forked from GitHub/gf-core
refactor the PGF.Expr type and the evaluation of abstract expressions
This commit is contained in:
krasimir
151
src/PGF/Expr.hs
151
src/PGF/Expr.hs
@@ -1,13 +1,13 @@
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module PGF.Expr(Tree(..), Literal(..),
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readTree, showTree, pTree, ppTree,
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Expr(..), Equation(..),
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readExpr, showExpr, pExpr, ppExpr,
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Expr(..), Patt(..), Equation(..),
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readExpr, showExpr, pExpr, ppExpr, ppPatt,
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tree2expr, expr2tree,
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-- needed in the typechecker
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Value(..), Env, eval, apply,
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Value(..), Env, eval, apply, eqValue,
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-- helpers
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pStr,pFactor,
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@@ -17,6 +17,7 @@ module PGF.Expr(Tree(..), Literal(..),
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) where
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import PGF.CId
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import PGF.Type
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import Data.Char
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import Data.Maybe
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@@ -29,7 +30,7 @@ data Literal =
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LStr String -- ^ string constant
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| LInt Integer -- ^ integer constant
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| LFlt Double -- ^ floating point constant
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deriving (Eq,Ord,Show)
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deriving (Eq,Ord)
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-- | The tree is an evaluated expression in the abstract syntax
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-- of the grammar. The type is especially restricted to not
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@@ -53,17 +54,24 @@ data Expr =
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| ELit Literal -- ^ literal
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| EMeta Int -- ^ meta variable
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| EVar CId -- ^ variable or function reference
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| EEq [Equation] -- ^ lambda function defined as a set of equations with pattern matching
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| EPi CId Expr Expr -- ^ dependent function type
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deriving (Eq,Ord)
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-- | The pattern is used to define equations in the abstract syntax of the grammar.
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data Patt =
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PApp CId [Patt] -- ^ application. The identifier should be constructor i.e. defined with 'data'
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| PLit Literal -- ^ literal
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| PVar CId -- ^ variable
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| PWild -- ^ wildcard
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deriving (Eq,Ord)
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-- | The equation is used to define lambda function as a sequence
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-- of equations with pattern matching. The list of 'Expr' represents
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-- the patterns and the second 'Expr' is the function body for this
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-- equation.
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data Equation =
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Equ [Expr] Expr
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deriving (Eq,Ord,Show)
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Equ [Patt] Expr
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deriving (Eq,Ord)
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-- | parses 'String' as an expression
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readTree :: String -> Maybe Tree
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@@ -120,24 +128,13 @@ pTree isNested = RP.skipSpaces >> (pParen RP.<++ pAbs RP.<++ pApp RP.<++ fmap Li
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return (Meta n)
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pExpr :: RP.ReadP Expr
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pExpr = RP.skipSpaces >> (pAbs RP.<++ pTerm RP.<++ pEqs)
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pExpr = RP.skipSpaces >> (pAbs RP.<++ pTerm)
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where
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pTerm = fmap (foldl1 EApp) (RP.sepBy1 pFactor RP.skipSpaces)
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pAbs = do xs <- RP.between (RP.char '\\') (RP.skipSpaces >> RP.string "->") (RP.sepBy1 (RP.skipSpaces >> pCId) (RP.skipSpaces >> RP.char ','))
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e <- pExpr
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return (foldr EAbs e xs)
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pEqs = fmap EEq $
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RP.between (RP.skipSpaces >> RP.char '{')
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(RP.skipSpaces >> RP.char '}')
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(RP.sepBy1 (RP.skipSpaces >> pEq)
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(RP.skipSpaces >> RP.string ";"))
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pEq = do pats <- (RP.sepBy1 pExpr RP.skipSpaces)
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RP.skipSpaces >> RP.string "=>"
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e <- pExpr
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return (Equ pats e)
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pFactor = fmap EVar pCId
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RP.<++ fmap ELit pLit
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@@ -176,6 +173,7 @@ ppTree d (Meta n) = PP.char '?' PP.<> PP.int n
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ppTree d (Var id) = PP.text (prCId id)
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ppExpr :: Int -> Expr -> PP.Doc
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ppExpr d (EAbs x e) = let (xs,e1) = getVars (EAbs x e)
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in ppParens (d > 0) (PP.char '\\' PP.<>
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PP.hsep (PP.punctuate PP.comma (map (PP.text . prCId) xs)) PP.<+>
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@@ -188,9 +186,11 @@ ppExpr d (EApp e1 e2) = ppParens (d > 1) ((ppExpr 1 e1) PP.<+> (ppExpr 2 e2))
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ppExpr d (ELit l) = ppLit l
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ppExpr d (EMeta n) = PP.char '?' PP.<+> PP.int n
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ppExpr d (EVar f) = PP.text (prCId f)
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ppExpr d (EEq eqs) = PP.braces (PP.sep (PP.punctuate PP.semi (map ppEquation eqs)))
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ppEquation (Equ pats e) = PP.hsep (map (ppExpr 2) pats) PP.<+> PP.text "=>" PP.<+> ppExpr 0 e
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ppPatt d (PApp f ps) = ppParens (d > 1) (PP.text (prCId f) PP.<+> PP.hsep (map (ppPatt 2) ps))
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ppPatt d (PLit l) = ppLit l
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ppPatt d (PVar f) = PP.text (prCId f)
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ppPatt d PWild = PP.char '_'
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ppLit (LStr s) = PP.text (show s)
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ppLit (LInt n) = PP.integer n
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@@ -212,46 +212,97 @@ tree2expr (Meta n) = EMeta n
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tree2expr (Abs xs t) = foldr EAbs (tree2expr t) xs
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tree2expr (Var x) = EVar x
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-- | Converts an expression to tree. If the expression
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-- contains unevaluated applications they will be applied.
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expr2tree :: Expr -> Tree
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expr2tree e = value2tree (eval Map.empty e) [] []
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-- | Converts an expression to tree. The expression
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-- is first reduced to beta-eta-alfa normal form and
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-- after that converted to tree.
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expr2tree :: Funs -> Expr -> Tree
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expr2tree funs e = value2tree [] (eval funs Map.empty e)
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where
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value2tree (VApp v1 v2) xs ts = value2tree v1 xs (value2tree v2 [] []:ts)
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value2tree (VVar x) xs ts = ret xs (fun xs x ts)
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value2tree (VMeta n) xs [] = ret xs (Meta n)
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value2tree (VLit l) xs [] = ret xs (Lit l)
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value2tree (VClosure env (EAbs x e)) xs [] = value2tree (eval (Map.insert x (VVar x) env) e) (x:xs) []
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fun xs x ts
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| x `elem` xs = Var x
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| otherwise = Fun x ts
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value2tree xs (VApp f vs) = case Map.lookup f funs of
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Just (DTyp hyps _ _,_) -> -- eta conversion
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let a1 = length hyps
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a2 = length vs
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a = a1 - a2
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i = length xs
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xs' = [var i | i <- [i..i+a-1]]
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in ret (reverse xs'++xs)
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(Fun f (map (value2tree []) vs++map Var xs'))
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Nothing -> error ("unknown variable "++prCId f)
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value2tree xs (VGen i) = ret xs (Var (var i))
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value2tree xs (VMeta n) = ret xs (Meta n)
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value2tree xs (VLit l) = ret xs (Lit l)
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value2tree xs (VClosure env (EAbs x e)) = let i = length xs
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in value2tree (var i:xs) (eval funs (Map.insert x (VGen i) env) e)
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var i = mkCId ('v':show i)
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ret [] t = t
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ret xs t = Abs (reverse xs) t
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data Value
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= VGen Int
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| VApp Value Value
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| VVar CId
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| VMeta Int
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= VApp CId [Value]
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| VLit Literal
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| VMeta Int
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| VGen Int
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| VClosure Env Expr
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deriving (Show,Eq,Ord)
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deriving (Eq,Ord)
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type Env = Map.Map CId Value
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type Funs = Map.Map CId (Type,[Equation]) -- type and def of a fun
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type Env = Map.Map CId Value
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eval :: Env -> Expr -> Value
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eval env (EVar x) = fromMaybe (VVar x) (Map.lookup x env)
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eval env (EApp e1 e2) = apply (eval env e1) (eval env e2)
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eval env (EAbs x e) = VClosure env (EAbs x e)
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eval env (EMeta k) = VMeta k
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eval env (ELit l) = VLit l
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eval env e = VClosure env e
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eval :: Funs -> Env -> Expr -> Value
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eval funs env (EVar x) = case Map.lookup x env of
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Just v -> v
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Nothing -> case Map.lookup x funs of
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Just (_,eqs) -> case eqs of
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Equ [] e : _ -> eval funs env e
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[] -> VApp x []
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Nothing -> error ("unknown variable "++prCId x)
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eval funs env (EApp e1 e2) = apply funs env e1 [eval funs env e2]
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eval funs env (EAbs x e) = VClosure env (EAbs x e)
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eval funs env (EMeta k) = VMeta k
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eval funs env (ELit l) = VLit l
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apply :: Value -> Value -> Value
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apply (VClosure env (EAbs x e)) v = eval (Map.insert x v env) e
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apply v0 v = VApp v0 v
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apply :: Funs -> Env -> Expr -> [Value] -> Value
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apply funs env e [] = eval funs env e
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apply funs env (EVar x) vs = case Map.lookup x env of
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Just v -> case (v,vs) of
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(VClosure env (EAbs x e),v:vs) -> apply funs (Map.insert x v env) e vs
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Nothing -> case Map.lookup x funs of
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Just (_,eqs) -> case match eqs vs of
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Just (e,vs,env) -> apply funs env e vs
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Nothing -> VApp x vs
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Nothing -> error ("unknown variable "++prCId x)
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apply funs env (EAbs x e) (v:vs) = apply funs (Map.insert x v env) e vs
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apply funs env (EApp e1 e2) vs = apply funs env e1 (eval funs env e2 : vs)
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match :: [Equation] -> [Value] -> Maybe (Expr, [Value], Env)
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match eqs vs =
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case eqs of
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[] -> Nothing
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(Equ ps res):eqs -> let (as,vs') = splitAt (length ps) vs
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in case zipWithM tryMatch ps as of
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Just envs -> Just (res, vs', Map.unions envs)
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Nothing -> match eqs vs
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where
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tryMatch p v = case (p, v) of
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(PVar x, _ ) -> Just (Map.singleton x v)
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(PApp f ps, VApp fe vs) | f == fe -> do envs <- zipWithM tryMatch ps vs
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return (Map.unions envs)
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(PLit l, VLit le ) | l == le -> Just Map.empty
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_ -> Nothing
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eqValue :: Int -> Value -> Value -> [(Value,Value)]
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eqValue k v1 v2 =
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case (v1,v2) of
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(VApp f1 vs1, VApp f2 vs2) | f1 == f2 -> concat (zipWith (eqValue k) vs1 vs2)
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(VLit l1, VLit l2 ) | l1 == l2 -> []
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(VMeta i, VMeta j ) | i == j -> []
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(VGen i, VGen j ) | i == j -> []
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(VClosure env1 (EAbs x1 e1), VClosure env2 (EAbs x2 e2)) ->
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let v = VGen k
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in eqValue (k+1) (VClosure (Map.insert x1 v env1) e1) (VClosure (Map.insert x2 v env2) e2)
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_ -> [(v1,v2)]
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--- use composOp and state monad...
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newMetas :: Expr -> Expr
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