On the Hoare theory of monadic recursion schemes

Konstantinos Mamouras
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引用次数: 6

Abstract

The equational theory of monadic recursion schemes is known to be decidable by the result of Sénizergues on the decidability of the problem of DPDA equivalence. In order to capture some properties of the domain of computation, we augment equations with certain hypotheses. This preserves the decidability of the theory, which we call simple implicational theory. The asymptotically fastest algorithm known for deciding the equational theory, and also for deciding the simple implicational theory, has running time that is non-elementary. We therefore consider a restriction of the properties about schemes to check: instead of arbitrary equations f ≡ g between schemes, we focus on propositional Hoare assertions {p}f{q}, where f is a scheme and p, q are tests. Such Hoare assertions have a straightforward encoding as equations. We investigate the Hoare theory of monadic recursion schemes, that is, the set of valid implications whose conclusions are Hoare assertions and whose premises are of a certain simple form. We present a sound and complete Hoare-style calculus for this theory. We also show that the Hoare theory can be decided in exponential time, and that it is complete for this class.
一元递归格式的Hoare理论
一元递推格式的方程理论是由samizizgues关于DPDA等价问题的可判定性的结果所决定的。为了捕捉计算域的一些性质,我们用一定的假设扩充方程。这保留了理论的可决性,我们称之为简单蕴涵理论。已知的用于确定方程理论和简单隐含理论的渐近最快算法,其运行时间是非初等的。因此,我们考虑一个关于方案的性质的限制来检验:代替方案之间的任意方程f≡g,我们关注于命题Hoare断言{p}f{q},其中f是一个方案,p, q是检验。这样的Hoare断言具有作为方程的直接编码。我们研究了一元递归格式的Hoare理论,即结论是Hoare断言且前提具有某种简单形式的有效蕴涵集。我们为这一理论提出了一个健全而完整的霍尔式演算。我们还证明了霍尔理论可以在指数时间内被决定,并且对于这门课来说它是完整的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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