Mercurial > hg > Gears > GearsAgda

changeset 660:712e2998c76b

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author Shinji KONO <kono@ie.u-ryukyu.ac.jp>
date Sun, 21 Nov 2021 19:03:22 +0900
parents afcccfaea264
children 323533798054
files hoareBinaryTree.agda
diffstat 1 files changed, 18 insertions(+), 23 deletions(-) [+]
line wrap: on
line diff
--- a/hoareBinaryTree.agda	Sun Nov 21 17:24:40 2021 +0900
+++ b/hoareBinaryTree.agda	Sun Nov 21 19:03:22 2021 +0900
@@ -103,8 +103,8 @@
        → treeInvariant (node key₁ value₁ (node key value t₁ t₂) (node key₂ value₂ t₃ t₄)) 
 
 data stackInvariant {n : Level} {A : Set n}  (key : ℕ) : (top orig : bt A) → (stack  : List (bt A)) → Set n where
-    s-nil :  {tree : bt A} → stackInvariant key tree tree []
-    s-single :  {tree tree0 : bt A} →  stackInvariant key tree tree0 [] →  stackInvariant key tree tree0 (tree ∷ [])
+    s-nil :  {tree tree0 : bt A} → stackInvariant key tree tree0 []
+    s-single :  {tree tree0 : bt A} →  stackInvariant key tree tree0 [] →  stackInvariant key tree0 tree0 (tree0 ∷ [])
     s-right :  {tree tree0 tree₁ : bt A} → {key₁ : ℕ } → {v1 : A } → {st : List (bt A)} 
         → key₁ < key  →  stackInvariant key (node key₁ v1 tree₁ tree) tree0 st → ¬ (st ≡ []) →  stackInvariant key tree tree0 (tree ∷ st)
     s-left :  {tree₁ tree0 tree : bt A} → {key₁ : ℕ } → {v1 : A } → {st : List (bt A)} 
@@ -149,9 +149,6 @@
 stackInvariantTest1 : stackInvariant 4 treeTest2 treeTest1 ( treeTest2 ∷ treeTest1 ∷ [] )
 stackInvariantTest1 = s-right (add< 2) (s-single s-nil) (λ ())
 
-si-nil :  {n : Level} {A : Set n} {key : ℕ} {tree tree0 : bt A} → (si : stackInvariant key tree tree0 []) → tree ≡ tree0
-si-nil s-nil = refl
-
 si-property1 :  {n : Level} {A : Set n} (key : ℕ) (tree tree0 : bt A) → (stack  : List (bt A)) → ¬ (stack ≡ [])  → stackInvariant key tree tree0 stack
    → stack-top stack ≡ just tree
 si-property1 key t t0 [] ne (s-nil ) = ⊥-elim ( ne refl )
@@ -183,15 +180,15 @@
 ti-left {_} {_} {.(node _ _ _ _)} {_} {key₁} {v1} (t-node x x₁ ti ti₁) = ti
 
 stackTreeInvariant : {n  : Level} {A : Set n} (key : ℕ) (sub tree : bt A) → (stack : List (bt A))
-   →  treeInvariant tree → stackInvariant key sub tree stack  → treeInvariant sub
-stackTreeInvariant {_} {A} key sub tree [] ti s-nil = ti
-stackTreeInvariant {_} {A} key sub tree (sub ∷ []) ti (s-single s-nil ) = ti
-stackTreeInvariant {_} {A} key sub tree (sub ∷ st) ti (s-right _ si _) = ti-right (si1 si) where
+   →  treeInvariant tree → stackInvariant key sub tree stack  → ¬ (stack ≡ [])  → treeInvariant sub
+stackTreeInvariant {_} {A} key sub tree [] ti s-nil ne = ⊥-elim ( ne refl )
+stackTreeInvariant {_} {A} key sub tree (sub ∷ []) ti (s-single s-nil ) _ = ti
+stackTreeInvariant {_} {A} key sub tree (sub ∷ st) ti (s-right _ si ne) _ = ti-right (si1 si) where
    si1 : {tree₁ : bt A} → {key₁ : ℕ} → {v1 : A} →  stackInvariant key (node key₁ v1 tree₁ sub ) tree st → treeInvariant  (node key₁ v1 tree₁ sub )
-   si1 {tree₁ }  {key₁ }  {v1 }  si = stackTreeInvariant  key (node key₁ v1 tree₁ sub ) tree st ti si
-stackTreeInvariant {_} {A} key sub tree (sub ∷ st) ti (s-left _ si _) = ti-left ( si2 si) where
+   si1 {tree₁ }  {key₁ }  {v1 }  si = stackTreeInvariant  key (node key₁ v1 tree₁ sub ) tree st ti si ne
+stackTreeInvariant {_} {A} key sub tree (sub ∷ st) ti (s-left _ si ne) _ = ti-left ( si2 si) where
    si2 : {tree₁ : bt A} → {key₁ : ℕ} → {v1 : A} →  stackInvariant key (node key₁ v1 sub tree₁ ) tree st → treeInvariant  (node key₁ v1 sub tree₁ )
-   si2 {tree₁ }  {key₁ }  {v1 }  si = stackTreeInvariant  key (node key₁ v1 sub tree₁ ) tree st ti si
+   si2 {tree₁ }  {key₁ }  {v1 }  si = stackTreeInvariant  key (node key₁ v1 sub tree₁ ) tree st ti si ne
 
 rt-property1 :  {n : Level} {A : Set n} (key : ℕ) (value : A) (tree tree1 : bt A ) → replacedTree key value tree tree1 → ¬ ( tree1 ≡ leaf )
 rt-property1 {n} {A} key value .leaf .(node key value leaf leaf) r-leaf ()
@@ -230,22 +227,20 @@
 open _∧_
 
 findP : {n m : Level} {A : Set n} {t : Set m} → (key : ℕ) → (tree tree0 : bt A ) → (stack : List (bt A))
-           →  treeInvariant tree ∧ stackInvariant key tree tree0 stack  
-           → (next : (tree1 tree0 : bt A) → (stack : List (bt A)) → treeInvariant tree1 ∧ stackInvariant key tree1 tree0 stack → bt-depth tree1 < bt-depth tree   → t )
-           → (exit : (tree1 tree0 : bt A) → (stack : List (bt A)) → treeInvariant tree1 ∧ stackInvariant key tree1 tree0 stack
+        →  treeInvariant tree ∧ ((¬ (stack ≡ []) → stackInvariant key tree tree0 stack ))
+        → (next : (tree1 tree0 : bt A) → (stack : List (bt A)) → treeInvariant tree1 ∧ ((¬ (stack ≡ []) → stackInvariant key tree1 tree0 stack)) → bt-depth tree1 < bt-depth tree   → t )
+        → (exit : (tree1 tree0 : bt A) → (stack : List (bt A)) → treeInvariant tree1 ∧ ((¬ (stack ≡ []) → stackInvariant key tree1 tree0 stack))
                  → (tree1 ≡ leaf ) ∨ ( node-key tree1 ≡ just key )  → t ) → t
 findP key leaf tree0 st Pre _ exit = exit leaf tree0 st Pre (case1 refl)
 findP key (node key₁ v1 tree tree₁) tree0 st Pre next exit with <-cmp key key₁
 findP key n tree0 st Pre _ exit | tri≈ ¬a refl ¬c = exit n tree0 st Pre (case2 refl)
 findP {n} {_} {A} key (node key₁ v1 tree tree₁) tree0 st Pre next _ | tri< a ¬b ¬c = next tree tree0 (tree ∷ st)
-       ⟪ treeLeftDown tree tree₁ (proj1 Pre)  , ? ⟫ depth-1< where
-   findP0 : key < key₁ → (st : List (bt A)) →  stackInvariant key (node key₁ v1 tree tree₁) tree0 st → Set n
-   findP0 a [] si = stackInvariant key tree0 tree0 (tree0 ∷ [])
-   findP0 a (x ∷ st) si = stackInvariant key tree tree0 (tree ∷ x ∷ st)
-   findP1 : (a : key < key₁ ) → (st : List (bt A)) →  (si : stackInvariant key (node key₁ v1 tree tree₁) tree0 st) → findP0 a st si
-   findP1 a (x ∷ st) si = s-left a si (λ ())
-   findP1 a [] s-nil = s-single  s-nil
-findP key n@(node key₁ v1 tree tree₁) tree0 st Pre next _ | tri> ¬a ¬b c = next tree₁ tree0 (tree₁ ∷ st) ⟪ treeRightDown tree tree₁ (proj1 Pre) , s-right c (proj2 Pre) {!!} ⟫ depth-2<
+       ⟪ treeLeftDown tree tree₁ (proj1 Pre)  , (λ ne → findP1 a st (proj2 Pre ))  ⟫ depth-1< where
+   findP1 : key < key₁ → (st : List (bt A)) →  ( ¬ (st ≡ [] ) → stackInvariant key (node key₁ v1 tree tree₁) tree0 st )  → stackInvariant key tree tree0 (tree ∷ st)
+   findP1 a [] si = {!!} -- s-single s-nil
+   findP1 a (x ∷ st) si  with si {!!}
+   ... | t = s-left a t {!!}
+findP key n@(node key₁ v1 tree tree₁) tree0 st Pre next _ | tri> ¬a ¬b c = next tree₁ tree0 (tree₁ ∷ st) ⟪ treeRightDown tree tree₁ (proj1 Pre) ,  {!!} ⟫ depth-2<
 
 replaceTree1 : {n  : Level} {A : Set n} {t t₁ : bt A } → ( k : ℕ ) → (v1 value : A ) →  treeInvariant (node k v1 t t₁) → treeInvariant (node k value t t₁)
 replaceTree1 k v1 value (t-single .k .v1) = t-single k value