  We present a unified framework on the limits of constraint satisfaction
problems (CSPs) and efficient parameter testing which depends only on array
exchangeability and the method of cut decomposition without recourse to the
weakly regular partitions. In particular, we formulate and prove a
representation theorem for compact colored $r$-uniform directed hypergraph
($r$-graph) limits, and apply this to $r$CSP limits. We investigate the sample
complexity of testable $r$-graph parameters, we discuss the generalized ground
state energies and demonstrate that they are efficiently testable.
