This paper presents CoreFun, a typed reversible functional language, which seeks to reduce typed reversible functional programming to its essentials. We present a complete formal definition of the language, including its formal semantics and type system, the latter of which is based on a combined reasoning logical system of unrestricted and relevantly typed terms, and allows special support for ancillary (read-only) variables through its unrestricted fragment. We show how, in many cases, the type system provides the possibility to statically check for the reversibility of programs. Finally, we detail how higher-level language features such as variants and type classes may be incorporated into CoreFun as syntactic sugar, such that CoreFun may be used as a core language for a reversible functional language in a more modern style.