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[ add ] Pointwise lifting of algebra to Data.Vec.Functional (Functional vector module #1945 redux) #2817

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[ add ] Pointwise lifting of algebra to Data.Vec.Functional (Functional vector module #1945 redux) #2817

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3cf9d5a
update of pr 1945
e-mniang Aug 28, 2025
c36797b
changes after review
e-mniang Aug 28, 2025
e67c13e
names changes
e-mniang Aug 29, 2025
e8de375
applying the reviews
e-mniang Oct 5, 2025
743ae6b
Update Base.agda
jamesmckinna Oct 10, 2025
ee19d44
Merge branch 'master' into updating-pr-1945
jamesmckinna Oct 10, 2025
5510128
Update CHANGELOG.md
JacquesCarette Jan 30, 2026
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120 changes: 54 additions & 66 deletions src/Data/Vec/Functional/Algebra/Base.agda
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Original file line number Diff line number Diff line change
@@ -1,7 +1,7 @@
------------------------------------------------------------------------
-- The Agda standard library
--
-- Some Vector-related module Definitions
-- Some VecF.Vector-related module Definitions

@JacquesCarette JacquesCarette Oct 10, 2025

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While importing Data.Vec.Functional as VecF makes sense, VecF in the top-comment does not. I would expand this out to "Functional Vector-related"

@jamesmckinna jamesmckinna Jan 8, 2026

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I presume that this is (something like) a global-search-and-replace that didn't get weeded out?

------------------------------------------------------------------------

{-# OPTIONS --cubical-compatible --safe #-}
Expand All @@ -12,128 +12,116 @@ open import Level using (Level; suc; _⊔_)
open import Function using (_$_)
open import Data.Nat using (ℕ)
open import Data.Fin using (Fin)
open import Data.Vec.Functional
import Data.Vec.Functional as VecF
open import Algebra.Core
open import Algebra.Bundles

@JacquesCarette JacquesCarette Dec 24, 2025

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using , here and below?

open import Algebra.Module
open import Relation.Binary using (Rel)
open import Data.Vec.Functional.Relation.Binary.Pointwise using (Pointwise)
import Data.Vec.Functional.Relation.Binary.Pointwise as Pointwise

private variable
a ℓ : Level
A : Set a
n : ℕ

------------------------------------------------------------------------
-- Vector-lifted relations & operators
-- VecF.Vector-lifted raw structures

@JacquesCarette JacquesCarette Oct 10, 2025

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Same comment. I would be tempted to go with just "Lifted raw structures" or if one wants more, "Raw structures lifted to Functional Vectors".


pointwiseᵛ : ( _≈_ : Rel A ℓ ) → Rel (Vector A n) ℓ
pointwiseᵛ _≈_ = Pointwise _≈_

zipWithᵛ : Op₂ A → Op₂ (Vector A n)
zipWithᵛ _∙_ = zipWith _∙_

mapᵛ : Op₁ A → Op₁ (Vector A n)
mapᵛ f = map f

------------------------------------------------------------------------
-- Vector-lifted raw structures

rawMagmaᵛ : RawMagma a ℓ → (n : ℕ) → RawMagma a ℓ
rawMagmaᵛ M n =
rawMagma : RawMagma a ℓ → (n : ℕ) → RawMagma a ℓ
rawMagma M n =
record
{ Carrier = Vector M.Carrier n
; _≈_ = pointwiseᵛ M._≈_
; _∙_ = zipWithᵛ M._∙_
{ Carrier = VecF.Vector M.Carrier n
; _≈_ = Pointwise.Pointwise M._≈_
; _∙_ = VecF.zipWith M._∙_
}
where module M = RawMagma M

rawMonoidᵛ : RawMonoid a ℓ → (n : ℕ) → RawMonoid a ℓ
rawMonoidᵛ M n =
rawMonoid : RawMonoid a ℓ → (n : ℕ) → RawMonoid a ℓ
rawMonoid M n =
record
{ RawMagma (rawMagmaᵛ M.rawMagma n)
{ RawMagma (rawMagma M.rawMagma n)
; ε = λ _ → M.ε
}
where module M = RawMonoid M

rawGroupᵛ : RawGroup a ℓ → (n : ℕ) → RawGroup a ℓ
rawGroupᵛ G n =
rawGroup : RawGroup a ℓ → (n : ℕ) → RawGroup a ℓ
rawGroup G n =
record
{ RawMonoid (rawMonoidᵛ G.rawMonoid n)
; _⁻¹ = mapᵛ G._⁻¹
{ RawMonoid (rawMonoid G.rawMonoid n)
; _⁻¹ = VecF.map G._⁻¹
}
where module G = RawGroup G

rawNearSemiringᵛ : RawNearSemiring a ℓ → (n : ℕ) → RawNearSemiring a ℓ
rawNearSemiringᵛ NS n =
rawNearSemiring : RawNearSemiring a ℓ → (n : ℕ) → RawNearSemiring a ℓ
rawNearSemiring NS n =
record
{ Carrier = Vector NS.Carrier n
; _≈_ = pointwiseᵛ NS._≈_
; _+_ = zipWithᵛ NS._+_
; _*_ = zipWithᵛ NS._*_
{ Carrier = VecF.Vector NS.Carrier n
; _≈_ = Pointwise.Pointwise NS._≈_
; _+_ = VecF.zipWith NS._+_
; _*_ = VecF.zipWith NS._*_
; 0# = λ _ → NS.0#
}
where module NS = RawNearSemiring NS

rawSemiringᵛ : RawSemiring a ℓ → (n : ℕ) → RawSemiring a ℓ
rawSemiringᵛ S n =
rawSemiring : RawSemiring a ℓ → (n : ℕ) → RawSemiring a ℓ
rawSemiring S n =
record
{ RawNearSemiring (rawNearSemiringᵛ S.rawNearSemiring n)
{ RawNearSemiring (rawNearSemiring S.rawNearSemiring n)
; 1# = λ _ → S.1#
}
where module S = RawSemiring S

rawRingᵛ : RawRing a ℓ → (n : ℕ) → RawRing a ℓ
rawRingᵛ R n =
rawRing : RawRing a ℓ → (n : ℕ) → RawRing a ℓ
rawRing R n =
record
{ RawSemiring (rawSemiringᵛ R.rawSemiring n)
; -_ = mapᵛ R.-_
{ RawSemiring (rawSemiring R.rawSemiring n)
; -_ = VecF.map R.-_
}
where module R = RawRing R

Comment thread
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------------------------------------------------------------------------
-- Vector actions (left/right scalar multiplication)
-- VecF.Vector actions (left/right scalar multiplication)

_*ₗᵛ_ : {S : Set a} → Op₂ S → Opₗ S (Vector S n)
_*ₗᵛ_ _*_ r xs = map (r *_) xs
_*ₗ_ : {S : Set a} → Op₂ S → Opₗ S (VecF.Vector S n)
_*ₗ_ _*_ r xs = VecF.map (r *_) xs

_*ᵣᵛ_ : {S : Set a} → Op₂ S → Opᵣ S (Vector S n)
_*ᵣᵛ_ _*_ xs r = map (_* r) xs
_*ᵣ_ : {S : Set a} → Op₂ S → Opᵣ S (VecF.Vector S n)
_*ᵣ_ _*_ xs r = VecF.map (_* r) xs

------------------------------------------------------------------------
-- Vector-lifted semimodule bundles
-- VecF.Vector-lifted semimodule bundles

rawLeftSemimoduleᵛ : (NS : RawNearSemiring a ℓ) (n : ℕ) → RawLeftSemimodule (RawNearSemiring.Carrier NS) a ℓ
rawLeftSemimoduleᵛ NS n =
rawLeftSemimodule : (NS : RawNearSemiring a ℓ) (n : ℕ) → RawLeftSemimodule (RawNearSemiring.Carrier NS) a ℓ
rawLeftSemimodule NS n =
record
{ Carrierᴹ = Vector NS.Carrier n
; _≈ᴹ_ = pointwiseᵛ NS._≈_
; _+ᴹ_ = zipWithᵛ NS._+_
; _*ₗ_ = _*ₗᵛ_ NS._*_
{ Carrierᴹ = VecF.Vector NS.Carrier n
; _≈ᴹ_ = Pointwise.Pointwise NS._≈_
; _+ᴹ_ = VecF.zipWith NS._+_
; _*ₗ_ = _*ₗ_ NS._*_
; 0ᴹ = λ _ → NS.0#
}
where module NS = RawNearSemiring NS

rawRightSemimoduleᵛ : (NS : RawNearSemiring a ℓ) (n : ℕ) → RawRightSemimodule (RawNearSemiring.Carrier NS) a ℓ
rawRightSemimoduleᵛ NS n =
rawRightSemimodule : (NS : RawNearSemiring a ℓ) (n : ℕ) → RawRightSemimodule (RawNearSemiring.Carrier NS) a ℓ
rawRightSemimodule NS n =
record
{ Carrierᴹ = Vector NS.Carrier n
; _≈ᴹ_ = pointwiseᵛ NS._≈_
; _+ᴹ_ = zipWithᵛ NS._+_
; _*ᵣ_ = _*ᵣᵛ_ NS._*_
{ Carrierᴹ = VecF.Vector NS.Carrier n
; _≈ᴹ_ = Pointwise.Pointwise NS._≈_
; _+ᴹ_ = VecF.zipWith NS._+_
; _*ᵣ_ = _*ᵣ_ NS._*_
; 0ᴹ = λ _ → NS.0#
}
where module NS = RawNearSemiring NS

rawBisemimoduleᵛ : (NS : RawNearSemiring a ℓ) (n : ℕ) → RawBisemimodule (RawNearSemiring.Carrier NS)
rawBisemimodule : (NS : RawNearSemiring a ℓ) (n : ℕ) → RawBisemimodule (RawNearSemiring.Carrier NS)
(RawNearSemiring.Carrier NS) a ℓ
rawBisemimoduleᵛ NS n =
rawBisemimodule NS n =
record
{ Carrierᴹ = Vector NS.Carrier n
; _≈ᴹ_ = pointwiseᵛ NS._≈_
; _+ᴹ_ = zipWithᵛ NS._+_
; _*ₗ_ = _*ₗᵛ_ NS._*_
; _*ᵣ_ = _*ᵣᵛ_ NS._*_
{ Carrierᴹ = VecF.Vector NS.Carrier n
; _≈ᴹ_ = Pointwise.Pointwise NS._≈_
; _+ᴹ_ = VecF.zipWith NS._+_
; _*ₗ_ = _*ₗ_ NS._*_
; _*ᵣ_ = _*ᵣ_ NS._*_
; 0ᴹ = λ _ → NS.0#
}
where module NS = RawNearSemiring NS
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