Abstract Logically constrained term rewriting systems (LCTRSs) are a formalism for program analysis with support for data types that are not (co)inductively defined. Only imperative programs have been considered through the lens of LCTRSs so far since LCTRSs were introduced as a first-order formalism. In this paper, we propose logically constrained simply-typed term rewriting systems (LCSTRSs), a higher-order generalization of LCTRSs, which suits the needs of representing and analyzing functional programs. We also study the termination problem of LCSTRSs and define a variant of the higher-order recursive path ordering (HORPO) for the newly proposed formalism.