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Animated Logic: Correct Functional Conversion to Conjunctive Normal Form
arXiv - CS - Logic in Computer Science Pub Date : 2020-03-11 , DOI: arxiv-2003.05081 Pedro Barroso, M\'ario Pereira and Ant\'onio Ravara
arXiv - CS - Logic in Computer Science Pub Date : 2020-03-11 , DOI: arxiv-2003.05081 Pedro Barroso, M\'ario Pereira and Ant\'onio Ravara
We present an approach to obtain formally verified implementations of
classical Computational Logic algorithms. We choose the Why3 platform because
it allows to implement functions in a style very close to the mathematical
definitions, as well as it allows a high degree of automation in the
verification process. As proof of concept, we present a mathematical definition of the algorithm to
convert propositional formulae to conjunctive normal form, implementations in
WhyML (the Why3 language, very similar to OCaml), and proofs of correctness of
the implementations. We apply our proposal on two variants of this algorithm:
one in direct-style and another with an explicit stack structure. Being both
first-order versions, Why3 processes the proofs naturally.
中文翻译:
动画逻辑:正确的功能转换为连接范式
我们提出了一种方法来获得经典计算逻辑算法的形式验证实现。我们选择 Why3 平台是因为它允许以非常接近数学定义的方式实现函数,并且它允许在验证过程中实现高度自动化。作为概念证明,我们提出了将命题公式转换为合取范式的算法的数学定义、WhyML(Why3 语言,非常类似于 OCaml)的实现,以及实现正确性的证明。我们将我们的建议应用于该算法的两种变体:一种是直接式的,另一种是具有显式堆栈结构的。作为两个一阶版本,Why3 自然地处理证明。
更新日期:2020-03-12
中文翻译:
动画逻辑:正确的功能转换为连接范式
我们提出了一种方法来获得经典计算逻辑算法的形式验证实现。我们选择 Why3 平台是因为它允许以非常接近数学定义的方式实现函数,并且它允许在验证过程中实现高度自动化。作为概念证明,我们提出了将命题公式转换为合取范式的算法的数学定义、WhyML(Why3 语言,非常类似于 OCaml)的实现,以及实现正确性的证明。我们将我们的建议应用于该算法的两种变体:一种是直接式的,另一种是具有显式堆栈结构的。作为两个一阶版本,Why3 自然地处理证明。