Interactive Theorem Proving

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.

This book describes an accurate analysis technique for energy systems based on formal methods—computer-based mathematical logic techniques for the specification, validation, and verification of the systems. Correctness and accuracy of the financial, operational, and implementation analysis are of the paramount importance for the materialization of the future energy systems, such as smart grids, to achieve the objectives of cost-effectiveness, efficiency, and quality-of-service. In this regard, the book develops formal theories of microeconomics, asymptotic, and stability to support the formal analysis of generation and distribution cost, smart operations, and processing of energy in a smart grid. These formal theories are also employed to formally verify the cost and utility modeling for: Energy generation and distribution; Asymptotic bounds for online scheduling algorithms for plug-in electric vehicles; and Stability of the power converters for wind turbines. The proposed approach results in mechanized proofs for the specification, validation, and verification of corresponding smart grid problems. The formal mathematical theories developed can be applied to the formal analysis of several other hardware and software systems as well, making this book of interest to researchers and practicing engineers in a variety of power electronic fields.

This book constitutes the thoroughly refereed proceedings of the Third International Conference on Interactive Theorem Proving, ITP 2012, held in Princeton, NJ, USA, in August 2012. The 21 revised full papers presented together with 4 rough diamond papers, 3 invited talks, and one invited tutorial were carefully reviewed and selected from 40 submissions. Among the topics covered are formalization of mathematics; program abstraction and logics; data structures and synthesis; security; (non-)termination and automata; program verification; theorem prover development; reasoning about program execution; and prover infrastructure and modeling styles.

This book constitutes the refereed proceedings of the 9th International Conference on Interactive Theorem Proving, ITP 2018, held in Oxford, UK, in July 2018. The 32 full papers and 5 short papers presented were carefully reviewed and selected from 65 submissions. The papers feature research in the area of logical frameworks and interactive proof assistants. The topics include theoretical foundations and implementation aspects of the technology, as well as applications to verifying hardware and software systems to ensure their safety and security, and applications to the formal verication of mathematical results. Chapters 2, 10, 26, 29, 30 and 37 are available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

This book constitutes the refereed proceedings of the 4th International Conference on Interactive Theorem Proving, ITP 2013, held in Rennes, France, in July 2013. The 26 regular full papers presented together with 7 rough diamond papers, 3 invited talks, and 2 invited tutorials were carefully reviewed and selected from 66 submissions. The papers are organized in topical sections such as program verfication, security, formalization of mathematics and theorem prover development.

This book constitutes the refereed proceedings of the 7th International Conference on Interactive Theorem Proving, ITP 2016, held in Nancy, France, in August 2016. The 27 full papers and 5 short papers presented were carefully reviewed and selected from 55 submissions. The topics range from theoretical foundations to implementation aspects and applications in program verification, security and formalization of mathematical theories.

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 proceedings of the 6th International Conference on Interactive Theorem Proving, ITP 2015, held in Nanjing, China, in August 2015. The 27 papers presented in this volume were carefully reviewed and selected from 54 submissions. The topics range from theoretical foundations to implementation aspects and applications in program verification, security and formalization of mathematics.