Construction and Deduction Methods for the Formal Development of Software

In this paper we present an approach towards a framework based on the type theory ECC Extended Calculus of Constructions in which speci cations programs and operators for modular development by stepwise re nement can be formally described and reasoned about We show that generic software development steps can be expressed as higher order functions and demonstrate that proofs about their asserted e ects can be carried out in the underlying logical calculus For transformations requiring syntactic manipulations of objects a two level system comprising a Meta and an Object level is provided and it is shown how transformations can be formalized that faithfully represent operators on the object level