# HG changeset patch # User Shinji KONO # Date 1638497659 -32400 # Node ID 578f29a76857d8d59068f6f723c0eb188e0b5748 # Parent ce6cd128595d77850fa2dcc560a9e5b1f7e4a468 ... diff -r ce6cd128595d -r 578f29a76857 hoareBinaryTree.agda --- a/hoareBinaryTree.agda Fri Dec 03 08:14:32 2021 +0900 +++ b/hoareBinaryTree.agda Fri Dec 03 11:14:19 2021 +0900 @@ -88,7 +88,7 @@ insertTest1 = insertTree leaf 1 1 (λ x → x ) insertTest2 = insertTree insertTest1 2 1 (λ x → x ) insertTest3 = insertTree insertTest2 3 2 (λ x → x ) -insertTest4 = insertTree insertTest3 2 2 (λ x → x ) +insertTest4 = insertTree insertTest3 2 2 (λ x → x ) -- this is wrong open import Data.Unit hiding ( _≟_ ; _≤?_ ; _≤_) @@ -534,21 +534,22 @@ RTtoTI1 = {!!} 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 + → (exit : (tree repl : bt A) → treeInvariant repl ∧ replacedTree key value tree repl → t ) → t insertTreeP {n} {m} {A} {t} tree key value P0 exit = TerminatingLoopS (bt A ∧ List (bt A) ) {λ p → treeInvariant (proj1 p) ∧ stackInvariant key (proj1 p) tree (proj2 p) } (λ p → bt-depth (proj1 p)) ⟪ tree , tree ∷ [] ⟫ ⟪ P0 , s-single ⟫ - $ λ p P loop → findP key (proj1 p) tree (proj2 p) P (λ t s P1 lt → loop ⟪ t , s ⟫ P1 lt ) -- treeInvariant t ∧ stackInvariant key t tree s + $ λ p P loop → findP key (proj1 p) tree (proj2 p) P (λ t s P1 lt → loop ⟪ t , s ⟫ P1 lt ) $ λ t s P C → replaceNodeP key value t C (proj1 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 ⊤ ) } - (λ p → length (proj1 p)) ⟪ s , ⟪ t , t1 ⟫ ⟫ record { tree0 = tree ; ti = P0 ; si = proj2 P ; ri = R ; ci = lift tt } -- replacedTree key value (child-replaced key t) t1 + (λ p → length (proj1 p)) ⟪ s , ⟪ t , t1 ⟫ ⟫ record { tree0 = tree ; ti = P0 ; si = proj2 P ; ri = R ; ci = lift tt } $ λ p P1 loop → replaceP key value (proj2 (proj2 p)) (proj1 p) P1 - (λ key value {tree1} repl1 stack P2 lt → loop ⟪ stack , ⟪ tree1 , repl1 ⟫ ⟫ P2 lt ) exit + (λ key value {tree1} repl1 stack P2 lt → loop ⟪ stack , ⟪ tree1 , repl1 ⟫ ⟫ P2 lt ) + $ λ tree repl P → exit tree repl ⟪ RTtoTI0 _ _ _ _ (proj1 P) (proj2 P) , proj2 P ⟫ -insertTestP1 = insertTreeP leaf 1 1 _ (λ _ x _ → x ) -insertTestP2 = insertTreeP insertTestP1 2 1 _ (λ _ x _ → x ) -insertTestP3 = insertTreeP insertTestP2 3 2 _ (λ _ x _ → x ) -insertTestP4 = insertTreeP insertTestP3 2 2 _ (λ _ x _ → x ) +insertTestP1 = insertTreeP leaf 1 1 t-leaf + $ λ _ x P → insertTreeP x 2 1 (proj1 P) + $ λ _ x P → insertTreeP x 3 2 (proj1 P) + $ λ _ x P → insertTreeP x 2 2 (proj1 P) (λ _ x _ → x ) top-value : {n : Level} {A : Set n} → (tree : bt A) → Maybe A top-value leaf = nothing @@ -560,6 +561,7 @@ 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 + ti0 : treeInvariant tree0 ti : treeInvariant tree si : stackInvariant key tree tree0 stack ci : C tree stack -- data continuation @@ -573,23 +575,23 @@ 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 ; ti = treeLeftDown tree tree₁ (findPR.ti Pre) ; si = findP1 a st (findPR.si Pre) ; ci = lift tt } depth-1< where + 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 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 ; ti = treeRightDown tree tree₁ (findPR.ti Pre) ; si = s-right c (findPR.si Pre) ; ci = lift tt } depth-2< + 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< 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 ; si = s-single ; ci = lift tt } + 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 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 ⊤ ) } - (λ p → length (proj1 p)) ⟪ s , ⟪ t , t1 ⟫ ⟫ record { tree0 = tree ; ti = P0 ; si = {!!} ; ri = R ; ci = lift tt } + (λ p → length (proj1 p)) ⟪ s , ⟪ t , t1 ⟫ ⟫ record { tree0 = findPR.tree0 P ; ti = findPR.ti0 P ; si = findPR.si P ; ri = R ; ci = lift tt } $ λ p P1 loop → replaceP key value (proj2 (proj2 p)) (proj1 p) P1 (λ key value {tree1} repl1 stack P2 lt → loop ⟪ stack , ⟪ tree1 , repl1 ⟫ ⟫ P2 lt ) exit @@ -608,18 +610,20 @@ findPPC key (node key₁ v1 tree tree₁) st Pre next exit with <-cmp key key₁ findPPC key n st Pre _ exit | tri≈ ¬a refl ¬c = exit n st Pre (case2 refl) findPPC {n} {_} {A} key (node key₁ v1 tree tree₁) st Pre next _ | tri< a ¬b ¬c = next tree (tree ∷ st) - record { tree0 = findPR.tree0 Pre ; ti = treeLeftDown tree tree₁ (findPR.ti Pre) ; si = findP1 a st (findPR.si Pre) ; ci = {!!} } depth-1< where + record { tree0 = findPR.tree0 Pre ; ti0 = findPR.ti0 Pre ; ti = treeLeftDown tree tree₁ (findPR.ti Pre) ; si = findP1 a st (findPR.si Pre) + ; ci = {!!} } depth-1< where 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 findPPC key n@(node key₁ v1 tree tree₁) st Pre next _ | tri> ¬a ¬b c = next tree₁ (tree₁ ∷ st) - record { tree0 = findPR.tree0 Pre ; ti = treeRightDown tree tree₁ (findPR.ti Pre) ; si = s-right c (findPR.si Pre) ; ci = {!!} } depth-2< + record { tree0 = findPR.tree0 Pre ; ti0 = findPR.ti0 Pre ; ti = treeRightDown tree tree₁ (findPR.ti Pre) ; si = s-right c (findPR.si Pre) + ; ci = {!!} } depth-2< containsTree : {n m : Level} {A : Set n} {t : Set m} → (tree tree1 : bt A) → (key : ℕ) → (value : A) → treeInvariant tree1 → replacedTree key value tree1 tree → ⊤ containsTree {n} {m} {A} {t} tree tree1 key value P RT = TerminatingLoopS (bt A ∧ List (bt A) ) {λ p → findPR key (proj1 p) (proj2 p) (findPC key ) } (λ p → bt-depth (proj1 p)) -- findPR key tree1 [] (findPC key value) - ⟪ tree1 , [] ⟫ record { tree0 = tree ; ti = {!!} ; si = {!!} ; ci = record { tree1 = tree ; ci = RT } } + ⟪ tree1 , [] ⟫ record { tree0 = tree ; ti0 = {!!} ; ti = {!!} ; si = {!!} ; ci = record { tree1 = tree ; ci = RT } } $ λ p P loop → findPPC key (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 )) → top-value t1 ≡ just value