Mercurial > hg > Gears > GearsAgda

changeset 621:6861bcb9c54d

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author Shinji KONO <kono@ie.u-ryukyu.ac.jp>
date Mon, 08 Nov 2021 16:36:26 +0900
parents fe8c2d82c05c
children a1849f24fa66
files hoareBinaryTree.agda
diffstat 1 files changed, 25 insertions(+), 27 deletions(-) [+]
line wrap: on
line diff
--- a/hoareBinaryTree.agda	Sun Nov 07 23:00:57 2021 +0900
+++ b/hoareBinaryTree.agda	Mon Nov 08 16:36:26 2021 +0900
@@ -98,15 +98,13 @@
 treeInvariantTest1  : treeInvariant (node 3 0 leaf (node 1 1 leaf (node 3 5 leaf leaf)))
 treeInvariantTest1  = {!!}
 
-data stackInvariant {n : Level} {A : Set n} : (tree0 : bt A) → (stack  : List (bt A)) → Set n where
-    s-nil : stackInvariant  leaf [] 
-    s-single : (tree : bt A) → stackInvariant tree (tree ∷ [] ) 
-    s-right  : (tree : bt A) → {key : ℕ } → {value : A } { left  : bt A} → stackInvariant (node key value left tree ) (tree ∷ node key value left tree  ∷ []) 
-    s-left   : (tree : bt A) → {key : ℕ } → {value : A } { right : bt A} → stackInvariant (node key value tree right) (tree ∷ node key value tree right  ∷ []) 
+data stackInvariant {n : Level} {A : Set n} : (tree tree0 : bt A) → (stack  : List (bt A)) → Set n where
+    s-nil : stackInvariant  leaf leaf [] 
+    s-single : (tree : bt A) → stackInvariant tree tree (tree ∷ [] ) 
     s-<      : (tree0 tree : bt A) → {key : ℕ } → {value : A } { left  : bt A} → {st : List (bt A)}
-         → stackInvariant tree0 (tree ∷ st )  → stackInvariant tree0 ((node key value left tree  ) ∷ tree ∷ st ) 
-    s->      : (tree0 tree : bt A) → {key : ℕ } → {value : A } { right : bt A} →  {st : List (bt A)}
-         → stackInvariant tree0 (tree ∷ st )  → stackInvariant tree0 ((node key value tree right ) ∷ tree ∷ st ) 
+         → stackInvariant (node key value left tree ) tree0 (node key value left tree ∷ st )  → stackInvariant tree tree0 (tree  ∷ node key value left tree ∷ st ) 
+    s->      : (tree0 tree : bt A) → {key : ℕ } → {value : A } { right  : bt A} → {st : List (bt A)}
+         → stackInvariant (node key value tree right ) tree0 (node key value tree right ∷ st )  → stackInvariant tree tree0 (tree  ∷ node key value tree right ∷ 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)
@@ -117,9 +115,9 @@
           → k < key → ( replacedTree key value t1 t2 →  replacedTree key value (node k v t1 t) (node k v t2 t) )
 
 findP : {n m : Level} {A : Set n} {t : Set m} → (key : ℕ) → (tree tree0 : bt A ) → (stack : List (bt A))
-           →  treeInvariant tree ∧ stackInvariant tree0 stack  
-           → (next : (tree1 tree0 : bt A) → (stack : List (bt A)) → treeInvariant tree1 ∧ stackInvariant tree0 stack → bt-depth tree1 < bt-depth tree   → t )
-           → (exit : (tree1 tree0 : bt A) → (stack : List (bt A)) → treeInvariant tree1 ∧ stackInvariant tree0 stack → t ) → t
+           →  treeInvariant tree ∧ stackInvariant tree tree0 stack  
+           → (next : (tree1 tree0 : bt A) → (stack : List (bt A)) → treeInvariant tree1 ∧ stackInvariant tree1 tree0 stack → bt-depth tree1 < bt-depth tree   → t )
+           → (exit : (tree1 tree0 : bt A) → (stack : List (bt A)) → treeInvariant tree1 ∧ stackInvariant tree1 tree0 stack → t ) → t
 findP key leaf tree0 st Pre _ exit = exit leaf tree0 st {!!}
 findP key (node key₁ v tree tree₁) tree0 st Pre next exit with <-cmp key key₁
 findP key n tree0 st Pre _ exit | tri≈ ¬a b ¬c = exit n tree0 st {!!}
@@ -132,8 +130,8 @@
 replaceNodeP k v (node key value t t₁) P next = next (node k v t t₁) {!!} {!!}
 
 replaceP : {n m : Level} {A : Set n} {t : Set m}
-     → (key : ℕ) → (value : A) → (tree repl : bt A) → (stack : List (bt A)) → treeInvariant tree ∧ stackInvariant tree stack ∧ replacedTree key value tree repl
-     → (next : ℕ → A → (tree1 repl : bt A) → (stack : List (bt A)) → treeInvariant tree1 ∧ stackInvariant tree1 stack ∧ replacedTree key value tree1 repl → bt-depth tree1 < bt-depth tree   → t )
+     → (key : ℕ) → (value : A) → (tree repl : bt A) → (stack : List (bt A)) → treeInvariant tree ∧ stackInvariant repl tree stack ∧ replacedTree key value tree repl
+     → (next : ℕ → A → (tree1 repl : bt A) → (stack : List (bt A)) → treeInvariant tree1 ∧ stackInvariant repl tree1 stack ∧ replacedTree key value tree1 repl → bt-depth tree1 < bt-depth tree   → t )
      → (exit : (tree1 repl : bt A) → treeInvariant tree1 ∧ replacedTree key value tree1 repl → t) → t
 replaceP key value tree repl [] Pre next exit = exit tree repl {!!} 
 replaceP key value tree repl (leaf ∷ st) Pre next exit = next key value tree {!!} st {!!} {!!}
@@ -177,14 +175,14 @@
 insertTreeP : {n m : Level} {A : Set n} {t : Set m} → (tree : bt A) → (key : ℕ) → (value : A) → treeInvariant tree
      → (exit : (tree repl : bt A) → treeInvariant tree ∧ replacedTree key value tree repl → t ) → t
 insertTreeP {n} {m} {A} {t} tree key value P exit =
-   TerminatingLoopS (bt A ∧ List (bt A) ) {λ p → treeInvariant (proj1 p) ∧ stackInvariant tree (proj2 p) } (λ p → bt-depth (proj1 p)) ⟪ tree , [] ⟫  ⟪ P , {!!}  ⟫
+   TerminatingLoopS (bt A ∧ List (bt A) ) {λ p → treeInvariant (proj1 p) ∧ stackInvariant (proj1 p) tree (proj2 p) } (λ p → bt-depth (proj1 p)) ⟪ tree , [] ⟫  ⟪ P , {!!}  ⟫
        $ λ p P loop → findP key (proj1 p)  tree (proj2 p) {!!} (λ t _ s P1 lt → loop ⟪ t ,  s  ⟫ {!!} lt )
        $ λ t _ s P → replaceNodeP key value t (proj1 P)
        $ λ t1 P1 R → TerminatingLoopS (List (bt A) ∧ (bt A ∧ bt A ))
-            {λ p → treeInvariant (proj1 (proj2 p)) ∧ stackInvariant (proj1 (proj2 p)) (proj1 p)  ∧ replacedTree key value (proj1 (proj2 p)) (proj2 (proj2 p)) }
+            {λ p → treeInvariant (proj1 (proj2 p)) ∧ stackInvariant (proj1 (proj2 p)) tree (proj1 p)  ∧ replacedTree key value (proj1 (proj2 p)) (proj2 (proj2 p)) }
                (λ p → bt-depth (proj1 (proj2 p))) ⟪ s , ⟪ t , t1 ⟫ ⟫　⟪ proj1 P , ⟪ {!!}  , R ⟫ ⟫
-       $  λ p P1 loop → replaceP key value (proj1 (proj2 p)) (proj2 (proj2 p)) (proj1 p) P1
-            (λ key value tree1 repl1 stack P2 lt → loop ⟪ stack , ⟪ tree1  , repl1  ⟫ ⟫ P2 lt )  exit 
+       $  λ p P1 loop → replaceP key value (proj1 (proj2 p)) (proj2 (proj2 p)) (proj1 p) {!!}
+            (λ key value tree1 repl1 stack P2 lt → loop ⟪ stack , ⟪ tree1  , repl1  ⟫ ⟫ {!!} lt )  exit 
 
 top-value : {n : Level} {A : Set n} → (tree : bt A) →  Maybe A 
 top-value leaf = nothing
@@ -197,24 +195,24 @@
    field
      tree0 : bt A
      ti : treeInvariant tree
-     si : stackInvariant tree0 stack
+     si : stackInvariant tree tree0 stack
    
 findPP : {n m : Level} {A : Set n} {t : Set m}
            → (key : ℕ) → (tree : bt A ) → (stack : List (bt A))
-           → (Pre :   bt A → List (bt A) →  findPR tree stack  )
+           → (Pre :  findPR tree stack  )
            → (next : (tree1 : bt A) → (stack1 : List (bt A)) → findPR tree1 stack1  →  bt-depth tree1 < bt-depth tree   → t )
            → (exit : (tree1 : bt A) → (stack1 : List (bt A)) → findPR tree1 stack1  → t) → t
-findPP key leaf st Pre next exit = exit leaf st (Pre leaf st ) 
+findPP key leaf st Pre next exit = exit leaf st Pre  
 findPP key (node key₁ v tree tree₁) st Pre next exit with <-cmp key key₁
-findPP key n st P next exit | tri≈ ¬a b ¬c = exit n st (P n st) 
+findPP key n st P next exit | tri≈ ¬a b ¬c = exit n st P 
 findPP {_} {_} {A} key n@(node key₁ v tree tree₁) st Pre next exit | tri< a ¬b ¬c =
-          next tree (n ∷ st) (record {ti = findPP0 tree tree₁ (findPR.ti (Pre n st)) ; si = findPP2 st (findPR.si (Pre n st))} ) findPP1 where 
-    tree0 =  findPR.tree0 (Pre n st)
+          next tree (n ∷ st) (record {ti = findPP0 tree tree₁ (findPR.ti Pre ) ; si = findPP2 st (findPR.si Pre)} ) findPP1 where 
+    tree0 =  findPR.tree0 Pre 
     findPP0 : (tree tree₁ : bt A) → treeInvariant ( node key₁ v tree tree₁ ) → treeInvariant tree
     findPP0 leaf t x = {!!}
     findPP0 (node key value tree tree₁) leaf x = proj1 {!!}
     findPP0 (node key value tree tree₁) (node key₁ value₁ t t₁) x = proj1 {!!}
-    findPP2 : (st : List (bt A)) → stackInvariant tree0 st →  stackInvariant tree0 (node key₁ v tree tree₁ ∷ st)
+    findPP2 : (st : List (bt A)) → stackInvariant {!!} tree0 st →  stackInvariant {!!} tree0 (node key₁ v tree tree₁ ∷ st)
     findPP2 [] = {!!}
     findPP2 (leaf ∷ st) x = {!!}
     findPP2 (node key value leaf leaf ∷ st) x = {!!}
@@ -234,10 +232,10 @@
        $ λ p P loop → findPP key (proj1 p) (proj2 p) {!!} (λ t s P1 lt → loop ⟪ t ,  s  ⟫ {!!} lt )
        $ λ t s P → replaceNodeP key value t {!!}
        $ λ t1 P1 R → TerminatingLoopS (List (bt A) ∧ (bt A ∧ bt A ))
-            {λ p → treeInvariant (proj1 (proj2 p)) ∧ stackInvariant (proj1 (proj2 p)) (proj1 p)  ∧ replacedTree key value (proj1 (proj2 p)) (proj2 (proj2 p)) }
+            {λ p → treeInvariant (proj1 (proj2 p)) ∧ stackInvariant (proj1 (proj2 p)) tree (proj1 p)  ∧ replacedTree key value (proj1 (proj2 p)) (proj2 (proj2 p)) }
                (λ p → bt-depth (proj1 (proj2 p))) ⟪ s , ⟪ t , t1 ⟫ ⟫　⟪ {!!} , ⟪ {!!}  , R ⟫ ⟫
-       $  λ p P1 loop → replaceP key value (proj1 (proj2 p)) (proj2 (proj2 p)) (proj1 p) P1
-            (λ key value tree1 repl1 stack P2 lt → loop ⟪ stack , ⟪ tree1  , repl1  ⟫ ⟫ P2 lt )  exit 
+       $  λ p P1 loop → replaceP key value (proj1 (proj2 p)) (proj2 (proj2 p)) (proj1 p) {!!}
+            (λ key value tree1 repl1 stack P2 lt → loop ⟪ stack , ⟪ tree1  , repl1  ⟫ ⟫ {!!} lt )  exit 
 
 -- findP key tree stack = findPP key tree stack {findPR} → record { ti = tree-invariant tree ; si stack-invariant tree stack } →