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A comparison of Landin's form of lambda calculus with Church's shows that,independently of the lambda calculus, there exists a mechanism for convertingfunctions with arguments indexed by variables to the usual kind of functionwhere the arguments are indexed numerically. We call this the "lambdamechanism" and show how it can be used in other calculi. In first-orderpredicate logic it can be used to define new functions and new predicates interms of existing ones. In a purely imperative programming language it can beused to provide an Algol-like procedure facility.

The lambda mechanism in lambda calculus and in other calculi