This new book on mathematical logic by Jeremy Avigad gives a thorough introduction to the fundamental results and methods of the subject from the syntactic point of view, emphasizing logic as the study of formal languages and systems and their proper use. Topics include proof theory, model theory, the theory of computability, and axiomatic foundations, with special emphasis given to aspects of mathematical logic that are fundamental to computer science, including deductive systems, constructive logic, the simply typed lambda calculus, and type-theoretic foundations.

Clear and engaging, with plentiful examples and exercises, it is an excellent introduction to the subject for graduate students and advanced undergraduates who are interested in logic in mathematics, computer science, and philosophy, and an invaluable reference for any practicing logician’s bookshelf.

This new book on mathematical logic by Jeremy Avigad gives a thorough introduction to the fundamental results and methods of the subject from the syntactic point of view, emphasizing logic as the study of formal languages and systems and their proper use. Topics include proof theory, model theory, the theory of computability, and axiomatic foundations, with special emphasis given to aspects of mathematical logic that are fundamental to computer science, including deductive systems, constructive logic, the simply typed lambda calculus, and type-theoretic foundations.

Clear and engaging, with plentiful examples and exercises, it is an excellent introduction to the subject for graduate students and advanced undergraduates who are interested in logic in mathematics, computer science, and philosophy, and an invaluable reference for any practicing logician’s bookshelf.

This new book on mathematical logic by Jeremy Avigad gives a thorough introduction to the fundamental results and methods of the subject from the syntactic point of view, emphasizing logic as the study of formal languages and systems and their proper use. Topics include proof theory, model theory, the theory of computability, and axiomatic foundations, with special emphasis given to aspects of mathematical logic that are fundamental to computer science, including deductive systems, constructive logic, the simply typed lambda calculus, and type-theoretic foundations.

Clear and engaging, with plentiful examples and exercises, it is an excellent introduction to the subject for graduate students and advanced undergraduates who are interested in logic in mathematics, computer science, and philosophy, and an invaluable reference for any practicing logician’s bookshelf.

This new book on mathematical logic by Jeremy Avigad gives a thorough introduction to the fundamental results and methods of the subject from the syntactic point of view, emphasizing logic as the study of formal languages and systems and their proper use. Topics include proof theory, model theory, the theory of computability, and axiomatic foundations, with special emphasis given to aspects of mathematical logic that are fundamental to computer science, including deductive systems, constructive logic, the simply typed lambda calculus, and type-theoretic foundations.

Clear and engaging, with plentiful examples and exercises, it is an excellent introduction to the subject for graduate students and advanced undergraduates who are interested in logic in mathematics, computer science, and philosophy, and an invaluable reference for any practicing logician’s bookshelf.

Scheme combines power and simplicity. Scheme is derived from Lisp, which John McCarthy developed—inspired in part by Alonzo Church’s work on the λ-calculus—while exploring ideas about computability, recursive functions, and models of computation. McCarthy intended Lisp for computing with symbolic data he called S-expressions. S-expressions are based on lists, and the name “Lisp” was formed from “list processing.” Lisp programs can be concise and natural programs, and they often resemble mathematical definitions of the functions they compute. Lisp has been used heavily in artificial intelligence for over fifty years, and in 1971, McCarthy received ACM’s Turing Award for contributions to artificial intelligence.

An abstract data type is not the only way to hide the representation of data: a representation can also be hidden in an object. An object is a bundle of operations—often called methods—that may share hidden state. An object interacts with other objects by sending messages; each message activates a method on the receiving object. An object’s methods can see the representation of the object’s own state, but not the representations of the states of other objects.

Chapters 1 to 7 don’t give us many ways to organize data. S-expressions are great, but you might have noticed that they serve as a kind of high-level assembly language on top of which you have to craft your own data structures. For programming at scale, that’s not good enough—programmers need to define proper data structures whose shapes and contents are known.

Congratulations! You now have some solid skills using functions, types, modules, objects, and more. You also have a cognitive framework that you can use to learn new programming languages, and if you’re like my students, you’ll be pleasantly surprised at how broadly your skills apply. Now you get the dessert menu. As your server, I recommend some tasty treats: languages that are superlative, unusual, or popular. Many are widely recognized as interesting or important, and some are just to my personal taste. Together, they offer a variety of jumping-off points, ranging from younger, less proven ideas to fashionable ideas drawn from the headlines.

In your prior programming experience, you may have used a procedural language such as Ada 83, Algol 60, C, Cobol, Fortran, Modula-2, or Pascal. Or you may have used a procedural language extended with object-oriented features, such as Ada 95, C#, C++, Eiffel, Java, Modula-3, Objective C, or Python—although these hybrid languages support an object-oriented style, they are often used procedurally.