We propose a paradigmatic programming language (called S PCF) which is linear in a semantic sense. S PCF is not syntactically linear, namely its programs can contain more than one occurrencies of the same variable. We give an interpretation of S PCF into a model of linear coherence spaces and we show that such semantics is fully abstract with respect to our language. Furthermore, we discuss the independence of new syntactical operators and we address the universality problem.

Essential and relational models † Intersection type assignment systems can be used as a general framework for building logical models of λ-calculus that allow to reason about the denotation of terms in a finitary way. We define essential models (a new class of logical models) through a parametric type assignment system using non-idempotent intersection types. Under an interpretation of terms based on typings instead than the usual one based on types, every suitable instance of the parameters induces a λ-model, whose theory is sensible. We prove that this type assignment system provides a logical description of a family of λ-models arising from a category of sets and relations.

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