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Cut Elimination for A WeaklyTyped Higher Order Logic James H. Andrews

Summary: Cut Elimination for A Weakly­Typed Higher Order Logic
James H. Andrews
Report No. 611
December 2003
Department of Computer Science
University of Western Ontario
London, Canada
N6A 5B7

Abstract: Cut­elimination is proved for a weakly­typed higher order logic
based on those presented by Gilmore. The logic allows lambda­abstraction over
terms and formulas, permitting all terms of the untyped lambda calculus includ­
ing the Y combinator, and providing various methods of expressing recursive
functions and predicates. Consistency is achieved in the logic via a nominalist
distinction between use and mention of terms. This report is intended as a
companion to Andrews, ``A Weakly­Typed Logic with General Lambda Terms
and Y­Combinator'', Works in Progress Track, TPHOLs 2002, which presented
the syntax, semantics and consistency of the logic.


Source: Andrews, Jamie - Department of Computer Science, University of Western Ontario


Collections: Computer Technologies and Information Sciences