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In computer science and mathematical logic, a proof assistant or interactive theorem prover is a software tool to assist with the development of formal proofs by human–machine collaboration. This involves some sort of interactive proof editor, or other interface , with which a human can guide the search for proofs, the details of which are ...
AlphaGeometry is an artificial intelligence (AI) program that can solve hard problems in Euclidean geometry.It was developed by DeepMind, a subsidiary of Google.The program solved 25 geometry problems out of 30 from the International Mathematical Olympiad (IMO) under competition time limits—a performance almost as good as the average human gold medallist.
The main trends of research on Wu's method concern systems of polynomial equations of positive dimension and differential algebra where Ritt's results have been made effective. [3] [4] Wu's method has been applied in various scientific fields, like biology, computer vision, robot kinematics and especially automatic proofs in geometry. [5]
An interactive proof session in CoqIDE, showing the proof script on the left and the proof state on the right. Coq is an interactive theorem prover first released in 1989. It allows for expressing mathematical assertions, mechanically checks proofs of these assertions, helps find formal proofs, and extracts a certified program from the constructive proof of its formal specification.
Since the proofs generated by automated theorem provers are typically very large, the problem of proof compression is crucial, and various techniques aiming at making the prover's output smaller, and consequently more easily understandable and checkable, have been developed. Proof assistants require a human user to give hints to the system ...
theorem and_swap (p q: Prop): p ∧ q → q ∧ p:= by intro h-- assume p ∧ q with proof h, the goal is q ∧ p apply And.intro-- the goal is split into two subgoals, one is q and the other is p · exact h.right-- the first subgoal is exactly the right part of h : p ∧ q · exact h.left-- the second subgoal is exactly the left part of h : p ...
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