Abstract

. This paper deals with formalizations and verifications in type theory that are abstracted with respect to a class of datatypes; i.e polytypic constructions. The main advantage of these developments are that they can not only be used to define functions in a generic way but also to formally state polytypic theorems and to synthesize polytypic proof objects in a formal way. This opens the door to mechanically proving many useful facts about large classes of datatypes once and for all. 1 Introduction It is a major challenge to design libraries for theorem proving systems that are both sufficiently complete and relatively easy to use in a wide range of applications (see e.g. [6, 26]). A library for abstract datatypes, in particular, is an essential component of every proof development system. The libraries of the Coq [1] and the Lego [13] system, for example, include a number of functions, theorems, and proofs for common datatypes like natural numbers or polymorphic lists. In th...

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