1 Introduction 2 Induction and sequences 2.1 Induction on natural numbers 2.2 Words and sequences 2.3 A digression on set theory 2.4 Induction on words 2.5 Grammar rules and string rewriting 3 Terms 3.1 Definition of terms 3.2 Knaster-Tarski's fixpoint theorem (1927) 3.3 Kleene's fixpoint theorem (1952?) 3.4 Pattern matching and term rewriting 3.5 Models of a term algebra 4 Lambda-calculus 4.1 Definition of λ-calculus 4.2 Church-computable functions 4.3 Kleene-computable functions 4.4 Turing-computable functions 5 Simply-typed lambda-calculus 5.1 Curry-style simply-typed λ-calculus . 5.2 Unification 5.3 Type inference 5.4 Church-style simply-typed λ-calculus 6 First-order logic 6.1 Formulas and truth 6.2 Provability and deduction systems 6.3 Proof terms and Curry-Howard correspondence 7 To go further 8 Solutions to exercises 8.1 Section 2: Induction and sequences 8.2 Section 3: Terms 8.3 Section 4: Lambda-calculus 8.4 Section 5: Simply-typed lambda-calculus 8.5 Section 6: First-order logic
