ACM Transactions on Programming Languages and Systems (TOPLAS)
Systematic software development using VDM (2nd ed.)
Systematic software development using VDM (2nd ed.)
Using Z: specification, refinement, and proof
Using Z: specification, refinement, and proof
Refinement in Z and object-Z: foundations and advanced applications
Refinement in Z and object-Z: foundations and advanced applications
Z: An Introduction to Formal Methods
Z: An Introduction to Formal Methods
The Theory and Practice of Concurrency
The Theory and Practice of Concurrency
How Firing Conditions Help Inheritance
ZUM '95 Proceedings of the 9th International Conference of Z Usres on The Z Formal Specification Notation
How to Combine Z with Process Algebra
ZUM '98 Proceedings of the 11th International Conference of Z Users on The Z Formal Specification Notation
Guards, Preconditions, and Refinement in Z
ZB '00 Proceedings of the First International Conference of B and Z Users on Formal Specification and Development in Z and B
VDM '91 Proceedings of the 4th International Symposium of VDM Europe on Formal Software Development-Volume 2: Tutorials
An Introduction to Refinement in Z
VDM '91 Proceedings of the 4th International Symposium of VDM Europe on Formal Software Development-Volume 2: Tutorials
On the Refinement and Simulation of Data Types and Processes
IFM '99 Proceedings of the 1st International Conference on Integrated Formal Methods
An Analysis of Backward Simulation Data-Refinement for Partial Relation Semantics
APSEC '03 Proceedings of the Tenth Asia-Pacific Software Engineering Conference Software Engineering Conference
Operation refinement and monotonicity in the schema calculus
ZB'03 Proceedings of the 3rd international conference on Formal specification and development in Z and B
An analysis of forward simulation data refinement
ZB'03 Proceedings of the 3rd international conference on Formal specification and development in Z and B
A relational investigation of UTP designs and prescriptions
UTP'06 Proceedings of the First international conference on Unifying Theories of Programming
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This paper begins a new strand of investigation which complements our previous investigation of refinement for specifications whose semantics is given by partial relations (using Z as a linguistic vehicle for this semantics). It revolves around extending our mathematical apparatus so as to continue our quest for examining mathematically the essence of the lifted-totalisation semantics (which underlies the de facto standard notion of refinement in Z) and the role of the semantic elements @? in model-theoretic refinement, but this time in the abortive paradigm. We conside the simpler framework of operation-refinement and, thus, (at least at this stage) abstract from the complications emerging when data simulations are involved: we examine the (de facto) standard account of operation-refinement in this regime by introducing a simpler, normative theory (SP-refinement) which captures the notion of firing conditions refinement directly in the language and in terms of the natural properties of preconditions and postconditions; we then summarise our observations and link them to the particular role each of the possible extreme specifications in Z plays in the abortive paradigm - this lays the foundations to a more intricate future investigation of data-refinement in this paradigm. We conclude by providing a detailed account of future work which generalises Miarka, Boiten and Derrick's work of combining the abortive and chaotic paradigms for refinement, in our mathematical framework of Z"C and Z"C^@?.