Proc. of the European symposium on programming on ESOP 86
The Z notation: a reference manual
The Z notation: a reference manual
Using Z: specification, refinement, and proof
Using Z: specification, refinement, and proof
A relational basis for program construction by parts
A relational basis for program construction by parts
Algebra of programming
Software Development: A Rigorous Approach
Software Development: A Rigorous Approach
Data Refinement: Model-Oriented Proof Methods and Their Comparison
Data Refinement: Model-Oriented Proof Methods and Their Comparison
MPC '02 Proceedings of the 6th International Conference on Mathematics of Program Construction
Safety of abstract interpretations for free, via logical relations and Galois connections
Science of Computer Programming - Special issue on mathematics of program construction (MPC 2002)
Transposing partial components: an exercise on coalgebraic refinement
Theoretical Computer Science - Components and objects
Calculating Invariants as Coreflexive Bisimulations
AMAST 2008 Proceedings of the 12th international conference on Algebraic Methodology and Software Technology
Transforming Data by Calculation
Generative and Transformational Techniques in Software Engineering II
A Single Complete Relational Rule for Coalgebraic Refinement
Electronic Notes in Theoretical Computer Science (ENTCS)
Programming from galois connections
RAMICS'11 Proceedings of the 12th international conference on Relational and algebraic methods in computer science
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The standard operation refinement ordering is a kind of “meet of opposites”: non-determinism reduction suggests “smaller” behaviour while increase of definition suggests “larger” behaviour. Groves' factorization of this ordering into two simpler relations, one per refinement concern, makes it more mathematically tractable but is far from fully exploited in the literature. We present a pointfree theory for this factorization which is more agile and calculational than the standard set-theoretic approach. In particular, we show that factorization leads to a simple proof of structural refinement for arbitrary parametric types and exploit factor instantiation across different subclasses of (relational) operation. The prospect of generalizing the factorization to coalgebraic refinement is discussed.