{bool} = \mt{False} \mid \mt{True} \\
adamc@542 1370 \\
adamc@785 1371 \mt{datatype} \; \mt{option} \; \mt{t} = \mt{None} \mid \mt{Some} \; \mt{of} \; \mt{t} \\
adamc@785 1372 \\
adamc@785 1373 \mt{datatype} \; \mt{list} \; \mt{t} = \mt{Nil} \mid \mt{Cons} \; \mt{of} \; \mt{t} \times \mt{list} \; \mt{t}
adamc@542 1374 \end{array}$$
adamc@542 1375
adamc@1123 1376 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 1377
adam@1297 1378 Ur also supports \emph{polymorphic variants}, a dual to extensible records that has been popularized by OCaml. A type $\mt{variant} \; r$ represents an $n$-ary sum type, with one constructor for each field of record $r$. Each constructor $c$ takes an argument of type $r.c$; the type $\{\}$ can be used to ``simulate'' a nullary constructor. The \cd{make} function builds a variant value, while \cd{match} implements pattern-matching, with match cases represented as records of functions.
adam@1297 1379 $$\begin{array}{l}
adam@1297 1380 \mt{con} \; \mt{variant} :: \{\mt{Type}\} \to \mt{Type} \\
adam@1297 1381 \mt{val} \; \mt{make} : \mt{nm} :: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{ts} ::: \{\mt{Type}\} \to [[\mt{nm}] \sim \mt{ts}] \Rightarrow \mt{t} \to \mt{variant} \; ([\mt{nm} = \mt{t}] \rc \mt{ts}) \\
adam@1297 1382 \mt{val} \; \mt{match} : \mt{ts} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{variant} \; \mt{ts} \to \$(\mt{map} \; (\lambda \mt{t'} \Rightarrow \mt{t'} \to \mt{t}) \; \mt{ts}) \to \mt{t}
adam@1297 1383 \end{array}$$
adam@1297 1384
adamc@657 1385 Another important generic Ur element comes at the beginning of \texttt{top.urs}.
adamc@657 1386
adamc@657 1387 $$\begin{array}{l}
adamc@657 1388 \mt{con} \; \mt{folder} :: \mt{K} \longrightarrow \{\mt{K}\} \to \mt{Type} \\
adamc@657 1389 \\
adamc@657 1390 \mt{val} \; \mt{fold} : \mt{K} \longrightarrow \mt{tf} :: (\{\mt{K}\} \to \mt{Type}) \\
adamc@657 1391 \hspace{.1in} \to (\mt{nm} :: \mt{Name} \to \mt{v} :: \mt{K} \to \mt{r} :: \{\mt{K}\} \to [[\mt{nm}] \sim \mt{r}] \Rightarrow \\
adamc@657 1392 \hspace{.2in} \mt{tf} \; \mt{r} \to \mt{tf} \; ([\mt{nm} = \mt{v}] \rc \mt{r})) \\
adamc@657 1393 \hspace{.1in} \to \mt{tf} \; [] \\
adamc@657 1394 \hspace{.1in} \to \mt{r} :: \{\mt{K}\} \to \mt{folder} \; \mt{r} \to \mt{tf} \; \mt{r}
adamc@657 1395 \end{array}$$
adamc@657 1396
adamc@657 1397 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 1398
adamc@664 1399 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 1400
adamc@542 1401
adamc@542 1402 \section{The Ur/Web Standard Library}
adamc@542 1403
adam@1400 1404 Some operations are only allowed in server-side code or only in client-side code. The type system does not enforce such restrictions, but the compiler enforces them in the process of whole-program compilation. In the discussion below, we note when a set of operations has a location restriction.
adam@1400 1405
adamc@658 1406 \subsection{Monads}
adamc@658 1407
adamc@658 1408 The Ur Basis defines the monad constructor class from Haskell.
adamc@658 1409
adamc@658 1410 $$\begin{array}{l}
adamc@658 1411 \mt{class} \; \mt{monad} :: \mt{Type} \to \mt{Type} \\
adamc@658 1412 \mt{val} \; \mt{return} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t} ::: \mt{Type} \\
adamc@658 1413 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658 1414 \hspace{.1in} \to \mt{t} \to \mt{m} \; \mt{t} \\
adamc@658 1415 \mt{val} \; \mt{bind} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t1} ::: \mt{Type} \to \mt{t2} ::: \mt{Type} \\
adamc@658 1416 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658 1417 \hspace{.1in} \to \mt{m} \; \mt{t1} \to (\mt{t1} \to \mt{m} \; \mt{t2}) \\
adam@1544 1418 \hspace{.1in} \to \mt{m} \; \mt{t2} \\
adam@1544 1419 \mt{val} \; \mt{mkMonad} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \\
adam@1544 1420 \hspace{.1in} \to \{\mt{Return} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{m} \; \mt{t}, \\
adam@1544 1421 \hspace{.3in} \mt{Bind} : \mt{t1} ::: \mt{Type} \to \mt{t2} ::: \mt{Type} \to \mt{m} \; \mt{t1} \to (\mt{t1} \to \mt{m} \; \mt{t2}) \to \mt{m} \; \mt{t2}\} \\
adam@1544 1422 \hspace{.1in} \to \mt{monad} \; \mt{m}
adamc@658 1423 \end{array}$$
adamc@658 1424
adam@1687 1425 The Ur/Web compiler provides syntactic sugar for monads, similar to Haskell's \cd{do} notation. An expression $x \leftarrow e_1; e_2$ is desugared to $\mt{bind} \; e_1 \; (\lambda x \Rightarrow e_2)$, and an expression $e_1; e_2$ is desugared to $\mt{bind} \; e_1 \; (\lambda () \Rightarrow e_2)$. Note a difference from Haskell: as the $e_1; e_2$ case desugaring involves a function with $()$ as its formal argument, the type of $e_1$ must be of the form $m \; \{\}$, rather than some arbitrary $m \; t$.
adam@1548 1426
adamc@542 1427 \subsection{Transactions}
adamc@542 1428
adamc@542 1429 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 1430 $$\begin{array}{l}
adamc@542 1431 \mt{con} \; \mt{transaction} :: \mt{Type} \to \mt{Type} \\
adamc@658 1432 \mt{val} \; \mt{transaction\_monad} : \mt{monad} \; \mt{transaction}
adamc@542 1433 \end{array}$$
adamc@542 1434
adamc@1123 1435 For debugging purposes, a transactional function is provided for outputting a string on the server process' \texttt{stderr}.
adamc@1123 1436 $$\begin{array}{l}
adamc@1123 1437 \mt{val} \; \mt{debug} : \mt{string} \to \mt{transaction} \; \mt{unit}
adamc@1123 1438 \end{array}$$
adamc@1123 1439
adamc@542 1440 \subsection{HTTP}
adamc@542 1441
adam@1797 1442 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. For now, cookie operations are server-side only.
adamc@542 1443 $$\begin{array}{l}
adamc@786 1444 \mt{con} \; \mt{http\_cookie} :: \mt{Type} \to \mt{Type} \\
adamc@786 1445 \mt{val} \; \mt{getCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; (\mt{option} \; \mt{t}) \\
adamc@1050 1446 \mt{val} \; \mt{setCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \{\mt{Value} : \mt{t}, \mt{Expires} : \mt{option} \; \mt{time}, \mt{Secure} : \mt{bool}\} \to \mt{transaction} \; \mt{unit} \\
adamc@1050 1447 \mt{val} \; \mt{clearCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; \mt{unit}
adamc@786 1448 \end{array}$$
adamc@786 1449
adamc@786 1450 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 1451 $$\begin{array}{l}
adamc@786 1452 \mt{type} \; \mt{url} \\
adamc@786 1453 \mt{val} \; \mt{bless} : \mt{string} \to \mt{url} \\
adamc@786 1454 \mt{val} \; \mt{checkUrl} : \mt{string} \to \mt{option} \; \mt{url}
adamc@786 1455 \end{array}$$
adamc@786 1456 $\mt{bless}$ raises a runtime error if the string passed to it fails the URL policy.
adamc@786 1457
adam@1400 1458 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. These are server-side operations.
adamc@1085 1459 $$\begin{array}{l}
adamc@1085 1460 \mt{val} \; \mt{currentUrl} : \mt{transaction} \; \mt{url} \\
adamc@1085 1461 \mt{val} \; \mt{url} : \mt{transaction} \; \mt{page} \to \mt{url}
adamc@1085 1462 \end{array}$$
adamc@1085 1463
adamc@1085 1464 Page generation may be interrupted at any time with a request to redirect to a particular URL instead.
adamc@1085 1465 $$\begin{array}{l}
adamc@1085 1466 \mt{val} \; \mt{redirect} : \mt{t} ::: \mt{Type} \to \mt{url} \to \mt{transaction} \; \mt{t}
adamc@1085 1467 \end{array}$$
adamc@1085 1468
adam@1400 1469 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. These functions and those described in the following paragraph are server-side.
adamc@786 1470 $$\begin{array}{l}
adamc@786 1471 \mt{type} \; \mt{file} \\
adamc@786 1472 \mt{val} \; \mt{fileName} : \mt{file} \to \mt{option} \; \mt{string} \\
adamc@786 1473 \mt{val} \; \mt{fileMimeType} : \mt{file} \to \mt{string} \\
adamc@786 1474 \mt{val} \; \mt{fileData} : \mt{file} \to \mt{blob}
adamc@786 1475 \end{array}$$
adamc@786 1476
adam@1799 1477 It is also possible to get HTTP request headers and environment variables, and set HTTP response headers, using abstract types similar to the one for URLs.
adam@1465 1478
adam@1465 1479 $$\begin{array}{l}
adam@1465 1480 \mt{type} \; \mt{requestHeader} \\
adam@1465 1481 \mt{val} \; \mt{blessRequestHeader} : \mt{string} \to \mt{requestHeader} \\
adam@1465 1482 \mt{val} \; \mt{checkRequestHeader} : \mt{string} \to \mt{option} \; \mt{requestHeader} \\
adam@1465 1483 \mt{val} \; \mt{getHeader} : \mt{requestHeader} \to \mt{transaction} \; (\mt{option} \; \mt{string}) \\
adam@1465 1484 \\
adam@1799 1485 \mt{type} \; \mt{envVar} \\
adam@1799 1486 \mt{val} \; \mt{blessEnvVar} : \mt{string} \to \mt{envVar} \\
adam@1799 1487 \mt{val} \; \mt{checkEnvVar} : \mt{string} \to \mt{option} \; \mt{envVar} \\
adam@1799 1488 \mt{val} \; \mt{getenv} : \mt{envVar} \to \mt{transaction} \; (\mt{option} \; \mt{string}) \\
adam@1799 1489 \\
adam@1465 1490 \mt{type} \; \mt{responseHeader} \\
adam@1465 1491 \mt{val} \; \mt{blessResponseHeader} : \mt{string} \to \mt{responseHeader} \\
adam@1465 1492 \mt{val} \; \mt{checkResponseHeader} : \mt{string} \to \mt{option} \; \mt{responseHeader} \\
adam@1465 1493 \mt{val} \; \mt{setHeader} : \mt{responseHeader} \to \mt{string} \to \mt{transaction} \; \mt{unit}
adam@1465 1494 \end{array}$$
adam@1465 1495
adamc@786 1496 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 1497 $$\begin{array}{l}
adamc@786 1498 \mt{type} \; \mt{mimeType} \\
adamc@786 1499 \mt{val} \; \mt{blessMime} : \mt{string} \to \mt{mimeType} \\
adamc@786 1500 \mt{val} \; \mt{checkMime} : \mt{string} \to \mt{option} \; \mt{mimeType} \\
adamc@786 1501 \mt{val} \; \mt{returnBlob} : \mt{t} ::: \mt{Type} \to \mt{blob} \to \mt{mimeType} \to \mt{transaction} \; \mt{t}
adamc@542 1502 \end{array}$$
adamc@542 1503
adamc@543 1504 \subsection{SQL}
adamc@543 1505
adam@1400 1506 Everything about SQL database access is restricted to server-side code.
adam@1400 1507
adamc@543 1508 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 1509 $$\begin{array}{l}
adamc@785 1510 \mt{con} \; \mt{sql\_table} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785 1511 \end{array}$$
adamc@785 1512 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 1513
adamc@785 1514 We also have the simpler type family of SQL views, which have no keys.
adamc@785 1515 $$\begin{array}{l}
adamc@785 1516 \mt{con} \; \mt{sql\_view} :: \{\mt{Type}\} \to \mt{Type}
adamc@543 1517 \end{array}$$
adamc@543 1518
adamc@785 1519 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 1520 $$\begin{array}{l}
adamc@785 1521 \mt{class} \; \mt{fieldsOf} :: \mt{Type} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1522 \mt{val} \; \mt{fieldsOf\_table} : \mt{fs} ::: \{\mt{Type}\} \to \mt{keys} ::: \{\{\mt{Unit}\}\} \to \mt{fieldsOf} \; (\mt{sql\_table} \; \mt{fs} \; \mt{keys}) \; \mt{fs} \\
adamc@785 1523 \mt{val} \; \mt{fieldsOf\_view} : \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; (\mt{sql\_view} \; \mt{fs}) \; \mt{fs}
adamc@785 1524 \end{array}$$
adamc@785 1525
adamc@785 1526 \subsubsection{Table Constraints}
adamc@785 1527
adamc@785 1528 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 1529
adamc@785 1530 $$\begin{array}{l}
adamc@785 1531 \mt{con} \; \mt{primary\_key} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type} \\
adamc@785 1532 \mt{val} \; \mt{no\_primary\_key} : \mt{fs} ::: \{\mt{Type}\} \to \mt{primary\_key} \; \mt{fs} \; [] \\
adamc@785 1533 \mt{val} \; \mt{primary\_key} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{key1} :: \mt{Name} \to \mt{keys} :: \{\mt{Type}\} \\
adamc@785 1534 \hspace{.1in} \to [[\mt{key1}] \sim \mt{keys}] \Rightarrow [[\mt{key1} = \mt{t}] \rc \mt{keys} \sim \mt{rest}] \\
adamc@785 1535 \hspace{.1in} \Rightarrow \$([\mt{key1} = \mt{sql\_injectable\_prim} \; \mt{t}] \rc \mt{map} \; \mt{sql\_injectable\_prim} \; \mt{keys}) \\
adamc@785 1536 \hspace{.1in} \to \mt{primary\_key} \; ([\mt{key1} = \mt{t}] \rc \mt{keys} \rc \mt{rest}) \; [\mt{Pkey} = [\mt{key1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{keys}]
adamc@785 1537 \end{array}$$
adamc@785 1538 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 1539
adamc@785 1540 A type family stands for sets of named constraints of the remaining varieties.
adamc@785 1541 $$\begin{array}{l}
adamc@785 1542 \mt{con} \; \mt{sql\_constraints} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785 1543 \end{array}$$
adamc@785 1544 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 1545
adamc@785 1546 There is a type family of individual, unnamed constraints.
adamc@785 1547 $$\begin{array}{l}
adamc@785 1548 \mt{con} \; \mt{sql\_constraint} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \mt{Type}
adamc@785 1549 \end{array}$$
adamc@785 1550 The first argument is the same as above, and the second argument gives the key columns for just this constraint.
adamc@785 1551
adamc@785 1552 We have operations for assembling constraints into constraint sets.
adamc@785 1553 $$\begin{array}{l}
adamc@785 1554 \mt{val} \; \mt{no\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_constraints} \; \mt{fs} \; [] \\
adamc@785 1555 \mt{val} \; \mt{one\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{unique} ::: \{\mt{Unit}\} \to \mt{name} :: \mt{Name} \\
adamc@785 1556 \hspace{.1in} \to \mt{sql\_constraint} \; \mt{fs} \; \mt{unique} \to \mt{sql\_constraints} \; \mt{fs} \; [\mt{name} = \mt{unique}] \\
adamc@785 1557 \mt{val} \; \mt{join\_constraints} : \mt{fs} ::: \{\mt{Type}\} \to \mt{uniques1} ::: \{\{\mt{Unit}\}\} \to \mt{uniques2} ::: \{\{\mt{Unit}\}\} \to [\mt{uniques1} \sim \mt{uniques2}] \\
adamc@785 1558 \hspace{.1in} \Rightarrow \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques1} \to \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques2} \to \mt{sql\_constraints} \; \mt{fs} \; (\mt{uniques1} \rc \mt{uniques2})
adamc@785 1559 \end{array}$$
adamc@785 1560
adamc@785 1561 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 1562 $$\begin{array}{l}
adamc@785 1563 \mt{val} \; \mt{unique} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{unique1} :: \mt{Name} \to \mt{unique} :: \{\mt{Type}\} \\
adamc@785 1564 \hspace{.1in} \to [[\mt{unique1}] \sim \mt{unique}] \Rightarrow [[\mt{unique1} = \mt{t}] \rc \mt{unique} \sim \mt{rest}] \\
adamc@785 1565 \hspace{.1in} \Rightarrow \mt{sql\_constraint} \; ([\mt{unique1} = \mt{t}] \rc \mt{unique} \rc \mt{rest}) \; ([\mt{unique1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{unique})
adamc@785 1566 \end{array}$$
adamc@785 1567
adamc@785 1568 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 1569 $$\begin{array}{l}
adamc@785 1570 \mt{class} \; \mt{linkable} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@785 1571 \mt{val} \; \mt{linkable\_same} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; \mt{t} \\
adamc@785 1572 \mt{val} \; \mt{linkable\_from\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; (\mt{option} \; \mt{t}) \; \mt{t} \\
adamc@785 1573 \mt{val} \; \mt{linkable\_to\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@785 1574 \end{array}$$
adamc@785 1575
adamc@785 1576 The $\mt{matching}$ type family uses $\mt{linkable}$ to define when two keys match up type-wise.
adamc@785 1577 $$\begin{array}{l}
adamc@785 1578 \mt{con} \; \mt{matching} :: \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1579 \mt{val} \; \mt{mat\_nil} : \mt{matching} \; [] \; [] \\
adamc@785 1580 \mt{val} \; \mt{mat\_cons} : \mt{t1} ::: \mt{Type} \to \mt{rest1} ::: \{\mt{Type}\} \to \mt{t2} ::: \mt{Type} \to \mt{rest2} ::: \{\mt{Type}\} \to \mt{nm1} :: \mt{Name} \to \mt{nm2} :: \mt{Name} \\
adamc@785 1581 \hspace{.1in} \to [[\mt{nm1}] \sim \mt{rest1}] \Rightarrow [[\mt{nm2}] \sim \mt{rest2}] \Rightarrow \mt{linkable} \; \mt{t1} \; \mt{t2} \to \mt{matching} \; \mt{rest1} \; \mt{rest2} \\
adamc@785 1582 \hspace{.1in} \to \mt{matching} \; ([\mt{nm1} = \mt{t1}] \rc \mt{rest1}) \; ([\mt{nm2} = \mt{t2}] \rc \mt{rest2})
adamc@785 1583 \end{array}$$
adamc@785 1584
adamc@785 1585 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 1586 $$\begin{array}{l}
adamc@785 1587 \mt{con} \; \mt{propagation\_mode} :: \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1588 \mt{val} \; \mt{restrict} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1589 \mt{val} \; \mt{cascade} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1590 \mt{val} \; \mt{no\_action} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1591 \mt{val} \; \mt{set\_null} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; (\mt{map} \; \mt{option} \; \mt{fs})
adamc@785 1592 \end{array}$$
adamc@785 1593
adamc@785 1594 Finally, we put these ingredient together to define the \texttt{FOREIGN KEY} constraint function.
adamc@785 1595 $$\begin{array}{l}
adamc@785 1596 \mt{val} \; \mt{foreign\_key} : \mt{mine1} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{mine} ::: \{\mt{Type}\} \to \mt{munused} ::: \{\mt{Type}\} \to \mt{foreign} ::: \{\mt{Type}\} \\
adamc@785 1597 \hspace{.1in} \to \mt{funused} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{uniques} ::: \{\{\mt{Unit}\}\} \\
adamc@785 1598 \hspace{.1in} \to [[\mt{mine1}] \sim \mt{mine}] \Rightarrow [[\mt{mine1} = \mt{t}] \rc \mt{mine} \sim \mt{munused}] \Rightarrow [\mt{foreign} \sim \mt{funused}] \Rightarrow [[\mt{nm}] \sim \mt{uniques}] \\
adamc@785 1599 \hspace{.1in} \Rightarrow \mt{matching} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}) \; \mt{foreign} \\
adamc@785 1600 \hspace{.1in} \to \mt{sql\_table} \; (\mt{foreign} \rc \mt{funused}) \; ([\mt{nm} = \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{foreign}] \rc \mt{uniques}) \\
adamc@785 1601 \hspace{.1in} \to \{\mt{OnDelete} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}), \\
adamc@785 1602 \hspace{.2in} \mt{OnUpdate} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine})\} \\
adamc@785 1603 \hspace{.1in} \to \mt{sql\_constraint} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine} \rc \mt{munused}) \; []
adamc@785 1604 \end{array}$$
adamc@785 1605
adamc@785 1606 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 1607 $$\begin{array}{l}
adam@1778 1608 \mt{val} \; \mt{check} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; [] \; [] \; \mt{fs} \; \mt{bool} \to \mt{sql\_constraint} \; \mt{fs} \; []
adamc@785 1609 \end{array}$$
adamc@785 1610
adamc@785 1611 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 1612
adamc@784 1613
adamc@543 1614 \subsubsection{Queries}
adamc@543 1615
adam@1400 1616 A final query is constructed via the $\mt{sql\_query}$ function. Constructor arguments respectively specify the unrestricted free table variables (which will only be available in subqueries), the free table variables that may only be mentioned within arguments to aggregate functions, 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 1617 $$\begin{array}{l}
adam@1400 1618 \mt{con} \; \mt{sql\_query} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@1193 1619 \mt{val} \; \mt{sql\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400 1620 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1621 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543 1622 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1623 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1193 1624 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adam@1400 1625 \hspace{.1in} \Rightarrow \{\mt{Rows} : \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}, \\
adamc@1193 1626 \hspace{.2in} \mt{OrderBy} : \mt{sql\_order\_by} \; (\mt{free} \rc \mt{tables}) \; \mt{selectedExps}, \\
adamc@543 1627 \hspace{.2in} \mt{Limit} : \mt{sql\_limit}, \\
adamc@543 1628 \hspace{.2in} \mt{Offset} : \mt{sql\_offset}\} \\
adam@1400 1629 \hspace{.1in} \to \mt{sql\_query} \; \mt{free} \; \mt{afree} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1630 \end{array}$$
adamc@543 1631
adamc@545 1632 Queries are used by folding over their results inside transactions.
adamc@545 1633 $$\begin{array}{l}
adam@1400 1634 \mt{val} \; \mt{query} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to [\mt{tables} \sim \mt{exps}] \Rightarrow \mt{state} ::: \mt{Type} \to \mt{sql\_query} \; [] \; [] \; \mt{tables} \; \mt{exps} \\
adamc@658 1635 \hspace{.1in} \to (\$(\mt{exps} \rc \mt{map} \; (\lambda \mt{fields} :: \{\mt{Type}\} \Rightarrow \$\mt{fields}) \; \mt{tables}) \\
adamc@545 1636 \hspace{.2in} \to \mt{state} \to \mt{transaction} \; \mt{state}) \\
adamc@545 1637 \hspace{.1in} \to \mt{state} \to \mt{transaction} \; \mt{state}
adamc@545 1638 \end{array}$$
adamc@545 1639
adam@1400 1640 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 unrestricted free table veriables, the aggregate-only free table variables, 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 1641 $$\begin{array}{l}
adam@1400 1642 \mt{con} \; \mt{sql\_query1} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@543 1643 \\
adamc@543 1644 \mt{type} \; \mt{sql\_relop} \\
adamc@543 1645 \mt{val} \; \mt{sql\_union} : \mt{sql\_relop} \\
adamc@543 1646 \mt{val} \; \mt{sql\_intersect} : \mt{sql\_relop} \\
adamc@543 1647 \mt{val} \; \mt{sql\_except} : \mt{sql\_relop} \\
adam@1400 1648 \mt{val} \; \mt{sql\_relop} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400 1649 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adam@1400 1650 \hspace{.1in} \to \mt{tables1} ::: \{\{\mt{Type}\}\} \\
adamc@543 1651 \hspace{.1in} \to \mt{tables2} ::: \{\{\mt{Type}\}\} \\
adamc@543 1652 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1653 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@543 1654 \hspace{.1in} \to \mt{sql\_relop} \\
adam@1458 1655 \hspace{.1in} \to \mt{bool} \; (* \; \mt{ALL} \; *) \\
adam@1400 1656 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables1} \; \mt{selectedFields} \; \mt{selectedExps} \\
adam@1400 1657 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables2} \; \mt{selectedFields} \; \mt{selectedExps} \\
adam@1400 1658 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{selectedFields} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1659 \end{array}$$
adamc@543 1660
adamc@543 1661 $$\begin{array}{l}
adamc@1193 1662 \mt{val} \; \mt{sql\_query1} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400 1663 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1664 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543 1665 \hspace{.1in} \to \mt{grouped} ::: \{\{\mt{Type}\}\} \\
adamc@543 1666 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1667 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1085 1668 \hspace{.1in} \to \mt{empties} :: \{\mt{Unit}\} \\
adamc@1193 1669 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adamc@1193 1670 \hspace{.1in} \Rightarrow [\mt{free} \sim \mt{grouped}] \\
adam@1400 1671 \hspace{.1in} \Rightarrow [\mt{afree} \sim \mt{tables}] \\
adamc@1193 1672 \hspace{.1in} \Rightarrow [\mt{empties} \sim \mt{selectedFields}] \\
adamc@1085 1673 \hspace{.1in} \Rightarrow \{\mt{Distinct} : \mt{bool}, \\
adamc@1193 1674 \hspace{.2in} \mt{From} : \mt{sql\_from\_items} \; \mt{free} \; \mt{tables}, \\
adam@1778 1675 \hspace{.2in} \mt{Where} : \mt{sql\_exp} \; (\mt{free} \rc \mt{tables}) \; \mt{afree} \; [] \; \mt{bool}, \\
adamc@543 1676 \hspace{.2in} \mt{GroupBy} : \mt{sql\_subset} \; \mt{tables} \; \mt{grouped}, \\
adam@1778 1677 \hspace{.2in} \mt{Having} : \mt{sql\_exp} \; (\mt{free} \rc \mt{grouped}) \; (\mt{afree} \rc \mt{tables}) \; [] \; \mt{bool}, \\
adamc@1085 1678 \hspace{.2in} \mt{SelectFields} : \mt{sql\_subset} \; \mt{grouped} \; (\mt{map} \; (\lambda \_ \Rightarrow []) \; \mt{empties} \rc \mt{selectedFields}), \\
adam@1778 1679 \hspace{.2in} \mt {SelectExps} : \$(\mt{map} \; (\mt{sql\_expw} \; (\mt{free} \rc \mt{grouped}) \; (\mt{afree} \rc \mt{tables}) \; []) \; \mt{selectedExps}) \} \\
adam@1400 1680 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1681 \end{array}$$
adamc@543 1682
adamc@543 1683 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 1684 $$\begin{array}{l}
adamc@543 1685 \mt{con} \; \mt{sql\_subset} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@543 1686 \mt{val} \; \mt{sql\_subset} : \mt{keep\_drop} :: \{(\{\mt{Type}\} \times \{\mt{Type}\})\} \\
adamc@543 1687 \hspace{.1in} \to \mt{sql\_subset} \\
adamc@658 1688 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1 \rc \mt{fields}.2)\; \mt{keep\_drop}) \\
adamc@658 1689 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1) \; \mt{keep\_drop}) \\
adamc@543 1690 \mt{val} \; \mt{sql\_subset\_all} : \mt{tables} :: \{\{\mt{Type}\}\} \to \mt{sql\_subset} \; \mt{tables} \; \mt{tables}
adamc@543 1691 \end{array}$$
adamc@543 1692
adam@1778 1693 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 1694 $$\begin{array}{l}
adam@1778 1695 \mt{con} \; \mt{sql\_exp} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}
adamc@543 1696 \end{array}$$
adamc@543 1697
adamc@543 1698 Any field in scope may be converted to an expression.
adamc@543 1699 $$\begin{array}{l}
adamc@543 1700 \mt{val} \; \mt{sql\_field} : \mt{otherTabs} ::: \{\{\mt{Type}\}\} \to \mt{otherFields} ::: \{\mt{Type}\} \\
adam@1778 1701 \hspace{.1in} \to \mt{fieldType} ::: \mt{Type} \to \mt{agg} ::: \{\{\mt{Type}\}\} \\
adamc@543 1702 \hspace{.1in} \to \mt{exps} ::: \{\mt{Type}\} \\
adamc@543 1703 \hspace{.1in} \to \mt{tab} :: \mt{Name} \to \mt{field} :: \mt{Name} \\
adam@1778 1704 \hspace{.1in} \to \mt{sql\_exp} \; ([\mt{tab} = [\mt{field} = \mt{fieldType}] \rc \mt{otherFields}] \rc \mt{otherTabs}) \; \mt{agg} \; \mt{exps} \; \mt{fieldType}
adamc@543 1705 \end{array}$$
adamc@543 1706
adamc@544 1707 There is an analogous function for referencing named expressions.
adamc@544 1708 $$\begin{array}{l}
adam@1778 1709 \mt{val} \; \mt{sql\_exp} : \mt{tabs} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{t} ::: \mt{Type} \to \mt{rest} ::: \{\mt{Type}\} \to \mt{nm} :: \mt{Name} \\
adam@1778 1710 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tabs} \; \mt{agg} \; ([\mt{nm} = \mt{t}] \rc \mt{rest}) \; \mt{t}
adamc@544 1711 \end{array}$$
adamc@544 1712
adamc@544 1713 Ur values of appropriate types may be injected into SQL expressions.
adamc@544 1714 $$\begin{array}{l}
adamc@786 1715 \mt{class} \; \mt{sql\_injectable\_prim} \\
adamc@786 1716 \mt{val} \; \mt{sql\_bool} : \mt{sql\_injectable\_prim} \; \mt{bool} \\
adamc@786 1717 \mt{val} \; \mt{sql\_int} : \mt{sql\_injectable\_prim} \; \mt{int} \\
adamc@786 1718 \mt{val} \; \mt{sql\_float} : \mt{sql\_injectable\_prim} \; \mt{float} \\
adamc@786 1719 \mt{val} \; \mt{sql\_string} : \mt{sql\_injectable\_prim} \; \mt{string} \\
adamc@786 1720 \mt{val} \; \mt{sql\_time} : \mt{sql\_injectable\_prim} \; \mt{time} \\
adamc@786 1721 \mt{val} \; \mt{sql\_blob} : \mt{sql\_injectable\_prim} \; \mt{blob} \\
adamc@786 1722 \mt{val} \; \mt{sql\_channel} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{channel} \; \mt{t}) \\
adamc@786 1723 \mt{val} \; \mt{sql\_client} : \mt{sql\_injectable\_prim} \; \mt{client} \\
adamc@786 1724 \\
adamc@544 1725 \mt{class} \; \mt{sql\_injectable} \\
adamc@786 1726 \mt{val} \; \mt{sql\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@786 1727 \mt{val} \; \mt{sql\_option\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; (\mt{option} \; \mt{t}) \\
adamc@786 1728 \\
adam@1778 1729 \mt{val} \; \mt{sql\_inject} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{sql\_injectable} \; \mt{t} \\
adam@1778 1730 \hspace{.1in} \to \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adamc@544 1731 \end{array}$$
adamc@544 1732
adamc@1123 1733 Additionally, most function-free types may be injected safely, via the $\mt{serialized}$ type family.
adamc@1123 1734 $$\begin{array}{l}
adamc@1123 1735 \mt{con} \; \mt{serialized} :: \mt{Type} \to \mt{Type} \\
adamc@1123 1736 \mt{val} \; \mt{serialize} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{serialized} \; \mt{t} \\
adamc@1123 1737 \mt{val} \; \mt{deserialize} : \mt{t} ::: \mt{Type} \to \mt{serialized} \; \mt{t} \to \mt{t} \\
adamc@1123 1738 \mt{val} \; \mt{sql\_serialized} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{serialized} \; \mt{t})
adamc@1123 1739 \end{array}$$
adamc@1123 1740
adamc@544 1741 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 1742 $$\begin{array}{l}
adam@1778 1743 \mt{val} \; \mt{sql\_is\_null} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778 1744 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; (\mt{option} \; \mt{t}) \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{bool}
adamc@544 1745 \end{array}$$
adamc@544 1746
adam@1602 1747 As another way of dealing with null values, there is also a restricted form of the standard \cd{COALESCE} function.
adam@1602 1748 $$\begin{array}{l}
adam@1602 1749 \mt{val} \; \mt{sql\_coalesce} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778 1750 \hspace{.1in} \to \mt{t} ::: \mt{Type} \\
adam@1778 1751 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; (\mt{option} \; \mt{t}) \\
adam@1778 1752 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1753 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adam@1602 1754 \end{array}$$
adam@1602 1755
adamc@559 1756 We have generic nullary, unary, and binary operators.
adamc@544 1757 $$\begin{array}{l}
adamc@544 1758 \mt{con} \; \mt{sql\_nfunc} :: \mt{Type} \to \mt{Type} \\
adamc@544 1759 \mt{val} \; \mt{sql\_current\_timestamp} : \mt{sql\_nfunc} \; \mt{time} \\
adam@1778 1760 \mt{val} \; \mt{sql\_nfunc} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778 1761 \hspace{.1in} \to \mt{sql\_nfunc} \; \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\\end{array}$$
adamc@544 1762
adamc@544 1763 $$\begin{array}{l}
adamc@544 1764 \mt{con} \; \mt{sql\_unary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544 1765 \mt{val} \; \mt{sql\_not} : \mt{sql\_unary} \; \mt{bool} \; \mt{bool} \\
adam@1778 1766 \mt{val} \; \mt{sql\_unary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adam@1778 1767 \hspace{.1in} \to \mt{sql\_unary} \; \mt{arg} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res} \\
adamc@544 1768 \end{array}$$
adamc@544 1769
adamc@544 1770 $$\begin{array}{l}
adamc@544 1771 \mt{con} \; \mt{sql\_binary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544 1772 \mt{val} \; \mt{sql\_and} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544 1773 \mt{val} \; \mt{sql\_or} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adam@1778 1774 \mt{val} \; \mt{sql\_binary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg_1} ::: \mt{Type} \to \mt{arg_2} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adam@1778 1775 \hspace{.1in} \to \mt{sql\_binary} \; \mt{arg_1} \; \mt{arg_2} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_1} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_2} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res}
adamc@544 1776 \end{array}$$
adamc@544 1777
adamc@544 1778 $$\begin{array}{l}
adamc@559 1779 \mt{class} \; \mt{sql\_arith} \\
adamc@559 1780 \mt{val} \; \mt{sql\_int\_arith} : \mt{sql\_arith} \; \mt{int} \\
adamc@559 1781 \mt{val} \; \mt{sql\_float\_arith} : \mt{sql\_arith} \; \mt{float} \\
adamc@559 1782 \mt{val} \; \mt{sql\_neg} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_unary} \; \mt{t} \; \mt{t} \\
adamc@559 1783 \mt{val} \; \mt{sql\_plus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1784 \mt{val} \; \mt{sql\_minus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1785 \mt{val} \; \mt{sql\_times} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1786 \mt{val} \; \mt{sql\_div} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1787 \mt{val} \; \mt{sql\_mod} : \mt{sql\_binary} \; \mt{int} \; \mt{int} \; \mt{int}
adamc@559 1788 \end{array}$$
adamc@544 1789
adam@1797 1790 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 1791 $$\begin{array}{l}
adam@1778 1792 \mt{val} \; \mt{sql\_count} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int}
adamc@544 1793 \end{array}$$
adamc@544 1794
adamc@544 1795 $$\begin{array}{l}
adamc@1188 1796 \mt{con} \; \mt{sql\_aggregate} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adam@1778 1797 \mt{val} \; \mt{sql\_aggregate} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{dom} ::: \mt{Type} \to \mt{ran} ::: \mt{Type} \\
adam@1778 1798 \hspace{.1in} \to \mt{sql\_aggregate} \; \mt{dom} \; \mt{ran} \to \mt{sql\_exp} \; \mt{agg} \; \mt{agg} \; \mt{exps} \; \mt{dom} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{ran}
adamc@1188 1799 \end{array}$$
adamc@1188 1800
adamc@1188 1801 $$\begin{array}{l}
adamc@1188 1802 \mt{val} \; \mt{sql\_count\_col} : \mt{t} ::: \mt{Type} \to \mt{sql\_aggregate} \; (\mt{option} \; \mt{t}) \; \mt{int}
adamc@544 1803 \end{array}$$
adam@1400 1804
adam@1400 1805 Most aggregate functions are typed using a two-parameter constructor class $\mt{nullify}$ which maps $\mt{option}$ types to themselves and adds $\mt{option}$ to others. That is, this constructor class represents the process of making an SQL type ``nullable.''
adamc@544 1806
adamc@544 1807 $$\begin{array}{l}
adamc@544 1808 \mt{class} \; \mt{sql\_summable} \\
adamc@544 1809 \mt{val} \; \mt{sql\_summable\_int} : \mt{sql\_summable} \; \mt{int} \\
adamc@544 1810 \mt{val} \; \mt{sql\_summable\_float} : \mt{sql\_summable} \; \mt{float} \\
adam@1777 1811 \mt{val} \; \mt{sql\_avg} : \mt{t} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{sql\_aggregate} \; \mt{t} \; (\mt{option} \; \mt{float}) \\
adam@1400 1812 \mt{val} \; \mt{sql\_sum} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt}
adamc@544 1813 \end{array}$$
adamc@544 1814
adamc@544 1815 $$\begin{array}{l}
adamc@544 1816 \mt{class} \; \mt{sql\_maxable} \\
adamc@544 1817 \mt{val} \; \mt{sql\_maxable\_int} : \mt{sql\_maxable} \; \mt{int} \\
adamc@544 1818 \mt{val} \; \mt{sql\_maxable\_float} : \mt{sql\_maxable} \; \mt{float} \\
adamc@544 1819 \mt{val} \; \mt{sql\_maxable\_string} : \mt{sql\_maxable} \; \mt{string} \\
adamc@544 1820 \mt{val} \; \mt{sql\_maxable\_time} : \mt{sql\_maxable} \; \mt{time} \\
adam@1400 1821 \mt{val} \; \mt{sql\_max} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt} \\
adam@1400 1822 \mt{val} \; \mt{sql\_min} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt}
adamc@544 1823 \end{array}$$
adamc@544 1824
adam@1778 1825 Any SQL query that returns single columns may be turned into a subquery expression.
adam@1777 1826
adam@1777 1827 $$\begin{array}{l}
adam@1778 1828 \mt{val} \; \mt{sql\_subquery} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \\
adam@1778 1829 \hspace{.1in} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_query} \; \mt{tables} \; \mt{agg} \; [\mt{nm} = \mt{t}] \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{nt}
adamc@1193 1830 \end{array}$$
adamc@1193 1831
adam@1573 1832 There is also an \cd{IF..THEN..ELSE..} construct that is compiled into standard SQL \cd{CASE} expressions.
adam@1573 1833 $$\begin{array}{l}
adam@1778 1834 \mt{val} \; \mt{sql\_if\_then\_else} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778 1835 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{bool} \\
adam@1778 1836 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1837 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1838 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adam@1573 1839 \end{array}$$
adam@1573 1840
adamc@1193 1841 \texttt{FROM} clauses are specified using a type family, whose arguments are the free table variables and the table variables bound by this clause.
adamc@1193 1842 $$\begin{array}{l}
adamc@1193 1843 \mt{con} \; \mt{sql\_from\_items} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@1193 1844 \mt{val} \; \mt{sql\_from\_table} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1845 \hspace{.1in} \to \mt{t} ::: \mt{Type} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; \mt{t} \; \mt{fs} \to \mt{name} :: \mt{Name} \to \mt{t} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193 1846 \mt{val} \; \mt{sql\_from\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{name} :: \mt{Name} \to \mt{sql\_query} \; \mt{free} \; [] \; \mt{fs} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193 1847 \mt{val} \; \mt{sql\_from\_comma} : \mt{free} ::: \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \to [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193 1848 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adamc@1193 1849 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2}) \\
adamc@1193 1850 \mt{val} \; \mt{sql\_inner\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1851 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193 1852 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adam@1778 1853 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193 1854 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2})
adamc@786 1855 \end{array}$$
adamc@786 1856
adamc@786 1857 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 1858 $$\begin{array}{l}
adamc@786 1859 \mt{class} \; \mt{nullify} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@786 1860 \mt{val} \; \mt{nullify\_option} : \mt{t} ::: \mt{Type} \to \mt{nullify} \; (\mt{option} \; \mt{t}) \; (\mt{option} \; \mt{t}) \\
adamc@786 1861 \mt{val} \; \mt{nullify\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{nullify} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@786 1862 \end{array}$$
adamc@786 1863
adamc@786 1864 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 1865
adamc@786 1866 $$\begin{array}{l}
adamc@1193 1867 \mt{val} \; \mt{sql\_left\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{(\mt{Type} \times \mt{Type})\}\} \\
adamc@1193 1868 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@786 1869 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\lambda \mt{r} \Rightarrow \$(\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{nullify} \; \mt{p}.1 \; \mt{p}.2) \; \mt{r})) \; \mt{tabs2}) \\
adamc@1193 1870 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \\
adam@1778 1871 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193 1872 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.2)) \; \mt{tabs2})
adamc@786 1873 \end{array}$$
adamc@786 1874
adamc@544 1875 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 1876 $$\begin{array}{l}
adamc@544 1877 \mt{type} \; \mt{sql\_direction} \\
adamc@544 1878 \mt{val} \; \mt{sql\_asc} : \mt{sql\_direction} \\
adamc@544 1879 \mt{val} \; \mt{sql\_desc} : \mt{sql\_direction} \\
adamc@544 1880 \\
adamc@544 1881 \mt{con} \; \mt{sql\_order\_by} :: \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@544 1882 \mt{val} \; \mt{sql\_order\_by\_Nil} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} :: \{\mt{Type}\} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adam@1778 1883 \mt{val} \; \mt{sql\_order\_by\_Cons} : \mt{tf} ::: (\{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}) \\
adam@1778 1884 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778 1885 \hspace{.1in} \to \mt{sql\_window} \; \mt{tf} \to \mt{tf} \; \mt{tables} \; [] \; \mt{exps} \; \mt{t} \to \mt{sql\_direction} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adam@1684 1886 \mt{val} \; \mt{sql\_order\_by\_random} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544 1887 \\
adamc@544 1888 \mt{type} \; \mt{sql\_limit} \\
adamc@544 1889 \mt{val} \; \mt{sql\_no\_limit} : \mt{sql\_limit} \\
adamc@544 1890 \mt{val} \; \mt{sql\_limit} : \mt{int} \to \mt{sql\_limit} \\
adamc@544 1891 \\
adamc@544 1892 \mt{type} \; \mt{sql\_offset} \\
adamc@544 1893 \mt{val} \; \mt{sql\_no\_offset} : \mt{sql\_offset} \\
adamc@544 1894 \mt{val} \; \mt{sql\_offset} : \mt{int} \to \mt{sql\_offset}
adamc@544 1895 \end{array}$$
adamc@544 1896
adam@1778 1897 When using Postgres, \cd{SELECT} and \cd{ORDER BY} are allowed to contain top-level uses of \emph{window functions}. A separate type family \cd{sql\_expw} is provided for such cases, with some type class convenience for overloading between normal and window expressions.
adam@1778 1898 $$\begin{array}{l}
adam@1778 1899 \mt{con} \; \mt{sql\_expw} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type} \\
adam@1778 1900 \\
adam@1778 1901 \mt{class} \; \mt{sql\_window} :: (\{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}) \to \mt{Type} \\
adam@1778 1902 \mt{val} \; \mt{sql\_window\_normal} : \mt{sql\_window} \; \mt{sql\_exp} \\
adam@1778 1903 \mt{val} \; \mt{sql\_window\_fancy} : \mt{sql\_window} \; \mt{sql\_expw} \\
adam@1778 1904 \mt{val} \; \mt{sql\_window} : \mt{tf} ::: (\{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}) \\
adam@1778 1905 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778 1906 \hspace{.1in} \to \mt{sql\_window} \; \mt{tf} \\
adam@1778 1907 \hspace{.1in} \to \mt{tf} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1908 \hspace{.1in} \to \mt{sql\_expw} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1909 \\
adam@1778 1910 \mt{con} \; \mt{sql\_partition} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adam@1778 1911 \mt{val} \; \mt{sql\_no\_partition} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778 1912 \hspace{.1in} \to \mt{sql\_partition} \; \mt{tables} \; \mt{agg} \; \mt{exps} \\
adam@1778 1913 \mt{val} \; \mt{sql\_partition} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778 1914 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1915 \hspace{.1in} \to \mt{sql\_partition} \; \mt{tables} \; \mt{agg} \; \mt{exps} \\
adam@1778 1916 \\
adam@1778 1917 \mt{con} \; \mt{sql\_window\_function} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type} \\
adam@1778 1918 \mt{val} \; \mt{sql\_window\_function} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778 1919 \hspace{.1in} \to \mt{t} ::: \mt{Type} \\
adam@1778 1920 \hspace{.1in} \to \mt{sql\_window\_function} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1921 \hspace{.1in} \to \mt{sql\_partition} \; \mt{tables} \; \mt{agg} \; \mt{exps} \\
adam@1778 1922 \hspace{.1in} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adam@1778 1923 \hspace{.1in} \to \mt{sql\_expw} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1924 \\
adam@1778 1925 \mt{val} \; \mt{sql\_window\_aggregate} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778 1926 \hspace{.1in} \to \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \\
adam@1778 1927 \hspace{.1in} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt} \\
adam@1778 1928 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1929 \hspace{.1in} \to \mt{sql\_window\_function} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{nt} \\
adam@1778 1930 \mt{val} \; \mt{sql\_window\_count} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778 1931 \hspace{.1in} \to \mt{sql\_window\_function} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int} \\
adam@1778 1932 \mt{val} \; \mt{sql\_rank} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778 1933 \hspace{.1in} \to \mt{sql\_window\_function} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int}
adam@1778 1934 \end{array}$$
adam@1778 1935
adamc@545 1936
adamc@545 1937 \subsubsection{DML}
adamc@545 1938
adamc@545 1939 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 1940
adamc@545 1941 $$\begin{array}{l}
adamc@545 1942 \mt{type} \; \mt{dml} \\
adamc@545 1943 \mt{val} \; \mt{dml} : \mt{dml} \to \mt{transaction} \; \mt{unit}
adamc@545 1944 \end{array}$$
adamc@545 1945
adam@1297 1946 The function $\mt{Basis.dml}$ will trigger a fatal application error if the command fails, for instance, because a data integrity constraint is violated. An alternate function returns an error message as a string instead.
adam@1297 1947
adam@1297 1948 $$\begin{array}{l}
adam@1297 1949 \mt{val} \; \mt{tryDml} : \mt{dml} \to \mt{transaction} \; (\mt{option} \; \mt{string})
adam@1297 1950 \end{array}$$
adam@1297 1951
adam@1797 1952 Properly typed records may be used to form $\mt{INSERT}$ commands.
adamc@545 1953 $$\begin{array}{l}
adamc@545 1954 \mt{val} \; \mt{insert} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \\
adam@1778 1955 \hspace{.1in} \to \$(\mt{map} \; (\mt{sql\_exp} \; [] \; [] \; []) \; \mt{fields}) \to \mt{dml}
adamc@545 1956 \end{array}$$
adamc@545 1957
adam@1578 1958 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. Note that, in the table environment applied to expressions, the table being updated is hardcoded at the name $\mt{T}$. The parsing extension for $\mt{UPDATE}$ will elaborate all table-free field references to use table variable $\mt{T}$.
adamc@545 1959 $$\begin{array}{l}
adam@1380 1960 \mt{val} \; \mt{update} : \mt{unchanged} ::: \{\mt{Type}\} \to \mt{changed} :: \{\mt{Type}\} \to [\mt{changed} \sim \mt{unchanged}] \\
adam@1778 1961 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; []) \; \mt{changed}) \\
adam@1778 1962 \hspace{.1in} \to \mt{sql\_table} \; (\mt{changed} \rc \mt{unchanged}) \to \mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545 1963 \end{array}$$
adamc@545 1964
adam@1578 1965 A $\mt{DELETE}$ command is formed from a table and a $\mt{WHERE}$ clause. The above use of $\mt{T}$ is repeated.
adamc@545 1966 $$\begin{array}{l}
adam@1778 1967 \mt{val} \; \mt{delete} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \to \mt{sql\_exp} \; [\mt{T} = \mt{fields}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545 1968 \end{array}$$
adamc@545 1969
adamc@546 1970 \subsubsection{Sequences}
adamc@546 1971
adamc@546 1972 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 1973
adamc@546 1974 $$\begin{array}{l}
adamc@546 1975 \mt{type} \; \mt{sql\_sequence} \\
adamc@1085 1976 \mt{val} \; \mt{nextval} : \mt{sql\_sequence} \to \mt{transaction} \; \mt{int} \\
adamc@1085 1977 \mt{val} \; \mt{setval} : \mt{sql\_sequence} \to \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@546 1978 \end{array}$$
adamc@546 1979
adamc@546 1980
adam@1648 1981 \subsection{\label{xml}XML}
adamc@547 1982
adam@1333 1983 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. The Ur/Web standard library encodes a very loose version of XHTML, where it is very easy to produce documents which are invalid XHTML, but which still display properly in all major browsers. The main purposes of the invariants that are enforced are first, to provide some documentation about the places where it would make sense to insert XML fragments; and second, to rule out code injection attacks and other abstraction violations related to HTML syntax.
adamc@547 1984
adam@1642 1985 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. For instance, the context for the \texttt{<td>} tag is $[\mt{Dyn}, \mt{MakeForm}, \mt{Tr}]$, to indicate nesting inside a \texttt{<tr>} tag with the ability to nest \texttt{<form>} and \texttt{<dyn>} tags (see below). Contexts are maintained in a somewhat ad-hoc way; the only definitive reference for their meanings is the types of the tag values in \texttt{basis.urs}. The arguments dealing with field binding are only relevant to HTML forms.
adamc@547 1986 $$\begin{array}{l}
adamc@547 1987 \mt{con} \; \mt{xml} :: \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547 1988 \end{array}$$
adamc@547 1989
adamc@547 1990 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 1991 $$\begin{array}{l}
adamc@547 1992 \mt{con} \; \mt{tag} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547 1993 \end{array}$$
adamc@547 1994
adamc@547 1995 Literal text may be injected into XML as ``CDATA.''
adamc@547 1996 $$\begin{array}{l}
adamc@547 1997 \mt{val} \; \mt{cdata} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{string} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adamc@547 1998 \end{array}$$
adamc@547 1999
adam@1358 2000 There is also a function to insert the literal value of a character. Since Ur/Web uses the UTF-8 text encoding, the $\mt{cdata}$ function is only sufficient to encode characters with ASCII codes below 128. Higher codes have alternate meanings in UTF-8 than in usual ASCII, so this alternate function should be used with them.
adam@1358 2001 $$\begin{array}{l}
adam@1358 2002 \mt{val} \; \mt{cdataChar} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{char} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adam@1358 2003 \end{array}$$
adam@1358 2004
adamc@547 2005 There is a function for producing an XML tree with a particular tag at its root.
adamc@547 2006 $$\begin{array}{l}
adamc@547 2007 \mt{val} \; \mt{tag} : \mt{attrsGiven} ::: \{\mt{Type}\} \to \mt{attrsAbsent} ::: \{\mt{Type}\} \to \mt{ctxOuter} ::: \{\mt{Unit}\} \to \mt{ctxInner} ::: \{\mt{Unit}\} \\
adamc@547 2008 \hspace{.1in} \to \mt{useOuter} ::: \{\mt{Type}\} \to \mt{useInner} ::: \{\mt{Type}\} \to \mt{bindOuter} ::: \{\mt{Type}\} \to \mt{bindInner} ::: \{\mt{Type}\} \\
adam@1380 2009 \hspace{.1in} \to [\mt{attrsGiven} \sim \mt{attrsAbsent}] \Rightarrow [\mt{useOuter} \sim \mt{useInner}] \Rightarrow [\mt{bindOuter} \sim \mt{bindInner}] \\
adam@1749 2010 \hspace{.1in} \Rightarrow \mt{css\_class} \\
adam@1643 2011 \hspace{.1in} \to \mt{option} \; (\mt{signal} \; \mt{css\_class}) \\
adam@1750 2012 \hspace{.1in} \to \mt{css\_style} \\
adam@1751 2013 \hspace{.1in} \to \mt{option} \; (\mt{signal} \; \mt{css\_style}) \\
adamc@787 2014 \hspace{.1in} \to \$\mt{attrsGiven} \\
adamc@547 2015 \hspace{.1in} \to \mt{tag} \; (\mt{attrsGiven} \rc \mt{attrsAbsent}) \; \mt{ctxOuter} \; \mt{ctxInner} \; \mt{useOuter} \; \mt{bindOuter} \\
adamc@547 2016 \hspace{.1in} \to \mt{xml} \; \mt{ctxInner} \; \mt{useInner} \; \mt{bindInner} \to \mt{xml} \; \mt{ctxOuter} \; (\mt{useOuter} \rc \mt{useInner}) \; (\mt{bindOuter} \rc \mt{bindInner})
adamc@547 2017 \end{array}$$
adam@1750 2018 Note that any tag may be assigned a CSS class, or left without a class by passing $\mt{Basis.null}$ as the first value-level argument. This is the sole way of making use of the values produced by $\mt{style}$ declarations. The function $\mt{Basis.classes}$ can be used to specify a list of CSS classes for a single tag. Stylesheets to assign properties to the classes can be linked via URL's with \texttt{link} tags. Ur/Web makes it easy to calculate upper bounds on usage of CSS classes through program analysis, with the \cd{-css} command-line flag.
adamc@547 2019
adam@1643 2020 Also note that two different arguments are available for setting CSS classes: the first, associated with the \texttt{class} pseudo-attribute syntactic sugar, fixes the class of a tag for the duration of the tag's life; while the second, associated with the \texttt{dynClass} pseudo-attribute, allows the class to vary over the tag's life. See Section \ref{signals} for an introduction to the $\mt{signal}$ type family.
adam@1643 2021
adam@1751 2022 The third and fourth value-level arguments makes it possible to generate HTML \cd{style} attributes, either with fixed content (\cd{style} attribute) or dynamic content (\cd{dynStyle} pseudo-attribute).
adam@1750 2023
adamc@547 2024 Two XML fragments may be concatenated.
adamc@547 2025 $$\begin{array}{l}
adamc@547 2026 \mt{val} \; \mt{join} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{bind_1} ::: \{\mt{Type}\} \to \mt{bind_2} ::: \{\mt{Type}\} \\
adam@1380 2027 \hspace{.1in} \to [\mt{use_1} \sim \mt{bind_1}] \Rightarrow [\mt{bind_1} \sim \mt{bind_2}] \\
adamc@547 2028 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind_1} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{bind_1}) \; \mt{bind_2} \to \mt{xml} \; \mt{ctx} \; \mt{use_1} \; (\mt{bind_1} \rc \mt{bind_2})
adamc@547 2029 \end{array}$$
adamc@547 2030
adamc@547 2031 Finally, any XML fragment may be updated to ``claim'' to use more form fields than it does.
adamc@547 2032 $$\begin{array}{l}
adam@1380 2033 \mt{val} \; \mt{useMore} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{use_2} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to [\mt{use_1} \sim \mt{use_2}] \\
adamc@547 2034 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{use_2}) \; \mt{bind}
adamc@547 2035 \end{array}$$
adamc@547 2036
adam@1344 2037 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. Also note that there is currently no way for the programmer to add his own tags. It \emph{is} possible to add new tags directly to \texttt{basis.urs}, but this should only be done as a prelude to suggesting a patch to the main distribution.
adamc@547 2038
adamc@547 2039 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 2040 $$\begin{array}{l}
adam@1641 2041 \mt{val} \; \mt{error} : \mt{t} ::: \mt{Type} \to \mt{xbody} \to \mt{t}
adamc@547 2042 \end{array}$$
adamc@547 2043
adamc@549 2044
adamc@701 2045 \subsection{Client-Side Programming}
adamc@659 2046
adamc@701 2047 Ur/Web supports running code on web browsers, via automatic compilation to JavaScript.
adamc@701 2048
adamc@701 2049 \subsubsection{The Basics}
adamc@701 2050
adam@1400 2051 All of the functions in this subsection are client-side only.
adam@1400 2052
adam@1297 2053 Clients can open alert and confirm dialog boxes, in the usual annoying JavaScript way.
adamc@701 2054 $$\begin{array}{l}
adam@1297 2055 \mt{val} \; \mt{alert} : \mt{string} \to \mt{transaction} \; \mt{unit} \\
adam@1297 2056 \mt{val} \; \mt{confirm} : \mt{string} \to \mt{transaction} \; \mt{bool}
adamc@701 2057 \end{array}$$
adamc@701 2058
adamc@701 2059 Any transaction may be run in a new thread with the $\mt{spawn}$ function.
adamc@701 2060 $$\begin{array}{l}
adamc@701 2061 \mt{val} \; \mt{spawn} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit}
adamc@701 2062 \end{array}$$
adamc@701 2063
adamc@701 2064 The current thread can be paused for at least a specified number of milliseconds.
adamc@701 2065 $$\begin{array}{l}
adamc@701 2066 \mt{val} \; \mt{sleep} : \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@701 2067 \end{array}$$
adamc@701 2068
adam@1770 2069 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 a JavaScript \cd{alert()} is used to announce its occurrence. When one of these functions is called multiple times within a single page, all registered handlers are run when appropriate events occur, with handlers run in the reverse of their registration order.
adamc@787 2070 $$\begin{array}{l}
adamc@787 2071 \mt{val} \; \mt{onError} : (\mt{xbody} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787 2072 \mt{val} \; \mt{onFail} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787 2073 \mt{val} \; \mt{onConnectFail} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787 2074 \mt{val} \; \mt{onDisconnect} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787 2075 \mt{val} \; \mt{onServerError} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit}
adamc@787 2076 \end{array}$$
adamc@787 2077
adam@1555 2078 There are also functions to register standard document-level event handlers.
adam@1555 2079
adam@1555 2080 $$\begin{array}{l}
adam@1783 2081 \mt{val} \; \mt{onClick} : (\mt{mouseEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783 2082 \mt{val} \; \mt{onDblclick} : (\mt{mouseEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783 2083 \mt{val} \; \mt{onKeydown} : (\mt{keyEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783 2084 \mt{val} \; \mt{onKeypress} : (\mt{keyEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783 2085 \mt{val} \; \mt{onKeyup} : (\mt{keyEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783 2086 \mt{val} \; \mt{onMousedown} : (\mt{mouseEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783 2087 \mt{val} \; \mt{onMouseup} : (\mt{mouseEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit}
adam@1555 2088 \end{array}$$
adam@1555 2089
adam@1559 2090 Versions of standard JavaScript functions are provided that event handlers may call to mask default handling or prevent bubbling of events up to parent DOM nodes, respectively.
adam@1559 2091
adam@1559 2092 $$\begin{array}{l}
adam@1559 2093 \mt{val} \; \mt{preventDefault} : \mt{transaction} \; \mt{unit} \\
adam@1559 2094 \mt{val} \; \mt{stopPropagation} : \mt{transaction} \; \mt{unit}
adam@1559 2095 \end{array}$$
adam@1559 2096
adam@1556 2097 \subsubsection{Node IDs}
adam@1556 2098
adam@1556 2099 There is an abstract type of node IDs that may be assigned to \cd{id} attributes of most HTML tags.
adam@1556 2100
adam@1556 2101 $$\begin{array}{l}
adam@1556 2102 \mt{type} \; \mt{id} \\
adam@1556 2103 \mt{val} \; \mt{fresh} : \mt{transaction} \; \mt{id}
adam@1556 2104 \end{array}$$
adam@1556 2105
adam@1785 2106 The \cd{fresh} function is allowed on both server and client, but there is no other way to create IDs, which includes lack of a way to force an ID to match a particular string. The main semantic importance of IDs within Ur/Web is in uses of the HTML \cd{<label>} tag. IDs play a much more central role in mainstream JavaScript programming, but Ur/Web uses a very different model to enable changes to particular nodes of a page tree, as the next manual subsection explains. IDs may still be useful in interfacing with JavaScript code (for instance, through Ur/Web's FFI).
adam@1785 2107
adam@1785 2108 One further use of IDs is as handles for requesting that \emph{focus} be given to specific tags.
adam@1785 2109
adam@1785 2110 $$\begin{array}{l}
adam@1785 2111 \mt{val} \; \mt{giveFocus} : \mt{id} \to \mt{transaction} \; \mt{unit}
adam@1785 2112 \end{array}$$
adam@1556 2113
adam@1643 2114 \subsubsection{\label{signals}Functional-Reactive Page Generation}
adamc@701 2115
adamc@701 2116 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 2117
adam@1403 2118 More operationally, you can think of a source as a mutable cell with facilities for subscription to change notifications. That level of detail is hidden behind a monadic facility to be described below. First, there are three primitive operations for working with sources just as if they were ML \cd{ref} cells, corresponding to ML's \cd{ref}, \cd{:=}, and \cd{!} operations.
adam@1403 2119
adamc@659 2120 $$\begin{array}{l}
adamc@659 2121 \mt{con} \; \mt{source} :: \mt{Type} \to \mt{Type} \\
adamc@659 2122 \mt{val} \; \mt{source} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{transaction} \; (\mt{source} \; \mt{t}) \\
adamc@659 2123 \mt{val} \; \mt{set} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@659 2124 \mt{val} \; \mt{get} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@659 2125 \end{array}$$
adamc@659 2126
adam@1400 2127 Only source creation and setting are supported server-side, as a convenience to help in setting up a page, where you may wish to allocate many sources that will be referenced through the page. All server-side storage of values inside sources uses string serializations of values, while client-side storage uses normal JavaScript values.
adam@1400 2128
adam@1608 2129 Pure functions over arbitrary numbers of sources are represented in a monad of \emph{signals}, which may only be used in client-side code. This is presented to the programmer in the form of a monad $\mt{signal}$, each of whose values represents (conceptually) some pure function over all sources that may be allocated in the course of program execution. A monad operation $\mt{signal}$ denotes the identity function over a particular source. By using $\mt{signal}$ on a source, you implicitly subscribe to change notifications for that source. That is, your signal will automatically be recomputed as that source changes. The usual monad operators make it possible to build up complex signals that depend on multiple sources; automatic updating upon source-value changes still happens automatically. There is also an operator for computing a signal's current value within a transaction.
adamc@659 2130
adamc@659 2131 $$\begin{array}{l}
adamc@659 2132 \mt{con} \; \mt{signal} :: \mt{Type} \to \mt{Type} \\
adamc@659 2133 \mt{val} \; \mt{signal\_monad} : \mt{monad} \; \mt{signal} \\
adam@1608 2134 \mt{val} \; \mt{signal} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{signal} \; \mt{t} \\
adam@1608 2135 \mt{val} \; \mt{current} : \mt{t} ::: \mt{Type} \to \mt{signal} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@659 2136 \end{array}$$
adamc@659 2137
adamc@659 2138 A reactive portion of an HTML page is injected with a $\mt{dyn}$ tag, which has a signal-valued attribute $\mt{Signal}$.
adamc@659 2139
adamc@659 2140 $$\begin{array}{l}
adam@1641 2141 \mt{val} \; \mt{dyn} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to [\mt{ctx} \sim [\mt{Dyn}]] \Rightarrow \mt{unit} \\
adam@1641 2142 \hspace{.1in} \to \mt{tag} \; [\mt{Signal} = \mt{signal} \; (\mt{xml} \; ([\mt{Dyn}] \rc \mt{ctx}) \; \mt{use} \; \mt{bind})] \; ([\mt{Dyn}] \rc \mt{ctx}) \; [] \; \mt{use} \; \mt{bind}
adamc@659 2143 \end{array}$$
adamc@659 2144
adam@1648 2145 The semantics of \cd{<dyn>} tags is somewhat subtle. When the signal associated with such a tag changes value, the associated subtree of the HTML page is recreated. Some properties of the subtree, such as attributes and client-side widget values, are specified explicitly in the signal value, so these may be counted on to remain the same after recreation. Other properties, like focus and cursor position within textboxes, are \emph{not} specified by signal values, and these properties will be \emph{reset} upon subtree regeneration. Furthermore, user interaction with widgets may not work properly during regeneration. For instance, clicking a button while it is being regenerated may not trigger its \cd{onclick} event code.
adam@1648 2146
adam@1648 2147 Currently, the only way to avoid undesired resets is to avoid regeneration of containing subtrees. There are two main strategies for achieving that goal. First, when changes to a subtree can be confined to CSS classes of tags, the \texttt{dynClass} pseudo-attribute may be used instead (see Section \ref{xml}), as it does not regenerate subtrees. Second, a single \cd{<dyn>} tag may be broken into multiple tags, in a way that makes finer-grained dependency structure explicit. This latter strategy can avoid ``spurious'' regenerations that are not actually required to achieve the intended semantics.
adam@1648 2148
adam@1786 2149 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. It is also possible to create an ``active'' HTML fragment that runs a $\mt{transaction}$ to determine its content, possibly allocating some sources in the process:
adam@1786 2150
adam@1786 2151 $$\begin{array}{l}
adam@1786 2152 \mt{val} \; \mt{active} : \mt{unit} \to \mt{tag} \; [\mt{Code} = \mt{transaction} \; \mt{xbody}] \; \mt{body} \; [] \; [] \; []
adam@1786 2153 \end{array}$$
adamc@701 2154
adamc@914 2155 \subsubsection{Remote Procedure Calls}
adamc@914 2156
adamc@914 2157 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 2158
adamc@914 2159 $$\begin{array}{l}
adamc@914 2160 \mt{val} \; \mt{rpc} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@914 2161 \end{array}$$
adamc@914 2162
adam@1848 2163 There is an alternate form that uses $\mt{None}$ to indicate that an error occurred during RPC processing, rather than raising an exception to abort this branch of control flow.
adam@1848 2164
adam@1848 2165 $$\begin{array}{l}
adam@1848 2166 \mt{val} \; \mt{tryRpc} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; \mt{t} \to \mt{transaction} \; (\mt{option} \; \mt{t})
adam@1848 2167 \end{array}$$
adam@1848 2168
adamc@701 2169 \subsubsection{Asynchronous Message-Passing}
adamc@701 2170
adamc@701 2171 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 2172
adamc@701 2173 $$\begin{array}{l}
adamc@701 2174 \mt{type} \; \mt{client} \\
adamc@701 2175 \mt{val} \; \mt{self} : \mt{transaction} \; \mt{client}
adamc@701 2176 \end{array}$$
adamc@701 2177
adamc@701 2178 \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 2179
adamc@701 2180 $$\begin{array}{l}
adamc@701 2181 \mt{con} \; \mt{channel} :: \mt{Type} \to \mt{Type} \\
adamc@701 2182 \mt{val} \; \mt{channel} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; (\mt{channel} \; \mt{t}) \\
adamc@701 2183 \mt{val} \; \mt{send} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@701 2184 \mt{val} \; \mt{recv} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@701 2185 \end{array}$$
adamc@701 2186
adamc@701 2187 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 2188
adamc@701 2189 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 2190
adam@1551 2191 \emph{Note}: Currently, there are known concurrency issues with multi-threaded applications that employ message-passing on top of database engines that don't support true serializable transactions. Postgres 9.1 is the only supported engine that does this properly.
adam@1551 2192
adamc@659 2193
adamc@549 2194 \section{Ur/Web Syntax Extensions}
adamc@549 2195
adamc@549 2196 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 2197
adamc@549 2198 \subsection{SQL}
adamc@549 2199
adamc@786 2200 \subsubsection{\label{tables}Table Declarations}
adamc@786 2201
adamc@788 2202 $\mt{table}$ declarations may include constraints, via these grammar rules.
adamc@788 2203 $$\begin{array}{rrcll}
adam@1594 2204 \textrm{Declarations} & d &::=& \mt{table} \; x : c \; [pk[,]] \; cts \mid \mt{view} \; x = V \\
adamc@788 2205 \textrm{Primary key constraints} & pk &::=& \mt{PRIMARY} \; \mt{KEY} \; K \\
adam@1722 2206 \textrm{Keys} & K &::=& f \mid (f, (f,)^+) \mid \{\{e\}\} \\
adamc@788 2207 \textrm{Constraint sets} & cts &::=& \mt{CONSTRAINT} f \; ct \mid cts, cts \mid \{\{e\}\} \\
adamc@788 2208 \textrm{Constraints} & ct &::=& \mt{UNIQUE} \; K \mid \mt{CHECK} \; E \\
adamc@788 2209 &&& \mid \mt{FOREIGN} \; \mt{KEY} \; K \; \mt{REFERENCES} \; F \; (K) \; [\mt{ON} \; \mt{DELETE} \; pr] \; [\mt{ON} \; \mt{UPDATE} \; pr] \\
adamc@788 2210 \textrm{Foreign tables} & F &::=& x \mid \{\{e\}\} \\
adam@1594 2211 \textrm{Propagation modes} & pr &::=& \mt{NO} \; \mt{ACTION} \mid \mt{RESTRICT} \mid \mt{CASCADE} \mid \mt{SET} \; \mt{NULL} \\
adam@1594 2212 \textrm{View expressions} & V &::=& Q \mid \{e\}
adamc@788 2213 \end{array}$$
adamc@788 2214
adamc@788 2215 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 2216
adamc@788 2217
adamc@549 2218 \subsubsection{Queries}
adamc@549 2219
adamc@550 2220 Queries $Q$ are added to the rules for expressions $e$.
adamc@550 2221
adamc@549 2222 $$\begin{array}{rrcll}
adam@1684 2223 \textrm{Queries} & Q &::=& (q \; [\mt{ORDER} \; \mt{BY} \; O] \; [\mt{LIMIT} \; N] \; [\mt{OFFSET} \; N]) \\
adamc@1085 2224 \textrm{Pre-queries} & q &::=& \mt{SELECT} \; [\mt{DISTINCT}] \; P \; \mt{FROM} \; F,^+ \; [\mt{WHERE} \; E] \; [\mt{GROUP} \; \mt{BY} \; p,^+] \; [\mt{HAVING} \; E] \\
adamc@1085 2225 &&& \mid q \; R \; q \mid \{\{\{e\}\}\} \\
adam@1684 2226 \textrm{Relational operators} & R &::=& \mt{UNION} \mid \mt{INTERSECT} \mid \mt{EXCEPT} \\
adam@1778 2227 \textrm{$\mt{ORDER \; BY}$ items} & O &::=& \mt{RANDOM} [()] \mid \hat{E} \; [o] \mid \hat{E} \; [o], O
adamc@549 2228 \end{array}$$
adamc@549 2229
adamc@549 2230 $$\begin{array}{rrcll}
adamc@549 2231 \textrm{Projections} & P &::=& \ast & \textrm{all columns} \\
adamc@549 2232 &&& p,^+ & \textrm{particular columns} \\
adamc@549 2233 \textrm{Pre-projections} & p &::=& t.f & \textrm{one column from a table} \\
adamc@558 2234 &&& t.\{\{c\}\} & \textrm{a record of columns from a table (of kind $\{\mt{Type}\}$)} \\
adam@1627 2235 &&& t.* & \textrm{all columns from a table} \\
adam@1778 2236 &&& \hat{E} \; [\mt{AS} \; f] & \textrm{expression column} \\
adamc@549 2237 \textrm{Table names} & t &::=& x & \textrm{constant table name (automatically capitalized)} \\
adamc@549 2238 &&& X & \textrm{constant table name} \\
adamc@549 2239 &&& \{\{c\}\} & \textrm{computed table name (of kind $\mt{Name}$)} \\
adamc@549 2240 \textrm{Column names} & f &::=& X & \textrm{constant column name} \\
adamc@549 2241 &&& \{c\} & \textrm{computed column name (of kind $\mt{Name}$)} \\
adamc@549 2242 \textrm{Tables} & T &::=& x & \textrm{table variable, named locally by its own capitalization} \\
adam@1756 2243 &&& x \; \mt{AS} \; X & \textrm{table variable, with local name} \\
adam@1756 2244 &&& x \; \mt{AS} \; \{c\} & \textrm{table variable, with computed local name} \\
adamc@549 2245 &&& \{\{e\}\} \; \mt{AS} \; t & \textrm{computed table expression, with local name} \\
adam@1756 2246 &&& \{\{e\}\} \; \mt{AS} \; \{c\} & \textrm{computed table expression, with computed local name} \\
adamc@1085 2247 \textrm{$\mt{FROM}$ items} & F &::=& T \mid \{\{e\}\} \mid F \; J \; \mt{JOIN} \; F \; \mt{ON} \; E \\
adamc@1085 2248 &&& \mid F \; \mt{CROSS} \; \mt{JOIN} \ F \\
adamc@1193 2249 &&& \mid (Q) \; \mt{AS} \; t \\
adamc@1085 2250 \textrm{Joins} & J &::=& [\mt{INNER}] \\
adamc@1085 2251 &&& \mid [\mt{LEFT} \mid \mt{RIGHT} \mid \mt{FULL}] \; [\mt{OUTER}] \\
adam@1587 2252 \textrm{SQL expressions} & E &::=& t.f & \textrm{column references} \\
adamc@549 2253 &&& X & \textrm{named expression references} \\
adam@1490 2254 &&& \{[e]\} & \textrm{injected native Ur expressions} \\
adam@1778 2255 &&& \{e\} & \textrm{computed expressions, probably using $\mt{sql\_exp}$ directly} \\
adamc@549 2256 &&& \mt{TRUE} \mid \mt{FALSE} & \textrm{boolean constants} \\
adamc@549 2257 &&& \ell & \textrm{primitive type literals} \\
adamc@549 2258 &&& \mt{NULL} & \textrm{null value (injection of $\mt{None}$)} \\
adamc@549 2259 &&& E \; \mt{IS} \; \mt{NULL} & \textrm{nullness test} \\
adam@1602 2260 &&& \mt{COALESCE}(E, E) & \textrm{take first non-null value} \\
adamc@549 2261 &&& n & \textrm{nullary operators} \\
adamc@549 2262 &&& u \; E & \textrm{unary operators} \\
adamc@549 2263 &&& E \; b \; E & \textrm{binary operators} \\
adam@1778 2264 &&& \mt{COUNT}(\ast) & \textrm{count number of rows} \\
adam@1778 2265 &&& a(E) & \textrm{other aggregate function} \\
adam@1573 2266 &&& \mt{IF} \; E \; \mt{THEN} \; E \; \mt{ELSE} \; E & \textrm{conditional} \\
adam@1778 2267 &&& (Q) & \textrm{subquery (must return a single expression column)} \\
adamc@549 2268 &&& (E) & \textrm{explicit precedence} \\
adamc@549 2269 \textrm{Nullary operators} & n &::=& \mt{CURRENT\_TIMESTAMP} \\
adamc@549 2270 \textrm{Unary operators} & u &::=& \mt{NOT} \\
adam@1688 2271 \textrm{Binary operators} & b &::=& \mt{AND} \mid \mt{OR} \mid = \mid \neq \mid < \mid \leq \mid > \mid \geq \\
adamc@1188 2272 \textrm{Aggregate functions} & a &::=& \mt{COUNT} \mid \mt{AVG} \mid \mt{SUM} \mid \mt{MIN} \mid \mt{MAX} \\
adam@1543 2273 \textrm{Directions} & o &::=& \mt{ASC} \mid \mt{DESC} \mid \{e\} \\
adamc@549 2274 \textrm{SQL integer} & N &::=& n \mid \{e\} \\
adam@1778 2275 \textrm{Windowable expressions} & \hat{E} &::=& E \\
adam@1778 2276 &&& w \; [\mt{OVER} \; ( & \textrm{(Postgres only)} \\
adam@1778 2277 &&& \hspace{.1in} [\mt{PARTITION} \; \mt{BY} \; E] \\
adam@1778 2278 &&& \hspace{.1in} [\mt{ORDER} \; \mt{BY} \; O])] \\
adam@1778 2279 \textrm{Window function} & w &::=& \mt{RANK}() \\
adam@1778 2280 &&& \mt{COUNT}(*) \\
adam@1778 2281 &&& a(E)
adamc@549 2282 \end{array}$$
adamc@549 2283
adamc@1085 2284 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 2285
adam@1683 2286 Unnamed expression columns in $\mt{SELECT}$ clauses are assigned consecutive natural numbers, starting with 1. Any expression in a $p$ position that is enclosed in parentheses is treated as an expression column, rather than a column pulled directly out of a table, even if it is only a field projection. (This distinction affects the record type used to describe query results.)
adamc@1194 2287
adamc@550 2288 \subsubsection{DML}
adamc@550 2289
adamc@550 2290 DML commands $D$ are added to the rules for expressions $e$.
adamc@550 2291
adamc@550 2292 $$\begin{array}{rrcll}
adamc@550 2293 \textrm{Commands} & D &::=& (\mt{INSERT} \; \mt{INTO} \; T^E \; (f,^+) \; \mt{VALUES} \; (E,^+)) \\
adamc@550 2294 &&& (\mt{UPDATE} \; T^E \; \mt{SET} \; (f = E,)^+ \; \mt{WHERE} \; E) \\
adamc@550 2295 &&& (\mt{DELETE} \; \mt{FROM} \; T^E \; \mt{WHERE} \; E) \\
adamc@550 2296 \textrm{Table expressions} & T^E &::=& x \mid \{\{e\}\}
adamc@550 2297 \end{array}$$
adamc@550 2298
adamc@550 2299 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 2300
adamc@551 2301 \subsection{XML}
adamc@551 2302
adamc@551 2303 XML fragments $L$ are added to the rules for expressions $e$.
adamc@551 2304
adamc@551 2305 $$\begin{array}{rrcll}
adamc@551 2306 \textrm{XML fragments} & L &::=& \texttt{<xml/>} \mid \texttt{<xml>}l^*\texttt{</xml>} \\
adamc@551 2307 \textrm{XML pieces} & l &::=& \textrm{text} & \textrm{cdata} \\
adamc@551 2308 &&& \texttt{<}g\texttt{/>} & \textrm{tag with no children} \\
adamc@551 2309 &&& \texttt{<}g\texttt{>}l^*\texttt{</}x\texttt{>} & \textrm{tag with children} \\
adamc@559 2310 &&& \{e\} & \textrm{computed XML fragment} \\
adamc@559 2311 &&& \{[e]\} & \textrm{injection of an Ur expression, via the $\mt{Top}.\mt{txt}$ function} \\
adamc@551 2312 \textrm{Tag} & g &::=& h \; (x = v)^* \\
adamc@551 2313 \textrm{Tag head} & h &::=& x & \textrm{tag name} \\
adamc@551 2314 &&& h\{c\} & \textrm{constructor parameter} \\
adamc@551 2315 \textrm{Attribute value} & v &::=& \ell & \textrm{literal value} \\
adamc@551 2316 &&& \{e\} & \textrm{computed value} \\
adamc@551 2317 \end{array}$$
adamc@551 2318
adam@1751 2319 Further, there is a special convenience and compatibility form for setting CSS classes of tags. If a \cd{class} attribute has a value that is a string literal, the literal is parsed in the usual HTML way and replaced with calls to appropriate Ur/Web combinators. Any dashes in the text are replaced with underscores to determine Ur identifiers. The same desugaring can be accessed in a normal expression context by calling the pseudo-function \cd{CLASS} on a string literal.
adam@1751 2320
adam@1751 2321 Similar support is provided for \cd{style} attributes. Normal CSS syntax may be used in string literals that are \cd{style} attribute values, and the desugaring may be accessed elsewhere with the pseudo-function \cd{STYLE}.
adamc@552 2322
adamc@1198 2323 \section{\label{structure}The Structure of Web Applications}
adamc@553 2324
adam@1797 2325 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. See Section \ref{cl} for information on the \texttt{prefix} and \texttt{rewrite url} directives, which can be used to rewrite the default URIs of different entry point functions. The final URL of a function is its default module-based URI, with \texttt{rewrite url} rules applied, and with the \texttt{prefix} prepended. Arguments to an entry-point function are deserialized from the part of the URI following \texttt{f}.
adamc@553 2326
adam@1532 2327 Elements of modules beside the main module, including page handlers, will only be included in the final application if they are transitive dependencies of the handlers in the main module.
adam@1532 2328
adam@1787 2329 Normal links are accessible via HTTP \texttt{GET}, which the relevant standard says should never cause side effects. To export a page which may cause side effects, accessible only via HTTP \texttt{POST}, include one argument of the page handler of type $\mt{Basis.postBody}$. When the handler is called, this argument will receive a value that can be deconstructed into a MIME type (with $\mt{Basis.postType}$) and payload (with $\mt{Basis.postData}$). This kind of handler should not be used with forms that exist solely within Ur/Web apps; for these, use Ur/Web's built-in support, as described below. It may still be useful to use $\mt{Basis.postBody}$ with form requests submitted by code outside an Ur/Web app. For such cases, the function $\mt{Top.postFields} : \mt{postBody} \to \mt{list} \; (\mt{string} \times \mt{string})$ may be useful, breaking a \texttt{POST} body of type \texttt{application/x-www-form-urlencoded} into its name-value pairs.
adam@1347 2330
adam@1370 2331 Any normal page handler may also include arguments of type $\mt{option \; Basis.queryString}$, which will be handled specially. Rather than being deserialized from the current URI, such an argument is passed the whole query string that the handler received. The string may be analyzed by calling $\mt{Basis.show}$ on it. A handler of this kind may be passed as an argument to $\mt{Basis.effectfulUrl}$ to generate a URL to a page that may be used as a ``callback'' by an external service, such that the handler is allowed to cause side effects.
adam@1370 2332
adamc@553 2333 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 2334
adamc@553 2335 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 2336
adam@1653 2337 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. Such serialized values may only be drawn from a limited set of types, and programs will fail to compile when the (implicit or explicit) arguments of page handler functions involve disallowed types. (Keep in mind that every free variable of a function is an implicit argument if it was not defined at the top level of a module.) For instance:
adam@1653 2338 \begin{itemize}
adam@1653 2339 \item Functions are disallowed, since there is no obvious way to serialize them safely.
adam@1653 2340 \item XML fragments are disallowed, since it is unclear how to check client-provided XML to be sure it doesn't break the HTML invariants of the application (for instance, by mutating the DOM in the conventional way, interfering with Ur/Web's functional-reactive regime).
adam@1653 2341 \item Blobs (``files'') are disallowed, since they can easily have very large serializations that could not fit within most web servers' URL size limits. (And you probably don't want to be serializing, e.g., image files in URLs, anyway.)
adam@1653 2342 \end{itemize}
adamc@553 2343
adamc@660 2344 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 2345
adamc@789 2346 \medskip
adamc@789 2347
adam@1347 2348 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, or via a direct call to a page handler with some argument of type $\mt{Basis.postBody}$. 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 2349
adamc@789 2350 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 2351
adam@1348 2352 \subsection{Tasks}
adam@1348 2353
adam@1348 2354 In many web applications, it's useful to run code at points other than requests from browsers. Ur/Web's \emph{task} mechanism facilitates this. A type family of \emph{task kinds} is in the standard library:
adam@1348 2355
adam@1348 2356 $$\begin{array}{l}
adam@1348 2357 \mt{con} \; \mt{task\_kind} :: \mt{Type} \to \mt{Type} \\
adam@1348 2358 \mt{val} \; \mt{initialize} : \mt{task\_kind} \; \mt{unit} \\
adam@1349 2359 \mt{val} \; \mt{clientLeaves} : \mt{task\_kind} \; \mt{client} \\
adam@1349 2360 \mt{val} \; \mt{periodic} : \mt{int} \to \mt{task\_kind} \; \mt{unit}
adam@1348 2361 \end{array}$$
adam@1348 2362
adam@1348 2363 A task kind names a particular extension point of generated applications, where the type parameter of a task kind describes which extra input data is available at that extension point. Add task code with the special declaration form $\mt{task} \; e_1 = e_2$, where $e_1$ is a task kind with data $\tau$, and $e_2$ is a function from $\tau$ to $\mt{transaction} \; \mt{unit}$.
adam@1348 2364
adam@1348 2365 The currently supported task kinds are:
adam@1348 2366 \begin{itemize}
adam@1349 2367 \item $\mt{initialize}$: Code that is run when the application starts up.
adam@1348 2368 \item $\mt{clientLeaves}$: Code that is run for each client that the runtime system decides has surfed away. When a request that generates a new client handle is aborted, that handle will still eventually be passed to $\mt{clientLeaves}$ task code, even though the corresponding browser was never informed of the client handle's existence. In other words, in general, $\mt{clientLeaves}$ handlers will be called more times than there are actual clients.
adam@1349 2369 \item $\mt{periodic} \; n$: Code that is run when the application starts up and then every $n$ seconds thereafter.
adam@1348 2370 \end{itemize}
adam@1348 2371
adamc@553 2372
adamc@897 2373 \section{The Foreign Function Interface}
adamc@897 2374
adamc@897 2375 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 2376
adamc@897 2377 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 2378
adamc@897 2379 \begin{itemize}
adamc@897 2380 \item \texttt{clientOnly Module.ident} registers a value as being allowed only in client-side code.
adamc@897 2381 \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.
adam@1699 2382 \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. (Note that merely assigning a function a \texttt{transaction}-based type does not mark it as effectful in this way!)
adamc@897 2383 \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 2384 \item \texttt{include FILE} requests inclusion of a C header file.
adamc@897 2385 \item \texttt{jsFunc Module.ident=name} gives a mapping from an Ur name for a value to a JavaScript name.
adamc@897 2386 \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 2387 \item \texttt{script URL} requests inclusion of a JavaScript source file within application HTML.
adamc@897 2388 \item \texttt{serverOnly Module.ident} registers a value as being allowed only in server-side code.
adamc@897 2389 \end{itemize}
adamc@897 2390
adamc@897 2391 \subsection{Writing C FFI Code}
adamc@897 2392
adamc@897 2393 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 2394
adamc@897 2395 \begin{itemize}
adamc@897 2396 \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 2397 \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 2398 \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*}.
adam@1686 2399 \item Ur/Web involves many types of program syntax, such as for HTML and SQL code. All of these types are implemented with normal C strings, and you may take advantage of that encoding to manipulate code as strings in C FFI code. Be mindful that, in writing such code, it is your responsibility to maintain the appropriate code invariants, or you may reintroduce the code injection vulnerabilities that Ur/Web rules out. The most convenient way to extend Ur/Web with functions that, e.g., use natively unsupported HTML tags is to generate the HTML code with the FFI.
adamc@897 2400 \end{itemize}
adamc@897 2401
adamc@897 2402 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 2403 \begin{itemize}
adamc@897 2404 \item \begin{verbatim}
adamc@897 2405 void uw_error(uw_context, failure_kind, const char *fmt, ...);
adamc@897 2406 \end{verbatim}
adamc@897 2407 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 2408
adam@1329 2409 All pointers to the context-local heap (see description below of \texttt{uw\_malloc()}) become invalid at the start and end of any execution of a main entry point function of an application. For example, if the request handler is restarted because of a \texttt{uw\_error()} call with \texttt{BOUNDED\_RETRY} or for any other reason, it is unsafe to access any local heap pointers that may have been stashed somewhere beforehand.
adam@1329 2410
adamc@897 2411 \item \begin{verbatim}
adam@1469 2412 void uw_set_error_message(uw_context, const char *fmt, ...);
adam@1469 2413 \end{verbatim}
adam@1469 2414 This simpler form of \texttt{uw\_error()} saves an error message without immediately aborting execution.
adam@1469 2415
adam@1469 2416 \item \begin{verbatim}
adamc@897 2417 void uw_push_cleanup(uw_context, void (*func)(void *), void *arg);
adamc@897 2418 void uw_pop_cleanup(uw_context);
adamc@897 2419 \end{verbatim}
adam@1329 2420 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. It is a bug to let a page request handler finish successfully with unpopped cleanup actions.
adam@1329 2421
adam@1329 2422 Pending cleanup actions aren't intended to have any complex relationship amongst themselves, so, upon request handler abort, pending actions are executed in first-in-first-out order.
adamc@897 2423
adamc@897 2424 \item \begin{verbatim}
adamc@897 2425 void *uw_malloc(uw_context, size_t);
adamc@897 2426 \end{verbatim}
adam@1329 2427 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. In general, \texttt{uw\_malloc()}ed memory should only be used in ways compatible with the computation model of pure Ur. This means it is fine to allocate and return a value that could just as well have been built with core Ur code. In contrast, it is almost never safe to store \texttt{uw\_malloc()}ed pointers in global variables, including when the storage happens implicitly by registering a callback that would take the pointer as an argument.
adam@1329 2428
adam@1329 2429 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. However, we emphasize again that \texttt{uw\_malloc()} should never be used to implement some logic that couldn't be implemented trivially by a constant-valued expression in Ur.
adamc@897 2430
adamc@897 2431 \item \begin{verbatim}
adamc@897 2432 typedef void (*uw_callback)(void *);
adam@1328 2433 typedef void (*uw_callback_with_retry)(void *, int will_retry);
adamc@897 2434 void uw_register_transactional(uw_context, void *data, uw_callback commit,
adam@1328 2435 uw_callback rollback, uw_callback_with_retry free);
adamc@897 2436 \end{verbatim}
adam@1328 2437 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. A free handler is told whether the runtime system expects to retry the current page request after rollback finishes.
adamc@897 2438
adamc@1085 2439 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 2440
adam@1329 2441 When a request handler ends with multiple pending transactional actions, their handlers are run in a first-in-last-out stack-like order, wherever the order would otherwise be ambiguous.
adam@1329 2442
adam@1329 2443 It is not safe for any of these handlers to access a context-local heap through a pointer returned previously by \texttt{uw\_malloc()}, nor should any new calls to that function be made. Think of the context-local heap as meant for use by the Ur/Web code itself, while transactional handlers execute after the Ur/Web code has finished.
adam@1329 2444
adam@1469 2445 A handler may signal an error by calling \texttt{uw\_set\_error\_message()}, but it is not safe to call \texttt{uw\_error()} from a handler. Signaling an error in a commit handler will cause the runtime system to switch to aborting the transaction, immediately after the current commit handler returns.
adam@1469 2446
adamc@1085 2447 \item \begin{verbatim}
adamc@1085 2448 void *uw_get_global(uw_context, char *name);
adamc@1085 2449 void uw_set_global(uw_context, char *name, void *data, uw_callback free);
adamc@1085 2450 \end{verbatim}
adam@1329 2451 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. It is never safe to store \texttt{uw\_malloc()}ed pointers in global variable slots.
adamc@1085 2452
adamc@897 2453 \end{itemize}
adamc@897 2454
adamc@897 2455 \subsection{Writing JavaScript FFI Code}
adamc@897 2456
adamc@897 2457 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 2458
adamc@897 2459 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 2460
adamc@897 2461 \begin{itemize}
adamc@897 2462 \item Integers, floats, strings, characters, and booleans are represented in the usual JavaScript way.
adam@1644 2463 \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)}. To lift a normal JavaScript function \cd{f} into an Ur/Web JavaScript function, run \cd{flift(f)}.
adamc@897 2464 \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 2465 \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 2466 \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.
adam@1686 2467 \item As in the C FFI, all abstract types of program syntax are implemented with strings in JavaScript.
adam@1844 2468 \item A value of Ur type \texttt{transaction t} is represented in the same way as for \texttt{unit -> t}.
adamc@897 2469 \end{itemize}
adamc@897 2470
adam@1644 2471 It is possible to write JavaScript FFI code that interacts with the functional-reactive structure of a document. Here is a quick summary of some of the simpler functions to use; descriptions of fancier stuff may be added later on request (and such stuff should be considered ``undocumented features'' until then).
adam@1644 2472
adam@1644 2473 \begin{itemize}
adam@1644 2474 \item Sources should be treated as an abstract type, manipulated via:
adam@1644 2475 \begin{itemize}
adam@1644 2476 \item \cd{sc(v)}, to create a source initialized to \cd{v}
adam@1644 2477 \item \cd{sg(s)}, to retrieve the current value of source \cd{s}
adam@1644 2478 \item \cd{sv(s, v)}, to set source \cd{s} to value \cd{v}
adam@1644 2479 \end{itemize}
adam@1644 2480
adam@1644 2481 \item Signals should be treated as an abstract type, manipulated via:
adam@1644 2482 \begin{itemize}
adam@1644 2483 \item \cd{sr(v)} and \cd{sb(s, f)}, the ``return'' and ``bind'' monad operators, respectively
adam@1644 2484 \item \cd{ss(s)}, to produce the signal corresponding to source \cd{s}
adam@1644 2485 \item \cd{scur(s)}, to get the current value of signal \cd{s}
adam@1644 2486 \end{itemize}
adam@1644 2487
adam@1644 2488 \item The behavior of the \cd{<dyn>} pseudo-tag may be mimicked by following the right convention in a piece of HTML source code with a type like $\mt{xbody}$. Such a piece of source code may be encoded with a JavaScript string. To insert a dynamic section, include a \cd{<script>} tag whose content is just a call \cd{dyn(pnode, s)}. The argument \cd{pnode} specifies what the relevant enclosing parent tag is. Use value \cd{"tr"} when the immediate parent is \cd{<tr>}, use \cd{"table"} when the immediate parent is \cd{<table>}, and use \cd{"span"} otherwise. The argument \cd{s} is a string-valued signal giving the HTML code to be inserted at this point. As with the usual \cd{<dyn>} tag, that HTML subtree is automatically updated as the value of \cd{s} changes.
adam@1644 2489
adam@1702 2490 \item There is only one supported method of taking HTML values generated in Ur/Web code and adding them to the DOM in FFI JavaScript code: call \cd{setInnerHTML(node, html)} to add HTML content \cd{html} within DOM node \cd{node}. Merely running \cd{node.innerHTML = html} is not guaranteed to get the job done, though programmers familiar with JavaScript will probably find it useful to think of \cd{setInnerHTML} as having this effect. The unusual idiom is required because Ur/Web uses a nonstandard representation of HTML, to support infinite nesting of code that may generate code that may generate code that.... The \cd{node} value must already be in the DOM tree at the point when \cd{setInnerHTML} is called, because some plumbing must be set up to interact sensibly with \cd{<dyn>} tags.
adam@1702 2491
adam@1644 2492 \item It is possible to use the more standard ``IDs and mutation'' style of JavaScript coding, though that style is unidiomatic for Ur/Web and should be avoided wherever possible. Recall the abstract type $\mt{id}$ and its constructor $\mt{fresh}$, which can be used to generate new unique IDs in Ur/Web code. Values of this type are represented as strings in JavaScript, and a function \cd{fresh()} is available to generate new unique IDs. Application-specific ID generation schemes may cause bad interactions with Ur/Web code that also generates IDs, so the recommended approach is to produce IDs only via calls to \cd{fresh()}. FFI code shouldn't depend on the ID generation scheme (on either server side or client side), but it is safe to include these IDs in tag attributes (in either server-side or client-side code) and manipulate the associated DOM nodes in the standard way (in client-side code). Be forewarned that this kind of imperative DOM manipulation may confuse the Ur/Web runtime system and interfere with proper behavior of tags like \cd{<dyn>}!
adam@1644 2493 \end{itemize}
adamc@897 2494
adam@1833 2495 \subsection{Introducing New HTML Tags}
adam@1833 2496
adam@1833 2497 FFI modules may introduce new tags as values with $\mt{Basis.tag}$ types. See \texttt{basis.urs} for examples of how tags are declared. The identifier of a tag value is used as its rendering in HTML. The Ur/Web syntax sugar for XML literals desugars each use of a tag into a reference to an identifier with the same name. There is no need to provide implementations (i.e., in C or JavaScript code) for such identifiers.
adam@1833 2498
adam@1833 2499 The onus is on the coder of a new tag's interface to think about consequences for code injection attacks, messing with the DOM in ways that may break Ur/Web reactive programming, etc.
adam@1833 2500
adamc@897 2501
adamc@552 2502 \section{Compiler Phases}
adamc@552 2503
adamc@552 2504 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 2505
adamc@552 2506 In this section, we step through the main phases of compilation, noting what consequences each phase has for effective programming.
adamc@552 2507
adamc@552 2508 \subsection{Parse}
adamc@552 2509
adamc@552 2510 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 2511
adamc@552 2512 \subsection{Elaborate}
adamc@552 2513
adamc@552 2514 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 2515
adam@1378 2516 Those crawling through the compiler source will also want to be aware of another compiler phase, Explify, that occurs immediately afterward. This phase just translates from an AST language that includes unification variables to a very similar language that doesn't; all variables should have been determined by the end of Elaborate, anyway. The new AST language also drops some features that are used only for static checking and that have no influence on runtime behavior, like disjointness constraints.
adam@1378 2517
adamc@552 2518 \subsection{Unnest}
adamc@552 2519
adamc@552 2520 Named local function definitions are moved to the top level, to avoid the need to generate closures.
adamc@552 2521
adamc@552 2522 \subsection{Corify}
adamc@552 2523
adamc@552 2524 Module system features are compiled away, through inlining of functor definitions at application sites. Afterward, most abstraction boundaries are broken, facilitating optimization.
adamc@552 2525
adamc@552 2526 \subsection{Especialize}
adamc@552 2527
adam@1356 2528 Functions are specialized to particular argument patterns. This is an important trick for avoiding the need to maintain any closures at runtime. Currently, specialization only happens for prefixes of a function's full list of parameters, so you may need to take care to put arguments of function types before other arguments. The optimizer will not be effective enough if you use arguments that mix functions and values that must be calculated at run-time. For instance, a tuple of a function and an integer counter would not lead to successful code generation; these should be split into separate arguments via currying.
adamc@552 2529
adamc@552 2530 \subsection{Untangle}
adamc@552 2531
adam@1797 2532 Remove unnecessary mutual recursion, splitting recursive groups into strongly connected components.
adamc@552 2533
adamc@552 2534 \subsection{Shake}
adamc@552 2535
adamc@552 2536 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 2537
adamc@661 2538 \subsection{Rpcify}
adamc@661 2539
adamc@661 2540 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 2541
adamc@661 2542 \subsection{Untangle, Shake}
adamc@661 2543
adamc@661 2544 Repeat these simplifications.
adamc@661 2545
adamc@553 2546 \subsection{\label{tag}Tag}
adamc@552 2547
adamc@552 2548 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 2549
adamc@552 2550 \subsection{Reduce}
adamc@552 2551
adamc@552 2552 Apply definitional equality rules to simplify the program as much as possible. This effectively includes inlining of every non-recursive definition.
adamc@552 2553
adamc@552 2554 \subsection{Unpoly}
adamc@552 2555
adamc@552 2556 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 2557
adamc@552 2558 \subsection{Specialize}
adamc@552 2559
adamc@558 2560 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 2561
adamc@552 2562 \subsection{Shake}
adamc@552 2563
adamc@558 2564 Here the compiler repeats the earlier Shake phase.
adamc@552 2565
adamc@552 2566 \subsection{Monoize}
adamc@552 2567
adamc@552 2568 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 2569
adamc@552 2570 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 2571
adamc@552 2572 \subsection{MonoOpt}
adamc@552 2573
adamc@552 2574 Simple algebraic laws are applied to simplify the program, focusing especially on efficient imperative generation of HTML pages.
adamc@552 2575
adamc@552 2576 \subsection{MonoUntangle}
adamc@552 2577
adamc@552 2578 Unnecessary mutual recursion is broken up again.
adamc@552 2579
adamc@552 2580 \subsection{MonoReduce}
adamc@552 2581
adamc@552 2582 Equivalents of the definitional equality rules are applied to simplify programs, with inlining again playing a major role.
adamc@552 2583
adamc@552 2584 \subsection{MonoShake, MonoOpt}
adamc@552 2585
adamc@552 2586 Unneeded declarations are removed, and basic optimizations are repeated.
adamc@552 2587
adamc@552 2588 \subsection{Fuse}
adamc@552 2589
adamc@552 2590 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 2591
adamc@552 2592 \subsection{MonoUntangle, MonoShake}
adamc@552 2593
adamc@552 2594 Fuse often creates more opportunities to remove spurious mutual recursion.
adamc@552 2595
adamc@552 2596 \subsection{Pathcheck}
adamc@552 2597
adamc@552 2598 The compiler checks that no link or action name has been used more than once.
adamc@552 2599
adamc@552 2600 \subsection{Cjrize}
adamc@552 2601
adamc@552 2602 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 2603
adamc@552 2604 \subsection{C Compilation and Linking}
adamc@552 2605
adam@1523 2606 The output of the last phase is pretty-printed as C source code and passed to the C compiler.
adamc@552 2607
adamc@552 2608
as@1564 2609 \end{document}