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Port two Endomorphism submodules over to new Function hierarchy #2342

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6619f11
port over two modules
JacquesCarette Apr 3, 2024
1af553e
and add to CHANGELOG
JacquesCarette Apr 3, 2024
81230ec
fix whitespace
JacquesCarette Apr 3, 2024
3305480
fix warning: it was pointing to a record that did not exist.
JacquesCarette Apr 4, 2024
e1e7c57
Merge branch 'FixWarning' into Endomorphism
JacquesCarette Apr 4, 2024
d1cae72
fix things as per Matthew's review - though this remains a breaking c…
JacquesCarette Apr 4, 2024
93e9e0f
take care of comments from James.
JacquesCarette Apr 9, 2024
35d3bb9
Merge branch 'master' into Endomorphism
JacquesCarette May 5, 2024
d258064
Merge branch 'master' into Endomorphism
JacquesCarette May 16, 2024
a2e3c26
adjust CHANGELOG for what will be implemented shortly
JacquesCarette May 16, 2024
e9fc145
Revert "take care of comments from James."
JacquesCarette May 16, 2024
9665443
Revert "fix things as per Matthew's review - though this remains a br…
JacquesCarette May 16, 2024
8cb04db
Revert "fix whitespace"
JacquesCarette May 16, 2024
154fb0e
Revert "port over two modules"
JacquesCarette May 16, 2024
d5d8113
rename these
JacquesCarette May 16, 2024
b04ab5d
fix tiny merge issue
JacquesCarette May 16, 2024
60ecbeb
get deprecations right (remove where not needed, make more global whe…
JacquesCarette May 22, 2024
08c8866
style guide - missing blank lines
JacquesCarette May 22, 2024
e7d4961
fix a bad merge
JacquesCarette May 22, 2024
b28f62d
fixed deprecations
jamesmckinna May 25, 2024
278547a
fix #2394
jamesmckinna Jun 5, 2024
c71cb83
minor tweaks
JacquesCarette Jun 7, 2024
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7 changes: 7 additions & 0 deletions CHANGELOG.md
Original file line number Diff line number Diff line change
Expand Up @@ -46,6 +46,13 @@ Deprecated modules
* `Data.List.Relation.Binary.Sublist.Propositional.Disjoint` deprecated in favour of
`Data.List.Relation.Binary.Sublist.Propositional.Slice`.

Un-deprecated modules
---------------------

* The modules `Function.Endomorphism.Propositional` and
`Function.Endomorphism.Setoid` previously used the old `Function`
hierarchy but have now been ported to using the new one.
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Deprecated names
----------------

Expand Down
1 change: 0 additions & 1 deletion src/Algebra/Morphism/Structures.agda
Original file line number Diff line number Diff line change
Expand Up @@ -116,7 +116,6 @@ module MagmaMorphisms (M₁ : RawMagma a ℓ₁) (M₂ : RawMagma b ℓ₂) wher
; surjective = surjective
}


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------------------------------------------------------------------------
-- Morphisms over monoid-like structures
------------------------------------------------------------------------
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58 changes: 41 additions & 17 deletions src/Function/Endomorphism/Propositional.agda
Original file line number Diff line number Diff line change
Expand Up @@ -5,21 +5,21 @@
------------------------------------------------------------------------

{-# OPTIONS --cubical-compatible --safe #-}

-- Disabled to prevent warnings from deprecated names
{-# OPTIONS --warn=noUserWarning #-}

module Function.Endomorphism.Propositional {a} (A : Set a) where

open import Algebra
open import Algebra.Morphism; open Definitions
open import Algebra using (Semigroup; Magma; RawMagma; Monoid; RawMonoid)
open import Algebra.Core
open import Algebra.Structures using (IsMagma; IsSemigroup; IsMonoid)
open import Algebra.Morphism
using (module Definitions; IsMagmaHomomorphism; IsMonoidHomomorphism)
open Definitions using (Homomorphic₂)

open import Data.Nat.Base using (ℕ; zero; suc; _+_)
open import Data.Nat.Base using (ℕ; zero; suc; _+_; +-rawMagma; +-0-rawMonoid)
open import Data.Nat.Properties using (+-0-monoid; +-semigroup)
open import Data.Product.Base using (_,_)

open import Function.Base using (id; _∘′_; _∋_)
open import Function.Equality using (_⟨$⟩_)
open import Function.Bundles using (Func; _⟶ₛ_; _⟨$⟩_)
open import Relation.Binary.Core using (_Preserves_⟶_)
open import Relation.Binary.PropositionalEquality.Core using (_≡_; refl; cong; cong₂)
import Relation.Binary.PropositionalEquality.Properties as ≡
Expand All @@ -37,7 +37,7 @@ fromSetoidEndo = _⟨$⟩_

toSetoidEndo : Endo → Setoid.Endo
toSetoidEndo f = record
{ _⟨$⟩_ = f
{ to = f
; cong = cong f
}

Expand Down Expand Up @@ -84,17 +84,41 @@ f ^ suc n = f ∘′ (f ^ n)
∘-id-monoid : Monoid _ _
∘-id-monoid = record { isMonoid = ∘-id-isMonoid }

private
∘-rawMagma : RawMagma a a
∘-rawMagma = Semigroup.rawMagma ∘-semigroup

∘-id-rawMonoid : RawMonoid a a
∘-id-rawMonoid = Monoid.rawMonoid ∘-id-monoid

------------------------------------------------------------------------
-- Homomorphism

^-isSemigroupMorphism : ∀ f → IsSemigroupMorphism +-semigroup ∘-semigroup (f ^_)
^-isSemigroupMorphism f = record
{ ⟦⟧-cong = cong (f ^_)
; ∙-homo = ^-homo f
^-isMagmaHomomorphism : ∀ f → IsMagmaHomomorphism +-rawMagma ∘-rawMagma (f ^_)
^-isMagmaHomomorphism f = record
{ isRelHomomorphism = record { cong = cong (f ^_) }
; homo = ^-homo f
}

^-isMonoidMorphism : ∀ f → IsMonoidMorphism +-0-monoid ∘-id-monoid (f ^_)
^-isMonoidMorphism f = record
{ sm-homo = ^-isSemigroupMorphism f
; ε-homo = refl
^-isMonoidHomomorphism : ∀ f → IsMonoidHomomorphism +-0-rawMonoid ∘-id-rawMonoid (f ^_)
^-isMonoidHomomorphism f = record
{ isMagmaHomomorphism = ^-isMagmaHomomorphism f
; ε-homo = refl
}

------------------------------------------------------------------------
-- Deprecations

-- Version 2.1

^-isSemigroupMorphism = ^-isMagmaHomomorphism
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{-# WARNING_ON_USAGE ^-isSemigroupMorphism
"Warning: ^-isSemigroupMorphism was deprecated in v2.1.
Please use ^-isMagmaHomomorphism instead."
#-}

^-isMonoidMorphism = ^-isMonoidHomomorphism
{-# WARNING_ON_USAGE ^-isMonoidMorphism
"Warning: ^-isMonoidMorphism was deprecated in v2.1.
Please use ^-isMonoidHomomorphism instead."
#-}
99 changes: 66 additions & 33 deletions src/Function/Endomorphism/Setoid.agda
Original file line number Diff line number Diff line change
Expand Up @@ -6,90 +6,123 @@

{-# OPTIONS --cubical-compatible --safe #-}

-- Disabled to prevent warnings from deprecated names
{-# OPTIONS --warn=noUserWarning #-}

open import Relation.Binary.Core using (_Preserves_⟶_)
open import Relation.Binary.Bundles using (Setoid)

module Function.Endomorphism.Setoid {c e} (S : Setoid c e) where

open import Agda.Builtin.Equality

open import Algebra
open import Algebra.Structures
open import Algebra.Morphism; open Definitions
open import Function.Equality using (setoid; _⟶_; id; _∘_; cong)
open import Data.Nat.Base using (ℕ; _+_); open ℕ
open import Data.Nat.Properties
open import Algebra using (Semigroup; Magma; RawMagma; Monoid; RawMonoid)
open import Algebra.Structures using (IsMagma; IsSemigroup; IsMonoid)
open import Algebra.Morphism
using (module Definitions; IsMagmaHomomorphism; IsMonoidHomomorphism)
open Definitions using (Homomorphic₂)
open import Data.Nat.Base using (ℕ; zero; suc; _+_; +-rawMagma; +-0-rawMonoid)
open import Data.Nat.Properties using (+-semigroup; +-identityʳ)
open import Data.Product.Base using (_,_)

import Relation.Binary.Indexed.Heterogeneous.Construct.Trivial as Trivial
open import Function.Bundles using (Func; _⟶ₛ_; _⟨$⟩_)
open import Function.Construct.Identity using () renaming (function to identity)
open import Function.Construct.Composition using () renaming (function to _∘_)
open import Function.Relation.Binary.Setoid.Equality as Eq using (_⇨_)
open import Level using (Level; _⊔_)
open import Relation.Binary.Core using (_Preserves_⟶_)

private
module E = Setoid (setoid S (Trivial.indexedSetoid S))
open E hiding (refl)

open module E = Setoid (S ⇨ S) hiding (refl)
module S = Setoid S
open Func using (cong)
------------------------------------------------------------------------
-- Basic type and functions

Endo : Set _
Endo = S ⟶ S
Endo = S ⟶ S
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infixr 8 _^_

private
id : Endo
id = identity S

_^_ : Endo → ℕ → Endo
f ^ zero = id
f ^ suc n = f ∘ (f ^ n)

^-cong₂ : ∀ f → (f ^_) Preserves _≡_ ⟶ _≈_
^-cong₂ f {n} refl = cong (f ^ n)
^-cong₂ f {n} refl = cong (f ^ n) S.refl

^-homo : ∀ f → Homomorphic₂ ℕ Endo _≈_ (f ^_) _+_ _∘_
^-homo f zero n x≈y = cong (f ^ n) x≈y
^-homo f (suc m) n x≈y = cong f (^-homo f m n x≈y)
^-homo f zero n = S.refl
^-homo f (suc m) zero = ^-cong₂ f (+-identityʳ m)
^-homo f (suc m) (suc n) = ^-homo f m (suc n)

------------------------------------------------------------------------
-- Structures

∘-isMagma : IsMagma _≈_ _∘_
∘-isMagma = record
{ isEquivalence = isEquivalence
; ∙-cong = λ g f x → g (f x)
; ∙-cong = λ {_} {_} {_} {v} x≈y u≈v → S.trans u≈v (cong v x≈y)
}

∘-magma : Magma _ _
∘-magma : Magma (c ⊔ e) (c ⊔ e)
∘-magma = record { isMagma = ∘-isMagma }

∘-isSemigroup : IsSemigroup _≈_ _∘_
∘-isSemigroup = record
{ isMagma = ∘-isMagma
; assoc = λ h g f x≈y → cong h (cong g (cong f x≈y))
; assoc = λ _ _ _ → S.refl
}

∘-semigroup : Semigroup _ _
∘-semigroup : Semigroup (c ⊔ e) (c ⊔ e)
∘-semigroup = record { isSemigroup = ∘-isSemigroup }

∘-id-isMonoid : IsMonoid _≈_ _∘_ id
∘-id-isMonoid = record
{ isSemigroup = ∘-isSemigroup
; identity = cong , cong
; identity = (λ _ → S.refl) , (λ _ → S.refl)
}

∘-id-monoid : Monoid _ _
∘-id-monoid : Monoid (c ⊔ e) (c ⊔ e)
∘-id-monoid = record { isMonoid = ∘-id-isMonoid }

private
∘-rawMagma : RawMagma (c ⊔ e) (c ⊔ e)
∘-rawMagma = Semigroup.rawMagma ∘-semigroup

∘-id-rawMonoid : RawMonoid (c ⊔ e) (c ⊔ e)
∘-id-rawMonoid = Monoid.rawMonoid ∘-id-monoid

------------------------------------------------------------------------
-- Homomorphism

^-isSemigroupMorphism : ∀ f → IsSemigroupMorphism +-semigroup ∘-semigroup (f ^_)
^-isSemigroupMorphism f = record
{ ⟦⟧-cong = ^-cong₂ f
; ∙-homo = ^-homo f
^-isMagmaHomomorphism : ∀ f → IsMagmaHomomorphism +-rawMagma ∘-rawMagma (f ^_)
^-isMagmaHomomorphism f = record
{ isRelHomomorphism = record { cong = ^-cong₂ f }
; homo = ^-homo f
}

^-isMonoidMorphism : ∀ f → IsMonoidMorphism +-0-monoid ∘-id-monoid (f ^_)
^-isMonoidMorphism f = record
{ sm-homo = ^-isSemigroupMorphism f
; ε-homo = λ x≈y → x≈y
^-isMonoidHomomorphism : ∀ f → IsMonoidHomomorphism +-0-rawMonoid ∘-id-rawMonoid (f ^_)
^-isMonoidHomomorphism f = record
{ isMagmaHomomorphism = record
{ isRelHomomorphism = record { cong = ^-cong₂ f }
; homo = ^-homo f
}
; ε-homo = S.refl
}

------------------------------------------------------------------------
-- Deprecations

-- Version 2.1

^-isSemigroupMorphism = ^-isMagmaHomomorphism
{-# WARNING_ON_USAGE ^-isSemigroupMorphism
"Warning: ^-isSemigroupMorphism was deprecated in v2.1.
Please use ^-isMagmaHomomorphism instead."
#-}

^-isMonoidMorphism = ^-isMonoidHomomorphism
{-# WARNING_ON_USAGE ^-isMonoidMorphism
"Warning: ^-isMonoidMorphism was deprecated in v2.1.
Please use ^-isMonoidHomomorphism instead."
#-}
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