Mario Coppo

A new type assignment for λ-terms

In the present paper we propose a new type assignment for λ-terms whose motivation is to introduce a system with simple inferential rules to study termination (i.e. the property of having a normal form) of λ-terms. The main results that will be proved in this paper are:a)all λ-terms in normal form possess a type,b)all λ-terms which possess a type reduce to normal form.

Global Progress in Dynamically Interleaved Multiparty Sessions

A multiparty session forms a unit of structured interactions among many participants which follow a prescribed scenario specified as a global type signature. This paper develops, besides a more traditional communicationtype system, a novel static interactiontype system for global progress in dynamically interleaved multiparty sessions.

Global Progress for Dynamically Interleaved Multiparty Sessions

A multiparty session forms a unit of structured communication among many participants which follow communication sequences specified as a global type. When a process is engaged in two or more sessions simultaneously, different sessions can be interleaved and can interfere at runtime. Previous work on multiparty session types has ignored session interleaving, providing a limited progress property ensured only within a single session, by assuming non-interference among different sessions and by forbidding delegation. This paper develops, besides a more traditional, compositional communication type system, a novel static interaction type system for global progress in dynamically interleaved and interfered multiparty sessions. The interaction type system infers causalities of channels making sure that processes do not get stuck at intermediate stages of sessions also in presence of delegation.

Type inference with recursive types: syntax and semantics

Abstract In this paper we study type inference systems for λ-calculus with a recursion operator over types. The main syntactical properties, notably the existence of principal type schemes, are proved to hold when recursive types are viewed as finite notations for infinite (regular) type expressions representing their infinite unfoldings. Exploiting the approximation structure of a model for the untyped language of terms, types are interpreted as limits of sequences of their approximations. We show that the interpretation is essentially unique and that two types have equal interpretation if and only if their infinite unfoldings are identical. Finally, a completeness theorem is proved to hold w.r.t. the specific model we consider for a natural (infinitary) extension of the type inference system.

Asynchronous session types and progress for object oriented languages

A session type is an abstraction of a sequence of heterogeneous values sent over one channel between two communicating processes. Session types have been introduced to guarantee consistency of the exchanged data and, more recently, progress of the session, i.e. the property that once a communication has been established, well-formed programs will never starve at communication points. A relevant feature which influences progress is whether the communication is synchronous or asynchronous. In this paper, we first formulate a typed asynchronous multi-threaded object-oriented language with thread spawning, iterative and higher order sessions. Then we study its progress through a new effect system. As far as we know, ours is the first session type system which assures progress in asynchronous communication.

M3 mobility types for mobile processes in mobile ambients

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.

An Extended Polymorphic Type System for Applicative Languages

This paper deals with the problem of finding a type system for programming languages, which allows the greatest generality in the definition of polymorphic procedures. The type system introduced in this paper can be seen as an extension of the one proposed in /MLN/ (which is implemented in the language ML).

Type inference, abstract interpretation and strictness analysis

Abstract Filter 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 Π 0 1 property), but a complete extension of the type inference system is presented.

Functional Characterization of Some Semantic Equalities inside Lambda-Calculus

Both (operational or denotational) semantics and type theories for λ-calculus induce in a natural way equivalence relations between terms. The aim of the present paper is to show that in some cases the semantic and functional equivalences coincide.

A Complete Type Inference Algorithm for Simple Intersection Types

In this paper we present a decidable restriction of the intersection type discipline, obtained by combining intersection and universal quantification over types. The system, which has a notion of principal type, is a proper extension of the ML type system. A sound and complete type checking algorithm is presented and proved correct.