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Find solution to Einstein's riddle with Apalache #113

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Jan 29, 2024
Merged

Find solution to Einstein's riddle with Apalache #113

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00b4d5e
Make Einstein work with Apalache
nano-o Jan 21, 2024
575c1a0
Avoid _OF_TYPE postfixes by using type Str
nano-o Jan 22, 2024
2f14b4d
improve comments
nano-o Jan 27, 2024
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24 changes: 20 additions & 4 deletions specifications/EinsteinRiddle/Einstein.tla
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Original file line number Diff line number Diff line change
Expand Up @@ -35,12 +35,14 @@

EXTENDS Naturals, FiniteSets

House == 1..5

\* Note that TLC!Permutations has a Java module override and, thus,
\* would be evaluated faster. However, TLC!Permutations equals a
\* set of records whereas Permutation below equals a set of tuples/
\* sequences. Also, Permutation expects Cardinality(S) = 5.
Permutation(S) ==
{ p \in [ 1..5 -> S ] :
Permutation(S) ==
{ p \in [ House -> S ] :
/\ p[2] \in S \ {p[1]}
/\ p[3] \in S \ {p[1], p[2]}
/\ p[4] \in S \ {p[1], p[2], p[3]}
Expand All @@ -58,10 +60,15 @@ PETS == Permutation({ "bird", "cat", "dog", "fish", "horse" })
CIGARS == Permutation({ "blend", "bm", "dh", "pm", "prince" })

VARIABLES
\* @type: Int -> Str;
nationality, \* tuple of nationalities
\* @type: Int -> Str;
colors, \* tuple of house colors
\* @type: Int -> Str;
pets, \* tuple of pets
\* @type: Int -> Str;
cigars, \* tuple of cigars
\* @type: Int -> Str;
drinks \* tuple of drinks

------------------------------------------------------------
Expand Down Expand Up @@ -122,10 +129,15 @@ Init ==
/\ pets \in PETS
/\ cigars \in CIGARS

\* Apalache cannot infer the type of `vars' because it could be a sequence or a tuple.
\* So we explicitely tell Apalache that it is a sequence by adding the following annotation:
\* @type: Seq(Int -> Str);
vars == <<nationality, colors, cigars, pets, drinks>>

Next ==
UNCHANGED <<nationality, colors, cigars, pets, drinks>>
UNCHANGED vars

Spec == Init /\ [][Next]_<<nationality, colors, cigars, pets, drinks>>
Spec == Init /\ [][Next]_vars

Solution ==
/\ BritLivesInTheRedHouse
Expand All @@ -146,4 +158,8 @@ Solution ==

FindSolution == ~Solution

\* To find the solution with the `^Apalache^' model-checker, run:
\* `^apalache-mc check --init=Init --inv=FindSolution --length=0 --run-dir=./outout Einstein.tla^'
\* You will then find the solution in `^./output/violation.tla^'.

============================================================