1,637 research outputs found
Sound and Complete Typing for lambda-mu
In this paper we define intersection and union type assignment for Parigot's
calculus lambda-mu. We show that this notion is complete (i.e. closed under
subject-expansion), and show also that it is sound (i.e. closed under
subject-reduction). This implies that this notion of intersection-union type
assignment is suitable to define a semantics.Comment: In Proceedings ITRS 2010, arXiv:1101.410
Semantic Predicate Types and Approximation for Class-based Object Oriented Programming
We apply the principles of the intersection type discipline to the study of
class-based object oriented programs and; our work follows from a similar
approach (in the context of Abadi and Cardelli's Varsigma-object calculus)
taken by van Bakel and de'Liguoro. We define an extension of Featherweight
Java, FJc and present a predicate system which we show to be sound and
expressive. We also show that our system provides a semantic underpinning for
the object oriented paradigm by generalising the concept of approximant from
the Lambda Calculus and demonstrating an approximation result: all expressions
to which we can assign a predicate have an approximant that satisfies the same
predicate. Crucial to this result is the notion of predicate language, which
associates a family of predicates with a class.Comment: Proceedings of 11th Workshop on Formal Techniques for Java-like
Programs (FTfJP'09), Genova, Italy, July 6 200
Polymorphic intersection type assignment for rewrite systems with abstraction and -rul
We define two type assignment systems for first-order rewriting extended with application, -abstraction, and -reduction, using a combination of intersection types and second-order polymorphic types. The first system is the general one, for which we prove subject reduction, and strong normalisation of typeable terms. The second is a decidable subsystem of the first, by restricting to rank 2 (intersection and quantified) types. For this system we define, using an extended notion of unification, a notion of principal typing which is more general than ML’s principal type property, since also the types for the free variables of terms are inferre
Approximation Semantics and Expressive Predicate Assignment for Object-Oriented Programming
We consider a semantics for a class-based object-oriented calculus based upon approximation; since in the context of LC such a semantics enjoys a strong correspondence with intersection type assignment systems, we also define such a system for our calculus and show that it is sound and complete. We establish the link with between type (we use the terminology predicate here) assignment and the approximation semantics by showing an approximation result, which leads to a sufficient condition for head-normalisation and termination.
We show the expressivity of our predicate system by defining an encoding of Combinatory Logic (and so also LC) into our calculus. We show that this encoding preserves predicate-ability and also that our system characterises the normalising and strongly normalising terms for this encoding, demonstrating that the great analytic capabilities of these predicates can be applied to OO
Functional Type Assignment for Featherweight Java
Abstract. We consider functional type assignment for the class-based objectoriented calculus Featherweight Java. We start with an intersection type assignment systems for this calculus for which types are preserved under conversion. We then define a variant for which type assignment is decidable, and define a notion of unification as well as a principal typeing algorithm. We show the expressivity of both our calculus and our type system by defining an encoding of Combinatory Logic into our calculus and showing that this encoding preserves typeability. We thus demonstrate that the great capabilities of functional types can be applied to the context of class-based object orientated programming
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