From 0a1d05785570c43688d7ffc8dee5bbd92b1b5f2e Mon Sep 17 00:00:00 2001 From: aarne Date: Mon, 13 Aug 2007 15:54:41 +0000 Subject: [PATCH] new tutorial version started --- doc/tutorial/Makefile | 8 +- doc/tutorial/gf-tutorial2_9.txt | 4160 +++++++++++++++++++++++++++++++ 2 files changed, 4164 insertions(+), 4 deletions(-) create mode 100644 doc/tutorial/gf-tutorial2_9.txt diff --git a/doc/tutorial/Makefile b/doc/tutorial/Makefile index 76ab130f1..5338adb6e 100644 --- a/doc/tutorial/Makefile +++ b/doc/tutorial/Makefile @@ -1,8 +1,8 @@ all: html tex html: - txt2tags -thtml --toc gf-tutorial2.txt + txt2tags -thtml --toc gf-tutorial2_9.txt tex: - txt2tags -ttex --toc gf-tutorial2.txt - pdflatex gf-tutorial2.tex - pdflatex gf-tutorial2.tex + txt2tags -ttex --toc gf-tutorial2_9.txt + pdflatex gf-tutorial2_9.tex + pdflatex gf-tutorial2_9.tex diff --git a/doc/tutorial/gf-tutorial2_9.txt b/doc/tutorial/gf-tutorial2_9.txt new file mode 100644 index 000000000..5ae0455f3 --- /dev/null +++ b/doc/tutorial/gf-tutorial2_9.txt @@ -0,0 +1,4160 @@ +Grammatical Framework Tutorial +Author: Aarne Ranta aarne (at) cs.chalmers.se +Last update: %%date(%c) + +% NOTE: this is a txt2tags file. +% Create an html file from this file using: +% txt2tags --toc gf-tutorial2.txt + +%!target:html +%!encoding: iso-8859-1 + +%!postproc(tex): "section\*" "section" + +%!postproc(html): #BCEN
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+ +%!postproc(tex): #BCEN "begin{center}" +%!postproc(tex): #ECEN "end{center}" + +%!preproc(html): #EDITORPNG [../quick-editor.png] +%!preproc(tex): #EDITORPNG [../../lib/resource-1.0/doc/10lang-small.png] + +%!preproc(html): #LOGOPNG [../gf-logo.png] +%!preproc(tex): #LOGOPNG "" + + +#LOGOPNG + + + +%--! +=Introduction= + +==Natural language application programming== + +Making computers understand human language is one of the oldest dreams of +programmers. Projects with machine translations started almost as soon as +the first computers appeared in the 1940's. This was partly encouraged by the +success of decryption during the Second World War. Thus some American scientists +had the vision that Russian can be seen as encrypted English, which can be +deciphered by similar algorithms as those used for cracking the Germans' Enigma. + +Despite substantial efforts on machine translation, the early visions were not +realized, and the general conclusion reached by the mid-1960's was that +high-quality broad-coverage machine translation is impossible. Machine +translation was translated to the less ambitious and more specialized tasks of +computational linguistics. Parallel to this, fantacies of "speaking robots" and +other language-understanding machines prevailed, exemplified by such science +fiction figures as the HAL computer in the film "2001: A Space Odyssey" from +1970. + +What we see in today's market of language understanding machines is a variety of +products, which focus on different aspects of the task and none of which comes +even close to HAL or a machine translator with human-like capacities. Here is a +list of some such applications: +- browse-quality machine translation: Systran +- machine translation specialized on weather reports: Meteo +- electronic dictionaries +- spelling and grammar checkers +- dialogue systems for enabling simple speech interaction with a computer + + +A common feature of these applications is that their construction requires +**linguistic knowledge**: theoretical understanding of languages. As opposed to +practical understanding, which means the ability to speak, listen, write, and +read, theoretical understanding means knowledge of the **rules** of language. +It is by expressing these rules in a programming language the we can hope to +make a computer understand at least something of a natural language. + +This is where GF comes into picture. GF, Grammatical Framework, is a programming +language designed for expressing linguistic rules. A set of such rules is called +a **grammar**. GF is designed in such a way that it is much easier to write +grammar rules in it than in a general-purpose programming language, such as +Java or C or Haskell. At the same time, GF is equipped with tools for +**embedded grammars**. This means that a GF grammar can be used as a component +of a program written in another language, such as Java or C or Haskell. To build +a language application usually involves much more than just a grammar, and it is +important that the grammar can be integrated seemlessly with the rest of the +application. + +Since natural language application programming requires linguistic knowledge, it +is usually considered to need linguistic training. The mission of GF is to relieve +some of this need. This is achieved in two ways: +- GF works in a way familiar to ordinary programmers, namely as a **compiler** + that analyses a language and generates a result. +- GF has a set of **resource grammar libraries**, which encapsulate much of + the linguistic knowledge needed when writing grammars. + + +This said, GF makes no claim to "fire linguists" from natural language programming +projects. The claim is rather one of the **division of labour**: GF enables the +division of grammar writing into different **modules**, where some modules +require linguistic knowledge and others don't. Linguists working on the linguistic +modules will appreciate the way GF supports abstractions and generalizations, and +also the grammar development tools that enable testing of linguistic rules. +Non-linguists working on the application-oriented modules will appreciate the +possibility to take grammar rules for granted and focus on other aspects of +the program. + + + +==The history of GF and its applications== + +GF belongs to the tradition of **functional programming languages**, exemplified +by Lisp and, as later and closer relatives, ML and Haskell. An important branch +of functional programming is **type theory**, which in turn has its roots in +logic and the foundations of mathematics. GF was, at the first place, created to +implement the idea that type theory can provide **semantics**, i.e. formalize +the meaning of natural languages. Several aspects of type-theoretical semantics +were covered in the monograph //Type-Theoretical Grammar// (A. Ranta, OUP 1994). +But a stronger aspect grew out of subsequent experiments dealing with different +languages: it is possible to have a common semantics for many language, and +thereby build systems that translate between languages via the semantics. During +this period, discussions with Per Martin-Löf (Ranta's PhD supervisor at the +University of Stockholm) had a major impact on the work, and cooperation +with Petri Mäenpää at the University of Helsinki led to the first computer +implementations. + +As a stand-alone programming language, GF was first implemented in 1998. This +took place at Xerox Research Centre Europe in Grenoble, within a project entitled +//Multilingual Document Authoring//. The leading idea in the project was to +enable writing documents in multiple languages simultaneously, so that the user +need only know one of the languages; the rest will be produced automatically +via translations from the type-theoretical semantics. The Xerox staff involved +in the project included Marc Dymetman, Lauri Karttunen, Veronika Lux, +Sylvain Pogodalla, and Annie Zaenen. + +The Xerox project produced some prototype applications, e.g. a restaurant phrase +book and an editor of medical drug descriptions. The grammars that were build +remained the property of Xerox, but the GF formalism and its implementation +were released as open-source software under GNU General Public License. The +principal author of GF got an academic position in 1999, at the Department of +Computing Science of Chalmers University of Technology and Gothenburg University. +At Chalmers, both functional programming and type theory flourish, and in this +environment, GF developed into a more stable and more full-fledged programming +language. In this process, collaboration with Koen Claessen, Thierry Coquand, +Thomas Hallgren, Patrik Jansson, and Bengt Nordström made important contributions. + +The idea of making GF into "the working programmer's grammar formalism", as +opposed to a tool requiring linguistic expertise, was confirmed at Chalmers +in courses given to computer science students and later in joint research +projects. A nice experience of the courses was that computer scientists are +often very interested in languages and have firm intuitions on grammar; given +a suitable programming tool, they can achieve impressive results. GF seemed to +be close to such a tool, and, in subsequent collaborations at the Department, +it evolved even more to a programming language with a virtues of familiarity +and "the least surprise". Issues of stability are also important, including +backward compatibility, and documentation is something there can hardly be +too much of. As a mark of stability, version 1.0 of GF was released in +2002. In 2004, a theoretical reference paper appeared in the Journal +of Functional Programming, as well as a long tutorial text in the ESSLLI +lecture notes post-publication. + +The first full-scale applications of GF emerged as natural-language interfaces. +The first one was for the proof editor Alfa, written with Thomas Hallgren. +The second one was a syntax editor and a natural-language interface to the +software specification language OCL (Object Constraint Language) built +within the KeY project. This work was done first with Reiner Hähnle, then +with the students Kristoffer Johannisson (PhD 2005), Hans-Joachim Daniels, +and David Burke. On the GF implementation side, Janna Khegai (PhD 2006) built +a Java-based syntax editor. Peter Ljunglöf (PhD 2004) succeeded to identify +the complexity of parsing in GF and found an algorithm that greatly improved +the use of GF in parsing. He implemented the algorithm with Håkan Burden, and +it was later still improved by Krasimir Angelov. + +At the same time, collaboration with the Linguistics Department of +Gothenburg University served as a "linguistic sanity check" of GF. +Robin Cooper, an eminent linguist working at the Department, initiated +two efforts that have formed the development of GF: +- resource grammar libraries +- dialogue system applications + + +It was the resource grammar libraries that made GF really usable for non-linguist +programmers in more serious projects. They were heavily missed in the Alfa +project, and heavily used and improved in the KeY project. The development of +the library started in 2002; a version stable enough to be released with number +1.0 was complete in 2006, comprising ten languages. + +Dialogue systems, on the other hand, turned +out to be a major source of interesting problems and also of successful solutions. +Much of this work was carried out in the European project TALK (Tools for Ambient +Linguistic Knowledge, 2004-2006), by Björn Bringert, Rebecca Jonson, and +Peter Ljunglöf in Gothenburg, and Oliver Lemon (Edinburgh), Nadine Perera (BMW), +and Karl Weilhammer (Cambridge) at the other sites. In addition to +complete systems, this project produced supporting tools for embedded grammars +and speech recognition, and additions to the resource grammar library. + +Besides dialogue systems, multilingual authoring and translation continues +to be the main application of GF. The European WebALT project (Web Advanced +Learning Technologies, 2005-2006), used GF to build a tool for translating +mathematical exercises from formal specifications (written in MathML) to +six language. Also tool integrating GF with a computer algebra system was +developed. The project gave rise to a company, WebALT Inc. Many members +of the WebALT staff also contributed to GF and the resource grammar library: +Lauri Carlson, Glòria Casanellas, Anni Laine, Wanjiku N'gan'ga, and +Jordi Saludes. + +As of the time of writing (August 2007), the release of GF has version +number 2.8. It is a stable system that has been built with contributions +of dozens of persons and been used by at least hundreds; download figures +are in thousands. New ideas of how to apply GF are posted by users almost +every week. These users are often programmers with good knowledge of +functional languages, highly developed instinct for programming language +design, and firm intuitions on natural language. Another group of users +are those that have been trained in GF on courses. + + + +==The purpose and scope of this book== + +The purpose of this book is to serve the growing user base of GF with +a manual that gathers all relevant information in one place. However, it +is also intended to serve those who want to get started with GF, and +who don't necessarily have the technical background of the typical +users. We believe that learning to program in GF is not more difficult +than learning some other programming language; as for the linguistic +aspects, we believe that writing grammars is an excellent introduction +to the problems of linguistics, where theory can be learnt at the +same time as it is motivated by concrete problems. + +The book thus starts with a tutorial, which gradually explains all +the constructs of the GF programming language. Also the design and style +aspects of grammar engineering are covered, to help the user to scale +up from small to large and possibly collaborative applications. +After the tutorial, the book continues with a "cook book" containing +hints and case studies for advanced users. Moreover, the resource +grammar library is covered in some detail, which will help the +programmers who want to port the library to new languages, but also +motivate linguistically the choices made in the libraries. +A complete reference manual concludes the book, with a quick reference +card as an appendix. + +What is not covered by the book is theoretical discussions of +GF, especially in comparison to other grammar formalism. Even though important +in the development of GF as a scientifically justified framework, such +discussions are not relevant for programmers who want to use GF - any more +than, say, a book on Haskell has to include comparisons with Java. In fact, +introducing Haskell by references to Java may have some point, since many +of the readers can already be assumed to know Java. But, even though some +readers will know DCG or HPSG or LFG, we will not assume this; we will just +note in passing the relation between GF and context-free grammars, also +known as BNF grammars in computer science. + + + + +==GF = Grammatical Framework== + +The term GF is used for different things: +- a **program** used for working with grammars +- a **programming language** in which grammars can be written +- a **theory** about grammars and languages + + +This tutorial is primarily about the GF program and +the GF programming language. +It will guide you +- to use the GF program +- to write GF grammars +- to write programs in which GF grammars are used as components + + + +%--! +==What are GF grammars used for== + +A grammar is a definition of a language. +From this definition, different language processing components +can be derived: +- **parsing**: to analyse the language +- **linearization**: to generate the language +- **translation**: to analyse one language and generate another + + +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: +- **morphological analysis**: find out the possible inflection forms of words +- **morphological synthesis**: generate all inflection forms of words +- **random generation**: generate random expressions +- **corpus generation**: generate all expressions +- **treebank generation**: generate a list of trees with multiple linearizations +- **teaching quizzes**: train morphology and translation +- **multilingual authoring**: create a document in many languages simultaneously +- **speech input**: optimize a speech recognition system for your grammar + + +A typical GF application is based on a **multilingual grammar** involving +translation on a special domain. Existing applications of this idea include +- [Alfa: http://www.cs.chalmers.se/~hallgren/Alfa/Tutorial/GFplugin.html]: + a natural-language interface to a proof editor + (languages: English, French, Swedish) +- [KeY http://www.key-project.org/]: + a multilingual authoring system for creating software specifications + (languages: OCL, English, German) +- [TALK http://www.talk-project.org]: + multilingual and multimodal dialogue systems + (languages: English, Finnish, French, German, Italian, Spanish, Swedish) +- [WebALT http://webalt.math.helsinki.fi/content/index_eng.html]: + a multilingual translator of mathematical exercises + (languages: Catalan, English, Finnish, French, Spanish, Swedish) +- [Numeral translator http://www.cs.chalmers.se/~bringert/gf/translate/]: + number words from 1 to 999,999 + (88 languages) + + +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 **application grammars**. +They are different from most grammars written by linguists just +because they are multilingual and domain-specific. + +However, there is another kind of grammars, which we call **resource grammars**. +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 **libraries** 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. + + + + +%--! +==Who is this tutorial for== + +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. + +A separate document has been written on how to write resource grammars: the +[Resource HOWTO ../../lib/resource-1.0/doc/Resource-HOWTO.html]. +In this tutorial, we will just cover the programming concepts that are used for +solving linguistic problems in the resource grammars. + +The easiest way to use GF is probably via the interactive syntax editor. +Its use does not require any knowledge of the GF formalism. There is +a separate +[Editor User Manual http://www.cs.chalmers.se/~aarne/GF2.0/doc/javaGUImanual/javaGUImanual.htm] +by Janna Khegai, covering the use of the editor. The editor is also a platform for many +kinds of GF applications, implementing the slogan + +//write a document in a language you don't know, while seeing it in a language you know//. + + +%--! +==The coverage of the tutorial== + +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 +``` + this Italian cheese is delicious +``` +in English and Italian. + +The first English grammar +[``food.cf`` food.cf] +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: +``` + Italian cheese ===> formaggio italiano +``` +The full GF grammar format is designed to support such +changes, by separating between the **abstract syntax** +(the logical structure) and the **concrete syntax** (the +sequence of words) of expressions. + +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: +``` + delicious (wine, wines, pizza, pizzas) + vino delizioso, vini deliziosi, pizza deliziosa, pizze deliziose +``` +The **morphology** 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 give an introduction to linguistically oriented grammar writing. + +Thus it is by elaborating the initial ``food.cf`` 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. + +To learn how to write GF grammars is not the only goal of +this tutorial. We will also explain the most important +commands of the GF system. With these commands, +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, moreover require programming in +some general-purpose language. Thus we will briefly explain how +GF grammars are used as components of Haskell programs. +Chapters on using them in Java and Javascript programs are +forthcoming; a comprehensive manual on GF embedded in Java, by Björn Bringert, is +available in +[``http://www.cs.chalmers.se/~bringert/gf/gf-java.html`` http://www.cs.chalmers.se/~bringert/gf/gf-java.html]. + + + +%--! +==Getting the GF program== + +The GF program is open-source free software, which you can download via the +GF Homepage: + +[``http://www.cs.chalmers.se/~aarne/GF`` http://www.cs.chalmers.se/~aarne/GF] + +There you can download +- binaries for Linux, Mac OS X, and Windows +- source code and documentation +- grammar libraries and examples + + +If you want to compile GF from source, you need a Haskell compiler. +To compile the interactive editor, you also need a Java compilers. +But normally you don't have to compile, and you definitely +don't need to know Haskell or Java to use GF. + +We are assuming the availability of a Unix shell. Linux and Mac OS X users +have it automatically, the latter under the name "terminal". +Windows users are recommended to install Cywgin, the free Unix shell for Windows. + + +%--! +==Running the GF program== + +To start the GF program, assuming you have installed it, just type +``` + % gf +``` +in the shell. +You will see GF's welcome message and the prompt ``>``. +The command +``` + > help +``` +will give you a list of available commands. + +As a common convention in this Tutorial, we will use +- ``%`` as a prompt that marks system commands +- ``>`` as a prompt that marks GF commands + + +Thus you should not type these prompts, but only the lines that +follow them. + + + +%--! +=The .cf grammar format= + +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. + +To get started, type (or copy) the following lines into a file named +``food.cf``: +``` +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" ; +``` +For those who know ordinary BNF, the +notation we use includes one extra element: a **label** appearing +as the first element of each rule and terminated by a full stop. + +The grammar we wrote defines a set of phrases usable for speaking about food. +It builds **sentences** (``S``) by assigning ``Quality``s to +``Item``s. ``Item``s are build from ``Kind``s by prepending the +word "this" or "that". ``Kind``s are either **atomic**, such as +"cheese" and "wine", or formed by prepending a ``Quality`` to a +``Kind``. A ``Quality`` is either atomic, such as "Italian" and "boring", +or built by another ``Quality`` 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: +``` + this delicious Italian wine is very very expensive +``` + + + +%--! +==Importing grammars and parsing strings== + +The first GF command needed when using a grammar is to **import** it. +The command has a long name, ``import``, and a short name, ``i``. +You can type either +``` + > import food.cf +``` +or +``` + > i food.cf +``` +to get the same effect. +The effect is that the GF program **compiles** your grammar into an internal +representation, and shows a new prompt when it is ready. It will also show how much +CPU time is consumed: +``` + > i food.cf + - parsing cf food.cf 12 msec + 16 msec + > +``` +You can now use GF for **parsing**: +``` + > parse "this cheese is delicious" + Is (This Cheese) Delicious + + > p "that wine is very very Italian" + Is (That Wine) (Very (Very Italian)) +``` +The ``parse`` (= ``p``) command takes a **string** +(in double quotes) and returns an **abstract syntax tree** - the thing +beginning with ``Is``. 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. + +Strings that return a tree when parsed do so in virtue of the grammar +you imported. Try parsing something else, and you fail +``` + > p "hello world" + Unknown words: hello world +``` + +**Exercise**. Extend the grammar ``food.cf`` by ten new food kinds and +qualities, and run the parser with new kinds of examples. + + +**Exercise**. Add a rule that enables questions of the form +//is this cheese Italian//. + + + +**Exercise**. Add the rule +``` + IsVery. S ::= Item "is" "very" Quality ; +``` +and see what happens when parsing ``this wine is very very Italian``. +You have just made the grammar **ambiguous**: it now assigns several +trees to some strings. + + +**Exercise**. Modify the grammar so that at most one ``Quality`` may +attach to a given ``Kind``. Thus //boring Italian fish// will no longer +be recognized. + + + + +%--! +==Generating trees and strings== + +You can also use GF for **linearizing** +(``linearize = l``). This is the inverse of +parsing, taking trees into strings: +``` + > linearize Is (That Wine) Warm + that wine is warm +``` +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 +**random generation** (``generate_random = gr``): +``` + > generate_random + Is (This (QKind Italian Fish)) Fresh +``` +Now you can copy the tree and paste it to the ``linearize command``. +Or, more conveniently, feed random generation into linearization by using +a **pipe**. +``` + > gr | l + this Italian fish is fresh +``` +Pipes in GF work much the same way as Unix pipes: they feed the output +of one command into another command as its input. + + +%--! +==Visualizing trees== + +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 **nesting**: 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 ``visualizre_tree = vt``, to which +parsing (and any other tree-producing command) can be piped: + +``` + > parse "this delicious cheese is very Italian" | vt +``` + +[Tree2.png] + +This command uses the programs Graphviz and Ghostview, which you +might not have, but which are freely available on the web. + + + +%--! +==Some random-generated sentences== + +Random generation is a good way to test a grammar; it can also +be fun. So you may want to +generate ten strings with one and the same command: +``` + > 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 +``` + + +%--! +==Systematic generation== + +To generate //all// sentence that a grammar +can generate, use the command ``generate_trees = gt``. +``` + > 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 + +``` +You get quite a few trees but not all of them: only up to a given +**depth** of trees. To see how you can get more, use the +``help = h`` command, +``` + > help gt +``` + +**Exercise**. If the command ``gt`` generated all +trees in your grammar, it would never terminate. Why? + +**Exercise**. Measure how many trees the grammar gives with depths 4 and 5, +respectively. You use the Unix **word count** command ``wc`` to count lines. +**Hint**. You can pipe the output of a GF command into a Unix command by +using the escape ``?``, as follows: +``` + > generate_trees | ? wc +``` + + + + + +%--! +==More on pipes; tracing== + +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. + +The intermediate results in a pipe can be observed by putting the +**tracing** flag ``-tr`` to each command whose output you +want to see: +``` + > gr -tr | l -tr | p + + Is (This Cheese) Boring + this cheese is boring + Is (This Cheese) Boring +``` +This facility is good for test purposes: for instance, you +may want to see if a grammar is **ambiguous**, i.e. +contains strings that can be parsed in more than one way. + +**Exercise**. Extend the grammar ``food.cf`` so that it produces ambiguous strings, +and try out the ambiguity test. + + + + +%--! +==Writing and reading files== + +To save the outputs of GF commands into a file, you can +pipe it to the ``write_file = wf`` command, +``` + > gr -number=10 | l | write_file exx.tmp +``` +You can read the file back to GF with the +``read_file = rf`` command, +``` + > read_file exx.tmp | p -lines +``` +Notice the flag ``-lines`` 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. + + + + +%--! +=The .gf grammar format= + +To see GF's internal representation of a grammar +that you have imported, you can give the command +``print_grammar = pg``, +``` + > print_grammar +``` +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. + +However, we will now start the demonstration +how GF's own notation gives you +much more expressive power than the ``.cf`` +format. We will introduce the ``.gf`` format by presenting +another way of defining the same grammar as in +``food.cf``. +Then we will show how the full GF grammar format enables you +to do things that are not possible in the context-free format. + + +%--! +==Abstract and concrete syntax== + +A GF grammar consists of two main parts: + +- **abstract syntax**, defining what syntax trees there are +- **concrete syntax**, defining how trees are linearized into strings + + +The context-free format fuses these two things together, but it is always +possible to take them apart. For instance, the sentence formation rule +``` + Is. S ::= Item "is" Quality ; +``` +is interpreted as the following pair of GF rules: +``` + fun Is : Item -> Quality -> S ; + lin Is item quality = {s = item.s ++ "is" ++ quality.s} ; +``` +The former rule, with the keyword ``fun``, belongs to the abstract syntax. +It defines the **function** +``Is`` which constructs syntax trees of form +(``Is`` //item// //quality//). + +The latter rule, with the keyword ``lin``, belongs to the concrete syntax. +It defines the **linearization function** for +syntax trees of form (``Is`` //item// //quality//). + + +%--! +==Judgement forms== + +Rules in a GF grammar are called **judgements**, and the keywords +``fun`` and ``lin`` are used for distinguishing between two +**judgement forms**. Here is a summary of the most important +judgement forms: + + - abstract syntax + + | form | reading | + | ``cat`` C | C is a category + | ``fun`` f ``:`` A | f is a function of type A + + - concrete syntax + + | form | reading | + | ``lincat`` C ``=`` T | category C has linearization type T + | ``lin`` f ``=`` t | function f has linearization t + + + +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. + + +%--! +==Module types== + +A GF grammar consists of **modules**, +into which judgements are grouped. The most important +module forms are + + - ``abstract`` A ``=`` M, abstract syntax A with judgements in + the module body M. + - ``concrete`` C ``of`` A ``=`` M, concrete syntax C of the + abstract syntax A, with judgements in the module body M. + + +%--! +==Basic types and function types== + +The nonterminals of a context-free grammar, i.e. categories, +are called **basic types** in the type system of GF. In addition +to them, there are **function types** such as +``` + Item -> Quality -> S +``` +This type is read "a function from iterms and qualities to sentences". +The last type in the arrow-separated sequence is the **value type** +of the function type, the earlier types are its **argument types**. + + + + +%--! +==Records and strings== + +The linearization type of a category is a **record type**, with +zero of more **fields** of different types. The simplest record +type used for linearization in GF is +``` + {s : Str} +``` +which has one field, with **label** ``s`` and type ``Str``. + +Examples of records of this type are +``` + {s = "foo"} + {s = "hello" ++ "world"} +``` + +Whenever a record ``r`` of type ``{s : Str}`` is given, +``r.s`` is an object of type ``Str``. This is +a special case of the **projection** rule, allowing the extraction +of fields from a record: + +- if //r// : ``{`` ... //p// : //T// ... ``}`` then //r.p// : //T// + + +The type ``Str`` is really the type of **token lists**, but +most of the time one can conveniently think of it as the type of strings, +denoted by string literals in double quotes. + +Notice that +``` "hello world" +is not recommended as an expression of type ``Str``. 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 +``` + ["hello world and people"] === "hello" ++ "world" ++ "and" ++ "people" +``` +can be used for lists of tokens. The expression +``` + [] +``` +denotes the empty token list. + + + +%--! +==An abstract syntax example== + +To express the abstract syntax of ``food.cf`` in +a file ``Food.gf``, we write two kinds of judgements: + +- Each category is introduced by a ``cat`` judgement. +- Each rule label is introduced by a ``fun`` judgement, + with the type formed from the nonterminals of the rule. + + +``` + 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 ; + } +``` +Notice the use of shorthands permitting the sharing of +the keyword in subsequent judgements, +``` + cat S ; Item ; === cat S ; cat Item ; +``` +and of the type in subsequent ``fun`` judgements, +``` + fun Wine, Fish : Kind ; === + fun Wine : Kind ; Fish : Kind ; === + fun Wine : Kind ; fun Fish : Kind ; +``` +The order of judgements in a module is free. + +**Exercise**. Extend the abstract syntax ``Food`` with ten new +kinds and qualities, and with questions of the form +//is this wine Italian//. + + + +%--! +==A concrete syntax example== + +Each category introduced in ``Food.gf`` is +given a ``lincat`` rule, and each +function is given a ``lin`` rule. Similar shorthands +apply as in ``abstract`` modules. +``` + 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"} ; + } +``` + +**Exercise**. Extend the concrete syntax ``FoodEng`` so that it +matches the abstract syntax defined in the exercise of the previous +section. What happens if the concrete syntax lacks some of the +new functions? + + + + +%--! +==Modules and files== + +GF uses suffixes to recognize different file formats. The most +important ones are: +- Source files: Module name + ``.gf`` = file name +- Target files: each module is compiled into a ``.gfc`` file. + + +Import ``FoodEng.gf`` and see what happens: +``` + > i FoodEng.gf + - compiling Food.gf... wrote file Food.gfc 16 msec + - compiling FoodEng.gf... wrote file FoodEng.gfc 20 msec +``` +The GF program does not only read the file +``FoodEng.gf``, but also all other files that it +depends on - in this case, ``Food.gf``. + +For each file that is compiled, a ``.gfc`` 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 ``.gfc`` file or to generate +a new one, by looking at modification times. + +**Exercise**. What happens when you import ``FoodEng.gf`` for +a second time? Try this in different situations: +- Right after importing it the first time (the modules are kept in + the memory of GF and need no reloading). +- After issuing the command ``empty`` (``e``), which clears the memory + of GF. +- After making a small change in ``FoodEng.gf``, be it only an added space. +- After making a change in ``Food.gf``. + + + +%--! +=Multilingual grammars and translation= + +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 **multilingual grammar**. + +Multilingual grammars can be used for applications such as +translation. Let us build an Italian concrete syntax for +``Food`` and then test the resulting +multilingual grammar. + + + + +%--! +==An Italian concrete syntax== + +``` +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"} ; + +} +``` + +**Exercise**. Write a concrete syntax of ``Food`` for some other language. +You will probably end up with grammatically incorrect output - but don't +worry about this yet. + +**Exercise**. If you have written ``Food`` for German, Swedish, or some +other language, test with random or exhaustive generation what constructs +come out incorrect, and prepare a list of those ones that cannot be helped +with the currently available fragment of GF. + + +%--! +==Using a multilingual grammar== + +Import the two grammars in the same GF session. +``` + > i FoodEng.gf + > i FoodIta.gf +``` +Try generation now: +``` + > gr | l + quello formaggio molto noioso è italiano + + > gr | l -lang=FoodEng + this fish is warm +``` +Translate by using a pipe: +``` + > p -lang=FoodEng "this cheese is very delicious" | l -lang=FoodIta + questo formaggio è molto delizioso +``` +Generate a **multilingual treebank**, i.e. a set of trees with their +translations in different languages: +``` + > gr -number=2 | tree_bank + + Is (That Cheese) (Very Boring) + quello formaggio è molto noioso + that cheese is very boring + + Is (That Cheese) Fresh + quello formaggio è fresco + that cheese is fresh +``` +The ``lang`` 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 +``print_options = po``: +``` + > print_options + main abstract : Food + main concrete : FoodIta + actual concretes : FoodIta FoodEng +``` +You can change the main grammar by the command ``change_main = cm``: +``` + > change_main FoodEng + main abstract : Food + main concrete : FoodEng + actual concretes : FoodIta FoodEng +``` + + +%--! +==Translation session== + +If translation is what you want to do with a set of grammars, a convenient +way to do it is to open a ``translation_session = ts``. In this session, +you can translate between all the languages that are in scope. +A dot ``.`` terminates the translation session. +``` + > 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> . + > +``` + + + +%--! +==Translation quiz== + +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 ``translation_quiz = tq`` +makes this in a subshell of GF. +``` + > 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 +``` +You can also generate a list of translation exercises and save it in a +file for later use, by the command ``translation_list = tl`` +``` + > translation_list -number=25 FoodEng FoodIta | write_file transl.txt +``` +The ``number`` flag gives the number of sentences generated. + + + + +%--! +=Grammar architecture= + +==Extending a grammar== + +The module system of GF makes it possible to **extend** a +grammar in different ways. The syntax of extension is +shown by the following example. We extend ``Food`` by +adding a category of questions and two new functions. +``` + abstract Morefood = Food ** { + cat + Question ; + fun + QIs : Item -> Quality -> Question ; + Pizza : Kind ; + + } +``` +Parallel to the abstract syntax, extensions can +be built for concrete syntaxes: +``` + concrete MorefoodEng of Morefood = FoodEng ** { + lincat + Question = {s : Str} ; + lin + QIs item quality = {s = "is" ++ item.s ++ quality.s} ; + Pizza = {s = "pizza"} ; + } +``` +The effect of extension is that all of the contents of the extended +and extending module are put together. We also say that the new +module **inherits** the contents of the old module. + + + +%--! +==Multiple inheritance== + +Specialized vocabularies can be represented as small grammars that +only do "one thing" each. For instance, the following are grammars +for fruit and mushrooms +``` + abstract Fruit = { + cat Fruit ; + fun Apple, Peach : Fruit ; + } + + abstract Mushroom = { + cat Mushroom ; + fun Cep, Agaric : Mushroom ; + } +``` +They can afterwards be combined into bigger grammars by using +**multiple inheritance**, i.e. extension of several grammars at the +same time: +``` + abstract Foodmarket = Food, Fruit, Mushroom ** { + fun + FruitKind : Fruit -> Kind ; + MushroomKind : Mushroom -> Kind ; + } +``` +At this point, you would perhaps like to go back to +``Food`` and take apart ``Wine`` to build a special +``Drink`` module. + + +%--! +==Visualizing module structure== + +When you have created all the abstract syntaxes and +one set of concrete syntaxes needed for ``Foodmarket``, +your grammar consists of eight GF modules. To see how their +dependences look like, you can use the command +``visualize_graph = vg``, +``` + > visualize_graph +``` +and the graph will pop up in a separate window. + +The graph uses + +- oval boxes for abstract modules +- square boxes for concrete modules +- black-headed arrows for inheritance +- white-headed arrows for the concrete-of-abstract relation + + +[Foodmarket.png] + + +Just as the ``visualize_tree = vt`` command, the open source tools +Ghostview and Graphviz are needed. + + +%--! +==System commands== + +To document your grammar, you may want to print the +graph into a file, e.g. a ``.png`` file that +can be included in an HTML document. You can do this +by first printing the graph into a file ``.dot`` and then +processing this file with the ``dot`` program (from the Graphviz package). +``` + > pm -printer=graph | wf Foodmarket.dot + > ! dot -Tpng Foodmarket.dot > Foodmarket.png +``` +The latter command is a Unix command, issued from GF by using the +shell escape symbol ``!``. The resulting graph was shown in the previous section. + +The command ``print_multi = pm`` is used for printing the current multilingual +grammar in various formats, of which the format ``-printer=graph`` just +shows the module dependencies. Use ``help`` to see what other formats +are available: +``` + > help pm + > help -printer + > help help +``` +Another form of system commands are those usable in GF pipes. The escape symbol +is then ``?``. +``` + > generate_trees | ? wc +``` + + + +%--! +=Resource modules= + + +==The golden rule of functional programming== + +In comparison to the ``.cf`` format, the ``.gf`` 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. + +However, there is a more elegant way to avoid repeating work than the copy-and-paste +method. The **golden rule of functional programming** says that +- whenever you find yourself programming by copy-and-paste, write a function instead. + + +A function separates the shared parts of different computations from the +changing parts, its **arguments**, or **parameters**. +In functional programming languages, such as +[Haskell http://www.haskell.org], it is possible to share much more +code with functions than in imperative languages such as C and Java. + + +==Operation definitions== + +GF is a functional programming language, not only in the sense that +the abstract syntax is a system of functions (``fun``), 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 ``oper`` (for +**operation**), distinct from ``fun`` for the sake of clarity. +Here is a simple example of an operation: +``` + oper ss : Str -> {s : Str} = \x -> {s = x} ; +``` +The operation can be **applied** to an argument, and GF will +**compute** the application into a value. For instance, +``` + ss "boy" ===> {s = "boy"} +``` +(We use the symbol ``===>`` to indicate how an expression is +computed into a value; this symbol is not a part of GF) + +Thus an ``oper`` 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 **lambda abstraction** form ``\x -> t`` of +the function. + + + +%--! +==The ``resource`` module type== + +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 **resources** +usable in many concrete syntaxes. + +The ``resource`` module type can be used to package +``oper`` definitions into reusable resources. Here is +an example, with a handful of operations to manipulate +strings and records. +``` + 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) ; + } +``` +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. + + + +%--! +==Opening a resource== + +Any number of ``resource`` modules can be +**opened** in a ``concrete`` syntax, which +makes definitions contained +in the resource usable in the concrete syntax. Here is +an example, where the resource ``StringOper`` is +opened in a new version of ``FoodEng``. +``` + concrete Food2Eng of Food = open StringOper in { + + lincat + S, Item, Kind, Quality = SS ; + + lin + Is item quality = cc item (prefix "is" quality) ; + This k = prefix "this" k ; + That k = prefix "that" k ; + QKind k q = cc k q ; + 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" ; + + } +``` +**Exercise**. Use the same string operations to write ``FoodIta`` +more concisely. + + + +%--! +==Partial application== + +GF, like Haskell, permits **partial application** of +functions. An example of this is the rule +``` + lin This k = prefix "this" k ; +``` +which can be written more concisely +``` + lin This = prefix "this" ; +``` +The first form is perhaps more intuitive to write +but, once you get used to partial application, you will appreciate its +conciseness and elegance. The logic of partial application +is known as **currying**, with a reference to Haskell B. Curry. +The idea is that any //n//-place function can be defined as a 1-place +function whose value is an //n-//1 -place function. Thus +``` + oper prefix : Str -> SS -> SS ; +``` +can be used as a 1-place function that takes a ``Str`` into a +function ``SS -> SS``. The expected linearization of ``This`` is exactly +a function of such a type, operating on an argument of type ``Kind`` +whose linearization is of type ``SS``. Thus we can define the +linearization directly as ``prefix "this"``. + +**Exercise**. Define an operation ``infix`` analogous to ``prefix``, +such that it allows you to write +``` + lin Is = infix "is" ; +``` + + +%--! +==Testing resource modules== + +To test a ``resource`` module independently, you must import it +with the flag ``-retain``, which tells GF to retain ``oper`` definitions +in the memory; the usual behaviour is that ``oper`` definitions +are just applied to compile linearization rules +(this is called **inlining**) and then thrown away. +``` + > i -retain StringOper.gf +``` +The command ``compute_concrete = cc`` computes any expression +formed by operations and other GF constructs. For example, +``` + > compute_concrete prefix "in" (ss "addition") + { + s : Str = "in" ++ "addition" + } +``` + + + +%--! +==Division of labour== + +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 their knowledge +available through resource grammar modules, whose users only need +to pick the right operations and not to know their implementation +details. + +In the following sections, we will go through some +such linguistic details. The programming constructs needed when +doing this are useful for all GF programmers, even if they don't +hand-code the linguistics of their applications but get them +from libraries. It is also useful to know something about the +linguistic concepts of inflection, agreement, and parts of speech. + + + + +%--! +=Morphology= + +Suppose we want to say, with the vocabulary included in +``Food.gf``, things like +``` + all Italian wines are delicious +``` +The new grammatical facility we need are the plural forms +of nouns and verbs (//wines, are//), as opposed to their +singular forms. + +The introduction of plural forms requires two things: +- the **inflection** of nouns and verbs in singular and plural +- the **agreement** of the verb to subject: + the verb must have the same number as the subject + + +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. + +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. + +**Exercise**. Make a list of the possible forms that nouns, +adjectives, and verbs can have in some languages that you know. + + +%--! +==Parameters and tables== + +We define the **parameter type** of number in Englisn by +using a new form of judgement: +``` + param Number = Sg | Pl ; +``` +To express that ``Kind`` expressions in English have a linearization +depending on number, we replace the linearization type ``{s : Str}`` +with a type where the ``s`` field is a **table** depending on number: +``` + lincat Kind = {s : Number => Str} ; +``` +The **table type** ``Number => Str`` is in many respects similar to +a function type (``Number -> Str``). 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: +``` + lin Cheese = {s = table { + Sg => "cheese" ; + Pl => "cheeses" + } + } ; +``` +The table consists of **branches**, where a **pattern** on the +left of the arrow ``=>`` is assigned a **value** on the right. + +The application of a table to a parameter is done by the **selection** +operator ``!``. For instance, +``` + table {Sg => "cheese" ; Pl => "cheeses"} ! Pl +``` +is a selection that computes into the value ``"cheeses"``. +This computation is performed by **pattern matching**: return +the value from the first branch whose pattern matches the +selection argument. Thus +``` + table {Sg => "cheese" ; Pl => "cheeses"} ! Pl + ===> "cheeses" +``` + +**Exercise**. In a previous exercise, we make a list of the possible +forms that nouns, adjectives, and verbs can have in some languages that +you know. Now take some of the results and implement them by +using parameter type definitions and tables. Write them into a ``resource`` +module, which you can test by using the command ``compute_concrete``. + + + +%--! +==Inflection tables and paradigms== + +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 //s//. This rule is an example of +a **paradigm** - a formula telling how the inflection +forms of a word are formed. + +From the GF point of view, a paradigm is a function that takes a **lemma** - +also known as a **dictionary form** - and returns an inflection +table of desired type. Paradigms are not functions in the sense of the +``fun`` judgements of abstract syntax (which operate on trees and not +on strings), but operations defined in ``oper`` judgements. +The following operation defines the regular noun paradigm of English: +``` + oper regNoun : Str -> {s : Number => Str} = \x -> { + s = table { + Sg => x ; + Pl => x + "s" + } + } ; +``` +The **gluing** operator ``+`` tells that +the string held in the variable ``x`` and the ending ``"s"`` +are written together to form one **token**. Thus, for instance, +``` + (regNoun "cheese").s ! Pl ---> "cheese" + "s" ---> "cheeses" +``` + +**Exercise**. Identify cases in which the ``regNoun`` paradigm does not +apply in English, and implement some alternative paradigms. + +**Exercise**. Implement a paradigm for regular verbs in English. + +**Exercise**. Implement some regular paradigms for other languages you have +considered in earlier exercises. + + +%--! +==Worst-case functions and data abstraction== + +Some English nouns, such as ``mouse``, are so irregular that +it makes no sense to see them as instances of a paradigm. Even +then, it is useful to perform **data abstraction** from the +definition of the type ``Noun``, and introduce a constructor +operation, a **worst-case function** for nouns: +``` + oper mkNoun : Str -> Str -> Noun = \x,y -> { + s = table { + Sg => x ; + Pl => y + } + } ; +``` +Thus we can define +``` + lin Mouse = mkNoun "mouse" "mice" ; +``` +and +``` + oper regNoun : Str -> Noun = \x -> + mkNoun x (x + "s") ; +``` +instead of writing the inflection tables explicitly. + +The grammar engineering advantage of worst-case functions is that +the author of the resource module may change the definitions of +``Noun`` and ``mkNoun``, 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, ``Noun`` is then treated as an **abstract datatype**. + + + +%--! +==A system of paradigms using Prelude operations== + +In addition to the completely regular noun paradigm ``regNoun``, +some other frequent noun paradigms deserve to be +defined, for instance, +``` + sNoun : Str -> Noun = \kiss -> mkNoun kiss (kiss + "es") ; +``` +What about nouns like //fly//, with the plural //flies//? The already +available solution is to use the longest common prefix +//fl// (also known as the **technical stem**) as argument, and define +``` + yNoun : Str -> Noun = \fl -> mkNoun (fl + "y") (fl + "ies") ; +``` +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 ``init``, which returns the initial segment (i.e. +all characters but the last) of a string: +``` + yNoun : Str -> Noun = \fly -> mkNoun fly (init fly + "ies") ; +``` +The operation ``init`` belongs to a set of operations in the +resource module ``Prelude``, which therefore has to be +``open``ed so that ``init`` can be used. Its dual is ``last``: +``` + > cc init "curry" + "curr" + + > cc last "curry" + "y" +``` +As generalizations of the library functions ``init`` and ``last``, GF has +two predefined funtions: +``Predef.dp``, which "drops" suffixes of any length, +and ``Predef.tk``, which "takes" a prefix +just omitting a number of characters from the end. For instance, +``` + > cc Predef.tk 3 "worried" + "worr" + > cc Predef.dp 3 "worried" + "ied" +``` +The prefix ``Predef`` is given to a handful of functions that could +not be defined internally in GF. They are available in all modules +without explicit ``open`` of the module ``Predef``. + + + + + +%--! +==Pattern matching== + +We have so far built all expressions of the ``table`` form +from branches whose patterns are constants introduced in +``param`` definitions, as well as constant strings. +But there are more expressive patterns. Here is a summary of the possible forms: +- a variable pattern (identifier other than constant parameter) matches anything +- the wild card ``_`` matches anything +- a string literal pattern, e.g. ``"s"``, matches the same string +- a disjunctive pattern ``P | ... | Q`` matches anything that + one of the disjuncts matches + + +Pattern matching is performed in the order in which the branches +appear in the table: the branch of the first matching pattern is followed. + +As syntactic sugar, one-branch tables can be written concisely, +``` + \\P,...,Q => t === table {P => ... table {Q => t} ...} +``` +Finally, the ``case`` expressions common in functional +programming languages are syntactic sugar for table selections: +``` + case e of {...} === table {...} ! e +``` + + +%--! +==An intelligent noun paradigm using pattern matching== + +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 ``last``). +``` + regNoun : Str -> Noun = \s -> case last s of { + "s" | "z" => mkNoun s (s + "es") ; + "y" => mkNoun s (init s + "ies") ; + _ => mkNoun s (s + "s") + } ; +``` +This definition displays many GF expression forms not shown befores; +these forms are explained in the next section. + +The paradigms ``regNoun`` does not give the correct forms for +all nouns. For instance, //mouse - mice// and +//fish - fish// must be given by using ``mkNoun``. +Also the word //boy// would be inflected incorrectly; to prevent +this, either use ``mkNoun`` or modify +``regNoun`` so that the ``"y"`` case does not +apply if the second-last character is a vowel. + +**Exercise**. Extend the ``regNoun`` paradigm so that it takes care +of all variations there are in English. Test it with the nouns +//ax//, //bamboo//, //boy//, //bush//, //hero//, //match//. +**Hint**. The library functions ``Predef.dp`` and ``Predef.tk`` +are useful in this task. + +**Exercise**. The same rules that form plural nouns in English also +apply in the formation of third-person singular verbs. +Write a regular verb paradigm that uses this idea, but first +rewrite ``regNoun`` so that the analysis needed to build //s//-forms +is factored out as a separate ``oper``, which is shared with +``regVerb``. + + + + +%--! +==Morphological resource modules== + +A common idiom is to +gather the ``oper`` and ``param`` definitions +needed for inflecting words in +a language into a morphology module. Here is a simple +example, [``MorphoEng`` resource/MorphoEng.gf]. +``` + --# -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") + } ; + } +``` +The first line gives as a hint to the compiler the +**search path** needed to find all the other modules that the +module depends on. The directory ``prelude`` is a subdirectory of +``GF/lib``; to be able to refer to it in this simple way, you can +set the environment variable ``GF_LIB_PATH`` to point to this +directory. + + + +=Using parameters in concrete syntax= + +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. + + +%--! +==Parametric vs. inherent features, agreement== + +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 +//has// a number, which it passes to the verb. The verb does not +//have// a number, but must be able to //receive// whatever number the +subject has. This distinction is nicely represented by the +different linearization types of **noun phrases** and **verb phrases**: +``` + lincat NP = {s : Str ; n : Number} ; + lincat VP = {s : Number => Str} ; +``` +We say that the number of ``NP`` is an **inherent feature**, +whereas the number of ``NP`` is a **variable feature** (or a +**parametric feature**). + +The agreement rule itself is expressed in the linearization rule of +the predication function: +``` + lin PredVP np vp = {s = np.s ++ vp.s ! np.n} ; +``` +The following section will present +``FoodsEng``, assuming the abstract syntax ``Foods`` +that is similar to ``Food`` but also has the +plural determiners ``These`` and ``Those``. +The reader is invited to inspect the way in which agreement works in +the formation of sentences. + + +%--! +==English concrete syntax with parameters== + +The grammar uses both +[``Prelude`` ../../lib/prelude/Prelude.gf] and +[``MorphoEng`` resource/MorphoEng]. +We will later see how to make the grammar even +more high-level by using a resource grammar library +and parametrized modules. +``` +--# -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 + } ; +} +``` + + + +%--! +==Hierarchic parameter types== + +The reader familiar with a functional programming language such as +[Haskell http://www.haskell.org] must have noticed the similarity +between parameter types in GF and **algebraic datatypes** (``data`` 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.) + +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. + +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 +``Gender => Number => Str``. The following hierarchic definition +yields an accurate system of three adjectival forms. +``` + param AdjForm = ASg Gender | APl ; + param Gender = Utr | Neutr ; +``` +Here is an example of pattern matching, the paradigm of regular adjectives. +``` + oper regAdj : Str -> AdjForm => Str = \fin -> table { + ASg Utr => fin ; + ASg Neutr => fin + "t" ; + APl => fin + "a" ; + } +``` +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 +``` + oper plattAdj : Str -> AdjForm => Str = \platt -> table { + ASg _ => platt ; + APl => platt + "a" ; + } +``` + + +%--! +==Morphological analysis and morphology quiz== + +Even though morphology is in GF +mostly used as an auxiliary for syntax, it +can also be useful on its own right. The command ``morpho_analyse = ma`` +can be used to read a text and return for each word the analyses that +it has in the current concrete syntax. +``` + > rf bible.txt | morpho_analyse +``` +In the same way as translation exercises, morphological exercises can +be generated, by the command ``morpho_quiz = mq``. Usually, +the category is set to be something else than ``S``. For instance, +``` + > cd GF/lib/resource-1.0/ + > i french/IrregFre.gf + > morpho_quiz -cat=V + + Welcome to GF Morphology Quiz. + ... + + réapparaître : VFin VCondit Pl P2 + réapparaitriez + > No, not réapparaitriez, but + réapparaîtriez + Score 0/1 +``` +Finally, a list of morphological exercises can be generated +off-line and saved in a +file for later use, by the command ``morpho_list = ml`` +``` + > morpho_list -number=25 -cat=V | wf exx.txt +``` +The ``number`` flag gives the number of exercises generated. + + + +%--! +==Discontinuous constituents== + +A linearization type may contain more strings than one. +An example of where this is useful are English particle +verbs, such as //switch off//. The linearization of +a sentence may place the object between the verb and the particle: +//he switched it off//. + +The following judgement defines transitive verbs as +**discontinuous constituents**, i.e. as having a linearization +type with two strings and not just one. +``` + lincat TV = {s : Number => Str ; part : Str} ; +``` +This linearization rule +shows how the constituents are separated by the object in complementization. +``` + lin PredTV tv obj = {s = \\n => tv.s ! n ++ obj.s ++ tv.part} ; +``` +There is no restriction in the number of discontinuous constituents +(or other fields) a ``lincat`` may contain. The only condition is that +the fields must be of finite types, i.e. built from records, tables, +parameters, and ``Str``, and not functions. + +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 ``Str`` +valued field labelled ``s``. Therefore, discontinuous constituents +are not a good idea in top-level categories accessed by the users +of a grammar application. + + +%--! +==Free variation== + +Sometimes there are many alternative ways to define a concrete syntax. +For instance, the verb negation in English can be expressed both by +//does not// and //doesn't//. In linguistic terms, these expressions +are in **free variation**. The ``variants`` construct of GF can +be used to give a list of strings in free variation. For example, +``` + NegVerb verb = {s = variants {["does not"] ; "doesn't} ++ verb.s ! Pl} ; +``` +An empty variant list +``` + variants {} +``` +can be used e.g. if a word lacks a certain form. + +In general, ``variants`` 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. + + + +==Overloading of operations== + +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 **overloading**: +the same name can be used for several functions. When such a name is used, the +compiler performs **overload resolution** 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. + +In C++, functions with the same name can be scattered everywhere in the program. +In GF, they must be grouped together in ``overload`` groups. Here is an example +of an overload group, defining four ways to define nouns in Italian: +``` + 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 + } +``` +All of the following uses of ``mkN`` are easy to resolve: +``` + lin Pizza = mkN "pizza" ; -- Str -> N + lin Hand = mkN "mano" Fem ; -- Str -> Gender -> N + lin Man = mkN "uomo" "uomini" ; -- Str -> Str -> N +``` + + + + + + +%--! +=More constructs for concrete syntax= + +In this chapter, we go through constructs that are not necessary in simple grammars +or when the concrete syntax relies on libraries. But they are useful when +writing advanced concrete syntax implementations, such as resource grammar libraries. +This chapter can safely be skipped if the reader prefers to continue to the +chapter on using libraries. + + +%--! +==Local definitions== + +Local definitions ("``let`` 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 +[``MorphoIta`` resource/MorphoIta.gf]: +``` + 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 + } ; +``` + + +==Record extension and subtyping== + +Record types and records can be **extended** with new fields. For instance, +in German it is natural to see transitive verbs as verbs with a case. +The symbol ``**`` is used for both constructs. +``` + lincat TV = Verb ** {c : Case} ; + + lin Follow = regVerb "folgen" ** {c = Dative} ; +``` +To extend a record type or a record with a field whose label it +already has is a type error. + +A record type //T// is a **subtype** of another one //R//, if //T// has +all the fields of //R// and possibly other fields. For instance, +an extension of a record type is always a subtype of it. + +If //T// is a subtype of //R//, an object of //T// can be used whenever +an object of //R// is required. For instance, a transitive verb can +be used whenever a verb is required. + +**Contravariance** means that a function taking an //R// as argument +can also be applied to any object of a subtype //T//. + + + +==Tuples and product types== + +Product types and tuples are syntactic sugar for record types and records: +``` + T1 * ... * Tn === {p1 : T1 ; ... ; pn : Tn} + === {p1 = T1 ; ... ; pn = Tn} +``` +Thus the labels ``p1, p2,...`` are hard-coded. + + +==Record and tuple patterns== + +Record types of parameter types are also parameter types. +A typical example is a record of agreement features, e.g. French +``` + oper Agr : PType = {g : Gender ; n : Number ; p : Person} ; +``` +Notice the term ``PType`` rather than just ``Type`` referring to +parameter types. Every ``PType`` is also a ``Type``, but not vice-versa. + +Pattern matching is done in the expected way, but it can moreover +utilize partial records: the branch +``` + {g = Fem} => t +``` +in a table of type ``Agr => T`` means the same as +``` + {g = Fem ; n = _ ; p = _} => t +``` +Tuple patterns are translated to record patterns in the +same way as tuples to records; partial patterns make it +possible to write, slightly surprisingly, +``` + case of { + => t + ... + } +``` + + +%--! +==Regular expression patterns== + +To define string operations computed at compile time, such +as in morphology, it is handy to use regular expression patterns: + - //p// ``+`` //q// : token consisting of //p// followed by //q// + - //p// ``*`` : token //p// repeated 0 or more times + (max the length of the string to be matched) + - ``-`` //p// : matches anything that //p// does not match + - //x// ``@`` //p// : bind to //x// what //p// matches + - //p// ``|`` //q// : matches what either //p// or //q// matches + + +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 //s// and used in the formation of both plural nouns and +third-person present-tense verbs. +``` + add_s : Str -> Str = \w -> case w of { + _ + "oo" => w + "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 + } ; +``` +Here is another example, the plural formation in Swedish 2nd declension. +The second branch uses a variable binding with ``@`` to cover the cases where an +unstressed pre-final vowel //e// disappears in the plural +(//nyckel-nycklar, seger-segrar, bil-bilar//): +``` + plural2 : Str -> Str = \w -> case w of { + pojk + "e" => pojk + "ar" ; + nyck + "e" + l@("l" | "r" | "n") => nyck + l + "ar" ; + bil => bil + "ar" + } ; +``` + + +Semantics: variables are always bound to the **first match**, which is the first +in the sequence of binding lists ``Match p v`` defined as follows. In the definition, +``p`` is a pattern and ``v`` is a value. The semantics is given in Haskell notation. +``` + Match (p1|p2) v = Match p1 ++ U 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 +``` +Examples: +- ``x + "e" + y`` matches ``"peter"`` with ``x = "p", y = "ter"`` +- ``x + "er"*`` matches ``"burgerer"`` with ``x = "burg" + + + +**Exercise**. Implement the German **Umlaut** operation on word stems. +The operation changes the vowel of the stressed stem syllable as follows: +//a// to //ä//, //au// to //äu//, //o// to //ö//, and //u// to //ü//. You +can assume that the operation only takes syllables as arguments. Test the +operation to see whether it correctly changes //Arzt// to //Ärzt//, +//Baum// to //Bäum//, //Topf// to //Töpf//, and //Kuh// to //Küh//. + + + + +%--! +==Prefix-dependent choices== + +Sometimes a token has different forms depending on the token +that follows. An example is the English indefinite article, +which is //an// if a vowel follows, //a// 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 ``pre`` construct exemplified in +``` + oper artIndef : Str = + pre {"a" ; "an" / strs {"a" ; "e" ; "i" ; "o"}} ; +``` +Thus +``` + artIndef ++ "cheese" ---> "a" ++ "cheese" + artIndef ++ "apple" ---> "an" ++ "apple" +``` +This very example does not work in all situations: the prefix +//u// has no general rules, and some problematic words are +//euphemism, one-eyed, n-gram//. It is possible to write +``` + oper artIndef : Str = + pre {"a" ; + "a" / strs {"eu" ; "one"} ; + "an" / strs {"a" ; "e" ; "i" ; "o" ; "n-"} + } ; +``` + + +==Predefined types== + +GF has the following predefined categories in abstract syntax: +``` + cat Int ; -- integers, e.g. 0, 5, 743145151019 + cat Float ; -- floats, e.g. 0.0, 3.1415926 + cat String ; -- strings, e.g. "", "foo", "123" +``` +The objects of each of these categories are **literals** +as indicated in the comments above. No ``fun`` definition +can have a predefined category as its value type, but +they can be used as arguments. For example: +``` + fun StreetAddress : Int -> String -> Address ; + lin StreetAddress number street = {s = number.s ++ street.s} ; + + -- e.g. (StreetAddress 10 "Downing Street") : Address +``` +FIXME: The linearization type is ``{s : Str}`` for all these categories. + + + +%--! + +=Using the resource grammar library= + +In this chapter, we will take a look at the GF resource grammar library. +We will use the library to implement a slightly extended ``Food`` grammar +and port it to some new languages. + + +==The coverage of the library== + +The GF Resource Grammar Library contains grammar rules for +10 languages (in addition, 2 languages are available as incomplete +implementations, and a few more are under construction). Its purpose +is to make these rules available for application programmers, +who can thereby concentrate on the semantic and stylistic +aspects of their grammars, without having to think about +grammaticality. The targeted level of application grammarians +is that of a skilled programmer with +a practical knowledge of the target languages, but without +theoretical knowledge about their grammars. +Such a combination of +skills is typical of programmers who, for instance, want to localize +software to new languages. + +The current resource languages are +- ``Ara``bic (incomplete) +- ``Cat``alan (incomplete) +- ``Dan``ish +- ``Eng``lish +- ``Fin``nish +- ``Fre``nch +- ``Ger``man +- ``Ita``lian +- ``Nor``wegian +- ``Rus``sian +- ``Spa``nish +- ``Swe``dish + + +The first three letters (``Eng`` etc) are used in grammar module names. +The incomplete Arabic and Catalan implementations are +enough to be used in many applications; they both contain, amoung other +things, complete inflectional morphology. + + +==The resource API== + +The resource library API is devided into language-specific +and language-independent parts. To put it roughly, +- the syntax API is language-independent, i.e. has the same types and functions for all + languages. + Its name is ``Syntax``//L// for each language //L// +- the morphology API is language-specific, i.e. has partly different types and functions + for different languages. + Its name is ``Paradigms``//L// for each language //L// + + +A full documentation of the API is available on-line in the +[resource synopsis ../../lib/resource-1.0/synopsis.html]. For our +examples, we will only need a fragment of the full API. + +In the first examples, +we will make use of the following categories, from the module ``Syntax``. + +|| Category | Explanation | Example || +| ``Utt`` | sentence, question, word... | "be quiet" | +| ``Adv`` | verb-phrase-modifying adverb, | "in the house" | +| ``AdA`` | adjective-modifying adverb, | "very" | +| ``S`` | declarative sentence | "she lived here" | +| ``Cl`` | declarative clause, with all tenses | "she looks at this" | +| ``AP`` | adjectival phrase | "very warm" | +| ``CN`` | common noun (without determiner) | "red house" | +| ``NP`` | noun phrase (subject or object) | "the red house" | +| ``Det`` | determiner phrase | "those seven" | +| ``Predet`` | predeterminer | "only" | +| ``Quant`` | quantifier with both sg and pl | "this/these" | +| ``Prep`` | preposition, or just case | "in" | +| ``A`` | one-place adjective | "warm" | +| ``N`` | common noun | "house" | + + +We will need the following syntax rules from ``Syntax``. + +|| Function | Type | Example || +| ``mkUtt`` | ``S -> Utt`` | //John walked// | +| ``mkUtt`` | ``Cl -> Utt`` | //John walks// | +| ``mkCl`` | ``NP -> AP -> Cl`` | //John is very old// | +| ``mkNP`` | ``Det -> CN -> NP`` | //the first old man// | +| ``mkNP`` | ``Predet -> NP -> NP`` | //only John// | +| ``mkDet`` | ``Quant -> Det`` | //this// | +| ``mkCN`` | ``N -> CN`` | //house// | +| ``mkCN`` | ``AP -> CN -> CN`` | //very big blue house// | +| ``mkAP`` | ``A -> AP`` | //old// | +| ``mkAP`` | ``AdA -> AP -> AP`` | //very very old// | + +We will also need the following structural words from ``Syntax``. + +|| Function | Type | Example || +| ``all_Predet`` | ``Predet`` | //all// | +| ``defPlDet`` | ``Det`` | //the (houses)// | +| ``this_Quant`` | ``Quant`` | //this// | +| ``very_AdA`` | ``AdA`` | //very// | + + +For French, we will use the following part of ``ParadigmsFre``. + +|| Function | Type | Example || +| ``Gender`` | ``Type`` | - | +| ``masculine`` | ``Gender`` | - | +| ``feminine`` | ``Gender`` | - | +| ``mkN`` | ``(cheval : Str) -> N`` | - | +| ``mkN`` | ``(foie : Str) -> Gender -> N`` | - | +| ``mkA`` | ``(cher : Str) -> A`` | - | +| ``mkA`` | ``(sec,seche : Str) -> A`` | - | + + +For German, we will use the following part of ``ParadigmsGer``. + +|| Function | Type | Example || +| ``Gender`` | ``Type`` | - | +| ``masculine`` | ``Gender`` | - | +| ``feminine`` | ``Gender`` | - | +| ``neuter`` | ``Gender`` | - | +| ``mkN`` | ``(Stufe : Str) -> N`` | - | +| ``mkN`` | ``(Bild,Bilder : Str) -> Gender -> N`` | - | +| ``mkA`` | ``Str -> A`` | - | +| ``mkA`` | ``(gut,besser,beste : Str) -> A`` | //gut,besser,beste// | + + +**Exercise**. Try out the morphological paradigms in different languages. Do +in this way: +``` + > i -path=alltenses:prelude -retain alltenses/ParadigmsGer.gfr + > cc mkN "Farbe" + > cc mkA "gut" "besser" "beste" +``` + + +==Example: French== + +We start with an abstract syntax that is like ``Food`` before, but +has a plural determiner (//all wines//) and some new nouns that will +need different genders in most languages. +``` + abstract Food = { + cat + S ; Item ; Kind ; Quality ; + fun + Is : Item -> Quality -> S ; + This, All : Kind -> Item ; + QKind : Quality -> Kind -> Kind ; + Wine, Cheese, Fish, Beer, Pizza : Kind ; + Very : Quality -> Quality ; + Fresh, Warm, Italian, Expensive, Delicious, Boring : Quality ; + } +``` +The French implementation opens ``SyntaxFre`` and ``ParadigmsFre`` +to get access to the resource libraries needed. In order to find +the libraries, a ``path`` directive is prepended; it is interpreted +relative to the environment variable ``GF_LIB_PATH``. +``` + --# -path=.:present:prelude + + concrete FoodFre of Food = open SyntaxFre,ParadigmsFre in { + lincat + S = Utt ; + Item = NP ; + Kind = CN ; + Quality = AP ; + lin + Is item quality = mkUtt (mkCl item quality) ; + This kind = mkNP (mkDet this_Quant) kind ; + All kind = mkNP all_Predet (mkNP defPlDet kind) ; + QKind quality kind = mkCN quality kind ; + Wine = mkCN (mkN "vin") ; + Beer = mkCN (mkN "bière") ; + Pizza = mkCN (mkN "pizza" feminine) ; + Cheese = mkCN (mkN "fromage" masculine) ; + Fish = mkCN (mkN "poisson") ; + Very quality = mkAP very_AdA quality ; + Fresh = mkAP (mkA "frais" "fraîche") ; + Warm = mkAP (mkA "chaud") ; + Italian = mkAP (mkA "italien") ; + Expensive = mkAP (mkA "cher") ; + Delicious = mkAP (mkA "délicieux") ; + Boring = mkAP (mkA "ennuyeux") ; + } +``` +The ``lincat`` definitions in ``FoodFre`` assign **resource categories** +to **application categories**. In a sense, the application categories +are **semantic**, as they correspond to concepts in the grammar application, +whereas the resource categories are **syntactic**: they give the linguistic +means to express concepts in any application. + +The ``lin`` definitions likewise assign resource functions to application +functions. Under the hood, there is a lot of matching with parameters to +take care of word order, inflection, and agreement. But the user of the +library sees nothing of this: the only parameters you need to give are +the genders of some nouns, which cannot be correctly inferred from the word. + +In French, for example, the one-argument ``mkN`` assigns the noun the feminine +gender if and only if it ends with an //e//. Therefore the words //fromage// and +//pizza// are given genders. One can of course always give genders manually, to +be on the safe side. + +As for inflection, the one-argument adjective pattern ``mkA`` takes care of +completely regular adjective such as //chaud-chaude//, but also of special +cases such as //italien-italienne//, //cher-chère//, and //délicieux-délicieuse//. +But it cannot form //frais-fraîche// properly. Once again, you can give more +forms to be on the safe side. You can also test the paradigms in the GF +program. + +**Exercise**. Compile the grammar ``FoodFre`` and generate and parse some sentences. + +**Exercise**. Write a concrete syntax of ``Food`` for English or some other language +included in the resource library. You can also compare the output with the hand-written +grammars presented earlier in this tutorial. + +**Exercise**. In particular, try to write a concrete syntax for Italian, even if +you don't know Italian. What you need to know is that "beer" is //birra// and +"pizza" is //pizza//, and that all the nouns and adjectives in the grammar +are regular. + + + +==Functor implementation of multilingual grammars== + +If you did the exercise of writing a concrete syntax of ``Food`` for some other +language, you probably noticed that much of the code looks exactly the same +as for French. The immediate reason for this is that the ``Syntax`` API is the +same for all languages; the deeper reason is that all languages (at least those +in the resource package) implement the same syntactic structures and tend to use them +in similar ways. Thus it is only the lexical parts of a concrete syntax that +you need to write anew for a new language. In brief, +- first copy the concrete syntax for one language +- then change the words (the strings and perhaps some paradigms) + + +But programming by copy-and-paste is not worthy of a functional programmer. +Can we write a function that takes care of the shared parts of grammar modules? +Yes, we can. It is not a function in the ``fun`` or ``oper`` sense, but +a function operating on modules, called a **functor**. This construct +is familiar from the functional languages ML and OCaml, but it does not +exist in Haskell. It also bears some resemblance to templates in C++. +Functors are also known as **parametrized modules**. + +In GF, a functor is a module that ``open``s one or more **interfaces**. +An ``interface`` is a module similar to a ``resource``, but it only +contains the types of ``oper``s, not their definitions. You can think +of an interface as a kind of a record type. Thus a functor is a kind +of a function taking records as arguments and producins a module +as value. + +Let us look at a functor implementation of the ``Food`` grammar. +Consider its module header first: +``` + incomplete concrete FoodI of Food = open Syntax, LexFood in +``` +In the functor-function analogy, ``FoodI`` would be presented as a function +with the following type signature: +``` + FoodI : instance of Syntax -> instance of LexFood -> concrete of Food +``` +It takes as arguments two interfaces: +- ``Syntax``, the resource grammar interface +- ``LexFood``, the domain-specific lexicon interface + + +Functors opening ``Syntax`` and a domain lexicon interface are in fact +so typical in GF applications, that this structure could be called a **design patter** +for GF grammars. The idea in this pattern is, again, that +the languages use the same syntactic structures but different words. + +Before going to the details of the module bodies, let us look at how functors +are concretely used. An interface has a header such as +``` + interface LexFood = open Syntax in +``` +To give an ``instance`` of it means that all ``oper``s are given definitione (of +appropriate types). For example, +``` + instance LexFoodGer of LexFood = open SyntaxGer, ParadigmsGer in +``` +Notice that when an interface opens an interface, such as ``Syntax``, then its instance +opens an instance of it. But the instance may also open some resources - typically, +a domain lexicon instance opens a ``Paradigms`` module. + +In the function-functor analogy, we now have +``` + SyntaxGer : instance of Syntax + LexFoodGer : instance of LexFood +``` +Thus we can complete the German implementation by "applying" the functor: +``` + FoodI SyntaxGer LexFoodGer : concrete of Food +``` +The GF syntax for doing so is +``` + concrete FoodGer of Food = FoodI with + (Syntax = SyntaxGer), + (LexFood = LexFoodGer) ; +``` +Notice that this is the //complete// module, not just a header of it. +The module body is received from ``FoodI``, by instantiating the +interface constants with their definitions given in the German +instances. + +A module of this form, characterized by the keyword ``with``, is +called a **functor instantiation**. + +Here is the complete code for the functor ``FoodI``: +``` + incomplete concrete FoodI of Food = open Syntax, LexFood in { + lincat + S = Utt ; + Item = NP ; + Kind = CN ; + Quality = AP ; + lin + Is item quality = mkUtt (mkCl item quality) ; + This kind = mkNP (mkDet this_Quant) kind ; + All kind = mkNP all_Predet (mkNP defPlDet kind) ; + QKind quality kind = mkCN quality kind ; + Wine = mkCN wine_N ; + Beer = mkCN beer_N ; + Pizza = mkCN pizza_N ; + Cheese = mkCN cheese_N ; + Fish = mkCN fish_N ; + Very quality = mkAP very_AdA quality ; + Fresh = mkAP fresh_A ; + Warm = mkAP warm_A ; + Italian = mkAP italian_A ; + Expensive = mkAP expensive_A ; + Delicious = mkAP delicious_A ; + Boring = mkAP boring_A ; +} +``` + + +==Interfaces and instances== + +Let us now define the ``LexFood`` interface: +``` + interface LexFood = open Syntax in { + oper + wine_N : N ; + beer_N : N ; + pizza_N : N ; + cheese_N : N ; + fish_N : N ; + fresh_A : A ; + warm_A : A ; + italian_A : A ; + expensive_A : A ; + delicious_A : A ; + boring_A : A ; +} +``` +In this interface, only lexical items are declared. In general, an +interface can declare any functions and also types. The ``Syntax`` +interface does so. + +Here is the German instance of the interface: +``` + instance LexFoodGer of LexFood = open SyntaxGer, ParadigmsGer in { + oper + wine_N = mkN "Wein" ; + beer_N = mkN "Bier" "Biere" neuter ; + pizza_N = mkN "Pizza" "Pizzen" feminine ; + cheese_N = mkN "Käse" "Käsen" masculine ; + fish_N = mkN "Fisch" ; + fresh_A = mkA "frisch" ; + warm_A = mkA "warm" "wärmer" "wärmste" ; + italian_A = mkA "italienisch" ; + expensive_A = mkA "teuer" ; + delicious_A = mkA "köstlich" ; + boring_A = mkA "langweilig" ; + } +``` +Just to complete the picture, we repeat the German functor instantiation +for ``FoodI``, this time with a path directive that makes it compilable. +``` + --# -path=.:present:prelude + + concrete FoodGer of Food = FoodI with + (Syntax = SyntaxGer), + (LexFood = LexFoodGer) ; +``` + + +**Exercise**. Compile and test ``FoodGer``. + +**Exercise**. Refactor ``FoodFre`` into a functor instantiation. + + + +==Adding languages to a functor implementation== + +Once we have an application grammar defined by using a functor, +adding a new language is simple. Just two modules need to be written: +- a domain lexicon instance +- a functor instantiation + + +The functor instantiation is completely mechanical to write. +Here is one for Finnish: +``` +--# -path=.:present:prelude + +concrete FoodFin of Food = FoodI with + (Syntax = SyntaxFin), + (LexFood = LexFoodFin) ; +``` +The domain lexicon instance requires some knowledge of the words of the +language: what words are used for which concepts, how the words are +inflected, plus features such as genders. Here is a lexicon instance for +Finnish: +``` + instance LexFoodFin of LexFood = open SyntaxFin, ParadigmsFin in { + oper + wine_N = mkN "viini" ; + beer_N = mkN "olut" ; + pizza_N = mkN "pizza" ; + cheese_N = mkN "juusto" ; + fish_N = mkN "kala" ; + fresh_A = mkA "tuore" ; + warm_A = mkA "lämmin" ; + italian_A = mkA "italialainen" ; + expensive_A = mkA "kallis" ; + delicious_A = mkA "herkullinen" ; + boring_A = mkA "tylsä" ; + } +``` + +**Exercise**. Instantiate the functor ``FoodI`` to some language of +your choice. + + +==Division of labour revisited== + +One purpose with the resource grammars was stated to be a division +of labour between linguists and application grammarians. We can now +reflect on what this means more precisely, by asking ourselves what +skills are required of grammarians working on different components. + +Building a GF application starts from the abstract syntax. Writing +an abstract syntax requires +- understanding the semantic structure of the application domain +- knowledge of the GF fragment with categories and functions + + +If the concrete syntax is written by means of a functor, the programmer +has to decide what parts of the implementation are put to the interface +and what parts are shared in the functor. This requires +- knowing how the domain concepts are expressed in natural language +- knowledge of the resource grammar library - the categories and combinators +- understanding what parts are likely to be expressed in language-dependent + ways, so that they must belong to the interface and not the functor +- knowledge of the GF fragment with function applications and strings + + +Instantiating a ready-made functor to a new language is less demanding. +It requires essentially +- knowing how the domain words are expressed in the language +- knowing, roughly, how these words are inflected +- knowledge of the paradigms available in the library +- knowledge of the GF fragment with function applications and strings + + +Notice that none of these tasks requires the use of GF records, tables, +or parameters. Thus only a small fragment of GF is needed; the rest of +GF is only relevant for those who write the libraries. + +Of course, grammar writing is not always straightforward usage of libraries. +For example, GF can be used for other languages than just those in the +libraries - for both natural and formal languages. A knowledge of records +and tables can, unfortunately, also be needed for understanding GF's error +messages. + +**Exercise**. Design a small grammar that can be used for controlling +an MP3 player. The grammar should be able to recognize commands such +as //play this song//, with the following variations: +- verbs: //play//, //remove// +- objects: //song//, //artist// +- determiners: //this//, //the previous// +- verbs without arguments: //stop//, //pause// + + +The implementation goes in the following phases: ++ abstract syntax ++ functor and lexicon interface ++ lexicon instance for the first language ++ functor instantiation for the first language ++ lexicon instance for the second language ++ functor instantiation for the second language ++ ... + + + +==Restricted inheritance== + +A functor implementation using the resource ``Syntax`` interface +works as long as all concepts are expressed by using the same structures +in all languages. If this is not the case, the deviant linearization can +be made into a parameter and moved to the domain lexicon interface. + +Let us take a slightly contrived example: assume that English has +no word for ``Pizza``, but has to use the paraphrase //Italian pie//. +This paraphrase is no longer a noun ``N``, but a complex phrase +in the category ``CN``. An obvious way to solve this problem is +to change interface ``LexEng`` so that the constant declared for +``Pizza`` gets a new type: +``` + oper pizza_CN : CN ; +``` +But this solution is unstable: we may end up changing the interface +and the function with each new language, and we must every time also +change the interface instances for the old languages to maintain +type correctness. + +A better solution is to use **restricted inheritance**: the English +instantiation inherits the functor implementation except for the +constant ``Pizza``. This is how we write: +``` + --# -path=.:present:prelude + + concrete FoodEng of Food = FoodI - [Pizza] with + (Syntax = SyntaxEng), + (LexFood = LexFoodEng) ** + open SyntaxEng, ParadigmsEng in { + + lin Pizza = mkCN (mkA "Italian") (mkN "pie") ; + } +``` +Restricted inheritance is available for all inherited modules. One can for +instance exclude some mushrooms and pick up just some fruit in +the ``FoodMarket`` example: +``` + abstract Foodmarket = Food, Fruit [Peach], Mushroom - [Agaric] +``` +A concrete syntax of ``Foodmarket`` must then indicate the same inheritance +restrictions. + + +**Exercise**. Change ``FoodGer`` in such a way that it says, instead of +//X is Y//, the equivalent of //X must be Y// (//X muss Y sein//). +You will have to browse the full resource API to find all +the functions needed. + + +==Browsing the resource with GF commands== + +In addition to reading the +[resource synopsis ../../lib/resource-1.0/synopsis.html], you +can find resource function combinations by using the parser. This +is so because the resource library is in the end implemented as +a top-level ``abstract-concrete`` grammar, on which parsing +and linearization work. + +Unfortunately, only English and the Scandinavian languages can be +parsed within acceptable computer resource limits when the full +resource is used. + +To look for a syntax tree in the overload API by parsing, do like this: +``` + > $GF_LIB_PATH + > i -path=alltenses:prelude alltenses/OverLangEng.gfc + > p -cat=S -overload "this grammar is too big" + mkS (mkCl (mkNP (mkDet this_Quant) grammar_N) (mkAP too_AdA big_A)) +``` +To view linearizations in all languages by parsing from English: +``` + > i alltenses/langs.gfcm + > p -cat=S -lang=LangEng "this grammar is too big" | tb + UseCl TPres ASimul PPos (PredVP (DetCN (DetSg (SgQuant this_Quant) + NoOrd) (UseN grammar_N)) (UseComp (CompAP (AdAP too_AdA (PositA big_A))))) + Den här grammatiken är för stor + Esta gramática es demasiado grande + (Cyrillic: eta grammatika govorit des'at' jazykov) + Denne grammatikken er for stor + Questa grammatica è troppo grande + Diese Grammatik ist zu groß + Cette grammaire est trop grande + Tämä kielioppi on liian suuri + This grammar is too big + Denne grammatik er for stor +``` +Unfortunately, the Russian grammar uses at the moment a different +character encoding than the rest and is therefore not displayed correctly +in a terminal window. However, the GF syntax editor does display all +examples correctly: +``` + % gfeditor alltenses/langs.gfcm +``` +When you have constructed the tree, you will see the following screen: + +#BCEN + + [../../lib/resource-1.0/doc/10lang-small.png] + +#ECEN + + +**Exercise**. Find the resource grammar translations for the following +English phrases (parse in the category ``Phr``). You can first try to +build the terms manually. + +//every man loves a woman// + +//this grammar speaks more than ten languages// + +//which languages aren't in the grammar// + +//which languages did you want to speak// + + + +=More concepts of abstract syntax= + +==GF as a logical framework== + +In this section, we will show how +to encode advanced semantic concepts in an abstract syntax. +We use concepts inherited from **type theory**. Type theory +is the basis of many systems known as **logical frameworks**, 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. + +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 ``abstract`` module in GF. +``` +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 + } +``` + +**Exercise**. Give a concrete syntax of ``Arithm``, either from scatch or +by using the resource library. + + + + +==Dependent types== + +**Dependent types** are a characteristic feature of GF, +inherited from the **constructive type theory** of Martin-Löf and +distinguishing GF from most other grammar formalisms and +functional programming languages. + +Dependent types can be used for stating stronger +**conditions of well-formedness** than ordinary types. +A simple example is a "smart house" system, which +defines voice commands for household appliances. This example +is borrowed from the +[Regulus Book http://cslipublications.stanford.edu/site/1575865262.html] +(Rayner & al. 2006). + +One who enters a smart house can use speech to dim lights, switch +on the fan, etc. For each ``Kind`` of a device, there is a set of +``Actions`` that can be performed on it; thus one can dim the lights but + not the fan, for example. These dependencies can be expressed by +by making the type ``Action`` dependent on ``Kind``. We express this +as follows in ``cat`` declarations: +``` + cat + Command ; + Kind ; + Action Kind ; + Device Kind ; +``` +The crucial use of the dependencies is made in the rule for forming commands: +``` + fun CAction : (k : Kind) -> Action k -> Device k -> Command ; +``` +In other words: an action and a device can be combined into a command only +if they are of the same ``Kind`` ``k``. If we have the functions +``` + DKindOne : (k : Kind) -> Device k ; -- the light + + light, fan : Kind ; + dim : Action light ; +``` +we can form the syntax tree +``` + CAction light dim (DKindOne light) +``` +but we cannot form the trees +``` + CAction light dim (DKindOne fan) + CAction fan dim (DKindOne light) + CAction fan dim (DKindOne fan) +``` +Linearization rules are written as usual: the concrete syntax does not +know if a category is a dependent type. In English, you can write as follows: +``` + lincat Action = {s : Str} ; + lin CAction kind act dev = {s = act.s ++ dev.s} ; +``` +Notice that the argument ``kind`` does not appear in the linearization. +The type checker will be able to reconstruct it from the ``dev`` argument. + +Parsing with dependent types is performed in two phases: ++ context-free parsing ++ filtering through type checker + + +If you just parse in the usual way, you don't enter the second phase, and +the ``kind`` argument is not found: +``` + > parse "dim the light" + CAction ? dim (DKindOne light) +``` +Moreover, type-incorrect commands are not rejected: +``` + > parse "dim the fan" + CAction ? dim (DKindOne fan) +``` +The question mark ``?`` is a **metavariable**, and is returned by the parser +for any subtree that is suppressed by a linearization rule. + +To get rid of metavariables, you must feed the parse result into the +second phase of **solving** them. The ``solve`` process uses the dependent +type checker to restore the values of the metavariables. It is invoked by +the command ``put_tree = pt`` with the flag ``-transform=solve``: +``` + > parse "dim the light" | put_tree -transform=solve + CAction light dim (DKindOne light) +``` +The ``solve`` process may fail, in which case no tree is returned: +``` + > parse "dim the fan" | put_tree -transform=solve + no tree found +``` + + +**Exercise**. Write an abstract syntax module with above contents +and an appropriate English concrete syntax. Try to parse the commands +//dim the light// and //dim the fan//, with and without ``solve`` filtering. + + +**Exercise**. Perform random and exhaustive generation, with and without +``solve`` filtering. + +**Exercise**. Add some device kinds and actions to the grammar. + + +==Polymorphism== + +Sometimes an action can be performed on all kinds of devices. It would be +possible to introduce separate ``fun`` constants for each kind-action pair, +but this would be tedious. Instead, one can use **polymorphic** actions, +i.e. actions that take a ``Kind`` as an argument and produce an ``Action`` +for that ``Kind``: +``` + fun switchOn, switchOff : (k : Kind) -> Action k ; +``` +Functions that are not polymorphic are **monomorphic**. However, the +dichotomy into monomorphism and full polymorphism is not always sufficien +for good semantic modelling: very typically, some actions are defined +for a proper subset of devices, but not just one. For instance, both doors and +windows can be opened, whereas lights cannot. +We will return to this problem by introducing the +concept of **restricted polymorphism** later, +after a chapter on proof objects. + + + +==Dependent types and spoken language models== + +We have used dependent types to control semantic well-formedness +in grammars. This is important in traditional type theory +applications such as proof assistants, where only mathematically +meaningful formulas should be constructed. But semantic filtering has +also proved important in speech recognition, because it reduces the +ambiguity of the results. + + +===Grammar-based language models=== + +The standard way of using GF in speech recognition is by building +**grammar-based language models**. To this end, GF comes with compilers +into several formats that are used in speech recognition systems. +One such format is GSL, used in the [Nuance speech recognizer www.nuance.com]. +It is produced from GF simply by printing a grammar with the flag +``-printer=gsl``. +``` + > import -conversion=finite SmartEng.gf + > print_grammar -printer=gsl + + ;GSL2.0 + ; Nuance speech recognition grammar for SmartEng + ; Generated by GF + + .MAIN SmartEng_2 + + SmartEng_0 [("switch" "off") ("switch" "on")] + SmartEng_1 ["dim" ("switch" "off") + ("switch" "on")] + SmartEng_2 [(SmartEng_0 SmartEng_3) + (SmartEng_1 SmartEng_4)] + SmartEng_3 ("the" SmartEng_5) + SmartEng_4 ("the" SmartEng_6) + SmartEng_5 "fan" + SmartEng_6 "light" +``` +Now, GSL is a context-free format, so how does it cope with dependent types? +In general, dependent types can give rise to infinitely many basic types +(exercise!), whereas a context-free grammar can by definition only have +finitely many nonterminals. + +This is where the flag ``-conversion=finite`` is needed in the ``import`` +command. Its effect is to convert a GF grammar with dependent types to +one without, so that each instance of a dependent type is replaced by +an atomic type. This can then be used as a nonterminal in a context-free +grammar. The ``finite`` conversion presupposes that every +dependent type has only finitely many instances, which is in fact +the case in the ``Smart`` grammar. + + +**Exercise**. If you have access to the Nuance speech recognizer, +test it with GF-generated language models for ``SmartEng``. Do this +both with and without ``-conversion=finite``. + +**Exercise**. Construct an abstract syntax with infinitely many instances +of dependent types. + + +===Statistical language models=== + +An alternative to grammar-based language models are +**statistical language models** (**SLM**s). An SLM is +built from a **corpus**, i.e. a set of utterances. It specifies the +probability of each **n-gram**, i.e. sequence of //n// words. The +typical value of //n// is 2 (bigrams) or 3 (trigrams). + +One advantage of SLMs over grammar-based models is that they are +**robust**, i.e. they can be used to recognize sequences that would +be out of the grammar or the corpus. Another advantage is that +an SLM can be built "for free" if a corpus is available. + +However, collecting a corpus can require a lot of work, and writing +a grammar can be less demanding, especially with tools such as GF or +Regulus. This advantage of grammars can be combined with robustness +by creating a back-up SLM from a **synthesized corpus**. This means +simply that the grammar is used for generating such a corpus. +In GF, this can be done with the ``generate_trees`` command. +As with grammar-based models, the quality of the SLM is better +if meaningless utterances are excluded from the corpus. Thus +a good way to generate an SLM from a GF grammar is by using +dependent types and filter the results through the type checker: +``` + > generate_trees | put_trees -transform=solve | linearize +``` + + +**Exercise**. Measure the size of the corpus generated from +``SmartEng``, with and without type checker filtering. + + + +==Digression: dependent types in concrete syntax== + +===Variables in function types=== + +A dependent function type needs to introduce a variable for +its argument type, as in +``` + switchOff : (k : Kind) -> Action k +``` +Function types //without// +variables are actually a shorthand notation: writing +``` + fun PredVP : NP -> VP -> S +``` +is shorthand for +``` + fun PredVP : (x : NP) -> (y : VP) -> S +``` +or any other naming of the variables. Actually the use of variables +sometimes shortens the code, since they can share a type: +``` + octuple : (x,y,z,u,v,w,s,t : Str) -> Str +``` +If a bound variable is not used, it can here, as elsewhere in GF, be replaced by +a wildcard: +``` + octuple : (_,_,_,_,_,_,_,_ : Str) -> Str +``` +A good practice for functions with many arguments of the same type +is to indicate the number of arguments: +``` + octuple : (x1,_,_,_,_,_,_,x8 : Str) -> Str +``` +One can also use the variables to document what each argument is expected +to provide, as is done in inflection paradigms in the resource grammar. +``` + mkV : (drink,drank,drunk : Str) -> V +``` + + +===Polymorphism in concrete syntax=== + +The **functional fragment** 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. + +Those readers who are familiar with functional programming languages +like ML and Haskell, may already have missed **polymorphic** +functions. For instance, Haskell programmers have access to +the functions +``` + const :: a -> b -> a + const c _ = c + + flip :: (a -> b -> c) -> b -> a -> c + flip f y x = f x y +``` +which can be used for any given types ``a``,``b``, and ``c``. + +The GF counterpart of polymorphic functions are **monomorphic** +functions with explicit **type variables**. Thus the above +definitions can be written +``` + 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 ; +``` +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. + + + +==Proof objects== + +Perhaps the most well-known idea in constructive type theory is +the **Curry-Howard isomorphism**, also known as the +**propositions as types principle**. 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. + +We first define the category of unary (also known as Peano-style) +natural numbers: +``` + cat Nat ; + fun Zero : Nat ; + fun Succ : Nat -> Nat ; +``` +The **successor function** ``Succ`` generates an infinite +sequence of natural numbers, beginning from ``Zero``. + +We then define what it means for a number //x// to be //less than// +a number //y//. Our definition is based on two axioms: +- ``Zero`` is less than ``Succ`` //y// for any //y//. +- If //x// is less than //y//, then ``Succ`` //x// is less than ``Succ`` //y//. + + +The most straightforward way of expressing these axioms in type theory +is as typing judgements that introduce objects of a type ``Less`` //x y//: +``` + 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) ; +``` +Objects formed by ``lessZ`` and ``lessS`` are +called **proof objects**: they establish the truth of certain +mathematical propositions. +For instance, the fact that 2 is less that +4 has the proof object +``` + lessS (Succ Zero) (Succ (Succ (Succ Zero))) + (lessS Zero (Succ (Succ Zero)) (lessZ (Succ Zero))) +``` +whose type is +``` + Less (Succ (Succ Zero)) (Succ (Succ (Succ (Succ Zero)))) +``` +which is the formalization of the proposition that 2 is less than 4. + +GF grammars can be used to provide a **semantic control** of +well-formedness of expressions. We have already seen examples of this: +the grammar of well-formed actions on household devices. By introducing proof objects +we have now added a very powerful technique of expressing semantic conditions. + +A simple example of the use of proof objects is the definition of +well-formed //time spans//: a time span is expected to be from an earlier to +a later time: +``` + from 3 to 8 +``` +is thus well-formed, whereas +``` + from 8 to 3 +``` +is not. The following rules for spans impose this condition +by using the ``Less`` predicate: +``` + cat Span ; + fun span : (m,n : Nat) -> Less m n -> Span ; +``` + +**Exercise**. Write an abstract and concrete syntax with the +concepts of this section, and experiment with it in GF. + + +**Exercise**. Define the notions of "even" and "odd" in terms +of proof objects. **Hint**. You need one function for proving +that 0 is even, and two other functions for propagating the +properties. + + + + +===Proof-carrying documents=== + +Another possible application of proof objects is **proof-carrying documents**: +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: + +//To fly from Gothenburg to Prague, first take LH3043 to Frankfurt, then OK0537 to Prague.// + +The well-formedness of this text is partly expressible by dependent typing: +``` + cat + City ; + Flight City City ; + fun + Gothenburg, Frankfurt, Prague : City ; + LH3043 : Flight Gothenburg Frankfurt ; + OK0537 : Flight Frankfurt Prague ; +``` +This rules out texts saying //take OK0537 from Gothenburg to Prague//. +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. +``` + 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 ; +``` + + +==Restricted polymorphism== + +In the first version of the smart house grammar ``Smart``, +all Actions were either of +- **monomorphic**: defined for one Kind +- **polymorphic**: defined for all Kinds + + +To make this scale up for new Kinds, we can refine this to +**restricted polymorphism**: defined for Kinds of a certain **class** + + +The notion of class can be expressed in abstract syntax +by using the Curry-Howard isomorphism as follows: +- a class is a **predicate** of Kinds - i.e. a type depending of Kinds +- a Kind is in a class if there is a proof object of this type + + +Here is an example with switching and dimming. The classes are called +``switchable`` and ``dimmable``. +``` +cat + Switchable Kind ; + Dimmable Kind ; +fun + switchable_light : Switchable light ; + switchable_fan : Switchable fan ; + dimmable_light : Dimmable light ; + + switchOn : (k : Kind) -> Switchable k -> Action k ; + dim : (k : Kind) -> Dimmable k -> Action k ; +``` +One advantage of this formalization is that classes for new +actions can be added incrementally. + +**Exercise**. Write a new version of the ``Smart`` grammar with +classes, and test it in GF. + +**Exercise**. Add some actions, kinds, and classes to the grammar. +Try to port the grammar to a new language. You will probably find +out that restricted polymorphism works differently in different languages. +For instance, in Finnish not only doors but also TVs and radios +can be "opened", which means switching them on. + + +==Variable bindings== + +Mathematical notation and programming languages have +expressions that **bind** variables. For instance, +a universally quantifier proposition +``` + (All x)B(x) +``` +consists of the **binding** ``(All x)`` of the variable ``x``, +and the **body** ``B(x)``, where the variable ``x`` can have +**bound occurrences**. + +Variable bindings appear in informal mathematical language as well, for +instance, +``` + 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 + + Let x be a natural number. Assume that x is even. Then x + 3 is odd. +``` +In type theory, variable-binding expression forms can be formalized +as functions that take functions as arguments. The universal +quantifier is defined +``` + fun All : (Ind -> Prop) -> Prop +``` +where ``Ind`` is the type of individuals and ``Prop``, +the type of propositions. If we have, for instance, the equality predicate +``` + fun Eq : Ind -> Ind -> Prop +``` +we may form the tree +``` + All (\x -> Eq x x) +``` +which corresponds to the ordinary notation +``` + (All x)(x = x). +``` +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 +``\x -> b``, 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 **higher-order abstract syntax**. + +The question now arises: how to define linearization rules +for variable-binding expressions? +Let us first consider universal quantification, +``` + fun All : (Ind -> Prop) -> Prop +``` +We write +``` + lin All B = {s = "(" ++ "All" ++ B.$0 ++ ")" ++ B.s} +``` +to obtain the form shown above. +This linearization rule brings in a new GF concept - the ``$0`` +field of ``B`` containing a bound variable symbol. +The general rule is that, if an argument type of a function is +itself a function type ``A -> C``, the linearization type of +this argument is the linearization type of ``C`` +together with a new field ``$0 : Str``. In the linearization rule +for ``All``, the argument ``B`` thus has the linearization +type +``` + {$0 : Str ; s : Str}, +``` +since the linearization type of ``Prop`` is +``` + {s : Str} +``` +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 +**eta-expanded** form in order to be linearizable: +any function of type +``` + A -> B +``` +always has a syntax tree of the form +``` + \x -> b +``` +where ``b : B`` under the assumption ``x : A``. +It is in this form that an expression can be analysed +as having a bound variable and a body. + + +Given the linearization rule +``` + lin Eq a b = {s = "(" ++ a.s ++ "=" ++ b.s ++ ")"} +``` +the linearization of +``` + \x -> Eq x x +``` +is the record +``` + {$0 = "x", s = ["( x = x )"]} +``` +Thus we can compute the linearization of the formula, +``` + All (\x -> Eq x x) --> {s = "[( All x ) ( x = x )]"}. +``` +How did we get the //linearization// of the variable ``x`` +into the string ``"x"``? 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. + +To be able to //parse// variable symbols, however, GF needs to know what +to look for (instead of e.g. trying to parse //any// +string as a variable). What strings are parsed as variable symbols +is defined in the lexical analysis part of GF parsing +``` + > p -cat=Prop -lexer=codevars "(All x)(x = x)" + All (\x -> Eq x x) +``` +(see more details on lexers below). If several variables are bound in the +same argument, the labels are ``$0, $1, $2``, etc. + + +**Exercise**. Write an abstract syntax of the whole +**predicate calculus**, with the +**connectives** "and", "or", "implies", and "not", and the +**quantifiers** "exists" and "for all". Use higher-order functions +to guarantee that unbounded variables do not occur. + +**Exercise**. Write a concrete syntax for your favourite +notation of predicate calculus. Use Latex as target language +if you want nice output. You can also try producing Haskell boolean +expressions. Use as many parenthesis as you need to +guarantee non-ambiguity. + + + +==Semantic definitions== + +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 **compute** +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. + +GF has a form of judgement for **semantic definitions**, +recognized by the key word ``def``. At its simplest, it is just +the definition of one constant, e.g. +``` + def one = Succ Zero ; +``` +We can also define a function with arguments, +``` + def Neg A = Impl A Abs ; +``` +which is still a special case of the most general notion of +definition, that of a group of **pattern equations**: +``` + def + sum x Zero = x ; + sum x (Succ y) = Succ (Sum x y) ; +``` +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 +``` + Sum one one --> + Sum (Succ Zero) (Succ Zero) --> + Succ (sum (Succ Zero) Zero) --> + Succ (Succ Zero) +``` +Computation in GF is performed with the ``pt`` command and the +``compute`` transformation, e.g. +``` + > p -tr "1 + 1" | pt -transform=compute -tr | l + sum one one + Succ (Succ Zero) + s(s(0)) +``` + +The ``def`` definitions of a grammar induce a notion of +**definitional equality** 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 +``` + sum Zero (Succ one) + Succ one + sum (sum Zero Zero) (sum (Succ Zero) one) +``` +and infinitely many other trees. + +A fact that has to be emphasized about ``def`` definitions is that +they are //not// performed as a first step of linearization. +We say that **linearization is intensional**, 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: +``` + 1 + 1 + s(0) + s(0) + s(s(0) + 0) + s(s(0)) + 0 + s(0) + s(1) + 0 + 0 + s(0) + 1 +``` +This notion of intensionality is +no more exotic than the intensionality of any **pretty-printing** +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. + +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 +**type checking is extensional**. 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, +``` + Proof (Odd one) + Proof (Odd (Succ Zero)) +``` +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.) + +In addition to computation, definitions impose a +**paraphrase** relation on expressions: +two strings are paraphrases if they +are linearizations of trees that are +definitionally equal. +Paraphrases are sometimes interesting for +translation: the **direct translation** +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. + +To stress express the distinction between +**constructors** (=**canonical** functions) +and other functions, GF has a judgement form +``data`` to tell that certain functions are canonical, e.g. +``` + data Nat = Succ | Zero ; +``` +Unlike in Haskell, but similarly to ALF (where constructor functions +are marked with a flag ``C``), +new constructors can be added to +a type with new ``data`` judgements. The type signatures of constructors +are given separately, in ordinary ``fun`` judgements. +One can also write directly +``` + data Succ : Nat -> Nat ; +``` +which is equivalent to the two judgements +``` + fun Succ : Nat -> Nat ; + data Nat = Succ ; +``` + +**Exercise**. Implement an interpreter of a small functional programming +language with natural numbers, lists, pairs, lambdas, etc. Use higher-order +abstract syntax with semantic definitions. As target language, use +your favourite programming language. + +**Exercise**. To make your interpreted language look nice, use +**precedences** instead of putting parentheses everywhere. +You can use the [precedence library ../../lib/prelude/Precedence.gf] +of GF to facilitate this. + + +=Practical issues= + +==Lexers and unlexers== + +Lexers and unlexers can be chosen from +a list of predefined ones, using the flags``-lexer`` and `` -unlexer`` either +in the grammar file or on the GF command line. Here are some often-used lexers +and unlexers: +``` + 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 + + The default is unwords. + -unlexer=unwords space-separated token list (like unwords) + -unlexer=text format as text: punctuation, capitals, paragraph

+ -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 +``` +More options can be found by ``help -lexer`` and ``help -unlexer``: + + + + +==Speech input and output== + +The ``speak_aloud = sa`` command sends a string to the speech +synthesizer +[Flite http://www.speech.cs.cmu.edu/flite/doc/]. +It is typically used via a pipe: +``` generate_random | linearize | speak_aloud +The result is only satisfactory for English. + +The ``speech_input = si`` command receives a string from a +speech recognizer that requires the installation of +[ATK http://mi.eng.cam.ac.uk/~sjy/software.htm]. +It is typically used to pipe input to a parser: +``` speech_input -tr | parse +The method words only for grammars of English. + +Both Flite and ATK are freely available through the links +above, but they are not distributed together with GF. + + + +==Multilingual syntax editor== + +The +[Editor User Manual http://www.cs.chalmers.se/~aarne/GF2.0/doc/javaGUImanual/javaGUImanual.htm] +describes the use of the editor, which works for any multilingual GF grammar. + +Here is a snapshot of the editor: + +#BCEN + +#EDITORPNG + +#ECEN + + +The grammars of the snapshot are from the +[Letter grammar package http://www.cs.chalmers.se/~aarne/GF/examples/letter]. + + +==Communicating with GF== + +Other processes can communicate with the GF command interpreter, +and also with the GF syntax editor. Useful flags when invoking GF are +- ``-batch`` suppresses the promps and structures the communication with XML tags. +- ``-s`` suppresses non-output non-error messages and XML tags. +- ``-nocpu`` suppresses CPU time indication. + + +Thus the most silent way to invoke GF is +``` + gf -batch -s -nocpu +``` + + + +=Embedded grammars in Haskell and Java= + +GF grammars can be used as parts of programs written in the +following languages. We will go through a skeleton application in +Haskell, while the next chapter will show how to build an +application in Java. + +We will show how to build a minimal resource grammar +application whose architecture scales up to much +larger applications. The application is run from the +shell by the command +``` + math +``` +whereafter it reads user input in English and French. +To each input line, it answers by the truth value of +the sentence. +``` + ./math + zéro est pair + True + zero is odd + False + zero is even and zero is odd + False +``` +The source of the application consists of the following +files: +``` + LexEng.gf -- English instance of Lex + LexFre.gf -- French instance of Lex + Lex.gf -- lexicon interface + Makefile -- a makefile + MathEng.gf -- English instantiation of MathI + MathFre.gf -- French instantiation of MathI + Math.gf -- abstract syntax + MathI.gf -- concrete syntax functor for Math + Run.hs -- Haskell Main module +``` +The system was built in 22 steps explained below. + + +==Writing GF grammars== + +===Creating the first grammar=== + +1. Write ``Math.gf``, which defines what you want to say. +``` + abstract Math = { + cat Prop ; Elem ; + fun + And : Prop -> Prop -> Prop ; + Even : Elem -> Prop ; + Zero : Elem ; + } +``` +2. Write ``Lex.gf``, which defines which language-dependent +parts are needed in the concrete syntax. These are mostly +words (lexicon), but can in fact be any operations. The definitions +only use resource abstract syntax, which is opened. +``` + interface Lex = open Syntax in { + oper + even_A : A ; + zero_PN : PN ; + } +``` +3. Write ``LexEng.gf``, the English implementation of ``Lex.gf`` +This module uses English resource libraries. +``` + instance LexEng of Lex = open GrammarEng, ParadigmsEng in { + oper + even_A = regA "even" ; + zero_PN = regPN "zero" ; + + } +``` +4. Write ``MathI.gf``, a language-independent concrete syntax of +``Math.gf``. It opens interfaces. +which makes it an incomplete module, aka. parametrized module, aka. +functor. +``` + incomplete concrete MathI of Math = + + open Syntax, Lex in { + + flags startcat = Prop ; + + lincat + Prop = S ; + Elem = NP ; + lin + And x y = mkS and_Conj x y ; + Even x = mkS (mkCl x even_A) ; + Zero = mkNP zero_PN ; + } +``` +5. Write ``MathEng.gf``, which is just an instatiation of ``MathI.gf``, +replacing the interfaces by their English instances. This is the module +that will be used as a top module in GF, so it contains a path to +the libraries. +``` + instance LexEng of Lex = open SyntaxEng, ParadigmsEng in { + oper + even_A = mkA "even" ; + zero_PN = mkPN "zero" ; + } +``` + + +===Testing=== + +6. Test the grammar in GF by random generation and parsing. +``` + $ gf + > i MathEng.gf + > gr -tr | l -tr | p + And (Even Zero) (Even Zero) + zero is evenand zero is even + And (Even Zero) (Even Zero) +``` +When importing the grammar, you will fail if you haven't +- correctly defined your ``GF_LIB_PATH`` as ``GF/lib`` +- installed the resource package or + compiled the resource from source by ``make`` in ``GF/lib/resource-1.0`` + + + +===Adding a new language=== + +7. Now it is time to add a new language. Write a French lexicon ``LexFre.gf``: +``` + instance LexFre of Lex = open SyntaxFre, ParadigmsFre in { + oper + even_A = mkA "pair" ; + zero_PN = mkPN "zéro" ; + } +``` +8. You also need a French concrete syntax, ``MathFre.gf``: +``` + --# -path=.:present:prelude + + concrete MathFre of Math = MathI with + (Syntax = SyntaxFre), + (Lex = LexFre) ; +``` +9. This time, you can test multilingual generation: +``` + > i MathFre.gf + > gr | tb + Even Zero + zéro est pair + zero is even +``` + + +===Extending the language=== + +10. You want to add a predicate saying that a number is odd. +It is first added to ``Math.gf``: +``` + fun Odd : Elem -> Prop ; +``` +11. You need a new word in ``Lex.gf``. +``` + oper odd_A : A ; +``` +12. Then you can give a language-independent concrete syntax in +``MathI.gf``: +``` + lin Odd x = mkS (mkCl x odd_A) ; +``` +13. The new word is implemented in ``LexEng.gf``. +``` + oper odd_A = mkA "odd" ; +``` +14. The new word is implemented in ``LexFre.gf``. +``` + oper odd_A = mkA "impair" ; +``` +15. Now you can test with the extended lexicon. First empty +the environment to get rid of the old abstract syntax, then +import the new versions of the grammars. +``` + > e + > i MathEng.gf + > i MathFre.gf + > gr | tb + And (Odd Zero) (Even Zero) + zéro est impair et zéro est pair + zero is odd and zero is even +``` + + +==Building a user program== + +===Producing a compiled grammar package=== + +16. Your grammar is going to be used by persons wh``MathEng.gf``o do not need +to compile it again. They may not have access to the resource library, +either. Therefore it is advisable to produce a multilingual grammar +package in a single file. We call this package ``math.gfcm`` and +produce it, when we have ``MathEng.gf`` and +``MathEng.gf`` in the GF state, by the command +``` + > pm | wf math.gfcm +``` + + +===Writing the Haskell application=== + +17. Write the Haskell main file ``Run.hs``. It uses the ``EmbeddedAPI`` +module defining some basic functionalities such as parsing. +The answer is produced by an interpreter of trees returned by the parser. +``` +module Main where + +import GSyntax +import GF.Embed.EmbedAPI + +main :: IO () +main = do + gr <- file2grammar "math.gfcm" + loop gr + +loop :: MultiGrammar -> IO () +loop gr = do + s <- getLine + interpret gr s + loop gr + +interpret :: MultiGrammar -> String -> IO () +interpret gr s = do + let tss = parseAll gr "Prop" s + case (concat tss) of + [] -> putStrLn "no parse" + t:_ -> print $ answer $ fg t + +answer :: GProp -> Bool +answer p = case p of + (GOdd x1) -> odd (value x1) + (GEven x1) -> even (value x1) + (GAnd x1 x2) -> answer x1 && answer x2 + +value :: GElem -> Int +value e = case e of + GZero -> 0 +``` + +18. The syntax trees manipulated by the interpreter are not raw +GF trees, but objects of the Haskell datatype ``GProp``. +From any GF grammar, a file ``GFSyntax.hs`` with +datatypes corresponding to its abstract +syntax can be produced by the command +``` + > pg -printer=haskell | wf GSyntax.hs +``` +The module also defines the overloaded functions +``gf`` and ``fg`` for translating from these types to +raw trees and back. + + +===Compiling the Haskell grammar=== + +19. Before compiling ``Run.hs``, you must check that the +embedded GF modules are found. The easiest way to do this +is by two symbolic links to your GF source directories: +``` + $ ln -s /home/aarne/GF/src/GF + $ ln -s /home/aarne/GF/src/Transfer/ +``` + +20. Now you can run the GHC Haskell compiler to produce the program. +``` + $ ghc --make -o math Run.hs +``` +The program can be tested with the command ``./math``. + + +===Building a distribution=== + +21. For a stand-alone binary-only distribution, only +the two files ``math`` and ``math.gfcm`` are needed. +For a source distribution, the files mentioned in +the beginning of this documents are needed. + + +===Using a Makefile=== + +22. As a part of the source distribution, a ``Makefile`` is +essential. The ``Makefile`` is also useful when developing the +application. It should always be possible to build an executable +from source by typing ``make``. Here is a minimal such ``Makefile``: +``` + all: + echo "pm | wf math.gfcm" | gf MathEng.gf MathFre.gf + echo "pg -printer=haskell | wf GSyntax.hs" | gf math.gfcm + ghc --make -o math Run.hs +``` + + + + +=Embedded grammars in Java= + +Forthcoming; at the moment, the document + + [``http://www.cs.chalmers.se/~bringert/gf/gf-java.html`` http://www.cs.chalmers.se/~bringert/gf/gf-java.html] + +by Björn Bringert gives more information on Java. + + + +=Further reading= + +Syntax Editor User Manual: + +[``http://www.cs.chalmers.se/~aarne/GF2.0/doc/javaGUImanual/javaGUImanual.htm`` http://www.cs.chalmers.se/~aarne/GF2.0/doc/javaGUImanual/javaGUImanual.htm] + +Resource Grammar Synopsis (on using resource grammars): + +[``http://www.cs.chalmers.se/~aarne/GF/lib/resource-1.0/synopsis.html`` ../../lib/resource-1.0/synopsis.html] + +Resource Grammar HOWTO (on writing resource grammars): + +[``http://www.cs.chalmers.se/~aarne/GF/lib/resource-1.0/synopsis.html`` ../../lib/resource-1.0/doc/Resource-HOWTO.html] + +GF Homepage: + +[``http://www.cs.chalmers.se/~aarne/GF/doc`` ../..] +