A Set of Combinators for Abstraction in Linear Space

Abstract A set of simple indexed combinators and an associated linear abstraction algorithm are presented, allowing to translate a combinator expression into a combinator code containing no variables, in such a way that the length of the generated code is less than twice the length of the original expression in the usual case. The key idea of this algorithm is to operate globally on all variables during the whole abstraction process. This set of combinators is intended for practical use as a reduction machine instruction set.