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jamesmckinnaMatthewDaggitt
jamesmckinna
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MatthewDaggitt
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Add bundled homomorphisms (#2383)
* Bundle `Algebra.Morphism`s * more bundles! * `RingWithoutOne` now exports a `RawRingWithoutOne` field * disambiguation error when trying to add `RingWithoutOneHomomorphism` record * FIXED: disambiguation error when trying to add `RingWithoutOneHomomorphism` * add `rawKleeneAlgebra` * add `KleeneAlgebra`, `Quasigroup`, and `Lopp` homomorphisms * add bundled `Identity` homomorphisms * avoid name clash: remove `open`ing of sub-homomorphism bundles * add bundled `Composition` of homomorphisms * more exported sub-bundles * removed redundant anonymous `module`s * removed redundant anonymous `module`s * add `isNearSemiring` to `IsRingWithoutOne` plus knock-on re-exports * add `nearSemiring` to `RingWithoutOne` plus knock-on re-exports * add `rawNearSemiring` to `RingWithoutOne` plus knock-on re-exports * lots more exported sub-structures and sub-bundles * fix bug: restrict exports * lots more exported sub-structures and sub-bundles * refactor: `RawX` parameterisation * knock-on: `Identity` takes a full `Bundle` * tighten imports * knock-on: `Composition` takes full `Bundle`s * `CHANGELOG` * `fix-whitespace` * fix `CHANGELOG` * update `CHANGELOG` --------- Co-authored-by: MatthewDaggitt <matthewdaggitt@gmail.com>
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‎CHANGELOG.md‎

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@@ -88,6 +88,11 @@ Deprecated names
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New modules
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-----------
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* Bundled morphisms between (raw) algebraic structures:
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```
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Algebra.Morphism.Bundles
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```
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* Properties of `IdempotentCommutativeMonoid`s refactored out from `Algebra.Solver.IdempotentCommutativeMonoid`:
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```agda
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Algebra.Properties.IdempotentCommutativeMonoid
@@ -140,6 +145,93 @@ New modules
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Additions to existing modules
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-----------------------------
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* In `Algebra.Bundles.KleeneAlgebra`:
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```agda
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rawKleeneAlgebra : RawKleeneAlgebra _ _
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```
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* In `Algebra.Bundles.Raw.RawRingWithoutOne`
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```agda
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rawNearSemiring : RawNearSemiring c ℓ
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```
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* Exporting more `Raw` substructures from `Algebra.Bundles.Ring`:
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```agda
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rawNearSemiring : RawNearSemiring _ _
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rawRingWithoutOne : RawRingWithoutOne _ _
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+-rawGroup : RawGroup _ _
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```
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* Exporting `RawRingWithoutOne` and `(Raw)NearSemiring` subbundles from
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`Algebra.Bundles.RingWithoutOne`:
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```agda
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nearSemiring : NearSemiring _ _
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rawNearSemiring : RawNearSemiring _ _
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rawRingWithoutOne : RawRingWithoutOne _ _
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```
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* In `Algebra.Morphism.Construct.Composition`:
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```agda
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magmaHomomorphism : MagmaHomomorphism M₁.rawMagma M₂.rawMagma →
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MagmaHomomorphism M₂.rawMagma M₃.rawMagma →
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MagmaHomomorphism M₁.rawMagma M₃.rawMagma
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monoidHomomorphism : MonoidHomomorphism M₁.rawMonoid M₂.rawMonoid →
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MonoidHomomorphism M₂.rawMonoid M₃.rawMonoid →
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MonoidHomomorphism M₁.rawMonoid M₃.rawMonoid
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groupHomomorphism : GroupHomomorphism M₁.rawGroup M₂.rawGroup →
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GroupHomomorphism M₂.rawGroup M₃.rawGroup →
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GroupHomomorphism M₁.rawGroup M₃.rawGroup
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nearSemiringHomomorphism : NearSemiringHomomorphism M₁.rawNearSemiring M₂.rawNearSemiring →
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NearSemiringHomomorphism M₂.rawNearSemiring M₃.rawNearSemiring →
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NearSemiringHomomorphism M₁.rawNearSemiring M₃.rawNearSemiring
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semiringHomomorphism : SemiringHomomorphism M₁.rawSemiring M₂.rawSemiring →
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SemiringHomomorphism M₂.rawSemiring M₃.rawSemiring →
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SemiringHomomorphism M₁.rawSemiring M₃.rawSemiring
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kleeneAlgebraHomomorphism : KleeneAlgebraHomomorphism M₁.rawKleeneAlgebra M₂.rawKleeneAlgebra →
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KleeneAlgebraHomomorphism M₂.rawKleeneAlgebra M₃.rawKleeneAlgebra →
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KleeneAlgebraHomomorphism M₁.rawKleeneAlgebra M₃.rawKleeneAlgebra
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nearSemiringHomomorphism : NearSemiringHomomorphism M₁.rawNearSemiring M₂.rawNearSemiring →
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NearSemiringHomomorphism M₂.rawNearSemiring M₃.rawNearSemiring →
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NearSemiringHomomorphism M₁.rawNearSemiring M₃.rawNearSemiring
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ringWithoutOneHomomorphism : RingWithoutOneHomomorphism M₁.rawRingWithoutOne M₂.rawRingWithoutOne →
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RingWithoutOneHomomorphism M₂.rawRingWithoutOne M₃.rawRingWithoutOne →
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RingWithoutOneHomomorphism M₁.rawRingWithoutOne M₃.rawRingWithoutOne
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ringHomomorphism : RingHomomorphism M₁.rawRing M₂.rawRing →
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RingHomomorphism M₂.rawRing M₃.rawRing →
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RingHomomorphism M₁.rawRing M₃.rawRing
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quasigroupHomomorphism : QuasigroupHomomorphism M₁.rawQuasigroup M₂.rawQuasigroup →
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QuasigroupHomomorphism M₂.rawQuasigroup M₃.rawQuasigroup →
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QuasigroupHomomorphism M₁.rawQuasigroup M₃.rawQuasigroup
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loopHomomorphism : LoopHomomorphism M₁.rawLoop M₂.rawLoop →
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LoopHomomorphism M₂.rawLoop M₃.rawLoop →
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LoopHomomorphism M₁.rawLoop M₃.rawLoop
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```
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* In `Algebra.Morphism.Construct.Identity`:
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```agda
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magmaHomomorphism : MagmaHomomorphism M.rawMagma M.rawMagma
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monoidHomomorphism : MonoidHomomorphism M.rawMonoid M.rawMonoid
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groupHomomorphism : GroupHomomorphism M.rawGroup M.rawGroup
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nearSemiringHomomorphism : NearSemiringHomomorphism M.raw M.raw
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semiringHomomorphism : SemiringHomomorphism M.rawNearSemiring M.rawNearSemiring
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kleeneAlgebraHomomorphism : KleeneAlgebraHomomorphism M.rawKleeneAlgebra M.rawKleeneAlgebra
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nearSemiringHomomorphism : NearSemiringHomomorphism M.rawNearSemiring M.rawNearSemiring
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ringWithoutOneHomomorphism : RingWithoutOneHomomorphism M.rawRingWithoutOne M.rawRingWithoutOne
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ringHomomorphism : RingHomomorphism M.rawRing M.rawRing
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quasigroupHomomorphism : QuasigroupHomomorphism M.rawQuasigroup M.rawQuasigroup
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loopHomomorphism : LoopHomomorphism M.rawLoop M.rawLoop
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```
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* In `Algebra.Morphism.Structures.RingMorphisms`
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```agda
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isRingWithoutOneHomomorphism : IsRingWithoutOneHomomorphism ⟦_⟧
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```
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* In `Algebra.Morphism.Structures.RingWithoutOneMorphisms`
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```agda
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isNearSemiringHomomorphism : IsNearSemiringHomomorphism ⟦_⟧
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```
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* Properties of non-divisibility in `Algebra.Properties.Magma.Divisibility`:
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```agda
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∤-respˡ-≈ : _∤_ Respectsˡ _≈_
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Env = Vec Carrier
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```
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* In `Algebra.Structures.RingWithoutOne`:
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```agda
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isNearSemiring : IsNearSemiring _ _
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```
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* In `Data.List.Membership.Setoid.Properties`:
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```agda
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∉⇒All[≉] : x ∉ xs → All (x ≉_) xs

‎src/Algebra/Bundles.agda‎

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@@ -873,6 +873,16 @@ record KleeneAlgebra c ℓ : Set (suc (c ⊔ ℓ)) where
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; rawSemiring; semiring
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)
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rawKleeneAlgebra : RawKleeneAlgebra _ _
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rawKleeneAlgebra = record
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{ _≈_ = _≈_
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; _+_ = _+_
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; _*_ = _*_
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; _⋆ = _⋆
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; 0# = 0#
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; 1# = 1#
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}
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record Quasiring c ℓ : Set (suc (c ⊔ ℓ)) where
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infixl 7 _*_
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infixl 6 _+_
@@ -931,20 +941,33 @@ record RingWithoutOne c ℓ : Set (suc (c ⊔ ℓ)) where
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open IsRingWithoutOne isRingWithoutOne public
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nearSemiring : NearSemiring _ _
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nearSemiring = record { isNearSemiring = isNearSemiring }
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open NearSemiring nearSemiring public
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using (*-semigroup; *-magma)
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+-abelianGroup : AbelianGroup _ _
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+-abelianGroup = record { isAbelianGroup = +-isAbelianGroup }
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*-semigroup : Semigroup _ _
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*-semigroup = record { isSemigroup = *-isSemigroup }
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open AbelianGroup +-abelianGroup public
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using () renaming (group to +-group; invertibleMagma to +-invertibleMagma; invertibleUnitalMagma to +-invertibleUnitalMagma)
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using ()
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renaming (group to +-group;
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invertibleMagma to +-invertibleMagma;
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invertibleUnitalMagma to +-invertibleUnitalMagma)
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rawRingWithoutOne : RawRingWithoutOne _ _
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rawRingWithoutOne = record
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{ _≈_ = _≈_
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; _+_ = _+_
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; _*_ = _*_
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; -_ = -_
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; 0# = 0#
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}
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open RawRingWithoutOne rawRingWithoutOne public
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using (+-rawGroup; *-rawMagma; rawNearSemiring)
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open Semigroup *-semigroup public
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using () renaming
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( rawMagma to *-rawMagma
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; magma to *-magma
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)
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------------------------------------------------------------------------
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-- Bundles with 2 binary operations, 1 unary operation & 2 elements

‎src/Algebra/Bundles/Raw.agda‎

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@@ -174,6 +174,17 @@ record RawRingWithoutOne c ℓ : Set (suc (c ⊔ ℓ)) where
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-_ : Op₁ Carrier
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0# : Carrier
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rawNearSemiring : RawNearSemiring c ℓ
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rawNearSemiring = record
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{ _≈_ = _≈_
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; _+_ = _+_
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; _*_ = _*_
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; 0# = 0#
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}
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open RawNearSemiring rawNearSemiring public
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using (_≉_; *-rawMagma; +-rawMagma; +-rawMonoid)
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+-rawGroup : RawGroup c ℓ
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+-rawGroup = record
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{ _≈_ = _≈_
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; _⁻¹ = -_
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}
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open RawGroup +-rawGroup public
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using (_≉_) renaming (rawMagma to +-rawMagma; rawMonoid to +-rawMonoid)
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*-rawMagma : RawMagma c ℓ
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*-rawMagma = record
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{ _≈_ = _≈_
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; _∙_ = _*_
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}
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------------------------------------------------------------------------
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-- Raw bundles with 2 binary operations, 1 unary operation & 2 elements
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------------------------------------------------------------------------

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