diff --git a/mlir/include/mlir/Analysis/Presburger/IntegerRelation.h b/mlir/include/mlir/Analysis/Presburger/IntegerRelation.h
--- a/mlir/include/mlir/Analysis/Presburger/IntegerRelation.h
+++ b/mlir/include/mlir/Analysis/Presburger/IntegerRelation.h
@@ -386,9 +386,13 @@
   /// O(VC) time.
   void removeRedundantConstraints();
 
-  /// Converts identifiers in the column range [idStart, idLimit) to local
-  /// variables.
-  void convertDimToLocal(unsigned dimStart, unsigned dimLimit);
+  /// Converts identifiers of kind srcKind in the range [idStart, idLimit) to variables
+  /// of kind dstKind and placed after all the other variables of kind dstKind. The
+  /// internal ordering among the moved variables is preserved.
+  void convertIdKind(IdKind srcKind, unsigned idStart, unsigned idLimit, IdKind dstKind);
+  void convertToLocal(IdKind kind, unsigned idStart, unsigned idLimit) {
+    convertIdKind(kind, idStart, idLimit, IdKind::Local);
+  }
 
   /// Adds additional local ids to the sets such that they both have the union
   /// of the local ids in each set, without changing the set of points that
diff --git a/mlir/lib/Analysis/Presburger/IntegerRelation.cpp b/mlir/lib/Analysis/Presburger/IntegerRelation.cpp
--- a/mlir/lib/Analysis/Presburger/IntegerRelation.cpp
+++ b/mlir/lib/Analysis/Presburger/IntegerRelation.cpp
@@ -1119,23 +1119,25 @@
   }
 }
 
-void IntegerRelation::convertDimToLocal(unsigned dimStart, unsigned dimLimit) {
-  assert(dimLimit <= getNumDimIds() && "Invalid dim pos range");
+void IntegerRelation::convertIdKind(IdKind srcKind, unsigned idStart,
+                                          unsigned idLimit, IdKind dstKind) {
+  assert(idLimit <= getNumIdKind(srcKind) && "Invalid id range");
 
-  if (dimStart >= dimLimit)
+  if (idStart >= idLimit)
     return;
 
   // Append new local variables corresponding to the dimensions to be converted.
-  unsigned convertCount = dimLimit - dimStart;
-  unsigned newLocalIdStart = getNumIds();
-  appendId(IdKind::Local, convertCount);
+  unsigned newIdsBegin = getIdKindEnd(dstKind);
+  unsigned convertCount = idLimit - idStart;
+  appendId(dstKind, convertCount);
 
   // Swap the new local variables with dimensions.
+  unsigned offset = getIdKindOffset(srcKind);
   for (unsigned i = 0; i < convertCount; ++i)
-    swapId(i + dimStart, i + newLocalIdStart);
+    swapId(offset + idStart + i, newIdsBegin + i);
 
   // Remove dimensions converted to local variables.
-  removeIdRange(IdKind::SetDim, dimStart, dimLimit);
+  removeIdRange(srcKind, idStart, idLimit);
 }
 
 void IntegerRelation::addBound(BoundType type, unsigned pos, int64_t value) {
diff --git a/mlir/lib/Dialect/Affine/Analysis/AffineStructures.cpp b/mlir/lib/Dialect/Affine/Analysis/AffineStructures.cpp
--- a/mlir/lib/Dialect/Affine/Analysis/AffineStructures.cpp
+++ b/mlir/lib/Dialect/Affine/Analysis/AffineStructures.cpp
@@ -1618,7 +1618,7 @@
 FlatAffineValueConstraints FlatAffineRelation::getDomainSet() const {
   FlatAffineValueConstraints domain = *this;
   // Convert all range variables to local variables.
-  domain.convertDimToLocal(getNumDomainDims(),
+  domain.convertToLocal(IdKind::SetDim, getNumDomainDims(),
                            getNumDomainDims() + getNumRangeDims());
   return domain;
 }
@@ -1626,7 +1626,7 @@
 FlatAffineValueConstraints FlatAffineRelation::getRangeSet() const {
   FlatAffineValueConstraints range = *this;
   // Convert all domain variables to local variables.
-  range.convertDimToLocal(0, getNumDomainDims());
+  range.convertToLocal(IdKind::SetDim, 0, getNumDomainDims());
   return range;
 }
 
@@ -1658,12 +1658,12 @@
   // Convert `rel` from [otherDomain] -> [otherRange thisRange] to
   // [otherDomain] -> [thisRange] by converting first otherRange range ids
   // to local ids.
-  rel.convertDimToLocal(rel.getNumDomainDims(),
+  rel.convertToLocal(IdKind::SetDim, rel.getNumDomainDims(),
                         rel.getNumDomainDims() + removeDims);
   // Convert `this` from [otherDomain thisDomain] -> [thisRange] to
   // [otherDomain] -> [thisRange] by converting last thisDomain domain ids
   // to local ids.
-  convertDimToLocal(getNumDomainDims() - removeDims, getNumDomainDims());
+  convertToLocal(IdKind::SetDim, getNumDomainDims() - removeDims, getNumDomainDims());
 
   auto thisMaybeValues = getMaybeDimValues();
   auto relMaybeValues = rel.getMaybeDimValues();
diff --git a/mlir/unittests/Analysis/Presburger/IntegerPolyhedronTest.cpp b/mlir/unittests/Analysis/Presburger/IntegerPolyhedronTest.cpp
--- a/mlir/unittests/Analysis/Presburger/IntegerPolyhedronTest.cpp
+++ b/mlir/unittests/Analysis/Presburger/IntegerPolyhedronTest.cpp
@@ -707,7 +707,7 @@
     IntegerPolyhedron poly =
         parsePoly("(i, j, q) : (4*q - i - j + 2 >= 0, -4*q + i + j >= 0)");
     // Convert `q` to a local variable.
-    poly.convertDimToLocal(2, 3);
+    poly.convertToLocal(IdKind::SetDim, 2, 3);
 
     std::vector<SmallVector<int64_t, 8>> divisions = {{1, 1, 0, 1}};
     SmallVector<unsigned, 8> denoms = {4};
@@ -721,7 +721,7 @@
   {
     IntegerPolyhedron poly = parsePoly("(i, j, q) : (-4*q + i + j == 0)");
     // Convert `q` to a local variable.
-    poly.convertDimToLocal(2, 3);
+    poly.convertToLocal(IdKind::SetDim, 2, 3);
 
     std::vector<SmallVector<int64_t, 8>> divisions = {{-1, -1, 0, 0}};
     SmallVector<unsigned, 8> denoms = {4};
@@ -731,7 +731,7 @@
   {
     IntegerPolyhedron poly = parsePoly("(i, j, q) : (4*q - i - j == 0)");
     // Convert `q` to a local variable.
-    poly.convertDimToLocal(2, 3);
+    poly.convertToLocal(IdKind::SetDim, 2, 3);
 
     std::vector<SmallVector<int64_t, 8>> divisions = {{-1, -1, 0, 0}};
     SmallVector<unsigned, 8> denoms = {4};
@@ -741,7 +741,7 @@
   {
     IntegerPolyhedron poly = parsePoly("(i, j, q) : (3*q + i + j - 2 == 0)");
     // Convert `q` to a local variable.
-    poly.convertDimToLocal(2, 3);
+    poly.convertToLocal(IdKind::SetDim, 2, 3);
 
     std::vector<SmallVector<int64_t, 8>> divisions = {{1, 1, 0, -2}};
     SmallVector<unsigned, 8> denoms = {3};
@@ -756,7 +756,7 @@
         parsePoly("(i, j, q, k) : (-3*k + i + j == 0, 4*q - "
                   "i - j + 2 >= 0, -4*q + i + j >= 0)");
     // Convert `q` and `k` to local variables.
-    poly.convertDimToLocal(2, 4);
+    poly.convertToLocal(IdKind::SetDim, 2, 4);
 
     std::vector<SmallVector<int64_t, 8>> divisions = {{1, 1, 0, 0, 1},
                                                       {-1, -1, 0, 0, 0}};
@@ -770,7 +770,7 @@
   IntegerPolyhedron poly =
       parsePoly("(x, q) : (x - 3 * q >= 0, -x + 3 * q + 3 >= 0)");
   // Convert q to a local variable.
-  poly.convertDimToLocal(1, 2);
+  poly.convertToLocal(IdKind::SetDim, 1, 2);
 
   std::vector<SmallVector<int64_t, 8>> divisions = {{0, 0, 0}};
   SmallVector<unsigned, 8> denoms = {0};
@@ -783,7 +783,7 @@
   IntegerPolyhedron poly =
       parsePoly("(x, q) : (-1 - 3*x - 6 * q >= 0, 6 + 3*x + 6*q >= 0)");
   // Convert q to a local variable.
-  poly.convertDimToLocal(1, 2);
+  poly.convertToLocal(IdKind::SetDim, 1, 2);
 
   // q = floor((-1/3 - x)/2)
   //   = floor((1/3) + (-1 - x)/2)