Show notes
An introduction to lambda-calculus and combinatory logic, two foundational systems of logic that function as abstract programming languages. Originally developed in the 1920s and 30s to investigate the foundations of mathematics, these systems now serve as critical tools for developing and studying the semantics of programming languages. The book covers essential concepts including term structure, substitution, and reduction, while exploring the power of these systems through the fixed-point theorem, Böhm’s theorem, and the representation of computable functions. It examines both typed and untyped versions of these theories, emphasizing their differences and practical applications. Designed for readers with basic logic experience, the text uses a systematic approach illustrated by examples and exercises to explain how operations can be combined to form complex functional structures. Finally, the material addresses the undecidability theorem and various models of lambda-calculus, offering a comprehensive overview of how these abstract calculi underpin modern computer science.
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