insertion-sort.timl

(* Insertion sort *)

structure InsertionSort = struct

open Basic
open List
       
absidx T_insert : BigO (fn m n => $m * $n) with
fun insert ['a] {m : Nat} {n : Nat} (le : 'a * 'a -- $m --> bool) (xs : list 'a {n}) x return list 'a {n + 1} using T_insert m n =
    case xs of
        Nil => Cons (x, Nil)
      | Cons (x', xs') =>
        case le (x, x') of
            true => Cons (x, xs)
          | false => Cons (x', insert le xs' x)
end

absidx T_isort : BigO (fn m n => $m * $n * $n) with
fun isort ['a] {m : Nat} {n : Nat} (le : 'a * 'a -- $m --> bool) (xs : list 'a {n}) return list 'a {n} using T_isort m n =
    case xs of
        Nil => Nil
      | Cons (x, xs) => insert le (isort le xs) x
end

end