no need for a lambda

lib/arel/algebra/attributes/attribute.rb

@@ -29,6 +29,8 @@ def == other
         @ancestor  == other.ancestor
     end
 
+    alias :eql? :==
+
     def named?(hypothetical_name)
       (@alias || name).to_s == hypothetical_name.to_s
     end
@@ -41,8 +43,6 @@ def eval(row)
       row[self]
     end
 
-    alias :eql? :==
-
     def hash
       @hash ||= name.hash + root.relation.hash
     end

lib/arel/algebra/relations/relation.rb

@@ -187,9 +187,11 @@ def find_attribute_matching_attribute(attribute)
     end
 
     def position_of(attribute)
-      (@position_of ||= Hash.new do |h, attribute|
-        h[attribute] = attributes.index(self[attribute])
-      end)[attribute]
+      @position_of ||= {}
+
+      return @position_of[attribute] if @position_of.key? attribute
+
+      @position_of[attribute] = attributes.index(attributes[attribute])
     end
 
     private