NDLI: Maximal sharing in the Lambda calculus with letrec

Content Provider	ACM Digital Library
Author	Grabmayer, Clemens Rochel, Jan
Abstract	Increasing sharing in programs is desirable to compactify the code, and to avoid duplication of reduction work at run-time, thereby speeding up execution. We show how a maximal degree of sharing can be obtained for programs expressed as terms in the lambda calculus with letrec. We introduce a notion of 'maximal compactness' for $λ_{letrec}-terms$ among all terms with the same infinite unfolding. Instead of defined purely syntactically, this notion is based on a graph semantics. $λ_{letrec}-terms$ are interpreted as first-order term graphs so that unfolding equivalence between terms is preserved and reflected through bisimilarity of the term graph interpretations. Compactness of the term graphs can then be compared via functional bisimulation. We describe practical and efficient methods for the following two problems: transforming a $λ_{letrec}-term$ into a maximally compact form; and deciding whether two $λ_{letrec}-terms$ are unfolding-equivalent. The transformation of a $λ_{letrec}-terms$ L into maximally compact form $L_{0}$ proceeds in three steps: (i) translate L into its term graph G = [[L]] ; (ii) compute the maximally shared form of G as its bisimulation collapse $G_{0}$ ; (iii) read back a $λ_{letrec}-term$ $L_{0}$ from the term graph $G_{0}$ with the property $[[L_{0}]]$ = $G_{0}.$ Then $L_{0}$ represents a maximally shared term graph, and it has the same unfolding as L. The procedure for deciding whether two given $λ_{letrec}-terms$ $L_{1}$ and $L_{2}$ are unfolding-equivalent computes their term graph interpretations $[[L_{1}]]$ and $[[L_{2}]],$ and checks whether these are bisimilar. For illustration, we also provide a readily usable implementation.
Starting Page	67
Ending Page	80
Page Count	14
File Format	PDF
ISSN	03621340 15581160
DOI	10.1145/2692915.2628148
Journal	ACM SIGPLAN Notices (SIGP)
Volume Number	49
Issue Number	9
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	1983-05-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Higher-order term graphs Maximal sharing Lambda calculus with letrec Subterm sharing Unfolding semantics
Content Type	Text
Resource Type	Article
Subject	Computer Graphics and Computer-Aided Design Software

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
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3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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