implementcomplete

Implementcomplete is a term in software engineering and formal methods used to describe a property of an implementation relative to a formal specification. An implementation is implementcomplete for a specification when the set of observable behaviors produced by the implementation exactly matches the set of behaviors permitted by the specification. Put another way, the implementation realizes every behavior the spec allows and exhibits no additional, unspecified behaviors. The concept combines fidelity to the specification with full behavioral coverage and is often discussed alongside soundness and refinement.

Formalization and relation to other concepts: In refinement theory, an implementation is correct if its observable behaviors are included in the specification. Implementcomplete would require equality of behavior sets, which can be difficult or impossible for non-deterministic or partially specified systems. The term is most meaningful when the specification is formal and precise enough to support exact comparisons.

Evaluation and usage: Assessing implementcomplete typically involves formal proofs, equivalence checking against a reference model, or exhaustive testing against a finite abstract model. Model checking and contract-based design approaches can help move toward implementcomplete by demonstrating that all specified cases are handled and no unwanted behaviors are introduced.

Examples and scope: For a function with a fully specified input-output relation, an implementcomplete implementation would produce exactly those outputs for every allowed input, including defined error signaling or exceptional conditions. In practice, achieving implementcomplete may require design choices that keep the specification complete yet tractable.

See also: refinement, total correctness, partial correctness, specification, model checking, code coverage.