higherorderover

Higherorderover is a neologism used in discussions of programming language theory to describe a pattern that merges higher-order functions with overloading semantics.

Definition and concept: Higherorderover refers to a construct in which a single higher-order operator or function can dispatch to multiple concrete implementations based on the type, structure, or shape of its function-valued arguments or contained values. It extends traditional operator overloading by allowing dispatch rules that consider the function-valued inputs themselves, not only the result types. In practice, higherorderover can be implemented with multimethods, type classes, or generics, enabling context-sensitive behavior that varies with the function arguments.

Relation to existing ideas: The concept sits at the intersection of higher-order functions, operator overloading, and ad hoc polymorphism. It is related to but distinct from standard operator overloading and to higher-order abstract interpretation in static analysis, as it emphasizes dispatch across higher-order inputs.

Usage and examples: A hypothetical example is a higherorderover combinator H that, given a function f: A -> B and a value x: F[A], applies a context-specific map selecting specialized implementations when F is a list, an option, or a promise. Another example is a dispatch mechanism that chooses different optimization strategies depending on whether f is curried or uncurried. The term is mostly used in theoretical discussions rather than as a widely implemented syntax.

See also: higher-order function, operator overloading, multimethod, type class, ad hoc polymorphism.

Status: The term is not standardized and usage varies across texts.