TAL.hs

-- | a. Fix that for me - write a list that allows me to hold any functions as
-- long as the input of one lines up with the output of the next.

data TypeAlignedList a b where
  TNil :: TypeAlignedList a a
  TCons :: (a -> r) -> TypeAlignedList r b -> TypeAlignedList a b
-- >>> f = TCons (+2) (TCons show TNil); f :: TypeAlignedList Int String

-- | b. Which types are existential?
-- r

-- | c. Write a function to append type-aligned lists. This is almost certainly
-- not as difficult as you'd initially think.

composeTALs :: TypeAlignedList b c -> TypeAlignedList a b -> TypeAlignedList a c
composeTALs bc TNil = bc -- a ~ b => TypeAlignedList b c ~ TypeAlignedList a c
composeTALs bc (TCons ax txb) = TCons ax (composeTALs bc txb)

evalTAL :: TypeAlignedList a b -> (a -> b)
evalTAL TNil = id
evalTAL (TCons ax txb) = evalTAL txb . ax
-- >>> f = (TCons show TNil); f :: TypeAlignedList Int String
-- >>> g = (TCons read TNil); g :: TypeAlignedList String Int
-- >>> gof = composeTALs g f
-- (evalTAL gof) 1234
-- 1234