module Quox.Thin.Cover

import public Quox.Thin.Base
import public Quox.Thin.List

%default total

||| an OPE list is a cover if at least one of the OPEs has `Keep` as the head,
||| and the tails are also a cover
|||
||| in @egtbs it is a binary relation which is fine for ×ᵣ but i don't want to
||| write my AST in universe-of-syntaxes style. sorry
public export data Cover : OPEList n -> Type

||| the "`Keep` in the head" condition of a cover
public export data Cover1 : OPEList n -> Type

data Cover where
  Nil  : Cover opes {n = 0}
  (::) : Cover1 opes -> All2 IsTail opes tails => Cover tails -> Cover opes
%name Cover cov

data Cover1 where
  Here  : Cover1 (Keep ope eq :: opes)
  There : Cover1 opes -> Cover1 (ope :: opes)
%name Cover1 cov1
%builtin Natural Cover1