Intersection types for λ-trees

  • Authors:
  • Steffan van Bakel;Franco Barbanera;Mariangiola Dezani-Diancaglini;Fer-Jan de Vries

  • Affiliations:
  • Imperial College, London, UK;Univ. degli Studi di Catania, Catania, Italy;Univ. delgi Studi di Tornio Corso, Turin, Italy;Univ. of Leicester, Leicester, UK

  • Venue:
  • Theoretical Computer Science - Special issue on theories of types and proofs
  • Year:
  • 2002

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Abstract

We introduce a type assignment system which is parametric withrespect to five families of trees obtained by evaluatingλ-terms (Bhm trees, Lvy-Longo trees, etc.). Then we prove,in an (almost) uniform way, that each type assignment system fullydescribes the observational equivalences induced by thecorresponding tree representation of λ-terms. Moreprecisely, for each family of trees, two λ-terms have thesame tree if and only if they get assigned the same types in thecorresponding type assignment system. Copyright 2002, ElsevierScience B.V.