Members/Moririn: hoareBinaryTree.agda annotate

annotate hoareBinaryTree.agda @ 588:8627d35d4bff

add data bt', and some function

author	ryokka
date	Thu, 05 Dec 2019 20:38:54 +0900
parents	f103f07c0552
children	37f5826ca7d2

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
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	78 bt-find' : {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	79 bt-find' key (bt'-leaf key₁) stack next = {!!}
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	80 bt-find' key (bt'-node key₁ value tree tree₁ x x₁) stack next with <-cmp key key₁
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	81 bt-find' {n} {m} {A} {t} key tr@(bt'-node {l} {r} key₁ value tree tree₁ x x₁) stack next \| tri< a ¬b ¬c =
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	82 bt-find' {n} {m} {A} {t} key tree ( (bt'-left {n} {A} key {key₁} {!!} {!!} ) ∷ stack) next
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	83 bt-find' key found@(bt'-node key₁ value tree tree₁ x x₁) stack next \| tri≈ ¬a b ¬c = next {!!} stack
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 \| tri> ¬a ¬b c = {!!}
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	85
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	86
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	87 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	88 bt-replace' = {!!}
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	89
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	90 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	91 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	92
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	93
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	94 -- 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	95
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	96 -- 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	97 -- 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	98 -- 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	99
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	100 -- 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	101 -- pushSingleLinkedStack st node
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	102 -- (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	103
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	104 -- 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	105 -- (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	106
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	107
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	108
587 f103f07c0552 add insert code ryokka parents: 586 diff changeset	109 lleaf : {n : Level} {a : Set n} → bt {n} {a}
586 0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	110 lleaf = (bt-leaf ⦃ 0 ⦄ ⦃ 3 ⦄ z≤n)
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	111
588 8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	112 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	113 lleaf1 0<3 a d = bt'-leaf d
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	114
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	115 test-node1 : bt' ℕ 3
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	116 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	117
8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	118
587 f103f07c0552 add insert code ryokka parents: 586 diff changeset	119 rleaf : {n : Level} {a : Set n} → bt {n} {a}
588 8627d35d4bff add data bt', and some function ryokka parents: 587 diff changeset	120 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	121
587 f103f07c0552 add insert code ryokka parents: 586 diff changeset	122 test-node : {n : Level} {a : Set n} → bt {n} {a}
586 0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	123 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	124
587 f103f07c0552 add insert code ryokka parents: 586 diff changeset	125 -- stt : {n m : Level} {a : Set n} {t : Set m} → {!!}
f103f07c0552 add insert code ryokka parents: 586 diff changeset	126 -- 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	127
586 0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	128
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	129
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	130 -- 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	131 -- 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	132 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	133 bt-search {n} {m} {a} {t} key (bt-leaf x) cg = cg nothing
587 f103f07c0552 add insert code ryokka parents: 586 diff changeset	134 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	135 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	136 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	137 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	138
f103f07c0552 add insert code ryokka parents: 586 diff changeset	139 -- 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	140 -- 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	141 -- 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	142
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	143
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	144 -- 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	145 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	146 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	147
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	148 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	149 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	150
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	151
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	152 -- 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	153 -- up-some (just (fst , snd)) = just fst
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	154 -- up-some nothing = nothing
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	155
587 f103f07c0552 add insert code ryokka parents: 586 diff changeset	156 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	157 search-lem {n} {m} {a} {t} key (bt-leaf x) = refl
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	158 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	159 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	160 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	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} ⦃ d ⦄ ⦃ lr' ⦄ key tree₂
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	162
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	163
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	164 -- bt-find
587 f103f07c0552 add insert code ryokka parents: 586 diff changeset	165 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	166
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	167 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	168 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	169 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	170
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	171 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	172 pushSingleLinkedStack st node
587 f103f07c0552 add insert code ryokka parents: 586 diff changeset	173 (λ st2 → find-support {n} {m} {a} {t} {{l'}} {{d}} key L st2 cg)
f103f07c0552 add insert code ryokka parents: 586 diff changeset	174
f103f07c0552 add insert code ryokka parents: 586 diff changeset	175 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	176 (λ st2 → find-support {n} {m} {a} {t} {{d}} {{lr'}} key R st2 cg)
f103f07c0552 add insert code ryokka parents: 586 diff changeset	177
f103f07c0552 add insert code ryokka parents: 586 diff changeset	178 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	179 bt-find {n} {m} {a} {t} ⦃ l ⦄ ⦃ u ⦄ key tr st cg = clearSingleLinkedStack st
f103f07c0552 add insert code ryokka parents: 586 diff changeset	180 (λ cst → find-support ⦃ l ⦄ ⦃ u ⦄ key tr cst cg)
586 0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	181
587 f103f07c0552 add insert code ryokka parents: 586 diff changeset	182 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	183 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	184 {-- result
f103f07c0552 add insert code ryokka parents: 586 diff changeset	185 λ {n} {m} {a} {t} ⦃ l ⦄ ⦃ u ⦄ →
f103f07c0552 add insert code ryokka parents: 586 diff changeset	186 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	187 --}
f103f07c0552 add insert code ryokka parents: 586 diff changeset	188
f103f07c0552 add insert code ryokka parents: 586 diff changeset	189 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	190 find-lem d (bt-leaf x) st = refl
f103f07c0552 add insert code ryokka parents: 586 diff changeset	191 find-lem d (bt-node d₁ tree tree₁ x x₁) st with <-cmp d d₁
f103f07c0552 add insert code ryokka parents: 586 diff changeset	192 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	193
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	194
587 f103f07c0552 add insert code ryokka parents: 586 diff changeset	195 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	196 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	197 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	198 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	199
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 = {!!}
f103f07c0552 add insert code ryokka parents: 586 diff changeset	201
f103f07c0552 add insert code ryokka parents: 586 diff changeset	202 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	203 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	204
f103f07c0552 add insert code ryokka parents: 586 diff changeset	205
f103f07c0552 add insert code ryokka parents: 586 diff changeset	206 singleton-test : {n m : Level} {a : Set n} {t : Set m} ⦃ l u : ℕ ⦄ → bt -- ?
f103f07c0552 add insert code ryokka parents: 586 diff changeset	207 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	208
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	209
587 f103f07c0552 add insert code ryokka parents: 586 diff changeset	210 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	211 replace-helper {n} {m} {a} {t} ⦃ l ⦄ ⦃ u ⦄ tree [] cg = cg tree
f103f07c0552 add insert code ryokka parents: 586 diff changeset	212 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	213 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	214 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	215 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	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> ¬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	217 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	218
f103f07c0552 add insert code ryokka parents: 586 diff changeset	219
f103f07c0552 add insert code ryokka parents: 586 diff changeset	220
f103f07c0552 add insert code ryokka parents: 586 diff changeset	221 bt-replace : {n m : Level} {a : Set n} {t : Set m} ⦃ l u : ℕ ⦄
f103f07c0552 add insert code ryokka parents: 586 diff changeset	222 → (d : ℕ) → (bt {n} {a} ) → SingleLinkedStack (bt {n} {a} )
f103f07c0552 add insert code ryokka parents: 586 diff changeset	223 → Maybe (Σ ℕ (λ d' → _iso_ {n} {a} d d')) → ( (bt {n} {a} ) → t ) → t
f103f07c0552 add insert code ryokka parents: 586 diff changeset	224 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	225
0ddfa505d612 isolate search function problem, and add hoareBinaryTree.agda. ryokka parents: diff changeset	226
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 -- 証明に insert がはいっててほしい
587 f103f07c0552 add insert code ryokka parents: 586 diff changeset	229 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	230 → ((bt {n} {a}) → t) → t
f103f07c0552 add insert code ryokka parents: 586 diff changeset	231
f103f07c0552 add insert code ryokka parents: 586 diff changeset	232 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	233
f103f07c0552 add insert code ryokka parents: 586 diff changeset	234 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	235 pickKey (bt-leaf x) = nothing
f103f07c0552 add insert code ryokka parents: 586 diff changeset	236 pickKey (bt-node d tree tree₁ x x₁) = just d
f103f07c0552 add insert code ryokka parents: 586 diff changeset	237
f103f07c0552 add insert code ryokka parents: 586 diff changeset	238 insert-test : {n m : Level} {a : Set n} {t : Set m} ⦃ l u : ℕ ⦄ → bt -- ?
f103f07c0552 add insert code ryokka parents: 586 diff changeset	239 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	240
f103f07c0552 add insert code ryokka parents: 586 diff changeset	241 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	242 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	243
f103f07c0552 add insert code ryokka parents: 586 diff changeset	244
f103f07c0552 add insert code ryokka parents: 586 diff changeset	245 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	246 → 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	247 (λ tt st ad → (pickKey {n} {m} {a} {t} ⦃ l ⦄ ⦃ u ⦄ tt) ≡ just d ) )
f103f07c0552 add insert code ryokka parents: 586 diff changeset	248
f103f07c0552 add insert code ryokka parents: 586 diff changeset	249
f103f07c0552 add insert code ryokka parents: 586 diff changeset	250 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	251 insert-lem d (bt-leaf x) \| tri< a ¬b ¬c = ⊥-elim (¬b refl)
f103f07c0552 add insert code ryokka parents: 586 diff changeset	252 insert-lem d (bt-leaf x) \| tri≈ ¬a b ¬c = refl
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-node d₁ tree tree₁ x x₁) with <-cmp d d₁
f103f07c0552 add insert code ryokka parents: 586 diff changeset	255 -- bt-insert d (bt-node d₁ tree tree₁ x x₁) (λ tree1 → {!!})
f103f07c0552 add insert code ryokka parents: 586 diff changeset	256 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	257 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	258 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	259 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	260
f103f07c0552 add insert code ryokka parents: 586 diff changeset	261 insert-lem d (bt-node d₁ tree tree₁ x x₁) \| tri< a ¬b ¬c = {!!}
f103f07c0552 add insert code ryokka parents: 586 diff changeset	262 where
f103f07c0552 add insert code ryokka parents: 586 diff changeset	263 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	264 lem-helper = {!!}
f103f07c0552 add insert code ryokka parents: 586 diff changeset	265
f103f07c0552 add insert code ryokka parents: 586 diff changeset	266 insert-lem d (bt-node d₁ tree tree₁ x x₁) \| tri> ¬a ¬b c = {!!}
f103f07c0552 add insert code ryokka parents: 586 diff changeset	267

Mercurial > hg > Members > Moririn

annotate hoareBinaryTree.agda @ 588:8627d35d4bff