A multi-level marketing case study : specifying forests and trees in Z

A formal specification of a multi-level marketing (MLM) business is presented. Specifying a MLM business boils down to specifying properties of and operations on mathematical forests and trees. The usefulness of the model-based specification language, Z, is investigated as a vehicle for a formal specification of these recursive structures. The specification is presented following a prescribed format, namely the Established Strategy for constructing a Z specification. The Established Strategy is augmented with the notion of proof aimed at corroborating the correctness of critical parts of a specification. We show how attempts at discharging two different proof obligations using the resolution-based, first-order theorem prover OTTER calls for the use of two automated reasoning strategies, namely avoiding equality and using resonance.

[1]  Paula Kotzé,et al.  Automated support for set-theoretic specifications , 2001 .

[2]  Journal of automated reasoning , 1986 .

[3]  Susan Stepney,et al.  Z in practice , 1995, BCS practitioner series.

[4]  Mark Saaltink,et al.  Z and Eves , 1991, Z User Workshop.

[5]  J. Michael Spivey,et al.  The Z notation - a reference manual , 1992, Prentice Hall International Series in Computer Science.

[6]  Antoni Diller,et al.  Z and Abstract Machine Notation: A Comparison , 1994, Z User Workshop.

[7]  Larry Wos.  The resonance strategy , 1995 .

[8]  Jane Sinclair,et al.  Introduction to formal specification and Z , 1991, Prentice Hall International Series in Computer Science.

[9]  John Wordsworth.  Practical Experience of Formal Specification: A Programming Interface for Communications , 1989, ESEC.

[10]  J. A. Van der Poll,et al.  Heuristics for resolution-based set-theoretic proofs , 1999 .

[11]  Thierry Scheurer.  Foundations of computing - system development with set theory and logic , 1994 .

[12]  Allen Van Gelder,et al.  Computer Algorithms: Introduction to Design and Analysis , 1978 .

[13]  J. W. Addison,et al.  Automated development of fundamental mathematical theories , 1992 .

[14]  Jim Woodcock,et al.  Using Z - specification, refinement, and proof , 1996, Prentice Hall international series in computer science.

[15]  Sidneyf Elder,et al.  ELEMENTS OF SET THEORY , 1995 .

[16]  Jean-Raymond Abrial,et al.  The B-book - assigning programs to meanings , 1996 .

[17]  William McCune,et al.  OTTER 3.0 Reference Manual and Guide , 1994 .