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|
import Control.Monad (ap)
import Control.Applicative (Applicative(..), (<$>))
-- Représenter la récursion au niveau du typage
newtype Mu f = Mu { unMu :: f (Mu f) }
-- Utiliser un fonction d'ordre supérieur pour parcourir une structure récursive
foldMu :: Functor f => (f a -> a) -> Mu f -> a
foldMu f = f . fmap (foldMu f) . unMu
-- Nos structures récursives
type Ids = String
type Exp = Mu Exp1
data Exp1 a = Id Ids
| Const Tree
| Add a a
| Sub a a
| Multi a a
| Comp a a
| Neg a
| And a a
| Or a a
| Equal a a
| Pair a a
| Fst a
| Snd a
| If a a a
type Tree = Mu Tree1
data Tree1 a = PairTree a a
| TreeValue Value deriving Show
data Value = Number Int
| Boolean Bool deriving Show
type Memory = [(Ids, Tree)]
-- Accès au point de récursion de chaque structure récursive
instance Functor Exp1 where
fmap _ (Id i) = Id i
fmap _ (Const t) = Const t
fmap f (Add x y) = Add (f x) (f y)
fmap f (Sub x y) = Sub (f x) (f y)
fmap f (Multi x y) = Multi (f x) (f y)
fmap f (Comp x y) = Comp (f x) (f y)
fmap f (Neg x) = Neg (f x)
fmap f (And x y) = And (f x) (f y)
fmap f (Or x y) = Or (f x) (f y)
fmap f (Equal x y) = Equal (f x) (f y)
fmap f (Pair x y) = Pair (f x) (f y)
fmap f (Fst x) = Fst (f x)
fmap f (Snd x) = Snd (f x)
fmap f (If x y z) = If (f x) (f y) (f z)
instance Functor Tree1 where
fmap f (PairTree x y) = PairTree (f x) (f y)
fmap _ (TreeValue v) = TreeValue v
-- Exp Api
newId :: Ids -> Exp
newId = Mu . Id
constExp :: Tree -> Exp
constExp = Mu . Const
add :: Exp -> Exp -> Exp
add x y = Mu $ Add x y
sub :: Exp -> Exp -> Exp
sub x y = Mu $ Sub x y
multi :: Exp -> Exp -> Exp
multi x y = Mu $ Multi x y
comp :: Exp -> Exp -> Exp
comp x y = Mu $ Comp x y
neg :: Exp -> Exp
neg = Mu . Neg
and :: Exp -> Exp -> Exp
and x y = Mu $ And x y
or :: Exp -> Exp -> Exp
or x y = Mu $ Or x y
equal :: Exp -> Exp -> Exp
equal x y = Mu $ Equal x y
pair :: Exp -> Exp -> Exp
pair x y = Mu $ Pair x y
-- Conflit possible si Control.Arrow est importé
first :: Exp -> Exp
first = Mu . Fst
-- Conflit possible si Control.Arrow est importé
second :: Exp -> Exp
second = Mu . Snd
ifExp :: Exp -> Exp -> Exp -> Exp
ifExp x y z = Mu $ If x y z
-- Tree Api
pairTree :: Tree -> Tree -> Tree
pairTree x y = Mu $ PairTree x y
treeValue :: Value -> Tree
treeValue = Mu . TreeValue
toNumber :: Int -> Tree
toNumber = treeValue . Number
toBoolean :: Bool -> Tree
toBoolean = treeValue . Boolean
-- eval Api
newtype Eval a = Eval { runEval :: Memory -> Maybe a } -- équivalent de ReaderT Memory Maybe a
instance Functor Eval where
fmap f (Eval k) = Eval (fmap f . k)
instance Applicative Eval where
pure = return
(<*>) = ap
instance Monad Eval where
return = Eval . const . Just
(Eval k) >>= f =
Eval $ \mem -> do
a <- k mem
runEval (f a) mem
askMemory :: Eval Memory
askMemory = Eval Just
evalError :: Eval a
evalError = Eval $ const Nothing
evalInt :: Tree -> Eval Int
evalInt = foldMu go
where
go (TreeValue v) =
case v of
Number i -> return i
_ -> evalError
go _ = evalError
evalBool :: Tree -> Eval Bool
evalBool = foldMu go
where
go (TreeValue v) =
case v of
Boolean b -> return b
_ -> evalError
go _ = evalError
evalPair :: Tree -> Eval (Tree, Tree)
evalPair tree = do
res <- foldMu go tree $ 0
case res of
(1, Mu(PairTree x y)) -> return (x, y)
_ -> evalError
where
go (PairTree kx ky) level = do
let level2 = level+1
(_,x) <- kx level2
(_,y) <- ky level2
let res = pairTree x y
if level == 0
then return (1, res) -- c'est un Pair !
else return (level, res)
go (TreeValue v) level = return (level, treeValue v)
lookupMemory :: Ids -> Eval Tree
lookupMemory x = do
mem <- askMemory
maybe evalError return (lookup x mem)
evalExp :: Exp -> Memory -> Maybe Tree
evalExp = runEval . foldMu go
where
go (Id x) = lookupMemory x
go (Const t) = return t
go (Add ex ey) = do
x <- ex >>= evalInt
y <- ey >>= evalInt
return $ toNumber (x + y)
go (Sub ex ey) = do
x <- ex >>= evalInt
y <- ey >>= evalInt
return $ toNumber (x - y)
go (Multi ex ey) = do
x <- ex >>= evalInt
y <- ey >>= evalInt
return $ toNumber (x * y)
go (Comp ex ey) = do
x <- ex >>= evalInt
y <- ey >>= evalInt
return $ toBoolean (x < y)
go (Neg ex) = do
x <- ex >>= evalBool
return $ toBoolean $ not x
go (And ex ey) = do
x <- ex >>= evalBool
y <- ey >>= evalBool
return $ toBoolean (x && y)
go (Or ex ey) = do
x <- ex >>= evalBool
y <- ey >>= evalBool
return $ toBoolean (x || y)
go (Equal ex ey) = do
x <- ex >>= evalInt
y <- ey >>= evalInt
return $ toBoolean (x == y)
go (Pair ex ey) = pairTree <$> ex <*> ey
go (Fst ex) = do
(l,_) <- ex >>= evalPair
return l
go (Snd ex) = do
(_,r) <- ex >>= evalPair
return r
go (If ep et ef) = do
p <- ep >>= evalBool
if p
then et
else ef |
simplifier mon where
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