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Fully Complete Minimal PER Models for the Simply Typed -calculus ?
 

Summary: Fully Complete Minimal PER Models for the
Simply Typed -calculus ?
Samson Abramsky 1 and Marina Lenisa 2
1 Oxford University Computing Laboratory
Wolfson Building, Parks Road, OX1 3QD, England.
e-mail: Samson.Abramsky@comlab.ox.ac.uk
2 Dipartimento di Matematica e Informatica, Universita di Udine,
Via delle Scienze 206, 33100 Udine, ITALY.
e-mail: lenisa@dimi.uniud.it.
Abstract. We show how to build a fully complete model for the maximal
theory of the simply typed -calculus with k ground constants, k . This
is obtained by linear realizability over an aĆne combinatory algebra of
partial involutions from natural numbers into natural numbers. For sim-
plicitly, we give the details of the construction of a fully complete model
for k extended with ground permutations. The fully complete minimal
model for k can be obtained by carrying out the previous construction
over a suitable subalgebra of partial involutions. The full completeness
result is then put to use in order to prove some simple results on the
maximal theory.
Introduction

  

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

 

Collections: Computer Technologies and Information Sciences; Mathematics