Notes (CTFP 06/31): Simple Algebraic Data Types

6 Simple Algebraic Data Types

6.5 Challenges

  1. Isomorphism:

    f :: Maybe a -> Either () a
f Nothing = Left ()
f Just a = Right a

g :: Either () a -> Maybe a
g (Left ()) = Nothing
g (Right a) = Just a

  2. Life is too short for OOP boilerplate. Break the cycle Morty, rise above, focus on FP.

  3. Let’s think about all the possible values of a + a and 2 x a:

    a + a ~ Either a a = Left a | Right a
2 x a ~ (Bool, a)

    But (Bool, a) is just

    (True, a)
(False, a)

    so we have the isomorphism:

    f :: Either a a -> (Bool, a)
f (Left a) = (True, a)
f (Right a) = (False, a)

g :: (Bool, a) -> Either a a
g (True, a) = Left a
g (False, a) = Right a