The Module System of GF

8/4/2005

Aarne Ranta

A GF grammar consists of a set of modules, which can be combined in different ways to build different grammars. There are several different types of modules: We will go through the module types in this order, which is also their order of "importance" from the most frequently used to the more esoteric/advanced ones.

This document is meant as an appendix to the GF tutorial, and presupposes knowledge of GF judgements and expressions. It aims just to tell what module system adds to the old functionality; some information is repeated to give understanding on how the module system related to the already familiar uses of GF grammars.

Abstract syntax

Any GF grammar that is used in an application will probably contain at least one module of the abstract module type. Here is an example of such a module, defining a fragment of propositional logic. 
  abstract Logic = {
    cat Prop ;
    fun Conj : Prop -> Prop -> Prop ;
    fun Disj : Prop -> Prop -> Prop ;
    fun Impl : Prop -> Prop -> Prop ;
    fun Falsum : Prop ;
    }
The name of this module is Logic.

An abstract module defines an abstract syntax, which is a language-independent representation of a fragment of language. It consists of two kinds of judgements:

There can also be def and data judgements in an abstract syntax.

Compilation of abstract syntax

The GF grammar compiler expects to find the module Logic in a file named Logic.gf. When the compiler is run, it produces another file, named Logic.gfc. This file is in the format called canonical GF, which is the "machine language" of GF. Next time that the module Logic is needed in compiling a grammar, it can be read from the compiled (gfc) file instead of the source (gf) file, unless the source has been changed after the compilation.

Concrete syntax

In order for a GF grammar to describe a concrete language, the abstract syntax must be completed with a concrete syntax of it. For this purpose, we use modules of type concrete: for instance, 
  concrete LogicEng of Logic = {
    lincat Prop = {s : Str} ;
    lin Conj a b = {s = a.s ++ "and" ++ b.s} ;
    lin Disj a b = {s = a.s ++ "or"  ++ b.s} ;
    lin Impl a b = {s = "if" ++ a.s ++ "then"  ++ b.s} ;
    lin Falsum = {s = ["we have a contradiction"]} ;
    }
The module LogicEng is a concrete syntax of the abstract syntax Logic. The GF grammar compiler checks that the concrete is valid with respect to the abstract syntax of which it is claimed to be. The validity requires that there has to be Validity also requires that the linearization functions defined by lin judgements are type-correct with respect to the linearization types of the arguments and value of the function.

There can also be lindef and printname judgements in a concrete syntax.

Top-level grammar

When a concrete module is successfully compiled, a gfc file is produced in the same way as for abstract modules. The pair of an abstract and a corresponding concrete module is a top-level grammar, which can be used in the GF system to perform various tasks. The most fundamental tasks are In the current grammar, infinitely many trees and strings are recognized, although no very interesting ones. For example, the tree 
  Impl (Disj Falsum Falsum) Falsum
has the linearization 
  if we have a contradiction or we have a contradiction then we have a contradiction
which in turn can be parsed uniquely as that tree.

Compiling top-level grammars

When GF compiles the module LogicEng it also has to compile all modules that it depends on (in this case, just Logic). The compilation process starts with dependency analysis to find all these modules, recursively, starting from the explicitly imported one. The compiler then reads either gf or gfc files, in a dependency order. The decision on which files to read depends on time stamps and dependencies in a natural way, so that all and only those modules that have to be compiled are compiled. (This behaviour can be changed with flags, see below.)

Using top-level grammars

To use a top-level grammar in the GF system, one uses the import command (short name i). For instance, 
  i LogicEng.gf
It is also possible to specify the imported grammar(s) on the command line when invoking GF: 
  gf LogicEng.gf
Various compilation flags can be added to both ways of compiling a module: Importing a grammar makes it visible in GF's internal state. To see what modules are available, use the command print_options (po). You can empty the state with the command empty (e); this is needed if you want to read in grammars with a different abstract syntax than the current one without exiting GF.

Grammar modules can reside in different directories. They can then be found by means of a search path, which is a flag such as 

  -path=.:../prelude
given to the import command or the shell command invoking GF. (It can also be defined in the grammar file; see below.) The compiler writes every gfc file in the same directory as the corresponding gf file.

Parsing and linearization can be performed with the parse (p) and linearize (l) commands, respectively. For instance, 

  > l Impl (Disj Falsum Falsum) Falsum
   if we have a contradiction or we have a contradiction then we have a contradiction

  > p -cat=Prop "we have a contradiction"
  Falsum
Notice that the parse command needs the parsing category as a flag. This necessary since a grammar can have several possible parsing categories ("entry points").

Multilingual grammar

One abstract syntax can have several concrete syntaxes. Here are two new ones for Logic: 
  concrete LogicFre of Logic = {
    lincat Prop = {s : Str} ;
    lin Conj a b = {s = a.s ++ "et" ++ b.s} ;
    lin Disj a b = {s = a.s ++ "ou"  ++ b.s} ;
    lin Impl a b = {s = "si" ++ a.s ++ "alors"  ++ b.s} ;
    lin Falsum = {s = ["nous avons une contradiction"]} ;
    }

  concrete LogicSymb of Logic = {
    lincat Prop = {s : Str} ;
    lin Conj a b = {s = "(" ++ a.s ++ "&" ++ b.s ++ ")"} ;
    lin Disj a b = {s = "(" ++ a.s ++ "v" ++ b.s ++ ")"} ;
    lin Impl a b = {s = "(" ++ a.s ++ "->" ++ b.s ++ ")"} ;
    lin Falsum = {s = "_|_"} ;
    }
The four modules Logic, LogicEng, LogicFre, and LogicSymb together form a multilingual grammar, in which it is possible to perform parsing and linearization with respect to any of the concrete syntaxes. As a combination of parsing and linearization, one can also perform translation from one language to another. (By language we mean the set of expressions generated by one concrete syntax.)

Using multilingual grammars

Any combination of abstract syntax and corresponding concrete syntaxes is thus a multilingual grammar. With many languages and other enrichments (as described below), a multilingual grammar easily grows to the size of tens of modules. The grammar developer, having finished her job, can package the result in a multilingual canonical grammar, a file with the suffix .gfcm. For instance, to compile the set of grammars described by now, the following sequence of GF commands can be used: 
  i LogicEng.gf
  i LogicFre.gf
  i LogicSymb.gf
  pm | wf logic.gfcm
The "end user" of the grammar only needs the file logic.gfcm to access all the functionality of the multilingual grammar. It can be imported in the GF system in the same way as .gf files. But it can also be used in the Embedded Java Interpreter for GF to build Java programs of which the multilingual grammar functionalities (linearization, parsing, translation) form a part.

In a multilingual grammar, the concrete syntax module names work as names of languages that can be selected for linearization and parsing: 

  > l -lang=LogicFre Impl Falsum Falsum
  si nous avons une contradiction alors nous avons une contradiction

  > l -lang=LogicSymb Impl Falsum Falsum
  ( _|_ -> _|_ )

  > p -cat=Prop -lang=LogicSymb "( _|_ & _|_ )"
  Conj Falsum Falsum
The option -multi gives linearization to all languages: 
  > l -multi Impl Falsum Falsum
  if we have a contradiction then we have a contradiction
  si nous avons une contradiction alors nous avons une contradiction
  ( _|_ -> _|_ )
Translation can be obtained by using a pipe from a parser to a linearizer: 
  > p -cat=Prop -lang=LogicSymb "( _|_ & _|_ )" | l -lang=LogicEng
  if we have a contradiction then we have a contradiction

Exercise

Write yet another concrete syntax of Logic, for a language or symbolic notation of your choice.

Resource modules

The concrete modules shown above would look much nicer if we used the main idea of functional programming: avoid repetitive code by using functions that capture repeated patterns of expressions. A collection of such functions can be a valuable resource for a programmer, reusable in many different top-level grammars. Thus we introduce the resource module type, with the first example 
  resource Util = {
    oper SS : Type = {s : Str} ;
    oper ss : Str -> SS = \s -> {s = s} ;
    oper paren : Str -> Str = \s -> "(" ++ s ++ ")" ;
    oper infix : Str -> SS -> SS -> SS = \h,x,y ->
      ss (x.s ++ h ++ y.s) ;
    oper infixp : Str -> SS -> SS -> SS = \h,x,y ->
      ss (paren (infix h x y)) ;
    }
Modules of resource type have two forms of judgement: A resource can be used in a concrete (or another resource) by opening it. This means that all operations (and parameter types) defined in the resource module become usable in module that opens it. For instance, we can rewrite the module LogicSymb much more concisely: 
  concrete LogicSymb of Logic = open Util in {
    lincat Prop = SS ;
    lin Conj = infixp "&" ;
    lin Disj = infixp "v" ;
    lin Impl = infixp "->" ;
    lin Falsum = ss "_|_" ;
    }
What happens when this variant of LogicSymb is compiled is that the oper-defined constants of Util are inlined in the right-hand-sides of the judgements of LogicSymb, and these expressions are partially evaluated, i.e. computed as far as possible. The generated gfc file will look just like the file generated for the first version of LogicSymb - at least, it will do the same job.

Several resource modules can be opened at the same time. If the modules contain same names, the conflict can be resolved by qualified opening and reference. For instance, 

  concrete LogicSymb of Logic = open Util, Prelude in { ...
    } ;
(where Prelude is a standard library of GF) brings into scope two definitions of the constant SS. To specify which one is used, you can write Util.SS or Prelude.SS instead of just SS. You can also introduce abbreviations to avoid long qualifiers, e.g. 
  concrete LogicSymb of Logic = open (U=Util), (P=Prelude) in { ...
    } ;
which means that you can write U.SS and P.SS.

Compiling resource modules

The compilation of a resource module differs from the compilation of abstract and concrete modules because oper operations do not in general have values in gfc. A gfc file is generated, but it contains only param judgements (also recall that opers are inlined in their top-level use sites, so it is not necessary to save them in the compiled grammar). However, since computing the operations over and over again can be time comsuming, and since type checking resource modules also takes time, a third kind of file is generated for resource modules: a .gfr file. This file is written in the GF source code notation, but it is type checked and type annotated, and opers are computed as far as possible.

If you look at any gfc or gfr file generated by the GF compiler, you see that all names have been replaced by their qualified variants. This is an important first step (after parsing) the compiler does. As for the commands in the GF shell, some output qualified names and some not. The difference does not always result from firm principles.

Using resource modules

The typical use is through open in a concrete module, which means that resource modules are not imported on their own. However, when developing and testing phase of grammars, it can be useful to evaluate opers with different arguments. To prevent them from being inlined away, the -retain option can be used: 
  > i -retain Util.gf
The command compute_concrete (cc) can now be used for evaluating expressions that may concain operations defined in Util: 
  > cc ss (paren "foo")
  {s = "(" ++ "foo" ++ ")"}
To find out, what opers are available for a given type, the command show_operations (so) can be used: 
  > so SS
  Util.ss : Str -> SS ;
  Util.infix : Str -> SS -> SS -> SS ;
  Util.infixp : Str -> SS -> SS -> SS ;

Exercise

Rewrite the modules LogicEng and LogicFre by making use of the resource.

Inheritance

The most characteristic modularity of GF lies in the division of grammars into abstract, concrete, and resource modules. This permits writing multilingual grammar and sharing the maximum of code between different languages.

In addition to its special modularity, GF provides inheritance, which is familiar from other programming languages (in particular, object-oriented ones). Inheritance means that a module inherits all judgements from another module; we also say that it extends the other module. Inheritance is useful to divide big grammars into smaller units, and also to reuse the same units in different bigger grammars.

The first example of inheritance is for abstract syntax. Let us extend the module Logic to Arithmetic: 

  abstract Arithmetic = Logic ** {
    cat Nat ;
    fun Even : Nat -> Prop ;
    fun Odd  : Nat -> Prop ;
    fun Zero : Nat ;
    fun Succ : Nat -> Nat ;
    }
In parallel with the extension of the abstract syntax Logic to Arithmetic, we can extend the concrete syntax LogicEng to ArithmeticEng: 
  concrete ArithmeticEng of Arithmetic = LogicEng ** open Util in {
    lincat Nat = SS ;
    lin Even x = ss (x.s ++ "is" ++ "even") ;
    lin Odd x = ss (x.s ++ "is" ++ "odd") ;
    lin Zero = ss "zero" ;
    lin Succ x = ss ("the" ++ "successor" ++ "of" ++ x.s) ;
    }
Another extension of Logic is Geometry, 
  abstract Geometry = Logic ** {
    cat Point ;
    cat Line ;
    fun Incident : Point -> Line -> Prop ;
    }
The corresponding concrete syntax is left as exercise.

Inheritance can be multiple, which means that a module may extend many modules at the same time. Suppose, for instance, that we want to build a module for mathematics covering both arithmetic and geometry, and the underlying logic. We then write 

  abstract Mathematics = Arithmetic, Geometry ** {
    } ;
We could of course add some new judgements in this module, but it is not necessary to do so.

The module Mathematics also shows that it is possibe to extend a module already built by extension. The correctness criterion for extensions is that the same name (cat, fun, oper, or param) may not be defined twice in the resulting union of names. That the names defined in Logic are "inherited twice" by Mathematics (via both Arithmetic and Geometry) is no violation of this rule; the usual problems of multiple inheritance do not arise, since the definitions of inherited constants cannot be changed.

Compiling inheritance

Inherited judgements are not copied into the inheriting modules. Instead, an indirection is created for each inherited name, as can be seen by looking into the generated gfc (and gfr) files. Thus for instance the names 
  Mathematics.Prop  Arithmetic.Prop  Logic.Prop
                    Geometry.Prop
all refer to the same category, declared in the module Logic.

Inspecting grammar hierarchies

The command visualize_graph (vg) shows the dependency graph in the current GF shell state. The graph can also be saved in a file and used e.g. in documentation.

Reuse of top-level grammars as resources

Interfaces, instances, and incomplete grammars

Transfer modules