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removed redundant use of with #1947

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Merged
merged 3 commits into from
Apr 24, 2023
Merged

removed redundant use of with #1947

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ba9f141
removed redundant use of `with`
jamesmckinna Apr 18, 2023
5e74e9a
some additional simplifications
jamesmckinna Apr 20, 2023
621ea0f
irrefutable `with` bindings for recursive calls/inductive hypotheses
jamesmckinna Apr 23, 2023
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4 changes: 1 addition & 3 deletions src/Algebra/Consequences/Base.agda
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Expand Up @@ -19,9 +19,7 @@ open import Relation.Binary.Definitions using (Reflexive)
module _ {ℓ} {_•_ : Op₂ A} (_≈_ : Rel A ℓ) where

sel⇒idem : Selective _≈_ _•_ → Idempotent _≈_ _•_
sel⇒idem sel x with sel x x
... | inj₁ x•x≈x = x•x≈x
... | inj₂ x•x≈x = x•x≈x
sel⇒idem sel x = reduce (sel x x)

module _ {ℓ} {f : Op₁ A} (_≈_ : Rel A ℓ) where

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22 changes: 10 additions & 12 deletions src/Data/List/Properties.agda
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Expand Up @@ -497,8 +497,8 @@ module _ {P : Pred A p} {f : A → A → A} where
foldr-forcesᵇ : (∀ x y → P (f x y) → P x × P y) →
∀ e xs → P (foldr f e xs) → All P xs
foldr-forcesᵇ _ _ [] _ = []
foldr-forcesᵇ forces _ (x ∷ xs) Pfold with forces _ _ Pfold
... | (px , pfxs) = px ∷ foldr-forcesᵇ forces _ xs pfxs
foldr-forcesᵇ forces _ (x ∷ xs) Pfold =
let px , pfxs = forces _ _ Pfold in px ∷ foldr-forcesᵇ forces _ xs pfxs

foldr-preservesᵇ : (∀ {x y} → P x → P y → P (f x y)) →
∀ {e xs} → P e → All P xs → P (foldr f e xs)
Expand Down Expand Up @@ -627,11 +627,10 @@ scanr-defn : ∀ (f : A → B → B) (e : B) →
scanr f e ≗ map (foldr f e) ∘ tails
scanr-defn f e [] = refl
scanr-defn f e (x ∷ []) = refl
scanr-defn f e (x ∷ y ∷ xs)
with scanr f e (y ∷ xs) | scanr-defn f e (y ∷ xs)
... | [] | ()
... | z ∷ zs | eq with ∷-injective eq
... | z≡fy⦇f⦈xs , _ = cong₂ (λ z → f x z ∷_) z≡fy⦇f⦈xs eq
scanr-defn f e (x ∷ y∷xs@(_ ∷ _))
with eq ← scanr-defn f e y∷xs
with z ∷ zs ← scanr f e y∷xs
= let z≡fy⦇f⦈xs , _ = ∷-injective eq in cong₂ (λ z → f x z ∷_) z≡fy⦇f⦈xs eq

------------------------------------------------------------------------
-- scanl
Expand Down Expand Up @@ -778,8 +777,7 @@ take++drop (suc n) (x ∷ xs) = cong (x ∷_) (take++drop n xs)
splitAt-defn : ∀ n → splitAt {A = A} n ≗ < take n , drop n >
splitAt-defn zero xs = refl
splitAt-defn (suc n) [] = refl
splitAt-defn (suc n) (x ∷ xs) with splitAt n xs | splitAt-defn n xs
... | (ys , zs) | ih = cong (Prod.map (x ∷_) id) ih
splitAt-defn (suc n) (x ∷ xs) = cong (Prod.map (x ∷_) id) (splitAt-defn n xs)

------------------------------------------------------------------------
-- takeWhile, dropWhile, and span
Expand Down Expand Up @@ -912,9 +910,9 @@ module _ {P : Pred A p} (P? : Decidable P) where
length-partition : ∀ xs → (let (ys , zs) = partition P? xs) →
length ys ≤ length xs × length zs ≤ length xs
length-partition [] = z≤n , z≤n
length-partition (x ∷ xs) with does (P? x) | length-partition xs
... | true | rec = Prod.map s≤s m≤n⇒m≤1+n rec
... | false | rec = Prod.map m≤n⇒m≤1+n s≤s rec
length-partition (x ∷ xs) with does (P? x)
... | true = Prod.map s≤s m≤n⇒m≤1+n (length-partition xs)
... | false = Prod.map m≤n⇒m≤1+n s≤s (length-partition xs)

------------------------------------------------------------------------
-- _ʳ++_
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