Duane Bibby – illustratör

An introduction to writing proofs about computer programs, written in an accessible question-and-answer style, complete with step-by-step examples and a simple proof assistant.

The Little Prover introduces inductive proofs as a way to determine facts about computer programs. It is written in an approachable, engaging style of question-and-answer, with the characteristic humor of The Little Schemer (fourth edition, MIT Press). Sometimes the best way to learn something is to sit down and do it; the book takes readers through step-by-step examples showing how to write inductive proofs. The Little Prover assumes only knowledge of recursive programs and lists (as presented in the first three chapters of The Little Schemer) and uses only a few terms beyond what novice programmers already know. The book comes with a simple proof assistant to help readers work through the book and complete solutions to every example.

A new edition of a book, written in a humorous question-and-answer style, that shows how to implement  and use an elegant little programming language for logic programming.

The goal of this book is to show the beauty and elegance of relational programming, which captures the essence of logic programming.  The book shows how to implement a relational programming language in Scheme, or in any other functional language, and demonstrates the remarkable flexibility of the resulting relational programs. As in the first edition, the pedagogical method is a series of questions and answers, which proceed with the characteristic humor that marked The Little Schemer and The Seasoned Schemer. Familiarity with a functional language or with the first five chapters of The Little Schemer is assumed. 

For this second edition, the authors have greatly simplified the programming language used in the book, as well as the implementation of the language. In addition to revising the text extensively, and simplifying and revising the “Laws” and “Commandments,” they have added explicit “Translation” rules to ease translation of Scheme functions into relations.

An introduction to dependent types, demonstrating the most beautiful aspects, one step at a time.

A program''s type describes its behavior. Dependent types are a first-class part of a language, and are much more powerful than other kinds of types; using just one language for types and programs allows program descriptions to be as powerful as the programs they describe. The Little Typer explains dependent types, beginning with a very small language that looks very much like Scheme and extending it to cover both programming with dependent types and using dependent types for mathematical reasoning. Readers should be familiar with the basics of a Lisp-like programming language, as presented in the first four chapters of The Little Schemer.

The first five chapters of The Little Typer provide the needed tools to understand dependent types; the remaining chapters use these tools to build a bridge between mathematics and programming. Readers will learn that tools they know from programming—pairs, lists, functions, and recursion—can also capture patterns of reasoning. The Little Typer does not attempt to teach either practical programming skills or a fully rigorous approach to types. Instead, it demonstrates the most beautiful aspects as simply as possible, one step at a time.