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2. Automated theorem proving - Wikipedia

   en.wikipedia.org/wiki/Automated_theorem_proving

   Automated theorem proving. Automated theorem proving (also known as ATP or automated deduction) is a subfield of automated reasoning and mathematical logic dealing with proving mathematical theorems by computer programs. Automated reasoning over mathematical proof was a major impetus for the development of computer science .

3. Lean (proof assistant) - Wikipedia

   en.wikipedia.org/wiki/Lean_(proof_assistant)

   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 ∧ q

4. Z3 Theorem Prover - Wikipedia

   en.wikipedia.org/wiki/Z3_Theorem_Prover

   Z3 was developed in the Research in Software Engineering (RiSE) group at Microsoft Research Redmond and is targeted at solving problems that arise in software verification and program analysis. Z3 supports arithmetic, fixed-size bit-vectors, extensional arrays, datatypes, uninterpreted functions, and quantifiers.

5. List of open-source software for mathematics - Wikipedia

   en.wikipedia.org/wiki/List_of_open-source...

   After a failure to launch as a product, NAG decided to release it as a free software in 2001 with more than 300 man-years worth of research involved. Axiom is licensed under a Modified BSD license. Cadabra. A Computer Algebra System designed for the solution of problems in field theory.

6. List of optimization software - Wikipedia

   en.wikipedia.org/wiki/List_of_optimization_software

   MIDACO – a software package for numerical optimization based on evolutionary computing. MINTO – integer programming solver using branch and bound algorithm; freeware for personal use. MOSEK – a large scale optimization software. Solves linear, quadratic, conic and convex nonlinear, continuous and integer optimization.

7. Proof assistant - Wikipedia

   en.wikipedia.org/wiki/Proof_assistant

   Proof assistant. 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 ...