Grammatical Framework Tutorial
Author: Aarne Ranta <aarne (at) cs.chalmers.se>
Last update: %%date(%c)

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[../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 <b>nesting</b>: trees are branching entities, and the branches
are themselves trees. Parentheses give a linear representation of trees,
useful for the computer. But the human eye may prefer to see a visualization;
for this purpose, GF provides the command ``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 ``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 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 knows 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 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
```



%--!
===Translation quiz===

This is a simple language exercise that can be automatically
generated from a multilingual grammar. The system generates a set of
random sentence, 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.


%--!
===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
```


%--!
==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.
```
  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 into 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

- oval boxes for abstract modules
- square boxes  for concrete modules
- black-headed arrows for inheritance
- white-headed arrows for the concrete-of-abstract relation




<img src="Gatherer.gif">


%--!
==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:

- 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 precisely in
concrete syntax while ignoring them in abstract syntax.



To be able to do all this, we need two new judgement forms,
a new module form, 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 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
``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
paradigms, 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.
```
  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 following 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.



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 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
```
Similarly to 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.



%--!
===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), in some sense
//has// a number, which it "sends" 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 page 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
<a href="http://www.haskell.org">Haskell<a> 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" ;
    }
```


%--!
===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===



===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===

