diff --git a/Lattice/Builder.agda b/Lattice/Builder.agda index f9f2374..4ba0465 100644 --- a/Lattice/Builder.agda +++ b/Lattice/Builder.agda @@ -129,10 +129,6 @@ record IsPartialSemilattice {a} {A : Set a} x-identityʳ : (a : A) → (a ⊔? x) ≈? just a x-identityʳ a = ≈?-trans (⊔-comm a x) (x-identityˡ a) -Maybe-≈ : ∀ {a} {A : Set a} → (_≈_ : A → A → Set a) → Maybe A → A → Set a -Maybe-≈ _≈_ (just a₁) a₂ = a₁ ≈ a₂ -Maybe-≈ {a} _≈_ nothing a₂ = Trivial a - record IsPartialLattice {a} {A : Set a} (_≈_ : A → A → Set a) (_⊔?_ : A → A → Maybe A) @@ -142,8 +138,8 @@ record IsPartialLattice {a} {A : Set a} {{partialJoinSemilattice}} : IsPartialSemilattice _≈_ _⊔?_ {{partialMeetSemilattice}} : IsPartialSemilattice _≈_ _⊓?_ - absorb-⊔-⊓ : (x y : A) → Maybe-≈ _≈_ ((x ⊓? y) >>= (x ⊔?_)) x - absorb-⊓-⊔ : (x y : A) → Maybe-≈ _≈_ ((x ⊔? y) >>= (x ⊓?_)) x + absorb-⊔-⊓ : (x y : A) → maybe (λ x⊓y → lift-≈ _≈_ (x ⊔? x⊓y) (just x)) (Trivial _) (x ⊓? y) + absorb-⊓-⊔ : (x y : A) → maybe (λ x⊔y → lift-≈ _≈_ (x ⊓? x⊔y) (just x)) (Trivial _) (x ⊔? y) open IsPartialSemilattice partialJoinSemilattice public open IsPartialSemilattice partialMeetSemilattice using ()