Abstract: This paper presents a new method for comparing computation-properties of λ-terms typeable with intersection types with respect to terms typeable with Curry types. In particular, strong normalization and λ-definability are investigated. A translation is introduced from intersection typing derivations to Curry typeable terms; the main feature of the proposed technique is that the translation is preserved by β-reduction. This allows to simulate a computation starting from a term typeable in the intersection discipline by means of a computation starting from a simply typeable term. Our approach naturally leads to prove strong normalization in the intersection system by means of purely syntactical techniques. In addition, the presented method enables us to give a proof of a conjecture proposed by Leivant in 1990, namely that all functions uniformly definable using intersection types are already definable using Curry types.

Abstract: In the type frame originating from the flat domain of boolean values, we single out elements which are hereditarily total. We show that these elements can be defined, up to total equivalence, by sequential programs. The elements of an equivalence class of the totality equivalence relation (totality class) can be seen as different algorithms for computing a given set-theoretic boolean function. We show that the bottom element of a totality class, which is sequential, corresponds to the most eager algorithm, and the top to the laziest one. Finally we suggest a link between size of totality classes and a well known measure of complexity of boolean functions, namely their sensitivity.

Abstract: We present an ambient-like calculus in which the open capability is dropped, and a new form of “lightweight� process mobility is introduced. The calculus comes equipped with a type system that allows the kind of values exchanged in communications and the access and mobility properties of processes to be controlled. A type inference procedure determines the “minimal� requirements to accept a system or a component as well typed. This gives a kind of principal typing. As an expressiveness test, we show that some well known calculi of concurrency and mobility can be encoded in our calculus in a natural way.

Abstract: Basic properties of rewriting systems can be stated in the framework of abstract reduction systems (ARS). Properties like confluence (or Church-Rosser, CR) and weak confluence (or weak Church-Rosser, WCR) and their relationships can be studied in this setting: as a matter of fact, well-known counterexamples to the implication WCR CR have been formulated as ARS. In this paper, starting from the observation that such counterexamples are structurally similar, we set out a graph-theoretic characterization of WCR ARS that is not CR in terms of a suitable class of reduction graphs, such that in every WCR not CR ARS, we can embed at least one element of this class. Moreover, we give a tighter characterization for a restricted class of ARS enjoying a suitable regularity condition. Finally, as a consequence of our approach, we prove some interesting results about ARS using the mathematical tools developed. In particular, we prove an extension of the Newman’s lemma and we find out conditions that, once assumed together with WCR property, ensure the unique normal form property. The Appendix treats two interesting examples, both generated by graph-rewriting rules, with specific combinatorial properties.