Formal Methods

Go beyond the basics of Lean 4. This practical deep dive explores functional programming, dependent types, theorem proving and formal verification. Learn how Lean works under the hood, build reliable proofs and automation, and tackle larger formal projects with confidence.

Programming languages are entering a new era. This book explores Vale, Valen, Bend and Revo, showing how they approach memory safety, concurrency, type systems and verification. With runnable examples and clear technical analysis, it offers experienced programmers a grounded look at where systems programming may be headed.

Formal verification does not have to live in research papers. This practical guide shows working software engineers how to turn real requirements into precise, machine-checkable guarantees, find bugs before they reach production and bring formal methods into everyday development, from application code to distributed and security-critical systems.

Make your Python AI code up to 100× faster using NumPy vectorization, Numba, parallel execution, and GPU acceleration. Learn through practical benchmarks and real-world optimization examples.

An introduction to actor-critic algorithms as dynamical systems: featuring hand-computable examples, fast-slow reductions, and machine-checked Lean 4 proofs