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JacquesCarettejamesmckinna
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jamesmckinna
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Port two Endomorphism submodules over to new Function hierarchy (#2342)
* port over two modules * and add to CHANGELOG * fix whitespace * fix warning: it was pointing to a record that did not exist. * fix things as per Matthew's review - though this remains a breaking change. * take care of comments from James. * adjust CHANGELOG for what will be implemented shortly * Revert "take care of comments from James." This reverts commit 93e9e0f. * Revert "fix things as per Matthew's review - though this remains a breaking change." This reverts commit d1cae72. * Revert "fix whitespace" This reverts commit 81230ec. * Revert "port over two modules" This reverts commit 6619f11. * rename these * fix tiny merge issue * get deprecations right (remove where not needed, make more global where needed) * style guide - missing blank lines * fix a bad merge * fixed deprecations * fix #2394 * minor tweaks --------- Co-authored-by: James McKinna <[email protected]>
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‎CHANGELOG.md

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@@ -51,6 +51,11 @@ Deprecated modules
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* `Data.List.Relation.Binary.Sublist.Propositional.Disjoint` deprecated in favour of
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`Data.List.Relation.Binary.Sublist.Propositional.Slice`.
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* The modules `Function.Endomorphism.Propositional` and
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`Function.Endomorphism.Setoid` that use the old `Function`
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hierarchy. Use `Function.Endo.Propositional` and
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`Function.Endo.Setoid` instead.
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Deprecated names
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----------------
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indexedSetoid : {A : Set a} → IndexedSetoid ℕ a _
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```
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* The modules `Function.Endo.Propositional` and
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`Function.Endo.Setoid` are new but are actually proper ports of
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`Function.Endomorphism.Propositional` and
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`Function.Endomorphism.Setoid`.
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* `Function.Relation.Binary.Equality`
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```agda
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setoid : Setoid a₁ a₂ → Setoid b₁ b₂ → Setoid _ _
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rawModule : RawModule R c ℓ
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```
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* In `Algebra.Morphism.Structures`
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* In `Algebra.Morphism.Structures`:
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```agda
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module SuccessorSetMorphisms (N₁ : RawSuccessorSet a ℓ₁) (N₂ : RawSuccessorSet b ℓ₂) where
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record IsSuccessorSetHomomorphism (⟦_⟧ : N₁.Carrier → N₂.Carrier) : Set _
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record IsSuccessorSetMonomorphism (⟦_⟧ : N₁.Carrier → N₂.Carrier) : Set _
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record IsSuccessorSetIsomorphism (⟦_⟧ : N₁.Carrier → N₂.Carrier) : Set _
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record IsSuccessorSetIsomorphism (⟦_⟧ : N₁.Carrier → N₂.Carrier) : Set _
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IsSemigroupHomomorphism : (A → B) → Set _
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IsSemigroupMonomorphism : (A → B) → Set _
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IsSemigroupIsomorphism : (A → B) → Set _
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```
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* In `Algebra.Properties.AbelianGroup`:
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```
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⁻¹-anti-homo‿- : (x - y) ⁻¹ ≈ y - x

‎src/Function/Endo/Propositional.agda

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------------------------------------------------------------------------
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-- The Agda standard library
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--
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-- Endomorphisms on a Set
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------------------------------------------------------------------------
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{-# OPTIONS --cubical-compatible --safe #-}
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module Function.Endo.Propositional {a} (A : Set a) where
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open import Algebra using (Semigroup; Magma; RawMagma; Monoid; RawMonoid)
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open import Algebra.Core
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import Algebra.Definitions.RawMonoid as RawMonoidDefinitions
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import Algebra.Properties.Monoid.Mult as MonoidMultProperties
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open import Algebra.Structures using (IsMagma; IsSemigroup; IsMonoid)
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open import Algebra.Morphism
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using (module Definitions; IsMagmaHomomorphism; IsMonoidHomomorphism)
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open Definitions using (Homomorphic₂)
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open import Data.Nat.Base using (ℕ; zero; suc; _+_; +-rawMagma; +-0-rawMonoid)
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open import Data.Nat.Properties using (+-0-monoid; +-semigroup)
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open import Data.Product.Base using (_,_)
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open import Function.Base using (id; _∘′_; _∋_; flip)
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open import Function.Bundles using (Func; _⟶ₛ_; _⟨$⟩_)
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open import Relation.Binary.Core using (_Preserves_⟶_)
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open import Relation.Binary.PropositionalEquality.Core using (_≡_; refl; cong; cong₂)
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import Relation.Binary.PropositionalEquality.Properties as ≡
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import Function.Endo.Setoid (≡.setoid A) as Setoid
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------------------------------------------------------------------------
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-- Basic type and raw bundles
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Endo : Set a
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Endo = A → A
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private
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_∘_ : Op₂ Endo
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_∘_ = _∘′_
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∘-id-rawMonoid : RawMonoid a a
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∘-id-rawMonoid = record { Carrier = Endo; _≈_ = _≡_ ; _∙_ = _∘_ ; ε = id }
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open RawMonoid ∘-id-rawMonoid
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using ()
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renaming (rawMagma to ∘-rawMagma)
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------------------------------------------------------------------------
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-- Conversion back and forth with the Setoid-based notion of Endomorphism
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fromSetoidEndo : Setoid.Endo → Endo
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fromSetoidEndo = _⟨$⟩_
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toSetoidEndo : Endo → Setoid.Endo
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toSetoidEndo f = record
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{ to = f
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; cong = cong f
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}
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------------------------------------------------------------------------
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-- Structures
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∘-isMagma : IsMagma _≡_ _∘_
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∘-isMagma = record
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{ isEquivalence = ≡.isEquivalence
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; ∙-cong = cong₂ _∘_
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}
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∘-magma : Magma _ _
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∘-magma = record { isMagma = ∘-isMagma }
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∘-isSemigroup : IsSemigroup _≡_ _∘_
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∘-isSemigroup = record
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{ isMagma = ∘-isMagma
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; assoc = λ _ _ _ → refl
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}
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∘-semigroup : Semigroup _ _
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∘-semigroup = record { isSemigroup = ∘-isSemigroup }
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∘-id-isMonoid : IsMonoid _≡_ _∘_ id
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∘-id-isMonoid = record
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{ isSemigroup = ∘-isSemigroup
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; identity = (λ _ → refl) , (λ _ → refl)
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}
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∘-id-monoid : Monoid _ _
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∘-id-monoid = record { isMonoid = ∘-id-isMonoid }
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------------------------------------------------------------------------
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-- n-th iterated composition
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infixr 8 _^_
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_^_ : Endo → ℕ → Endo
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_^_ = flip _×_ where open RawMonoidDefinitions ∘-id-rawMonoid using (_×_)
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------------------------------------------------------------------------
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-- Homomorphism
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module _ (f : Endo) where
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open MonoidMultProperties ∘-id-monoid using (×-homo-+)
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^-homo : Homomorphic₂ ℕ Endo _≡_ (f ^_) _+_ _∘_
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^-homo = ×-homo-+ f
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^-isMagmaHomomorphism : IsMagmaHomomorphism +-rawMagma ∘-rawMagma (f ^_)
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^-isMagmaHomomorphism = record
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{ isRelHomomorphism = record { cong = cong (f ^_) }
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; homo = ^-homo
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}
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^-isMonoidHomomorphism : IsMonoidHomomorphism +-0-rawMonoid ∘-id-rawMonoid (f ^_)
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^-isMonoidHomomorphism = record
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{ isMagmaHomomorphism = ^-isMagmaHomomorphism
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; ε-homo = refl
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}

‎src/Function/Endo/Setoid.agda

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------------------------------------------------------------------------
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-- The Agda standard library
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--
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-- Endomorphisms on a Setoid
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------------------------------------------------------------------------
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{-# OPTIONS --cubical-compatible --safe #-}
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open import Relation.Binary.Bundles using (Setoid)
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module Function.Endo.Setoid {c e} (S : Setoid c e) where
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open import Agda.Builtin.Equality using (_≡_)
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open import Algebra using (Semigroup; Magma; RawMagma; Monoid; RawMonoid)
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import Algebra.Definitions.RawMonoid as RawMonoidDefinitions
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import Algebra.Properties.Monoid.Mult as MonoidMultProperties
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open import Algebra.Structures using (IsMagma; IsSemigroup; IsMonoid)
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open import Algebra.Morphism
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using (module Definitions; IsMagmaHomomorphism; IsMonoidHomomorphism)
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open Definitions using (Homomorphic₂)
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open import Data.Nat.Base using (ℕ; zero; suc; _+_; +-rawMagma; +-0-rawMonoid)
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open import Data.Nat.Properties using (+-semigroup; +-identityʳ)
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open import Data.Product.Base using (_,_)
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open import Function.Bundles using (Func; _⟶ₛ_; _⟨$⟩_)
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open import Function.Construct.Identity using () renaming (function to identity)
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open import Function.Construct.Composition using () renaming (function to _∘_)
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open import Function.Relation.Binary.Setoid.Equality as Eq using (_⇨_)
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open import Level using (Level; _⊔_)
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open import Relation.Binary.Core using (_Preserves_⟶_)
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private
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open module E = Setoid (S ⇨ S) hiding (refl)
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module S = Setoid S
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open Func using (cong)
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------------------------------------------------------------------------
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-- Basic type and raw bundles
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Endo : Set _
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Endo = S ⟶ₛ S
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private
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id : Endo
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id = identity S
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∘-id-rawMonoid : RawMonoid (c ⊔ e) (c ⊔ e)
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∘-id-rawMonoid = record { Carrier = Endo; _≈_ = _≈_ ; _∙_ = _∘_ ; ε = id }
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open RawMonoid ∘-id-rawMonoid
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using ()
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renaming (rawMagma to ∘-rawMagma)
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--------------------------------------------------------------
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-- Structures
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∘-isMagma : IsMagma _≈_ _∘_
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∘-isMagma = record
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{ isEquivalence = isEquivalence
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; ∙-cong = λ {_} {_} {_} {v} x≈y u≈v → S.trans u≈v (cong v x≈y)
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}
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∘-magma : Magma (c ⊔ e) (c ⊔ e)
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∘-magma = record { isMagma = ∘-isMagma }
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∘-isSemigroup : IsSemigroup _≈_ _∘_
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∘-isSemigroup = record
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{ isMagma = ∘-isMagma
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; assoc = λ _ _ _ → S.refl
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}
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∘-semigroup : Semigroup (c ⊔ e) (c ⊔ e)
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∘-semigroup = record { isSemigroup = ∘-isSemigroup }
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∘-id-isMonoid : IsMonoid _≈_ _∘_ id
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∘-id-isMonoid = record
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{ isSemigroup = ∘-isSemigroup
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; identity = (λ _ → S.refl) , (λ _ → S.refl)
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}
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∘-id-monoid : Monoid (c ⊔ e) (c ⊔ e)
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∘-id-monoid = record { isMonoid = ∘-id-isMonoid }
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------------------------------------------------------------------------
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-- -- n-th iterated composition
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infixr 8 _^_
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_^_ : Endo → ℕ → Endo
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f ^ n = n × f where open RawMonoidDefinitions ∘-id-rawMonoid using (_×_)
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------------------------------------------------------------------------
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-- Homomorphism
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module _ (f : Endo) where
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open MonoidMultProperties ∘-id-monoid using (×-congˡ; ×-homo-+)
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^-cong₂ : (f ^_) Preserves _≡_ ⟶ _≈_
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^-cong₂ = ×-congˡ {f}
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^-homo : Homomorphic₂ ℕ Endo _≈_ (f ^_) _+_ _∘_
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^-homo = ×-homo-+ f
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^-isMagmaHomomorphism : IsMagmaHomomorphism +-rawMagma ∘-rawMagma (f ^_)
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^-isMagmaHomomorphism = record
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{ isRelHomomorphism = record { cong = ^-cong₂ }
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; homo = ^-homo
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}
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^-isMonoidHomomorphism : IsMonoidHomomorphism +-0-rawMonoid ∘-id-rawMonoid (f ^_)
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^-isMonoidHomomorphism = record
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{ isMagmaHomomorphism = ^-isMagmaHomomorphism
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; ε-homo = S.refl
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}
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‎src/Function/Endomorphism/Propositional.agda

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------------------------------------------------------------------------
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-- The Agda standard library
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--
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-- Endomorphisms on a Set
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-- This module is DEPRECATED.
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------------------------------------------------------------------------
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{-# OPTIONS --cubical-compatible --safe #-}
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-- Disabled to prevent warnings from deprecated names
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{-# OPTIONS --warn=noUserWarning #-}
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module Function.Endomorphism.Propositional {a} (A : Set a) where
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{-# WARNING_ON_IMPORT
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"Function.Endomorphism.Propositional was deprecated in v2.1.
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Use Function.Endo.Propositional instead."
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#-}
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open import Algebra
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open import Algebra.Morphism; open Definitions
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‎src/Function/Endomorphism/Setoid.agda

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------------------------------------------------------------------------
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-- The Agda standard library
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--
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-- Endomorphisms on a Setoid
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-- This module is DEPRECATED.
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------------------------------------------------------------------------
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{-# OPTIONS --cubical-compatible --safe #-}
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-- Disabled to prevent warnings from deprecated names
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{-# OPTIONS --warn=noUserWarning #-}
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open import Relation.Binary.Core using (_Preserves_⟶_)
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open import Relation.Binary.Bundles using (Setoid)
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module Function.Endomorphism.Setoid {c e} (S : Setoid c e) where
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{-# WARNING_ON_IMPORT
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"Function.Endomorphism.Setoid was deprecated in v2.1.
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Use Function.Endo.Setoid instead."
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#-}
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open import Agda.Builtin.Equality
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open import Algebra

‎src/Function/Equality.agda

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------------------------------------------------------------------------
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{-# OPTIONS --cubical-compatible --safe #-}
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{-# OPTIONS --warn=noUserWarning #-}
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module Function.Equality where
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