Friday, 24 July 2026

Theorem Proving in Lean - Three Definitions to Get Started

This is an abridged account of Theorem Proving in Lean capturing only the SSPs, or super salient points.

Here are some three starting definitions essential for understanding this topic:

Formal verification - using logical and computational methods to establish claims that are expressed in precise mathematical terms. Example claims - mathematical theorem /hypothesis, claims that pieces of hardware or software, network protocols, security protocols - do what they say they actually do.  The process is "describe your system in mathematical terms" ,then use "theorem proving" to establish truth.

Automated theorem proving - focused on "finding". The "ATP" toolkit includes: resolution theorem provers, tableau theorem provers, fast satisfiability solvers to provide means of establishing validity of formulas in propositional and first-order logic.  Computer algebra systems may be used in concert to carry out mathematical computations.  

Automated reasoning - differs; not as "cast iron" as theorem proving. Automated reasoning is a superset of automated theorem proving, which includes imprecise techniques such as heuristic search and fuzzy logic.





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