Restrictionapply

Restrictionapply is a term used in computer science and mathematics to describe an operation that combines restricting a domain with applying a function. It is often realized as a higher-order function or operator that, given a predicate and a function, yields a new function that only produces a result when the input satisfies the predicate. If the input does not meet the restriction, the operation may return a default value or signal that the result is undefined.

Conceptually, restrictionapply merges two ideas: restriction and application. The restriction component filters inputs or defines a domain where the operation is valid, while the application component computes a result using the provided function. This approach can help enforce safety in APIs, constrain computations to valid inputs, or express partial functions in a total form by wrapping results in optional types or error signals.

Common implementations treat restrictionapply as a wrapper around an existing function. For example, a predicate p and a function f yield a new function g such that g(x) equals f(x) when p(x) is true, and g(x) returns a default, raises an exception, or yields an empty value otherwise. Variants may use Option/Maybe types, either monads, or error handling to represent undefined results.

Applications include data processing pipelines where only records meeting certain criteria are transformed, mathematical formalisms that require domain restrictions, and safe APIs that prevent invalid operations from propagating. Related concepts include restriction operators, filtering, partial vs total functions, and function composition.

See also: restriction operator, filter, partial function, option/Maybe type, function composition.