Function Application

In Lambda Calculus, a function application refers to applying the Transformation defined by a Function Abstraction, $\lambda x.E$, to an argument $A$. This works through Beta Reduction.

$$(\lambda x.E)A$$

For example, the function that adds one to its input, being applied to 1.

$$\begin{array}{c}(\lambda x.x+1)1\\ 1+1\\ 2\end{array}$$