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Simplify type of Basis.tag, regarding 'class' attribute; new compatibility parsing of 'class' values given as string literals
author Adam Chlipala <adam@chlipala.net>
date Sun, 06 May 2012 13:07:13 -0400
parents 518e0b23c4ef
children 277480862cef
rev   line source
adamc@524 1 \documentclass{article}
adamc@554 2 \usepackage{fullpage,amsmath,amssymb,proof,url}
rmbruijn@1568 3 \usepackage[T1]{fontenc}
adamc@524 4 \newcommand{\cd}[1]{\texttt{#1}}
adamc@524 5 \newcommand{\mt}[1]{\mathsf{#1}}
adamc@524 6
adamc@524 7 \newcommand{\rc}{+ \hspace{-.075in} + \;}
adamc@527 8 \newcommand{\rcut}{\; \texttt{--} \;}
adamc@527 9 \newcommand{\rcutM}{\; \texttt{---} \;}
adamc@524 10
adamc@524 11 \begin{document}
adamc@524 12
adamc@524 13 \title{The Ur/Web Manual}
adamc@524 14 \author{Adam Chlipala}
adamc@524 15
adamc@524 16 \maketitle
adamc@524 17
adamc@540 18 \tableofcontents
adamc@540 19
adamc@554 20
adamc@554 21 \section{Introduction}
adamc@554 22
adamc@1160 23 \emph{Ur} is a programming language designed to introduce richer type system features into functional programming in the tradition of ML and Haskell. Ur is functional, pure, statically-typed, and strict. Ur supports a powerful kind of \emph{metaprogramming} based on \emph{type-level computation with type-level records}.
adamc@554 24
adamc@554 25 \emph{Ur/Web} is Ur plus a special standard library and associated rules for parsing and optimization. Ur/Web supports construction of dynamic web applications backed by SQL databases. The signature of the standard library is such that well-typed Ur/Web programs ``don't go wrong'' in a very broad sense. Not only do they not crash during particular page generations, but they also may not:
adamc@554 26
adamc@554 27 \begin{itemize}
adamc@554 28 \item Suffer from any kinds of code-injection attacks
adamc@554 29 \item Return invalid HTML
adamc@554 30 \item Contain dead intra-application links
adamc@554 31 \item Have mismatches between HTML forms and the fields expected by their handlers
adamc@652 32 \item Include client-side code that makes incorrect assumptions about the ``AJAX''-style services that the remote web server provides
adamc@554 33 \item Attempt invalid SQL queries
adamc@652 34 \item Use improper marshaling or unmarshaling in communication with SQL databases or between browsers and web servers
adamc@554 35 \end{itemize}
adamc@554 36
adamc@554 37 This type safety is just the foundation of the Ur/Web methodology. It is also possible to use metaprogramming to build significant application pieces by analysis of type structure. For instance, the demo includes an ML-style functor for building an admin interface for an arbitrary SQL table. The type system guarantees that the admin interface sub-application that comes out will always be free of the above-listed bugs, no matter which well-typed table description is given as input.
adamc@554 38
adamc@652 39 The Ur/Web compiler also produces very efficient object code that does not use garbage collection. These compiled programs will often be even more efficient than what most programmers would bother to write in C. The compiler also generates JavaScript versions of client-side code, with no need to write those parts of applications in a different language.
adamc@554 40
adamc@554 41 \medskip
adamc@554 42
adamc@554 43 The official web site for Ur is:
adamc@554 44 \begin{center}
adamc@554 45 \url{http://www.impredicative.com/ur/}
adamc@554 46 \end{center}
adamc@554 47
adamc@555 48
adamc@555 49 \section{Installation}
adamc@555 50
adamc@555 51 If you are lucky, then the following standard command sequence will suffice for installation, in a directory to which you have unpacked the latest distribution tarball.
adamc@555 52
adamc@555 53 \begin{verbatim}
adamc@555 54 ./configure
adamc@555 55 make
adamc@555 56 sudo make install
adamc@555 57 \end{verbatim}
adamc@555 58
adam@1523 59 Some other packages must be installed for the above to work. At a minimum, you need a standard UNIX shell, with standard UNIX tools like sed and GCC (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 60 \begin{verbatim}
adam@1368 61 apt-get install mlton libssl-dev
adamc@896 62 \end{verbatim}
adamc@555 63
adamc@896 64 To build programs that access SQL databases, you also need one of these client libraries for supported backends.
adamc@555 65 \begin{verbatim}
adamc@896 66 apt-get install libpq-dev libmysqlclient15-dev libsqlite3-dev
adamc@555 67 \end{verbatim}
adamc@555 68
adamc@555 69 It is also possible to access the modules of the Ur/Web compiler interactively, within Standard ML of New Jersey. To install the prerequisites in Debian testing:
adamc@555 70 \begin{verbatim}
adamc@555 71 apt-get install smlnj libsmlnj-smlnj ml-yacc ml-lpt
adamc@555 72 \end{verbatim}
adamc@555 73
adamc@555 74 To begin an interactive session with the Ur compiler modules, run \texttt{make smlnj}, and then, from within an \texttt{sml} session, run \texttt{CM.make "src/urweb.cm";}. The \texttt{Compiler} module is the main entry point.
adamc@555 75
adamc@896 76 To run an SQL-backed application with a backend besides SQLite, you will probably want to install one of these servers.
adamc@555 77
adamc@555 78 \begin{verbatim}
adam@1400 79 apt-get install postgresql-8.4 mysql-server-5.1
adamc@555 80 \end{verbatim}
adamc@555 81
adamc@555 82 To use the Emacs mode, you must have a modern Emacs installed. We assume that you already know how to do this, if you're in the business of looking for an Emacs mode. The demo generation facility of the compiler will also call out to Emacs to syntax-highlight code, and that process depends on the \texttt{htmlize} module, which can be installed in Debian testing via:
adamc@555 83
adamc@555 84 \begin{verbatim}
adamc@555 85 apt-get install emacs-goodies-el
adamc@555 86 \end{verbatim}
adamc@555 87
adam@1441 88 If you don't want to install the Emacs mode, run \texttt{./configure} with the argument \texttt{--without-emacs}.
adam@1441 89
adam@1523 90 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 91
adamc@555 92 \begin{verbatim}
adam@1523 93 CCARGS=-fno-inline ./configure
adamc@555 94 \end{verbatim}
adamc@555 95
adam@1523 96 Since the author is still getting a handle on the GNU Autotools that provide the build system, you may need to do some further work to get started, especially in environments with significant differences from Linux (where most testing is done). 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 97
adamc@555 98 The Emacs mode can be set to autoload by adding the following to your \texttt{.emacs} file.
adamc@555 99
adamc@555 100 \begin{verbatim}
adamc@555 101 (add-to-list 'load-path "/usr/local/share/emacs/site-lisp/urweb-mode")
adamc@555 102 (load "urweb-mode-startup")
adamc@555 103 \end{verbatim}
adamc@555 104
adamc@555 105 Change the path in the first line if you chose a different Emacs installation path during configuration.
adamc@555 106
adamc@555 107
adamc@556 108 \section{Command-Line Compiler}
adamc@556 109
adam@1604 110 \subsection{\label{cl}Project Files}
adamc@556 111
adamc@556 112 The basic inputs to the \texttt{urweb} compiler are project files, which have the extension \texttt{.urp}. Here is a sample \texttt{.urp} file.
adamc@556 113
adamc@556 114 \begin{verbatim}
adamc@556 115 database dbname=test
adamc@556 116 sql crud1.sql
adamc@556 117
adamc@556 118 crud
adamc@556 119 crud1
adamc@556 120 \end{verbatim}
adamc@556 121
adamc@556 122 The \texttt{database} line gives the database information string to pass to libpq. In this case, the string only says to connect to a local database named \texttt{test}.
adamc@556 123
adamc@556 124 The \texttt{sql} line asks for an SQL source file to be generated, giving the commands to run to create the tables and sequences that this application expects to find. After building this \texttt{.urp} file, the following commands could be used to initialize the database, assuming that the current UNIX user exists as a Postgres user with database creation privileges:
adamc@556 125
adamc@556 126 \begin{verbatim}
adamc@556 127 createdb test
adamc@556 128 psql -f crud1.sql test
adamc@556 129 \end{verbatim}
adamc@556 130
adam@1331 131 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@556 132
adamc@556 133 For each entry \texttt{M} in the module list, the file \texttt{M.urs} is included in the project if it exists, and the file \texttt{M.ur} must exist and is always included.
adamc@556 134
adamc@783 135 Here is the complete list of directive forms. ``FFI'' stands for ``foreign function interface,'' Ur's facility for interaction between Ur programs and C and JavaScript libraries.
adamc@783 136 \begin{itemize}
adam@1465 137 \item \texttt{[allow|deny] [url|mime|requestHeader|responseHeader] PATTERN} registers a rule governing which URLs, MIME types, HTTP request headers, or HTTP response headers 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 138 \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 139 \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@783 140 \item \texttt{clientOnly Module.ident} registers an FFI function or transaction that may only be run in client browsers.
adamc@783 141 \item \texttt{clientToServer Module.ident} adds FFI type \texttt{Module.ident} to the list of types that are OK to marshal from clients to servers. Values like XML trees and SQL queries are hard to marshal without introducing expensive validity checks, so it's easier to ensure that the server never trusts clients to send such values. The file \texttt{include/urweb.h} shows examples of the C support functions that are required of any type that may be marshalled. These include \texttt{attrify}, \texttt{urlify}, and \texttt{unurlify} functions.
adamc@783 142 \item \texttt{database DBSTRING} sets the string to pass to libpq to open a database connection.
adamc@783 143 \item \texttt{debug} saves some intermediate C files, which is mostly useful to help in debugging the compiler itself.
adam@1699 144 \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@783 145 \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@783 146 \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 147 \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@783 148 \item \texttt{jsFunc Module.ident=name} gives the JavaScript name of an FFI value.
adamc@1089 149 \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 150 \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 151 \begin{itemize}
adam@1309 152 \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@1309 153 \item \texttt{database}: maximum size of database files (currently only used by SQLite)
adam@1309 154 \item \texttt{deltas}: maximum number of messages sendable in a single request handler with \texttt{Basis.send}
adam@1309 155 \item \texttt{globals}: maximum number of global variables that FFI libraries may set in a single request context
adam@1309 156 \item \texttt{headers}: maximum size (in bytes) of per-request buffer used to hold HTTP headers for generated pages
adam@1309 157 \item \texttt{heap}: maximum size (in bytes) of per-request heap for dynamically-allocated data
adam@1309 158 \item \texttt{inputs}: maximum number of top-level form fields per request
adam@1309 159 \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 160 \item \texttt{page}: maximum size (in bytes) of per-request buffer used to hold HTML content of generated pages
adam@1309 161 \item \texttt{script}: maximum size (in bytes) of per-request buffer used to hold JavaScript content of generated pages
adam@1309 162 \item \texttt{subinputs}: maximum number of form fields per request, excluding top-level fields
adam@1309 163 \item \texttt{time}: maximum running time of a single page request, in units of approximately 0.1 seconds
adam@1309 164 \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 165 \end{itemize}
adam@1523 166 \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 167 \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 168 \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@1478 169 \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 170 \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@852 171 \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@783 172 \item \texttt{prefix PREFIX} sets the prefix included before every URI within the generated application. The default is \texttt{/}.
adamc@783 173 \item \texttt{profile} generates an executable that may be used with gprof.
adam@1300 174 \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.
adamc@1183 175 \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@783 176 \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@783 177 \item \texttt{serverOnly Module.ident} registers an FFI function or transaction that may only be run on the server.
adamc@1164 178 \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@783 179 \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 180 \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@783 181 \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@783 182 \end{itemize}
adamc@701 183
adamc@701 184
adamc@557 185 \subsection{Building an Application}
adamc@557 186
adamc@557 187 To compile project \texttt{P.urp}, simply run
adamc@557 188 \begin{verbatim}
adamc@557 189 urweb P
adamc@557 190 \end{verbatim}
adamc@1198 191 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@557 192
adamc@557 193 To time how long the different compiler phases run, without generating an executable, run
adamc@557 194 \begin{verbatim}
adamc@557 195 urweb -timing P
adamc@557 196 \end{verbatim}
adamc@557 197
adamc@1086 198 To stop the compilation process after type-checking, run
adamc@1086 199 \begin{verbatim}
adamc@1086 200 urweb -tc P
adamc@1086 201 \end{verbatim}
adam@1530 202 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 203
adam@1745 204 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 205
adam@1723 206 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 207
adamc@1170 208 To output information relevant to CSS stylesheets (and not finish regular compilation), run
adamc@1170 209 \begin{verbatim}
adamc@1170 210 urweb -css P
adamc@1170 211 \end{verbatim}
adamc@1170 212 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 213
adam@1733 214 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 215 \begin{verbatim}
adam@1733 216 urweb daemon start
adam@1733 217 \end{verbatim}
adam@1733 218 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 219 \begin{verbatim}
adam@1733 220 urweb daemon stop
adam@1733 221 \end{verbatim}
adam@1733 222 Communication happens via a UNIX domain socket in file \cd{.urweb\_daemon} in the working directory.
adam@1733 223
adam@1733 224 \medskip
adam@1733 225
adamc@896 226 Some other command-line parameters are accepted:
adamc@896 227 \begin{itemize}
ezyang@1739 228 \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 229
adamc@896 230 \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@896 231
adamc@896 232 \item \texttt{-dbms [postgres|mysql|sqlite]}: Sets the database backend to use.
adamc@896 233 \begin{itemize}
adamc@896 234 \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@896 235
adamc@896 236 A command sequence like this can initialize a Postgres database, using a file \texttt{app.sql} generated by the compiler:
adamc@896 237 \begin{verbatim}
adamc@896 238 createdb app
adamc@896 239 psql -f app.sql app
adamc@896 240 \end{verbatim}
adamc@896 241
adamc@896 242 \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@896 243
adamc@896 244 A command sequence like this can initialize a MySQL database:
adamc@896 245 \begin{verbatim}
adamc@896 246 echo "CREATE DATABASE app" | mysql
adamc@896 247 mysql -D app <app.sql
adamc@896 248 \end{verbatim}
adamc@896 249
adamc@896 250 \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@896 251
adamc@896 252 A command like this can initialize an SQLite database:
adamc@896 253 \begin{verbatim}
adamc@896 254 sqlite3 path/to/database/file <app.sql
adamc@896 255 \end{verbatim}
adamc@896 256 \end{itemize}
adamc@896 257
adam@1693 258 \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 259
adam@1309 260 \item \texttt{-limit class num}: Equivalent to the \texttt{limit} directive from \texttt{.urp} files
adam@1309 261
adamc@896 262 \item \texttt{-output FILENAME}: Set where the application executable is written.
adamc@896 263
adamc@1127 264 \item \texttt{-path NAME VALUE}: Set the value of path variable \texttt{\$NAME} to \texttt{VALUE}, for use in \texttt{.urp} files.
adamc@1127 265
adam@1335 266 \item \texttt{-prefix PREFIX}: Equivalent to the \texttt{prefix} directive from \texttt{.urp} files
adam@1335 267
adamc@896 268 \item \texttt{-protocol [http|cgi|fastcgi]}: Set the protocol that the generated application speaks.
adamc@896 269 \begin{itemize}
adamc@896 270 \item \texttt{http}: This is the default. It is for building standalone web servers that can be accessed by web browsers directly.
adamc@896 271
adamc@896 272 \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@896 273
adamc@896 274 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@896 275 \begin{verbatim}
adamc@896 276 ScriptAlias /Hello /path/to/hello.exe
adamc@896 277 \end{verbatim}
adamc@896 278
adamc@1163 279 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 280 \begin{verbatim}
adamc@1163 281 Options +ExecCGI
adamc@1163 282 AddHandler cgi-script .exe
adamc@1163 283 \end{verbatim}
adamc@1163 284
adamc@1163 285 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 286 \begin{verbatim}
adamc@1163 287 prefix /dir/script.exe/
adamc@1163 288 \end{verbatim}
adamc@1163 289
adamc@1163 290 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 291
adamc@1164 292 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 293
adamc@896 294 \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@896 295
adamc@896 296 To configure a FastCGI program with Apache, one could combine the above \texttt{ScriptAlias} line with a line like this:
adamc@896 297 \begin{verbatim}
adamc@896 298 FastCgiServer /path/to/hello.exe -idle-timeout 99999
adamc@896 299 \end{verbatim}
adamc@896 300 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@896 301
adamc@896 302 Here is some lighttpd configuration for the same application.
adamc@896 303 \begin{verbatim}
adamc@896 304 fastcgi.server = (
adamc@896 305 "/Hello/" =>
adamc@896 306 (( "bin-path" => "/path/to/hello.exe",
adamc@896 307 "socket" => "/tmp/hello",
adamc@896 308 "check-local" => "disable",
adamc@896 309 "docroot" => "/",
adamc@896 310 "max-procs" => "1"
adamc@896 311 ))
adamc@896 312 )
adamc@896 313 \end{verbatim}
adamc@896 314 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@896 315
adamc@896 316 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 317
adam@1509 318 \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@896 319 \end{itemize}
adamc@896 320
adamc@1127 321 \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 322
adamc@1164 323 \item \texttt{-sigfile PATH}: Same as the \texttt{sigfile} directive in \texttt{.urp} files
adamc@1164 324
adamc@896 325 \item \texttt{-sql FILENAME}: Set where a database set-up SQL script is written.
adamc@1095 326
adamc@1095 327 \item \texttt{-static}: Link the runtime system statically. The default is to link against dynamic libraries.
adamc@896 328 \end{itemize}
adamc@896 329
adam@1297 330 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@556 331
adam@1509 332 \subsection{Tutorial Formatting}
adam@1509 333
adam@1509 334 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 335
adam@1509 336 These input files follow normal Ur syntax, with a few exceptions:
adam@1509 337 \begin{itemize}
adam@1509 338 \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 339 \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 340 \item A comment like \cd{(* * HEADING *)} introduces a section heading, with text \cd{HEADING} of your choice.
adam@1509 341 \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 342 \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 343 \end{itemize}
adam@1509 344
adam@1509 345 A word of warning: as for demo generation, tutorial generation calls Emacs to syntax-highlight Ur code.
adam@1509 346
adam@1522 347 \subsection{Run-Time Options}
adam@1522 348
adam@1522 349 Compiled applications consult a few environment variables to modify their behavior:
adam@1522 350
adam@1522 351 \begin{itemize}
adam@1522 352 \item \cd{URWEB\_NUM\_THREADS}: alternative to the \cd{-t} command-line argument (currently used only by FastCGI)
adam@1522 353 \item \cd{URWEB\_STACK\_SIZE}: size of per-thread stacks, in bytes
as@1564 354 \item \cd{URWEB\_PQ\_CON}: when using PostgreSQL, overrides the compiled-in connection string
adam@1522 355 \end{itemize}
adam@1522 356
adam@1509 357
adamc@529 358 \section{Ur Syntax}
adamc@529 359
adamc@784 360 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@524 361
adamc@524 362 \subsection{Lexical Conventions}
adamc@524 363
adamc@524 364 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@524 365
adamc@524 366 \begin{center}
adamc@524 367 \begin{tabular}{rl}
adamc@524 368 \textbf{\LaTeX} & \textbf{ASCII} \\
adamc@524 369 $\to$ & \cd{->} \\
adam@1687 370 $\longrightarrow$ & \cd{-{}->} \\
adamc@524 371 $\times$ & \cd{*} \\
adamc@524 372 $\lambda$ & \cd{fn} \\
adamc@524 373 $\Rightarrow$ & \cd{=>} \\
adamc@652 374 $\Longrightarrow$ & \cd{==>} \\
adamc@529 375 $\neq$ & \cd{<>} \\
adamc@529 376 $\leq$ & \cd{<=} \\
adamc@529 377 $\geq$ & \cd{>=} \\
adamc@524 378 \\
adamc@524 379 $x$ & Normal textual identifier, not beginning with an uppercase letter \\
adamc@525 380 $X$ & Normal textual identifier, beginning with an uppercase letter \\
adamc@524 381 \end{tabular}
adamc@524 382 \end{center}
adamc@524 383
adamc@525 384 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@524 385
adamc@873 386 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@526 387
adamc@527 388 This version of the manual doesn't include operator precedences; see \texttt{src/urweb.grm} for that.
adamc@527 389
adam@1297 390 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 391
adamc@552 392 \subsection{\label{core}Core Syntax}
adamc@524 393
adamc@524 394 \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@524 395 $$\begin{array}{rrcll}
adamc@524 396 \textrm{Kinds} & \kappa &::=& \mt{Type} & \textrm{proper types} \\
adamc@525 397 &&& \mt{Unit} & \textrm{the trivial constructor} \\
adamc@525 398 &&& \mt{Name} & \textrm{field names} \\
adamc@525 399 &&& \kappa \to \kappa & \textrm{type-level functions} \\
adamc@525 400 &&& \{\kappa\} & \textrm{type-level records} \\
adamc@525 401 &&& (\kappa\times^+) & \textrm{type-level tuples} \\
adamc@652 402 &&& X & \textrm{variable} \\
adam@1574 403 &&& X \longrightarrow \kappa & \textrm{kind-polymorphic type-level function} \\
adamc@529 404 &&& \_\_ & \textrm{wildcard} \\
adamc@525 405 &&& (\kappa) & \textrm{explicit precedence} \\
adamc@524 406 \end{array}$$
adamc@524 407
adamc@524 408 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@524 409 $$\begin{array}{rrcll}
adamc@524 410 \textrm{Explicitness} & ? &::=& :: & \textrm{explicit} \\
adamc@558 411 &&& ::: & \textrm{implicit}
adamc@524 412 \end{array}$$
adamc@524 413
adamc@524 414 \emph{Constructors} are the main class of compile-time-only data. They include proper types and are classified by kinds.
adamc@524 415 $$\begin{array}{rrcll}
adamc@524 416 \textrm{Constructors} & c, \tau &::=& (c) :: \kappa & \textrm{kind annotation} \\
adamc@530 417 &&& \hat{x} & \textrm{constructor variable} \\
adamc@524 418 \\
adamc@525 419 &&& \tau \to \tau & \textrm{function type} \\
adamc@525 420 &&& x \; ? \; \kappa \to \tau & \textrm{polymorphic function type} \\
adamc@652 421 &&& X \longrightarrow \tau & \textrm{kind-polymorphic function type} \\
adamc@525 422 &&& \$ c & \textrm{record type} \\
adamc@524 423 \\
adamc@525 424 &&& c \; c & \textrm{type-level function application} \\
adamc@530 425 &&& \lambda x \; :: \; \kappa \Rightarrow c & \textrm{type-level function abstraction} \\
adamc@524 426 \\
adamc@652 427 &&& X \Longrightarrow c & \textrm{type-level kind-polymorphic function abstraction} \\
adamc@655 428 &&& c [\kappa] & \textrm{type-level kind-polymorphic function application} \\
adamc@652 429 \\
adamc@525 430 &&& () & \textrm{type-level unit} \\
adamc@525 431 &&& \#X & \textrm{field name} \\
adamc@524 432 \\
adamc@525 433 &&& [(c = c)^*] & \textrm{known-length type-level record} \\
adamc@525 434 &&& c \rc c & \textrm{type-level record concatenation} \\
adamc@652 435 &&& \mt{map} & \textrm{type-level record map} \\
adamc@524 436 \\
adamc@558 437 &&& (c,^+) & \textrm{type-level tuple} \\
adamc@525 438 &&& c.n & \textrm{type-level tuple projection ($n \in \mathbb N^+$)} \\
adamc@524 439 \\
adamc@652 440 &&& [c \sim c] \Rightarrow \tau & \textrm{guarded type} \\
adamc@524 441 \\
adamc@529 442 &&& \_ :: \kappa & \textrm{wildcard} \\
adamc@525 443 &&& (c) & \textrm{explicit precedence} \\
adamc@530 444 \\
adamc@530 445 \textrm{Qualified uncapitalized variables} & \hat{x} &::=& x & \textrm{not from a module} \\
adamc@530 446 &&& M.x & \textrm{projection from a module} \\
adamc@525 447 \end{array}$$
adamc@525 448
adam@1579 449 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@655 450
adamc@525 451 Modules of the module system are described by \emph{signatures}.
adamc@525 452 $$\begin{array}{rrcll}
adamc@525 453 \textrm{Signatures} & S &::=& \mt{sig} \; s^* \; \mt{end} & \textrm{constant} \\
adamc@525 454 &&& X & \textrm{variable} \\
adamc@525 455 &&& \mt{functor}(X : S) : S & \textrm{functor} \\
adamc@529 456 &&& S \; \mt{where} \; \mt{con} \; x = c & \textrm{concretizing an abstract constructor} \\
adamc@525 457 &&& M.X & \textrm{projection from a module} \\
adamc@525 458 \\
adamc@525 459 \textrm{Signature items} & s &::=& \mt{con} \; x :: \kappa & \textrm{abstract constructor} \\
adamc@525 460 &&& \mt{con} \; x :: \kappa = c & \textrm{concrete constructor} \\
adamc@528 461 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529 462 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@525 463 &&& \mt{val} \; x : \tau & \textrm{value} \\
adamc@525 464 &&& \mt{structure} \; X : S & \textrm{sub-module} \\
adamc@525 465 &&& \mt{signature} \; X = S & \textrm{sub-signature} \\
adamc@525 466 &&& \mt{include} \; S & \textrm{signature inclusion} \\
adamc@525 467 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@654 468 &&& \mt{class} \; x :: \kappa & \textrm{abstract constructor class} \\
adamc@654 469 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@525 470 \\
adamc@525 471 \textrm{Datatype constructors} & dc &::=& X & \textrm{nullary constructor} \\
adamc@525 472 &&& X \; \mt{of} \; \tau & \textrm{unary constructor} \\
adamc@524 473 \end{array}$$
adamc@524 474
adamc@526 475 \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@526 476 $$\begin{array}{rrcll}
adamc@526 477 \textrm{Patterns} & p &::=& \_ & \textrm{wildcard} \\
adamc@526 478 &&& x & \textrm{variable} \\
adamc@526 479 &&& \ell & \textrm{constant} \\
adamc@526 480 &&& \hat{X} & \textrm{nullary constructor} \\
adamc@526 481 &&& \hat{X} \; p & \textrm{unary constructor} \\
adamc@526 482 &&& \{(x = p,)^*\} & \textrm{rigid record pattern} \\
adamc@526 483 &&& \{(x = p,)^+, \ldots\} & \textrm{flexible record pattern} \\
adamc@852 484 &&& p : \tau & \textrm{type annotation} \\
adamc@527 485 &&& (p) & \textrm{explicit precedence} \\
adamc@526 486 \\
adamc@529 487 \textrm{Qualified capitalized variables} & \hat{X} &::=& X & \textrm{not from a module} \\
adamc@526 488 &&& M.X & \textrm{projection from a module} \\
adamc@526 489 \end{array}$$
adamc@526 490
adamc@527 491 \emph{Expressions} are the main run-time entities, corresponding to both ``expressions'' and ``statements'' in mainstream imperative languages.
adamc@527 492 $$\begin{array}{rrcll}
adamc@527 493 \textrm{Expressions} & e &::=& e : \tau & \textrm{type annotation} \\
adamc@529 494 &&& \hat{x} & \textrm{variable} \\
adamc@529 495 &&& \hat{X} & \textrm{datatype constructor} \\
adamc@527 496 &&& \ell & \textrm{constant} \\
adamc@527 497 \\
adamc@527 498 &&& e \; e & \textrm{function application} \\
adamc@527 499 &&& \lambda x : \tau \Rightarrow e & \textrm{function abstraction} \\
adamc@527 500 &&& e [c] & \textrm{polymorphic function application} \\
adamc@852 501 &&& \lambda [x \; ? \; \kappa] \Rightarrow e & \textrm{polymorphic function abstraction} \\
adamc@655 502 &&& e [\kappa] & \textrm{kind-polymorphic function application} \\
adamc@652 503 &&& X \Longrightarrow e & \textrm{kind-polymorphic function abstraction} \\
adamc@527 504 \\
adamc@527 505 &&& \{(c = e,)^*\} & \textrm{known-length record} \\
adamc@527 506 &&& e.c & \textrm{record field projection} \\
adamc@527 507 &&& e \rc e & \textrm{record concatenation} \\
adamc@527 508 &&& e \rcut c & \textrm{removal of a single record field} \\
adamc@527 509 &&& e \rcutM c & \textrm{removal of multiple record fields} \\
adamc@527 510 \\
adamc@527 511 &&& \mt{let} \; ed^* \; \mt{in} \; e \; \mt{end} & \textrm{local definitions} \\
adamc@527 512 \\
adamc@527 513 &&& \mt{case} \; e \; \mt{of} \; (p \Rightarrow e|)^+ & \textrm{pattern matching} \\
adamc@527 514 \\
adamc@654 515 &&& \lambda [c \sim c] \Rightarrow e & \textrm{guarded expression abstraction} \\
adamc@654 516 &&& e \; ! & \textrm{guarded expression application} \\
adamc@527 517 \\
adamc@527 518 &&& \_ & \textrm{wildcard} \\
adamc@527 519 &&& (e) & \textrm{explicit precedence} \\
adamc@527 520 \\
adamc@527 521 \textrm{Local declarations} & ed &::=& \cd{val} \; x : \tau = e & \textrm{non-recursive value} \\
adamc@527 522 &&& \cd{val} \; \cd{rec} \; (x : \tau = e \; \cd{and})^+ & \textrm{mutually-recursive values} \\
adamc@527 523 \end{array}$$
adamc@527 524
adamc@655 525 As with constructors, we include both abstraction and application for kind polymorphism, but applications are only inferred internally.
adamc@655 526
adamc@528 527 \emph{Declarations} primarily bring new symbols into context.
adamc@528 528 $$\begin{array}{rrcll}
adamc@528 529 \textrm{Declarations} & d &::=& \mt{con} \; x :: \kappa = c & \textrm{constructor synonym} \\
adamc@528 530 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529 531 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@528 532 &&& \mt{val} \; x : \tau = e & \textrm{value} \\
adamc@528 533 &&& \mt{val} \; \cd{rec} \; (x : \tau = e \; \mt{and})^+ & \textrm{mutually-recursive values} \\
adamc@528 534 &&& \mt{structure} \; X : S = M & \textrm{module definition} \\
adamc@528 535 &&& \mt{signature} \; X = S & \textrm{signature definition} \\
adamc@528 536 &&& \mt{open} \; M & \textrm{module inclusion} \\
adamc@528 537 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@528 538 &&& \mt{open} \; \mt{constraints} \; M & \textrm{inclusion of just the constraints from a module} \\
adamc@528 539 &&& \mt{table} \; x : c & \textrm{SQL table} \\
adam@1594 540 &&& \mt{view} \; x = e & \textrm{SQL view} \\
adamc@528 541 &&& \mt{sequence} \; x & \textrm{SQL sequence} \\
adamc@535 542 &&& \mt{cookie} \; x : \tau & \textrm{HTTP cookie} \\
adamc@784 543 &&& \mt{style} \; x : \tau & \textrm{CSS class} \\
adamc@654 544 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@1085 545 &&& \mt{task} \; e = e & \textrm{recurring task} \\
adamc@528 546 \\
adamc@529 547 \textrm{Modules} & M &::=& \mt{struct} \; d^* \; \mt{end} & \textrm{constant} \\
adamc@529 548 &&& X & \textrm{variable} \\
adamc@529 549 &&& M.X & \textrm{projection} \\
adamc@529 550 &&& M(M) & \textrm{functor application} \\
adamc@529 551 &&& \mt{functor}(X : S) : S = M & \textrm{functor abstraction} \\
adamc@528 552 \end{array}$$
adamc@528 553
adamc@528 554 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@527 555
adam@1594 556 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@784 557
adamc@529 558 \subsection{Shorthands}
adamc@529 559
adamc@529 560 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@529 561
adamc@529 562 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@529 563
adamc@529 564 A record type may be written $\{(c = c,)^*\}$, which elaborates to $\$[(c = c,)^*]$.
adamc@529 565
adamc@533 566 The notation $[c_1, \ldots, c_n]$ is shorthand for $[c_1 = (), \ldots, c_n = ()]$.
adamc@533 567
adam@1350 568 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@529 569
adam@1687 570 The syntax $()$ expands to $\{\}$ as a pattern or expression.
adam@1687 571
adamc@852 572 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@529 573
adam@1574 574 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 575
adam@1306 576 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 577
adamc@529 578 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@529 579
adamc@529 580 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@529 581
adamc@654 582 A signature item or declaration $\mt{class} \; x = \lambda y \Rightarrow c$ may be abbreviated $\mt{class} \; x \; y = c$.
adamc@529 583
adam@1738 584 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@529 585
adamc@852 586 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@529 587
adamc@852 588 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@852 589
adamc@852 590 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@529 591
adamc@529 592 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@529 593
adamc@852 594 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@852 595
adamc@853 596 A declaration $\mt{table} \; x : \{(c = c,)^*\}$ is elaborated into $\mt{table} \; x : [(c = c,)^*]$.
adamc@529 597
adamc@529 598 The syntax $\mt{where} \; \mt{type}$ is an alternate form of $\mt{where} \; \mt{con}$.
adamc@529 599
adamc@529 600 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@529 601
adamc@529 602 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@529 603
adamc@784 604 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@529 605
adamc@530 606
adamc@530 607 \section{Static Semantics}
adamc@530 608
adamc@530 609 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@530 610
adamc@530 611 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@530 612 \begin{itemize}
adamc@655 613 \item $\Gamma \vdash \kappa$ expresses kind well-formedness.
adamc@530 614 \item $\Gamma \vdash c :: \kappa$ assigns a kind to a constructor in a context.
adamc@530 615 \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@531 616 \item $\Gamma \vdash c \hookrightarrow C$ proves that record constructor $c$ decomposes into set $C$ of field names and record constructors.
adamc@530 617 \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@530 618 \item $\Gamma \vdash e : \tau$ is a standard typing judgment.
adamc@534 619 \item $\Gamma \vdash p \leadsto \Gamma; \tau$ combines typing of patterns with calculation of which new variables they bind.
adamc@537 620 \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@537 621 \item $\Gamma \vdash S \equiv S$ is the signature equivalence judgment.
adamc@536 622 \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@530 623 \item $\Gamma \vdash M : S$ is the module signature checking judgment.
adamc@537 624 \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@539 625 \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@530 626 \end{itemize}
adamc@530 627
adamc@655 628
adamc@655 629 \subsection{Kind Well-Formedness}
adamc@655 630
adamc@655 631 $$\infer{\Gamma \vdash \mt{Type}}{}
adamc@655 632 \quad \infer{\Gamma \vdash \mt{Unit}}{}
adamc@655 633 \quad \infer{\Gamma \vdash \mt{Name}}{}
adamc@655 634 \quad \infer{\Gamma \vdash \kappa_1 \to \kappa_2}{
adamc@655 635 \Gamma \vdash \kappa_1
adamc@655 636 & \Gamma \vdash \kappa_2
adamc@655 637 }
adamc@655 638 \quad \infer{\Gamma \vdash \{\kappa\}}{
adamc@655 639 \Gamma \vdash \kappa
adamc@655 640 }
adamc@655 641 \quad \infer{\Gamma \vdash (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@655 642 \forall i: \Gamma \vdash \kappa_i
adamc@655 643 }$$
adamc@655 644
adamc@655 645 $$\infer{\Gamma \vdash X}{
adamc@655 646 X \in \Gamma
adamc@655 647 }
adamc@655 648 \quad \infer{\Gamma \vdash X \longrightarrow \kappa}{
adamc@655 649 \Gamma, X \vdash \kappa
adamc@655 650 }$$
adamc@655 651
adamc@530 652 \subsection{Kinding}
adamc@530 653
adamc@655 654 We write $[X \mapsto \kappa_1]\kappa_2$ for capture-avoiding substitution of $\kappa_1$ for $X$ in $\kappa_2$.
adamc@655 655
adamc@530 656 $$\infer{\Gamma \vdash (c) :: \kappa :: \kappa}{
adamc@530 657 \Gamma \vdash c :: \kappa
adamc@530 658 }
adamc@530 659 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530 660 x :: \kappa \in \Gamma
adamc@530 661 }
adamc@530 662 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530 663 x :: \kappa = c \in \Gamma
adamc@530 664 }$$
adamc@530 665
adamc@530 666 $$\infer{\Gamma \vdash M.x :: \kappa}{
adamc@537 667 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 668 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = \kappa
adamc@530 669 }
adamc@530 670 \quad \infer{\Gamma \vdash M.x :: \kappa}{
adamc@537 671 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 672 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@530 673 }$$
adamc@530 674
adamc@530 675 $$\infer{\Gamma \vdash \tau_1 \to \tau_2 :: \mt{Type}}{
adamc@530 676 \Gamma \vdash \tau_1 :: \mt{Type}
adamc@530 677 & \Gamma \vdash \tau_2 :: \mt{Type}
adamc@530 678 }
adamc@530 679 \quad \infer{\Gamma \vdash x \; ? \: \kappa \to \tau :: \mt{Type}}{
adamc@530 680 \Gamma, x :: \kappa \vdash \tau :: \mt{Type}
adamc@530 681 }
adamc@655 682 \quad \infer{\Gamma \vdash X \longrightarrow \tau :: \mt{Type}}{
adamc@655 683 \Gamma, X \vdash \tau :: \mt{Type}
adamc@655 684 }
adamc@530 685 \quad \infer{\Gamma \vdash \$c :: \mt{Type}}{
adamc@530 686 \Gamma \vdash c :: \{\mt{Type}\}
adamc@530 687 }$$
adamc@530 688
adamc@530 689 $$\infer{\Gamma \vdash c_1 \; c_2 :: \kappa_2}{
adamc@530 690 \Gamma \vdash c_1 :: \kappa_1 \to \kappa_2
adamc@530 691 & \Gamma \vdash c_2 :: \kappa_1
adamc@530 692 }
adamc@530 693 \quad \infer{\Gamma \vdash \lambda x \; :: \; \kappa_1 \Rightarrow c :: \kappa_1 \to \kappa_2}{
adamc@530 694 \Gamma, x :: \kappa_1 \vdash c :: \kappa_2
adamc@530 695 }$$
adamc@530 696
adamc@655 697 $$\infer{\Gamma \vdash c[\kappa'] :: [X \mapsto \kappa']\kappa}{
adamc@655 698 \Gamma \vdash c :: X \to \kappa
adamc@655 699 & \Gamma \vdash \kappa'
adamc@655 700 }
adamc@655 701 \quad \infer{\Gamma \vdash X \Longrightarrow c :: X \to \kappa}{
adamc@655 702 \Gamma, X \vdash c :: \kappa
adamc@655 703 }$$
adamc@655 704
adamc@530 705 $$\infer{\Gamma \vdash () :: \mt{Unit}}{}
adamc@530 706 \quad \infer{\Gamma \vdash \#X :: \mt{Name}}{}$$
adamc@530 707
adamc@530 708 $$\infer{\Gamma \vdash [\overline{c_i = c'_i}] :: \{\kappa\}}{
adamc@530 709 \forall i: \Gamma \vdash c_i : \mt{Name}
adamc@530 710 & \Gamma \vdash c'_i :: \kappa
adamc@530 711 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@530 712 }
adamc@530 713 \quad \infer{\Gamma \vdash c_1 \rc c_2 :: \{\kappa\}}{
adamc@530 714 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530 715 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@530 716 & \Gamma \vdash c_1 \sim c_2
adamc@530 717 }$$
adamc@530 718
adamc@655 719 $$\infer{\Gamma \vdash \mt{map} :: (\kappa_1 \to \kappa_2) \to \{\kappa_1\} \to \{\kappa_2\}}{}$$
adamc@530 720
adamc@573 721 $$\infer{\Gamma \vdash (\overline c) :: (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@573 722 \forall i: \Gamma \vdash c_i :: \kappa_i
adamc@530 723 }
adamc@573 724 \quad \infer{\Gamma \vdash c.i :: \kappa_i}{
adamc@573 725 \Gamma \vdash c :: (\kappa_1 \times \ldots \times \kappa_n)
adamc@530 726 }$$
adamc@530 727
adamc@655 728 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow \tau :: \mt{Type}}{
adamc@655 729 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530 730 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@655 731 & \Gamma, c_1 \sim c_2 \vdash \tau :: \mt{Type}
adamc@530 732 }$$
adamc@530 733
adamc@531 734 \subsection{Record Disjointness}
adamc@531 735
adamc@531 736 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@558 737 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@558 738 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@558 739 & \forall c'_1 \in C_1, c'_2 \in C_2: \Gamma \vdash c'_1 \sim c'_2
adamc@531 740 }
adamc@531 741 \quad \infer{\Gamma \vdash X \sim X'}{
adamc@531 742 X \neq X'
adamc@531 743 }$$
adamc@531 744
adamc@531 745 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@531 746 c'_1 \sim c'_2 \in \Gamma
adamc@558 747 & \Gamma \vdash c'_1 \hookrightarrow C_1
adamc@558 748 & \Gamma \vdash c'_2 \hookrightarrow C_2
adamc@558 749 & c_1 \in C_1
adamc@558 750 & c_2 \in C_2
adamc@531 751 }$$
adamc@531 752
adamc@531 753 $$\infer{\Gamma \vdash c \hookrightarrow \{c\}}{}
adamc@531 754 \quad \infer{\Gamma \vdash [\overline{c = c'}] \hookrightarrow \{\overline{c}\}}{}
adamc@531 755 \quad \infer{\Gamma \vdash c_1 \rc c_2 \hookrightarrow C_1 \cup C_2}{
adamc@531 756 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@531 757 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@531 758 }
adamc@531 759 \quad \infer{\Gamma \vdash c \hookrightarrow C}{
adamc@531 760 \Gamma \vdash c \equiv c'
adamc@531 761 & \Gamma \vdash c' \hookrightarrow C
adamc@531 762 }
adamc@531 763 \quad \infer{\Gamma \vdash \mt{map} \; f \; c \hookrightarrow C}{
adamc@531 764 \Gamma \vdash c \hookrightarrow C
adamc@531 765 }$$
adamc@531 766
adamc@541 767 \subsection{\label{definitional}Definitional Equality}
adamc@532 768
adamc@655 769 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@532 770
adamc@532 771 $$\infer{\Gamma \vdash c \equiv c}{}
adamc@532 772 \quad \infer{\Gamma \vdash c_1 \equiv c_2}{
adamc@532 773 \Gamma \vdash c_2 \equiv c_1
adamc@532 774 }
adamc@532 775 \quad \infer{\Gamma \vdash c_1 \equiv c_3}{
adamc@532 776 \Gamma \vdash c_1 \equiv c_2
adamc@532 777 & \Gamma \vdash c_2 \equiv c_3
adamc@532 778 }
adamc@532 779 \quad \infer{\Gamma \vdash \mathcal C[c_1] \equiv \mathcal C[c_2]}{
adamc@532 780 \Gamma \vdash c_1 \equiv c_2
adamc@532 781 }$$
adamc@532 782
adamc@532 783 $$\infer{\Gamma \vdash x \equiv c}{
adamc@532 784 x :: \kappa = c \in \Gamma
adamc@532 785 }
adamc@532 786 \quad \infer{\Gamma \vdash M.x \equiv c}{
adamc@537 787 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 788 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@532 789 }
adamc@532 790 \quad \infer{\Gamma \vdash (\overline c).i \equiv c_i}{}$$
adamc@532 791
adamc@532 792 $$\infer{\Gamma \vdash (\lambda x :: \kappa \Rightarrow c) \; c' \equiv [x \mapsto c'] c}{}
adamc@655 793 \quad \infer{\Gamma \vdash (X \Longrightarrow c) [\kappa] \equiv [X \mapsto \kappa] c}{}$$
adamc@655 794
adamc@655 795 $$\infer{\Gamma \vdash c_1 \rc c_2 \equiv c_2 \rc c_1}{}
adamc@532 796 \quad \infer{\Gamma \vdash c_1 \rc (c_2 \rc c_3) \equiv (c_1 \rc c_2) \rc c_3}{}$$
adamc@532 797
adamc@532 798 $$\infer{\Gamma \vdash [] \rc c \equiv c}{}
adamc@532 799 \quad \infer{\Gamma \vdash [\overline{c_1 = c'_1}] \rc [\overline{c_2 = c'_2}] \equiv [\overline{c_1 = c'_1}, \overline{c_2 = c'_2}]}{}$$
adamc@532 800
adamc@655 801 $$\infer{\Gamma \vdash \mt{map} \; f \; [] \equiv []}{}
adamc@655 802 \quad \infer{\Gamma \vdash \mt{map} \; f \; ([c_1 = c_2] \rc c) \equiv [c_1 = f \; c_2] \rc \mt{map} \; f \; c}{}$$
adamc@532 803
adamc@532 804 $$\infer{\Gamma \vdash \mt{map} \; (\lambda x \Rightarrow x) \; c \equiv c}{}
adamc@655 805 \quad \infer{\Gamma \vdash \mt{map} \; f \; (\mt{map} \; f' \; c)
adamc@655 806 \equiv \mt{map} \; (\lambda x \Rightarrow f \; (f' \; x)) \; c}{}$$
adamc@532 807
adamc@532 808 $$\infer{\Gamma \vdash \mt{map} \; f \; (c_1 \rc c_2) \equiv \mt{map} \; f \; c_1 \rc \mt{map} \; f \; c_2}{}$$
adamc@531 809
adamc@534 810 \subsection{Expression Typing}
adamc@533 811
adamc@873 812 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@533 813
adamc@533 814 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@533 815
adamc@533 816 $$\infer{\Gamma \vdash e : \tau : \tau}{
adamc@533 817 \Gamma \vdash e : \tau
adamc@533 818 }
adamc@533 819 \quad \infer{\Gamma \vdash e : \tau}{
adamc@533 820 \Gamma \vdash e : \tau'
adamc@533 821 & \Gamma \vdash \tau' \equiv \tau
adamc@533 822 }
adamc@533 823 \quad \infer{\Gamma \vdash \ell : T(\ell)}{}$$
adamc@533 824
adamc@533 825 $$\infer{\Gamma \vdash x : \mathcal I(\tau)}{
adamc@533 826 x : \tau \in \Gamma
adamc@533 827 }
adamc@533 828 \quad \infer{\Gamma \vdash M.x : \mathcal I(\tau)}{
adamc@537 829 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 830 & \mt{proj}(M, \overline{s}, \mt{val} \; x) = \tau
adamc@533 831 }
adamc@533 832 \quad \infer{\Gamma \vdash X : \mathcal I(\tau)}{
adamc@533 833 X : \tau \in \Gamma
adamc@533 834 }
adamc@533 835 \quad \infer{\Gamma \vdash M.X : \mathcal I(\tau)}{
adamc@537 836 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 837 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \tau
adamc@533 838 }$$
adamc@533 839
adamc@533 840 $$\infer{\Gamma \vdash e_1 \; e_2 : \tau_2}{
adamc@533 841 \Gamma \vdash e_1 : \tau_1 \to \tau_2
adamc@533 842 & \Gamma \vdash e_2 : \tau_1
adamc@533 843 }
adamc@533 844 \quad \infer{\Gamma \vdash \lambda x : \tau_1 \Rightarrow e : \tau_1 \to \tau_2}{
adamc@533 845 \Gamma, x : \tau_1 \vdash e : \tau_2
adamc@533 846 }$$
adamc@533 847
adamc@533 848 $$\infer{\Gamma \vdash e [c] : [x \mapsto c]\tau}{
adamc@533 849 \Gamma \vdash e : x :: \kappa \to \tau
adamc@533 850 & \Gamma \vdash c :: \kappa
adamc@533 851 }
adamc@852 852 \quad \infer{\Gamma \vdash \lambda [x \; ? \; \kappa] \Rightarrow e : x \; ? \; \kappa \to \tau}{
adamc@533 853 \Gamma, x :: \kappa \vdash e : \tau
adamc@533 854 }$$
adamc@533 855
adamc@655 856 $$\infer{\Gamma \vdash e [\kappa] : [X \mapsto \kappa]\tau}{
adamc@655 857 \Gamma \vdash e : X \longrightarrow \tau
adamc@655 858 & \Gamma \vdash \kappa
adamc@655 859 }
adamc@655 860 \quad \infer{\Gamma \vdash X \Longrightarrow e : X \longrightarrow \tau}{
adamc@655 861 \Gamma, X \vdash e : \tau
adamc@655 862 }$$
adamc@655 863
adamc@533 864 $$\infer{\Gamma \vdash \{\overline{c = e}\} : \{\overline{c : \tau}\}}{
adamc@533 865 \forall i: \Gamma \vdash c_i :: \mt{Name}
adamc@533 866 & \Gamma \vdash e_i : \tau_i
adamc@533 867 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@533 868 }
adamc@533 869 \quad \infer{\Gamma \vdash e.c : \tau}{
adamc@533 870 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533 871 }
adamc@533 872 \quad \infer{\Gamma \vdash e_1 \rc e_2 : \$(c_1 \rc c_2)}{
adamc@533 873 \Gamma \vdash e_1 : \$c_1
adamc@533 874 & \Gamma \vdash e_2 : \$c_2
adamc@573 875 & \Gamma \vdash c_1 \sim c_2
adamc@533 876 }$$
adamc@533 877
adamc@533 878 $$\infer{\Gamma \vdash e \rcut c : \$c'}{
adamc@533 879 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533 880 }
adamc@533 881 \quad \infer{\Gamma \vdash e \rcutM c : \$c'}{
adamc@533 882 \Gamma \vdash e : \$(c \rc c')
adamc@533 883 }$$
adamc@533 884
adamc@533 885 $$\infer{\Gamma \vdash \mt{let} \; \overline{ed} \; \mt{in} \; e \; \mt{end} : \tau}{
adamc@533 886 \Gamma \vdash \overline{ed} \leadsto \Gamma'
adamc@533 887 & \Gamma' \vdash e : \tau
adamc@533 888 }
adamc@533 889 \quad \infer{\Gamma \vdash \mt{case} \; e \; \mt{of} \; \overline{p \Rightarrow e} : \tau}{
adamc@533 890 \forall i: \Gamma \vdash p_i \leadsto \Gamma_i, \tau'
adamc@533 891 & \Gamma_i \vdash e_i : \tau
adamc@533 892 }$$
adamc@533 893
adamc@573 894 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow e : \lambda [c_1 \sim c_2] \Rightarrow \tau}{
adamc@533 895 \Gamma \vdash c_1 :: \{\kappa\}
adamc@655 896 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@533 897 & \Gamma, c_1 \sim c_2 \vdash e : \tau
adamc@662 898 }
adamc@662 899 \quad \infer{\Gamma \vdash e \; ! : \tau}{
adamc@662 900 \Gamma \vdash e : [c_1 \sim c_2] \Rightarrow \tau
adamc@662 901 & \Gamma \vdash c_1 \sim c_2
adamc@533 902 }$$
adamc@533 903
adamc@534 904 \subsection{Pattern Typing}
adamc@534 905
adamc@534 906 $$\infer{\Gamma \vdash \_ \leadsto \Gamma; \tau}{}
adamc@534 907 \quad \infer{\Gamma \vdash x \leadsto \Gamma, x : \tau; \tau}{}
adamc@534 908 \quad \infer{\Gamma \vdash \ell \leadsto \Gamma; T(\ell)}{}$$
adamc@534 909
adamc@534 910 $$\infer{\Gamma \vdash X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534 911 X : \overline{x ::: \mt{Type}} \to \tau \in \Gamma
adamc@534 912 & \textrm{$\tau$ not a function type}
adamc@534 913 }
adamc@534 914 \quad \infer{\Gamma \vdash X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534 915 X : \overline{x ::: \mt{Type}} \to \tau'' \to \tau \in \Gamma
adamc@534 916 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534 917 }$$
adamc@534 918
adamc@534 919 $$\infer{\Gamma \vdash M.X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537 920 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 921 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau
adamc@534 922 & \textrm{$\tau$ not a function type}
adamc@534 923 }$$
adamc@534 924
adamc@534 925 $$\infer{\Gamma \vdash M.X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537 926 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 927 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau'' \to \tau
adamc@534 928 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534 929 }$$
adamc@534 930
adamc@534 931 $$\infer{\Gamma \vdash \{\overline{x = p}\} \leadsto \Gamma_n; \{\overline{x = \tau}\}}{
adamc@534 932 \Gamma_0 = \Gamma
adamc@534 933 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534 934 }
adamc@534 935 \quad \infer{\Gamma \vdash \{\overline{x = p}, \ldots\} \leadsto \Gamma_n; \$([\overline{x = \tau}] \rc c)}{
adamc@534 936 \Gamma_0 = \Gamma
adamc@534 937 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534 938 }$$
adamc@534 939
adamc@852 940 $$\infer{\Gamma \vdash p : \tau \leadsto \Gamma'; \tau}{
adamc@852 941 \Gamma \vdash p \leadsto \Gamma'; \tau'
adamc@852 942 & \Gamma \vdash \tau' \equiv \tau
adamc@852 943 }$$
adamc@852 944
adamc@535 945 \subsection{Declaration Typing}
adamc@535 946
adamc@535 947 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@535 948
adamc@655 949 This is the first judgment where we deal with constructor classes, for the $\mt{class}$ declaration form. We will omit their special handling in this formal specification. Section \ref{typeclasses} gives an informal description of how constructor classes influence type inference.
adamc@535 950
adamc@558 951 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@537 952 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@535 953
adamc@535 954 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535 955 \quad \infer{\Gamma \vdash d, \overline{d} \leadsto \Gamma''}{
adamc@535 956 \Gamma \vdash d \leadsto \Gamma'
adamc@535 957 & \Gamma' \vdash \overline{d} \leadsto \Gamma''
adamc@535 958 }$$
adamc@535 959
adamc@535 960 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@535 961 \Gamma \vdash c :: \kappa
adamc@535 962 }
adamc@535 963 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@535 964 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@535 965 }$$
adamc@535 966
adamc@535 967 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537 968 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 969 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@535 970 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@535 971 }$$
adamc@535 972
adamc@535 973 $$\infer{\Gamma \vdash \mt{val} \; x : \tau = e \leadsto \Gamma, x : \tau}{
adamc@535 974 \Gamma \vdash e : \tau
adamc@535 975 }$$
adamc@535 976
adamc@535 977 $$\infer{\Gamma \vdash \mt{val} \; \mt{rec} \; \overline{x : \tau = e} \leadsto \Gamma, \overline{x : \tau}}{
adamc@535 978 \forall i: \Gamma, \overline{x : \tau} \vdash e_i : \tau_i
adamc@535 979 & \textrm{$e_i$ starts with an expression $\lambda$, optionally preceded by constructor and disjointness $\lambda$s}
adamc@535 980 }$$
adamc@535 981
adamc@535 982 $$\infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : S}{
adamc@535 983 \Gamma \vdash M : S
adamc@558 984 & \textrm{ $M$ not a constant or application}
adamc@535 985 }
adamc@558 986 \quad \infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : \mt{selfify}(X, \overline{s})}{
adamc@558 987 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@539 988 }$$
adamc@539 989
adamc@539 990 $$\infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@535 991 \Gamma \vdash S
adamc@535 992 }$$
adamc@535 993
adamc@537 994 $$\infer{\Gamma \vdash \mt{open} \; M \leadsto \Gamma, \mathcal O(M, \overline{s})}{
adamc@537 995 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535 996 }$$
adamc@535 997
adamc@535 998 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma}{
adamc@535 999 \Gamma \vdash c_1 :: \{\kappa\}
adamc@535 1000 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@535 1001 & \Gamma \vdash c_1 \sim c_2
adamc@535 1002 }
adamc@537 1003 \quad \infer{\Gamma \vdash \mt{open} \; \mt{constraints} \; M \leadsto \Gamma, \mathcal O_c(M, \overline{s})}{
adamc@537 1004 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535 1005 }$$
adamc@535 1006
adamc@784 1007 $$\infer{\Gamma \vdash \mt{table} \; x : c \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_table} \; c \; []}{
adamc@535 1008 \Gamma \vdash c :: \{\mt{Type}\}
adamc@535 1009 }
adam@1594 1010 \quad \infer{\Gamma \vdash \mt{view} \; x = e \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_view} \; c}{
adam@1594 1011 \Gamma \vdash e :: \mt{Basis}.\mt{sql\_query} \; [] \; [] \; (\mt{map} \; (\lambda \_ \Rightarrow []) \; c') \; c
adamc@784 1012 }$$
adamc@784 1013
adamc@784 1014 $$\infer{\Gamma \vdash \mt{sequence} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_sequence}}{}$$
adamc@535 1015
adamc@535 1016 $$\infer{\Gamma \vdash \mt{cookie} \; x : \tau \leadsto \Gamma, x : \mt{Basis}.\mt{http\_cookie} \; \tau}{
adamc@535 1017 \Gamma \vdash \tau :: \mt{Type}
adamc@784 1018 }
adamc@784 1019 \quad \infer{\Gamma \vdash \mt{style} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{css\_class}}{}$$
adamc@535 1020
adamc@1085 1021 $$\infer{\Gamma \vdash \mt{task} \; e_1 = e_2 \leadsto \Gamma}{
adam@1348 1022 \Gamma \vdash e_1 :: \mt{Basis}.\mt{task\_kind} \; \tau
adam@1348 1023 & \Gamma \vdash e_2 :: \tau \to \mt{Basis}.\mt{transaction} \; \{\}
adamc@1085 1024 }$$
adamc@1085 1025
adamc@784 1026 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784 1027 \Gamma \vdash c :: \kappa
adamc@535 1028 }$$
adamc@535 1029
adamc@535 1030 $$\infer{\overline{y}; x; \Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535 1031 \quad \infer{\overline{y}; x; \Gamma \vdash X \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to x \; \overline{y}}{
adamc@535 1032 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535 1033 }
adamc@535 1034 \quad \infer{\overline{y}; x; \Gamma \vdash X \; \mt{of} \; \tau \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to \tau \to x \; \overline{y}}{
adamc@535 1035 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535 1036 }$$
adamc@535 1037
adamc@537 1038 \subsection{Signature Item Typing}
adamc@537 1039
adamc@537 1040 We appeal to a signature item analogue of the $\mathcal O$ function from the last subsection.
adamc@537 1041
adamc@537 1042 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@537 1043 \quad \infer{\Gamma \vdash s, \overline{s} \leadsto \Gamma''}{
adamc@537 1044 \Gamma \vdash s \leadsto \Gamma'
adamc@537 1045 & \Gamma' \vdash \overline{s} \leadsto \Gamma''
adamc@537 1046 }$$
adamc@537 1047
adamc@537 1048 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}
adamc@537 1049 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@537 1050 \Gamma \vdash c :: \kappa
adamc@537 1051 }
adamc@537 1052 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@537 1053 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@537 1054 }$$
adamc@537 1055
adamc@537 1056 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537 1057 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1058 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1059 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@537 1060 }$$
adamc@537 1061
adamc@537 1062 $$\infer{\Gamma \vdash \mt{val} \; x : \tau \leadsto \Gamma, x : \tau}{
adamc@537 1063 \Gamma \vdash \tau :: \mt{Type}
adamc@537 1064 }$$
adamc@537 1065
adamc@537 1066 $$\infer{\Gamma \vdash \mt{structure} \; X : S \leadsto \Gamma, X : S}{
adamc@537 1067 \Gamma \vdash S
adamc@537 1068 }
adamc@537 1069 \quad \infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@537 1070 \Gamma \vdash S
adamc@537 1071 }$$
adamc@537 1072
adamc@537 1073 $$\infer{\Gamma \vdash \mt{include} \; S \leadsto \Gamma, \mathcal O(\overline{s})}{
adamc@537 1074 \Gamma \vdash S
adamc@537 1075 & \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1076 }$$
adamc@537 1077
adamc@537 1078 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma, c_1 \sim c_2}{
adamc@537 1079 \Gamma \vdash c_1 :: \{\kappa\}
adamc@537 1080 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@537 1081 }$$
adamc@537 1082
adamc@784 1083 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784 1084 \Gamma \vdash c :: \kappa
adamc@537 1085 }
adamc@784 1086 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}$$
adamc@537 1087
adamc@536 1088 \subsection{Signature Compatibility}
adamc@536 1089
adamc@558 1090 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 1091
adamc@537 1092 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 1093
adamc@536 1094 $$\infer{\Gamma \vdash S \equiv S}{}
adamc@536 1095 \quad \infer{\Gamma \vdash S_1 \equiv S_2}{
adamc@536 1096 \Gamma \vdash S_2 \equiv S_1
adamc@536 1097 }
adamc@536 1098 \quad \infer{\Gamma \vdash X \equiv S}{
adamc@536 1099 X = S \in \Gamma
adamc@536 1100 }
adamc@536 1101 \quad \infer{\Gamma \vdash M.X \equiv S}{
adamc@537 1102 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1103 & \mt{proj}(M, \overline{s}, \mt{signature} \; X) = S
adamc@536 1104 }$$
adamc@536 1105
adamc@536 1106 $$\infer{\Gamma \vdash S \; \mt{where} \; \mt{con} \; x = c \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa = c \; \overline{s_2} \; \mt{end}}{
adamc@536 1107 \Gamma \vdash S \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa \; \overline{s_2} \; \mt{end}
adamc@536 1108 & \Gamma \vdash c :: \kappa
adamc@537 1109 }
adamc@537 1110 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s^1} \; \mt{include} \; S \; \overline{s^2} \; \mt{end} \equiv \mt{sig} \; \overline{s^1} \; \overline{s} \; \overline{s^2} \; \mt{end}}{
adamc@537 1111 \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@536 1112 }$$
adamc@536 1113
adamc@536 1114 $$\infer{\Gamma \vdash S_1 \leq S_2}{
adamc@536 1115 \Gamma \vdash S_1 \equiv S_2
adamc@536 1116 }
adamc@536 1117 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \mt{end}}{}
adamc@537 1118 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; s' \; \overline{s'} \; \mt{end}}{
adamc@537 1119 \Gamma \vdash \overline{s} \leq s'
adamc@537 1120 & \Gamma \vdash s' \leadsto \Gamma'
adamc@537 1121 & \Gamma' \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \overline{s'} \; \mt{end}
adamc@537 1122 }$$
adamc@537 1123
adamc@537 1124 $$\infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537 1125 \Gamma \vdash s \leq s'
adamc@537 1126 }
adamc@537 1127 \quad \infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537 1128 \Gamma \vdash s \leadsto \Gamma'
adamc@537 1129 & \Gamma' \vdash \overline{s} \leq s'
adamc@536 1130 }$$
adamc@536 1131
adamc@536 1132 $$\infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 \leq \mt{functor} (X : S'_1) : S'_2}{
adamc@536 1133 \Gamma \vdash S'_1 \leq S_1
adamc@536 1134 & \Gamma, X : S'_1 \vdash S_2 \leq S'_2
adamc@536 1135 }$$
adamc@536 1136
adamc@537 1137 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@537 1138 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}
adamc@558 1139 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type}}{}$$
adamc@537 1140
adamc@537 1141 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(y)} \to \mt{Type}}{
adamc@537 1142 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1143 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1144 }$$
adamc@537 1145
adamc@784 1146 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@784 1147 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}$$
adamc@537 1148
adamc@537 1149 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \mt{\kappa} = c_2}{
adamc@537 1150 \Gamma \vdash c_1 \equiv c_2
adamc@537 1151 }
adamc@784 1152 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \kappa = c_2}{
adamc@537 1153 \Gamma \vdash c_1 \equiv c_2
adamc@537 1154 }$$
adamc@537 1155
adamc@537 1156 $$\infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537 1157 \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1158 }$$
adamc@537 1159
adamc@537 1160 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537 1161 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1162 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1163 & \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1164 }$$
adamc@537 1165
adamc@537 1166 $$\infer{\Gamma \vdash \cdot \leq \cdot}{}
adamc@537 1167 \quad \infer{\Gamma \vdash X; \overline{dc} \leq X; \overline{dc'}}{
adamc@537 1168 \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1169 }
adamc@537 1170 \quad \infer{\Gamma \vdash X \; \mt{of} \; \tau_1; \overline{dc} \leq X \; \mt{of} \; \tau_2; \overline{dc'}}{
adamc@537 1171 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537 1172 & \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1173 }$$
adamc@537 1174
adamc@537 1175 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x = \mt{datatype} \; M'.z'}{
adamc@537 1176 \Gamma \vdash M.z \equiv M'.z'
adamc@537 1177 }$$
adamc@537 1178
adamc@537 1179 $$\infer{\Gamma \vdash \mt{val} \; x : \tau_1 \leq \mt{val} \; x : \tau_2}{
adamc@537 1180 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537 1181 }
adamc@537 1182 \quad \infer{\Gamma \vdash \mt{structure} \; X : S_1 \leq \mt{structure} \; X : S_2}{
adamc@537 1183 \Gamma \vdash S_1 \leq S_2
adamc@537 1184 }
adamc@537 1185 \quad \infer{\Gamma \vdash \mt{signature} \; X = S_1 \leq \mt{signature} \; X = S_2}{
adamc@537 1186 \Gamma \vdash S_1 \leq S_2
adamc@537 1187 & \Gamma \vdash S_2 \leq S_1
adamc@537 1188 }$$
adamc@537 1189
adamc@537 1190 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leq \mt{constraint} \; c'_1 \sim c'_2}{
adamc@537 1191 \Gamma \vdash c_1 \equiv c'_1
adamc@537 1192 & \Gamma \vdash c_2 \equiv c'_2
adamc@537 1193 }$$
adamc@537 1194
adamc@655 1195 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{class} \; x :: \kappa}{}
adamc@655 1196 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{class} \; x :: \kappa}{}
adamc@655 1197 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{class} \; x :: \kappa = c_2}{
adamc@537 1198 \Gamma \vdash c_1 \equiv c_2
adamc@537 1199 }$$
adamc@537 1200
adamc@538 1201 \subsection{Module Typing}
adamc@538 1202
adamc@538 1203 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 1204
adamc@538 1205 $$\infer{\Gamma \vdash M : S}{
adamc@538 1206 \Gamma \vdash M : S'
adamc@538 1207 & \Gamma \vdash S' \leq S
adamc@538 1208 }
adamc@538 1209 \quad \infer{\Gamma \vdash \mt{struct} \; \overline{d} \; \mt{end} : \mt{sig} \; \mt{sigOf}(\overline{d}) \; \mt{end}}{
adamc@538 1210 \Gamma \vdash \overline{d} \leadsto \Gamma'
adamc@538 1211 }
adamc@538 1212 \quad \infer{\Gamma \vdash X : S}{
adamc@538 1213 X : S \in \Gamma
adamc@538 1214 }$$
adamc@538 1215
adamc@538 1216 $$\infer{\Gamma \vdash M.X : S}{
adamc@538 1217 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@538 1218 & \mt{proj}(M, \overline{s}, \mt{structure} \; X) = S
adamc@538 1219 }$$
adamc@538 1220
adamc@538 1221 $$\infer{\Gamma \vdash M_1(M_2) : [X \mapsto M_2]S_2}{
adamc@538 1222 \Gamma \vdash M_1 : \mt{functor}(X : S_1) : S_2
adamc@538 1223 & \Gamma \vdash M_2 : S_1
adamc@538 1224 }
adamc@538 1225 \quad \infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 = M : \mt{functor} (X : S_1) : S_2}{
adamc@538 1226 \Gamma \vdash S_1
adamc@538 1227 & \Gamma, X : S_1 \vdash S_2
adamc@538 1228 & \Gamma, X : S_1 \vdash M : S_2
adamc@538 1229 }$$
adamc@538 1230
adamc@538 1231 \begin{eqnarray*}
adamc@538 1232 \mt{sigOf}(\cdot) &=& \cdot \\
adamc@538 1233 \mt{sigOf}(s \; \overline{s'}) &=& \mt{sigOf}(s) \; \mt{sigOf}(\overline{s'}) \\
adamc@538 1234 \\
adamc@538 1235 \mt{sigOf}(\mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@538 1236 \mt{sigOf}(\mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \overline{dc} \\
adamc@538 1237 \mt{sigOf}(\mt{datatype} \; x = \mt{datatype} \; M.z) &=& \mt{datatype} \; x = \mt{datatype} \; M.z \\
adamc@538 1238 \mt{sigOf}(\mt{val} \; x : \tau = e) &=& \mt{val} \; x : \tau \\
adamc@538 1239 \mt{sigOf}(\mt{val} \; \mt{rec} \; \overline{x : \tau = e}) &=& \overline{\mt{val} \; x : \tau} \\
adamc@538 1240 \mt{sigOf}(\mt{structure} \; X : S = M) &=& \mt{structure} \; X : S \\
adamc@538 1241 \mt{sigOf}(\mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@538 1242 \mt{sigOf}(\mt{open} \; M) &=& \mt{include} \; S \textrm{ (where $\Gamma \vdash M : S$)} \\
adamc@538 1243 \mt{sigOf}(\mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@538 1244 \mt{sigOf}(\mt{open} \; \mt{constraints} \; M) &=& \cdot \\
adamc@538 1245 \mt{sigOf}(\mt{table} \; x : c) &=& \mt{table} \; x : c \\
adam@1594 1246 \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 1247 \mt{sigOf}(\mt{sequence} \; x) &=& \mt{sequence} \; x \\
adamc@538 1248 \mt{sigOf}(\mt{cookie} \; x : \tau) &=& \mt{cookie} \; x : \tau \\
adamc@784 1249 \mt{sigOf}(\mt{style} \; x) &=& \mt{style} \; x \\
adamc@655 1250 \mt{sigOf}(\mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@538 1251 \end{eqnarray*}
adamc@539 1252 \begin{eqnarray*}
adamc@539 1253 \mt{selfify}(M, \cdot) &=& \cdot \\
adamc@558 1254 \mt{selfify}(M, s \; \overline{s'}) &=& \mt{selfify}(M, s) \; \mt{selfify}(M, \overline{s'}) \\
adamc@539 1255 \\
adamc@539 1256 \mt{selfify}(M, \mt{con} \; x :: \kappa) &=& \mt{con} \; x :: \kappa = M.x \\
adamc@539 1257 \mt{selfify}(M, \mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@539 1258 \mt{selfify}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \mt{datatype} \; M.x \\
adamc@539 1259 \mt{selfify}(M, \mt{datatype} \; x = \mt{datatype} \; M'.z) &=& \mt{datatype} \; x = \mt{datatype} \; M'.z \\
adamc@539 1260 \mt{selfify}(M, \mt{val} \; x : \tau) &=& \mt{val} \; x : \tau \\
adamc@539 1261 \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 1262 \mt{selfify}(M, \mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@539 1263 \mt{selfify}(M, \mt{include} \; S) &=& \mt{include} \; S \\
adamc@539 1264 \mt{selfify}(M, \mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@655 1265 \mt{selfify}(M, \mt{class} \; x :: \kappa) &=& \mt{class} \; x :: \kappa = M.x \\
adamc@655 1266 \mt{selfify}(M, \mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@539 1267 \end{eqnarray*}
adamc@539 1268
adamc@540 1269 \subsection{Module Projection}
adamc@540 1270
adamc@540 1271 \begin{eqnarray*}
adamc@540 1272 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \\
adamc@540 1273 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa, c) \\
adamc@540 1274 \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 1275 \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 1276 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})$)} \\
adamc@655 1277 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \to \mt{Type} \\
adamc@655 1278 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa \to \mt{Type}, c) \\
adamc@540 1279 \\
adamc@540 1280 \mt{proj}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc} \; \overline{s}, \mt{datatype} \; x) &=& (\overline{y}, \overline{dc}) \\
adamc@540 1281 \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 1282 \\
adamc@540 1283 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, \mt{val} \; x) &=& \tau \\
adamc@540 1284 \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 1285 \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 1286 \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 1287 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \in \overline{dc}$)} \\
adamc@540 1288 \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 1289 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \; \mt{of} \; \tau \in \overline{dc}$)} \\
adamc@540 1290 \\
adamc@540 1291 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, \mt{structure} \; X) &=& S \\
adamc@540 1292 \\
adamc@540 1293 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, \mt{signature} \; X) &=& S \\
adamc@540 1294 \\
adamc@540 1295 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1296 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1297 \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 1298 \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 1299 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@540 1300 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1301 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1302 \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 1303 \mt{proj}(M, \mt{constraint} \; c_1 \sim c_2 \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@655 1304 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@655 1305 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1306 \end{eqnarray*}
adamc@540 1307
adamc@541 1308
adamc@541 1309 \section{Type Inference}
adamc@541 1310
adamc@541 1311 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 1312
adamc@541 1313 \subsection{Basic Unification}
adamc@541 1314
adamc@560 1315 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 1316
adamc@656 1317 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 1318
adamc@541 1319 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 1320
adamc@541 1321 \subsection{Unifying Record Types}
adamc@541 1322
adamc@570 1323 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 1324
adamc@656 1325 \subsection{\label{typeclasses}Constructor Classes}
adamc@541 1326
adamc@784 1327 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 1328
adamc@784 1329 Constructor classes are integrated with the module system. A constructor class of kind $\kappa$ is just a constructor of kind $\kappa$. By marking such a constructor $c$ as a constructor class, the programmer instructs the type inference engine to, in each scope, record all values of types $c \; c_1 \; \ldots \; c_n$ as \emph{instances}. Any function argument whose type is of such a form is treated as implicit, to be determined by examining the current instance database.
adamc@541 1330
adamc@656 1331 The ``dictionary encoding'' often used in Haskell implementations is made explicit in Ur. Constructor class instances are just properly-typed values, and they can also be considered as ``proofs'' of membership in the class. In some cases, it is useful to pass these proofs around explicitly. An underscore written where a proof is expected will also be inferred, if possible, from the current instance database.
adamc@541 1332
adamc@656 1333 Just as for constructors, constructors classes may be exported from modules, and they may be exported as concrete or abstract. Concrete constructor classes have their ``real'' definitions exposed, so that client code may add new instances freely. Abstract constructor classes are useful as ``predicates'' that can be used to enforce invariants, as we will see in some definitions of SQL syntax in the Ur/Web standard library.
adamc@541 1334
adamc@541 1335 \subsection{Reverse-Engineering Record Types}
adamc@541 1336
adamc@656 1337 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 1338
adamc@541 1339 \subsection{Implicit Arguments in Functor Applications}
adamc@541 1340
adamc@656 1341 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 1342
adamc@541 1343
adamc@542 1344 \section{The Ur Standard Library}
adamc@542 1345
adamc@542 1346 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 1347
adamc@542 1348 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 1349
adamc@542 1350 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 1351 $$\begin{array}{l}
adamc@542 1352 \mt{type} \; \mt{int} \\
adamc@542 1353 \mt{type} \; \mt{float} \\
adamc@873 1354 \mt{type} \; \mt{char} \\
adamc@542 1355 \mt{type} \; \mt{string} \\
adamc@542 1356 \mt{type} \; \mt{time} \\
adamc@785 1357 \mt{type} \; \mt{blob} \\
adamc@542 1358 \\
adamc@542 1359 \mt{type} \; \mt{unit} = \{\} \\
adamc@542 1360 \\
adamc@542 1361 \mt{datatype} \; \mt{bool} = \mt{False} \mid \mt{True} \\
adamc@542 1362 \\
adamc@785 1363 \mt{datatype} \; \mt{option} \; \mt{t} = \mt{None} \mid \mt{Some} \; \mt{of} \; \mt{t} \\
adamc@785 1364 \\
adamc@785 1365 \mt{datatype} \; \mt{list} \; \mt{t} = \mt{Nil} \mid \mt{Cons} \; \mt{of} \; \mt{t} \times \mt{list} \; \mt{t}
adamc@542 1366 \end{array}$$
adamc@542 1367
adamc@1123 1368 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 1369
adam@1297 1370 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 1371 $$\begin{array}{l}
adam@1297 1372 \mt{con} \; \mt{variant} :: \{\mt{Type}\} \to \mt{Type} \\
adam@1297 1373 \mt{val} \; \mt{make} : \mt{nm} :: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{ts} ::: \{\mt{Type}\} \to [[\mt{nm}] \sim \mt{ts}] \Rightarrow \mt{t} \to \mt{variant} \; ([\mt{nm} = \mt{t}] \rc \mt{ts}) \\
adam@1297 1374 \mt{val} \; \mt{match} : \mt{ts} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{variant} \; \mt{ts} \to \$(\mt{map} \; (\lambda \mt{t'} \Rightarrow \mt{t'} \to \mt{t}) \; \mt{ts}) \to \mt{t}
adam@1297 1375 \end{array}$$
adam@1297 1376
adamc@657 1377 Another important generic Ur element comes at the beginning of \texttt{top.urs}.
adamc@657 1378
adamc@657 1379 $$\begin{array}{l}
adamc@657 1380 \mt{con} \; \mt{folder} :: \mt{K} \longrightarrow \{\mt{K}\} \to \mt{Type} \\
adamc@657 1381 \\
adamc@657 1382 \mt{val} \; \mt{fold} : \mt{K} \longrightarrow \mt{tf} :: (\{\mt{K}\} \to \mt{Type}) \\
adamc@657 1383 \hspace{.1in} \to (\mt{nm} :: \mt{Name} \to \mt{v} :: \mt{K} \to \mt{r} :: \{\mt{K}\} \to [[\mt{nm}] \sim \mt{r}] \Rightarrow \\
adamc@657 1384 \hspace{.2in} \mt{tf} \; \mt{r} \to \mt{tf} \; ([\mt{nm} = \mt{v}] \rc \mt{r})) \\
adamc@657 1385 \hspace{.1in} \to \mt{tf} \; [] \\
adamc@657 1386 \hspace{.1in} \to \mt{r} :: \{\mt{K}\} \to \mt{folder} \; \mt{r} \to \mt{tf} \; \mt{r}
adamc@657 1387 \end{array}$$
adamc@657 1388
adamc@657 1389 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 1390
adamc@664 1391 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 1392
adamc@542 1393
adamc@542 1394 \section{The Ur/Web Standard Library}
adamc@542 1395
adam@1400 1396 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 1397
adamc@658 1398 \subsection{Monads}
adamc@658 1399
adamc@658 1400 The Ur Basis defines the monad constructor class from Haskell.
adamc@658 1401
adamc@658 1402 $$\begin{array}{l}
adamc@658 1403 \mt{class} \; \mt{monad} :: \mt{Type} \to \mt{Type} \\
adamc@658 1404 \mt{val} \; \mt{return} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t} ::: \mt{Type} \\
adamc@658 1405 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658 1406 \hspace{.1in} \to \mt{t} \to \mt{m} \; \mt{t} \\
adamc@658 1407 \mt{val} \; \mt{bind} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t1} ::: \mt{Type} \to \mt{t2} ::: \mt{Type} \\
adamc@658 1408 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658 1409 \hspace{.1in} \to \mt{m} \; \mt{t1} \to (\mt{t1} \to \mt{m} \; \mt{t2}) \\
adam@1544 1410 \hspace{.1in} \to \mt{m} \; \mt{t2} \\
adam@1544 1411 \mt{val} \; \mt{mkMonad} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \\
adam@1544 1412 \hspace{.1in} \to \{\mt{Return} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{m} \; \mt{t}, \\
adam@1544 1413 \hspace{.3in} \mt{Bind} : \mt{t1} ::: \mt{Type} \to \mt{t2} ::: \mt{Type} \to \mt{m} \; \mt{t1} \to (\mt{t1} \to \mt{m} \; \mt{t2}) \to \mt{m} \; \mt{t2}\} \\
adam@1544 1414 \hspace{.1in} \to \mt{monad} \; \mt{m}
adamc@658 1415 \end{array}$$
adamc@658 1416
adam@1687 1417 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 1418
adamc@542 1419 \subsection{Transactions}
adamc@542 1420
adamc@542 1421 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 1422 $$\begin{array}{l}
adamc@542 1423 \mt{con} \; \mt{transaction} :: \mt{Type} \to \mt{Type} \\
adamc@658 1424 \mt{val} \; \mt{transaction\_monad} : \mt{monad} \; \mt{transaction}
adamc@542 1425 \end{array}$$
adamc@542 1426
adamc@1123 1427 For debugging purposes, a transactional function is provided for outputting a string on the server process' \texttt{stderr}.
adamc@1123 1428 $$\begin{array}{l}
adamc@1123 1429 \mt{val} \; \mt{debug} : \mt{string} \to \mt{transaction} \; \mt{unit}
adamc@1123 1430 \end{array}$$
adamc@1123 1431
adamc@542 1432 \subsection{HTTP}
adamc@542 1433
adam@1400 1434 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 1435 $$\begin{array}{l}
adamc@786 1436 \mt{con} \; \mt{http\_cookie} :: \mt{Type} \to \mt{Type} \\
adamc@786 1437 \mt{val} \; \mt{getCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; (\mt{option} \; \mt{t}) \\
adamc@1050 1438 \mt{val} \; \mt{setCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \{\mt{Value} : \mt{t}, \mt{Expires} : \mt{option} \; \mt{time}, \mt{Secure} : \mt{bool}\} \to \mt{transaction} \; \mt{unit} \\
adamc@1050 1439 \mt{val} \; \mt{clearCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; \mt{unit}
adamc@786 1440 \end{array}$$
adamc@786 1441
adamc@786 1442 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 1443 $$\begin{array}{l}
adamc@786 1444 \mt{type} \; \mt{url} \\
adamc@786 1445 \mt{val} \; \mt{bless} : \mt{string} \to \mt{url} \\
adamc@786 1446 \mt{val} \; \mt{checkUrl} : \mt{string} \to \mt{option} \; \mt{url}
adamc@786 1447 \end{array}$$
adamc@786 1448 $\mt{bless}$ raises a runtime error if the string passed to it fails the URL policy.
adamc@786 1449
adam@1400 1450 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 1451 $$\begin{array}{l}
adamc@1085 1452 \mt{val} \; \mt{currentUrl} : \mt{transaction} \; \mt{url} \\
adamc@1085 1453 \mt{val} \; \mt{url} : \mt{transaction} \; \mt{page} \to \mt{url}
adamc@1085 1454 \end{array}$$
adamc@1085 1455
adamc@1085 1456 Page generation may be interrupted at any time with a request to redirect to a particular URL instead.
adamc@1085 1457 $$\begin{array}{l}
adamc@1085 1458 \mt{val} \; \mt{redirect} : \mt{t} ::: \mt{Type} \to \mt{url} \to \mt{transaction} \; \mt{t}
adamc@1085 1459 \end{array}$$
adamc@1085 1460
adam@1400 1461 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 1462 $$\begin{array}{l}
adamc@786 1463 \mt{type} \; \mt{file} \\
adamc@786 1464 \mt{val} \; \mt{fileName} : \mt{file} \to \mt{option} \; \mt{string} \\
adamc@786 1465 \mt{val} \; \mt{fileMimeType} : \mt{file} \to \mt{string} \\
adamc@786 1466 \mt{val} \; \mt{fileData} : \mt{file} \to \mt{blob}
adamc@786 1467 \end{array}$$
adamc@786 1468
adam@1465 1469 It is also possible to get HTTP request headers and set HTTP response headers, using abstract types similar to the one for URLs.
adam@1465 1470
adam@1465 1471 $$\begin{array}{l}
adam@1465 1472 \mt{type} \; \mt{requestHeader} \\
adam@1465 1473 \mt{val} \; \mt{blessRequestHeader} : \mt{string} \to \mt{requestHeader} \\
adam@1465 1474 \mt{val} \; \mt{checkRequestHeader} : \mt{string} \to \mt{option} \; \mt{requestHeader} \\
adam@1465 1475 \mt{val} \; \mt{getHeader} : \mt{requestHeader} \to \mt{transaction} \; (\mt{option} \; \mt{string}) \\
adam@1465 1476 \\
adam@1465 1477 \mt{type} \; \mt{responseHeader} \\
adam@1465 1478 \mt{val} \; \mt{blessResponseHeader} : \mt{string} \to \mt{responseHeader} \\
adam@1465 1479 \mt{val} \; \mt{checkResponseHeader} : \mt{string} \to \mt{option} \; \mt{responseHeader} \\
adam@1465 1480 \mt{val} \; \mt{setHeader} : \mt{responseHeader} \to \mt{string} \to \mt{transaction} \; \mt{unit}
adam@1465 1481 \end{array}$$
adam@1465 1482
adamc@786 1483 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 1484 $$\begin{array}{l}
adamc@786 1485 \mt{type} \; \mt{mimeType} \\
adamc@786 1486 \mt{val} \; \mt{blessMime} : \mt{string} \to \mt{mimeType} \\
adamc@786 1487 \mt{val} \; \mt{checkMime} : \mt{string} \to \mt{option} \; \mt{mimeType} \\
adamc@786 1488 \mt{val} \; \mt{returnBlob} : \mt{t} ::: \mt{Type} \to \mt{blob} \to \mt{mimeType} \to \mt{transaction} \; \mt{t}
adamc@542 1489 \end{array}$$
adamc@542 1490
adamc@543 1491 \subsection{SQL}
adamc@543 1492
adam@1400 1493 Everything about SQL database access is restricted to server-side code.
adam@1400 1494
adamc@543 1495 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 1496 $$\begin{array}{l}
adamc@785 1497 \mt{con} \; \mt{sql\_table} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785 1498 \end{array}$$
adamc@785 1499 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 1500
adamc@785 1501 We also have the simpler type family of SQL views, which have no keys.
adamc@785 1502 $$\begin{array}{l}
adamc@785 1503 \mt{con} \; \mt{sql\_view} :: \{\mt{Type}\} \to \mt{Type}
adamc@543 1504 \end{array}$$
adamc@543 1505
adamc@785 1506 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 1507 $$\begin{array}{l}
adamc@785 1508 \mt{class} \; \mt{fieldsOf} :: \mt{Type} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1509 \mt{val} \; \mt{fieldsOf\_table} : \mt{fs} ::: \{\mt{Type}\} \to \mt{keys} ::: \{\{\mt{Unit}\}\} \to \mt{fieldsOf} \; (\mt{sql\_table} \; \mt{fs} \; \mt{keys}) \; \mt{fs} \\
adamc@785 1510 \mt{val} \; \mt{fieldsOf\_view} : \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; (\mt{sql\_view} \; \mt{fs}) \; \mt{fs}
adamc@785 1511 \end{array}$$
adamc@785 1512
adamc@785 1513 \subsubsection{Table Constraints}
adamc@785 1514
adamc@785 1515 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 1516
adamc@785 1517 $$\begin{array}{l}
adamc@785 1518 \mt{con} \; \mt{primary\_key} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type} \\
adamc@785 1519 \mt{val} \; \mt{no\_primary\_key} : \mt{fs} ::: \{\mt{Type}\} \to \mt{primary\_key} \; \mt{fs} \; [] \\
adamc@785 1520 \mt{val} \; \mt{primary\_key} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{key1} :: \mt{Name} \to \mt{keys} :: \{\mt{Type}\} \\
adamc@785 1521 \hspace{.1in} \to [[\mt{key1}] \sim \mt{keys}] \Rightarrow [[\mt{key1} = \mt{t}] \rc \mt{keys} \sim \mt{rest}] \\
adamc@785 1522 \hspace{.1in} \Rightarrow \$([\mt{key1} = \mt{sql\_injectable\_prim} \; \mt{t}] \rc \mt{map} \; \mt{sql\_injectable\_prim} \; \mt{keys}) \\
adamc@785 1523 \hspace{.1in} \to \mt{primary\_key} \; ([\mt{key1} = \mt{t}] \rc \mt{keys} \rc \mt{rest}) \; [\mt{Pkey} = [\mt{key1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{keys}]
adamc@785 1524 \end{array}$$
adamc@785 1525 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 1526
adamc@785 1527 A type family stands for sets of named constraints of the remaining varieties.
adamc@785 1528 $$\begin{array}{l}
adamc@785 1529 \mt{con} \; \mt{sql\_constraints} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785 1530 \end{array}$$
adamc@785 1531 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 1532
adamc@785 1533 There is a type family of individual, unnamed constraints.
adamc@785 1534 $$\begin{array}{l}
adamc@785 1535 \mt{con} \; \mt{sql\_constraint} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \mt{Type}
adamc@785 1536 \end{array}$$
adamc@785 1537 The first argument is the same as above, and the second argument gives the key columns for just this constraint.
adamc@785 1538
adamc@785 1539 We have operations for assembling constraints into constraint sets.
adamc@785 1540 $$\begin{array}{l}
adamc@785 1541 \mt{val} \; \mt{no\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_constraints} \; \mt{fs} \; [] \\
adamc@785 1542 \mt{val} \; \mt{one\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{unique} ::: \{\mt{Unit}\} \to \mt{name} :: \mt{Name} \\
adamc@785 1543 \hspace{.1in} \to \mt{sql\_constraint} \; \mt{fs} \; \mt{unique} \to \mt{sql\_constraints} \; \mt{fs} \; [\mt{name} = \mt{unique}] \\
adamc@785 1544 \mt{val} \; \mt{join\_constraints} : \mt{fs} ::: \{\mt{Type}\} \to \mt{uniques1} ::: \{\{\mt{Unit}\}\} \to \mt{uniques2} ::: \{\{\mt{Unit}\}\} \to [\mt{uniques1} \sim \mt{uniques2}] \\
adamc@785 1545 \hspace{.1in} \Rightarrow \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques1} \to \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques2} \to \mt{sql\_constraints} \; \mt{fs} \; (\mt{uniques1} \rc \mt{uniques2})
adamc@785 1546 \end{array}$$
adamc@785 1547
adamc@785 1548 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 1549 $$\begin{array}{l}
adamc@785 1550 \mt{val} \; \mt{unique} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{unique1} :: \mt{Name} \to \mt{unique} :: \{\mt{Type}\} \\
adamc@785 1551 \hspace{.1in} \to [[\mt{unique1}] \sim \mt{unique}] \Rightarrow [[\mt{unique1} = \mt{t}] \rc \mt{unique} \sim \mt{rest}] \\
adamc@785 1552 \hspace{.1in} \Rightarrow \mt{sql\_constraint} \; ([\mt{unique1} = \mt{t}] \rc \mt{unique} \rc \mt{rest}) \; ([\mt{unique1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{unique})
adamc@785 1553 \end{array}$$
adamc@785 1554
adamc@785 1555 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 1556 $$\begin{array}{l}
adamc@785 1557 \mt{class} \; \mt{linkable} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@785 1558 \mt{val} \; \mt{linkable\_same} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; \mt{t} \\
adamc@785 1559 \mt{val} \; \mt{linkable\_from\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; (\mt{option} \; \mt{t}) \; \mt{t} \\
adamc@785 1560 \mt{val} \; \mt{linkable\_to\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@785 1561 \end{array}$$
adamc@785 1562
adamc@785 1563 The $\mt{matching}$ type family uses $\mt{linkable}$ to define when two keys match up type-wise.
adamc@785 1564 $$\begin{array}{l}
adamc@785 1565 \mt{con} \; \mt{matching} :: \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1566 \mt{val} \; \mt{mat\_nil} : \mt{matching} \; [] \; [] \\
adamc@785 1567 \mt{val} \; \mt{mat\_cons} : \mt{t1} ::: \mt{Type} \to \mt{rest1} ::: \{\mt{Type}\} \to \mt{t2} ::: \mt{Type} \to \mt{rest2} ::: \{\mt{Type}\} \to \mt{nm1} :: \mt{Name} \to \mt{nm2} :: \mt{Name} \\
adamc@785 1568 \hspace{.1in} \to [[\mt{nm1}] \sim \mt{rest1}] \Rightarrow [[\mt{nm2}] \sim \mt{rest2}] \Rightarrow \mt{linkable} \; \mt{t1} \; \mt{t2} \to \mt{matching} \; \mt{rest1} \; \mt{rest2} \\
adamc@785 1569 \hspace{.1in} \to \mt{matching} \; ([\mt{nm1} = \mt{t1}] \rc \mt{rest1}) \; ([\mt{nm2} = \mt{t2}] \rc \mt{rest2})
adamc@785 1570 \end{array}$$
adamc@785 1571
adamc@785 1572 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 1573 $$\begin{array}{l}
adamc@785 1574 \mt{con} \; \mt{propagation\_mode} :: \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1575 \mt{val} \; \mt{restrict} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1576 \mt{val} \; \mt{cascade} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1577 \mt{val} \; \mt{no\_action} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1578 \mt{val} \; \mt{set\_null} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; (\mt{map} \; \mt{option} \; \mt{fs})
adamc@785 1579 \end{array}$$
adamc@785 1580
adamc@785 1581 Finally, we put these ingredient together to define the \texttt{FOREIGN KEY} constraint function.
adamc@785 1582 $$\begin{array}{l}
adamc@785 1583 \mt{val} \; \mt{foreign\_key} : \mt{mine1} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{mine} ::: \{\mt{Type}\} \to \mt{munused} ::: \{\mt{Type}\} \to \mt{foreign} ::: \{\mt{Type}\} \\
adamc@785 1584 \hspace{.1in} \to \mt{funused} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{uniques} ::: \{\{\mt{Unit}\}\} \\
adamc@785 1585 \hspace{.1in} \to [[\mt{mine1}] \sim \mt{mine}] \Rightarrow [[\mt{mine1} = \mt{t}] \rc \mt{mine} \sim \mt{munused}] \Rightarrow [\mt{foreign} \sim \mt{funused}] \Rightarrow [[\mt{nm}] \sim \mt{uniques}] \\
adamc@785 1586 \hspace{.1in} \Rightarrow \mt{matching} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}) \; \mt{foreign} \\
adamc@785 1587 \hspace{.1in} \to \mt{sql\_table} \; (\mt{foreign} \rc \mt{funused}) \; ([\mt{nm} = \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{foreign}] \rc \mt{uniques}) \\
adamc@785 1588 \hspace{.1in} \to \{\mt{OnDelete} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}), \\
adamc@785 1589 \hspace{.2in} \mt{OnUpdate} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine})\} \\
adamc@785 1590 \hspace{.1in} \to \mt{sql\_constraint} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine} \rc \mt{munused}) \; []
adamc@785 1591 \end{array}$$
adamc@785 1592
adamc@785 1593 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 1594 $$\begin{array}{l}
adamc@785 1595 \mt{val} \; \mt{check} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; [] \; [] \; \mt{fs} \; \mt{bool} \to \mt{sql\_constraint} \; \mt{fs} \; []
adamc@785 1596 \end{array}$$
adamc@785 1597
adamc@785 1598 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 1599
adamc@784 1600
adamc@543 1601 \subsubsection{Queries}
adamc@543 1602
adam@1400 1603 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 1604 $$\begin{array}{l}
adam@1400 1605 \mt{con} \; \mt{sql\_query} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@1193 1606 \mt{val} \; \mt{sql\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400 1607 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1608 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543 1609 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1610 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1193 1611 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adam@1400 1612 \hspace{.1in} \Rightarrow \{\mt{Rows} : \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}, \\
adamc@1193 1613 \hspace{.2in} \mt{OrderBy} : \mt{sql\_order\_by} \; (\mt{free} \rc \mt{tables}) \; \mt{selectedExps}, \\
adamc@543 1614 \hspace{.2in} \mt{Limit} : \mt{sql\_limit}, \\
adamc@543 1615 \hspace{.2in} \mt{Offset} : \mt{sql\_offset}\} \\
adam@1400 1616 \hspace{.1in} \to \mt{sql\_query} \; \mt{free} \; \mt{afree} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1617 \end{array}$$
adamc@543 1618
adamc@545 1619 Queries are used by folding over their results inside transactions.
adamc@545 1620 $$\begin{array}{l}
adam@1400 1621 \mt{val} \; \mt{query} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to [\mt{tables} \sim \mt{exps}] \Rightarrow \mt{state} ::: \mt{Type} \to \mt{sql\_query} \; [] \; [] \; \mt{tables} \; \mt{exps} \\
adamc@658 1622 \hspace{.1in} \to (\$(\mt{exps} \rc \mt{map} \; (\lambda \mt{fields} :: \{\mt{Type}\} \Rightarrow \$\mt{fields}) \; \mt{tables}) \\
adamc@545 1623 \hspace{.2in} \to \mt{state} \to \mt{transaction} \; \mt{state}) \\
adamc@545 1624 \hspace{.1in} \to \mt{state} \to \mt{transaction} \; \mt{state}
adamc@545 1625 \end{array}$$
adamc@545 1626
adam@1400 1627 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 1628 $$\begin{array}{l}
adam@1400 1629 \mt{con} \; \mt{sql\_query1} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@543 1630 \\
adamc@543 1631 \mt{type} \; \mt{sql\_relop} \\
adamc@543 1632 \mt{val} \; \mt{sql\_union} : \mt{sql\_relop} \\
adamc@543 1633 \mt{val} \; \mt{sql\_intersect} : \mt{sql\_relop} \\
adamc@543 1634 \mt{val} \; \mt{sql\_except} : \mt{sql\_relop} \\
adam@1400 1635 \mt{val} \; \mt{sql\_relop} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400 1636 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adam@1400 1637 \hspace{.1in} \to \mt{tables1} ::: \{\{\mt{Type}\}\} \\
adamc@543 1638 \hspace{.1in} \to \mt{tables2} ::: \{\{\mt{Type}\}\} \\
adamc@543 1639 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1640 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@543 1641 \hspace{.1in} \to \mt{sql\_relop} \\
adam@1458 1642 \hspace{.1in} \to \mt{bool} \; (* \; \mt{ALL} \; *) \\
adam@1400 1643 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables1} \; \mt{selectedFields} \; \mt{selectedExps} \\
adam@1400 1644 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables2} \; \mt{selectedFields} \; \mt{selectedExps} \\
adam@1400 1645 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{selectedFields} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1646 \end{array}$$
adamc@543 1647
adamc@543 1648 $$\begin{array}{l}
adamc@1193 1649 \mt{val} \; \mt{sql\_query1} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400 1650 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1651 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543 1652 \hspace{.1in} \to \mt{grouped} ::: \{\{\mt{Type}\}\} \\
adamc@543 1653 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1654 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1085 1655 \hspace{.1in} \to \mt{empties} :: \{\mt{Unit}\} \\
adamc@1193 1656 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adamc@1193 1657 \hspace{.1in} \Rightarrow [\mt{free} \sim \mt{grouped}] \\
adam@1400 1658 \hspace{.1in} \Rightarrow [\mt{afree} \sim \mt{tables}] \\
adamc@1193 1659 \hspace{.1in} \Rightarrow [\mt{empties} \sim \mt{selectedFields}] \\
adamc@1085 1660 \hspace{.1in} \Rightarrow \{\mt{Distinct} : \mt{bool}, \\
adamc@1193 1661 \hspace{.2in} \mt{From} : \mt{sql\_from\_items} \; \mt{free} \; \mt{tables}, \\
adam@1400 1662 \hspace{.2in} \mt{Where} : \mt{sql\_exp} \; (\mt{free} \rc \mt{tables}) \; \mt{afree} \; [] \; \mt{bool}, \\
adamc@543 1663 \hspace{.2in} \mt{GroupBy} : \mt{sql\_subset} \; \mt{tables} \; \mt{grouped}, \\
adam@1400 1664 \hspace{.2in} \mt{Having} : \mt{sql\_exp} \; (\mt{free} \rc \mt{grouped}) \; (\mt{afree} \rc \mt{tables}) \; [] \; \mt{bool}, \\
adamc@1085 1665 \hspace{.2in} \mt{SelectFields} : \mt{sql\_subset} \; \mt{grouped} \; (\mt{map} \; (\lambda \_ \Rightarrow []) \; \mt{empties} \rc \mt{selectedFields}), \\
adam@1400 1666 \hspace{.2in} \mt {SelectExps} : \$(\mt{map} \; (\mt{sql\_exp} \; (\mt{free} \rc \mt{grouped}) \; (\mt{afree} \rc \mt{tables}) \; []) \; \mt{selectedExps}) \} \\
adam@1400 1667 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1668 \end{array}$$
adamc@543 1669
adamc@543 1670 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 1671 $$\begin{array}{l}
adamc@543 1672 \mt{con} \; \mt{sql\_subset} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@543 1673 \mt{val} \; \mt{sql\_subset} : \mt{keep\_drop} :: \{(\{\mt{Type}\} \times \{\mt{Type}\})\} \\
adamc@543 1674 \hspace{.1in} \to \mt{sql\_subset} \\
adamc@658 1675 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1 \rc \mt{fields}.2)\; \mt{keep\_drop}) \\
adamc@658 1676 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1) \; \mt{keep\_drop}) \\
adamc@543 1677 \mt{val} \; \mt{sql\_subset\_all} : \mt{tables} :: \{\{\mt{Type}\}\} \to \mt{sql\_subset} \; \mt{tables} \; \mt{tables}
adamc@543 1678 \end{array}$$
adamc@543 1679
adamc@560 1680 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 1681 $$\begin{array}{l}
adamc@543 1682 \mt{con} \; \mt{sql\_exp} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}
adamc@543 1683 \end{array}$$
adamc@543 1684
adamc@543 1685 Any field in scope may be converted to an expression.
adamc@543 1686 $$\begin{array}{l}
adamc@543 1687 \mt{val} \; \mt{sql\_field} : \mt{otherTabs} ::: \{\{\mt{Type}\}\} \to \mt{otherFields} ::: \{\mt{Type}\} \\
adamc@543 1688 \hspace{.1in} \to \mt{fieldType} ::: \mt{Type} \to \mt{agg} ::: \{\{\mt{Type}\}\} \\
adamc@543 1689 \hspace{.1in} \to \mt{exps} ::: \{\mt{Type}\} \\
adamc@543 1690 \hspace{.1in} \to \mt{tab} :: \mt{Name} \to \mt{field} :: \mt{Name} \\
adamc@543 1691 \hspace{.1in} \to \mt{sql\_exp} \; ([\mt{tab} = [\mt{field} = \mt{fieldType}] \rc \mt{otherFields}] \rc \mt{otherTabs}) \; \mt{agg} \; \mt{exps} \; \mt{fieldType}
adamc@543 1692 \end{array}$$
adamc@543 1693
adamc@544 1694 There is an analogous function for referencing named expressions.
adamc@544 1695 $$\begin{array}{l}
adamc@544 1696 \mt{val} \; \mt{sql\_exp} : \mt{tabs} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{t} ::: \mt{Type} \to \mt{rest} ::: \{\mt{Type}\} \to \mt{nm} :: \mt{Name} \\
adamc@544 1697 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tabs} \; \mt{agg} \; ([\mt{nm} = \mt{t}] \rc \mt{rest}) \; \mt{t}
adamc@544 1698 \end{array}$$
adamc@544 1699
adamc@544 1700 Ur values of appropriate types may be injected into SQL expressions.
adamc@544 1701 $$\begin{array}{l}
adamc@786 1702 \mt{class} \; \mt{sql\_injectable\_prim} \\
adamc@786 1703 \mt{val} \; \mt{sql\_bool} : \mt{sql\_injectable\_prim} \; \mt{bool} \\
adamc@786 1704 \mt{val} \; \mt{sql\_int} : \mt{sql\_injectable\_prim} \; \mt{int} \\
adamc@786 1705 \mt{val} \; \mt{sql\_float} : \mt{sql\_injectable\_prim} \; \mt{float} \\
adamc@786 1706 \mt{val} \; \mt{sql\_string} : \mt{sql\_injectable\_prim} \; \mt{string} \\
adamc@786 1707 \mt{val} \; \mt{sql\_time} : \mt{sql\_injectable\_prim} \; \mt{time} \\
adamc@786 1708 \mt{val} \; \mt{sql\_blob} : \mt{sql\_injectable\_prim} \; \mt{blob} \\
adamc@786 1709 \mt{val} \; \mt{sql\_channel} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{channel} \; \mt{t}) \\
adamc@786 1710 \mt{val} \; \mt{sql\_client} : \mt{sql\_injectable\_prim} \; \mt{client} \\
adamc@786 1711 \\
adamc@544 1712 \mt{class} \; \mt{sql\_injectable} \\
adamc@786 1713 \mt{val} \; \mt{sql\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@786 1714 \mt{val} \; \mt{sql\_option\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; (\mt{option} \; \mt{t}) \\
adamc@786 1715 \\
adamc@544 1716 \mt{val} \; \mt{sql\_inject} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@544 1717 \hspace{.1in} \to \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adamc@544 1718 \end{array}$$
adamc@544 1719
adamc@1123 1720 Additionally, most function-free types may be injected safely, via the $\mt{serialized}$ type family.
adamc@1123 1721 $$\begin{array}{l}
adamc@1123 1722 \mt{con} \; \mt{serialized} :: \mt{Type} \to \mt{Type} \\
adamc@1123 1723 \mt{val} \; \mt{serialize} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{serialized} \; \mt{t} \\
adamc@1123 1724 \mt{val} \; \mt{deserialize} : \mt{t} ::: \mt{Type} \to \mt{serialized} \; \mt{t} \to \mt{t} \\
adamc@1123 1725 \mt{val} \; \mt{sql\_serialized} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{serialized} \; \mt{t})
adamc@1123 1726 \end{array}$$
adamc@1123 1727
adamc@544 1728 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 1729 $$\begin{array}{l}
adamc@544 1730 \mt{val} \; \mt{sql\_is\_null} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544 1731 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; (\mt{option} \; \mt{t}) \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{bool}
adamc@544 1732 \end{array}$$
adamc@544 1733
adam@1602 1734 As another way of dealing with null values, there is also a restricted form of the standard \cd{COALESCE} function.
adam@1602 1735 $$\begin{array}{l}
adam@1602 1736 \mt{val} \; \mt{sql\_coalesce} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1602 1737 \hspace{.1in} \to \mt{t} ::: \mt{Type} \\
adam@1602 1738 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; (\mt{option} \; \mt{t}) \\
adam@1602 1739 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1602 1740 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adam@1602 1741 \end{array}$$
adam@1602 1742
adamc@559 1743 We have generic nullary, unary, and binary operators.
adamc@544 1744 $$\begin{array}{l}
adamc@544 1745 \mt{con} \; \mt{sql\_nfunc} :: \mt{Type} \to \mt{Type} \\
adamc@544 1746 \mt{val} \; \mt{sql\_current\_timestamp} : \mt{sql\_nfunc} \; \mt{time} \\
adamc@544 1747 \mt{val} \; \mt{sql\_nfunc} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544 1748 \hspace{.1in} \to \mt{sql\_nfunc} \; \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\\end{array}$$
adamc@544 1749
adamc@544 1750 $$\begin{array}{l}
adamc@544 1751 \mt{con} \; \mt{sql\_unary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544 1752 \mt{val} \; \mt{sql\_not} : \mt{sql\_unary} \; \mt{bool} \; \mt{bool} \\
adamc@544 1753 \mt{val} \; \mt{sql\_unary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adamc@544 1754 \hspace{.1in} \to \mt{sql\_unary} \; \mt{arg} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res} \\
adamc@544 1755 \end{array}$$
adamc@544 1756
adamc@544 1757 $$\begin{array}{l}
adamc@544 1758 \mt{con} \; \mt{sql\_binary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544 1759 \mt{val} \; \mt{sql\_and} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544 1760 \mt{val} \; \mt{sql\_or} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544 1761 \mt{val} \; \mt{sql\_binary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg_1} ::: \mt{Type} \to \mt{arg_2} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adamc@544 1762 \hspace{.1in} \to \mt{sql\_binary} \; \mt{arg_1} \; \mt{arg_2} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_1} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_2} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res}
adamc@544 1763 \end{array}$$
adamc@544 1764
adamc@544 1765 $$\begin{array}{l}
adamc@559 1766 \mt{class} \; \mt{sql\_arith} \\
adamc@559 1767 \mt{val} \; \mt{sql\_int\_arith} : \mt{sql\_arith} \; \mt{int} \\
adamc@559 1768 \mt{val} \; \mt{sql\_float\_arith} : \mt{sql\_arith} \; \mt{float} \\
adamc@559 1769 \mt{val} \; \mt{sql\_neg} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_unary} \; \mt{t} \; \mt{t} \\
adamc@559 1770 \mt{val} \; \mt{sql\_plus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1771 \mt{val} \; \mt{sql\_minus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1772 \mt{val} \; \mt{sql\_times} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1773 \mt{val} \; \mt{sql\_div} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1774 \mt{val} \; \mt{sql\_mod} : \mt{sql\_binary} \; \mt{int} \; \mt{int} \; \mt{int}
adamc@559 1775 \end{array}$$
adamc@544 1776
adamc@656 1777 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 1778 $$\begin{array}{l}
adamc@544 1779 \mt{val} \; \mt{sql\_count} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int}
adamc@544 1780 \end{array}$$
adamc@544 1781
adamc@544 1782 $$\begin{array}{l}
adamc@1188 1783 \mt{con} \; \mt{sql\_aggregate} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@1188 1784 \mt{val} \; \mt{sql\_aggregate} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{dom} ::: \mt{Type} \to \mt{ran} ::: \mt{Type} \\
adamc@1188 1785 \hspace{.1in} \to \mt{sql\_aggregate} \; \mt{dom} \; \mt{ran} \to \mt{sql\_exp} \; \mt{agg} \; \mt{agg} \; \mt{exps} \; \mt{dom} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{ran}
adamc@1188 1786 \end{array}$$
adamc@1188 1787
adamc@1188 1788 $$\begin{array}{l}
adamc@1188 1789 \mt{val} \; \mt{sql\_count\_col} : \mt{t} ::: \mt{Type} \to \mt{sql\_aggregate} \; (\mt{option} \; \mt{t}) \; \mt{int}
adamc@544 1790 \end{array}$$
adam@1400 1791
adam@1400 1792 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 1793
adamc@544 1794 $$\begin{array}{l}
adamc@544 1795 \mt{class} \; \mt{sql\_summable} \\
adamc@544 1796 \mt{val} \; \mt{sql\_summable\_int} : \mt{sql\_summable} \; \mt{int} \\
adamc@544 1797 \mt{val} \; \mt{sql\_summable\_float} : \mt{sql\_summable} \; \mt{float} \\
adam@1400 1798 \mt{val} \; \mt{sql\_avg} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt} \\
adam@1400 1799 \mt{val} \; \mt{sql\_sum} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt}
adamc@544 1800 \end{array}$$
adamc@544 1801
adamc@544 1802 $$\begin{array}{l}
adamc@544 1803 \mt{class} \; \mt{sql\_maxable} \\
adamc@544 1804 \mt{val} \; \mt{sql\_maxable\_int} : \mt{sql\_maxable} \; \mt{int} \\
adamc@544 1805 \mt{val} \; \mt{sql\_maxable\_float} : \mt{sql\_maxable} \; \mt{float} \\
adamc@544 1806 \mt{val} \; \mt{sql\_maxable\_string} : \mt{sql\_maxable} \; \mt{string} \\
adamc@544 1807 \mt{val} \; \mt{sql\_maxable\_time} : \mt{sql\_maxable} \; \mt{time} \\
adam@1400 1808 \mt{val} \; \mt{sql\_max} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt} \\
adam@1400 1809 \mt{val} \; \mt{sql\_min} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt}
adamc@544 1810 \end{array}$$
adamc@544 1811
adamc@1193 1812 Any SQL query that returns single columns may be turned into a subquery expression.
adamc@1193 1813
adamc@786 1814 $$\begin{array}{l}
adam@1421 1815 \mt{val} \; \mt{sql\_subquery} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \\
adam@1421 1816 \hspace{.1in} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_query} \; \mt{tables} \; \mt{agg} \; [\mt{nm} = \mt{t}] \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{nt}
adamc@1193 1817 \end{array}$$
adamc@1193 1818
adam@1573 1819 There is also an \cd{IF..THEN..ELSE..} construct that is compiled into standard SQL \cd{CASE} expressions.
adam@1573 1820 $$\begin{array}{l}
adam@1573 1821 \mt{val} \; \mt{sql\_if\_then\_else} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1573 1822 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{bool} \\
adam@1573 1823 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1573 1824 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1573 1825 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adam@1573 1826 \end{array}$$
adam@1573 1827
adamc@1193 1828 \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 1829 $$\begin{array}{l}
adamc@1193 1830 \mt{con} \; \mt{sql\_from\_items} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@1193 1831 \mt{val} \; \mt{sql\_from\_table} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1832 \hspace{.1in} \to \mt{t} ::: \mt{Type} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; \mt{t} \; \mt{fs} \to \mt{name} :: \mt{Name} \to \mt{t} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193 1833 \mt{val} \; \mt{sql\_from\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{name} :: \mt{Name} \to \mt{sql\_query} \; \mt{free} \; [] \; \mt{fs} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193 1834 \mt{val} \; \mt{sql\_from\_comma} : \mt{free} ::: \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \to [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193 1835 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adamc@1193 1836 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2}) \\
adamc@1193 1837 \mt{val} \; \mt{sql\_inner\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1838 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193 1839 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adamc@1193 1840 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193 1841 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2})
adamc@786 1842 \end{array}$$
adamc@786 1843
adamc@786 1844 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 1845 $$\begin{array}{l}
adamc@786 1846 \mt{class} \; \mt{nullify} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@786 1847 \mt{val} \; \mt{nullify\_option} : \mt{t} ::: \mt{Type} \to \mt{nullify} \; (\mt{option} \; \mt{t}) \; (\mt{option} \; \mt{t}) \\
adamc@786 1848 \mt{val} \; \mt{nullify\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{nullify} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@786 1849 \end{array}$$
adamc@786 1850
adamc@786 1851 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 1852
adamc@786 1853 $$\begin{array}{l}
adamc@1193 1854 \mt{val} \; \mt{sql\_left\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{(\mt{Type} \times \mt{Type})\}\} \\
adamc@1193 1855 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@786 1856 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\lambda \mt{r} \Rightarrow \$(\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{nullify} \; \mt{p}.1 \; \mt{p}.2) \; \mt{r})) \; \mt{tabs2}) \\
adamc@1193 1857 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \\
adamc@1193 1858 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193 1859 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.2)) \; \mt{tabs2})
adamc@786 1860 \end{array}$$
adamc@786 1861
adamc@544 1862 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 1863 $$\begin{array}{l}
adamc@544 1864 \mt{type} \; \mt{sql\_direction} \\
adamc@544 1865 \mt{val} \; \mt{sql\_asc} : \mt{sql\_direction} \\
adamc@544 1866 \mt{val} \; \mt{sql\_desc} : \mt{sql\_direction} \\
adamc@544 1867 \\
adamc@544 1868 \mt{con} \; \mt{sql\_order\_by} :: \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@544 1869 \mt{val} \; \mt{sql\_order\_by\_Nil} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} :: \{\mt{Type}\} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544 1870 \mt{val} \; \mt{sql\_order\_by\_Cons} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544 1871 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; [] \; \mt{exps} \; \mt{t} \to \mt{sql\_direction} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adam@1684 1872 \mt{val} \; \mt{sql\_order\_by\_random} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544 1873 \\
adamc@544 1874 \mt{type} \; \mt{sql\_limit} \\
adamc@544 1875 \mt{val} \; \mt{sql\_no\_limit} : \mt{sql\_limit} \\
adamc@544 1876 \mt{val} \; \mt{sql\_limit} : \mt{int} \to \mt{sql\_limit} \\
adamc@544 1877 \\
adamc@544 1878 \mt{type} \; \mt{sql\_offset} \\
adamc@544 1879 \mt{val} \; \mt{sql\_no\_offset} : \mt{sql\_offset} \\
adamc@544 1880 \mt{val} \; \mt{sql\_offset} : \mt{int} \to \mt{sql\_offset}
adamc@544 1881 \end{array}$$
adamc@544 1882
adamc@545 1883
adamc@545 1884 \subsubsection{DML}
adamc@545 1885
adamc@545 1886 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 1887
adamc@545 1888 $$\begin{array}{l}
adamc@545 1889 \mt{type} \; \mt{dml} \\
adamc@545 1890 \mt{val} \; \mt{dml} : \mt{dml} \to \mt{transaction} \; \mt{unit}
adamc@545 1891 \end{array}$$
adamc@545 1892
adam@1297 1893 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 1894
adam@1297 1895 $$\begin{array}{l}
adam@1297 1896 \mt{val} \; \mt{tryDml} : \mt{dml} \to \mt{transaction} \; (\mt{option} \; \mt{string})
adam@1297 1897 \end{array}$$
adam@1297 1898
adamc@545 1899 Properly-typed records may be used to form $\mt{INSERT}$ commands.
adamc@545 1900 $$\begin{array}{l}
adamc@545 1901 \mt{val} \; \mt{insert} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \\
adamc@658 1902 \hspace{.1in} \to \$(\mt{map} \; (\mt{sql\_exp} \; [] \; [] \; []) \; \mt{fields}) \to \mt{dml}
adamc@545 1903 \end{array}$$
adamc@545 1904
adam@1578 1905 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 1906 $$\begin{array}{l}
adam@1380 1907 \mt{val} \; \mt{update} : \mt{unchanged} ::: \{\mt{Type}\} \to \mt{changed} :: \{\mt{Type}\} \to [\mt{changed} \sim \mt{unchanged}] \\
adamc@658 1908 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; []) \; \mt{changed}) \\
adamc@545 1909 \hspace{.1in} \to \mt{sql\_table} \; (\mt{changed} \rc \mt{unchanged}) \to \mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545 1910 \end{array}$$
adamc@545 1911
adam@1578 1912 A $\mt{DELETE}$ command is formed from a table and a $\mt{WHERE}$ clause. The above use of $\mt{T}$ is repeated.
adamc@545 1913 $$\begin{array}{l}
adamc@545 1914 \mt{val} \; \mt{delete} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \to \mt{sql\_exp} \; [\mt{T} = \mt{fields}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545 1915 \end{array}$$
adamc@545 1916
adamc@546 1917 \subsubsection{Sequences}
adamc@546 1918
adamc@546 1919 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 1920
adamc@546 1921 $$\begin{array}{l}
adamc@546 1922 \mt{type} \; \mt{sql\_sequence} \\
adamc@1085 1923 \mt{val} \; \mt{nextval} : \mt{sql\_sequence} \to \mt{transaction} \; \mt{int} \\
adamc@1085 1924 \mt{val} \; \mt{setval} : \mt{sql\_sequence} \to \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@546 1925 \end{array}$$
adamc@546 1926
adamc@546 1927
adam@1648 1928 \subsection{\label{xml}XML}
adamc@547 1929
adam@1333 1930 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 1931
adam@1642 1932 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 1933 $$\begin{array}{l}
adamc@547 1934 \mt{con} \; \mt{xml} :: \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547 1935 \end{array}$$
adamc@547 1936
adamc@547 1937 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 1938 $$\begin{array}{l}
adamc@547 1939 \mt{con} \; \mt{tag} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547 1940 \end{array}$$
adamc@547 1941
adamc@547 1942 Literal text may be injected into XML as ``CDATA.''
adamc@547 1943 $$\begin{array}{l}
adamc@547 1944 \mt{val} \; \mt{cdata} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{string} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adamc@547 1945 \end{array}$$
adamc@547 1946
adam@1358 1947 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 1948 $$\begin{array}{l}
adam@1358 1949 \mt{val} \; \mt{cdataChar} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{char} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adam@1358 1950 \end{array}$$
adam@1358 1951
adamc@547 1952 There is a function for producing an XML tree with a particular tag at its root.
adamc@547 1953 $$\begin{array}{l}
adamc@547 1954 \mt{val} \; \mt{tag} : \mt{attrsGiven} ::: \{\mt{Type}\} \to \mt{attrsAbsent} ::: \{\mt{Type}\} \to \mt{ctxOuter} ::: \{\mt{Unit}\} \to \mt{ctxInner} ::: \{\mt{Unit}\} \\
adamc@547 1955 \hspace{.1in} \to \mt{useOuter} ::: \{\mt{Type}\} \to \mt{useInner} ::: \{\mt{Type}\} \to \mt{bindOuter} ::: \{\mt{Type}\} \to \mt{bindInner} ::: \{\mt{Type}\} \\
adam@1380 1956 \hspace{.1in} \to [\mt{attrsGiven} \sim \mt{attrsAbsent}] \Rightarrow [\mt{useOuter} \sim \mt{useInner}] \Rightarrow [\mt{bindOuter} \sim \mt{bindInner}] \\
adam@1749 1957 \hspace{.1in} \Rightarrow \mt{css\_class} \\
adam@1643 1958 \hspace{.1in} \to \mt{option} \; (\mt{signal} \; \mt{css\_class}) \\
adamc@787 1959 \hspace{.1in} \to \$\mt{attrsGiven} \\
adamc@547 1960 \hspace{.1in} \to \mt{tag} \; (\mt{attrsGiven} \rc \mt{attrsAbsent}) \; \mt{ctxOuter} \; \mt{ctxInner} \; \mt{useOuter} \; \mt{bindOuter} \\
adamc@547 1961 \hspace{.1in} \to \mt{xml} \; \mt{ctxInner} \; \mt{useInner} \; \mt{bindInner} \to \mt{xml} \; \mt{ctxOuter} \; (\mt{useOuter} \rc \mt{useInner}) \; (\mt{bindOuter} \rc \mt{bindInner})
adamc@547 1962 \end{array}$$
adam@1749 1963 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. Ur/Web itself doesn't deal with the syntax or semantics of style sheets; they can be linked via URLs with \texttt{link} tags. However, Ur/Web does make it easy to calculate upper bounds on usage of CSS classes through program analysis. The function $\mt{Basis.classes}$ can be used to specify a list of CSS classes for a single tag.
adamc@547 1964
adam@1643 1965 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 1966
adamc@547 1967 Two XML fragments may be concatenated.
adamc@547 1968 $$\begin{array}{l}
adamc@547 1969 \mt{val} \; \mt{join} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{bind_1} ::: \{\mt{Type}\} \to \mt{bind_2} ::: \{\mt{Type}\} \\
adam@1380 1970 \hspace{.1in} \to [\mt{use_1} \sim \mt{bind_1}] \Rightarrow [\mt{bind_1} \sim \mt{bind_2}] \\
adamc@547 1971 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind_1} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{bind_1}) \; \mt{bind_2} \to \mt{xml} \; \mt{ctx} \; \mt{use_1} \; (\mt{bind_1} \rc \mt{bind_2})
adamc@547 1972 \end{array}$$
adamc@547 1973
adamc@547 1974 Finally, any XML fragment may be updated to ``claim'' to use more form fields than it does.
adamc@547 1975 $$\begin{array}{l}
adam@1380 1976 \mt{val} \; \mt{useMore} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{use_2} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to [\mt{use_1} \sim \mt{use_2}] \\
adamc@547 1977 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{use_2}) \; \mt{bind}
adamc@547 1978 \end{array}$$
adamc@547 1979
adam@1344 1980 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 1981
adamc@547 1982 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 1983 $$\begin{array}{l}
adam@1641 1984 \mt{val} \; \mt{error} : \mt{t} ::: \mt{Type} \to \mt{xbody} \to \mt{t}
adamc@547 1985 \end{array}$$
adamc@547 1986
adamc@549 1987
adamc@701 1988 \subsection{Client-Side Programming}
adamc@659 1989
adamc@701 1990 Ur/Web supports running code on web browsers, via automatic compilation to JavaScript.
adamc@701 1991
adamc@701 1992 \subsubsection{The Basics}
adamc@701 1993
adam@1400 1994 All of the functions in this subsection are client-side only.
adam@1400 1995
adam@1297 1996 Clients can open alert and confirm dialog boxes, in the usual annoying JavaScript way.
adamc@701 1997 $$\begin{array}{l}
adam@1297 1998 \mt{val} \; \mt{alert} : \mt{string} \to \mt{transaction} \; \mt{unit} \\
adam@1297 1999 \mt{val} \; \mt{confirm} : \mt{string} \to \mt{transaction} \; \mt{bool}
adamc@701 2000 \end{array}$$
adamc@701 2001
adamc@701 2002 Any transaction may be run in a new thread with the $\mt{spawn}$ function.
adamc@701 2003 $$\begin{array}{l}
adamc@701 2004 \mt{val} \; \mt{spawn} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit}
adamc@701 2005 \end{array}$$
adamc@701 2006
adamc@701 2007 The current thread can be paused for at least a specified number of milliseconds.
adamc@701 2008 $$\begin{array}{l}
adamc@701 2009 \mt{val} \; \mt{sleep} : \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@701 2010 \end{array}$$
adamc@701 2011
adamc@787 2012 A few functions are available to registers callbacks for particular error events. Respectively, they are triggered on calls to $\mt{error}$, uncaught JavaScript exceptions, failure of remote procedure calls, the severance of the connection serving asynchronous messages, or the occurrence of some other error with that connection. If no handlers are registered for a kind of error, then occurrences of that error are ignored silently.
adamc@787 2013 $$\begin{array}{l}
adamc@787 2014 \mt{val} \; \mt{onError} : (\mt{xbody} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787 2015 \mt{val} \; \mt{onFail} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787 2016 \mt{val} \; \mt{onConnectFail} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787 2017 \mt{val} \; \mt{onDisconnect} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787 2018 \mt{val} \; \mt{onServerError} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit}
adamc@787 2019 \end{array}$$
adamc@787 2020
adam@1555 2021 There are also functions to register standard document-level event handlers.
adam@1555 2022
adam@1555 2023 $$\begin{array}{l}
adam@1555 2024 \mt{val} \; \mt{onClick} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adam@1555 2025 \mt{val} \; \mt{onDblclick} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adam@1555 2026 \mt{val} \; \mt{onKeydown} : (\mt{int} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1555 2027 \mt{val} \; \mt{onKeypress} : (\mt{int} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1555 2028 \mt{val} \; \mt{onKeyup} : (\mt{int} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1555 2029 \mt{val} \; \mt{onMousedown} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adam@1555 2030 \mt{val} \; \mt{onMouseup} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit}
adam@1555 2031 \end{array}$$
adam@1555 2032
adam@1559 2033 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 2034
adam@1559 2035 $$\begin{array}{l}
adam@1559 2036 \mt{val} \; \mt{preventDefault} : \mt{transaction} \; \mt{unit} \\
adam@1559 2037 \mt{val} \; \mt{stopPropagation} : \mt{transaction} \; \mt{unit}
adam@1559 2038 \end{array}$$
adam@1559 2039
adam@1556 2040 \subsubsection{Node IDs}
adam@1556 2041
adam@1556 2042 There is an abstract type of node IDs that may be assigned to \cd{id} attributes of most HTML tags.
adam@1556 2043
adam@1556 2044 $$\begin{array}{l}
adam@1556 2045 \mt{type} \; \mt{id} \\
adam@1556 2046 \mt{val} \; \mt{fresh} : \mt{transaction} \; \mt{id}
adam@1556 2047 \end{array}$$
adam@1556 2048
adam@1556 2049 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 only 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@1556 2050
adam@1643 2051 \subsubsection{\label{signals}Functional-Reactive Page Generation}
adamc@701 2052
adamc@701 2053 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 2054
adam@1403 2055 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 2056
adamc@659 2057 $$\begin{array}{l}
adamc@659 2058 \mt{con} \; \mt{source} :: \mt{Type} \to \mt{Type} \\
adamc@659 2059 \mt{val} \; \mt{source} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{transaction} \; (\mt{source} \; \mt{t}) \\
adamc@659 2060 \mt{val} \; \mt{set} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@659 2061 \mt{val} \; \mt{get} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@659 2062 \end{array}$$
adamc@659 2063
adam@1400 2064 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 2065
adam@1608 2066 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 2067
adamc@659 2068 $$\begin{array}{l}
adamc@659 2069 \mt{con} \; \mt{signal} :: \mt{Type} \to \mt{Type} \\
adamc@659 2070 \mt{val} \; \mt{signal\_monad} : \mt{monad} \; \mt{signal} \\
adam@1608 2071 \mt{val} \; \mt{signal} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{signal} \; \mt{t} \\
adam@1608 2072 \mt{val} \; \mt{current} : \mt{t} ::: \mt{Type} \to \mt{signal} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@659 2073 \end{array}$$
adamc@659 2074
adamc@659 2075 A reactive portion of an HTML page is injected with a $\mt{dyn}$ tag, which has a signal-valued attribute $\mt{Signal}$.
adamc@659 2076
adamc@659 2077 $$\begin{array}{l}
adam@1641 2078 \mt{val} \; \mt{dyn} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to [\mt{ctx} \sim [\mt{Dyn}]] \Rightarrow \mt{unit} \\
adam@1641 2079 \hspace{.1in} \to \mt{tag} \; [\mt{Signal} = \mt{signal} \; (\mt{xml} \; ([\mt{Dyn}] \rc \mt{ctx}) \; \mt{use} \; \mt{bind})] \; ([\mt{Dyn}] \rc \mt{ctx}) \; [] \; \mt{use} \; \mt{bind}
adamc@659 2080 \end{array}$$
adamc@659 2081
adam@1648 2082 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 2083
adam@1648 2084 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 2085
adamc@701 2086 Transactions can be run on the client by including them in attributes like the $\mt{Onclick}$ attribute of $\mt{button}$, and GUI widgets like $\mt{ctextbox}$ have $\mt{Source}$ attributes that can be used to connect them to sources, so that their values can be read by code running because of, e.g., an $\mt{Onclick}$ event.
adamc@701 2087
adamc@914 2088 \subsubsection{Remote Procedure Calls}
adamc@914 2089
adamc@914 2090 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 2091
adamc@914 2092 $$\begin{array}{l}
adamc@914 2093 \mt{val} \; \mt{rpc} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@914 2094 \end{array}$$
adamc@914 2095
adamc@701 2096 \subsubsection{Asynchronous Message-Passing}
adamc@701 2097
adamc@701 2098 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 2099
adamc@701 2100 $$\begin{array}{l}
adamc@701 2101 \mt{type} \; \mt{client} \\
adamc@701 2102 \mt{val} \; \mt{self} : \mt{transaction} \; \mt{client}
adamc@701 2103 \end{array}$$
adamc@701 2104
adamc@701 2105 \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 2106
adamc@701 2107 $$\begin{array}{l}
adamc@701 2108 \mt{con} \; \mt{channel} :: \mt{Type} \to \mt{Type} \\
adamc@701 2109 \mt{val} \; \mt{channel} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; (\mt{channel} \; \mt{t}) \\
adamc@701 2110 \mt{val} \; \mt{send} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@701 2111 \mt{val} \; \mt{recv} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@701 2112 \end{array}$$
adamc@701 2113
adamc@701 2114 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 2115
adamc@701 2116 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 2117
adam@1551 2118 \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 2119
adamc@659 2120
adamc@549 2121 \section{Ur/Web Syntax Extensions}
adamc@549 2122
adamc@549 2123 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 2124
adamc@549 2125 \subsection{SQL}
adamc@549 2126
adamc@786 2127 \subsubsection{\label{tables}Table Declarations}
adamc@786 2128
adamc@788 2129 $\mt{table}$ declarations may include constraints, via these grammar rules.
adamc@788 2130 $$\begin{array}{rrcll}
adam@1594 2131 \textrm{Declarations} & d &::=& \mt{table} \; x : c \; [pk[,]] \; cts \mid \mt{view} \; x = V \\
adamc@788 2132 \textrm{Primary key constraints} & pk &::=& \mt{PRIMARY} \; \mt{KEY} \; K \\
adam@1722 2133 \textrm{Keys} & K &::=& f \mid (f, (f,)^+) \mid \{\{e\}\} \\
adamc@788 2134 \textrm{Constraint sets} & cts &::=& \mt{CONSTRAINT} f \; ct \mid cts, cts \mid \{\{e\}\} \\
adamc@788 2135 \textrm{Constraints} & ct &::=& \mt{UNIQUE} \; K \mid \mt{CHECK} \; E \\
adamc@788 2136 &&& \mid \mt{FOREIGN} \; \mt{KEY} \; K \; \mt{REFERENCES} \; F \; (K) \; [\mt{ON} \; \mt{DELETE} \; pr] \; [\mt{ON} \; \mt{UPDATE} \; pr] \\
adamc@788 2137 \textrm{Foreign tables} & F &::=& x \mid \{\{e\}\} \\
adam@1594 2138 \textrm{Propagation modes} & pr &::=& \mt{NO} \; \mt{ACTION} \mid \mt{RESTRICT} \mid \mt{CASCADE} \mid \mt{SET} \; \mt{NULL} \\
adam@1594 2139 \textrm{View expressions} & V &::=& Q \mid \{e\}
adamc@788 2140 \end{array}$$
adamc@788 2141
adamc@788 2142 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 2143
adamc@788 2144
adamc@549 2145 \subsubsection{Queries}
adamc@549 2146
adamc@550 2147 Queries $Q$ are added to the rules for expressions $e$.
adamc@550 2148
adamc@549 2149 $$\begin{array}{rrcll}
adam@1684 2150 \textrm{Queries} & Q &::=& (q \; [\mt{ORDER} \; \mt{BY} \; O] \; [\mt{LIMIT} \; N] \; [\mt{OFFSET} \; N]) \\
adamc@1085 2151 \textrm{Pre-queries} & q &::=& \mt{SELECT} \; [\mt{DISTINCT}] \; P \; \mt{FROM} \; F,^+ \; [\mt{WHERE} \; E] \; [\mt{GROUP} \; \mt{BY} \; p,^+] \; [\mt{HAVING} \; E] \\
adamc@1085 2152 &&& \mid q \; R \; q \mid \{\{\{e\}\}\} \\
adam@1684 2153 \textrm{Relational operators} & R &::=& \mt{UNION} \mid \mt{INTERSECT} \mid \mt{EXCEPT} \\
adam@1684 2154 \textrm{$\mt{ORDER \; BY}$ items} & O &::=& \mt{RANDOM} [()] \mid E \; [o] \mid E \; [o], O
adamc@549 2155 \end{array}$$
adamc@549 2156
adamc@549 2157 $$\begin{array}{rrcll}
adamc@549 2158 \textrm{Projections} & P &::=& \ast & \textrm{all columns} \\
adamc@549 2159 &&& p,^+ & \textrm{particular columns} \\
adamc@549 2160 \textrm{Pre-projections} & p &::=& t.f & \textrm{one column from a table} \\
adamc@558 2161 &&& t.\{\{c\}\} & \textrm{a record of columns from a table (of kind $\{\mt{Type}\}$)} \\
adam@1627 2162 &&& t.* & \textrm{all columns from a table} \\
adamc@1194 2163 &&& E \; [\mt{AS} \; f] & \textrm{expression column} \\
adamc@549 2164 \textrm{Table names} & t &::=& x & \textrm{constant table name (automatically capitalized)} \\
adamc@549 2165 &&& X & \textrm{constant table name} \\
adamc@549 2166 &&& \{\{c\}\} & \textrm{computed table name (of kind $\mt{Name}$)} \\
adamc@549 2167 \textrm{Column names} & f &::=& X & \textrm{constant column name} \\
adamc@549 2168 &&& \{c\} & \textrm{computed column name (of kind $\mt{Name}$)} \\
adamc@549 2169 \textrm{Tables} & T &::=& x & \textrm{table variable, named locally by its own capitalization} \\
adamc@549 2170 &&& x \; \mt{AS} \; t & \textrm{table variable, with local name} \\
adamc@549 2171 &&& \{\{e\}\} \; \mt{AS} \; t & \textrm{computed table expression, with local name} \\
adamc@1085 2172 \textrm{$\mt{FROM}$ items} & F &::=& T \mid \{\{e\}\} \mid F \; J \; \mt{JOIN} \; F \; \mt{ON} \; E \\
adamc@1085 2173 &&& \mid F \; \mt{CROSS} \; \mt{JOIN} \ F \\
adamc@1193 2174 &&& \mid (Q) \; \mt{AS} \; t \\
adamc@1085 2175 \textrm{Joins} & J &::=& [\mt{INNER}] \\
adamc@1085 2176 &&& \mid [\mt{LEFT} \mid \mt{RIGHT} \mid \mt{FULL}] \; [\mt{OUTER}] \\
adam@1587 2177 \textrm{SQL expressions} & E &::=& t.f & \textrm{column references} \\
adamc@549 2178 &&& X & \textrm{named expression references} \\
adam@1490 2179 &&& \{[e]\} & \textrm{injected native Ur expressions} \\
adamc@549 2180 &&& \{e\} & \textrm{computed expressions, probably using $\mt{sql\_exp}$ directly} \\
adamc@549 2181 &&& \mt{TRUE} \mid \mt{FALSE} & \textrm{boolean constants} \\
adamc@549 2182 &&& \ell & \textrm{primitive type literals} \\
adamc@549 2183 &&& \mt{NULL} & \textrm{null value (injection of $\mt{None}$)} \\
adamc@549 2184 &&& E \; \mt{IS} \; \mt{NULL} & \textrm{nullness test} \\
adam@1602 2185 &&& \mt{COALESCE}(E, E) & \textrm{take first non-null value} \\
adamc@549 2186 &&& n & \textrm{nullary operators} \\
adamc@549 2187 &&& u \; E & \textrm{unary operators} \\
adamc@549 2188 &&& E \; b \; E & \textrm{binary operators} \\
adamc@549 2189 &&& \mt{COUNT}(\ast) & \textrm{count number of rows} \\
adamc@549 2190 &&& a(E) & \textrm{other aggregate function} \\
adam@1573 2191 &&& \mt{IF} \; E \; \mt{THEN} \; E \; \mt{ELSE} \; E & \textrm{conditional} \\
adamc@1193 2192 &&& (Q) & \textrm{subquery (must return a single expression column)} \\
adamc@549 2193 &&& (E) & \textrm{explicit precedence} \\
adamc@549 2194 \textrm{Nullary operators} & n &::=& \mt{CURRENT\_TIMESTAMP} \\
adamc@549 2195 \textrm{Unary operators} & u &::=& \mt{NOT} \\
adam@1688 2196 \textrm{Binary operators} & b &::=& \mt{AND} \mid \mt{OR} \mid = \mid \neq \mid < \mid \leq \mid > \mid \geq \\
adamc@1188 2197 \textrm{Aggregate functions} & a &::=& \mt{COUNT} \mid \mt{AVG} \mid \mt{SUM} \mid \mt{MIN} \mid \mt{MAX} \\
adam@1543 2198 \textrm{Directions} & o &::=& \mt{ASC} \mid \mt{DESC} \mid \{e\} \\
adamc@549 2199 \textrm{SQL integer} & N &::=& n \mid \{e\} \\
adamc@549 2200 \end{array}$$
adamc@549 2201
adamc@1085 2202 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 2203
adam@1683 2204 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 2205
adamc@550 2206 \subsubsection{DML}
adamc@550 2207
adamc@550 2208 DML commands $D$ are added to the rules for expressions $e$.
adamc@550 2209
adamc@550 2210 $$\begin{array}{rrcll}
adamc@550 2211 \textrm{Commands} & D &::=& (\mt{INSERT} \; \mt{INTO} \; T^E \; (f,^+) \; \mt{VALUES} \; (E,^+)) \\
adamc@550 2212 &&& (\mt{UPDATE} \; T^E \; \mt{SET} \; (f = E,)^+ \; \mt{WHERE} \; E) \\
adamc@550 2213 &&& (\mt{DELETE} \; \mt{FROM} \; T^E \; \mt{WHERE} \; E) \\
adamc@550 2214 \textrm{Table expressions} & T^E &::=& x \mid \{\{e\}\}
adamc@550 2215 \end{array}$$
adamc@550 2216
adamc@550 2217 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 2218
adamc@551 2219 \subsection{XML}
adamc@551 2220
adamc@551 2221 XML fragments $L$ are added to the rules for expressions $e$.
adamc@551 2222
adamc@551 2223 $$\begin{array}{rrcll}
adamc@551 2224 \textrm{XML fragments} & L &::=& \texttt{<xml/>} \mid \texttt{<xml>}l^*\texttt{</xml>} \\
adamc@551 2225 \textrm{XML pieces} & l &::=& \textrm{text} & \textrm{cdata} \\
adamc@551 2226 &&& \texttt{<}g\texttt{/>} & \textrm{tag with no children} \\
adamc@551 2227 &&& \texttt{<}g\texttt{>}l^*\texttt{</}x\texttt{>} & \textrm{tag with children} \\
adamc@559 2228 &&& \{e\} & \textrm{computed XML fragment} \\
adamc@559 2229 &&& \{[e]\} & \textrm{injection of an Ur expression, via the $\mt{Top}.\mt{txt}$ function} \\
adamc@551 2230 \textrm{Tag} & g &::=& h \; (x = v)^* \\
adamc@551 2231 \textrm{Tag head} & h &::=& x & \textrm{tag name} \\
adamc@551 2232 &&& h\{c\} & \textrm{constructor parameter} \\
adamc@551 2233 \textrm{Attribute value} & v &::=& \ell & \textrm{literal value} \\
adamc@551 2234 &&& \{e\} & \textrm{computed value} \\
adamc@551 2235 \end{array}$$
adamc@551 2236
adam@1749 2237 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.
adamc@552 2238
adamc@1198 2239 \section{\label{structure}The Structure of Web Applications}
adamc@553 2240
adam@1604 2241 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 2242
adam@1532 2243 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 2244
adam@1347 2245 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 will only work with \texttt{POST} payloads of MIME types besides those associated with HTML forms; for these, use Ur/Web's built-in support, as described below.
adam@1347 2246
adam@1370 2247 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 2248
adamc@553 2249 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 2250
adamc@553 2251 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 2252
adam@1653 2253 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 2254 \begin{itemize}
adam@1653 2255 \item Functions are disallowed, since there is no obvious way to serialize them safely.
adam@1653 2256 \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 2257 \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 2258 \end{itemize}
adamc@553 2259
adamc@660 2260 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 2261
adamc@789 2262 \medskip
adamc@789 2263
adam@1347 2264 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 2265
adamc@789 2266 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 2267
adam@1348 2268 \subsection{Tasks}
adam@1348 2269
adam@1348 2270 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 2271
adam@1348 2272 $$\begin{array}{l}
adam@1348 2273 \mt{con} \; \mt{task\_kind} :: \mt{Type} \to \mt{Type} \\
adam@1348 2274 \mt{val} \; \mt{initialize} : \mt{task\_kind} \; \mt{unit} \\
adam@1349 2275 \mt{val} \; \mt{clientLeaves} : \mt{task\_kind} \; \mt{client} \\
adam@1349 2276 \mt{val} \; \mt{periodic} : \mt{int} \to \mt{task\_kind} \; \mt{unit}
adam@1348 2277 \end{array}$$
adam@1348 2278
adam@1348 2279 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 2280
adam@1348 2281 The currently supported task kinds are:
adam@1348 2282 \begin{itemize}
adam@1349 2283 \item $\mt{initialize}$: Code that is run when the application starts up.
adam@1348 2284 \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 2285 \item $\mt{periodic} \; n$: Code that is run when the application starts up and then every $n$ seconds thereafter.
adam@1348 2286 \end{itemize}
adam@1348 2287
adamc@553 2288
adamc@897 2289 \section{The Foreign Function Interface}
adamc@897 2290
adamc@897 2291 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 2292
adamc@897 2293 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 2294
adamc@897 2295 \begin{itemize}
adamc@897 2296 \item \texttt{clientOnly Module.ident} registers a value as being allowed only in client-side code.
adamc@897 2297 \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 2298 \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 2299 \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 2300 \item \texttt{include FILE} requests inclusion of a C header file.
adamc@897 2301 \item \texttt{jsFunc Module.ident=name} gives a mapping from an Ur name for a value to a JavaScript name.
adamc@897 2302 \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 2303 \item \texttt{script URL} requests inclusion of a JavaScript source file within application HTML.
adamc@897 2304 \item \texttt{serverOnly Module.ident} registers a value as being allowed only in server-side code.
adamc@897 2305 \end{itemize}
adamc@897 2306
adamc@897 2307 \subsection{Writing C FFI Code}
adamc@897 2308
adamc@897 2309 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 2310
adamc@897 2311 \begin{itemize}
adamc@897 2312 \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 2313 \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 2314 \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 2315 \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 2316 \end{itemize}
adamc@897 2317
adamc@897 2318 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 2319 \begin{itemize}
adamc@897 2320 \item \begin{verbatim}
adamc@897 2321 void uw_error(uw_context, failure_kind, const char *fmt, ...);
adamc@897 2322 \end{verbatim}
adamc@897 2323 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 2324
adam@1329 2325 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 2326
adamc@897 2327 \item \begin{verbatim}
adam@1469 2328 void uw_set_error_message(uw_context, const char *fmt, ...);
adam@1469 2329 \end{verbatim}
adam@1469 2330 This simpler form of \texttt{uw\_error()} saves an error message without immediately aborting execution.
adam@1469 2331
adam@1469 2332 \item \begin{verbatim}
adamc@897 2333 void uw_push_cleanup(uw_context, void (*func)(void *), void *arg);
adamc@897 2334 void uw_pop_cleanup(uw_context);
adamc@897 2335 \end{verbatim}
adam@1329 2336 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 2337
adam@1329 2338 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 2339
adamc@897 2340 \item \begin{verbatim}
adamc@897 2341 void *uw_malloc(uw_context, size_t);
adamc@897 2342 \end{verbatim}
adam@1329 2343 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 2344
adam@1329 2345 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 2346
adamc@897 2347 \item \begin{verbatim}
adamc@897 2348 typedef void (*uw_callback)(void *);
adam@1328 2349 typedef void (*uw_callback_with_retry)(void *, int will_retry);
adamc@897 2350 void uw_register_transactional(uw_context, void *data, uw_callback commit,
adam@1328 2351 uw_callback rollback, uw_callback_with_retry free);
adamc@897 2352 \end{verbatim}
adam@1328 2353 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 2354
adamc@1085 2355 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 2356
adam@1329 2357 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 2358
adam@1329 2359 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 2360
adam@1469 2361 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 2362
adamc@1085 2363 \item \begin{verbatim}
adamc@1085 2364 void *uw_get_global(uw_context, char *name);
adamc@1085 2365 void uw_set_global(uw_context, char *name, void *data, uw_callback free);
adamc@1085 2366 \end{verbatim}
adam@1329 2367 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 2368
adamc@897 2369 \end{itemize}
adamc@897 2370
adamc@897 2371 \subsection{Writing JavaScript FFI Code}
adamc@897 2372
adamc@897 2373 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 2374
adamc@897 2375 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 2376
adamc@897 2377 \begin{itemize}
adamc@897 2378 \item Integers, floats, strings, characters, and booleans are represented in the usual JavaScript way.
adam@1644 2379 \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 2380 \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 2381 \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 2382 \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 2383 \item As in the C FFI, all abstract types of program syntax are implemented with strings in JavaScript.
adamc@897 2384 \end{itemize}
adamc@897 2385
adam@1644 2386 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 2387
adam@1644 2388 \begin{itemize}
adam@1644 2389 \item Sources should be treated as an abstract type, manipulated via:
adam@1644 2390 \begin{itemize}
adam@1644 2391 \item \cd{sc(v)}, to create a source initialized to \cd{v}
adam@1644 2392 \item \cd{sg(s)}, to retrieve the current value of source \cd{s}
adam@1644 2393 \item \cd{sv(s, v)}, to set source \cd{s} to value \cd{v}
adam@1644 2394 \end{itemize}
adam@1644 2395
adam@1644 2396 \item Signals should be treated as an abstract type, manipulated via:
adam@1644 2397 \begin{itemize}
adam@1644 2398 \item \cd{sr(v)} and \cd{sb(s, f)}, the ``return'' and ``bind'' monad operators, respectively
adam@1644 2399 \item \cd{ss(s)}, to produce the signal corresponding to source \cd{s}
adam@1644 2400 \item \cd{scur(s)}, to get the current value of signal \cd{s}
adam@1644 2401 \end{itemize}
adam@1644 2402
adam@1644 2403 \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 2404
adam@1702 2405 \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 2406
adam@1644 2407 \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 2408 \end{itemize}
adamc@897 2409
adamc@897 2410
adamc@552 2411 \section{Compiler Phases}
adamc@552 2412
adamc@552 2413 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 2414
adamc@552 2415 In this section, we step through the main phases of compilation, noting what consequences each phase has for effective programming.
adamc@552 2416
adamc@552 2417 \subsection{Parse}
adamc@552 2418
adamc@552 2419 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 2420
adamc@552 2421 \subsection{Elaborate}
adamc@552 2422
adamc@552 2423 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 2424
adam@1378 2425 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 2426
adamc@552 2427 \subsection{Unnest}
adamc@552 2428
adamc@552 2429 Named local function definitions are moved to the top level, to avoid the need to generate closures.
adamc@552 2430
adamc@552 2431 \subsection{Corify}
adamc@552 2432
adamc@552 2433 Module system features are compiled away, through inlining of functor definitions at application sites. Afterward, most abstraction boundaries are broken, facilitating optimization.
adamc@552 2434
adamc@552 2435 \subsection{Especialize}
adamc@552 2436
adam@1356 2437 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 2438
adamc@552 2439 \subsection{Untangle}
adamc@552 2440
adamc@552 2441 Remove unnecessary mutual recursion, splitting recursive groups into strongly-connected components.
adamc@552 2442
adamc@552 2443 \subsection{Shake}
adamc@552 2444
adamc@552 2445 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 2446
adamc@661 2447 \subsection{Rpcify}
adamc@661 2448
adamc@661 2449 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 2450
adamc@661 2451 \subsection{Untangle, Shake}
adamc@661 2452
adamc@661 2453 Repeat these simplifications.
adamc@661 2454
adamc@553 2455 \subsection{\label{tag}Tag}
adamc@552 2456
adamc@552 2457 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 2458
adamc@552 2459 \subsection{Reduce}
adamc@552 2460
adamc@552 2461 Apply definitional equality rules to simplify the program as much as possible. This effectively includes inlining of every non-recursive definition.
adamc@552 2462
adamc@552 2463 \subsection{Unpoly}
adamc@552 2464
adamc@552 2465 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 2466
adamc@552 2467 \subsection{Specialize}
adamc@552 2468
adamc@558 2469 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 2470
adamc@552 2471 \subsection{Shake}
adamc@552 2472
adamc@558 2473 Here the compiler repeats the earlier Shake phase.
adamc@552 2474
adamc@552 2475 \subsection{Monoize}
adamc@552 2476
adamc@552 2477 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 2478
adamc@552 2479 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 2480
adamc@552 2481 \subsection{MonoOpt}
adamc@552 2482
adamc@552 2483 Simple algebraic laws are applied to simplify the program, focusing especially on efficient imperative generation of HTML pages.
adamc@552 2484
adamc@552 2485 \subsection{MonoUntangle}
adamc@552 2486
adamc@552 2487 Unnecessary mutual recursion is broken up again.
adamc@552 2488
adamc@552 2489 \subsection{MonoReduce}
adamc@552 2490
adamc@552 2491 Equivalents of the definitional equality rules are applied to simplify programs, with inlining again playing a major role.
adamc@552 2492
adamc@552 2493 \subsection{MonoShake, MonoOpt}
adamc@552 2494
adamc@552 2495 Unneeded declarations are removed, and basic optimizations are repeated.
adamc@552 2496
adamc@552 2497 \subsection{Fuse}
adamc@552 2498
adamc@552 2499 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 2500
adamc@552 2501 \subsection{MonoUntangle, MonoShake}
adamc@552 2502
adamc@552 2503 Fuse often creates more opportunities to remove spurious mutual recursion.
adamc@552 2504
adamc@552 2505 \subsection{Pathcheck}
adamc@552 2506
adamc@552 2507 The compiler checks that no link or action name has been used more than once.
adamc@552 2508
adamc@552 2509 \subsection{Cjrize}
adamc@552 2510
adamc@552 2511 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 2512
adamc@552 2513 \subsection{C Compilation and Linking}
adamc@552 2514
adam@1523 2515 The output of the last phase is pretty-printed as C source code and passed to the C compiler.
adamc@552 2516
adamc@552 2517
as@1564 2518 \end{document}