module Quox.OPE.Cover

import Quox.OPE.Basics
import Quox.OPE.Length
import Quox.OPE.Sub

%default total


public export
data Cover_ : (overlap : Bool) -> xs `Sub` zs -> ys `Sub` zs -> Type where
  CE : Cover_ ov End End
  CL : Cover_ ov p q -> Cover_ ov   (Keep p) (Drop q)
  CR : Cover_ ov p q -> Cover_ ov   (Drop p) (Keep q)
  C2 : Cover_ ov p q -> Cover_ True (Keep p) (Keep q)

public export
Cover : xs `Sub` zs -> ys `Sub` zs -> Type
Cover = Cover_ True

public export
Partition : xs `Sub` zs -> ys `Sub` zs -> Type
Partition = Cover_ False