Mercurial > hg > Gears > GearsAgda

changeset 702:5959f7aa0960

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author Shinji KONO <kono@ie.u-ryukyu.ac.jp>
date Sun, 05 Dec 2021 11:46:20 +0900
parents 690da797cf40
children 23e0b9df7896
files hoareBinaryTree.agda
diffstat 1 files changed, 35 insertions(+), 16 deletions(-) [+]
line wrap: on
line diff
--- a/hoareBinaryTree.agda	Sun Dec 05 10:40:44 2021 +0900
+++ b/hoareBinaryTree.agda	Sun Dec 05 11:46:20 2021 +0900
@@ -585,9 +585,6 @@
 top-value leaf = nothing
 top-value (node key value tree tree₁) = just value
 
-insertTreeSpec0 : {n : Level} {A : Set n} → (tree : bt A) → (value : A) → top-value tree ≡ just value → ⊤
-insertTreeSpec0 _ _ _ = tt
-
 record findPR {n : Level} {A : Set n} (key : ℕ) (tree : bt A ) (stack : List (bt A)) (C : bt A → List (bt A) → Set n) : Set n where
    field
      tree0 : bt A
@@ -595,29 +592,36 @@
      ti : treeInvariant tree
      si : stackInvariant key tree tree0 stack
      ci : C tree stack     -- data continuation
+
+record findExt {n : Level} {A : Set n} (C : bt A → List (bt A) → Set n) : Set (Level.suc n) where
+   field
+      c1 : {key key₁ : ℕ} {tree tree₁ : bt A } {st : List (bt A)} {v1 : A}
+        → findPR key (node key₁ v1 tree tree₁) st C → key < key₁  → C tree (tree ∷ st)
+      c2 : {key key₁ : ℕ} {tree tree₁ : bt A } {st : List (bt A)} {v1 : A}
+        → findPR key (node key₁ v1 tree tree₁) st C → key > key₁  → C tree₁ (tree₁ ∷ st)
    
 findPP : {n m : Level} {A : Set n} {t : Set m} → (key : ℕ) → (tree : bt A ) → (stack : List (bt A))
-           →  findPR key tree stack (λ _ _ → Lift n ⊤)
-           → (next : (tree1 : bt A) → (stack : List (bt A)) → findPR key tree1 stack (λ _ _ → Lift n ⊤) → bt-depth tree1 < bt-depth tree   → t )
-           → (exit : (tree1 : bt A) → (stack : List (bt A)) → findPR key tree1 stack (λ _ _ → Lift n ⊤)
+           →  {C : bt A → List (bt A) → Set n } → findPR key tree stack C  → findExt C
+           → (next : (tree1 : bt A) → (stack : List (bt A)) → findPR key tree1 stack C → bt-depth tree1 < bt-depth tree   → t )
+           → (exit : (tree1 : bt A) → (stack : List (bt A)) → findPR key tree1 stack C
                  → (tree1 ≡ leaf ) ∨ ( node-key tree1 ≡ just key )  → t ) → t
-findPP key leaf st Pre _ exit = exit leaf st Pre (case1 refl)
-findPP key (node key₁ v1 tree tree₁) st Pre next exit with <-cmp key key₁
-findPP key n st Pre _ exit | tri≈ ¬a refl ¬c = exit n st Pre (case2 refl)
-findPP {n} {_} {A} key (node key₁ v1 tree tree₁) st  Pre next _ | tri< a ¬b ¬c = next tree (tree ∷ st)
-       record { tree0 = findPR.tree0 Pre ; ti0 = findPR.ti0 Pre ; ti = treeLeftDown tree tree₁ (findPR.ti Pre)  ; si =  findP1 a st (findPR.si Pre) ; ci = lift tt } depth-1< where
+findPP key leaf st Pre _ _ exit = exit leaf st Pre (case1 refl)
+findPP key (node key₁ v1 tree tree₁) st Pre _ next exit with <-cmp key key₁
+findPP key n st Pre _ _ exit | tri≈ ¬a refl ¬c = exit n st Pre (case2 refl)
+findPP {n} {_} {A} key (node key₁ v1 tree tree₁) st  Pre e next _ | tri< a ¬b ¬c = next tree (tree ∷ st)
+       record { tree0 = findPR.tree0 Pre ; ti0 = findPR.ti0 Pre ; ti = treeLeftDown tree tree₁ (findPR.ti Pre)  ; si =  findP1 a st (findPR.si Pre) ; ci = findExt.c1 e Pre a } depth-1< where -- findPR key (node key₁ v1 tree tree₁) st C → key < key₁  → C tree (tree ∷ st)
    findP1 : key < key₁ → (st : List (bt A)) →  stackInvariant key (node key₁ v1 tree tree₁)
          (findPR.tree0 Pre) st → stackInvariant key tree (findPR.tree0 Pre) (tree ∷ st)
    findP1 a (x ∷ st) si = s-left a si
-findPP key n@(node key₁ v1 tree tree₁) st Pre next _ | tri> ¬a ¬b c = next tree₁ (tree₁ ∷ st)
-       record { tree0 = findPR.tree0 Pre ; ti0 = findPR.ti0 Pre ; ti = treeRightDown tree tree₁ (findPR.ti Pre) ; si =  s-right c (findPR.si Pre) ; ci = lift tt }  depth-2<
+findPP key n@(node key₁ v1 tree tree₁) st Pre e next _ | tri> ¬a ¬b c = next tree₁ (tree₁ ∷ st)
+       record { tree0 = findPR.tree0 Pre ; ti0 = findPR.ti0 Pre ; ti = treeRightDown tree tree₁ (findPR.ti Pre) ; si =  s-right c (findPR.si Pre) ; ci = findExt.c2 e Pre c }  depth-2<
 
 insertTreePP : {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
 insertTreePP {n} {m} {A} {t} tree key value P0 exit =
    TerminatingLoopS (bt A ∧ List (bt A) ) {λ p → findPR key (proj1 p) (proj2 p) (λ _ _ → Lift n ⊤) } (λ p → bt-depth (proj1 p)) ⟪ tree , tree ∷ [] ⟫
            record { tree0 = tree ; ti = P0 ; ti0 = P0 ;si = s-single ; ci = lift tt }
-       $ λ p P loop → findPP key (proj1 p)  (proj2 p) P (λ t s P1 lt → loop ⟪ t ,  s  ⟫ P1 lt ) 
+       $ λ p P loop → findPP key (proj1 p)  (proj2 p) P record { c1 = λ _ _ → lift tt ; c2 =  λ _ _ → lift tt } (λ t s P1 lt → loop ⟪ t ,  s  ⟫ P1 lt ) 
        $ λ t s P C → replaceNodeP key value t C (findPR.ti P)
        $ λ t1 P1 R → TerminatingLoopS (List (bt A) ∧ bt A ∧ bt A )
             {λ p → replacePR key value  (proj1 (proj2 p)) (proj2 (proj2 p)) (proj1 p)  (λ _ _ _ → Lift n ⊤ ) }
@@ -659,13 +663,28 @@
    findP2 | r-right x ri | node key value t t₁ | record { eq = refl } = record { tree1 = t₁ ; ci =  ri }
    findP2 | r-leaf | leaf | record { eq = eq } = ⊥-elim ( nat-≤> c ≤-refl )
 
+findPPC1 : {n m : Level} {A : Set n} {t : Set m} → (key : ℕ) → (value : A) → (tree : bt A ) → (stack : List (bt A))
+   →  findPR key tree stack (findPC key value )
+   → (next : (tree1 : bt A) → (stack : List (bt A)) → findPR key tree1 stack (findPC key value ) → bt-depth tree1 < bt-depth tree   → t )
+   → (exit : (tree1 : bt A) → (stack : List (bt A)) → findPR key tree1 stack (findPC key value )
+                 → (tree1 ≡ leaf ) ∨ ( node-key tree1 ≡ just key )  → t ) → t
+findPPC1 {n} {_} {A} key value tree stack Pr next exit = findPP key tree stack Pr findext next exit where
+   findext01 : {key₁ : ℕ} {key₂ : ℕ} {tree₁ : bt A} {tree₂ : bt A} {st : List (bt A)} {v1 : A} →
+    findPR key₁ (node key₂ v1 tree₁ tree₂) st (findPC key value) → key₁ < key₂ → findPC key value tree₁ (tree₁ ∷ st)
+   findext01 = {!!}
+   findext : findExt (findPC key value)
+   findext = record { c1 = findext01 ; c2 = {!!} }
+
+insertTreeSpec0 : {n : Level} {A : Set n} → (tree : bt A) → (value : A) → top-value tree ≡ just value → ⊤
+insertTreeSpec0 _ _ _ = tt
+
 containsTree : {n : Level} {A : Set n} → (tree tree1 : bt A) → (key : ℕ) → (value : A) → treeInvariant tree1 → replacedTree key value tree1 tree  → ⊤
 containsTree {n}  {A}  tree tree1 key value P RT =
    TerminatingLoopS (bt A ∧ List (bt A) )
      {λ p → findPR key (proj1 p) (proj2 p) (findPC key value ) } (λ p → bt-depth (proj1 p)) 
               ⟪ tree , tree ∷ []  ⟫ record { tree0 = tree ; ti0 = RTtoTI0 _ _ _ _ P RT ; ti = RTtoTI0 _ _ _ _ P RT ; si = s-single
                     ; ci = record { tree1 = tree1 ; ci = RT } }
-       $ λ p P loop → findPPC key value (proj1 p) (proj2 p) P (λ t s P1 lt → loop ⟪ t , s ⟫ P1 lt )  
+       $ λ p P loop → findPPC1 key value (proj1 p) (proj2 p) P (λ t s P1 lt → loop ⟪ t , s ⟫ P1 lt )  
        $ λ t1 s1 P2 found? → insertTreeSpec0 t1 value (lemma6 t1 s1 found? P2) where
            lemma6 : (t1 : bt A) (s1 : List (bt A)) (found? : (t1 ≡ leaf) ∨ (node-key t1 ≡ just key)) (P2 : findPR key t1 s1 (findPC key value )) → top-value t1 ≡ just value
            lemma6 t1 s1 found? P2 = lemma7 t1 s1 (findPR.tree0 P2) ( findPC.tree1  (findPR.ci P2)) (findPC.ci  (findPR.ci P2)) (findPR.si P2) found? where
@@ -686,6 +705,6 @@
 containsTree1 : {n : Level} {A : Set n}  → (tree : bt A) → (key : ℕ) → (value : A) → treeInvariant tree → ⊤
 containsTree1 {n} {A} tree key value ti =
        insertTreeP tree key value ti
-     $ λ tree0 tree1 P → containsTree tree1 tree0 key value (RTtoTI1 _ _ _ _ (proj1 P) (proj2 P) ) (proj2 P) -- (proj1 P) (proj2 P)
+     $ λ tree0 tree1 P → containsTree tree1 tree0 key value (RTtoTI1 _ _ _ _ (proj1 P) (proj2 P) ) (proj2 P)