  We examine the connections between deterministic, complete, and general
global optimisation of continuous functions and a general concept of regression
from the perspective of constructive type theory via the concept of
'searchability'. We see how the property of convergence of global optimisation
is a straightforward consequence of searchability. The abstract setting allows
us to generalise searchability and continuity to higher-order functions, so
that we can formulate novel convergence criteria for regression, derived from
the convergence of global optimisation. All the theory and the motivating
examples are fully formalised in the proof assistant Agda.
