Barriers to the widespread adoption of formal methods include perceived high costs and a lack of applicability to certain domains. Historical context reveals that these methods have not been effectively integrated into mainstream software development practices.

Mathematicians, logicians, and computer scientists have developed various calculi, including lambda calculus, relational calculus, and predicate calculus. Lambda calculus, created by Alonzo Church, serves as a foundational model of computation, while relational calculus underpins SQL and predicate calculus is essential in formal methods.

LLMs can be evaluated for their ability to model system code using TLA+, a specification language for concurrent and distributed systems. The Specula team explored using Claude to create a TLA+ specification for Etcd.