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Explore the cutting-edge field of formal software verification in this 51-minute conference talk from the PLMW @ ICFP/SPLASH 2025 workshop. Discover how machine-assisted reasoning is transforming software specification and verification, bringing mathematical rigor to large-scale industrial systems. Learn about recent breakthroughs in proof assistants, verification tools, and their real-world applications in both academic and industrial settings. Examine the mechanised specification of the W3C WebAssembly language standard through the innovative Wasm SpecTec process, and understand compositional software analysis techniques based on separation logic that enable independent function specification within complex, open industrial codebases. Gain insights into compositional techniques for verified specification of shared-memory concurrent programs and understand what makes a specification appropriate, well-evaluated, and useful for practical applications. Understand the historical context from Turing, Hoare, and Milner's original vision to today's mature mathematical techniques and well-engineered tools that make large-scale formal verification possible, while also learning about the challenges that remain in bringing scientific methods to modern software system verification.