Mercurial > hg > Gears > GearsAgda

changeset 653:a8e7d1f20ce6

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author Shinji KONO <kono@ie.u-ryukyu.ac.jp>
date Sun, 21 Nov 2021 09:22:59 +0900
parents 8c7446829b99
children 48c6e6961ea5
files hoareBinaryTree.agda
diffstat 1 files changed, 19 insertions(+), 17 deletions(-) [+]
line wrap: on
line diff
--- a/hoareBinaryTree.agda	Sun Nov 21 07:23:08 2021 +0900
+++ b/hoareBinaryTree.agda	Sun Nov 21 09:22:59 2021 +0900
@@ -103,14 +103,14 @@
        → 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-left0 :  {tree tree₁ : bt A} → {key₁ : ℕ } → {v1 : A } 
+        →  key < key₁  → stackInvariant key (node key₁ v1 tree tree₁) (node key₁ v1 tree tree₁) (node key₁ v1 tree tree₁ ∷ [])
     s-right0 :  {tree₁ tree : bt A} → {key₁ : ℕ } → {v1 : A } 
-        →  key₁ > key  → stackInvariant key (node key₁ v1 tree tree₁) (node key₁ v1 tree tree₁) (node key₁ v1 tree tree₁ ∷ [])
-    s-left0 :  {tree tree₁ : bt A} → {key₁ : ℕ } → {v1 : A } 
-        →  key > key₁  → stackInvariant key (node key₁ v1 tree tree₁) (node key₁ v1 tree tree₁) (node key₁ v1 tree tree₁ ∷ [])
-    s-right :  {tree₁ tree0 tree : bt A} → {key₁ : ℕ } → {v1 : A } → {st : List (bt A)} 
-        → key₁ > key  →  stackInvariant key (node key₁ v1 tree tree₁) tree0 st →  stackInvariant key tree₁ tree0 (tree₁ ∷ st)
-    s-left :  {tree tree0 tree₁ : bt A} → {key₁ : ℕ } → {v1 : A } → {st : List (bt A)} 
-        → key  > key₁ →  stackInvariant key (node key₁ v1 tree₁ tree) tree0 st →  stackInvariant key tree tree0 (tree ∷ st)
+        →  key₁ < key  → stackInvariant key (node key₁ v1 tree tree₁) (node key₁ v1 tree tree₁) (node key₁ v1 tree tree₁ ∷ [])
+    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 →  stackInvariant key tree tree0 (tree ∷ st)
+    s-left :  {tree₁ tree0 tree : bt A} → {key₁ : ℕ } → {v1 : A } → {st : List (bt A)} 
+        → key  < key₁ →  stackInvariant key (node key₁ v1 tree₁ tree) tree0 st →  stackInvariant key tree₁ tree0 (tree₁ ∷ st)
 
 data replacedTree  {n : Level} {A : Set n} (key : ℕ) (value : A)  : (tree tree1 : bt A ) → Set n where
     r-leaf : replacedTree key value leaf (node key value leaf leaf)
@@ -155,7 +155,7 @@
 stack-last (x ∷ s) = stack-last s
 
 stackInvariantTest1 : stackInvariant 4 treeTest2 treeTest1 ( treeTest2 ∷ treeTest1 ∷ [] )
-stackInvariantTest1 = s-left (add< 2) (s-left0 (add< 2))
+stackInvariantTest1 = s-right (add< 2) (s-right0 (add< 2))
 
 si-property1 :  {n : Level} {A : Set n} (key : ℕ) (tree tree0 : bt A) → (stack  : List (bt A)) → stackInvariant key tree tree0 stack
    → stack-top stack ≡ just tree
@@ -167,7 +167,7 @@
 si-property-last :  {n : Level} {A : Set n}  (key : ℕ) (tree tree0 : bt A) → (stack  : List (bt A)) → stackInvariant key tree tree0 stack
    → stack-last stack ≡ just tree0
 si-property-last key t t0 (.t ∷ []) (s-right0 _ ) = refl
-si-property-last key t t0 (.t ∷ []) (s-left0 _ ) = {!!}
+si-property-last key t t0 (.t ∷ []) (s-left0 _ ) = refl
 si-property-last key t t0 (.t ∷ x ∷ st) (s-right _ si) with  si-property1 key _ _ (x ∷ st) si
 ... | refl = si-property-last key x t0 (x ∷ st) si
 si-property-last key t t0 (.t ∷ x ∷ st) (s-left _ si) with  si-property1 key _ _ (x ∷ st) si
@@ -185,14 +185,16 @@
 ti-left {_} {_} {_} {_} {key₁} {v1} (t-left x ti) = ti
 ti-left {_} {_} {.(node _ _ _ _)} {_} {key₁} {v1} (t-node x x₁ ti ti₁) = ti
 
-stackTreeInvariant : {n  : Level} {A : Set n} (key : ℕ) (repl tree : bt A) → (stack : List (bt A))
-   →  treeInvariant tree → stackInvariant key repl tree stack  → treeInvariant repl
-stackTreeInvariant {_} {A} key repl tree (repl ∷ st) ti (s-right _ si) = ti-right (si1 {!!}) where
-   si1 : {tree₁ : bt A} → {key₁ : ℕ} → {v1 : A} →  stackInvariant key (node key₁ v1 tree₁ repl) tree st → treeInvariant  (node key₁ v1 tree₁ repl)
-   si1 {tree₁ }  {key₁ }  {v1 }  si = stackTreeInvariant  key (node key₁ v1 tree₁ repl) tree st ti si
-stackTreeInvariant {_} {A} key repl tree (repl ∷ st) ti (s-left _ si) = ti-left ( si2 {!!} ) where
-   si2 : {tree₁ : bt A} → {key₁ : ℕ} → {v1 : A} →  stackInvariant key (node key₁ v1 repl tree₁ ) tree st → treeInvariant  (node key₁ v1 repl tree₁ )
-   si2 {tree₁ }  {key₁ }  {v1 }  si = stackTreeInvariant  key (node key₁ v1 repl tree₁ ) tree st ti si
+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 (sub ∷ []) ti (s-right0 _ ) = ti
+stackTreeInvariant {_} {A} key sub tree (sub ∷ []) ti (s-left0 _ ) = ti
+stackTreeInvariant {_} {A} key sub tree (sub ∷ st) ti (s-right _ si) = 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
+   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
 
 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 ()