Editing Lambda calculus (section)

==== Functions that operate on functions ====
In lambda calculus, functions are taken to be '[[First-class object|first class values]]', so functions may be used as the inputs, or be returned as outputs from other functions.

For example, the lambda term <math>\lambda x.x</math> represents the [[identity function]], <math>x \mapsto x</math>. Further, <math>\lambda x.y</math> represents the ''constant function'' <math>x \mapsto y</math>, the function that always returns <math>y</math>, no matter the input. As an example of a function operating on functions, the [[function composition]] can be defined as <math>\lambda f. \lambda g. \lambda x. (f ( g x))</math>.<!---Notational conventions should be explained elsewhere in this article; they differ by author, anyway:---In lambda calculus, function application is regarded as [[Operator associativity|left-associative]], so that <math>stx</math> means <math>(st)x</math>.--->

There are several notions of "equivalence" and "reduction" that allow lambda terms to be "reduced" to "equivalent" lambda terms.