Revised

What is Closure?

A closure is the combination of a function and the lexical environment within which that function was declared.

The concept of closure comes from Lambda Calculus (also written as λ-calculus). λ-calculus is a formal system in mathematical logic for expressing computation based on function abstraction and application using variable binding and substitution. It is a universal model of computation that can be used to simulate any Turing machine.

Yet, there is one basic difference between closure and λ-calculus. This can be understood when we consider a function as a black-box.

function h is some black-box in λ-calculus

In Closure, the function’s output is also influenced by other environment variables. Meaning, it can be influenced by variables (a.k.a environment variables, free variables, … as part of the same lexical scope) that are not formal parameters to the function.

Relationship(s)

At times other names are used inter-changeably with closure. This sections attempts to clarify on those.

Closure is one of the fundamental units of Functional Programing (FP). In fact, this is the basis for a higher order function in FP.

A higher order function is closure that returns another function. Example uses of this being the infamous map, reduce, filter.

A first class function is one where a language construct supports passing a closure as a parameter.

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