An algorithm for optimal lambda calculus reduction

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An algorithm for optimal lambda calculus reduction

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Annual Symposium on Principles of Programming Languages archive
Proceedings of the 17th ACM SIGPLAN-SIGACT symposium on Principles of programming languages table of contents

San Francisco, California, United States

Pages: 16 - 30

Year of Publication: 1989

ISBN:0-89791-343-4

Author

John Lamping

Xerox PARC

Sponsors

SIGACT: ACM Special Interest Group on Algorithms and Computation Theory
SIGPLAN: ACM Special Interest Group on Programming Languages

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ACM New York, NY, USA

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Downloads (6 Weeks): 15, Downloads (12 Months): 61, Citation Count: 42

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ABSTRACT

We present an algorithm for lambda expression reduction that avoids any copying that could later cause duplication of work. It is optimal in the sense defined by Lévy. The basis of the algorithm is a graphical representation of the kinds of commonality that can arise from substitutions; the idea can be adapted to represent other kinds of expressions besides lambda expressions. The algorithm is also well suited to parallel implementations, consisting of a fixed set of local graph rewrite rules.

REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	H. P. Barendregt. The Lambda Calculus its Syntax: and Semantics, volume 103 of Studies in logic and the foundations of mathemalies. North-Holland, 1981.
	2	ti. P. Barendregt et al. LEAN, an intermediate language based on graph rewriting. Parallel Compulin9, 9:163-177, 1989.
	3	Vinod Kathail. private communication, 1989.
	4	jean-Jacques L~vy. R~ductions correctes et optimales dans le lambda-calcul. PhD thesis, Universit6 de Paris, 1978.
	5	Jean-Jacques Ldvy. Optimal reductions in the lambda-calculus. In J.P. Seldin and J.R. Hindley, editors, To H.B. Curry: Essays on Combinalory Logic, Lambda Calculus and Formalism, pages 159- 191. Academic Press, 1980.
	6	John Staples. Efficient evaluation of lambda expressions: a new strategy. Technical Report 23, University of Queensland, Department of Computer Science, St. Lucia, Queensland, 4067, Australia, 1980.
	7	John Staples, Two-level expression representation for faster evaluation, Proceedings of the 2nd International Workshop on Graph-Grammars and Their Application to Computer Science, p.392-404, October 04-08, 1982
	8	D. A. Turner. A new implementation technique for applicative languages. Software Practice and Experience, 9(1), 1979.
	9	C. P. Wadsworth. Semantics and Pragmatics of the )~-calculus. PhD thesis, Oxford University , 1971.

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