  Louveau showed that if a Borel set in a Polish space happens to be in a Borel
Wadge class $\Gamma$, then its $\Gamma$-code can be obtained from its Borel
code in a hyperarithmetical manner. We extend Louveau's theorem to Borel
functions: If a Borel function on a Polish space happens to be a
$\Sigma_t$-function, then one can effectively find its $\Sigma_t$-code
hyperarithmetically relative to its Borel code. More generally, we prove
extension-type, domination-type, and decomposition-type variants of Louveau's
theorem for Borel functions.
