The system F of variable types, fifteen years later
Theoretical Computer Science
Understanding Z: a specification language and its formal semantics
Understanding Z: a specification language and its formal semantics
A higher-order calculus and theory abstraction
Information and Computation
Proceedings of the 10th International Conference on Theorem Proving in Higher Order Logics
TPHOLs '97 Proceedings of the 10th International Conference on Theorem Proving in Higher Order Logics
A Structure Preserving Encoding of Z in Isabelle/HOL
TPHOLs '96 Proceedings of the 9th International Conference on Theorem Proving in Higher Order Logics
Set Theory, Higher Order Logic or Both?
TPHOLs '96 Proceedings of the 9th International Conference on Theorem Proving in Higher Order Logics
Type Classes and Overloading in Higher-Order Logic
TPHOLs '97 Proceedings of the 10th International Conference on Theorem Proving in Higher Order Logics
A Logic for the Schema Calculus
ZUM '98 Proceedings of the 11th International Conference of Z Users on The Z Formal Specification Notation
A Fixedpoint Approach to Implementing (Co)Inductive Definitions
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
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The standard versions of HOL only support disjoint sums over finite families of types. This paper introduces disjoint sums over type classes containing possibly a countably infinite number of monomorphic types. The result is a monomorphic sum type together with an overloaded function which represents the family of injections. Model-theoretic reasoning shows the soundness of the construction. In order to axiomatize the disjoint sums in HOL, datatypes are introduced which mirror the syntactic structure of type classes. The association of a type with its image in the sum type is represented by a HOL function carrier. This allows a translation of the set-theoretic axiomatization of disjoint sums to HOL. As an application, a sum type U is presented which contains isomorphic copies of many familiar HOL types. Finally, a Z universe is constructed which can server as the basis of a HOL model of the Z schema calculus.