Logic And Proof In Computer Science: Categories And Limits Of Proof Techniques

Computer software pervades our lives today. Nevertheless, software is one of the few products for which producers generally provide no express or implied warranties, a truly striking fact since peoples' lives depend in such fundamental ways on these products. This article addresses why such an unintuitive (and undesirable) situation might exist. It will catalog a range of computer science proof techniques and their historical antecedents, the purposes they serve, and several foundational concerns that elude proof techniques of any kind. Along the way, the concept of intractability and its role in computing will be explored as it pertains to algorithmic complexity and to proofs of the meanings of computer programs.