# Grammatical Framework Tutorial

Author: Aarne Ranta <aarne (at) cs.chalmers.se>
Last update: Mon Dec 19 17:31:35 2005

- Introduction
  - GF = Grammatical Framework
  - What are GF grammars used for
  - Who is this tutorial for
  - The coverage of the tutorial
  - Getting the GF program
- The .cf grammar format
  - Importing grammars and parsing strings
  - Generating trees and strings
  - Visualizing trees
  - Some random-generated sentences
  - Systematic generation
  - More on pipes; tracing
  - Writing and reading files
  - Labelled context-free grammars
  - The labelled context-free format
- The ``.gf`` grammar format
  - Abstract and concrete syntax
  - Judgement forms
  - Module types
  - Record types, records, and ``Str``s
  - An abstract syntax example
  - A concrete syntax example
  - Modules and files
- Multilingual grammars and translation
  - An Italian concrete syntax
  - Using a multilingual grammar
  - Translation session
  - Translation quiz
- Grammar architecture
  - Extending a grammar
  - Multiple inheritance
  - Visualizing module structure
- System commands
- Resource modules
  - The golden rule of functional programming
  - Operation definitions
  - The ``resource`` module type
  - Opening a ``resource``
  - Division of labour
- Morphology
  - Parameters and tables
  - Inflection tables, paradigms, and ``oper`` definitions
  - Worst-case macros and data abstraction
  - A system of paradigms using ``Prelude`` operations
  - An intelligent noun paradigm using ``case`` expressions
  - Pattern matching
  - Morphological ``resource`` modules
  - Testing ``resource`` modules
- Using morphology in concrete syntax
  - Parametric vs. inherent features, agreement
  - English concrete syntax with parameters
  - Hierarchic parameter types
  - Morphological analysis and morphology quiz
  - Discontinuous constituents
- More constructs for concrete syntax
  - Local definitions
  - Free variation
  - Record extension and subtyping
  - Tuples and product types
  - Prefix-dependent choices
  - Predefined types and operations
- More features of the module system
  - Resource grammars and their reuse
  - Interfaces, instances, and functors
  - Restricted inheritance and qualified opening
- More concepts of abstract syntax
  - Dependent types
  - Higher-order abstract syntax
  - Semantic definitions
- Transfer modules
- Practical issues
  - Lexers and unlexers
  - Efficiency of grammars
  - Speech input and output
  - Multilingual syntax editor
  - Interactive Development Environment (IDE)
  - Communicating with GF
  - Embedded grammars in Haskell, Java, and Prolog
  - Alternative input and output grammar formats
- Case studies
  - Interfacing formal and natural languages

## 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:: a natural-language interface to a proof editor (languages: English, French, Swedish)
- KeY: a multilingual authoring system for creating software specifications (languages: OCL, English, German)
- TALK: multilingual and multimodal dialogue systems
- WebALT: a multilingual translator of mathematical exercises (languages: Catalan, English, Finnish, French, Spanish, Swedish)
- Numeral translator: 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.

### 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` 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 the words contained in a BNF grammar to another language, proper translation usually involves more, e.g. changing the word order in

      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, the tutorial will explain the main programming concepts involved. 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`

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

### 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 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

        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 `paleolithic.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)

## 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 EBNF and CF formats fuse 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 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"}

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 buid 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

## 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 the `help` to see what other formats are available:

        > help pm
        > help -printer

## Resource modules

### The golden rule of functional programming

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

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

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

A function separates the shared parts of different computations from the changing parts, parameters. In functional programming languages, such as Haskell, it is possible to share muc more than in the languages such as C and Java.

### Operation definitions

GF is a functional programming language, not only in the sense that the abstract syntax is a system of functions (`fun`), but also because functional programming can be used to define concrete syntax. This is done by using a new form of judgement, with the keyword `oper` (for operation), distinct from `fun` for the sake of clarity. Here is a simple example of an operation:

        oper ss : Str -> {s : Str} = \x -> {s = x} ;

The operation can be applied to an argument, and GF will compute the application into a value. For instance,

        ss "boy"  --->  {s = "boy"}

(We use the symbol `--->` to indicate how an expression is computed into a value; this symbol is not a part of GF)

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

### The ``resource`` module type

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

The `resource` module type can be used to package `oper` definitions into reusable resources. Here is an example, with a handful of operations to manipulate strings and records.

        resource StringOper = {
          oper
            SS : Type = {s : Str} ;

            ss : Str -> SS = \x -> {s = x} ;

            cc : SS -> SS -> SS = \x,y -> ss (x.s ++ y.s) ;

            prefix : Str -> SS -> SS = \p,x -> ss (p ++ x.s) ;
        }

Resource modules can extend other resource modules, in the same way as modules of other types can extend modules of the same type. Thus it is possible to build resource hierarchies.

### Opening a ``resource``

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

        Cheese.s ! 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 - a string also known as a dictionary form - and returns an inflection table of desired type. Paradigms are not functions in the sense of the `fun` judgements of abstract syntax (which operate on trees and not on strings), but operations defined in `oper` judgements. The following operation defines the regular noun paradigm of English:

        oper regNoun : Str -> {s : Number => Str} = \x -> {
          s = table {
            Sg => x ;
            Pl => x + "s"
            }
          } ;

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

### A system of paradigms using ``Prelude`` operations

In addition to the completely regular noun paradigm `regNoun`, some other frequent noun paradigms deserve to be defined, for instance,

        sNoun : Str -> Noun = \kiss  -> mkNoun kiss  (kiss  + "es") ;

What about nouns like fly, with the plural flies? The already available solution is to use the longest common prefix fl (also known as the technical stem) as argument, and define

        yNoun : Str -> Noun = \fl -> mkNoun (fl  + "y") (fl  + "ies") ;

But this paradigm would be very unintuitive to use, because the technical stem is not an existing form of the word. A better solution is to use the lemma and a string operator `init`, which returns the initial segment (i.e. all characters but the last) of a string:

        yNoun : Str -> Noun = \fly -> mkNoun fly (init fly  + "ies") ;

The operator `init` belongs to a set of operations in the resource module `Prelude`, which therefore has to be `open`ed so that `init` can be used.

### An intelligent noun paradigm using ``case`` expressions

It may be hard for the user of a resource morphology to pick the right inflection paradigm. A way to help this is to define a more intelligent paradigm, which chooses the ending by first analysing the lemma. The following variant for English regular nouns puts together all the previously shown paradigms, and chooses one of them on the basis of the final letter of the lemma (found by the prelude operator `last`).

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

This definition displays many GF expression forms not shown befores; these forms are explained in the next section.

The paradigms `regNoun` does not give the correct forms for all nouns. For instance, 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`.

        --# -path=.:prelude

        resource MorphoEng = open Prelude in {

          param
            Number = Sg | Pl ;

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

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

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

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

            regVerb : Str -> Verb = \s -> case last s of {
              "s" | "z" => mkVerb s (s + "es") ;
              "y"       => mkVerb s (init s + "ies") ;
              "o"       => mkVerb s (s + "es") ;
              _         => mkVerb s (s + "s")
              } ;
        }

The first line gives as a hint to the compiler the search path needed to find all the other modules that the module depends on. The directory `prelude` is a subdirectory of `GF/lib`; to be able to refer to it in this simple way, you can set the environment variable `GF_LIB_PATH` to point to this directory.

### Testing ``resource`` modules

To test a `resource` module independently, you can import it with a flag that tells GF to retain the `oper` definitions in the memory; the usual behaviour is that `oper` definitions are just applied to compile linearization rules (this is called inlining) and then thrown away.

       > i -retain MorphoEng.gf

The command `compute_concrete = cc` computes any expression formed by operations and other GF constructs. For example,

        > cc regVerb "echo"
        {s : Number => Str = table Number {
          Sg => "echoes" ;
          Pl => "echo"
          }
        }

The command `show_operations = so`` shows the type signatures of all operations returning a given value type:

        > so Verb
        MorphoEng.mkNoun : Str -> Str -> {s : {MorphoEng.Number} => Str}
        MorphoEng.mkVerb : Str -> Str -> {s : {MorphoEng.Number} => Str}
        MorphoEng.regNoun : Str -> {s : {MorphoEng.Number} => Str}
        MorphoEng.regVerb : Str -> { s : {MorphoEng.Number} => Str}

Why does the command also show the operations that form `Noun`s? The reason is that the type expression `Verb` is first computed, and its value happens to be the same as the value of `Noun`.

## Using morphology in concrete syntax

We can now enrich the concrete syntax definitions to comprise morphology. This will involve a more radical variation between languages (e.g. English and Italian) then just the use of different words. In general, parameters and linearization types are different in different languages - but this does not prevent the use of a common abstract syntax.

### Parametric vs. inherent features, agreement

The rule of subject-verb agreement in English says that the verb phrase must be inflected in the number of the subject. This means that a noun phrase (functioning as a subject), inherently has a number, which it passes to the verb. The verb does not have a number, but must be able to receive whatever number the subject has. This distinction is nicely represented by the different linearization types of noun phrases and verb phrases:

        lincat NP = {s : Str ; n : Number} ;
        lincat VP = {s : Number => Str} ;

We say that the number of `NP` is an inherent feature, whereas the number of `NP` is parametric.

The agreement rule itself is expressed in the linearization rule of the predication structure:

        lin PredVP np vp = {s = np.s ++ vp.s ! np.n} ;

The following section will present `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` and `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 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 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 = \platt -> table {
          ASg _ => platt ;
          APl   => platt + "a" ;
          }

### Morphological analysis and morphology quiz

Even though in GF morphology is mostly seen as an auxiliary of syntax, a morphology once defined can be used on its own right. The command `morpho_analyse = ma` can be used to read a text and return for each word the analyses that it has in the current concrete syntax.

        > rf bible.txt | morpho_analyse

In the same way as translation exercises, morphological exercises can be generated, by the command `morpho_quiz = mq`. Usually, the category is set to be something else than `S`. For instance,

        > i lib/resource/french/VerbsFre.gf
        > morpho_quiz -cat=V

        Welcome to GF Morphology Quiz.
        ...

        réapparaître : VFin VCondit  Pl  P2
        réapparaitriez
        > No, not réapparaitriez, but
        réapparaîtriez
        Score 0/1

Finally, a list of morphological exercises and save it in a file for later use, by the command `morpho_list = ml`

        > morpho_list -number=25 -cat=V

The `number` flag gives the number of exercises generated.

### Discontinuous constituents

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

The first of the following judgements defines transitive verbs as 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 ; part : Str} ;
        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. Moreover, the parsing and linearization commands only give reliable results for categories whose linearization type has a unique `Str` valued field labelled `s`.

## 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:

        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, even though `variants` admits lists of any type, its semantics for complex types can cause surprises.

### 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.

### Prefix-dependent choices

The 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

## More features of the module system

### Resource grammars and their reuse

See resource library documentation

### Interfaces, instances, and functors

See an example built this way

### Restricted inheritance and qualified opening

## More concepts of abstract syntax

### Dependent types

### Higher-order abstract syntax

### Semantic definitions

## 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 of this example.

See the transfer language documentation 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. 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. 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 describes the use of the editor, which works for any multilingual GF grammar.

Here is a snapshot of the editor:

The grammars of the snapshot are from the Letter grammar package.

### Interactive Development Environment (IDE)

Forthcoming.

### Communicating with GF

Other processes can communicate with the GF command interpreter, and also with the GF syntax editor.

### 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
- Haskell
- Prolog

### Alternative input and output grammar formats

A summary is given in the following chart of GF grammar compiler phases:

## Case studies

### Interfacing formal and natural languages

Formal and Informal Software Specifications, PhD Thesis by Kristofer Johannisson, 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.