Abstract

ion in Type Theory H. Pfeifer and H. Rueß Universitat Ulm Fakultat fur Informatik D-89069 Ulm, Germany fpfeifer,ruessg@informatik.uni-ulm.de Abstract. This paper is concerned with formalizations and verifications in type theory that are abstracted with respect to a large class of datatypes; i.e polytypic formalizations. The main advantage of these developments are that they can not only be used to polytypically define functions but also to formally state polytypic theorems and to interactively develop polytypic proofs using existing proof editors. Polytypic program and proof construction in a type-theoretic setting is exemplified by the definition of a polytypic map function and by mechanized proofs of corresponding properties such as preservation of composition and fusion theorems. 1 Introduction Many functional programming languages provide a predefined map functional on the list datatype. Applying this functional to a function f and a source list l yields a target list obtained b...

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