 Since this definition determines \(\mu yf(\vec{x},y)\) uniquely, (\ref{murec}) can also be regarded as defining a functional \(\mathcal{Min}_k\) which maps \(k+1\)-ary partial functions into \(k\)-ary partial functions. We now define the classes of functions \(\mathbf{PartREC}\)  and \(\mathbf{REC}\)  as follow: