We describe a macro for introducing \partial functions" into ACL2, i.e., functions not dened everywhere. The function \denitions" are actually admitted via the encapsulation principle. We discuss the basic issues surrounding partial functions in ACL2 and illustrate theorems that can be proved about such functions.

Several induction theorem provers have been developed which support mechanized verification of functional programs. Unfortunately, a major problem is that they often fail in verifying tail recursive functions (which correspond to imperative programs). However, in practice imperative programs are used almost exclusively. We present an automatic transformation to tackle this problem. It transforms functions which are hard to verify into functions whose correctness can be shown by the existing provers. In contrast to classical program transformations, the aim of our technique is not to increase efficiency, but to increase veriability. Therefore, this paper introduces a novel application area for program transformations and it shows that such techniques can in fact solve some of the most urgent current challenge problems in automated verification and induction theorem proving.

We present a method for automated induction proofs about partial functions. This method cannot only be used to verify the partial correctness of functional programs, but it also solves some other challenge problems where reasoning about partial functions is necessary. For a further analysis of partial functions we also developed a method to determine (non-trivial subsets of) their domains automatically.