- Introduction to Coq: What Is Coq and Why Use It?
- Setting Up Your Coq Development Environment
- Your First Coq Program: Hello World
- Understanding Coq Syntax and Structure
- Basic Data Types in Coq
- Working with Numbers and Arithmetic in Coq
- Defining Variables and Expressions in Coq
- Basic Control Structures in Coq: if, then, else
- Working with Functions in Coq
- Using Inductive Types in Coq
- Basic Proofs in Coq: Introduction to Proof Scripts
- Understanding Coq's Logical Foundations
- Simple Proofs in Coq: Proof by Reflexivity and Symmetry
- Introduction to the Coq Proof Assistant
- Working with Lists and Sequences in Coq
- Basic Set Theory and Coq’s Set Notation
- Using
Prop for Logical Propositions in Coq
- Introduction to Tactics:
intro, apply, and exact
- The
induction Tactic in Coq
- Basic Arithmetic Proofs in Coq
- Understanding the
exists Quantifier in Coq
- Working with Theorems and Lemmas in Coq
- Understanding the Coq Proof Engine
- Coq's
Fixpoint and Recursive Definitions
- Building Basic Algorithms in Coq
- Understanding Types and Type Systems in Coq
- Data Structures in Coq: Lists, Trees, and More
- Proof by Induction in Coq
- Working with Higher-Order Logic in Coq
- Understanding
forall Quantifiers in Coq
- Coq’s Logical Connectives: AND, OR, IMPLIES
- Proving Equality in Coq
- Using the
rewrite Tactic in Coq
- Defining Functions and Relations in Coq
- Manipulating Proof Contexts in Coq
- Advanced Proof Techniques in Coq
- The
destruct and case Tactics in Coq
- Coq's Strong and Weak Normalization
- Understanding and Using Universes in Coq
- Working with Parametric Polymorphism in Coq
- Proof Automation in Coq:
auto and eauto Tactics
- Coq's Constructive Logic and its Applications
- Working with Coq’s
Set and Type Hierarchy
- Defining and Proving Recursive Functions in Coq
- Using
Inductive and CoInductive Types in Coq
- Defining and Proving Properties of Lists in Coq
- Coq's
Prop, Set, and Type: Understanding the Difference
- Working with Proofs by Contradiction in Coq
- Coq's
match and Pattern Matching in Functions and Proofs
- Using the
firstorder Tactic in Coq for Automatic Proofs
- Working with Coq’s Logical Connectives in Proofs
- Advanced Manipulation of Tactics and Proof Context
- Introducing Coq's
Not and Exists Quantifiers in Proofs
- The
cbv and simpl Tactics for Simplification in Coq
- Defining and Proving Inductive Families in Coq
- Defining and Using Lists in Coq’s Proof Assistant
- Modular Proofs and Proof General in Coq
- The
focus Tactic in Coq for Focusing on Proof Goals
- Using the
intros and apply Tactics Together
- Using Recursion and Induction for Mathematical Proofs in Coq
- Proving Program Correctness with Coq
- Understanding and Using Coq’s Functional Programming Features
- Working with Coq’s
forall and exists in Proofs
- Proving Equivalence in Coq
- Building and Using Functions with Dependent Types in Coq
- Advanced Type Theory in Coq
- Working with Coq’s
Universe Polymorphism
- Defining and Using Coq’s Dependently-Typed Functions
- Coq's Reflection and Meta-Programming Capabilities
- Constructing Complex Proofs in Coq
- Using
Setoid and Equivalence Relations in Coq
- Proving the Correctness of Algorithms in Coq
- Advanced Recursion Patterns and Proofs in Coq
- Coq and Higher-Order Logic: Applications and Limitations
- Working with Coq’s Library and the Mathematical Components Library
- Formal Verification of Cryptographic Protocols in Coq
- Extending Coq: Writing and Using Coq Plugins
- Using Coq to Prove Properties of Recursive Data Structures
- Advanced Techniques for Managing Proof Contexts
- The
Program Tactic for Defining Programs in Coq
- Coq’s Inductive and CoInductive Types in Advanced Proofs
- The
Setoid Approach to Equivalence and Normalization
- Using Coq’s Tactics for Interactive Theorem Proving
- Proving Termination and Totality in Coq
- Coq and Proof-Carrying Code (PCC)
- Advanced Automation: Building Proof Automation Tools in Coq
- Using Coq with Haskell and F# for Program Verification
- Working with Coq’s
Prop for Constructive Proofs
- Coq’s Logical Foundations: Intuitionistic vs Classical Logic
- The
Qed Command and Finalizing Proofs in Coq
- Coq and Homotopy Type Theory (HoTT)
- Proof Development Strategies: Combining Induction and Structural Recursion
- Exploring Proof Search and Automation in Coq
- Building Proof Assistants and Custom Tactics with Coq
- Using Coq for Formalizing Mathematical Theorems
- Implementing Dependent Types and GADTs in Coq
- Building and Managing Libraries in Coq
- Coq’s Metaprogramming: Writing Advanced Tactics
- Formalizing and Proving Properties of Software with Coq
- The Future of Coq: Trends and Innovations in Proof Engineering
These 100 chapters cover the full spectrum of Coq programming, from introductory topics on syntax and basic proofs to more advanced concepts such as dependent types, meta-programming, and formal verification of algorithms. This guide will help you master Coq for a variety of tasks, including software verification, mathematical proofs, and building proof assistants. Whether you're a beginner or an advanced user, this structure provides a clear progression for learning Coq.