Deriving Mixed Evaluation from Standard Evaluation for a Simple Functional Language

We demonstrate how a specification for the standard evaluation of a simple functional programming language can be systematically extended to a specification for mixed evaluation. Using techniques inspired by natural semantics we specify a standard evaluator by a set of inference rules. The evaluation of programs is then performed by a restricted kind of theorem proving in this logic. We then describe a systematic method for extending the proof system for standard evaluation to a new proof system that provides greater flexibility in treating bound variables in the object-level functional programs. We demonstrate how this extended proof system provides the capabilities of a mixed evaluator and how correctness with respect to standard evaluation can be proved in a simple and direct manner. The current work focuses only on a primitive notion of mixed evaluation for a simple functional programming language, but we believe that our methods will extend to more sophisticated kinds of evaluations and richer languages. Comments University of Pennsylvania Department of Computer and Information Science Technical Report No. MSCIS-89-28. This technical report is available at ScholarlyCommons: http://repository.upenn.edu/cis_reports/787 Deriving Mixed Evaluation From Standard Evaluation For A Simple Functional Language MS-CIS-89-28 LINC LAB 150 John Hannan Dale Miller Department of Computer and Information Science School of Engineering and Applied Science University of Pennsylvania Philadelphia, PA 19104-6389 May 1989 This is a revised version os a paper appearing at the International Conference on the Mathematics of Program Construction, Twente University, The Netherlands, June 1989. Acknowledgements: The first author is supported in part by a fellowship from the Corporate Research and Architecture Group, Digital Equipment Corporation, Maynard, MA USA. Both authors are supported in part by NSF grants CCR-05596-MCS-8219196-CER, IRI84-10413-A02, ONR N00014-88-K-0633, DARPA grant N00014-85-K-0018 and U.S. Army grants DAA29-84-K-0061, DAA29-84-9-0027 Deriving Mixed Evaluation from Standard Evaluation for a Simple Functional Language1 JOHN HANNAN and DALE MILLER Department of Computer and Information Science University of Pennsylvania Philadelphia, PA 191 04-6389 USA We demonstrate how a specification for the standard evaluation of a simple functional programming language can be systematically extended to a specification for mixed evaluation. Using techniques inspired by natural semantics we specify a standard evaluator by a set of inference rules. The evalu a, t' lon of programs is then performed by a restricted liind of theorem proving in this logic. We then describe a systematic method for extending the proof system for standard evaluation to a new proof system that provides greater flexibility in treating bound variables in the object-level functional programs. We demonstrate how this extended proof system provides the capabilities of a mixed evaluator and how correctness with respect to standard evaluation can be proved in a simple and direct manner. The current work focuses only on a primitive notion of mixed evaluation for a simple functional programming language, but we believe that our methods will extend to more sophisticated liinds of evaluations and richer languages.