demibindings

Demibindings is a term used in some areas of programming language theory and knowledge representation to describe a partially specified binding of a variable or symbol. A demibinding pairs a binding target with a partial specification: the bound portion provides a concrete value while the remaining aspects are constrained but not fixed. This notion is useful in settings where information arrives gradually, such as incremental type checking, constraint solving, or partial evaluation.

Formalism and operations: A demibinding consists of a map from variables to a binding structure that includes a value component and a constraint set. Operations include extending a demibinding with new information, refining the constraints, or issuing a projection to expose only information that is determined. Demibindings are typically monotone: adding constraints does not remove already bound values, though it may tighten or invalidate less constrained bindings. They can be composed or dissolved as inference proceeds.

Applications and examples: In gradual typing, a demibinding might bind a variable to a static type alongside a set of unknowns that will be resolved by type inference. In constraint-based program analysis, demibindings represent partially solved variables that will be fully bound when constraints are satisfied. They also appear in interactive theorem proving where user input supplies partial evidence.

Relation to related concepts: Demibindings are related to partial bindings, unification, and constraint solving. They are distinct from fully bound environments and from complete unification in that they maintain explicit constraints about unresolved portions.

Limitations and debate: Because the term is not universally standardized, definitions vary across communities; some critics argue that demibindings add complexity without ensuring decisive benefits in all contexts.