NDLI: A theory of using history for equational systems with applications

Content Provider	ACM Digital Library
Author	Verma, Rakesh M.
Copyright Year	1995
Abstract	Implementation of programming language interpreters, proving theorem of the form A=B, implementation of abstract data types, and program optimization are all problems that can be reduced to the problem of finding a normal form for an expression with respect to a finite set of equations. In 1980, Chew proposed an elegant congruence closure based simplifier (CCNS) for computing with regular systems, which stores the history of it computations in a compact data structure. In 1990, Verma and Ramakrishnan showed that it can also be used for noetherian systems with no overlaps.In this paper, we develop a general theory of using CCNS for computing normal forms and present several applications. Our results are more powerful and widely applicable than earlier work. We present an independent set of postulates and prove that CCNS can be used for any system that satisfies them. (This proof is based on the notion of strong closure). We then show that CCNS can be used for consistent convergent systems and for various kinds of priority rewrite systems. This is the first time that the applicability of CCNS has been shown for priority systems. Finally, we present a new and simpler translation scheme for converting convergent systems into effectively nonoverlapping convergent priority systems. Such a translation scheme has been proposed earlier, but we show that it is incorrect.Because CCNS requires some strong properties of the given system, our demonstration of its wide applicability is both difficult and surprising. The tension between demands imposed by CCNS and our efforts to satisfy them gives our work much general significance. Our results are partly achieved through the idea of effectively simulating “bad” systems by almost-equivalent “good” ones, partly through our theory that substantially weakens the demands, and partly through the design of a powerful and unifying reduction proof method.
Starting Page	984
Ending Page	1020
Page Count	37
File Format	PDF
ISSN	00045411
e-ISSN	1557735X
DOI	10.1145/210118.210130
Journal	Journal of the ACM (JACM)
Volume Number	42
Issue Number	5
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	1995-09-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Congruence-closure algorithm Equational logic Proof theory Rewrite system transformation Term rewrite systems
Content Type	Text
Resource Type	Article
Subject	Hardware and Architecture Information Systems Control and Systems Engineering Artificial Intelligence Software

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
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
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Equational inference, canonical proofs, and proof orderings

An algorithm for finding canonical sets of ground rewrite rules in polynomial time

Ordered chaining calculi for first-order theories of transitive relations

Fast Decision Procedures Based on Congruence Closure

Completeness of rewrite rules and rewrite strategies for FP

Partial completion of equational theories

Transitive closure logic, nested tree walking automata, and XPath

A Proof Procedure Using Connection Graphs

A needed narrowing strategy

A theory of using history for equational systems with applications

Similar Documents

Equational inference, canonical proofs, and proof orderings

An algorithm for finding canonical sets of ground rewrite rules in polynomial time

Ordered chaining calculi for first-order theories of transitive relations

Fast Decision Procedures Based on Congruence Closure

Completeness of rewrite rules and rewrite strategies for FP

Partial completion of equational theories

Transitive closure logic, nested tree walking automata, and XPath

A Proof Procedure Using Connection Graphs

A needed narrowing strategy

A theory of using history for equational systems with applications