We adapt Kahn-style (\big-step") natural semantics to take on desirable aspects of small-step and denotational semantics forms, more precisely: (i) the ability to express divergent computations; (ii) the ability to reason about the (length of a) computation of a derivation; and (iii) the ability to compute upon and reason about higher-order values. To accomplish these results, we extend the cla...

We show that  higher derivations on a Hilbert$C^{*}-$module associated with the Cauchy functional equation satisfying generalized Hyers--Ulam stability.