We present a Java-like language in which objects are explicitly put in regions. The language has constructs for allocating, updating and deallocating regions, as well as region types for objects. For this language we present a static semantics ensuring that well-typed programs use regions safely, and we present a dynamic semantics that is intentional with respect to a region-based store. We formulate and prove a soundness theorem stating that well-typed programs do not go wrong. Finally, we develop a concrete model for implementing regions, and we compare this model to garbage collection for small examples.

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The Calculus of Inductive Constructions (CIC) is a powerful type system, featuring dependent types and inductive definitions, that forms the basis of proof-assistant systems such as Coq and Lego. We extend CIC with constructor subtyping, a basic form of subtyping in which an inductive type σ is viewed as a subtype of another inductive type τ if τ has more elements than σ. It is shown that the calculus is well-behaved and provides a suitable basis for formalizing natural semantics in proof-development systems.

Proof tools must be well designed if they...

We present a natural semantics for the untyped lazy -calculus plus McCarthy's amb, a nondeterministic choice operator. The natural semantics includes rules for both convergent behaviour (dened inductively) and divergent behaviour (dened co-inductively). This semantics is equivalent to a small step reduction semantics that corresponds closely to our operational intuitions about McCarthy's amb. We present equivalences for convergent and divergent behaviour based on the natural semantics and prove a Context Lemma for the convergence equivalence. We then give a -theory l 8 , based on the equivalences for convergent and divergent behaviour. Since it is able to distinguish between programs that dier only in their divergent behaviour, the -theory is more discriminating than equational theories based on current domain-theoretic models. It is therefore more suitable for reasoning about functional programs containing McCarthy's amb. Contents 1 Introduction 2 2 Related Work 3 3 ...

This paper focuses on the assignment of meaning to infinite derivations in logic programming. Several approaches have been developped by considering infinite elements in the universe of the discourse but none are complete. By considering proofs as objects in a co-inductive set, standard properties of co-inductive definitions are used both to explain this incompleteness and to define a sound and complete semantics, based on the logic program as co-inductive denition paradigm, for a subclass of infinite derivations, called infinite derivations over a finite domain (i.e. derivations which do not compute infinite terms).