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This text develops a comprehensive theory of programming languages based on type systems and structural operational semantics. Language concepts are precisely defined by their static and dynamic semantics, presenting the essential tools both intuitively and rigorously while relying on only elementary mathematics. These tools are used to analyze and prove properties of languages and provide the framework for combining and comparing language features. The broad range of concepts includes fundamental data types such as sums and products, polymorphic and abstract types, dynamic typing, dynamic dispatch, subtyping and refinement types, symbols and dynamic classification, parallelism and cost semantics, and concurrency and distribution. The methods are directly applicable to language implementation, to the development of logics for reasoning about programs, and to the formal verification language properties such as type safety. This thoroughly revised second edition includes exercises at the end of nearly every chapter and a new chapter on type refinements. Table of Contents Part I Judgments and Rules Chapter 1 Abstract Syntax Chapter 2 Inductive Definitions Chapter 3 Hypothetical and General Judgments Part II Statics and Dynamics Chapter 4 Statics Chapter 5 Dynamics Chapter 6 Type Safety Chapter 7 Evaluation Dynamics Part III Total Functions Chapter 8 Function Definitions and Values Chapter 9 System T of Higher-Order Recursion Part IV Finite Data Types Chapter 10 Product Types Chapter 11 Sum Types Part V Types and Propositions Chapter 12 Constructive Logic Chapter 13 Classical Logic Part VI Infinite Data Types Chapter 14 Generic Programming Chapter 15 Inductive and Coinductive Types Part VII Variable Types Chapter 16 System F of Polymorphic Types Chapter 17 Abstract Types Chapter 18 Higher Kinds Part VIII Partiality and Recursive Types Chapter 19 System PCF of Recursive Functions Chapter 20 System FPC of Recursive Types Part IX Dynamic Types Chapter 21 The Untyp
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