This paper introduces a compositional program logic for higherorder polymorphic functions and standard data types. The logic enables us to reason about observable properties of polymorphic programs starting from those of their constituents. Just as types attached to programs offer information on their composability so as to guarantee basic safety of composite programs, formulae of the proposed logic attached to programs offer information on their composability so as to guarantee fine-grained behavioural properties of polymorphic programs. The central feature of the logic is a systematic usage of names and operations on them, whose origin is in the logics for typed π-calculi. The paper introduces the program logic and its proof rules and illustrates their usage by non-trivial reasoning examples, taking a prototypical call-by-value functional language with impredicative polymorphism and recursive types as a target language.

By using intersection types and filter models we formulate a theory of types for a λ-calculus with record subtyping via a finitary programming logic. Types are interpreted as spaces of filters over a subset of the language of properties (the intersection types) which describes the underlying type free realizability structure. We show that such an interpretation is a PER semantics, proving that the quotient space arising from “logical” PERs taken with the intrinsic ordering is isomorphic to the filter semantics of types.

Subtyping in first order object calculi is studied with respect to the logical semantics obtained by identifying terms that satisfy the same set of predicates, as formalised through an assignment system. It is shown that equality in the full first order ς-calculus is modelled by this notion, which in turn is included in a Morris-style contextual equivalence.

In this note we consider a restricted version of the intersection types for a #-calculus with records as presented in [5, 6] w.r.t. principal typing property and expressivity. We sketch how the classical approach to principal typing for intersection type assignment system can be adapted to cope with record types. We then exemplify typings in our system of self-application and recursive record interpretations of objects. 1

We investigate logical semantics of the first order #-calculus. An assignment system of predicates to first order typed terms of the OB1 calculus is introduced. We define retraction models for that calculus and an interpretation of terms, types and predicates into such models. The assignment system is then proved to be sound and complete w.r.t. retraction models. 1

this paper we show how they can be recast into algorithmic inference rules by applying a combination of standard techniques, among which constraint handling plays a central role. We then analyse the generated constraint sets and show that they share a common structure which can be simplified with a specialised algorithm we present. As the constraint simplification procedure is mainly based on unification, we implemented the whole inference algorithm in a Prolog program which we will comment upon

We present a procedure for computing normal forms of terms in Abadi and Cardelli’s functional object calculus. Even when equipped with simple types, terms of this calculus are not terminating in general, and we draw on recent ideas about the normalization by evaluation paradigm for the untyped lambda calculus. Technically, we work in the framework of Shinwell and Pitts ’ FM-domain theory, which leads to a normalization procedure for the object calculus that is directly implementable in a language like Fresh O’Caml.