diff --git a/pymbolic/mapper/__init__.py b/pymbolic/mapper/__init__.py
index 678b3c6bfb2f210190328fd365c18d24b7393895..686e682b4816c805f44f5391b7d055a43753d730 100644
--- a/pymbolic/mapper/__init__.py
+++ b/pymbolic/mapper/__init__.py
@@ -63,6 +63,8 @@ class Mapper(object):
             return self.map_constant(expr, *args)
         elif isinstance(expr, list):
             return self.map_list(expr, *args)
+        elif isinstance(expr, tuple):
+            return self.map_tuple(expr, *args)
         elif is_numpy_array(expr):
             return self.map_numpy_array(expr, *args)
         else:
@@ -138,8 +140,10 @@ class CombineMapper(RecursiveMapper):
                     self.rec(coeff, *args) for exp, coeff in expr.data)
                 )
 
-    map_list = map_sum
-    map_vector = map_sum
+    def map_list(self, expr, *args):
+        return self.combine(self.rec(child, *args) for child in expr)
+
+    map_tuple = map_list
 
     def map_numpy_array(self, expr, *args):
         return self.combine(self.rec(el) for el in expr.flat)
@@ -153,11 +157,6 @@ class CombineMapper(RecursiveMapper):
             self.rec(expr.then),
             self.rec(expr.else_)])
 
-    def map_foreign(self, expr, *args):
-        if isinstance(expr, tuple):
-            return self.combine([self.rec(child) for child in expr])
-        else:
-            return RecursiveMapper.map_foreign(self, expr, *args)
 
 
 
@@ -215,8 +214,11 @@ class IdentityMapperBase(object):
                               ((exp, self.rec(coeff, *args))
                                   for exp, coeff in expr.data))
 
-    map_list = map_sum
-    map_vector = map_sum
+    def map_list(self, expr, *args):
+        return [self.rec(child, *args) for child in expr]
+
+    def map_tuple(self, expr, *args):
+        return tuple(self.rec(child, *args) for child in expr)
 
     def map_numpy_array(self, expr):
         import numpy