A necessary and sufficient condition in order that a Herbrand interpretation be expressive relative to recursive programs

It is proved that a recursive program (without counters) is able to enumerate all elements in any Herbrand interpretation. It follows that all recursive program domains in a Herbrand interpretation can be defined by first-order formulas iff there are first-order formulas expressing integer arithmetic in that interpretation

Kripke Semantics for Intersection Formulas

We propose a notion of the Kripke-style model for intersection logic. Using a game interpretation, we prove soundness and completeness of the proposed semantics. In other words, a formula is provable (a type is inhabited) if and only if it is forced in every model. As a by-product, we obtain another proof of normalization for the Barendregt–Coppo–Dezani intersection type assignment system

Using Inhabitation in Bounded Combinatory Logic with Intersection Types for Composition Synthesis

We describe ongoing work on a framework for automatic composition synthesis from a repository of software components. This work is based on combinatory logic with intersection types. The idea is that components are modeled as typed combinators, and an algorithm for inhabitation {\textemdash} is there a combinatory term e with type tau relative to an environment Gamma? {\textemdash} can be used to synthesize compositions. Here, Gamma represents the repository in the form of typed combinators, tau specifies the synthesis goal, and e is the synthesized program. We illustrate our approach by examples, including an application to synthesis from GUI-components.Comment: In Proceedings ITRS 2012, arXiv:1307.784

Discrimination by Parallel Observers: the Algorithm

The main result of the paper is a constructive proof of the following equivalence: two pure λ-terms are observationally equivalent in the lazy concurrent λ-calculus iff they have the same Lévy-Longo trees. An algorithm which allows to build a context discriminating any two pure λ-terms with different Lévy-Longo trees is described. It follows that contextual equivalence coincides with behavioural equivalence (bisimulation) as considered by Sangiorgi. Another consequence is that the discriminating power of concurrent lambda contexts is the same as that of Boudol-Laneve's contexts with multiplicities