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authoraarne <aarne@cs.chalmers.se>2008-06-25 16:43:48 +0000
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-The GFCC Grammar Format
-Aarne Ranta
-December 14, 2007
-
-Author's address:
-[``http://www.cs.chalmers.se/~aarne`` http://www.cs.chalmers.se/~aarne]
-
-% to compile: txt2tags -thtml --toc gfcc.txt
-
-History:
-- 14 Dec 2007: simpler, Lisp-like concrete syntax of GFCC
-- 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`` ../DataGFCC.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`` ../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`` ../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
- (FV ts, _ ) -> FV $ Prelude.map (\t -> proj t p) 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
-+ type check and partially evaluate GF source
-+ create a symbol table mapping the GF 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 GF grammar so that it has just one abstract syntax
- and one concrete syntax per language
-+ TODO: apply UTF8 encoding to the grammar, if not yet applied (this is told by the
- ``coding`` flag)
-+ translate the GF grammar object to a GFCC grammar object, 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
-
-
-
-
-===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 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.
-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
-```
-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 http://www.cs.chalmers.se/Cs/Research/Language-technology/darcs/GF/doc/darcs.html]
-of GF, in the subdirectories [``GF/src/GF/GFCC`` ../] and
-[``GF/src/GF/Devel`` ../../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.
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-Hand-written parsers for GFCC grammars to reduce code size
-(and efficiency?) of interpreters.
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-Binary format and/or file compression of GFCC output.
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-Syntax editor based on GFCC.
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-Rewriting of resource libraries in order to exploit the
-word-suffix sharing better (depth-one tables, as in FM).
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