An important philosophical issue concerning the \(\lambda\)-calculus is the question of its underlying concept of functions. In set theory, a function is standardly understood as a set of argument-value pairs. More specifically, a function is understood as a set \(f\) of ordered pairs satisfying the property that \((x,y) \in f\) and \((x,z) \in f\) implies \(y = z\). If \(f\) is a function and \((x,y) \in f\), this means that the function f assigns the value \(y\) to the argument \(x\). This is the concept of functions-as-sets. Consequently, the notion of equality of functions-as-sets is equality qua sets, which, under the standard principle of extensionality, entails that two functions are equal precisely when they contain the same ordered pairs. In other words, two functions are identical if and only if they assign the same values to the same arguments. In this sense, functions-as-sets are extensional objects.