Typed Lambda Calculus and Formal Type Theory

Mastering formal type theory provides a rigorous understanding of how modern compilers, type checkers, and functional programming languages operate. This text-based course guides you through the foundational mechanics of typed lambda calculus, demystifying abstract mathematical logic into clear, approachable concepts. What you'll learn: - Understand the core syntax, terms, and structural rules of typed lambda calculus - Master key decision problems including type checking, type synthesis, and type inhabitation - Analyze reduction strategies, redex creation properties, and delta-reductions - Explore proofs and implications of weak and strong normalization - Learn how to extend basic type systems with constants and primitive operations - Connect classical type theory principles to modern type inference and compiler design. The curriculum starts with essential definitions and notation before guiding you through reduction mechanics, formal semantics, and normalization proofs using comprehensive explanations and text exercises. This course is created for programmers, computer science students, and curious learners seeking a clear entry point into programming language theory without advanced prerequisites. Start reading today to deepen your command of type systems and computational logic.