Logical Semantics for Stability

  • Authors:

  • Luca Paolini;Mauro Piccolo;Simona Ronchi Della Rocca

  • Affiliations:

  • Dipartimento di Informatica, Università di Torino, Torino, Italy;Dipartimento di Informatica, Università di Torino, Torino, Italy and Laboratoire PPS, Universitè de Paris VII, Paris, France;Dipartimento di Informatica, Università di Torino, Torino, Italy

  • Venue:
  • Electronic Notes in Theoretical Computer Science (ENTCS)
  • Year:
  • 2009

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Abstract

Type assignment systems for @l-calculus based on intersection types are a general framework for building models of @l-calculus (known as filter-models) which are useful tools for reasoning in a finitary way about the denotational interpretation of terms. Indeed the denotation of a term is the set of types derivable for it and a type is a ''finite piece'' of information on such a denotation. This approach to the @l-calculus semantics is called in the literature logical semantics, and it has been intensively studied in relation with @l-models in the Scott's domain setting. In this paper we define two intersection type assignment systems for @l-calculus, parametric with respect to a coherence relation between types. We prove that, when the instantiation of the parameter satisfies a given condition, our two type systems induce models of @l-calculus, that we call clique-models. Lastly we show that such systems give a logical characterization of two classes of models built on the category of Girard's coherence spaces and stable functions