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-
-\achapter{Calling external provers}
-
-\asection{The \texttt{gappa} tactic}
-\aauthor{Sylvie Boldo, Guillaume Melquiond, Jean-Christophe Filliātre}
-\tacindex{gappa}
-
-The \texttt{gappa} tactic invokes the Gappa
-tool\footnote{\url{http://lipforge.ens-lyon.fr/www/gappa/}} to solve
-properties about floating-point or fixed-point arithmetic. It can also
-solve simple inequalities over real numbers.
-
-The Gappa tool must be installed and its executable (called
-\texttt{gappa}) must be in the user program path. The Coq support
-library for Gappa must also be installed (it is available from Gappa's
-web site). This library provides a \texttt{Gappa\_tactic} module,
-which must be loaded for the tactic to work properly.
-
-The \texttt{gappa} tactic only handles goals and hypotheses that are
-double inequalities $f_1 \le e \le f_2$ where $f_1$ and $f_2$ are
-dyadic constants and $e$ a real-valued expression. Here is an example
-of a goal solved by \texttt{gappa}:
-\begin{verbatim}
-Lemma test_gappa :
- forall x y:R,
- 3/4 <= x <= 3 ->
- 0 <= sqrt x <= 1775 * (powerRZ 2 (-10)).
-Proof.
- gappa.
-Qed.
-\end{verbatim}
-
-Gappa supports floating-point rounding operations (as functions over
-real numbers). Here is an example involving double-precision
-floating-point numbers with rounding toward zero:
-\begin{verbatim}
-Definition rnd := gappa_rounding (rounding_float roundZR 53 1074).
-
-Lemma test_gappa2 :
- forall a_ b_ a b : R,
- a = rnd a_ ->
- b = rnd b_ ->
- 52 / 16 <= a <= 53 / 16 ->
- 22 / 16 <= b <= 30 / 16 ->
- 0 <= rnd (a - b) - (a - b) <= 0.
-Proof.
- unfold rnd; gappa.
-Qed.
-\end{verbatim}
-The function \texttt{gappa\_rounding} declares a rounding mode
-recognized by the \texttt{gappa} tactic. Rounding modes are built
-using constants such as \texttt{rounding\_float} and
-\texttt{roundZR} provided by the Gappa support library.
-
-%%% Local Variables:
-%%% mode: latex
-%%% TeX-master: t
-%%% End: