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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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14 changes: 14 additions & 0 deletions CHANGELOG.md
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Expand Up @@ -231,6 +231,11 @@ Deprecated names
^-monoid-morphism ↦ ^-isMonoidHomomorphism
```

* In `Data.Tree.AVL.Indexed.Relation.Unary.Any.Properties`:
```agda
insertWith-just ↦ insertWith-just-update
```

* In `Effect.Monad.Partiality`:
```agda
_≟-Kind_ ↦ _≡?-Kind_
Expand Down Expand Up @@ -486,6 +491,15 @@ Additions to existing modules
Pointwise R S =[ Sum.[ f , g ]′ ]⇒ T
```

* In `Data.Tree.AVL.Indexed.Relation.Unary.Any.Properties.Insert`:
```agda
insertWith-just-update : ∀ t l<k<u →
(∀ 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))
```

* In `Data.Vec.Properties`:
```agda
lookup-head : (xs : Vec A (suc n)) → lookup xs zero ≡ head xs
Expand Down
82 changes: 58 additions & 24 deletions src/Data/Tree/AVL/Indexed/Relation/Unary/Any/Properties/Insert.agda
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Expand Up @@ -16,16 +16,19 @@ open import Data.Maybe.Base using (Maybe; nothing; just)
open import Data.Nat.Base using (ℕ)
open import Data.Product.Base using (_×_; _,_; proj₁; proj₂)
open import Data.Sum.Base as Sum using (_⊎_; inj₁; inj₂)
open import Data.Unit.Base using (⊤; tt)
open import Function.Base as F using (_∘′_)
open import Level using (Level)
open import Level using (Level; 0ℓ)
open import Relation.Binary.Definitions using (tri<; tri≈; tri>)
open import Relation.Binary.PropositionalEquality.Core as ≡ using (_≡_; subst; cong)
open import Relation.Nullary.Negation.Core using (¬_; contradiction)
open import Relation.Unary using (Pred)

open import Data.Tree.AVL.Indexed sto as AVL
open import Data.Tree.AVL.Indexed.Relation.Unary.Any sto as Any
open import Data.Tree.AVL.Indexed.Relation.Unary.Any.Properties.Lookup sto
using (lookup-result; lookup-bounded; lookup-rebuild-accum)
using (lookup-result; lookup-bounded; lookup-rebuild;
lookup-rebuild-accum; lookup-lookup-rebuild)
open import Data.Tree.AVL.Indexed.Relation.Unary.Any.Properties.JoinLemmas sto
using (joinˡ⁺-left⁺; joinʳ⁺-right⁺; joinˡ⁺-here⁺; joinʳ⁺-here⁺;
joinʳ⁺-left⁺; joinˡ⁺-right⁺; joinˡ⁺⁻; joinʳ⁺⁻)
Expand All @@ -41,11 +44,12 @@ import Relation.Binary.Reasoning.StrictPartialOrder as <-Reasoning

private
variable
v p : Level
v p q : Level
V : Value v
l u : Key⁺
h : ℕ
P : Pred (K& V) p
Q : Pred (K& V) q


module _ {V : Value v} (open Value V using (respects) renaming (family to Val)) where
Expand Down Expand Up @@ -73,56 +77,58 @@ module _ {V : Value v} (open Value V using (respects) renaming (family to Val))
ku′ = insertWith k f ku l<k<u′
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
insertWith-just-update : (t : Tree V l u h) (l<k<u : l < k < u) →
(∀ 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-update (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-update 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-update 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 +139,8 @@ 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-update 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 Expand Up @@ -217,6 +224,28 @@ module _ {V : Value v} (open Value V using (respects) renaming (family to Val))

-- Version 2.4

module _ {V : Value v} (open Value V using (respects) renaming (family to Val)) where

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

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 {P = P} t l<k<u pr p =
insertWith-just-update k f {P = P′} {Q = P} t l<k<u
(λ k′ v eq _ → pr k′ v eq)
p′ k≈p′
where
P′ : Pred (K& V) 0ℓ
P′ _ = ⊤
p′ : Any P′ t
p′ = lookup-rebuild p tt
k≈p′ : k ≈ lookupKey p′
k≈p′ = subst (k ≈_)
(≡.sym (cong key (lookup-lookup-rebuild p tt)))
(lookup-result p)


Any-insertWith-nothing = insertWith-nothing
{-# WARNING_ON_USAGE Any-insertWith-nothing
"Warning: Any-insertWith-nothing was deprecated in v2.4.
Expand All @@ -225,7 +254,7 @@ Please use insertWith-nothing instead."
Any-insertWith-just = insertWith-just
{-# WARNING_ON_USAGE Any-insertWith-just
"Warning: Any-insertWith-just was deprecated in v2.4.
Please use insertWith-just instead."
Please use insertWith-just-update instead."
#-}
Any-insert-nothing = insert-nothing
{-# WARNING_ON_USAGE Any-insert-nothing
Expand All @@ -237,3 +266,8 @@ Any-insert-just = insert-just
"Warning: Any-insert-just was deprecated in v2.4.
Please use insert-just instead."
#-}

{-# WARNING_ON_USAGE insertWith-just
"Warning: insertWith-just was deprecated in v2.4.
Comment thread
mikedelorimier marked this conversation as resolved.
Outdated
Please use insertWith-just-update instead."
#-}
7 changes: 6 additions & 1 deletion src/Data/Tree/AVL/Indexed/Relation/Unary/Any/Properties/Lookup.agda
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Expand Up @@ -43,7 +43,6 @@ private
t : Tree V l u h



----------------------------------------------------------------------
-- lookup

Expand All @@ -67,6 +66,12 @@ lookup-rebuild (right p) q = right (lookup-rebuild p q)
lookup-rebuild-accum : (p : Any P t) → Q (lookup p) → Any (Q ∩ P) t
lookup-rebuild-accum p q = lookup-rebuild p (q , lookup-result p)

lookup-lookup-rebuild : (p : Any P t) (q : Q (lookup p)) →
lookup {P = Q} (lookup-rebuild p q) ≡ lookup p
lookup-lookup-rebuild (here _) _ = refl
lookup-lookup-rebuild (left p) q = lookup-lookup-rebuild p q
lookup-lookup-rebuild (right p) q = lookup-lookup-rebuild p q


----------------------------------------------------------------------
-- Relating Any.lookup to AVL.lookup
Expand Down
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