An Analysis of Forward Simulation Data Refinement

An alternative approach to handling nondeterminism in model-oriented data-refinement

“…and, if it is, what is its relationship to the normative theory that we established in [8,9,7]? Our normative theories, SX-refinement 11 , are the proof-theoretic benchmarks, each characterised by two elimination rules (which account for 11 These theories are closely connected to sufficient refinement conditions introduced by Spivey [26] (for forward simulation necessary conditions for refinement), guaranteeing a rudimentary property one expects in a (simulation-based) refinement: first, that requirements in the domains of definitions do not disappear in a refinement step and, second, that nondeterminism does not increase in a refinement step.…”

“…We then define the notions of implementation by means of this operator and establish the induced theories of data-refinement (sections 4.3 and 4.4). In section 5, we show that each of the implementation-based theories is equivalent to the corresponding standard characterisation of data-refinement, demonstrating that reallocation of nondeterminism does not modify the intentions manifested by our normative characterisation of data-refinement (shown to be equivalent to standard account in [8,9,7]). Our paper concludes with a review of what has been established and an agenda for further investigation (section 6).…”

“…For reasons thoroughly discussed in e.g. [8,9,7], we prefer to call it simply the "distinguished" element. 6 Lifting signifies mapping ⊥ of the source set of the relation onto all the states of its target set.…”

“…In the W • -family of refinement theories, the divergence, at the points of partiality, arising due to lifted-totalisation is crucial in preventing augmentation of undefinedness. 8 Thus, being defined as a subset relation on lifted-totalisations, refinement simply amounts to reduction of nondeterminism. This enables us to treat underspecification and nondeterminism in a uniform manner, by adopting the way algebraic specifications treat underspecification [29,30].…”

“…in [11,12]) as well as data-refinement (e.g. in [8,9,7]), answering various questions raised by the technical machinery; in particular, precisely explaining the extent to which this approach is canonical and the extent to which it is arbitrary. The modus operandi we have employed in that work is to investigate the relationship amongst a variety of refinement theories, each of which is based on a distinct notion of relational completion.…”