Created
January 10, 2012 14:14
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Classic example on how to use GADTs
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{-# LANGUAGE GADTs #-} | |
data Expr t where | |
Con :: Int -> Expr Int | |
Add :: Expr Int -> Expr Int -> Expr Int | |
Mult :: Expr Int -> Expr Int -> Expr Int | |
IsZ :: Expr Int -> Expr Bool | |
If :: Expr Bool -> Expr t -> Expr t -> Expr t | |
And :: Expr Bool -> Expr Bool -> Expr Bool | |
Or :: Expr Bool -> Expr Bool -> Expr Bool | |
Tuple :: Expr t -> Expr s -> Expr (t,s) | |
Fst :: Expr(t,s) -> Expr t | |
Snd :: Expr(t,s) -> Expr s | |
unop op e = op ++ "(" ++ show e ++ ")" | |
binop op e1 e2 = op ++ "(" ++ show e1 ++ "," ++ show e2 ++ ")" | |
instance Show (Expr t) where | |
show (Con i) = "Con " ++ show i | |
show (Add e1 e2) = binop "Add" e1 e2 | |
show (Mult e1 e2) = binop "Mult" e1 e2 | |
show (IsZ e) = unop "IsZ" e | |
show (If b e1 e2) = "If(" ++ show b ++ "," ++ show e1 ++ "," ++ show e2 ++ ")" | |
show (And e1 e2) = binop "And" e1 e2 | |
show (Or e1 e2) = binop "Or" e1 e2 | |
show (Tuple e1 e2) = binop "Pair" e1 e2 | |
show (Fst e) = unop "Fst" e | |
show (Snd e) = unop "Snd" e | |
--v1 = Add (IsZ $ Con 0) (Con 1) --Not allowed | |
v2 = Fst $ Tuple (Add (Con 41) (Con 1)) (Con 2) --All fine | |
eval :: Expr t -> t | |
eval (Con i) = i | |
eval (Add e1 e2) = eval e1 + eval e2 | |
eval (Mult e1 e2) = eval e1 * eval e2 | |
eval (IsZ e) = eval e == 0 | |
eval (If b e1 e2) = if eval b then eval e1 else eval e2 | |
eval (And e1 e2) = eval e1 && eval e2 | |
eval (Or e1 e2) = eval e1 || eval e2 | |
eval (Tuple e1 e2) = (eval e1, eval e2) | |
eval (Fst e) = fst $ eval e | |
eval (Snd e) = snd $ eval e |
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