Definition
Plain language
A method for getting AI to grow code and machine-checked proofs of correctness side by side.
As stated in the literature
A verified-systems synthesis framework where an inner deductive agent grows code and proof in small steps with Rocq's Admitted-based partial-verification feedback, and an outer inductive agent pivots strategy or proposes lemmas when the inner agent stalls.
Also called: IDS
Why it matters: It offers a way to produce code that's both written and formally verified by AI, rather than trusting a model's claim that its output is correct.
For example, the inner agent grows a key-value store implementation while incrementally proving each operation correct in Rocq, and the outer agent steps in to suggest a new invariant when proofs stop closing.