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author | blanchet |

Fri, 27 May 2011 10:30:08 +0200 | |

changeset 43036 | 0ef380310863 |

parent 43035 | 31182f0ec04d |

child 43037 | ade5c84f860f |

more Sledgehammer documentation updates

--- a/doc-src/Sledgehammer/sledgehammer.tex Fri May 27 10:30:08 2011 +0200 +++ b/doc-src/Sledgehammer/sledgehammer.tex Fri May 27 10:30:08 2011 +0200 @@ -101,9 +101,9 @@ The result of a successful proof search is some source text that usually (but not always) reconstructs the proof within Isabelle. For ATPs, the reconstructed -proof relies on the general-purpose Metis prover \cite{metis}, which is fully -integrated into Isabelle/HOL, with explicit inferences going through the kernel. -Thus its results are correct by construction. +proof relies on the general-purpose Metis prover, which is fully integrated into +Isabelle/HOL, with explicit inferences going through the kernel. Thus its +results are correct by construction. In this manual, we will explicitly invoke the \textbf{sledgehammer} command. Sledgehammer also provides an automatic mode that can be enabled via the @@ -249,33 +249,33 @@ \slshape Sledgehammer: ``\textit{e}'' on goal \\ $[a] = [b] \,\Longrightarrow\, a = b$ \\ -Try this: \textbf{by} (\textit{metis last\_ConsL}). \\ +Try this: \textbf{by} (\textit{metis last\_ConsL}) (46 ms). \\ To minimize: \textbf{sledgehammer} \textit{min} [\textit{e}] (\textit{last\_ConsL}). \\[3\smallskipamount] % Sledgehammer: ``\textit{vampire}'' on goal \\ $[a] = [b] \,\Longrightarrow\, a = b$ \\ -Try this: \textbf{by} (\textit{metis hd.simps}). \\ +Try this: \textbf{by} (\textit{metis hd.simps}) (17 ms). \\ To minimize: \textbf{sledgehammer} \textit{min} [\textit{vampire}] (\textit{hd.simps}). \\[3\smallskipamount] % Sledgehammer: ``\textit{spass}'' on goal \\ $[a] = [b] \,\Longrightarrow\, a = b$ \\ -Try this: \textbf{by} (\textit{metis list.inject}). \\ +Try this: \textbf{by} (\textit{metis list.inject}) (20 ms). \\ To minimize: \textbf{sledgehammer} \textit{min} [\textit{spass}]~(\textit{list.inject}). \\[3\smallskipamount] % Sledgehammer: ``\textit{remote\_waldmeister}'' on goal \\ $[a] = [b] \,\Longrightarrow\, a = b$ \\ -Try this: \textbf{by} (\textit{metis hd.simps insert\_Nil}). \\ +Try this: \textbf{by} (\textit{metis hd.simps insert\_Nil}) (25 ms). \\ To minimize: \textbf{sledgehammer} \textit{min} [\textit{remote\_waldmeister}] \\ \phantom{To minimize: \textbf{sledgehammer}~}(\textit{hd.simps insert\_Nil}). \\[3\smallskipamount] % Sledgehammer: ``\textit{remote\_sine\_e}'' on goal \\ $[a] = [b] \,\Longrightarrow\, a = b$ \\ -Try this: \textbf{by} (\textit{metis hd.simps}). \\ +Try this: \textbf{by} (\textit{metis hd.simps}) (17 ms). \\ To minimize: \textbf{sledgehammer} \textit{min} [\textit{remote\_sine\_e}]~(\textit{hd.simps}). \\[3\smallskipamount] % Sledgehammer: ``\textit{remote\_z3}'' on goal \\ $[a] = [b] \,\Longrightarrow\, a = b$ \\ -Try this: \textbf{by} (\textit{metis hd.simps}). \\ +Try this: \textbf{by} (\textit{metis hd.simps}) (17 ms). \\ To minimize: \textbf{sledgehammer} \textit{min} [\textit{remote\_z3}]~(\textit{hd.simps}). \postw @@ -285,11 +285,12 @@ \textit{remote\_} prefix. Waldmeister is run only for unit equational problems, where the goal's conclusion is a (universally quantified) equation. -For each successful prover, Sledgehammer gives a one-liner proof that uses the -\textit{metis} or \textit{smt} method. You can click the proof to insert it into -the theory text. You can click the ``\textbf{sledgehammer} \textit{minimize}'' +For each successful prover, Sledgehammer gives a one-liner proof that uses Metis +or the \textit{smt} proof method. For Metis, timings are shown in parentheses, +indicating how fast the call is. You can click the proof to insert it into the +theory text. You can click the ``\textbf{sledgehammer} \textit{minimize}'' command if you want to look for a shorter (and probably faster) proof. But here -the proof found by E looks perfect, so click it to finish the proof. +the proof found by Vampire is both short and fast already. You can ask Sledgehammer for an Isar text proof by passing the \textit{isar\_proof} option (\S\ref{output-format}): @@ -299,8 +300,8 @@ \postw When Isar proof construction is successful, it can yield proofs that are more -readable and also faster than the \textit{metis} one-liners. This feature is -experimental and is only available for ATPs. +readable and also faster than the Metis one-liners. This feature is experimental +and is only available for ATPs. \section{Hints} \label{hints} @@ -383,38 +384,44 @@ \point{Why does Metis fail to reconstruct the proof?} There are many reasons. If Metis runs seemingly forever, that is a sign that the -proof is too difficult for it. Metis is complete, so it should eventually find -it, but that's little consolation. There are several possible solutions: +proof is too difficult for it. Metis's search is complete, so it should +eventually find it, but that's little consolation. There are several possible +solutions: \begin{enum} \item[$\bullet$] Try the \textit{isar\_proof} option (\S\ref{output-format}) to obtain a step-by-step Isar proof where each step is justified by Metis. Since the steps are fairly small, Metis is more likely to be able to replay them. -\item[$\bullet$] Try the \textit{smt} proof method instead of \textit{metis}. It -is usually stronger, but you need to have Z3 available to replay the proofs, -trust the SMT solver, or use certificates. See the documentation in the -\emph{SMT} theory (\texttt{\$ISABELLE\_HOME/src/HOL/SMT.thy}) for details. +\item[$\bullet$] Try the \textit{smt} proof method instead of Metis. It is +usually stronger, but you need to have Z3 available to replay the proofs, trust +the SMT solver, or use certificates. See the documentation in the \emph{SMT} +theory (\texttt{\$ISABELLE\_HOME/src/HOL/SMT.thy}) for details. \item[$\bullet$] Try the \textit{blast} or \textit{auto} proof methods, passing the necessary facts via \textbf{unfolding}, \textbf{using}, \textit{intro}{:}, \textit{elim}{:}, \textit{dest}{:}, or \textit{simp}{:}, as appropriate. \end{enum} -In some rare cases, Metis fails fairly quickly. This usually indicates that -Sledgehammer found a type-incorrect proof. Sledgehammer erases some type -information to speed up the search. Try Sledgehammer again with full type -information: \textit{full\_types} (\S\ref{problem-encoding}), or choose a -specific type encoding with \textit{type\_sys} (\S\ref{problem-encoding}). Older -versions of Sledgehammer were frequent victims of this problem. Now this should -very seldom be an issue, but if you notice many unsound proofs, contact the -author at \authoremail. +In some rare cases, Metis fails fairly quickly, and you get the error message + +\prew +\slshape +Proof reconstruction failed. +\postw + +This usually indicates that Sledgehammer found a type-incorrect proof. +Sledgehammer erases some type information to speed up the search. Try +Sledgehammer again with full type information: \textit{full\_types} +(\S\ref{problem-encoding}), or choose a specific type encoding with +\textit{type\_sys} (\S\ref{problem-encoding}). Older versions of Sledgehammer +were frequent victims of this problem. Now this should very seldom be an issue, +but if you notice many unsound proofs, contact the author at \authoremail. \point{How can I tell whether a generated proof is sound?} -First, if \emph{metis} (or \emph{metisFT}) can reconstruct it, the proof is -sound (modulo soundness of Isabelle's inference kernel). If it fails or runs -seemingly forever, you can try +First, if Metis can reconstruct it, the proof is sound (modulo soundness of +Isabelle's inference kernel). If it fails or runs seemingly forever, you can try \prew \textbf{apply}~\textbf{--} \\ @@ -494,21 +501,6 @@ set the \textit{isar\_shrink\_factor} option (\S\ref{output-format}) to a larger value or to try several provers and keep the nicest-looking proof. -\point{Should I minimize the number of lemmas?} - -In general, minimization is a good idea, because proofs involving fewer lemmas -tend to be shorter as well, and hence easier to re-find by Metis. But the -opposite is sometimes the case. - -\point{Why does the minimizer sometimes starts on its own?} - -There are two scenarios in which this can happen. First, some provers (notably -CVC3, Satallax, and Yices) do not provide proofs or sometimes provide incomplete -proofs. The minimizer is then invoked to find out which facts are actually -needed from the (large) set of facts that was initinally given to the prover. -Second, if a prover returns a proof with lots of facts, the minimizer is invoked -automatically since Metis would be unlikely to re-find the proof. - \point{What is metisFT?} The \textit{metisFT} proof method is the fully-typed version of Metis. It is @@ -517,7 +509,12 @@ \mathrel{\lor} x = \mathit{False}$'' for reasoning in higher-order places (e.g., in set comprehensions). The method kicks in automatically as a fallback when \textit{metis} fails, and it is sometimes generated by Sledgehammer instead of -\textit{metis} if the proof obviously requires type information. +\textit{metis} if the proof obviously requires type information or if +\textit{metis} failed when Sledgehammer preplayed the proof. (By default, +Sledgehammer tries to run \textit{metis} and/or \textit{metisFT} for 4 seconds +to ensure that the generated one-line proofs actually work and to display timing +information. This can be configured using the \textit{preplay\_timeout} option +(\S\ref{mode-of-operation}).) If you see the warning @@ -529,6 +526,22 @@ in a successful Metis proof, you can advantageously replace the \textit{metis} call with \textit{metisFT}. +\point{Should I minimize the number of lemmas?} + +In general, minimization is a good idea, because proofs involving fewer lemmas +tend to be shorter as well, and hence easier to re-find by Metis. But the +opposite is sometimes the case. Keep an eye on the timing information displayed +next to the suggested Metis calls. + +\point{Why does the minimizer sometimes starts on its own?} + +There are two scenarios in which this can happen. First, some provers (notably +CVC3, Satallax, and Yices) do not provide proofs or sometimes provide incomplete +proofs. The minimizer is then invoked to find out which facts are actually +needed from the (large) set of facts that was initinally given to the prover. +Second, if a prover returns a proof with lots of facts, the minimizer is invoked +automatically since Metis would be unlikely to re-find the proof. + \point{A strange error occurred---what should I do?} Sledgehammer tries to give informative error messages. Please report any strange @@ -679,9 +692,9 @@ \item[$\bullet$] \qtybf{float\_pair\/}: A pair of floating-point numbers (e.g., 0.6 0.95). \item[$\bullet$] \qtybf{smart\_int\/}: An integer or \textit{smart}. -\item[$\bullet$] \qtybf{float\_or\_none\/}: An integer (e.g., 60) or -floating-point number (e.g., 0.5) expressing a number of seconds, or the keyword -\textit{none} ($\infty$ seconds). +\item[$\bullet$] \qtybf{float\_or\_none\/}: A floating-point number (e.g., 60 or +0.5) expressing a number of seconds, or the keyword \textit{none} ($\infty$ +seconds). \end{enum} Default values are indicated in braces. Boolean options have a negated @@ -817,6 +830,11 @@ the option ``Sledgehammer: Time Limit'' from the ``Isabelle'' menu in Proof General. +\opdefault{preplay\_timeout}{float\_or\_none}{\upshape 4} +Specifies the maximum number of seconds that Metis should be spent trying to +``preplay'' the found proof. If this option is set to 0, no preplaying takes +place, and no timing information is displayed next to the suggested Metis calls. + \opfalse{blocking}{non\_blocking} Specifies whether the \textbf{sledgehammer} command should operate synchronously. The asynchronous (non-blocking) mode lets the user start proving