The core principle of higher-order functions in functional programming is the ability to treat functions as first-class objects that can be passed as arguments to other functions. This mechanism relies on the formal concept of a "callable" object, where a function accepts another function, typically referred to as a key, to transform individual items based on specific criteria before processing. Within the domain of algorithmic sorting and data manipulation, this rule enables generic operations like sorting to adapt to custom ordering logic without requiring changes to the primary function's implementation.
Prerequisite chain context: requires Python function decorator syntax and wrapper implementation.