Ines Margaria

A characterization of F-complete type assignments

The aim of this paper is to investigate the soundness and completeness of the intersection type discipline (for terms of the (untyped ?-calculus) with respect to the F-semantics (F-soundness and F-completeness).As pointed out by Scott, if D is the domain of a ?-model, there is a subset F of D whose elements are the `canonical? representatives of functions. The F-semantics of types takes into account that theintuitive meaning of “???” is `the type of functions with domain ? and range ?? and interprets ??? as a subset of F.The type theories which induce F-complete type assignments are characterized. It follows that a type assignment is F-complete iff equal terms get equal types and, whenever M has a type ???n, where ? is a type variable and ? is the `universal? type, the term ?z1?zn?Mz1?zn has type ?. Here we assume that z1?z.n do not occur free in M.

Filter models with polymorphic types

Abstract Using ideas and results from Barendrecht (1983) and Coppo (1984) on intersection types, a comparable theory is developed for (second order) polymorphic types. The set of filters constructed with polymorphic type forms, with inclusion, a continuous lattice which yields a model of what we call βη-expansion (i.e. the value of a term increases under βη-reduction), but not of β-conversion. Combining intersection with polymorphic types does give filter λ-models, but the two standard ways of interpreting λ-terms do not coincide.

F-semantics for intersection type discipline

Aim of this paper is to investigate the soundness and completeness for the F-semantics (F-soundness and F-completeness) of some modifications of the intersection type discipline for terms of the (untyped) λ-calculus.

Principal Typing in a ∀Λ-Discipline

In this paper we study the problem of finding a principal typing for a A-term in a polymorphic intersection type assignment system. Following the approach of Coppo el aL, Ronchi and Venneri, the principal type is proved to exist for any A-term with a finite set of approximants. In the same way the existence of the principal type is shown for BCKA-terms in a polymorphic type assignment system. Keywordr. A-calculus, approximation theorem, intersection types, polymorphic types, principal typing.

Isomorphism of intersection and union types

This paper investigates type isomorphism in a lambda-calculus with intersection and union types. It is known that in lambda-calculus, the isomorphism between two types is realised by a pair of terms inverse one each other. Notably, invertible terms are linear terms of a particular shape, called finite hereditary permutators. Typing properties of finite hereditary permutators are then studied in a relevant type inference system with intersection and union types for linear terms. In particular, an isomorphism preserving reduction between types is defined. Type reduction is confluent and terminating, and induces a notion of normal form of types. The properties of normal types are a crucial step toward the complete characterisation of type isomorphism. The main results of this paper are, on one hand, the fact that two types with the same normal form are isomorphic, on the other hand, the characterisation of the isomorphism between types in normal form, modulo isomorphism of arrow types.

Toward Isomorphism of Intersection and Union Types

This paper investigates type isomorphism in a λ-calculus with intersection and union types. It is known that in λ-calculus, the isomorphism between two types is realised by a pair of terms inverse one each other. Notably, invertible terms are linear terms of a particular shape, called finite hereditary permutators. Typing properties of finite hereditary permutators are then studied in a relevant type inference system with intersection and union types for linear terms. In particular, an isomorphism preserving reduction between types is defined. Reduction of types is confluent and terminating, and induces a notion of normal form of types. The properties of normal types are a crucial step toward the complete characterisation of type isomorphism. The main results of this paper are, on one hand, the fact that two types with the same normal form are isomorphic, on the other hand, the characterisation of the isomorphism between types in normal form, modulo isomorphism of arrow types.

On Isomorphism of "Functional" Intersection and Union Types.

Type isomorphism is useful for retrieving library components, since a function in a library can have a type different from, but isomorphic to, the one expected by the user. Moreover type isomorphism gives for free the coercion required to include the function in the user program with the right type. The present paper faces the problem of type isomorphism in a system with intersection and union types. In the presence of intersection and union, isomorphism is not a congruence and cannot be characterised in an equational way. A characterisation can still be given, quite complicated by the interference between functional and non functional types. This drawback is faced in the paper by interpreting each atomic type as the set of functions mapping any argument into the interpretation of the type itself. This choice has been suggested by the initial projection of Scotts inverse limit lambda-model. The main result of this paper is a condition assuring type isomorphism, based on an isomorphism preserving reduction.

Access control in mobile ambient calculi: A comparative view

Ambient Calculi represent a class of process calculi used to describe and model mobile and distributed computations. This paper examines the most relevant of these calculi and focuses on an important dimension: the access control problem. In the security world, a system is considered trusted if it controls the access to its resources, i.e. every request for the access to a resource is honored if and only if the subject requiring the resource is an authorized user of the system and the request agrees with a given policy. So the security problem for ambient calculi is investigated considering the authentication mechanism and the possibility to implement security policies. Two examples have been chosen to illustrate these topics: the firewall and the communication by means of named channels.

Retractions in Intersection Types.

This paper deals with retraction - intended as isomorphic embedding - in intersection types building left and right inverses as terms of a lambda calculus with a bottom constant. The main result is a necessary and sufficient condition two strict intersection types must satisfy in order to assure the existence of two terms showing the first type to be a retract of the second one. Moreover, the characterisation of retraction in the standard intersection types is discussed.

Partial and Complete Processes in Multiparty Sessions

Multiparty sessions describe the interactions among multiple agents in a distributed environment and require essentially two steps: the specification of the communication protocols and the implementation of such protocols as processes. Multiparty session types address this methodology: global and session types provide the communication protocols, whereas the processes describe the behaviour of the peers involved in the sessions. Because of the close relationships between types and processes, some information, such as the names of senders and receivers, are replicated both in types and in processes. In multiparty conversations it is quite natural that participants with essentially the same role are implemented by processes that follow the same pattern, differing only in the senders and receivers of communication actions. In order to allow for a lighter and less rigid development of processes, we propose a translation tool which allows one to write processes in a simplified syntax, called partial syntax, where the names of senders/receivers for input/output operations are omitted. By adding the missing information, partial processes can be automatically translated in complete processes, for which an operational semantics is defined. The partial syntax, in particular, allows one to use the same process template to implement similar participants. In this paper we present a translation and type checking algorithm from partial to complete processes, which, if successful, also assures that the target processes are well typed. The algorithm is synthesised from a rule-based description of the translation in natural semantics and it is proved sound and complete with respect to the translation rules.