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@alex28sh
alex28sh committed Sep 9, 2024
1 parent 0862d52 commit 1e2ad08
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Showing 107 changed files with 1,824 additions and 77 deletions.
25 changes: 22 additions & 3 deletions Bench/000-has-close-elements.py
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Original file line number Diff line number Diff line change
Expand Up @@ -4,48 +4,65 @@

@Pure
def abs_value(val: int) -> int:
# post-conditions-start
Ensures(Implies(val < 0, Result() == -val))
Ensures(Implies(val >= 0, Result() == val))
# post-conditions-end

# impl-start
if val < 0:
return -val
else:
return val
# impl-end


@Pure
def abs1(x: int, threshold: int) -> bool:
# impl-start
return x >= threshold or x <= -threshold
# impl-end

@Pure
def fn(x: int, numbers: List[int], threshold: int) -> bool:
# pre-conditions-start
Requires(threshold > 0)
Requires(Acc(list_pred(numbers)))
Requires(x >= 0 and x < len(numbers))
# pre-conditions-end

# impl-start
return Forall(range(len(numbers)), lambda y :
x == y or
abs1(numbers[x] - numbers[y], threshold)
)
# impl-end


def has_close_elements(numbers: List[int], threshold: int) -> bool:
# pre-conditions-start
Requires(threshold > 0)
Requires(Acc(list_pred(numbers)))
# pre-conditions-end
# post-conditions-start
Ensures(Implies(Result() != True, Forall(range(len(numbers)), lambda x :
fn(x, numbers, threshold)
)))
# post-conditions-end


# impl-start
flag = False
i = 0
while i < len(numbers):
# invariants-start
Invariant(Acc(list_pred(numbers)))
Invariant(0 <= i and i <= len(numbers))
Invariant(Implies(flag != True,
Forall(range(i), lambda x : fn(x, numbers, threshold))))

# invariants-end
j = 0
while j < len(numbers):
# invariants-start
Invariant(Acc(list_pred(numbers)))
Invariant(0 <= i and i < len(numbers))
Invariant(0 <= j and j <= len(numbers))
Expand All @@ -57,6 +74,7 @@ def has_close_elements(numbers: List[int], threshold: int) -> bool:
Forall(range(j), lambda y : i == y or abs1(numbers[i] - numbers[y], threshold))
)
)
# invariants-end

if i != j:
distance = abs_value(numbers[i] - numbers[j])
Expand All @@ -66,4 +84,5 @@ def has_close_elements(numbers: List[int], threshold: int) -> bool:
j += 1
i += 1

return flag
return flag
# impl-end
24 changes: 24 additions & 0 deletions Bench/001-separate-paren-groups.py
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Original file line number Diff line number Diff line change
Expand Up @@ -3,8 +3,12 @@

@Pure
def IsValidParentheses(s : List[int], i : int, depth : int) -> bool :
# pre-conditions-start
Requires(Acc(list_pred(s), 1/2))
Requires(i >= 0 and i <= len(s))
# pre-conditions-end

# impl-start
if (i) == (len(s)):
return (depth) >= (0)
elif (depth) < (0):
Expand All @@ -15,11 +19,16 @@ def IsValidParentheses(s : List[int], i : int, depth : int) -> bool :
return ((depth) > (0)) and (IsValidParentheses(s, (i) + (1), (depth) - (1)))
elif True:
return IsValidParentheses(s, (i) + (1), depth)
# impl-end

@Pure
def IsValidParentheses2(s : List[int], i : int, depth : int) -> bool :
# pre-conditions-start
Requires(Acc(list_pred(s), 1/2))
Requires(i >= 0 and i <= len(s))
# pre-conditions-end

# impl-start
if (i) == (len(s)):
return (depth) >= (0)
elif (depth) < (0):
Expand All @@ -30,11 +39,16 @@ def IsValidParentheses2(s : List[int], i : int, depth : int) -> bool :
return ((depth) > (0)) and (IsValidParentheses(s, (i) + (1), (depth) - (1)))
elif True:
return IsValidParentheses(s, (i) + (1), depth)
# impl-end

@Pure
def IsValidParentheses1(s : List[int], i : int, depth : int) -> bool :
# pre-conditions-start
Requires(Acc(list_pred(s), 1/2))
Requires(i >= 0 and i <= len(s))
# pre-conditions-end

# impl-start
if (i) == (len(s)):
return (depth) == (0)
elif ((depth) <= (0)) and ((i) != (0)):
Expand All @@ -45,23 +59,31 @@ def IsValidParentheses1(s : List[int], i : int, depth : int) -> bool :
return ((depth) > (0)) and (IsValidParentheses1(s, (i) + (1), (depth) - (1)))
elif True:
return IsValidParentheses1(s, (i) + (1), depth)
# impl-end

def separate__paren__groups(paren__string : List[int]) -> List[List[int]]:
# pre-conditions-start
Requires(Acc(list_pred(paren__string)))
Requires(Forall(int, lambda d_0_i_:
not (((d_0_i_) >= (0)) and ((d_0_i_) < (len(paren__string)))) or ((((paren__string)[d_0_i_]) == (0)) or (((paren__string)[d_0_i_]) == (1)))))
Requires(Forall(int, lambda d_1_i_:
not (((0) <= (d_1_i_)) and ((d_1_i_) <= (len(paren__string)))) or (IsValidParentheses(paren__string, d_1_i_, 0))))
Requires(IsValidParentheses2(paren__string, 0, 0))
# pre-conditions-end
# post-conditions-start
Ensures(Acc(list_pred(ResultT(List[List[int]]))))
Ensures(Forall(ResultT(List[List[int]]), lambda x: Acc(list_pred(x), 1/2)))
Ensures((Forall(int, lambda d_2_i_:
not (((0) <= (d_2_i_)) and ((d_2_i_) < (len(Result())))) or (IsValidParentheses1((Result())[d_2_i_], 0, 0)))))
# post-conditions-end

# impl-start
res : List[List[int]] = []
d_3_current__string_ : List[int] = []
d_4_current__depth_ = int(0) # type : int
d_5_i_ = int(0) # type : int
while (d_5_i_) < (len(paren__string)):
# invariants-start
Invariant(Acc(list_pred(res)))
Invariant(Acc(list_pred(d_3_current__string_)))
Invariant(Acc(list_pred(paren__string)))
Expand All @@ -74,6 +96,7 @@ def separate__paren__groups(paren__string : List[int]) -> List[List[int]]:
Invariant((Forall(int, lambda d_6_i1_:
not (((0) <= (d_6_i1_)) and ((d_6_i1_) < (len(res)))) or (IsValidParentheses1((res)[d_6_i1_], 0, 0)))))
Invariant(IsValidParentheses(paren__string, d_5_i_, 0))
# invariants-end
d_7_c_ = (paren__string)[d_5_i_]
if (d_7_c_) == (0):
d_4_current__depth_ = (d_4_current__depth_) + (1)
Expand All @@ -86,4 +109,5 @@ def separate__paren__groups(paren__string : List[int]) -> List[List[int]]:
d_3_current__string_ = []
d_5_i_ = (d_5_i_) + (1)
return res
# impl-end

20 changes: 20 additions & 0 deletions Bench/003-below-zero.py
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Original file line number Diff line number Diff line change
Expand Up @@ -3,37 +3,57 @@

@Pure
def psum(i : int, j : int, s : List[int]) -> int :
# pre-conditions-start
Requires(Acc(list_pred(s)))
Requires(0 <= i and i <= j and j <= len(s))
# pre-conditions-end

# impl-start
if i == j:
return 0
else:
return (s)[j - 1] + (psum(i, j - 1, s))
# impl-end

def below__zero(ops : List[int]) -> bool:
# pre-conditions-start
Requires(Acc(list_pred(ops)))
# pre-conditions-end
# post-conditions-start
Ensures(Acc(list_pred(ops)))
Ensures(not (Result()) or (Forall(int, lambda d_1_i_:
not (((0) <= (d_1_i_)) and ((d_1_i_) <= (len(ops)))) or ((psum(0, d_1_i_, ops)) >= (0)))))
Ensures(not (not(Result())) or (Exists(int, lambda d_2_i_:
(((0) <= (d_2_i_)) and ((d_2_i_) <= (len(ops)))) and ((psum(0, d_2_i_, ops)) < (0)))))
# post-conditions-end

# impl-start
res = False # type : bool
d_3_balance_ = int(0) # type : int
d_3_balance_ = 0
d_4_i_ = int(0) # type : int
d_4_i_ = 0

while (d_4_i_) < (len(ops)):
# invariants-start
Invariant(Acc(list_pred(ops)))
Invariant(((0) <= (d_4_i_)) and ((d_4_i_) <= (len(ops))))
Invariant((d_3_balance_) == (psum(0, d_4_i_, ops)))
Invariant(Forall(int, lambda d_2_i_: (not (((0) <= (d_2_i_)) and ((d_2_i_) < (len(ops)))) or ((psum(0, d_2_i_ + 1, ops)) == (psum(0, d_2_i_, ops) + ops[d_2_i_])), [[psum(0, d_2_i_ + 1, ops)]])))
Invariant(Forall(int, lambda d_5_j_:
(not (((0) <= (d_5_j_)) and ((d_5_j_) <= (d_4_i_))) or ((psum(0, d_5_j_, ops)) >= (0)), [[psum(0, d_5_j_, ops)]])))
# invariants-end

# assert-start
Assert((psum(0, (d_4_i_) + (1), ops)) == ((psum(0, d_4_i_, ops)) + ((ops)[d_4_i_])))
# assert-end

d_3_balance_ = (d_3_balance_) + ((ops)[d_4_i_])
if (d_3_balance_) < (0):
res = False
return res
d_4_i_ = (d_4_i_) + (1)

res = True
return res
# impl-end
12 changes: 10 additions & 2 deletions Bench/005-intersperse.py
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Original file line number Diff line number Diff line change
Expand Up @@ -2,29 +2,37 @@
from nagini_contracts.contracts import *

def intersperse(numbers: List[int], delimiter: int) -> List[int]:
# pre-conditions-start
Requires(Acc(list_pred(numbers)))
# pre-conditions-end
# post-conditions-start
Ensures(Acc(list_pred(numbers)))
Ensures(Acc(list_pred(Result())))
Ensures(Implies(len(numbers) != 0, len(Result()) == len(numbers) * 2 - 1))
Ensures(Implies(len(numbers) == 0, len(Result()) == 0))
Ensures(Forall(range(len(Result())), lambda i: i % 2 == 1 or Result()[i] == numbers[i // 2]))
Ensures(Forall(range(len(Result())), lambda i: i % 2 == 0 or Result()[i] == delimiter))

# post-conditions-end

# impl-start
res = [] # type: List[int]
if len(numbers) != 0:
i = 0
while i + 1 < len(numbers):
# invariants-start
Invariant(Acc(list_pred(numbers)))
Invariant(Acc(list_pred(res)))
Invariant(0 <= i and i < len(numbers))
Invariant(len(res) == 2 * i)
Invariant(Forall(range(len(res)), lambda i: i % 2 == 1 or res[i] == numbers[i // 2]))
Invariant(Forall(range(len(res)), lambda i: i % 2 == 0 or res[i] == delimiter))
# invariants-end

res.append(numbers[i])
res.append(delimiter)
i += 1

res.append(numbers[i])

return res
return res
# impl-end
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