Abstract
Transformations of graphlike expressions are called correct if they preserve a given functional semantics of the expressions. Combining the algebraic theory of graph grammars (cf./Eh 78/) and the ADJ approach to semantics of programming languages it will be proved that the correctness of transformation rules carries over to the correctness of derivations via such rules. Applying this result to LISP we show that a LISP interpreter represented by a graph grammar is correct with respect to the functional semantics of graphlike LISP expressions.
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References
J. Backus: Can Programming be Liberated from the von Neumann Style? A Functional Style and its Algebra of Programs; CACM Vol. 21, No.8, August 1978
J.M. Cadiou/ Z. Manna: Recursive Definitions of Partial Functions and their Computations; SIGPLAN Notices, Vol. 7, No. 1, 58–65, 1972
H. Ehrig: Introduction to the Algebraic Theory of Graph Grammars; this volume
H. Ehrig/ B.K. Rosen: The Mathematics of Record Handling; Proc. 4th International Colloquium on Automata, Languages and Programming, Turku 1977, Springer Lect. Notes in Comp. Sci. 52, 206–220
J.V. Guttag/ E. Horowitz/ D.R. Musser: Abstract Data Types and Software Validation; University of Southern California Information Sci. Institute RR-76-48, 1976
J.A. Goguen/ J.W. Thatcher/ E.G. Wagner: Initial Algebra Semantics and Continuous Algebras; J.ACM, Vol.24, No. 1, 68–95, 1977
P.Henderson/J.H.Morris: A Lazy Evaluator; Proc.Third ACM Symposium on Principles of Programming Languages (1976), 95–103
D.J.Lehmann/M.B.Smyth: Data Types; University of Warwick, Dept.of Comp.Sci., Theory of Computation Report No.19,1977
M.Nivat: On the Interpretation of Recursive Program Schemes; Universität Saarbrücken, Technical Report A74/09, 1974
P.Padawitz: Operationelle und funktionale Semantik von Σ-Graphen; Forschungsbericht der TU Berlin, FB 20, Nr. 78-23, 1978
—: Graph Grammars and Operational Semantics; Forschungsbericht der TU Berlin, FB 20, Nr.78-33,1978
B.K. Rosen: Tree-Manipulating Systems and Church-Rosser Theorems; J.ACM,Vol.20,No.1,160–187, 1973
D. Scott: Continuous Lattices, in: Toposes, Algebraic Geometry and Logic (ed. by F.W.Lawvere), Springer Lect. Notes in Mathematics 274, 97–136, 1972
—: Data Types as Lattices; Proc. International Summer Institute and Logic Colloquium, Kiel 1974, Springer Lect. Notes in Math. 499, and SIAM Journ. on Computing 5 (1976) 522–587
J. Vuillemin: Correct and Optimal Implementations of Recursion in a Simple Programming Language, J.Comp. Syst.Sci., Vol.9,No.3, 332–354, 1974
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© 1979 Springer-Verlag Berlin Heidelberg
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Padawitz, P. (1979). Graph grammars and operational semantics. In: Claus, V., Ehrig, H., Rozenberg, G. (eds) Graph-Grammars and Their Application to Computer Science and Biology. Graph Grammars 1978. Lecture Notes in Computer Science, vol 73. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0025732
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DOI: https://doi.org/10.1007/BFb0025732
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