MaybeA

MaybeA is a theoretical data type used in programming language theory to represent values that may be present, absent, or uncertain. It is described as an extension of the conventional Maybe or Optional type to capture partial knowledge about a value in computation or data sources.

In MaybeA, a value of type A can be in three states: Some(a) indicating definite presence, None indicating absence, and Unknown(p, a) indicating uncertainty with probability p that the value is the intended one or that a given predicate holds. The parameter p lies in the interval [0,1], with higher values indicating higher confidence. Some formulations allow Unknown to carry no explicit value, while others attach a provisional candidate value to guide subsequent computations.

Common operations mirror those of Maybe/Optional types but propagate uncertainty. For example, map applies a function to the contained value when in Some or Unknown states, while flatMap composes computations that may themselves yield Unknown. getOrElse provides a fallback for Some or Unknown with a default, and None yields the default unconditionally.

Use cases include data integration from unreliable sources, probabilistic reasoning, and user interfaces that must portray partial information without failing. Example (pseudo-code): a = MaybeA.present(5); b = MaybeA.none(); c = MaybeA.unknown(0.6, 7); d = a.map(f); e = b.getOrElse(0); f = c.map(g).

Compared with Optional or Maybe, MaybeA emphasizes uncertainty in addition to presence or absence. It is primarily a theoretical construct and is not part of a standard library in mainstream languages.