In the book "Haskell programming from first principles" it is said that:
If you are using GHC 7.10 or newer, you’ll see an Applicative constraint in
> the definition of Monad, as it should be:
class Applicative m => Monad m where
> (>>=) :: m a -> (a -> m b) -> m b
> (>>) :: m a -> m b -> m b
> return :: a -> m a
I have created the following applicative functor.
data WhoCares a = ItDoesnt | Matter a | WhatThisIsCalled deriving (Eq, Show)
instance Functor WhoCares where
fmap _ ItDoesnt = ItDoesnt
fmap _ WhatThisIsCalled = WhatThisIsCalled
fmap f (Matter a) = Matter (f a)
instance Applicative WhoCares where
pure = Matter
Matter f <*> Matter a = Matter (f a)
main = do
-- fmap id == id
let funcx = fmap id "Hi Julie"
let funcy = id "Hi Julie"
print(funcx)
print(funcy)
print(funcx == funcy)
-- fmap (f . g) == fmap f . fmap g
let funcx' = fmap ((+1) . (*2)) [1..5]
let funcy' = fmap (+1) . fmap (*2) $ [1..5]
print(funcx')
print(funcy')
print(funcx' == funcy')
-- pure id <*> v = v
print(pure id <*> (Matter 10))
-- pure (.) <*> u <*> v <*> w = u <*> (v <*> w)
let appx = pure (.) <*> (Matter (+1)) <*> (Matter (*2)) <*> (Matter 10)
let appy = (Matter (+1)) <*> ((Matter (*2)) <*> (Matter 10))
print(appx)
print(appy)
print(appx == appy)
-- pure f <*> pure x = pure (f x)
let appx' = pure (+1) <*> pure 1 :: WhoCares Int
let appy' = pure ((+1) 1) :: WhoCares Int
print(appx')
print(appy')
print(appx' == appy')
-- u <*> pure y = pure ($ y) <*> u
let appx'' = Matter (+2) <*> pure 2
let appy'' = pure ($ 2) <*> Matter (+ 2)
print(appx'')
print(appy'')
print(appx'' == appy'')
Due to lack of examples, I am not understanding how to implement >>= and
>>. The code I came up with so far is:
instance Monad (WhoCares a) where
(>>=) :: Matter a -> (a -> Matter b) -> Matter b
(>>) :: Matter a -> Matter b -> Matter b
return :: a -> Matter a
return = pure
So, that I can do stuff like:
half x = if even x
then Matter (x `div` 2)
else ItDoesnt
incVal :: (Ord a, Num a) => a -> WhoCares a
incVal x
| x + 1 <= 10 = return (x + 1)
| otherwise = ItDoesnt
decVal :: (Ord a, Num a) => a -> WhoCares a
decVal x
| x - 1 >= 0 = return (x - 1)
| otherwise = ItDoesnt
main = do
print (Matter 7 >>= incVal >>= incVal >>= incVal)
print (Matter 7 >>= incVal >>= incVal >>= incVal >>= incVal)
print (Matter 7 >>= incVal >>= incVal >>= incVal >>= incVal >>= decVal
>>= decVal)
print (Matter 2 >>= decVal >>= decVal >>= decVal)
print(Matter 20 >>= half >>= half)
With Output:
10
ItDoesnt
ItDoesnt
ItDoesnt
5
Please help.
*Thanks and Best Regards,Ahmad Ismail*
