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Merge pull request #15 from alex28sh/38,56,90
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@alex28sh
alex28sh authored Sep 9, 2024
2 parents 2cda672 + b1a50e5 commit 05e1fc5
Showing 1 changed file with 85 additions and 19 deletions.
104 changes: 85 additions & 19 deletions Bench/034-unique.py
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Original file line number Diff line number Diff line change
Expand Up @@ -3,32 +3,42 @@

@Pure
def InArray(a : List[int], x : int) -> bool:
# pre-conditions-start
Requires(Acc(list_pred(a), 1/2))
# pre-conditions-end

# impl-start
return Exists(int, lambda d_0_i_:
((((0) <= (d_0_i_)) and ((d_0_i_) < (len((a)))) and ((a)[d_0_i_]) == (x))))
# impl-end



def uniqueSorted(s : List[int]) -> List[int]:
Requires(Acc(list_pred(s)))
# pre-conditions-start
Requires(Acc(list_pred(s), 1/2))
Requires(Forall(int, lambda d_0_i_:
Forall(int, lambda d_1_j_:
Implies((((0) <= (d_0_i_)) and ((d_0_i_) < (d_1_j_))) and ((d_1_j_) < (len(s))),
((s)[d_0_i_]) <= ((s)[d_1_j_])))))
Ensures(Acc(list_pred(s)))
# pre-conditions-end
# post-conditions-start
Ensures(Acc(list_pred(s), 1/2))
Ensures(Acc(list_pred(Result())))
Ensures(Forall(int, lambda d_9_k_:
(Implies(((0) <= (d_9_k_)) and ((d_9_k_) < (len(Result()))), InArray(s, Result()[d_9_k_])))))
Ensures(Forall(int, lambda d_2_i_:
Forall(int, lambda d_3_j_:
not ((((0) <= (d_2_i_)) and ((d_2_i_) < (d_3_j_))) and ((d_3_j_) < (len(Result())))) or (((Result())[d_2_i_]) < ((Result())[d_3_j_])))))
Ensures(Forall(int, lambda d_11_j_:
(Implies(((0) <= (d_11_j_)) and ((d_11_j_) < (len(s))), InArray(Result(), s[d_11_j_])))))
# post-conditions-end

# impl-start
result = list([int(0)] * 0) # type : List[int]
result = list([])
d_6_i_ = int(0) # type : int
d_6_i_ = 0
while (d_6_i_) < (len(s)):
# invariants-start
Invariant(Acc(list_pred(result)))
Invariant(Acc(list_pred(s), 1/2))
Invariant(Forall(int, lambda d_0_i_:
Expand All @@ -46,42 +56,90 @@ def uniqueSorted(s : List[int]) -> List[int]:
(not ((((0) <= (d_7_k_)) and ((d_7_k_) < (d_8_l_))) and ((d_8_l_) < (len(result)))) or (((result)[d_7_k_]) < ((result)[d_8_l_])),
[[(result)[d_8_l_]]])),
[[(result)[d_7_k_]]])))
Invariant(Forall(int, lambda d_11_j_:
(Implies(((0) <= (d_11_j_)) and ((d_11_j_) < (d_6_i_)), InArray(result, s[d_11_j_])), [[]])))
# invariants-end
if ((len(result)) == (0)) or (((result)[(len(result)) - (1)]) != ((s)[d_6_i_])):
# assert-start
Assert(Implies(len(result) > 0, result[len(result) - 1] < s[d_6_i_]))
Assert(Implies(len(result) > 0,
Forall(int, lambda d_11_j_:
Implies(0 <= d_11_j_ and d_11_j_ < len(result), result[d_11_j_] < s[d_6_i_]))))
# assert-end
result = (result) + [(s)[d_6_i_]]
d_6_i_ = (d_6_i_) + (1)
return result
# impl-end

# def unique(s : List[int]) -> List[int]:
# Requires(Acc(list_pred(s)))
# Ensures(Acc(list_pred(s)))
# Ensures(Acc(list_pred(Result())))
# Ensures(Forall(int, lambda d_9_k_:
# (Implies(((0) <= (d_9_k_)) and ((d_9_k_) < (len(Result()))), InArray(s, Result()[d_9_k_])))))
# Ensures(Forall(int, lambda d_2_i_:
# Forall(int, lambda d_3_j_:
# not ((((0) <= (d_2_i_)) and ((d_2_i_) < (d_3_j_))) and ((d_3_j_) < (len(Result())))) or (((Result())[d_2_i_]) < ((Result())[d_3_j_])))))
# # Ensures(Forall(int, lambda d_11_j_:
# # (Implies(((0) <= (d_11_j_)) and ((d_11_j_) < (len(s))), InArray(Result(), s[d_11_j_])))))
# return uniqueSorted(BubbleSort(s))
def unique(s : List[int]) -> List[int]:
# pre-conditions-start
Requires(Acc(list_pred(s)))
# pre-conditions-end
# post-conditions-start
Ensures(Acc(list_pred(s)))
Ensures(Acc(list_pred(Result())))
Ensures(Forall(int, lambda d_9_k_:
(Implies(((0) <= (d_9_k_)) and ((d_9_k_) < (len(Result()))), InArray(s, Result()[d_9_k_])))))
Ensures(Forall(int, lambda d_2_i_:
Forall(int, lambda d_3_j_:
not ((((0) <= (d_2_i_)) and ((d_2_i_) < (d_3_j_))) and ((d_3_j_) < (len(Result())))) or (((Result())[d_2_i_]) < ((Result())[d_3_j_])))))
# post-conditions-end

# impl-start
a = BubbleSort(s)
# assert-start
Assert(Forall(int, lambda d_9_k_:
(Implies(((0) <= (d_9_k_)) and ((d_9_k_) < (len(a))), InArray(s, a[d_9_k_])))))
# assert-end
b = uniqueSorted(a)
# assert-start
Assert(Forall(int, lambda d_9_k_:
(Implies(((0) <= (d_9_k_)) and ((d_9_k_) < (len(a))), InArray(s, a[d_9_k_])))))
Assert(Forall(int, lambda d_9_k_:
(Implies(((0) <= (d_9_k_)) and ((d_9_k_) < (len(b))), InArray(a, b[d_9_k_])))))
Assert(Forall(int, lambda d_9_k_:
(Implies(((0) <= (d_9_k_)) and ((d_9_k_) < (len(b))), InArray(s, b[d_9_k_])))))
# assert-end
return b
# impl-end

def BubbleSort(a1 : List[int]) -> List[int]:
# pre-conditions-start
Requires(Acc(list_pred(a1), 1/2))
# pre-conditions-end
# post-conditions-start
Ensures(Acc(list_pred(a1), 1/2))
Ensures(Acc(list_pred(Result())))
Ensures((len(a1)) == (len(Result())))
Ensures(Forall(int, lambda d_0_i_:
Forall(int, lambda d_1_j_:
Implies((((0) <= (d_0_i_)) and ((d_0_i_) < (d_1_j_))) and ((d_1_j_) < (len((Result())))), ((Result())[d_0_i_]) <= ((Result())[d_1_j_])))))
a = list(a1) # type : List[int]
Ensures(Forall(int, lambda d_9_k_:
(Implies(((0) <= (d_9_k_)) and ((d_9_k_) < (len(Result()))), InArray(a1, Result()[d_9_k_])))))
# post-conditions-end

# impl-start
a : List[int] = []
d_2_i_ = int(0) # type : int
while d_2_i_ < len(a1):
# invariants-start
Invariant(Acc(list_pred(a)))
Invariant(Acc(list_pred(a1), 1/2))
Invariant(len(a) == d_2_i_)
Invariant(0 <= d_2_i_ and d_2_i_ <= len(a1))
Invariant(Forall(int, lambda d_9_k_:
(Implies(((0) <= (d_9_k_)) and ((d_9_k_) < (d_2_i_)), a[d_9_k_] == a1[d_9_k_]))))
Invariant(Forall(int, lambda d_9_k_:
(Implies(((0) <= (d_9_k_)) and ((d_9_k_) < (d_2_i_)), InArray(a1, a[d_9_k_])), [[InArray(a1, a[d_9_k_])]])))
Invariant(Forall(int, lambda d_9_k_:
(Implies(((0) <= (d_9_k_)) and ((d_9_k_) < (d_2_i_)), InArray(a, a1[d_9_k_])), [[InArray(a, a1[d_9_k_])]])))
# invariants-end
a = a + [a1[d_2_i_]]
# assert-start
Assert(InArray(a1, a[d_2_i_]))
# assert-end
d_2_i_ = d_2_i_ + 1
d_2_i_ = (len((a))) - (1)
while (d_2_i_) > (0):
# invariants-start
Invariant(Acc(list_pred(a)))
Invariant(Acc(list_pred(a1), 1/2))
Invariant((len(a1)) == (len(a)))
Expand All @@ -97,9 +155,13 @@ def BubbleSort(a1 : List[int]) -> List[int]:
(Implies(((((0) <= (d_5_k_)) and ((d_5_k_) <= (d_2_i_))) and ((d_2_i_) < (d_6_k_k_)) and (d_6_k_k_) < (len((a)))), ((a)[d_5_k_]) <= ((a)[d_6_k_k_])),
[[(a)[d_6_k_k_]]])),
[[(a)[d_5_k_]]])))
Invariant(Forall(int, lambda d_9_k_:
(Implies(((0) <= (d_9_k_)) and ((d_9_k_) < (len(a))), InArray(a1, a[d_9_k_])), [[InArray(a1, a[d_9_k_])]])))
# invariants-end
d_7_j_ = int(0) # type : int
d_7_j_ = 0
while (d_7_j_) < (d_2_i_):
# invariants-start
Invariant(Acc(list_pred(a)))
Invariant(Acc(list_pred(a1), 1/2))
Invariant((len(a1)) == (len(a)))
Expand All @@ -117,10 +179,14 @@ def BubbleSort(a1 : List[int]) -> List[int]:
Invariant(Forall(int, lambda d_12_k_:
(Implies(((0) <= (d_12_k_)) and ((d_12_k_) <= (d_7_j_)), ((a)[d_12_k_]) <= ((a)[d_7_j_])),
[[(a)[d_12_k_]]])))
Invariant(Forall(int, lambda d_9_k_:
(Implies(((0) <= (d_9_k_)) and ((d_9_k_) < (len(a))), InArray(a1, a[d_9_k_])), [[InArray(a1, a[d_9_k_])]])))
# invariants-end
if ((a)[d_7_j_]) > ((a)[(d_7_j_) + (1)]):
rhs0_ = (a)[(d_7_j_) + (1)] # type : int
(a)[(d_7_j_) + (1)] = (a)[d_7_j_]
(a)[d_7_j_] = rhs0_
d_7_j_ = (d_7_j_) + (1)
d_2_i_ = (d_2_i_) - (1)
return a
# impl-end

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