------------------------------------------------------------------------
-- The Agda standard library
--
-- Modalities used in the reflection machinery
------------------------------------------------------------------------
 
{-# OPTIONS --cubical-compatible --safe #-}
 
module Reflection.AST.Argument.Modality where
 
open import Data.Product.Base                          using (_×_; <_,_>; uncurry)
open import Relation.Nullary.Decidable.Core            using (map′; _×-dec_)
open import Relation.Binary.Definitions                using (DecidableEquality)
open import Relation.Binary.PropositionalEquality.Core using (_≡_; refl; cong₂)
 
open import Reflection.AST.Argument.Relevance as Relevance using (Relevance)
open import Reflection.AST.Argument.Quantity as Quantity using (Quantity)
 
private
  variable
    r r′ : Relevance
    q q′ : Quantity
 
------------------------------------------------------------------------
-- Re-exporting the builtins publicly
 
open import Agda.Builtin.Reflection public using (Modality)
open Modality public
 
------------------------------------------------------------------------
-- Operations
 
relevance : Modality → Relevance
relevance (modality r _) = r
 
quantity : Modality → Quantity
quantity (modality _ q) = q
 
------------------------------------------------------------------------
-- Decidable equality
 
modality-injective₁ : modality r q ≡ modality r′ q′ → r ≡ r′
modality-injective₁ refl = refl
 
modality-injective₂ : modality r q ≡ modality r′ q′ → q ≡ q′
modality-injective₂ refl = refl
 
modality-injective : modality r q ≡ modality r′ q′ → r ≡ r′ × q ≡ q′
modality-injective = < modality-injective₁ , modality-injective₂ >
 
infix  _≟_
 
_≟_ : DecidableEquality Modality
modality r q ≟ modality r′ q′ =
  map′
    (uncurry (cong₂ modality))
    modality-injective
    (r Relevance.≟ r′ ×-dec q Quantity.≟ q′)