A comparison of HOL-ST and Isabelle/ZF

The use of higher order logic simple type theory is often limited by its restrictive type system Set theory allows many constructions on sets that are not possible on types in higher order logic This paper presents a comparison of two theorem provers supporting set theory namely HOL ST and Isabelle ZF based on a formalization of the inverse limit construction of domain theory this construction cannot be formalized in higher order logic directly We argue that whilst the combination of higher order logic and set theory in HOL ST has advantages over the rst order set theory in Isabelle ZF the proof infrastructure of Isabelle ZF has better support for set theory proofs than HOL ST Proofs in Isabelle ZF are both considerably shorter and easier to write