# Grammatical Framework Tutorial

Author: Aarne Ranta <aarne (at) cs.chalmers.se>
Last update: Thu Dec 15 16:43:59 2005

- Grammatical Framework Tutorial
  - GF = Grammatical Framework
    - Getting the GF program
  - My first grammar
    - Importing grammars and parsing strings
    - Generating trees and strings
    - Some random-generated sentences
    - Systematic generation
    - More on pipes; tracing
    - Writing and reading files
    - Labelled context-free grammars
  - The GF grammar format
    - Abstract and concrete syntax
    - Resource modules
    - Opening a ``resource``
  - Topics still to be written

# Grammatical Framework Tutorial

3rd Edition, for GF version 2.2 or later

Aarne Ranta

`aarne@cs.chalmers.se`

## GF = Grammatical Framework

The term GF is used for different things:

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

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

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

### Getting the GF program

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

There you can download

- ready-made binaries for Linux, Solaris, Macintosh, and Windows
- source code and documentation
- grammar libraries and examples

If you want to compile GF from source, you need Haskell and Java compilers. But normally you don't have to compile, and you definitely don't need to know Haskell or Java to use GF.

To start the GF program, assuming you have installed it, just type

        gf

in the shell. You will see GF's welcome message and the prompt `>`.

## My first grammar

Now you are ready to try out your first grammar. We start with one that is not written in GF language, but in the EBNF notation (Extended Backus Naur Form), which GF can also understand. Type (or copy) the following lines in a file named `paleolithic.ebnf`:

        S   ::= NP VP ;
        VP  ::= V | TV NP | "is" A ;
        NP  ::= ("this" | "that" | "the" | "a") CN ;
        CN  ::= A CN ;
        CN  ::= "boy" | "louse" | "snake" | "worm" ;
        A   ::= "green" | "rotten" | "thick" | "warm" ;
        V   ::= "laughs" | "sleeps" | "swims" ;
        TV  ::= "eats" | "kills" | "washes" ;

### Importing grammars and parsing strings

The first GF command when using a grammar is to import it. The command has a long name, `import`, and a short name, `i`.

        import paleolithic.gf

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

You can use GF for parsing:

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

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

The `parse` (= `p`) command takes a string (in double quotes) and returns an abstract syntax tree - the thing with `Mks`s and parentheses. We will see soon how to make sense of the abstract syntax trees - now you should just notice that the tree is different for the two strings.

Strings that return a tree when parsed do so in virtue of the grammar you imported. Try parsing something else, and you fail

        > p "hello world"
        No success in cf parsing
        no tree found

### Generating trees and strings

You can also use GF for linearizing (`linearize = l`). This is the inverse of parsing, taking trees into strings:

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

What is the use of this? Typically not that you type in a tree at the GF prompt. The utility of linearization comes from the fact that you can obtain a tree from somewhere else. One way to do so is random generation (`generate_random = gr`):

        > generate_random
        Mks_0 (Mks_4 Mks_11) (Mks_3 Mks_15)

Now you can copy the tree and paste it to the `linearize command`. Or, more efficiently, feed random generation into parsing by using a pipe.

        > gr | l
        this worm is warm

### Some random-generated sentences

Random generation can be quite amusing. So you may want to generate ten strings with one and the same command:

        > gr -number=10 | l
        this boy is green
        a snake laughs
        the rotten boy is thick
        a boy washes this worm
        a boy is warm
        this green warm boy is rotten
        the green thick green louse is rotten
        that boy is green
        this thick thick boy laughs
        a boy is green

### Systematic generation

To generate <i>all<i> sentence that a grammar can generate, use the command `generate_trees = gt`.

        > generate_trees | l
        this louse laughs
        this louse sleeps
        this louse swims
        this louse is green
        this louse is rotten
        ...
        a boy is rotten
        a boy is thick
        a boy is warm

You get quite a few trees but not all of them: only up to a given depth of trees. To see how you can get more, use the `help = h` command,

        help gr

Quiz. If the command `gt` generated all trees in your grammar, it would never terminate. Why?

### More on pipes; tracing

A pipe of GF commands can have any length, but the "output type" (either string or tree) of one command must always match the "input type" of the next command.

The intermediate results in a pipe can be observed by putting the tracing flag `-tr` to each command whose output you want to see:

        > gr -tr | l -tr | p
        Mks_0 (Mks_7 Mks_10) (Mks_1 Mks_18)
        a louse sleeps
        Mks_0 (Mks_7 Mks_10) (Mks_1 Mks_18)

This facility is good for test purposes: for instance, you may want to see if a grammar is ambiguous, i.e. contains strings that can be parsed in more than one way.

### Writing and reading files

To save the outputs of GF commands into a file, you can pipe it to the `write_file = wf` command,

        > gr -number=10 | l | write_file exx.tmp

You can read the file back to GF with the `read_file = rf` command,

        > read_file exx.tmp | l -tr | p -lines

Notice the flag `-lines` given to the parsing command. This flag tells GF to parse each line of the file separately. Without the flag, the grammar could not recognize the string in the file, because it is not a sentence but a sequence of ten sentences.

### Labelled context-free grammars

The syntax trees returned by GF's parser in the previous examples are not so nice to look at. The identifiers of form `Mks` are labels of the EBNF rules. To see which label corresponds to which rule, you can use the `print_grammar = pg` command with the `printer` flag set to `cf` (which means context-free):

        > print_grammar -printer=cf
        Mks_10. CN ::= "louse" ;
        Mks_11. CN ::= "snake" ;
        Mks_12. CN ::= "worm" ;
        Mks_8.  CN ::= A CN ;
        Mks_9.  CN ::= "boy" ;
        Mks_4.  NP ::= "this" CN ;
        Mks_15. A  ::= "thick" ;
        ...

A syntax tree such as

        Mks_4 (Mks_8 Mks_15 Mks_12)
        this thick worm

encodes the sequence of grammar rules used for building the expression. If you look at this tree, you will notice that `Mks_4` is the label of the rule prefixing `this` to a common noun, `Mks_15` is the label of the adjective `thick`, and so on.

<h4>The labelled context-free format<h4>

The labelled context-free grammar format permits user-defined labels to each rule. GF recognizes files of this format by the suffix `.cf`. It is intermediate between EBNF and full GF format. Let us include the following rules in the file `paleolithic.cf`.

        PredVP.  S   ::= NP VP ;
        UseV.    VP  ::= V ;
        ComplTV. VP  ::= TV NP ;
        UseA.    VP  ::= "is" A ;
        This.    NP  ::= "this" CN ;
        That.    NP  ::= "that" CN ;
        Def.     NP  ::= "the" CN ;
        Indef.   NP  ::= "a" CN ;
        ModA.    CN  ::= A CN ;
        Boy.     CN  ::= "boy" ;
        Louse.   CN  ::= "louse" ;
        Snake.   CN  ::= "snake" ;
        Worm.    CN  ::= "worm" ;
        Green.   A   ::= "green" ;
        Rotten.  A   ::= "rotten" ;
        Thick.   A   ::= "thick" ;
        Warm.    A   ::= "warm" ;
        Laugh.   V   ::= "laughs" ;
        Sleep.   V   ::= "sleeps" ;
        Swim.    V   ::= "swims" ;
        Eat.     TV  ::= "eats" ;
        Kill.    TV  ::= "kills"
        Wash.    TV  ::= "washes" ;

<h4>Using the labelled context-free format<h4>

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

        > empty

        > i paleolithic.cf

        > p "the boy eats a snake"
        PredVP (Def Boy) (ComplTV Eat (Indef Snake))

        > gr -tr | l
        PredVP (Indef Louse) (UseA Thick)
        a louse is thick

## The GF grammar format

To see what there really is in GF's shell state when a grammar has been imported, you can give the plain command `print_grammar = pg`.

        > print_grammar

The output is quite unreadable at this stage, and you may feel happy that you did not need to write the grammar in that notation, but that the GF grammar compiler produced it.

However, we will now start to show how GF's own notation gives you much more expressive power than the `.cf` and `.ebnf` formats. We will introduce the `.gf` format by presenting one more way of defining the same grammar as in `paleolithic.cf` and `paleolithic.ebnf`. Then we will show how the full GF grammar format enables you to do things that are not possible in the weaker formats.

### Abstract and concrete syntax

A GF grammar consists of two main parts:

- abstract syntax, defining what syntax trees there are
- concrete syntax, defining how trees are linearized into strings

The EBNF and CF formats fuse these two things together, but it is possible to take them apart. For instance, the verb phrase predication rule

        PredVP. S ::= NP VP ;

is interpreted as the following pair of rules:

        fun PredVP : NP -> VP -> S ;
        lin PredVP x y = {s = x.s ++ y.s} ;

The former rule, with the keyword `fun`, belongs to the abstract syntax. It defines the function `PredVP` which constructs syntax trees of form (`PredVP` <i>x<i> <i>y<i>).

The latter rule, with the keyword `lin`, belongs to the concrete syntax. It defines the linearization function for syntax trees of form (`PredVP` <i>x<i> <i>y<i>).

<h4>Judgement forms<h4>

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 grammar `paleolithic.cf` is expressed by using modules and judgements.

<h4>Module types<h4>

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.

<h4>Record types, records, and `Str`s<h4>

The linearization type of a category is a record type, with zero of more fields of different types. The simplest record type used for linearization in GF is

        {s : Str}

which has one field, with label `s` and type `Str`.

Examples of records of this type are

        [s = "foo"}
        [s = "hello" ++ "world"}

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

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

<h4>An abstract syntax example<h4>

Each nonterminal occurring in the grammar `paleolithic.cf` is introduced by a `cat` judgement. Each rule label is introduced by a `fun` judgement.

      abstract Paleolithic = {
      cat
        S ; NP ; VP ; CN ; A ; V ; TV ;
      fun
        PredVP  : NP -> VP -> S ;
        UseV    : V -> VP ;
        ComplTV : TV -> NP -> VP ;
        UseA    : A -> VP ;
        ModA    : A -> CN -> CN ;
        This, That, Def, Indef : CN -> NP ;
        Boy, Louse, Snake, Worm : CN ;
        Green, Rotten, Thick, Warm : A ;
        Laugh, Sleep, Swim : V ;
        Eat, Kill, Wash : TV ;
      }

Notice the use of shorthands permitting the sharing of the keyword in subsequent judgements, and of the type in subsequent `fun` judgements.

<h4>A concrete syntax example<h4>

Each category introduced in `Paleolithic.gf` is given a `lincat` rule, and each function is given a `fun` rule. Similar shorthands apply as in `abstract` modules.

      concrete PaleolithicEng of Paleolithic = {
      lincat
        S, NP, VP, CN, A, V, TV = {s : Str} ;
      lin
        PredVP np vp  = {s = np.s ++ vp.s} ;
        UseV   v      = v ;
        ComplTV tv np = {s = tv.s ++ np.s} ;
        UseA   a   = {s = "is" ++ a.s} ;
        This  cn   = {s = "this" ++ cn.s} ;
        That  cn   = {s = "that" ++ cn.s} ;
        Def   cn   = {s = "the" ++ cn.s} ;
        Indef cn   = {s = "a" ++ cn.s} ;
        ModA  a cn = {s = a.s ++ cn.s} ;
        Boy    = {s = "boy"} ;
        Louse  = {s = "louse"} ;
        Snake  = {s = "snake"} ;
        Worm   = {s = "worm"} ;
        Green  = {s = "green"} ;
        Rotten = {s = "rotten"} ;
        Thick  = {s = "thick"} ;
        Warm   = {s = "warm"} ;
        Laugh  = {s = "laughs"} ;
        Sleep  = {s = "sleeps"} ;
        Swim   = {s = "swims"} ;
        Eat    = {s = "eats"} ;
        Kill   = {s = "kills"} ;
        Wash   = {s = "washes"} ;
      }

<h4>Modules and files<h4>

Module name + `.gf` = file name

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

Import `PaleolithicEng.gf` and try what happens

        > i PaleolithicEng.gf

The GF program does not only read the file `PaleolithicEng.gf`, but also all other files that it depends on - in this case, `Paleolithic.gf`.

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

<h4>Multilingual grammar<h4>

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

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

<h4>An Italian concrete syntax<h4>

      concrete PaleolithicIta of Paleolithic = {
      lincat
        S, NP, VP, CN, A, V, TV = {s : Str} ;
      lin
        PredVP np vp  = {s = np.s ++ vp.s} ;
        UseV   v      = v ;
        ComplTV tv np = {s = tv.s ++ np.s} ;
        UseA   a   = {s = "è" ++ a.s} ;
        This  cn   = {s = "questo" ++ cn.s} ;
        That  cn   = {s = "quello" ++ cn.s} ;
        Def   cn   = {s = "il" ++ cn.s} ;
        Indef cn   = {s = "un" ++ cn.s} ;
        ModA  a cn = {s = cn.s ++ a.s} ;
        Boy    = {s = "ragazzo"} ;
        Louse  = {s = "pidocchio"} ;
        Snake  = {s = "serpente"} ;
        Worm   = {s = "verme"} ;
        Green  = {s = "verde"} ;
        Rotten = {s = "marcio"} ;
        Thick  = {s = "grosso"} ;
        Warm   = {s = "caldo"} ;
        Laugh  = {s = "ride"} ;
        Sleep  = {s = "dorme"} ;
        Swim   = {s = "nuota"} ;
        Eat    = {s = "mangia"} ;
        Kill   = {s = "uccide"} ;
        Wash   = {s = "lava"} ;
      }

<h4>Using a multilingual grammar<h4>

Import without first emptying

        > i PaleolithicEng.gf
        > i PaleolithicIta.gf

Try generation now:

        > gr | l
        un pidocchio uccide questo ragazzo

        > gr | l -lang=PaleolithicEng
        that louse eats a louse

Translate by using a pipe:

        > p -lang=PaleolithicEng "the boy eats the snake" | l -lang=PaleolithicIta
        il ragazzo mangia il serpente

<h4>Translation quiz<h4>

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

        > translation_quiz PaleolithicEng PaleolithicIta

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

        a green boy washes the louse
        un ragazzo verde lava il gatto

        No, not un ragazzo verde lava il gatto, but
        un ragazzo verde lava il pidocchio
        Score 0/1

You can also generate a list of translation exercises and save it in a file for later use, by the command `translation_list = tl`

        > translation_list -number=25 PaleolithicEng PaleolithicIta

The number flag gives the number of sentences generated.

<h4>The multilingual shell state<h4>

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

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

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

<h4>Extending a grammar<h4>

The module system of GF makes it possible to extend a grammar in different ways. The syntax of extension is shown by the following example.

        abstract Neolithic = Paleolithic ** {
          fun
            Fire, Wheel : CN ;
            Think : V ;
        }

Parallel to the abstract syntax, extensions can be built for concrete syntaxes:

        concrete NeolithicEng of Neolithic = PaleolithicEng ** {
          lin
            Fire  = {s = "fire"} ;
            Wheel = {s = "wheel"} ;
            Think = {s = "thinks"} ;
        }

The effect of extension is that all of the contents of the extended and extending module are put together.

<h4>Multiple inheritance<h4>

Specialized vocabularies can be represented as small grammars that only do "one thing" each, e.g.

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

        abstract Mushrooms = {
          cat Mushroom ;
          fun Cep, Agaric : Mushroom ;
        }

They can afterwards be combined into bigger grammars by using multiple inheritance, i.e. extension of several grammars at the same time:

        abstract Gatherer = Paleolithic, Fish, Mushrooms ** {
          fun
            UseFish     : Fish     -> CN ;
            UseMushroom : Mushroom -> CN ;
          }

<h4>Visualizing module structure<h4>

When you have created all the abstract syntaxes and one set of concrete syntaxes needed for `Gatherer`, your grammar consists of eight GF modules. To see how their dependences look like, you can use the command `visualize_graph = vg`,

        > visualize_graph

and the graph will pop up in a separate window. It can also be printed out into a file, e.g. a `.gif` file that can be included in an HTML document

        > pm -printer=graph | wf Gatherer.dot
        > ! dot -Tgif Gatherer.dot > Gatherer.gif

The latter command is a Unix command, issued from GF by using the shell escape symbol `!`. The resulting graph is shown in the next section.

The command `print_multi = pm` is used for printing the current multilingual grammar in various formats, of which the format `-printer=graph` just shows the module dependencies.

<h4>The module structure of `GathererEng`<h4>

The graph uses

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

<img src="Gatherer.gif">

### Resource modules

Suppose we want to say, with the vocabulary included in `Paleolithic.gf`, things like

        the boy eats two snakes
        all boys sleep

The new grammatical facility we need are the plural forms of nouns and verbs (<i>boys, sleep<i>), as opposed to their singular forms.

The introduction of plural forms requires two things:

- to inflect nouns and verbs in singular and plural number
- to describe the agreement of the verb to subject: the rule that the verb must have the same number as the subject

Different languages have different rules of inflection and agreement. For instance, Italian has also agreement in gender (masculine vs. feminine). We want to express such special features of languages precisely in concrete syntax while ignoring them in abstract syntax.

To be able to do all this, we need two new judgement forms, a new module form, and a generalizarion of linearization types from strings to more complex types.

<h4>Parameters and tables<h4>

We define the parameter type of number in Englisn by using a new form of judgement:

        param Number = Sg | Pl ;

To express that nouns in English have a linearization depending on number, we replace the linearization type `{s : Str}` with a type where the `s` field is a table depending on number:

        lincat CN = {s : Number => Str} ;

The table type `Number => Str` is in many respects similar to a function type (`Number -> Str`). The main restriction is that the argument type of a table type must always be a parameter type. This means that the argument-value pairs can be listed in a finite table. The following example shows such a table:

        lin Boy = {s = table {
          Sg => "boy" ;
          Pl => "boys"
          }
        } ;

The application of a table to a parameter is done by the selection operator `!`. For instance,

        Boy.s ! Pl

is a selection, whose value is `"boys"`.

<h4>Inflection tables, paradigms, and `oper` definitions<h4>

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 <i>s<i>. This rule is an example of a paradigm - a formula telling how the inflection forms of a word are formed.

From GF point of view, a paradigm is a function that takes a lemma - a string also known as a dictionary form - and returns an inflection table of desired type. Paradigms are not functions in the sense of the `fun` judgements of abstract syntax (which operate on trees and not on strings). Thus we call them operations for the sake of clarity, introduce one one form of judgement, with the keyword `oper`. As an example, the following operation defines the regular noun paradigm of English:

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

Thus an `oper` judgement includes the name of the defined operation, its type, and an expression defining it. As for the syntax of the defining expression, notice the lambda abstraction form `\x -> t` of the function, and the glueing operator `+` telling that the string held in the variable `x` and the ending `"s"` are written together to form one token.

<h4>The `resource` module type<h4>

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

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

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

Resource modules can extend other resource modules, in the same way as modules of other types can extend modules of the same type.

### Opening a ``resource``

Any number of `resource` modules can be opened in a `concrete` syntax, which makes the parameter and operation definitions contained in the resource usable in the concrete syntax. Here is an example, where the resource `MorphoEng` is open in (the fragment of) a new version of `PaleolithicEng`.

      concrete PaleolithicEng of Paleolithic = open MorphoEng in {
        lincat
          CN = Noun ;
        lin
          Boy   = regNoun "boy" ;
          Snake = regNoun "snake" ;
          Worm  = regNoun "worm" ;
        }

Notice that, just like in abstract syntax, function application is written by juxtaposition of the function and the argument.

Using operations defined in resource modules is clearly a concise way of giving e.g. inflection tables and other repeated patterns of expression. In addition, it enables a new kind of modularity and division of labour in grammar writing: grammarians familiar with the linguistic details of a language can put this knowledge available through resource grammars, whose users only need to pick the right operations and not to know their implementation details.

<h4>Worst-case macros and data abstraction<h4>

Some English nouns, such as `louse`, are so irregular that it makes little sense to see them as instances of a paradigm. Even then, it is useful to perform data abstraction from the definition of the type `Noun`, and introduce a constructor operation, a worst-case macro for nouns:

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

Thus we define

        lin Louse = mkNoun "louse" "lice" ;

instead of writing the inflection table explicitly.

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

<h4>A system of paradigms using `Prelude` operations<h4>

The regular noun paradigm `regNoun` can - and should - of course be defined by the worst-case macro `mkNoun`. In addition, some more noun paradigms could be defined, for instance,

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

What about nouns like <i>fly<i>, with the plural <i>flies<i>? The already available solution is to use the so-called "technical stem" <i>fl<i> as argument, and define

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

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

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

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

<h4>An intelligent noun paradigm using `case` expressions<h4>

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

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

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

The paradigms `regNoun` does not give the correct forms for all nouns. For instance, <i>louse - lice<i> and <i>fish - fish<i> must be given by using `mkNoun`. Also the word <i>boy<i> 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.

<h4>Pattern matching<h4>

Expressions of the `table` form are built from lists of argument-value pairs. These pairs are called the branches of the table. In addition to constants introduced in `param` definitions, the left-hand side of a branch can more generally be a pattern, and the computation of selection is then performed by pattern matching:

- a variable pattern (identifier other than constant parameter) matches anything
- the wild card `_` matches anything
- a string literal pattern, e.g. `"s"`, matches the same string
- a disjunctive pattern `P | ... | Q` matches anything that one of the disjuncts matches

Pattern matching is performed in the order in which the branches appear in the table.

As syntactic sugar, one-branch tables can be written concisely,

        \\P,...,Q => t  ===  table {P => ... table {Q => t} ...}

Finally, the `case` expressions common in functional programming languages are syntactic sugar for table selections:

        case e of {...} ===  table {...} ! e

<h4>Morphological analysis and morphology quiz<h4>

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

        > rf bible.txt | morpho_analyse

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

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

        Welcome to GF Morphology Quiz.
        ...

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

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

        > morpho_list -number=25 -cat=V

The number flag gives the number of exercises generated.

<h4>Parametric vs. inherent features, agreement<h4>

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

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

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

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

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

The following page will present a new version of `PaleolithingEng`, assuming an abstract syntax xextended with `All` and `Two`. It also assumes that `MorphoEng` has a paradigm `regVerb` for regular verbs (which need only be regular only in the present tensse). The reader is invited to inspect the way in which agreement works in the formation of noun phrases and verb phrases.

<h4>English concrete syntax with parameters<h4>

      concrete PaleolithicEng of Paleolithic = open MorphoEng in {
      lincat
        S, A          = {s : Str} ;
        VP, CN, V, TV = {s : Number => Str} ;
        NP            = {s : Str ; n : Number} ;
      lin
        PredVP np vp  = {s = np.s ++ vp.s ! np.n} ;
        UseV   v      = v ;
        ComplTV tv np = {s = \\n => tv.s ! n ++ np.s} ;
        UseA   a   = {s = \\n => case n of {Sg => "is" ; Pl => "are"} ++ a.s} ;
        This  cn   = {s = "this" ++ cn.s ! Sg } ;
        Indef cn   = {s = "a" ++ cn.s ! Sg} ;
        All   cn   = {s = "all" ++ cn.s ! Pl} ;
        Two   cn   = {s = "two" ++ cn.s ! Pl} ;
        ModA  a cn = {s = \\n => a.s ++ cn.s ! n} ;
        Louse  = mkNoun "louse" "lice" ;
        Snake  = regNoun "snake" ;
        Green  = {s = "green"} ;
        Warm   = {s = "warm"} ;
        Laugh  = regVerb "laugh" ;
        Sleep  = regVerb "sleep" ;
        Kill   = regVerb "kill" ;
      }

<h4>Hierarchic parameter types<h4>

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

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

To give an example, Swedish adjectives are inflected in number (singular or plural) and gender (uter or neuter). These parameters would suggest 2*2=4 different forms. However, the gender distinction is done only in the singular. Therefore, it would be inaccurate to define adjective paradigms using the type `Gender => Number => Str`. The following hierarchic definition yields an accurate system of three adjectival forms.

        param AdjForm = ASg Gender | APl ;
        param Gender  = Uter | Neuter ;

In pattern matching, a constructor can have patterns as arguments. For instance, the adjectival paradigm in which the two singular forms are the same, can be defined

        oper plattAdj : Str -> AdjForm => Str = \x -> table {
          ASg _ => x ;
          APl   => x + "a" ;
          }

<h4>Discontinuous constituents<h4>

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

The first of the following judgements defines transitive verbs as a discontinuous constituents, i.e. as having a linearization type with two strings and not just one. The second judgement shows how the constituents are separated by the object in complementization.

        lincat TV = {s : Number => Str ; s2 : Str} ;
        lin ComplTV tv obj = {s = \\n => tv.s ! n ++ obj.s ++ tv.s2} ;

GF currently requires that all fields in linearization records that have a table with value type `Str` have as labels either `s` or `s` with an integer index.

## Topics still to be written

Free variation

Record extension, tuples

Predefined types and operations

Lexers and unlexers

Grammars of formal languages

Resource grammars and their reuse

Embedded grammars in Haskell and Java

Dependent types, variable bindings, semantic definitions

Transfer rules

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