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Consistency of the theory of contexts

Published online by Cambridge University Press:  25 October 2016

ANNA BUCALO
Affiliation:
Department of Mathematics and Computer Science, University of Udine, Italy email: miculan@dimi.uniud.it
FURIO HONSELL
Affiliation:
Department of Mathematics and Computer Science, University of Udine, Italy email: miculan@dimi.uniud.it
MARINO MICULAN
Affiliation:
Department of Mathematics and Computer Science, University of Udine, Italy email: miculan@dimi.uniud.it
IVAN SCAGNETTO
Affiliation:
Department of Mathematics and Computer Science, University of Udine, Italy email: miculan@dimi.uniud.it
MARTIN HOFFMAN
Affiliation:
Institut für Informatik, Ludwig-Maximilians-Universität, München, Germany
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Abstract

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The Theory of Contexts is a type-theoretic axiomatization aiming to give a metalogical account of the fundamental notions of variable and context as they appear in Higher Order Abstract Syntax. In this paper, we prove that this theory is consistent by building a model based on functor categories. By means of a suitable notion of forcing, we prove that this model validates Classical Higher Order Logic, the Theory of Contexts, and also (parametrised) structural induction and recursion principles over contexts. Our approach, which we present in full detail, should also be useful for reasoning on other models based on functor categories. Moreover, the construction could also be adopted, and possibly generalized, for validating other theories of names and binders.

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Article
Copyright
2006 Cambridge University Press
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