Content deleted Content added
Cander0000 (talk | contribs) refined category using AWB |
Belovedfreak (talk | contribs) m Disambiguate Member to Element (mathematics) using popups |
||
Line 1:
In [[formal methods]], '''program refinement''' is the [[formal verification|verifiable]] transformation of an ''abstract'' (high-level) [[formal specification]] into a ''concrete'' (low-level) [[executable program]]. ''[[Stepwise refinement]]'' allows this process to be done in stages. Logically, refinement normally involves [[implication]], but there can be additional complications. ''[[Data refinement]]'' is used to convert an abstract data model (in terms of [[set|sets]] for example) into implementable [[data structures]] (such as [[Array|arrays]]). ''[[Operation refinement]]'' converts a [[specification]] of an operation on a system into an implementable [[computer program|program]] (e.g., a [[Procedure (computer science)|procedure]]). The [[postcondition]] can be strengthened and/or the [[precondition]] weakened in this process. This reduces any [[nondeterminism]] in the specification, typically to a completely [[deterministic]] implementation.
For example, <i>x'</i> ∈ {1,2,3} (where <i>x'</i> is the value of the [[variable]] <i>x</i> after an operation) could be refined to <i>x'</i> ∈ {1,2}, then <i>x'</i> ∈ {1}, and implemented as <i>x</i> := 1. Implementations of <i>x</i> := 2 and <i>x</i> := 3 would be equally acceptable in this case, using a different route for the refinement. However, we must be careful not to refine to <i>x'</i> ∈ {} (equivalent to <i>false</i>) since this is unimplementable; it is impossible to select a [[Element (mathematics)|member]] from the [[empty set]].
The term [[Reification (computer science)|reification]] is also sometimes used (coined by [[Cliff Jones]]). [[Retrenchment (computing)|Retrenchment]] is an alternative technique when formal refinement is not possible. The opposite of refinement is [[Abstraction (computer science)|abstraction]].
| |||