diff --git a/loopy/check.py b/loopy/check.py
index 6c26e15109d6250211fdec96ebbe07d7ddf25689..e200dab85ddc4d637c795cbcf6e7983b3a6d6b9a 100644
--- a/loopy/check.py
+++ b/loopy/check.py
@@ -1,5 +1,6 @@
 from __future__ import division
 from islpy import dim_type
+import islpy as isl
 
 
 
@@ -219,15 +220,18 @@ def check_implemented_domains(kernel, implemented_domains):
         insn_impl_domain = idomains[0]
         for idomain in idomains[1:]:
             insn_impl_domain = insn_impl_domain | idomain
-        assumptions = align_spaces(kernel.assumptions, insn_impl_domain,
-                obj_bigger_ok=True)
+        assumption_non_param = isl.BasicSet.from_params(kernel.assumptions)
+        assumptions = align_spaces(
+                assumption_non_param,
+                insn_impl_domain, obj_bigger_ok=True)
         insn_impl_domain = (
                 (insn_impl_domain & assumptions)
                 .project_out_except(kernel.insn_inames(insn), [dim_type.set]))
 
         insn_inames = kernel.insn_inames(insn)
         insn_domain = kernel.get_inames_domain(insn_inames)
-        assumptions = align_spaces(kernel.assumptions, insn_domain,
+        assumptions = align_spaces(
+                assumption_non_param, insn_domain,
                 obj_bigger_ok=True)
         desired_domain = ((insn_domain & assumptions)
             .project_out_except(kernel.insn_inames(insn), [dim_type.set]))
diff --git a/loopy/codegen/__init__.py b/loopy/codegen/__init__.py
index e25f0af365f62137e35657617a8e7fcfe55ff7b2..69739ed69e3b97dcefd368cb99fb34e562cb0444 100644
--- a/loopy/codegen/__init__.py
+++ b/loopy/codegen/__init__.py
@@ -292,7 +292,7 @@ def generate_code(kernel, with_annotation=False,
 
     # }}}
 
-    initial_implemented_domain = kernel.assumptions
+    initial_implemented_domain = isl.BasicSet.from_params(kernel.assumptions)
     codegen_state = CodeGenerationState(initial_implemented_domain, c_code_mapper=ccm)
 
     from loopy.codegen.loop import set_up_hw_parallel_loops
diff --git a/loopy/kernel.py b/loopy/kernel.py
index 2f1d1516d7fbf31ea33b414d983549c349a6fb58..6fd09982ae6d0a38b6c68259ad5b2f2054e18774 100644
--- a/loopy/kernel.py
+++ b/loopy/kernel.py
@@ -915,7 +915,7 @@ class LoopKernel(Record):
             for i in xrange(dom0_space.dim(dim_type.param)):
                 assumptions_space = assumptions_space.set_dim_name(
                         dim_type.param, i, dom0_space.get_dim_name(dim_type.param, i))
-            assumptions = isl.Set.universe(assumptions_space)
+            assumptions = isl.BasicSet.universe(assumptions_space)
 
         elif isinstance(assumptions, str):
             all_inames = set()
@@ -1144,8 +1144,8 @@ class LoopKernel(Record):
         assert isinstance(domains, tuple) # for caching
 
         if not domains:
-            return isl.BasicSet.universe(isl.Space.alloc(
-                self.isl_context, 0, 0, 0))
+            return isl.BasicSet.universe(isl.Space.set_alloc(
+                self.isl_context, 0, 0))
 
         result = None
         for dom_index in domains: