A Mechanised Semantics for HOL with Ad-hoc Overloading

Isabelle/HOL augments classical higher-order logic with ad-hoc overloading of constant definitions—that is, one constant may have several definitions for non-overlapping types. In this paper, we present a mechanised proof that HOL with ad-hoc overloading is consistent. All our results have been formalised in the HOL4 theorem prover.