Add delete, nub, sort to Data.List

lib/Haskell/Data/List.agda

@@ -2,10 +2,39 @@ module Haskell.Data.List where
 
 open import Haskell.Prelude
 
+open import Haskell.Data.Ord using (comparing)
+
+open import Haskell.Law.Eq
+open import Haskell.Law.Equality
+
 {-----------------------------------------------------------------------------
     Operations
 ------------------------------------------------------------------------------}
 
 partition : (a → Bool) → List a → (List a × List a)
 partition p xs = (filter p xs , filter (not ∘ p) xs)
 
+deleteBy : (a → a → Bool) → a → List a → List a
+deleteBy eq x ys = filter (not ∘ (eq x)) ys
+
+delete : ⦃ Eq a ⦄ → a → List a → List a
+delete = deleteBy (_==_)
+
+-- | These semantics of 'nub' assume that the 'Eq' instance
+-- is lawful.
+-- These semantics are inefficient, but good for proofs.
+nub : ⦃ _ : Eq a ⦄ → @0 ⦃ IsLawfulEq a ⦄ → List a → List a
+nub [] = []
+nub (x ∷ xs) = x ∷ delete x (nub xs)
+
+postulate
+  sortBy : (a → a → Ordering) → List a → List a
+
+sort : ⦃ Ord a ⦄ → List a → List a
+sort = sortBy compare
+
+sortOn : ⦃ Ord b ⦄ → (a → b) → List a → List a
+sortOn f =
+    map snd
+    ∘ sortBy (comparing fst)
+    ∘ map (λ x → let y = f x in seq y (y , x))