| M. Poppleton and R. Banach. Retrenchment: a relational theory. 1999. in preparation. |
....note that retrenchment liberalizes refinement: every refinement yields a retrenchment, using abstract precondition as WITHIN constraint and a false concession. 3 A relational theory of retrenchment We give an overview of a relational model for retrenchment; a full development is in preparation [25]. In section 1, B relational semantics was expressed in terms of state variables, with I O afforded no special status. The more fluid world of retrenchment requires that I O variables become first class citizens . This is achieved by adding appropriate dimensionality to the semantic model; that ....
....is associative, modulo cancellation of all intermediate state invariant terms. 4 Monotonicity properties It is straightforward to show that the simple GSL constructors are monotonic w.r.t. the retrenchment ordering, as is required in order that retrenchment be a piecewise development step (see [25]) Monotonicity results are stated for the four primitive GSL constructors. Theorem RetMono : Retrenchment is monotonic w.r.t. the precondition, guard, bounded and unbounded choice constructors of B. Case j : Assume S(u; i; o) G;P;C;A T(v; j; p) Assume Q is a predicate either on a common ....
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M. Poppleton and R. Banach. Retrenchment: a relational theory. 1999. in preparation.
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