-- merge sort
module test032;

open import Stdlib.Prelude;
open import Stdlib.Data.Nat.Ord;

split : {A : Type} → Nat → List A → List A × List A;
split zero xs := (nil, xs);
split (suc n) nil := (nil, nil);
split (suc n) (x :: xs) := case split n xs
  | l1, l2 := (x :: l1, l2);

terminating
merge' : List Nat → List Nat → List Nat;
merge' nil ys := ys;
merge' xs nil := xs;
merge' xs@(x :: xs') ys@(y :: ys') := if (x <= y) (x :: merge' xs' ys) (y :: merge' xs ys');

terminating
sort : List Nat → List Nat;
sort xs :=
  let n : Nat; n := length xs in
  if (n <= 1)
    xs
    (case split (div n 2) xs
      | l1, l2 := merge' (sort l1) (sort l2)
    );

terminating
uniq : List Nat → List Nat;
uniq nil := nil;
uniq (x :: nil) := x :: nil;
uniq (x :: xs@(x' :: _)) := if (x == x') (uniq xs) (x :: uniq xs);

gen : List Nat → Nat → (Nat → Nat) → List Nat;
gen acc zero f := acc;
gen acc (suc n) f := gen (f (suc n) :: acc) n f;

gen2 : List (List Nat) → Nat → Nat → List (List Nat);
gen2 acc m zero := acc;
gen2 acc m (suc n) := gen2 (gen nil m ((+) (suc n)) :: acc) m n;

printListNatLn : List Nat → IO;
printListNatLn nil := printStringLn "nil";
printListNatLn (x :: xs) := printNat x >> printString " :: " >> printListNatLn xs;

main : IO;
main :=
  printListNatLn (take 10 (uniq (sort (flatten (gen2 nil 6 40))))) >>
  printListNatLn (take 10 (uniq (sort (flatten (gen2 nil 9 80))))) >>
  printListNatLn (take 10 (uniq (sort (flatten (gen2 nil 6 80)))));

end;