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|
module Rewriting.Term
( VarIdx, Term (..), TermEq, TermEqs
, showVarIdx, showTerm, showTermEq, showTermEqs, tConst, tOp, tRoot, tCons
, tConsAll, tVars, tVarsAll, isConsTerm, isVarTerm, isGround, isLinear
, isNormal, maxVarInTerm, minVarInTerm, normalizeTerm, renameTermVars
, mapTerm, eqConsPattern
) where
import FiniteMap (listToFM, lookupFM)
import List (nub, intercalate, maximum, minimum)
import Maybe (fromMaybe)
type VarIdx = Int
data Term f = TermVar VarIdx | TermCons f [Term f]
type TermEq f = (Term f, Term f)
type TermEqs f = [TermEq f]
showVarIdx :: VarIdx -> String
showVarIdx v | v >= 0 = if q == 0 then [c] else c:(show q)
| otherwise = ""
where
(q, r) = divMod v 26
c = "abcdefghijklmnopqrstuvwxyz" !! r
showTerm :: (f -> String) -> Term f -> String
showTerm s = showTerm' False
where
showTerm' _ (TermVar v) = showVarIdx v
showTerm' b (TermCons c ts)
= case ts of
[] -> s c
[l, r] -> parensIf b ((showTerm' True l) ++ " " ++ (s c) ++ " "
++ (showTerm' True r))
_ -> (s c) ++ "("
++ (intercalate "," (map (showTerm' False) ts)) ++ ")"
showTermEq :: (f -> String) -> TermEq f -> String
showTermEq s (l, r) = (showTerm s l) ++ " = " ++ (showTerm s r)
showTermEqs :: (f -> String) -> TermEqs f -> String
showTermEqs s = unlines . (map (showTermEq s))
tConst :: f -> Term f
tConst c = TermCons c []
tOp :: Term f -> f -> Term f -> Term f
tOp l c r = TermCons c [l, r]
tRoot :: Term f -> Either VarIdx f
tRoot (TermVar v) = Left v
tRoot (TermCons c _) = Right c
tCons :: Term f -> [f]
tCons = nub . tConsAll
tConsAll :: Term f -> [f]
tConsAll (TermVar _) = []
tConsAll (TermCons c ts) = c:(concatMap tConsAll ts)
tVars :: Term _ -> [VarIdx]
tVars = nub . tVarsAll
tVarsAll :: Term _ -> [VarIdx]
tVarsAll (TermVar v) = [v]
tVarsAll (TermCons _ ts) = concatMap tVarsAll ts
isConsTerm :: Term _ -> Bool
isConsTerm (TermVar _) = False
isConsTerm (TermCons _ _) = True
isVarTerm :: Term _ -> Bool
isVarTerm = not . isConsTerm
isGround :: Term _ -> Bool
isGround = null . tVarsAll
isLinear :: Term _ -> Bool
isLinear = unique . tVarsAll
isNormal :: Term _ -> Bool
isNormal (TermVar _) = True
isNormal (TermCons _ []) = True
isNormal (TermCons c (t:ts))
= case t of
(TermVar _) -> all isVarTerm ts
(TermCons _ _) -> (isNormal t) && (isNormal (TermCons c ts))
maxVarInTerm :: Term _ -> Maybe VarIdx
maxVarInTerm t = case tVars t of
[] -> Nothing
vs@(_:_) -> Just (maximum vs)
minVarInTerm :: Term _ -> Maybe VarIdx
minVarInTerm t = case tVars t of
[] -> Nothing
vs@(_:_) -> Just (minimum vs)
normalizeTerm :: Term f -> Term f
normalizeTerm t = normalize t
where
sub = listToFM (<) (zip (tVars t) (map TermVar [0..]))
normalize t'@(TermVar v) = fromMaybe t' (lookupFM sub v)
normalize (TermCons c ts) = TermCons c (map normalize ts)
renameTermVars :: Int -> Term f -> Term f
renameTermVars i (TermVar v) = TermVar (v + i)
renameTermVars i (TermCons c ts) = TermCons c (map (renameTermVars i) ts)
mapTerm :: (a -> b) -> Term a -> Term b
mapTerm _ (TermVar v) = TermVar v
mapTerm f (TermCons c ts) = TermCons (f c) (map (mapTerm f) ts)
eqConsPattern :: Term f -> Term f -> Bool
eqConsPattern (TermVar _) _ = False
eqConsPattern (TermCons _ _) (TermVar _) = False
eqConsPattern (TermCons c1 ts1) (TermCons c2 ts2) =
c1 == c2 && length ts1 == length ts2
parensIf :: Bool -> String -> String
parensIf b s = if b then "(" ++ s ++ ")" else s
unique :: [_] -> Bool
unique [] = True
unique (x:xs) | notElem x xs = unique xs
| otherwise = False |