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2. 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 ...

3. 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 .

4. Lean (proof assistant) - Wikipedia

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

   Lean is a proof assistant and a functional programming language. [ 1] It is based on the calculus of constructions with inductive types. It is an open-source project hosted on GitHub. It was developed primarily by Leonardo de Moura while employed by Microsoft Research and now Amazon Web Services, and has had significant contributions from other ...

5. Isabelle (proof assistant) - Wikipedia

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

   The Isabelle [a] automated theorem prover is a higher-order logic (HOL) theorem prover, written in Standard ML and Scala.As an LCF-style theorem prover, it is based on a small logical core (kernel) to increase the trustworthiness of proofs without requiring — yet supporting — explicit proof objects.

6. Logic for Computable Functions - Wikipedia

   en.wikipedia.org/wiki/Logic_for_Computable_Functions

   Logic for Computable Functions ( LCF) is an interactive automated theorem prover developed at Stanford and Edinburgh by Robin Milner and collaborators in early 1970s, based on the theoretical foundation of logic of computable functions previously proposed by Dana Scott. Work on the LCF system introduced the general-purpose programming language ...

7. Mathematical proof - Wikipedia

   en.wikipedia.org/wiki/Mathematical_proof

   The concept of proof is formalized in the field of mathematical logic. [ 12] A formal proof is written in a formal language instead of natural language. A formal proof is a sequence of formulas in a formal language, starting with an assumption, and with each subsequent formula a logical consequence of the preceding ones.

8. MU puzzle - Wikipedia

   en.wikipedia.org/wiki/MU_puzzle

   MU puzzle. The MU puzzle is a puzzle stated by Douglas Hofstadter and found in Gödel, Escher, Bach involving a simple formal system called "MIU". Hofstadter's motivation is to contrast reasoning within a formal system (i.e., deriving theorems) against reasoning about the formal system itself.

9. Resolution (logic) - Wikipedia

   en.wikipedia.org/wiki/Resolution_(logic)

   In mathematical logic and automated theorem proving, resolution is a rule of inference leading to a refutation-complete theorem-proving technique for sentences in propositional logic and first-order logic. For propositional logic, systematically applying the resolution rule acts as a decision procedure for formula unsatisfiability, solving the ...