Exception Monado

gistfile1.hs

--
-- Excerpt from Monads for functional programming
-- http://homepages.inf.ed.ac.uk/wadler/papers/marktoberdorf/baastad.pdf
--

-- 2.1 Variation zero: The basic evaluator 
--
data Term = Con Int | Div Term Term

eval :: Term -> Int
eval (Con a) = a 
eval (Div t v) = div (eval t) (eval v)

answer :: Term
answer = Div (Div (Con 1972) (Con 2)) (Con 23) 

err :: Term
err = Div (Con 1) (Con 0)

-- 2.2 Variation one: Exceptions
--
data M a = Raise Exception | Return a deriving (Show)
type Exception = String

eval1 :: Term -> M Int
eval1 (Con a) = Return a
eval1 (Div t v) = case eval1 t of
                       Raise e -> Raise e
                       Return a -> case eval1 v of
                                        Raise e -> Raise e
                                        Return b -> if b==0
                                                    then Raise "divide by zero (eval1)"
                                                    else Return (div a b)

-- 2.7 Variation one, revisited: Exceptions
--              
unit :: a -> M a
unit a = Return a

bind :: M a -> (a -> M b) -> M b
bind m k = case m of
                Raise e -> Raise e
                Return a -> k a

raise :: Exception -> M a
raise e = Raise e 

eval2 :: Term -> M Int
eval2 (Con a) = unit a
eval2 (Div t v) = (eval2 t) `bind` λa -> eval2 v `bind` λb -> unit (div a b)

eval2' :: Term -> M Int
eval2' (Con a) = unit a
eval2' (Div t v) = (eval2' t) `bind` λa -> eval2' v `bind` λb -> if b == 0 then raise "divide by zero (eval2')" else unit (div a b)