Members/Moririn: hoareBinaryTree.agda annotate

annotate hoareBinaryTree.agda @ 589:37f5826ca7d2

minor fix

author	Shinji KONO <kono@ie.u-ryukyu.ac.jp>
date	Fri, 06 Dec 2019 13:01:53 +0900
parents	8627d35d4bff
children	7c424dd0945d

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
588 8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	65 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	66 bt'-leaf : (key : ℕ) → bt' A key
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	67 bt'-node : { l r : ℕ } → (key : ℕ) → (value : A) →
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	68 bt' {n} A l → bt' {n} A r → l < key → key < r → bt' A key
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	69
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	70 data bt'-path {n : Level} (A : Set n) : Set n where -- (a : Setn)
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	71 bt'-left : (key : ℕ) → {left-key : ℕ} → (bt' A left-key ) → (key < left-key) → bt'-path A
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	72 bt'-right : (key : ℕ) → {right-key : ℕ} → (bt' A right-key ) → (right-key < key) → bt'-path A
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	73 bt'-null : bt'-path A
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	74
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	75
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	76 test = bt'-left {Z} {ℕ} 3 {5} (bt'-leaf 5) (s≤s (s≤s (s≤s (s≤s z≤n))))
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	77
589 37f5826ca7d2 minor fix Shinji KONO <kono@ie.u-ryukyu.ac.jp> parents: 588 diff changeset	78 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	79 → ( {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	80 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	81 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	82 bt-find' key tr@(bt'-node {l} {r} key₁ value tree tree₁ x x₁) stack next \| tri< a ¬b ¬c =
37f5826ca7d2 minor fix Shinji KONO <kono@ie.u-ryukyu.ac.jp> parents: 588 diff changeset	83 bt-find' key tree ( (bt'-left key {key₁} tr a ) ∷ stack) next
37f5826ca7d2 minor fix Shinji KONO <kono@ie.u-ryukyu.ac.jp> parents: 588 diff changeset	84 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	85 bt-find' key tr@(bt'-node key₁ value tree tree₁ x x₁) stack next \| tri> ¬a ¬b c =
37f5826ca7d2 minor fix Shinji KONO <kono@ie.u-ryukyu.ac.jp> parents: 588 diff changeset	86 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	87
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	88
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	89 bt-replace' : {n m : Level} {A : Set n} {t : Set m} {tn : ℕ} → (key : ℕ) → (tree : bt' ℕ tn ) → List (bt'-path A ) → ( {key1 : ℕ } → bt' A key1 → List (bt'-path A ) → t ) → t
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	90 bt-replace' = {!!}
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	91
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	92 bt-find'-assert1 : {n m : Level} {A : Set n} {t : Set m} → Set n
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	93 bt-find'-assert1 {n} {m} {A} {t} = (key : ℕ) → (val : A) → bt-find' key {!!} {!!} (λ tree stack → {!!})
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	94
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	95
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	96 -- 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	97
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	98 -- 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	99 -- 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	100 -- 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	101
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	102 -- 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	103 -- pushSingleLinkedStack st node
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	104 -- (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	105
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	106 -- 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	107 -- (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	108
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	109
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	110
587 f103f07c0552 add insert code ryokka parents: 586 diff changeset	111 lleaf : {n : Level} {a : Set n} → bt {n} {a}
586 0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	112 lleaf = (bt-leaf ⦃ 0 ⦄ ⦃ 3 ⦄ z≤n)
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	113
588 8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	114 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	115 lleaf1 0<3 a d = bt'-leaf d
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	116
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	117 test-node1 : bt' ℕ 3
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	118 test-node1 = bt'-node (3) 3 (bt'-leaf 2) (bt'-leaf 4) (s≤s (s≤s (s≤s z≤n))) (s≤s (s≤s (s≤s (s≤s z≤n))))
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	119
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	120
587 f103f07c0552 add insert code ryokka parents: 586 diff changeset	121 rleaf : {n : Level} {a : Set n} → bt {n} {a}
588 8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	122 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	123
587 f103f07c0552 add insert code ryokka parents: 586 diff changeset	124 test-node : {n : Level} {a : Set n} → bt {n} {a}
586 0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	125 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	126
587 f103f07c0552 add insert code ryokka parents: 586 diff changeset	127 -- stt : {n m : Level} {a : Set n} {t : Set m} → {!!}
f103f07c0552 add insert code ryokka parents: 586 diff changeset	128 -- 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	129
586 0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	130
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	131
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	132 -- 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	133 -- 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	134 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	135 bt-search {n} {m} {a} {t} key (bt-leaf x) cg = cg nothing
587 f103f07c0552 add insert code ryokka parents: 586 diff changeset	136 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	137 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	138 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	139 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	140
f103f07c0552 add insert code ryokka parents: 586 diff changeset	141 -- 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	142 -- 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	143 -- 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	144
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	145
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	146 -- 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	147 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	148 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	149
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	150 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	151 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	152
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	153
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	154 -- 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	155 -- up-some (just (fst , snd)) = just fst
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	156 -- up-some nothing = nothing
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	157
587 f103f07c0552 add insert code ryokka parents: 586 diff changeset	158 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	159 search-lem {n} {m} {a} {t} key (bt-leaf x) = refl
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	160 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	161 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	162 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	163 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	164
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 -- bt-find
587 f103f07c0552 add insert code ryokka parents: 586 diff changeset	167 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	168
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	169 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	170 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	171 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	172
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	173 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	174 pushSingleLinkedStack st node
587 f103f07c0552 add insert code ryokka parents: 586 diff changeset	175 (λ st2 → find-support {n} {m} {a} {t} {{l'}} {{d}} key L st2 cg)
f103f07c0552 add insert code ryokka parents: 586 diff changeset	176
f103f07c0552 add insert code ryokka parents: 586 diff changeset	177 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	178 (λ st2 → find-support {n} {m} {a} {t} {{d}} {{lr'}} key R st2 cg)
f103f07c0552 add insert code ryokka parents: 586 diff changeset	179
f103f07c0552 add insert code ryokka parents: 586 diff changeset	180 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	181 bt-find {n} {m} {a} {t} ⦃ l ⦄ ⦃ u ⦄ key tr st cg = clearSingleLinkedStack st
f103f07c0552 add insert code ryokka parents: 586 diff changeset	182 (λ cst → find-support ⦃ l ⦄ ⦃ u ⦄ key tr cst cg)
586 0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	183
587 f103f07c0552 add insert code ryokka parents: 586 diff changeset	184 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	185 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	186 {-- result
f103f07c0552 add insert code ryokka parents: 586 diff changeset	187 λ {n} {m} {a} {t} ⦃ l ⦄ ⦃ u ⦄ →
f103f07c0552 add insert code ryokka parents: 586 diff changeset	188 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	189 --}
f103f07c0552 add insert code ryokka parents: 586 diff changeset	190
f103f07c0552 add insert code ryokka parents: 586 diff changeset	191 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	192 find-lem d (bt-leaf x) st = refl
f103f07c0552 add insert code ryokka parents: 586 diff changeset	193 find-lem d (bt-node d₁ tree tree₁ x x₁) st with <-cmp d d₁
f103f07c0552 add insert code ryokka parents: 586 diff changeset	194 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	195
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	196
587 f103f07c0552 add insert code ryokka parents: 586 diff changeset	197 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	198 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	199 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	200 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	201
f103f07c0552 add insert code ryokka parents: 586 diff changeset	202 find-lem d (bt-node d₁ tree tree₁ x x₁) st \| tri> ¬a ¬b c = {!!}
f103f07c0552 add insert code ryokka parents: 586 diff changeset	203
f103f07c0552 add insert code ryokka parents: 586 diff changeset	204 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	205 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	206
f103f07c0552 add insert code ryokka parents: 586 diff changeset	207
f103f07c0552 add insert code ryokka parents: 586 diff changeset	208 singleton-test : {n m : Level} {a : Set n} {t : Set m} ⦃ l u : ℕ ⦄ → bt -- ?
f103f07c0552 add insert code ryokka parents: 586 diff changeset	209 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	210
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	211
587 f103f07c0552 add insert code ryokka parents: 586 diff changeset	212 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	213 replace-helper {n} {m} {a} {t} ⦃ l ⦄ ⦃ u ⦄ tree [] cg = cg tree
f103f07c0552 add insert code ryokka parents: 586 diff changeset	214 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	215 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	216 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	217 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	218 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	219 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	220
f103f07c0552 add insert code ryokka parents: 586 diff changeset	221
f103f07c0552 add insert code ryokka parents: 586 diff changeset	222
f103f07c0552 add insert code ryokka parents: 586 diff changeset	223 bt-replace : {n m : Level} {a : Set n} {t : Set m} ⦃ l u : ℕ ⦄
f103f07c0552 add insert code ryokka parents: 586 diff changeset	224 → (d : ℕ) → (bt {n} {a} ) → SingleLinkedStack (bt {n} {a} )
f103f07c0552 add insert code ryokka parents: 586 diff changeset	225 → Maybe (Σ ℕ (λ d' → _iso_ {n} {a} d d')) → ( (bt {n} {a} ) → t ) → t
f103f07c0552 add insert code ryokka parents: 586 diff changeset	226 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	227
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	228
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	229
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	230 -- 証明に insert がはいっててほしい
587 f103f07c0552 add insert code ryokka parents: 586 diff changeset	231 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	232 → ((bt {n} {a}) → t) → t
f103f07c0552 add insert code ryokka parents: 586 diff changeset	233
f103f07c0552 add insert code ryokka parents: 586 diff changeset	234 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	235
f103f07c0552 add insert code ryokka parents: 586 diff changeset	236 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	237 pickKey (bt-leaf x) = nothing
f103f07c0552 add insert code ryokka parents: 586 diff changeset	238 pickKey (bt-node d tree tree₁ x x₁) = just d
f103f07c0552 add insert code ryokka parents: 586 diff changeset	239
f103f07c0552 add insert code ryokka parents: 586 diff changeset	240 insert-test : {n m : Level} {a : Set n} {t : Set m} ⦃ l u : ℕ ⦄ → bt -- ?
f103f07c0552 add insert code ryokka parents: 586 diff changeset	241 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	242
f103f07c0552 add insert code ryokka parents: 586 diff changeset	243 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	244 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	245
f103f07c0552 add insert code ryokka parents: 586 diff changeset	246
f103f07c0552 add insert code ryokka parents: 586 diff changeset	247 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	248 → 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	249 (λ tt st ad → (pickKey {n} {m} {a} {t} ⦃ l ⦄ ⦃ u ⦄ tt) ≡ just d ) )
f103f07c0552 add insert code ryokka parents: 586 diff changeset	250
f103f07c0552 add insert code ryokka parents: 586 diff changeset	251
f103f07c0552 add insert code ryokka parents: 586 diff changeset	252 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	253 insert-lem d (bt-leaf x) \| tri< a ¬b ¬c = ⊥-elim (¬b refl)
f103f07c0552 add insert code ryokka parents: 586 diff changeset	254 insert-lem d (bt-leaf x) \| tri≈ ¬a b ¬c = refl
f103f07c0552 add insert code ryokka parents: 586 diff changeset	255 insert-lem d (bt-leaf x) \| tri> ¬a ¬b c = ⊥-elim (¬b refl)
f103f07c0552 add insert code ryokka parents: 586 diff changeset	256 insert-lem d (bt-node d₁ tree tree₁ x x₁) with <-cmp d d₁
f103f07c0552 add insert code ryokka parents: 586 diff changeset	257 -- bt-insert d (bt-node d₁ tree tree₁ x x₁) (λ tree1 → {!!})
f103f07c0552 add insert code ryokka parents: 586 diff changeset	258 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	259 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	260 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	261 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	262
f103f07c0552 add insert code ryokka parents: 586 diff changeset	263 insert-lem d (bt-node d₁ tree tree₁ x x₁) \| tri< a ¬b ¬c = {!!}
f103f07c0552 add insert code ryokka parents: 586 diff changeset	264 where
f103f07c0552 add insert code ryokka parents: 586 diff changeset	265 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	266 lem-helper = {!!}
f103f07c0552 add insert code ryokka parents: 586 diff changeset	267
f103f07c0552 add insert code ryokka parents: 586 diff changeset	268 insert-lem d (bt-node d₁ tree tree₁ x x₁) \| tri> ¬a ¬b c = {!!}
f103f07c0552 add insert code ryokka parents: 586 diff changeset	269

Mercurial > hg > Members > Moririn

annotate hoareBinaryTree.agda @ 589:37f5826ca7d2