A formal definition of what it means for a machine to learn a collecti
on of concepts in an order determined by a finite acyclic digraph of r
ecursive functions is presented. We show that given a labelled graph G
=(V, E) representing the learning structure, there are sets S such tha
t in order to learn a program corresponding to some node i, a machine
must have precisely learned programs corresponding to all the predeces
sor nodes.