|20-CS-4003-001||Organization of Programming Languages||Fall 2018|
import Control.Monad f = (\ x -> if (x == 0) then fail "zero" else Just (x+1)) v1 = Just 5 >>= f v2 = Just 0 >>= f v3 = Nothing >>= f v4 = f 0 v5 = f 5 v1' = f =<< Just 5 v2' = f =<< Just 0 v3' = f =<< Nothing v6 = ap [(+1),(+2),(+3)] [1,2,3] v7 = fail "test" :: Maybe Int v8 = fail "test" :: Maybe [Int] v9 = fail "test" :: IO () v10 = filterM (\x -> Just (x > 0)) [2, 1, 0, -1] (./.) :: Fractional a => a -> a -> Maybe a x ./. 0 = Nothing x ./. y = Just (x / y) divide :: Fractional a => a -> [a] -> Maybe a divide x ys = foldM (./.) x ys v11 = divide 128 [2,4,8] v12 = divide 8 [2,3,4,0,6,7] v13 = guard True >> Just 3 v14 = guard False >> Just 3 v15 = liftM head (Just [23,24,25]) v16 = liftM tail (Just [23,24,25]) v17 = mzero :: [Int] v18 = mzero :: Maybe Int v19 = mplus "a" "b" v20 = mplus (Just "a") (Just "b") v21 = mplus (Just 10) (Just 20) v22 = mplus mzero (Just 10) v23 = mplus (Just 10) mzero v24 = (return 3) :: Maybe Int v25 = (return 3) :: [Int] v26 = getLine >>= (\x -> return (x ++ " " ++ x)) >>= print v27 = sequence [print 1, print 2, print 3] >>= print v28 = sequence [Just 1, Just 2, Just 3] v29 = unless (0 == 1) (print "OK") v30 = when (1 == 1) (print "OK")
The operator filerM filters out all elements of 2nd argument
that do not satisfy the 1st argument which is a function that returns
a value of type |
The operator foldM is the monadic version of fold:
that is, it takes a function of type
The operator guard returns () if its argument is True, otherwise it returns mzero. The value of v13 is Just 3 and the value of v14 is Nothing.
The operator liftM lets a non-monadic function (1st argument) operate on the contents of a monad (2nd argument). To the left, v15 has value Just 23 and v16 has value Just [24,25].
The operator mapM applies a monadic function (1st argument)
The operator mzero is the zero of the MonadPlus class.
To the left, the value of v17 is  and the value of
v18 is Nothing. Its type is
The operator mplus is the plus of the MonadPlus class. To the left, v19 has value "ab", v20 has value Just "a", v21 has value Just 10, v22 has value Just 10, v23 has value Just 10.
The operator sequence evaluates all monadic values in the
input list from left to right and returns a list of the "contents" of
these monads, placing this list in a monad of the same type.
Evaluating can be interpreted as "performing an action", for example
in the case of print. To the left v27 displays
The operator unless executes a monadic expression (2nd argument) when the first argument evaluates to False. Looking at v29 shows "OK".
The operator when executes a monadic expression (2nd argument) when the first argument evaluates to True. Looking at v30 shows "OK".
Monads are useful in any situation where the programmer wants to carry out a purely functional computation while a related computation is carried out on the side. In imperative programming the side effects are embedded in the semantics of the programming language; with monads, they are made explicit in the monad definition, thus avoiding errors by action at a distance.