Recursion removal/introduction by formal transformation: an aid to program development and program comprehension

Computer Journal

Volumn 42, Issue 8, 1999, Pages 650-673

  Ward, Martin P ^a   Bennett, Keith H ^a  

^a DURHAM UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ITERATIVE METHODS; MATHEMATICAL TRANSFORMATIONS; RECURSIVE FUNCTIONS; REVERSE ENGINEERING; STRUCTURED PROGRAMMING; THEOREM PROVING;

FORMAL TRANSFORMATION; PROGRAM COMPREHENSION; PROGRAM DEVELOPMENT; RECURSION REMOVAL;

SOFTWARE ENGINEERING;

EID: 0033310419     PISSN: 00104620     EISSN: None     Source Type: Journal    
DOI: 10.1093/comjnl/42.8.650     Document Type: Article

References (49)

1. Knuth, D. E. (1974) Structured programming with the GOTO statement. Comput. Surv., 6, 261-301.
2. Bird, R. (1977) Notes on recursion removal. Comm. ACM, 20, 434-439.
3. Ward, M. (1989) Proving Program Refinements and Transformations. DPhil Thesis, Oxford University.
4. Ward, M. (1989) Iterative Procedures for Computing Ackermann's Function. Technical Report 89-3. Durham University. http://www.dur.ac.uk/~dcsOmpw/martin/papers/ack-t.ps.gz
5. Ward, M. (1994) Foundations for a Practical Theory of Program Refinement and Transformation. Technical Report, Durham University. http://www.dur.ac.uk/~dcsOmpw/martin/papers/foundation2-t.ps.gz
6. Ward, M. (1994) Language oriented programming. Softw. Concepts Tools, 15, 147-161. http://www.dur.ac.uk/~dcsOmpw/martin/papers/middle-out-t.ps.gz
7. Ward, M. and Bennett, K. H. (1995) Formal methods to aid the evolution of software. Int. J. Softw. Eng. Knowl. Eng., 5, 25-47. http://www.dur.ac.uk/~dcsOmpw/martin/papers/evolution-t.ps.gz
8. Ward, M. and Bennett, K. H. (1995) Formal methods for legacy systems. J. Softw. Maint. Res. Pract., 7, 203-219. http://www.dur.ac.uk/~dcsOmpw/martin/papers/legacy-t.ps.gz
9. Ward, M. (1990) Derivation of a Sorting Algorithm. Technical Report, Durham University. http://www.dur.ac.uk/~dcsOmpw/martin/papers/sorting-t.ps.gz
10. Ward, M. (1996) Derivation of data intensive algorithms by formal transformation. IEEE Trans. Softw. Eng., 22, 665-686. http://www.dur.ac.uk/~dcsOmpw/martin/papers/sw-alg.ps.gz
11. Ward, M. (1993) Abstracting a specification from code. J. Softw. Maint. Res. Pract., 5, 101-122. http://www.dur.ac.uk/~dcsOmpw/martin/papers/prog-spec.ps.gz
12. Hoare, C. A. R., Hayes, I. J., Jifeng, H. E., Morgan, C. C., Roscoe, A. W., Sanders, J. W., Sørensen, I. H., Spivey, J. M. and Sufrin, B. A. (1987) Laws of programming. Comm. ACM, 30, 672-686.
13. Morgan, C. C. (1994) Programming from Specifications (2nd edn). Prentice-Hall, Englewood Cliffs, NJ.
14. Morgan, C. C., Robinson, K. and Gardiner, P. (1988) On the Refinement Calculus. Technical Monograph PRG-70, Oxford University.
15. Morgan, C. C. (1988) The specification statement. Trans. Prog. Lang. Syst., 10, 403-419.
16. Dijkstra, E. W. (1976) A Discipline of Programming. Prentice-Hall, Englewood Cliffs, NJ.
17. Jones, C. B., Jones, K. D., Lindsay, P. A. and Moore, R. (1991) Mural: A Formal Development Support System. Springer, New York, Berlin, Heidelberg.
18. Neilson, M., Havelund, K., Wagner, K. R. and Saaman, E. (1989) The RAISE language, method and tools. Form. Asp. Comput., 1, 85-114.
19. Abrial, J. R., Davis, S. T., Lee, M. K. O., Neilson, D. S., Scharbach, P. N. and Sørensen, I. H. (1991) The B Method. BP Research, Sunbury Research Centre, UK.
20. Sennett, C. T. (1990) Royal Signals and Radar Establishment. Using refinement to convince: lessons learned from a case study. Refinement Workshop, 8th-11th January, Hursley Park, Winchester.
21. Bauer, F. L., Moller, B., Partsch, H. and Pepper, P. (1989) Formal construction by transformation - computer aided intuition guided programming. IEEE Trans. Softw. Eng., 15.
22. Bauer, F. L. and The CIP Language Group (1985) The Munich Project CIP, Volume I: The Wide Spectrum Language CIP-L (Lecture Notes in Computer Science, vol. 183). Springer, New York, Berlin, Heidelberg.
23. Bauer, F. L. and The CIP System Group (1987) The Munich Project CIP, Volume II: The Program Transformation System CIP-S (Lecture Notes in Computer Science, vol. 292). Springer, New York, Berlin, Heidelberg.
24. Majester, M. E. (1977) Limits of the 'algebraic' specification of abstract data types. SIGPLAN Not., 12, 37-42.
25. Ward, M. (1992) A recursion removal theorem. Proc. 5th Refinement Workshop, London, January 8-11. Springer, New York, Berlin, Heidelberg, pp. 43-69. http://www.dur.ac.uk/~dcsOmpw/martin/papers/ref-ws-5.ps.gz
26. Bird, R. (1989) Lectures on constructive functional programming. In Broy, M. (ed.), Constructive Methods in Computing Science (NATO ASI Series, vol. F55). Springer, New York, Berlin, Heidelberg, pp. 155-218.
27. Partsch, H. (1984) The CIP transformation system. In Pepper, P. (ed.), Program Transformation and Programming Environments (Report on a Workshop directed by F. L. Bauer and H. Remus). Springer, New York, Heidelberg, Berlin, pp. 305-323.
28. Karp, C. R. (1964) Languages with Expressions of Infinite Length. North-Holland, Amsterdam.
29. Engeler, E. (1968) Formal Languages: Automata and Structures. Markham, Chicago.
30. Back, R. J. R. (1980) Correctness Preserving Program Refinements (Mathematical Centre Tracts, vol. 131). Mathematisch Centrum, Amsterdam.
31. Back, R. J. R. and von Wright, J. (1990) Refinement concepts formalised in higher-order logic. Form. Asp. Comput., 2, 247-272.
32. Hayes, I. J. (1987) Specification Case Studies. Prentice-Hall, Englewood Cliffs, NJ.
33. Jones, C. B. (1986) Systematic Software Development Using VDM. Prentice-Hall, Englewood Cliffs, NJ.
34. Younger, E. J. and Ward, M. (1993) Inverse engineering a simple real time program. J. Softw. Maint. Res. Pract., 6, 197-234. http://www.dur.ac.uk/~dcsOmpw/martin/papers/eddy-t.ps.gz
35. Ward, M. and Bennett, K. H. (1993) A practical program transformation system for reverse engineering. Working Conference on Reverse Engineering, May 21-23, 1993. IEEE Computer Society, Baltimore MA. http://www.dur.ac.uk/~dcsOmpw/martin/papers/icse.ps.gz
36. Taylor, D. (1984) An alternative to current looping syntax. SIGPLAN Not., 19, 48-53.
37. Arsac, J. (1978) An Interactive Program Manipulation System for Non-Naïve Users. LITP Research Report, Institut de Programmation Paris.
38. Arsac, J. (1982) Transformation of recursive procedures. In Neel, D. (ed.), Tools and Notations for Program Construction, pp. 211-265. Cambridge University Press, Cambridge.
39. Arsac, J. (1982) Syntactic source to source program transformations and program manipulation. Comm. ACM, 22, 43-54.
40. Davey, B. A. and Priestley, H. A. (1990) Introduction to Lattices and Order. Cambridge University Press, Cambridge.
41. Priestley, H. A. and Ward, M. (1994) A multipurpose backtracking algorithm. J. Symb. Comput., 18, 1-40. http://www.dur.ac.uk/~dcsOmpw/martin/papers/backtr-t.ps.gz
42. Ward, M. (1991) A Recursion Removal Theorem - Proof and Applications. Technical Report, Durham University. http://www.dur.ac.uk/~dcsOmpw/martin/papers/rec-proof-t.ps.gz
43. Burstall, R. M. and Darlington, J. A. (1977) A transformation system for developing recursive programs. J. Assoc. Comput. Mach., 24, 44-67.
44. Hoare, C. A. R. (1962) Quicksort. Comput. J., 5, 10-15.
45. Darlington, J. (1978) A synthesis of several sort programs. Acta Inform., 11, 1-30.
46. Sedgewick, R. (1988) Algorithms. Addison-Wesley, Reading, MA.
47. Breuer, P. T., Lano, K. and Bowen, J. (1991) Understanding Programs Through Formal Methods. Programming Research Group, Oxford University.
48. Ackermann, W. (1928) Zum Hilbertschen Aufbau der reellen Zahlen. Math. Ann., 99, 118-133.
49. Church, A. (1951) The calculi of lambda conversion. Ann. Math. Stud., 6.