Transitions and Trees

Transitions and Trees provides a clear and self-contained introduction to the mathematical foundations of program semantics. The book examines how transition systems and tree structures can be used to describe the behavior of programs in an implementation-independent manner. By presenting definitions through both big-step and small-step semantics, it covers a range of programming language constructs—from control structures and structured declarations to objects, parameter mechanisms, and procedural abstraction. Throughout the text, the reader is introduced to important proof techniques, including various forms of induction and notions of semantic equivalence such as bisimilarity. Developed from comprehensive lecture notes and refined over many years of teaching, this book offers a rigorous yet accessible exploration of the subject, making it suitable for both undergraduate and graduate students, as well as computing professionals seeking a deeper theoretical understanding.