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@@ -263,4 +263,3 @@ def check(candidate): | |
assert candidate('( ) (( )) (( )( ))') == ['()', '(())', '(()())'] | ||
*/ | ||
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@@ -1,9 +1,7 @@ | ||
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/* | ||
### ID | ||
HumanEval/3 | ||
*/ | ||
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/* | ||
### VERUS BEGIN | ||
*/ | ||
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@@ -13,34 +11,40 @@ verus! { | |
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// This function is part of the specification | ||
pub open spec fn sum(s: Seq<int>) -> int | ||
decreases s.len() | ||
decreases s.len(), | ||
{ | ||
if s.len() == 0 { 0 } else { s[0] + sum(s.skip(1)) } | ||
if s.len() == 0 { | ||
0 | ||
} else { | ||
s[0] + sum(s.skip(1)) | ||
} | ||
} | ||
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// This function is also part of the specification | ||
pub open spec fn first_n(s: Seq<i32>, n: int) -> Seq<int> | ||
{ | ||
pub open spec fn first_n(s: Seq<i32>, n: int) -> Seq<int> { | ||
s.take(n).map(|_idx, j: i32| j as int) | ||
} | ||
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// This function is used by the proof | ||
pub open spec fn sum_other_way(s: Seq<int>) -> int | ||
decreases s.len() | ||
decreases s.len(), | ||
{ | ||
if s.len() == 0 { 0 } else { s.last() + sum_other_way(s.drop_last()) } | ||
if s.len() == 0 { | ||
0 | ||
} else { | ||
s.last() + sum_other_way(s.drop_last()) | ||
} | ||
} | ||
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proof fn lemma_sum_equals_sum_other_way(s: Seq<int>) | ||
ensures | ||
sum(s) == sum_other_way(s), | ||
decreases s.len() | ||
decreases s.len(), | ||
{ | ||
if s.len() == 1 { | ||
assert(sum(s.skip(1)) == 0); | ||
assert(sum_other_way(s.drop_last()) == 0); | ||
} | ||
else if s.len() > 1 { | ||
} else if s.len() > 1 { | ||
let ss = s.skip(1); | ||
lemma_sum_equals_sum_other_way(ss); | ||
assert(sum_other_way(ss) == ss.last() + sum_other_way(ss.drop_last())); | ||
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@@ -52,7 +56,8 @@ proof fn lemma_sum_equals_sum_other_way(s: Seq<int>) | |
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fn below_zero(operations: Vec<i32>) -> (result: bool) | ||
ensures | ||
result <==> exists |i: int| 0 <= i <= [email protected]() && #[trigger] sum(first_n(operations@, i)) < 0, | ||
result <==> exists|i: int| | ||
0 <= i <= [email protected]() && #[trigger] sum(first_n(operations@, i)) < 0, | ||
{ | ||
let mut s = 0i32; | ||
let mut num_overflows: usize = 0; | ||
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@@ -63,9 +68,11 @@ fn below_zero(operations: Vec<i32>) -> (result: bool) | |
max_plus == i32::MAX + 1, | ||
s >= 0, | ||
s + num_overflows * max_plus == sum(first_n(operations@, k as int)), | ||
forall |i: int| 0 <= i <= k ==> #[trigger] sum(first_n(operations@, i)) >= 0, | ||
forall|i: int| 0 <= i <= k ==> #[trigger] sum(first_n(operations@, i)) >= 0, | ||
{ | ||
assert(sum(first_n(operations@, k as int)) + operations@[k as int] == sum(first_n(operations@, k + 1))) by { | ||
assert(sum(first_n(operations@, k as int)) + operations@[k as int] == sum( | ||
first_n(operations@, k + 1), | ||
)) by { | ||
let q1 = first_n(operations@, k as int); | ||
let q2 = first_n(operations@, k + 1); | ||
assert(q2.last() == operations@[k as int] as int); | ||
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@@ -78,12 +85,10 @@ fn below_zero(operations: Vec<i32>) -> (result: bool) | |
if s > i32::MAX - op { | ||
s += op - i32::MAX - 1; | ||
num_overflows += 1; | ||
} | ||
else { | ||
} else { | ||
s += op; | ||
} | ||
} | ||
else { | ||
} else { | ||
s += op; | ||
if s < 0 { | ||
if num_overflows == 0 { | ||
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@@ -98,7 +103,6 @@ fn below_zero(operations: Vec<i32>) -> (result: bool) | |
} | ||
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} // verus! | ||
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fn main() {} | ||
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/* | ||
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@@ -159,4 +163,3 @@ def check(candidate): | |
assert candidate([1, -2, 2, -2, 5, -5, 4, -4]) == True | ||
*/ | ||
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