The library has been tested using Agda 2.7.0 and 2.7.0.1.
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Algebra.Apartness.Structures, renamedsymfromIsApartnessRelationto#-symin order to avoid overloaded projection.irreflandcotransare similarly renamed for the sake of consistency.
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The implementation of
≤-totalinData.Nat.Propertieshas been altered to use operations backed by primitives, rather than recursion, making it significantly faster. However, its reduction behaviour on open terms may have changed. -
The definition of
AdjointinRelation.Binary.Definitionshas been altered to be the conjunction of two universally quantifiedHalf*Adjointproperties, rather than to be a universally quantified conjunction, for better compatibility withFunction.Definitions.
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Algebra.Definitions.RawMagma:_∣∣_ ↦ _∥_ _∤∤_ ↦ _∦_
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Algebra.Module.Consequences*ₗ-assoc+comm⇒*ᵣ-assoc ↦ *ₗ-assoc∧comm⇒*ᵣ-assoc *ₗ-assoc+comm⇒*ₗ-*ᵣ-assoc ↦ *ₗ-assoc∧comm⇒*ₗ-*ᵣ-assoc *ᵣ-assoc+comm⇒*ₗ-assoc ↦ *ᵣ-assoc∧comm⇒*ₗ-assoc *ₗ-assoc+comm⇒*ₗ-*ᵣ-assoc ↦ *ₗ-assoc∧comm⇒*ₗ-*ᵣ-assoc
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Algebra.Properties.Magma.Divisibility:∣∣-sym ↦ ∥-sym ∣∣-respˡ-≈ ↦ ∥-respˡ-≈ ∣∣-respʳ-≈ ↦ ∥-respʳ-≈ ∣∣-resp-≈ ↦ ∥-resp-≈ ∤∤-sym -≈ ↦ ∦-sym ∤∤-respˡ-≈ ↦ ∦-respˡ-≈ ∤∤-respʳ-≈ ↦ ∦-respʳ-≈ ∤∤-resp-≈ ↦ ∦-resp-≈
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Algebra.Properties.Monoid.Divisibility:∣∣-refl ↦ ∥-refl ∣∣-reflexive ↦ ∥-reflexive ∣∣-isEquivalence ↦ ∥-isEquivalence
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Algebra.Properties.Semigroup.Divisibility:∣∣-trans ↦ ∥-trans
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Data.List.Base:and ↦ Data.Bool.ListAction.and or ↦ Data.Bool.ListAction.or any ↦ Data.Bool.ListAction.any all ↦ Data.Bool.ListAction.all sum ↦ Data.Nat.ListAction.sum product ↦ Data.Nat.ListAction.product
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Data.List.Properties:sum-++ ↦ Data.Nat.ListAction.Properties.sum-++ ∈⇒∣product ↦ Data.Nat.ListAction.Properties.∈⇒∣product product≢0 ↦ Data.Nat.ListAction.Properties.product≢0 ∈⇒≤product ↦ Data.Nat.ListAction.Properties.∈⇒≤product
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Data.List.Relation.Binary.Permutation.Propositional.Properties:sum-↭ ↦ Data.Nat.ListAction.Properties.sum-↭ product-↭ ↦ Data.Nat.ListAction.Properties.product-↭
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Data.List.Base.{and|or|any|all}have been lifted out intoData.Bool.ListAction. -
Data.List.Base.{sum|product}and their properties have been lifted out intoData.Nat.ListActionandData.Nat.ListAction.Properties.
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Algebra.Construct.Pointwise:isNearSemiring : IsNearSemiring _≈_ _+_ _*_ 0# → IsNearSemiring (liftRel _≈_) (lift₂ _+_) (lift₂ _*_) (lift₀ 0#) isSemiringWithoutOne : IsSemiringWithoutOne _≈_ _+_ _*_ 0# → IsSemiringWithoutOne (liftRel _≈_) (lift₂ _+_) (lift₂ _*_) (lift₀ 0#) isCommutativeSemiringWithoutOne : IsCommutativeSemiringWithoutOne _≈_ _+_ _*_ 0# → IsCommutativeSemiringWithoutOne (liftRel _≈_) (lift₂ _+_) (lift₂ _*_) (lift₀ 0#) isCommutativeSemiring : IsCommutativeSemiring _≈_ _+_ _*_ 0# 1# → IsCommutativeSemiring (liftRel _≈_) (lift₂ _+_) (lift₂ _*_) (lift₀ 0#) (lift₀ 1#) isIdempotentSemiring : IsIdempotentSemiring _≈_ _+_ _*_ 0# 1# → IsIdempotentSemiring (liftRel _≈_) (lift₂ _+_) (lift₂ _*_) (lift₀ 0#) (lift₀ 1#) isKleeneAlgebra : IsKleeneAlgebra _≈_ _+_ _*_ _⋆ 0# 1# → IsKleeneAlgebra (liftRel _≈_) (lift₂ _+_) (lift₂ _*_) (lift₁ _⋆) (lift₀ 0#) (lift₀ 1#) isQuasiring : IsQuasiring _≈_ _+_ _*_ 0# 1# → IsQuasiring (liftRel _≈_) (lift₂ _+_) (lift₂ _*_) (lift₀ 0#) (lift₀ 1#) isCommutativeRing : IsCommutativeRing _≈_ _+_ _*_ -_ 0# 1# → IsCommutativeRing (liftRel _≈_) (lift₂ _+_) (lift₂ _*_) (lift₁ -_) (lift₀ 0#) (lift₀ 1#) commutativeMonoid : CommutativeMonoid c ℓ → CommutativeMonoid (a ⊔ c) (a ⊔ ℓ) nearSemiring : NearSemiring c ℓ → NearSemiring (a ⊔ c) (a ⊔ ℓ) semiringWithoutOne : SemiringWithoutOne c ℓ → SemiringWithoutOne (a ⊔ c) (a ⊔ ℓ) commutativeSemiringWithoutOne : CommutativeSemiringWithoutOne c ℓ → CommutativeSemiringWithoutOne (a ⊔ c) (a ⊔ ℓ) commutativeSemiring : CommutativeSemiring c ℓ → CommutativeSemiring (a ⊔ c) (a ⊔ ℓ) idempotentSemiring : IdempotentSemiring c ℓ → IdempotentSemiring (a ⊔ c) (a ⊔ ℓ) kleeneAlgebra : KleeneAlgebra c ℓ → KleeneAlgebra (a ⊔ c) (a ⊔ ℓ) quasiring : Quasiring c ℓ → Quasiring (a ⊔ c) (a ⊔ ℓ) commutativeRing : CommutativeRing c ℓ → CommutativeRing (a ⊔ c) (a ⊔ ℓ)
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Data.List.Properties:map-applyUpTo : ∀ (f : ℕ → A) (g : A → B) n → map g (applyUpTo f n) ≡ applyUpTo (g ∘ f) n map-applyDownFrom : ∀ (f : ℕ → A) (g : A → B) n → map g (applyDownFrom f n) ≡ applyDownFrom (g ∘ f) n map-upTo : ∀ (f : ℕ → A) n → map f (upTo n) ≡ applyUpTo f n map-downFrom : ∀ (f : ℕ → A) n → map f (downFrom n) ≡ applyDownFrom f n
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Data.List.Relation.Binary.Permutation.PropositionalProperties:filter-↭ : ∀ (P? : Pred.Decidable P) → xs ↭ ys → filter P? xs ↭ filter P? ys
* In `Function.Consequences`:
```agda
inverseˡ⇒halfLeftAdjoint : Inverseˡ ≈₁ ≈₂ f f⁻¹ → HalfLeftAdjoint ≈₁ ≈₂ f f⁻¹
halfLeftAdjoint⇒inverseˡ : HalfLeftAdjoint ≈₁ ≈₂ f f⁻¹ → Inverseˡ ≈₁ ≈₂ f f⁻¹
inverseˡ⇒halfRightAdjoint : Symmetric ≈₁ → Symmetric ≈₂ →
Inverseʳ ≈₁ ≈₂ f f⁻¹ → HalfRightAdjoint ≈₁ ≈₂ f f⁻¹
halfRightAdjoint⇒inverseˡ : Symmetric ≈₁ → Symmetric ≈₂ →
HalfRightAdjoint ≈₁ ≈₂ f f⁻¹ → Inverseʳ ≈₁ ≈₂ f f⁻¹
inverseᵇ⇒adjoint : Symmetric ≈₁ → Symmetric ≈₂ →
Inverseᵇ ≈₁ ≈₂ f f⁻¹ → Adjoint ≈₁ ≈₂ f f⁻¹
adjoint⇒inverseᵇ : Symmetric ≈₁ → Symmetric ≈₂ →
Adjoint ≈₁ ≈₂ f f⁻¹ → Inverseᵇ ≈₁ ≈₂ f f⁻¹
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Function.Consequences.Setoid:inverseˡ⇒halfLeftAdjoint : Inverseˡ ≈₁ ≈₂ f f⁻¹ → HalfLeftAdjoint ≈₁ ≈₂ f f⁻¹ halfLeftAdjoint⇒inverseˡ : HalfLeftAdjoint ≈₁ ≈₂ f f⁻¹ → Inverseˡ ≈₁ ≈₂ f f⁻¹ inverseʳ⇒halfRightAdjoint : Inverseʳ ≈₁ ≈₂ f f⁻¹ → HalfRightAdjoint ≈₁ ≈₂ f f⁻¹ halfRightAdjoint⇒inverseʳ : HalfRightAdjoint ≈₁ ≈₂ f f⁻¹ → Inverseʳ ≈₁ ≈₂ f f⁻¹ inverseᵇ⇒adjoint : Inverseᵇ ≈₁ ≈₂ f f⁻¹ → Adjoint ≈₁ ≈₂ f f⁻¹ adjoint⇒inverseᵇ : Adjoint ≈₁ ≈₂ f f⁻¹ → Inverseᵇ ≈₁ ≈₂ f f⁻¹
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Relation.Binary.Definitions:HalfLeftAdjoint : Rel A ℓ₁ → Rel B ℓ₂ → (A → B) → (B → A) → Set _ HalfLeftAdjoint _≤_ _⊑_ f g = ∀ {x y} → (x ≤ g y → f x ⊑ y) HalfRightAdjoint : Rel A ℓ₁ → Rel B ℓ₂ → (A → B) → (B → A) → Set _ HalfRightAdjoint _≤_ _⊑_ f g = ∀ {x y} → (f x ⊑ y → x ≤ g y)