Theorem Proving with the Real Numbers

The book explores the integration of real numbers in theorem proving, expanding beyond traditional discrete datatypes like natural numbers. It highlights the significance of real numbers for applications in verifying floating point hardware and enhancing computer algebra systems. Utilizing a version of the HOL theorem prover, it details the rigorous construction of real numbers and formalizes substantial aspects of real analysis. Additionally, it presents a decision procedure for real algebra and discusses practical tools for automating calculations, alongside case studies on correctness specifications in floating point verification.