simplify mkSkolem naming system: don't use $$

Short summary: By default NODEID is appeneded, just continue doing what you
were, just don't add the _$$ at the end.

Long summary:

Before this commit there were four (yes!) ways to specify the names for new
skolems, which result in names as given below

1) mkSkolem("name", ..., SKOLEM_FLAG_DEFAULT)  -> "name_NODEID"
2) mkSkolem("name", ..., SKOLEM_EXACT_NAME)  -> "name"
3) mkSkolem("name_$$", ..., SKOLEM_FLAG_DEFAULT) -> "name_NODEID"
4) mkSkolem("na_$$_me", ..., SKOLEM_FLAG_DEFAULT) -> "na_NODEID_me"

After this commit, only 1) and 2) stay.

90% usage is of 1) or 3), which results in exact same behavior (and
looking at the source code it doesn't look like everyone realized that
the _$$ is just redundant).

Almost no one used 4), which is the only reason to even have $$. Post this
commit if you really want a number in the middle, manually construct the
name and use the SKOLEM_EXACT_NAME flag.

2 files changed, 5 insertions, 5 deletions

diff --git a/src/theory/arith/arith_ite_utils.cpp b/src/theory/arith/arith_ite_utils.cpp
index 4f182fb69..d5dcae726 100644
--- a/src/theory/arith/arith_ite_utils.cpp
+++ b/src/theory/arith/arith_ite_utils.cpp
@@ -418,7 +418,7 @@ bool ArithIteUtils::solveBinOr(TNode binor){
 
         Node cnd = findIteCnd(binor[0], binor[1]);
 
-        Node sk = nm->mkSkolem("deor$$", nm->booleanType());
+        Node sk = nm->mkSkolem("deor", nm->booleanType());
         Node ite = sk.iteNode(otherL, otherR);
         d_skolems.insert(sk, cnd);
         d_skolemsAdded.push_back(sk);
diff --git a/src/theory/arith/theory_arith_private.cpp b/src/theory/arith/theory_arith_private.cpp
index a63de446c..0c8ca7507 100644
--- a/src/theory/arith/theory_arith_private.cpp
+++ b/src/theory/arith/theory_arith_private.cpp
@@ -226,7 +226,7 @@ Node TheoryArithPrivate::getRealDivideBy0Func(){
 
   if(d_realDivideBy0Func.isNull()){
     TypeNode realType = NodeManager::currentNM()->realType();
-    d_realDivideBy0Func = skolemFunction("/by0_$$", realType, realType);
+    d_realDivideBy0Func = skolemFunction("/by0", realType, realType);
   }
   return d_realDivideBy0Func;
 }
@@ -237,7 +237,7 @@ Node TheoryArithPrivate::getIntDivideBy0Func(){
 
   if(d_intDivideBy0Func.isNull()){
     TypeNode intType = NodeManager::currentNM()->integerType();
-    d_intDivideBy0Func = skolemFunction("divby0_$$", intType, intType);
+    d_intDivideBy0Func = skolemFunction("divby0", intType, intType);
   }
   return d_intDivideBy0Func;
 }
@@ -248,7 +248,7 @@ Node TheoryArithPrivate::getIntModulusBy0Func(){
 
   if(d_intModulusBy0Func.isNull()){
     TypeNode intType = NodeManager::currentNM()->integerType();
-    d_intModulusBy0Func = skolemFunction("modby0_$$", intType, intType);
+    d_intModulusBy0Func = skolemFunction("modby0", intType, intType);
   }
   return d_intModulusBy0Func;
 }
@@ -1498,7 +1498,7 @@ Node TheoryArithPrivate::axiomIteForTotalIntDivision(Node int_div_like){
   Polynomial qp = Polynomial::parsePolynomial(q);
 
   Node abs_d = (n.isConstant()) ?
-    d.getHead().getConstant().abs().getNode() : mkIntSkolem("abs_$$");
+    d.getHead().getConstant().abs().getNode() : mkIntSkolem("abs");
 
   Node eq = Comparison::mkComparison(EQUAL, n, d * qp + rp).getNode();
   Node leq0 = currNM->mkNode(LEQ, zero, r);