Parametric λ-theories

  • Authors:
  • Luca Paolini

  • Affiliations:
  • Dipartimento di Informatica, Università degli Studi di Torino, Corso Svizzera, 185, 10149 Torino, Italy

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2008

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Abstract

The parametric lambda calculus subsumes different existing @l-calculi, in particular the classical @l@b-calculus and the @l@b"v-calculus of Plotkin. Previously established results on the parametric calculus, such as confluence and standardization, are primarily syntactical. In this paper our attention is mainly addressed to semantics, although we start again from a syntactical point of view. We propose an analysis of the notion of contextual preorders of usual operational semantics. Given a contextual preorder, we build a parametric complete lattice based on a closure operator. This lattice provides a fully abstract model for the considered preorder, via a completion.