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A Consistent Foundation for Isabelle/HOL
"... Abstract. The interactive theorem prover Isabelle/HOL is based on the well un-derstood Higher-Order Logic (HOL), which is widely believed to be consistent (and provably consistent in set theory by a standard semantic argument). How-ever, Isabelle/HOL brings its own personal touch to HOL: overloaded ..."
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Abstract. The interactive theorem prover Isabelle/HOL is based on the well un-derstood Higher-Order Logic (HOL), which is widely believed to be consistent (and provably consistent in set theory by a standard semantic argument). How-ever, Isabelle/HOL brings its own personal touch to HOL: overloaded constant definitions, used to achieve Haskell-like type classes in the user space. These fea-tures are a delight for the users, but unfortunately are not easy to get right as an extension of HOL—they have a history of inconsistent behavior. It has been an open question under which criteria overloaded constant definitions and type defi-nitions can be combined together while still guaranteeing consistency. This paper presents a solution to this problem: non-overlapping definitions and termination of the definition-dependency relation (tracked not only through constants but also through types) ensures relative consistency of Isabelle/HOL. 1