Abstract

In this paper the reader will be introduced to type theories (predicative and impredicative, with and without inductive types) by ashort section giving theoretical background and by another section with exercises about thecalculusofconstructions and its ne structure the lambda cube. 1. Background Mathematics consists of de ning, reasoning and computing. Type systems are designed to represent mathematics in such a way that it can be veri ed automatically whether the de nitions are well-formed, the derivations are correct and the computations are performed by a simple underlying reduction system. This veri cation method is expected to be useful for the development of mathematics and the teaching of it. Also for the veri cation of hardware and software systems. See Barendregt [1996] and [1997] for a discussion and more information. Type systems as presented are based on work of Russell and Whitehead

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