The Lambda Calculus

Lambda calculus is a logical system of rules for expressing computation using variable binding, abstraction, and function application. We can define anonymous functions and apply those functions. Lambda calculus would be limited if it weren't for recursion. Pure functional programming languages derived from lambda calculus include LISP, Haskell, and ML.

Lambda Expressions

A lambda expression is an instance of a functional interface consisting of a set of terms. These terms can be variables like x, y, and z. These are not mutating variables, but rather placeholders for values or other lambda terms. The variable inside of x is applied to whatever it is bound to. The variable x is inside the term t. The lambda abstraction is defined as λ x.t.

For example, if we have the equation f(x) = x2 and replace x with 5, we have f(5) =  52.

When the function f is applied to x, we get x². In our example, the function f is applied to the argument 5 and we get 52.

We can eliminate the parentheses...