Remove subtyping for sets theory (#5179)

This PR removes subtyping for sets theory due to issues like #4502, #4507 and #4631.
Changes:

Add SingletonOp for singletons to specify the type of the single element in the set.
Add mkSingleton to the solver to enable the user to pass the sort of the single element.
Update smt and cvc parsers to use mkSingleton when the kind is SINGLETON

2 files changed, 8 insertions, 2 deletions

diff --git a/src/theory/quantifiers/fmf/bounded_integers.cpp b/src/theory/quantifiers/fmf/bounded_integers.cpp
index 28731b371..2d6af9a63 100644
--- a/src/theory/quantifiers/fmf/bounded_integers.cpp
+++ b/src/theory/quantifiers/fmf/bounded_integers.cpp
@@ -676,7 +676,7 @@ Node BoundedIntegers::getSetRangeValue( Node q, Node v, RepSetIterator * rsi ) {
     Assert(i < d_setm_choice[sro].size());
     choice_i = d_setm_choice[sro][i];
     choices.push_back(choice_i);
-    Node sChoiceI = nm->mkNode(SINGLETON, choice_i);
+    Node sChoiceI = nm->mkSingleton(choice_i.getType(), choice_i);
     if (nsr.isNull())
     {
       nsr = sChoiceI;
diff --git a/src/theory/quantifiers/sygus/sygus_grammar_cons.cpp b/src/theory/quantifiers/sygus/sygus_grammar_cons.cpp
index 1b86afb85..ba9962bd9 100644
--- a/src/theory/quantifiers/sygus/sygus_grammar_cons.cpp
+++ b/src/theory/quantifiers/sygus/sygus_grammar_cons.cpp
@@ -965,7 +965,13 @@ void CegGrammarConstructor::mkSygusDefaultGrammar(
       Trace("sygus-grammar-def") << "...add for singleton" << std::endl;
       std::vector<TypeNode> cargsSingleton;
       cargsSingleton.push_back(unresElemType);
-      sdts[i].addConstructor(SINGLETON, cargsSingleton);
+
+      // lambda x . (singleton (singleton_op T) x) where T = x.getType()
+      Node x = nm->mkBoundVar(etype);
+      Node vars = nm->mkNode(BOUND_VAR_LIST, x);
+      Node singleton = nm->mkSingleton(etype, x);
+      Node lambda = nm->mkNode(LAMBDA,vars, singleton);
+      sdts[i].addConstructor(lambda, "singleton", cargsSingleton);
 
       // add for union, difference, intersection
       std::vector<Kind> bin_kinds = {UNION, INTERSECTION, SETMINUS};