A theoretical basis for stepwise refinement and the programming calculus
Science of Computer Programming
ACM Transactions on Programming Languages and Systems (TOPLAS)
A calculus of refinements for program derivations
Acta Informatica
A generalization of Dijkstra's calculus
ACM Transactions on Programming Languages and Systems (TOPLAS)
Systematic software development using VDM (2nd ed.)
Systematic software development using VDM (2nd ed.)
Programming from specifications (2nd ed.)
Programming from specifications (2nd ed.)
Using Z: specification, refinement, and proof
Using Z: specification, refinement, and proof
The B-book: assigning programs to meanings
The B-book: assigning programs to meanings
A Discipline of Programming
Refinement Calculus: A Systematic Introduction
Refinement Calculus: A Systematic Introduction
Recursive Schema Definitions in Object-Z
ZB '00 Proceedings of the First International Conference of B and Z Users on Formal Specification and Development in Z and B
Formalisation of B in Isabelle/HOL
B '98 Proceedings of the Second International B Conference on Recent Advances in the Development and Use of the B Method
Invariants, Frames and Postconditions: a Comparison of the VDM and B Notations
FME '93 Proceedings of the First International Symposium of Formal Methods Europe on Industrial-Strength Formal Methods
Interpreting the B-Method in the Refinement Calculus
FM '99 Proceedings of the Wold Congress on Formal Methods in the Development of Computing Systems-Volume I - Volume I
The Safe Machine: A New Specification Construct for B
FM '99 Proceedings of the Wold Congress on Formal Methods in the Development of Computing Systems-Volume I - Volume I
FME '02 Proceedings of the International Symposium of Formal Methods Europe on Formal Methods - Getting IT Right
Compound monads in specification languages
PLPV '07 Proceedings of the 2007 workshop on Programming languages meets program verification
A Practical Single Refinement Method for B
ABZ '08 Proceedings of the 1st international conference on Abstract State Machines, B and Z
Introducing backward refinement into B
ZB'03 Proceedings of the 3rd international conference on Formal specification and development in Z and B
Towards dynamic population management of abstract machines in the B method
ZB'03 Proceedings of the 3rd international conference on Formal specification and development in Z and B
Formalising generalised substitutions
TPHOLs'07 Proceedings of the 20th international conference on Theorem proving in higher order logics
ABZ'10 Proceedings of the Second international conference on Abstract State Machines, Alloy, B and Z
ZB'05 Proceedings of the 4th international conference on Formal Specification and Development in Z and B
A stepwise development of the peterson's mutual exclusion algorithm using b abstract systems
ZB'05 Proceedings of the 4th international conference on Formal Specification and Development in Z and B
A prospective-value semantics for the GSL
ZB'05 Proceedings of the 4th international conference on Formal Specification and Development in Z and B
Component reuse in b using ACL2
ZB'05 Proceedings of the 4th international conference on Formal Specification and Development in Z and B
B'07 Proceedings of the 7th international conference on Formal Specification and Development in B
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We augment the usual wp semantics of substitutions with an explicit notion of frame, which allows us to develop a simple self-contained theory of generalised substitutions outside their usual context of the B Method. We formulate three fundamental healthiness conditions which semantically characterise all substitutions, and from which we are able to derive directly, without need of any explicit further appeal to syntax, a number of familiar properties of substitutions, as well as several new ones specifically concerning frames. In doing so we gain some useful insights about the nature of substitutions, which enables us to resolve some hitherto problematic issues concerning substitutions within the B Method.