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
alpha 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].