Find solution to Einstein's riddle with Apalache (tlaplus#113)

Make Einstein work with Apalache

Signed-off-by: Giuliano Losa <giuliano@losa.fr>

specifications/EinsteinRiddle/Einstein.tla

@@ -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]}
@@ -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
 
 ------------------------------------------------------------
@@ -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
@@ -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^'.
+
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