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Handbook of Practical Logic and Automated Reasoning by John Harrison

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6

Interactive theorem proving

 

 

Our efforts so far have been aimed at making the computer prove theorems completely automatically. But the scope of fully automatic methods, subject to any remotely realistic limitations on computing power, covers only a very small part of present-day mathematics. Here we develop an alternative: an interactive proof assistant that can help to precisely state and formalize a proof, while still dealing with some boring details automatically. Moreover, to ensure its reliability, we design the proof assistant based on a very simple logical kernel.

6.1 Human-oriented methods

We’ve devoted quite a lot of energy to making computers prove statements completely automatically. The methods we’ve implemented are fairly ...

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