Chapter

Computer Science Logic

Volume 1862 of the series Lecture Notes in Computer Science pp 140-155

Date:

A Fully Complete PER Model for ML Polymorphic Types

  • Samson AbramskyAffiliated withLFCS, Division of Informatics, University of Edinburgh
  • , Marina LenisaAffiliated withDipartimento di Matematica e Informatica, Università di Udine

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Abstract

We present a linear realizability technique for building Partial Equivalence Relations (PER) categories over Linear Combinatory Algebras. These PER categories turn out to be linear categories and to form an adjoint model with their co-Kleisli categories. We show that a special linear combinatory algebra of partial involutions, arising from Geometry of Interaction constructions, gives rise to a fully and faithfully complete model for ML polymorphic types of system F.

Keywords

ML-polymorphic types linear logic PER models Geometry of Interaction full completeness