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veriT
Alethe
Commits
31d52ce0
Commit
31d52ce0
authored
4 months ago
by
Lachnitt
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Revert "Merge branch 'add/shuffle' into 'master'"
This reverts merge request
!17
parent
c9505bb8
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revert-c9505bb8
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#50387
passed
4 months ago
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spec/changelog.tex
+0
-2
0 additions, 2 deletions
spec/changelog.tex
spec/rule_list.tex
+3
-24
3 additions, 24 deletions
spec/rule_list.tex
with
3 additions
and
26 deletions
spec/changelog.tex
+
0
−
2
View file @
31d52ce0
...
...
@@ -18,8 +18,6 @@ Proof rules:
\item
Addition of the
\proofRule
{
bind
_
let
}
rule. This rule can be used to
preprocess
\inlineAlethe
{
let
}
expressions similar to the
\proofRule
{
bind
}
rule used with ordinary quantifiers.
\item
Additon of the
\proofRule
{
shuffle
}
to permute the arguments of a
commutative operator.
\end{itemize}
\noindent
...
...
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spec/rule_list.tex
+
3
−
24
View file @
31d52ce0
...
...
@@ -256,13 +256,12 @@ simplifications.}
\ruleref
{
la
_
mult
_
neg
}
&
Multiplication with a negative factor.
\\
\ruleref
{
symm
}
&
Symmetry of equality.
\\
\ruleref
{
not
_
symm
}
&
Symmetry of not-equal.
\\
\ruleref
{
reordering
}
&
Permutation of the literals in a clause.
\\
\ruleref
{
shuffle
}
&
Permutation of the arguments of a commutative operator.
\\
\ruleref
{
reordering
}
&
Reording of the literals in a clause.
\\
\end{xltabular}
\begin{xltabular}
{
\linewidth
}{
l X
}
\caption
{
Rules used by the Carcara elaborator.
}
\label
{
rule-tab:c
arcara
}
\\
\label
{
rule-tab:c
vc5
}
\\
Rule
&
Description
\\
\hline
\ruleref
{
weakening
}
&
Weakening of a clause.
\\
...
...
@@ -487,7 +486,7 @@ A simple \proofRule{la_generic} step in the logic \textsf{LRA} might look like t
:rule la
_
generic :args (1.0 -1.0))
\end{AletheVerb}
To verify this we have to check the
u
nsatisfiability of
$
(
f
\,
a
)
>
(
f
\,
b
)
\land
To verify this we have to check the
i
nsatisfiability of
$
(
f
\,
a
)
>
(
f
\,
b
)
\land
(
f
\,
a
)
≈
(
f
\,
b
)
$
(step 2). After step~3 we get
$
(
f
\,
a
)
-
(
f
\,
b
)
>
0
\land
(
f
\,
a
)
-
(
f
\,
b
)
≈
0
$
. Since we don't have an integer sort in this logic step~4 does
not apply. Finally, after step~5 the conjunction is
$
(
f
\,
a
)
-
(
f
\,
b
)
>
0
\land
...
...
@@ -866,26 +865,6 @@ are the same. That is, the conclusion of the rule is a reordering of the
literals in the premise.
\end{RuleDescription}
\begin{RuleDescription}
{
shuffle
}
\begin{AletheXS}
$
i
$
.
&
\ctxsep
&
$
\Gamma
$
&
$
\circ\
t
_
1
\dots
t
_
n ≈
\circ\
u
_
1
\dots
u
_
n
$
&
\currule
\\
\end{AletheXS}
where
$
\circ
$
is a commutative operator, and
the multisets
$
\{
t
_
1
,
\cdots
, t
_
n
\}
$
and
$
\{
u
_
1
,
\cdots
, u
_
n
\}
$
are the same.
In the logics currently supported
by Alethe
$
\circ
\in\{
+
,
*
,
\land
,
\lor\}
$
.
\ruleparagraph
{
Remark.
}
To permute the literals in a clause the
\proofRule
{
reordering
}
rule can be used.
\end{RuleDescription}
\begin{RuleDescription}
{
not
_
and
}
\begin{AletheX}
$
i
$
.
&
\ctxsep
&
$
\neg
(
\varphi
_
1
\land
\dots
\land
\varphi
_
n
)
$
&
(
$
\dots
$
)
\\
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...
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