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Generalise Data.Product.Relation.Binary.Pointwise.NonDependent.Pointwise #2401

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Jun 4, 2024
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Generalise Data.Product.Relation.Binary.Pointwise.NonDependent.Pointwise #2401

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11 changes: 8 additions & 3 deletions CHANGELOG.md
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Expand Up @@ -36,9 +36,14 @@ Other major improvements

Minor improvements
------------------
The size of the dependency graph for many modules has been
reduced. This may lead to speed ups for first-time loading of some
modules.

* The size of the dependency graph for many modules has been
reduced. This may lead to speed ups for first-time loading of some
modules.

* The definition of the `Pointwise` relational combinator in
`Data.Product.Relation.Binary.Pointwise.NonDependent.Pointwise`
has been generalised to take heterogeneous arguments in `REL`.

Deprecated modules
------------------
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10 changes: 5 additions & 5 deletions src/Data/Product/Relation/Binary/Pointwise/NonDependent.agda
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Expand Up @@ -11,10 +11,10 @@ module Data.Product.Relation.Binary.Pointwise.NonDependent where
open import Data.Product.Base as Product
open import Data.Sum.Base using (inj₁; inj₂)
open import Level using (Level; _⊔_; 0ℓ)
open import Function.Base using (_on_; id)
open import Function.Base using (id)
open import Function.Bundles using (Inverse)
open import Relation.Nullary.Decidable using (_×-dec_)
open import Relation.Binary.Core using (Rel; _⇒_)
open import Relation.Binary.Core using (REL; Rel; _⇒_)
open import Relation.Binary.Bundles
using (Setoid; DecSetoid; Preorder; Poset; StrictPartialOrder)
open import Relation.Binary.Definitions
Expand All @@ -25,14 +25,14 @@ import Relation.Binary.PropositionalEquality.Properties as ≡
private
variable
a b ℓ₁ ℓ₂ ℓ₃ ℓ₄ : Level
A B : Set a
A B C D : Set a
R S ≈₁ ≈₂ : Rel A ℓ₁

------------------------------------------------------------------------
-- Definition

Pointwise : Rel A ℓ₁ → Rel B ℓ₂ → Rel (A × B) (ℓ₁ ⊔ ℓ₂)
Pointwise R S = (R on proj₁) -×- (S on proj₂)
Pointwise : REL A B ℓ₁ → REL C D ℓ₂ → REL (A × C) (B × D) (ℓ₁ ⊔ ℓ₂)
Pointwise R S (a , c) (b , d) = (R a b) × (S c d)

------------------------------------------------------------------------
-- Pointwise preserves many relational properties
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6 changes: 2 additions & 4 deletions src/Data/Vec/Functional/Relation/Binary/Pointwise/Properties.agda
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Expand Up @@ -172,12 +172,10 @@ module _ {R : REL A B r} {S : REL A′ B′ s} {T : REL A″ B″ t} where
module _ {R : REL A B r} {S : REL A′ B′ s} {n xs ys xs′ ys′} where

zip⁺ : Pointwise R xs ys → Pointwise S xs′ ys′ →
Pointwise (λ xx yy → R (proj₁ xx) (proj₁ yy) × S (proj₂ xx) (proj₂ yy))
(zip xs xs′) (zip {n = n} ys ys′)
Pointwise (×-Pointwise R S) (zip xs xs′) (zip {n = n} ys ys′)
zip⁺ rs ss i = rs i , ss i

zip⁻ : Pointwise (λ xx yy → R (proj₁ xx) (proj₁ yy) × S (proj₂ xx) (proj₂ yy))
(zip xs xs′) (zip {n = n} ys ys′) →
zip⁻ : Pointwise (×-Pointwise R S) (zip xs xs′) (zip {n = n} ys ys′) →
Pointwise R xs ys × Pointwise S xs′ ys′
zip⁻ rss = proj₁ ∘ rss , proj₂ ∘ rss

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