@article{oai:ipsj.ixsq.nii.ac.jp:00059885,
 author = {Masato, Takeichi and Masato, Takeichi},
 issue = {4},
 journal = {Journal of Information Processing},
 month = {Feb},
 note = {Turner shows how combinators can be used for implementing applicative languages. In his method  a combinator expression is represented by a graph with the nodes comprising functions and their arguments. Application of a function to an argument causes graph reduction which corresponds to the beta-reduction of lambda calculus. Graph reduction is performed in a way such that the node representing a functional application is over-written by its result. Another scheme for combinator expression evaluation is proposed by Jones and Muchnick. Although their evaluator is a fixed-program and would have some advantages over Turner's graph reduction scheme  it seems unusual in dealing with higher order functions. In this paper we describe an alternative scheme for evaluating combinator expressions. The evaluator is almost a fixed-program and is easily extended to include new combinators. It deals with higher order functions consistently as Turner's evaluator does. That is  the proposed scheme shares both advantages of Turner's graph reduction and of a fixed-program. And it is most attractive in implementing the evaluator on conventional hardware. An experimental evaluator is also presented., Turner shows how combinators can be used for implementing applicative languages. In his method, a combinator expression is represented by a graph with the nodes comprising functions and their arguments. Application of a function to an argument causes graph reduction which corresponds to the beta-reduction of lambda calculus. Graph reduction is performed in a way such that the node representing a functional application is over-written by its result. Another scheme for combinator expression evaluation is proposed by Jones and Muchnick. Although their evaluator is a fixed-program and would have some advantages over Turner's graph reduction scheme, it seems unusual in dealing with higher order functions. In this paper we describe an alternative scheme for evaluating combinator expressions. The evaluator is almost a fixed-program and is easily extended to include new combinators. It deals with higher order functions consistently as Turner's evaluator does. That is, the proposed scheme shares both advantages of Turner's graph reduction and of a fixed-program. And it is most attractive in implementing the evaluator on conventional hardware. An experimental evaluator is also presented.},
 pages = {246--253},
 title = {An Alternative Scheme for Evaluating Combinator Expressions},
 volume = {7},
 year = {1985}
}