A Formal Calculus for Informal Equality with Binding [chapter]

Murdoch J. Gabbay, Aad Mathijssen
2007 Lecture Notes in Computer Science  
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
more » ... -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.
doi:10.1007/978-3-540-73445-1_12 fatcat:wntzp5iacrhtzfifjyyxcsae6m