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changeset 693:49dd82f49fa1

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insertTreeP
author Shinji KONO <kono@ie.u-ryukyu.ac.jp>
date Thu, 02 Dec 2021 00:27:11 +0900
parents 9f1ccc8a0e1d
children da42fe4eda54
files hoareBinaryTree.agda
diffstat 1 files changed, 19 insertions(+), 21 deletions(-) [+]
line wrap: on
line diff
--- a/hoareBinaryTree.agda	Wed Dec 01 23:04:55 2021 +0900
+++ b/hoareBinaryTree.agda	Thu Dec 02 00:27:11 2021 +0900
@@ -239,17 +239,17 @@
 
 findP : {n m : Level} {A : Set n} {t : Set m} → (key : ℕ) → (tree tree0 : bt A ) → (stack : List (bt A))
            →  treeInvariant tree ∧ stackInvariant key tree tree0 stack  
-           → (next : (tree1 tree0 : bt A) → (stack : List (bt A)) → treeInvariant tree1 ∧ stackInvariant key tree1 tree0 stack → bt-depth tree1 < bt-depth tree   → t )
-           → (exit : (tree1 tree0 : bt A) → (stack : List (bt A)) → treeInvariant tree1 ∧ stackInvariant key tree1 tree0 stack
+           → (next : (tree1 : bt A) → (stack : List (bt A)) → treeInvariant tree1 ∧ stackInvariant key tree1 tree0 stack → bt-depth tree1 < bt-depth tree   → t )
+           → (exit : (tree1 : bt A) → (stack : List (bt A)) → treeInvariant tree1 ∧ stackInvariant key tree1 tree0 stack
                  → (tree1 ≡ leaf ) ∨ ( node-key tree1 ≡ just key )  → t ) → t
-findP key leaf tree0 st Pre _ exit = exit leaf tree0 st Pre (case1 refl)
+findP key leaf tree0 st Pre _ exit = exit leaf st Pre (case1 refl)
 findP key (node key₁ v1 tree tree₁) tree0 st Pre next exit with <-cmp key key₁
-findP key n tree0 st Pre _ exit | tri≈ ¬a refl ¬c = exit n tree0 st Pre (case2 refl)
-findP {n} {_} {A} key (node key₁ v1 tree tree₁) tree0 st  Pre next _ | tri< a ¬b ¬c = next tree tree0 (tree ∷ st)
+findP key n tree0 st Pre _ exit | tri≈ ¬a refl ¬c = exit n st Pre (case2 refl)
+findP {n} {_} {A} key (node key₁ v1 tree tree₁) tree0 st  Pre next _ | tri< a ¬b ¬c = next tree (tree ∷ st)
        ⟪ treeLeftDown tree tree₁ (proj1 Pre)  , findP1 a st (proj2 Pre) ⟫ depth-1< where
    findP1 : key < key₁ → (st : List (bt A)) →  stackInvariant key (node key₁ v1 tree tree₁) tree0 st → stackInvariant key tree tree0 (tree ∷ st)
    findP1 a (x ∷ st) si = s-left a si
-findP key n@(node key₁ v1 tree tree₁) tree0 st Pre next _ | tri> ¬a ¬b c = next tree₁ tree0 (tree₁ ∷ st) ⟪ treeRightDown tree tree₁ (proj1 Pre) , s-right c (proj2 Pre) ⟫ depth-2<
+findP key n@(node key₁ v1 tree tree₁) tree0 st Pre next _ | tri> ¬a ¬b c = next tree₁ (tree₁ ∷ st) ⟪ treeRightDown tree tree₁ (proj1 Pre) , s-right c (proj2 Pre) ⟫ depth-2<
 
 replaceTree1 : {n  : Level} {A : Set n} {t t₁ : bt A } → ( k : ℕ ) → (v1 value : A ) →  treeInvariant (node k v1 t t₁) → treeInvariant (node k value t t₁)
 replaceTree1 k v1 value (t-single .k .v1) = t-single k value
@@ -514,15 +514,13 @@
 RTtoTI0 .(node key _ (node _ _ _ _) (node _ _ _ _)) .(node key value (node _ _ _ _) (node _ _ _ _)) key value (t-node x x₁ ti ti₁) r-node = t-node x x₁ ti ti₁
 RTtoTI0 (node _ _ leaf leaf) (node _ _ leaf .(node key value leaf leaf)) key value (t-single _ _) (r-right x r-leaf) = t-right x (t-single key value)
 RTtoTI0 (node _ _ leaf right@(node _ _ _ _)) (node key₁ value₁ leaf leaf) key value (t-right x₁ ti) (r-right x ri) = t-single key₁ value₁
-RTtoTI0 (node key₁ _ leaf right@(node key₂ _ _ _)) (node key₁ value₁ leaf right₁@(node key₃ _ _ _)) key value (t-right x₁ ti) (r-right x ri) = t-right rt2 rt1 where
-    rt2 : key₁ < key₃
-    rt2 = subst (λ k → key₁ < k ) (rt-property-key ri) x₁
-    rt1 : treeInvariant right₁   
-    rt1 = RTtoTI0 _ _ key value ti ri 
+RTtoTI0 (node key₁ _ leaf right@(node key₂ _ _ _)) (node key₁ value₁ leaf right₁@(node key₃ _ _ _)) key value (t-right x₁ ti) (r-right x ri) = 
+      t-right (subst (λ k → key₁ < k ) (rt-property-key ri) x₁) (RTtoTI0 _ _ key value ti ri)
 RTtoTI0 (node key₁ _ (node _ _ _ _) leaf) (node key₁ _ (node key₃ value left right) leaf) key value₁ (t-left x₁ ti) (r-right x ())
 RTtoTI0 (node key₁ _ (node key₃ _ _ _) leaf) (node key₁ _ (node key₃ value₃ _ _) (node key value leaf leaf)) key value (t-left x₁ ti) (r-right x r-leaf) =
       t-node x₁ x ti (t-single key value) 
-RTtoTI0 .(node _ _ (node _ _ _ _) (node _ _ _ _)) .(node _ _ (node _ _ _ _) _) key value (t-node x₁ x₂ ti ti₁) (r-right x ri) = {!!}
+RTtoTI0 (node key₁ _ (node _ _ _ _) (node key₂ _ _ _)) (node key₁ _ (node _ _ _ _) (node key₃ _ _ _)) key value (t-node x₁ x₂ ti ti₁) (r-right x ri) =
+      t-node x₁ (subst (λ k → key₁ < k) (rt-property-key ri) x₂) ti (RTtoTI0 _ _ key value ti₁ ri)
 RTtoTI0 .(node _ _ _ _) .(node _ _ _ _) key value ti (r-left x ri) = {!!}
 
 RTtoTI1  : {n : Level} {A : Set n}  → (tree repl : bt A) → (key : ℕ) → (value : A) → treeInvariant repl
@@ -531,15 +529,15 @@
 
 insertTreeP : {n m : Level} {A : Set n} {t : Set m} → (tree : bt A) → (key : ℕ) → (value : A) → treeInvariant tree
      → (exit : (tree repl : bt A) → treeInvariant tree ∧ replacedTree key value tree repl → t ) → t
-insertTreeP {n} {m} {A} {t} tree key value P exit =
-   TerminatingLoopS (bt A ∧ List (bt A) ) {λ p → treeInvariant (proj1 p) ∧ stackInvariant key (proj1 p) tree (proj2 p) } (λ p → bt-depth (proj1 p)) ⟪ tree , [] ⟫  ⟪ P , {!!}  ⟫
-       $ λ p P loop → findP key (proj1 p)  tree (proj2 p) {!!} (λ t _ s P1 lt → loop ⟪ t ,  s  ⟫ {!!} lt )
-       $ λ t _ s P C → replaceNodeP key value t C (proj1 P)
-       $ λ t1 P1 R → TerminatingLoopS (List (bt A) ∧ (bt A ∧ bt A ))
-            {λ p → treeInvariant (proj1 (proj2 p)) ∧ stackInvariant key (proj1 (proj2 p)) tree (proj1 p)  ∧ replacedTree key value (proj1 (proj2 p)) (proj2 (proj2 p)) }
-               (λ p → length (proj1 p)) ⟪ s , ⟪ t , t1 ⟫ ⟫　⟪ proj1 P , ⟪ {!!}  , R ⟫ ⟫
-       $  λ p P1 loop → replaceP key value  (proj2 (proj2 p)) (proj1 p) {!!}
-            (λ key value repl1 stack P2 lt → loop ⟪ stack , ⟪ {!!} , repl1  ⟫ ⟫ {!!} lt )  exit 
+insertTreeP {n} {m} {A} {t} tree key value P0 exit =
+   TerminatingLoopS (bt A ∧ List (bt A) ) {λ p → treeInvariant (proj1 p) ∧ stackInvariant key (proj1 p) tree (proj2 p) } (λ p → bt-depth (proj1 p)) ⟪ tree , tree ∷ [] ⟫  ⟪ P0 , s-single ⟫
+       $ λ p P loop → findP key (proj1 p)  tree (proj2 p) P (λ t s P1 lt → loop ⟪ t ,  s  ⟫ P1 lt ) -- treeInvariant t ∧ stackInvariant key t tree s
+       $ λ t s P C → replaceNodeP key value t C (proj1 P)
+       $ λ t1 P1 R → TerminatingLoopS (List (bt A) ∧ bt A ∧ bt A )
+            {λ p → replacePR key value  (proj1 (proj2 p)) (proj2 (proj2 p)) (proj1 p)  (λ _ _ _ → Lift n ⊤ ) }
+               (λ p → length (proj1 p)) ⟪ s , ⟪ t , t1 ⟫ ⟫ record { tree0 = tree ; ti = P0 ; si = proj2 P ; ri = {!!} ; ci = lift tt } -- replacedTree key value (child-replaced key t) t1
+       $  λ p P1 loop → replaceP key value  (proj2 (proj2 p)) (proj1 p) P1
+            (λ key value {tree1} repl1 stack P2 lt → loop ⟪ stack , ⟪ tree1 , repl1  ⟫ ⟫ P2 lt )  exit 
 
 top-value : {n : Level} {A : Set n} → (tree : bt A) →  Maybe A 
 top-value leaf = nothing