@MISC{Kamareddine96auseful, author = {Fairouz Kamareddine and Rob Nederpelt}, title = {A Useful λ-Notation}, year = {1996} }

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Abstract

In this article, we introduce a -notation that is useful for many concepts of the - calculus. The new notation is a simple translation of the classical one. Yet, it provides many nice advantages. First, we show that definitions such as compatibility, the heart of a term and fi-redexes become simpler in item notation. Second, we show that with this item notation, reduction can be generalised in a nice way. We find a relation ; fi which extends ! fi , which is Church Rosser and Strongly Normalising. This reduction relation may be the way to new reduction strategies. In classical notation, it is much harder to present this generalised reduction in a convincing manner. Third, we show that the item notation enables one to represent in a very simple way the canonical type ø (\Gamma; A) of a term A in context \Gamma. This canonical type plays the role of a preference type and can be used to split \Gamma ` A : B in the two parts: \Gamma ` A and ø (\Gamma; A) = B. This means that the questio...