module PGF.Paraphrase (
paraphrase,
paraphraseN
) where
import PGF.Data
import PGF.Tree
import PGF.Macros (lookDef,isData)
import PGF.CId
import Data.List (nub,sort,group)
import qualified Data.Map as Map
import Debug.Trace
paraphrase :: PGF -> Expr -> [Expr]
paraphrase pgf t = nub (paraphraseN 2 pgf t)
paraphraseN :: Int -> PGF -> Expr -> [Expr]
paraphraseN i pgf = map tree2expr . paraphraseN' i pgf . expr2tree
paraphraseN' :: Int -> PGF -> Tree -> [Tree]
paraphraseN' 0 _ t = [t]
paraphraseN' i pgf t =
step i t ++ [Fun g ts' | Fun g ts <- step (i1) t, ts' <- sequence (map par ts)]
where
par = paraphraseN' (i1) pgf
step 0 t = [t]
step i t = let stept = step (i1) t in stept ++ concat [def u | u <- stept]
def = fromDef pgf
fromDef :: PGF -> Tree -> [Tree]
fromDef pgf t@(Fun f ts) = defDown t ++ defUp t where
defDown t = [subst g u | let equ = equsFrom f, (u,g) <- match equ ts, trequ "U" f equ]
defUp t = [subst g u | equ <- equsTo f, (u,g) <- match [equ] ts, trequ "D" f equ]
equsFrom f = [(ps,d) | Just equs <- [lookup f equss], (Fun _ ps,d) <- equs]
equsTo f = [c | (_,equs) <- equss, c <- casesTo f equs]
casesTo f equs =
[(ps,p) | (p,d@(Fun g ps)) <- equs, g==f,
isClosed d || (length equs == 1 && isLinear d)]
equss = [(f,[(Fun f (map patt2tree ps), expr2tree d) | (Equ ps d) <- eqs]) |
(f,(_,_,Just eqs,_,_)) <- Map.assocs (funs (abstract pgf)), not (null eqs)]
trequ s f e = True
subst :: Subst -> Tree -> Tree
subst g e = case e of
Fun f ts -> Fun f (map substg ts)
Var x -> maybe e id $ lookup x g
_ -> e
where
substg = subst g
type Subst = [(CId,Tree)]
isClosed :: Tree -> Bool
isClosed t = case t of
Fun _ ts -> all isClosed ts
Var _ -> False
_ -> True
isLinear :: Tree -> Bool
isLinear = nodup . vars where
vars t = case t of
Fun _ ts -> concatMap vars ts
Var x -> [x]
_ -> []
nodup = all ((<2) . length) . group . sort
match :: [([Tree],Tree)] -> [Tree] -> [(Tree, Subst)]
match cases terms = case cases of
[] -> []
(patts,_):_ | length patts /= length terms -> []
(patts,val):cc -> case mapM tryMatch (zip patts terms) of
Just substs -> return (val, concat substs)
_ -> match cc terms
where
tryMatch (p,t) = case (p, t) of
(Var x, _) | notMeta t -> return [(x,t)]
(Fun p pp, Fun f tt) | p == f && length pp == length tt -> do
matches <- mapM tryMatch (zip pp tt)
return (concat matches)
_ -> if p==t then return [] else Nothing
notMeta e = case e of
Meta _ -> False
Fun f ts -> all notMeta ts
_ -> True
patt2tree :: Patt -> Tree
patt2tree (PApp f ps) = Fun f (map patt2tree ps)
patt2tree (PLit l) = Lit l
patt2tree (PVar x) = Var x
patt2tree PWild = Meta 0