Second-Order Logic and System F: Type Theory Fundamentals

Modern type systems and functional programming languages rest on powerful theoretical foundations developed in logic and type theory. This text-based course guides you through second-order intuitionistic propositional logic and polymorphic lambda calculus (System F) step by step, transforming abstract formalisms into clear, accessible concepts. You will build a rigorous foundation in formal logic, understanding how proofs correspond to programs and how polymorphism is expressed mathematically. Through structured explanations and written exercises, you will learn to represent core data structures and logic connectives purely through types. What you'll learn: - Understand the core principles of intuitionistic logic and the Curry-Howard isomorphism - Master second-order propositional logic and the syntax of polymorphic lambda calculus (System F) - Encode standard logical connectives, booleans, and empty types using universal quantification - Construct Church numerals, pairs, sum types, and inductive data structures such as lists - Apply existential types to model data abstraction and modular program components - Practice formal proof construction and type-checking through focused written exercises The course begins with foundational definitions, core terminology, and basic lambda calculus before progressing systematically into polymorphic types, encodings, and algebraic structures. Designed for learners interested in computer science theory and functional programming foundations, no advanced theoretical background is required. Start reading today to deepen your understanding of type systems and mathematical logic.