Reasoning algebraically about loops

Acta Informatica

Volumn 36, Issue 4, 1999, Pages 295-334

  Back, R J R ^a   Von Wright, J ^a  

^a ÅBO AKADEMI UNIVERSITY   (Finland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033153875     PISSN: 00015903     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002360050163     Document Type: Article

References (27)

1. 1. C. Aarts et al.: Fixpoint calculus. Information Processing Letters 53(3), February 1995
2. 2. R.J. Back: Correctness Preserving Program Refinements: Proof Theory and Applications, volume 131 of Mathematical Centre Tracts. Mathematical Centre, Amsterdam, 1980
3. 3. R.J. Back: A calculus of refinements for program derivations. Acta Informatica 25, 593-624 (1988)
4. 4. R.J. Back: Refining atomicity in parallel algorithms. In PARLE Conference on Parallel Architectures and Languages Europe, Eindhoven, the Netherlands. Berlin Heidelberg New York: Springer 1989
5. 5. R.J. Back: Atomicity refinement in a refinement calculus framework. Reports on computer science and mathematics 141, Åbo Akademi, 1992
6. 6. R.J. Back, K. Sere: Stepwise refinement of parallel algorithms. Science of Computer Programming 13, 133-180 (1990)
7. 7. R.J. Back, K. Sere: Stepwise refinement of action systems. Structured Programming 12, 17-30 (1991)
8. 8. R.J. Back, K. Sere: Superposition refinement of parallel algorithms. In K.R. Parker, G. A. Rose, editors, Formal Description Techniques IV, pages 475-493. North-Holland: Elsevier Science Publishers 1992
9. 9. R.J. Back, J. von Wright: Refinement Calculus: A Systematic Introduction. Berlin Heidelberg New York: Springer 1998
10. 10. R.C. Backhouse, B. A. Carré: Regular algebra applied to path finding problems. Journal Inst. Math. Appl. 15, 161-186 (1975)
11. 11. G. Birkhoff: Lattice Theory. American Mathematical Society, Providence, 1961
12. 12. M.J. Butler, C.C. Morgan: Action systems, unbounded nondeterminism and infinite traces. Formal Aspects of Computing 7(1), 37-53 (1995)
13. 13. K.M. Chandy, J. Misra: Parallel Program Design: A Foundation. Addison-Wesley 1988
14. 14. E.W. Dijkstra: A Discipline of Programming. Prentice-Hall 1976
15. 15. E.W. Dijkstra, C.S. Scholten: Predicate Calculus and Program Semantics. Berlin Heidelberg New York: Springer 1990
16. 16. R.M. Dijkstra: Relational calculus and relational program semantics. Tech. Rpt. 9408, Rijksuniversiteit Groningen, 1994
17. 17. P.H. Gardiner, C.C. Morgan: Data refinement of predicate transformers. Theoretical Computer Science 87(1), 143-162 (1991)
18. 18. L. Lamport: A theorem on atomicity in destributed algorithms. Distributed Computing 4, 59-68 (1990)
19. 19. R.J. Lipton: Reduction: A method of proving properties of parallel programs. Communications of the ACM 18(12), 717-721 (1975)
20. 20. M.S. Manasse, C.G. Nelson: Correct compilation of control structures. Techn. Memo. 11271-840909-09TM, AT&T Bell Laboratories, September 1984
21. 21. C.C. Morgan: The specification statement. ACM Transactions on Programming Languages and Systems 10(3), 403-419 (1988)
22. 22. J.M. Morris: A theoretical basis for stepwise refinement and the programming calculus. Science of Computer Programming 9, 287-306 (1987)
23. 23. S. Rönn: On the Regularity Calculus and its Role in Distributed Programming. PhD thesis, Helsinki University of technology, Helsinki, Finland, 1992
24. 24. J.L. A. van de Snepscheut: On lattice theory and program semantics. Technical Report CS-TR-93-19, Caltech, Pasadena, California, USA, 1993
25. 25. A. Tarski: A lattice theoretical fixed point theorem and its applications. Pacific J. Mathematics 5, 285-309 (1955)
26. 26. J. von Wright: Data refinement with stuttering. Reports on computer science and mathematics 137, Åbo Akademi, 1992
27. 27. J. von Wright: The lattice of data refinement. Acta Informatica 31, 105-135 (1994)