Members/Moririn: hoareBinaryTree.agda annotate

annotate hoareBinaryTree.agda @ 593:063274f64a77

bt-replace-hoare

author	kono
date	Sat, 07 Dec 2019 08:50:54 +0900
parents	7fb57243a8c9
children	4bbeb8d9e250

rev	line source
586 0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	1 module hoareBinaryTree where
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	2
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	3 open import Level renaming (zero to Z ; suc to succ)
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	4
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	5 open import Data.Nat hiding (compare)
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	6 open import Data.Nat.Properties as NatProp
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	7 open import Data.Maybe
588 8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	8 -- open import Data.Maybe.Properties
586 0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	9 open import Data.Empty
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	10 open import Data.List
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	11 open import Data.Product
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	12
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	13 open import Function as F hiding (const)
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	14
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	15 open import Relation.Binary
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	16 open import Relation.Binary.PropositionalEquality
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	17 open import Relation.Nullary
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	18 open import logic
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	19
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	20
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	21 SingleLinkedStack = List
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	22
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	23 emptySingleLinkedStack : {n : Level } {Data : Set n} -> SingleLinkedStack Data
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	24 emptySingleLinkedStack = []
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	25
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	26 clearSingleLinkedStack : {n m : Level } {Data : Set n} {t : Set m} -> SingleLinkedStack Data → ( SingleLinkedStack Data → t) → t
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	27 clearSingleLinkedStack [] cg = cg []
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	28 clearSingleLinkedStack (x ∷ as) cg = cg []
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	29
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	30 pushSingleLinkedStack : {n m : Level } {t : Set m } {Data : Set n} -> List Data -> Data -> (Code : SingleLinkedStack Data -> t) -> t
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	31 pushSingleLinkedStack stack datum next = next ( datum ∷ stack )
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	32
587 f103f07c0552 add insert code ryokka parents: 586 diff changeset	33
586 0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	34 popSingleLinkedStack : {n m : Level } {t : Set m } {a : Set n} -> SingleLinkedStack a -> (Code : SingleLinkedStack a -> (Maybe a) -> t) -> t
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	35 popSingleLinkedStack [] cs = cs [] nothing
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	36 popSingleLinkedStack (data1 ∷ s) cs = cs s (just data1)
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	37
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	38
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	39
587 f103f07c0552 add insert code ryokka parents: 586 diff changeset	40 emptySigmaStack : {n : Level } { Data : Set n} → List Data
f103f07c0552 add insert code ryokka parents: 586 diff changeset	41 emptySigmaStack = []
f103f07c0552 add insert code ryokka parents: 586 diff changeset	42
f103f07c0552 add insert code ryokka parents: 586 diff changeset	43 pushSigmaStack : {n m : Level} {d d2 : Set n} {t : Set m} → d2 → List d → (List (d × d2) → t) → t
f103f07c0552 add insert code ryokka parents: 586 diff changeset	44 pushSigmaStack {n} {m} {d} d2 st next = next (Data.List.zip (st) (d2 ∷ []) )
f103f07c0552 add insert code ryokka parents: 586 diff changeset	45
f103f07c0552 add insert code ryokka parents: 586 diff changeset	46 tt = pushSigmaStack 3 (true ∷ []) (λ st → st)
f103f07c0552 add insert code ryokka parents: 586 diff changeset	47
588 8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	48 _iso_ : {n : Level} {a : Set n} → ℕ → ℕ → Set
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	49 d iso d' = (¬ (suc d ≤ d')) ∧ (¬ (suc d' ≤ d))
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	50
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	51 iso-intro : {n : Level} {a : Set n} {x y : ℕ} → ¬ (suc x ≤ y) → ¬ (suc y ≤ x) → _iso_ {n} {a} x y
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	52 iso-intro = λ z z₁ → record { proj1 = z ; proj2 = z₁ }
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	53
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	54
587 f103f07c0552 add insert code ryokka parents: 586 diff changeset	55 {--
f103f07c0552 add insert code ryokka parents: 586 diff changeset	56 data A B : C → D → Set where の A B と C → D の差は？
f103f07c0552 add insert code ryokka parents: 586 diff changeset	57
f103f07c0552 add insert code ryokka parents: 586 diff changeset	58 --}
588 8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	59
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	60 data bt {n : Level} {a : Set n} : Set n where -- (a : Setn)
587 f103f07c0552 add insert code ryokka parents: 586 diff changeset	61 bt-leaf : ⦃ l u : ℕ ⦄ → l ≤ u → bt
586 0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	62 bt-node : ⦃ l l' u u' : ℕ ⦄ → (d : ℕ) →
587 f103f07c0552 add insert code ryokka parents: 586 diff changeset	63 bt {n} {a} → bt {n} {a} → l ≤ l' → u' ≤ u → bt
586 0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	64
590 7c424dd0945d ... Shinji KONO <kono@ie.u-ryukyu.ac.jp> parents: 589 diff changeset	65 --
7c424dd0945d ... Shinji KONO <kono@ie.u-ryukyu.ac.jp> parents: 589 diff changeset	66 --
7c424dd0945d ... Shinji KONO <kono@ie.u-ryukyu.ac.jp> parents: 589 diff changeset	67 -- no children , having left node , having right node , having both
7c424dd0945d ... Shinji KONO <kono@ie.u-ryukyu.ac.jp> parents: 589 diff changeset	68 --
588 8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	69 data bt' {n : Level} (A : Set n) : (key : ℕ) → Set n where -- (a : Setn)
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	70 bt'-leaf : (key : ℕ) → bt' A key
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	71 bt'-node : { l r : ℕ } → (key : ℕ) → (value : A) →
591 8ab2e2f9469f use <= Shinji KONO <kono@ie.u-ryukyu.ac.jp> parents: 590 diff changeset	72 bt' {n} A l → bt' {n} A r → l ≤ key → key ≤ r → bt' A key
588 8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	73
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	74 data bt'-path {n : Level} (A : Set n) : Set n where -- (a : Setn)
592 7fb57243a8c9 fix ryokka parents: 591 diff changeset	75 bt'-left : (key : ℕ) → {left-key : ℕ} → (bt' A left-key ) → (key ≤ left-key) → bt'-path A
591 8ab2e2f9469f use <= Shinji KONO <kono@ie.u-ryukyu.ac.jp> parents: 590 diff changeset	76 bt'-right : (key : ℕ) → {right-key : ℕ} → (bt' A right-key ) → (right-key ≤ key) → bt'-path A
588 8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	77
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	78
593 063274f64a77 bt-replace-hoare kono parents: 592 diff changeset	79 test = bt'-left {Z} {ℕ} 3 {5} (bt'-leaf 5) (s≤s (s≤s (s≤s z≤n)))
588 8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	80
589 37f5826ca7d2 minor fix Shinji KONO <kono@ie.u-ryukyu.ac.jp> parents: 588 diff changeset	81 bt-find' : {n m : Level} {A : Set n} {t : Set m} {tn : ℕ} → (key : ℕ) → (tree : bt' A tn ) → List (bt'-path A )
37f5826ca7d2 minor fix Shinji KONO <kono@ie.u-ryukyu.ac.jp> parents: 588 diff changeset	82 → ( {key1 : ℕ } → bt' A key1 → List (bt'-path A ) → t ) → t
37f5826ca7d2 minor fix Shinji KONO <kono@ie.u-ryukyu.ac.jp> parents: 588 diff changeset	83 bt-find' key tr@(bt'-leaf key₁) stack next = next tr stack -- no key found
588 8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	84 bt-find' key (bt'-node key₁ value tree tree₁ x x₁) stack next with <-cmp key key₁
589 37f5826ca7d2 minor fix Shinji KONO <kono@ie.u-ryukyu.ac.jp> parents: 588 diff changeset	85 bt-find' key tr@(bt'-node {l} {r} key₁ value tree tree₁ x x₁) stack next \| tri< a ¬b ¬c =
592 7fb57243a8c9 fix ryokka parents: 591 diff changeset	86 bt-find' key tree ( (bt'-left key {key₁} tr (<⇒≤ a) ) ∷ stack) next
589 37f5826ca7d2 minor fix Shinji KONO <kono@ie.u-ryukyu.ac.jp> parents: 588 diff changeset	87 bt-find' key found@(bt'-node key₁ value tree tree₁ x x₁) stack next \| tri≈ ¬a b ¬c = next found stack
37f5826ca7d2 minor fix Shinji KONO <kono@ie.u-ryukyu.ac.jp> parents: 588 diff changeset	88 bt-find' key tr@(bt'-node key₁ value tree tree₁ x x₁) stack next \| tri> ¬a ¬b c =
592 7fb57243a8c9 fix ryokka parents: 591 diff changeset	89 bt-find' key tree ( (bt'-right key {key₁} tr (<⇒≤ c) ) ∷ stack) next
588 8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	90
590 7c424dd0945d ... Shinji KONO <kono@ie.u-ryukyu.ac.jp> parents: 589 diff changeset	91 a<sa : { a : ℕ } → a < suc a
7c424dd0945d ... Shinji KONO <kono@ie.u-ryukyu.ac.jp> parents: 589 diff changeset	92 a<sa {zero} = s≤s z≤n
7c424dd0945d ... Shinji KONO <kono@ie.u-ryukyu.ac.jp> parents: 589 diff changeset	93 a<sa {suc a} = s≤s a<sa
588 8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	94
592 7fb57243a8c9 fix ryokka parents: 591 diff changeset	95 a≤sa : { a : ℕ } → a ≤ suc a
7fb57243a8c9 fix ryokka parents: 591 diff changeset	96 a≤sa {zero} = z≤n
7fb57243a8c9 fix ryokka parents: 591 diff changeset	97 a≤sa {suc a} = s≤s a≤sa
7fb57243a8c9 fix ryokka parents: 591 diff changeset	98
590 7c424dd0945d ... Shinji KONO <kono@ie.u-ryukyu.ac.jp> parents: 589 diff changeset	99 pa<a : { a : ℕ } → pred (suc a) < suc a
7c424dd0945d ... Shinji KONO <kono@ie.u-ryukyu.ac.jp> parents: 589 diff changeset	100 pa<a {zero} = s≤s z≤n
7c424dd0945d ... Shinji KONO <kono@ie.u-ryukyu.ac.jp> parents: 589 diff changeset	101 pa<a {suc a} = s≤s pa<a
7c424dd0945d ... Shinji KONO <kono@ie.u-ryukyu.ac.jp> parents: 589 diff changeset	102
7c424dd0945d ... Shinji KONO <kono@ie.u-ryukyu.ac.jp> parents: 589 diff changeset	103 bt-replace' : {n m : Level} {A : Set n} {t : Set m} {tn : ℕ} → (key : ℕ) → (value : A ) → (tree : bt' A tn ) → List (bt'-path A )
7c424dd0945d ... Shinji KONO <kono@ie.u-ryukyu.ac.jp> parents: 589 diff changeset	104 → ( {key1 : ℕ } → bt' A key1 → t ) → t
7c424dd0945d ... Shinji KONO <kono@ie.u-ryukyu.ac.jp> parents: 589 diff changeset	105 bt-replace' {n} {m} {A} {t} {tn} key value node stack next = bt-replace1 tn node where
7c424dd0945d ... Shinji KONO <kono@ie.u-ryukyu.ac.jp> parents: 589 diff changeset	106 bt-replace0 : {tn : ℕ } (node : bt' A tn ) → List (bt'-path A ) → t
7c424dd0945d ... Shinji KONO <kono@ie.u-ryukyu.ac.jp> parents: 589 diff changeset	107 bt-replace0 node [] = next node
592 7fb57243a8c9 fix ryokka parents: 591 diff changeset	108 bt-replace0 node (bt'-left key (bt'-leaf key₁) x₁ ∷ stack) = {!!}
7fb57243a8c9 fix ryokka parents: 591 diff changeset	109 bt-replace0 {tn} node (bt'-left key (bt'-node key₁ value x x₂ x₃ x₄) x₁ ∷ stack) = bt-replace0 {key₁} (bt'-node key₁ value node x₂ {!!} x₄ ) stack
590 7c424dd0945d ... Shinji KONO <kono@ie.u-ryukyu.ac.jp> parents: 589 diff changeset	110 bt-replace0 node (bt'-right key x x₁ ∷ stack) = {!!}
7c424dd0945d ... Shinji KONO <kono@ie.u-ryukyu.ac.jp> parents: 589 diff changeset	111 bt-replace1 : (tn : ℕ ) (tree : bt' A tn ) → t
591 8ab2e2f9469f use <= Shinji KONO <kono@ie.u-ryukyu.ac.jp> parents: 590 diff changeset	112 bt-replace1 tn (bt'-leaf key0) = bt-replace0 (bt'-node tn value
592 7fb57243a8c9 fix ryokka parents: 591 diff changeset	113 (bt'-leaf (pred tn)) (bt'-leaf (suc tn) ) (≤⇒pred≤ ≤-refl) a≤sa) stack
590 7c424dd0945d ... Shinji KONO <kono@ie.u-ryukyu.ac.jp> parents: 589 diff changeset	114 bt-replace1 tn (bt'-node key value node node₁ x x₁) = bt-replace0 (bt'-node key value node node₁ x x₁) stack
588 8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	115
593 063274f64a77 bt-replace-hoare kono parents: 592 diff changeset	116 tree->key : {n : Level} {tn : ℕ} → (A : Set n) → (tree : bt' A tn ) → ℕ
063274f64a77 bt-replace-hoare kono parents: 592 diff changeset	117 tree->key {n} {.key} (A) (bt'-leaf key) = key
063274f64a77 bt-replace-hoare kono parents: 592 diff changeset	118 tree->key {n} {.key} (A) (bt'-node key value tree tree₁ x x₁) = key
063274f64a77 bt-replace-hoare kono parents: 592 diff changeset	119
063274f64a77 bt-replace-hoare kono parents: 592 diff changeset	120
063274f64a77 bt-replace-hoare kono parents: 592 diff changeset	121 bt-find'-assert1 : {n m : Level} {A : Set n} {t : Set m} {tn : ℕ} → (tree : bt' A tn ) → Set n
063274f64a77 bt-replace-hoare kono parents: 592 diff changeset	122 bt-find'-assert1 {n} {m} {A} {t} {tn} tree = (key : ℕ) → (val : A) → bt-find' key tree [] (λ tree1 stack → key ≡ (tree->key A tree1))
063274f64a77 bt-replace-hoare kono parents: 592 diff changeset	123
063274f64a77 bt-replace-hoare kono parents: 592 diff changeset	124
063274f64a77 bt-replace-hoare kono parents: 592 diff changeset	125 bt-replace-hoare : {n m : Level} {A : Set n} {t : Set m} {tn : ℕ} → (key : ℕ) → (value : A ) → (tree : bt' A tn )
063274f64a77 bt-replace-hoare kono parents: 592 diff changeset	126 → (pre : bt-find'-assert1 {n} {m} {A} {t} tree → bt-replace' {!!} {!!} {!!} {!!} {!!}) → t
063274f64a77 bt-replace-hoare kono parents: 592 diff changeset	127 bt-replace-hoare key value tree stack = {!!}
063274f64a77 bt-replace-hoare kono parents: 592 diff changeset	128
588 8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	129
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	130
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	131 -- find'-support : {n m : Level} {a : Set n} {t : Set m} ⦃ l u : ℕ ⦄ → (d : ℕ) → (tree : bt' {n} {a} ) → SingleLinkedStack (bt' {n} {a} ) → ( (bt' {n} {a} ) → SingleLinkedStack (bt' {n} {a} ) → Maybe (Σ ℕ (λ d' → _iso_ {n} {a} d d')) → t ) → t
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	132
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	133 -- find'-support {n} {m} {a} {t} ⦃ l ⦄ ⦃ u ⦄ key leaf@(bt'-leaf x) st cg = cg leaf st nothing
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	134 -- find'-support {n} {m} {a} {t} ⦃ l ⦄ ⦃ u ⦄ key (bt'-node d tree₁ tree₂ x x₁) st cg with <-cmp key d
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	135 -- find'-support {n} {m} {a} {t} ⦃ l ⦄ ⦃ u ⦄ key node@(bt'-node d tree₁ tree₂ x x₁) st cg \| tri≈ ¬a b ¬c = cg node st (just (d , iso-intro {n} {a} ¬a ¬c))
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	136
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	137 -- find'-support {n} {m} {a} {t} key node@(bt'-node ⦃ nl ⦄ ⦃ l' ⦄ ⦃ nu ⦄ ⦃ u' ⦄ d L R x x₁) st cg \| tri< a₁ ¬b ¬c =
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	138 -- pushSingleLinkedStack st node
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	139 -- (λ st2 → find'-support {n} {m} {a} {t} {{l'}} {{d}} key L st2 cg)
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	140
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	141 -- find'-support {n} {m} {a} {t} ⦃ l ⦄ ⦃ u ⦄ key node@(bt'-node ⦃ ll ⦄ ⦃ ll' ⦄ ⦃ lr ⦄ ⦃ lr' ⦄ d L R x x₁) st cg \| tri> ¬a ¬b c = pushSingleLinkedStack st node
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	142 -- (λ st2 → find'-support {n} {m} {a} {t} {{d}} {{lr'}} key R st2 cg)
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	143
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	144
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	145
587 f103f07c0552 add insert code ryokka parents: 586 diff changeset	146 lleaf : {n : Level} {a : Set n} → bt {n} {a}
586 0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	147 lleaf = (bt-leaf ⦃ 0 ⦄ ⦃ 3 ⦄ z≤n)
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	148
588 8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	149 lleaf1 : {n : Level} {A : Set n} → (0 < 3) → (a : A) → (d : ℕ ) → bt' {n} A d
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	150 lleaf1 0<3 a d = bt'-leaf d
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	151
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	152 test-node1 : bt' ℕ 3
591 8ab2e2f9469f use <= Shinji KONO <kono@ie.u-ryukyu.ac.jp> parents: 590 diff changeset	153 test-node1 = bt'-node (3) 3 (bt'-leaf 2) (bt'-leaf 4) (s≤s (s≤s {!!})) (s≤s (s≤s (s≤s {!!})))
588 8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	154
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	155
587 f103f07c0552 add insert code ryokka parents: 586 diff changeset	156 rleaf : {n : Level} {a : Set n} → bt {n} {a}
588 8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	157 rleaf = (bt-leaf ⦃ 3 ⦄ ⦃ 3 ⦄ (s≤s (s≤s (s≤s z≤n))))
586 0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	158
587 f103f07c0552 add insert code ryokka parents: 586 diff changeset	159 test-node : {n : Level} {a : Set n} → bt {n} {a}
586 0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	160 test-node {n} {a} = (bt-node ⦃ 0 ⦄ ⦃ 0 ⦄ ⦃ 4 ⦄ ⦃ 4 ⦄ 3 lleaf rleaf z≤n ≤-refl )
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	161
587 f103f07c0552 add insert code ryokka parents: 586 diff changeset	162 -- stt : {n m : Level} {a : Set n} {t : Set m} → {!!}
f103f07c0552 add insert code ryokka parents: 586 diff changeset	163 -- stt {n} {m} {a} {t} = pushSingleLinkedStack [] (test-node ) (λ st → pushSingleLinkedStack st lleaf (λ st2 → st2) )
f103f07c0552 add insert code ryokka parents: 586 diff changeset	164
586 0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	165
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	166
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	167 -- search の {{ l }} {{ u }} はその時みている node の大小。 l が小さく u が大きい
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	168 -- ここでは d が現在の node のkey値なので比較後のsearch では値が変わる
587 f103f07c0552 add insert code ryokka parents: 586 diff changeset	169 bt-search : {n m : Level} {a : Set n} {t : Set m} ⦃ l u : ℕ ⦄ → (d : ℕ) → bt {n} {a} → (Maybe (Σ ℕ (λ d' → _iso_ {n} {a} d d')) → t ) → t
586 0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	170 bt-search {n} {m} {a} {t} key (bt-leaf x) cg = cg nothing
587 f103f07c0552 add insert code ryokka parents: 586 diff changeset	171 bt-search {n} {m} {a} {t} ⦃ l ⦄ ⦃ u ⦄ key (bt-node ⦃ ll ⦄ ⦃ l' ⦄ ⦃ uu ⦄ ⦃ u' ⦄ d L R x x₁) cg with <-cmp key d
f103f07c0552 add insert code ryokka parents: 586 diff changeset	172 bt-search {n} {m} {a} {t} ⦃ l ⦄ ⦃ u ⦄ key (bt-node ⦃ ll ⦄ ⦃ l' ⦄ ⦃ uu ⦄ ⦃ u' ⦄ d L R x x₁) cg \| tri< a₁ ¬b ¬c = bt-search ⦃ l' ⦄ ⦃ d ⦄ key L cg
f103f07c0552 add insert code ryokka parents: 586 diff changeset	173 bt-search {n} {m} {a} {t} ⦃ l ⦄ ⦃ u ⦄ key (bt-node ⦃ ll ⦄ ⦃ l' ⦄ ⦃ uu ⦄ ⦃ u' ⦄ d L R x x₁) cg \| tri≈ ¬a b ¬c = cg (just (d , iso-intro {n} {a} ¬a ¬c))
f103f07c0552 add insert code ryokka parents: 586 diff changeset	174 bt-search {n} {m} {a} {t} ⦃ l ⦄ ⦃ u ⦄ key (bt-node ⦃ ll ⦄ ⦃ l' ⦄ ⦃ uu ⦄ ⦃ u' ⦄ d L R x x₁) cg \| tri> ¬a ¬b c = bt-search ⦃ d ⦄ ⦃ u' ⦄ key R cg
f103f07c0552 add insert code ryokka parents: 586 diff changeset	175
f103f07c0552 add insert code ryokka parents: 586 diff changeset	176 -- bt-search {n} {m} {a} {t} ⦃ l ⦄ ⦃ u ⦄ key (bt-node ⦃ l ⦄ ⦃ l' ⦄ ⦃ u ⦄ ⦃ u' ⦄ d L R x x₁) cg \| tri< a₁ ¬b ¬c = ? -- bt-search ⦃ l' ⦄ ⦃ d ⦄ key L cg
f103f07c0552 add insert code ryokka parents: 586 diff changeset	177 -- bt-search {n} {m} {a} {t} ⦃ l ⦄ ⦃ u ⦄ key (bt-node d L R x x₁) cg \| tri≈ ¬a b ¬c = cg (just (d , iso-intro {n} {a} ¬a ¬c))
f103f07c0552 add insert code ryokka parents: 586 diff changeset	178 -- bt-search {n} {m} {a} {t} ⦃ l ⦄ ⦃ u ⦄ key (bt-node ⦃ l ⦄ ⦃ l' ⦄ ⦃ u ⦄ ⦃ u' ⦄ d L R x x₁) cg \| tri> ¬a ¬b c = bt-search ⦃ d ⦄ ⦃ u' ⦄ key R cg
586 0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	179
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	180
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	181 -- この辺の test を書くときは型を考えるのがやや面倒なので先に動作を書いてから型を ? から補間するとよさそう
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	182 bt-search-test : {n m : Level} {a : Set n} {t : Set m} ⦃ l u : ℕ ⦄ → (x : (x₁ : Maybe (Σ ℕ (λ z → ((x₂ : 4 ≤ z) → ⊥) ∧ ((x₂ : suc z ≤ 3) → ⊥)))) → t) → t
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	183 bt-search-test {n} {m} {a} {t} = bt-search {n} {m} {a} {t} ⦃ zero ⦄ ⦃ 4 ⦄ 3 test-node
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	184
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	185 bt-search-test-bad : {n m : Level} {a : Set n} {t : Set m} ⦃ l u : ℕ ⦄ → (x : (x₁ : Maybe (Σ ℕ (λ z → ((x₂ : 8 ≤ z) → ⊥) ∧ ((x₂ : suc z ≤ 7) → ⊥)))) → t) → t
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	186 bt-search-test-bad {n} {m} {a} {t} = bt-search {n} {m} {a} {t} ⦃ zero ⦄ ⦃ 4 ⦄ 7 test-node
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	187
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	188
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	189 -- up-some : {n m : Level} {a : Set n} {t : Set m} ⦃ l u : ℕ ⦄ {d : ℕ} → (Maybe (Σ ℕ (λ d' → _iso_ {n} {a} d d'))) → (Maybe ℕ)
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	190 -- up-some (just (fst , snd)) = just fst
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	191 -- up-some nothing = nothing
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	192
587 f103f07c0552 add insert code ryokka parents: 586 diff changeset	193 search-lem : {n m : Level} {a : Set n} {t : Set m} ⦃ l u : ℕ ⦄ → (key : ℕ) → (tree : bt {n} {a} ) → bt-search ⦃ l ⦄ ⦃ u ⦄ key tree (λ gdata → gdata ≡ gdata)
586 0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	194 search-lem {n} {m} {a} {t} key (bt-leaf x) = refl
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	195 search-lem {n} {m} {a} {t} key (bt-node d tree₁ tree₂ x x₁) with <-cmp key d
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	196 search-lem {n} {m} {a} {t} key (bt-node ⦃ ll ⦄ ⦃ ll' ⦄ ⦃ lr ⦄ ⦃ lr' ⦄ d tree₁ tree₂ x x₁) \| tri< lt ¬eq ¬gt = search-lem {n} {m} {a} {t} ⦃ ll' ⦄ ⦃ d ⦄ key tree₁
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	197 search-lem {n} {m} {a} {t} key (bt-node d tree₁ tree₂ x x₁) \| tri≈ ¬lt eq ¬gt = refl
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	198 search-lem {n} {m} {a} {t} key (bt-node ⦃ ll ⦄ ⦃ ll' ⦄ ⦃ lr ⦄ ⦃ lr' ⦄ d tree₁ tree₂ x x₁) \| tri> ¬lt ¬eq gt = search-lem {n} {m} {a} {t} ⦃ d ⦄ ⦃ lr' ⦄ key tree₂
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	199
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	200
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	201 -- bt-find
587 f103f07c0552 add insert code ryokka parents: 586 diff changeset	202 find-support : {n m : Level} {a : Set n} {t : Set m} ⦃ l u : ℕ ⦄ → (d : ℕ) → (tree : bt {n} {a} ) → SingleLinkedStack (bt {n} {a} ) → ( (bt {n} {a} ) → SingleLinkedStack (bt {n} {a} ) → Maybe (Σ ℕ (λ d' → _iso_ {n} {a} d d')) → t ) → t
586 0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	203
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	204 find-support {n} {m} {a} {t} ⦃ l ⦄ ⦃ u ⦄ key leaf@(bt-leaf x) st cg = cg leaf st nothing
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	205 find-support {n} {m} {a} {t} ⦃ l ⦄ ⦃ u ⦄ key (bt-node d tree₁ tree₂ x x₁) st cg with <-cmp key d
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	206 find-support {n} {m} {a} {t} ⦃ l ⦄ ⦃ u ⦄ key node@(bt-node d tree₁ tree₂ x x₁) st cg \| tri≈ ¬a b ¬c = cg node st (just (d , iso-intro {n} {a} ¬a ¬c))
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	207
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	208 find-support {n} {m} {a} {t} key node@(bt-node ⦃ nl ⦄ ⦃ l' ⦄ ⦃ nu ⦄ ⦃ u' ⦄ d L R x x₁) st cg \| tri< a₁ ¬b ¬c =
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	209 pushSingleLinkedStack st node
587 f103f07c0552 add insert code ryokka parents: 586 diff changeset	210 (λ st2 → find-support {n} {m} {a} {t} {{l'}} {{d}} key L st2 cg)
f103f07c0552 add insert code ryokka parents: 586 diff changeset	211
f103f07c0552 add insert code ryokka parents: 586 diff changeset	212 find-support {n} {m} {a} {t} ⦃ l ⦄ ⦃ u ⦄ key node@(bt-node ⦃ ll ⦄ ⦃ ll' ⦄ ⦃ lr ⦄ ⦃ lr' ⦄ d L R x x₁) st cg \| tri> ¬a ¬b c = pushSingleLinkedStack st node
f103f07c0552 add insert code ryokka parents: 586 diff changeset	213 (λ st2 → find-support {n} {m} {a} {t} {{d}} {{lr'}} key R st2 cg)
f103f07c0552 add insert code ryokka parents: 586 diff changeset	214
f103f07c0552 add insert code ryokka parents: 586 diff changeset	215 bt-find : {n m : Level} {a : Set n} {t : Set m} ⦃ l u : ℕ ⦄ → (d : ℕ) → (tree : bt {n} {a} ) → SingleLinkedStack (bt {n} {a} ) → ( (bt {n} {a} ) → SingleLinkedStack (bt {n} {a} ) → Maybe (Σ ℕ (λ d' → _iso_ {n} {a} d d')) → t ) → t
f103f07c0552 add insert code ryokka parents: 586 diff changeset	216 bt-find {n} {m} {a} {t} ⦃ l ⦄ ⦃ u ⦄ key tr st cg = clearSingleLinkedStack st
f103f07c0552 add insert code ryokka parents: 586 diff changeset	217 (λ cst → find-support ⦃ l ⦄ ⦃ u ⦄ key tr cst cg)
586 0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	218
587 f103f07c0552 add insert code ryokka parents: 586 diff changeset	219 find-test : {n m : Level} {a : Set n} {t : Set m} ⦃ l u : ℕ ⦄ → List bt -- ?
f103f07c0552 add insert code ryokka parents: 586 diff changeset	220 find-test {n} {m} {a} {t} ⦃ l ⦄ ⦃ u ⦄ = bt-find {n} {_} {a} ⦃ l ⦄ ⦃ u ⦄ 3 test-node [] (λ tt st ad → st)
f103f07c0552 add insert code ryokka parents: 586 diff changeset	221 {-- result
f103f07c0552 add insert code ryokka parents: 586 diff changeset	222 λ {n} {m} {a} {t} ⦃ l ⦄ ⦃ u ⦄ →
f103f07c0552 add insert code ryokka parents: 586 diff changeset	223 bt-node 3 (bt-leaf z≤n) (bt-leaf (s≤s (s≤s (s≤s z≤n)))) z≤n (s≤s (s≤s (s≤s (s≤s z≤n)))) ∷ []
f103f07c0552 add insert code ryokka parents: 586 diff changeset	224 --}
f103f07c0552 add insert code ryokka parents: 586 diff changeset	225
f103f07c0552 add insert code ryokka parents: 586 diff changeset	226 find-lem : {n m : Level} {a : Set n} {t : Set m} ⦃ l u : ℕ ⦄ → (d : ℕ) → (tree : bt {n} {a}) → (st : List (bt {n} {a})) → find-support {{l}} {{u}} d tree st (λ ta st ad → ta ≡ ta)
f103f07c0552 add insert code ryokka parents: 586 diff changeset	227 find-lem d (bt-leaf x) st = refl
f103f07c0552 add insert code ryokka parents: 586 diff changeset	228 find-lem d (bt-node d₁ tree tree₁ x x₁) st with <-cmp d d₁
f103f07c0552 add insert code ryokka parents: 586 diff changeset	229 find-lem d (bt-node d₁ tree tree₁ x x₁) st \| tri≈ ¬a b ¬c = refl
586 0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	230
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	231
587 f103f07c0552 add insert code ryokka parents: 586 diff changeset	232 find-lem d (bt-node d₁ tree tree₁ x x₁) st \| tri< a ¬b ¬c with tri< a ¬b ¬c
f103f07c0552 add insert code ryokka parents: 586 diff changeset	233 find-lem {n} {m} {a} {t} {{l}} {{u}} d (bt-node d₁ tree tree₁ x x₁) st \| tri< lt ¬b ¬c \| tri< a₁ ¬b₁ ¬c₁ = find-lem {n} {m} {a} {t} {{l}} {{u}} d tree {!!}
f103f07c0552 add insert code ryokka parents: 586 diff changeset	234 find-lem d (bt-node d₁ tree tree₁ x x₁) st \| tri< a ¬b ¬c \| tri≈ ¬a b ¬c₁ = {!!}
f103f07c0552 add insert code ryokka parents: 586 diff changeset	235 find-lem d (bt-node d₁ tree tree₁ x x₁) st \| tri< a ¬b ¬c \| tri> ¬a ¬b₁ c = {!!}
f103f07c0552 add insert code ryokka parents: 586 diff changeset	236
f103f07c0552 add insert code ryokka parents: 586 diff changeset	237 find-lem d (bt-node d₁ tree tree₁ x x₁) st \| tri> ¬a ¬b c = {!!}
f103f07c0552 add insert code ryokka parents: 586 diff changeset	238
f103f07c0552 add insert code ryokka parents: 586 diff changeset	239 bt-singleton :{n m : Level} {a : Set n} {t : Set m} ⦃ l u : ℕ ⦄ → (d : ℕ) → ( (bt {n} {a} ) → t ) → t
f103f07c0552 add insert code ryokka parents: 586 diff changeset	240 bt-singleton {n} {m} {a} {t} ⦃ l ⦄ ⦃ u ⦄ d cg = cg (bt-node ⦃ 0 ⦄ ⦃ 0 ⦄ ⦃ d ⦄ ⦃ d ⦄ d (bt-leaf ⦃ 0 ⦄ ⦃ d ⦄ z≤n ) (bt-leaf ⦃ d ⦄ ⦃ d ⦄ ≤-refl) z≤n ≤-refl)
f103f07c0552 add insert code ryokka parents: 586 diff changeset	241
f103f07c0552 add insert code ryokka parents: 586 diff changeset	242
f103f07c0552 add insert code ryokka parents: 586 diff changeset	243 singleton-test : {n m : Level} {a : Set n} {t : Set m} ⦃ l u : ℕ ⦄ → bt -- ?
f103f07c0552 add insert code ryokka parents: 586 diff changeset	244 singleton-test {n} {m} {a} {t} ⦃ l ⦄ ⦃ u ⦄ = bt-singleton {n} {_} {a} ⦃ l ⦄ ⦃ u ⦄ 10 λ x → x
586 0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	245
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	246
587 f103f07c0552 add insert code ryokka parents: 586 diff changeset	247 replace-helper : {n m : Level} {a : Set n} {t : Set m} ⦃ l u : ℕ ⦄ → (tree : bt {n} {a} ) → SingleLinkedStack (bt {n} {a} ) → ( (bt {n} {a} ) → t ) → t
f103f07c0552 add insert code ryokka parents: 586 diff changeset	248 replace-helper {n} {m} {a} {t} ⦃ l ⦄ ⦃ u ⦄ tree [] cg = cg tree
f103f07c0552 add insert code ryokka parents: 586 diff changeset	249 replace-helper {n} {m} {a} {t} ⦃ l ⦄ ⦃ u ⦄ tree@(bt-node d L R x₁ x₂) (bt-leaf x ∷ st) cg = replace-helper ⦃ l ⦄ ⦃ u ⦄ tree st cg -- Unknown Case
f103f07c0552 add insert code ryokka parents: 586 diff changeset	250 replace-helper {n} {m} {a} {t} ⦃ l ⦄ ⦃ u ⦄ (bt-node d tree tree₁ x₁ x₂) (bt-node d₁ x x₃ x₄ x₅ ∷ st) cg with <-cmp d d₁
f103f07c0552 add insert code ryokka parents: 586 diff changeset	251 replace-helper {n} {m} {a} {t} ⦃ l ⦄ ⦃ u ⦄ subt@(bt-node d tree tree₁ x₁ x₂) (bt-node d₁ x x₃ x₄ x₅ ∷ st) cg \| tri< a₁ ¬b ¬c = replace-helper ⦃ l ⦄ ⦃ u ⦄ (bt-node d₁ subt x₃ x₄ x₅) st cg
f103f07c0552 add insert code ryokka parents: 586 diff changeset	252 replace-helper {n} {m} {a} {t} ⦃ l ⦄ ⦃ u ⦄ subt@(bt-node d tree tree₁ x₁ x₂) (bt-node d₁ x x₃ x₄ x₅ ∷ st) cg \| tri≈ ¬a b ¬c = replace-helper ⦃ l ⦄ ⦃ u ⦄ (bt-node d₁ subt x₃ x₄ x₅) st cg
f103f07c0552 add insert code ryokka parents: 586 diff changeset	253 replace-helper {n} {m} {a} {t} ⦃ l ⦄ ⦃ u ⦄ subt@(bt-node d tree tree₁ x₁ x₂) (bt-node d₁ x x₃ x₄ x₅ ∷ st) cg \| tri> ¬a ¬b c = replace-helper ⦃ l ⦄ ⦃ u ⦄ (bt-node d₁ x₃ subt x₄ x₅) st cg
f103f07c0552 add insert code ryokka parents: 586 diff changeset	254 replace-helper {n} {m} {a} {t} ⦃ l ⦄ ⦃ u ⦄ tree (x ∷ st) cg = replace-helper ⦃ l ⦄ ⦃ u ⦄ tree st cg -- Unknown Case
f103f07c0552 add insert code ryokka parents: 586 diff changeset	255
f103f07c0552 add insert code ryokka parents: 586 diff changeset	256
f103f07c0552 add insert code ryokka parents: 586 diff changeset	257
f103f07c0552 add insert code ryokka parents: 586 diff changeset	258 bt-replace : {n m : Level} {a : Set n} {t : Set m} ⦃ l u : ℕ ⦄
f103f07c0552 add insert code ryokka parents: 586 diff changeset	259 → (d : ℕ) → (bt {n} {a} ) → SingleLinkedStack (bt {n} {a} )
f103f07c0552 add insert code ryokka parents: 586 diff changeset	260 → Maybe (Σ ℕ (λ d' → _iso_ {n} {a} d d')) → ( (bt {n} {a} ) → t ) → t
f103f07c0552 add insert code ryokka parents: 586 diff changeset	261 bt-replace {n} {m} {a} {t} ⦃ l ⦄ ⦃ u ⦄ d tree st eqP cg = replace-helper {n} {m} {a} {t} ⦃ l ⦄ ⦃ u ⦄ ((bt-node ⦃ 0 ⦄ ⦃ 0 ⦄ ⦃ d ⦄ ⦃ d ⦄ d (bt-leaf ⦃ 0 ⦄ ⦃ d ⦄ z≤n ) (bt-leaf ⦃ d ⦄ ⦃ d ⦄ ≤-refl) z≤n ≤-refl)) st cg
586 0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	262
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	263
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	264
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	265 -- 証明に insert がはいっててほしい
587 f103f07c0552 add insert code ryokka parents: 586 diff changeset	266 bt-insert : {n m : Level} {a : Set n} {t : Set m} ⦃ l u : ℕ ⦄ → (d : ℕ) → (tree : bt {n} {a})
f103f07c0552 add insert code ryokka parents: 586 diff changeset	267 → ((bt {n} {a}) → t) → t
f103f07c0552 add insert code ryokka parents: 586 diff changeset	268
f103f07c0552 add insert code ryokka parents: 586 diff changeset	269 bt-insert {n} {m} {a} {t} ⦃ l ⦄ ⦃ u ⦄ d tree cg = bt-find {n} {_} {a} ⦃ l ⦄ ⦃ u ⦄ d tree [] (λ tt st ad → bt-replace ⦃ l ⦄ ⦃ u ⦄ d tt st ad cg )
f103f07c0552 add insert code ryokka parents: 586 diff changeset	270
f103f07c0552 add insert code ryokka parents: 586 diff changeset	271 pickKey : {n m : Level} {a : Set n} {t : Set m} ⦃ l u : ℕ ⦄ → (tree : bt {n} {a}) → Maybe ℕ
f103f07c0552 add insert code ryokka parents: 586 diff changeset	272 pickKey (bt-leaf x) = nothing
f103f07c0552 add insert code ryokka parents: 586 diff changeset	273 pickKey (bt-node d tree tree₁ x x₁) = just d
f103f07c0552 add insert code ryokka parents: 586 diff changeset	274
f103f07c0552 add insert code ryokka parents: 586 diff changeset	275 insert-test : {n m : Level} {a : Set n} {t : Set m} ⦃ l u : ℕ ⦄ → bt -- ?
f103f07c0552 add insert code ryokka parents: 586 diff changeset	276 insert-test {n} {m} {a} {t} ⦃ l ⦄ ⦃ u ⦄ = bt-insert {n} {_} {a} ⦃ l ⦄ ⦃ u ⦄ 1 test-node λ x → x
f103f07c0552 add insert code ryokka parents: 586 diff changeset	277
f103f07c0552 add insert code ryokka parents: 586 diff changeset	278 insert-test-l : {n m : Level} {a : Set n} {t : Set m} ⦃ l u : ℕ ⦄ → bt -- ?
f103f07c0552 add insert code ryokka parents: 586 diff changeset	279 insert-test-l {n} {m} {a} {t} ⦃ l ⦄ ⦃ u ⦄ = bt-insert {n} {_} {a} ⦃ l ⦄ ⦃ u ⦄ 1 (lleaf) λ x → x
f103f07c0552 add insert code ryokka parents: 586 diff changeset	280
f103f07c0552 add insert code ryokka parents: 586 diff changeset	281
f103f07c0552 add insert code ryokka parents: 586 diff changeset	282 insert-lem : {n m : Level} {a : Set n} {t : Set m} ⦃ l u : ℕ ⦄ → (d : ℕ) → (tree : bt {n} {a})
f103f07c0552 add insert code ryokka parents: 586 diff changeset	283 → bt-insert {n} {_} {a} ⦃ l ⦄ ⦃ u ⦄ d tree (λ tree1 → bt-find ⦃ l ⦄ ⦃ u ⦄ d tree1 []
f103f07c0552 add insert code ryokka parents: 586 diff changeset	284 (λ tt st ad → (pickKey {n} {m} {a} {t} ⦃ l ⦄ ⦃ u ⦄ tt) ≡ just d ) )
f103f07c0552 add insert code ryokka parents: 586 diff changeset	285
f103f07c0552 add insert code ryokka parents: 586 diff changeset	286
f103f07c0552 add insert code ryokka parents: 586 diff changeset	287 insert-lem d (bt-leaf x) with <-cmp d d -- bt-insert d (bt-leaf x) (λ tree1 → {!!})
f103f07c0552 add insert code ryokka parents: 586 diff changeset	288 insert-lem d (bt-leaf x) \| tri< a ¬b ¬c = ⊥-elim (¬b refl)
f103f07c0552 add insert code ryokka parents: 586 diff changeset	289 insert-lem d (bt-leaf x) \| tri≈ ¬a b ¬c = refl
f103f07c0552 add insert code ryokka parents: 586 diff changeset	290 insert-lem d (bt-leaf x) \| tri> ¬a ¬b c = ⊥-elim (¬b refl)
f103f07c0552 add insert code ryokka parents: 586 diff changeset	291 insert-lem d (bt-node d₁ tree tree₁ x x₁) with <-cmp d d₁
f103f07c0552 add insert code ryokka parents: 586 diff changeset	292 -- bt-insert d (bt-node d₁ tree tree₁ x x₁) (λ tree1 → {!!})
f103f07c0552 add insert code ryokka parents: 586 diff changeset	293 insert-lem d (bt-node d₁ tree tree₁ x x₁) \| tri≈ ¬a b ¬c with <-cmp d d
f103f07c0552 add insert code ryokka parents: 586 diff changeset	294 insert-lem d (bt-node d₁ tree tree₁ x x₁) \| tri≈ ¬a b ¬c \| tri< a ¬b ¬c₁ = ⊥-elim (¬b refl)
f103f07c0552 add insert code ryokka parents: 586 diff changeset	295 insert-lem d (bt-node d₁ tree tree₁ x x₁) \| tri≈ ¬a b ¬c \| tri≈ ¬a₁ b₁ ¬c₁ = refl
f103f07c0552 add insert code ryokka parents: 586 diff changeset	296 insert-lem d (bt-node d₁ tree tree₁ x x₁) \| tri≈ ¬a b ¬c \| tri> ¬a₁ ¬b c = ⊥-elim (¬b refl)
f103f07c0552 add insert code ryokka parents: 586 diff changeset	297
f103f07c0552 add insert code ryokka parents: 586 diff changeset	298 insert-lem d (bt-node d₁ tree tree₁ x x₁) \| tri< a ¬b ¬c = {!!}
f103f07c0552 add insert code ryokka parents: 586 diff changeset	299 where
f103f07c0552 add insert code ryokka parents: 586 diff changeset	300 lem-helper : find-support ⦃ {!!} ⦄ ⦃ {!!} ⦄ d tree (bt-node d₁ tree tree₁ x x₁ ∷ []) (λ tt₁ st ad → replace-helper ⦃ {!!} ⦄ ⦃ {!!} ⦄ (bt-node ⦃ {!!} ⦄ ⦃ {!!} ⦄ ⦃ {!!} ⦄ ⦃ {!!} ⦄ d (bt-leaf ⦃ 0 ⦄ ⦃ d ⦄ z≤n) (bt-leaf ⦃ {!!} ⦄ ⦃ {!!} ⦄ (≤-reflexive refl)) z≤n (≤-reflexive refl)) st (λ tree1 → find-support ⦃ {!!} ⦄ ⦃ {!!} ⦄ d tree1 [] (λ tt₂ st₁ ad₁ → pickKey {{!!}} {{!!}} {{!!}} {{!!}} ⦃ {!!} ⦄ ⦃ {!!} ⦄ tt₂ ≡ just d)))
f103f07c0552 add insert code ryokka parents: 586 diff changeset	301 lem-helper = {!!}
f103f07c0552 add insert code ryokka parents: 586 diff changeset	302
f103f07c0552 add insert code ryokka parents: 586 diff changeset	303 insert-lem d (bt-node d₁ tree tree₁ x x₁) \| tri> ¬a ¬b c = {!!}
f103f07c0552 add insert code ryokka parents: 586 diff changeset	304

Mercurial > hg > Members > Moririn

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