copumpkin

-- This is the type we're working with.
data List a = List (forall r. (a -> r -> r) -> r -> r)

-- Implement this signature. It should not be inefficient, so if you're planning
-- on writing something like tail (notoriously inefficient using foldr) on our
-- List type, think again! It should be possible to write with the same time
-- complexity as the original. And of course, converting to/from a conventional
-- list is cheating :)

zipWith :: (a -> b -> c) -> List a -> List b -> List c

copumpkin

module Nicomachus where

open import Function
open import Relation.Binary.PropositionalEquality
import Relation.Binary.EqReasoning as EqReasoning

open import Data.Nat
open import Data.Nat.Properties

-- http://en.wikipedia.org/wiki/Nicomachus%27s_theorem