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Regular corecursion in Prolog
No full textCorecursion is the ability of defining a function that produces some infinite data in terms of the function and the data itself, as supported by lazy evaluation. However, in languages such as Haskell strict operations fail to terminate even on infinite regular data, that is, cyclic data. Regular corecursion is naturally supported by coinductive Prolog, an extension where predicates can be interpreted either inductively or coinductively, that has proved to be useful for formal verification, static analysis and symbolic evaluation of programs. In this paper we use the meta-programming facilities offered by Prolog to propose extensions to coinductive Prolog aiming to make regular corecursion more expressive and easier to program with. First, we propose a new interpreter to solve the problem of non-terminating failure as experienced with the standard semantics of coinduction (as supported, for instance, in SWI-Prolog). Another problem with the standard semantics is that predicates expressed in terms of existential quantification over a regular term cannot directly defined by coinduction; to this aim, we introduce finally clauses, to allow more flexibility in coinductive definitions. Then we investigate the possibility of annotating arguments of coinductive predicates, to restrict coinductive definitions to a subset of the arguments; this allows more efficient definitions, and further enhance the expressive power of coinductive Prolog. We investigate the effectiveness of such features by showing different example programs manipulating several kinds of cyclic values, ranging from automata and context free grammars to graphs and repeating decimals; the examples show how computations on cyclic values can be expressed with concise and relatively simple programs. The semantics defined by these vanilla meta-interpreters are an interesting starting point for a more mature design and implementation of coinductive Prolog
Preface to the special section on Object-Oriented Programming and Systems (OOPS 2009), a special track at the 24th ACM Symposium on Applied Computing
No full textRegular corecursion in Prolog
No full textCo-recursion is the ability of defining a function that produces some infinite data in terms of the function and the data itself, and is typically supported by languages with lazy evaluation. However, in languages as Haskell strict operations fail to terminate even on infinite regular data. Regular co-recursion is naturally supported by co-inductive Prolog, an extension where predicates can be interpreted either inductively or co-inductively, that has proved to be useful for formal verification, static analysis and symbolic evaluation of programs. In this paper we propose two main alternative vanilla meta-interpreters to support regular co-recursion in Prolog as an interesting programming style in its own right, able to elegantly solve problems that would require more complex code if conventional recursion were used. In particular, the second meta-interpreters avoids non termination in several cases, by restricting the set of possible answers. The semantics defined by these vanilla meta-interpreters are an interesting starting point to study new semantics able to support regular co-recursion for non logical languages
How to prove type soundness of Java-like languages without forgoing big-step semantics
No full textSmall-step operational semantics is the most commonly employed formalism for
proving type soundness of statically typed programming languages, because
of its ability to distinguish stuck from non-terminating computations,
as opposed to big-step operational semantics.
Despite this, big-step operational semantics is more abstract, and more
useful for specifying interpreters.
In previous work we have proposed a new proof technique to prove type soundness
of a Java-like language expressed in terms of its big-step operational semantics.
However the presented proof is rather involved, since it
requires showing that the set of proof trees defining the semantic judgment forms a complete metric space
when equipped with a specific distance function.
In this paper we propose a more direct and abstract approach that exploits a standard and general compactness property
of the metric space of values, that allows approximation of the coinductive big-step semantics in terms of the small-step one;
in this way type soundness can be proved by standard mathematical induction
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