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| author | aarne <aarne@cs.chalmers.se> | 2008-06-27 11:27:40 +0000 |
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| committer | aarne <aarne@cs.chalmers.se> | 2008-06-27 11:27:40 +0000 |
| commit | 032531c6a690edbb377ff11ee2a743a30c5bf500 (patch) | |
| tree | 21842e9061dc8dd54e2666c65160d2616537dae7 /doc/tutorial/gf-tutorial2_1.html | |
| parent | e4e64c13a69db6505df499a0c3445ada9b1b2d88 (diff) | |
rm old tutorials
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diff --git a/doc/tutorial/gf-tutorial2_1.html b/doc/tutorial/gf-tutorial2_1.html deleted file mode 100644 index 5576428b5..000000000 --- a/doc/tutorial/gf-tutorial2_1.html +++ /dev/null @@ -1,3504 +0,0 @@ -<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> -<HTML> -<HEAD> -<META NAME="generator" CONTENT="http://txt2tags.sf.net"> -<META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=iso-8859-1"> -<TITLE>Grammatical Framework Tutorial</TITLE> -</HEAD><BODY BGCOLOR="white" TEXT="black"> -<P ALIGN="center"><CENTER><H1>Grammatical Framework Tutorial</H1> -<FONT SIZE="4"> -<I>Author: Aarne Ranta aarne (at) cs.chalmers.se</I><BR> -Last update: Wed May 30 21:26:11 2007 -</FONT></CENTER> - -<P></P> -<HR NOSHADE SIZE=1> -<P></P> - <UL> - <LI><A HREF="#toc1">Introduction</A> - <UL> - <LI><A HREF="#toc2">GF = Grammatical Framework</A> - <LI><A HREF="#toc3">What are GF grammars used for</A> - <LI><A HREF="#toc4">Who is this tutorial for</A> - <LI><A HREF="#toc5">The coverage of the tutorial</A> - <LI><A HREF="#toc6">Getting the GF program</A> - </UL> - <LI><A HREF="#toc7">The .cf grammar format</A> - <UL> - <LI><A HREF="#toc8">Importing grammars and parsing strings</A> - <LI><A HREF="#toc9">Generating trees and strings</A> - <LI><A HREF="#toc10">Visualizing trees</A> - <LI><A HREF="#toc11">Some random-generated sentences</A> - <LI><A HREF="#toc12">Systematic generation</A> - <LI><A HREF="#toc13">More on pipes; tracing</A> - <LI><A HREF="#toc14">Writing and reading files</A> - </UL> - <LI><A HREF="#toc15">The .gf grammar format</A> - <UL> - <LI><A HREF="#toc16">Abstract and concrete syntax</A> - <LI><A HREF="#toc17">Judgement forms</A> - <LI><A HREF="#toc18">Module types</A> - <LI><A HREF="#toc19">Records and strings</A> - <LI><A HREF="#toc20">An abstract syntax example</A> - <LI><A HREF="#toc21">A concrete syntax example</A> - <LI><A HREF="#toc22">Modules and files</A> - </UL> - <LI><A HREF="#toc23">Multilingual grammars and translation</A> - <UL> - <LI><A HREF="#toc24">An Italian concrete syntax</A> - <LI><A HREF="#toc25">Using a multilingual grammar</A> - <LI><A HREF="#toc26">Translation session</A> - <LI><A HREF="#toc27">Translation quiz</A> - </UL> - <LI><A HREF="#toc28">Grammar architecture</A> - <UL> - <LI><A HREF="#toc29">Extending a grammar</A> - <LI><A HREF="#toc30">Multiple inheritance</A> - <LI><A HREF="#toc31">Visualizing module structure</A> - <LI><A HREF="#toc32">System commands</A> - </UL> - <LI><A HREF="#toc33">Resource modules</A> - <UL> - <LI><A HREF="#toc34">The golden rule of functional programming</A> - <LI><A HREF="#toc35">Operation definitions</A> - <LI><A HREF="#toc36">The ``resource`` module type</A> - <LI><A HREF="#toc37">Opening a ``resource``</A> - <LI><A HREF="#toc38">Division of labour</A> - </UL> - <LI><A HREF="#toc39">Morphology</A> - <UL> - <LI><A HREF="#toc40">Parameters and tables</A> - <LI><A HREF="#toc41">Inflection tables, paradigms, and ``oper`` definitions</A> - <LI><A HREF="#toc42">Worst-case functions and data abstraction</A> - <LI><A HREF="#toc43">A system of paradigms using Prelude operations</A> - <LI><A HREF="#toc44">An intelligent noun paradigm using ``case`` expressions</A> - <LI><A HREF="#toc45">Pattern matching</A> - <LI><A HREF="#toc46">Morphological resource modules</A> - <LI><A HREF="#toc47">Testing resource modules</A> - </UL> - <LI><A HREF="#toc48">Using parameters in concrete syntax</A> - <UL> - <LI><A HREF="#toc49">Parametric vs. inherent features, agreement</A> - <LI><A HREF="#toc50">English concrete syntax with parameters</A> - <LI><A HREF="#toc51">Hierarchic parameter types</A> - <LI><A HREF="#toc52">Morphological analysis and morphology quiz</A> - <LI><A HREF="#toc53">Discontinuous constituents</A> - <LI><A HREF="#toc54">Free variation</A> - <LI><A HREF="#toc55">Overloading of operations</A> - </UL> - <LI><A HREF="#toc56">Using the resource grammar library TODO</A> - <UL> - <LI><A HREF="#toc57">Interfaces, instances, and functors</A> - <LI><A HREF="#toc58">The simplest way</A> - <LI><A HREF="#toc59">How to find resource functions</A> - <LI><A HREF="#toc60">A functor implementation</A> - <LI><A HREF="#toc61">Restricted inheritance and qualified opening</A> - </UL> - <LI><A HREF="#toc62">More constructs for concrete syntax</A> - <UL> - <LI><A HREF="#toc63">Local definitions</A> - <LI><A HREF="#toc64">Record extension and subtyping</A> - <LI><A HREF="#toc65">Tuples and product types</A> - <LI><A HREF="#toc66">Record and tuple patterns</A> - <LI><A HREF="#toc67">Regular expression patterns</A> - <LI><A HREF="#toc68">Prefix-dependent choices</A> - <LI><A HREF="#toc69">Predefined types and operations</A> - </UL> - <LI><A HREF="#toc70">More concepts of abstract syntax</A> - <UL> - <LI><A HREF="#toc71">GF as a logical framework</A> - <LI><A HREF="#toc72">Dependent types</A> - <LI><A HREF="#toc73">Dependent types in concrete syntax</A> - <LI><A HREF="#toc74">Expressing selectional restrictions</A> - <LI><A HREF="#toc75">Case study: selectional restrictions and statistical language models TODO</A> - <LI><A HREF="#toc76">Proof objects</A> - <LI><A HREF="#toc77">Variable bindings</A> - <LI><A HREF="#toc78">Semantic definitions</A> - <LI><A HREF="#toc79">Case study: representing anaphoric reference TODO</A> - </UL> - <LI><A HREF="#toc80">Transfer modules TODO</A> - <LI><A HREF="#toc81">Practical issues TODO</A> - <UL> - <LI><A HREF="#toc82">Lexers and unlexers</A> - <LI><A HREF="#toc83">Efficiency of grammars</A> - <LI><A HREF="#toc84">Speech input and output</A> - <LI><A HREF="#toc85">Multilingual syntax editor</A> - <LI><A HREF="#toc86">Interactive Development Environment (IDE)</A> - <LI><A HREF="#toc87">Communicating with GF</A> - <LI><A HREF="#toc88">Embedded grammars in Haskell, Java, and Prolog</A> - <LI><A HREF="#toc89">Alternative input and output grammar formats</A> - </UL> - <LI><A HREF="#toc90">Larger case studies TODO</A> - <UL> - <LI><A HREF="#toc91">Interfacing formal and natural languages</A> - <LI><A HREF="#toc92">A multimodal dialogue system</A> - </UL> - </UL> - -<P></P> -<HR NOSHADE SIZE=1> -<P></P> -<P> -<IMG ALIGN="middle" SRC="../gf-logo.png" BORDER="0" ALT=""> -</P> -<A NAME="toc1"></A> -<H2>Introduction</H2> -<A NAME="toc2"></A> -<H3>GF = Grammatical Framework</H3> -<P> -The term GF is used for different things: -</P> -<UL> -<LI>a <B>program</B> used for working with grammars -<LI>a <B>programming language</B> in which grammars can be written -<LI>a <B>theory</B> about grammars and languages -</UL> - -<P> -This tutorial is primarily about the GF program and -the GF programming language. -It will guide you -</P> -<UL> -<LI>to use the GF program -<LI>to write GF grammars -<LI>to write programs in which GF grammars are used as components -</UL> - -<A NAME="toc3"></A> -<H3>What are GF grammars used for</H3> -<P> -A grammar is a definition of a language. -From this definition, different language processing components -can be derived: -</P> -<UL> -<LI>parsing: to analyse the language -<LI>linearization: to generate the language -<LI>translation: to analyse one language and generate another -</UL> - -<P> -A GF grammar can be seen as a declarative program from which these -processing tasks can be automatically derived. In addition, many -other tasks are readily available for GF grammars: -</P> -<UL> -<LI>morphological analysis: find out the possible inflection forms of words -<LI>morphological synthesis: generate all inflection forms of words -<LI>random generation: generate random expressions -<LI>corpus generation: generate all expressions -<LI>teaching quizzes: train morphology and translation -<LI>multilingual authoring: create a document in many languages simultaneously -<LI>speech input: optimize a speech recognition system for your grammar -</UL> - -<P> -A typical GF application is based on a <B>multilingual grammar</B> involving -translation on a special domain. Existing applications of this idea include -</P> -<UL> -<LI><A HREF="http://www.cs.chalmers.se/~hallgren/Alfa/Tutorial/GFplugin.html">Alfa:</A>: - a natural-language interface to a proof editor - (languages: English, French, Swedish) -<LI><A HREF="http://www.key-project.org/">KeY</A>: - a multilingual authoring system for creating software specifications - (languages: OCL, English, German) -<LI><A HREF="http://www.talk-project.org">TALK</A>: - multilingual and multimodal dialogue systems - (languages: English, Finnish, French, German, Italian, Spanish, Swedish) -<LI><A HREF="http://webalt.math.helsinki.fi/content/index_eng.html">WebALT</A>: - a multilingual translator of mathematical exercises - (languages: Catalan, English, Finnish, French, Spanish, Swedish) -<LI><A HREF="http://www.cs.chalmers.se/~bringert/gf/translate/">Numeral translator</A>: - number words from 1 to 999,999 - (88 languages) -</UL> - -<P> -The specialization of a grammar to a domain makes it possible to -obtain much better translations than in an unlimited machine translation -system. This is due to the well-defined semantics of such domains. -Grammars having this character are called <B>application grammars</B>. -They are different from most grammars written by linguists just -because they are multilingual and domain-specific. -</P> -<P> -However, there is another kind of grammars, which we call <B>resource grammars</B>. -These are large, comprehensive grammars that can be used on any domain. -The GF Resource Grammar Library has resource grammars for 10 languages. -These grammars can be used as <B>libraries</B> to define application grammars. -In this way, it is possible to write a high-quality grammar without -knowing about linguistics: in general, to write an application grammar -by using the resource library just requires practical knowledge of -the target language. and all theoretical knowledge about its grammar -is given by the libraries. -</P> -<A NAME="toc4"></A> -<H3>Who is this tutorial for</H3> -<P> -This tutorial is mainly for programmers who want to learn to write -application grammars. It will go through GF's programming concepts -without entering too deep into linguistics. Thus it should -be accessible to anyone who has some previous programming experience. -</P> -<P> -A separate document is being written on how to write resource grammars. -This includes the ways in which linguistic problems posed by different -languages are solved in GF. -</P> -<A NAME="toc5"></A> -<H3>The coverage of the tutorial</H3> -<P> -The tutorial gives a hands-on introduction to grammar writing. -We start by building a small grammar for the domain of food: -in this grammar, you can say things like -</P> -<PRE> - this Italian cheese is delicious -</PRE> -<P> -in English and Italian. -</P> -<P> -The first English grammar -<A HREF="food.cf"><CODE>food.cf</CODE></A> -is written in a context-free -notation (also known as BNF). The BNF format is often a good -starting point for GF grammar development, because it is -simple and widely used. However, the BNF format is not -good for multilingual grammars. While it is possible to -"translate" by just changing the words contained in a -BNF grammar to words of some other -language, proper translation usually involves more. -For instance, the order of words may have to be changed: -</P> -<PRE> - Italian cheese ===> formaggio italiano -</PRE> -<P> -The full GF grammar format is designed to support such -changes, by separating between the <B>abstract syntax</B> -(the logical structure) and the <B>concrete syntax</B> (the -sequence of words) of expressions. -</P> -<P> -There is more than words and word order that makes languages -different. Words can have different forms, and which forms -they have vary from language to language. For instance, -Italian adjectives usually have four forms where English -has just one: -</P> -<PRE> - delicious (wine, wines, pizza, pizzas) - vino delizioso, vini deliziosi, pizza deliziosa, pizze deliziose -</PRE> -<P> -The <B>morphology</B> of a language describes the -forms of its words. While the complete description of morphology -belongs to resource grammars, this tutorial will explain the -programming concepts involved in morphology. This will moreover -make it possible to grow the fragment covered by the food example. -The tutorial will in fact build a miniature resource grammar in order -to illustrate the module structure of library-based application -grammar writing. -</P> -<P> -Thus it is by elaborating the initial <CODE>food.cf</CODE> example that -the tutorial makes a guided tour through all concepts of GF. -While the constructs of the GF language are the main focus, -also the commands of the GF system are introduced as they -are needed. -</P> -<P> -To learn how to write GF grammars is not the only goal of -this tutorial. To learn the commands of the GF system means -that simple applications of grammars, such as translation and -quiz systems, can be built simply by writing scripts for the -system. More complicated applications, such as natural-language -interfaces and dialogue systems, also require programming in -some general-purpose language. We will briefly explain how -GF grammars are used as components of Haskell, Java, Javascript, -and Prolog grammars. The tutorial concludes with a couple of -case studies showing how such complete systems can be built. -</P> -<A NAME="toc6"></A> -<H3>Getting the GF program</H3> -<P> -The GF program is open-source free software, which you can download via the -GF Homepage: -<A HREF="http://www.cs.chalmers.se/~aarne/GF"><CODE>http://www.cs.chalmers.se/~aarne/GF</CODE></A> -</P> -<P> -There you can download -</P> -<UL> -<LI>binaries for Linux, Solaris, Macintosh, and Windows -<LI>source code and documentation -<LI>grammar libraries and examples -</UL> - -<P> -If you want to compile GF from source, you need Haskell and Java -compilers. But normally you don't have to compile, and you definitely -don't need to know Haskell or Java to use GF. -</P> -<P> -To start the GF program, assuming you have installed it, just type -</P> -<PRE> - % gf -</PRE> -<P> -in the shell. You will see GF's welcome message and the prompt <CODE>></CODE>. -The command -</P> -<PRE> - > help -</PRE> -<P> -will give you a list of available commands. -</P> -<P> -As a common convention in this Tutorial, we will use -</P> -<UL> -<LI><CODE>%</CODE> as a prompt that marks system commands -<LI><CODE>></CODE> as a prompt that marks GF commands -</UL> - -<P> -Thus you should not type these prompts, but only the lines that -follow them. -</P> -<A NAME="toc7"></A> -<H2>The .cf grammar format</H2> -<P> -Now you are ready to try out your first grammar. -We start with one that is not written in the GF language, but -in the much more common BNF notation (Backus Naur Form). The GF -program understands a variant of this notation and translates it -internally to GF's own representation. -</P> -<P> -To get started, type (or copy) the following lines into a file named -<CODE>food.cf</CODE>: -</P> -<PRE> - Is. S ::= Item "is" Quality ; - That. Item ::= "that" Kind ; - This. Item ::= "this" Kind ; - QKind. Kind ::= Quality Kind ; - Cheese. Kind ::= "cheese" ; - Fish. Kind ::= "fish" ; - Wine. Kind ::= "wine" ; - Italian. Quality ::= "Italian" ; - Boring. Quality ::= "boring" ; - Delicious. Quality ::= "delicious" ; - Expensive. Quality ::= "expensive" ; - Fresh. Quality ::= "fresh" ; - Very. Quality ::= "very" Quality ; - Warm. Quality ::= "warm" ; -</PRE> -<P> -For those who know ordinary BNF, the -notation we use includes one extra element: a <B>label</B> appearing -as the first element of each rule and terminated by a full stop. -</P> -<P> -The grammar we wrote defines a set of phrases usable for speaking about food. -It builds <B>sentences</B> (<CODE>S</CODE>) by assigning <CODE>Quality</CODE>s to -<CODE>Item</CODE>s. <CODE>Item</CODE>s are build from <CODE>Kind</CODE>s by prepending the -word "this" or "that". <CODE>Kind</CODE>s are either <B>atomic</B>, such as -"cheese" and "wine", or formed by prepending a <CODE>Quality</CODE> to a -<CODE>Kind</CODE>. A <CODE>Quality</CODE> is either atomic, such as "Italian" and "boring", -or built by another <CODE>Quality</CODE> by prepending "very". Those familiar with -the context-free grammar notation will notice that, for instance, the -following sentence can be built using this grammar: -</P> -<PRE> - this delicious Italian wine is very very expensive -</PRE> -<P></P> -<A NAME="toc8"></A> -<H3>Importing grammars and parsing strings</H3> -<P> -The first GF command needed when using a grammar is to <B>import</B> it. -The command has a long name, <CODE>import</CODE>, and a short name, <CODE>i</CODE>. -You can type either -</P> -<PRE> - > import food.cf -</PRE> -<P> -or -</P> -<PRE> - > i food.cf -</PRE> -<P> -to get the same effect. -The effect is that the GF program <B>compiles</B> your grammar into an internal -representation, and shows a new prompt when it is ready. -</P> -<P> -You can now use GF for <B>parsing</B>: -</P> -<PRE> - > parse "this cheese is delicious" - Is (This Cheese) Delicious - - > p "that wine is very very Italian" - Is (That Wine) (Very (Very Italian)) -</PRE> -<P> -The <CODE>parse</CODE> (= <CODE>p</CODE>) command takes a <B>string</B> -(in double quotes) and returns an <B>abstract syntax tree</B> - the thing -beginning with <CODE>Is</CODE>. Trees are built from the rule labels given in the -grammar, and record the ways in which the rules are used to produce the -strings. A tree is, in general, something easier than a string -for a machine to understand and to process further. -</P> -<P> -Strings that return a tree when parsed do so in virtue of the grammar -you imported. Try parsing something else, and you fail -</P> -<PRE> - > p "hello world" - No success in cf parsing hello world - no tree found -</PRE> -<P></P> -<A NAME="toc9"></A> -<H3>Generating trees and strings</H3> -<P> -You can also use GF for <B>linearizing</B> -(<CODE>linearize = l</CODE>). This is the inverse of -parsing, taking trees into strings: -</P> -<PRE> - > linearize Is (That Wine) Warm - that wine is warm -</PRE> -<P> -What is the use of this? Typically not that you type in a tree at -the GF prompt. The utility of linearization comes from the fact that -you can obtain a tree from somewhere else. One way to do so is -<B>random generation</B> (<CODE>generate_random = gr</CODE>): -</P> -<PRE> - > generate_random - Is (This (QKind Italian Fish)) Fresh -</PRE> -<P> -Now you can copy the tree and paste it to the <CODE>linearize command</CODE>. -Or, more conveniently, feed random generation into linearization by using -a <B>pipe</B>. -</P> -<PRE> - > gr | l - this Italian fish is fresh -</PRE> -<P></P> -<A NAME="toc10"></A> -<H3>Visualizing trees</H3> -<P> -The gibberish code with parentheses returned by the parser does not -look like trees. Why is it called so? From the abstract mathematical -point of view, trees are a data structure that -represents <B>nesting</B>: trees are branching entities, and the branches -are themselves trees. Parentheses give a linear representation of trees, -useful for the computer. But the human eye may prefer to see a visualization; -for this purpose, GF provides the command <CODE>visualizre_tree = vt</CODE>, to which -parsing (and any other tree-producing command) can be piped: -</P> -<PRE> - parse "this delicious cheese is very Italian" | vt -</PRE> -<P></P> -<P> -<IMG ALIGN="middle" SRC="Tree2.png" BORDER="0" ALT=""> -</P> -<A NAME="toc11"></A> -<H3>Some random-generated sentences</H3> -<P> -Random generation is a good way to test a grammar; it can also -be quite amusing. So you may want to -generate ten strings with one and the same command: -</P> -<PRE> - > gr -number=10 | l - that wine is boring - that fresh cheese is fresh - that cheese is very boring - this cheese is Italian - that expensive cheese is expensive - that fish is fresh - that wine is very Italian - this wine is Italian - this cheese is boring - this fish is boring -</PRE> -<P></P> -<A NAME="toc12"></A> -<H3>Systematic generation</H3> -<P> -To generate <I>all</I> sentence that a grammar -can generate, use the command <CODE>generate_trees = gt</CODE>. -</P> -<PRE> - > generate_trees | l - that cheese is very Italian - that cheese is very boring - that cheese is very delicious - that cheese is very expensive - that cheese is very fresh - ... - this wine is expensive - this wine is fresh - this wine is warm - -</PRE> -<P> -You get quite a few trees but not all of them: only up to a given -<B>depth</B> of trees. To see how you can get more, use the -<CODE>help = h</CODE> command, -</P> -<PRE> - help gt -</PRE> -<P> -<B>Quiz</B>. If the command <CODE>gt</CODE> generated all -trees in your grammar, it would never terminate. Why? -</P> -<A NAME="toc13"></A> -<H3>More on pipes; tracing</H3> -<P> -A pipe of GF commands can have any length, but the "output type" -(either string or tree) of one command must always match the "input type" -of the next command. -</P> -<P> -The intermediate results in a pipe can be observed by putting the -<B>tracing</B> flag <CODE>-tr</CODE> to each command whose output you -want to see: -</P> -<PRE> - > gr -tr | l -tr | p - - Is (This Cheese) Boring - this cheese is boring - Is (This Cheese) Boring -</PRE> -<P> -This facility is good for test purposes: for instance, you -may want to see if a grammar is <B>ambiguous</B>, i.e. -contains strings that can be parsed in more than one way. -</P> -<A NAME="toc14"></A> -<H3>Writing and reading files</H3> -<P> -To save the outputs of GF commands into a file, you can -pipe it to the <CODE>write_file = wf</CODE> command, -</P> -<PRE> - > gr -number=10 | l | write_file exx.tmp -</PRE> -<P> -You can read the file back to GF with the -<CODE>read_file = rf</CODE> command, -</P> -<PRE> - > read_file exx.tmp | p -lines -</PRE> -<P> -Notice the flag <CODE>-lines</CODE> given to the parsing -command. This flag tells GF to parse each line of -the file separately. Without the flag, the grammar could -not recognize the string in the file, because it is not -a sentence but a sequence of ten sentences. -</P> -<A NAME="toc15"></A> -<H2>The .gf grammar format</H2> -<P> -To see GF's internal representation of a grammar -that you have imported, you can give the command -<CODE>print_grammar = pg</CODE>, -</P> -<PRE> - > print_grammar -</PRE> -<P> -The output is quite unreadable at this stage, and you may feel happy that -you did not need to write the grammar in that notation, but that the -GF grammar compiler produced it. -</P> -<P> -However, we will now start the demonstration -how GF's own notation gives you -much more expressive power than the <CODE>.cf</CODE> -format. We will introduce the <CODE>.gf</CODE> format by presenting -another way of defining the same grammar as in -<CODE>food.cf</CODE>. -Then we will show how the full GF grammar format enables you -to do things that are not possible in the context-free format. -</P> -<A NAME="toc16"></A> -<H3>Abstract and concrete syntax</H3> -<P> -A GF grammar consists of two main parts: -</P> -<UL> -<LI><B>abstract syntax</B>, defining what syntax trees there are -<LI><B>concrete syntax</B>, defining how trees are linearized into strings -</UL> - -<P> -The context-free format fuses these two things together, but it is always -possible to take them apart. For instance, the sentence formation rule -</P> -<PRE> - Is. S ::= Item "is" Quality ; -</PRE> -<P> -is interpreted as the following pair of GF rules: -</P> -<PRE> - fun Is : Item -> Quality -> S ; - lin Is item quality = {s = item.s ++ "is" ++ quality.s} ; -</PRE> -<P> -The former rule, with the keyword <CODE>fun</CODE>, belongs to the abstract syntax. -It defines the <B>function</B> -<CODE>Is</CODE> which constructs syntax trees of form -(<CODE>Is</CODE> <I>item</I> <I>quality</I>). -</P> -<P> -The latter rule, with the keyword <CODE>lin</CODE>, belongs to the concrete syntax. -It defines the <B>linearization function</B> for -syntax trees of form (<CODE>Is</CODE> <I>item</I> <I>quality</I>). -</P> -<A NAME="toc17"></A> -<H3>Judgement forms</H3> -<P> -Rules in a GF grammar are called <B>judgements</B>, and the keywords -<CODE>fun</CODE> and <CODE>lin</CODE> are used for distinguishing between two -<B>judgement forms</B>. Here is a summary of the most important -judgement forms: -</P> - <UL> - <LI>abstract syntax - <P></P> - </UL> - -<TABLE ALIGN="center" CELLPADDING="4" BORDER="1"> -<TR> -<TD>form</TD> -<TD>reading</TD> -</TR> -<TR> -<TD><CODE>cat</CODE> C</TD> -<TD>C is a category</TD> -</TR> -<TR> -<TD><CODE>fun</CODE> f <CODE>:</CODE> A</TD> -<TD>f is a function of type A</TD> -</TR> -</TABLE> - - <UL> - <LI>concrete syntax - <P></P> - </UL> - -<TABLE ALIGN="center" CELLPADDING="4" BORDER="1"> -<TR> -<TD>form</TD> -<TD>reading</TD> -</TR> -<TR> -<TD><CODE>lincat</CODE> C <CODE>=</CODE> T</TD> -<TD>category C has linearization type T</TD> -</TR> -<TR> -<TD><CODE>lin</CODE> f <CODE>=</CODE> t</TD> -<TD>function f has linearization t</TD> -</TR> -</TABLE> - -<P> -We return to the precise meanings of these judgement forms later. -First we will look at how judgements are grouped into modules, and -show how the food grammar is -expressed by using modules and judgements. -</P> -<A NAME="toc18"></A> -<H3>Module types</H3> -<P> -A GF grammar consists of <B>modules</B>, -into which judgements are grouped. The most important -module forms are -</P> - <UL> - <LI><CODE>abstract</CODE> A <CODE>=</CODE> M, abstract syntax A with judgements in - the module body M. - <LI><CODE>concrete</CODE> C <CODE>of</CODE> A <CODE>=</CODE> M, concrete syntax C of the - abstract syntax A, with judgements in the module body M. - </UL> - -<A NAME="toc19"></A> -<H3>Records and strings</H3> -<P> -The linearization type of a category is a <B>record type</B>, with -zero of more <B>fields</B> of different types. The simplest record -type used for linearization in GF is -</P> -<PRE> - {s : Str} -</PRE> -<P> -which has one field, with <B>label</B> <CODE>s</CODE> and type <CODE>Str</CODE>. -</P> -<P> -Examples of records of this type are -</P> -<PRE> - {s = "foo"} - {s = "hello" ++ "world"} -</PRE> -<P></P> -<P> -Whenever a record <CODE>r</CODE> of type <CODE>{s : Str}</CODE> is given, -<CODE>r.s</CODE> is an object of type <CODE>Str</CODE>. This is -a special case of the <B>projection</B> rule, allowing the extraction -of fields from a record: -</P> -<UL> -<LI>if <I>r</I> : <CODE>{</CODE> ... <I>p</I> : <I>T</I> ... <CODE>}</CODE> then <I>r.p</I> : <I>T</I> -</UL> - -<P> -The type <CODE>Str</CODE> is really the type of <B>token lists</B>, but -most of the time one can conveniently think of it as the type of strings, -denoted by string literals in double quotes. -</P> -<P> -Notice that -</P> -<PRE> - "hello world" -</PRE> -<P> -is not recommended as an expression of type <CODE>Str</CODE>. It denotes -a token with a space in it, and will usually -not work with the lexical analysis that precedes parsing. A shorthand -exemplified by -</P> -<PRE> - ["hello world and people"] === "hello" ++ "world" ++ "and" ++ "people" -</PRE> -<P> -can be used for lists of tokens. The expression -</P> -<PRE> - [] -</PRE> -<P> -denotes the empty token list. -</P> -<A NAME="toc20"></A> -<H3>An abstract syntax example</H3> -<P> -To express the abstract syntax of <CODE>food.cf</CODE> in -a file <CODE>Food.gf</CODE>, we write two kinds of judgements: -</P> -<UL> -<LI>Each category is introduced by a <CODE>cat</CODE> judgement. -<LI>Each rule label is introduced by a <CODE>fun</CODE> judgement, - with the type formed from the nonterminals of the rule. -</UL> - -<PRE> - abstract Food = { - - cat - S ; Item ; Kind ; Quality ; - - fun - Is : Item -> Quality -> S ; - This, That : Kind -> Item ; - QKind : Quality -> Kind -> Kind ; - Wine, Cheese, Fish : Kind ; - Very : Quality -> Quality ; - Fresh, Warm, Italian, Expensive, Delicious, Boring : Quality ; - } -</PRE> -<P> -Notice the use of shorthands permitting the sharing of -the keyword in subsequent judgements, -</P> -<PRE> - cat S ; Item ; === cat S ; cat Item ; -</PRE> -<P> -and of the type in subsequent <CODE>fun</CODE> judgements, -</P> -<PRE> - fun Wine, Fish : Kind ; === - fun Wine : Kind ; Fish : Kind ; === - fun Wine : Kind ; fun Fish : Kind ; -</PRE> -<P> -The order of judgements in a module is free. -</P> -<A NAME="toc21"></A> -<H3>A concrete syntax example</H3> -<P> -Each category introduced in <CODE>Food.gf</CODE> is -given a <CODE>lincat</CODE> rule, and each -function is given a <CODE>lin</CODE> rule. Similar shorthands -apply as in <CODE>abstract</CODE> modules. -</P> -<PRE> - concrete FoodEng of Food = { - - lincat - S, Item, Kind, Quality = {s : Str} ; - - lin - Is item quality = {s = item.s ++ "is" ++ quality.s} ; - This kind = {s = "this" ++ kind.s} ; - That kind = {s = "that" ++ kind.s} ; - QKind quality kind = {s = quality.s ++ kind.s} ; - Wine = {s = "wine"} ; - Cheese = {s = "cheese"} ; - Fish = {s = "fish"} ; - Very quality = {s = "very" ++ quality.s} ; - Fresh = {s = "fresh"} ; - Warm = {s = "warm"} ; - Italian = {s = "Italian"} ; - Expensive = {s = "expensive"} ; - Delicious = {s = "delicious"} ; - Boring = {s = "boring"} ; - } -</PRE> -<P></P> -<A NAME="toc22"></A> -<H3>Modules and files</H3> -<P> -Source files: Module name + <CODE>.gf</CODE> = file name -</P> -<P> -Target files: each module is compiled into a <CODE>.gfc</CODE> file. -</P> -<P> -Import <CODE>FoodEng.gf</CODE> and see what happens -</P> -<PRE> - > i FoodEng.gf -</PRE> -<P> -The GF program does not only read the file -<CODE>FoodEng.gf</CODE>, but also all other files that it -depends on - in this case, <CODE>Food.gf</CODE>. -</P> -<P> -For each file that is compiled, a <CODE>.gfc</CODE> file -is generated. The GFC format (="GF Canonical") is the -"machine code" of GF, which is faster to process than -GF source files. When reading a module, GF decides whether -to use an existing <CODE>.gfc</CODE> file or to generate -a new one, by looking at modification times. -</P> -<A NAME="toc23"></A> -<H2>Multilingual grammars and translation</H2> -<P> -The main advantage of separating abstract from concrete syntax is that -one abstract syntax can be equipped with many concrete syntaxes. -A system with this property is called a <B>multilingual grammar</B>. -</P> -<P> -Multilingual grammars can be used for applications such as -translation. Let us build an Italian concrete syntax for -<CODE>Food</CODE> and then test the resulting -multilingual grammar. -</P> -<A NAME="toc24"></A> -<H3>An Italian concrete syntax</H3> -<PRE> - concrete FoodIta of Food = { - - lincat - S, Item, Kind, Quality = {s : Str} ; - - lin - Is item quality = {s = item.s ++ "è" ++ quality.s} ; - This kind = {s = "questo" ++ kind.s} ; - That kind = {s = "quello" ++ kind.s} ; - QKind quality kind = {s = kind.s ++ quality.s} ; - Wine = {s = "vino"} ; - Cheese = {s = "formaggio"} ; - Fish = {s = "pesce"} ; - Very quality = {s = "molto" ++ quality.s} ; - Fresh = {s = "fresco"} ; - Warm = {s = "caldo"} ; - Italian = {s = "italiano"} ; - Expensive = {s = "caro"} ; - Delicious = {s = "delizioso"} ; - Boring = {s = "noioso"} ; - - } - -</PRE> -<P></P> -<A NAME="toc25"></A> -<H3>Using a multilingual grammar</H3> -<P> -Import the two grammars in the same GF session. -</P> -<PRE> - > i FoodEng.gf - > i FoodIta.gf -</PRE> -<P> -Try generation now: -</P> -<PRE> - > gr | l - quello formaggio molto noioso è italiano - - > gr | l -lang=FoodEng - this fish is warm -</PRE> -<P> -Translate by using a pipe: -</P> -<PRE> - > p -lang=FoodEng "this cheese is very delicious" | l -lang=FoodIta - questo formaggio è molto delizioso -</PRE> -<P> -The <CODE>lang</CODE> flag tells GF which concrete syntax to use in parsing and -linearization. By default, the flag is set to the last-imported grammar. -To see what grammars are in scope and which is the main one, use the command -<CODE>print_options = po</CODE>: -</P> -<PRE> - > print_options - main abstract : Food - main concrete : FoodIta - actual concretes : FoodIta FoodEng -</PRE> -<P></P> -<A NAME="toc26"></A> -<H3>Translation session</H3> -<P> -If translation is what you want to do with a set of grammars, a convenient -way to do it is to open a <CODE>translation_session = ts</CODE>. In this session, -you can translate between all the languages that are in scope. -A dot <CODE>.</CODE> terminates the translation session. -</P> -<PRE> - > ts - - trans> that very warm cheese is boring - quello formaggio molto caldo è noioso - that very warm cheese is boring - - trans> questo vino molto italiano è molto delizioso - questo vino molto italiano è molto delizioso - this very Italian wine is very delicious - - trans> . - > -</PRE> -<P></P> -<A NAME="toc27"></A> -<H3>Translation quiz</H3> -<P> -This is a simple language exercise that can be automatically -generated from a multilingual grammar. The system generates a set of -random sentences, displays them in one language, and checks the user's -answer given in another language. The command <CODE>translation_quiz = tq</CODE> -makes this in a subshell of GF. -</P> -<PRE> - > translation_quiz FoodEng FoodIta - - Welcome to GF Translation Quiz. - The quiz is over when you have done at least 10 examples - with at least 75 % success. - You can interrupt the quiz by entering a line consisting of a dot ('.'). - - this fish is warm - questo pesce è caldo - > Yes. - Score 1/1 - - this cheese is Italian - questo formaggio è noioso - > No, not questo formaggio è noioso, but - questo formaggio è italiano - - Score 1/2 - this fish is expensive -</PRE> -<P> -You can also generate a list of translation exercises and save it in a -file for later use, by the command <CODE>translation_list = tl</CODE> -</P> -<PRE> - > translation_list -number=25 FoodEng FoodIta -</PRE> -<P> -The <CODE>number</CODE> flag gives the number of sentences generated. -</P> -<A NAME="toc28"></A> -<H2>Grammar architecture</H2> -<A NAME="toc29"></A> -<H3>Extending a grammar</H3> -<P> -The module system of GF makes it possible to <B>extend</B> a -grammar in different ways. The syntax of extension is -shown by the following example. We extend <CODE>Food</CODE> by -adding a category of questions and two new functions. -</P> -<PRE> - abstract Morefood = Food ** { - cat - Question ; - fun - QIs : Item -> Quality -> Question ; - Pizza : Kind ; - - } -</PRE> -<P> -Parallel to the abstract syntax, extensions can -be built for concrete syntaxes: -</P> -<PRE> - concrete MorefoodEng of Morefood = FoodEng ** { - lincat - Question = {s : Str} ; - lin - QIs item quality = {s = "is" ++ item.s ++ quality.s} ; - Pizza = {s = "pizza"} ; - } -</PRE> -<P> -The effect of extension is that all of the contents of the extended -and extending module are put together. -</P> -<A NAME="toc30"></A> -<H3>Multiple inheritance</H3> -<P> -Specialized vocabularies can be represented as small grammars that -only do "one thing" each. For instance, the following are grammars -for fruit and mushrooms -</P> -<PRE> - abstract Fruit = { - cat Fruit ; - fun Apple, Peach : Fruit ; - } - - abstract Mushroom = { - cat Mushroom ; - fun Cep, Agaric : Mushroom ; - } -</PRE> -<P> -They can afterwards be combined into bigger grammars by using -<B>multiple inheritance</B>, i.e. extension of several grammars at the -same time: -</P> -<PRE> - abstract Foodmarket = Food, Fruit, Mushroom ** { - fun - FruitKind : Fruit -> Kind ; - MushroomKind : Mushroom -> Kind ; - } -</PRE> -<P> -At this point, you would perhaps like to go back to -<CODE>Food</CODE> and take apart <CODE>Wine</CODE> to build a special -<CODE>Drink</CODE> module. -</P> -<A NAME="toc31"></A> -<H3>Visualizing module structure</H3> -<P> -When you have created all the abstract syntaxes and -one set of concrete syntaxes needed for <CODE>Foodmarket</CODE>, -your grammar consists of eight GF modules. To see how their -dependences look like, you can use the command -<CODE>visualize_graph = vg</CODE>, -</P> -<PRE> - > visualize_graph -</PRE> -<P> -and the graph will pop up in a separate window. -</P> -<P> -The graph uses -</P> -<UL> -<LI>oval boxes for abstract modules -<LI>square boxes for concrete modules -<LI>black-headed arrows for inheritance -<LI>white-headed arrows for the concrete-of-abstract relation -</UL> - -<P> -<IMG ALIGN="middle" SRC="Foodmarket.png" BORDER="0" ALT=""> -</P> -<A NAME="toc32"></A> -<H3>System commands</H3> -<P> -To document your grammar, you may want to print the -graph into a file, e.g. a <CODE>.png</CODE> file that -can be included in an HTML document. You can do this -by first printing the graph into a file <CODE>.dot</CODE> and then -processing this file with the <CODE>dot</CODE> program. -</P> -<PRE> - > pm -printer=graph | wf Foodmarket.dot - > ! dot -Tpng Foodmarket.dot > Foodmarket.png -</PRE> -<P> -The latter command is a Unix command, issued from GF by using the -shell escape symbol <CODE>!</CODE>. The resulting graph was shown in the previous section. -</P> -<P> -The command <CODE>print_multi = pm</CODE> is used for printing the current multilingual -grammar in various formats, of which the format <CODE>-printer=graph</CODE> just -shows the module dependencies. Use <CODE>help</CODE> to see what other formats -are available: -</P> -<PRE> - > help pm - > help -printer -</PRE> -<P></P> -<A NAME="toc33"></A> -<H2>Resource modules</H2> -<A NAME="toc34"></A> -<H3>The golden rule of functional programming</H3> -<P> -In comparison to the <CODE>.cf</CODE> format, the <CODE>.gf</CODE> format looks rather -verbose, and demands lots more characters to be written. You have probably -done this by the copy-paste-modify method, which is a common way to -avoid repeating work. -</P> -<P> -However, there is a more elegant way to avoid repeating work than the copy-and-paste -method. The <B>golden rule of functional programming</B> says that -</P> -<UL> -<LI>whenever you find yourself programming by copy-and-paste, write a function instead. -</UL> - -<P> -A function separates the shared parts of different computations from the -changing parts, parameters. In functional programming languages, such as -<A HREF="http://www.haskell.org">Haskell</A>, it is possible to share much more than in -languages such as C and Java. -</P> -<A NAME="toc35"></A> -<H3>Operation definitions</H3> -<P> -GF is a functional programming language, not only in the sense that -the abstract syntax is a system of functions (<CODE>fun</CODE>), but also because -functional programming can be used to define concrete syntax. This is -done by using a new form of judgement, with the keyword <CODE>oper</CODE> (for -<B>operation</B>), distinct from <CODE>fun</CODE> for the sake of clarity. -Here is a simple example of an operation: -</P> -<PRE> - oper ss : Str -> {s : Str} = \x -> {s = x} ; -</PRE> -<P> -The operation can be <B>applied</B> to an argument, and GF will -<B>compute</B> the application into a value. For instance, -</P> -<PRE> - ss "boy" ---> {s = "boy"} -</PRE> -<P> -(We use the symbol <CODE>---></CODE> to indicate how an expression is -computed into a value; this symbol is not a part of GF) -</P> -<P> -Thus an <CODE>oper</CODE> judgement includes the name of the defined operation, -its type, and an expression defining it. As for the syntax of the defining -expression, notice the <B>lambda abstraction</B> form <CODE>\x -> t</CODE> of -the function. -</P> -<A NAME="toc36"></A> -<H3>The ``resource`` module type</H3> -<P> -Operator definitions can be included in a concrete syntax. -But they are not really tied to a particular set of linearization rules. -They should rather be seen as <B>resources</B> -usable in many concrete syntaxes. -</P> -<P> -The <CODE>resource</CODE> module type can be used to package -<CODE>oper</CODE> definitions into reusable resources. Here is -an example, with a handful of operations to manipulate -strings and records. -</P> -<PRE> - resource StringOper = { - oper - SS : Type = {s : Str} ; - ss : Str -> SS = \x -> {s = x} ; - cc : SS -> SS -> SS = \x,y -> ss (x.s ++ y.s) ; - prefix : Str -> SS -> SS = \p,x -> ss (p ++ x.s) ; - } -</PRE> -<P> -Resource modules can extend other resource modules, in the -same way as modules of other types can extend modules of the -same type. Thus it is possible to build resource hierarchies. -</P> -<A NAME="toc37"></A> -<H3>Opening a ``resource``</H3> -<P> -Any number of <CODE>resource</CODE> modules can be -<B>opened</B> in a <CODE>concrete</CODE> syntax, which -makes definitions contained -in the resource usable in the concrete syntax. Here is -an example, where the resource <CODE>StringOper</CODE> is -opened in a new version of <CODE>FoodEng</CODE>. -</P> -<PRE> - concrete Food2Eng of Food = open StringOper in { - - lincat - S, Item, Kind, Quality = SS ; - - lin - Is item quality = cc item (prefix "is" quality) ; - This = prefix "this" ; - That = prefix "that" ; - QKind = cc ; - Wine = ss "wine" ; - Cheese = ss "cheese" ; - Fish = ss "fish" ; - Very = prefix "very" ; - Fresh = ss "fresh" ; - Warm = ss "warm" ; - Italian = ss "Italian" ; - Expensive = ss "expensive" ; - Delicious = ss "delicious" ; - Boring = ss "boring" ; - - } -</PRE> -<P> -The same string operations could be used to write <CODE>FoodIta</CODE> -more concisely. -</P> -<A NAME="toc38"></A> -<H3>Division of labour</H3> -<P> -Using operations defined in resource modules is a -way to avoid repetitive code. -In addition, it enables a new kind of modularity -and division of labour in grammar writing: grammarians familiar with -the linguistic details of a language can make this knowledge -available through resource grammar modules, whose users only need -to pick the right operations and not to know their implementation -details. -</P> -<A NAME="toc39"></A> -<H2>Morphology</H2> -<P> -Suppose we want to say, with the vocabulary included in -<CODE>Food.gf</CODE>, things like -</P> -<PRE> - all Italian wines are delicious -</PRE> -<P> -The new grammatical facility we need are the plural forms -of nouns and verbs (<I>wines, are</I>), as opposed to their -singular forms. -</P> -<P> -The introduction of plural forms requires two things: -</P> -<UL> -<LI>the <B>inflection</B> of nouns and verbs in singular and plural -<LI>the <B>agreement</B> of the verb to subject: - the verb must have the same number as the subject -</UL> - -<P> -Different languages have different rules of inflection and agreement. -For instance, Italian has also agreement in gender (masculine vs. feminine). -We want to express such special features of languages in the -concrete syntax while ignoring them in the abstract syntax. -</P> -<P> -To be able to do all this, we need one new judgement form -and many new expression forms. -We also need to generalize linearization types -from strings to more complex types. -</P> -<A NAME="toc40"></A> -<H3>Parameters and tables</H3> -<P> -We define the <B>parameter type</B> of number in Englisn by -using a new form of judgement: -</P> -<PRE> - param Number = Sg | Pl ; -</PRE> -<P> -To express that <CODE>Kind</CODE> expressions in English have a linearization -depending on number, we replace the linearization type <CODE>{s : Str}</CODE> -with a type where the <CODE>s</CODE> field is a <B>table</B> depending on number: -</P> -<PRE> - lincat Kind = {s : Number => Str} ; -</PRE> -<P> -The <B>table type</B> <CODE>Number => Str</CODE> is in many respects similar to -a function type (<CODE>Number -> Str</CODE>). The main difference is that the -argument type of a table type must always be a parameter type. This means -that the argument-value pairs can be listed in a finite table. The following -example shows such a table: -</P> -<PRE> - lin Cheese = {s = table { - Sg => "cheese" ; - Pl => "cheeses" - } - } ; -</PRE> -<P> -The table consists of <B>branches</B>, where a <B>pattern</B> on the -left of the arrow <CODE>=></CODE> is assigned a <B>value</B> on the right. -</P> -<P> -The application of a table to a parameter is done by the <B>selection</B> -operator <CODE>!</CODE>. For instance, -</P> -<PRE> - table {Sg => "cheese" ; Pl => "cheeses"} ! Pl -</PRE> -<P> -is a selection that computes into the value <CODE>"cheeses"</CODE>. -This computation is performed by <B>pattern matching</B>: return -the value from the first branch whose pattern matches the -selection argument. -</P> -<A NAME="toc41"></A> -<H3>Inflection tables, paradigms, and ``oper`` definitions</H3> -<P> -All English common nouns are inflected in number, most of them in the -same way: the plural form is obtained from the singular by adding the -ending <I>s</I>. This rule is an example of -a <B>paradigm</B> - a formula telling how the inflection -forms of a word are formed. -</P> -<P> -From the GF point of view, a paradigm is a function that takes a <B>lemma</B> - -also known as a <B>dictionary form</B> - and returns an inflection -table of desired type. Paradigms are not functions in the sense of the -<CODE>fun</CODE> judgements of abstract syntax (which operate on trees and not -on strings), but operations defined in <CODE>oper</CODE> judgements. -The following operation defines the regular noun paradigm of English: -</P> -<PRE> - oper regNoun : Str -> {s : Number => Str} = \x -> { - s = table { - Sg => x ; - Pl => x + "s" - } - } ; -</PRE> -<P> -The <B>gluing</B> operator <CODE>+</CODE> tells that -the string held in the variable <CODE>x</CODE> and the ending <CODE>"s"</CODE> -are written together to form one <B>token</B>. Thus, for instance, -</P> -<PRE> - (regNoun "cheese").s ! Pl ---> "cheese" + "s" ---> "cheeses" -</PRE> -<P></P> -<A NAME="toc42"></A> -<H3>Worst-case functions and data abstraction</H3> -<P> -Some English nouns, such as <CODE>mouse</CODE>, are so irregular that -it makes no sense to see them as instances of a paradigm. Even -then, it is useful to perform <B>data abstraction</B> from the -definition of the type <CODE>Noun</CODE>, and introduce a constructor -operation, a <B>worst-case function</B> for nouns: -</P> -<PRE> - oper mkNoun : Str -> Str -> Noun = \x,y -> { - s = table { - Sg => x ; - Pl => y - } - } ; -</PRE> -<P> -Thus we could define -</P> -<PRE> - lin Mouse = mkNoun "mouse" "mice" ; -</PRE> -<P> -and -</P> -<PRE> - oper regNoun : Str -> Noun = \x -> - mkNoun x (x + "s") ; -</PRE> -<P> -instead of writing the inflection table explicitly. -</P> -<P> -The grammar engineering advantage of worst-case functions is that -the author of the resource module may change the definitions of -<CODE>Noun</CODE> and <CODE>mkNoun</CODE>, and still retain the -interface (i.e. the system of type signatures) that makes it -correct to use these functions in concrete modules. In programming -terms, <CODE>Noun</CODE> is then treated as an <B>abstract datatype</B>. -</P> -<A NAME="toc43"></A> -<H3>A system of paradigms using Prelude operations</H3> -<P> -In addition to the completely regular noun paradigm <CODE>regNoun</CODE>, -some other frequent noun paradigms deserve to be -defined, for instance, -</P> -<PRE> - sNoun : Str -> Noun = \kiss -> mkNoun kiss (kiss + "es") ; -</PRE> -<P> -What about nouns like <I>fly</I>, with the plural <I>flies</I>? The already -available solution is to use the longest common prefix -<I>fl</I> (also known as the <B>technical stem</B>) as argument, and define -</P> -<PRE> - yNoun : Str -> Noun = \fl -> mkNoun (fl + "y") (fl + "ies") ; -</PRE> -<P> -But this paradigm would be very unintuitive to use, because the technical stem -is not an existing form of the word. A better solution is to use -the lemma and a string operator <CODE>init</CODE>, which returns the initial segment (i.e. -all characters but the last) of a string: -</P> -<PRE> - yNoun : Str -> Noun = \fly -> mkNoun fly (init fly + "ies") ; -</PRE> -<P> -The operation <CODE>init</CODE> belongs to a set of operations in the -resource module <CODE>Prelude</CODE>, which therefore has to be -<CODE>open</CODE>ed so that <CODE>init</CODE> can be used. -</P> -<A NAME="toc44"></A> -<H3>An intelligent noun paradigm using ``case`` expressions</H3> -<P> -It may be hard for the user of a resource morphology to pick the right -inflection paradigm. A way to help this is to define a more intelligent -paradigm, which chooses the ending by first analysing the lemma. -The following variant for English regular nouns puts together all the -previously shown paradigms, and chooses one of them on the basis of -the final letter of the lemma (found by the prelude operator <CODE>last</CODE>). -</P> -<PRE> - regNoun : Str -> Noun = \s -> case last s of { - "s" | "z" => mkNoun s (s + "es") ; - "y" => mkNoun s (init s + "ies") ; - _ => mkNoun s (s + "s") - } ; -</PRE> -<P> -This definition displays many GF expression forms not shown befores; -these forms are explained in the next section. -</P> -<P> -The paradigms <CODE>regNoun</CODE> does not give the correct forms for -all nouns. For instance, <I>mouse - mice</I> and -<I>fish - fish</I> must be given by using <CODE>mkNoun</CODE>. -Also the word <I>boy</I> would be inflected incorrectly; to prevent -this, either use <CODE>mkNoun</CODE> or modify -<CODE>regNoun</CODE> so that the <CODE>"y"</CODE> case does not -apply if the second-last character is a vowel. -</P> -<A NAME="toc45"></A> -<H3>Pattern matching</H3> -<P> -We have so far built all expressions of the <CODE>table</CODE> form -from branches whose patterns are constants introduced in -<CODE>param</CODE> definitions, as well as constant strings. -But there are more expressive patterns. Here is a summary of the possible forms: -</P> -<UL> -<LI>a variable pattern (identifier other than constant parameter) matches anything -<LI>the wild card <CODE>_</CODE> matches anything -<LI>a string literal pattern, e.g. <CODE>"s"</CODE>, matches the same string -<LI>a disjunctive pattern <CODE>P | ... | Q</CODE> matches anything that - one of the disjuncts matches -</UL> - -<P> -Pattern matching is performed in the order in which the branches -appear in the table: the branch of the first matching pattern is followed. -</P> -<P> -As syntactic sugar, one-branch tables can be written concisely, -</P> -<PRE> - \\P,...,Q => t === table {P => ... table {Q => t} ...} -</PRE> -<P> -Finally, the <CODE>case</CODE> expressions common in functional -programming languages are syntactic sugar for table selections: -</P> -<PRE> - case e of {...} === table {...} ! e -</PRE> -<P></P> -<A NAME="toc46"></A> -<H3>Morphological resource modules</H3> -<P> -A common idiom is to -gather the <CODE>oper</CODE> and <CODE>param</CODE> definitions -needed for inflecting words in -a language into a morphology module. Here is a simple -example, <A HREF="resource/MorphoEng.gf"><CODE>MorphoEng</CODE></A>. -</P> -<PRE> - --# -path=.:prelude - - resource MorphoEng = open Prelude in { - - param - Number = Sg | Pl ; - - oper - Noun, Verb : Type = {s : Number => Str} ; - - mkNoun : Str -> Str -> Noun = \x,y -> { - s = table { - Sg => x ; - Pl => y - } - } ; - - regNoun : Str -> Noun = \s -> case last s of { - "s" | "z" => mkNoun s (s + "es") ; - "y" => mkNoun s (init s + "ies") ; - _ => mkNoun s (s + "s") - } ; - - mkVerb : Str -> Str -> Verb = \x,y -> mkNoun y x ; - - regVerb : Str -> Verb = \s -> case last s of { - "s" | "z" => mkVerb s (s + "es") ; - "y" => mkVerb s (init s + "ies") ; - "o" => mkVerb s (s + "es") ; - _ => mkVerb s (s + "s") - } ; - } -</PRE> -<P> -The first line gives as a hint to the compiler the -<B>search path</B> needed to find all the other modules that the -module depends on. The directory <CODE>prelude</CODE> is a subdirectory of -<CODE>GF/lib</CODE>; to be able to refer to it in this simple way, you can -set the environment variable <CODE>GF_LIB_PATH</CODE> to point to this -directory. -</P> -<A NAME="toc47"></A> -<H3>Testing resource modules</H3> -<P> -To test a <CODE>resource</CODE> module independently, you must import it -with the flag <CODE>-retain</CODE>, which tells GF to retain <CODE>oper</CODE> definitions -in the memory; the usual behaviour is that <CODE>oper</CODE> definitions -are just applied to compile linearization rules -(this is called <B>inlining</B>) and then thrown away. -</P> -<PRE> - > i -retain MorphoEng.gf -</PRE> -<P> -The command <CODE>compute_concrete = cc</CODE> computes any expression -formed by operations and other GF constructs. For example, -</P> -<PRE> - > cc regVerb "echo" - {s : Number => Str = table Number { - Sg => "echoes" ; - Pl => "echo" - } - } -</PRE> -<P></P> -<P> -The command <CODE>show_operations = so`</CODE> shows the type signatures -of all operations returning a given value type: -</P> -<PRE> - > so Verb - MorphoEng.mkNoun : Str -> Str -> {s : {MorphoEng.Number} => Str} - MorphoEng.mkVerb : Str -> Str -> {s : {MorphoEng.Number} => Str} - MorphoEng.regNoun : Str -> {s : {MorphoEng.Number} => Str} - MorphoEng.regVerb : Str -> { s : {MorphoEng.Number} => Str} -</PRE> -<P> -Why does the command also show the operations that form -<CODE>Noun</CODE>s? The reason is that the type expression -<CODE>Verb</CODE> is first computed, and its value happens to be -the same as the value of <CODE>Noun</CODE>. -</P> -<A NAME="toc48"></A> -<H2>Using parameters in concrete syntax</H2> -<P> -We can now enrich the concrete syntax definitions to -comprise morphology. This will involve a more radical -variation between languages (e.g. English and Italian) -then just the use of different words. In general, -parameters and linearization types are different in -different languages - but this does not prevent the -use of a common abstract syntax. -</P> -<A NAME="toc49"></A> -<H3>Parametric vs. inherent features, agreement</H3> -<P> -The rule of subject-verb agreement in English says that the verb -phrase must be inflected in the number of the subject. This -means that a noun phrase (functioning as a subject), inherently -<I>has</I> a number, which it passes to the verb. The verb does not -<I>have</I> a number, but must be able to <I>receive</I> whatever number the -subject has. This distinction is nicely represented by the -different linearization types of <B>noun phrases</B> and <B>verb phrases</B>: -</P> -<PRE> - lincat NP = {s : Str ; n : Number} ; - lincat VP = {s : Number => Str} ; -</PRE> -<P> -We say that the number of <CODE>NP</CODE> is an <B>inherent feature</B>, -whereas the number of <CODE>NP</CODE> is a <B>variable feature</B> (or a -<B>parametric feature</B>). -</P> -<P> -The agreement rule itself is expressed in the linearization rule of -the predication function: -</P> -<PRE> - lin PredVP np vp = {s = np.s ++ vp.s ! np.n} ; -</PRE> -<P> -The following section will present -<CODE>FoodsEng</CODE>, assuming the abstract syntax <CODE>Foods</CODE> -that is similar to <CODE>Food</CODE> but also has the -plural determiners <CODE>These</CODE> and <CODE>Those</CODE>. -The reader is invited to inspect the way in which agreement works in -the formation of sentences. -</P> -<A NAME="toc50"></A> -<H3>English concrete syntax with parameters</H3> -<P> -The grammar uses both -<A HREF="../../lib/prelude/Prelude.gf"><CODE>Prelude</CODE></A> and -<A HREF="resource/MorphoEng"><CODE>MorphoEng</CODE></A>. -We will later see how to make the grammar even -more high-level by using a resource grammar library -and parametrized modules. -</P> -<PRE> - --# -path=.:resource:prelude - - concrete FoodsEng of Foods = open Prelude, MorphoEng in { - - lincat - S, Quality = SS ; - Kind = {s : Number => Str} ; - Item = {s : Str ; n : Number} ; - - lin - Is item quality = ss (item.s ++ (mkVerb "are" "is").s ! item.n ++ quality.s) ; - This = det Sg "this" ; - That = det Sg "that" ; - These = det Pl "these" ; - Those = det Pl "those" ; - QKind quality kind = {s = \\n => quality.s ++ kind.s ! n} ; - Wine = regNoun "wine" ; - Cheese = regNoun "cheese" ; - Fish = mkNoun "fish" "fish" ; - Very = prefixSS "very" ; - Fresh = ss "fresh" ; - Warm = ss "warm" ; - Italian = ss "Italian" ; - Expensive = ss "expensive" ; - Delicious = ss "delicious" ; - Boring = ss "boring" ; - - oper - det : Number -> Str -> Noun -> {s : Str ; n : Number} = \n,d,cn -> { - s = d ++ cn.s ! n ; - n = n - } ; - - } -</PRE> -<P></P> -<A NAME="toc51"></A> -<H3>Hierarchic parameter types</H3> -<P> -The reader familiar with a functional programming language such as -<A HREF="http://www.haskell.org">Haskell</A> must have noticed the similarity -between parameter types in GF and <B>algebraic datatypes</B> (<CODE>data</CODE> definitions -in Haskell). The GF parameter types are actually a special case of algebraic -datatypes: the main restriction is that in GF, these types must be finite. -(It is this restriction that makes it possible to invert linearization rules into -parsing methods.) -</P> -<P> -However, finite is not the same thing as enumerated. Even in GF, parameter -constructors can take arguments, provided these arguments are from other -parameter types - only recursion is forbidden. Such parameter types impose a -hierarchic order among parameters. They are often needed to define -the linguistically most accurate parameter systems. -</P> -<P> -To give an example, Swedish adjectives -are inflected in number (singular or plural) and -gender (uter or neuter). These parameters would suggest 2*2=4 different -forms. However, the gender distinction is done only in the singular. Therefore, -it would be inaccurate to define adjective paradigms using the type -<CODE>Gender => Number => Str</CODE>. The following hierarchic definition -yields an accurate system of three adjectival forms. -</P> -<PRE> - param AdjForm = ASg Gender | APl ; - param Gender = Utr | Neutr ; -</PRE> -<P> -Here is an example of pattern matching, the paradigm of regular adjectives. -</P> -<PRE> - oper regAdj : Str -> AdjForm => Str = \fin -> table { - ASg Utr => fin ; - ASg Neutr => fin + "t" ; - APl => fin + "a" ; - } -</PRE> -<P> -A constructor can be used as a pattern that has patterns as arguments. For instance, -the adjectival paradigm in which the two singular forms are the same, -can be defined -</P> -<PRE> - oper plattAdj : Str -> AdjForm => Str = \platt -> table { - ASg _ => platt ; - APl => platt + "a" ; - } -</PRE> -<P></P> -<A NAME="toc52"></A> -<H3>Morphological analysis and morphology quiz</H3> -<P> -Even though morphology is in GF -mostly used as an auxiliary for syntax, it -can also be useful on its own right. The command <CODE>morpho_analyse = ma</CODE> -can be used to read a text and return for each word the analyses that -it has in the current concrete syntax. -</P> -<PRE> - > rf bible.txt | morpho_analyse -</PRE> -<P> -In the same way as translation exercises, morphological exercises can -be generated, by the command <CODE>morpho_quiz = mq</CODE>. Usually, -the category is set to be something else than <CODE>S</CODE>. For instance, -</P> -<PRE> - > i lib/resource/french/VerbsFre.gf - > morpho_quiz -cat=V - - Welcome to GF Morphology Quiz. - ... - - réapparaître : VFin VCondit Pl P2 - réapparaitriez - > No, not réapparaitriez, but - réapparaîtriez - Score 0/1 -</PRE> -<P> -Finally, a list of morphological exercises can be generated -off-line and saved in a -file for later use, by the command <CODE>morpho_list = ml</CODE> -</P> -<PRE> - > morpho_list -number=25 -cat=V | wf exx.txt -</PRE> -<P> -The <CODE>number</CODE> flag gives the number of exercises generated. -</P> -<A NAME="toc53"></A> -<H3>Discontinuous constituents</H3> -<P> -A linearization type may contain more strings than one. -An example of where this is useful are English particle -verbs, such as <I>switch off</I>. The linearization of -a sentence may place the object between the verb and the particle: -<I>he switched it off</I>. -</P> -<P> -The following judgement defines transitive verbs as -<B>discontinuous constituents</B>, i.e. as having a linearization -type with two strings and not just one. -</P> -<PRE> - lincat TV = {s : Number => Str ; part : Str} ; -</PRE> -<P> -This linearization rule -shows how the constituents are separated by the object in complementization. -</P> -<PRE> - lin PredTV tv obj = {s = \\n => tv.s ! n ++ obj.s ++ tv.part} ; -</PRE> -<P> -There is no restriction in the number of discontinuous constituents -(or other fields) a <CODE>lincat</CODE> may contain. The only condition is that -the fields must be of finite types, i.e. built from records, tables, -parameters, and <CODE>Str</CODE>, and not functions. -</P> -<P> -A mathematical result -about parsing in GF says that the worst-case complexity of parsing -increases with the number of discontinuous constituents. This is -potentially a reason to avoid discontinuous constituents. -Moreover, the parsing and linearization commands only give accurate -results for categories whose linearization type has a unique <CODE>Str</CODE> -valued field labelled <CODE>s</CODE>. Therefore, discontinuous constituents -are not a good idea in top-level categories accessed by the users -of a grammar application. -</P> -<A NAME="toc54"></A> -<H3>Free variation</H3> -<P> -Sometimes there are many alternative ways to define a concrete syntax. -For instance, the verb negation in English can be expressed both by -<I>does not</I> and <I>doesn't</I>. In linguistic terms, these expressions -are in <B>free variation</B>. The <CODE>variants</CODE> construct of GF can -be used to give a list of strings in free variation. For example, -</P> -<PRE> - NegVerb verb = {s = variants {["does not"] ; "doesn't} ++ verb.s ! Pl} ; -</PRE> -<P> -An empty variant list -</P> -<PRE> - variants {} -</PRE> -<P> -can be used e.g. if a word lacks a certain form. -</P> -<P> -In general, <CODE>variants</CODE> should be used cautiously. It is not -recommended for modules aimed to be libraries, because the -user of the library has no way to choose among the variants. -</P> -<A NAME="toc55"></A> -<H3>Overloading of operations</H3> -<P> -Large libraries, such as the GF Resource Grammar Library, may define -hundreds of names, which can be unpractical -for both the library writer and the user. The writer has to invent longer -and longer names which are not always intuitive, -and the user has to learn or at least be able to find all these names. -A solution to this problem, adopted by languages such as C++, is <B>overloading</B>: -the same name can be used for several functions. When such a name is used, the -compiler performs <B>overload resolution</B> to find out which of the possible functions -is meant. The resolution is based on the types of the functions: all functions that -have the same name must have different types. -</P> -<P> -In C++, functions with the same name can be scattered everywhere in the program. -In GF, they must be grouped together in <CODE>overload</CODE> groups. Here is an example -of an overload group, defining four ways to define nouns in Italian: -</P> -<PRE> - oper mkN = overload { - mkN : Str -> N = -- regular nouns - mkN : Str -> Gender -> N = -- regular nouns with unexpected gender - mkN : Str -> Str -> N = -- irregular nouns - mkN : Str -> Str -> Gender -> N = -- irregular nouns with unexpected gender - } -</PRE> -<P> -All of the following uses of <CODE>mkN</CODE> are easy to resolve: -</P> -<PRE> - lin Pizza = mkN "pizza" ; -- Str -> N - lin Hand = mkN "mano" Fem ; -- Str -> Gender -> N - lin Man = mkN "uomo" "uomini" ; -- Str -> Str -> N -</PRE> -<P></P> -<A NAME="toc56"></A> -<H2>Using the resource grammar library TODO</H2> -<P> -A resource grammar is a grammar built on linguistic grounds, -to describe a language rather than a domain. -The GF resource grammar library, which contains resource grammars for -10 languages, is described more closely in the following -documents: -</P> -<UL> -<LI><A HREF="../../lib/resource-1.0/doc/">Resource library API documentation</A>: - for application grammarians using the resource. -<LI><A HREF="../../lib/resource-1.0/doc/Resource-HOWTO.html">Resource writing HOWTO</A>: - for resource grammarians developing the resource. -</UL> - -<A NAME="toc57"></A> -<H3>Interfaces, instances, and functors</H3> -<A NAME="toc58"></A> -<H3>The simplest way</H3> -<P> -The simplest way is to <CODE>open</CODE> a top-level <CODE>Lang</CODE> module -and a <CODE>Paradigms</CODE> module: -</P> -<PRE> - abstract Foo = ... - - concrete FooEng = open LangEng, ParadigmsEng in ... - concrete FooSwe = open LangSwe, ParadigmsSwe in ... -</PRE> -<P> -Here is an example. -</P> -<PRE> - abstract Arithm = { - cat - Prop ; - Nat ; - fun - Zero : Nat ; - Succ : Nat -> Nat ; - Even : Nat -> Prop ; - And : Prop -> Prop -> Prop ; - } - - --# -path=.:alltenses:prelude - - concrete ArithmEng of Arithm = open LangEng, ParadigmsEng in { - lincat - Prop = S ; - Nat = NP ; - lin - Zero = - UsePN (regPN "zero" nonhuman) ; - Succ n = - DetCN (DetSg (SgQuant DefArt) NoOrd) (ComplN2 (regN2 "successor") n) ; - Even n = - UseCl TPres ASimul PPos - (PredVP n (UseComp (CompAP (PositA (regA "even"))))) ; - And x y = - ConjS and_Conj (BaseS x y) ; - - } - - --# -path=.:alltenses:prelude - - concrete ArithmSwe of Arithm = open LangSwe, ParadigmsSwe in { - lincat - Prop = S ; - Nat = NP ; - lin - Zero = - UsePN (regPN "noll" neutrum) ; - Succ n = - DetCN (DetSg (SgQuant DefArt) NoOrd) - (ComplN2 (mkN2 (mk2N "efterföljare" "efterföljare") - (mkPreposition "till")) n) ; - Even n = - UseCl TPres ASimul PPos - (PredVP n (UseComp (CompAP (PositA (regA "jämn"))))) ; - And x y = - ConjS and_Conj (BaseS x y) ; - } -</PRE> -<P></P> -<A NAME="toc59"></A> -<H3>How to find resource functions</H3> -<P> -The definitions in this example were found by parsing: -</P> -<PRE> - > i LangEng.gf - - -- for Successor: - > p -cat=NP -mcfg -parser=topdown "the mother of Paris" - - -- for Even: - > p -cat=S -mcfg -parser=topdown "Paris is old" - - -- for And: - > p -cat=S -mcfg -parser=topdown "Paris is old and I am old" -</PRE> -<P> -The use of parsing can be systematized by <B>example-based grammar writing</B>, -to which we will return later. -</P> -<A NAME="toc60"></A> -<H3>A functor implementation</H3> -<P> -The interesting thing now is that the -code in <CODE>ArithmSwe</CODE> is similar to the code in <CODE>ArithmEng</CODE>, except for -some lexical items ("noll" vs. "zero", "efterföljare" vs. "successor", -"jämn" vs. "even"). How can we exploit the similarities and -actually share code between the languages? -</P> -<P> -The solution is to use a functor: an <CODE>incomplete</CODE> module that opens -an <CODE>abstract</CODE> as an <CODE>interface</CODE>, and then instantiate it to different -languages that implement the interface. The structure is as follows: -</P> -<PRE> - abstract Foo ... - - incomplete concrete FooI = open Lang, Lex in ... - - concrete FooEng of Foo = FooI with (Lang=LangEng), (Lex=LexEng) ; - concrete FooSwe of Foo = FooI with (Lang=LangSwe), (Lex=LexSwe) ; -</PRE> -<P> -where <CODE>Lex</CODE> is an abstract lexicon that includes the vocabulary -specific to this application: -</P> -<PRE> - abstract Lex = Cat ** ... - - concrete LexEng of Lex = CatEng ** open ParadigmsEng in ... - concrete LexSwe of Lex = CatSwe ** open ParadigmsSwe in ... -</PRE> -<P> -Here, again, a complete example (<CODE>abstract Arithm</CODE> is as above): -</P> -<PRE> - incomplete concrete ArithmI of Arithm = open Lang, Lex in { - lincat - Prop = S ; - Nat = NP ; - lin - Zero = - UsePN zero_PN ; - Succ n = - DetCN (DetSg (SgQuant DefArt) NoOrd) (ComplN2 successor_N2 n) ; - Even n = - UseCl TPres ASimul PPos - (PredVP n (UseComp (CompAP (PositA even_A)))) ; - And x y = - ConjS and_Conj (BaseS x y) ; - } - - --# -path=.:alltenses:prelude - concrete ArithmEng of Arithm = ArithmI with - (Lang = LangEng), - (Lex = LexEng) ; - - --# -path=.:alltenses:prelude - concrete ArithmSwe of Arithm = ArithmI with - (Lang = LangSwe), - (Lex = LexSwe) ; - - abstract Lex = Cat ** { - fun - zero_PN : PN ; - successor_N2 : N2 ; - even_A : A ; - } - - concrete LexSwe of Lex = CatSwe ** open ParadigmsSwe in { - lin - zero_PN = regPN "noll" neutrum ; - successor_N2 = - mkN2 (mk2N "efterföljare" "efterföljare") (mkPreposition "till") ; - even_A = regA "jämn" ; - } -</PRE> -<P></P> -<A NAME="toc61"></A> -<H3>Restricted inheritance and qualified opening</H3> -<A NAME="toc62"></A> -<H2>More constructs for concrete syntax</H2> -<P> -In this chapter, we go through constructs that are not necessary in simple grammars -or when the concrete syntax relies on libraries, but very useful when writing advanced -concrete syntax implementations, such as resource grammar libraries. -</P> -<A NAME="toc63"></A> -<H3>Local definitions</H3> -<P> -Local definitions ("<CODE>let</CODE> expressions") are used in functional -programming for two reasons: to structure the code into smaller -expressions, and to avoid repeated computation of one and -the same expression. Here is an example, from -<A HREF="resource/MorphoIta.gf"><CODE>MorphoIta</CODE></A>: -</P> -<PRE> - oper regNoun : Str -> Noun = \vino -> - let - vin = init vino ; - o = last vino - in - case o of { - "a" => mkNoun Fem vino (vin + "e") ; - "o" | "e" => mkNoun Masc vino (vin + "i") ; - _ => mkNoun Masc vino vino - } ; -</PRE> -<P></P> -<A NAME="toc64"></A> -<H3>Record extension and subtyping</H3> -<P> -Record types and records can be <B>extended</B> with new fields. For instance, -in German it is natural to see transitive verbs as verbs with a case. -The symbol <CODE>**</CODE> is used for both constructs. -</P> -<PRE> - lincat TV = Verb ** {c : Case} ; - - lin Follow = regVerb "folgen" ** {c = Dative} ; -</PRE> -<P> -To extend a record type or a record with a field whose label it -already has is a type error. -</P> -<P> -A record type <I>T</I> is a <B>subtype</B> of another one <I>R</I>, if <I>T</I> has -all the fields of <I>R</I> and possibly other fields. For instance, -an extension of a record type is always a subtype of it. -</P> -<P> -If <I>T</I> is a subtype of <I>R</I>, an object of <I>T</I> can be used whenever -an object of <I>R</I> is required. For instance, a transitive verb can -be used whenever a verb is required. -</P> -<P> -<B>Contravariance</B> means that a function taking an <I>R</I> as argument -can also be applied to any object of a subtype <I>T</I>. -</P> -<A NAME="toc65"></A> -<H3>Tuples and product types</H3> -<P> -Product types and tuples are syntactic sugar for record types and records: -</P> -<PRE> - T1 * ... * Tn === {p1 : T1 ; ... ; pn : Tn} - <t1, ..., tn> === {p1 = T1 ; ... ; pn = Tn} -</PRE> -<P> -Thus the labels <CODE>p1, p2,...</CODE> are hard-coded. -</P> -<A NAME="toc66"></A> -<H3>Record and tuple patterns</H3> -<P> -Record types of parameter types are also parameter types. -A typical example is a record of agreement features, e.g. French -</P> -<PRE> - oper Agr : PType = {g : Gender ; n : Number ; p : Person} ; -</PRE> -<P> -Notice the term <CODE>PType</CODE> rather than just <CODE>Type</CODE> referring to -parameter types. Every <CODE>PType</CODE> is also a <CODE>Type</CODE>, but not vice-versa. -</P> -<P> -Pattern matching is done in the expected way, but it can moreover -utilize partial records: the branch -</P> -<PRE> - {g = Fem} => t -</PRE> -<P> -in a table of type <CODE>Agr => T</CODE> means the same as -</P> -<PRE> - {g = Fem ; n = _ ; p = _} => t -</PRE> -<P> -Tuple patterns are translated to record patterns in the -same way as tuples to records; partial patterns make it -possible to write, slightly surprisingly, -</P> -<PRE> - case <g,n,p> of { - <Fem> => t - ... - } -</PRE> -<P></P> -<A NAME="toc67"></A> -<H3>Regular expression patterns</H3> -<P> -To define string operations computed at compile time, such -as in morphology, it is handy to use regular expression patterns: -</P> - <UL> - <LI><I>p</I> <CODE>+</CODE> <I>q</I> : token consisting of <I>p</I> followed by <I>q</I> - <LI><I>p</I> <CODE>*</CODE> : token <I>p</I> repeated 0 or more times - (max the length of the string to be matched) - <LI><CODE>-</CODE> <I>p</I> : matches anything that <I>p</I> does not match - <LI><I>x</I> <CODE>@</CODE> <I>p</I> : bind to <I>x</I> what <I>p</I> matches - <LI><I>p</I> <CODE>|</CODE> <I>q</I> : matches what either <I>p</I> or <I>q</I> matches - </UL> - -<P> -The last three apply to all types of patterns, the first two only to token strings. -As an example, we give a rule for the formation of English word forms -ending with an <I>s</I> and used in the formation of both plural nouns and -third-person present-tense verbs. -</P> -<PRE> - add_s : Str -> Str = \w -> case w of { - _ + "oo" => s + "s" ; -- bamboo - _ + ("s" | "z" | "x" | "sh" | "o") => w + "es" ; -- bus, hero - _ + ("a" | "o" | "u" | "e") + "y" => w + "s" ; -- boy - x + "y" => x + "ies" ; -- fly - _ => w + "s" -- car - } ; -</PRE> -<P> -Here is another example, the plural formation in Swedish 2nd declension. -The second branch uses a variable binding with <CODE>@</CODE> to cover the cases where an -unstressed pre-final vowel <I>e</I> disappears in the plural -(<I>nyckel-nycklar, seger-segrar, bil-bilar</I>): -</P> -<PRE> - plural2 : Str -> Str = \w -> case w of { - pojk + "e" => pojk + "ar" ; - nyck + "e" + l@("l" | "r" | "n") => nyck + l + "ar" ; - bil => bil + "ar" - } ; -</PRE> -<P></P> -<P> -Semantics: variables are always bound to the <B>first match</B>, which is the first -in the sequence of binding lists <CODE>Match p v</CODE> defined as follows. In the definition, -<CODE>p</CODE> is a pattern and <CODE>v</CODE> is a value. -</P> -<PRE> - Match (p1|p2) v = Match p1 v ++ Match p2 v - Match (p1+p2) s = [Match p1 s1 ++ Match p2 s2 | - i <- [0..length s], (s1,s2) = splitAt i s] - Match p* s = [[]] if Match "" s ++ Match p s ++ Match (p+p) s ++... /= [] - Match -p v = [[]] if Match p v = [] - Match c v = [[]] if c == v -- for constant and literal patterns c - Match x v = [[(x,v)]] -- for variable patterns x - Match x@p v = [[(x,v)]] + M if M = Match p v /= [] - Match p v = [] otherwise -- failure -</PRE> -<P> -Examples: -</P> -<UL> -<LI><CODE>x + "e" + y</CODE> matches <CODE>"peter"</CODE> with <CODE>x = "p", y = "ter"</CODE> -<LI><CODE>x + "er"*</CODE> matches <CODE>"burgerer"</CODE> with ``x = "burg" -</UL> - -<A NAME="toc68"></A> -<H3>Prefix-dependent choices</H3> -<P> -Sometimes a token has different forms depending on the token -that follows. An example is the English indefinite article, -which is <I>an</I> if a vowel follows, <I>a</I> otherwise. -Which form is chosen can only be decided at run time, i.e. -when a string is actually build. GF has a special construct for -such tokens, the <CODE>pre</CODE> construct exemplified in -</P> -<PRE> - oper artIndef : Str = - pre {"a" ; "an" / strs {"a" ; "e" ; "i" ; "o"}} ; -</PRE> -<P> -Thus -</P> -<PRE> - artIndef ++ "cheese" ---> "a" ++ "cheese" - artIndef ++ "apple" ---> "an" ++ "apple" -</PRE> -<P> -This very example does not work in all situations: the prefix -<I>u</I> has no general rules, and some problematic words are -<I>euphemism, one-eyed, n-gram</I>. It is possible to write -</P> -<PRE> - oper artIndef : Str = - pre {"a" ; - "a" / strs {"eu" ; "one"} ; - "an" / strs {"a" ; "e" ; "i" ; "o" ; "n-"} - } ; -</PRE> -<P></P> -<A NAME="toc69"></A> -<H3>Predefined types and operations</H3> -<P> -GF has the following predefined categories in abstract syntax: -</P> -<PRE> - cat Int ; -- integers, e.g. 0, 5, 743145151019 - cat Float ; -- floats, e.g. 0.0, 3.1415926 - cat String ; -- strings, e.g. "", "foo", "123" -</PRE> -<P> -The objects of each of these categories are <B>literals</B> -as indicated in the comments above. No <CODE>fun</CODE> definition -can have a predefined category as its value type, but -they can be used as arguments. For example: -</P> -<PRE> - fun StreetAddress : Int -> String -> Address ; - lin StreetAddress number street = {s = number.s ++ street.s} ; - - -- e.g. (StreetAddress 10 "Downing Street") : Address -</PRE> -<P> -FIXME: The linearization type is <CODE>{s : Str}</CODE> for all these categories. -</P> -<A NAME="toc70"></A> -<H2>More concepts of abstract syntax</H2> -<P> -This section is about the use of the type theory part of GF for -including more semantics in grammars. Some of the subsections present -ideas that have not yet been used in real-world applications, and whose -tool support outside the GF program is not complete. -</P> -<A NAME="toc71"></A> -<H3>GF as a logical framework</H3> -<P> -In this section, we will show how -to encode advanced semantic concepts in an abstract syntax. -We use concepts inherited from <B>type theory</B>. Type theory -is the basis of many systems known as <B>logical frameworks</B>, which are -used for representing mathematical theorems and their proofs on a computer. -In fact, GF has a logical framework as its proper part: -this part is the abstract syntax. -</P> -<P> -In a logical framework, the formalization of a mathematical theory -is a set of type and function declarations. The following is an example -of such a theory, represented as an <CODE>abstract</CODE> module in GF. -</P> -<PRE> - abstract Arithm = { - cat - Prop ; -- proposition - Nat ; -- natural number - fun - Zero : Nat ; -- 0 - Succ : Nat -> Nat ; -- successor of x - Even : Nat -> Prop ; -- x is even - And : Prop -> Prop -> Prop ; -- A and B - } -</PRE> -<P> -A concrete syntax is given below, as an example of using the resource grammar -library. -</P> -<A NAME="toc72"></A> -<H3>Dependent types</H3> -<P> -<B>Dependent types</B> are a characteristic feature of GF, -inherited from the -<B>constructive type theory</B> of Martin-Löf and -distinguishing GF from most other grammar formalisms and -functional programming languages. -The initial main motivation for developing GF was, indeed, -to have a grammar formalism with dependent types. -As can be inferred from the fact that we introduce them only now, -after having written lots of grammars without them, -dependent types are no longer the only motivation for GF. -But they are still important and interesting. -</P> -<P> -Dependent types can be used for stating stronger -<B>conditions of well-formedness</B> than non-dependent types. -A simple example is postal addresses. Ignoring the other details, -let us take a look at addresses consisting of -a street, a city, and a country. -</P> -<PRE> - abstract Address = { - cat - Address ; Country ; City ; Street ; - - fun - mkAddress : Country -> City -> Street -> Address ; - - UK, France : Country ; - Paris, London, Grenoble : City ; - OxfordSt, ShaftesburyAve, BdRaspail, RueBlondel, AvAlsaceLorraine : Street ; - } -</PRE> -<P> -The linearization rules are straightforward, -</P> -<PRE> - lin - mkAddress country city street = - ss (street.s ++ "," ++ city.s ++ "," ++ country.s) ; - UK = ss ("U.K.") ; - France = ss ("France") ; - Paris = ss ("Paris") ; - London = ss ("London") ; - Grenoble = ss ("Grenoble") ; - OxfordSt = ss ("Oxford" ++ "Street") ; - ShaftesburyAve = ss ("Shaftesbury" ++ "Avenue") ; - BdRaspail = ss ("boulevard" ++ "Raspail") ; - RueBlondel = ss ("rue" ++ "Blondel") ; - AvAlsaceLorraine = ss ("avenue" ++ "Alsace-Lorraine") ; -</PRE> -<P> -Notice that, in <CODE>mkAddress</CODE>, we have -reversed the order of the constituents. The type of <CODE>mkAddress</CODE> -in the abstract syntax takes its arguments in a "logical" order, -with increasing precision. (This order is sometimes even used in the -concrete syntax of addresses, e.g. in Russia). -</P> -<P> -Both existing and non-existing addresses are recognized by this -grammar. The non-existing ones in the following randomly generated -list have afterwards been marked by *: -</P> -<PRE> - > gr -cat=Address -number=7 | l - - * Oxford Street , Paris , France - * Shaftesbury Avenue , Grenoble , U.K. - boulevard Raspail , Paris , France - * rue Blondel , Grenoble , U.K. - * Shaftesbury Avenue , Grenoble , France - * Oxford Street , London , France - * Shaftesbury Avenue , Grenoble , France -</PRE> -<P> -Dependent types provide a way to guarantee that addresses are -well-formed. What we do is to include <B>contexts</B> in -<CODE>cat</CODE> judgements: -</P> -<PRE> - cat - Address ; - Country ; - City Country ; - Street (x : Country)(City x) ; -</PRE> -<P> -The first two judgements are as before, but the third one makes -<CODE>City</CODE> dependent on <CODE>Country</CODE>: there are no longer just cities, -but cities of the U.K. and cities of France. The fourth judgement -makes <CODE>Street</CODE> dependent on <CODE>City</CODE>; but since -<CODE>City</CODE> is itself dependent on <CODE>Country</CODE>, we must -include them both in the context, moreover guaranteeing that -the city is one of the given country. Since the context itself -is built by using a dependent type, we have to use variables -to indicate the dependencies. The judgement we used for <CODE>City</CODE> -is actually shorthand for -</P> -<PRE> - cat City (x : Country) -</PRE> -<P> -which is only possible if the subsequent context does not depend on <CODE>x</CODE>. -</P> -<P> -The <CODE>fun</CODE> judgements of the grammar are modified accordingly: -</P> -<PRE> - fun - mkAddress : (x : Country) -> (y : City x) -> Street x y -> Address ; - - UK : Country ; - France : Country ; - Paris : City France ; - London : City UK ; - Grenoble : City France ; - OxfordSt : Street UK London ; - ShaftesburyAve : Street UK London ; - BdRaspail : Street France Paris ; - RueBlondel : Street France Paris ; - AvAlsaceLorraine : Street France Grenoble ; -</PRE> -<P> -Since the type of <CODE>mkAddress</CODE> now has dependencies among -its argument types, we have to use variables just like we used in -the context of <CODE>Street</CODE> above. What we claimed to be the -"logical" order of the arguments is now forced by the type system -of GF: a variable must be declared (=bound) before it can be -referenced (=used). -</P> -<P> -The effect of dependent types is that the *-marked addresses above are -no longer well-formed. What the GF parser actually does is that it -initially accepts them (by using a context-free parsing algorithm) -and then rejects them (by type checking). The random generator does not produce -illegal addresses (this could be useful in bulk mailing!). -The linearization algorithm does not care about type dependencies; -actually, since the <I>categories</I> (ignoring their arguments) -are the same in both abstract syntaxes, -we use the same concrete syntax -for both of them. -</P> -<P> -<B>Remark</B>. Function types <I>without</I> -variables are actually a shorthand notation: writing -</P> -<PRE> - fun PredV1 : NP -> V1 -> S -</PRE> -<P> -is shorthand for -</P> -<PRE> - fun PredV1 : (x : NP) -> (y : V1) -> S -</PRE> -<P> -or any other naming of the variables. Actually the use of variables -sometimes shortens the code, since we can write e.g. -</P> -<PRE> - oper triple : (x,y,z : Str) -> Str = ... -</PRE> -<P> -If a bound variable is not used, it can here, as elswhere in GF, be replaced by -a wildcard: -</P> -<PRE> - oper triple : (_,_,_ : Str) -> Str = ... -</PRE> -<P></P> -<A NAME="toc73"></A> -<H3>Dependent types in concrete syntax</H3> -<P> -The <B>functional fragment</B> of GF -terms and types comprises function types, applications, lambda -abstracts, constants, and variables. This fragment is similar in -abstract and concrete syntax. In particular, -dependent types are also available in concrete syntax. -We have not made use of them yet, -but we will now look at one example of how they -can be used. -</P> -<P> -Those readers who are familiar with functional programming languages -like ML and Haskell, may already have missed <B>polymorphic</B> -functions. For instance, Haskell programmers have access to -the functions -</P> -<PRE> - const :: a -> b -> a - const c _ = c - - flip :: (a -> b -> c) -> b -> a -> c - flip f y x = f x y -</PRE> -<P> -which can be used for any given types <CODE>a</CODE>,<CODE>b</CODE>, and <CODE>c</CODE>. -</P> -<P> -The GF counterpart of polymorphic functions are <B>monomorphic</B> -functions with explicit <B>type variables</B>. Thus the above -definitions can be written -</P> -<PRE> - oper const :(a,b : Type) -> a -> b -> a = - \_,_,c,_ -> c ; - - oper flip : (a,b,c : Type) -> (a -> b ->c) -> b -> a -> c = - \_,_,_,f,x,y -> f y x ; -</PRE> -<P> -When the operations are used, the type checker requires -them to be equipped with all their arguments; this may be a nuisance -for a Haskell or ML programmer. -</P> -<A NAME="toc74"></A> -<H3>Expressing selectional restrictions</H3> -<P> -This section introduces a way of using dependent types to -formalize a notion known as <B>selectional restrictions</B> -in linguistics. We first present a mathematical model -of the notion, and then integrate it in a linguistically -motivated syntax. -</P> -<P> -In linguistics, a -grammar is usually thought of as being about <B>syntactic well-formedness</B> -in a rather liberal sense: an expression can be well-formed without -being meaningful, in other words, without being -<B>semantically well-formed</B>. -For instance, the sentence -</P> -<PRE> - the number 2 is equilateral -</PRE> -<P> -is syntactically well-formed but semantically ill-formed. -It is well-formed because it combines a well-formed -noun phrase ("the number 2") with a well-formed -verb phrase ("is equilateral") and satisfies the agreement -rule saying that the verb phrase is inflected in the -number of the noun phrase: -</P> -<PRE> - fun PredVP : NP -> VP -> S ; - lin PredVP np v = {s = np.s ++ vp.s ! np.n} ; -</PRE> -<P> -It is ill-formed because the predicate "is equilateral" -is only defined for triangles, not for numbers. -</P> -<P> -In a straightforward type-theoretical formalization of -mathematics, domains of mathematical objects -are defined as types. In GF, we could write -</P> -<PRE> - cat Nat ; - cat Triangle ; - cat Prop ; -</PRE> -<P> -for the types of natural numbers, triangles, and propositions, -respectively. -Noun phrases are typed as objects of basic types other than -<CODE>Prop</CODE>, whereas verb phrases are functions from basic types -to <CODE>Prop</CODE>. For instance, -</P> -<PRE> - fun two : Nat ; - fun Even : Nat -> Prop ; - fun Equilateral : Triangle -> Prop ; -</PRE> -<P> -With these judgements, and the linearization rules -</P> -<PRE> - lin two = ss ["the number 2"] ; - lin Even x = ss (x.s ++ ["is even"]) ; - lin Equilateral x = ss (x.s ++ ["is equilateral"]) ; -</PRE> -<P> -we can form the proposition <CODE>Even two</CODE> -</P> -<PRE> - the number 2 is even -</PRE> -<P> -but no proposition linearized to -</P> -<PRE> - the number 2 is equilateral -</PRE> -<P> -since <CODE>Equilateral two</CODE> is not a well-formed type-theoretical object. -It is not even accepted by the context-free parser. -</P> -<P> -When formalizing mathematics, e.g. in the purpose of -computer-assisted theorem proving, we are certainly interested -in semantic well-formedness: we want to be sure that a proposition makes -sense before we make the effort of proving it. The straightforward typing -of nouns and predicates shown above is the way in which this -is guaranteed in various proof systems based on type theory. -(Notice that it is still possible to form <I>false</I> propositions, -e.g. "the number 3 is even". -False and meaningless are different things.) -</P> -<P> -As shown by the linearization rules for <CODE>two</CODE>, <CODE>Even</CODE>, -etc, it <I>is</I> possible to use straightforward mathematical typings -as the abstract syntax of a grammar. However, this syntax is not very -expressive linguistically: for instance, there is no distinction between -adjectives and verbs. It is hard to give rules for structures like -adjectival modification ("even number") and conjunction of predicates -("even or odd"). -</P> -<P> -By using dependent types, it is simple to combine a linguistically -motivated system of categories with mathematically motivated -type restrictions. What we need is a category of domains of -individual objects, -</P> -<PRE> - cat Dom -</PRE> -<P> -and dependencies of other categories on this: -</P> -<PRE> - cat - S ; -- sentence - V1 Dom ; -- one-place verb with specific subject type - V2 Dom Dom ; -- two-place verb with specific subject and object types - A1 Dom ; -- one-place adjective - A2 Dom Dom ; -- two-place adjective - NP Dom ; -- noun phrase for an object of specific type - Conj ; -- conjunction - Det ; -- determiner -</PRE> -<P> -Having thus parametrized categories on domains, we have to reformulate -the rules of predication, etc, accordingly. This is straightforward: -</P> -<PRE> - fun - PredV1 : (A : Dom) -> NP A -> V1 A -> S ; - ComplV2 : (A,B : Dom) -> V2 A B -> NP B -> V1 A ; - DetCN : Det -> (A : Dom) -> NP A ; - ModA1 : (A : Dom) -> A1 A -> Dom ; - ConjS : Conj -> S -> S -> S ; - ConjV1 : (A : Dom) -> Conj -> V1 A -> V1 A -> V1 A ; -</PRE> -<P> -In linearization rules, -we use wildcards for the domain arguments, -because they don't affect linearization: -</P> -<PRE> - lin - PredV1 _ np vp = ss (np.s ++ vp.s) ; - ComplV2 _ _ v2 np = ss (v2.s ++ np.s) ; - DetCN det cn = ss (det.s ++ cn.s) ; - ModA1 cn a1 = ss (a1.s ++ cn.s) ; - ConjS conj s1 s2 = ss (s1.s ++ conj.s ++ s2.s) ; - ConjV1 _ conj v1 v2 = ss (v1.s ++ conj.s ++ v2.s) ; -</PRE> -<P> -The domain arguments thus get suppressed in linearization. -Parsing initially returns metavariables for them, -but type checking can usually restore them -by inference from those arguments that are not suppressed. -</P> -<P> -One traditional linguistic example of domain restrictions -(= selectional restrictions) is the contrast between the two sentences -</P> -<PRE> - John plays golf - golf plays John -</PRE> -<P> -To explain the contrast, we introduce the functions -</P> -<PRE> - human : Dom ; - game : Dom ; - play : V2 human game ; - John : NP human ; - Golf : NP game ; -</PRE> -<P> -Both sentences still pass the context-free parser, -returning trees with lots of metavariables of type <CODE>Dom</CODE>: -</P> -<PRE> - PredV1 ?0 John (ComplV2 ?1 ?2 play Golf) - PredV1 ?0 Golf (ComplV2 ?1 ?2 play John) -</PRE> -<P> -But only the former sentence passes the type checker, which moreover -infers the domain arguments: -</P> -<PRE> - PredV1 human John (ComplV2 human game play Golf) -</PRE> -<P> -To try this out in GF, use <CODE>pt = put_term</CODE> with the <B>tree transformation</B> -that solves the metavariables by type checking: -</P> -<PRE> - > p -tr "John plays golf" | pt -transform=solve - > p -tr "golf plays John" | pt -transform=solve -</PRE> -<P> -In the latter case, no solutions are found. -</P> -<P> -A known problem with selectional restrictions is that they can be more -or less liberal. For instance, -</P> -<PRE> - John loves Mary - John loves golf -</PRE> -<P> -should both make sense, even though <CODE>Mary</CODE> and <CODE>golf</CODE> -are of different types. A natural solution in this case is to -formalize <CODE>love</CODE> as a <B>polymorphic</B> verb, which takes -a human as its first argument but an object of any type as its second -argument: -</P> -<PRE> - fun love : (A : Dom) -> V2 human A ; - lin love _ = ss "loves" ; -</PRE> -<P> -In other words, it is possible for a human to love anything. -</P> -<P> -A problem related to polymorphism is <B>subtyping</B>: what -is meaningful for a <CODE>human</CODE> is also meaningful for -a <CODE>man</CODE> and a <CODE>woman</CODE>, but not the other way round. -One solution to this is <B>coercions</B>: functions that -"lift" objects from subtypes to supertypes. -</P> -<A NAME="toc75"></A> -<H3>Case study: selectional restrictions and statistical language models TODO</H3> -<A NAME="toc76"></A> -<H3>Proof objects</H3> -<P> -Perhaps the most well-known idea in constructive type theory is -the <B>Curry-Howard isomorphism</B>, also known as the -<B>propositions as types principle</B>. Its earliest formulations -were attempts to give semantics to the logical systems of -propositional and predicate calculus. In this section, we will consider -a more elementary example, showing how the notion of proof is useful -outside mathematics, as well. -</P> -<P> -We first define the category of unary (also known as Peano-style) -natural numbers: -</P> -<PRE> - cat Nat ; - fun Zero : Nat ; - fun Succ : Nat -> Nat ; -</PRE> -<P> -The <B>successor function</B> <CODE>Succ</CODE> generates an infinite -sequence of natural numbers, beginning from <CODE>Zero</CODE>. -</P> -<P> -We then define what it means for a number <I>x</I> to be <I>less than</I> -a number <I>y</I>. Our definition is based on two axioms: -</P> -<UL> -<LI><CODE>Zero</CODE> is less than <CODE>Succ</CODE> <I>y</I> for any <I>y</I>. -<LI>If <I>x</I> is less than <I>y</I>, then<CODE>Succ</CODE> <I>x</I> is less than <CODE>Succ</CODE> <I>y</I>. -</UL> - -<P> -The most straightforward way of expressing these axioms in type theory -is as typing judgements that introduce objects of a type <CODE>Less</CODE> //x y //: -</P> -<PRE> - cat Less Nat Nat ; - fun lessZ : (y : Nat) -> Less Zero (Succ y) ; - fun lessS : (x,y : Nat) -> Less x y -> Less (Succ x) (Succ y) ; -</PRE> -<P> -Objects formed by <CODE>lessZ</CODE> and <CODE>lessS</CODE> are -called <B>proof objects</B>: they establish the truth of certain -mathematical propositions. -For instance, the fact that 2 is less that -4 has the proof object -</P> -<PRE> - lessS (Succ Zero) (Succ (Succ (Succ Zero))) - (lessS Zero (Succ (Succ Zero)) (lessZ (Succ Zero))) -</PRE> -<P> -whose type is -</P> -<PRE> - Less (Succ (Succ Zero)) (Succ (Succ (Succ (Succ Zero)))) -</PRE> -<P> -which is the formalization of the proposition that 2 is less than 4. -</P> -<P> -GF grammars can be used to provide a <B>semantic control</B> of -well-formedness of expressions. We have already seen examples of this: -the grammar of well-formed addresses and the grammar with -selectional restrictions above. By introducing proof objects -we have now added a very powerful technique of expressing semantic conditions. -</P> -<P> -A simple example of the use of proof objects is the definition of -well-formed <I>time spans</I>: a time span is expected to be from an earlier to -a later time: -</P> -<PRE> - from 3 to 8 -</PRE> -<P> -is thus well-formed, whereas -</P> -<PRE> - from 8 to 3 -</PRE> -<P> -is not. The following rules for spans impose this condition -by using the <CODE>Less</CODE> predicate: -</P> -<PRE> - cat Span ; - fun span : (m,n : Nat) -> Less m n -> Span ; -</PRE> -<P> -A possible practical application of this idea is <B>proof-carrying documents</B>: -to be semantically well-formed, the abstract syntax of a document must contain a proof -of some property, although the proof is not shown in the concrete document. -Think, for instance, of small documents describing flight connections: -</P> -<P> -<I>To fly from Gothenburg to Prague, first take LH3043 to Frankfurt, then OK0537 to Prague.</I> -</P> -<P> -The well-formedness of this text is partly expressible by dependent typing: -</P> -<PRE> - cat - City ; - Flight City City ; - fun - Gothenburg, Frankfurt, Prague : City ; - LH3043 : Flight Gothenburg Frankfurt ; - OK0537 : Flight Frankfurt Prague ; -</PRE> -<P> -This rules out texts saying <I>take OK0537 from Gothenburg to Prague</I>. However, there is a -further condition saying that it must be possible to change from LH3043 to OK0537 in Frankfurt. -This can be modelled as a proof object of a suitable type, which is required by the constructor -that connects flights. -</P> -<PRE> - cat - IsPossible (x,y,z : City)(Flight x y)(Flight y z) ; - fun - Connect : (x,y,z : City) -> - (u : Flight x y) -> (v : Flight y z) -> - IsPossible x y z u v -> Flight x z ; -</PRE> -<P></P> -<A NAME="toc77"></A> -<H3>Variable bindings</H3> -<P> -Mathematical notation and programming languages have lots of -expressions that <B>bind</B> variables. For instance, -a universally quantifier proposition -</P> -<PRE> - (All x)B(x) -</PRE> -<P> -consists of the <B>binding</B> <CODE>(All x)</CODE> of the variable <CODE>x</CODE>, -and the <B>body</B> <CODE>B(x)</CODE>, where the variable <CODE>x</CODE> can have -<B>bound occurrences</B>. -</P> -<P> -Variable bindings appear in informal mathematical language as well, for -instance, -</P> -<PRE> - for all x, x is equal to x - - the function that for any numbers x and y returns the maximum of x+y - and x*y -</PRE> -<P> -In type theory, variable-binding expression forms can be formalized -as functions that take functions as arguments. The universal -quantifier is defined -</P> -<PRE> - fun All : (Ind -> Prop) -> Prop -</PRE> -<P> -where <CODE>Ind</CODE> is the type of individuals and <CODE>Prop</CODE>, -the type of propositions. If we have, for instance, the equality predicate -</P> -<PRE> - fun Eq : Ind -> Ind -> Prop -</PRE> -<P> -we may form the tree -</P> -<PRE> - All (\x -> Eq x x) -</PRE> -<P> -which corresponds to the ordinary notation -</P> -<PRE> - (All x)(x = x). -</PRE> -<P></P> -<P> -An abstract syntax where trees have functions as arguments, as in -the two examples above, has turned out to be precisely the right -thing for the semantics and computer implementation of -variable-binding expressions. The advantage lies in the fact that -only one variable-binding expression form is needed, the lambda abstract -<CODE>\x -> b</CODE>, and all other bindings can be reduced to it. -This makes it easier to implement mathematical theories and reason -about them, since variable binding is tricky to implement and -to reason about. The idea of using functions as arguments of -syntactic constructors is known as <B>higher-order abstract syntax</B>. -</P> -<P> -The question now arises: how to define linearization rules -for variable-binding expressions? -Let us first consider universal quantification, -</P> -<PRE> - fun All : (Ind -> Prop) -> Prop -</PRE> -<P> -We write -</P> -<PRE> - lin All B = {s = "(" ++ "All" ++ B.$0 ++ ")" ++ B.s} -</PRE> -<P> -to obtain the form shown above. -This linearization rule brings in a new GF concept - the <CODE>$0</CODE> -field of <CODE>B</CODE> containing a bound variable symbol. -The general rule is that, if an argument type of a function is -itself a function type <CODE>A -> C</CODE>, the linearization type of -this argument is the linearization type of <CODE>C</CODE> -together with a new field <CODE>$0 : Str</CODE>. In the linearization rule -for <CODE>All</CODE>, the argument <CODE>B</CODE> thus has the linearization -type -</P> -<PRE> - {$0 : Str ; s : Str}, -</PRE> -<P> -since the linearization type of <CODE>Prop</CODE> is -</P> -<PRE> - {s : Str} -</PRE> -<P> -In other words, the linearization of a function -consists of a linearization of the body together with a -field for a linearization of the bound variable. -Those familiar with type theory or lambda calculus -should notice that GF requires trees to be in -<B>eta-expanded</B> form in order to be linearizable: -any function of type -</P> -<PRE> - A -> B -</PRE> -<P> -always has a syntax tree of the form -</P> -<PRE> - \x -> b -</PRE> -<P> -where <CODE>b : B</CODE> under the assumption <CODE>x : A</CODE>. -It is in this form that an expression can be analysed -as having a bound variable and a body. -</P> -<P> -Given the linearization rule -</P> -<PRE> - lin Eq a b = {s = "(" ++ a.s ++ "=" ++ b.s ++ ")"} -</PRE> -<P> -the linearization of -</P> -<PRE> - \x -> Eq x x -</PRE> -<P> -is the record -</P> -<PRE> - {$0 = "x", s = ["( x = x )"]} -</PRE> -<P> -Thus we can compute the linearization of the formula, -</P> -<PRE> - All (\x -> Eq x x) --> {s = "[( All x ) ( x = x )]"}. -</PRE> -<P></P> -<P> -How did we get the <I>linearization</I> of the variable <CODE>x</CODE> -into the string <CODE>"x"</CODE>? GF grammars have no rules for -this: it is just hard-wired in GF that variable symbols are -linearized into the same strings that represent them in -the print-out of the abstract syntax. -</P> -<P> -To be able to <I>parse</I> variable symbols, however, GF needs to know what -to look for (instead of e.g. trying to parse <I>any</I> -string as a variable). What strings are parsed as variable symbols -is defined in the lexical analysis part of GF parsing -</P> -<PRE> - > p -cat=Prop -lexer=codevars "(All x)(x = x)" - All (\x -> Eq x x) -</PRE> -<P> -(see more details on lexers below). If several variables are bound in the -same argument, the labels are <CODE>$0, $1, $2</CODE>, etc. -</P> -<A NAME="toc78"></A> -<H3>Semantic definitions</H3> -<P> -We have seen that, -just like functional programming languages, GF has declarations -of functions, telling what the type of a function is. -But we have not yet shown how to <B>compute</B> -these functions: all we can do is provide them with arguments -and linearize the resulting terms. -Since our main interest is the well-formedness of expressions, -this has not yet bothered -us very much. As we will see, however, computation does play a role -even in the well-formedness of expressions when dependent types are -present. -</P> -<P> -GF has a form of judgement for <B>semantic definitions</B>, -recognized by the key word <CODE>def</CODE>. At its simplest, it is just -the definition of one constant, e.g. -</P> -<PRE> - def one = Succ Zero ; -</PRE> -<P> -We can also define a function with arguments, -</P> -<PRE> - def Neg A = Impl A Abs ; -</PRE> -<P> -which is still a special case of the most general notion of -definition, that of a group of <B>pattern equations</B>: -</P> -<PRE> - def - sum x Zero = x ; - sum x (Succ y) = Succ (Sum x y) ; -</PRE> -<P> -To compute a term is, as in functional programming languages, -simply to follow a chain of reductions until no definition -can be applied. For instance, we compute -</P> -<PRE> - Sum one one --> - Sum (Succ Zero) (Succ Zero) --> - Succ (sum (Succ Zero) Zero) --> - Succ (Succ Zero) -</PRE> -<P> -Computation in GF is performed with the <CODE>pt</CODE> command and the -<CODE>compute</CODE> transformation, e.g. -</P> -<PRE> - > p -tr "1 + 1" | pt -transform=compute -tr | l - sum one one - Succ (Succ Zero) - s(s(0)) -</PRE> -<P></P> -<P> -The <CODE>def</CODE> definitions of a grammar induce a notion of -<B>definitional equality</B> among trees: two trees are -definitionally equal if they compute into the same tree. -Thus, trivially, all trees in a chain of computation -(such as the one above) -are definitionally equal to each other. So are the trees -</P> -<PRE> - sum Zero (Succ one) - Succ one - sum (sum Zero Zero) (sum (Succ Zero) one) -</PRE> -<P> -and infinitely many other trees. -</P> -<P> -A fact that has to be emphasized about <CODE>def</CODE> definitions is that -they are <I>not</I> performed as a first step of linearization. -We say that <B>linearization is intensional</B>, which means that -the definitional equality of two trees does not imply that -they have the same linearizations. For instance, each of the seven terms -shown above has a different linearizations in arithmetic notation: -</P> -<PRE> - 1 + 1 - s(0) + s(0) - s(s(0) + 0) - s(s(0)) - 0 + s(0) - s(1) - 0 + 0 + s(0) + 1 -</PRE> -<P> -This notion of intensionality is -no more exotic than the intensionality of any <B>pretty-printing</B> -function of a programming language (function that shows -the expressions of the language as strings). It is vital for -pretty-printing to be intensional in this sense - if we want, -for instance, to trace a chain of computation by pretty-printing each -intermediate step, what we want to see is a sequence of different -expression, which are definitionally equal. -</P> -<P> -What is more exotic is that GF has two ways of referring to the -abstract syntax objects. In the concrete syntax, the reference is intensional. -In the abstract syntax, the reference is extensional, since -<B>type checking is extensional</B>. The reason is that, -in the type theory with dependent types, types may depend on terms. -Two types depending on terms that are definitionally equal are -equal types. For instance, -</P> -<PRE> - Proof (Odd one) - Proof (Odd (Succ Zero)) -</PRE> -<P> -are equal types. Hence, any tree that type checks as a proof that -1 is odd also type checks as a proof that the successor of 0 is odd. -(Recall, in this connection, that the -arguments a category depends on never play any role -in the linearization of trees of that category, -nor in the definition of the linearization type.) -</P> -<P> -In addition to computation, definitions impose a -<B>paraphrase</B> relation on expressions: -two strings are paraphrases if they -are linearizations of trees that are -definitionally equal. -Paraphrases are sometimes interesting for -translation: the <B>direct translation</B> -of a string, which is the linearization of the same tree -in the targer language, may be inadequate because it is e.g. -unidiomatic or ambiguous. In such a case, -the translation algorithm may be made to consider -translation by a paraphrase. -</P> -<P> -To stress express the distinction between -<B>constructors</B> (=<B>canonical</B> functions) -and other functions, GF has a judgement form -<CODE>data</CODE> to tell that certain functions are canonical, e.g. -</P> -<PRE> - data Nat = Succ | Zero ; -</PRE> -<P> -Unlike in Haskell, but similarly to ALF (where constructor functions -are marked with a flag <CODE>C</CODE>), -new constructors can be added to -a type with new <CODE>data</CODE> judgements. The type signatures of constructors -are given separately, in ordinary <CODE>fun</CODE> judgements. -One can also write directly -</P> -<PRE> - data Succ : Nat -> Nat ; -</PRE> -<P> -which is equivalent to the two judgements -</P> -<PRE> - fun Succ : Nat -> Nat ; - data Nat = Succ ; -</PRE> -<P></P> -<A NAME="toc79"></A> -<H3>Case study: representing anaphoric reference TODO</H3> -<A NAME="toc80"></A> -<H2>Transfer modules TODO</H2> -<P> -Transfer means noncompositional tree-transforming operations. -The command <CODE>apply_transfer = at</CODE> is typically used in a pipe: -</P> -<PRE> - > p "John walks and John runs" | apply_transfer aggregate | l - John walks and runs -</PRE> -<P> -See the -<A HREF="../../transfer/examples/aggregation">sources</A> of this example. -</P> -<P> -See the -<A HREF="../transfer.html">transfer language documentation</A> -for more information. -</P> -<A NAME="toc81"></A> -<H2>Practical issues TODO</H2> -<A NAME="toc82"></A> -<H3>Lexers and unlexers</H3> -<P> -Lexers and unlexers can be chosen from -a list of predefined ones, using the flags<CODE>-lexer</CODE> and `` -unlexer`` either -in the grammar file or on the GF command line. -</P> -<P> -Given by <CODE>help -lexer</CODE>, <CODE>help -unlexer</CODE>: -</P> -<PRE> - The default is words. - -lexer=words tokens are separated by spaces or newlines - -lexer=literals like words, but GF integer and string literals recognized - -lexer=vars like words, but "x","x_...","$...$" as vars, "?..." as meta - -lexer=chars each character is a token - -lexer=code use Haskell's lex - -lexer=codevars like code, but treat unknown words as variables, ?? as meta - -lexer=text with conventions on punctuation and capital letters - -lexer=codelit like code, but treat unknown words as string literals - -lexer=textlit like text, but treat unknown words as string literals - -lexer=codeC use a C-like lexer - -lexer=ignore like literals, but ignore unknown words - -lexer=subseqs like ignore, but then try all subsequences from longest - - The default is unwords. - -unlexer=unwords space-separated token list (like unwords) - -unlexer=text format as text: punctuation, capitals, paragraph <p> - -unlexer=code format as code (spacing, indentation) - -unlexer=textlit like text, but remove string literal quotes - -unlexer=codelit like code, but remove string literal quotes - -unlexer=concat remove all spaces - -unlexer=bind like identity, but bind at "&+" -</PRE> -<P></P> -<A NAME="toc83"></A> -<H3>Efficiency of grammars</H3> -<P> -Issues: -</P> -<UL> -<LI>the choice of datastructures in <CODE>lincat</CODE>s -<LI>the value of the <CODE>optimize</CODE> flag -<LI>parsing efficiency: <CODE>-fcfg</CODE> vs. others -</UL> - -<A NAME="toc84"></A> -<H3>Speech input and output</H3> -<P> -The<CODE>speak_aloud = sa</CODE> command sends a string to the speech -synthesizer -<A HREF="http://www.speech.cs.cmu.edu/flite/doc/">Flite</A>. -It is typically used via a pipe: -</P> -<PRE> - generate_random | linearize | speak_aloud -</PRE> -<P> -The result is only satisfactory for English. -</P> -<P> -The <CODE>speech_input = si</CODE> command receives a string from a -speech recognizer that requires the installation of -<A HREF="http://mi.eng.cam.ac.uk/~sjy/software.htm">ATK</A>. -It is typically used to pipe input to a parser: -</P> -<PRE> - speech_input -tr | parse -</PRE> -<P> -The method words only for grammars of English. -</P> -<P> -Both Flite and ATK are freely available through the links -above, but they are not distributed together with GF. -</P> -<A NAME="toc85"></A> -<H3>Multilingual syntax editor</H3> -<P> -The -<A HREF="http://www.cs.chalmers.se/~aarne/GF2.0/doc/javaGUImanual/javaGUImanual.htm">Editor User Manual</A> -describes the use of the editor, which works for any multilingual GF grammar. -</P> -<P> -Here is a snapshot of the editor: -</P> -<P> -<IMG ALIGN="middle" SRC="../quick-editor.png" BORDER="0" ALT=""> -</P> -<P> -The grammars of the snapshot are from the -<A HREF="http://www.cs.chalmers.se/~aarne/GF/examples/letter">Letter grammar package</A>. -</P> -<A NAME="toc86"></A> -<H3>Interactive Development Environment (IDE)</H3> -<P> -Forthcoming. -</P> -<A NAME="toc87"></A> -<H3>Communicating with GF</H3> -<P> -Other processes can communicate with the GF command interpreter, -and also with the GF syntax editor. Useful flags when invoking GF are -</P> -<UL> -<LI><CODE>-batch</CODE> suppresses the promps and structures the communication with XML tags. -<LI><CODE>-s</CODE> suppresses non-output non-error messages and XML tags. --- <CODE>-nocpu</CODE> suppresses CPU time indication. -<P></P> -Thus the most silent way to invoke GF is -<PRE> - gf -batch -s -nocpu -</PRE> -</UL> - -<A NAME="toc88"></A> -<H3>Embedded grammars in Haskell, Java, and Prolog</H3> -<P> -GF grammars can be used as parts of programs written in the -following languages. The links give more documentation. -</P> -<UL> -<LI><A HREF="http://www.cs.chalmers.se/~bringert/gf/gf-java.html">Java</A> -<LI><A HREF="http://www.cs.chalmers.se/~aarne/GF/src/GF/Embed/EmbedAPI.hs">Haskell</A> -<LI><A HREF="http://www.cs.chalmers.se/~peb/software.html">Prolog</A> -</UL> - -<A NAME="toc89"></A> -<H3>Alternative input and output grammar formats</H3> -<P> -A summary is given in the following chart of GF grammar compiler phases: -<IMG ALIGN="middle" SRC="../gf-compiler.png" BORDER="0" ALT=""> -</P> -<A NAME="toc90"></A> -<H2>Larger case studies TODO</H2> -<A NAME="toc91"></A> -<H3>Interfacing formal and natural languages</H3> -<P> -<A HREF="http://www.cs.chalmers.se/~krijo/thesis/thesisA4.pdf">Formal and Informal Software Specifications</A>, -PhD Thesis by -<A HREF="http://www.cs.chalmers.se/~krijo">Kristofer Johannisson</A>, is an extensive example of this. -The system is based on a multilingual grammar relating the formal language OCL with -English and German. -</P> -<P> -A simpler example will be explained here. -</P> -<A NAME="toc92"></A> -<H3>A multimodal dialogue system</H3> -<P> -See TALK project deliverables, <A HREF="http://www.talk-project.org">TALK homepage</A> -</P> - -<!-- html code generated by txt2tags 2.4 (http://txt2tags.sf.net) --> -<!-- cmdline: txt2tags -thtml -\-toc gf-tutorial2.txt --> -</BODY></HTML> |