Mercurial > hg > Gears > GearsAgda
view stackTest.agda @ 842:ee2dd920e414
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author | Shinji KONO <kono@ie.u-ryukyu.ac.jp> |
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date | Thu, 21 Mar 2024 15:25:37 +0900 |
parents | 0b791ae19543 |
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open import Level renaming (suc to succ ; zero to Zero ) module stackTest where open import stack open import Relation.Binary.PropositionalEquality open import Relation.Binary.Core open import Data.Nat open import Function open SingleLinkedStack open Stack ---- -- -- proof of properties ( concrete cases ) -- test01 : {n : Level } {a : Set n} -> SingleLinkedStack a -> Maybe a -> Bool {n} test01 stack _ with (top stack) ... | (Just _) = True ... | Nothing = False test02 : {n : Level } {a : Set n} -> SingleLinkedStack a -> Bool test02 stack = popSingleLinkedStack stack test01 test03 : {n : Level } {a : Set n} -> a -> Bool test03 v = pushSingleLinkedStack emptySingleLinkedStack v test02 -- after a push and a pop, the stack is empty lemma : {n : Level} {A : Set n} {a : A} -> test03 a ≡ False lemma = refl testStack01 : {n m : Level } {a : Set n} -> a -> Bool {m} testStack01 v = pushStack createSingleLinkedStack v ( \s -> popStack s (\s1 d1 -> True)) -- after push 1 and 2, pop2 get 1 and 2 testStack02 : {m : Level } -> ( Stack ℕ (SingleLinkedStack ℕ) -> Bool {m} ) -> Bool {m} testStack02 cs = pushStack createSingleLinkedStack 1 ( \s -> pushStack s 2 cs) testStack031 : (d1 d2 : ℕ ) -> Bool {Zero} testStack031 2 1 = True testStack031 _ _ = False testStack032 : (d1 d2 : Maybe ℕ) -> Bool {Zero} testStack032 (Just d1) (Just d2) = testStack031 d1 d2 testStack032 _ _ = False testStack03 : {m : Level } -> Stack ℕ (SingleLinkedStack ℕ) -> ((Maybe ℕ) -> (Maybe ℕ) -> Bool {m} ) -> Bool {m} testStack03 s cs = pop2Stack s ( \s d1 d2 -> cs d1 d2 ) testStack04 : Bool testStack04 = testStack02 (\s -> testStack03 s testStack032) testStack05 : testStack04 ≡ True testStack05 = refl testStack06 : {m : Level } -> Maybe (Element ℕ) testStack06 = pushStack createSingleLinkedStack 1 ( \s -> pushStack s 2 (\s -> top (stack s))) testStack07 : {m : Level } -> Maybe (Element ℕ) testStack07 = pushSingleLinkedStack emptySingleLinkedStack 1 ( \s -> pushSingleLinkedStack s 2 (\s -> top s)) testStack08 = pushSingleLinkedStack emptySingleLinkedStack 1 $ \s -> pushSingleLinkedStack s 2 $ \s -> pushSingleLinkedStack s 3 $ \s -> pushSingleLinkedStack s 4 $ \s -> pushSingleLinkedStack s 5 $ \s -> top s ------ -- -- proof of properties with indefinite state of stack -- -- this should be proved by properties of the stack inteface, not only by the implementation, -- and the implementation have to provides the properties. -- -- we cannot write "s ≡ s3", since level of the Set does not fit , but use stack s ≡ stack s3 is ok. -- anyway some implementations may result s != s3 -- stackInSomeState : {l m : Level } {D : Set l} {t : Set m } (s : SingleLinkedStack D ) -> Stack {l} {m} D {t} ( SingleLinkedStack D ) stackInSomeState s = record { stack = s ; stackMethods = singleLinkedStackSpec } push->push->pop2 : {l : Level } {D : Set l} (x y : D ) (s : SingleLinkedStack D ) -> pushStack ( stackInSomeState s ) x ( \s1 -> pushStack s1 y ( \s2 -> pop2Stack s2 ( \s3 y1 x1 -> (Just x ≡ x1 ) ∧ (Just y ≡ y1 ) ) )) push->push->pop2 {l} {D} x y s = record { pi1 = refl ; pi2 = refl } -- id : {n : Level} {A : Set n} -> A -> A -- id a = a -- push a, n times n-push : {n : Level} {A : Set n} {a : A} -> ℕ -> SingleLinkedStack A -> SingleLinkedStack A n-push zero s = s n-push {l} {A} {a} (suc n) s = pushSingleLinkedStack (n-push {l} {A} {a} n s) a (\s -> s ) n-pop : {n : Level}{A : Set n} {a : A} -> ℕ -> SingleLinkedStack A -> SingleLinkedStack A n-pop zero s = s n-pop {_} {A} {a} (suc n) s = popSingleLinkedStack (n-pop {_} {A} {a} n s) (\s _ -> s ) open ≡-Reasoning push-pop-equiv : {n : Level} {A : Set n} {a : A} (s : SingleLinkedStack A) -> (popSingleLinkedStack (pushSingleLinkedStack s a (\s -> s)) (\s _ -> s) ) ≡ s push-pop-equiv s = refl push-and-n-pop : {n : Level} {A : Set n} {a : A} (n : ℕ) (s : SingleLinkedStack A) -> n-pop {_} {A} {a} (suc n) (pushSingleLinkedStack s a id) ≡ n-pop {_} {A} {a} n s push-and-n-pop zero s = refl push-and-n-pop {_} {A} {a} (suc n) s = begin n-pop {_} {A} {a} (suc (suc n)) (pushSingleLinkedStack s a id) ≡⟨ refl ⟩ popSingleLinkedStack (n-pop {_} {A} {a} (suc n) (pushSingleLinkedStack s a id)) (\s _ -> s) ≡⟨ cong (\s -> popSingleLinkedStack s (\s _ -> s )) (push-and-n-pop n s) ⟩ popSingleLinkedStack (n-pop {_} {A} {a} n s) (\s _ -> s) ≡⟨ refl ⟩ n-pop {_} {A} {a} (suc n) s ∎ n-push-pop-equiv : {n : Level} {A : Set n} {a : A} (n : ℕ) (s : SingleLinkedStack A) -> (n-pop {_} {A} {a} n (n-push {_} {A} {a} n s)) ≡ s n-push-pop-equiv zero s = refl n-push-pop-equiv {_} {A} {a} (suc n) s = begin n-pop {_} {A} {a} (suc n) (n-push (suc n) s) ≡⟨ refl ⟩ n-pop {_} {A} {a} (suc n) (pushSingleLinkedStack (n-push n s) a (\s -> s)) ≡⟨ push-and-n-pop n (n-push n s) ⟩ n-pop {_} {A} {a} n (n-push n s) ≡⟨ n-push-pop-equiv n s ⟩ s ∎ n-push-pop-equiv-empty : {n : Level} {A : Set n} {a : A} -> (n : ℕ) -> n-pop {_} {A} {a} n (n-push {_} {A} {a} n emptySingleLinkedStack) ≡ emptySingleLinkedStack n-push-pop-equiv-empty n = n-push-pop-equiv n emptySingleLinkedStack