Certified Programs And Proofs

A handbook to the Coq software for writing and checking mathematical proofs, with a practical engineering focus. The technology of mechanized program verification can play a supporting role in many kinds of research projects in computer science, and related tools for formal proof-checking are seeing increasing adoption in mathematics and engineering. This book provides an introduction to the Coq software for writing and checking mathematical proofs. It takes a practical engineering focus throughout, emphasizing techniques that will help users to build, understand, and maintain large Coq developments and minimize the cost of code change over time. Two topics, rarely discussed elsewhere, are covered in detail: effective dependently typed programming (making productive use of a feature at the heart of the Coq system) and construction of domain-specific proof tactics. Almost every subject covered is also relevant to interactive computer theorem proving in general, not just program verification, demonstrated through examples of verified programs applied in many different sorts of formalizations. The book develops a unique automated proof style and applies it throughout; even experienced Coq users may benefit from reading about basic Coq concepts from this novel perspective. The book also offers a library of tactics, or programs that find proofs, designed for use with examples in the book. Readers will acquire the necessary skills to reimplement these tactics in other settings by the end of the book. All of the code appearing in the book is freely available online.

This book constitutes the referred proceedings of the First International Conference on Certified Programs and Proofs, CPP 2011, held in Kenting, Taiwan, in December 2011. The 24 revised regular papers presented together with 4 invited talks were carefully reviewed and selected from 49 submissions. They are organized in topical sections on logic and types, certificates, formalization, proof assistants, teaching, programming languages, hardware certification, miscellaneous, and proof perls.

This book constitutes the refereed proceedings of the Second International Conference on Certified Programs and Proofs, CPP 2012, held in Kyoto, Japan, in December 2012. The 18 revised regular papers presented were carefully reviewed and selected from 37 submissions. They deal with those topics in computer science and mathematics in which certification via formal techniques is crucial.

This book constitutes the refereed proceedings of the Third International Conference on Certified Programs and Proofs, CPP 2013, colocated with APLAS 2013 held in Melbourne, Australia, in December 2013. The 18 revised regular papers presented together with 1 invited lecture were carefully reviewed and selected from 39 submissions. The papers are organized in topical sections on code verification, elegant proofs, proof libraries, certified transformations and security.

This book constitutes the referred proceedings of the First International Conference on Certified Programs and Proofs, CPP 2011, held in Kenting, Taiwan, in December 2011. The 24 revised regular papers presented together with 4 invited talks were carefully reviewed and selected from 49 submissions. They are organized in topical sections on logic and types, certificates, formalization, proof assistants, teaching, programming languages, hardware certification, miscellaneous, and proof perls.

This book constitutes the thoroughly refereed post-proceedings of the Second International Workshop of the TYPES Working Group, TYPES 2002, held in Berg en Dal, The Netherlands in April 2002. The 18 revised full papers presented were carefully selected during two rounds of reviewing and improvement. All current issues in type theory and type systems and their applications to programming, systems design, and proof theory are addressed. Among the systems dealt with are Coq and Isar/HOL.

This book constitutes the thoroughly refereed post-proceedings of the Third International Workshop of the Types Working Group, TYPES 2003, held in Torino, Italy in April/May 2003. The 25 revised full papers presented were carefully selected during two rounds of reviewing and improvement. All current issues in type theory and type systems and their applications to programming, systems design, and proof theory are addressed. Among the systems dealt with are Isabelle/Isar, PAF!, and Coq.

A practical introduction to the development of proofs and certified programs using Coq. An invaluable tool for researchers, students, and engineers interested in formal methods and the development of zero-fault software.