Rewrite for set membership of the powerset of a record where the reco…

…rd has infinite co-domains.

Simplified real-world scenario:
```tla
EXTENDS Integers

VARIABLE
  \* @type: Set({ p: (Int) });
  v

TypeOK ==
  v \in SUBSET [ p: Int ]

Init ==
  v = { [p |-> 42] }

Next ==
  UNCHANGED v
```

Apalache Error:
```sh
$ apalache-mc check --inv=TypeOK APARecSub.tla
[...]
Input error (see the manual): Found a set map over an infinite set of CellTFrom(Int). Not supported.
```

Rewrite:
```tla
S \in SUBSET [a : T] ~~> \A r \in S: DOMAIN r = { "a" } /\ r.a \in T
```

Related commits, issues, PRs:
* 625a164
* 785e269

* apalache-mc#723
* apalache-mc#1627
* apalache-mc#2762

* apalache-mc#1453
* apalache-mc#1629

Signed-off-by: Markus Alexander Kuppe <[email protected]>

tla-pp/src/main/scala/at/forsyte/apalache/tla/pp/ExprOptimizer.scala

@@ -97,6 +97,31 @@ class ExprOptimizer(nameGen: UniqueNameGenerator, tracker: TransformationTracker
         }
         apply(tla.and(domEq +: fieldsEq: _*).as(b))
       }
+
+    // S ∈ SUBSET { ["a" ↦ x] : x ∈ T }
+    case memEx @ OperEx(TlaSetOper.in, setRec,
+            OperEx(TlaSetOper.powerset,
+                OperEx(TlaSetOper.map, OperEx(TlaFunOper.rec, fieldsAndValues @ _*), varsAndSets @ _*)))
+        if fieldsAndValues.length == varsAndSets.length =>
+      val (fields, values) = TlaOper.deinterleave(fieldsAndValues)
+      val (vars, sets) = TlaOper.deinterleave(varsAndSets)
+      assert(fields.length == vars.length)
+      if (values.zip(vars).exists(p => p._1 != p._2)) {
+        memEx
+      } else {
+        val strSetT = SetT1(StrT1)
+        val b = BoolT1
+
+        val domType = getElemType(setRec)
+        val r = tla.name(nameGen.newName()).as(domType)
+
+        val domEq = tla.eql(tla.dom(r).as(SetT1(domType)), tla.enumSet(fields: _*).as(strSetT)).as(b)
+
+        val fieldsEq = fields.zip(values.zip(sets)).map { case (key, (value, set)) =>
+          tla.in(tla.appFun(r, key).as(value.typeTag.asTlaType1()), set).as(b)
+        }
+        apply(tla.forall(r, setRec, tla.and(domEq +: fieldsEq: _*).as(b)).as(b))
+      }
   }
 
   /**

tla-pp/src/test/scala/at/forsyte/apalache/tla/pp/TestExprOptimizer.scala

@@ -87,22 +87,76 @@ class TestExprOptimizer extends AnyFunSuite with BeforeAndAfterEach {
 
   // An optimization for set membership over sets of records. Note that this is the standard form produced by Keramelizer.
   test("""r \in { [a |-> x, b |-> y]: x \in S, y \in T } becomes DOMAIN r = { "a", "b" } /\ r.a \in S /\ r.b \in T""") {
+    // ... [a |-> x, b |-> y] ...
     val recT = RecT1("a" -> IntT1, "b" -> IntT1)
-    val recSetT = SetT1(recT)
+    // ... x \in S, y \in T ...
     val record =
       enumFun(str("a"), name("x").as(intT), str("b"), name("y").as(intT)).as(recT)
+    // ... S ...
     val S = name("S").as(intSetT)
+    // ... T ...
     val T = name("T").as(intSetT)
+    // { ... }
+    val recSetT = SetT1(recT)
     val recordSet = map(record, name("x").as(intT), S, name("y").as(intT), T).as(recSetT)
+    // r ...
     val r = name("r").as(recT)
+    // ... \in ...
     val input = in(r, recordSet).as(boolT)
 
+    // ~~>
+
+    // DOMAIN r = { "a", "b" }
     val strSetT = SetT1(StrT1)
     val domEq = eql(dom(r).as(strSetT), enumSet(str("a"), str("b")).as(strSetT)).as(boolT)
+    // r.a \in S
     val memA = in(appFun(r, str("a")).as(intT), S).as(boolT)
+    // r.b \in T
     val memB = in(appFun(r, str("b")).as(intT), T).as(boolT)
+    // ... /\ ... /\ ...
     val expected = and(domEq, memA, memB).as(boolT)
     val output = optimizer.apply(input)
+
+    assert(expected == output)
+  }
+
+  // An optimization for set membership of the powerset of a record where the record has infinite co-domains.
+  test("""S \in SUBSET [a : T] ~~> \A r \in S: DOMAIN r = { "a" } /\ r.a \in T""") {
+
+    // ... { [a |-> x] : x \in T } ...
+    val recT = RecT1("a" -> IntT1)
+    val record =
+      enumFun(str("a"), name("x").as(intT)).as(recT)
+    val T = name("T").as(intSetT)
+    val recSetT = SetT1(recT)
+    val recordSet = map(record, name("x").as(intT), T).as(recSetT)
+
+    // ... SUBSET ...
+    val powSetT = powSet(recordSet).as(recSetT)
+
+    // S ...
+    val s = name("S").as(recSetT)
+
+    // ... \in ...
+    val input = in(s, powSetT).as(boolT)
+    val output = optimizer.apply(input)
+
+    // ~~>
+
+    // DOMAIN r = { "a" }
+    val r = name("t_1").as(recT)
+    val strSetT = SetT1(StrT1)
+    val domEq = eql(dom(r).as(strSetT), enumSet(str("a")).as(strSetT)).as(boolT)
+
+    // r.a \in T
+    val memA = in(appFun(r, str("a")).as(intT), T).as(boolT)
+
+    // ... /\ ...
+    val conjunct = and(domEq, memA).as(boolT)
+
+    // \A ...
+    val expected = forall(r, s, conjunct).as(boolT)
+
     assert(expected == output)
   }