Source : Free On-Line Dictionary of Computing

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 {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].
     
        (2003-06-15)