structural:expansion
CL versus CL calculus

A distinction must be made between the CL as described in this article and the CL calculus. The distinction corresponds to that between the λ and the λ calculus. Unlike the λ calculus, the λ calculus restricts abstractions to:

As a consequence, combinator K is not present in the λ calculus nor in the CL calculus. The constants of CL are: I, B, C and S, which form a basis from which all CL terms can be composed (modulo equality). Every λ term can be converted into an equal CL combinator according to rules similar to those presented above for the conversion of λ terms into CL combinators. See chapter 9 in Barendregt (1984).