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Why3
why3
Commits
c2cc7aee
Commit
c2cc7aee
authored
May 13, 2016
by
MARCHE Claude
Browse files
quick fix of Einstein's problem in doc
parent
bd2e2dd1
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doc/syntax.tex
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c2cc7aee
...
...
@@ 322,6 +322,9 @@ problem''.%
\footnote
{
This
\why
example was contributed by St
\'
ephane Lescuyer.
}
%END LATEX
%HEVEA {} (This \why example was contributed by St\'ephane Lescuyer.)
The code given below is available in the source distribution in
directory
\verb

examples/logic/einstein.why

.
The problem is stated as follows. Five persons, of five
different nationalities, live in five houses in a row, all
painted with different colors.
...
...
@@ 371,10 +374,10 @@ theory Bijection
type u
function of t : u
function to u : t
function to
_
u : t
axiom To
_
of : forall x : t. to (of x) = x
axiom Of
_
to : forall y : u. of (to y) = y
axiom To
_
of : forall x : t. to
_
(of x) = x
axiom Of
_
to : forall y : u. of (to
_
y) = y
end
\end{whycode}
...
...
@@ 399,7 +402,7 @@ by cloning the \texttt{Bijection} theory appropriately.
clone Bijection as Color with type t = house, type u = color
\end{whycode}
It introduces two functions, namely
\texttt
{
Color.of
}
and
\texttt
{
Color.to
}
, from houses to colors and colors to houses,
\texttt
{
Color.to
\_
}
, from houses to colors and colors to houses,
respectively, and the two axioms relating them.
Similarly, we express that each house is associated bijectively to a
person
...
...
@@ 442,11 +445,11 @@ theory \texttt{Einstein}.
theory EinsteinHints "Hints"
use import Einstein
\end{whycode}
Then each hypothesis is stated in terms of
\texttt
{
to
}
and
\texttt
{
of
}
Then each hypothesis is stated in terms of
\texttt
{
to
\_
}
and
\texttt
{
of
}
functions. For instance, the hypothesis ``The Englishman lives in a
red house'' is declared as the following axiom.
\begin{whycode}
axiom Hint1: Color.of (Owner.to Englishman) = Red
axiom Hint1: Color.of (Owner.to
_
Englishman) = Red
\end{whycode}
And so on for all other hypotheses, up to
``The man who smokes Blends has a neighbour who drinks water'', which completes
...
...
@@ 454,7 +457,7 @@ this theory.
\begin{whycode}
...
axiom Hint15:
neighbour (Owner.to (Cigar.to Blend)) (Owner.to (Drink.to Water))
neighbour (Owner.to
_
(Cigar.to
_
Blend)) (Owner.to
_
(Drink.to
_
Water))
end
\end{whycode}
Finally, we declare the goal in the fourth theory:
...
...
@@ 463,7 +466,7 @@ theory Problem "Goal of Einstein's problem"
use import Einstein
use import EinsteinHints
goal G: Pet.to Fish = German
goal G: Pet.to
_
Fish = German
end
\end{whycode}
and we are ready to use
\why
to discharge this goal with any prover
...
...
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