module Chapter11.Patch where

open import Level

open import Data.Unit
open import Data.Product

open import Chapter2.Logic

open import Chapter6.IDesc.Fixpoint

open import Chapter10.Ornament
open import Chapter10.Reornament

open import Chapter11.Functions
open import Chapter11.FunOrnament



Patch : ∀{}{T : Type }   T ⟧Type  FunctionOrn T  Set 
Patch {T = μ D [ ._ ]→ T} f (μ⁺ o [ inv i⁺ ]→ T⁺) = 
      (x : μ D _)  
         μ (reornD o) (i⁺ , x)  Patch (f x) T⁺
Patch {T = μ D [ ._  T} (x , t) (μ⁺ o [ inv i⁺  T⁺) =
      μ (reornD o) (i⁺ , x) × Patch t T⁺
Patch {T = `⊤} (lift tt) `⊤ = Lift