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Add Dec for unit and empty types #2647

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Merged
merged 2 commits into from
Mar 6, 2025
Merged

Add Dec for unit and empty types #2647

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e820bd7
Add Dec for unit and empty types
carlostome Mar 6, 2025
30cfba0
Add changes to CHANGELOG.md
carlostome Mar 6, 2025
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6 changes: 6 additions & 0 deletions CHANGELOG.md
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Original file line number Diff line number Diff line change
Expand Up @@ -149,3 +149,9 @@ Additions to existing modules
```agda
filter-↭ : ∀ (P? : Pred.Decidable P) → xs ↭ ys → filter P? xs ↭ filter P? ys
```

* In `Relation.Nullary.Decidable.Core`:
```agda
⊤-dec : Dec {a} ⊤
⊥-dec : Dec {a} ⊥
```
11 changes: 10 additions & 1 deletion src/Relation/Nullary/Decidable/Core.agda
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Expand Up @@ -18,7 +18,8 @@ open import Agda.Builtin.Maybe using (Maybe; just; nothing)
open import Agda.Builtin.Equality using (_≡_)
open import Level using (Level)
open import Data.Bool.Base using (Bool; T; false; true; not; _∧_; _∨_)
open import Data.Unit.Polymorphic.Base using (⊤)
open import Data.Unit.Polymorphic.Base using (⊤; tt)
open import Data.Empty.Polymorphic using (⊥)
open import Data.Product.Base using (_×_)
open import Data.Sum.Base using (_⊎_; inj₁; inj₂)
open import Function.Base using (_∘_; const; _$_; flip)
Expand Down Expand Up @@ -95,10 +96,18 @@ T? x = x because T-reflects x
does (¬? a?) = not (does a?)
proof (¬? a?) = ¬-reflects (proof a?)

⊤-dec : Dec {a} ⊤
does ⊤-dec = true
proof ⊤-dec = ofʸ tt

_×-dec_ : Dec A → Dec B → Dec (A × B)
does (a? ×-dec b?) = does a? ∧ does b?
proof (a? ×-dec b?) = proof a? ×-reflects proof b?

⊥-dec : Dec {a} ⊥
does ⊥-dec = false
proof ⊥-dec = ofⁿ λ ()

_⊎-dec_ : Dec A → Dec B → Dec (A ⊎ B)
does (a? ⊎-dec b?) = does a? ∨ does b?
proof (a? ⊎-dec b?) = proof a? ⊎-reflects proof b?
Expand Down