irrelevance of recompute

CHANGELOG.md

@@ -407,6 +407,11 @@ Additions to existing modules
  WeaklyDecidable : Set _
  ```
 
+* Added new proof in `Relation.Nullary.Decidable.Core`:
+ ```agda
+ recompute-irr : (a? : Dec A) (p q : A) → recompute a? p ≡ recompute a? q
+ ```
+
 * Added new proof in `Relation.Nullary.Decidable`:
  ```agda
  ⌊⌋-map′ : (a? : Dec A) → ⌊ map′ t f a? ⌋ ≡ ⌊ a? ⌋
@@ -419,13 +424,8 @@ Additions to existing modules
 
 * Added new definitions in `Relation.Nullary.Reflects`:
  ```agda
- recompute : Reflects A b → Recomputable A
- ```
-
-* Added new definitions in `Relation.Unary`
- ```
- Stable : Pred A ℓ → Set _
- WeaklyDecidable : Pred A ℓ → Set _
+ recompute : Reflects A b → Recomputable A
+ recompute-irr : (r : Reflects A b) (p q : A) → recompute r p ≡ recompute r q
  ```
 
 * Added new definitions in `Relation.Unary`

src/Relation/Nullary/Decidable/Core.agda

@@ -18,9 +18,10 @@ open import Data.Product.Base using (_×_)
 open import Data.Sum.Base using (_⊎_)
 open import Function.Base using (_∘_; const; _$_; flip)
 open import Relation.Nullary.Recomputable
-open import Relation.Nullary.Reflects as Reflects hiding (recompute)
+open import Relation.Nullary.Reflects as Reflects hiding (recompute; recompute-irr)
 open import Relation.Nullary.Negation.Core
  using (¬_; Stable; negated-stable; contradiction; DoubleNegation)
+open import Agda.Builtin.Equality using (_≡_)
 
 private
  variable
@@ -73,6 +74,9 @@ module _ {A : Set a} where
 recompute : Dec A → Recomputable A
 recompute = Reflects.recompute ∘ proof
 
+recompute-irr : (a? : Dec A) (p q : A) → recompute a? p ≡ recompute a? q
+recompute-irr = Reflects.recompute-irr ∘ proof
+
 ------------------------------------------------------------------------
 -- Interaction with negation, sum, product etc.
 

src/Relation/Nullary/Reflects.agda

@@ -61,6 +61,9 @@ recompute : ∀ {b} → Reflects A b → Recomputable A
 recompute (ofʸ a) _ = a
 recompute (ofⁿ ¬a) a = contradiction-irr a ¬a
 
+recompute-irr : ∀ {b} (r : Reflects A b) (p q : A) → recompute r p ≡ recompute r q
+recompute-irr r p q = refl
+
 ------------------------------------------------------------------------
 -- Interaction with negation, product, sums etc.