Refinement

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In mathematics, refinement (topology) often refers to the refinement of an open cover.

(See also selectivity for a non-computer science meaning.)

In formal methods, refinement is the 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 sets for example) into implementable data structures (such as arrays). Operation refinement converts a specification of an operation on a system into an implementable program (e.g., a 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, x' ∈ {1,2,3} (where x' is the value of the variable x after an operation) could be refined to x' ∈ {1,2}, then x' ∈ {1}, and implemented as x := 1. Implementations of x := 2 and x := 3 would be equally acceptable in this case, using a different route for the refinement. However, we must be careful not to refine to x' ∈ {} (equivalent to false) since this is unimplementable; it is impossible to select a member from the empty set.

The term reification is also sometimes used (coined by Cliff Jones). Retrenchment is an alternative technique when formal refinement is not possible. The opposite of refinement is abstraction.

The FermaT Transformation System is an industrial-strengh implementation of refinement.