diff --git a/loopy/expression.py b/loopy/expression.py
index e3eb65dc5c6e100d427f78dfd7e8da41d21e9b17..64172b88a6cc2dda17b60a6427cfcf9bf430600f 100644
--- a/loopy/expression.py
+++ b/loopy/expression.py
@@ -22,14 +22,22 @@ LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
 THE SOFTWARE.
 """
-
+from typing import TYPE_CHECKING
 
 import numpy as np
 
+import pymbolic.primitives as p
 from pymbolic.mapper import Mapper
 
 from loopy.codegen import UnvectorizableError
 from loopy.diagnostic import LoopyError
+from loopy.symbolic import simplify_using_aff
+
+
+if TYPE_CHECKING:
+    from loopy.kernel import LoopKernel
+    from loopy.kernel.data import Iname
+    from loopy.symbolic import LinearSubscript, Reduction
 
 
 # type_context may be:
@@ -58,7 +66,7 @@ def dtype_to_type_context(target, dtype):
 
 # {{{ vectorizability checker
 
-class VectorizabilityChecker(Mapper):
+class VectorizabilityChecker(Mapper[bool, []]):
     """The return value from this mapper is a :class:`bool` indicating whether
     the result of the expression is vectorized along :attr:`vec_iname`.
     If the expression is not vectorizable, the mapper raises
@@ -67,31 +75,32 @@ class VectorizabilityChecker(Mapper):
     .. attribute:: vec_iname
     """
 
-    def __init__(self, kernel, vec_iname, vec_iname_length):
+    def __init__(self,
+                kernel: LoopKernel,
+                vec_iname: Iname,
+                vec_iname_length: int
+            ) -> None:
         self.kernel = kernel
         self.vec_iname = vec_iname
         self.vec_iname_length = vec_iname_length
 
-    @staticmethod
-    def combine(vectorizabilities):
-        from functools import reduce
-        from operator import and_
-        return reduce(and_, vectorizabilities)
-
-    def map_sum(self, expr):
+    def map_sum(self, expr: p.Sum) -> bool:
         return any(self.rec(child) for child in expr.children)
 
-    map_product = map_sum
+    def map_product(self, expr: p.Product) -> bool:
+        return any(self.rec(child) for child in expr.children)
 
-    def map_quotient(self, expr):
+    def map_quotient(self, expr: p.QuotientBase) -> bool:
         return (self.rec(expr.numerator)
                 or
                 self.rec(expr.denominator))
 
-    def map_linear_subscript(self, expr):
-        return False
+    map_remainder = map_quotient
+
+    def map_linear_subscript(self, expr: LinearSubscript) -> bool:
+        raise UnvectorizableError("linear subscripts cannot be vectorized")
 
-    def map_call(self, expr):
+    def map_call(self, expr: p.Call) -> bool:
         # FIXME: Should implement better vectorization check for function calls
 
         rec_pars = [
@@ -101,16 +110,11 @@ class VectorizabilityChecker(Mapper):
 
         return False
 
-    def map_subscript(self, expr):
+    def map_subscript(self, expr: p.Subscript) -> bool:
+        assert isinstance(expr.aggregate, p.Variable)
         name = expr.aggregate.name
 
-        var = self.kernel.arg_dict.get(name)
-        if var is None:
-            var = self.kernel.temporary_variables.get(name)
-
-        if var is None:
-            raise LoopyError("unknown array variable in subscript: %s"
-                    % name)
+        var = self.kernel.get_var_descriptor(name)
 
         from loopy.kernel.array import ArrayBase
         if not isinstance(var, ArrayBase):
@@ -124,11 +128,16 @@ class VectorizabilityChecker(Mapper):
         from loopy.symbolic import get_dependencies
 
         possible = None
+
+        assert isinstance(var.shape, tuple)
+        assert var.dim_tags is not None
+
         for i in range(len(var.shape)):
+            idx_i = index[i]
             if (
                     isinstance(var.dim_tags[i], VectorArrayDimTag)
-                    and isinstance(index[i], Variable)
-                    and index[i].name == self.vec_iname):
+                    and isinstance(idx_i, Variable)
+                    and idx_i.name == self.vec_iname):
                 if var.shape[i] != self.vec_iname_length:
                     raise UnvectorizableError("vector length was mismatched")
 
@@ -136,7 +145,7 @@ class VectorizabilityChecker(Mapper):
                     possible = True
 
             else:
-                if self.vec_iname in get_dependencies(index[i]):
+                if self.vec_iname in get_dependencies(idx_i):
                     raise UnvectorizableError("vectorizing iname '%s' occurs in "
                             "unvectorized subscript axis %d (1-based) of "
                             "expression '%s'"
@@ -145,10 +154,11 @@ class VectorizabilityChecker(Mapper):
 
         return bool(possible)
 
-    def map_constant(self, expr):
+    def map_constant(self, expr: object) -> bool:
+        # Loopy does not have vector literals.
         return False
 
-    def map_variable(self, expr):
+    def map_variable(self, expr: p.Variable) -> bool:
         if expr.name == self.vec_iname:
             # Technically, this is doable. But we're not going there.
             raise UnvectorizableError()
@@ -158,7 +168,7 @@ class VectorizabilityChecker(Mapper):
 
     map_tagged_variable = map_variable
 
-    def map_lookup(self, expr):
+    def map_lookup(self, expr: p.Lookup) -> bool:
         if self.rec(expr.aggregate):
             raise UnvectorizableError()
 
@@ -170,13 +180,13 @@ class VectorizabilityChecker(Mapper):
 
         raise UnvectorizableError()
 
-    def map_logical_not(self, expr):
+    def map_logical_not(self, expr: object) -> bool:
         raise UnvectorizableError()
 
     map_logical_and = map_logical_not
     map_logical_or = map_logical_not
 
-    def map_reduction(self, expr):
+    def map_reduction(self, expr: Reduction) -> bool:
         # FIXME: Do this more carefully
         raise UnvectorizableError()