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[refactor] Relation.Nulllary.Decidable.Core #2329

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Merged
merged 2 commits into from
Mar 27, 2024
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[refactor] Relation.Nulllary.Decidable.Core #2329

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847b270
minor refactor: use Data.Unit.Polymorphic instead of an explicit Lift.
JacquesCarette Mar 26, 2024
20dfc42
additional tweak: use contradiction where possible.
JacquesCarette Mar 26, 2024
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10 changes: 5 additions & 5 deletions src/Relation/Nullary/Decidable/Core.agda
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Original file line number Diff line number Diff line change
Expand Up @@ -13,14 +13,14 @@ module Relation.Nullary.Decidable.Core where

open import Level using (Level; Lift)
open import Data.Bool.Base using (Bool; T; false; true; not; _∧_; _∨_)
open import Data.Unit.Base using (⊤)
open import Data.Empty using (⊥)
open import Data.Unit.Polymorphic.Base using (⊤)
open import Data.Empty.Irrelevant using (⊥-elim)
open import Data.Product.Base using (_×_)
open import Data.Sum.Base using (_⊎_)
open import Function.Base using (_∘_; const; _$_; flip)
open import Relation.Nullary.Reflects
open import Relation.Nullary.Negation.Core
using (¬_; Stable; negated-stable; contradiction; DoubleNegation)

private
variable
Expand Down Expand Up @@ -58,11 +58,11 @@ module _ {A : Set a} where

From-yes : Dec A → Set a
From-yes (true because _) = A
From-yes (false because _) = Lift a ⊤
From-yes (false because _) = ⊤

From-no : Dec A → Set a
From-no (false because _) = ¬ A
From-no (true because _) = Lift a ⊤
From-no (true because _) = ⊤

------------------------------------------------------------------------
-- Recompute
Expand Down Expand Up @@ -171,7 +171,7 @@ proof (map′ A→B B→A (false because [¬a])) = ofⁿ (invert [¬a] ∘ B→A

decidable-stable : Dec A → Stable A
decidable-stable (yes a) ¬¬a = a
decidable-stable (no ¬a) ¬¬a = ⊥-elim (¬¬a ¬a)
decidable-stable (no ¬a) ¬¬a = contradiction ¬a ¬¬a

¬-drop-Dec : Dec (¬ ¬ A) → Dec (¬ A)
¬-drop-Dec ¬¬a? = map′ negated-stable contradiction (¬? ¬¬a?)
Expand Down