Abstract
AbstractCategorical combinators form a formal system similar to Curry's combinatory logic. The original system was developed by Curien, inspired by the equivalence of the theories of typed λ‐calculus and Cartesian closed categories, as shown by Lambek and Scott. A new system for categorical combinators was introduced by the author. This system uses a more compact notation for the code and needs a smaller set of rewriting rules.The aim of this paper is to analyse these two different rewriting systems for categorical combinators as a basis for implementation of applicative languages, and compare them with the classical approach due to Turner, using combinatory logic.
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