Grammatical Framework Tutorial

3rd Edition, for GF version 2.2 or later

Aarne Ranta

aarne@cs.chalmers.se

12 May 2005

GF = Grammatical Framework

The term GF is used for different things:

This tutorial is primarily about the GF program and the GF programming language. It will guide you

Getting the GF program

The program is open-source free software, which you can download from the GF Homepage:
http://www.cs.chalmers.se/~aarne/GF

There you can download

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 >.

My first grammar

Now you are ready to try out your first grammar. We start with one that is not written in GF language, but in the EBNF notation (Extended Backus Naur Form), which GF can also understand. Type (or copy) the following lines in a file named paleolithic.ebnf: 
  S   ::= NP VP ;
  VP  ::= V | TV NP | "is" A ;
  NP  ::= ("this" | "that" | "the" | "a") CN ;
  CN  ::= A CN ;
  CN  ::= "boy" | "louse" | "snake" | "worm" ;
  A   ::= "green" | "rotten" | "thick" | "warm" ;
  V   ::= "laughs" | "sleeps" | "swims" ;
  TV  ::= "eats" | "kills" | "washes" ;

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. 
  import paleolithic.gf
The GF program now compiles your grammar into an internal representation, and shows a new prompt when it is ready.

You can use GF for parsing: 

  > parse "the boy eats a snake"
  Mks_0 (Mks_6 Mks_9) (Mks_2 Mks_20 (Mks_7 Mks_11))

  > parse "the snake eats a boy"
  Mks_0 (Mks_6 Mks_11) (Mks_2 Mks_20 (Mks_7 Mks_9))
The parse (= p) command takes a string (in double quotes) and returns an abstract syntax tree - the thing with Mkss and parentheses. 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
  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 Mks_0 (Mks_6 Mks_11) (Mks_2 Mks_20 (Mks_7 Mks_9))
  the snake eats a boy
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
  Mks_0 (Mks_4 Mks_11) (Mks_3 Mks_15)
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

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
  Mks_0 (Mks_7 Mks_10) (Mks_1 Mks_18)
  a louse sleeps
  Mks_0 (Mks_7 Mks_10) (Mks_1 Mks_18)
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 | l -tr | 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 EBNF 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
  Mks_10. CN ::= "louse" ;
  Mks_11. CN ::= "snake" ;
  Mks_12. CN ::= "worm" ;
  Mks_8.  CN ::= A CN ;
  Mks_9.  CN ::= "boy" ;
  Mks_4.  NP ::= "this" CN ;
  Mks_15. A  ::= "thick" ;
  ...
A syntax tree such as 
  Mks_4 (Mks_8 Mks_15 Mks_12)
  this thick worm
encodes the sequence of grammar rules used for building the expression. If you look at this tree, you will notice that Mks_4 is the label of the rule prefixing this to a common noun, Mks_15 is the label of the adjective thick, and so on.

The labelled context-free format

The labelled context-free grammar format permits user-defined labels to each rule. GF recognizes files of this format by the suffix .cf. Let us include the following rules in the file paleolithic.cf. 
  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" ;

Using the labelled context-free format

The GF commands for the .cf format are exactly the same as for the .ebnf format. Just the syntax trees become nicer to read and to remember. Notice that before reading in a new grammar in GF you often (but not always, as we will see later) have first to give the command (empty = e), which removes the old grammar from the GF shell state. 
  > empty

  > i paleolithic.cf

  > 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 really 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 to show how GF's own notation gives you much more expressive power than the .cf and .ebnf formats. We will introduce the .gf format by presenting one more way of defining the same grammar as in paleolithic.cf and paleolithic.ebnf. 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: 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: 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 grammar paleolithic.cf 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

An abstract syntax example

Each nonterminal occurring in paleolithic.cf is introduced by a cat judgement. Each rule label is introduced by a fun judgement. 
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 fun 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 compiles, 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 knows whether to use an existing .gfc file or to generate a new one, by looking at modification times.

Multilingual grammar

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 without first emptying 
  > 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 multilingual shell state

A GF shell is at any time in a state, which contains a multilingual grammar. One of the concrete syntaxes is the "main" one, which means that parsing and linearization are performed by using it. By default, the main concrete syntax is the last-imported one. As we saw on previous slide, the lang flag can be used to change the linearization and parsing grammar.

To see what the multilingual grammar is (as well as some other things), you can use the command print_options = po: 

  > print_options
  main abstract :     Paleolithic
  main concrete :     PaleolithicIta
  all concretes :     PaleolithicIta PaleolithicEng

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. 
  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, e.g. 
  abstract Fish = {
    cat Fish ;
    fun Salmon, Perch : Fish ;
  }

  abstract Mushrooms = {
    cat Mushroom ;
    fun Cep, Agaric : Mushroom ;
  }
They can afterwards be combined in bigger grammars by using multiple inheritance, i.e. extension of several grammars at the same time: 
  abstract Gatherer = Paleolithic, Fish, Mushrooms ** {
    fun 
      UseFish     : Fish     -> CN ;
      UseMushroom : 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. It can also be printed out into a file, e.g. a .gif file that can be included in an HTML document 
  > 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.

The module structure of GathererEng

The graph uses

Resource modules

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:

Different languages have different rules of inflection and agreement. For instance, Italian has also agreement in gender (masculine vs. feminine). We want to be able to ignore such differences in the abstract syntax.

To be able to do all this, we need a couple of new judgement forms, a new module form, and a more powerful way of expressing linearization rules.

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 restriction 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). Thus we call them operations for the sake of clarity, introduce one one form of judgement, with the keyword oper. As an example, the following operation defines the regular noun paradigm of English: 

  oper regNoun : Str -> {s : Number => Str} = \x -> {
    s = table {
      Sg => x ;
      Pl => x + "s"
      }
    } ;
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, and the glueing operator + telling that the string held in the variable x and the ending "s" are written together to form one token.

The resource module type

Parameter and operator definitions do not belong to the abstract syntax. They can be used when defining concrete syntax - but they are not tied to a particular set of linearization rules. The proper way to see them is as auxiliary concepts, as resources usable in many concrete syntaxes.

The resource module type thus consists of param and oper definitions. Here is an example. 

  resource MorphoEng = {
    param
      Number = Sg | Pl ;
    oper
      Noun  : Type = {s : Number => Str} ;
      regNoun : Str -> Noun = \x -> {
        s = table {
          Sg => x ;
          Pl => 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.

Opening a resource

Any number of resource modules can be opened in a concrete syntax, which makes the parameter and operation definitions contained in the resource usable in the concrete syntax. Here is an example, where the resource MorphoEng is open in (the fragment of) a new version of PaleolithicEng. 
concrete PaleolithicEng of Paleolithic = open MorphoEng in {
  lincat 
    CN = Noun ;
  lin
    Boy   = regNoun "boy" ;
    Snake = regNoun "snake" ;
    Worm  = regNoun "worm" ;
  }
Notice that, just like in abstract syntax, function application is written by juxtaposition of the function and the argument.

Using operations defined in resource modules is clearly a concise way of giving e.g. inflection tables and other repeated patterns of expression. 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 grammars, whose users only need to pick the right operations and not to know their implementation details.

Worst-case macros and data abstraction

Some English nouns, such as louse, are so irregular that it makes little 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" ;
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

The regular noun paradigm regNoun can - and should - of course be defined by the worst-case macro mkNoun. In addition, some more noun paradigms could be defined, for instance, 
  regNoun : Str -> Noun = \snake -> mkNoun snake (snake + "s") ;
  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 so-called "technical stem" fl 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 even an existing form of the word. A better solution is to use the 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 opened so that init can be used.

An intelligent noun paradigm using case expressions

Topics still to be written

Morpho and translation quiz

Predefined types and operations

Lexers and unlexers

Grammars of formal languages

Resource grammars and their reuse

Embedded grammars in Haskell and Java

Dependent types, variable bindings, semantic definitions

Transfer rules