1. De Bruijn notation A variation of lambda notation for specifying functions using numbers instead of names to refer to formal parameters. A reference to a formal parameter is a number which gives the number of lambdas written as here between the reference and the lambda which binds the parameter. E. g. the function f . x . f x would be written . . 1 0. The 0 refers to the innermost lambda, the 1 to the next etc. The chief advantage of this notation is that it avoids the possibility of name capture and removes the need for al conversion. [N. G. De Bruijn, "Lambda Calculus Notation with Nameless Dummies: A Tool for Automatic Formula Manipulation, with Application to the Church-Rosser Theorem", Indag Math. 34, pp 381-392].
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