# Divergence

**November 22, 2022**, tags: computation.

In computer science, a computation is said to diverge if it does not terminate or terminates in an exceptional state. Otherwise it is said to converge.

In the *λ*-calculus an expression is *divergent* if it has no normal form.

In *denotational semantics* an object function *f* : *A* → *B* can be modelled as a mathematical function *f* : *A* ∪ { ⊥ } → *B* ∪ { ⊥ } where ⊥ indicates that the object function or its argument *diverges*.