Grammatical Framework Tutorial Author: Aarne Ranta 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 [../gf-logo.gif] %--! ==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 %--! ===Getting the GF program=== The 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 - ready-made binaries for Linux, Solaris, Macintosh, and Windows - source code and documentation - grammar libraries and examples If you want to compile GF from source, you need Haskell and Java compilers. But normally you don't have to compile, and you definitely don't need to know Haskell or Java to use GF. 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 ``.cf`` grammar format== Now you are ready to try out your first grammar. We start with one that is not written in GF language, but in the ubiquitous BNF notation (Backus Naur Form), which GF can also understand. Type (or copy) the following lines in a file named ``paleolithic.cf``: ``` S ::= NP VP ; VP ::= V | TV NP | "is" A ; NP ::= "this" CN | "that" CN | "the" CN | "a" CN ; CN ::= A CN ; CN ::= "boy" | "louse" | "snake" | "worm" ; A ::= "green" | "rotten" | "thick" | "warm" ; V ::= "laughs" | "sleeps" | "swims" ; TV ::= "eats" | "kills" | "washes" ; ``` (The name ``paleolithic`` refers to a larger package [stoneage http://www.cs.chalmers.se/~aarne/GF/examples/stoneage/], which implements a fragment of primitive language. This fragment was defined by the linguist Morris Swadesh as a tool for studying the historical relations of languages. But as suggested in the Wiktionary article on [Swadesh list http://en.wiktionary.org/wiki/Wiktionary:Swadesh_list], the fragment is also usable for basic communication between foreigners.) %--! ===Importing grammars and parsing strings=== The first GF command 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 paleolithic.cf or ``` i paleolithic.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. You can now use GF for **parsing**: ``` > parse "the boy eats a snake" S_NP_VP (NP_the_CN CN_boy) (VP_TV_NP TV_eats (NP_a_CN CN_snake)) > parse "the snake eats a boy" S_NP_VP (NP_the_CN CN_snake) (VP_TV_NP TV_eats (NP_a_CN CN_boy)) ``` The ``parse`` (= ``p``) command takes a **string** (in double quotes) and returns an **abstract syntax tree** - the thing beginning with ``S_NP_VP``. We will see soon how to make sense of the abstract syntax trees - now you should just notice that the tree is different for the two strings. 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" No success in cf parsing hello world no tree found ``` %--! ===Generating trees and strings=== You can also use GF for **linearizing** (``linearize = l``). This is the inverse of parsing, taking trees into strings: ``` > linearize S_NP_VP (NP_the_CN CN_boy) (VP_TV_NP TV_eats (NP_a_CN CN_snake)) the boy eats a snake ``` 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 S_NP_VP (NP_this_CN (CN_A_CN A_thick CN_worm)) (VP_V V_sleeps) ``` Now you can copy the tree and paste it to the ``linearize command``. Or, more efficiently, feed random generation into parsing by using a **pipe**. ``` > gr | l this worm is warm ``` %--! ===Visualizing trees=== The gibberish code with parentheses returned by the parser does not look like trees. Why is it called so? Trees are a data structure that represent 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 "the green boy eats a warm snake" | vt [Tree.png] %--! ===Some random-generated sentences=== Random generation can be quite amusing. So you may want to generate ten strings with one and the same command: ``` > gr -number=10 | l this boy is green a snake laughs the rotten boy is thick a boy washes this worm a boy is warm this green warm boy is rotten the green thick green louse is rotten that boy is green this thick thick boy laughs a boy is green ``` %--! ===Systematic generation=== To generate //all// sentence that a grammar can generate, use the command ``generate_trees = gt``. ``` > generate_trees | l this louse laughs this louse sleeps this louse swims this louse is green this louse is rotten ... a boy is rotten a boy is thick a boy 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 gr ``` **Quiz**. If the command ``gt`` generated all trees in your grammar, it would never terminate. Why? %--! ===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 S_NP_VP (NP_the_CN CN_snake) (VP_V V_sleeps) the snake sleeps S_NP_VP (NP_the_CN CN_snake) (VP_V V_sleeps) ``` 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. %--! ===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. %--! ===Labelled context-free grammars=== The syntax trees returned by GF's parser in the previous examples are not so nice to look at. The identifiers of form ``Mks`` are **labels** of the BNF rules. To see which label corresponds to which rule, you can use the ``print_grammar = pg`` command with the ``printer`` flag set to ``cf`` (which means context-free): ``` > print_grammar -printer=cf V_laughs. V ::= "laughs" ; V_sleeps. V ::= "sleeps" ; V_swims. V ::= "swims" ; VP_TV_NP. VP ::= TV NP ; VP_V. VP ::= V ; VP_is_A. VP ::= "is" A ; TV_eats. TV ::= "eats" ; TV_kills. TV ::= "kills" ; TV_washes. TV ::= "washes" ; S_NP_VP. S ::= NP VP ; NP_a_CN. NP ::= "a" ; ... ``` A syntax tree such as ``` NP_this_CN (CN_A_CN A_thick CN_worm) this thick worm ``` encodes the sequence of grammar rules used for building the expression. If you look at this tree, you will notice that ``NP_this_CN`` is the label of the rule prefixing ``this`` to a common noun (``CN``), thereby forming a noun phrase (``NP``). ``A_thick`` is the label of the adjective ``thick``, and so on. These labels are formed automatically when the grammar is compiled by GF. %--! ===The labelled context-free format=== The **labelled context-free grammar** format permits user-defined labels to each rule. In files with the suffix ``.cf``, you can prefix rules with labels that you provide yourself - these may be more useful than the automatically generated ones. The following is a possible labelling of ``paleolithic.cf`` with nicer-looking labels. ``` PredVP. S ::= NP VP ; UseV. VP ::= V ; ComplTV. VP ::= TV NP ; UseA. VP ::= "is" A ; This. NP ::= "this" CN ; That. NP ::= "that" CN ; Def. NP ::= "the" CN ; Indef. NP ::= "a" CN ; ModA. CN ::= A CN ; Boy. CN ::= "boy" ; Louse. CN ::= "louse" ; Snake. CN ::= "snake" ; Worm. CN ::= "worm" ; Green. A ::= "green" ; Rotten. A ::= "rotten" ; Thick. A ::= "thick" ; Warm. A ::= "warm" ; Laugh. V ::= "laughs" ; Sleep. V ::= "sleeps" ; Swim. V ::= "swims" ; Eat. TV ::= "eats" ; Kill. TV ::= "kills" Wash. TV ::= "washes" ; ``` With this grammar, the trees look as follows: ``` > p "the boy eats a snake" PredVP (Def Boy) (ComplTV Eat (Indef Snake)) > gr -tr | l PredVP (Indef Louse) (UseA Thick) a louse is thick ``` %--! ==The ``.gf`` grammar format== To see what there is in GF's shell state when a grammar has been imported, you can give the plain 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 one more way of defining the same grammar as in ``paleolithic.cf``. Then we will show how the full GF grammar format enables you to do things that are not possible in the weaker formats. %--! ===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 EBNF and CF formats fuse these two things together, but it is possible to take them apart. For instance, the verb phrase predication rule ``` PredVP. S ::= NP VP ; ``` is interpreted as the following pair of rules: ``` fun PredVP : NP -> VP -> S ; lin PredVP x y = {s = x.s ++ y.s} ; ``` The former rule, with the keyword ``fun``, belongs to the abstract syntax. It defines the **function** ``PredVP`` which constructs syntax trees of form (``PredVP`` //x// //y//). The latter rule, with the keyword ``lin``, belongs to the concrete syntax. It defines the **linearization function** for syntax trees of form (``PredVP`` //x// //y//). %--! ===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 paleolithic 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. %--! ===Record types, records, and ``Str``s=== 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"} ``` 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. 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// %--! ===An abstract syntax example=== To express the abstract syntax of ``paleolithic.cf`` in a file ``Paleolithic.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 Paleolithic = { cat S ; NP ; VP ; CN ; A ; V ; TV ; fun PredVP : NP -> VP -> S ; UseV : V -> VP ; ComplTV : TV -> NP -> VP ; UseA : A -> VP ; ModA : A -> CN -> CN ; This, That, Def, Indef : CN -> NP ; Boy, Louse, Snake, Worm : CN ; Green, Rotten, Thick, Warm : A ; Laugh, Sleep, Swim : V ; Eat, Kill, Wash : TV ; } ``` Notice the use of shorthands permitting the sharing of the keyword in subsequent judgements, and of the type in subsequent ``fun`` judgements. %--! ===A concrete syntax example=== Each category introduced in ``Paleolithic.gf`` is given a ``lincat`` rule, and each function is given a ``lin`` rule. Similar shorthands apply as in ``abstract`` modules. ``` concrete PaleolithicEng of Paleolithic = { lincat S, NP, VP, CN, A, V, TV = {s : Str} ; lin PredVP np vp = {s = np.s ++ vp.s} ; UseV v = v ; ComplTV tv np = {s = tv.s ++ np.s} ; UseA a = {s = "is" ++ a.s} ; This cn = {s = "this" ++ cn.s} ; That cn = {s = "that" ++ cn.s} ; Def cn = {s = "the" ++ cn.s} ; Indef cn = {s = "a" ++ cn.s} ; ModA a cn = {s = a.s ++ cn.s} ; Boy = {s = "boy"} ; Louse = {s = "louse"} ; Snake = {s = "snake"} ; Worm = {s = "worm"} ; Green = {s = "green"} ; Rotten = {s = "rotten"} ; Thick = {s = "thick"} ; Warm = {s = "warm"} ; Laugh = {s = "laughs"} ; Sleep = {s = "sleeps"} ; Swim = {s = "swims"} ; Eat = {s = "eats"} ; Kill = {s = "kills"} ; Wash = {s = "washes"} ; } ``` %--! ===Modules and files=== Module name + ``.gf`` = file name Each module is compiled into a ``.gfc`` file. Import ``PaleolithicEng.gf`` and try what happens ``` > i PaleolithicEng.gf ``` The GF program does not only read the file ``PaleolithicEng.gf``, but also all other files that it depends on - in this case, ``Paleolithic.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. %--! ==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 buid an Italian concrete syntax for ``Paleolithic`` and then test the resulting multilingual grammar. %--! ===An Italian concrete syntax=== ``` concrete PaleolithicIta of Paleolithic = { lincat S, NP, VP, CN, A, V, TV = {s : Str} ; lin PredVP np vp = {s = np.s ++ vp.s} ; UseV v = v ; ComplTV tv np = {s = tv.s ++ np.s} ; UseA a = {s = "è" ++ a.s} ; This cn = {s = "questo" ++ cn.s} ; That cn = {s = "quello" ++ cn.s} ; Def cn = {s = "il" ++ cn.s} ; Indef cn = {s = "un" ++ cn.s} ; ModA a cn = {s = cn.s ++ a.s} ; Boy = {s = "ragazzo"} ; Louse = {s = "pidocchio"} ; Snake = {s = "serpente"} ; Worm = {s = "verme"} ; Green = {s = "verde"} ; Rotten = {s = "marcio"} ; Thick = {s = "grosso"} ; Warm = {s = "caldo"} ; Laugh = {s = "ride"} ; Sleep = {s = "dorme"} ; Swim = {s = "nuota"} ; Eat = {s = "mangia"} ; Kill = {s = "uccide"} ; Wash = {s = "lava"} ; } ``` %--! ===Using a multilingual grammar=== Import the two grammars in the same GF session. ``` > i PaleolithicEng.gf > i PaleolithicIta.gf ``` Try generation now: ``` > gr | l un pidocchio uccide questo ragazzo > gr | l -lang=PaleolithicEng that louse eats a louse ``` Translate by using a pipe: ``` > p -lang=PaleolithicEng "the boy eats the snake" | l -lang=PaleolithicIta il ragazzo mangia il serpente ``` 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 : Paleolithic main concrete : PaleolithicIta actual concretes : PaleolithicIta PaleolithicEng ``` %--! ===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 PaleolithicEng PaleolithicIta 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 ('.'). a green boy washes the louse un ragazzo verde lava il gatto No, not un ragazzo verde lava il gatto, but un ragazzo verde lava il pidocchio Score 0/1 ``` 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 PaleolithicEng PaleolithicIta ``` 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. This is how language was extended when civilization advanced from the paleolithic to the neolithic age: ``` abstract Neolithic = Paleolithic ** { fun Fire, Wheel : CN ; Think : V ; } ``` Parallel to the abstract syntax, extensions can be built for concrete syntaxes: ``` concrete NeolithicEng of Neolithic = PaleolithicEng ** { lin Fire = {s = "fire"} ; Wheel = {s = "wheel"} ; Think = {s = "thinks"} ; } ``` The effect of extension is that all of the contents of the extended and extending module are put together. %--! ===Multiple inheritance=== Specialized vocabularies can be represented as small grammars that only do "one thing" each. For instance, the following are grammars for fish names and mushroom names. ``` abstract Fish = { cat Fish ; fun Salmon, Perch : Fish ; } abstract Mushrooms = { 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 Gatherer = Paleolithic, Fish, Mushrooms ** { fun FishCN : Fish -> CN ; MushroomCN : Mushroom -> CN ; } ``` %--! ===Visualizing module structure=== When you have created all the abstract syntaxes and one set of concrete syntaxes needed for ``Gatherer``, 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 [Gatherer.gif] %--! ==System commands== To document your grammar, you may want to print the graph into a file, e.g. a ``.gif`` 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. ``` > pm -printer=graph | wf Gatherer.dot > ! dot -Tgif Gatherer.dot > Gatherer.gif ``` The latter command is a Unix command, issued from GF by using the shell escape symbol ``!``. The resulting graph is shown in the next 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 the ``help`` to see what other formats are available: ``` > help pm > help -printer ``` %--! ==Resource modules== ===The golden rule of functional programming=== In comparison to the ``.cf`` format, the ``.gf`` format still 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 standard 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, parameters. In functional programming languages, such as [Haskell http://www.haskell.org], it is possible to share muc more than in the 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 ``PaleolithicEng``. ``` concrete PalEng of Paleolithic = open StringOper in { lincat S, NP, VP, CN, A, V, TV = SS ; lin PredVP = cc ; UseV v = v ; ComplTV = cc ; UseA = prefix "is" ; This = prefix "this" ; That = prefix "that" ; Def = prefix "the" ; Indef = prefix "a" ; ModA = cc ; Boy = ss "boy" ; Louse = ss "louse" ; Snake = ss "snake" ; -- etc } ``` The same string operations could be use to write ``PaleolithicIta`` more concisely. %--! ===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 put this knowledge available through resource grammar modules, whose users only need to pick the right operations and not to know their implementation details. %--! ==Morphology== Suppose we want to say, with the vocabulary included in ``Paleolithic.gf``, things like ``` the boy eats two snakes all boys sleep ``` The new grammatical facility we need are the plural forms of nouns and verbs (//boys, sleep//), as opposed to their singular forms. The introduction of plural forms requires two things: - to **inflect** nouns and verbs in singular and plural number - to describe the **agreement** of the verb to subject: the rule that 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, many new expression forms, and a generalizarion of linearization types from strings to more complex types. %--! ===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 nouns 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 CN = {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 Boy = {s = table { Sg => "boy" ; Pl => "boys" } } ; ``` The application of a table to a parameter is done by the **selection** operator ``!``. For instance, ``` Boy.s ! Pl ``` is a selection, whose value is ``"boys"``. %--! ===Inflection tables, paradigms, and ``oper`` definitions=== All English common nouns are inflected in number, most of them in the same way: the plural form is formed from the singular form 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 GF point of view, a paradigm is a function that takes a **lemma** - a string 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 **glueing** 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 "boy").s ! Pl ---> "boy" + "s" ---> "boys" ``` %--! ===Worst-case macros and data abstraction=== Some English nouns, such as ``louse``, 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 macro** for nouns: ``` oper mkNoun : Str -> Str -> Noun = \x,y -> { s = table { Sg => x ; Pl => y } } ; ``` Thus we define ``` lin Louse = mkNoun "louse" "lice" ; ``` and ``` oper regNoun : Str -> Noun = \x -> mkNoun x (x + "s") ; ``` instead of writing the inflection table explicitly. The grammar engineering advantage of worst-case macros 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 operator ``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. %--! ===An intelligent noun paradigm using ``case`` expressions=== 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, //louse - lice// 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. %--! ===Pattern matching=== Expressions of the ``table`` form are built from lists of argument-value pairs. These pairs are called the **branches** of the table. In addition to constants introduced in ``param`` definitions, the left-hand side of a branch can more generally be a **pattern**, and the computation of selection is then performed by **pattern matching**: - 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 ``` %--! ===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`` 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. %--! ===Testing ``resource`` modules=== To test a ``resource`` module independently, you can import it with a flag that tells GF to retain the ``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 MorphoEng.gf The command ``compute_concrete = cc`` computes any expression formed by operations and other GF constructs. For example, ``` > cc regVerb "echo" {s : Number => Str = table Number { Sg => "echoes" ; Pl => "echo" } } ``` The command ``show_operations = so``` shows the type signatures of all operations returning a given value type: ``` > so Verb MorphoEng.mkNoun : Str -> Str -> {s : {MorphoEng.Number} => Str} MorphoEng.mkVerb : Str -> Str -> {s : {MorphoEng.Number} => Str} MorphoEng.regNoun : Str -> {s : {MorphoEng.Number} => Str} MorphoEng.regVerb : Str -> { s : {MorphoEng.Number} => Str} ``` Why does the command also show the operations that form ``Noun``s? The reason is that the type expression ``Verb`` is first computed, and its value happens to be the same as the value of ``Noun``. ==Using morphology 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 **parametric**. The agreement rule itself is expressed in the linearization rule of the predication structure: ``` lin PredVP np vp = {s = np.s ++ vp.s ! np.n} ; ``` The following section will present a new version of ``PaleolithingEng``, assuming an abstract syntax xextended with ``All`` and ``Two``. It also assumes that ``MorphoEng`` has a paradigm ``regVerb`` for regular verbs (which need only be regular only in the present tensse). The reader is invited to inspect the way in which agreement works in the formation of noun phrases and verb phrases. %--! ===English concrete syntax with parameters=== ``` concrete PaleolithicEng of Paleolithic = open MorphoEng in { lincat S, A = {s : Str} ; VP, CN, V, TV = {s : Number => Str} ; NP = {s : Str ; n : Number} ; lin PredVP np vp = {s = np.s ++ vp.s ! np.n} ; UseV v = v ; ComplTV tv np = {s = \\n => tv.s ! n ++ np.s} ; UseA a = {s = \\n => case n of {Sg => "is" ; Pl => "are"} ++ a.s} ; This cn = {s = "this" ++ cn.s ! Sg } ; Indef cn = {s = "a" ++ cn.s ! Sg} ; All cn = {s = "all" ++ cn.s ! Pl} ; Two cn = {s = "two" ++ cn.s ! Pl} ; ModA a cn = {s = \\n => a.s ++ cn.s ! n} ; Louse = mkNoun "louse" "lice" ; Snake = regNoun "snake" ; Green = {s = "green"} ; Warm = {s = "warm"} ; Laugh = regVerb "laugh" ; Sleep = regVerb "sleep" ; Kill = regVerb "kill" ; } ``` %--! ===Hierarchic parameter types=== The reader familiar with a functional programming language such as Haskell 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. (This restriction 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 (recursion is forbidden). Such parameter types impose a hierarchic order among parameters. They are often useful to define linguistically 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 = Uter | Neuter ; ``` In pattern matching, a constructor can have 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 = \x -> table { ASg _ => x ; APl => x + "a" ; } ``` %--! ===Morphological analysis and morphology quiz=== Even though in GF morphology is mostly seen as an auxiliary of syntax, a morphology once defined can be used 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, ``` > i lib/resource/french/VerbsFre.gf > morpho_quiz -cat=V Welcome to GF Morphology Quiz. ... réapparaître : VFin VCondit Pl P2 réapparaitriez > No, not réapparaitriez, but réapparaîtriez Score 0/1 ``` Finally, a list of morphological exercises and save it in a file for later use, by the command ``morpho_list = ml`` ``` > morpho_list -number=25 -cat=V ``` 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 first of the following judgements defines transitive verbs as a **discontinuous constituents**, i.e. as having a linearization type with two strings and not just one. The second judgement shows how the constituents are separated by the object in complementization. ``` lincat TV = {s : Number => Str ; s2 : Str} ; lin ComplTV tv obj = {s = \\n => tv.s ! n ++ obj.s ++ tv.s2} ; ``` GF currently requires that all fields in linearization records that have a table with value type ``Str`` have as labels either ``s`` or ``s`` with an integer index. %--! ==Topics still to be written== ===Free variation=== ===Record extension, tuples=== ===Predefined types and operations=== ===Lexers and unlexers=== ===Grammars of formal languages=== ===Resource grammars and their reuse=== ===Interfaces, instances, and functors=== ===Speech input and output=== ===Embedded grammars in Haskell, Java, and Prolog=== ===Dependent types, variable bindings, semantic definitions=== ===Transfer modules=== ===Alternative input and output grammar formats===