Haskell/Solutions/More on functions

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Operators

Exercises
  • Lambdas are a nice way to avoid defining unnecessary separate functions. Convert the following let- or where-bindings to lambdas:
    • map f xs where f x = x * 2 + 3
    • let f x y = read x + y in foldr f 1 xs
  • Sections are just syntactic sugar for lambda operations. I.e. (+2) is equivalent to \x -> x + 2. What would the following sections 'desugar' to? What would be their types?
    • (4+)
    • (1 `elem`)
    • (`notElem` "abc")

1.

  • Substitute f to get map (\ x -> x * 2 + 3) xs
  • Substitute f to get foldr (\ x y -> read x + y) 1 xs

2.

  • (4+)
    • Becomes (\ x -> 4 + x)
    • Has type Num a => a -> a
  • (1 `elem`)
    • Becomes(\ x -> 1 `elem` x)
    • Alternately written as (\ x -> elem 1 x)
    • Has type Num a :: a -> Bool
      • Note: The full type is (Foldable t, Eq a, Num a) => t a -> Bool but this has not been covered yet.
  • (`notElem` "abc")
    • Becomes (\ x -> x `notElem` "abc")
    • Alternately written as (\ x -> notElem x "abc")
    • Has type Char -> Bool
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