Theorem Prover
A core component of the formal verification toolchain that requires users to supply step-by-step proof scripts, with a kernel mechanically checking the validity of each inference step. Representative tools include Coq, Isabelle and Lean.
Timeline (last 90 days)
The relationship among type systems, proof systems, and theorem provers can be understood as a continuum of strength and cost: type systems are the most automated and cheapest; theorem provers are the most expressive but have the highest barrier; dependent types, refinement types, and design by contract fall in between.
Verification artifacts generated by the LLM need to be handed to a theorem prover or SMT solver for checking, forming a "generate-check" loop, which is the mechanistic basis for LLM-assisted verification being trustworthy.
The kernel of a theorem prover is the smallest trusted component responsible for checking the correctness of proofs.
All Facts (3)
The relationship among type systems, proof systems, and theorem provers can be understood as a continuum of strength and cost: type systems are the most automated and cheapest; theorem provers are the most expressive but have the highest barrier; dependent types, refinement types, and design by contract fall in between.
50%UnverifiedVerification artifacts generated by the LLM need to be handed to a theorem prover or SMT solver for checking, forming a "generate-check" loop, which is the mechanistic basis for LLM-assisted verification being trustworthy.
50%UnverifiedThe kernel of a theorem prover is the smallest trusted component responsible for checking the correctness of proofs.
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