refactor the PGF.Expr type and the evaluation of abstract expressions

This commit is contained in:
krasimir
2009-05-20 21:03:56 +00:00
parent f9574dcf77
commit e5399f2d0e
32 changed files with 245 additions and 360 deletions

View File

@@ -1,106 +0,0 @@
----------------------------------------------------------------------
-- |
-- Module : AbsCompute
-- Maintainer : AR
-- Stability : (stable)
-- Portability : (portable)
--
-- computation in abstract syntax with def definitions.
--
-- modified from src GF computation
-----------------------------------------------------------------------------
module PGF.AbsCompute (
compute
) where
import PGF.Data
import PGF.Macros (lookDef,isData)
import PGF.Expr
import PGF.CId
compute :: PGF -> Tree -> Tree
compute pgf = computeAbsTermIn pgf []
computeAbsTermIn :: PGF -> [CId] -> Tree -> Tree
computeAbsTermIn pgf vv = expr2tree . compt vv . tree2expr where
compt vv t =
let
t' = beta vv t
(yy,f,aa) = exprForm t'
vv' = yy ++ vv
aa' = map (compt vv') aa
in
mkAbs yy $ case look f of
Left (EEq eqs) -> case match eqs aa' of
Just (d,g) -> compt vv' $ subst vv' g d
_ -> mkApp f aa'
Left (EMeta _) -> mkApp f aa' -- canonical or primitive
Left d -> compt vv' $ mkApp d aa'
_ -> mkApp f aa' -- literal
look f = case f of
EVar c -> Left $ lookDef pgf c
_ -> Right f
match = findMatch pgf
beta :: [CId] -> Expr -> Expr
beta vv c = case c of
EApp f a ->
let (a',f') = (beta vv a, beta vv f) in
case f' of
EAbs x b -> beta vv $ subst vv [(x,a')] (beta (x:vv) b)
_ -> (if a'==a && f'==f then id else beta vv) $ EApp f' a'
EAbs x b -> EAbs x (beta (x:vv) b)
_ -> c
subst :: [CId] -> Subst -> Expr -> Expr
subst xs g e = case e of
EAbs x b -> EAbs x (subst (x:xs) g e) ---- TODO: refresh variables
EApp f a -> EApp (substg f) (substg a)
EVar x -> maybe e id $ lookup x g
_ -> e
where
substg = subst xs g
type Subst = [(CId,Expr)]
type Patt = Expr
exprForm :: Expr -> ([CId],Expr,[Expr])
exprForm exp = upd ([],exp,[]) where
upd (xs,f,es) = case f of
EAbs x b -> upd (x:xs,b,es)
EApp c a -> upd (xs,c,a:es)
_ -> (reverse xs,f,es)
mkAbs xs b = foldr EAbs b xs
mkApp f es = foldl EApp f es
-- special version of pattern matching, to deal with comp under lambda
findMatch :: PGF -> [Equation] -> [Expr] -> Maybe (Expr, Subst)
findMatch pgf cases terms = case cases of
[] -> Nothing
(Equ patts _):_ | length patts /= length terms -> Nothing
(Equ patts val):cc -> case mapM tryMatch (zip patts terms) of
Just substs -> return (val, concat substs)
_ -> findMatch pgf cc terms
where
tryMatch (p,t) = case (exprForm p, exprForm t) of
(([],EVar c,[]),_) | constructor c -> if p==t then return [] else Nothing
(([],EVar x,[]),_) | notMeta t -> return [(x,t)]
(([],p, pp), ([], 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
EMeta _ -> False
EApp f a -> notMeta f && notMeta a
EAbs _ b -> notMeta b
_ -> True
constructor = isData pgf

View File

@@ -109,7 +109,6 @@ instance Binary Expr where
put (ELit (LFlt d)) = putWord8 4 >> put d
put (ELit (LInt i)) = putWord8 5 >> put i
put (EMeta i) = putWord8 6 >> put i
put (EEq eqs) = putWord8 7 >> put eqs
get = do tag <- getWord8
case tag of
0 -> liftM2 EAbs get get
@@ -119,9 +118,25 @@ instance Binary Expr where
4 -> liftM (ELit . LFlt) get
5 -> liftM (ELit . LInt) get
6 -> liftM EMeta get
7 -> liftM EEq get
_ -> decodingError
instance Binary Patt where
put (PApp f ps) = putWord8 0 >> put (f,ps)
put (PVar x) = putWord8 1 >> put x
put PWild = putWord8 2
put (PLit (LStr s)) = putWord8 3 >> put s
put (PLit (LFlt d)) = putWord8 4 >> put d
put (PLit (LInt i)) = putWord8 5 >> put i
get = do tag <- getWord8
case tag of
0 -> liftM2 PApp get get
1 -> liftM PVar get
2 -> return PWild
3 -> liftM (PLit . LStr) get
4 -> liftM (PLit . LFlt) get
5 -> liftM (PLit . LInt) get
_ -> decodingError
instance Binary Equation where
put (Equ ps e) = put (ps,e)
get = liftM2 Equ get get

View File

@@ -24,7 +24,7 @@ data PGF = PGF {
data Abstr = Abstr {
aflags :: Map.Map CId String, -- value of a flag
funs :: Map.Map CId (Type,Expr), -- type and def of a fun
funs :: Map.Map CId (Type,[Equation]), -- type and def of a fun
cats :: Map.Map CId [Hypo], -- context of a cat
catfuns :: Map.Map CId [CId] -- funs to a cat (redundant, for fast lookup)
}

View File

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

13
src/PGF/Expr.hs-boot Normal file
View File

@@ -0,0 +1,13 @@
module PGF.Expr where
import qualified Text.PrettyPrint as PP
import qualified Text.ParserCombinators.ReadP as RP
data Expr
instance Eq Expr
instance Ord Expr
pFactor :: RP.ReadP Expr
ppExpr :: Int -> Expr -> PP.Doc

View File

@@ -37,14 +37,15 @@ lookType :: PGF -> CId -> Type
lookType pgf f =
fst $ lookMap (error $ "lookType " ++ show f) f (funs (abstract pgf))
lookDef :: PGF -> CId -> Expr
lookDef :: PGF -> CId -> [Equation]
lookDef pgf f =
snd $ lookMap (error $ "lookDef " ++ show f) f (funs (abstract pgf))
isData :: PGF -> CId -> Bool
isData pgf f = case Map.lookup f (funs (abstract pgf)) of
Just (_,EMeta 0) -> True ---- the encoding of data constrs
_ -> False
isData pgf f =
case Map.lookup f (funs (abstract pgf)) of
Just (_,[]) -> True -- the encoding of data constrs
_ -> False
lookValCat :: PGF -> CId -> CId
lookValCat pgf = valCat . lookType pgf
@@ -120,9 +121,6 @@ contextLength :: Type -> Int
contextLength ty = case ty of
DTyp hyps _ _ -> length hyps
primNotion :: Expr
primNotion = EEq []
term0 :: CId -> Term
term0 = TM . prCId

View File

@@ -49,13 +49,8 @@ fromDef pgf t@(Fun f ts) = defDown t ++ defUp t where
[(ps,p) | (p,d@(Fun g ps)) <- equs, g==f,
isClosed d || (length equs == 1 && isLinear d)]
equss = [(f,[(Fun f (map expr2tree ps), expr2tree d) | (Equ ps d) <- eqs]) |
(f,(_,d)) <- Map.assocs (funs (abstract pgf)), eqs <- defs d]
defs d = case d of
EEq eqs -> [eqs]
EMeta _ -> []
_ -> [[Equ [] d]]
equss = [(f,[(Fun f (map patt2tree ps), expr2tree (funs (abstract pgf)) d) | (Equ ps d) <- eqs]) |
(f,(_,eqs)) <- Map.assocs (funs (abstract pgf)), not (null eqs)]
trequ s f e = True ----trace (s ++ ": " ++ show f ++ " " ++ show e) True
@@ -86,8 +81,6 @@ isLinear = nodup . vars where
nodup = all ((<2) . length) . group . sort
-- special version of AbsCompute.findMatch, working on Tree
match :: [([Tree],Tree)] -> [Tree] -> [(Tree, Subst)]
match cases terms = case cases of
[] -> []
@@ -108,3 +101,9 @@ match cases terms = case cases of
Fun f ts -> all notMeta ts
_ -> True
-- | Converts a pattern to tree.
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

View File

@@ -3,7 +3,7 @@ module PGF.Type ( Type(..), Hypo(..),
pType, ppType, ppHypo ) where
import PGF.CId
import PGF.Expr
import {-# SOURCE #-} PGF.Expr
import Data.Char
import qualified Text.PrettyPrint as PP
import qualified Text.ParserCombinators.ReadP as RP

View File

@@ -17,7 +17,6 @@ module PGF.TypeCheck (
import PGF.Data
import PGF.Macros (lookDef,isData)
import PGF.Expr
import PGF.AbsCompute
import PGF.CId
import GF.Data.ErrM
@@ -29,7 +28,7 @@ import Debug.Trace
typecheck :: PGF -> Tree -> [Tree]
typecheck pgf t = case inferExpr pgf (newMetas (tree2expr t)) of
Ok t -> [expr2tree t]
Ok t -> [expr2tree (funs (abstract pgf)) t]
Bad s -> trace s []
inferExpr :: PGF -> Expr -> Err Expr
@@ -50,26 +49,24 @@ infer pgf tenv@(k,rho,gamma) e = case e of
-- K i -> return (AStr i, valAbsString, [])
EApp f t -> do
(f',w,csf) <- infer pgf tenv f
typ <- whnf w
(f',typ,csf) <- infer pgf tenv f
case typ of
VClosure env (EPi x a b) -> do
(a',csa) <- checkExp pgf tenv t (VClosure env a)
b' <- whnf $ VClosure (eins x (VClosure rho t) env) b
let b' = eval (funs (abstract pgf)) (eins x (VClosure rho t) env) b
return $ (EApp f' a', b', csf ++ csa)
_ -> Bad ("function type expected for function " ++ show f)
_ -> Bad ("cannot infer type of expression" ++ show e)
checkExp :: PGF -> TCEnv -> Expr -> Value -> Err (Expr, [(Value,Value)])
checkExp pgf tenv@(k,rho,gamma) e ty = do
typ <- whnf ty
checkExp pgf tenv@(k,rho,gamma) e typ = do
let v = VGen k
case e of
EMeta m -> return $ (e,[])
EAbs x t -> case typ of
VClosure env (EPi y a b) -> do
a' <- whnf $ VClosure env a
let a' = eval (funs (abstract pgf)) env a
(t',cs) <- checkExp pgf (k+1,eins x v rho, eins x a' gamma) t
(VClosure (eins y v env) b)
return (EAbs x t', cs)
@@ -79,7 +76,7 @@ checkExp pgf tenv@(k,rho,gamma) e ty = do
checkInferExp :: PGF -> TCEnv -> Expr -> Value -> Err (Expr, [(Value,Value)])
checkInferExp pgf tenv@(k,_,_) e typ = do
(e',w,cs1) <- infer pgf tenv e
cs2 <- eqValue k w typ
let cs2 = eqValue k w typ
return (e',cs1 ++ cs2)
lookupEVar :: PGF -> TCEnv -> CId -> Err Value
@@ -100,40 +97,12 @@ eins = Map.insert
emptyTCEnv :: TCEnv
emptyTCEnv = (0,eempty,eempty)
whnf :: Value -> Err Value
whnf v = case v of
VApp u w -> do
u' <- whnf u
w' <- whnf w
return $ apply u' w'
VClosure env e -> return $ eval env e
_ -> return v
eqValue :: Int -> Value -> Value -> Err [(Value,Value)]
eqValue k u1 u2 = do
w1 <- whnf u1
w2 <- whnf u2
let v = VGen k
case (w1,w2) of
(VApp f1 a1, VApp f2 a2) -> liftM2 (++) (eqValue k f1 f2) (eqValue k a1 a2)
(VClosure env1 (EAbs x1 e1), VClosure env2 (EAbs x2 e2)) ->
eqValue (k+1) (VClosure (eins x1 v env1) e1) (VClosure (eins x2 v env2) e2)
(VClosure env1 (EPi x1 a1 b1), VClosure env2 (EPi x2 a2 b2)) ->
liftM2 (++)
(eqValue k (VClosure env1 a1) (VClosure env2 a2))
(eqValue (k+1) (VClosure (eins x1 v env1) b1) (VClosure (eins x2 v env2) b2))
(VGen i, VGen j) -> return [(w1,w2) | i /= j]
(VVar i, VVar j) -> return [(w1,w2) | i /= j]
_ -> return [(w1,w2) | w1 /= w2]
-- invariant: constraints are in whnf
-- this is not given in Expr
prValue = showExpr . value2expr
value2expr v = case v of
VApp v u -> EApp (value2expr v) (value2expr u)
VVar x -> EVar x
VApp f vs -> foldl EApp (EVar f) (map value2expr vs)
VMeta i -> EMeta i
VClosure g e -> e ----
VLit l -> ELit l