Behavioural inverse limit λ-models

  • Authors:

  • Mariangiola Dezani-Ciancaglini;Silvia Ghilezan;Silvia Likavec

  • Affiliations:

  • Dipartimento di Informatica, Università di Torino, Corso Svizzera 185, 10149 Torino, Italy;Faculty of Engineering, University of Novi Sad, Trg D. Obradovića 6, Novi Sad 21000, Yugoslavia;Dipartimento di Informatica, Università di Torino, 10149 Torino, Italy and Faculty of Eng., Univ. of Novi Sad, Trg D. Obradovića 6, Novi Sad 21000, Yugoslavia and École Normale Sup& ...

  • Venue:
  • Theoretical Computer Science - Logic, semantics and theory of programming
  • Year:
  • 2004

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Abstract

We construct two inverse limit λ-models which completely characterise sets of terms with similar computational behaviours: the sets of normalising, head normalising, weak head normalising λ-terms, those corresponding to the persistent versions of these notions, and the sets of closable, closable normalising, and closable head normalising λ-terms. More precisely, for each of these sets of terms there is a corresponding element in at least one of the two models such that a term belongs to the set if and only if its interpretation (in a suitable environment) is greater than or equal to that element. We use the finitary logical description of the models, obtained by defining suitable intersection type assignment systems, to prove this.