Program Proofs demonstrates what it means to write specifications for programs, what it means for programs to satisfy those specifications, and how to write proofs that connect specifications and programs. Writing with clarity and humor, K. Rustan M. Leino first provides an overview of the basic theory behind reasoning about programs. He then gradually builds up to complex concepts and applications until students are facing real programs using objects, data structures, and nontrivial recursion. To emphasize the practical nature of program proofs, all material and examples use the verification aware programming language Dafny, but no previous knowledge of Dafny is assumed. Comprehensively covers how to write proofs and how to specify and verify both functional programs and imperative programs, Uses program text from a real programming language, not pseudocode, Features engaging illustrations and hands-on learning exercises