Cubical.Data.NatMinusOne.Base

{-# OPTIONS --no-exact-split #-}
module Cubical.Data.NatMinusOne.Base where

open import Cubical.Core.Primitives
open import Cubical.Data.Nat
open import Cubical.Data.Empty

record ℕ₋₁ : Type₀ where
  constructor -1+_
  field
    n : ℕ

pattern neg1 = -1+ zero
pattern ℕ→ℕ₋₁ n = -1+ (suc n)

1+_ : ℕ₋₁ → ℕ
1+_ (-1+ n) = n

suc₋₁ : ℕ₋₁ → ℕ₋₁
suc₋₁ (-1+ n) = -1+ (suc n)

-- Natural number and negative integer literals for ℕ₋₁

open import Cubical.Data.Nat.Literals public

instance
  fromNatℕ₋₁ : HasFromNat ℕ₋₁
  fromNatℕ₋₁ = record { Constraint = λ _ → Unit ; fromNat = ℕ→ℕ₋₁ }

instance
  fromNegℕ₋₁ : HasFromNeg ℕ₋₁
  fromNegℕ₋₁ = record { Constraint = λ { (suc (suc _)) → ⊥ ; _ → Unit }
                       ; fromNeg = λ { zero →  ; (suc zero) → neg1 } }