Editing Fixed-point combinator (section)

===Function versus implementation===

The fixed-point combinator may be defined in mathematics and then implemented in other languages. General mathematics defines a function based on its [[extensionality|extensional]] properties.<ref>{{cite web |last1=Selinger |first1=Peter |date=2001–2013 |title=Lecture notes on the lambda calculus: Expository course notes |url=https://www.mscs.dal.ca/~selinger/papers/#lambdanotes |page=6 |format=PDF}} </ref> That is, two functions are equal if they perform the same mapping. Lambda calculus and programming languages regard function identity as an [[Intensional definition|intensional]] property. A function's identity is based on its implementation. 

A lambda calculus function (or term) is an implementation of a mathematical function. In the lambda calculus there are a number of combinators (implementations) that satisfy the mathematical definition of a fixed-point combinator.