module Chapter5.Brady.Fin where open import Function open import Data.Empty open import Data.Unit open import Data.Nat open import Data.Fin open import Data.Vec open import Data.Product open import Relation.Binary.PropositionalEquality open import Chapter1.Logic open import Chapter2.IDesc.Tagged open import Chapter2.IDesc.Fixpoint open import Chapter2.IDesc.Examples.Fin open import Chapter5.Ornament FinO : orn (toDesc Constraint.FinD) id id FinO = orn.mk λ { zero → insert ⊥ ⊥-elim ; (suc n) → `Σ {S = Fin 2} λ { zero → deleteΣ n (deleteΣ refl `1) ; (suc zero) → deleteΣ n (deleteΣ refl (`var (inv n) `× `1)) ; (suc (suc ())) } } Fin' : ℕ → Set Fin' = μ ⟦ FinO ⟧orn fz : ∀{n} → Fin' (suc n) fz = ⟨ zero , tt ⟩ fs : ∀{n} → Fin' n → Fin' (suc n) fs k = ⟨ suc zero , k , tt ⟩