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sav08:theorem_prover [2008/02/20 09:22] vkuncak |
sav08:theorem_prover [2008/02/20 10:31] vkuncak |
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=== Notion of Automated Theorem Prover === | === Notion of Automated Theorem Prover === | ||
- | Theorem prover (TP) accepts a logical formula and tries to prove that the formula is valid. Possible outcomes: | + | Theorem prover (TP) accepts a //logical formula// and tries to prove that the formula is valid. Possible outcomes: |
* TP says: "Yes, formula is valid" | * TP says: "Yes, formula is valid" | ||
* TP says: "No, formula is not valid, here is a counterexample which shows it is false" | * TP says: "No, formula is not valid, here is a counterexample which shows it is false" | ||
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Semidecision procedure: must terminate if answer is "yes", need not terminate if answer is "no". | Semidecision procedure: must terminate if answer is "yes", need not terminate if answer is "no". | ||
* Example: first-order logic | * Example: first-order logic | ||
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+ | **Important question**: combining different decision procedures and using them inside provers | ||
+ | * we will explore this question as well in this course | ||
=== Prover in Analysis === | === Prover in Analysis === | ||
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+ | Recall the big picture in [[Verification as Science]]. What is the role of the theorem prover? | ||
Role of prover in analysis: analyzer asks theorem prover questions | Role of prover in analysis: analyzer asks theorem prover questions |