From 23d8ebeb26892c8d831a8b5324fece62f6c6687c Mon Sep 17 00:00:00 2001 From: aarne Date: Sun, 8 Jul 2007 16:36:56 +0000 Subject: tutorial in final form --- doc/tutorial/gf-tutorial2_8.txt | 3542 --------------------------------------- 1 file changed, 3542 deletions(-) delete mode 100644 doc/tutorial/gf-tutorial2_8.txt (limited to 'doc/tutorial/gf-tutorial2_8.txt') diff --git a/doc/tutorial/gf-tutorial2_8.txt b/doc/tutorial/gf-tutorial2_8.txt deleted file mode 100644 index 9820a7354..000000000 --- a/doc/tutorial/gf-tutorial2_8.txt +++ /dev/null @@ -1,3542 +0,0 @@ -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): "subsection\*" "section" - -% workaround for some missing things in the format -% %!postproc(html): C-
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-% %!postproc(html): t- -% %!postproc(html): -t - - - - -[../gf-logo.png] - - - -%--! -=Introduction= - -==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. -Nevertheless, we will cover some linguistic problems posed by different -languages and how they are solved in GF. - - -%--! -==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 will briefly explain how -GF grammars are used as components of Haskell, Java, Javascript, -and Prolog grammars. -%The tutorial concludes with a couple of -%case studies showing how such complete systems can be built. - - - -%--! -==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. -For 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 very useful when writing advanced -concrete syntax implementations, such as resource grammar 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" - - - - - -%--! -==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`` assignes 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-italien//, //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. - - - -==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) have 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 this. - -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`` as 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" -``` -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 -``` - -**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). - -In a smart house, the owner or tennant can use speech to dim lights, swith -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 show in the linearization. -The type checker will be able to reconstruct it from the ``dev`` argument. - -Parsing with dependent types happens in two phases. If you just parse in -the usual way, 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 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 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 hte ``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 only has 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 with 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 we can write e.g. -``` - 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 such functions is to indicate the number of arguments -in the type: -``` - 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 addresses and the grammar with -selectional restrictions above. 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 - a type depending of Kinds -- a Kind is in a xlass if there is of proof object of this type - - -Here is an example with switching and dimming. -``` -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 for 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 lots of -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 -``` -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. - - - -==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 ; -``` - - -=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. - -Given by ``help -lexer``, ``help -unlexer``: -``` - The default is words. - -lexer=words tokens are separated by spaces or newlines - -lexer=literals like words, but GF integer and string literals recognized - -lexer=vars like words, but "x","x_...","$...$" as vars, "?..." as meta - -lexer=chars each character is a token - -lexer=code use Haskell's lex - -lexer=codevars like code, but treat unknown words as variables, ?? as meta - -lexer=text with conventions on punctuation and capital letters - -lexer=codelit like code, but treat unknown words as string literals - -lexer=textlit like text, but treat unknown words as string literals - -lexer=codeC use a C-like lexer - -lexer=ignore like literals, but ignore unknown words - -lexer=subseqs like ignore, but then try all subsequences from longest - - The default is unwords. - -unlexer=unwords space-separated token list (like unwords) - -unlexer=text format as text: punctuation, capitals, paragraph

- -unlexer=code format as code (spacing, indentation) - -unlexer=textlit like text, but remove string literal quotes - -unlexer=codelit like code, but remove string literal quotes - -unlexer=concat remove all spaces - -unlexer=bind like identity, but bind at "&+" -``` - - - - -==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: - -[../quick-editor.png] - -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, Java, and Prolog== - -GF grammars can be used as parts of programs written in the -following languages. The links give more documentation. -- [Java http://www.cs.chalmers.se/~bringert/gf/gf-java.html] -- [Haskell http://www.cs.chalmers.se/~aarne/GF/src/GF/Embed/EmbedAPI.hs] -- [Prolog http://www.cs.chalmers.se/~peb/software.html] - - -==Alternative input and output grammar formats== - -A summary is given in the following chart of GF grammar compiler phases: -[../gf-compiler.png] - - - -=Further reading= - -- cgit v1.2.3