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