Simply Typed Lambda Calculus and Type Inference

Understanding how modern compilers verify code safety and infer data types begins with the mathematical foundations of typed lambda calculus. This text-based course breaks down formal type theory into clear, structured explanations, helping you understand how static type systems ensure program correctness without requiring an advanced background in logic. You will build a deep conceptual foundation in formal typing systems, comparing Church-style explicit typing with Curry-style implicit typing. Through carefully explained derivations and written exercises, you will explore structural properties such as subject reduction, the substitution lemma, and principal type generation, culminating in the practical mechanics of automated type inference. What you will learn: - Understand the core terminology and syntax of simply typed lambda calculus in Church and Curry styles - Examine subterm typability, context management, and the substitution lemma - Analyze subject reduction and the theoretical guarantees of type preservation - Master term unification algorithms and how they resolve type constraints - Apply the Hindley-Milner type inference algorithm step by step - Connect classical type theoretical principles to type checkers in modern programming languages The material begins with fundamental definitions and typing rules before guiding you through formal properties and algorithmic type reconstruction. Designed for programmers, computer science students, and language enthusiasts, this course requires only basic familiarity with programming logic. Begin reading today to discover how static type systems work beneath the surface.