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changeset 862:28e3ea66e4da

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author Shinji KONO <kono@ie.u-ryukyu.ac.jp>
date Tue, 02 Apr 2024 10:23:48 +0900
parents 0ede876fdc4c
children 5a34330bc850
files hoareBinaryTree1.agda
diffstat 1 files changed, 9 insertions(+), 28 deletions(-) [+]
line wrap: on
line diff
--- a/hoareBinaryTree1.agda	Tue Apr 02 08:38:40 2024 +0900
+++ b/hoareBinaryTree1.agda	Tue Apr 02 10:23:48 2024 +0900
@@ -1113,36 +1113,17 @@
         rr04 = RTtoTI0 _ _ _ _ (t-left _ _ (proj1 x₃) (proj1 (proj2 x₃)) (proj2 (proj2 x₃)) ti₁ ) (r-left (proj1 x₃) r-node) 
         rr05 : treeInvariant (node key₁ value₁ t₂ t₃)
         rr05 = RB-repl→ti _ _ _ _ ti trb
-RB-repl→ti (node key₁ ⟪ Black , c1 ⟫ (node key₂ ⟪ Red , c2 ⟫ .leaf .leaf) (node key₃ v3 t₂ t₃)) (node _ ⟪ Black , _ ⟫ (node key₄ value₁ t₄ t₅) (node _ ⟪ Red , _ ⟫ .leaf (node key₃ _ _ _))) key value (t-node _ _ key₃ x₁ x₂ x₃ x₄ x₅ x₆ (t-single .key₂ .(⟪ Red , c2 ⟫)) ti₁) (rbr-rotate-ll x lt trb) = t-node _ _ _ ? x₁ ? ? tt ? rr02 ? where
+RB-repl→ti (node key₁ ⟪ Black , c1 ⟫ (node key₂ ⟪ Red , c2 ⟫ .leaf .leaf) (node key₃ v3 t₂ t₃)) (node _ ⟪ Black , _ ⟫ (node key₄ value₁ t₄ t₅) (node _ ⟪ Red , _ ⟫ .leaf (node key₃ _ _ _))) key value (t-node _ _ key₃ x₁ x₂ x₃ x₄ x₅ x₆ (t-single .key₂ .(⟪ Red , c2 ⟫)) ti₁) (rbr-rotate-ll x lt trb) = t-node _ _ _ ? x₁ ? ? ? ? ? ?
+RB-repl→ti (node key₁ ⟪ Black , c1 ⟫ (node key₂ ⟪ Red , c2 ⟫ .leaf .(node key₅ _ _ _)) (node key₃ v3 t₂ t₃)) (node _ ⟪ Black , _ ⟫ (node key₄ value₁ t₄ t₅) (node _ ⟪ Red , _ ⟫ .(node key₅ _ _ _) (node key₃ _ _ _))) key value (t-node _ _ key₃ x₁ x₂ x₃ x₄ x₅ x₆ (t-right .key₂ key₅ x₇ x₈ x₉ ti) ti₁) (rbr-rotate-ll x lt trb) = t-node _ _ _ ? x₁ ? ? ? ? ? ?
+RB-repl→ti (node key₁ ⟪ Black , c1 ⟫ (node key₂ ⟪ Red , c2 ⟫ .(node key₅ _ _ _) .leaf) (node key₃ v3 t₂ t₃)) (node _ ⟪ Black , _ ⟫ (node key₄ value₁ t₄ t₅) (node _ ⟪ Red , _ ⟫ .leaf (node key₃ _ _ _))) key value (t-node _ _ key₃ x₁ x₂ x₃ x₄ x₅ x₆ (t-left key₅ .key₂ x₇ x₈ x₉ ti) ti₁) (rbr-rotate-ll x lt trb) = t-node _ _ _ ? x₁ ? ? ? ? ? ?
+RB-repl→ti (node key₁ ⟪ Black , c1 ⟫ (node key₂ ⟪ Red , c2 ⟫ .(node key₅ _ _ _) (node key₆ value₆ t₆ t₇)) (node key₃ v3 t₂ t₃)) (node _ ⟪ Black , _ ⟫ (node key₄ value₁ t₄ t₅) (node _ ⟪ Red , _ ⟫ .(node key₆ _ _ _) (node key₃ _ _ _))) key value 
+  (t-node _ _ key₃ x₁ x₂ x₃ x₄ x₅ x₆ (t-node key₅ .key₂ key₆ x₇ x₈ x₉ x₁₀ x₁₁ x₁₂ ti ti₂) ti₁) (rbr-rotate-ll x lt trb) = t-node _ _ _ ? x₁ ? ? ⟪ ? , ⟪ ? , ? ⟫ ⟫  ? rr02 rr03 where
         rr00 : (key₄ < key₂) ∧ tr< key₂ t₄ ∧ tr< key₂ t₅
-        rr00 = RB-repl→ti< _ _ _ _ _ trb lt tt
-        rr02 : treeInvariant (node key₄ value₁ t₄ t₅)
-        rr02 = RB-repl→ti _ _ _ _ t-leaf trb
-        rr03 : treeInvariant (node key₁ ⟪ Red , c1 ⟫ leaf (node key₃ v3 t₂ t₃))
-        rr03 = RTtoTI0 _ _ _ _ (t-right key₁ key₃ x₂ x₄ x₅ (t-right ? ?  ? ? ? ?)) r-node
-RB-repl→ti (node key₁ ⟪ Black , c1 ⟫ (node key₂ ⟪ Red , c2 ⟫ .leaf .(node key₅ _ _ _)) (node key₃ v3 t₂ t₃)) (node _ ⟪ Black , _ ⟫ (node key₄ value₁ t₄ t₅) (node _ ⟪ Red , _ ⟫ .(node key₅ _ _ _) (node key₃ _ _ _))) key value (t-node _ _ key₃ x₁ x₂ x₃ x₄ x₅ x₆ (t-right .key₂ key₅ x₇ x₈ x₉ ti) ti₁) (rbr-rotate-ll x lt trb) = t-node _ _ _ ? x₁ ? ? ? ? rr02 rr03 where
-        rr00 : (key₄ < key₂) ∧ tr< key₂ t₄ ∧ tr< key₂ t₅
-        rr00 = RB-repl→ti< _ _ _ _ _ trb lt ?
+        rr00 = RB-repl→ti< _ _ _ _ _ trb lt ⟪ x₇ , ⟪ x₉ , x₁₀ ⟫ ⟫
         rr02 : treeInvariant (node key₄ value₁ t₄ t₅)
-        rr02 = RB-repl→ti _ _ _ _ ti₁ ?
-        rr03 : treeInvariant (node key₁ ⟪ Red , c1 ⟫ ? (node key₃ v3 t₂ t₃))
-        rr03 = RTtoTI0 _ _ _ _ ? r-node
-RB-repl→ti (node key₁ ⟪ Black , c1 ⟫ (node key₂ ⟪ Red , c2 ⟫ .(node key₅ _ _ _) .leaf) (node key₃ v3 t₂ t₃)) (node _ ⟪ Black , _ ⟫ (node key₄ value₁ t₄ t₅) (node _ ⟪ Red , _ ⟫ .leaf (node key₃ _ _ _))) key value (t-node _ _ key₃ x₁ x₂ x₃ x₄ x₅ x₆ (t-left key₅ .key₂ x₇ x₈ x₉ ti) ti₁) (rbr-rotate-ll x lt trb) = t-node _ _ _ ? x₁ ? ? ? ? rr02 rr03 where
-        rr00 : (key₄ < key₂) ∧ tr< key₂ t₄ ∧ tr< key₂ t₅
-        rr00 = RB-repl→ti< _ _ _ _ _ trb lt ?
-        rr02 : treeInvariant (node key₄ value₁ t₄ t₅)
-        rr02 = RB-repl→ti _ _ _ _ ti₁ ?
-        rr03 : treeInvariant (node key₁ ⟪ Red , c1 ⟫ ? (node key₃ v3 t₂ t₃))
-        rr03 = RTtoTI0 _ _ _ _ ? r-node
-RB-repl→ti (node key₁ ⟪ Black , c1 ⟫ (node key₂ ⟪ Red , c2 ⟫ .(node key₅ _ _ _) .(node key₆ _ _ _)) (node key₃ v3 t₂ t₃)) (node _ ⟪ Black , _ ⟫ (node key₄ value₁ t₄ t₅) (node _ ⟪ Red , _ ⟫ .(node key₆ _ _ _) (node key₃ _ _ _))) key value (t-node _ _ key₃ x₁ x₂ x₃ x₄ x₅ x₆ (t-node key₅ .key₂ key₆ x₇ x₈ x₉ x₁₀ x₁₁ x₁₂ ti ti₂) ti₁) (rbr-rotate-ll x lt trb) = t-node _ _ _ ? x₁ ? ? ? ? rr02 rr03 where
-        rr00 : (key₄ < key₂) ∧ tr< key₂ t₄ ∧ tr< key₂ t₅
-        rr00 = RB-repl→ti< _ _ _ _ _ trb lt ?
-        rr02 : treeInvariant (node key₄ value₁ t₄ t₅)
-        rr02 = RB-repl→ti _ _ _ _ ti₁ ?
-        rr03 : treeInvariant (node key₁ ⟪ Red , c1 ⟫ ? (node key₃ v3 t₂ t₃))
-        rr03 = RTtoTI0 _ _ _ _ ? r-node
-        rr04 : (key₂ < key₃) ∧ tr> key₂ t₂ ∧ tr> key₂ t₃
-        rr04 = ?
+        rr02 = RB-repl→ti _ _ _ _ ti trb
+        rr03 : treeInvariant (node key₁ ⟪ Red , c1 ⟫ (node key₆ value₆ t₆ t₇) (node key₃ v3 t₂ t₃))
+        rr03 = RTtoTI0 _ _ _ _(t-node _ _ _ ? ? ? ? ? ? ti₂ ti₁) r-node
 RB-repl→ti .(node _ ⟪ Black , _ ⟫ _ (node _ ⟪ Red , _ ⟫ _ _)) .(node _ ⟪ Black , _ ⟫ (node _ ⟪ Red , _ ⟫ _ _) _) key value ti (rbr-rotate-rr x lt trb) = ?
 RB-repl→ti .(node kg ⟪ Black , _ ⟫ (node kp ⟪ Red , _ ⟫ _ _) _) .(node kn ⟪ Black , _ ⟫ (node kp ⟪ Red , _ ⟫ _ t₂) (node kg ⟪ Red , _ ⟫ t₃ _)) key value ti (rbr-rotate-lr t₂ t₃ kg kp kn trb) = ?
 RB-repl→ti .(node kg ⟪ Black , _ ⟫ _ (node kp ⟪ Red , _ ⟫ _ _)) .(node kn ⟪ Black , _ ⟫ (node kg ⟪ Red , _ ⟫ _ t₂) (node kp ⟪ Red , _ ⟫ t₃ _)) key value ti (rbr-rotate-rl t₂ t₃ kg kp kn trb) = ?