  The Higher-Order $\Psi$-calculus framework (HO$\Psi$) is a generalisation of
many first- and higher-order extensions of the $\pi$-calculus. It was proposed
by Parrow et al. who showed that higher-order calculi such as HO$\pi$ and CHOCS
can be expressed as HO$\Psi$-calculi. In this paper we present a generic type
system for HO$\Psi$-calculi which extends previous work by H\"uttel on a
generic type system for first-order $\Psi$-calculi. Our generic type system
satisfies the usual property of subject reduction and can be instantiated to
yield type systems for variants of HO{\pi}, including the type system for
termination due to Demangeon et al. Moreover, we derive a type system for the
$\rho$-calculus, a reflective higher-order calculus proposed by Meredith and
Radestock. This establishes that our generic type system is richer than its
predecessor, as the $\rho$-calculus cannot be encoded in the $\pi$-calculus in
a way that satisfies standard criteria of encodability.
