- Introduction to Lean: What is Lean and Why Learn It?
- Setting Up the Lean Development Environment
- Your First Lean Program: "Hello, World!"
- Understanding Lean Syntax: Structure and Formatting
- Lean Data Types: Basic Types and Simple Variables
- Working with Numbers in Lean: Integers, Reals, and Arithmetic
- Lean Logic: Boolean Types and Logical Operations
- Control Flow in Lean:
if Statements and Conditionals
- Loops and Recursion in Lean: Basics of Iteration
- Functions in Lean: Defining and Calling Functions
- Basic Input and Output in Lean: Reading and Printing Data
- Understanding Variables and Scope in Lean
- Using
let and def to Bind Values and Define Functions
- Pattern Matching in Lean: Basic Techniques
- Lean’s
match Expression: Matching Values and Types
- Introduction to Lists and Collections in Lean
- Using Tuples in Lean: Pairing Data Together
- Working with Strings in Lean: Basic String Operations
- Understanding Lean’s
Option and Either Types
- Error Handling and Exceptions in Lean: Using
Option and Result
- Introduction to Lean’s Type System: Types and Type Inference
- Defining and Using Custom Types in Lean
- Working with Algebraic Data Types (ADTs) in Lean
- Type Constructors in Lean:
Option, List, and More
- Advanced Functions in Lean: Higher-Order Functions
- First-Class Functions in Lean: Passing Functions as Arguments
- Lean's
bind and map for Functional Programming
- Polymorphism in Lean: Using Generics for Flexibility
- Lean’s
mutual Definitions: Interdependent Functions and Types
- Modules and Namespaces in Lean: Organizing Code
- Lean's
inductive Types: Defining Recursive Data Types
- Working with Lean’s Theorem Proving System
- Introduction to Lean’s
proof and theorem Syntax
- Using Lean for Formal Verification and Proofs
- Lean’s Mathematical Libraries: Basic Theorems and Definitions
- Defining Recursive Functions in Lean
- Working with Lean’s Built-in Libraries for Lists and Sets
- Introduction to Lean’s
nat (Natural Numbers) Type
- Advanced List Operations in Lean: Mapping, Filtering, and Reducing
- Lean’s
predicate Logic: Using Functions to Model Conditions
- Using Lean’s
tactic Mode for Proof Development
- Lean’s
inductive Theorem Proving: Proof by Induction
- Pattern Matching with
match Expressions in Lean
- Defining and Working with Complex Recursive Functions
- Lean’s
record Types: Modeling Structured Data
- Understanding Lean’s Proof and Refinement System
- Using Lean's
meta Programming Capabilities
- Introduction to Lean’s
setoid Theory: Equivalence Relations
- The Lean Community: Where to Find Resources and Support
- Interfacing Lean with Other Languages: Calling C and Python
- Advanced Theorem Proving in Lean: Tactics and Strategies
- Advanced Recursive Types in Lean: Universes and Inductive Families
- Lean and Dependent Types: Introduction and Benefits
- Proving Properties of Functions in Lean
- Constructing Proofs by Induction and Recursion in Lean
- Lean’s Type-Level Programming: Using
universe Polymorphism
- Homotopy Type Theory in Lean: Introduction and Basics
- Writing Efficient Lean Code: Performance Considerations
- Formalizing Mathematics in Lean: Set Theory and Functions
- Lean’s
category Theory: Modeling Algebraic Structures
- Building Interactive Proofs with Lean: Using
tactic Mode
- Using Lean for Formalizing Programming Language Semantics
- Advanced Pattern Matching in Lean: Customizing Matching Behavior
- Proving Correctness of Algorithms in Lean
- Building a Custom Proof Engine in Lean
- The Lean 4 Update: New Features and Improvements
- Lean's
quote and unquote: Meta-Programming in Lean
- Writing Custom Proof Tactics in Lean
- Building a Lean Proof Checker for Formal Verification
- Implementing Real-World Algorithms in Lean
- Advanced Lean Theorems: Formalizing Complex Mathematical Proofs
- Implementing Proofs of Correctness for Sorting Algorithms
- Working with Lean’s
class System for Type Classes
- Combining Lean with Other Formal Methods and Tools
- Lean for Formal Software Engineering: Specification and Verification
- Using Lean for Automated Theorem Proving in Cryptography
- Building Advanced Data Structures in Lean: Trees and Graphs
- Proving Termination and Complexity of Functions in Lean
- Lean for Machine Learning: Formalizing Neural Networks and Models
- Building a Proof-Assistive IDE for Lean
- Using Lean in Collaborative Formal Verification Projects
- Introduction to Lean’s
algebra Library: Vector Spaces and Groups
- Using Lean for Cryptographic Protocol Verification
- Extending Lean’s Proof Engine with Custom Logic
- Implementing Dynamic Typing in Lean: Advanced Type Manipulation
- Proving Properties of Recursive Algorithms in Lean
- Combining Lean and Coq for Advanced Formal Verification
- Lean for Compiler Verification: Building a Formal Compiler
- Formalizing the Lambda Calculus in Lean
- Understanding Lean’s
congruence Tactics: Advanced Proof Techniques
- Formalizing the Zermelo-Fraenkel Set Theory in Lean
- Advanced Category Theory in Lean: Monoidal Categories and Functors
- Creating Formal Libraries in Lean for Mathematical Domains
- Using Lean for Formal Verification in High-Assurance Systems
- Lean for Parallel and Distributed Systems Verification
- Working with Lean's Proof Search Capabilities
- Applying Lean to Formalize and Prove Security Protocols
- Combining Lean with Model-Checking Techniques
- Writing Lean Libraries for Advanced Data Structures and Algorithms
- The Future of Lean: Trends, Community, and New Directions in Formal Proofs
This list spans a journey from the basics of understanding Lean's syntax, to the complexities of formal proofs, type theory, and advanced metaprogramming. With this progression, learners will gain expertise in using Lean not only as a programming language but also as a powerful tool for formal verification, theorem proving, and mathematical modeling.