This book is an introduction to programming language theory using the proof assistant Agda.

Comments on all matters—organisation, material to add, material to remove, parts that require better explanation, good exercises, errors, and typos—are welcome. The book repository is on GitHub. Pull requests are encouraged.

Front matter

Part 1: Logical Foundations

Part 2: Programming Language Foundations

  • Lambda: Introduction to Lambda Calculus
  • Properties: Progress and Preservation
  • DeBruijn: Intrinsically-typed de Bruijn representation
  • More: Additional constructs of simply-typed lambda calculus
  • Bisimulation: Relating reduction systems
  • Inference: Bidirectional type inference
  • Untyped: Untyped lambda calculus with full normalisation
  • Confluence: Confluence of untyped lambda calculus
  • BigStep: Big-step semantics of untyped lambda calculus

Part 3: Denotational Semantics

  • Denotational: Denotational semantics of untyped lambda calculus
  • Compositional: The denotational semantics is compositional
  • Soundness: Soundness of reduction with respect to denotational semantics
  • Adequacy: Adequacy of denotational semantics with respect to operational semantics
  • ContextualEquivalence: Denotational equality implies contextual equivalence


Back matter

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