Certified Programming With Dependent Types - 9780262026659

The technology of mechanized program verification can play a supporting role in manykinds of research projects in computer science, and related tools for formal proof-checking areseeing increasing adoption in mathematics and engineering. This book provides an introduction to theCoq software for writing and checking mathematical proofs. It takes a practical engineering focusthroughout, emphasizing techniques that will help users to build, understand, and maintain large Coqdevelopments 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 featureat the heart of the Coq system) and construction of domain-specific proof tactics. Almost everysubject covered is also relevant to interactive computer theorem proving in general, not justprogram verification, demonstrated through examples of verified programs applied in many differentsorts 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 novelperspective. The book also offers a library of tactics, or programs that find proofs, designed foruse with examples in the book. Readers will acquire the necessary skills to reimplement thesetactics in other settings by the end of the book. All of the code appearing in the book is freelyavailable online.