Theorem prover

Theorem provers as assistants
A theorem prover can also act as a proof-checker, where the proof is given by a human as a
series of fairly large steps; ...

EQP theorem prover at Argonne National Labs proves the Robbins Conjecture in mathematics (October-November, 1996).

Carine theorem prover
Automated theorem proving
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v - d - e ...

sound of a theorem prover or algorithm, guaranteed to produce only correct results, i.e., anything that is proved is indeed a theorem. cf. complete.
specular describes a surface whose reflectance is mirror-like. cf. Lambertian.

Some examples of Symbolic AI programs are chess-playing programs, expert systems such as theorem provers, ELIZA, STUDENT (which solves calculus problems) etc. Just about any task-center AI program is a symbolic AI program.

Otter: a theorem prover. C.
DTP: a theorem prover. Common Lisp.
Epilog: theorem prover and logical language toolkit. Binary for Mac, HP.
CLIPS: a Tool for Building Expert Systems. C.

Herbert Gelernter wrote the Geometry Theorem Prover which used information to prune a search with a billion alternatives (for a 3-step proof of a geometry theorem) to only 25 alternatives. He was the first to demonstrate "model referencing." ...

The "Theorem Prover" systems have not been oriented toward making it easy to employ the second and the third kinds of knowledge. We have just given an example of how the second type of knowledge can be used.

main approaches to implementing formal verification include state space enumeration, symbolic state space enumeration, abstract interpretation, abstraction refinement, process-algebraic methods, and reasoning with the aid of automatic theorem provers ...

See also: Artificial intelligence, Knowledge, Inference, AI, Expert system