Discernment is all you need

Abstract

We explore the expressive power of HOL, a system of higher-order logic, and its relationship to the simply-typed lambda calculus and Church's simple theory of types, arguing for the potential of HOL as a unifying logical framework, capable of encoding a broad range of logical systems, including modal and non-classical logics. Along the way, we emphasize the essential role of discernment, the ability to tell things apart, as a language primitive; highlighting how it endows HOL with practical expressivity superpowers while elegantly enriching its theoretical properties.