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(HOF) A function that can take one or more functions as
argument and/or return a function as its value. E.g. map in
(map f l) which returns the list of results of applying
function f to each of the elements of list l. See also
curried function.

Higher-order thinking, known as higher order thinking skills (HOTS), is a concept of education reform based on learning taxonomies (such as Bloom's taxonomy). The idea is that some types of learning require more cognitive processing than others, but also have more generalized benefits.

In mathematics and logic, a higher-order logic is a form of predicate logic that is distinguished from first-order logic by additional quantifiers and, sometimes, stronger semantics. Higher-order logics with their standard semantics are more expressive, but their model-theoretic properties are less well-behaved than those of first-order logic.

Higher-order function

In mathematics and computer science, a **higher-order function** (HOF) is a function that does at least one of the following:

- takes one or more functions as arguments (i.e. a procedural parameter, which is a parameter of a procedure that is itself a procedure),
- returns a function as its result.

All other functions are *first-order functions*. In mathematics higher-order functions are also termed *operators* or *functionals*. The differential operator in calculus is a common example, since it maps a function to its derivative, also a function. Higher-order functions should not be confused with other uses of the word "functor" throughout mathematics, see Functor (disambiguation).

In the untyped lambda calculus, all functions are higher-order; in a typed lambda calculus, from which most functional programming languages are derived, higher-order functions that take one function as argument are values with types of the form $(\tau _{1}\to \tau _{2})\to \tau _{3}$.