Generalized filter models

AbstractIn this paper, starting from filters which are a natural generalization of intersection filters (Barendregt et al., J. Symbolic Logic 48 (1983) 931–940), the existence of filter models and filter semimodels for the λ-calculus is investigated. The construction of filters is based on a Z-semilattice of types in which the subsets having infimum are given by a collection Z, called subset system. The set of representable functions is characterized in the obtained domain. In the case where the properties of the subset system Z guarantee the existence of a filter model, the proof of soundness and completeness of the associated natural Z-type assignment system is routine

Foundations of session types and behavioural contracts

Behavioural type systems, usually associated to concurrent or distributed computations, encompass concepts such as interfaces, communication protocols, and contracts, in addition to the traditional input/output operations. The behavioural type of a software component specifies its expected patterns of interaction using expressive type languages, so types can be used to determine automatically whether the component interacts correctly with other components. Two related important notions of behavioural types are those of session types and behavioural contracts. This article surveys the main accomplishments of the last 20 years within these two approaches

Type Inference, Abstract Interpretation and Strictness Analysis.

AbstractFilter domains (Coppo et al.,1984) can be seen as abstract domains for the interpretation of (functional) type-free programming languages. What is remarkable is the fact that in filter domains the interpretation of a term is given by the set of its types in the intersection type discipline with inclusion, thus reducing the computation of an abstract interpretation to typechecking. As a main example, an abstract filter domain for strictness analysis of type-free functional languages is presented. The inclusion relation between types representing strictness properties has a complete recursive axiomatization. Type inference rules cannot be complete (strictness being a Π01 property), but a complete extension of the type inference system is presented