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strengthen the AVL tree's insertWith-just #3087

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strengthen the AVL tree's insertWith-just #3087

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7e67f24
Added insertWith-just-update, which is stronger than insertWith-just.
mikedelorimier Jul 23, 2026
e524799
Made breaking change instead of complicated deprecation.
mikedelorimier Jul 28, 2026
296ac1d
Removed now unused code.
mikedelorimier Jul 28, 2026
a281ac4
Removed now unused code.
mikedelorimier Jul 28, 2026
561e2cd
resolved merge conflict
mikedelorimier Jul 28, 2026
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4 changes: 4 additions & 0 deletions CHANGELOG.md
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Original file line number Diff line number Diff line change
Expand Up @@ -157,6 +157,10 @@ Non-backwards compatible changes
defined in `Data.List.Relation.Binary.Permutation.{Propositional|Setoid}`,
has been removed.

* In `Data.Tree.AVL.Indexed.Relation.Unary.Any.Properties.Insert`:
`insertWith-just` is strengthened to prevent the possibility of `insertWith`
ignoring the old value.

* In `Data.Product.Relation.Binary.Pointwise.Dependent`, the universe level of
the `record POINTWISE` has been lowered to `ℓ₁ ⊔ ℓ₂` given the universe levels
`ℓ₁`, resp. `ℓ₂` of the argument relations `_R₁_`, resp. `_R₂_`.
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42 changes: 23 additions & 19 deletions src/Data/Tree/AVL/Indexed/Relation/Unary/Any/Properties/Insert.agda
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Expand Up @@ -46,6 +46,7 @@ private
l u : Key⁺
h : ℕ
P : Pred (K& V) p
Q : Pred (K& V) p


module _ {V : Value v} (open Value V using (respects) renaming (family to Val)) where
Expand Down Expand Up @@ -74,55 +75,57 @@ module _ {V : Value v} (open Value V using (respects) renaming (family to Val))
ih = insertWith-nothing ku l<k<u′ pr (λ p → ¬p (right p))

insertWith-just : (t : Tree V l u h) (l<k<u : l < k < u) →
(pr : ∀ k′ v → (eq : k ≈ k′) → P (k′ , respects eq (f (just (respects (sym eq) v))))) →
Any ((k ≈_) ∘′ key) t → Any P (proj₂ (insertWith k f t l<k<u))
insertWith-just (node kv@(k′ , v) lk ku bal) (l<k , k<u) pr p
(∀ k′ v → (eq : k ≈ k′) → P (k′ , v) →
Q (k′ , respects eq (f (just (respects (sym eq) v))))) →
(p : Any P t) → k ≈ lookupKey p →
Any Q (proj₂ (insertWith k f t l<k<u))
insertWith-just (node kv@(k′ , v) lk ku bal) (l<k , k<u) pr p k≈p
with p | compare k k′
-- happy paths
... | here _ | tri≈ _ k≈k′ _ = here (pr k′ v k≈k′)
... | here p | tri≈ _ k≈k′ _ = here (pr k′ v k≈k′ p)
... | left lp | tri< k<k′ _ _ =
joinˡ⁺-left⁺ kv lk′ ku bal (insertWith-just lk l<k<u′ pr lp)
joinˡ⁺-left⁺ kv lk′ ku bal (insertWith-just lk l<k<u′ pr lp k≈p)
where
l<k<u′ = l<k , [ k<k′ ]ᴿ
lk′ = insertWith k f lk l<k<u′
... | right rp | tri> _ _ k>k′ =
joinʳ⁺-right⁺ kv lk ku′ bal (insertWith-just ku l<k<u′ pr rp)
joinʳ⁺-right⁺ kv lk ku′ bal (insertWith-just ku l<k<u′ pr rp k≈p)
where
l<k<u′ = [ k>k′ ]ᴿ , k<u
ku′ = insertWith k f ku l<k<u′

-- impossible cases
... | here eq | tri< k<k′ _ _ = begin-contradiction
... | here _ | tri< k<k′ _ _ = begin-contradiction
[ k ] <⟨ [ k<k′ ]ᴿ ⟩
[ k′ ] ≈⟨ [ sym eq ]ᴱ ⟩
[ k′ ] ≈⟨ [ sym k≈p ]ᴱ ⟩
[ k ] ∎
... | here eq | tri> _ _ k>k′ = begin-contradiction
[ k ] ≈⟨ [ eq ]ᴱ ⟩
... | here _ | tri> _ _ k>k′ = begin-contradiction
[ k ] ≈⟨ [ k≈p ]ᴱ ⟩
[ k′ ] <⟨ [ k>k′ ]ᴿ ⟩
[ k ] ∎
... | left lp | tri≈ _ k≈k′ _ = begin-contradiction
let k″ = Any.lookup lp .key; k≈k″ = lookup-result lp; (_ , k″<k′) = lookup-bounded lp in
[ k ] ≈⟨ [ k≈k″ ]ᴱ ⟩
let k″ = Any.lookup lp .key; (_ , k″<k′) = lookup-bounded lp in
[ k ] ≈⟨ [ k≈p ]ᴱ ⟩
[ k″ ] <⟨ k″<k′ ⟩
[ k′ ] ≈⟨ [ sym k≈k′ ]ᴱ ⟩
[ k ] ∎
... | left lp | tri> _ _ k>k′ = begin-contradiction
let k″ = Any.lookup lp .key; k≈k″ = lookup-result lp; (_ , k″<k′) = lookup-bounded lp in
[ k ] ≈⟨ [ k≈k″ ]ᴱ ⟩
let k″ = Any.lookup lp .key; (_ , k″<k′) = lookup-bounded lp in
[ k ] ≈⟨ [ k≈p ]ᴱ ⟩
[ k″ ] <⟨ k″<k′ ⟩
[ k′ ] <⟨ [ k>k′ ]ᴿ ⟩
[ k ] ∎
... | right rp | tri< k<k′ _ _ = begin-contradiction
let k″ = Any.lookup rp .key; k≈k″ = lookup-result rp; (k′<k″ , _) = lookup-bounded rp in
let k″ = Any.lookup rp .key; (k′<k″ , _) = lookup-bounded rp in
[ k ] <⟨ [ k<k′ ]ᴿ ⟩
[ k′ ] <⟨ k′<k″ ⟩
[ k″ ] ≈⟨ [ sym k≈k″ ]ᴱ ⟩
[ k″ ] ≈⟨ [ sym k≈p ]ᴱ ⟩
[ k ] ∎
... | right rp | tri≈ _ k≈k′ _ = begin-contradiction
let k″ = Any.lookup rp .key; k≈k″ = lookup-result rp; (k′<k″ , _) = lookup-bounded rp in
let k″ = Any.lookup rp .key; (k′<k″ , _) = lookup-bounded rp in
[ k ] ≈⟨ [ k≈k′ ]ᴱ ⟩
[ k′ ] <⟨ k′<k″ ⟩
[ k″ ] ≈⟨ [ sym k≈k″ ]ᴱ ⟩
[ k″ ] ≈⟨ [ sym k≈p ]ᴱ ⟩
[ k ] ∎

module _ (k : Key) (v : Val k) (t : Tree V l u h) (l<k<u : l < k < u) where
Expand All @@ -133,7 +136,8 @@ module _ {V : Value v} (open Value V using (respects) renaming (family to Val))

insert-just : (pr : ∀ k′ → (eq : k ≈ k′) → P (k′ , respects eq v)) →
Any ((k ≈_) ∘′ key) t → Any P (proj₂ (insert k v t l<k<u))
insert-just pr = insertWith-just k (F.const v) t l<k<u (λ k′ _ → pr k′)
insert-just pr p = insertWith-just k (F.const v) t l<k<u
(λ k′ _ eq _ → pr k′ eq) p (lookup-result p)

module _ (k : Key) (f : Maybe (Val k) → Val k) where

Expand Down
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