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Submodule HumanEval-Dafny
updated
160 files
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def truncate_number(number: float) -> float: | ||
""" Given a positive floating point number, it can be decomposed into | ||
and integer part (largest integer smaller than given number) and decimals | ||
(leftover part always smaller than 1). | ||
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Return the decimal part of the number. | ||
>>> truncate_number(3.5) | ||
0.5 | ||
""" |
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The following errors occurred during verification: | ||
{error} | ||
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Please fix the error by adding, removing or modifying the invariants and/or assertions and return the fixed program. |
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prompts/humaneval-dafny-cot-onestep/ask_for_fixed_had_errors.txt
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There are still some errors: | ||
{error} | ||
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Could you please fix them? |
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prompts/humaneval-dafny-cot-onestep/rewrite/examples/001/answer.txt
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Let's go over the provided program step by step. | ||
First, we'll identify what each function does and what its input and output are. | ||
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1. The function `sum` takes a `seq<int>` as input and returns an `int` as output. Looking at it's body, we see that it takes the first element of the sequence, adds it to the sum of the rest of the elements, and returns the result. | ||
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2. The lemma `sum_prop` states that given that length of a sequence is greater than 0, the sum of the sequence is equal to the sum of first `|s| - 1` elements plus the last element. | ||
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3. The method `sum_loop` takes a `seq<int>` as input and returns an `int` as output. It has an accumulator variable `s` that starts at 0. It then loops through the sequence, adding each element to the accumulator. As we see, it uses a `while` loop, so one of the invariants dafny requires is that `0 <= i <= |s|`. | ||
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Now, let's try to prove the `sum_loop` method. We'll start by adding the `0 <= i <= |s|` invariant to the while loop: | ||
``` | ||
while (i < |numbers|) | ||
invariant 0 <= i <= |numbers| | ||
``` | ||
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Next, we need to use the `sum_prop` lemma to prove that `s == sum(numbers[0..i])`. To do this, we'll need to prove that adding `numbers[i]` to `sum(numbers[0..i])` results in `sum(numbers[0..i + 1])`. That's exactly what `sum_prop(numbers[0..i + 1])` does. For dafny to be able to ensure that, we'll need to prove that `numbers[0..i + 1][..i] == numbers[0..i]`. This is an automatic proof that dafny can do, so we don't need to add any extra proof steps, let's just add an assertion: | ||
``` | ||
assert numbers[0..i + 1][..i] == numbers[0..i]; | ||
``` | ||
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Finally, we'll add the `s == sum(numbers[0..i])` invariant to the while loop: | ||
``` | ||
while (i < |numbers|) | ||
invariant 0 <= i <= |numbers| | ||
invariant s = sum(numbers[0..i]) | ||
``` | ||
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Now, we can use the `sum_prop` lemma to prove that `s == sum(numbers[0..i])`: | ||
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``` | ||
assert numbers[0..i + 1][..i] == numbers[0..i]; | ||
sum_prop(numbers[0..i + 1]); | ||
assert sum(numbers[0..i + 1]) == sum(numbers[0..i]) + numbers[i]; | ||
``` | ||
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Now, the proof is complete: | ||
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<answer> | ||
function sum(s: seq<int>) : int { | ||
if |s| == 0 then 0 else s[0] + sum(s[1..]) | ||
} | ||
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lemma sum_prop(s: seq<int>) | ||
requires |s| > 0 | ||
ensures sum(s) == sum(s[..|s| - 1]) + s[ |s| - 1 ] | ||
{ | ||
if (|s| > 1) { | ||
assert (s[1..][..|s[1..]| - 1]) == s[1..|s| - 1]; | ||
} | ||
} | ||
method sum_loop(numbers: seq<int>) returns (s: int) | ||
ensures s == sum(numbers) | ||
{ | ||
s := 0; | ||
var i := 0; | ||
while (i < |numbers|) | ||
invariant 0 <= i <= |numbers| | ||
invariant s == sum(numbers[0..i]) | ||
{ | ||
s := s + numbers[i]; | ||
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assert numbers[0..i + 1][..i] == numbers[0..i]; | ||
sum_prop(numbers[0..i + 1]); | ||
assert sum(numbers[0..i + 1]) == sum(numbers[0..i]) + numbers[i]; | ||
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i := i + 1; | ||
} | ||
} | ||
</answer> |
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prompts/humaneval-dafny-cot-onestep/rewrite/examples/001/question.txt
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Rewrite the following dafny program, adding correct invariants into the loops and adding assertions in nessesary places. | ||
Do not change the code, only add invariants and assertions. Don't remove any helper functions, they are there to help you. | ||
Explain all your reasoning in detail before answering. Put the answer in <answer></answer> tags without markdown backticks. | ||
The program: | ||
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```dafny | ||
function sum(s: seq<int>) : int { | ||
if |s| == 0 then 0 else s[0] + sum(s[1..]) | ||
} | ||
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lemma sum_prop(s: seq<int>) | ||
requires |s| > 0 | ||
ensures sum(s) == sum(s[..|s| - 1]) + s[ |s| - 1 ] | ||
{ | ||
if (|s| > 1) { | ||
assert (s[1..][..|s[1..]| - 1]) == s[1..|s| - 1]; | ||
} | ||
} | ||
method sum_loop(numbers: seq<int>) returns (s: int) | ||
ensures s == sum(numbers) | ||
{ | ||
s := 0; | ||
var i := 0; | ||
while (i < |numbers|) | ||
{ | ||
s := s + numbers[i]; | ||
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i := i + 1; | ||
} | ||
} | ||
``` |
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Rewrite the following dafny program, adding correct invariants into the loops and adding assertions in nessesary places. | ||
Do not change the code, only add invariants and assertions. Don't remove any helper functions, they are there to help you. | ||
Explain all your reasoning in detail before answering. Put the answer in <answer></answer> tags without markdown backticks. | ||
The program: | ||
{program} |
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You are an expert in Dafny. | ||
You will be given tasks dealing with Dafny programs including precise annotations. | ||
You respond only with code blocks. |
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The verifier timed out during the verification. | ||
This usually means that the provided invariants were too broad or were difficult to check. | ||
Could you please try to improve the invariants and try again? |
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prompts/humaneval-dafny-without-conditions-cot-onestep/ask_for_fixed.txt
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The following errors occurred during verification: | ||
{error} | ||
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Please fix the error by adding, removing or modifying the invariants and/or assertions and return the fixed program. |
4 changes: 4 additions & 0 deletions
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prompts/humaneval-dafny-without-conditions-cot-onestep/ask_for_fixed_had_errors.txt
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There are still some errors: | ||
{error} | ||
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Could you please fix them? |
Oops, something went wrong.