Coinductive big-step operational semantics for type soundness of Java-like languages

Proceedings of the 15th Workshop on Formal Techniques for Java-Like Programs

2013

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In previous work we have presented COFJ, an extension to Featherweight Java that promotes coinductive programming, a sub-paradigm expressly devised to ease high-level programming and reasoning with cyclic data structures.The COFJ language supports cyclic objects and regularly corecursive methods, that is, methods whose invocation terminates not only when the corresponding call trace is finite (as happens with ordinary recursion), but also when such a trace is infinite but cyclic, that is, can be specified by a regular term, or, equivalently, by a finite set of recursive syntactic equations.In COFJ it is not easy to ensure that the invocation of a corecursive method will return a well-defined value, since the recursive equations corresponding to the regular trace of the recursive calls may not admit a (unique) solution; in such cases we say that the value returned by the method call is undetermined.In this paper we propose two new contributions. First, we design a simpler construct for defining corecursive methods and, correspondingly, provide a more intuitive operational semantics. For this COFJ variant, we are able to define a type system that allows the user to specify that certain corecursive methods cannot return an undetermined value; in this way, it is possible to prevent unsafe use of such a value.The operational semantics and the type system of COFJ are fully formalized, and the soundness of the type system is proved.

Section: Formal Definitionmentioning

confidence: 99%

“…In comparison with the more foundational studies [1,2] on the use of coinductive big-step operational semantics of Java-like languages for proving type soundness properties, this paper is more focused on the challenge of extending object-oriented languages to support coinductive programming.…”

Section: Related Work and Conclusionmentioning

confidence: 99%

Safe corecursion in coFJ

Proceedings of the 15th Workshop on Formal Techniques for Java-Like Programs

2013

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“…We show now an example which illustrates the difference with the approach in [Ancona 2011[Ancona , 2012[Ancona , 2014, where, in order to have soundness of the type system, non well-founded values (that is, values corresponding to infinite trees) were considered. In an imperative language, this would correspond to allowing heaps to have infinite domain, since the abstract structure of values can be recovered from the heap.…”

Section: An Imperative Java-like Languagementioning

confidence: 99%

Reasoning on divergent computations with coaxioms

Dagnino

Proc. ACM Program. Lang.

2017

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Coaxioms have been recently introduced to enhance the expressive power of inference systems, by supporting interpretations which are neither purely inductive, nor coinductive. This paper proposes a novel approach based on coaxioms to capture divergence in semantic definitions by allowing inductive and coinductive semantic rules to be merged together for defining a unique semantic judgment. In particular, coinduction is used to derive a special result which models divergence. In this way, divergent, terminating, and stuck computations can be properly distinguished even in semantic definitions where this is typically difficult, as in big-step style. We show how the proposed approach can be applied to several languages; in particular, we first illustrate it on the paradigmatic example of the λ-calculus, then show how it can be adopted for defining the big-step semantics of a simple imperative Java-like language. We provide proof techniques to show classical results, including equivalence with small-step semantics, and type soundness for typed versions of both languages.

“…In comparison with the more foundational studies [1,3] on the use of coinductive big-step operational semantics of Java-like languages for proving type soundness properties, the main contribution and aim of this paper is to propose a novel programming paradigm to support useful abstractions for the convenient creation and manipulation of cyclic data structures.…”

Section: Related Work and Conclusionmentioning

confidence: 99%

Corecursive Featherweight Java

Proceedings of the 14th Workshop on Formal Techniques for Java-Like Programs

2012

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Despite cyclic data structures occur often in many application domains, object-oriented programming languages provide poor abstraction mechanisms for dealing with cyclic objects.Such a deficiency is reflected also in the research on theoretical foundation of object-oriented languages; for instance, Featherweigh Java (FJ), which is one of the most widespread objectoriented calculi, does not allow creation and manipulation of cyclic objects.We propose an extension to Featherweight Java, called COFJ, where it is possible to define cyclic objects, abstractly corresponding to regular terms, and where an abstraction mechanism, called regular corecursion, is provided for supporting implementation of coinductive operations on cyclic objects.We formally define the operational semantics of COFJ, and provide a handful of examples showing the expressive power of regular corecursion; such a mechanism promotes a novel programming style particularly well-suited for implementing cyclic data structures, and for supporting coinductive reasoning.