Haskell applicative functor - compilation failure

Question

I'm trying to chain together functions via the applicative functor pattern, but I'm having a problem compiling my code:

import Control.Applicative

buildMyList :: Float -> Float -> [Float]
buildMyList ul tick = [p | p <- [0,tick..ul]]

myFunctionChain :: [Float]
myFunctionChain = reverse <$> buildMyList 100 1

When I attempt to compile this I get the following compilation error:

Couldn't match type 'Float' with '[a0]'
Expected type: [[a0]]
  Actual type: [Float]
In the return type of call of 'buildMyList'

It seems to me that I haven't managed to match the expected return context with the actual context. Not having enough experience in this area, I cant get any further!

Answer 1

The Applicative could be better explained using bulldMyList . Assume you want to build an array of square matrix: [(0,0), (0,1), (0,2), (1, 0) ...] . Using list comprehensions:

buildMyMatrix :: Int -> Int -> [(Int, Int)]
buildMyMatrix maxX maxY = [(x, y) | x <- [0..maxX], y <- [0..maxY]]

Using applicative combinators it can be rewritten as:

buildMyMatrix maxX maxY = pure (\x y -> (x, y)) <*> [0..maxX] <*> [0..maxY]

And according to applicative laws we can rewrite pure f <*> x = f <$> x , for all f and x :

buildMyMatrix maxX maxY = (\x y -> (x, y)) <$> [0..maxX] <*> [0..maxY]

---

I had to use slightly more complicated buildMyMatrix , as your buildMyList is too trivial to benefit from Applicative:

buildMyList :: Float -> Float -> [Float]
buildMyList ul tick = [p | p <- [0,tick..ul]]
buildMyList ul tick = id <$> [0,tick..ul] -- [by functor identity law]:
buildMyList ul tick = [0,tick..ul]