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Simplification by Cooperating Decision Procedures
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Source ACM Transactions on Programming Languages and Systems (TOPLAS) archive
Volume 1 ,  Issue 2  (October 1979) table of contents
Pages: 245 - 257  
Year of Publication: 1979
ISSN:0164-0925
Authors
Greg Nelson  Artificial Intelligence Laboratory, Computer Science Department, Stanford University, Stanford, CA
Derek C. Oppen  Artificial Intelligence Laboratory, Computer Science Department, Stanford University, Stanford, CA
Publisher
ACM  New York, NY, USA
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Downloads (6 Weeks): 13,   Downloads (12 Months): 129,   Citation Count: 87
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ABSTRACT

A method for combining decision procedures for several theories into a single decision procedure for their combination is described, and a simplifier based on this method is discussed. The simplifier finds a normal form for any expression formed from individual variables, the usual Boolean connectives, the equality predicate =, the conditional function if-then-else, the integers, the arithmetic functions and predicates +, -, and ≤, the Lisp functions and predicates car, cdr, cons, and atom, the functions store and select for storing into and selecting from arrays, and uninterpreted function symbols. If the expression is a theorem it is simplified to the constant true, so the simplifier can be used as a decision procedure for the quantifier-free theory containing these functions and predicates. The simplifier is currently used in the Stanford Pascal Verifier.


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
CRAIG, W. Three uses of the Herbrand-Gentzen theorem in relating model theory and proof theory. J. Symbolic Logic 22 (1955).
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MATIYASEVlCH, Y.V. Diophantine representation ofrecursively enumerable predicates. Proc. 2nd Scandinavian Logic Symposium, North-Holland Publ. Co., 1970.
 
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MCCARTHY, J. A basis for a mathematical theory of computation. In Computing Programming and Formal Systems, P. Braffort and D. Hirshberg, Eds. North-Holland Publ. Co., 1963.
 
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OPPEN, D.C. Convexity, complexity, and combinations of theories. To appear in Theoretical Comptr. Sci.
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SCHOENFIELD, J.R. Mathematical Logic. Addison-Wesley, Reading, Mass., 1967.
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SuzuKI, N., AND JEFFERSON, D. Verification decidability of Presburger array programs. Proc. Conf. on Theoretical Computer Science, U. of Waterloo, Aug. 1977.
 
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TAKEUC}II, I. Private communication to J. McCarthy.
 
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TARSKI, A. A decision method for elementary algebra and geometry. Berkeley, 1951.

CITED BY  87

Collaborative Colleagues:
Greg Nelson: colleagues
Derek C. Oppen: colleagues