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A Fully Complete PER Model for ML Polymorphic Types

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.
e­mail: samson@dcs.ed.ac.uk
2 Dipartimento di Matematica e Informatica, Universit`a di Udine,
Viale delle Scienze 206, 33100 Udine, ITALY.
e­mail: lenisa@dimi.uniud.it
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


Source: Abramsky, Samson - Computing Laboratory, University of Oxford
Lenisa, Marina - Dipartimento di Matematica e Informatica, Università degli Studi di Udine


Collections: Computer Technologies and Information Sciences; Mathematics