Programming Language Theory

  1. Mathematical Foundations
    1. Formal Logic
      1. Propositional Logic
        1. Syntax and Formation Rules
          1. Semantics and Truth Conditions
            1. Truth Tables
              1. Logical Connectives
                1. Tautologies and Contradictions
                2. Predicate Logic
                  1. Quantifiers
                    1. Variables and Domains
                      1. Logical Inference Rules
                        1. Satisfiability
                        2. Proof Systems
                          1. Natural Deduction
                            1. Introduction Rules
                              1. Elimination Rules
                                1. Proof Trees
                                2. Sequent Calculus
                                  1. Sequent Structure
                                    1. Structural Rules
                                      1. Logical Rules
                                  2. Set Theory and Relations
                                    1. Basic Set Operations
                                      1. Functions and Mappings
                                        1. Partial Functions
                                          1. Total Functions
                                            1. Injective and Surjective Functions
                                            2. Relations and Properties
                                              1. Reflexivity
                                                1. Symmetry
                                                  1. Transitivity
                                                    1. Equivalence Relations
                                                  2. Mathematical Induction
                                                    1. Principle of Mathematical Induction
                                                      1. Structural Induction
                                                        1. Inductive Definitions
                                                          1. Inductive Proofs for Language Properties
                                                          2. Formal Languages and Automata
                                                            1. Regular Languages
                                                              1. Regular Expressions
                                                                1. Deterministic Finite Automata
                                                                  1. Nondeterministic Finite Automata
                                                                    1. Equivalence of Representations
                                                                    2. Context-Free Languages
                                                                      1. Context-Free Grammars
                                                                        1. Parse Trees and Derivations
                                                                          1. Pushdown Automata
                                                                            1. Parsing Algorithms

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                                                                        1. Introduction to Programming Language Theory

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                                                                        3. Lambda Calculus