A formal calculus for informal equality with binding

Authors:
Murdoch J. Gabbay;Aad Mathijssen
Affiliations:
School of Mathematical and Computer Sciences, Heriot-Watt University, Scotland, Great Britain;Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands
Venue:
WoLLIC'07 Proceedings of the 14th international conference on Logic, language, information and computation
Year:
2007

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Abstract

In informal mathematical usage we often reason using languages with binding.We usually find ourselves placing capture-avoidance constraints on where variables can and cannot occur free. We describe a logical derivation system which allows a direct formalisation of such assertions, along with a direct formalisation of their constraints. We base our logic on equality, probably the simplest available judgement form. In spite of this, we can axiomatise systems of logic and computation such as first-order logic or the lambda-calculus in a very direct and natural way. We investigate the theory of derivations, prove a suitable semantics sound and complete, and discuss existing and future research.