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veriT
Alethe
Commits
77b4700a
Commit
77b4700a
authored
3 years ago
by
Haniel Barbosa
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[Calculus] Clarify lack of confluence for ITE_simp
parent
0c249e12
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#4478
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3 years ago
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spec/rule_list.tex
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spec/rule_list.tex
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77b4700a
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@@ -1136,8 +1136,14 @@ The possible transformations are:
\label
{
sec:ite-simp-rules
}
\begin{proof-rule}
{
ite
_
simplify
}{
veriT
}
This rule simplifies an if-then-else term by applying equivalent
transformations as long as possible. Depending on the sort of the
This rule simplifies an if-then-else term by applying equivalent
transformations until fix point
\footnote
{
Note however that the order of the
application is important, since the set of rules is not confluent. For
example, the term
$
(
\operatorname
{
ite
}
\top
\;
t
_
1
\;
t
_
2
\leftrightarrow
t
_
1
)
$
can be simplified into both
$
p
$
and
$
(
not
(
not p
))
$
depending on the
order of applications.
}
%
Depending on the sort of the
$
\operatorname
{
ite
}$
-term the rule can have one of two forms. If the sort
is
$
\mathbf
{
Bool
}$
it has the form
\begin{plContainer}
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