Categorical Combinators arose from the intertranslation between lambda-calculus and Cartesian Closed Categories. Their theory is fairly similar to classical Combinatory Logic, and they also have been used for the design of the so called Categorical A

A technique is presented for comparing the performance of functional languages with different evaluation strategies running on different machines. A set of small benchmarks is used, and th execution times of these programs running in the functional language and in the implementation language of the functional system are compared. The ratio of these execution times measured how well the functional system used the resources of the underlying hardware and implementation language. Also two functional programming systems are described. One system is a graph reduction interpreter for lambda calculus. The other is a DEL-style intermediate instruction set architecture for FP. The benchmarks in FP and the performances of the two systems on these benchmarks are presented.>

In the standard presentations of $\lambda $-calculus (e.g., in [H. Barendregt, The Lambda Calculus, Its Syntax and Semantics, North-Holland, Amsterdam, 1981] or [J. R. Hindley, B. Lecher, J. P. Seldin, Introduction to Combinatory Logic, Cambridge Univ. Press, London, 1972]) the operation of substitution is defined as a primitive operation and used in the definition of convertibility. In the present paper we show that the axioms for the theory of lambda-conversion can be simplified in such a way that substitution is not needed at all, as it is reduced to a more elementary operation of replacement without giving up the intuitive simplicity of the lambda-notation. This is achieved by making essential use of the properties of substitution in formulating the axiom system. Also, another unusual axiom system will be presented which uses renaming that replaces every (free or bound) occurrence of a variable by another. Finally, we give the outline of a program written in PL/I that computes the normal form (if any) of $\lambda $-terms by using our axioms.