- Introduction to Agda: What is it and Why Use It?
- Setting Up the Agda Development Environment
- Your First Agda Program: Hello World
- Basic Syntax and Structure of Agda Programs
- Understanding Agda's Type System
- Types and Terms in Agda: A Basic Overview
- Variables and Functions in Agda
- Working with Data Types in Agda
- Introduction to Dependent Types
- Using Lists and Basic Data Structures in Agda
- Defining and Using Records in Agda
- Understanding Agda’s Pattern Matching
- Introduction to Proofs and Theorems in Agda
- Creating Simple Functions in Agda
- Working with Natural Numbers in Agda
- Boolean Types and Operations in Agda
- Tuples and Pairs in Agda
- Using Lists and List Functions in Agda
- Basic Control Structures in Agda: if, case, and let
- Writing Recursive Functions in Agda
- Introduction to Inductive Types in Agda
- The Role of Proofs in Agda Programming
- Understanding Agda’s Interactive Proof Assistant
- Creating Simple Theorems in Agda
- Defining and Using Constants in Agda
- Advanced Pattern Matching in Agda
- Defining and Using Custom Data Types in Agda
- Understanding Dependent Function Types in Agda
- Working with Coinductive Types in Agda
- Handling Universes in Agda
- Exploring Agda’s Module System
- Creating and Using Agda Modules
- The Relationship Between Types and Proofs in Agda
- Inductive and Coinductive Definitions in Agda
- Writing Functions with Dependent Types in Agda
- Understanding and Using Inductive Families
- Proofs by Induction in Agda
- Using Agda’s Built-in Proofs and Lemmas
- Understanding Agda’s Universe Polymorphism
- Type Classes and Type-Directed Programming in Agda
- Working with Vectors and Arrays in Agda
- Using Agda for Metaprogramming
- Creating and Using Generic Functions in Agda
- Integrating Agda with Haskell for Practical Applications
- Using Agda for Functional Programming
- Reasoning About Programs with Agda
- Defining and Proving Properties of Functions in Agda
- Using Agda’s Reflection and Unification Features
- Testing and Debugging Agda Programs
- Understanding the Agda Proof Engine and Tactics
- Exploring Agda's List Library and Standard Library
- Type-Safe Programming in Agda
- Advanced Record Definitions in Agda
- Creating Recursive Data Structures in Agda
- Understanding Agda’s Type Inference Mechanism
- Working with Higher-Kinded Types in Agda
- Using Agda's Coercions and Subtyping Features
- Writing and Proving Properties of Algorithms in Agda
- Building and Managing Large Agda Projects
- Best Practices for Proof Engineering in Agda
- Working with Agda’s Iterators and Traversable Data Types
- Understanding Functors, Monads, and Applicative in Agda
- Building Efficient Algorithms in Agda
- Creating Type-Level Computations in Agda
- Handling Finite Sets and Data Types in Agda
- Mastering Dependent Pattern Matching in Agda
- Advanced Inductive and Coinductive Types in Agda
- Creating and Proving Parametric Polymorphic Functions in Agda
- Designing Complex Theorems in Agda
- Using Agda’s Reflection Mechanism for Code Generation
- Formal Verification of Algorithms with Agda
- Creating and Verifying Cryptographic Algorithms in Agda
- Proving Termination of Recursive Functions in Agda
- Understanding the Formal Semantics of Agda
- Mastering Agda’s Metaprogramming Capabilities
- Building Type-Theoretic Libraries in Agda
- Reasoning About Mutually Recursive Data Types in Agda
- Advanced Proof Techniques: Dependent Induction and Recursion
- Designing and Implementing Domain-Specific Languages with Agda
- Exploring the Agda Interactive Theorem Prover
- Creating Proofs of Correctness for Software Systems in Agda
- Advanced Functional Programming Patterns in Agda
- Integrating Agda with Other Proof Assistants
- Formalizing Mathematics with Agda: Algebraic Structures
- Proving Properties of Infinite Data Structures in Agda
- Mastering Type Families and Indexed Data Types in Agda
- Understanding and Implementing Category Theory in Agda
- Building Highly Generic Libraries in Agda
- Proofs in Agda: The Role of Automating Proof Search
- Using Agda for Knowledge Representation and AI
- Working with Computational Interpretations of Agda's Proofs
- Building Verified Software Systems with Agda
- Integrating Agda with Other Functional Programming Languages
- Designing and Proving Security Protocols in Agda
- Agda for Formalizing Software Engineering Principles
- Verification and Synthesis of Embedded Systems with Agda
- Automating Proofs in Agda with Tactics and Automation Libraries
- Advanced Program Synthesis Techniques in Agda
- Exploring Agda’s Integration with the Lambda Calculus
- The Future of Agda and its Role in Proof Assistants
These chapter titles cover a broad range of topics, from the fundamentals of Agda and dependent types to advanced topics like program synthesis, formal verification, and integrating Agda with other languages and systems. This list would guide a learner from basic programming to expert-level formal verification and theorem proving.