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associativity for vectors #1621

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Merged
merged 4 commits into from
Nov 20, 2021
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associativity for vectors #1621

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c7f1ef3
associativity for vectors
o-da Nov 14, 2021
0c53066
improving style of associativity for vectors
o-da Nov 14, 2021
bdc233b
+ associativity for vectors in CHANGELOG.md
o-da Nov 14, 2021
c37059d
- implementaion for vect. concat. from changelog
o-da Nov 14, 2021
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5 changes: 5 additions & 0 deletions src/Data/Vec/Relation/Binary/Equality/Setoid.agda
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Original file line number Diff line number Diff line change
Expand Up @@ -68,6 +68,11 @@ open PW public using (++⁺ ; ++⁻ ; ++ˡ⁻; ++ʳ⁻)
++-identityʳ [] = []
++-identityʳ (x ∷ xs) = refl ∷ ++-identityʳ xs

++-assoc : ∀ {n m k} (xs : Vec A n) → (ys : Vec A m)
→ (zs : Vec A k) → (xs ++ ys) ++ zs ≋ xs ++ (ys ++ zs)
++-assoc [] ys zs = ≋-refl
++-assoc (x ∷ xs) ys zs = refl ∷ ++-assoc xs ys zs

map-++-commute : ∀ {b m n} {B : Set b}
(f : B → A) (xs : Vec B m) {ys : Vec B n} →
map f (xs ++ ys) ≋ map f xs ++ map f ys
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