A Purely Definitional Universal Domain (Draft)

Existing theorem prover tools do not adequately support reasoning about general recursive datatypes. Better support for such datatypes would facilitate reasoning about a wide variety of real-world programs, including those written in continuation-passing style, that are beyond the scope of current tools. This paper introduces a new formalization of a universal domain that is suitable for modeling general recursive datatypes. The construction is purely definitional, introducing no new axioms. Defining recursive types in terms of this universal domain will allow a theorem prover to derive strong reasoning principles, with soundness ensured by construction.