Theorem Proving with the Real Numbers

The book explores the integration of real numbers into theorem proving, expanding beyond traditional discrete datatypes. It highlights the implications for 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 through a novel approach to Cantor's method and formalizes significant elements of real analysis. Additionally, it presents an advanced decision procedure for real algebra and practical tools for automating calculations, alongside case studies on correctness specifications in floating point verification.