Fully Complete Minimal PER Models for the Simply Typed lambda-Calculus

Authors:
Samson Abramsky;Marina Lenisa
Affiliations:
-;-
Venue:
CSL '01 Proceedings of the 15th International Workshop on Computer Science Logic
Year:
2001

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Abstract

We show how to build a fully complete model for the maximal theory of the simply typed λ-calculus with k ground constants, λk. This is obtained by linear realizability over an affine combinatory algebra of partial involutions from natural numbers into natural numbers. For simplicitly, we give the details of the construction of a fully complete model for λk extended with ground permutations. The fully complete minimal model for λk 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.