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-The GFCC Grammar Format
-Aarne Ranta
-October 19, 2006
-
-Author's address:
-[``http://www.cs.chalmers.se/~aarne`` http://www.cs.chalmers.se/~aarne]
-
-% to compile: txt2tags -thtml --toc gfcc.txt
-
-History:
-- 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
-
-
-The idea is that all embedded GF applications are compiled to 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++, Haskell, Java, and OCaml. Also an XML 
-representation is 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.
-
-The main differences of GFCC compared with GFC 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
-- there is (so far) no support for dependent types or higher-order abstract
-  syntax (which would be easy to add, but make interpreters much more difficult
-  to write)
-
-
-Here is an example of a GF grammar, consisting of three modules, 
-as translated to GFCC. The representations are aligned, with the exceptions
-due to the alphabetical sorting of GFCC grammars.
-```  
-                                    grammar Ex(Eng,Swe);
-
-abstract Ex = {                     abstract {
-  cat 
-    S ; NP ; VP ;
-  fun 
-    Pred : NP -> VP -> S ;            Pred : NP,VP -> S = (Pred);
-    She, They : NP ;                  She : -> NP = (She);
-    Sleep : VP ;                      Sleep : -> VP = (Sleep); 
-                                      They : -> NP = (They);
-}                                     } ;
-                                    
-concrete Eng of Ex = {              concrete Eng {
-  lincat
-    S  = {s : Str} ;
-    NP = {s : Str ; n : Num} ;
-    VP = {s : Num => Str} ;
-  param
-    Num = Sg | Pl ;
-  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} ;    
-    Sleep = {s = table {              Sleep = [("sleep" + ["s",""])];
-      Sg => "sleeps" ; 
-      Pl => "sleep"                   They = [1, "they"];
-      }                               } ;
-    } ;
-}
-
-concrete Swe of Ex = {              concrete Swe {
-  lincat
-    S  = {s : Str} ;
-    NP = {s : Str} ;
-    VP = {s : Str} ;
-  param
-    Num = Sg | Pl ;
-  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==
-
-===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.
-```
-  Grammar  ::= Header ";" Abstract ";" [Concrete] ;
-  Header   ::= "grammar" CId "(" [CId] ")" ;
-  Abstract ::= "abstract" "{" [AbsDef] "}" ;
-  Concrete ::= "concrete" CId "{" [CncDef] "}" ;
-```
-Abstract syntax judgements give typings and semantic definitions.
-Concrete syntax judgements give linearizations.
-```
-  AbsDef   ::= CId ":" Type "=" Exp ;
-  CncDef   ::= CId "=" Term ;
-```
-Also flags are possible, local to each "module" (i.e. abstract and concretes).
-```
-  AbsDef   ::= "%" CId "=" String ;
-  CncDef   ::= "%" CId "=" String ;
-```
-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 {
-    funs :: Map CId Type,   -- find the type of a fun
-    cats :: Map CId [CId]   -- find the funs giving a cat
-    }
-
-  type Concr = Map CId Term
-```
-
-
-===Abstract syntax===
-
-Types are first-order function types built from
-category symbols. Syntax trees (``Exp``) are
-rose trees with the head (``Atom``) either a function
-constant, a metavariable, or a string, integer, or float
-literal.
-```
-  Type     ::= [CId] "->" CId ;
-  Exp      ::= "(" Atom [Exp] ")" ;
-  Atom     ::= CId ;        -- function constant
-  Atom     ::= "?" ;        -- metavariable
-  Atom     ::= String ;     -- string literal
-  Atom     ::= Integer ;    -- integer literal
-  Atom     ::= Double ;     -- float literal
-```
-
-
-===Concrete syntax===
-
-Linearization terms (``Term``) are built as follows.
-Constructor names are shown to make the later code
-examples readable.
-```
-  R.  Term ::= "[" [Term] "]" ;        -- array
-  P.  Term ::= "(" Term "!" Term ")" ; -- access to indexed field
-  S.  Term ::= "(" [Term] ")" ;        -- sequence with ++
-  K.  Term ::= Tokn ;                  -- token
-  V.  Term ::= "$" Integer ;           -- argument
-  C.  Term ::= Integer ;               -- array index
-  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] ;
-```
-Three 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
-  RP. Term ::= "(" Term "@" Term ")";    -- record parameter alias
-```
-Identifiers are like ``Ident`` in GF and GFC, except that
-the compiler produces constants prefixed with ``_`` in
-the common subterm elimination optimization.
-```
-  token CId (('_' | letter) (letter | digit | '\'' | '_')*) ;
-```
-
-
-==The semantics of concrete syntax terms==
-
-===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 mcfg lang tree@(Tr 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 mcfg lang
-     comp = compute mcfg lang
-     look = lookLin mcfg lang
-```
-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       -> "?"
-```
-Since the order of record fields is not necessarily
-the same as in GF source,
-this realization does not work securely for
-categories whose lincats more than one field.
-
-
-===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 mcfg lang args = comp where
-  comp trm = case trm of
-    P r p  -> proj (comp r) (comp p)
-    RP i t -> RP (comp i) (comp t)
-    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 = lookLin mcfg 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.
-
-The most curious construct of GFCC is the parameter array alias, 
-```
-  Term ::= "(" Term "@" Term ")";
-```
-This form is used as the value of parameter records, such as the type
-```
-  {n : Number ; p : Person}
-```
-The problem with parameter records is their double role.
-They can be used like parameter values, as indices in selection,
-```
-  VP.s ! {n = Sg ; p = P3}
-```
-but also as records, from which parameters can be projected:
-```
-  {n = Sg ; p = P3}.n
-```
-Whichever use is selected as primary, a prohibitively complex
-case expression must be generated at compilation to GFCC to get the
-other use. The adopted
-solution is to generate a pair containing both a parameter value index 
-and an array of indices of record fields. For instance, if we have
-```
-  param Number = Sg | Pl ; Person = P1 | P2 | P3 ;
-```
-we get the encoding
-```
-  {n = Sg ; p = P3}  ---> (2 @ [0,2])
-```
-The GFCC computation rules are essentially
-```
-  (t ! (i @ _)) = (t ! i)
-  ((_ @ r) ! j)  =(r ! j)
-```
-
-
-==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
-+ translate GF source to GFC, as always in GF
-+ undo GFC back-end optimizations
-+ perform the ``values`` optimization to normalize tables
-+ create a symbol table mapping the GFC parameter and record types to
-  fixed-size arrays, and parameter values and record labels to integers
-+ traverse the linearization rules replacing parameters and labels by integers
-+ reorganize the created GFC grammar so that it has just one abstract syntax
-  and one concrete syntax per language
-+ apply UTF8 encoding to the grammar, if not yet applied (this is told by the
-  ``coding`` flag)
-+ translate the GFC syntax tree to a GFCC syntax tree, using a simple
-  compositional mapping
-+ perform the word-suffix optimization on GFCC linearization terms
-+ perform subexpression elimination on each concrete syntax module
-+ print out the GFCC code
-
-
-Notice that a major part of the compilation is done within GFC, so that
-GFC-related tasks (such as parser generation) could be performed by
-using the old algorithms.
-
-
-===Problems in GFCC compilation===
-
-Two major problems had to be solved in compiling GFC 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 different ways for tables and records.
-For tables, the ``values`` optimization of GFC already manages to
-maintain a canonical order. But this order can be destroyed by the
-``share`` optimization. To make sure that GFCC compilation works properly,
-it is safest to recompile the GF grammar by using the ``values``
-optimization flag.
-
-Records can be canonically ordered by sorting them by labels.
-In fact, this was done in connection of the GFCC work as a part
-of the GFC generation, to guarantee consistency. 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 GFC 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 chose the alias representation
-which is easy enough to deal with in interpreters.
-
-
-===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*                         = size(P)        -- parameter type              
-  {_ : I ; __ : R}*          = (I* @ R*)      -- record of parameters
-  {r1 : T1 ; ... ; rn : Tn}* = [T1*,...,Tn*]  -- other record
-  (P => T)*                  = [T* ,...,T*]   -- size(P) times
-  Str*                       = ()
-```
-The category symbols are prefixed with two underscores (``__``).
-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 = [(6@[2,3]),[(),(),()]]
-```
-
-
-
-
-===Running the compiler and the GFCC interpreter===
-
-GFCC generation is a part of the 
-[developers' version http://www.cs.chalmers.se/Cs/Research/Language-technology/darcs/GF/doc/darcs.html] 
-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. To ``strip`` the grammar before
-GFCC translation removes unnecessary interface references.
-Here is an example, performed in
-[example/bronzeage ../../../../../examples/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
-```
-
-
-
-==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 of gfcc
-  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   -- post-parser grammar creation, linearization and evaluation
-  GenGFCC.hs    -- random and exhaustive generation, generate-and-test parsing
-  RunGFCC.hs    -- main function - a simple command interpreter
-```
-It is included in the
-[developers' version http://www.cs.chalmers.se/Cs/Research/Language-technology/darcs/GF/doc/darcs.html]
-of GF, in the subdirectory [``GF/src/GF/Canon/GFCC`` ../].
-
-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 <Int> <Cat> <String>``: "parse", i.e. generate trees until match or 
-  until the given number have been generated
-- ``<Tree>``: linearize tree in all languages, also showing full records
-- ``quit``: terminate the system cleanly
-
-
-==Interpreter in C++==
-
-A base-line interpreter in C++ has been started.
-Its main functionality is random generation of trees and linearization of them.
-
-Here are some results from running the different interpreters, compared
-to running the same grammar in GF, saved in ``.gfcm`` format.
-The grammar contains the English, German, and Norwegian
-versions of Bronzeage. The experiment was carried out on
-Ubuntu Linux laptop with 1.5 GHz Intel centrino processor.
-
-||                | GF        | gfcc(hs) | gfcc++ |
-| program size    |   7249k   |   803k   |  113k
-| grammar size    |    336k   |  119k    |  119k
-| read grammar    |   1150ms  |  510ms   |  100ms
-| generate 222    |   9500ms  |  450ms   |  800ms
-| memory          |     21M   |   10M    |   20M
-
-
-
-To summarize:
-- going from GF to gfcc is a major win in both code size and efficiency
-- going from Haskell to C++ interpreter is not a win yet, because of a space
-  leak in the C++ version
-
-
-
-==Some things to do==
-
-Interpreter in Java.
-
-Parsing via MCFG 
-- the FCFG format can possibly be simplified
-- parser grammars should be saved in files to make interpreters easier
-
-
-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).
-
-
-