null

Definition

null

null is a distinguished value used to represent the absence of an ordinary value. For a nullable form of a type $Y$, its possible values may be modelled as

$$Y_{\mathrm{null}}=Y\cup \{\mathrm{null}\}.$$

The surrounding program or interface determines what this absence means. null does not inherently mean false, zero, failure, or unknown.

As an inconclusive result

An algorithm may use null as the distinguished result of an inconclusive algorithm:

$$A:X\to Y\cup \{\mathrm{null}\},A(x)=\mathrm{null}⟺\text{A makes no claim on x}.$$

Under this explicit contract, null plays the role of $\perp$. Without such a contract, a null result indicates only absence and need not mean that the algorithm is inconclusive.