# The GFCC Grammar Format

Aarne Ranta
October 5, 2007

Author's address: `http://www.cs.chalmers.se/~aarne`

History:

- 5 Oct 2007: new, better structured GFCC with full expressive power
- 19 Oct: translation of lincats, new figures on C++
- 3 Oct 2006: first version

## What is GFCC

GFCC is a low-level format for GF grammars. Its aim is to contain the minimum that is needed to process GF grammars at runtime. This minimality has three advantages:

- compact grammar files and run-time objects
- time and space efficient processing
- simple definition of interpreters

Thus we also want to call GFCC the portable grammar format.

The idea is that all embedded GF applications use GFCC. The GF system would be primarily used as a compiler and as a grammar development tool.

Since GFCC is implemented in BNFC, a parser of the format is readily available for C, C++, C#, Haskell, Java, and OCaml. Also an XML representation can be generated in BNFC. A reference implementation of linearization and some other functions has been written in Haskell.

## GFCC vs. GFC

GFCC is aimed to replace GFC as the run-time grammar format. GFC was designed to be a run-time format, but also to support separate compilation of grammars, i.e. to store the results of compiling individual GF modules. But this means that GFC has to contain extra information, such as type annotations, which is only needed in compilation and not at run-time. In particular, the pattern matching syntax and semantics of GFC is complex and therefore difficult to implement in new platforms.

Actually, GFC is planned to be omitted also as the target format of separate compilation, where plain GF (type annotated and partially evaluated) will be used instead. GFC provides only marginal advantages as a target format compared with GF, and it is therefore just extra weight to carry around this format.

The main differences of GFCC compared with GFC (and GF) can be summarized as follows:

- there are no modules, and therefore no qualified names
- a GFCC grammar is multilingual, and consists of a common abstract syntax together with one concrete syntax per language
- records and tables are replaced by arrays
- record labels and parameter values are replaced by integers
- record projection and table selection are replaced by array indexing
- even though the format does support dependent types and higher-order abstract syntax, there is no interpreted yet that does this

Here is an example of a GF grammar, consisting of three modules, as translated to GFCC. The representations are aligned; thus they do not completely reflect the order of judgements in GFCC files, which have different orders of blocks of judgements, and alphabetical sorting.

                                          grammar Ex(Eng,Swe);

      abstract Ex = {                     abstract {
        cat                                 cat
          S ; NP ; VP ;                      NP[]; S[]; VP[];
        fun                                 fun
          Pred : NP -> VP -> S ;             Pred=[(($ 0! 1),(($ 1! 0)!($ 0! 0)))];
          She, They : NP ;                   She=[0,"she"];
          Sleep : VP ;                       They=[1,"they"];
                                             Sleep=[["sleeps","sleep"]];
      }                                     } ;

      concrete Eng of Ex = {              concrete Eng {
        lincat                             lincat
          S  = {s : Str} ;                  S=[()];
          NP = {s : Str ; n : Num} ;        NP=[1,()];
          VP = {s : Num => Str} ;           VP=[[(),()]];
        param
          Num = Sg | Pl ;
        lin                                lin
          Pred np vp = {                    Pred=[(($ 0! 1),(($ 1! 0)!($ 0! 0)))];
            s = np.s ++ vp.s ! np.n} ;
          She = {s = "she" ; n = Sg} ;      She=[0,"she"];
          They = {s = "they" ; n = Pl} ;    They = [1, "they"];
          Sleep = {s = table {              Sleep=[["sleeps","sleep"]];
            Sg => "sleeps" ;
            Pl => "sleep"
            }
          } ;
      }                                   } ;

      concrete Swe of Ex = {              concrete Swe {
        lincat                             lincat
          S  = {s : Str} ;                  S=[()];
          NP = {s : Str} ;                  NP=[()];
          VP = {s : Str} ;                  VP=[()];
        param
          Num = Sg | Pl ;
        lin                                lin
          Pred np vp = {                    Pred = [(($0!0),($1!0))];
            s = np.s ++ vp.s} ;
          She = {s = "hon"} ;               She = ["hon"];
          They = {s = "de"} ;               They = ["de"];
          Sleep = {s = "sover"} ;           Sleep = ["sover"];
      }                                     } ;

## The syntax of GFCC files

The complete BNFC grammar, from which the rules in this section are taken, is in the file `GF/GFCC/GFCC.cf`.

### Top level

A grammar has a header telling the name of the abstract syntax (often specifying an application domain), and the names of the concrete languages. The abstract syntax and the concrete syntaxes themselves follow.

        Grm. Grammar  ::=
          "grammar" CId "(" [CId] ")" ";"
          Abstract ";"
          [Concrete] ;

        Abs. Abstract ::=
          "abstract" "{"
            "flags" [Flag]
            "fun"   [FunDef]
            "cat"   [CatDef]
          "}" ;

        Cnc. Concrete ::=
          "concrete" CId "{"
            "flags"  [Flag]
            "lin"    [LinDef]
            "oper"   [LinDef]
            "lincat" [LinDef]
            "lindef" [LinDef]
            "printname" [LinDef]
          "}" ;

This syntax organizes each module to a sequence of fields, such as flags, linearizations, operations, linearization types, etc. It is envisaged that particular applications can ignore some of the fields, typically so that earlier fields are more important than later ones.

The judgement forms have the following syntax.

        Flg. Flag     ::= CId "=" String ;
        Cat. CatDef   ::= CId "[" [Hypo] "]" ;
        Fun. FunDef   ::= CId ":" Type "=" Exp ;
        Lin. LinDef   ::= CId "=" Term ;

For the run-time system, the reference implementation in Haskell uses a structure that gives efficient look-up:

        data GFCC = GFCC {
          absname   :: CId ,
          cncnames  :: [CId] ,
          abstract  :: Abstr ,
          concretes :: Map CId Concr
          }

        data Abstr = Abstr {
          aflags  :: Map CId String,     -- value of a flag
          funs    :: Map CId (Type,Exp), -- type and def of a fun
          cats    :: Map CId [Hypo],     -- context of a cat
          catfuns :: Map CId [CId]       -- funs yielding a cat (redundant, for fast lookup)
          }

        data Concr = Concr {
          flags   :: Map CId String, -- value of a flag
          lins    :: Map CId Term,   -- lin of a fun
          opers   :: Map CId Term,   -- oper generated by subex elim
          lincats :: Map CId Term,   -- lin type of a cat
          lindefs :: Map CId Term,   -- lin default of a cat
          printnames :: Map CId Term -- printname of a cat or a fun
          }

These definitions are from `GF/GFCC/DataGFCC.hs`.

Identifiers (`CId`) are like `Ident` in GF, except that the compiler produces constants prefixed with `_` in the common subterm elimination optimization.

        token CId (('_' | letter) (letter | digit | '\'' | '_')*) ;

### Abstract syntax

Types are first-order function types built from argument type contexts and value types. category symbols. Syntax trees (`Exp`) are rose trees with nodes consisting of a head (`Atom`) and bound variables (`CId`).

        DTyp. Type  ::= "[" [Hypo] "]" CId [Exp] ;
        DTr.  Exp   ::= "[" "(" [CId] ")" Atom [Exp] "]" ;
        Hyp.  Hypo  ::= CId ":" Type ;

The head Atom is either a function constant, a bound variable, or a metavariable, or a string, integer, or float literal.

        AC.   Atom  ::= CId ;
        AS.   Atom  ::= String ;
        AI.   Atom  ::= Integer ;
        AF.   Atom  ::= Double ;
        AM.   Atom  ::= "?" Integer ;

The context-free types and trees of the "old GFCC" are special cases, which can be defined as follows:

        Typ.  Type  ::= [CId] "->" CId
        Typ args val = DTyp [Hyp (CId "_") arg | arg <- args] val

        Tr.   Exp   ::= "(" CId [Exp] ")"
        Tr fun exps  = DTr [] fun exps

To store semantic (`def`) definitions by cases, the following expression form is provided, but it is only meaningful in the last field of a function declaration in an abstract syntax:

        EEq. Exp      ::= "{" [Equation] "}" ;
        Equ. Equation ::= [Exp] "->" Exp ;

Notice that expressions are used to encode patterns. Primitive notions (the default semantics in GF) are encoded as empty sets of equations (`[]`). For a constructor (canonical form) of a category `C`, we aim to use the encoding as the application `(_constr C)`.

### Concrete syntax

Linearization terms (`Term`) are built as follows. Constructor names are shown to make the later code examples readable.

        R.  Term ::= "[" [Term] "]" ;        -- array (record/table)
        P.  Term ::= "(" Term "!" Term ")" ; -- access to field (projection/selection)
        S.  Term ::= "(" [Term] ")" ;        -- concatenated sequence
        K.  Term ::= Tokn ;                  -- token
        V.  Term ::= "$" Integer ;           -- argument (subtree)
        C.  Term ::= Integer ;               -- array index (label/parameter value)
        FV. Term ::= "[|" [Term] "|]" ;      -- free variation
        TM. Term ::= "?" ;                   -- linearization of metavariable

Tokens are strings or (maybe obsolescent) prefix-dependent variant lists.

        KS.  Tokn     ::= String ;
        KP.  Tokn     ::= "[" "pre" [String] "[" [Variant] "]" "]" ;
        Var. Variant  ::= [String] "/" [String] ;

Two special forms of terms are introduced by the compiler as optimizations. They can in principle be eliminated, but their presence makes grammars much more compact. Their semantics will be explained in a later section.

        F.  Term ::= CId ;                     -- global constant
        W.  Term ::= "(" String "+" Term ")" ; -- prefix + suffix table

There is also a deprecated form of "record parameter alias",

        RP. Term ::= "(" Term "@" Term ")";    -- DEPRECATED

which will be removed when the migration to new GFCC is complete.

## The semantics of concrete syntax terms

The code in this section is from `GF/GFCC/Linearize.hs`.

### Linearization and realization

The linearization algorithm is essentially the same as in GFC: a tree is linearized by evaluating its linearization term in the environment of the linearizations of the subtrees. Literal atoms are linearized in the obvious way. The function also needs to know the language (i.e. concrete syntax) in which linearization is performed.

        linExp :: GFCC -> CId -> Exp -> Term
        linExp gfcc lang tree@(DTr _ at trees) = case at of
          AC fun -> comp (Prelude.map lin trees) $ look fun
          AS s   -> R [kks (show s)] -- quoted
          AI i   -> R [kks (show i)]
          AF d   -> R [kks (show d)]
          AM     -> TM
         where
           lin  = linExp gfcc lang
           comp = compute gfcc lang
           look = lookLin gfcc lang

TODO: bindings must be supported.

The result of linearization is usually a record, which is realized as a string using the following algorithm.

        realize :: Term -> String
        realize trm = case trm of
          R (t:_)  -> realize t
          S ss     -> unwords $ Prelude.map realize ss
          K (KS s) -> s
          K (KP s _) -> unwords s ---- prefix choice TODO
          W s t    -> s ++ realize t
          FV (t:_) -> realize t
          TM       -> "?"

Notice that realization always picks the first field of a record. If a linearization type has more than one field, the first field does not necessarily contain the desired string. Also notice that the order of record fields in GFCC is not necessarily the same as in GF source.

### Term evaluation

Evaluation follows call-by-value order, with two environments needed:

- the grammar (a concrete syntax) to give the global constants
- an array of terms to give the subtree linearizations

The code is presented in one-level pattern matching, to enable reimplementations in languages that do not permit deep patterns (such as Java and C++).

      compute :: GFCC -> CId -> [Term] -> Term -> Term
      compute gfcc lang args = comp where
        comp trm = case trm of
          P r p  -> proj (comp r) (comp p)
          W s t  -> W s (comp t)
          R ts   -> R $ Prelude.map comp ts
          V i    -> idx args (fromInteger i)  -- already computed
          F c    -> comp $ look c             -- not computed (if contains V)
          FV ts  -> FV $ Prelude.map comp ts
          S ts   -> S $ Prelude.filter (/= S []) $ Prelude.map comp ts
          _ -> trm

        look = lookOper gfcc lang

        idx xs i = xs !! i

        proj r p = case (r,p) of
          (_,     FV ts) -> FV $ Prelude.map (proj r) ts
          (W s t, _)     -> kks (s ++ getString (proj t p))
          _              -> comp $ getField r (getIndex p)

        getString t = case t of
          K (KS s) -> s
          _ -> trace ("ERROR in grammar compiler: string from "++ show t) "ERR"

        getIndex t =  case t of
          C i    -> fromInteger i
          RP p _ -> getIndex p
          TM     -> 0  -- default value for parameter
          _ -> trace ("ERROR in grammar compiler: index from " ++ show t) 0

        getField t i = case t of
          R rs   -> idx rs i
          RP _ r -> getField r i
          TM     -> TM
          _ -> trace ("ERROR in grammar compiler: field from " ++ show t) t

### The special term constructors

The three forms introduced by the compiler may a need special explanation.

Global constants

        Term ::= CId ;

are shorthands for complex terms. They are produced by the compiler by (iterated) common subexpression elimination. They are often more powerful than hand-devised code sharing in the source code. They could be computed off-line by replacing each identifier by its definition.

Prefix-suffix tables

        Term ::= "(" String "+" Term ")" ;

represent tables of word forms divided to the longest common prefix and its array of suffixes. In the example grammar above, we have

        Sleep = [("sleep" + ["s",""])]

which in fact is equal to the array of full forms

        ["sleeps", "sleep"]

The power of this construction comes from the fact that suffix sets tend to be repeated in a language, and can therefore be collected by common subexpression elimination. It is this technique that explains the used syntax rather than the more accurate

        "(" String "+" [String] ")"

since we want the suffix part to be a `Term` for the optimization to take effect.

## Compiling to GFCC

Compilation to GFCC is performed by the GF grammar compiler, and GFCC interpreters need not know what it does. For grammar writers, however, it might be interesting to know what happens to the grammars in the process.

The compilation phases are the following

1. type check and partially evaluate GF source
2. create a symbol table mapping the GF parameter and record types to fixed-size arrays, and parameter values and record labels to integers
3. traverse the linearization rules replacing parameters and labels by integers
4. reorganize the created GF grammar so that it has just one abstract syntax and one concrete syntax per language
5. TODO: apply UTF8 encoding to the grammar, if not yet applied (this is told by the `coding` flag)
6. translate the GF grammar object to a GFCC grammar object, using a simple compositional mapping
7. perform the word-suffix optimization on GFCC linearization terms
8. perform subexpression elimination on each concrete syntax module
9. print out the GFCC code

### Problems in GFCC compilation

Two major problems had to be solved in compiling GF to GFCC:

- consistent order of tables and records, to permit the array translation
- run-time variables in complex parameter values.

The current implementation is still experimental and may fail to generate correct code. Any errors remaining are likely to be related to the two problems just mentioned.

The order problem is solved in slightly different ways for tables and records. In both cases, eta expansion is used to establish a canonical order. Tables are ordered by applying the preorder induced by `param` definitions. Records are ordered by sorting them by labels. This means that e.g. the `s` field will in general no longer appear as the first field, even if it does so in the GF source code. But relying on the order of fields in a labelled record would be misplaced anyway.

The canonical form of records is further complicated by lock fields, i.e. dummy fields of form `lock_C = <>`, which are added to grammar libraries to force intensionality of linearization types. The problem is that the absence of a lock field only generates a warning, not an error. Therefore a GF grammar can contain objects of the same type with and without a lock field. This problem was solved in GFCC generation by just removing all lock fields (defined as fields whose type is the empty record type). This has the further advantage of (slightly) reducing the grammar size. More importantly, it is safe to remove lock fields, because they are never used in computation, and because intensional types are only needed in grammars reused as libraries, not in grammars used at runtime.

While the order problem is rather bureaucratic in nature, run-time variables are an interesting problem. They arise in the presence of complex parameter values, created by argument-taking constructors and parameter records. To give an example, consider the GF parameter type system

        Number = Sg | Pl ;
        Person = P1 | P2 | P3 ;
        Agr = Ag Number Person ;

The values can be translated to integers in the expected way,

        Sg = 0, Pl = 1
        P1 = 0, P2 = 1, P3 = 2
        Ag Sg P1 = 0, Ag Sg P2 = 1, Ag Sg P3 = 2,
        Ag Pl P1 = 3, Ag Pl P2 = 4, Ag Pl P3 = 5

However, an argument of `Agr` can be a run-time variable, as in

        Ag np.n P3

This expression must first be translated to a case expression,

        case np.n of {
          0 => 2 ;
          1 => 5
          }

which can then be translated to the GFCC term

        ([2,5] ! ($0 ! $1))

assuming that the variable `np` is the first argument and that its `Number` field is the second in the record.

This transformation of course has to be performed recursively, since there can be several run-time variables in a parameter value:

        Ag np.n np.p

A similar transformation would be possible to deal with the double role of parameter records discussed above. Thus the type

        RNP = {n : Number ; p : Person}

could be uniformly translated into the set `{0,1,2,3,4,5}` as `Agr` above. Selections would be simple instances of indexing. But any projection from the record should be translated into a case expression,

        rnp.n  ===>
        case rnp of {
          0 => 0 ;
          1 => 0 ;
          2 => 0 ;
          3 => 1 ;
          4 => 1 ;
          5 => 1
          }

To avoid the code bloat resulting from this, we have chosen to deal with records by a currying transformation:

        table {n : Number ; p : Person} {... ...}
         ===>
        table Number {Sg => table Person {...} ; table Person {...}}

This is performed when GFCC is generated. Selections with records have to be treated likewise,

        t ! r   ===> t ! r.n ! r.p

### The representation of linearization types

Linearization types (`lincat`) are not needed when generating with GFCC, but they have been added to enable parser generation directly from GFCC. The linearization type definitions are shown as a part of the concrete syntax, by using terms to represent types. Here is the table showing how different linearization types are encoded.

        P*                         = max(P)         -- parameter type
        {r1 : T1 ; ... ; rn : Tn}* = [T1*,...,Tn*]  -- record
        (P => T)*                  = [T* ,...,T*]   -- table, size(P) cases
        Str*                       = ()

For example, the linearization type `present/CatEng.NP` is translated as follows:

        NP = {
          a : {                     -- 6 = 2*3 values
            n : {ParamX.Number} ;   -- 2 values
            p : {ParamX.Person}     -- 3 values
          } ;
          s : {ResEng.Case} => Str  -- 3 values
        }

        __NP = [[1,2],[(),(),()]]

### Running the compiler and the GFCC interpreter

GFCC generation is a part of the developers' version of GF since September 2006. To invoke the compiler, the flag `-printer=gfcc` to the command `pm = print_multi` is used. It is wise to recompile the grammar from source, since previously compiled libraries may not obey the canonical order of records. Here is an example, performed in example/bronzeage.

        i -src -path=.:prelude:resource-1.0/* -optimize=all_subs BronzeageEng.gf
        i -src -path=.:prelude:resource-1.0/* -optimize=all_subs BronzeageGer.gf
        strip
        pm -printer=gfcc | wf bronze.gfcc

There is also an experimental batch compiler, which does not use the GFC format or the record aliases. It can be produced by

        make gfc

in `GF/src`, and invoked by

        gfc --make FILES

## The reference interpreter

The reference interpreter written in Haskell consists of the following files:

        -- source file for BNFC
        GFCC.cf       -- labelled BNF grammar of gfcc

        -- files generated by BNFC
        AbsGFCC.hs    -- abstrac syntax datatypes
        ErrM.hs       -- error monad used internally
        LexGFCC.hs    -- lexer of gfcc files
        ParGFCC.hs    -- parser of gfcc files and syntax trees
        PrintGFCC.hs  -- printer of gfcc files and syntax trees

        -- hand-written files
        DataGFCC.hs   -- grammar datatype, post-parser grammar creation
        Linearize.hs  -- linearization and evaluation
        Macros.hs     -- utilities abstracting away from GFCC datatypes
        Generate.hs   -- random and exhaustive generation, generate-and-test parsing
        API.hs        -- functionalities accessible in embedded GF applications
        Generate.hs   -- random and exhaustive generation
        Shell.hs      -- main function - a simple command interpreter

It is included in the developers' version of GF, in the subdirectories `GF/src/GF/GFCC` and `GF/src/GF/Devel`.

As of September 2007, default parsing in main GF uses GFCC (implemented by Krasimir Angelov). The interpreter uses the relevant modules

        GF/Conversions/SimpleToFCFG.hs  -- generate parser from GFCC
        GF/Parsing/FCFG.hs              -- run the parser

To compile the interpreter, type

        make gfcc

in `GF/src`. To run it, type

        ./gfcc <GFCC-file>

The available commands are

- `gr <Cat> <Int>`: generate a number of random trees in category. and show their linearizations in all languages
- `grt <Cat> <Int>`: generate a number of random trees in category. and show the trees and their linearizations in all languages
- `gt <Cat> <Int>`: generate a number of trees in category from smallest, and show their linearizations in all languages
- `gtt <Cat> <Int>`: generate a number of trees in category from smallest, and show the trees and their linearizations in all languages
- `p <Lang> <Cat> <String>`: parse a string into a set of trees
- `lin <Tree>`: linearize tree in all languages, also showing full records
- `q`: terminate the system cleanly

## Embedded formats

- JavaScript: compiler of linearization and abstract syntax

- Haskell: compiler of abstract syntax and interpreter with parsing, linearization, and generation

- C: compiler of linearization (old GFCC)

- C++: embedded interpreter supporting linearization (old GFCC)

## Some things to do

Support for dependent types, higher-order abstract syntax, and semantic definition in GFCC generation and interpreters.

Replacing the entire GF shell by one based on GFCC.

Interpreter in Java.

Hand-written parsers for GFCC grammars to reduce code size (and efficiency?) of interpreters.

Binary format and/or file compression of GFCC output.

Syntax editor based on GFCC.

Rewriting of resource libraries in order to exploit the word-suffix sharing better (depth-one tables, as in FM).