Mercurial > hg > Gears > GearsAgda
changeset 874:3fd3ab3bff54
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| author | Shinji KONO <kono@ie.u-ryukyu.ac.jp> |
|---|---|
| date | Thu, 02 May 2024 11:02:02 +0900 |
| parents | 0c36153cd08f |
| children | d7e255dbaa84 |
| files | hoareBinaryTree1.agda |
| diffstat | 1 files changed, 22 insertions(+), 7 deletions(-) [+] |
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--- a/hoareBinaryTree1.agda Thu May 02 01:19:15 2024 +0900 +++ b/hoareBinaryTree1.agda Thu May 02 11:02:02 2024 +0900 @@ -1202,15 +1202,30 @@ RB-repl→ti (node kg ⟪ Black , v1 ⟫ (node kp ⟪ Red , v2 ⟫ (node key₁ value₁ t t₁) leaf) .leaf) (node kn ⟪ Black , v3 ⟫ (node kp ⟪ Red , _ ⟫ _ leaf) (node kg ⟪ Red , _ ⟫ leaf _)) .kn .v3 (t-left .kp .kg x x₁ x₂ (t-left .key₁ .kp x₃ x₄ x₅ ti)) (rbr-rotate-lr .leaf .leaf kg kp kn lt1 lt2 rbr-leaf) = t-node _ _ _ lt1 lt2 ⟪ <-trans x₃ lt1 , ⟪ >-tr< x₄ lt1 , >-tr< x₅ lt1 ⟫ ⟫ tt tt tt (t-left _ _ x₃ x₄ x₅ ti) (t-single _ _) RB-repl→ti (node kg ⟪ Black , v1 ⟫ (node kp ⟪ Red , v2 ⟫ .leaf (node key₁ .(⟪ Red , _ ⟫) .leaf .leaf)) .leaf) (node .key₁ ⟪ Black , _ ⟫ (node kp ⟪ Red , _ ⟫ _ leaf) (node kg ⟪ Red , _ ⟫ leaf _)) .key₁ _ (t-left .kp .kg x x₁ x₂ (t-right .kp .key₁ x₃ x₄ x₅ ti)) (rbr-rotate-lr .leaf .leaf kg kp .key₁ lt1 lt2 rbr-node) = t-node _ _ _ lt1 lt2 tt tt tt tt (t-single _ _) (t-single _ _) -RB-repl→ti (node kg ⟪ Black , v1 ⟫ (node kp ⟪ Red , v2 ⟫ .leaf (node key₁ value₁ t₁ t₂)) .leaf) (node kn ⟪ Black , _ ⟫ (node kp ⟪ Red , _ ⟫ _ leaf) (node kg ⟪ Red , _ ⟫ (node key₂ value₂ t₄ t₅) t₆)) key value (t-left .kp .kg x x₁ x₂ (t-right .kp .key₁ x₃ x₄ x₅ ti)) (rbr-rotate-lr .leaf .(node key₂ value₂ t₄ t₅) kg kp kn lt1 lt2 trb) = t-node _ _ _ (proj1 rr00) (proj1 rr01) tt tt ? tt (t-single _ _) (t-left _ _ ? ? ? (treeRightDown _ _ ( RB-repl→ti _ _ _ _ ti trb))) where - rr00 : (kp < kn) ∧ ⊤ ∧ tr> kp (node key₂ value₂ t₄ t₅) +RB-repl→ti (node kg ⟪ Black , v1 ⟫ (node kp ⟪ Red , v2 ⟫ .leaf (node key₁ value₁ t₁ t₂)) .leaf) (node kn ⟪ Black , value₃ ⟫ (node kp ⟪ Red , _ ⟫ _ leaf) (node kg ⟪ Red , _ ⟫ (node key₂ value₂ t₄ t₅) t₆)) key value (t-left .kp .kg x x₁ x₂ (t-right .kp .key₁ x₃ x₄ x₅ ti)) (rbr-rotate-lr .leaf .(node key₂ value₂ t₄ t₅) kg kp kn lt1 lt2 trb) = + t-node _ _ _ (proj1 rr00) (proj1 rr01) tt tt rr03 tt (t-single _ _) (t-left _ _ (proj1 rr02) (proj1 (proj2 rr02)) (proj2 (proj2 rr02)) (treeRightDown _ _ ( RB-repl→ti _ _ _ _ ti trb))) where + rr00 : (kp < kn) ∧ ⊤ ∧ ((kp < key₂) ∧ tr> kp t₄ ∧ tr> kp t₅ ) rr00 = RB-repl→ti> _ _ _ _ _ trb lt1 ⟪ x₃ , ⟪ x₄ , x₅ ⟫ ⟫ - rr01 : (kn < kg) ∧ tr< kg leaf ∧ tr< kg (node key₂ value₂ t₄ t₅) + rr01 : (kn < kg) ∧ ⊤ ∧ ((key₂ < kg ) ∧ tr< kg t₄ ∧ tr< kg t₅ ) -- tr< kg (node key₂ value₂ t₄ t₅) rr01 = RB-repl→ti< _ _ _ _ _ trb lt2 x₂ -RB-repl→ti (node kg ⟪ Black , v1 ⟫ (node kp ⟪ Red , v2 ⟫ .leaf (node key₁ value₁ t₁ t₂)) .leaf) (node kn ⟪ Black , _ ⟫ (node kp ⟪ Red , _ ⟫ _ (node key₂ value₂ t₃ t₅)) (node kg ⟪ Red , _ ⟫ leaf _)) key value (t-left .kp .kg x x₁ x₂ (t-right .kp .key₁ x₃ x₄ x₅ ti)) (rbr-rotate-lr .(node key₂ value₂ t₃ t₅) .leaf kg kp kn lt1 lt2 trb) = t-node _ _ _ ? ? ? ? ? ? ? ? -RB-repl→ti (node kg ⟪ Black , v1 ⟫ (node kp ⟪ Red , v2 ⟫ .leaf (node key₁ value₁ t₁ t₂)) .leaf) (node kn ⟪ Black , _ ⟫ (node kp ⟪ Red , _ ⟫ _ (node key₂ value₂ t₃ t₅)) (node kg ⟪ Red , _ ⟫ (node key₃ value₃ t₄ t₆) _)) key value (t-left .kp .kg x x₁ x₂ (t-right .kp .key₁ x₃ x₄ x₅ ti)) (rbr-rotate-lr .(node key₂ value₂ t₃ t₅) .(node key₃ value₃ t₄ t₆) kg kp kn lt1 lt2 trb) = t-node _ _ _ ? ? ? ? ? ? ? ? --- rr00 : (kp < kn) ∧ tr> kp t₃ ∧ tr> kp t₄ --- rr00 = RB-repl→ti> _ _ _ _ _ trb lt1 ⟪ x₃ , ⟪ x₄ , x₅ ⟫ ⟫ + rr02 = proj2 (proj2 rr01) + rr03 : (kn < key₂) ∧ tr> kn t₄ ∧ tr> kn t₅ + rr03 with RB-repl→ti _ _ _ _ ti trb + ... | t-right .kn .key₂ x x₁ x₂ t = ⟪ x , ⟪ x₁ , x₂ ⟫ ⟫ +RB-repl→ti (node kg ⟪ Black , v1 ⟫ (node kp ⟪ Red , v2 ⟫ .leaf (node key₁ value₁ t₁ t₂)) .leaf) (node kn ⟪ Black , value₃ ⟫ (node kp ⟪ Red , _ ⟫ _ (node key₂ value₂ t₃ t₅)) (node kg ⟪ Red , _ ⟫ leaf _)) key value (t-left .kp .kg x x₁ x₂ (t-right .kp .key₁ x₃ x₄ x₅ ti)) (rbr-rotate-lr .(node key₂ value₂ t₃ t₅) .leaf kg kp kn lt1 lt2 trb) with RB-repl→ti _ _ _ _ ti trb +... | t-left .key₂ .kn x₆ x₇ x₈ t = + t-node _ _ _ (proj1 rr00) (proj1 rr01) tt ⟪ x₆ , ⟪ x₇ , x₈ ⟫ ⟫ tt tt (t-right _ _ (proj1 rr02) (proj1 (proj2 rr02)) (proj2 (proj2 rr02)) t) (t-single _ _) where + rr00 : (kp < kn) ∧ ((kp < key₂) ∧ tr> kp t₃ ∧ tr> kp t₅) ∧ ⊤ + rr00 = RB-repl→ti> _ _ _ _ _ trb lt1 ⟪ x₃ , ⟪ x₄ , x₅ ⟫ ⟫ + rr02 = proj1 (proj2 rr00) + rr01 : (kn < kg) ∧ ((key₂ < kg) ∧ tr< kg t₃ ∧ tr< kg t₅) ∧ ⊤ + rr01 = RB-repl→ti< _ _ _ _ _ trb lt2 x₂ +RB-repl→ti (node kg ⟪ Black , v1 ⟫ (node kp ⟪ Red , v2 ⟫ .leaf (node key₁ value₁ t₁ t₂)) .leaf) (node kn ⟪ Black , value₄ ⟫ (node kp ⟪ Red , _ ⟫ _ (node key₂ value₂ t₃ t₅)) (node kg ⟪ Red , _ ⟫ (node key₃ value₃ t₄ t₆) _)) key value (t-left .kp .kg x x₁ x₂ (t-right .kp .key₁ x₃ x₄ x₅ ti)) (rbr-rotate-lr .(node key₂ value₂ t₃ t₅) .(node key₃ value₃ t₄ t₆) kg kp kn lt1 lt2 trb) with RB-repl→ti _ _ _ _ ti trb +... | t-node .key₂ .kn .key₃ x₆ x₇ x₈ x₉ x₁₀ x₁₁ t t₇ = t-node _ _ _ ? ? ? ? ? ? (t-right _ _ ? ? ? t) (RB-repl→ti _ _ _ _ t₇ trb) where + rr00 : ? + rr00 = RB-repl→ti> _ _ _ _ _ trb lt1 ⟪ x₃ , ⟪ x₄ , x₅ ⟫ ⟫ + rr01 : ? + rr01 = RB-repl→ti< _ _ _ _ _ trb lt2 x₂ RB-repl→ti (node kg ⟪ Black , v1 ⟫ (node kp ⟪ Red , v2 ⟫ .(node key₂ _ _ _) (node key₁ value₁ t₁ t₂)) .leaf) (node kn ⟪ Black , _ ⟫ (node kp ⟪ Red , _ ⟫ _ t₃) (node kg ⟪ Red , _ ⟫ t₄ _)) key value (t-left .kp .kg x x₁ x₂ (t-node key₂ .kp .key₁ x₃ x₄ x₅ x₆ x₇ x₈ ti ti₁)) (rbr-rotate-lr t₃ t₄ kg kp kn lt1 lt2 trb) = t-node _ _ _ ? ? ? ? ? ? ? ? RB-repl→ti (node kg ⟪ Black , v1 ⟫ (node kp ⟪ Red , v2 ⟫ t leaf) .(node key₂ _ _ _)) (node kn ⟪ Black , _ ⟫ (node kp ⟪ Red , _ ⟫ _ t₃) (node kg ⟪ Red , _ ⟫ t₄ _)) key value (t-node .kp .kg key₂ x x₁ x₂ x₃ x₄ x₅ ti ti₁) (rbr-rotate-lr t₃ t₄ kg kp kn lt1 lt2 trb) = ? RB-repl→ti (node kg ⟪ Black , v1 ⟫ (node kp ⟪ Red , v2 ⟫ t (node key₁ value₁ t₁ t₂)) .(node key₂ _ _ _)) (node kn ⟪ Black , _ ⟫ (node kp ⟪ Red , _ ⟫ _ t₃) (node kg ⟪ Red , _ ⟫ t₄ _)) key value (t-node .kp .kg key₂ x x₁ x₂ x₃ x₄ x₅ ti ti₁) (rbr-rotate-lr t₃ t₄ kg kp kn lt1 lt2 trb) = ?