Dependent Record Types, Subtyping and Proof Reutilization

We present an example of formalization of systems of algebras using an extension of Martin-LL of's theory of types with record types and subtyping. This extension has been presented in 5]. In this paper we intend to illustrate all the features of the extended theory that we consider relevant for the task of formalizing algebraic constructions. We also provide code of the formalization as accepted by a type checker that has been implemented. 1. Introduction We shall use an extension of Martin-LL of's theory of logical types 14] with dependent record types and subtyping as the formal language in which constructions concerning systems of algebras are going to be represented. The original formulation of Martin-LL of's theory of types, from now on referred to as the logical framework, has been presented in 15, 7]. The system of types that this calculus embodies are the type Set (the type of inductively deened sets), dependent function types

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