 The \(\lambda\)-calculus is an elegant notation for working with applications of functions to arguments. To take a mathematical example, suppose we are given a simple polynomial such as \(x^2 -2\cdot x+5\). What is the value of this expression when \(x = 2\)? We compute this by ‘plugging in’ 2 for \(x\) in the expression: we get \(2^2 -2\cdot 2+5\), which we can further reduce to get the answer 5. To use the \(\lambda\)-calculus to represent the situation, we start with the \(\lambda\)-term