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annotate hoareRedBlackTree.agda @ 583:d18df2e6135d

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add replaceNode
author Shinji KONO <kono@ie.u-ryukyu.ac.jp>
date Sun, 03 Nov 2019 08:53:00 +0900
parents 1a5dd71199f1
children 7e551cef35d7
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1 module hoareRedBlackTree where
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2
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3
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4 open import Level hiding (zero)
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5
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6 open import Data.Nat hiding (compare)
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7 open import Data.Nat.Properties as NatProp
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8 open import Data.Maybe
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9 -- open import Data.Bool
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10 open import Data.Empty
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11 open import Data.List
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12
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13 open import Relation.Binary
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14 open import Relation.Binary.PropositionalEquality
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15 open import logic
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16
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17
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18 record TreeMethods {n m : Level } {a : Set n } {t : Set m } (treeImpl : Set n ) : Set (m Level.⊔ n) where
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19 field
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20 putImpl : treeImpl → a → (treeImpl → t) → t
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21 getImpl : treeImpl → (treeImpl → Maybe a → t) → t
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22 open TreeMethods
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23
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24 record Tree {n m : Level } {a : Set n } {t : Set m } (treeImpl : Set n ) : Set (m Level.⊔ n) where
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25 field
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26 tree : treeImpl
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27 treeMethods : TreeMethods {n} {m} {a} {t} treeImpl
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28 putTree : a → (Tree treeImpl → t) → t
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29 putTree d next = putImpl (treeMethods ) tree d (\t1 → next (record {tree = t1 ; treeMethods = treeMethods} ))
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30 getTree : (Tree treeImpl → Maybe a → t) → t
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31 getTree next = getImpl (treeMethods ) tree (\t1 d → next (record {tree = t1 ; treeMethods = treeMethods} ) d )
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32
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33 open Tree
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34
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35 SingleLinkedStack = List
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36
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37 emptySingleLinkedStack : {n : Level } {Data : Set n} -> SingleLinkedStack Data
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38 emptySingleLinkedStack = []
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39
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40 pushSingleLinkedStack : {n m : Level } {t : Set m } {Data : Set n} -> List Data -> Data -> (Code : SingleLinkedStack Data -> t) -> t
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41 pushSingleLinkedStack stack datum next = next ( datum ∷ stack )
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42
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43 popSingleLinkedStack : {n m : Level } {t : Set m } {a : Set n} -> SingleLinkedStack a -> (Code : SingleLinkedStack a -> (Maybe a) -> t) -> t
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44 popSingleLinkedStack [] cs = cs [] nothing
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45 popSingleLinkedStack (data1 ∷ s) cs = cs s (just data1)
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46
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47 data Color {n : Level } : Set n where
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48 Red : Color
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49 Black : Color
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50
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51 record Node {n : Level } (a : Set n) : Set n where
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52 inductive
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53 field
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54 key : ℕ
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55 value : a
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56 right : Maybe (Node a )
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57 left : Maybe (Node a )
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58 color : Color {n}
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59 open Node
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60
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61 record RedBlackTree {n : Level } (a : Set n) : Set n where
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62 field
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63 root : Maybe (Node a )
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64 nodeStack : SingleLinkedStack (Node a )
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65 -- compare : k → k → Tri A B C
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66 -- <-cmp
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67
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68 open RedBlackTree
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69
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70
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71 ----
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72 -- find node potition to insert or to delete, the path will be in the stack
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73 --
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74
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75 {-# TERMINATING #-}
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76 findNode : {n m : Level } {a : Set n} {t : Set m} → RedBlackTree {n} a → (Node a ) → (RedBlackTree {n} a → t) → t
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77 findNode {n} {m} {a} {t} tree n0 next with root tree
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78 findNode {n} {m} {a} {t} tree n0 next | nothing = next tree
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79 findNode {n} {m} {a} {t} tree n0 next | just x with <-cmp (key x) (key n0)
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80 findNode {n} {m} {a} {t} tree n0 next | just x | tri≈ ¬a b ¬c = next tree
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81 findNode {n} {m} {a} {t} tree n0 next | just x | tri< a₁ ¬b ¬c = pushSingleLinkedStack (nodeStack tree) x (λ s → findNode (record {root = (left x) ; nodeStack = s}) n0 next)
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82 findNode {n} {m} {a} {t} tree n0 next | just x | tri> ¬a ¬b c = pushSingleLinkedStack (nodeStack tree) x (λ s → findNode (record {root = (right x) ; nodeStack = s}) n0 next)
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84
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85 findNode1 : {n m : Level } {a : Set n} {t : Set m} → RedBlackTree {n} a → (Node a ) → (RedBlackTree {n} a → t) → t
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86 findNode1 {n} {m} {a} {t} tree n0 next = findNode2 (root tree) (nodeStack tree)
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87 module FindNode where
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88 findNode2 : (Maybe (Node a )) → SingleLinkedStack (Node a ) → t
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89 findNode2 nothing st = next record { root = nothing ; nodeStack = st }
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90 findNode2 (just x) st with <-cmp (key n0) (key x)
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91 ... | tri≈ ¬a b ¬c = next (record {root = just x ; nodeStack = st })
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92 ... | tri< a ¬b ¬c = pushSingleLinkedStack st x (λ s1 → findNode2 (right x) s1)
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93 ... | tri> ¬a ¬b c = pushSingleLinkedStack st x (λ s1 → findNode2 (left x) s1)
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94
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95 node001 : Node ℕ
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96 node001 = record { key = 2 ; value = 3 ; left = nothing ; right = nothing ; color = Black }
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97 node002 : Node ℕ
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98 node002 = record { key = 1 ; value = 3 ; left = just node001 ; right = nothing ; color = Black }
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99 node003 : Node ℕ
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100 node003 = record { key = 0 ; value = 3 ; left = just node002 ; right = nothing ; color = Black }
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101
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102 test001 = findNode1 {Level.zero} {Level.zero} {ℕ} {RedBlackTree ℕ} ( record { root = nothing ; nodeStack = emptySingleLinkedStack } )
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103 node001 ( λ tree → tree )
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104 test002 = findNode1 {Level.zero} {Level.zero} {ℕ} {RedBlackTree ℕ} ( record { root = just node001 ; nodeStack = emptySingleLinkedStack } )
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105 node001 ( λ tree → tree )
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106 test003 = findNode1 {Level.zero} {Level.zero} {ℕ} {RedBlackTree ℕ} ( record { root = just node003 ; nodeStack = emptySingleLinkedStack } )
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107 node001 ( λ tree → tree )
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108 test004 = findNode {Level.zero} {Level.zero} {ℕ} {RedBlackTree ℕ} ( record { root = just node003 ; nodeStack = emptySingleLinkedStack } )
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109 node001 ( λ tree → tree )
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110
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111 replaceNode : {n m : Level } {a : Set n} {t : Set m} → RedBlackTree {n} a → (Node a ) → (RedBlackTree {n} a → t) → t
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112 replaceNode {n} {m} {a} {t} tree n0 next = replaceNode2 (nodeStack tree) (λ newNode → next record { root = just newNode ; nodeStack = emptySingleLinkedStack } )
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113 module FindNodeR where
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114 replaceNode1 : (Maybe (Node a )) → Node a
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115 replaceNode1 nothing = record n0 { left = nothing ; right = nothing }
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116 replaceNode1 (just x) = record n0 { left = left x ; right = right x }
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117 replaceNode2 : SingleLinkedStack (Node a ) → (Node a → t) → t
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118 replaceNode2 [] next = next ( replaceNode1 (root tree) )
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119 replaceNode2 (x ∷ st) next with <-cmp (key x) (key n0)
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120 replaceNode2 (x ∷ st) next | tri< a ¬b ¬c = replaceNode2 st ( λ new → next ( record x { left = left new } ) )
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121 replaceNode2 (x ∷ st) next | tri≈ ¬a b ¬c = replaceNode2 st ( λ new → next ( record x { left = left new ; right = right new } ) )
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122 replaceNode2 (x ∷ st) next | tri> ¬a ¬b c = replaceNode2 st ( λ new → next ( record x { right = right new } ) )
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123
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124 insertNode : {n m : Level } {a : Set n} {t : Set m} → RedBlackTree {n} a → (Node a ) → (RedBlackTree {n} a → t) → t
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125 insertNode tree n0 next = findNode1 tree n0 ( λ new → replaceNode tree n0 next )
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126
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127 createEmptyRedBlackTreeℕ : {n m : Level} {t : Set m} (a : Set n) (b : ℕ)
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128 → RedBlackTree {n} a
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129 createEmptyRedBlackTreeℕ a b = record {
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130 root = nothing
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131 ; nodeStack = emptySingleLinkedStack
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132 }
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133
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134 findNodeLeft : {n : Level } {a : Set n} (r : Node a ) (t : SingleLinkedStack (Node a)) → Set n
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135 findNodeLeft x [] = (left x ≡ nothing ) ∧ (right x ≡ nothing )
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136 findNodeLeft {n} x (h ∷ t) = Lift n ((key x) < (key h))
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137 findNodeRight : {n : Level } {a : Set n} (r : Node a ) (t : SingleLinkedStack (Node a)) → Set n
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138 findNodeRight x [] = (left x ≡ nothing ) ∧ (right x ≡ nothing )
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139 findNodeRight {n} x (h ∷ t) = Lift n ((key x) > (key h))
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140
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141 data FindNodeInvariant {n : Level } {a : Set n} : (t : SingleLinkedStack (Node a)) (original : RedBlackTree {n} a ) → Set n where
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142 fni-Top : (now : RedBlackTree {n} a ) → FindNodeInvariant [] now
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143 fni-Left : (x : Node a) (t : SingleLinkedStack (Node a)) (original : RedBlackTree {n} a )
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144 → FindNodeInvariant ( x ∷ t ) original → findNodeLeft x t → FindNodeInvariant t original
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145 fni-Right : (x : Node a) (t : SingleLinkedStack (Node a)) (original : RedBlackTree {n} a )
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents: 580
diff changeset
146 → FindNodeInvariant ( x ∷ t ) original → findNodeRight x t → FindNodeInvariant t original
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents: 580
diff changeset
147
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents: 580
diff changeset
148
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents: 580
diff changeset
149 findNode1h : {n m : Level } {a : Set n} {t : Set m} → (tree : RedBlackTree {n} a ) → (Node a )
582
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents: 581
diff changeset
150 → ((new : RedBlackTree {n} a) → FindNodeInvariant (nodeStack new) tree → t )
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents: 581
diff changeset
151 → ( FindNodeInvariant (nodeStack tree) tree) → t
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents: 581
diff changeset
152 findNode1h {n} {m} {a} {t} tree n0 next prev = findNode2h (root tree) (nodeStack tree) prev
581
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents: 580
diff changeset
153 module FindNodeH where
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents: 580
diff changeset
154 findNode2h : (Maybe (Node a )) → (s : SingleLinkedStack (Node a )) → FindNodeInvariant s tree → t
582
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents: 581
diff changeset
155 findNode2h nothing st prev = next record { root = nothing ; nodeStack = st } {!!}
581
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents: 580
diff changeset
156 findNode2h (just x) st prev with <-cmp (key n0) (key x)
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents: 580
diff changeset
157 ... | tri≈ ¬a b ¬c = next (record {root = just x ; nodeStack = st }) {!!} -- ( fni-Last ? )
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents: 580
diff changeset
158 ... | tri< a ¬b ¬c = pushSingleLinkedStack st x (λ s1 → findNode2h (right x) s1 (fni-Left x s1 tree {!!} {!!}) )
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents: 580
diff changeset
159 ... | tri> ¬a ¬b c = pushSingleLinkedStack st x (λ s1 → findNode2h (left x) s1 (fni-Right x s1 tree {!!} {!!}) )
578
7bacba816277 use list base simple stack
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents: 577
diff changeset
160
7bacba816277 use list base simple stack
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents: 577
diff changeset
161
583
d18df2e6135d add replaceNode
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents: 582
diff changeset
162 replaceNodeH : {n m : Level } {a : Set n} {t : Set m} → RedBlackTree {n} a → (Node a ) → (RedBlackTree {n} a → {!!} → t) → {!!} → t
d18df2e6135d add replaceNode
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents: 582
diff changeset
163 replaceNodeH = {!!}
578
7bacba816277 use list base simple stack
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents: 577
diff changeset
164