Software tool to assist with the development of formal proofs by human-machine collaboration
For verification in computer science, see formal verification.
For the academic conference, see Interactive Theorem Proving (conference).
Not to be confused with Interactive proof system.
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An interactive proof session in CoqIDE, showing the proof script on the left and the proof state on the right
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 stored in, and some steps provided by, a computer.
A recent effort within this field is making these tools use artificial intelligence to automate the formalization of ordinary mathematics.[1]
^Ornes, Stephen (August 27, 2020). "Quanta Magazine – How Close Are Computers to Automating Mathematical Reasoning?".
mathematical logic, a proofassistant or interactive theorem prover is a software tool to assist with the development of formal proofs by human-machine collaboration...
that a published proof can, in principle, be converted into a formal proof. However, outside the field of automated proofassistants, this is rarely done...
computer proofassistants. Type theory is an active area of research, one direction being the development of homotopy type theory. The first computer proof assistant...
essentially another proofassistant for classical higher order logic. Coq Developed in France, Coq is another automated proofassistant, which can automatically...
formal proof; it was finished (and verified) in 2015. Once written formally, a proof can be verified using a program called a proofassistant. These programs...
Mathematical software is software used to model, analyze or calculate numeric, symbolic or geometric data. Numerical analysis and symbolic computation...
and verified proof. Over a 6-month period, a group led by Johan Commelin verified the central part of the proof using the proofassistant Lean. As of 14...
language and an associated computer program (a proofassistant) for archiving and verifying mathematical proofs. Several databases of proved theorems have...
for writing mathematical definitions and proofs, a proofassistant, which is able to mechanically check proofs written in this language, and a library...
villages), mines, and dams Locale (Isabelle), a module of the Isabelle proofassistant Locale ('Ndrangheta), the main local organizational unit of the 'Ndrangheta...
and hence consistent. The CoC has been developed alongside the Coq proofassistant. As features were added (or possible liabilities removed) to the theory...
Interactive Proof. Proofs have been done using embeddings of Separation Logic into interactive theorem provers such as the Coq proofassistant and HOL (proof assistant)...
make possible); and the formalization of each of these in computer proofassistants. There is a large overlap between the work referred to as homotopy...
of a formal proof of the Kepler conjecture using a combination of the Isabelle and HOL Light proofassistants. In 2017, the formal proof was accepted...
errors". In 2024, Sky Wilshaw formalized a version of Holmes' proof using the proofassistant Lean, finally resolving the question of NF's consistency. Timothy...
by zero, which can be handled in another part of the program. Many proofassistants, such as Coq and Lean, define 1/0 = 0. This is due to the requirement...
theorem and Feit–Thompson proof of the odd-order theorem. (Both were written using the proofassistant Coq.) Flyspeck proof led by Thomas Callister Hales...
HOL, HOL Light, and the Isabelle proofassistant that supports various logics. As of 2019, the Isabelle proofassistant still contains an implementation...
In automated theorem proving, PhoX is a proofassistant based on higher-order logic which is eXtensible. The user gives PhoX an initial goal and guides...
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