diff --git a/polly/lib/Analysis/DependenceInfo.cpp b/polly/lib/Analysis/DependenceInfo.cpp
--- a/polly/lib/Analysis/DependenceInfo.cpp
+++ b/polly/lib/Analysis/DependenceInfo.cpp
@@ -642,8 +642,7 @@
     return true;
 
   isl::union_map Dependences = getDependences(TYPE_RAW | TYPE_WAW | TYPE_WAR);
-  isl::space Space = S.getParamSpace();
-  isl::union_map Schedule = isl::union_map::empty(Space);
+  isl::union_map Schedule = isl::union_map::empty(S.getIslCtx());
 
   isl::space ScheduleSpace;
 
@@ -778,7 +777,7 @@
 isl::union_map Dependences::getDependences(int Kinds) const {
   assert(hasValidDependences() && "No valid dependences available");
   isl::space Space = isl::manage_copy(RAW).get_space();
-  isl::union_map Deps = Deps.empty(Space);
+  isl::union_map Deps = Deps.empty(Space.ctx());
 
   if (Kinds & TYPE_RAW)
     Deps = Deps.unite(isl::manage_copy(RAW));
diff --git a/polly/lib/Analysis/ScopBuilder.cpp b/polly/lib/Analysis/ScopBuilder.cpp
--- a/polly/lib/Analysis/ScopBuilder.cpp
+++ b/polly/lib/Analysis/ScopBuilder.cpp
@@ -3366,7 +3366,7 @@
   MinMaxAccesses.reserve(AliasGroup.size());
 
   isl::union_set Domains = scop->getDomains();
-  isl::union_map Accesses = isl::union_map::empty(scop->getParamSpace());
+  isl::union_map Accesses = isl::union_map::empty(scop->getIslCtx());
 
   for (MemoryAccess *MA : AliasGroup)
     Accesses = Accesses.add_map(MA->getAccessRelation());
diff --git a/polly/lib/Analysis/ScopInfo.cpp b/polly/lib/Analysis/ScopInfo.cpp
--- a/polly/lib/Analysis/ScopInfo.cpp
+++ b/polly/lib/Analysis/ScopInfo.cpp
@@ -2314,7 +2314,7 @@
 
 isl::union_map
 Scop::getAccessesOfType(std::function<bool(MemoryAccess &)> Predicate) {
-  isl::union_map Accesses = isl::union_map::empty(getParamSpace());
+  isl::union_map Accesses = isl::union_map::empty(getIslCtx());
 
   for (ScopStmt &Stmt : *this) {
     for (MemoryAccess *MA : Stmt) {
diff --git a/polly/lib/CodeGen/PPCGCodeGeneration.cpp b/polly/lib/CodeGen/PPCGCodeGeneration.cpp
--- a/polly/lib/CodeGen/PPCGCodeGeneration.cpp
+++ b/polly/lib/CodeGen/PPCGCodeGeneration.cpp
@@ -219,8 +219,8 @@
       KillMemIds.push_back(isl::manage(SAI->getBasePtrId().release()));
   }
 
-  Info.TaggedMustKills = isl::union_map::empty(ParamSpace);
-  Info.MustKills = isl::union_map::empty(ParamSpace);
+  Info.TaggedMustKills = isl::union_map::empty(ParamSpace.ctx());
+  Info.MustKills = isl::union_map::empty(ParamSpace.ctx());
 
   // Initialising KillsSchedule to `isl_set_empty` creates an empty node in the
   // schedule:
diff --git a/polly/lib/Exchange/JSONExporter.cpp b/polly/lib/Exchange/JSONExporter.cpp
--- a/polly/lib/Exchange/JSONExporter.cpp
+++ b/polly/lib/Exchange/JSONExporter.cpp
@@ -321,7 +321,7 @@
     return false;
   }
 
-  auto ScheduleMap = isl::union_map::empty(S.getParamSpace());
+  auto ScheduleMap = isl::union_map::empty(S.getIslCtx());
   for (ScopStmt &Stmt : S) {
     if (NewSchedule.find(&Stmt) != NewSchedule.end())
       ScheduleMap = ScheduleMap.add_map(NewSchedule[&Stmt]);
diff --git a/polly/lib/External/isl/include/isl/isl-noexceptions.h b/polly/lib/External/isl/include/isl/isl-noexceptions.h
--- a/polly/lib/External/isl/include/isl/isl-noexceptions.h
+++ b/polly/lib/External/isl/include/isl/isl-noexceptions.h
@@ -5,6 +5,8 @@
 /// polyhedral compilation, ranging from dependence analysis over scheduling
 /// to AST generation.
 
+// clang-format off
+
 #ifndef ISL_CPP_CHECKED
 #define ISL_CPP_CHECKED
 
@@ -3228,9 +3230,7 @@
   inline isl::union_map domain_map() const;
   inline isl::union_pw_multi_aff domain_map_union_pw_multi_aff() const;
   inline isl::union_map domain_product(isl::union_map umap2) const;
-  static inline isl::union_map empty(isl::space space);
   static inline isl::union_map empty(isl::ctx ctx);
-  static inline isl::union_map empty_space(isl::space space);
   inline isl::union_map eq_at(isl::multi_union_pw_aff mupa) const;
   inline isl::map extract_map(isl::space space) const;
   inline isl::union_map factor_domain() const;
@@ -3708,9 +3708,7 @@
   inline boolean contains(const isl::space &space) const;
   inline isl::union_set detect_equalities() const;
   inline isl_size dim(isl::dim type) const;
-  static inline isl::union_set empty(isl::space space);
   static inline isl::union_set empty(isl::ctx ctx);
-  static inline isl::union_set empty_space(isl::space space);
   inline isl::set extract_set(isl::space space) const;
   inline stat foreach_point(const std::function<stat(point)> &fn) const;
   inline stat foreach_set(const std::function<stat(set)> &fn) const;
@@ -17579,24 +17577,12 @@
   return manage(res);
 }
 
-isl::union_map union_map::empty(isl::space space)
-{
-  auto res = isl_union_map_empty(space.release());
-  return manage(res);
-}
-
 isl::union_map union_map::empty(isl::ctx ctx)
 {
   auto res = isl_union_map_empty_ctx(ctx.release());
   return manage(res);
 }
 
-isl::union_map union_map::empty_space(isl::space space)
-{
-  auto res = isl_union_map_empty_space(space.release());
-  return manage(res);
-}
-
 isl::union_map union_map::eq_at(isl::multi_union_pw_aff mupa) const
 {
   auto res = isl_union_map_eq_at_multi_union_pw_aff(copy(), mupa.release());
@@ -19793,24 +19779,12 @@
   return res;
 }
 
-isl::union_set union_set::empty(isl::space space)
-{
-  auto res = isl_union_set_empty(space.release());
-  return manage(res);
-}
-
 isl::union_set union_set::empty(isl::ctx ctx)
 {
   auto res = isl_union_set_empty_ctx(ctx.release());
   return manage(res);
 }
 
-isl::union_set union_set::empty_space(isl::space space)
-{
-  auto res = isl_union_set_empty_space(space.release());
-  return manage(res);
-}
-
 isl::set union_set::extract_set(isl::space space) const
 {
   auto res = isl_union_set_extract_set(get(), space.release());
diff --git a/polly/lib/Support/ISLTools.cpp b/polly/lib/Support/ISLTools.cpp
--- a/polly/lib/Support/ISLTools.cpp
+++ b/polly/lib/Support/ISLTools.cpp
@@ -90,7 +90,7 @@
 }
 
 isl::union_map polly::beforeScatter(isl::union_map UMap, bool Strict) {
-  isl::union_map Result = isl::union_map::empty(UMap.get_space());
+  isl::union_map Result = isl::union_map::empty(UMap.ctx());
 
   for (isl::map Map : UMap.get_map_list()) {
     isl::map After = beforeScatter(Map, Strict);
@@ -108,7 +108,7 @@
 }
 
 isl::union_map polly::afterScatter(const isl::union_map &UMap, bool Strict) {
-  isl::union_map Result = isl::union_map::empty(UMap.get_space());
+  isl::union_map Result = isl::union_map::empty(UMap.ctx());
   for (isl::map Map : UMap.get_map_list()) {
     isl::map After = afterScatter(Map, Strict);
     Result = Result.add_map(After);
@@ -188,7 +188,7 @@
 
 isl::union_map polly::makeIdentityMap(const isl::union_set &USet,
                                       bool RestrictDomain) {
-  isl::union_map Result = isl::union_map::empty(USet.get_space());
+  isl::union_map Result = isl::union_map::empty(USet.ctx());
   for (isl::set Set : USet.get_set_list()) {
     isl::map IdentityMap = makeIdentityMap(Set, RestrictDomain);
     Result = Result.add_map(IdentityMap);
@@ -205,7 +205,7 @@
 }
 
 isl::union_map polly::reverseDomain(const isl::union_map &UMap) {
-  isl::union_map Result = isl::union_map::empty(UMap.get_space());
+  isl::union_map Result = isl::union_map::empty(UMap.ctx());
   for (isl::map Map : UMap.get_map_list()) {
     auto Reversed = reverseDomain(std::move(Map));
     Result = Result.add_map(Reversed);
@@ -226,7 +226,7 @@
 }
 
 isl::union_set polly::shiftDim(isl::union_set USet, int Pos, int Amount) {
-  isl::union_set Result = isl::union_set::empty(USet.get_space());
+  isl::union_set Result = isl::union_set::empty(USet.ctx());
   for (isl::set Set : USet.get_set_list()) {
     isl::set Shifted = shiftDim(Set, Pos, Amount);
     Result = Result.unite(Shifted);
@@ -265,7 +265,7 @@
 
 isl::union_map polly::shiftDim(isl::union_map UMap, isl::dim Dim, int Pos,
                                int Amount) {
-  isl::union_map Result = isl::union_map::empty(UMap.get_space());
+  isl::union_map Result = isl::union_map::empty(UMap.ctx());
 
   for (isl::map Map : UMap.get_map_list()) {
     isl::map Shifted = shiftDim(Map, Dim, Pos, Amount);
@@ -486,7 +486,7 @@
 }
 
 isl::union_map polly::distributeDomain(isl::union_map UMap) {
-  isl::union_map Result = isl::union_map::empty(UMap.get_space());
+  isl::union_map Result = isl::union_map::empty(UMap.ctx());
   for (isl::map Map : UMap.get_map_list()) {
     auto Distributed = distributeDomain(Map);
     Result = Result.add_map(Distributed);
@@ -824,7 +824,7 @@
 ///
 /// @see expand(const isl::set)
 static isl::union_set expand(const isl::union_set &USet) {
-  isl::union_set Expanded = isl::union_set::empty(USet.get_space());
+  isl::union_set Expanded = isl::union_set::empty(USet.ctx());
   for (isl::set Set : USet.get_set_list()) {
     isl::set SetExpanded = expand(Set);
     Expanded = Expanded.unite(SetExpanded);
diff --git a/polly/lib/Transform/DeLICM.cpp b/polly/lib/Transform/DeLICM.cpp
--- a/polly/lib/Transform/DeLICM.cpp
+++ b/polly/lib/Transform/DeLICM.cpp
@@ -882,7 +882,7 @@
     simplify(WritesTarget);
 
     // { DomainWrite[] }
-    auto UniverseWritesDom = isl::union_set::empty(ParamSpace);
+    auto UniverseWritesDom = isl::union_set::empty(ParamSpace.ctx());
 
     for (auto *MA : S->getPHIIncomings(SAI))
       UniverseWritesDom = UniverseWritesDom.unite(getDomainFor(MA));
diff --git a/polly/lib/Transform/FlattenAlgo.cpp b/polly/lib/Transform/FlattenAlgo.cpp
--- a/polly/lib/Transform/FlattenAlgo.cpp
+++ b/polly/lib/Transform/FlattenAlgo.cpp
@@ -116,7 +116,7 @@
     return UMap; /* isl_map_project_out would also reset the tuple, which should
                     have no effect on schedule ranges */
 
-  auto Result = isl::union_map::empty(UMap.get_space());
+  auto Result = isl::union_map::empty(UMap.ctx());
   for (isl::map Map : UMap.get_map_list()) {
     auto Outprojected = Map.project_out(isl::dim::out, first, n);
     Result = Result.add_map(Outprojected);
@@ -142,7 +142,7 @@
 
 /// Return the @p pos' range dimension, converted to an isl_union_pw_aff.
 isl::union_pw_aff scheduleExtractDimAff(isl::union_map UMap, unsigned pos) {
-  auto SingleUMap = isl::union_map::empty(UMap.get_space());
+  auto SingleUMap = isl::union_map::empty(UMap.ctx());
   for (isl::map Map : UMap.get_map_list()) {
     unsigned MapDims = Map.range_tuple_dim();
     isl::map SingleMap = Map.project_out(isl::dim::out, 0, pos);
@@ -191,7 +191,7 @@
   auto AllDomains = Schedule.domain();
   auto AllDomainsToNull = isl::union_pw_multi_aff(AllDomains);
 
-  auto NewSchedule = isl::union_map::empty(ParamSpace);
+  auto NewSchedule = isl::union_map::empty(ParamSpace.ctx());
   auto Counter = isl::pw_aff(isl::local_space(ParamSpace.set_from_params()));
 
   while (!ScatterSet.is_empty()) {
diff --git a/polly/lib/Transform/MaximalStaticExpansion.cpp b/polly/lib/Transform/MaximalStaticExpansion.cpp
--- a/polly/lib/Transform/MaximalStaticExpansion.cpp
+++ b/polly/lib/Transform/MaximalStaticExpansion.cpp
@@ -136,7 +136,7 @@
   auto AccessDomainSet = MA->getAccessRelation().domain();
   auto AccessDomainId = AccessDomainSet.get_tuple_id();
 
-  isl::union_map MapDependences = isl::union_map::empty(S.getParamSpace());
+  isl::union_map MapDependences = isl::union_map::empty(S.getIslCtx());
 
   for (isl::map Map : Dependences.get_map_list()) {
     // Filter out Statement to Statement dependences.
@@ -184,7 +184,7 @@
     auto Writes = S.getPHIIncomings(SAI);
 
     // Get the domain where all the writes are writing to.
-    auto WriteDomain = isl::union_set::empty(S.getParamSpace());
+    auto WriteDomain = isl::union_set::empty(S.getIslCtx());
 
     for (auto Write : Writes) {
       auto MapDeps = filterDependences(S, Dependences, Write);
@@ -209,8 +209,8 @@
 
   int NumberWrites = 0;
   for (ScopStmt &Stmt : S) {
-    auto StmtReads = isl::union_map::empty(S.getParamSpace());
-    auto StmtWrites = isl::union_map::empty(S.getParamSpace());
+    auto StmtReads = isl::union_map::empty(S.getIslCtx());
+    auto StmtWrites = isl::union_map::empty(S.getIslCtx());
 
     for (MemoryAccess *MA : Stmt) {
       // Check if the current MemoryAccess involved the current SAI.
diff --git a/polly/lib/Transform/ScheduleTreeTransform.cpp b/polly/lib/Transform/ScheduleTreeTransform.cpp
--- a/polly/lib/Transform/ScheduleTreeTransform.cpp
+++ b/polly/lib/Transform/ScheduleTreeTransform.cpp
@@ -217,8 +217,7 @@
   isl::schedule visitLeaf(const isl::schedule_node &Leaf,
                           const isl::union_set &Domain,
                           isl::union_map &Extensions) {
-    isl::ctx Ctx = Leaf.ctx();
-    Extensions = isl::union_map::empty(isl::space::params_alloc(Ctx, 0));
+    Extensions = isl::union_map::empty(Leaf.ctx());
     return isl::schedule::from_domain(Domain);
   }
 
@@ -233,7 +232,7 @@
     isl::schedule NewChild = visit(OldChild, Domain, NewChildExtensions);
 
     // Add the extensions to the partial schedule.
-    OuterExtensions = isl::union_map::empty(NewChildExtensions.get_space());
+    OuterExtensions = isl::union_map::empty(NewChildExtensions.ctx());
     isl::union_map NewPartialSchedMap = isl::union_map::from(PartialSched);
     unsigned BandDims = isl_schedule_node_band_n_member(OldNode.get());
     for (isl::map Ext : NewChildExtensions.get_map_list()) {
diff --git a/polly/lib/Transform/Simplify.cpp b/polly/lib/Transform/Simplify.cpp
--- a/polly/lib/Transform/Simplify.cpp
+++ b/polly/lib/Transform/Simplify.cpp
@@ -248,8 +248,7 @@
 void SimplifyImpl::removeOverwrites() {
   for (auto &Stmt : *S) {
     isl::set Domain = Stmt.getDomain();
-    isl::union_map WillBeOverwritten =
-        isl::union_map::empty(S->getParamSpace());
+    isl::union_map WillBeOverwritten = isl::union_map::empty(S->getIslCtx());
 
     SmallVector<MemoryAccess *, 32> Accesses(getAccessesInOrder(Stmt));
 
@@ -330,7 +329,7 @@
 
     // List of all eligible (for coalescing) writes of the future.
     // { [Domain[] -> Element[]] -> [Value[] -> MemoryAccess[]] }
-    isl::union_map FutureWrites = isl::union_map::empty(S->getParamSpace());
+    isl::union_map FutureWrites = isl::union_map::empty(S->getIslCtx());
 
     // Iterate over accesses from the last to the first.
     SmallVector<MemoryAccess *, 32> Accesses(getAccessesInOrder(Stmt));
@@ -444,7 +443,7 @@
         TouchedAccesses.insert(MA);
       }
       isl::union_map NewFutureWrites =
-          isl::union_map::empty(FutureWrites.get_space());
+          isl::union_map::empty(FutureWrites.ctx());
       for (isl::map FutureWrite : FutureWrites.get_map_list()) {
         MemoryAccess *MA = (MemoryAccess *)FutureWrite.get_space()
                                .range()
@@ -499,7 +498,7 @@
     // List of element reads that still have the same value while iterating
     // through the MemoryAccesses.
     // { [Domain[] -> Element[]] -> Val[] }
-    isl::union_map Known = isl::union_map::empty(S->getParamSpace());
+    isl::union_map Known = isl::union_map::empty(S->getIslCtx());
 
     SmallVector<MemoryAccess *, 32> Accesses(getAccessesInOrder(Stmt));
     for (MemoryAccess *MA : Accesses) {
diff --git a/polly/lib/Transform/ZoneAlgo.cpp b/polly/lib/Transform/ZoneAlgo.cpp
--- a/polly/lib/Transform/ZoneAlgo.cpp
+++ b/polly/lib/Transform/ZoneAlgo.cpp
@@ -250,7 +250,7 @@
 }
 
 isl::union_map polly::filterKnownValInst(const isl::union_map &UMap) {
-  isl::union_map Result = isl::union_map::empty(UMap.get_space());
+  isl::union_map Result = isl::union_map::empty(UMap.ctx());
   for (isl::map Map : UMap.get_map_list()) {
     if (!isMapToUnknown(Map))
       Result = Result.add_map(Map);
@@ -587,11 +587,11 @@
 }
 
 isl::union_set ZoneAlgorithm::makeEmptyUnionSet() const {
-  return isl::union_set::empty(ParamSpace);
+  return isl::union_set::empty(ParamSpace.ctx());
 }
 
 isl::union_map ZoneAlgorithm::makeEmptyUnionMap() const {
-  return isl::union_map::empty(ParamSpace);
+  return isl::union_map::empty(ParamSpace.ctx());
 }
 
 void ZoneAlgorithm::collectCompatibleElts() {
@@ -845,7 +845,7 @@
 static isl::union_map normalizeValInst(isl::union_map Input,
                                        const DenseSet<PHINode *> &ComputedPHIs,
                                        isl::union_map NormalizeMap) {
-  isl::union_map Result = isl::union_map::empty(Input.get_space());
+  isl::union_map Result = isl::union_map::empty(Input.ctx());
   for (isl::map Map : Input.get_map_list()) {
     isl::space Space = Map.get_space();
     isl::space RangeSpace = Space.range();
diff --git a/polly/unittests/DeLICM/DeLICMTest.cpp b/polly/unittests/DeLICM/DeLICMTest.cpp
--- a/polly/unittests/DeLICM/DeLICMTest.cpp
+++ b/polly/unittests/DeLICM/DeLICMTest.cpp
@@ -23,7 +23,7 @@
 
 /// Get the universes of all spaces in @p USet.
 isl::union_set unionSpace(const isl::union_set &USet) {
-  auto Result = isl::union_set::empty(USet.get_space());
+  auto Result = isl::union_set::empty(USet.ctx());
   for (isl::set Set : USet.get_set_list()) {
     isl::space Space = Set.get_space();
     isl::set Universe = isl::set::universe(Space);
@@ -45,7 +45,7 @@
   if (!OccupiedAndKnown.is_null()) {
     assert(Known.is_null());
 
-    Known = isl::union_map::empty(ParamSpace);
+    Known = isl::union_map::empty(ParamSpace.ctx());
 
     if (Occupied.is_null())
       Occupied = OccupiedAndKnown.domain();
@@ -63,7 +63,7 @@
   }
 
   if (Known.is_null()) { // By default, nothing is known.
-    Known = isl::union_map::empty(ParamSpace);
+    Known = isl::union_map::empty(ParamSpace.ctx());
   }
 
   // Conditions that must hold when returning.
@@ -96,7 +96,7 @@
     isl::union_map ProposedOccupiedAndKnown, isl::union_set ProposedUnused,
     isl::union_map ProposedWritten) {
   // Determine universe (set of all possible domains).
-  auto Universe = isl::union_set::empty(isl::space::params_alloc(Ctx, 0));
+  auto Universe = isl::union_set::empty(Ctx);
   if (!ExistingOccupiedAndKnown.is_null())
     Universe = Universe.unite(ExistingOccupiedAndKnown.domain());
   if (!ExistingUnused.is_null())