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

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[../gf-logo.gif]



%--!
==Introduction==

===GF = Grammatical Framework===

The term GF is used for different things:

- a **program** used for working with grammars
- a **programming language** in which grammars can be written
- a **theory** about grammars and languages


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

- to use the GF program
- to write GF grammars
- to write programs in which GF grammars are used as components



%--!
===What are GF grammars used for===

A grammar is a definition of a language.
From this definition, different language processing components 
can be derived:

- parsing: to analyse the language
- linearization: to generate the language
- translation: to analyse one language and generate another


A GF grammar can be seen as a declarative program from which these
processing tasks can be automatically derived. In addition, many
other tasks are readily available for GF grammars:

- morphological analysis: find out the possible inflection forms of words
- morphological synthesis: generate all inflection forms of words
- random generation: generate random expressions
- corpus generation: generate all expressions
- teaching quizzes: train morphology and translation
- multilingual authoring: create a document in many languages simultaneously
- speech input: optimize a speech recognition system for your grammar


A typical GF application is based on a **multilingual grammar** involving
translation on a special domain. Existing applications of this idea include

- [Alfa: http://www.cs.chalmers.se/%7Ehallgren/Alfa/Tutorial/GFplugin.html]:
  a natural-language interface to a proof editor
  (languages: English, French, Swedish)
- [KeY http://www.key-project.org/]: 
  a multilingual authoring system for creating software specifications
  (languages: OCL, English, German)
- [TALK http://www.talk-project.org]:
  multilingual and multimodal dialogue systems
- [WebALT http://webalt.math.helsinki.fi/content/index_eng.html]: 
  a multilingual translator of mathematical exercises
  (languages: Catalan, English, Finnish, French, Spanish, Swedish)
- [Numeral translator http://www.cs.chalmers.se/~bringert/gf/translate/]: 
  number words from 1 to 999,999
  (88 languages)


The specialization of a grammar to a domain makes it possible to
obtain much better translations than in an unlimited machine translation
system. This is due to the well-defined semantics of such domains.
Grammars having this character are called **application grammars**.
They are different from most grammars written by linguists just
because they are multilingual and domain-specific.

However, there is another kind of grammars, which we call **resource grammars**.
These are large, comprehensive grammars that can be used on any domain.
The GF Resource Grammar Library has resource grammars for 10 languages.
These grammars can be used as **libraries** to define application grammars.
In this way, it is possible to write a high-quality grammar without
knowing about linguistics: in general, to write an application grammar
by using the resource library just requires practical knowledge of
the target language. and all theoretical knowledge about its grammar
is given by the libraries.




%--!
===Who is this tutorial for===

This tutorial is mainly for programmers who want to learn to write
application grammars. It will go through GF's programming concepts
without entering too deep into linguistics. Thus it should
be accessible to anyone who has some previous programming experience.

A separate document is being written on how to write resource grammars.
This includes the ways in which linguistic problems posed by different
languages are solved in GF.


%--!
===The coverage of the tutorial===

The tutorial gives a hands-on introduction to grammar writing.
We start by building a small grammar for the domain of food:
in this grammar, you can say things like
``` this Italian cheese is delicious
in English and Italian.

The first English grammar 
[``food.cf`` food.cf]
is written in a context-free
notation (also known as BNF). The BNF format is often a good
starting point for GF grammar development, because it is
simple and widely used. However, the BNF format is not
good for multilingual grammars. While it is possible to
"translate" by just changing the words contained in a 
BNF grammar to words of some other
language, proper translation usually involves more.
For instance, the order of words may have to be changed:
``` Italian cheese ===> formaggio italiano
The full GF grammar format is designed to support such
changes, by separating between the **abstract syntax**
(the logical structure) and the **concrete syntax** (the
sequence of words) of expressions. 

There is more than words and word order that makes languages
different. Words can have different forms, and which forms
they have vary from language to language. For instance,
Italian adjectives usually have four forms where English
has just one:
```
  delicious (wine, wines, pizza, pizzas)
  vino delizioso, vini deliziosi, pizza deliziosa, pizze deliziose
```
The **morphology** of a language describes the
forms of its words. While the complete description of morphology
belongs to resource grammars, this tutorial will explain the
programming concepts involved in morphology. This will moreover
make it possible to grow the fragment covered by the food example.
The tutorial will in fact build a toy resource grammar in order
to illustrate the module structure of library-based application
grammar writing.

Thus it is by elaborating the initial ``food.cf`` example that
the tutorial makes a guided tour through all concepts of GF.
While the constructs of the GF language are the main focus,
also the commands of the GF system are introduced as they
are needed. 

To learn how to write GF grammars is not the only goal of
this tutorial. To learn the commands of the GF system means
that simple applications of grammars, such as translation and
quiz systems, can be built simply by writing scripts for the
system. More complicated applications, such as natural-language
interfaces and dialogue systems, also require programming in
some general-purpose language. We will briefly explain how
GF grammars are used as components of Haskell, Java, and
Prolog grammars. The tutorial concludes with a couple of
case studies showing how such complete systems can be built.



%--!
===Getting the GF program===

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

There you can download

- binaries for Linux, 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 command
```
  > help
```
will give you a list of available commands.

As a common convention in this Tutorial, we will use
- ``%`` as a prompt that marks system commands
- ``>`` as a prompt that marks GF commands


Thus you should not type these prompts, but only the lines that
follow them.


%--!
==The .cf grammar format==

Now you are ready to try out your first grammar.
We start with one that is not written in 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
``food.cf``:
```
  S       ::= Item "is" Quality ;
  Item    ::= "this" Kind | "that" Kind ;
  Kind    ::= Quality Kind ;
  Kind    ::= "wine" | "cheese" | "fish" ;
  Quality ::= "very" Quality ;
  Quality ::= "fresh" | "warm" | "Italian" | "expensive" | "delicious" | "boring" ;
```
This grammar defines a set of phrases usable to speak about food.
It builds **sentences** (``S``) by assigning ``Qualities`` to
``Item``s. The grammar shows a typical character of GF grammars:
they are small grammars describing some more or less well-defined
domain, such as in this case food.


%--!
===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 food.cf

or

```> i food.cf

to get the same effect.
The effect is that the GF program **compiles** your grammar into an internal
representation, and shows a new prompt when it is ready.
 
You can now use GF for **parsing**:
```
  > parse "this cheese is delicious"
  S_Item_is_Quality (Item_this_Kind Kind_cheese) Quality_delicious

  > p "that wine is very very Italian"
  S_Item_is_Quality (Item_that_Kind Kind_wine) 
    (Quality_very_Quality (Quality_very_Quality Quality_Italian))
```
The ``parse`` (= ``p``) command takes a **string**
(in double quotes) and returns an **abstract syntax tree** - the thing
beginning with ``S_Item_Is_Quality``. 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_Item_is_Quality (Item_that_Kind Kind_wine) Quality_warm
  that wine is warm
```
What is the use of this? Typically not that you type in a tree at
the GF prompt. The utility of linearization comes from the fact that
you can obtain a tree from somewhere else. One way to do so is
**random generation** (``generate_random = gr``):
```
  > generate_random
  S_Item_is_Quality (Item_this_Kind Kind_wine) Quality_delicious
```
Now you can copy the tree and paste it to the ``linearize command``.
Or, more efficiently, feed random generation into linearization by using
a **pipe**.
```
  > gr | l
  this fresh cheese is delicious
```

%--!
===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 "this delicious cheese is very Italian" | 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
  that wine is boring
  that fresh cheese is fresh
  that cheese is very boring
  this cheese is Italian
  that expensive cheese is expensive
  that fish is fresh
  that wine is very Italian
  this wine is Italian
  this cheese is boring
  this fish is boring
```


%--!
===Systematic generation===

To generate //all// sentence that a grammar
can generate, use the command ``generate_trees = gt``.
```
  > generate_trees | l
  that cheese is very Italian
  that cheese is very boring
  that cheese is very delicious
  that cheese is very expensive
  that cheese is very fresh
  ...
  this wine is expensive
  this wine is fresh
  this wine is warm

```
You get quite a few trees but not all of them: only up to a given
**depth** of trees. To see how you can get more, use the
``help = h`` command,
```
  help gt
```
**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_Item_is_Quality (Item_this_Kind Kind_cheese) Quality_boring
  this cheese is boring
  S_Item_is_Quality (Item_this_Kind Kind_cheese) Quality_boring
```
This facility is good for test purposes: for instance, you
may want to see if a grammar is **ambiguous**, i.e.
contains strings that can be parsed in more than one way.



%--!
===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 that form the tree
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

  S_Item_is_Quality. S ::= Item "is" Quality ;
  Quality_Italian. Quality ::= "Italian" ;
  Quality_boring. Quality ::= "boring" ;
  Quality_delicious. Quality ::= "delicious" ;
  Quality_expensive. Quality ::= "expensive" ;
  Quality_fresh. Quality ::= "fresh" ;
  Quality_very_Quality. Quality ::= "very" Quality ;
  Quality_warm. Quality ::= "warm" ;
  Kind_Quality_Kind. Kind ::= Quality Kind ;
  Kind_cheese. Kind ::= "cheese" ;
  Kind_fish. Kind ::= "fish" ;
  Kind_wine. Kind ::= "wine" ;
  Item_that_Kind. Item ::= "that" Kind ;
  Item_this_Kind. Item ::= "this" Kind ;
```
A syntax tree such as
```
  S_Item_is_Quality (Item_this_Kind Kind_wine) Quality_delicious
```
encodes the sequence of grammar rules used for building the
tree. If you look at this tree, you will notice that ``Item_this_Kind``
is the label of the rule prefixing ``this`` to a ``Kind``,
thereby forming an ``Item``.
``Kind_wine`` is the label of the kind ``"wine"``,
and so on. These labels are formed automatically when the grammar
is compiled by GF, in a way that guarantees that different rules
get different labels.


%--!
===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 ``food.cf`` with nicer-looking labels.
```
  Is.        S       ::= Item "is" Quality ;
  That.      Item    ::= "that" Kind ;
  This.      Item    ::= "this" Kind ;
  QKind.     Kind    ::= Quality Kind ;
  Cheese.    Kind    ::= "cheese" ;
  Fish.      Kind    ::= "fish" ;
  Wine.      Kind    ::= "wine" ;
  Italian.   Quality ::= "Italian" ;
  Boring.    Quality ::= "boring" ;
  Delicious. Quality ::= "delicious" ;
  Expensive. Quality ::= "expensive" ;
  Fresh.     Quality ::= "fresh" ;
  Very.      Quality ::= "very" Quality ;
  Warm.      Quality ::= "warm" ;
```
With this grammar, the trees look as follows:
```
  > parse -tr "this delicious cheese is very Italian" | vt
  Is (This (QKind Delicious Cheese)) (Very Italian)
```

[Tree2.png]


%--!
==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
``food.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 CF format fuses these two things together, but it is possible
to take them apart. For instance, the sentence formation rule
```
  Is. S ::= Item "is" Quality ;
```
is interpreted as the following pair of rules:
```
  fun Is : Item -> Quality -> S ;
  lin Is item quality = {s = item.s ++ "is" ++ quality.s} ;
```
The former rule, with the keyword ``fun``, belongs to the abstract syntax.
It defines the **function**
``Is`` which constructs syntax trees of form
(``Is`` //item// //quality//). 

The latter rule, with the keyword ``lin``, belongs to the concrete syntax.
It defines the **linearization function** for
syntax trees of form (``Is`` //item// //quality//). 


%--!
===Judgement forms===

Rules in a GF grammar are called **judgements**, and the keywords
``fun`` and ``lin`` are used for distinguishing between two
**judgement forms**. Here is a summary of the most important
judgement forms:

  - abstract syntax
  
     | form               | reading                   | 
     | ``cat`` C          | C is a category
     | ``fun`` f ``:`` A  | f is a function of type A 

  - concrete syntax
  
     | form                 | reading        | 
     | ``lincat`` C ``=`` T | category C has linearization type T 
     | ``lin`` f ``=`` t    | function f has linearization t
  


We return to the precise meanings of these judgement forms later.
First we will look at how judgements are grouped into modules, and
show how the food grammar is
expressed by using modules and judgements.


%--!
===Module types===

A GF grammar consists of **modules**, 
into which judgements are grouped. The most important
module forms are

  - ``abstract`` A ``=`` M, abstract syntax A with judgements in
  the module body M.
  - ``concrete`` C ``of`` A ``=`` M, concrete syntax C of the
       abstract syntax A, with judgements in the module body M.



%--!
===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"}
```

Whenever a record ``r`` of type ``{s : Str}`` is given,
``r.s`` is an object of type ``Str``. This is
a special case of the **projection** rule, allowing the extraction
of fields from a record:

- if //r// : ``{`` ... //p// : //T// ... ``}`` then //r.p// : //T//


The type ``Str`` is really the type of **token lists**, but
most of the time one can conveniently think of it as the type of strings,
denoted by string literals in double quotes. 

Notice that
```  "hello world"
is not recommended as an expression of type ``Str``. It denotes
a token with a space in it, and will usually 
not work with the lexical analysis that precedes parsing. A shorthand
exemplified by
```  ["hello world and people"]  === "hello" ++ "world" ++ "and" ++ "people"
can be used for lists of tokens. The expression
```  []
denotes the empty token list.



%--!
===An abstract syntax example===

To express the abstract syntax of ``food.cf`` in
a file ``Food.gf``, we write two kinds of judgements:

- Each category is introduced by a ``cat`` judgement.
- Each rule label is introduced by a ``fun`` judgement,
  with the type formed from the nonterminals of the rule.


```
abstract Food = {

  cat
    S ; Item ; Kind ; Quality ;

  fun
    Is : Item -> Quality -> S ;
    This, That : Kind -> Item ;
    QKind : Quality -> Kind -> Kind ;
    Wine, Cheese, Fish : Kind ;
    Very : Quality -> Quality ;
    Fresh, Warm, Italian, Expensive, Delicious, Boring : Quality ;
}
```
Notice the use of shorthands permitting the sharing of
the keyword in subsequent judgements, and of the type
in subsequent ``fun`` judgements.


%--!
===A concrete syntax example===

Each category introduced in ``Food.gf`` is
given a ``lincat`` rule, and each
function is given a ``lin`` rule. Similar shorthands
apply as in ``abstract`` modules.
```
concrete FoodEng of Food = {

  lincat
    S, Item, Kind, Quality = {s : Str} ;

  lin
    Is item quality = {s = item.s ++ "is" ++ quality.s} ;
    This kind = {s = "this" ++ kind.s} ;
    That kind = {s = "that" ++ kind.s} ;
    QKind quality kind = {s = quality.s ++ kind.s} ;
    Wine = {s = "wine"} ;
    Cheese = {s = "cheese"} ;
    Fish = {s = "fish"} ;
    Very quality = {s = "very" ++ quality.s} ;
    Fresh = {s = "fresh"} ;
    Warm = {s = "warm"} ;
    Italian = {s = "Italian"} ;
    Expensive = {s = "expensive"} ;
    Delicious = {s = "delicious"} ;
    Boring = {s = "boring"} ;
}
```


%--!
===Modules and files===

Module name + ``.gf`` = file name

Each module is compiled into a ``.gfc`` file.

Import ``FoodEng.gf`` and see what happens
```
  > i FoodEng.gf
```
The GF program does not only read the file 
``FoodEng.gf``, but also all other files that it
depends on - in this case, ``Food.gf``.

For each file that is compiled, a ``.gfc`` file
is generated. The GFC format (="GF Canonical") is the
"machine code" of GF, which is faster to process than
GF source files. When reading a module, GF decides whether
to use an existing ``.gfc`` file or to generate
a new one, by looking at modification times.



%--!
==Multilingual grammars and translation==

The main advantage of separating abstract from concrete syntax is that
one abstract syntax can be equipped with many concrete syntaxes.
A system with this property is called a **multilingual grammar**.

Multilingual grammars can be used for applications such as
translation. Let us build an Italian concrete syntax for
``Food`` and then test the resulting 
multilingual grammar.




%--!
===An Italian concrete syntax===

```
concrete FoodIta of Food = {

  lincat
    S, Item, Kind, Quality = {s : Str} ;

  lin
    Is item quality = {s = item.s ++ "è" ++ quality.s} ;
    This kind = {s = "questo" ++ kind.s} ;
    That kind = {s = "quello" ++ kind.s} ;
    QKind quality kind = {s = kind.s ++ quality.s} ;
    Wine = {s = "vino"} ;
    Cheese = {s = "formaggio"} ;
    Fish = {s = "pesce"} ;
    Very quality = {s = "molto" ++ quality.s} ;
    Fresh = {s = "fresco"} ;
    Warm = {s = "caldo"} ;
    Italian = {s = "italiano"} ;
    Expensive = {s = "caro"} ;
    Delicious = {s = "delizioso"} ;
    Boring = {s = "noioso"} ;

}

```

%--!
===Using a multilingual grammar===

Import the two grammars in the same GF session.
```
  > i FoodEng.gf
  > i FoodIta.gf
```
Try generation now:
```
  > gr | l
  quello formaggio molto noioso è italiano

  > gr | l -lang=FoodEng
  this fish is warm
```
Translate by using a pipe:
```
  > p -lang=FoodEng "this cheese is very delicious" | l -lang=FoodIta
  questo formaggio è molto delizioso
```
The ``lang`` flag tells GF which concrete syntax to use in parsing and
linearization. By default, the flag is set to the last-imported grammar.
To see what grammars are in scope and which is the main one, use the command
``print_options = po``:
```
  > print_options
  main abstract :     Food
  main concrete :     FoodIta
  actual concretes :  FoodIta FoodEng
```


%--!
===Translation session===

If translation is what you want to do with a set of grammars, a convenient
way to do it is to open a ``translation_session = ts``. In this session,
you can translate between all the languages that are in scope.
A dot ``.`` terminates the translation session.
```
  > ts

  trans> that very warm cheese is boring
  quello formaggio molto caldo è noioso
  that very warm cheese is boring

  trans> questo vino molto italiano è molto delizioso
  questo vino molto italiano è molto delizioso
  this very Italian wine is very delicious

  trans> .
  >
```



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

This is a simple language exercise that can be automatically
generated from a multilingual grammar. The system generates a set of
random sentences, displays them in one language, and checks the user's
answer given in another language. The command ``translation_quiz = tq``
makes this in a subshell of GF.
```
  > translation_quiz FoodEng FoodIta

  Welcome to GF Translation Quiz.
  The quiz is over when you have done at least 10 examples
  with at least 75 % success.
  You can interrupt the quiz by entering a line consisting of a dot ('.').

  this fish is warm
  questo pesce è caldo
  > Yes.
  Score 1/1

  this cheese is Italian
  questo formaggio è noioso
  > No, not questo formaggio è noioso, but
  questo formaggio è italiano

  Score 1/2
  this fish is expensive
```
You can also generate a list of translation exercises and save it in a
file for later use, by the command ``translation_list = tl``
```
  > translation_list -number=25 FoodEng FoodIta
```
The ``number`` flag gives the number of sentences generated.



%--!
==Grammar architecture==

===Extending a grammar===

The module system of GF makes it possible to **extend** a
grammar in different ways. The syntax of extension is
shown by the following example. We extend ``Food`` by
adding a category of questions and two new functions.
```
  abstract Morefood = Food ** {
    cat
      Question ;
    fun
      QIs : Item -> Quality -> Question ;
      Pizza : Kind ;
      
  }
```
Parallel to the abstract syntax, extensions can
be built for concrete syntaxes:
```
  concrete MorefoodEng of Morefood = FoodEng ** {
    lincat
      Question = {s : Str} ;
    lin
      QIs item quality = {s = "is" ++ item.s ++ quality.s} ;
      Pizza = {s = "pizza"} ;
  }
```
The effect of extension is that all of the contents of the extended
and extending module are put together.



%--!
===Multiple inheritance===

Specialized vocabularies can be represented as small grammars that
only do "one thing" each. For instance, the following are grammars
for fruit and mushrooms
```
  abstract Fruit = {
    cat Fruit ;
    fun Apple, Peach : Fruit ;
  }

  abstract Mushroom = {
    cat Mushroom ;
    fun Cep, Agaric : Mushroom ;
  }
```
They can afterwards be combined into bigger grammars by using
**multiple inheritance**, i.e. extension of several grammars at the
same time:
```
  abstract Foodmarket = Food, Fruit, Mushroom ** {
    fun 
      FruitKind    : Fruit    -> Kind ;
      MushroomKind : Mushroom -> Kind ;
    }
```
At this point, you would perhaps like to go back to
``Food`` and take apart ``Wine`` to build a special
``Drink`` module.


%--!
===Visualizing module structure===

When you have created all the abstract syntaxes and
one set of concrete syntaxes needed for ``Foodmarket``,
your grammar consists of eight GF modules. To see how their
dependences look like, you can use the command 
``visualize_graph = vg``,
```
  > visualize_graph
```
and the graph will pop up in a separate window. 

The graph uses

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


[Foodmarket.png]



%--!
==System commands==

To document your grammar, you may want to print the
graph into a file, e.g. a ``.png`` file that
can be included in an HTML document. You can do this
by first printing the graph into a file ``.dot`` and then
processing this file with the ``dot`` program.
```
  > pm -printer=graph | wf Foodmarket.dot
  > ! dot -Tpng Foodmarket.dot > Foodmarket.png
```
The latter command is a Unix command, issued from GF by using the
shell escape symbol ``!``. The resulting graph was shown in the previous section.

The command ``print_multi = pm`` is used for printing the current multilingual
grammar in various formats, of which the format ``-printer=graph`` just
shows the module dependencies. Use ``help`` to see what other formats
are available:
```
  > help pm
  > help -printer
```



%--!
==Resource modules==


===The golden rule of functional programming===

In comparison to the ``.cf`` format, the ``.gf`` format looks rather
verbose, and demands lots more characters to be written. You have probably
done this by the copy-paste-modify method, which is a common way to
avoid repeating work.

However, there is a more elegant way to avoid repeating work than the copy-and-paste
method. The **golden rule of functional programming** says that

- whenever you find yourself programming by copy-and-paste, write a function instead.


A function separates the shared parts of different computations from the
changing parts, parameters. In functional programming languages, such as
[Haskell http://www.haskell.org], it is possible to share much more than in
languages such as C and Java.


===Operation definitions===

GF is a functional programming language, not only in the sense that
the abstract syntax is a system of functions (``fun``), but also because
functional programming can be used to define concrete syntax. This is
done by using a new form of judgement, with the keyword ``oper`` (for
**operation**), distinct from ``fun`` for the sake of clarity.
Here is a simple example of an operation:
```
  oper ss : Str -> {s : Str} = \x -> {s = x} ;
```
The operation can be **applied** to an argument, and GF will
**compute** the application into a value. For instance,
```
  ss "boy"  --->  {s = "boy"}
```
(We use the symbol ``--->`` to indicate how an expression is 
computed into a value; this symbol is not a part of GF)

Thus an ``oper`` judgement includes the name of the defined operation,
its type, and an expression defining it. As for the syntax of the defining
expression, notice the **lambda abstraction** form ``\x -> t`` of
the function.



%--!
===The ``resource`` module type===

Operator definitions can be included in a concrete syntax. 
But they are not really tied to a particular set of linearization rules.
They should rather be seen as **resources**
usable in many concrete syntaxes.

The ``resource`` module type can be used to package
``oper`` definitions into reusable resources. Here is
an example, with a handful of operations to manipulate
strings and records.
```
  resource StringOper = {
    oper
      SS : Type = {s : Str} ;
      ss : Str -> SS = \x -> {s = x} ;
      cc : SS -> SS -> SS = \x,y -> ss (x.s ++ y.s) ;
      prefix : Str -> SS -> SS = \p,x -> ss (p ++ x.s) ;
  }
```
Resource modules can extend other resource modules, in the
same way as modules of other types can extend modules of the
same type. Thus it is possible to build resource hierarchies.



%--!
===Opening a ``resource``===

Any number of ``resource`` modules can be
**opened** in a ``concrete`` syntax, which
makes definitions contained
in the resource usable in the concrete syntax. Here is
an example, where the resource ``StringOper`` is
opened in a new version of ``FoodEng``.
```
  concrete Food2Eng of Food = open StringOper in {

  lincat
    S, Item, Kind, Quality = SS ;

  lin
    Is item quality = cc item (prefix "is" quality) ;
    This = prefix "this" ;
    That = prefix "that" ;
    QKind = cc ;
    Wine = ss "wine" ;
    Cheese = ss "cheese" ;
    Fish = ss "fish" ;
    Very = prefix "very" ;
    Fresh = ss "fresh" ;
    Warm = ss "warm" ;
    Italian = ss "Italian" ;
    Expensive = ss "expensive" ;
    Delicious = ss "delicious" ;
    Boring = ss "boring" ;

  }
```
The same string operations could be use to write ``FoodIta``
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
``Food.gf``, things like
```
  all Italian wines are delicious
```
The new grammatical facility we need are the plural forms
of nouns and verbs (//wines, are//), as opposed to their
singular forms.

The introduction of plural forms requires two things:

- 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
and many new expression forms.
We also need to generalize 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 ``Kind`` expressions in English have a linearization
depending on number, we replace the linearization type ``{s : Str}``
with a type where the ``s`` field is a **table** depending on number:
```
  lincat Kind = {s : Number => Str} ;
```
The **table type** ``Number => Str`` is in many respects similar to
a function type (``Number -> Str``). The main difference is that the
argument type of a table type must always be a parameter type. This means
that the argument-value pairs can be listed in a finite table. The following
example shows such a table:
```
  lin Cheese = {s = table {
    Sg => "cheese" ;
    Pl => "cheeses"
    }
  } ;
```
The application of a table to a parameter is done by the **selection**
operator ``!``. For instance,
```
   table {Sg => "cheese" ; Pl => "cheeses"} ! Pl
```
is a selection, whose value is ``"cheeses"``.


%--!
===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** -
also known as a **dictionary form** - and returns an inflection
table of desired type. Paradigms are not functions in the sense of the
``fun`` judgements of abstract syntax (which operate on trees and not
on strings), but operations defined in ``oper`` judgements.
The following operation defines the regular noun paradigm of English:
```
  oper regNoun : Str -> {s : Number => Str} = \x -> {
    s = table {
      Sg => x ;
      Pl => x + "s"
      }
    } ;
```
The **gluing** operator ``+`` tells that
the string held in the variable ``x`` and the ending ``"s"`` 
are written together to form one **token**. Thus, for instance,
```
  (regNoun "cheese").s ! Pl  ---> "cheese" + "s"  --->  "cheeses"
```



%--!
===Worst-case functions and data abstraction===

Some English nouns, such as ``mouse``, are so irregular that
it makes no sense to see them as instances of a paradigm. Even
then, it is useful to perform **data abstraction** from the
definition of the type ``Noun``, and introduce a constructor
operation, a **worst-case function** for nouns:
```
  oper mkNoun : Str -> Str -> Noun = \x,y -> {
    s = table {
      Sg => x ;
      Pl => y
      }
    } ;
```
Thus we could define
```
  lin Mouse = mkNoun "mouse" "mice" ;
```
and
```
  oper regNoun : Str -> Noun = \x -> 
    mkNoun x (x + "s") ;
```
instead of writing the inflection table explicitly.

The grammar engineering advantage of worst-case functions is that
the author of the resource module may change the definitions of
``Noun`` and ``mkNoun``, and still retain the
interface (i.e. the system of type signatures) that makes it
correct to use these functions in concrete modules. In programming
terms, ``Noun`` is then treated as an **abstract datatype**.



%--!
===A system of paradigms using Prelude operations===

In addition to the completely regular noun paradigm ``regNoun``, 
some other frequent noun paradigms deserve to be
defined, for instance,
```
  sNoun : Str -> Noun = \kiss  -> mkNoun kiss  (kiss  + "es") ;
```
What about nouns like //fly//, with the plural //flies//? The already
available solution is to use the longest common prefix
//fl// (also known as the **technical stem**) as argument, and define
```
  yNoun : Str -> Noun = \fl -> mkNoun (fl  + "y") (fl  + "ies") ;
```
But this paradigm would be very unintuitive to use, because the technical stem
is not an existing form of the word. A better solution is to use
the lemma and a string operator ``init``, which returns the initial segment (i.e.
all characters but the last) of a string:
```
  yNoun : Str -> Noun = \fly -> mkNoun fly (init fly  + "ies") ;  
```
The 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, //mouse - mice// and
//fish - fish// must be given by using ``mkNoun``.
Also the word //boy// would be inflected incorrectly; to prevent
this, either use ``mkNoun`` or modify 
``regNoun`` so that the ``"y"`` case does not
apply if the second-last character is a vowel.



%--!
===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`` resource/MorphoEng.gf].
```
  --# -path=.:prelude

  resource MorphoEng = open Prelude in {

    param
      Number = Sg | Pl ;

    oper
      Noun, Verb : Type = {s : Number => Str} ;

      mkNoun : Str -> Str -> Noun = \x,y -> {
        s = table {
          Sg => x ;
          Pl => y
          }
        } ;

      regNoun : Str -> Noun = \s -> case last s of {
        "s" | "z" => mkNoun s (s + "es") ;
        "y"       => mkNoun s (init s + "ies") ;
        _         => mkNoun s (s + "s")
        } ;

      mkVerb : Str -> Str -> Verb = \x,y -> mkNoun y x ;

      regVerb : Str -> Verb = \s -> case last s of {
        "s" | "z" => mkVerb s (s + "es") ;
        "y"       => mkVerb s (init s + "ies") ;
        "o"       => mkVerb s (s + "es") ;
        _         => mkVerb s (s + "s")
        } ;
  }
```
The first line gives as a hint to the compiler the
**search path** needed to find all the other modules that the
module depends on. The directory ``prelude`` is a subdirectory of
``GF/lib``; to be able to refer to it in this simple way, you can
set the environment variable ``GF_LIB_PATH`` to point to this
directory.


%--!
===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 a **variable feature** (or a
**parametric feature**).

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
``FoodsEng``, assuming the abstract syntax ``Foods`` 
that is similar to ``Food`` but also has the
plural determiners ``These`` and ``Those``.
The reader is invited to inspect the way in which agreement works in
the formation of sentences.


%--!
===English concrete syntax with parameters===

The grammar uses both 
[``Prelude`` ../../lib/prelude/Prelude.gf] and
[``MorphoEng`` resource/MorphoEng].
We will later see how to make the grammar even
more high-level by using a resource grammar library
and parametrized modules.
```
--# -path=.:resource:prelude

concrete FoodsEng of Foods = open Prelude, MorphoEng in {

  lincat
    S, Quality = SS ; 
    Kind = {s : Number => Str} ; 
    Item = {s : Str ; n : Number} ; 

  lin
    Is item quality = ss (item.s ++ (mkVerb "are" "is").s ! item.n ++ quality.s) ;
    This  = det Sg "this" ;
    That  = det Sg "that" ;
    These = det Pl "these" ;
    Those = det Pl "those" ;
    QKind quality kind = {s = \\n => quality.s ++ kind.s ! n} ;
    Wine = regNoun "wine" ;
    Cheese = regNoun "cheese" ;
    Fish = mkNoun "fish" "fish" ;
    Very = prefixSS "very" ;
    Fresh = ss "fresh" ;
    Warm = ss "warm" ;
    Italian = ss "Italian" ;
    Expensive = ss "expensive" ;
    Delicious = ss "delicious" ;
    Boring = ss "boring" ;

  oper
    det : Number -> Str -> Noun -> {s : Str ; n : Number} = \n,d,cn -> {
      s = d ++ cn.s ! n ;
      n = n
      } ;

}
```



%--!
===Hierarchic parameter types===

The reader familiar with a functional programming language such as
[Haskell http://www.haskell.org] must have noticed the similarity
between parameter types in GF and **algebraic datatypes** (``data`` definitions
in Haskell). The GF parameter types are actually a special case of algebraic
datatypes: the main restriction is that in GF, these types must be finite.
(It is this restriction that makes it possible to invert linearization rules into
parsing methods.)

However, finite is not the same thing as enumerated. Even in GF, parameter
constructors can take arguments, provided these arguments are from other
parameter types - only recursion is forbidden. Such parameter types impose a
hierarchic order among parameters. They are often needed to define
the linguistically most accurate parameter systems.

To give an example, Swedish adjectives
are inflected in number (singular or plural) and
gender (uter or neuter). These parameters would suggest 2*2=4 different
forms. However, the gender distinction is done only in the singular. Therefore,
it would be inaccurate to define adjective paradigms using the type
``Gender => Number => Str``. The following hierarchic definition
yields an accurate system of three adjectival forms.
```
  param AdjForm = ASg Gender | APl ;
  param Gender  = Utr | Neutr ;
```
Here is an example of pattern matching, the paradigm of regular adjectives.
```
  oper regAdj : Str -> AdjForm => Str = \fin -> table {
    ASg Utr   => fin ;
    ASg Neutr => fin + "t" ;
    APl       => fin + "a" ;
    }
```
A constructor can be used as a pattern that has patterns as arguments. For instance,
the adjectival paradigm in which the two singular forms are the same, 
can be defined
```
  oper plattAdj : Str -> AdjForm => Str = \platt -> table {
    ASg _ => platt ;
    APl   => platt + "a" ;
    }
```


%--!
===Morphological analysis and morphology quiz===

Even though morphology is in GF
mostly used as an auxiliary for syntax, it
can also be useful on its own right. The command ``morpho_analyse = ma``
can be used to read a text and return for each word the analyses that
it has in the current concrete syntax.
```
  > rf bible.txt | morpho_analyse
```
In the same way as translation exercises, morphological exercises can
be generated, by the command ``morpho_quiz = mq``. Usually,
the category is set to be something else than ``S``. For instance,
```
  > 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 can be generated
off-line saved in a
file for later use, by the command ``morpho_list = ml``
```
  > morpho_list -number=25 -cat=V | wf exx.txt
```
The ``number`` flag gives the number of exercises generated.



%--!
===Discontinuous constituents===

A linearization type may contain more strings than one. 
An example of where this is useful are English particle
verbs, such as //switch off//. The linearization of
a sentence may place the object between the verb and the particle:
//he switched it off//.

The following judgement defines transitive verbs as
**discontinuous constituents**, i.e. as having a linearization
type with two strings and not just one. 
```
  lincat TV = {s : Number => Str ; part : Str} ;
```
This linearization rule
shows how the constituents are separated by the object in complementization.
```
  lin PredTV tv obj = {s = \\n => tv.s ! n ++ obj.s ++ tv.part} ;
```
There is no restriction in the number of discontinuous constituents
(or other fields) a  ``lincat`` may contain. The only condition is that
the fields must be of finite types, i.e. built from records, tables,
parameters, and ``Str``, and not functions. 

A mathematical result
about parsing in GF says that the worst-case complexity of parsing
increases with the number of discontinuous constituents. This is
potentially a reason to avoid discontinuous constituents.
Moreover, the parsing and linearization commands only give accurate
results for categories whose linearization type has a unique ``Str`` 
valued field labelled ``s``. Therefore, discontinuous constituents
are not a good idea in top-level categories accessed by the users
of a grammar application.


%--!
==More constructs for concrete syntax==


%--!
===Local definitions===

Local definitions ("``let`` expressions") are used in functional
programming for two reasons: to structure the code into smaller
expressions, and to avoid repeated computation of one and
the same expression. Here is an example, from 
[``MorphoIta resource/MorphoIta.gf]:
```
  oper regNoun : Str -> Noun = \vino -> 
        let 
          vin = init vino ;
          o   = last vino
        in
        case o of {
          "a"       => mkNoun Fem  vino (vin + "e") ;
          "o" | "e" => mkNoun Masc vino (vin + "i") ;
          _         => mkNoun Masc vino vino         
          } ;
```




%--!
===Free variation===

Sometimes there are many alternative ways to define a concrete syntax.
For instance, the verb negation in English can be expressed both by
//does not// and //doesn't//. In linguistic terms, these expressions
are in **free variation**. The ``variants`` construct of GF can
be used to give a list of strings in free variation. For example,
```
  NegVerb verb = {s = variants {["does not"] ; "doesn't} ++ verb.s ! Pl} ;
```
An empty variant list
```
  variants {}
```
can be used e.g. if a word lacks a certain form.

In general, ``variants`` should be used cautiously. It is not
recommended for modules aimed to be libraries, because the
user of the library has no way to choose among the variants.
Moreover, ``variants`` is only defined for basic types (``Str``
and parameter types). The grammar compiler will admit
``variants`` for any types, but it will push it to the
level of basic types in a way that may be unwanted.
For instance, German has two words meaning "car", 
//Wagen//, which is Masculine, and //Auto//, which is Neuter.
However, if one writes
```
  variants {{s = "Wagen" ; g = Masc} ; {s = "Auto" ; g = Neutr}}
```
this will compute to
```
  {s = variants {"Wagen" ; "Auto"} ; g = variants {Masc ; Neutr}}
```
which will also accept erroneous combinations of strings and genders.




===Record extension and subtyping===

Record types and records can be **extended** with new fields. For instance,
in German it is natural to see transitive verbs as verbs with a case.
The symbol ``**`` is used for both constructs.
```
  lincat TV = Verb ** {c : Case} ;

  lin Follow = regVerb "folgen" ** {c = Dative} ; 
```
To extend a record type or a record with a field whose label it
already has is a type error.

A record type //T// is a **subtype** of another one //R//, if //T// has
all the fields of //R// and possibly other fields. For instance,
an extension of a record type is always a subtype of it.

If //T// is a subtype of //R//, an object of //T// can be used whenever
an object of //R// is required. For instance, a transitive verb can
be used whenever a verb is required.

**Contravariance** means that a function taking an //R// as argument
can also be applied to any object of a subtype //T//.



===Tuples and product types===

Product types and tuples are syntactic sugar for record types and records:
```
  T1 * ... * Tn   ===   {p1 : T1 ; ... ; pn : Tn}
  <t1, ...,  tn>  ===   {p1 = T1 ; ... ; pn = Tn}
```
Thus the labels ``p1, p2,...``` are hard-coded.


===Record and tuple patterns===

Record types of parameter types are also parameter types.
A typical example is a record of agreement features, e.g. French
```
  oper Agr : PType = {g : Gender ; n : Number ; p : Person} ;
```
Notice the term ``PType`` rather than just ``Type`` referring to
parameter types. Every ``PType`` is also a ``Type``.

Pattern matching is done in the expected way, but it can moreover
utilize partial records: the branch
```
  {g = Fem} => t
```
in a table of type ``Agr => T`` means the same as
```
  {g = Fem ; n = _ ; p = _} => t
```
Tuple patterns are translated to record patterns in the
same way as tuples to records; partial patterns make it
possible to write, slightly surprisingly,
```
  case <g,n,p> of {
    <Fem> => t
    ...
    }
```

%--!
===Regular expression patterns===

To define string operations computed at compile time, such
as in morphology, it is handy to use regular expression patterns:
 - //p// ``+`` //q// : token consisting of //p// followed by //q//
 - //p// ``*``       : token //p// repeated 0 or more times
                                     (max the length of the string to be matched)
 - ``-`` //p//       : matches anything that //p// does not match
 - //x// ``@`` //p// : bind to //x// what //p// matches
 - //p// ``|`` //q// : matches what either //p// or //q// matches


The last three apply to all types of patterns, the first two only to token strings.
Example: plural formation in Swedish 2nd declension
(//pojke-pojkar, nyckel-nycklar, seger-segrar, bil-bilar//):
```
  plural2 : Str -> Str = \w -> case w of {
    pojk + "e"                       => pojk + "ar" ;
    nyck + "e" + l@("l" | "r" | "n") => nyck + l + "ar" ;
    bil                              => bil + "ar"
    } ;
```
Another example: English noun plural formation.
```
  plural : Str -> Str = \w -> case w of {
    _ + ("s" | "z" | "x" | "sh")      => w + "es" ;
    _ + ("a" | "o" | "u" | "e") + "y" => w + "s" ;
    x + "y"                           => x + "ies" ;
    _                                 => w + "s"
    } ;
```
Semantics: variables are always bound to the **first match**, which is the first
in the sequence of binding lists ``Match p v`` defined as follows. In the definition,
``p`` is a pattern and ``v`` is a value.
```
  Match (p1|p2) v = Match p1 v ++ Match p2 v
  Match (p1+p2) s = [Match p1 s1 ++ Match p2 s2 | 
                       i <- [0..length s], (s1,s2) = splitAt i s]
  Match p*      s = [[]] if Match "" s ++ Match p s ++ Match (p+p) s ++... /= []
  Match -p      v = [[]] if Match p v = []
  Match c       v = [[]] if c == v  -- for constant and literal patterns c
  Match x       v = [[(x,v)]]       -- for variable patterns x
  Match x@p     v = [[(x,v)]] + M   if M = Match p v /= []
  Match p       v = [] otherwise    -- failure
```
Examples:
- ``x + "e" + y`` matches ``"peter"`` with ``x = "p", y = "ter"``
- ``x + "er"*`` matches ``"burgerer"`` with ``x = "burg"





%--!
===Prefix-dependent choices===

Sometimes a token has different forms depending on the token
that follows. An example is the English indefinite article,
which is //an// if a vowel follows, //a// otherwise.
Which form is chosen can only be decided at run time, i.e.
when a string is actually build. GF has a special construct for
such tokens, the ``pre`` construct exemplified in
```
  oper artIndef : Str = 
    pre {"a" ; "an" / strs {"a" ; "e" ; "i" ; "o"}} ;
```
Thus
```
  artIndef ++ "cheese"  --->  "a" ++ "cheese"
  artIndef ++ "apple"   --->  "an" ++ "cheese"
```
This very example does not work in all situations: the prefix
//u// has no general rules, and some problematic words are
//euphemism, one-eyed, n-gram//. It is possible to write
```
  oper artIndef : Str = 
    pre {"a" ; 
         "a"  / strs {"eu" ; "one"} ;
         "an" / strs {"a" ; "e" ; "i" ; "o" ; "n-"}
        } ;
```


===Predefined types and operations===

GF has the following predefined categories in abstract syntax:
```
  cat Int ;     -- integers, e.g. 0, 5, 743145151019
  cat Float ;   -- floats,   e.g. 0.0, 3.1415926
  cat String ;  -- strings,  e.g. "", "foo", "123"
```
The objects of each of these categories are **literals**
as indicated in the comments above. No ``fun`` definition
can have a predefined category as its value type, but
they can be used as arguments. For example:
```
  fun StreetAddress : Int -> String -> Address ;
  lin StreetAddress number street = {s = number.s ++ street.s} ;

  -- e.g. (StreetAddress 10 "Downing Street") : Address
```
The linearization type is ``{s : Str}`` for all these categories.


==More concepts of abstract syntax==

===GF as a logical framework===

In this section, we will introduce concepts that make it possible
to encode advanced semantic concepts in an abstract syntax.
These concepts are inherited from **type theory**. Type theory
is the basis of many systems known as **logical frameworks**, which are
used for representing mathematical theorems and their proofs on a computer.
In fact, GF has a logical framework as its proper part:
this part is the abstract syntax.

In a logical framework, the formalization of a mathematical theory
is a set of type and function declarations. The following is an example
of such a theory, represented as an ``abstract`` module in GF.
```
  abstract Geometry = {
    cat 
      Line ; Point ; Circle ;            -- basic types of figures
      Prop ;                             -- proposition
    fun
      Parallel : Line -> Line -> Prop ;  -- x is parallel to y
      Centre : Circle -> Point ;         -- the centre of c
    } 
```



===Dependent types===

===Higher-order abstract syntax===

===Semantic definitions===

===List categories===





%--!
==More features of the module system==

===Interfaces, instances, and functors===


===Resource grammars and their reuse===

A resource grammar is a grammar built on linguistic grounds,
to describe a language rather than a domain.
The GF resource grammar library contains resource grammars for
10 languages, is described more closely in the following
documents:
- [Resource library API documentation ../../lib/resource/doc/gf-resource.html]:
  for application grammarians using the resource.
- [Resource writing HOWTO ../../lib/resource-1.0/doc/Resource-HOWTO.html]:
  for resource grammarians developing the resource.


However, to give a flavour of both using and writing resource grammars,
we have created a miniature resource, which resides in the
subdirectory [``resource`` resource]. Its API consists of the following
three modules:

[Syntax resource/Syntax.gf] - syntactic structures, language-independent:
```

```
[LexEng resource/LexEng.gf] - lexical paradigms, English:
```

```
[LexIta resource/LexIta.gf] - lexical paradigms, Italian:
```

```


Only these three modules should be ``open``ed in applications.
The implementations of the resource are given in the following four modules:

[MorphoEng resource/MorphoEng.gf],
```

```
[MorphoIta resource/MorphoIta.gf]: low-level morphology
- [SyntaxEng resource/SyntaxEng.gf].
  [SyntaxIta resource/SyntaxIta.gf]: definitions of syntactic structures


An example use of the resource resides in the
subdirectory [``applications`` applications].
It implements the abstract syntax 
[``FoodComments`` applications/FoodComments.gf] for English and Italian.
The following diagram shows the module structure, indicating by
colours which modules are written by the grammarian. The two blue modules
form the abstract syntax. The three red modules form the concrete syntax.
The two green modules are trivial instantiations of a functor.
The rest of the modules (black) come from the resource.

[Multi.png]



===Restricted inheritance and qualified opening===



==Transfer modules==

Transfer means noncompositional tree-transforming operations.
The command ``apply_transfer = at`` is typically used in a pipe:
```
  > p "John walks and John runs" | apply_transfer aggregate | l
  John walks and runs
```
See the
[sources ../../transfer/examples/aggregation] of this example.

See the
[transfer language documentation  ../transfer.html]
for more information.


==Practical issues==


===Lexers and unlexers===

Lexers and unlexers can be chosen from
a list of predefined ones, using the flags``-lexer`` and `` -unlexer`` either
in the grammar file or on the GF command line.

Given by ``help -lexer``, ``help -unlexer``:
```
    The default is words.
    -lexer=words         tokens are separated by spaces or newlines
    -lexer=literals      like words, but GF integer and string literals recognized
    -lexer=vars          like words, but "x","x_...","$...$" as vars, "?..." as meta
    -lexer=chars         each character is a token
    -lexer=code          use Haskell's lex
    -lexer=codevars      like code, but treat unknown words as variables, ?? as meta
    -lexer=text          with conventions on punctuation and capital letters
    -lexer=codelit       like code, but treat unknown words as string literals
    -lexer=textlit       like text, but treat unknown words as string literals
    -lexer=codeC         use a C-like lexer
    -lexer=ignore        like literals, but ignore unknown words
    -lexer=subseqs       like ignore, but then try all subsequences from longest

    The default is unwords.
    -unlexer=unwords     space-separated token list (like unwords)
    -unlexer=text        format as text: punctuation, capitals, paragraph <p>
    -unlexer=code        format as code (spacing, indentation)
    -unlexer=textlit     like text, but remove string literal quotes
    -unlexer=codelit     like code, but remove string literal quotes
    -unlexer=concat      remove all spaces
    -unlexer=bind        like identity, but bind at "&+"

```


===Efficiency of grammars===

Issues:

- the choice of datastructures in ``lincat``s
- the value of the ``optimize`` flag 
- parsing efficiency: ``-mcfg`` vs. others


===Speech input and output===

The``speak_aloud = sa`` command sends a string to the speech
synthesizer 
[Flite http://www.speech.cs.cmu.edu/flite/doc/].
It is typically used via a pipe:
```  generate_random | linearize | speak_aloud
The result is only satisfactory for English.

The ``speech_input = si`` command receives a string from a
speech recognizer that requires the installation of
[ATK http://mi.eng.cam.ac.uk/~sjy/software.htm].
It is typically used to pipe input to a parser:
```  speech_input -tr | parse
The method words only for grammars of English.

Both Flite and ATK are freely available through the links
above, but they are not distributed together with GF.




===Multilingual syntax editor===

The 
[Editor User Manual http://www.cs.chalmers.se/~aarne/GF2.0/doc/javaGUImanual/javaGUImanual.htm]
describes the use of the editor, which works for any multilingual GF grammar.

Here is a snapshot of the editor:

[../quick-editor.gif]
 
The grammars of the snapshot are from the
[Letter grammar package http://www.cs.chalmers.se/~aarne/GF/examples/letter].



===Interactive Development Environment (IDE)===

Forthcoming.


===Communicating with GF===

Other processes can communicate with the GF command interpreter,
and also with the GF syntax editor. Useful flags when invoking GF are
- ``-batch`` suppresses the promps and structures the communication with XML tags.
- ``-s`` suppresses non-output non-error messages and XML tags.
-- ``-nocpu`` suppresses CPU time indication.

Thus the most silent way to invoke GF is
```
  gf -batch -s -nocpu
```



===Embedded grammars in Haskell, Java, and Prolog===

GF grammars can be used as parts of programs written in the
following languages. The links give more documentation.

- [Java http://www.cs.chalmers.se/~bringert/gf/gf-java.html]
- [Haskell http://www.cs.chalmers.se/~aarne/GF/src/GF/Embed/EmbedAPI.hs]
- [Prolog http://www.cs.chalmers.se/~peb/software.html]


===Alternative input and output grammar formats===

A summary is given in the following chart of GF grammar compiler phases:
[../gf-compiler.png]


==Case studies==

===Interfacing formal and natural languages===

[Formal and Informal Software Specifications http://www.cs.chalmers.se/~krijo/thesis/thesisA4.pdf],
PhD Thesis by
[Kristofer Johannisson http://www.cs.chalmers.se/~krijo], is an extensive example of this.
The system is based on a multilingual grammar relating the formal language OCL with
English and German.

A simpler example will be explained here.

