module Quox.Thin.Coprod

import public Quox.Thin.Base
import public Quox.Thin.Comp
import public Quox.Thin.View
import public Quox.Thin.List
import public Quox.Thin.Cover
import Data.DPair

%default total

public export
record Coprod2 (ope1 : OPE m1 n mask1) (ope2 : OPE m2 n mask2) where
  constructor MkCoprod2
  {sizeMask  : Nat}
  {leftMask  : Nat}
  {rightMask : Nat}
  {0 sub     : OPE size n sizeMask}
  {0 left    : OPE m1 size leftMask}
  {0 right   : OPE m2 size rightMask}
  0 leftComp  : Comp sub left  ope1
  0 rightComp : Comp sub right ope2
  {auto 0 isCover : Cover [left, right]}
%name Coprod2 cop

export
coprod2 : {n, mask1, mask2 : Nat} ->
          (0 ope1 : OPE m1 n mask1) -> (0 ope2 : OPE m2 n mask2) ->
          Coprod2 ope1 ope2
coprod2 ope1 ope2 with (view ope1) | (view ope2)
  coprod2 Stop Stop | StopV | StopV = MkCoprod2 StopZ StopZ
  coprod2 (Drop ope1 Refl) (Drop ope2 Refl) | DropV _ ope1 | DropV _ ope2 =
    let MkCoprod2 l r = coprod2 ope1 ope2 in MkCoprod2 (DropZ l) (DropZ r)
  coprod2 (Drop ope1 Refl) (Keep ope2 Refl) | DropV _ ope1 | KeepV _ ope2 =
    let MkCoprod2 l r = coprod2 ope1 ope2 in MkCoprod2 (KDZ l) (KeepZ r)
  coprod2 (Keep ope1 Refl) (Drop ope2 Refl) | KeepV _ ope1 | DropV _ ope2 =
    let MkCoprod2 l r = coprod2 ope1 ope2 in MkCoprod2 (KeepZ l) (KDZ r)
  coprod2 (Keep ope1 Refl) (Keep ope2 Refl) | KeepV _ ope1 | KeepV _ ope2 =
    let MkCoprod2 l r = coprod2 ope1 ope2 in MkCoprod2 (KeepZ l) (KeepZ r)

-- [todo] n-ary coprod