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Add '-q' option to HTTP binaries
author Adam Chlipala <adam@chlipala.net>
date Wed, 11 Dec 2013 11:06:08 -0500
parents f1c211936557
children 1484ba362062
rev   line source
adamc@524 1 \documentclass{article}
adamc@554 2 \usepackage{fullpage,amsmath,amssymb,proof,url}
rmbruijn@1568 3 \usepackage[T1]{fontenc}
vshabanoff@1765 4 \usepackage{ae,aecompl}
adamc@524 5 \newcommand{\cd}[1]{\texttt{#1}}
adamc@524 6 \newcommand{\mt}[1]{\mathsf{#1}}
adamc@524 7
adamc@524 8 \newcommand{\rc}{+ \hspace{-.075in} + \;}
adamc@527 9 \newcommand{\rcut}{\; \texttt{--} \;}
adamc@527 10 \newcommand{\rcutM}{\; \texttt{---} \;}
adamc@524 11
adamc@524 12 \begin{document}
adamc@524 13
adamc@524 14 \title{The Ur/Web Manual}
adamc@524 15 \author{Adam Chlipala}
adamc@524 16
adamc@524 17 \maketitle
adamc@524 18
adamc@540 19 \tableofcontents
adamc@540 20
adamc@554 21
adamc@554 22 \section{Introduction}
adamc@554 23
adam@1797 24 \emph{Ur} is a programming language designed to introduce richer type system features into functional programming in the tradition of ML and Haskell. Ur is functional, pure, statically typed, and strict. Ur supports a powerful kind of \emph{metaprogramming} based on \emph{type-level computation with type-level records}.
adamc@554 25
adamc@554 26 \emph{Ur/Web} is Ur plus a special standard library and associated rules for parsing and optimization. Ur/Web supports construction of dynamic web applications backed by SQL databases. The signature of the standard library is such that well-typed Ur/Web programs ``don't go wrong'' in a very broad sense. Not only do they not crash during particular page generations, but they also may not:
adamc@554 27
adamc@554 28 \begin{itemize}
adamc@554 29 \item Suffer from any kinds of code-injection attacks
adamc@554 30 \item Return invalid HTML
adamc@554 31 \item Contain dead intra-application links
adamc@554 32 \item Have mismatches between HTML forms and the fields expected by their handlers
adamc@652 33 \item Include client-side code that makes incorrect assumptions about the ``AJAX''-style services that the remote web server provides
adamc@554 34 \item Attempt invalid SQL queries
adamc@652 35 \item Use improper marshaling or unmarshaling in communication with SQL databases or between browsers and web servers
adamc@554 36 \end{itemize}
adamc@554 37
adamc@554 38 This type safety is just the foundation of the Ur/Web methodology. It is also possible to use metaprogramming to build significant application pieces by analysis of type structure. For instance, the demo includes an ML-style functor for building an admin interface for an arbitrary SQL table. The type system guarantees that the admin interface sub-application that comes out will always be free of the above-listed bugs, no matter which well-typed table description is given as input.
adamc@554 39
adamc@652 40 The Ur/Web compiler also produces very efficient object code that does not use garbage collection. These compiled programs will often be even more efficient than what most programmers would bother to write in C. The compiler also generates JavaScript versions of client-side code, with no need to write those parts of applications in a different language.
adamc@554 41
adamc@554 42 \medskip
adamc@554 43
adamc@554 44 The official web site for Ur is:
adamc@554 45 \begin{center}
adamc@554 46 \url{http://www.impredicative.com/ur/}
adamc@554 47 \end{center}
adamc@554 48
adamc@555 49
adamc@555 50 \section{Installation}
adamc@555 51
adamc@555 52 If you are lucky, then the following standard command sequence will suffice for installation, in a directory to which you have unpacked the latest distribution tarball.
adamc@555 53
adamc@555 54 \begin{verbatim}
adamc@555 55 ./configure
adamc@555 56 make
adamc@555 57 sudo make install
adamc@555 58 \end{verbatim}
adamc@555 59
adam@1523 60 Some other packages must be installed for the above to work. At a minimum, you need a standard UNIX shell, with standard UNIX tools like sed and GCC (or an alternate C compiler) in your execution path; MLton, the whole-program optimizing compiler for Standard ML; and the development files for the OpenSSL C library. As of this writing, in the ``testing'' version of Debian Linux, this command will install the more uncommon of these dependencies:
adamc@896 61 \begin{verbatim}
adam@1368 62 apt-get install mlton libssl-dev
adamc@896 63 \end{verbatim}
adamc@555 64
adamc@896 65 To build programs that access SQL databases, you also need one of these client libraries for supported backends.
adamc@555 66 \begin{verbatim}
adamc@896 67 apt-get install libpq-dev libmysqlclient15-dev libsqlite3-dev
adamc@555 68 \end{verbatim}
adamc@555 69
adamc@555 70 It is also possible to access the modules of the Ur/Web compiler interactively, within Standard ML of New Jersey. To install the prerequisites in Debian testing:
adamc@555 71 \begin{verbatim}
adamc@555 72 apt-get install smlnj libsmlnj-smlnj ml-yacc ml-lpt
adamc@555 73 \end{verbatim}
adamc@555 74
adamc@555 75 To begin an interactive session with the Ur compiler modules, run \texttt{make smlnj}, and then, from within an \texttt{sml} session, run \texttt{CM.make "src/urweb.cm";}. The \texttt{Compiler} module is the main entry point.
adamc@555 76
adamc@896 77 To run an SQL-backed application with a backend besides SQLite, you will probably want to install one of these servers.
adamc@555 78
adamc@555 79 \begin{verbatim}
adam@1400 80 apt-get install postgresql-8.4 mysql-server-5.1
adamc@555 81 \end{verbatim}
adamc@555 82
adamc@555 83 To use the Emacs mode, you must have a modern Emacs installed. We assume that you already know how to do this, if you're in the business of looking for an Emacs mode. The demo generation facility of the compiler will also call out to Emacs to syntax-highlight code, and that process depends on the \texttt{htmlize} module, which can be installed in Debian testing via:
adamc@555 84
adamc@555 85 \begin{verbatim}
adamc@555 86 apt-get install emacs-goodies-el
adamc@555 87 \end{verbatim}
adamc@555 88
adam@1441 89 If you don't want to install the Emacs mode, run \texttt{./configure} with the argument \texttt{--without-emacs}.
adam@1441 90
adam@1523 91 Even with the right packages installed, configuration and building might fail to work. After you run \texttt{./configure}, you will see the values of some named environment variables printed. You may need to adjust these values to get proper installation for your system. To change a value, store your preferred alternative in the corresponding UNIX environment variable, before running \texttt{./configure}. For instance, here is how to change the list of extra arguments that the Ur/Web compiler will pass to the C compiler and linker on every invocation. Some older GCC versions need this setting to mask a bug in function inlining.
adamc@555 92
adamc@555 93 \begin{verbatim}
adam@1523 94 CCARGS=-fno-inline ./configure
adamc@555 95 \end{verbatim}
adamc@555 96
adam@1523 97 Since the author is still getting a handle on the GNU Autotools that provide the build system, you may need to do some further work to get started, especially in environments with significant differences from Linux (where most testing is done). The variables \texttt{PGHEADER}, \texttt{MSHEADER}, and \texttt{SQHEADER} may be used to set the proper C header files to include for the development libraries of PostgreSQL, MySQL, and SQLite, respectively. To get libpq to link, one OS X user reported setting \texttt{CCARGS="-I/opt/local/include -L/opt/local/lib/postgresql84"}, after creating a symbolic link with \texttt{ln -s /opt/local/include/postgresql84 /opt/local/include/postgresql}.
adamc@555 98
adamc@555 99 The Emacs mode can be set to autoload by adding the following to your \texttt{.emacs} file.
adamc@555 100
adamc@555 101 \begin{verbatim}
adamc@555 102 (add-to-list 'load-path "/usr/local/share/emacs/site-lisp/urweb-mode")
adamc@555 103 (load "urweb-mode-startup")
adamc@555 104 \end{verbatim}
adamc@555 105
adamc@555 106 Change the path in the first line if you chose a different Emacs installation path during configuration.
adamc@555 107
adamc@555 108
adamc@556 109 \section{Command-Line Compiler}
adamc@556 110
adam@1604 111 \subsection{\label{cl}Project Files}
adamc@556 112
adamc@556 113 The basic inputs to the \texttt{urweb} compiler are project files, which have the extension \texttt{.urp}. Here is a sample \texttt{.urp} file.
adamc@556 114
adamc@556 115 \begin{verbatim}
adamc@556 116 database dbname=test
adamc@556 117 sql crud1.sql
adamc@556 118
adamc@556 119 crud
adamc@556 120 crud1
adamc@556 121 \end{verbatim}
adamc@556 122
adamc@556 123 The \texttt{database} line gives the database information string to pass to libpq. In this case, the string only says to connect to a local database named \texttt{test}.
adamc@556 124
adamc@556 125 The \texttt{sql} line asks for an SQL source file to be generated, giving the commands to run to create the tables and sequences that this application expects to find. After building this \texttt{.urp} file, the following commands could be used to initialize the database, assuming that the current UNIX user exists as a Postgres user with database creation privileges:
adamc@556 126
adamc@556 127 \begin{verbatim}
adamc@556 128 createdb test
adamc@556 129 psql -f crud1.sql test
adamc@556 130 \end{verbatim}
adamc@556 131
adam@1331 132 A blank line separates the named directives from a list of modules to include in the project. Any line may contain a shell-script-style comment, where any suffix of a line starting at a hash character \texttt{\#} is ignored.
adamc@556 133
adamc@556 134 For each entry \texttt{M} in the module list, the file \texttt{M.urs} is included in the project if it exists, and the file \texttt{M.ur} must exist and is always included.
adamc@556 135
adamc@783 136 Here is the complete list of directive forms. ``FFI'' stands for ``foreign function interface,'' Ur's facility for interaction between Ur programs and C and JavaScript libraries.
adamc@783 137 \begin{itemize}
adam@1799 138 \item \texttt{[allow|deny] [url|mime|requestHeader|responseHeader|env] PATTERN} registers a rule governing which URLs, MIME types, HTTP request headers, HTTP response headers, or environment variable names are allowed to appear explicitly in this application. The first such rule to match a name determines the verdict. If \texttt{PATTERN} ends in \texttt{*}, it is interpreted as a prefix rule. Otherwise, a string must match it exactly.
adam@1400 139 \item \texttt{alwaysInline PATH} requests that every call to the referenced function be inlined. Section \ref{structure} explains how functions are assigned path strings.
adam@1462 140 \item \texttt{benignEffectful Module.ident} registers an FFI function or transaction as having side effects. The optimizer avoids removing, moving, or duplicating calls to such functions. Every effectful FFI function must be registered, or the optimizer may make invalid transformations. This version of the \texttt{effectful} directive registers that this function only has side effects that remain local to a single page generation.
adamc@783 141 \item \texttt{clientOnly Module.ident} registers an FFI function or transaction that may only be run in client browsers.
adam@1881 142 \item \texttt{clientToServer Module.ident} adds FFI type \texttt{Module.ident} to the list of types that are OK to marshal from clients to servers. Values like XML trees and SQL queries are hard to marshal without introducing expensive validity checks, so it's easier to ensure that the server never trusts clients to send such values. The file \texttt{include/urweb/urweb\_cpp.h} shows examples of the C support functions that are required of any type that may be marshalled. These include \texttt{attrify}, \texttt{urlify}, and \texttt{unurlify} functions.
adam@1816 143 \item \texttt{coreInline TREESIZE} sets how many nodes the AST of a function definition may have before the optimizer stops trying hard to inline calls to that function. (This is one of two options for one of two intermediate languages within the compiler.)
adamc@783 144 \item \texttt{database DBSTRING} sets the string to pass to libpq to open a database connection.
adamc@783 145 \item \texttt{debug} saves some intermediate C files, which is mostly useful to help in debugging the compiler itself.
adam@1878 146 \item \texttt{effectful Module.ident} registers an FFI function or transaction as having side effects. The optimizer avoids removing, moving, or duplicating calls to such functions. This is the default behavior for \texttt{transaction}-based types.
adamc@783 147 \item \texttt{exe FILENAME} sets the filename to which to write the output executable. The default for file \texttt{P.urp} is \texttt{P.exe}.
adam@1881 148 \item \texttt{ffi FILENAME} reads the file \texttt{FILENAME.urs} to determine the interface to a new FFI module. The name of the module is calculated from \texttt{FILENAME} in the same way as for normal source files. See the files \texttt{include/urweb/urweb\_cpp.h} and \texttt{src/c/urweb.c} for examples of C headers and implementations for FFI modules. In general, every type or value \texttt{Module.ident} becomes \texttt{uw\_Module\_ident} in C.
adamc@1099 149 \item \texttt{include FILENAME} adds \texttt{FILENAME} to the list of files to be \texttt{\#include}d in C sources. This is most useful for interfacing with new FFI modules.
adamc@783 150 \item \texttt{jsFunc Module.ident=name} gives the JavaScript name of an FFI value.
adamc@1089 151 \item \texttt{library FILENAME} parses \texttt{FILENAME.urp} and merges its contents with the rest of the current file's contents. If \texttt{FILENAME.urp} doesn't exist, the compiler also tries \texttt{FILENAME/lib.urp}.
adam@1309 152 \item \texttt{limit class num} sets a resource usage limit for generated applications. The limit \texttt{class} will be set to the non-negative integer \texttt{num}. The classes are:
adam@1309 153 \begin{itemize}
adam@1309 154 \item \texttt{cleanup}: maximum number of cleanup operations (e.g., entries recording the need to deallocate certain temporary objects) that may be active at once per request
adam@1850 155 \item \texttt{clients}: maximum number of simultaneous connections to one application by web clients waiting for new asynchronous messages sent with \texttt{Basis.send}
adam@1850 156 \item \texttt{database}: maximum size of a database file (currently only used by SQLite, which interprets the parameter as a number of pages, where page size is itself a quantity configurable in SQLite)
adam@1309 157 \item \texttt{deltas}: maximum number of messages sendable in a single request handler with \texttt{Basis.send}
adam@1309 158 \item \texttt{globals}: maximum number of global variables that FFI libraries may set in a single request context
adam@1309 159 \item \texttt{headers}: maximum size (in bytes) of per-request buffer used to hold HTTP headers for generated pages
adam@1797 160 \item \texttt{heap}: maximum size (in bytes) of per-request heap for dynamically allocated data
adam@1309 161 \item \texttt{inputs}: maximum number of top-level form fields per request
adam@1309 162 \item \texttt{messages}: maximum size (in bytes) of per-request buffer used to hold a single outgoing message sent with \texttt{Basis.send}
adam@1309 163 \item \texttt{page}: maximum size (in bytes) of per-request buffer used to hold HTML content of generated pages
adam@1309 164 \item \texttt{script}: maximum size (in bytes) of per-request buffer used to hold JavaScript content of generated pages
adam@1309 165 \item \texttt{subinputs}: maximum number of form fields per request, excluding top-level fields
adam@1309 166 \item \texttt{time}: maximum running time of a single page request, in units of approximately 0.1 seconds
adam@1309 167 \item \texttt{transactionals}: maximum number of custom transactional actions (e.g., sending an e-mail) that may be run in a single page generation
adam@1309 168 \end{itemize}
adam@1523 169 \item \texttt{link FILENAME} adds \texttt{FILENAME} to the list of files to be passed to the linker at the end of compilation. This is most useful for importing extra libraries needed by new FFI modules.
adam@1725 170 \item \texttt{linker CMD} sets \texttt{CMD} as the command line prefix to use for linking C object files. The command line will be completed with a space-separated list of \texttt{.o} and \texttt{.a} files, \texttt{-L} and \texttt{-l} flags, and finally with a \texttt{-o} flag to set the location where the executable should be written.
adam@1332 171 \item \texttt{minHeap NUMBYTES} sets the initial size for thread-local heaps used in handling requests. These heaps grow automatically as needed (up to any maximum set with \texttt{limit}), but each regrow requires restarting the request handling process.
adam@1816 172 \item \texttt{monoInline TREESIZE} sets how many nodes the AST of a function definition may have before the optimizer stops trying hard to inline calls to that function. (This is one of two options for one of two intermediate languages within the compiler.)
adam@1478 173 \item \texttt{noXsrfProtection URIPREFIX} turns off automatic cross-site request forgery protection for the page handler identified by the given URI prefix. This will avoid checking cryptographic signatures on cookies, which is generally a reasonable idea for some pages, such as login pages that are going to discard all old cookie values, anyway.
adam@1297 174 \item \texttt{onError Module.var} changes the handling of fatal application errors. Instead of displaying a default, ugly error 500 page, the error page will be generated by calling function \texttt{Module.var} on a piece of XML representing the error message. The error handler should have type $\mt{xbody} \to \mt{transaction} \; \mt{page}$. Note that the error handler \emph{cannot} be in the application's main module, since that would register it as explicitly callable via URLs.
adamc@852 175 \item \texttt{path NAME=VALUE} creates a mapping from \texttt{NAME} to \texttt{VALUE}. This mapping may be used at the beginnings of filesystem paths given to various other configuration directives. A path like \texttt{\$NAME/rest} is expanded to \texttt{VALUE/rest}. There is an initial mapping from the empty name (for paths like \texttt{\$/list}) to the directory where the Ur/Web standard library is installed. If you accept the default \texttt{configure} options, this directory is \texttt{/usr/local/lib/urweb/ur}.
adamc@783 176 \item \texttt{prefix PREFIX} sets the prefix included before every URI within the generated application. The default is \texttt{/}.
adamc@783 177 \item \texttt{profile} generates an executable that may be used with gprof.
adam@1752 178 \item \texttt{rewrite KIND FROM TO} gives a rule for rewriting canonical module paths. For instance, the canonical path of a page may be \texttt{Mod1.Mod2.mypage}, while you would rather the page were accessed via a URL containing only \texttt{page}. The directive \texttt{rewrite url Mod1/Mod2/mypage page} would accomplish that. The possible values of \texttt{KIND} determine which kinds of objects are affected. The kind \texttt{all} matches any object, and \texttt{url} matches page URLs. The kinds \texttt{table}, \texttt{sequence}, and \texttt{view} match those sorts of SQL entities, and \texttt{relation} matches any of those three. \texttt{cookie} matches HTTP cookies, and \texttt{style} matches CSS class names. If \texttt{FROM} ends in \texttt{/*}, it is interpreted as a prefix matching rule, and rewriting occurs by replacing only the appropriate prefix of a path with \texttt{TO}. The \texttt{TO} field may be left empty to express the idea of deleting a prefix. For instance, \texttt{rewrite url Main/*} will strip all \texttt{Main/} prefixes from URLs. While the actual external names of relations and styles have parts separated by underscores instead of slashes, all rewrite rules must be written in terms of slashes. An optional suffix of \cd{[-]} for a \cd{rewrite} directive asks to additionally replace all \cd{\_} characters with \cd{-} characters, which can be handy for, e.g., interfacing with an off-the-shelf CSS library that prefers hyphens over underscores.
adamc@1183 179 \item \texttt{safeGet URI} asks to allow the page handler assigned this canonical URI prefix to cause persistent side effects, even if accessed via an HTTP \cd{GET} request.
adamc@783 180 \item \texttt{script URL} adds \texttt{URL} to the list of extra JavaScript files to be included at the beginning of any page that uses JavaScript. This is most useful for importing JavaScript versions of functions found in new FFI modules.
adamc@783 181 \item \texttt{serverOnly Module.ident} registers an FFI function or transaction that may only be run on the server.
adamc@1164 182 \item \texttt{sigfile PATH} sets a path where your application should look for a key to use in cryptographic signing. This is used to prevent cross-site request forgery attacks for any form handler that both reads a cookie and creates side effects. If the referenced file doesn't exist, an application will create it and read its saved data on future invocations. You can also initialize the file manually with any contents at least 16 bytes long; the first 16 bytes will be treated as the key.
adamc@783 183 \item \texttt{sql FILENAME} sets where to write an SQL file with the commands to create the expected database schema. The default is not to create such a file.
adam@1629 184 \item \texttt{timeFormat FMT} accepts a time format string, as processed by the POSIX C function \texttt{strftime()}. This controls the default rendering of $\mt{time}$ values, via the $\mt{show}$ instance for $\mt{time}$.
adamc@783 185 \item \texttt{timeout N} sets to \texttt{N} seconds the amount of time that the generated server will wait after the last contact from a client before determining that that client has exited the application. Clients that remain active will take the timeout setting into account in determining how often to ping the server, so it only makes sense to set a high timeout to cope with browser and network delays and failures. Higher timeouts can lead to more unnecessary client information taking up memory on the server. The timeout goes unused by any page that doesn't involve the \texttt{recv} function, since the server only needs to store per-client information for clients that receive asynchronous messages.
adamc@783 186 \end{itemize}
adamc@701 187
adamc@701 188
adamc@557 189 \subsection{Building an Application}
adamc@557 190
adamc@557 191 To compile project \texttt{P.urp}, simply run
adamc@557 192 \begin{verbatim}
adamc@557 193 urweb P
adamc@557 194 \end{verbatim}
adamc@1198 195 The output executable is a standalone web server. Run it with the command-line argument \texttt{-h} to see which options it takes. If the project file lists a database, the web server will attempt to connect to that database on startup. See Section \ref{structure} for an explanation of the URI mapping convention, which determines how each page of your application may be accessed via URLs.
adamc@557 196
adamc@557 197 To time how long the different compiler phases run, without generating an executable, run
adamc@557 198 \begin{verbatim}
adamc@557 199 urweb -timing P
adamc@557 200 \end{verbatim}
adamc@557 201
adamc@1086 202 To stop the compilation process after type-checking, run
adamc@1086 203 \begin{verbatim}
adamc@1086 204 urweb -tc P
adamc@1086 205 \end{verbatim}
adam@1530 206 It is often worthwhile to run \cd{urweb} in this mode, because later phases of compilation can take significantly longer than type-checking alone, and the type checker catches many errors that would traditionally be found through debugging a running application.
adamc@1086 207
adam@1745 208 A related option is \cd{-dumpTypes}, which, as long as parsing succeeds, outputs to stdout a summary of the kinds of all identifiers declared with \cd{con} and the types of all identifiers declared with \cd{val} or \cd{val rec}. This information is dumped even if there are errors during type inference. Compiler error messages go to stderr, not stdout, so it is easy to distinguish the two kinds of output programmatically. A refined version of this option is \cd{-dumpTypesOnError}, which only has an effect when there are compilation errors.
adam@1531 209
adam@1723 210 It may be useful to combine another option \cd{-unifyMore} with \cd{-dumpTypes}. Ur/Web type inference proceeds in a series of stages, where the first is standard Hindley-Milner type inference as in ML, and the later phases add more complex aspects. By default, an error detected in one phase cuts off the execution of later phases. However, the later phases might still determine more values of unification variables. These value choices might be ``misguided,'' since earlier phases have not come up with reasonable types at a coarser detail level; but the unification decisions may still be useful for debugging and program understanding. So, if a run with \cd{-dumpTypes} leaves unification variables undetermined in positions where you would like to see best-effort guesses instead, consider \cd{-unifyMore}. Note that \cd{-unifyMore} has no effect when type inference succeeds fully, but it may lead to many more error messages when inference fails.
adam@1723 211
adamc@1170 212 To output information relevant to CSS stylesheets (and not finish regular compilation), run
adamc@1170 213 \begin{verbatim}
adamc@1170 214 urweb -css P
adamc@1170 215 \end{verbatim}
adamc@1170 216 The first output line is a list of categories of CSS properties that would be worth setting on the document body. The remaining lines are space-separated pairs of CSS class names and categories of properties that would be worth setting for that class. The category codes are divided into two varieties. Codes that reveal properties of a tag or its (recursive) children are \cd{B} for block-level elements, \cd{C} for table captions, \cd{D} for table cells, \cd{L} for lists, and \cd{T} for tables. Codes that reveal properties of the precise tag that uses a class are \cd{b} for block-level elements, \cd{t} for tables, \cd{d} for table cells, \cd{-} for table rows, \cd{H} for the possibility to set a height, \cd{N} for non-replaced inline-level elements, \cd{R} for replaced inline elements, and \cd{W} for the possibility to set a width.
adamc@1170 217
adam@1733 218 Ur/Web type inference can take a significant amount of time, so it can be helpful to cache type-inferred versions of source files. This mode can be activated by running
adam@1733 219 \begin{verbatim}
adam@1733 220 urweb daemon start
adam@1733 221 \end{verbatim}
adam@1733 222 Further \cd{urweb} invocations in the same working directory will send requests to a background daemon process that reuses type inference results whenever possible, tracking source file dependencies and modification times. To stop the background daemon, run
adam@1733 223 \begin{verbatim}
adam@1733 224 urweb daemon stop
adam@1733 225 \end{verbatim}
adam@1733 226 Communication happens via a UNIX domain socket in file \cd{.urweb\_daemon} in the working directory.
adam@1733 227
adam@1733 228 \medskip
adam@1733 229
adamc@896 230 Some other command-line parameters are accepted:
adamc@896 231 \begin{itemize}
ezyang@1739 232 \item \texttt{-boot}: Run Ur/Web from a build tree (and not from a system install). This is useful if you're testing the compiler and don't want to install it. It forces generation of statically linked executables.
ezyang@1739 233
adam@1875 234 \item \texttt{-ccompiler <PROGRAM>}: Select an alternative C compiler to call with command lines in compiling Ur/Web applications. (It's possible to set the default compiler as part of the \texttt{configure} process, but it may sometimes be useful to override the default.)
adam@1875 235
adamc@896 236 \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@896 237
adamc@896 238 \item \texttt{-dbms [postgres|mysql|sqlite]}: Sets the database backend to use.
adamc@896 239 \begin{itemize}
adamc@896 240 \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@896 241
adamc@896 242 A command sequence like this can initialize a Postgres database, using a file \texttt{app.sql} generated by the compiler:
adamc@896 243 \begin{verbatim}
adamc@896 244 createdb app
adamc@896 245 psql -f app.sql app
adamc@896 246 \end{verbatim}
adamc@896 247
adamc@896 248 \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@896 249
adamc@896 250 A command sequence like this can initialize a MySQL database:
adamc@896 251 \begin{verbatim}
adamc@896 252 echo "CREATE DATABASE app" | mysql
adamc@896 253 mysql -D app <app.sql
adamc@896 254 \end{verbatim}
adamc@896 255
adamc@896 256 \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@896 257
adamc@896 258 A command like this can initialize an SQLite database:
adamc@896 259 \begin{verbatim}
adamc@896 260 sqlite3 path/to/database/file <app.sql
adamc@896 261 \end{verbatim}
adamc@896 262 \end{itemize}
adamc@896 263
adam@1693 264 \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 265
adam@1309 266 \item \texttt{-limit class num}: Equivalent to the \texttt{limit} directive from \texttt{.urp} files
adam@1309 267
adam@1850 268 \item \texttt{-moduleOf FILENAME}: Prints the Ur/Web module name corresponding to source file \texttt{FILENAME}, exiting immediately afterward.
adam@1850 269
adamc@896 270 \item \texttt{-output FILENAME}: Set where the application executable is written.
adamc@896 271
adamc@1127 272 \item \texttt{-path NAME VALUE}: Set the value of path variable \texttt{\$NAME} to \texttt{VALUE}, for use in \texttt{.urp} files.
adamc@1127 273
adam@1335 274 \item \texttt{-prefix PREFIX}: Equivalent to the \texttt{prefix} directive from \texttt{.urp} files
adam@1335 275
adam@1875 276 \item \texttt{-print-ccompiler}: Print the C compiler being used.
adam@1875 277
adam@1923 278 \item \texttt{-print-cinclude}: Print the name of the directory where C/C++ header files are installed.
adam@1923 279
adam@1753 280 \item \texttt{-protocol [http|cgi|fastcgi|static]}: Set the protocol that the generated application speaks.
adamc@896 281 \begin{itemize}
adamc@896 282 \item \texttt{http}: This is the default. It is for building standalone web servers that can be accessed by web browsers directly.
adamc@896 283
adamc@896 284 \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@896 285
adamc@896 286 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@896 287 \begin{verbatim}
adamc@896 288 ScriptAlias /Hello /path/to/hello.exe
adamc@896 289 \end{verbatim}
adamc@896 290
adamc@1163 291 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 292 \begin{verbatim}
adamc@1163 293 Options +ExecCGI
adamc@1163 294 AddHandler cgi-script .exe
adamc@1163 295 \end{verbatim}
adamc@1163 296
adamc@1163 297 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 298 \begin{verbatim}
adamc@1163 299 prefix /dir/script.exe/
adamc@1163 300 \end{verbatim}
adamc@1163 301
adamc@1163 302 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 303
adamc@1164 304 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 305
adamc@896 306 \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@896 307
adamc@896 308 To configure a FastCGI program with Apache, one could combine the above \texttt{ScriptAlias} line with a line like this:
adamc@896 309 \begin{verbatim}
adamc@896 310 FastCgiServer /path/to/hello.exe -idle-timeout 99999
adamc@896 311 \end{verbatim}
adamc@896 312 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@896 313
adam@1753 314 Also see the discussion of the \cd{prefix} directive for CGI above; similar configuration is likely to be necessary for FastCGI. An Ur/Web application won't generally run correctly if it doesn't have a unique URI prefix assigned to it and configured with \cd{prefix}.
adam@1753 315
adamc@896 316 Here is some lighttpd configuration for the same application.
adamc@896 317 \begin{verbatim}
adamc@896 318 fastcgi.server = (
adamc@896 319 "/Hello/" =>
adamc@896 320 (( "bin-path" => "/path/to/hello.exe",
adamc@896 321 "socket" => "/tmp/hello",
adamc@896 322 "check-local" => "disable",
adamc@896 323 "docroot" => "/",
adamc@896 324 "max-procs" => "1"
adamc@896 325 ))
adamc@896 326 )
adamc@896 327 \end{verbatim}
adamc@896 328 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@896 329
adamc@896 330 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 331
adam@1509 332 \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@896 333 \end{itemize}
adamc@896 334
adamc@1127 335 \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 336
adamc@1164 337 \item \texttt{-sigfile PATH}: Same as the \texttt{sigfile} directive in \texttt{.urp} files
adamc@1164 338
adamc@896 339 \item \texttt{-sql FILENAME}: Set where a database set-up SQL script is written.
adamc@1095 340
adamc@1095 341 \item \texttt{-static}: Link the runtime system statically. The default is to link against dynamic libraries.
adamc@896 342 \end{itemize}
adamc@896 343
adam@1297 344 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@556 345
adam@1509 346 \subsection{Tutorial Formatting}
adam@1509 347
adam@1509 348 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 349
adam@1509 350 These input files follow normal Ur syntax, with a few exceptions:
adam@1509 351 \begin{itemize}
adam@1509 352 \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 353 \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 354 \item A comment like \cd{(* * HEADING *)} introduces a section heading, with text \cd{HEADING} of your choice.
adam@1509 355 \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 356 \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 357 \end{itemize}
adam@1509 358
adam@1509 359 A word of warning: as for demo generation, tutorial generation calls Emacs to syntax-highlight Ur code.
adam@1509 360
adam@1522 361 \subsection{Run-Time Options}
adam@1522 362
adam@1522 363 Compiled applications consult a few environment variables to modify their behavior:
adam@1522 364
adam@1522 365 \begin{itemize}
adam@1522 366 \item \cd{URWEB\_NUM\_THREADS}: alternative to the \cd{-t} command-line argument (currently used only by FastCGI)
adam@1522 367 \item \cd{URWEB\_STACK\_SIZE}: size of per-thread stacks, in bytes
as@1564 368 \item \cd{URWEB\_PQ\_CON}: when using PostgreSQL, overrides the compiled-in connection string
adam@1522 369 \end{itemize}
adam@1522 370
adam@1509 371
adamc@529 372 \section{Ur Syntax}
adamc@529 373
adamc@784 374 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@524 375
adamc@524 376 \subsection{Lexical Conventions}
adamc@524 377
adamc@524 378 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@524 379
adamc@524 380 \begin{center}
adamc@524 381 \begin{tabular}{rl}
adamc@524 382 \textbf{\LaTeX} & \textbf{ASCII} \\
adamc@524 383 $\to$ & \cd{->} \\
adam@1687 384 $\longrightarrow$ & \cd{-{}->} \\
adamc@524 385 $\times$ & \cd{*} \\
adamc@524 386 $\lambda$ & \cd{fn} \\
adamc@524 387 $\Rightarrow$ & \cd{=>} \\
adamc@652 388 $\Longrightarrow$ & \cd{==>} \\
adamc@529 389 $\neq$ & \cd{<>} \\
adamc@529 390 $\leq$ & \cd{<=} \\
adamc@529 391 $\geq$ & \cd{>=} \\
adamc@524 392 \\
adamc@524 393 $x$ & Normal textual identifier, not beginning with an uppercase letter \\
adamc@525 394 $X$ & Normal textual identifier, beginning with an uppercase letter \\
adamc@524 395 \end{tabular}
adamc@524 396 \end{center}
adamc@524 397
adamc@525 398 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@524 399
adamc@873 400 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@526 401
adamc@527 402 This version of the manual doesn't include operator precedences; see \texttt{src/urweb.grm} for that.
adamc@527 403
adam@1297 404 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 405
adamc@552 406 \subsection{\label{core}Core Syntax}
adamc@524 407
adamc@524 408 \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@524 409 $$\begin{array}{rrcll}
adamc@524 410 \textrm{Kinds} & \kappa &::=& \mt{Type} & \textrm{proper types} \\
adamc@525 411 &&& \mt{Unit} & \textrm{the trivial constructor} \\
adamc@525 412 &&& \mt{Name} & \textrm{field names} \\
adamc@525 413 &&& \kappa \to \kappa & \textrm{type-level functions} \\
adamc@525 414 &&& \{\kappa\} & \textrm{type-level records} \\
adamc@525 415 &&& (\kappa\times^+) & \textrm{type-level tuples} \\
adamc@652 416 &&& X & \textrm{variable} \\
adam@1574 417 &&& X \longrightarrow \kappa & \textrm{kind-polymorphic type-level function} \\
adamc@529 418 &&& \_\_ & \textrm{wildcard} \\
adamc@525 419 &&& (\kappa) & \textrm{explicit precedence} \\
adamc@524 420 \end{array}$$
adamc@524 421
adamc@524 422 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@524 423 $$\begin{array}{rrcll}
adamc@524 424 \textrm{Explicitness} & ? &::=& :: & \textrm{explicit} \\
adamc@558 425 &&& ::: & \textrm{implicit}
adamc@524 426 \end{array}$$
adamc@524 427
adamc@524 428 \emph{Constructors} are the main class of compile-time-only data. They include proper types and are classified by kinds.
adamc@524 429 $$\begin{array}{rrcll}
adamc@524 430 \textrm{Constructors} & c, \tau &::=& (c) :: \kappa & \textrm{kind annotation} \\
adamc@530 431 &&& \hat{x} & \textrm{constructor variable} \\
adamc@524 432 \\
adamc@525 433 &&& \tau \to \tau & \textrm{function type} \\
adamc@525 434 &&& x \; ? \; \kappa \to \tau & \textrm{polymorphic function type} \\
adamc@652 435 &&& X \longrightarrow \tau & \textrm{kind-polymorphic function type} \\
adamc@525 436 &&& \$ c & \textrm{record type} \\
adamc@524 437 \\
adamc@525 438 &&& c \; c & \textrm{type-level function application} \\
adamc@530 439 &&& \lambda x \; :: \; \kappa \Rightarrow c & \textrm{type-level function abstraction} \\
adamc@524 440 \\
adamc@652 441 &&& X \Longrightarrow c & \textrm{type-level kind-polymorphic function abstraction} \\
adamc@655 442 &&& c [\kappa] & \textrm{type-level kind-polymorphic function application} \\
adamc@652 443 \\
adamc@525 444 &&& () & \textrm{type-level unit} \\
adamc@525 445 &&& \#X & \textrm{field name} \\
adamc@524 446 \\
adamc@525 447 &&& [(c = c)^*] & \textrm{known-length type-level record} \\
adamc@525 448 &&& c \rc c & \textrm{type-level record concatenation} \\
adamc@652 449 &&& \mt{map} & \textrm{type-level record map} \\
adamc@524 450 \\
adamc@558 451 &&& (c,^+) & \textrm{type-level tuple} \\
adamc@525 452 &&& c.n & \textrm{type-level tuple projection ($n \in \mathbb N^+$)} \\
adamc@524 453 \\
adamc@652 454 &&& [c \sim c] \Rightarrow \tau & \textrm{guarded type} \\
adamc@524 455 \\
adamc@529 456 &&& \_ :: \kappa & \textrm{wildcard} \\
adamc@525 457 &&& (c) & \textrm{explicit precedence} \\
adamc@530 458 \\
adamc@530 459 \textrm{Qualified uncapitalized variables} & \hat{x} &::=& x & \textrm{not from a module} \\
adamc@530 460 &&& M.x & \textrm{projection from a module} \\
adamc@525 461 \end{array}$$
adamc@525 462
adam@1579 463 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@655 464
adamc@525 465 Modules of the module system are described by \emph{signatures}.
adamc@525 466 $$\begin{array}{rrcll}
adamc@525 467 \textrm{Signatures} & S &::=& \mt{sig} \; s^* \; \mt{end} & \textrm{constant} \\
adamc@525 468 &&& X & \textrm{variable} \\
adamc@525 469 &&& \mt{functor}(X : S) : S & \textrm{functor} \\
adamc@529 470 &&& S \; \mt{where} \; \mt{con} \; x = c & \textrm{concretizing an abstract constructor} \\
adamc@525 471 &&& M.X & \textrm{projection from a module} \\
adamc@525 472 \\
adamc@525 473 \textrm{Signature items} & s &::=& \mt{con} \; x :: \kappa & \textrm{abstract constructor} \\
adamc@525 474 &&& \mt{con} \; x :: \kappa = c & \textrm{concrete constructor} \\
adamc@528 475 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529 476 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@525 477 &&& \mt{val} \; x : \tau & \textrm{value} \\
adamc@525 478 &&& \mt{structure} \; X : S & \textrm{sub-module} \\
adamc@525 479 &&& \mt{signature} \; X = S & \textrm{sub-signature} \\
adamc@525 480 &&& \mt{include} \; S & \textrm{signature inclusion} \\
adamc@525 481 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@654 482 &&& \mt{class} \; x :: \kappa & \textrm{abstract constructor class} \\
adamc@654 483 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@525 484 \\
adamc@525 485 \textrm{Datatype constructors} & dc &::=& X & \textrm{nullary constructor} \\
adamc@525 486 &&& X \; \mt{of} \; \tau & \textrm{unary constructor} \\
adamc@524 487 \end{array}$$
adamc@524 488
adamc@526 489 \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@526 490 $$\begin{array}{rrcll}
adamc@526 491 \textrm{Patterns} & p &::=& \_ & \textrm{wildcard} \\
adamc@526 492 &&& x & \textrm{variable} \\
adamc@526 493 &&& \ell & \textrm{constant} \\
adamc@526 494 &&& \hat{X} & \textrm{nullary constructor} \\
adamc@526 495 &&& \hat{X} \; p & \textrm{unary constructor} \\
adamc@526 496 &&& \{(x = p,)^*\} & \textrm{rigid record pattern} \\
adamc@526 497 &&& \{(x = p,)^+, \ldots\} & \textrm{flexible record pattern} \\
adamc@852 498 &&& p : \tau & \textrm{type annotation} \\
adamc@527 499 &&& (p) & \textrm{explicit precedence} \\
adamc@526 500 \\
adamc@529 501 \textrm{Qualified capitalized variables} & \hat{X} &::=& X & \textrm{not from a module} \\
adamc@526 502 &&& M.X & \textrm{projection from a module} \\
adamc@526 503 \end{array}$$
adamc@526 504
adamc@527 505 \emph{Expressions} are the main run-time entities, corresponding to both ``expressions'' and ``statements'' in mainstream imperative languages.
adamc@527 506 $$\begin{array}{rrcll}
adamc@527 507 \textrm{Expressions} & e &::=& e : \tau & \textrm{type annotation} \\
adamc@529 508 &&& \hat{x} & \textrm{variable} \\
adamc@529 509 &&& \hat{X} & \textrm{datatype constructor} \\
adamc@527 510 &&& \ell & \textrm{constant} \\
adamc@527 511 \\
adamc@527 512 &&& e \; e & \textrm{function application} \\
adamc@527 513 &&& \lambda x : \tau \Rightarrow e & \textrm{function abstraction} \\
adamc@527 514 &&& e [c] & \textrm{polymorphic function application} \\
adamc@852 515 &&& \lambda [x \; ? \; \kappa] \Rightarrow e & \textrm{polymorphic function abstraction} \\
adamc@655 516 &&& e [\kappa] & \textrm{kind-polymorphic function application} \\
adamc@652 517 &&& X \Longrightarrow e & \textrm{kind-polymorphic function abstraction} \\
adamc@527 518 \\
adamc@527 519 &&& \{(c = e,)^*\} & \textrm{known-length record} \\
adamc@527 520 &&& e.c & \textrm{record field projection} \\
adamc@527 521 &&& e \rc e & \textrm{record concatenation} \\
adamc@527 522 &&& e \rcut c & \textrm{removal of a single record field} \\
adamc@527 523 &&& e \rcutM c & \textrm{removal of multiple record fields} \\
adamc@527 524 \\
adamc@527 525 &&& \mt{let} \; ed^* \; \mt{in} \; e \; \mt{end} & \textrm{local definitions} \\
adamc@527 526 \\
adamc@527 527 &&& \mt{case} \; e \; \mt{of} \; (p \Rightarrow e|)^+ & \textrm{pattern matching} \\
adamc@527 528 \\
adamc@654 529 &&& \lambda [c \sim c] \Rightarrow e & \textrm{guarded expression abstraction} \\
adamc@654 530 &&& e \; ! & \textrm{guarded expression application} \\
adamc@527 531 \\
adamc@527 532 &&& \_ & \textrm{wildcard} \\
adamc@527 533 &&& (e) & \textrm{explicit precedence} \\
adamc@527 534 \\
adamc@527 535 \textrm{Local declarations} & ed &::=& \cd{val} \; x : \tau = e & \textrm{non-recursive value} \\
adam@1797 536 &&& \cd{val} \; \cd{rec} \; (x : \tau = e \; \cd{and})^+ & \textrm{mutually recursive values} \\
adamc@527 537 \end{array}$$
adamc@527 538
adamc@655 539 As with constructors, we include both abstraction and application for kind polymorphism, but applications are only inferred internally.
adamc@655 540
adamc@528 541 \emph{Declarations} primarily bring new symbols into context.
adamc@528 542 $$\begin{array}{rrcll}
adamc@528 543 \textrm{Declarations} & d &::=& \mt{con} \; x :: \kappa = c & \textrm{constructor synonym} \\
adamc@528 544 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529 545 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@528 546 &&& \mt{val} \; x : \tau = e & \textrm{value} \\
adam@1797 547 &&& \mt{val} \; \cd{rec} \; (x : \tau = e \; \mt{and})^+ & \textrm{mutually recursive values} \\
adamc@528 548 &&& \mt{structure} \; X : S = M & \textrm{module definition} \\
adamc@528 549 &&& \mt{signature} \; X = S & \textrm{signature definition} \\
adamc@528 550 &&& \mt{open} \; M & \textrm{module inclusion} \\
adamc@528 551 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@528 552 &&& \mt{open} \; \mt{constraints} \; M & \textrm{inclusion of just the constraints from a module} \\
adamc@528 553 &&& \mt{table} \; x : c & \textrm{SQL table} \\
adam@1594 554 &&& \mt{view} \; x = e & \textrm{SQL view} \\
adamc@528 555 &&& \mt{sequence} \; x & \textrm{SQL sequence} \\
adamc@535 556 &&& \mt{cookie} \; x : \tau & \textrm{HTTP cookie} \\
adamc@784 557 &&& \mt{style} \; x : \tau & \textrm{CSS class} \\
adamc@1085 558 &&& \mt{task} \; e = e & \textrm{recurring task} \\
adamc@528 559 \\
adamc@529 560 \textrm{Modules} & M &::=& \mt{struct} \; d^* \; \mt{end} & \textrm{constant} \\
adamc@529 561 &&& X & \textrm{variable} \\
adamc@529 562 &&& M.X & \textrm{projection} \\
adamc@529 563 &&& M(M) & \textrm{functor application} \\
adamc@529 564 &&& \mt{functor}(X : S) : S = M & \textrm{functor abstraction} \\
adamc@528 565 \end{array}$$
adamc@528 566
adamc@528 567 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@527 568
adam@1594 569 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@784 570
adamc@529 571 \subsection{Shorthands}
adamc@529 572
adamc@529 573 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@529 574
adamc@529 575 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@529 576
adamc@529 577 A record type may be written $\{(c = c,)^*\}$, which elaborates to $\$[(c = c,)^*]$.
adamc@529 578
adamc@533 579 The notation $[c_1, \ldots, c_n]$ is shorthand for $[c_1 = (), \ldots, c_n = ()]$.
adamc@533 580
adam@1350 581 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@529 582
adam@1687 583 The syntax $()$ expands to $\{\}$ as a pattern or expression.
adam@1687 584
adamc@852 585 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@529 586
adam@1574 587 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 588
adam@1306 589 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 590
adamc@529 591 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@529 592
adamc@529 593 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@529 594
adamc@654 595 A signature item or declaration $\mt{class} \; x = \lambda y \Rightarrow c$ may be abbreviated $\mt{class} \; x \; y = c$.
adamc@529 596
adam@1738 597 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@529 598
adamc@852 599 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@529 600
adamc@852 601 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@852 602
adam@1797 603 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@529 604
adamc@529 605 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@529 606
adamc@852 607 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@852 608
adamc@853 609 A declaration $\mt{table} \; x : \{(c = c,)^*\}$ is elaborated into $\mt{table} \; x : [(c = c,)^*]$.
adamc@529 610
adamc@529 611 The syntax $\mt{where} \; \mt{type}$ is an alternate form of $\mt{where} \; \mt{con}$.
adamc@529 612
adamc@529 613 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@529 614
adamc@529 615 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@529 616
adamc@784 617 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@529 618
adamc@530 619
adamc@530 620 \section{Static Semantics}
adamc@530 621
adamc@530 622 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@530 623
adam@1891 624 The notations used here are the standard ones of programming language semantics. They are probably the most effective way to convey this information. At the same time, most Ur/Web users can probably get by \emph{without} knowing the contents of this section! If you're interested in diving into the details of Ur typing but are unfamiliar with ``inference rule notation,'' I recommend the following book:
adam@1891 625 \begin{quote}
adam@1891 626 Benjamin C. Pierce, \emph{Types and Programming Languages}, MIT Press, 2002.
adam@1891 627 \end{quote}
adam@1891 628
adamc@530 629 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@530 630 \begin{itemize}
adamc@655 631 \item $\Gamma \vdash \kappa$ expresses kind well-formedness.
adamc@530 632 \item $\Gamma \vdash c :: \kappa$ assigns a kind to a constructor in a context.
adamc@530 633 \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@531 634 \item $\Gamma \vdash c \hookrightarrow C$ proves that record constructor $c$ decomposes into set $C$ of field names and record constructors.
adamc@530 635 \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@530 636 \item $\Gamma \vdash e : \tau$ is a standard typing judgment.
adamc@534 637 \item $\Gamma \vdash p \leadsto \Gamma; \tau$ combines typing of patterns with calculation of which new variables they bind.
adamc@537 638 \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@537 639 \item $\Gamma \vdash S \equiv S$ is the signature equivalence judgment.
adamc@536 640 \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@530 641 \item $\Gamma \vdash M : S$ is the module signature checking judgment.
adamc@537 642 \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@539 643 \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@530 644 \end{itemize}
adamc@530 645
adamc@655 646
adamc@655 647 \subsection{Kind Well-Formedness}
adamc@655 648
adamc@655 649 $$\infer{\Gamma \vdash \mt{Type}}{}
adamc@655 650 \quad \infer{\Gamma \vdash \mt{Unit}}{}
adamc@655 651 \quad \infer{\Gamma \vdash \mt{Name}}{}
adamc@655 652 \quad \infer{\Gamma \vdash \kappa_1 \to \kappa_2}{
adamc@655 653 \Gamma \vdash \kappa_1
adamc@655 654 & \Gamma \vdash \kappa_2
adamc@655 655 }
adamc@655 656 \quad \infer{\Gamma \vdash \{\kappa\}}{
adamc@655 657 \Gamma \vdash \kappa
adamc@655 658 }
adamc@655 659 \quad \infer{\Gamma \vdash (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@655 660 \forall i: \Gamma \vdash \kappa_i
adamc@655 661 }$$
adamc@655 662
adamc@655 663 $$\infer{\Gamma \vdash X}{
adamc@655 664 X \in \Gamma
adamc@655 665 }
adamc@655 666 \quad \infer{\Gamma \vdash X \longrightarrow \kappa}{
adamc@655 667 \Gamma, X \vdash \kappa
adamc@655 668 }$$
adamc@655 669
adamc@530 670 \subsection{Kinding}
adamc@530 671
adamc@655 672 We write $[X \mapsto \kappa_1]\kappa_2$ for capture-avoiding substitution of $\kappa_1$ for $X$ in $\kappa_2$.
adamc@655 673
adamc@530 674 $$\infer{\Gamma \vdash (c) :: \kappa :: \kappa}{
adamc@530 675 \Gamma \vdash c :: \kappa
adamc@530 676 }
adamc@530 677 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530 678 x :: \kappa \in \Gamma
adamc@530 679 }
adamc@530 680 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530 681 x :: \kappa = c \in \Gamma
adamc@530 682 }$$
adamc@530 683
adamc@530 684 $$\infer{\Gamma \vdash M.x :: \kappa}{
adamc@537 685 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 686 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = \kappa
adamc@530 687 }
adamc@530 688 \quad \infer{\Gamma \vdash M.x :: \kappa}{
adamc@537 689 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 690 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@530 691 }$$
adamc@530 692
adamc@530 693 $$\infer{\Gamma \vdash \tau_1 \to \tau_2 :: \mt{Type}}{
adamc@530 694 \Gamma \vdash \tau_1 :: \mt{Type}
adamc@530 695 & \Gamma \vdash \tau_2 :: \mt{Type}
adamc@530 696 }
adamc@530 697 \quad \infer{\Gamma \vdash x \; ? \: \kappa \to \tau :: \mt{Type}}{
adamc@530 698 \Gamma, x :: \kappa \vdash \tau :: \mt{Type}
adamc@530 699 }
adamc@655 700 \quad \infer{\Gamma \vdash X \longrightarrow \tau :: \mt{Type}}{
adamc@655 701 \Gamma, X \vdash \tau :: \mt{Type}
adamc@655 702 }
adamc@530 703 \quad \infer{\Gamma \vdash \$c :: \mt{Type}}{
adamc@530 704 \Gamma \vdash c :: \{\mt{Type}\}
adamc@530 705 }$$
adamc@530 706
adamc@530 707 $$\infer{\Gamma \vdash c_1 \; c_2 :: \kappa_2}{
adamc@530 708 \Gamma \vdash c_1 :: \kappa_1 \to \kappa_2
adamc@530 709 & \Gamma \vdash c_2 :: \kappa_1
adamc@530 710 }
adamc@530 711 \quad \infer{\Gamma \vdash \lambda x \; :: \; \kappa_1 \Rightarrow c :: \kappa_1 \to \kappa_2}{
adamc@530 712 \Gamma, x :: \kappa_1 \vdash c :: \kappa_2
adamc@530 713 }$$
adamc@530 714
adamc@655 715 $$\infer{\Gamma \vdash c[\kappa'] :: [X \mapsto \kappa']\kappa}{
adamc@655 716 \Gamma \vdash c :: X \to \kappa
adamc@655 717 & \Gamma \vdash \kappa'
adamc@655 718 }
adamc@655 719 \quad \infer{\Gamma \vdash X \Longrightarrow c :: X \to \kappa}{
adamc@655 720 \Gamma, X \vdash c :: \kappa
adamc@655 721 }$$
adamc@655 722
adamc@530 723 $$\infer{\Gamma \vdash () :: \mt{Unit}}{}
adamc@530 724 \quad \infer{\Gamma \vdash \#X :: \mt{Name}}{}$$
adamc@530 725
adamc@530 726 $$\infer{\Gamma \vdash [\overline{c_i = c'_i}] :: \{\kappa\}}{
adamc@530 727 \forall i: \Gamma \vdash c_i : \mt{Name}
adamc@530 728 & \Gamma \vdash c'_i :: \kappa
adamc@530 729 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@530 730 }
adamc@530 731 \quad \infer{\Gamma \vdash c_1 \rc c_2 :: \{\kappa\}}{
adamc@530 732 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530 733 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@530 734 & \Gamma \vdash c_1 \sim c_2
adamc@530 735 }$$
adamc@530 736
adamc@655 737 $$\infer{\Gamma \vdash \mt{map} :: (\kappa_1 \to \kappa_2) \to \{\kappa_1\} \to \{\kappa_2\}}{}$$
adamc@530 738
adamc@573 739 $$\infer{\Gamma \vdash (\overline c) :: (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@573 740 \forall i: \Gamma \vdash c_i :: \kappa_i
adamc@530 741 }
adamc@573 742 \quad \infer{\Gamma \vdash c.i :: \kappa_i}{
adamc@573 743 \Gamma \vdash c :: (\kappa_1 \times \ldots \times \kappa_n)
adamc@530 744 }$$
adamc@530 745
adamc@655 746 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow \tau :: \mt{Type}}{
adamc@655 747 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530 748 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@655 749 & \Gamma, c_1 \sim c_2 \vdash \tau :: \mt{Type}
adamc@530 750 }$$
adamc@530 751
adamc@531 752 \subsection{Record Disjointness}
adamc@531 753
adamc@531 754 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@558 755 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@558 756 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@558 757 & \forall c'_1 \in C_1, c'_2 \in C_2: \Gamma \vdash c'_1 \sim c'_2
adamc@531 758 }
adamc@531 759 \quad \infer{\Gamma \vdash X \sim X'}{
adamc@531 760 X \neq X'
adamc@531 761 }$$
adamc@531 762
adamc@531 763 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@531 764 c'_1 \sim c'_2 \in \Gamma
adamc@558 765 & \Gamma \vdash c'_1 \hookrightarrow C_1
adamc@558 766 & \Gamma \vdash c'_2 \hookrightarrow C_2
adamc@558 767 & c_1 \in C_1
adamc@558 768 & c_2 \in C_2
adamc@531 769 }$$
adamc@531 770
adamc@531 771 $$\infer{\Gamma \vdash c \hookrightarrow \{c\}}{}
adamc@531 772 \quad \infer{\Gamma \vdash [\overline{c = c'}] \hookrightarrow \{\overline{c}\}}{}
adamc@531 773 \quad \infer{\Gamma \vdash c_1 \rc c_2 \hookrightarrow C_1 \cup C_2}{
adamc@531 774 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@531 775 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@531 776 }
adamc@531 777 \quad \infer{\Gamma \vdash c \hookrightarrow C}{
adamc@531 778 \Gamma \vdash c \equiv c'
adamc@531 779 & \Gamma \vdash c' \hookrightarrow C
adamc@531 780 }
adamc@531 781 \quad \infer{\Gamma \vdash \mt{map} \; f \; c \hookrightarrow C}{
adamc@531 782 \Gamma \vdash c \hookrightarrow C
adamc@531 783 }$$
adamc@531 784
adamc@541 785 \subsection{\label{definitional}Definitional Equality}
adamc@532 786
adamc@655 787 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@532 788
adamc@532 789 $$\infer{\Gamma \vdash c \equiv c}{}
adamc@532 790 \quad \infer{\Gamma \vdash c_1 \equiv c_2}{
adamc@532 791 \Gamma \vdash c_2 \equiv c_1
adamc@532 792 }
adamc@532 793 \quad \infer{\Gamma \vdash c_1 \equiv c_3}{
adamc@532 794 \Gamma \vdash c_1 \equiv c_2
adamc@532 795 & \Gamma \vdash c_2 \equiv c_3
adamc@532 796 }
adamc@532 797 \quad \infer{\Gamma \vdash \mathcal C[c_1] \equiv \mathcal C[c_2]}{
adamc@532 798 \Gamma \vdash c_1 \equiv c_2
adamc@532 799 }$$
adamc@532 800
adamc@532 801 $$\infer{\Gamma \vdash x \equiv c}{
adamc@532 802 x :: \kappa = c \in \Gamma
adamc@532 803 }
adamc@532 804 \quad \infer{\Gamma \vdash M.x \equiv c}{
adamc@537 805 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 806 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@532 807 }
adamc@532 808 \quad \infer{\Gamma \vdash (\overline c).i \equiv c_i}{}$$
adamc@532 809
adamc@532 810 $$\infer{\Gamma \vdash (\lambda x :: \kappa \Rightarrow c) \; c' \equiv [x \mapsto c'] c}{}
adamc@655 811 \quad \infer{\Gamma \vdash (X \Longrightarrow c) [\kappa] \equiv [X \mapsto \kappa] c}{}$$
adamc@655 812
adamc@655 813 $$\infer{\Gamma \vdash c_1 \rc c_2 \equiv c_2 \rc c_1}{}
adamc@532 814 \quad \infer{\Gamma \vdash c_1 \rc (c_2 \rc c_3) \equiv (c_1 \rc c_2) \rc c_3}{}$$
adamc@532 815
adamc@532 816 $$\infer{\Gamma \vdash [] \rc c \equiv c}{}
adamc@532 817 \quad \infer{\Gamma \vdash [\overline{c_1 = c'_1}] \rc [\overline{c_2 = c'_2}] \equiv [\overline{c_1 = c'_1}, \overline{c_2 = c'_2}]}{}$$
adamc@532 818
adamc@655 819 $$\infer{\Gamma \vdash \mt{map} \; f \; [] \equiv []}{}
adamc@655 820 \quad \infer{\Gamma \vdash \mt{map} \; f \; ([c_1 = c_2] \rc c) \equiv [c_1 = f \; c_2] \rc \mt{map} \; f \; c}{}$$
adamc@532 821
adamc@532 822 $$\infer{\Gamma \vdash \mt{map} \; (\lambda x \Rightarrow x) \; c \equiv c}{}
adamc@655 823 \quad \infer{\Gamma \vdash \mt{map} \; f \; (\mt{map} \; f' \; c)
adamc@655 824 \equiv \mt{map} \; (\lambda x \Rightarrow f \; (f' \; x)) \; c}{}$$
adamc@532 825
adamc@532 826 $$\infer{\Gamma \vdash \mt{map} \; f \; (c_1 \rc c_2) \equiv \mt{map} \; f \; c_1 \rc \mt{map} \; f \; c_2}{}$$
adamc@531 827
adamc@534 828 \subsection{Expression Typing}
adamc@533 829
adamc@873 830 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@533 831
adamc@533 832 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@533 833
adamc@533 834 $$\infer{\Gamma \vdash e : \tau : \tau}{
adamc@533 835 \Gamma \vdash e : \tau
adamc@533 836 }
adamc@533 837 \quad \infer{\Gamma \vdash e : \tau}{
adamc@533 838 \Gamma \vdash e : \tau'
adamc@533 839 & \Gamma \vdash \tau' \equiv \tau
adamc@533 840 }
adamc@533 841 \quad \infer{\Gamma \vdash \ell : T(\ell)}{}$$
adamc@533 842
adamc@533 843 $$\infer{\Gamma \vdash x : \mathcal I(\tau)}{
adamc@533 844 x : \tau \in \Gamma
adamc@533 845 }
adamc@533 846 \quad \infer{\Gamma \vdash M.x : \mathcal I(\tau)}{
adamc@537 847 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 848 & \mt{proj}(M, \overline{s}, \mt{val} \; x) = \tau
adamc@533 849 }
adamc@533 850 \quad \infer{\Gamma \vdash X : \mathcal I(\tau)}{
adamc@533 851 X : \tau \in \Gamma
adamc@533 852 }
adamc@533 853 \quad \infer{\Gamma \vdash M.X : \mathcal I(\tau)}{
adamc@537 854 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 855 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \tau
adamc@533 856 }$$
adamc@533 857
adamc@533 858 $$\infer{\Gamma \vdash e_1 \; e_2 : \tau_2}{
adamc@533 859 \Gamma \vdash e_1 : \tau_1 \to \tau_2
adamc@533 860 & \Gamma \vdash e_2 : \tau_1
adamc@533 861 }
adamc@533 862 \quad \infer{\Gamma \vdash \lambda x : \tau_1 \Rightarrow e : \tau_1 \to \tau_2}{
adamc@533 863 \Gamma, x : \tau_1 \vdash e : \tau_2
adamc@533 864 }$$
adamc@533 865
adamc@533 866 $$\infer{\Gamma \vdash e [c] : [x \mapsto c]\tau}{
adamc@533 867 \Gamma \vdash e : x :: \kappa \to \tau
adamc@533 868 & \Gamma \vdash c :: \kappa
adamc@533 869 }
adamc@852 870 \quad \infer{\Gamma \vdash \lambda [x \; ? \; \kappa] \Rightarrow e : x \; ? \; \kappa \to \tau}{
adamc@533 871 \Gamma, x :: \kappa \vdash e : \tau
adamc@533 872 }$$
adamc@533 873
adamc@655 874 $$\infer{\Gamma \vdash e [\kappa] : [X \mapsto \kappa]\tau}{
adamc@655 875 \Gamma \vdash e : X \longrightarrow \tau
adamc@655 876 & \Gamma \vdash \kappa
adamc@655 877 }
adamc@655 878 \quad \infer{\Gamma \vdash X \Longrightarrow e : X \longrightarrow \tau}{
adamc@655 879 \Gamma, X \vdash e : \tau
adamc@655 880 }$$
adamc@655 881
adamc@533 882 $$\infer{\Gamma \vdash \{\overline{c = e}\} : \{\overline{c : \tau}\}}{
adamc@533 883 \forall i: \Gamma \vdash c_i :: \mt{Name}
adamc@533 884 & \Gamma \vdash e_i : \tau_i
adamc@533 885 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@533 886 }
adamc@533 887 \quad \infer{\Gamma \vdash e.c : \tau}{
adamc@533 888 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533 889 }
adamc@533 890 \quad \infer{\Gamma \vdash e_1 \rc e_2 : \$(c_1 \rc c_2)}{
adamc@533 891 \Gamma \vdash e_1 : \$c_1
adamc@533 892 & \Gamma \vdash e_2 : \$c_2
adamc@573 893 & \Gamma \vdash c_1 \sim c_2
adamc@533 894 }$$
adamc@533 895
adamc@533 896 $$\infer{\Gamma \vdash e \rcut c : \$c'}{
adamc@533 897 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533 898 }
adamc@533 899 \quad \infer{\Gamma \vdash e \rcutM c : \$c'}{
adamc@533 900 \Gamma \vdash e : \$(c \rc c')
adamc@533 901 }$$
adamc@533 902
adamc@533 903 $$\infer{\Gamma \vdash \mt{let} \; \overline{ed} \; \mt{in} \; e \; \mt{end} : \tau}{
adamc@533 904 \Gamma \vdash \overline{ed} \leadsto \Gamma'
adamc@533 905 & \Gamma' \vdash e : \tau
adamc@533 906 }
adamc@533 907 \quad \infer{\Gamma \vdash \mt{case} \; e \; \mt{of} \; \overline{p \Rightarrow e} : \tau}{
adamc@533 908 \forall i: \Gamma \vdash p_i \leadsto \Gamma_i, \tau'
adamc@533 909 & \Gamma_i \vdash e_i : \tau
adamc@533 910 }$$
adamc@533 911
adamc@573 912 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow e : \lambda [c_1 \sim c_2] \Rightarrow \tau}{
adamc@533 913 \Gamma \vdash c_1 :: \{\kappa\}
adamc@655 914 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@533 915 & \Gamma, c_1 \sim c_2 \vdash e : \tau
adamc@662 916 }
adamc@662 917 \quad \infer{\Gamma \vdash e \; ! : \tau}{
adamc@662 918 \Gamma \vdash e : [c_1 \sim c_2] \Rightarrow \tau
adamc@662 919 & \Gamma \vdash c_1 \sim c_2
adamc@533 920 }$$
adamc@533 921
adamc@534 922 \subsection{Pattern Typing}
adamc@534 923
adamc@534 924 $$\infer{\Gamma \vdash \_ \leadsto \Gamma; \tau}{}
adamc@534 925 \quad \infer{\Gamma \vdash x \leadsto \Gamma, x : \tau; \tau}{}
adamc@534 926 \quad \infer{\Gamma \vdash \ell \leadsto \Gamma; T(\ell)}{}$$
adamc@534 927
adamc@534 928 $$\infer{\Gamma \vdash X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534 929 X : \overline{x ::: \mt{Type}} \to \tau \in \Gamma
adamc@534 930 & \textrm{$\tau$ not a function type}
adamc@534 931 }
adamc@534 932 \quad \infer{\Gamma \vdash X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534 933 X : \overline{x ::: \mt{Type}} \to \tau'' \to \tau \in \Gamma
adamc@534 934 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534 935 }$$
adamc@534 936
adamc@534 937 $$\infer{\Gamma \vdash M.X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537 938 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 939 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau
adamc@534 940 & \textrm{$\tau$ not a function type}
adamc@534 941 }$$
adamc@534 942
adamc@534 943 $$\infer{\Gamma \vdash M.X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537 944 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 945 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau'' \to \tau
adamc@534 946 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534 947 }$$
adamc@534 948
adamc@534 949 $$\infer{\Gamma \vdash \{\overline{x = p}\} \leadsto \Gamma_n; \{\overline{x = \tau}\}}{
adamc@534 950 \Gamma_0 = \Gamma
adamc@534 951 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534 952 }
adamc@534 953 \quad \infer{\Gamma \vdash \{\overline{x = p}, \ldots\} \leadsto \Gamma_n; \$([\overline{x = \tau}] \rc c)}{
adamc@534 954 \Gamma_0 = \Gamma
adamc@534 955 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534 956 }$$
adamc@534 957
adamc@852 958 $$\infer{\Gamma \vdash p : \tau \leadsto \Gamma'; \tau}{
adamc@852 959 \Gamma \vdash p \leadsto \Gamma'; \tau'
adamc@852 960 & \Gamma \vdash \tau' \equiv \tau
adamc@852 961 }$$
adamc@852 962
adamc@535 963 \subsection{Declaration Typing}
adamc@535 964
adamc@535 965 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@535 966
adamc@558 967 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@537 968 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@535 969
adamc@535 970 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535 971 \quad \infer{\Gamma \vdash d, \overline{d} \leadsto \Gamma''}{
adamc@535 972 \Gamma \vdash d \leadsto \Gamma'
adamc@535 973 & \Gamma' \vdash \overline{d} \leadsto \Gamma''
adamc@535 974 }$$
adamc@535 975
adamc@535 976 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@535 977 \Gamma \vdash c :: \kappa
adamc@535 978 }
adamc@535 979 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@535 980 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@535 981 }$$
adamc@535 982
adamc@535 983 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537 984 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 985 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@535 986 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@535 987 }$$
adamc@535 988
adamc@535 989 $$\infer{\Gamma \vdash \mt{val} \; x : \tau = e \leadsto \Gamma, x : \tau}{
adamc@535 990 \Gamma \vdash e : \tau
adamc@535 991 }$$
adamc@535 992
adamc@535 993 $$\infer{\Gamma \vdash \mt{val} \; \mt{rec} \; \overline{x : \tau = e} \leadsto \Gamma, \overline{x : \tau}}{
adamc@535 994 \forall i: \Gamma, \overline{x : \tau} \vdash e_i : \tau_i
adamc@535 995 & \textrm{$e_i$ starts with an expression $\lambda$, optionally preceded by constructor and disjointness $\lambda$s}
adamc@535 996 }$$
adamc@535 997
adamc@535 998 $$\infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : S}{
adamc@535 999 \Gamma \vdash M : S
adamc@558 1000 & \textrm{ $M$ not a constant or application}
adamc@535 1001 }
adamc@558 1002 \quad \infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : \mt{selfify}(X, \overline{s})}{
adamc@558 1003 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@539 1004 }$$
adamc@539 1005
adamc@539 1006 $$\infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@535 1007 \Gamma \vdash S
adamc@535 1008 }$$
adamc@535 1009
adamc@537 1010 $$\infer{\Gamma \vdash \mt{open} \; M \leadsto \Gamma, \mathcal O(M, \overline{s})}{
adamc@537 1011 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535 1012 }$$
adamc@535 1013
adamc@535 1014 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma}{
adamc@535 1015 \Gamma \vdash c_1 :: \{\kappa\}
adamc@535 1016 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@535 1017 & \Gamma \vdash c_1 \sim c_2
adamc@535 1018 }
adamc@537 1019 \quad \infer{\Gamma \vdash \mt{open} \; \mt{constraints} \; M \leadsto \Gamma, \mathcal O_c(M, \overline{s})}{
adamc@537 1020 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535 1021 }$$
adamc@535 1022
adamc@784 1023 $$\infer{\Gamma \vdash \mt{table} \; x : c \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_table} \; c \; []}{
adamc@535 1024 \Gamma \vdash c :: \{\mt{Type}\}
adamc@535 1025 }
adam@1594 1026 \quad \infer{\Gamma \vdash \mt{view} \; x = e \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_view} \; c}{
adam@1594 1027 \Gamma \vdash e :: \mt{Basis}.\mt{sql\_query} \; [] \; [] \; (\mt{map} \; (\lambda \_ \Rightarrow []) \; c') \; c
adamc@784 1028 }$$
adamc@784 1029
adamc@784 1030 $$\infer{\Gamma \vdash \mt{sequence} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_sequence}}{}$$
adamc@535 1031
adamc@535 1032 $$\infer{\Gamma \vdash \mt{cookie} \; x : \tau \leadsto \Gamma, x : \mt{Basis}.\mt{http\_cookie} \; \tau}{
adamc@535 1033 \Gamma \vdash \tau :: \mt{Type}
adamc@784 1034 }
adamc@784 1035 \quad \infer{\Gamma \vdash \mt{style} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{css\_class}}{}$$
adamc@535 1036
adamc@1085 1037 $$\infer{\Gamma \vdash \mt{task} \; e_1 = e_2 \leadsto \Gamma}{
adam@1348 1038 \Gamma \vdash e_1 :: \mt{Basis}.\mt{task\_kind} \; \tau
adam@1348 1039 & \Gamma \vdash e_2 :: \tau \to \mt{Basis}.\mt{transaction} \; \{\}
adamc@1085 1040 }$$
adamc@1085 1041
adamc@535 1042 $$\infer{\overline{y}; x; \Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535 1043 \quad \infer{\overline{y}; x; \Gamma \vdash X \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to x \; \overline{y}}{
adamc@535 1044 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535 1045 }
adamc@535 1046 \quad \infer{\overline{y}; x; \Gamma \vdash X \; \mt{of} \; \tau \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to \tau \to x \; \overline{y}}{
adamc@535 1047 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535 1048 }$$
adamc@535 1049
adamc@537 1050 \subsection{Signature Item Typing}
adamc@537 1051
adamc@537 1052 We appeal to a signature item analogue of the $\mathcal O$ function from the last subsection.
adamc@537 1053
adam@1797 1054 This is the first judgment where we deal with constructor classes, for the $\mt{class}$ forms. We will omit their special handling in this formal specification. Section \ref{typeclasses} gives an informal description of how constructor classes influence type inference.
adam@1797 1055
adamc@537 1056 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@537 1057 \quad \infer{\Gamma \vdash s, \overline{s} \leadsto \Gamma''}{
adamc@537 1058 \Gamma \vdash s \leadsto \Gamma'
adamc@537 1059 & \Gamma' \vdash \overline{s} \leadsto \Gamma''
adamc@537 1060 }$$
adamc@537 1061
adamc@537 1062 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}
adamc@537 1063 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@537 1064 \Gamma \vdash c :: \kappa
adamc@537 1065 }
adamc@537 1066 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@537 1067 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@537 1068 }$$
adamc@537 1069
adamc@537 1070 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537 1071 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1072 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1073 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@537 1074 }$$
adamc@537 1075
adamc@537 1076 $$\infer{\Gamma \vdash \mt{val} \; x : \tau \leadsto \Gamma, x : \tau}{
adamc@537 1077 \Gamma \vdash \tau :: \mt{Type}
adamc@537 1078 }$$
adamc@537 1079
adamc@537 1080 $$\infer{\Gamma \vdash \mt{structure} \; X : S \leadsto \Gamma, X : S}{
adamc@537 1081 \Gamma \vdash S
adamc@537 1082 }
adamc@537 1083 \quad \infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@537 1084 \Gamma \vdash S
adamc@537 1085 }$$
adamc@537 1086
adamc@537 1087 $$\infer{\Gamma \vdash \mt{include} \; S \leadsto \Gamma, \mathcal O(\overline{s})}{
adamc@537 1088 \Gamma \vdash S
adamc@537 1089 & \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1090 }$$
adamc@537 1091
adamc@537 1092 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma, c_1 \sim c_2}{
adamc@537 1093 \Gamma \vdash c_1 :: \{\kappa\}
adamc@537 1094 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@537 1095 }$$
adamc@537 1096
adamc@784 1097 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784 1098 \Gamma \vdash c :: \kappa
adamc@537 1099 }
adamc@784 1100 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}$$
adamc@537 1101
adamc@536 1102 \subsection{Signature Compatibility}
adamc@536 1103
adam@1797 1104 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 1105
adamc@537 1106 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 1107
adamc@536 1108 $$\infer{\Gamma \vdash S \equiv S}{}
adamc@536 1109 \quad \infer{\Gamma \vdash S_1 \equiv S_2}{
adamc@536 1110 \Gamma \vdash S_2 \equiv S_1
adamc@536 1111 }
adamc@536 1112 \quad \infer{\Gamma \vdash X \equiv S}{
adamc@536 1113 X = S \in \Gamma
adamc@536 1114 }
adamc@536 1115 \quad \infer{\Gamma \vdash M.X \equiv S}{
adamc@537 1116 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1117 & \mt{proj}(M, \overline{s}, \mt{signature} \; X) = S
adamc@536 1118 }$$
adamc@536 1119
adamc@536 1120 $$\infer{\Gamma \vdash S \; \mt{where} \; \mt{con} \; x = c \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa = c \; \overline{s_2} \; \mt{end}}{
adamc@536 1121 \Gamma \vdash S \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa \; \overline{s_2} \; \mt{end}
adamc@536 1122 & \Gamma \vdash c :: \kappa
adamc@537 1123 }
adamc@537 1124 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s^1} \; \mt{include} \; S \; \overline{s^2} \; \mt{end} \equiv \mt{sig} \; \overline{s^1} \; \overline{s} \; \overline{s^2} \; \mt{end}}{
adamc@537 1125 \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@536 1126 }$$
adamc@536 1127
adamc@536 1128 $$\infer{\Gamma \vdash S_1 \leq S_2}{
adamc@536 1129 \Gamma \vdash S_1 \equiv S_2
adamc@536 1130 }
adamc@536 1131 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \mt{end}}{}
adamc@537 1132 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; s' \; \overline{s'} \; \mt{end}}{
adamc@537 1133 \Gamma \vdash \overline{s} \leq s'
adamc@537 1134 & \Gamma \vdash s' \leadsto \Gamma'
adamc@537 1135 & \Gamma' \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \overline{s'} \; \mt{end}
adamc@537 1136 }$$
adamc@537 1137
adamc@537 1138 $$\infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537 1139 \Gamma \vdash s \leq s'
adamc@537 1140 }
adamc@537 1141 \quad \infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537 1142 \Gamma \vdash s \leadsto \Gamma'
adamc@537 1143 & \Gamma' \vdash \overline{s} \leq s'
adamc@536 1144 }$$
adamc@536 1145
adamc@536 1146 $$\infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 \leq \mt{functor} (X : S'_1) : S'_2}{
adamc@536 1147 \Gamma \vdash S'_1 \leq S_1
adamc@536 1148 & \Gamma, X : S'_1 \vdash S_2 \leq S'_2
adamc@536 1149 }$$
adamc@536 1150
adamc@537 1151 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@537 1152 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}
adamc@558 1153 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type}}{}$$
adamc@537 1154
adamc@537 1155 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(y)} \to \mt{Type}}{
adamc@537 1156 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1157 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1158 }$$
adamc@537 1159
adamc@784 1160 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@784 1161 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}$$
adamc@537 1162
adamc@537 1163 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \mt{\kappa} = c_2}{
adamc@537 1164 \Gamma \vdash c_1 \equiv c_2
adamc@537 1165 }
adamc@784 1166 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \kappa = c_2}{
adamc@537 1167 \Gamma \vdash c_1 \equiv c_2
adamc@537 1168 }$$
adamc@537 1169
adamc@537 1170 $$\infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537 1171 \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1172 }$$
adamc@537 1173
adamc@537 1174 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537 1175 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1176 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1177 & \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1178 }$$
adamc@537 1179
adamc@537 1180 $$\infer{\Gamma \vdash \cdot \leq \cdot}{}
adamc@537 1181 \quad \infer{\Gamma \vdash X; \overline{dc} \leq X; \overline{dc'}}{
adamc@537 1182 \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1183 }
adamc@537 1184 \quad \infer{\Gamma \vdash X \; \mt{of} \; \tau_1; \overline{dc} \leq X \; \mt{of} \; \tau_2; \overline{dc'}}{
adamc@537 1185 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537 1186 & \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1187 }$$
adamc@537 1188
adamc@537 1189 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x = \mt{datatype} \; M'.z'}{
adamc@537 1190 \Gamma \vdash M.z \equiv M'.z'
adamc@537 1191 }$$
adamc@537 1192
adamc@537 1193 $$\infer{\Gamma \vdash \mt{val} \; x : \tau_1 \leq \mt{val} \; x : \tau_2}{
adamc@537 1194 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537 1195 }
adamc@537 1196 \quad \infer{\Gamma \vdash \mt{structure} \; X : S_1 \leq \mt{structure} \; X : S_2}{
adamc@537 1197 \Gamma \vdash S_1 \leq S_2
adamc@537 1198 }
adamc@537 1199 \quad \infer{\Gamma \vdash \mt{signature} \; X = S_1 \leq \mt{signature} \; X = S_2}{
adamc@537 1200 \Gamma \vdash S_1 \leq S_2
adamc@537 1201 & \Gamma \vdash S_2 \leq S_1
adamc@537 1202 }$$
adamc@537 1203
adamc@537 1204 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leq \mt{constraint} \; c'_1 \sim c'_2}{
adamc@537 1205 \Gamma \vdash c_1 \equiv c'_1
adamc@537 1206 & \Gamma \vdash c_2 \equiv c'_2
adamc@537 1207 }$$
adamc@537 1208
adamc@655 1209 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{class} \; x :: \kappa}{}
adamc@655 1210 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{class} \; x :: \kappa}{}
adamc@655 1211 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{class} \; x :: \kappa = c_2}{
adamc@537 1212 \Gamma \vdash c_1 \equiv c_2
adamc@537 1213 }$$
adamc@537 1214
adam@1797 1215 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leq \mt{class} \; x :: \kappa}{}
adam@1797 1216 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leq \mt{class} \; x :: \kappa}{}
adam@1797 1217 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c_1 \leq \mt{class} \; x :: \kappa = c_2}{
adam@1797 1218 \Gamma \vdash c_1 \equiv c_2
adam@1797 1219 }$$
adam@1797 1220
adamc@538 1221 \subsection{Module Typing}
adamc@538 1222
adamc@538 1223 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 1224
adamc@538 1225 $$\infer{\Gamma \vdash M : S}{
adamc@538 1226 \Gamma \vdash M : S'
adamc@538 1227 & \Gamma \vdash S' \leq S
adamc@538 1228 }
adamc@538 1229 \quad \infer{\Gamma \vdash \mt{struct} \; \overline{d} \; \mt{end} : \mt{sig} \; \mt{sigOf}(\overline{d}) \; \mt{end}}{
adamc@538 1230 \Gamma \vdash \overline{d} \leadsto \Gamma'
adamc@538 1231 }
adamc@538 1232 \quad \infer{\Gamma \vdash X : S}{
adamc@538 1233 X : S \in \Gamma
adamc@538 1234 }$$
adamc@538 1235
adamc@538 1236 $$\infer{\Gamma \vdash M.X : S}{
adamc@538 1237 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@538 1238 & \mt{proj}(M, \overline{s}, \mt{structure} \; X) = S
adamc@538 1239 }$$
adamc@538 1240
adamc@538 1241 $$\infer{\Gamma \vdash M_1(M_2) : [X \mapsto M_2]S_2}{
adamc@538 1242 \Gamma \vdash M_1 : \mt{functor}(X : S_1) : S_2
adamc@538 1243 & \Gamma \vdash M_2 : S_1
adamc@538 1244 }
adamc@538 1245 \quad \infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 = M : \mt{functor} (X : S_1) : S_2}{
adamc@538 1246 \Gamma \vdash S_1
adamc@538 1247 & \Gamma, X : S_1 \vdash S_2
adamc@538 1248 & \Gamma, X : S_1 \vdash M : S_2
adamc@538 1249 }$$
adamc@538 1250
adamc@538 1251 \begin{eqnarray*}
adamc@538 1252 \mt{sigOf}(\cdot) &=& \cdot \\
adamc@538 1253 \mt{sigOf}(s \; \overline{s'}) &=& \mt{sigOf}(s) \; \mt{sigOf}(\overline{s'}) \\
adamc@538 1254 \\
adamc@538 1255 \mt{sigOf}(\mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@538 1256 \mt{sigOf}(\mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \overline{dc} \\
adamc@538 1257 \mt{sigOf}(\mt{datatype} \; x = \mt{datatype} \; M.z) &=& \mt{datatype} \; x = \mt{datatype} \; M.z \\
adamc@538 1258 \mt{sigOf}(\mt{val} \; x : \tau = e) &=& \mt{val} \; x : \tau \\
adamc@538 1259 \mt{sigOf}(\mt{val} \; \mt{rec} \; \overline{x : \tau = e}) &=& \overline{\mt{val} \; x : \tau} \\
adamc@538 1260 \mt{sigOf}(\mt{structure} \; X : S = M) &=& \mt{structure} \; X : S \\
adamc@538 1261 \mt{sigOf}(\mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@538 1262 \mt{sigOf}(\mt{open} \; M) &=& \mt{include} \; S \textrm{ (where $\Gamma \vdash M : S$)} \\
adamc@538 1263 \mt{sigOf}(\mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@538 1264 \mt{sigOf}(\mt{open} \; \mt{constraints} \; M) &=& \cdot \\
adamc@538 1265 \mt{sigOf}(\mt{table} \; x : c) &=& \mt{table} \; x : c \\
adam@1594 1266 \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 1267 \mt{sigOf}(\mt{sequence} \; x) &=& \mt{sequence} \; x \\
adamc@538 1268 \mt{sigOf}(\mt{cookie} \; x : \tau) &=& \mt{cookie} \; x : \tau \\
adam@1797 1269 \mt{sigOf}(\mt{style} \; x) &=& \mt{style} \; x
adamc@538 1270 \end{eqnarray*}
adamc@539 1271 \begin{eqnarray*}
adamc@539 1272 \mt{selfify}(M, \cdot) &=& \cdot \\
adamc@558 1273 \mt{selfify}(M, s \; \overline{s'}) &=& \mt{selfify}(M, s) \; \mt{selfify}(M, \overline{s'}) \\
adamc@539 1274 \\
adamc@539 1275 \mt{selfify}(M, \mt{con} \; x :: \kappa) &=& \mt{con} \; x :: \kappa = M.x \\
adamc@539 1276 \mt{selfify}(M, \mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@539 1277 \mt{selfify}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \mt{datatype} \; M.x \\
adamc@539 1278 \mt{selfify}(M, \mt{datatype} \; x = \mt{datatype} \; M'.z) &=& \mt{datatype} \; x = \mt{datatype} \; M'.z \\
adamc@539 1279 \mt{selfify}(M, \mt{val} \; x : \tau) &=& \mt{val} \; x : \tau \\
adamc@539 1280 \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 1281 \mt{selfify}(M, \mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@539 1282 \mt{selfify}(M, \mt{include} \; S) &=& \mt{include} \; S \\
adamc@539 1283 \mt{selfify}(M, \mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@655 1284 \mt{selfify}(M, \mt{class} \; x :: \kappa) &=& \mt{class} \; x :: \kappa = M.x \\
adamc@655 1285 \mt{selfify}(M, \mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@539 1286 \end{eqnarray*}
adamc@539 1287
adamc@540 1288 \subsection{Module Projection}
adamc@540 1289
adamc@540 1290 \begin{eqnarray*}
adamc@540 1291 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \\
adamc@540 1292 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa, c) \\
adamc@540 1293 \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 1294 \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 1295 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})$)} \\
adamc@655 1296 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \to \mt{Type} \\
adamc@655 1297 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa \to \mt{Type}, c) \\
adamc@540 1298 \\
adamc@540 1299 \mt{proj}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc} \; \overline{s}, \mt{datatype} \; x) &=& (\overline{y}, \overline{dc}) \\
adamc@540 1300 \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 1301 \\
adamc@540 1302 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, \mt{val} \; x) &=& \tau \\
adamc@540 1303 \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 1304 \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 1305 \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 1306 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \in \overline{dc}$)} \\
adamc@540 1307 \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 1308 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \; \mt{of} \; \tau \in \overline{dc}$)} \\
adamc@540 1309 \\
adamc@540 1310 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, \mt{structure} \; X) &=& S \\
adamc@540 1311 \\
adamc@540 1312 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, \mt{signature} \; X) &=& S \\
adamc@540 1313 \\
adamc@540 1314 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1315 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1316 \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 1317 \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 1318 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@540 1319 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1320 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1321 \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 1322 \mt{proj}(M, \mt{constraint} \; c_1 \sim c_2 \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@655 1323 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@655 1324 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1325 \end{eqnarray*}
adamc@540 1326
adamc@541 1327
adamc@541 1328 \section{Type Inference}
adamc@541 1329
adamc@541 1330 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 1331
adamc@541 1332 \subsection{Basic Unification}
adamc@541 1333
adamc@560 1334 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 1335
adamc@656 1336 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 1337
adamc@541 1338 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 1339
adamc@541 1340 \subsection{Unifying Record Types}
adamc@541 1341
adamc@570 1342 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 1343
adamc@656 1344 \subsection{\label{typeclasses}Constructor Classes}
adamc@541 1345
adamc@784 1346 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 1347
adam@1797 1348 Constructor classes are integrated with the module system. A constructor class of kind $\kappa$ is just a constructor of kind $\kappa$. By marking such a constructor $c$ as a constructor class, the programmer instructs the type inference engine to, in each scope, record all values of types $c \; c_1 \; \ldots \; c_n$ as \emph{instances}. Any function argument whose type is of such a form is treated as implicit, to be determined by examining the current instance database. Any suitably kinded constructor within a module may be exposed as a constructor class from outside the module, simply by using a $\mt{class}$ signature item instead of a $\mt{con}$ signature item in the module's signature.
adam@1797 1349
adam@1797 1350 The ``dictionary encoding'' often used in Haskell implementations is made explicit in Ur. Constructor class instances are just properly typed values, and they can also be considered as ``proofs'' of membership in the class. In some cases, it is useful to pass these proofs around explicitly. An underscore written where a proof is expected will also be inferred, if possible, from the current instance database.
adam@1797 1351
adam@1797 1352 Just as for constructors, constructors classes may be exported from modules, and they may be exported as concrete or abstract. Concrete constructor classes have their ``real'' definitions exposed, so that client code may add new instances freely. Automatic inference of concrete class instances will not generally work, so abstract classes are almost always the right choice. They are useful as ``predicates'' that can be used to enforce invariants, as we will see in some definitions of SQL syntax in the Ur/Web standard library. Free extension of a concrete class is easily supported by exporting a constructor function from a module, since the class implementation will be concrete within the module.
adamc@541 1353
adamc@541 1354 \subsection{Reverse-Engineering Record Types}
adamc@541 1355
adamc@656 1356 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 1357
adamc@541 1358 \subsection{Implicit Arguments in Functor Applications}
adamc@541 1359
adamc@656 1360 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 1361
adamc@541 1362
adamc@542 1363 \section{The Ur Standard Library}
adamc@542 1364
adamc@542 1365 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 1366
adamc@542 1367 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 1368
adamc@542 1369 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 1370 $$\begin{array}{l}
adamc@542 1371 \mt{type} \; \mt{int} \\
adamc@542 1372 \mt{type} \; \mt{float} \\
adamc@873 1373 \mt{type} \; \mt{char} \\
adamc@542 1374 \mt{type} \; \mt{string} \\
adamc@542 1375 \mt{type} \; \mt{time} \\
adamc@785 1376 \mt{type} \; \mt{blob} \\
adamc@542 1377 \\
adamc@542 1378 \mt{type} \; \mt{unit} = \{\} \\
adamc@542 1379 \\
adamc@542 1380 \mt{datatype} \; \mt{bool} = \mt{False} \mid \mt{True} \\
adamc@542 1381 \\
adamc@785 1382 \mt{datatype} \; \mt{option} \; \mt{t} = \mt{None} \mid \mt{Some} \; \mt{of} \; \mt{t} \\
adamc@785 1383 \\
adamc@785 1384 \mt{datatype} \; \mt{list} \; \mt{t} = \mt{Nil} \mid \mt{Cons} \; \mt{of} \; \mt{t} \times \mt{list} \; \mt{t}
adamc@542 1385 \end{array}$$
adamc@542 1386
adamc@1123 1387 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 1388
adam@1297 1389 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 1390 $$\begin{array}{l}
adam@1297 1391 \mt{con} \; \mt{variant} :: \{\mt{Type}\} \to \mt{Type} \\
adam@1297 1392 \mt{val} \; \mt{make} : \mt{nm} :: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{ts} ::: \{\mt{Type}\} \to [[\mt{nm}] \sim \mt{ts}] \Rightarrow \mt{t} \to \mt{variant} \; ([\mt{nm} = \mt{t}] \rc \mt{ts}) \\
adam@1297 1393 \mt{val} \; \mt{match} : \mt{ts} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{variant} \; \mt{ts} \to \$(\mt{map} \; (\lambda \mt{t'} \Rightarrow \mt{t'} \to \mt{t}) \; \mt{ts}) \to \mt{t}
adam@1297 1394 \end{array}$$
adam@1297 1395
adamc@657 1396 Another important generic Ur element comes at the beginning of \texttt{top.urs}.
adamc@657 1397
adamc@657 1398 $$\begin{array}{l}
adamc@657 1399 \mt{con} \; \mt{folder} :: \mt{K} \longrightarrow \{\mt{K}\} \to \mt{Type} \\
adamc@657 1400 \\
adamc@657 1401 \mt{val} \; \mt{fold} : \mt{K} \longrightarrow \mt{tf} :: (\{\mt{K}\} \to \mt{Type}) \\
adamc@657 1402 \hspace{.1in} \to (\mt{nm} :: \mt{Name} \to \mt{v} :: \mt{K} \to \mt{r} :: \{\mt{K}\} \to [[\mt{nm}] \sim \mt{r}] \Rightarrow \\
adamc@657 1403 \hspace{.2in} \mt{tf} \; \mt{r} \to \mt{tf} \; ([\mt{nm} = \mt{v}] \rc \mt{r})) \\
adamc@657 1404 \hspace{.1in} \to \mt{tf} \; [] \\
adamc@657 1405 \hspace{.1in} \to \mt{r} :: \{\mt{K}\} \to \mt{folder} \; \mt{r} \to \mt{tf} \; \mt{r}
adamc@657 1406 \end{array}$$
adamc@657 1407
adamc@657 1408 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 1409
adamc@664 1410 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 1411
adamc@542 1412
adamc@542 1413 \section{The Ur/Web Standard Library}
adamc@542 1414
adam@1400 1415 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 1416
adamc@658 1417 \subsection{Monads}
adamc@658 1418
adamc@658 1419 The Ur Basis defines the monad constructor class from Haskell.
adamc@658 1420
adamc@658 1421 $$\begin{array}{l}
adamc@658 1422 \mt{class} \; \mt{monad} :: \mt{Type} \to \mt{Type} \\
adamc@658 1423 \mt{val} \; \mt{return} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t} ::: \mt{Type} \\
adamc@658 1424 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658 1425 \hspace{.1in} \to \mt{t} \to \mt{m} \; \mt{t} \\
adamc@658 1426 \mt{val} \; \mt{bind} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t1} ::: \mt{Type} \to \mt{t2} ::: \mt{Type} \\
adamc@658 1427 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658 1428 \hspace{.1in} \to \mt{m} \; \mt{t1} \to (\mt{t1} \to \mt{m} \; \mt{t2}) \\
adam@1544 1429 \hspace{.1in} \to \mt{m} \; \mt{t2} \\
adam@1544 1430 \mt{val} \; \mt{mkMonad} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \\
adam@1544 1431 \hspace{.1in} \to \{\mt{Return} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{m} \; \mt{t}, \\
adam@1544 1432 \hspace{.3in} \mt{Bind} : \mt{t1} ::: \mt{Type} \to \mt{t2} ::: \mt{Type} \to \mt{m} \; \mt{t1} \to (\mt{t1} \to \mt{m} \; \mt{t2}) \to \mt{m} \; \mt{t2}\} \\
adam@1544 1433 \hspace{.1in} \to \mt{monad} \; \mt{m}
adamc@658 1434 \end{array}$$
adamc@658 1435
adam@1687 1436 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 1437
adamc@542 1438 \subsection{Transactions}
adamc@542 1439
adamc@542 1440 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 1441 $$\begin{array}{l}
adamc@542 1442 \mt{con} \; \mt{transaction} :: \mt{Type} \to \mt{Type} \\
adamc@658 1443 \mt{val} \; \mt{transaction\_monad} : \mt{monad} \; \mt{transaction}
adamc@542 1444 \end{array}$$
adamc@542 1445
adamc@1123 1446 For debugging purposes, a transactional function is provided for outputting a string on the server process' \texttt{stderr}.
adamc@1123 1447 $$\begin{array}{l}
adamc@1123 1448 \mt{val} \; \mt{debug} : \mt{string} \to \mt{transaction} \; \mt{unit}
adamc@1123 1449 \end{array}$$
adamc@1123 1450
adamc@542 1451 \subsection{HTTP}
adamc@542 1452
adam@1797 1453 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 1454 $$\begin{array}{l}
adamc@786 1455 \mt{con} \; \mt{http\_cookie} :: \mt{Type} \to \mt{Type} \\
adamc@786 1456 \mt{val} \; \mt{getCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; (\mt{option} \; \mt{t}) \\
adamc@1050 1457 \mt{val} \; \mt{setCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \{\mt{Value} : \mt{t}, \mt{Expires} : \mt{option} \; \mt{time}, \mt{Secure} : \mt{bool}\} \to \mt{transaction} \; \mt{unit} \\
adamc@1050 1458 \mt{val} \; \mt{clearCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; \mt{unit}
adamc@786 1459 \end{array}$$
adamc@786 1460
adamc@786 1461 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 1462 $$\begin{array}{l}
adamc@786 1463 \mt{type} \; \mt{url} \\
adamc@786 1464 \mt{val} \; \mt{bless} : \mt{string} \to \mt{url} \\
adamc@786 1465 \mt{val} \; \mt{checkUrl} : \mt{string} \to \mt{option} \; \mt{url}
adamc@786 1466 \end{array}$$
adamc@786 1467 $\mt{bless}$ raises a runtime error if the string passed to it fails the URL policy.
adamc@786 1468
adam@1400 1469 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 1470 $$\begin{array}{l}
adamc@1085 1471 \mt{val} \; \mt{currentUrl} : \mt{transaction} \; \mt{url} \\
adamc@1085 1472 \mt{val} \; \mt{url} : \mt{transaction} \; \mt{page} \to \mt{url}
adamc@1085 1473 \end{array}$$
adamc@1085 1474
adamc@1085 1475 Page generation may be interrupted at any time with a request to redirect to a particular URL instead.
adamc@1085 1476 $$\begin{array}{l}
adamc@1085 1477 \mt{val} \; \mt{redirect} : \mt{t} ::: \mt{Type} \to \mt{url} \to \mt{transaction} \; \mt{t}
adamc@1085 1478 \end{array}$$
adamc@1085 1479
adam@1400 1480 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 1481 $$\begin{array}{l}
adamc@786 1482 \mt{type} \; \mt{file} \\
adamc@786 1483 \mt{val} \; \mt{fileName} : \mt{file} \to \mt{option} \; \mt{string} \\
adamc@786 1484 \mt{val} \; \mt{fileMimeType} : \mt{file} \to \mt{string} \\
adamc@786 1485 \mt{val} \; \mt{fileData} : \mt{file} \to \mt{blob}
adamc@786 1486 \end{array}$$
adamc@786 1487
adam@1799 1488 It is also possible to get HTTP request headers and environment variables, and set HTTP response headers, using abstract types similar to the one for URLs.
adam@1465 1489
adam@1465 1490 $$\begin{array}{l}
adam@1465 1491 \mt{type} \; \mt{requestHeader} \\
adam@1465 1492 \mt{val} \; \mt{blessRequestHeader} : \mt{string} \to \mt{requestHeader} \\
adam@1465 1493 \mt{val} \; \mt{checkRequestHeader} : \mt{string} \to \mt{option} \; \mt{requestHeader} \\
adam@1465 1494 \mt{val} \; \mt{getHeader} : \mt{requestHeader} \to \mt{transaction} \; (\mt{option} \; \mt{string}) \\
adam@1465 1495 \\
adam@1799 1496 \mt{type} \; \mt{envVar} \\
adam@1799 1497 \mt{val} \; \mt{blessEnvVar} : \mt{string} \to \mt{envVar} \\
adam@1799 1498 \mt{val} \; \mt{checkEnvVar} : \mt{string} \to \mt{option} \; \mt{envVar} \\
adam@1799 1499 \mt{val} \; \mt{getenv} : \mt{envVar} \to \mt{transaction} \; (\mt{option} \; \mt{string}) \\
adam@1799 1500 \\
adam@1465 1501 \mt{type} \; \mt{responseHeader} \\
adam@1465 1502 \mt{val} \; \mt{blessResponseHeader} : \mt{string} \to \mt{responseHeader} \\
adam@1465 1503 \mt{val} \; \mt{checkResponseHeader} : \mt{string} \to \mt{option} \; \mt{responseHeader} \\
adam@1465 1504 \mt{val} \; \mt{setHeader} : \mt{responseHeader} \to \mt{string} \to \mt{transaction} \; \mt{unit}
adam@1465 1505 \end{array}$$
adam@1465 1506
adamc@786 1507 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 1508 $$\begin{array}{l}
adamc@786 1509 \mt{type} \; \mt{mimeType} \\
adamc@786 1510 \mt{val} \; \mt{blessMime} : \mt{string} \to \mt{mimeType} \\
adamc@786 1511 \mt{val} \; \mt{checkMime} : \mt{string} \to \mt{option} \; \mt{mimeType} \\
adamc@786 1512 \mt{val} \; \mt{returnBlob} : \mt{t} ::: \mt{Type} \to \mt{blob} \to \mt{mimeType} \to \mt{transaction} \; \mt{t}
adamc@542 1513 \end{array}$$
adamc@542 1514
adamc@543 1515 \subsection{SQL}
adamc@543 1516
adam@1400 1517 Everything about SQL database access is restricted to server-side code.
adam@1400 1518
adamc@543 1519 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 1520 $$\begin{array}{l}
adamc@785 1521 \mt{con} \; \mt{sql\_table} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785 1522 \end{array}$$
adamc@785 1523 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 1524
adamc@785 1525 We also have the simpler type family of SQL views, which have no keys.
adamc@785 1526 $$\begin{array}{l}
adamc@785 1527 \mt{con} \; \mt{sql\_view} :: \{\mt{Type}\} \to \mt{Type}
adamc@543 1528 \end{array}$$
adamc@543 1529
adamc@785 1530 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 1531 $$\begin{array}{l}
adamc@785 1532 \mt{class} \; \mt{fieldsOf} :: \mt{Type} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1533 \mt{val} \; \mt{fieldsOf\_table} : \mt{fs} ::: \{\mt{Type}\} \to \mt{keys} ::: \{\{\mt{Unit}\}\} \to \mt{fieldsOf} \; (\mt{sql\_table} \; \mt{fs} \; \mt{keys}) \; \mt{fs} \\
adamc@785 1534 \mt{val} \; \mt{fieldsOf\_view} : \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; (\mt{sql\_view} \; \mt{fs}) \; \mt{fs}
adamc@785 1535 \end{array}$$
adamc@785 1536
adamc@785 1537 \subsubsection{Table Constraints}
adamc@785 1538
adamc@785 1539 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 1540
adamc@785 1541 $$\begin{array}{l}
adamc@785 1542 \mt{con} \; \mt{primary\_key} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type} \\
adamc@785 1543 \mt{val} \; \mt{no\_primary\_key} : \mt{fs} ::: \{\mt{Type}\} \to \mt{primary\_key} \; \mt{fs} \; [] \\
adamc@785 1544 \mt{val} \; \mt{primary\_key} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{key1} :: \mt{Name} \to \mt{keys} :: \{\mt{Type}\} \\
adamc@785 1545 \hspace{.1in} \to [[\mt{key1}] \sim \mt{keys}] \Rightarrow [[\mt{key1} = \mt{t}] \rc \mt{keys} \sim \mt{rest}] \\
adamc@785 1546 \hspace{.1in} \Rightarrow \$([\mt{key1} = \mt{sql\_injectable\_prim} \; \mt{t}] \rc \mt{map} \; \mt{sql\_injectable\_prim} \; \mt{keys}) \\
adamc@785 1547 \hspace{.1in} \to \mt{primary\_key} \; ([\mt{key1} = \mt{t}] \rc \mt{keys} \rc \mt{rest}) \; [\mt{Pkey} = [\mt{key1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{keys}]
adamc@785 1548 \end{array}$$
adamc@785 1549 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 1550
adamc@785 1551 A type family stands for sets of named constraints of the remaining varieties.
adamc@785 1552 $$\begin{array}{l}
adamc@785 1553 \mt{con} \; \mt{sql\_constraints} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785 1554 \end{array}$$
adamc@785 1555 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 1556
adamc@785 1557 There is a type family of individual, unnamed constraints.
adamc@785 1558 $$\begin{array}{l}
adamc@785 1559 \mt{con} \; \mt{sql\_constraint} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \mt{Type}
adamc@785 1560 \end{array}$$
adamc@785 1561 The first argument is the same as above, and the second argument gives the key columns for just this constraint.
adamc@785 1562
adamc@785 1563 We have operations for assembling constraints into constraint sets.
adamc@785 1564 $$\begin{array}{l}
adamc@785 1565 \mt{val} \; \mt{no\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_constraints} \; \mt{fs} \; [] \\
adamc@785 1566 \mt{val} \; \mt{one\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{unique} ::: \{\mt{Unit}\} \to \mt{name} :: \mt{Name} \\
adamc@785 1567 \hspace{.1in} \to \mt{sql\_constraint} \; \mt{fs} \; \mt{unique} \to \mt{sql\_constraints} \; \mt{fs} \; [\mt{name} = \mt{unique}] \\
adamc@785 1568 \mt{val} \; \mt{join\_constraints} : \mt{fs} ::: \{\mt{Type}\} \to \mt{uniques1} ::: \{\{\mt{Unit}\}\} \to \mt{uniques2} ::: \{\{\mt{Unit}\}\} \to [\mt{uniques1} \sim \mt{uniques2}] \\
adamc@785 1569 \hspace{.1in} \Rightarrow \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques1} \to \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques2} \to \mt{sql\_constraints} \; \mt{fs} \; (\mt{uniques1} \rc \mt{uniques2})
adamc@785 1570 \end{array}$$
adamc@785 1571
adamc@785 1572 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 1573 $$\begin{array}{l}
adamc@785 1574 \mt{val} \; \mt{unique} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{unique1} :: \mt{Name} \to \mt{unique} :: \{\mt{Type}\} \\
adamc@785 1575 \hspace{.1in} \to [[\mt{unique1}] \sim \mt{unique}] \Rightarrow [[\mt{unique1} = \mt{t}] \rc \mt{unique} \sim \mt{rest}] \\
adamc@785 1576 \hspace{.1in} \Rightarrow \mt{sql\_constraint} \; ([\mt{unique1} = \mt{t}] \rc \mt{unique} \rc \mt{rest}) \; ([\mt{unique1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{unique})
adamc@785 1577 \end{array}$$
adamc@785 1578
adamc@785 1579 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 1580 $$\begin{array}{l}
adamc@785 1581 \mt{class} \; \mt{linkable} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@785 1582 \mt{val} \; \mt{linkable\_same} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; \mt{t} \\
adamc@785 1583 \mt{val} \; \mt{linkable\_from\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; (\mt{option} \; \mt{t}) \; \mt{t} \\
adamc@785 1584 \mt{val} \; \mt{linkable\_to\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@785 1585 \end{array}$$
adamc@785 1586
adamc@785 1587 The $\mt{matching}$ type family uses $\mt{linkable}$ to define when two keys match up type-wise.
adamc@785 1588 $$\begin{array}{l}
adamc@785 1589 \mt{con} \; \mt{matching} :: \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1590 \mt{val} \; \mt{mat\_nil} : \mt{matching} \; [] \; [] \\
adamc@785 1591 \mt{val} \; \mt{mat\_cons} : \mt{t1} ::: \mt{Type} \to \mt{rest1} ::: \{\mt{Type}\} \to \mt{t2} ::: \mt{Type} \to \mt{rest2} ::: \{\mt{Type}\} \to \mt{nm1} :: \mt{Name} \to \mt{nm2} :: \mt{Name} \\
adamc@785 1592 \hspace{.1in} \to [[\mt{nm1}] \sim \mt{rest1}] \Rightarrow [[\mt{nm2}] \sim \mt{rest2}] \Rightarrow \mt{linkable} \; \mt{t1} \; \mt{t2} \to \mt{matching} \; \mt{rest1} \; \mt{rest2} \\
adamc@785 1593 \hspace{.1in} \to \mt{matching} \; ([\mt{nm1} = \mt{t1}] \rc \mt{rest1}) \; ([\mt{nm2} = \mt{t2}] \rc \mt{rest2})
adamc@785 1594 \end{array}$$
adamc@785 1595
adamc@785 1596 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 1597 $$\begin{array}{l}
adamc@785 1598 \mt{con} \; \mt{propagation\_mode} :: \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1599 \mt{val} \; \mt{restrict} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1600 \mt{val} \; \mt{cascade} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1601 \mt{val} \; \mt{no\_action} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1602 \mt{val} \; \mt{set\_null} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; (\mt{map} \; \mt{option} \; \mt{fs})
adamc@785 1603 \end{array}$$
adamc@785 1604
adamc@785 1605 Finally, we put these ingredient together to define the \texttt{FOREIGN KEY} constraint function.
adamc@785 1606 $$\begin{array}{l}
adamc@785 1607 \mt{val} \; \mt{foreign\_key} : \mt{mine1} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{mine} ::: \{\mt{Type}\} \to \mt{munused} ::: \{\mt{Type}\} \to \mt{foreign} ::: \{\mt{Type}\} \\
adamc@785 1608 \hspace{.1in} \to \mt{funused} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{uniques} ::: \{\{\mt{Unit}\}\} \\
adamc@785 1609 \hspace{.1in} \to [[\mt{mine1}] \sim \mt{mine}] \Rightarrow [[\mt{mine1} = \mt{t}] \rc \mt{mine} \sim \mt{munused}] \Rightarrow [\mt{foreign} \sim \mt{funused}] \Rightarrow [[\mt{nm}] \sim \mt{uniques}] \\
adamc@785 1610 \hspace{.1in} \Rightarrow \mt{matching} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}) \; \mt{foreign} \\
adamc@785 1611 \hspace{.1in} \to \mt{sql\_table} \; (\mt{foreign} \rc \mt{funused}) \; ([\mt{nm} = \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{foreign}] \rc \mt{uniques}) \\
adamc@785 1612 \hspace{.1in} \to \{\mt{OnDelete} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}), \\
adamc@785 1613 \hspace{.2in} \mt{OnUpdate} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine})\} \\
adamc@785 1614 \hspace{.1in} \to \mt{sql\_constraint} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine} \rc \mt{munused}) \; []
adamc@785 1615 \end{array}$$
adamc@785 1616
adamc@785 1617 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 1618 $$\begin{array}{l}
adam@1778 1619 \mt{val} \; \mt{check} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; [] \; [] \; \mt{fs} \; \mt{bool} \to \mt{sql\_constraint} \; \mt{fs} \; []
adamc@785 1620 \end{array}$$
adamc@785 1621
adamc@785 1622 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 1623
adamc@784 1624
adamc@543 1625 \subsubsection{Queries}
adamc@543 1626
adam@1400 1627 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 1628 $$\begin{array}{l}
adam@1400 1629 \mt{con} \; \mt{sql\_query} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@1193 1630 \mt{val} \; \mt{sql\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400 1631 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1632 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543 1633 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1634 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1193 1635 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adam@1400 1636 \hspace{.1in} \Rightarrow \{\mt{Rows} : \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}, \\
adamc@1193 1637 \hspace{.2in} \mt{OrderBy} : \mt{sql\_order\_by} \; (\mt{free} \rc \mt{tables}) \; \mt{selectedExps}, \\
adamc@543 1638 \hspace{.2in} \mt{Limit} : \mt{sql\_limit}, \\
adamc@543 1639 \hspace{.2in} \mt{Offset} : \mt{sql\_offset}\} \\
adam@1400 1640 \hspace{.1in} \to \mt{sql\_query} \; \mt{free} \; \mt{afree} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1641 \end{array}$$
adamc@543 1642
adamc@545 1643 Queries are used by folding over their results inside transactions.
adamc@545 1644 $$\begin{array}{l}
adam@1400 1645 \mt{val} \; \mt{query} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to [\mt{tables} \sim \mt{exps}] \Rightarrow \mt{state} ::: \mt{Type} \to \mt{sql\_query} \; [] \; [] \; \mt{tables} \; \mt{exps} \\
adamc@658 1646 \hspace{.1in} \to (\$(\mt{exps} \rc \mt{map} \; (\lambda \mt{fields} :: \{\mt{Type}\} \Rightarrow \$\mt{fields}) \; \mt{tables}) \\
adamc@545 1647 \hspace{.2in} \to \mt{state} \to \mt{transaction} \; \mt{state}) \\
adamc@545 1648 \hspace{.1in} \to \mt{state} \to \mt{transaction} \; \mt{state}
adamc@545 1649 \end{array}$$
adamc@545 1650
adam@1400 1651 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 1652 $$\begin{array}{l}
adam@1400 1653 \mt{con} \; \mt{sql\_query1} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@543 1654 \\
adamc@543 1655 \mt{type} \; \mt{sql\_relop} \\
adamc@543 1656 \mt{val} \; \mt{sql\_union} : \mt{sql\_relop} \\
adamc@543 1657 \mt{val} \; \mt{sql\_intersect} : \mt{sql\_relop} \\
adamc@543 1658 \mt{val} \; \mt{sql\_except} : \mt{sql\_relop} \\
adam@1400 1659 \mt{val} \; \mt{sql\_relop} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400 1660 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adam@1400 1661 \hspace{.1in} \to \mt{tables1} ::: \{\{\mt{Type}\}\} \\
adamc@543 1662 \hspace{.1in} \to \mt{tables2} ::: \{\{\mt{Type}\}\} \\
adamc@543 1663 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1664 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@543 1665 \hspace{.1in} \to \mt{sql\_relop} \\
adam@1458 1666 \hspace{.1in} \to \mt{bool} \; (* \; \mt{ALL} \; *) \\
adam@1400 1667 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables1} \; \mt{selectedFields} \; \mt{selectedExps} \\
adam@1400 1668 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables2} \; \mt{selectedFields} \; \mt{selectedExps} \\
adam@1400 1669 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{selectedFields} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1670 \end{array}$$
adamc@543 1671
adamc@543 1672 $$\begin{array}{l}
adamc@1193 1673 \mt{val} \; \mt{sql\_query1} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400 1674 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1675 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543 1676 \hspace{.1in} \to \mt{grouped} ::: \{\{\mt{Type}\}\} \\
adamc@543 1677 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1678 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1085 1679 \hspace{.1in} \to \mt{empties} :: \{\mt{Unit}\} \\
adamc@1193 1680 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adamc@1193 1681 \hspace{.1in} \Rightarrow [\mt{free} \sim \mt{grouped}] \\
adam@1400 1682 \hspace{.1in} \Rightarrow [\mt{afree} \sim \mt{tables}] \\
adamc@1193 1683 \hspace{.1in} \Rightarrow [\mt{empties} \sim \mt{selectedFields}] \\
adamc@1085 1684 \hspace{.1in} \Rightarrow \{\mt{Distinct} : \mt{bool}, \\
adamc@1193 1685 \hspace{.2in} \mt{From} : \mt{sql\_from\_items} \; \mt{free} \; \mt{tables}, \\
adam@1778 1686 \hspace{.2in} \mt{Where} : \mt{sql\_exp} \; (\mt{free} \rc \mt{tables}) \; \mt{afree} \; [] \; \mt{bool}, \\
adamc@543 1687 \hspace{.2in} \mt{GroupBy} : \mt{sql\_subset} \; \mt{tables} \; \mt{grouped}, \\
adam@1778 1688 \hspace{.2in} \mt{Having} : \mt{sql\_exp} \; (\mt{free} \rc \mt{grouped}) \; (\mt{afree} \rc \mt{tables}) \; [] \; \mt{bool}, \\
adamc@1085 1689 \hspace{.2in} \mt{SelectFields} : \mt{sql\_subset} \; \mt{grouped} \; (\mt{map} \; (\lambda \_ \Rightarrow []) \; \mt{empties} \rc \mt{selectedFields}), \\
adam@1778 1690 \hspace{.2in} \mt {SelectExps} : \$(\mt{map} \; (\mt{sql\_expw} \; (\mt{free} \rc \mt{grouped}) \; (\mt{afree} \rc \mt{tables}) \; []) \; \mt{selectedExps}) \} \\
adam@1400 1691 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1692 \end{array}$$
adamc@543 1693
adamc@543 1694 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 1695 $$\begin{array}{l}
adamc@543 1696 \mt{con} \; \mt{sql\_subset} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@543 1697 \mt{val} \; \mt{sql\_subset} : \mt{keep\_drop} :: \{(\{\mt{Type}\} \times \{\mt{Type}\})\} \\
adamc@543 1698 \hspace{.1in} \to \mt{sql\_subset} \\
adamc@658 1699 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1 \rc \mt{fields}.2)\; \mt{keep\_drop}) \\
adamc@658 1700 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1) \; \mt{keep\_drop}) \\
adamc@543 1701 \mt{val} \; \mt{sql\_subset\_all} : \mt{tables} :: \{\{\mt{Type}\}\} \to \mt{sql\_subset} \; \mt{tables} \; \mt{tables}
adamc@543 1702 \end{array}$$
adamc@543 1703
adam@1778 1704 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 1705 $$\begin{array}{l}
adam@1778 1706 \mt{con} \; \mt{sql\_exp} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}
adamc@543 1707 \end{array}$$
adamc@543 1708
adamc@543 1709 Any field in scope may be converted to an expression.
adamc@543 1710 $$\begin{array}{l}
adamc@543 1711 \mt{val} \; \mt{sql\_field} : \mt{otherTabs} ::: \{\{\mt{Type}\}\} \to \mt{otherFields} ::: \{\mt{Type}\} \\
adam@1778 1712 \hspace{.1in} \to \mt{fieldType} ::: \mt{Type} \to \mt{agg} ::: \{\{\mt{Type}\}\} \\
adamc@543 1713 \hspace{.1in} \to \mt{exps} ::: \{\mt{Type}\} \\
adamc@543 1714 \hspace{.1in} \to \mt{tab} :: \mt{Name} \to \mt{field} :: \mt{Name} \\
adam@1778 1715 \hspace{.1in} \to \mt{sql\_exp} \; ([\mt{tab} = [\mt{field} = \mt{fieldType}] \rc \mt{otherFields}] \rc \mt{otherTabs}) \; \mt{agg} \; \mt{exps} \; \mt{fieldType}
adamc@543 1716 \end{array}$$
adamc@543 1717
adamc@544 1718 There is an analogous function for referencing named expressions.
adamc@544 1719 $$\begin{array}{l}
adam@1778 1720 \mt{val} \; \mt{sql\_exp} : \mt{tabs} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{t} ::: \mt{Type} \to \mt{rest} ::: \{\mt{Type}\} \to \mt{nm} :: \mt{Name} \\
adam@1778 1721 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tabs} \; \mt{agg} \; ([\mt{nm} = \mt{t}] \rc \mt{rest}) \; \mt{t}
adamc@544 1722 \end{array}$$
adamc@544 1723
adamc@544 1724 Ur values of appropriate types may be injected into SQL expressions.
adamc@544 1725 $$\begin{array}{l}
adamc@786 1726 \mt{class} \; \mt{sql\_injectable\_prim} \\
adamc@786 1727 \mt{val} \; \mt{sql\_bool} : \mt{sql\_injectable\_prim} \; \mt{bool} \\
adamc@786 1728 \mt{val} \; \mt{sql\_int} : \mt{sql\_injectable\_prim} \; \mt{int} \\
adamc@786 1729 \mt{val} \; \mt{sql\_float} : \mt{sql\_injectable\_prim} \; \mt{float} \\
adamc@786 1730 \mt{val} \; \mt{sql\_string} : \mt{sql\_injectable\_prim} \; \mt{string} \\
adamc@786 1731 \mt{val} \; \mt{sql\_time} : \mt{sql\_injectable\_prim} \; \mt{time} \\
adamc@786 1732 \mt{val} \; \mt{sql\_blob} : \mt{sql\_injectable\_prim} \; \mt{blob} \\
adamc@786 1733 \mt{val} \; \mt{sql\_channel} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{channel} \; \mt{t}) \\
adamc@786 1734 \mt{val} \; \mt{sql\_client} : \mt{sql\_injectable\_prim} \; \mt{client} \\
adamc@786 1735 \\
adamc@544 1736 \mt{class} \; \mt{sql\_injectable} \\
adamc@786 1737 \mt{val} \; \mt{sql\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@786 1738 \mt{val} \; \mt{sql\_option\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; (\mt{option} \; \mt{t}) \\
adamc@786 1739 \\
adam@1778 1740 \mt{val} \; \mt{sql\_inject} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{sql\_injectable} \; \mt{t} \\
adam@1778 1741 \hspace{.1in} \to \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adamc@544 1742 \end{array}$$
adamc@544 1743
adamc@1123 1744 Additionally, most function-free types may be injected safely, via the $\mt{serialized}$ type family.
adamc@1123 1745 $$\begin{array}{l}
adamc@1123 1746 \mt{con} \; \mt{serialized} :: \mt{Type} \to \mt{Type} \\
adamc@1123 1747 \mt{val} \; \mt{serialize} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{serialized} \; \mt{t} \\
adamc@1123 1748 \mt{val} \; \mt{deserialize} : \mt{t} ::: \mt{Type} \to \mt{serialized} \; \mt{t} \to \mt{t} \\
adamc@1123 1749 \mt{val} \; \mt{sql\_serialized} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{serialized} \; \mt{t})
adamc@1123 1750 \end{array}$$
adamc@1123 1751
adamc@544 1752 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 1753 $$\begin{array}{l}
adam@1778 1754 \mt{val} \; \mt{sql\_is\_null} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778 1755 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; (\mt{option} \; \mt{t}) \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{bool}
adamc@544 1756 \end{array}$$
adamc@544 1757
adam@1602 1758 As another way of dealing with null values, there is also a restricted form of the standard \cd{COALESCE} function.
adam@1602 1759 $$\begin{array}{l}
adam@1602 1760 \mt{val} \; \mt{sql\_coalesce} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778 1761 \hspace{.1in} \to \mt{t} ::: \mt{Type} \\
adam@1778 1762 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; (\mt{option} \; \mt{t}) \\
adam@1778 1763 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1764 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adam@1602 1765 \end{array}$$
adam@1602 1766
adamc@559 1767 We have generic nullary, unary, and binary operators.
adamc@544 1768 $$\begin{array}{l}
adamc@544 1769 \mt{con} \; \mt{sql\_nfunc} :: \mt{Type} \to \mt{Type} \\
adamc@544 1770 \mt{val} \; \mt{sql\_current\_timestamp} : \mt{sql\_nfunc} \; \mt{time} \\
adam@1778 1771 \mt{val} \; \mt{sql\_nfunc} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778 1772 \hspace{.1in} \to \mt{sql\_nfunc} \; \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\\end{array}$$
adamc@544 1773
adamc@544 1774 $$\begin{array}{l}
adamc@544 1775 \mt{con} \; \mt{sql\_unary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544 1776 \mt{val} \; \mt{sql\_not} : \mt{sql\_unary} \; \mt{bool} \; \mt{bool} \\
adam@1778 1777 \mt{val} \; \mt{sql\_unary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adam@1778 1778 \hspace{.1in} \to \mt{sql\_unary} \; \mt{arg} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res} \\
adamc@544 1779 \end{array}$$
adamc@544 1780
adamc@544 1781 $$\begin{array}{l}
adamc@544 1782 \mt{con} \; \mt{sql\_binary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544 1783 \mt{val} \; \mt{sql\_and} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544 1784 \mt{val} \; \mt{sql\_or} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adam@1778 1785 \mt{val} \; \mt{sql\_binary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg_1} ::: \mt{Type} \to \mt{arg_2} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adam@1778 1786 \hspace{.1in} \to \mt{sql\_binary} \; \mt{arg_1} \; \mt{arg_2} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_1} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_2} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res}
adamc@544 1787 \end{array}$$
adamc@544 1788
adamc@544 1789 $$\begin{array}{l}
adamc@559 1790 \mt{class} \; \mt{sql\_arith} \\
adamc@559 1791 \mt{val} \; \mt{sql\_int\_arith} : \mt{sql\_arith} \; \mt{int} \\
adamc@559 1792 \mt{val} \; \mt{sql\_float\_arith} : \mt{sql\_arith} \; \mt{float} \\
adamc@559 1793 \mt{val} \; \mt{sql\_neg} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_unary} \; \mt{t} \; \mt{t} \\
adamc@559 1794 \mt{val} \; \mt{sql\_plus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1795 \mt{val} \; \mt{sql\_minus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1796 \mt{val} \; \mt{sql\_times} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1797 \mt{val} \; \mt{sql\_div} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1798 \mt{val} \; \mt{sql\_mod} : \mt{sql\_binary} \; \mt{int} \; \mt{int} \; \mt{int}
adamc@559 1799 \end{array}$$
adamc@544 1800
adam@1797 1801 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 1802 $$\begin{array}{l}
adam@1778 1803 \mt{val} \; \mt{sql\_count} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int}
adamc@544 1804 \end{array}$$
adamc@544 1805
adamc@544 1806 $$\begin{array}{l}
adamc@1188 1807 \mt{con} \; \mt{sql\_aggregate} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adam@1778 1808 \mt{val} \; \mt{sql\_aggregate} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{dom} ::: \mt{Type} \to \mt{ran} ::: \mt{Type} \\
adam@1778 1809 \hspace{.1in} \to \mt{sql\_aggregate} \; \mt{dom} \; \mt{ran} \to \mt{sql\_exp} \; \mt{agg} \; \mt{agg} \; \mt{exps} \; \mt{dom} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{ran}
adamc@1188 1810 \end{array}$$
adamc@1188 1811
adamc@1188 1812 $$\begin{array}{l}
adamc@1188 1813 \mt{val} \; \mt{sql\_count\_col} : \mt{t} ::: \mt{Type} \to \mt{sql\_aggregate} \; (\mt{option} \; \mt{t}) \; \mt{int}
adamc@544 1814 \end{array}$$
adam@1400 1815
adam@1400 1816 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 1817
adamc@544 1818 $$\begin{array}{l}
adamc@544 1819 \mt{class} \; \mt{sql\_summable} \\
adamc@544 1820 \mt{val} \; \mt{sql\_summable\_int} : \mt{sql\_summable} \; \mt{int} \\
adamc@544 1821 \mt{val} \; \mt{sql\_summable\_float} : \mt{sql\_summable} \; \mt{float} \\
adam@1777 1822 \mt{val} \; \mt{sql\_avg} : \mt{t} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{sql\_aggregate} \; \mt{t} \; (\mt{option} \; \mt{float}) \\
adam@1400 1823 \mt{val} \; \mt{sql\_sum} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt}
adamc@544 1824 \end{array}$$
adamc@544 1825
adamc@544 1826 $$\begin{array}{l}
adamc@544 1827 \mt{class} \; \mt{sql\_maxable} \\
adamc@544 1828 \mt{val} \; \mt{sql\_maxable\_int} : \mt{sql\_maxable} \; \mt{int} \\
adamc@544 1829 \mt{val} \; \mt{sql\_maxable\_float} : \mt{sql\_maxable} \; \mt{float} \\
adamc@544 1830 \mt{val} \; \mt{sql\_maxable\_string} : \mt{sql\_maxable} \; \mt{string} \\
adamc@544 1831 \mt{val} \; \mt{sql\_maxable\_time} : \mt{sql\_maxable} \; \mt{time} \\
adam@1400 1832 \mt{val} \; \mt{sql\_max} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt} \\
adam@1400 1833 \mt{val} \; \mt{sql\_min} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt}
adamc@544 1834 \end{array}$$
adamc@544 1835
adam@1778 1836 Any SQL query that returns single columns may be turned into a subquery expression.
adam@1777 1837
adam@1777 1838 $$\begin{array}{l}
adam@1778 1839 \mt{val} \; \mt{sql\_subquery} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \\
adam@1778 1840 \hspace{.1in} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_query} \; \mt{tables} \; \mt{agg} \; [\mt{nm} = \mt{t}] \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{nt}
adamc@1193 1841 \end{array}$$
adamc@1193 1842
adam@1573 1843 There is also an \cd{IF..THEN..ELSE..} construct that is compiled into standard SQL \cd{CASE} expressions.
adam@1573 1844 $$\begin{array}{l}
adam@1778 1845 \mt{val} \; \mt{sql\_if\_then\_else} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778 1846 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{bool} \\
adam@1778 1847 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1848 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1849 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adam@1573 1850 \end{array}$$
adam@1573 1851
adamc@1193 1852 \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 1853 $$\begin{array}{l}
adamc@1193 1854 \mt{con} \; \mt{sql\_from\_items} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@1193 1855 \mt{val} \; \mt{sql\_from\_table} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1856 \hspace{.1in} \to \mt{t} ::: \mt{Type} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; \mt{t} \; \mt{fs} \to \mt{name} :: \mt{Name} \to \mt{t} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193 1857 \mt{val} \; \mt{sql\_from\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{name} :: \mt{Name} \to \mt{sql\_query} \; \mt{free} \; [] \; \mt{fs} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193 1858 \mt{val} \; \mt{sql\_from\_comma} : \mt{free} ::: \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \to [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193 1859 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adamc@1193 1860 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2}) \\
adamc@1193 1861 \mt{val} \; \mt{sql\_inner\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1862 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193 1863 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adam@1778 1864 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193 1865 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2})
adamc@786 1866 \end{array}$$
adamc@786 1867
adamc@786 1868 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 1869 $$\begin{array}{l}
adamc@786 1870 \mt{class} \; \mt{nullify} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@786 1871 \mt{val} \; \mt{nullify\_option} : \mt{t} ::: \mt{Type} \to \mt{nullify} \; (\mt{option} \; \mt{t}) \; (\mt{option} \; \mt{t}) \\
adamc@786 1872 \mt{val} \; \mt{nullify\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{nullify} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@786 1873 \end{array}$$
adamc@786 1874
adamc@786 1875 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 1876
adamc@786 1877 $$\begin{array}{l}
adamc@1193 1878 \mt{val} \; \mt{sql\_left\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{(\mt{Type} \times \mt{Type})\}\} \\
adamc@1193 1879 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@786 1880 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\lambda \mt{r} \Rightarrow \$(\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{nullify} \; \mt{p}.1 \; \mt{p}.2) \; \mt{r})) \; \mt{tabs2}) \\
adamc@1193 1881 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \\
adam@1778 1882 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193 1883 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.2)) \; \mt{tabs2})
adamc@786 1884 \end{array}$$
adamc@786 1885
adamc@544 1886 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 1887 $$\begin{array}{l}
adamc@544 1888 \mt{type} \; \mt{sql\_direction} \\
adamc@544 1889 \mt{val} \; \mt{sql\_asc} : \mt{sql\_direction} \\
adamc@544 1890 \mt{val} \; \mt{sql\_desc} : \mt{sql\_direction} \\
adamc@544 1891 \\
adamc@544 1892 \mt{con} \; \mt{sql\_order\_by} :: \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@544 1893 \mt{val} \; \mt{sql\_order\_by\_Nil} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} :: \{\mt{Type}\} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adam@1778 1894 \mt{val} \; \mt{sql\_order\_by\_Cons} : \mt{tf} ::: (\{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}) \\
adam@1778 1895 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778 1896 \hspace{.1in} \to \mt{sql\_window} \; \mt{tf} \to \mt{tf} \; \mt{tables} \; [] \; \mt{exps} \; \mt{t} \to \mt{sql\_direction} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adam@1684 1897 \mt{val} \; \mt{sql\_order\_by\_random} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544 1898 \\
adamc@544 1899 \mt{type} \; \mt{sql\_limit} \\
adamc@544 1900 \mt{val} \; \mt{sql\_no\_limit} : \mt{sql\_limit} \\
adamc@544 1901 \mt{val} \; \mt{sql\_limit} : \mt{int} \to \mt{sql\_limit} \\
adamc@544 1902 \\
adamc@544 1903 \mt{type} \; \mt{sql\_offset} \\
adamc@544 1904 \mt{val} \; \mt{sql\_no\_offset} : \mt{sql\_offset} \\
adamc@544 1905 \mt{val} \; \mt{sql\_offset} : \mt{int} \to \mt{sql\_offset}
adamc@544 1906 \end{array}$$
adamc@544 1907
adam@1778 1908 When using Postgres, \cd{SELECT} and \cd{ORDER BY} are allowed to contain top-level uses of \emph{window functions}. A separate type family \cd{sql\_expw} is provided for such cases, with some type class convenience for overloading between normal and window expressions.
adam@1778 1909 $$\begin{array}{l}
adam@1778 1910 \mt{con} \; \mt{sql\_expw} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type} \\
adam@1778 1911 \\
adam@1778 1912 \mt{class} \; \mt{sql\_window} :: (\{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}) \to \mt{Type} \\
adam@1778 1913 \mt{val} \; \mt{sql\_window\_normal} : \mt{sql\_window} \; \mt{sql\_exp} \\
adam@1778 1914 \mt{val} \; \mt{sql\_window\_fancy} : \mt{sql\_window} \; \mt{sql\_expw} \\
adam@1778 1915 \mt{val} \; \mt{sql\_window} : \mt{tf} ::: (\{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}) \\
adam@1778 1916 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778 1917 \hspace{.1in} \to \mt{sql\_window} \; \mt{tf} \\
adam@1778 1918 \hspace{.1in} \to \mt{tf} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1919 \hspace{.1in} \to \mt{sql\_expw} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1920 \\
adam@1778 1921 \mt{con} \; \mt{sql\_partition} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adam@1778 1922 \mt{val} \; \mt{sql\_no\_partition} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778 1923 \hspace{.1in} \to \mt{sql\_partition} \; \mt{tables} \; \mt{agg} \; \mt{exps} \\
adam@1778 1924 \mt{val} \; \mt{sql\_partition} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adam@1778 1925 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1926 \hspace{.1in} \to \mt{sql\_partition} \; \mt{tables} \; \mt{agg} \; \mt{exps} \\
adam@1778 1927 \\
adam@1778 1928 \mt{con} \; \mt{sql\_window\_function} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type} \\
adam@1778 1929 \mt{val} \; \mt{sql\_window\_function} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778 1930 \hspace{.1in} \to \mt{t} ::: \mt{Type} \\
adam@1778 1931 \hspace{.1in} \to \mt{sql\_window\_function} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1932 \hspace{.1in} \to \mt{sql\_partition} \; \mt{tables} \; \mt{agg} \; \mt{exps} \\
adam@1778 1933 \hspace{.1in} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adam@1778 1934 \hspace{.1in} \to \mt{sql\_expw} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1935 \\
adam@1778 1936 \mt{val} \; \mt{sql\_window\_aggregate} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778 1937 \hspace{.1in} \to \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \\
adam@1778 1938 \hspace{.1in} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt} \\
adam@1778 1939 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\
adam@1778 1940 \hspace{.1in} \to \mt{sql\_window\_function} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{nt} \\
adam@1778 1941 \mt{val} \; \mt{sql\_window\_count} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778 1942 \hspace{.1in} \to \mt{sql\_window\_function} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int} \\
adam@1778 1943 \mt{val} \; \mt{sql\_rank} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \\
adam@1778 1944 \hspace{.1in} \to \mt{sql\_window\_function} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int}
adam@1778 1945 \end{array}$$
adam@1778 1946
adamc@545 1947
adamc@545 1948 \subsubsection{DML}
adamc@545 1949
adamc@545 1950 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 1951
adamc@545 1952 $$\begin{array}{l}
adamc@545 1953 \mt{type} \; \mt{dml} \\
adamc@545 1954 \mt{val} \; \mt{dml} : \mt{dml} \to \mt{transaction} \; \mt{unit}
adamc@545 1955 \end{array}$$
adamc@545 1956
adam@1297 1957 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 1958
adam@1297 1959 $$\begin{array}{l}
adam@1297 1960 \mt{val} \; \mt{tryDml} : \mt{dml} \to \mt{transaction} \; (\mt{option} \; \mt{string})
adam@1297 1961 \end{array}$$
adam@1297 1962
adam@1797 1963 Properly typed records may be used to form $\mt{INSERT}$ commands.
adamc@545 1964 $$\begin{array}{l}
adamc@545 1965 \mt{val} \; \mt{insert} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \\
adam@1778 1966 \hspace{.1in} \to \$(\mt{map} \; (\mt{sql\_exp} \; [] \; [] \; []) \; \mt{fields}) \to \mt{dml}
adamc@545 1967 \end{array}$$
adamc@545 1968
adam@1578 1969 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 1970 $$\begin{array}{l}
adam@1380 1971 \mt{val} \; \mt{update} : \mt{unchanged} ::: \{\mt{Type}\} \to \mt{changed} :: \{\mt{Type}\} \to [\mt{changed} \sim \mt{unchanged}] \\
adam@1778 1972 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; []) \; \mt{changed}) \\
adam@1778 1973 \hspace{.1in} \to \mt{sql\_table} \; (\mt{changed} \rc \mt{unchanged}) \to \mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545 1974 \end{array}$$
adamc@545 1975
adam@1578 1976 A $\mt{DELETE}$ command is formed from a table and a $\mt{WHERE}$ clause. The above use of $\mt{T}$ is repeated.
adamc@545 1977 $$\begin{array}{l}
adam@1778 1978 \mt{val} \; \mt{delete} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \to \mt{sql\_exp} \; [\mt{T} = \mt{fields}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545 1979 \end{array}$$
adamc@545 1980
adamc@546 1981 \subsubsection{Sequences}
adamc@546 1982
adamc@546 1983 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 1984
adamc@546 1985 $$\begin{array}{l}
adamc@546 1986 \mt{type} \; \mt{sql\_sequence} \\
adamc@1085 1987 \mt{val} \; \mt{nextval} : \mt{sql\_sequence} \to \mt{transaction} \; \mt{int} \\
adamc@1085 1988 \mt{val} \; \mt{setval} : \mt{sql\_sequence} \to \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@546 1989 \end{array}$$
adamc@546 1990
adamc@546 1991
adam@1648 1992 \subsection{\label{xml}XML}
adamc@547 1993
adam@1333 1994 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 1995
adam@1642 1996 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 1997 $$\begin{array}{l}
adamc@547 1998 \mt{con} \; \mt{xml} :: \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547 1999 \end{array}$$
adamc@547 2000
adamc@547 2001 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 2002 $$\begin{array}{l}
adamc@547 2003 \mt{con} \; \mt{tag} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547 2004 \end{array}$$
adamc@547 2005
adamc@547 2006 Literal text may be injected into XML as ``CDATA.''
adamc@547 2007 $$\begin{array}{l}
adamc@547 2008 \mt{val} \; \mt{cdata} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{string} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adamc@547 2009 \end{array}$$
adamc@547 2010
adam@1358 2011 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 2012 $$\begin{array}{l}
adam@1358 2013 \mt{val} \; \mt{cdataChar} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{char} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adam@1358 2014 \end{array}$$
adam@1358 2015
adamc@547 2016 There is a function for producing an XML tree with a particular tag at its root.
adamc@547 2017 $$\begin{array}{l}
adamc@547 2018 \mt{val} \; \mt{tag} : \mt{attrsGiven} ::: \{\mt{Type}\} \to \mt{attrsAbsent} ::: \{\mt{Type}\} \to \mt{ctxOuter} ::: \{\mt{Unit}\} \to \mt{ctxInner} ::: \{\mt{Unit}\} \\
adamc@547 2019 \hspace{.1in} \to \mt{useOuter} ::: \{\mt{Type}\} \to \mt{useInner} ::: \{\mt{Type}\} \to \mt{bindOuter} ::: \{\mt{Type}\} \to \mt{bindInner} ::: \{\mt{Type}\} \\
adam@1380 2020 \hspace{.1in} \to [\mt{attrsGiven} \sim \mt{attrsAbsent}] \Rightarrow [\mt{useOuter} \sim \mt{useInner}] \Rightarrow [\mt{bindOuter} \sim \mt{bindInner}] \\
adam@1749 2021 \hspace{.1in} \Rightarrow \mt{css\_class} \\
adam@1643 2022 \hspace{.1in} \to \mt{option} \; (\mt{signal} \; \mt{css\_class}) \\
adam@1750 2023 \hspace{.1in} \to \mt{css\_style} \\
adam@1751 2024 \hspace{.1in} \to \mt{option} \; (\mt{signal} \; \mt{css\_style}) \\
adamc@787 2025 \hspace{.1in} \to \$\mt{attrsGiven} \\
adamc@547 2026 \hspace{.1in} \to \mt{tag} \; (\mt{attrsGiven} \rc \mt{attrsAbsent}) \; \mt{ctxOuter} \; \mt{ctxInner} \; \mt{useOuter} \; \mt{bindOuter} \\
adamc@547 2027 \hspace{.1in} \to \mt{xml} \; \mt{ctxInner} \; \mt{useInner} \; \mt{bindInner} \to \mt{xml} \; \mt{ctxOuter} \; (\mt{useOuter} \rc \mt{useInner}) \; (\mt{bindOuter} \rc \mt{bindInner})
adamc@547 2028 \end{array}$$
adam@1750 2029 Note that any tag may be assigned a CSS class, or left without a class by passing $\mt{Basis.null}$ as the first value-level argument. This is the sole way of making use of the values produced by $\mt{style}$ declarations. The function $\mt{Basis.classes}$ can be used to specify a list of CSS classes for a single tag. Stylesheets to assign properties to the classes can be linked via URL's with \texttt{link} tags. Ur/Web makes it easy to calculate upper bounds on usage of CSS classes through program analysis, with the \cd{-css} command-line flag.
adamc@547 2030
adam@1643 2031 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 2032
adam@1751 2033 The third and fourth value-level arguments makes it possible to generate HTML \cd{style} attributes, either with fixed content (\cd{style} attribute) or dynamic content (\cd{dynStyle} pseudo-attribute).
adam@1750 2034
adamc@547 2035 Two XML fragments may be concatenated.
adamc@547 2036 $$\begin{array}{l}
adamc@547 2037 \mt{val} \; \mt{join} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{bind_1} ::: \{\mt{Type}\} \to \mt{bind_2} ::: \{\mt{Type}\} \\
adam@1380 2038 \hspace{.1in} \to [\mt{use_1} \sim \mt{bind_1}] \Rightarrow [\mt{bind_1} \sim \mt{bind_2}] \\
adamc@547 2039 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind_1} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{bind_1}) \; \mt{bind_2} \to \mt{xml} \; \mt{ctx} \; \mt{use_1} \; (\mt{bind_1} \rc \mt{bind_2})
adamc@547 2040 \end{array}$$
adamc@547 2041
adamc@547 2042 Finally, any XML fragment may be updated to ``claim'' to use more form fields than it does.
adamc@547 2043 $$\begin{array}{l}
adam@1380 2044 \mt{val} \; \mt{useMore} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{use_2} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to [\mt{use_1} \sim \mt{use_2}] \\
adamc@547 2045 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{use_2}) \; \mt{bind}
adamc@547 2046 \end{array}$$
adamc@547 2047
adam@1344 2048 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 2049
adamc@547 2050 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 2051 $$\begin{array}{l}
adam@1641 2052 \mt{val} \; \mt{error} : \mt{t} ::: \mt{Type} \to \mt{xbody} \to \mt{t}
adamc@547 2053 \end{array}$$
adamc@547 2054
adamc@549 2055
adamc@701 2056 \subsection{Client-Side Programming}
adamc@659 2057
adamc@701 2058 Ur/Web supports running code on web browsers, via automatic compilation to JavaScript.
adamc@701 2059
adamc@701 2060 \subsubsection{The Basics}
adamc@701 2061
adam@1400 2062 All of the functions in this subsection are client-side only.
adam@1400 2063
adam@1297 2064 Clients can open alert and confirm dialog boxes, in the usual annoying JavaScript way.
adamc@701 2065 $$\begin{array}{l}
adam@1297 2066 \mt{val} \; \mt{alert} : \mt{string} \to \mt{transaction} \; \mt{unit} \\
adam@1297 2067 \mt{val} \; \mt{confirm} : \mt{string} \to \mt{transaction} \; \mt{bool}
adamc@701 2068 \end{array}$$
adamc@701 2069
adamc@701 2070 Any transaction may be run in a new thread with the $\mt{spawn}$ function.
adamc@701 2071 $$\begin{array}{l}
adamc@701 2072 \mt{val} \; \mt{spawn} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit}
adamc@701 2073 \end{array}$$
adamc@701 2074
adamc@701 2075 The current thread can be paused for at least a specified number of milliseconds.
adamc@701 2076 $$\begin{array}{l}
adamc@701 2077 \mt{val} \; \mt{sleep} : \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@701 2078 \end{array}$$
adamc@701 2079
adam@1770 2080 A few functions are available to registers callbacks for particular error events. Respectively, they are triggered on calls to $\mt{error}$, uncaught JavaScript exceptions, failure of remote procedure calls, the severance of the connection serving asynchronous messages, or the occurrence of some other error with that connection. If no handlers are registered for a kind of error, then a JavaScript \cd{alert()} is used to announce its occurrence. When one of these functions is called multiple times within a single page, all registered handlers are run when appropriate events occur, with handlers run in the reverse of their registration order.
adamc@787 2081 $$\begin{array}{l}
adamc@787 2082 \mt{val} \; \mt{onError} : (\mt{xbody} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787 2083 \mt{val} \; \mt{onFail} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787 2084 \mt{val} \; \mt{onConnectFail} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787 2085 \mt{val} \; \mt{onDisconnect} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787 2086 \mt{val} \; \mt{onServerError} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit}
adamc@787 2087 \end{array}$$
adamc@787 2088
adam@1555 2089 There are also functions to register standard document-level event handlers.
adam@1555 2090
adam@1555 2091 $$\begin{array}{l}
adam@1783 2092 \mt{val} \; \mt{onClick} : (\mt{mouseEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783 2093 \mt{val} \; \mt{onDblclick} : (\mt{mouseEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783 2094 \mt{val} \; \mt{onKeydown} : (\mt{keyEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783 2095 \mt{val} \; \mt{onKeypress} : (\mt{keyEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783 2096 \mt{val} \; \mt{onKeyup} : (\mt{keyEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783 2097 \mt{val} \; \mt{onMousedown} : (\mt{mouseEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adam@1783 2098 \mt{val} \; \mt{onMouseup} : (\mt{mouseEvent} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit}
adam@1555 2099 \end{array}$$
adam@1555 2100
adam@1559 2101 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 2102
adam@1559 2103 $$\begin{array}{l}
adam@1559 2104 \mt{val} \; \mt{preventDefault} : \mt{transaction} \; \mt{unit} \\
adam@1559 2105 \mt{val} \; \mt{stopPropagation} : \mt{transaction} \; \mt{unit}
adam@1559 2106 \end{array}$$
adam@1559 2107
adam@1926 2108 Finally, here is an HTML tag to leave a marker in the \cd{<head>} of a document asking for some side-effecting code to be run. This pattern is \emph{much} less common in Ur/Web applications than in normal HTML/JavaScript applications; see Section \ref{signals} for the more idiomatic, functional way of manipulating the visible page.
adam@1926 2109
adam@1926 2110 $$\begin{array}{l}
adam@1926 2111 \mt{val} \; \mt{script} : \mt{unit} \to \mt{tag} \; [\mt{Code} = \mt{transaction} \; \mt{unit}] \; \mt{head} \; [] \; [] \; []
adam@1926 2112 \end{array}$$
adam@1926 2113
adam@1926 2114 Note that the Ur/Web version of \cd{<script>} is used like \cd{<script code=\{...\}/>}, rather than \cd{<script>...</script>}.
adam@1926 2115
adam@1556 2116 \subsubsection{Node IDs}
adam@1556 2117
adam@1556 2118 There is an abstract type of node IDs that may be assigned to \cd{id} attributes of most HTML tags.
adam@1556 2119
adam@1556 2120 $$\begin{array}{l}
adam@1556 2121 \mt{type} \; \mt{id} \\
adam@1556 2122 \mt{val} \; \mt{fresh} : \mt{transaction} \; \mt{id}
adam@1556 2123 \end{array}$$
adam@1556 2124
adam@1785 2125 The \cd{fresh} function is allowed on both server and client, but there is no other way to create IDs, which includes lack of a way to force an ID to match a particular string. The main semantic importance of IDs within Ur/Web is in uses of the HTML \cd{<label>} tag. IDs play a much more central role in mainstream JavaScript programming, but Ur/Web uses a very different model to enable changes to particular nodes of a page tree, as the next manual subsection explains. IDs may still be useful in interfacing with JavaScript code (for instance, through Ur/Web's FFI).
adam@1785 2126
adam@1785 2127 One further use of IDs is as handles for requesting that \emph{focus} be given to specific tags.
adam@1785 2128
adam@1785 2129 $$\begin{array}{l}
adam@1785 2130 \mt{val} \; \mt{giveFocus} : \mt{id} \to \mt{transaction} \; \mt{unit}
adam@1785 2131 \end{array}$$
adam@1556 2132
adam@1643 2133 \subsubsection{\label{signals}Functional-Reactive Page Generation}
adamc@701 2134
adamc@701 2135 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 2136
adam@1403 2137 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 2138
adamc@659 2139 $$\begin{array}{l}
adamc@659 2140 \mt{con} \; \mt{source} :: \mt{Type} \to \mt{Type} \\
adamc@659 2141 \mt{val} \; \mt{source} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{transaction} \; (\mt{source} \; \mt{t}) \\
adamc@659 2142 \mt{val} \; \mt{set} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@659 2143 \mt{val} \; \mt{get} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@659 2144 \end{array}$$
adamc@659 2145
adam@1400 2146 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 2147
adam@1608 2148 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 2149
adamc@659 2150 $$\begin{array}{l}
adamc@659 2151 \mt{con} \; \mt{signal} :: \mt{Type} \to \mt{Type} \\
adamc@659 2152 \mt{val} \; \mt{signal\_monad} : \mt{monad} \; \mt{signal} \\
adam@1608 2153 \mt{val} \; \mt{signal} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{signal} \; \mt{t} \\
adam@1608 2154 \mt{val} \; \mt{current} : \mt{t} ::: \mt{Type} \to \mt{signal} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@659 2155 \end{array}$$
adamc@659 2156
adamc@659 2157 A reactive portion of an HTML page is injected with a $\mt{dyn}$ tag, which has a signal-valued attribute $\mt{Signal}$.
adamc@659 2158
adamc@659 2159 $$\begin{array}{l}
adam@1641 2160 \mt{val} \; \mt{dyn} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to [\mt{ctx} \sim [\mt{Dyn}]] \Rightarrow \mt{unit} \\
adam@1641 2161 \hspace{.1in} \to \mt{tag} \; [\mt{Signal} = \mt{signal} \; (\mt{xml} \; ([\mt{Dyn}] \rc \mt{ctx}) \; \mt{use} \; \mt{bind})] \; ([\mt{Dyn}] \rc \mt{ctx}) \; [] \; \mt{use} \; \mt{bind}
adamc@659 2162 \end{array}$$
adamc@659 2163
adam@1648 2164 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 2165
adam@1648 2166 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 2167
adam@1786 2168 Transactions can be run on the client by including them in attributes like the $\mt{Onclick}$ attribute of $\mt{button}$, and GUI widgets like $\mt{ctextbox}$ have $\mt{Source}$ attributes that can be used to connect them to sources, so that their values can be read by code running because of, e.g., an $\mt{Onclick}$ event. It is also possible to create an ``active'' HTML fragment that runs a $\mt{transaction}$ to determine its content, possibly allocating some sources in the process:
adam@1786 2169
adam@1786 2170 $$\begin{array}{l}
adam@1786 2171 \mt{val} \; \mt{active} : \mt{unit} \to \mt{tag} \; [\mt{Code} = \mt{transaction} \; \mt{xbody}] \; \mt{body} \; [] \; [] \; []
adam@1786 2172 \end{array}$$
adamc@701 2173
adamc@914 2174 \subsubsection{Remote Procedure Calls}
adamc@914 2175
adamc@914 2176 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 2177
adamc@914 2178 $$\begin{array}{l}
adamc@914 2179 \mt{val} \; \mt{rpc} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@914 2180 \end{array}$$
adamc@914 2181
adam@1848 2182 There is an alternate form that uses $\mt{None}$ to indicate that an error occurred during RPC processing, rather than raising an exception to abort this branch of control flow.
adam@1848 2183
adam@1848 2184 $$\begin{array}{l}
adam@1848 2185 \mt{val} \; \mt{tryRpc} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; \mt{t} \to \mt{transaction} \; (\mt{option} \; \mt{t})
adam@1848 2186 \end{array}$$
adam@1848 2187
adamc@701 2188 \subsubsection{Asynchronous Message-Passing}
adamc@701 2189
adamc@701 2190 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 2191
adamc@701 2192 $$\begin{array}{l}
adamc@701 2193 \mt{type} \; \mt{client} \\
adamc@701 2194 \mt{val} \; \mt{self} : \mt{transaction} \; \mt{client}
adamc@701 2195 \end{array}$$
adamc@701 2196
adamc@701 2197 \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 2198
adamc@701 2199 $$\begin{array}{l}
adamc@701 2200 \mt{con} \; \mt{channel} :: \mt{Type} \to \mt{Type} \\
adamc@701 2201 \mt{val} \; \mt{channel} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; (\mt{channel} \; \mt{t}) \\
adamc@701 2202 \mt{val} \; \mt{send} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@701 2203 \mt{val} \; \mt{recv} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@701 2204 \end{array}$$
adamc@701 2205
adamc@701 2206 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 2207
adamc@701 2208 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 2209
adam@1551 2210 \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 2211
adamc@659 2212
adamc@549 2213 \section{Ur/Web Syntax Extensions}
adamc@549 2214
adamc@549 2215 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 2216
adamc@549 2217 \subsection{SQL}
adamc@549 2218
adamc@786 2219 \subsubsection{\label{tables}Table Declarations}
adamc@786 2220
adamc@788 2221 $\mt{table}$ declarations may include constraints, via these grammar rules.
adamc@788 2222 $$\begin{array}{rrcll}
adam@1594 2223 \textrm{Declarations} & d &::=& \mt{table} \; x : c \; [pk[,]] \; cts \mid \mt{view} \; x = V \\
adamc@788 2224 \textrm{Primary key constraints} & pk &::=& \mt{PRIMARY} \; \mt{KEY} \; K \\
adam@1722 2225 \textrm{Keys} & K &::=& f \mid (f, (f,)^+) \mid \{\{e\}\} \\
adamc@788 2226 \textrm{Constraint sets} & cts &::=& \mt{CONSTRAINT} f \; ct \mid cts, cts \mid \{\{e\}\} \\
adamc@788 2227 \textrm{Constraints} & ct &::=& \mt{UNIQUE} \; K \mid \mt{CHECK} \; E \\
adamc@788 2228 &&& \mid \mt{FOREIGN} \; \mt{KEY} \; K \; \mt{REFERENCES} \; F \; (K) \; [\mt{ON} \; \mt{DELETE} \; pr] \; [\mt{ON} \; \mt{UPDATE} \; pr] \\
adamc@788 2229 \textrm{Foreign tables} & F &::=& x \mid \{\{e\}\} \\
adam@1594 2230 \textrm{Propagation modes} & pr &::=& \mt{NO} \; \mt{ACTION} \mid \mt{RESTRICT} \mid \mt{CASCADE} \mid \mt{SET} \; \mt{NULL} \\
adam@1594 2231 \textrm{View expressions} & V &::=& Q \mid \{e\}
adamc@788 2232 \end{array}$$
adamc@788 2233
adamc@788 2234 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 2235
adamc@788 2236
adamc@549 2237 \subsubsection{Queries}
adamc@549 2238
adamc@550 2239 Queries $Q$ are added to the rules for expressions $e$.
adamc@550 2240
adamc@549 2241 $$\begin{array}{rrcll}
adam@1684 2242 \textrm{Queries} & Q &::=& (q \; [\mt{ORDER} \; \mt{BY} \; O] \; [\mt{LIMIT} \; N] \; [\mt{OFFSET} \; N]) \\
adamc@1085 2243 \textrm{Pre-queries} & q &::=& \mt{SELECT} \; [\mt{DISTINCT}] \; P \; \mt{FROM} \; F,^+ \; [\mt{WHERE} \; E] \; [\mt{GROUP} \; \mt{BY} \; p,^+] \; [\mt{HAVING} \; E] \\
adamc@1085 2244 &&& \mid q \; R \; q \mid \{\{\{e\}\}\} \\
adam@1684 2245 \textrm{Relational operators} & R &::=& \mt{UNION} \mid \mt{INTERSECT} \mid \mt{EXCEPT} \\
adam@1778 2246 \textrm{$\mt{ORDER \; BY}$ items} & O &::=& \mt{RANDOM} [()] \mid \hat{E} \; [o] \mid \hat{E} \; [o], O
adamc@549 2247 \end{array}$$
adamc@549 2248
adamc@549 2249 $$\begin{array}{rrcll}
adamc@549 2250 \textrm{Projections} & P &::=& \ast & \textrm{all columns} \\
adamc@549 2251 &&& p,^+ & \textrm{particular columns} \\
adamc@549 2252 \textrm{Pre-projections} & p &::=& t.f & \textrm{one column from a table} \\
adamc@558 2253 &&& t.\{\{c\}\} & \textrm{a record of columns from a table (of kind $\{\mt{Type}\}$)} \\
adam@1627 2254 &&& t.* & \textrm{all columns from a table} \\
adam@1778 2255 &&& \hat{E} \; [\mt{AS} \; f] & \textrm{expression column} \\
adamc@549 2256 \textrm{Table names} & t &::=& x & \textrm{constant table name (automatically capitalized)} \\
adamc@549 2257 &&& X & \textrm{constant table name} \\
adamc@549 2258 &&& \{\{c\}\} & \textrm{computed table name (of kind $\mt{Name}$)} \\
adamc@549 2259 \textrm{Column names} & f &::=& X & \textrm{constant column name} \\
adamc@549 2260 &&& \{c\} & \textrm{computed column name (of kind $\mt{Name}$)} \\
adamc@549 2261 \textrm{Tables} & T &::=& x & \textrm{table variable, named locally by its own capitalization} \\
adam@1756 2262 &&& x \; \mt{AS} \; X & \textrm{table variable, with local name} \\
adam@1756 2263 &&& x \; \mt{AS} \; \{c\} & \textrm{table variable, with computed local name} \\
adamc@549 2264 &&& \{\{e\}\} \; \mt{AS} \; t & \textrm{computed table expression, with local name} \\
adam@1756 2265 &&& \{\{e\}\} \; \mt{AS} \; \{c\} & \textrm{computed table expression, with computed local name} \\
adamc@1085 2266 \textrm{$\mt{FROM}$ items} & F &::=& T \mid \{\{e\}\} \mid F \; J \; \mt{JOIN} \; F \; \mt{ON} \; E \\
adamc@1085 2267 &&& \mid F \; \mt{CROSS} \; \mt{JOIN} \ F \\
adamc@1193 2268 &&& \mid (Q) \; \mt{AS} \; t \\
adamc@1085 2269 \textrm{Joins} & J &::=& [\mt{INNER}] \\
adamc@1085 2270 &&& \mid [\mt{LEFT} \mid \mt{RIGHT} \mid \mt{FULL}] \; [\mt{OUTER}] \\
adam@1587 2271 \textrm{SQL expressions} & E &::=& t.f & \textrm{column references} \\
adamc@549 2272 &&& X & \textrm{named expression references} \\
adam@1490 2273 &&& \{[e]\} & \textrm{injected native Ur expressions} \\
adam@1778 2274 &&& \{e\} & \textrm{computed expressions, probably using $\mt{sql\_exp}$ directly} \\
adamc@549 2275 &&& \mt{TRUE} \mid \mt{FALSE} & \textrm{boolean constants} \\
adamc@549 2276 &&& \ell & \textrm{primitive type literals} \\
adamc@549 2277 &&& \mt{NULL} & \textrm{null value (injection of $\mt{None}$)} \\
adamc@549 2278 &&& E \; \mt{IS} \; \mt{NULL} & \textrm{nullness test} \\
adam@1602 2279 &&& \mt{COALESCE}(E, E) & \textrm{take first non-null value} \\
adamc@549 2280 &&& n & \textrm{nullary operators} \\
adamc@549 2281 &&& u \; E & \textrm{unary operators} \\
adamc@549 2282 &&& E \; b \; E & \textrm{binary operators} \\
adam@1778 2283 &&& \mt{COUNT}(\ast) & \textrm{count number of rows} \\
adam@1778 2284 &&& a(E) & \textrm{other aggregate function} \\
adam@1573 2285 &&& \mt{IF} \; E \; \mt{THEN} \; E \; \mt{ELSE} \; E & \textrm{conditional} \\
adam@1778 2286 &&& (Q) & \textrm{subquery (must return a single expression column)} \\
adamc@549 2287 &&& (E) & \textrm{explicit precedence} \\
adamc@549 2288 \textrm{Nullary operators} & n &::=& \mt{CURRENT\_TIMESTAMP} \\
adamc@549 2289 \textrm{Unary operators} & u &::=& \mt{NOT} \\
adam@1688 2290 \textrm{Binary operators} & b &::=& \mt{AND} \mid \mt{OR} \mid = \mid \neq \mid < \mid \leq \mid > \mid \geq \\
adamc@1188 2291 \textrm{Aggregate functions} & a &::=& \mt{COUNT} \mid \mt{AVG} \mid \mt{SUM} \mid \mt{MIN} \mid \mt{MAX} \\
adam@1543 2292 \textrm{Directions} & o &::=& \mt{ASC} \mid \mt{DESC} \mid \{e\} \\
adamc@549 2293 \textrm{SQL integer} & N &::=& n \mid \{e\} \\
adam@1778 2294 \textrm{Windowable expressions} & \hat{E} &::=& E \\
adam@1778 2295 &&& w \; [\mt{OVER} \; ( & \textrm{(Postgres only)} \\
adam@1778 2296 &&& \hspace{.1in} [\mt{PARTITION} \; \mt{BY} \; E] \\
adam@1778 2297 &&& \hspace{.1in} [\mt{ORDER} \; \mt{BY} \; O])] \\
adam@1778 2298 \textrm{Window function} & w &::=& \mt{RANK}() \\
adam@1778 2299 &&& \mt{COUNT}(*) \\
adam@1778 2300 &&& a(E)
adamc@549 2301 \end{array}$$
adamc@549 2302
adamc@1085 2303 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 2304
adam@1683 2305 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 2306
adamc@550 2307 \subsubsection{DML}
adamc@550 2308
adamc@550 2309 DML commands $D$ are added to the rules for expressions $e$.
adamc@550 2310
adamc@550 2311 $$\begin{array}{rrcll}
adamc@550 2312 \textrm{Commands} & D &::=& (\mt{INSERT} \; \mt{INTO} \; T^E \; (f,^+) \; \mt{VALUES} \; (E,^+)) \\
adamc@550 2313 &&& (\mt{UPDATE} \; T^E \; \mt{SET} \; (f = E,)^+ \; \mt{WHERE} \; E) \\
adamc@550 2314 &&& (\mt{DELETE} \; \mt{FROM} \; T^E \; \mt{WHERE} \; E) \\
adamc@550 2315 \textrm{Table expressions} & T^E &::=& x \mid \{\{e\}\}
adamc@550 2316 \end{array}$$
adamc@550 2317
adamc@550 2318 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 2319
adamc@551 2320 \subsection{XML}
adamc@551 2321
adamc@551 2322 XML fragments $L$ are added to the rules for expressions $e$.
adamc@551 2323
adamc@551 2324 $$\begin{array}{rrcll}
adamc@551 2325 \textrm{XML fragments} & L &::=& \texttt{<xml/>} \mid \texttt{<xml>}l^*\texttt{</xml>} \\
adamc@551 2326 \textrm{XML pieces} & l &::=& \textrm{text} & \textrm{cdata} \\
adamc@551 2327 &&& \texttt{<}g\texttt{/>} & \textrm{tag with no children} \\
adamc@551 2328 &&& \texttt{<}g\texttt{>}l^*\texttt{</}x\texttt{>} & \textrm{tag with children} \\
adamc@559 2329 &&& \{e\} & \textrm{computed XML fragment} \\
adamc@559 2330 &&& \{[e]\} & \textrm{injection of an Ur expression, via the $\mt{Top}.\mt{txt}$ function} \\
adamc@551 2331 \textrm{Tag} & g &::=& h \; (x = v)^* \\
adamc@551 2332 \textrm{Tag head} & h &::=& x & \textrm{tag name} \\
adamc@551 2333 &&& h\{c\} & \textrm{constructor parameter} \\
adamc@551 2334 \textrm{Attribute value} & v &::=& \ell & \textrm{literal value} \\
adamc@551 2335 &&& \{e\} & \textrm{computed value} \\
adamc@551 2336 \end{array}$$
adamc@551 2337
adam@1751 2338 Further, there is a special convenience and compatibility form for setting CSS classes of tags. If a \cd{class} attribute has a value that is a string literal, the literal is parsed in the usual HTML way and replaced with calls to appropriate Ur/Web combinators. Any dashes in the text are replaced with underscores to determine Ur identifiers. The same desugaring can be accessed in a normal expression context by calling the pseudo-function \cd{CLASS} on a string literal.
adam@1751 2339
adam@1751 2340 Similar support is provided for \cd{style} attributes. Normal CSS syntax may be used in string literals that are \cd{style} attribute values, and the desugaring may be accessed elsewhere with the pseudo-function \cd{STYLE}.
adamc@552 2341
adamc@1198 2342 \section{\label{structure}The Structure of Web Applications}
adamc@553 2343
adam@1797 2344 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 2345
adam@1532 2346 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 2347
adam@1787 2348 Normal links are accessible via HTTP \texttt{GET}, which the relevant standard says should never cause side effects. To export a page which may cause side effects, accessible only via HTTP \texttt{POST}, include one argument of the page handler of type $\mt{Basis.postBody}$. When the handler is called, this argument will receive a value that can be deconstructed into a MIME type (with $\mt{Basis.postType}$) and payload (with $\mt{Basis.postData}$). This kind of handler should not be used with forms that exist solely within Ur/Web apps; for these, use Ur/Web's built-in support, as described below. It may still be useful to use $\mt{Basis.postBody}$ with form requests submitted by code outside an Ur/Web app. For such cases, the function $\mt{Top.postFields} : \mt{postBody} \to \mt{list} \; (\mt{string} \times \mt{string})$ may be useful, breaking a \texttt{POST} body of type \texttt{application/x-www-form-urlencoded} into its name-value pairs.
adam@1347 2349
adam@1370 2350 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 2351
adamc@553 2352 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 2353
adamc@553 2354 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 2355
adam@1653 2356 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 2357 \begin{itemize}
adam@1653 2358 \item Functions are disallowed, since there is no obvious way to serialize them safely.
adam@1653 2359 \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 2360 \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 2361 \end{itemize}
adamc@553 2362
adamc@660 2363 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 2364
adamc@789 2365 \medskip
adamc@789 2366
adam@1347 2367 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 2368
adamc@789 2369 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 2370
adam@1348 2371 \subsection{Tasks}
adam@1348 2372
adam@1348 2373 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 2374
adam@1348 2375 $$\begin{array}{l}
adam@1348 2376 \mt{con} \; \mt{task\_kind} :: \mt{Type} \to \mt{Type} \\
adam@1348 2377 \mt{val} \; \mt{initialize} : \mt{task\_kind} \; \mt{unit} \\
adam@1349 2378 \mt{val} \; \mt{clientLeaves} : \mt{task\_kind} \; \mt{client} \\
adam@1349 2379 \mt{val} \; \mt{periodic} : \mt{int} \to \mt{task\_kind} \; \mt{unit}
adam@1348 2380 \end{array}$$
adam@1348 2381
adam@1348 2382 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 2383
adam@1348 2384 The currently supported task kinds are:
adam@1348 2385 \begin{itemize}
adam@1349 2386 \item $\mt{initialize}$: Code that is run when the application starts up.
adam@1348 2387 \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 2388 \item $\mt{periodic} \; n$: Code that is run when the application starts up and then every $n$ seconds thereafter.
adam@1348 2389 \end{itemize}
adam@1348 2390
adamc@553 2391
adamc@897 2392 \section{The Foreign Function Interface}
adamc@897 2393
adamc@897 2394 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 2395
adamc@897 2396 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 2397
adamc@897 2398 \begin{itemize}
adamc@897 2399 \item \texttt{clientOnly Module.ident} registers a value as being allowed only in client-side code.
adamc@897 2400 \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@1878 2401 \item \texttt{effectful Module.ident} registers a function that can have side effects. This is the default for \texttt{transaction}-based types, and, actually, this directive is mostly present for legacy compatibility reasons, since it used to be required explicitly for each \texttt{transaction}al function.
adamc@897 2402 \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 2403 \item \texttt{include FILE} requests inclusion of a C header file.
adamc@897 2404 \item \texttt{jsFunc Module.ident=name} gives a mapping from an Ur name for a value to a JavaScript name.
adamc@897 2405 \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 2406 \item \texttt{script URL} requests inclusion of a JavaScript source file within application HTML.
adamc@897 2407 \item \texttt{serverOnly Module.ident} registers a value as being allowed only in server-side code.
adamc@897 2408 \end{itemize}
adamc@897 2409
adamc@897 2410 \subsection{Writing C FFI Code}
adamc@897 2411
adam@1881 2412 C source files connecting to the Ur/Web FFI should include \texttt{urweb.h}, and C++ source files should include \texttt{urweb\_cpp.h}.
adam@1881 2413
adamc@897 2414 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 2415
adamc@897 2416 \begin{itemize}
adam@1881 2417 \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/urweb/types.h} for their definitions.
adamc@897 2418 \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 2419 \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 2420 \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 2421 \end{itemize}
adamc@897 2422
adam@1881 2423 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/urweb\_cpp.h}. Most should only be used internally by the compiler. A few are useful in general FFI implementation:
adamc@897 2424 \begin{itemize}
adamc@897 2425 \item \begin{verbatim}
adamc@897 2426 void uw_error(uw_context, failure_kind, const char *fmt, ...);
adamc@897 2427 \end{verbatim}
adamc@897 2428 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 2429
adam@1329 2430 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 2431
adamc@897 2432 \item \begin{verbatim}
adam@1469 2433 void uw_set_error_message(uw_context, const char *fmt, ...);
adam@1469 2434 \end{verbatim}
adam@1469 2435 This simpler form of \texttt{uw\_error()} saves an error message without immediately aborting execution.
adam@1469 2436
adam@1469 2437 \item \begin{verbatim}
adamc@897 2438 void uw_push_cleanup(uw_context, void (*func)(void *), void *arg);
adamc@897 2439 void uw_pop_cleanup(uw_context);
adamc@897 2440 \end{verbatim}
adam@1329 2441 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 2442
adam@1329 2443 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 2444
adamc@897 2445 \item \begin{verbatim}
adamc@897 2446 void *uw_malloc(uw_context, size_t);
adamc@897 2447 \end{verbatim}
adam@1329 2448 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 2449
adam@1329 2450 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 2451
adamc@897 2452 \item \begin{verbatim}
adamc@897 2453 typedef void (*uw_callback)(void *);
adam@1328 2454 typedef void (*uw_callback_with_retry)(void *, int will_retry);
adamc@897 2455 void uw_register_transactional(uw_context, void *data, uw_callback commit,
adam@1328 2456 uw_callback rollback, uw_callback_with_retry free);
adamc@897 2457 \end{verbatim}
adam@1328 2458 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 2459
adamc@1085 2460 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 2461
adam@1329 2462 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 2463
adam@1329 2464 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 2465
adam@1469 2466 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 2467
adamc@1085 2468 \item \begin{verbatim}
adamc@1085 2469 void *uw_get_global(uw_context, char *name);
adamc@1085 2470 void uw_set_global(uw_context, char *name, void *data, uw_callback free);
adamc@1085 2471 \end{verbatim}
adam@1329 2472 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 2473
adamc@897 2474 \end{itemize}
adamc@897 2475
adamc@897 2476 \subsection{Writing JavaScript FFI Code}
adamc@897 2477
adamc@897 2478 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 2479
adamc@897 2480 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 2481
adamc@897 2482 \begin{itemize}
adamc@897 2483 \item Integers, floats, strings, characters, and booleans are represented in the usual JavaScript way.
adam@1644 2484 \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 2485 \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 2486 \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 2487 \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 2488 \item As in the C FFI, all abstract types of program syntax are implemented with strings in JavaScript.
adam@1844 2489 \item A value of Ur type \texttt{transaction t} is represented in the same way as for \texttt{unit -> t}.
adamc@897 2490 \end{itemize}
adamc@897 2491
adam@1644 2492 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 2493
adam@1644 2494 \begin{itemize}
adam@1644 2495 \item Sources should be treated as an abstract type, manipulated via:
adam@1644 2496 \begin{itemize}
adam@1644 2497 \item \cd{sc(v)}, to create a source initialized to \cd{v}
adam@1644 2498 \item \cd{sg(s)}, to retrieve the current value of source \cd{s}
adam@1644 2499 \item \cd{sv(s, v)}, to set source \cd{s} to value \cd{v}
adam@1644 2500 \end{itemize}
adam@1644 2501
adam@1644 2502 \item Signals should be treated as an abstract type, manipulated via:
adam@1644 2503 \begin{itemize}
adam@1644 2504 \item \cd{sr(v)} and \cd{sb(s, f)}, the ``return'' and ``bind'' monad operators, respectively
adam@1644 2505 \item \cd{ss(s)}, to produce the signal corresponding to source \cd{s}
adam@1644 2506 \item \cd{scur(s)}, to get the current value of signal \cd{s}
adam@1644 2507 \end{itemize}
adam@1644 2508
adam@1644 2509 \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 2510
adam@1702 2511 \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 2512
adam@1644 2513 \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 2514 \end{itemize}
adamc@897 2515
adam@1833 2516 \subsection{Introducing New HTML Tags}
adam@1833 2517
adam@1833 2518 FFI modules may introduce new tags as values with $\mt{Basis.tag}$ types. See \texttt{basis.urs} for examples of how tags are declared. The identifier of a tag value is used as its rendering in HTML. The Ur/Web syntax sugar for XML literals desugars each use of a tag into a reference to an identifier with the same name. There is no need to provide implementations (i.e., in C or JavaScript code) for such identifiers.
adam@1833 2519
adam@1833 2520 The onus is on the coder of a new tag's interface to think about consequences for code injection attacks, messing with the DOM in ways that may break Ur/Web reactive programming, etc.
adam@1833 2521
adamc@897 2522
adamc@552 2523 \section{Compiler Phases}
adamc@552 2524
adamc@552 2525 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 2526
adamc@552 2527 In this section, we step through the main phases of compilation, noting what consequences each phase has for effective programming.
adamc@552 2528
adamc@552 2529 \subsection{Parse}
adamc@552 2530
adamc@552 2531 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 2532
adamc@552 2533 \subsection{Elaborate}
adamc@552 2534
adamc@552 2535 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 2536
adam@1378 2537 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 2538
adamc@552 2539 \subsection{Unnest}
adamc@552 2540
adamc@552 2541 Named local function definitions are moved to the top level, to avoid the need to generate closures.
adamc@552 2542
adamc@552 2543 \subsection{Corify}
adamc@552 2544
adamc@552 2545 Module system features are compiled away, through inlining of functor definitions at application sites. Afterward, most abstraction boundaries are broken, facilitating optimization.
adamc@552 2546
adamc@552 2547 \subsection{Especialize}
adamc@552 2548
adam@1356 2549 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 2550
adamc@552 2551 \subsection{Untangle}
adamc@552 2552
adam@1797 2553 Remove unnecessary mutual recursion, splitting recursive groups into strongly connected components.
adamc@552 2554
adamc@552 2555 \subsection{Shake}
adamc@552 2556
adamc@552 2557 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 2558
adamc@661 2559 \subsection{Rpcify}
adamc@661 2560
adamc@661 2561 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 2562
adamc@661 2563 \subsection{Untangle, Shake}
adamc@661 2564
adamc@661 2565 Repeat these simplifications.
adamc@661 2566
adamc@553 2567 \subsection{\label{tag}Tag}
adamc@552 2568
adamc@552 2569 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 2570
adamc@552 2571 \subsection{Reduce}
adamc@552 2572
adamc@552 2573 Apply definitional equality rules to simplify the program as much as possible. This effectively includes inlining of every non-recursive definition.
adamc@552 2574
adamc@552 2575 \subsection{Unpoly}
adamc@552 2576
adamc@552 2577 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 2578
adamc@552 2579 \subsection{Specialize}
adamc@552 2580
adamc@558 2581 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 2582
adamc@552 2583 \subsection{Shake}
adamc@552 2584
adamc@558 2585 Here the compiler repeats the earlier Shake phase.
adamc@552 2586
adamc@552 2587 \subsection{Monoize}
adamc@552 2588
adamc@552 2589 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 2590
adamc@552 2591 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 2592
adamc@552 2593 \subsection{MonoOpt}
adamc@552 2594
adamc@552 2595 Simple algebraic laws are applied to simplify the program, focusing especially on efficient imperative generation of HTML pages.
adamc@552 2596
adamc@552 2597 \subsection{MonoUntangle}
adamc@552 2598
adamc@552 2599 Unnecessary mutual recursion is broken up again.
adamc@552 2600
adamc@552 2601 \subsection{MonoReduce}
adamc@552 2602
adamc@552 2603 Equivalents of the definitional equality rules are applied to simplify programs, with inlining again playing a major role.
adamc@552 2604
adamc@552 2605 \subsection{MonoShake, MonoOpt}
adamc@552 2606
adamc@552 2607 Unneeded declarations are removed, and basic optimizations are repeated.
adamc@552 2608
adamc@552 2609 \subsection{Fuse}
adamc@552 2610
adamc@552 2611 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 2612
adamc@552 2613 \subsection{MonoUntangle, MonoShake}
adamc@552 2614
adamc@552 2615 Fuse often creates more opportunities to remove spurious mutual recursion.
adamc@552 2616
adamc@552 2617 \subsection{Pathcheck}
adamc@552 2618
adamc@552 2619 The compiler checks that no link or action name has been used more than once.
adamc@552 2620
adamc@552 2621 \subsection{Cjrize}
adamc@552 2622
adamc@552 2623 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 2624
adamc@552 2625 \subsection{C Compilation and Linking}
adamc@552 2626
adam@1523 2627 The output of the last phase is pretty-printed as C source code and passed to the C compiler.
adamc@552 2628
adamc@552 2629
as@1564 2630 \end{document}