determineddefined

Determineddefined is a concept in theoretical computer science and programming language design that describes a property of values or computations as being both determinate and defined. In this sense, a value is determined if, for any valid execution path, the result is the same; it is defined if it yields a concrete value rather than an undefined result.

Origin and usage: The term is used in discussions about total correctness, semantic modeling, and functional purity to emphasize the combination of determinism and definedness. It is not a standard language feature in mainstream languages, but the idea appears in various forms under labels such as totality, total functions, or definedness within academic and methodological contexts.

Definition: A computation is determineddefined if it terminates with a single, well-defined value for every valid input, and no execution path leads to undefined or divergent outcomes. In practice, this requires two properties: determinism (no randomness or nondeterministic branching) and definedness (no null or bottom results). Ensuring determineddefined behavior often involves proving termination and ruling out partial or undefined cases.

Implications and enforcement: Programs that are determineddefined are easier to reason about, support stronger optimizations, and enable formal verification and total correctness proofs. Enforcement can be achieved through type systems, effect systems, or static analysis that mark functions as total and defined, or by requiring totality checks at compile time or during verification.

Relation to related concepts: Determineddefined overlaps with determinism, total functions, and definedness, and contrasts with partial or nondeterministic computations.

See also: determinism, total function, definedness, total correctness, partial function, type system.