diff options
Diffstat (limited to 'Data/Matrix/Transform.agda')
| -rw-r--r-- | Data/Matrix/Transform.agda | 17 |
1 files changed, 16 insertions, 1 deletions
diff --git a/Data/Matrix/Transform.agda b/Data/Matrix/Transform.agda index 671725f..87b8020 100644 --- a/Data/Matrix/Transform.agda +++ b/Data/Matrix/Transform.agda @@ -27,7 +27,7 @@ open import Data.Matrix.Monoid R.+-monoid using (𝟎; 𝟎ᵀ; _[+]_) open import Data.Vector.Core R.setoid using (Vector; Vectorₛ; ⟨⟩; module ≊; _≊_; _++_; ⟨⟩-++) open import Data.Vector.Vec using (zipWith-map; map-zipWith; zipWith-map-map) open import Data.Vector.Monoid R.+-monoid using (_⊕_; ⊕-cong; ⊕-identityˡ; ⊕-identityʳ) renaming (⟨ε⟩ to ⟨0⟩) -open import Data.Vector.Bisemimodule R using (_∙_; ∙-cong; ∙-zeroˡ; ∙-zeroʳ; _⟨_⟩; *-∙ˡ; ∙-distribʳ) +open import Data.Vector.Bisemimodule R using (_∙_; ∙-cong; ∙-zeroˡ; ∙-zeroʳ; _⟨_⟩; *-∙ˡ; *-∙ʳ; ∙-distribˡ; ∙-distribʳ) open Vec open ℕ @@ -55,6 +55,9 @@ opaque -[-]-cong : {x y : Vector n} (A : Matrix n m) → x ≊ y → A [ x ] ≊ A [ y ] -[-]-cong {x = x} {y} A ≋V = PW.map⁺ (λ ≋w → ∙-cong ≋w ≋V) {xs = A} ≋.refl + -[-]-cong₁ : {M M′ : Matrix n m} → M ≋ M′ → (V : Vector n) → M [ V ] ≊ M′ [ V ] + -[-]-cong₁ {n} {m} {M} {M′} ≋M V = PW.map⁺ (λ ≊V → ∙-cong ≊V ≊.refl) ≋M + [-]--cong : {x y : Vector m} {A B : Matrix n m} → x ≊ y → A ≋ B → [ x ] A ≊ [ y ] B [-]--cong ≋V A≋B = PW.map⁺ (∙-cong ≋V) (-ᵀ-cong A≋B) @@ -74,6 +77,12 @@ opaque [-]-[]ₕ {zero} [] = ≡.refl [-]-[]ₕ {suc A} [] = ≡.cong (0# ∷_) ([-]-[]ₕ []) + opaque + unfolding _⊕_ + -[⊕] : (M : Matrix A B) (V W : Vector A) → M [ V ⊕ W ] ≊ (M [ V ]) ⊕ (M [ W ]) + -[⊕] [] V W = PW.[] + -[⊕] (x ∷ M) V W = ∙-distribˡ x V W PW.∷ -[⊕] M V W + opaque unfolding Matrix Vector @@ -296,3 +305,9 @@ opaque 0# ∷ ⟨0⟩ ∎ where open ≈-Reasoning (Vectorₛ _) + +opaque + unfolding _[_] ⟨0⟩ + -[⟨0⟩] : (M : Matrix A B) → M [ ⟨0⟩ ] ≊ ⟨0⟩ + -[⟨0⟩] {A} {B} [] = PW.[] + -[⟨0⟩] {A} {B} (M₀ ∷ M) = ∙-zeroʳ M₀ PW.∷ -[⟨0⟩] M |