Foundations of Typed Lambda Calculus and Curry-Howard

Have you ever wondered how programming languages guarantee type safety, or how mathematical proofs relate to computer code? Understanding the typed lambda calculus is the key to unlocking the formal foundations of modern functional programming and type systems. This text-based course guides you through the core concepts of mathematical logic and computation, taking you from raw terms to formal proof systems. You will develop a solid theoretical foundation that explains how compilers verify program correctness. What you'll learn: 1. Understand the structure of pre-terms, types, and contexts in lambda calculus. 2. Compare Curry-style and Church-style typing rules. 3. Construct type derivation trees to formally verify program correctness. 4. Explore the system of minimal propositional logic. 5. Apply the Curry-Howard isomorphism to translate proofs into programs. 6. Analyze modern type system concepts like type safety, progress, and preservation. The course begins with foundational definitions of terms and types, establishing a clear mathematical vocabulary. You will then progress through formal typing rules, derivation trees, and propositional logic, culminating in a deep exploration of the Curry-Howard correspondence. This course is designed for beginner computer scientists, mathematicians, and functional programmers who want to understand the theoretical foundations of types without needing advanced prerequisites. Start reading today to bridge the gap between mathematical logic and software design.