Summary: A Fully Complete PER Model for
ML Polymorphic Types
Samson Abramsky 1 and Marina Lenisa 2 ?
1 LFCS, Division of Informatics, University of Edinburgh,
The King's Buildings, Mayfield Road, Edinburgh EH9 3JZ, UK.
2 Dipartimento di Matematica e Informatica, Universit`a di Udine,
Viale delle Scienze 206, 33100 Udine, ITALY.
Abstract. We present a linear realizability technique for building Par
tial 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 coKleisli 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: MLpolymorphic types, linear logic, PER models, Geometry
of Interaction, full completeness.
Recently, Game Semantics has been used to define fullycomplete models for