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Why3
why3
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eb7bb11c
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eb7bb11c
authored
Sep 17, 2014
by
JeanChristophe Filliâtre
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doc: transformation induction_ty_lex
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doc/technical.tex
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eb7bb11c
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@@ 184,22 +184,45 @@ each $x_1 \dots x_n$ occurs at most once in all the $e_i$.
\subsection
{
Induction Transformations
}
\begin{itemize}
\item
Induction on an algebraic data type:
\verb

induction_ty_lex

\index
{
inductiontylex@
\verb
+
induction_ty_lex
+
}
[TO BE COMPLETED]
\begin{description}
\item
[induction\_ty\_lex]
:
\index
{
inductiontylex@
\verb
+
induction_ty_lex
+
}
This transformation performs structural, lexicographic induction on
goals involving universally quantified variables of algebraic data
types, such as lists, trees, etc. For instance, it transforms the
following goal
\begin{whycode}
goal G: forall l: list 'a. length l >= 0
\end{whycode}
into this one:
\begin{whycode}
goal G :
forall l:list 'a.
match l with
 Nil > length l >= 0
 Cons a l1 > length l1 >= 0 > length l >= 0
end
\end{whycode}
When induction can be applied to several variables, the transformation
picks one heuristically. A label
\verb

induction

can be used to
force induction over one particular variable,
\emph
{
e.g.
}
,
\begin{whycode}
goal G: forall l1 "induction" l2 l3: list 'a.
l1 ++ (l2 ++ l3) = (l1 ++ l2) ++ l3
\end{whycode}
If such a label is used on several variables, a lexicographic
induction is performed on these variables, from left to right.
\item
Induction on a inductive predicate:
\item
[]
Induction on inductive predicates.
[TO BE COMPLETED]
\end{
itemize
}
\end{
description
}
\subsection
{
Simplification by Computation
}
Th
ose transformations simplifies the goal by applying several kind
of
simplification
s
. The transformations differ only by the kind of rules they
Th
ese transformations simplify the goal by applying several kinds
of
simplification. The transformations differ only by the kind of rules they
apply:
\verb

compute_in_goal

aggressively apply all known
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