Abstract
The proof-theoretical nature of initial algebra semantics provides us with the basis for showing the completeness of Data Type Specifications by term rewriting methods. Based upon these methods- in which the equations of a specification are regarded as rewriting rules- we show the decidability of completeness in a very large subclass of algebraic specifications including non-linear and/ or non-normalizing ones.
Furthermore the decision algorithm allows us to complete partial specifications and to ”reason” about the structure of specifications.
Some computer experiments illustrating its behavior are also given.
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6. Bibliography
DERSHOWITZ N:”Ordering for term rewriting systems” TCS 17(3) 1983
EHRIG H,KREOWSKY H, PADAWITZ P: ”Stepwise specifications and implementeation of ADTs. ICALP 78.
GOGUEN J.A, THATCHER J.W, WAGNER E.G ”Abstract data types as initial algebras and the correctness of data representations” Con. on computer Grafics, Pattern recognition,and data structures 1975.
GOGUEN J.A., THATCHER J.W., WAGNER E.G.: ”An initial algebra approach to the specification, correctness and implementation of abstract data types” in ”Current trends in programming methodology”, vol. 4, pp 80–149, Ed. Yeh R., Prentice-Hall (1978)
GUTTANG J, HORNING J: ”The algebraic specifications of ADTs” Acta Informatica 10 1978 p 27–52
HUET G., HULLOT J.M.:”Proofs by induction in equational theories with constructors” Proc. 21th FOCS (1980) and JCSS 25-2 (1982)
HUET G., OPPEN D.: ”Equations and rewrite rules: a survey” in ”Formal languages: perspectives and open problems” Ed. Book R.,Academic Press (1980)
JOUANNAUD J.P, KIRCHNER ”Completion of a set of rules modulo a set of equations,” Proc. 11th ACM Conference of Principles of Programming Languages (1984), also SIAM to appear
KIRCHNER C.,KIRCHNER H.: ”New applicatons of the REVE system” Rep. CRIN (1984) to appear.
KNUTH D., BENDIX P. ”Simple Word Problems in Universal Algebras,” Computational problems in Abstract Algebra Ed.Pergamon Press pp.263–297 (1970)
LESCANNE P.:”Computer experimentswith the REVE term rewriting system generator” Proc. 10th POPL Conference (1983)
NIPKOW T, WEIKUM” A decidability result about sufficient completeness of axiomaticaly specified ADTs.LNCS 146 (1983) p 257–268
MUSSER D.R.: ”On proving inductive properties of abstract data types” Proc. 7th POPL Conference, Las Vegas (1980)
PADAWITZ P: ”New results on completeness and consinsency of ADTs” LNCS 88 (1980) 460–473
—: ”Correctess,Completeness, Consinstency of Equational Data type specifications” TUBerlin Bericht Nr 83-15
REMY J.L, ZHANG H.”REVEUR 4:a System for validating Conditional Algebraic Specifications of Abstract Data Types” Proc. of 5th ECAI (1984)
THIEL J.J.: ”Stop loosing sleep over uncompleteness of Data Type Specifications” Proc of 11th ACM Conference of Principles of Programming Languages POPL (1984).
WAND M: ”Algebraic theories and Tree Replacements Systems.” T.R 66 Undiana Univer. Bloomington (1977).
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Emmanuel, K. (1985). Completeness in data type specifications. In: Caviness, B.F. (eds) EUROCAL '85. EUROCAL 1985. Lecture Notes in Computer Science, vol 204. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-15984-3_291
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DOI: https://doi.org/10.1007/3-540-15984-3_291
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