gistfile1.txt

Given:

pure ∷ a → f a
⊛ ∷ f (a → b) → f a → f b

(.) ∷ (b → c) → (a → b) → a → c

show:

pure (.) ⊛ u ⊛ v ⊛ = u ⊛ (v ⊛ w)

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LHS:

pure (.)
  ∷ f ((b → c) -> ((a → b) → a → c))
pure (.) ⊛ u
  ∷ f ((a → b) → a → c)
pure (.) ⊛ u ⊛ v
  ∷ f (a → c)
pure (.) ⊛ u ⊛ v ⊛ w
  ∷ f c

So:
u ∷ f (b → c)
v ∷ f (a → b)
w ∷ f a

RHS:
u ⊛ (v ⊛ w) ∷ f c