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When I state a lemma in Isabelle, I often type nitpick, and if that doesn't give me a counterexample. I then type sledgehammer to try to find a proof automatically.

I wonder: is it possible to invoke Nitpick and Sledgehammer so that they run concurrently? Since Sledgehammer is already sending off my lemma to a bunch of automatic provers, couldn't one of those provers actually be a counterexample-finder such as Nitpick?

John Wickerson
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1 Answers1

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You can try using the try command in Isabelle; it runs sledgehammer, nitpick, quickcheck and a number of other solvers (such as auto, simp, force, etc) in parallel, giving you the results of the first one that finishes.

For example, running the following:

lemma "(a * (b + 1)) = (a * b + a)"
  try

will return a counter-example from nitpick, indicating that the theorem is not true in general. Adding a type constraint:

lemma "((a :: nat) * (b + 1)) = (a * b + a)"
  try

will now return a message telling you that simp is able to solve the goal.

Finally, changing the type constraint to the more challenging 32 word type (available from Word in HOL-Word):

lemma "((a :: 32 word) * (b + 1)) = (a * b + a)"
  try

will return a result from sledgehammer.

davidg
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    A more lightweight variant is `try0`, which only tries proof methods, but leaves out the more heavyweight `sledeghammer`, `nitpick`, `quickcheck` calls. – Lars Noschinski Mar 01 '13 at 15:33