De Bruijn notation

(language)A variation of lambda notation for specifyingfunctions using numbers instead of names to refer to formal parameters. A reference to a formal parameter is a numberwhich gives the number of lambdas (written as \\ here) betweenthe reference and the lambda which binds the parameter.E.g. the function \\ f . \\ x . f x would be written \\ . \\ . 10. The 0 refers to the innermost lambda, the 1 to the nextetc. The chief advantage of this notation is that it avoidsthe possibility of name capture and removes the need for alpha conversion.

[N.G. De Bruijn, "Lambda Calculus Notation with NamelessDummies: A Tool for Automatic Formula Manipulation, withApplication to the Church-Rosser Theorem", Indag Math. 34, pp381-392].

单词	de bruijn notation
释义	De Bruijn notation De Bruijn notation (language)A variation of lambda notation for specifyingfunctions using numbers instead of names to refer to formal parameters. A reference to a formal parameter is a numberwhich gives the number of lambdas (written as \\ here) betweenthe reference and the lambda which binds the parameter.E.g. the function \\ f . \\ x . f x would be written \\ . \\ . 10. The 0 refers to the innermost lambda, the 1 to the nextetc. The chief advantage of this notation is that it avoidsthe possibility of name capture and removes the need for alpha conversion. [N.G. De Bruijn, "Lambda Calculus Notation with NamelessDummies: A Tool for Automatic Formula Manipulation, withApplication to the Church-Rosser Theorem", Indag Math. 34, pp381-392].
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