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<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">Joachim<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">I was talking to Stepanie about newtype wrappers, and realised that<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">a) there are two very different ways to use type classes to<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> implement the feature, one good and one bad<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">b) the one I thought we were using is the Bad One<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">c) the one on the wiki page is sketched in far too little detail<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> but is the Good One<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">
<a href="http://ghc.haskell.org/trac/ghc/wiki/NewtypeWrappers">http://ghc.haskell.org/trac/ghc/wiki/NewtypeWrappers</a><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">Also, there’s an interaction with “roles” which Richard is on the point of committing.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">Below are some detailed notes.
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">Before too long, could you refresh the wiki page to:<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">* demote rejected ideas<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">* explain the accepted plan in more detail<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">* discuss implementation aspects<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">Thanks<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">Simon<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">Bad version<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">~~~~~~~~~~~<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> class NT a b
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> rep :: NT a b => a -> b<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> wrap :: NT a b => b -> a<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">Then for each newtype<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> newtype Age = Int<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">we generate<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> axiom axAge :: Age ~ Int<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> instance NT Age Int
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">and for data types<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> data (a,b) = (a,b)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">we generate<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> instance (NT a a', NT b b') => NT (a,b) (a',b')<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">Internally (NT a b) is implemented as a simple boxing of a
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">representational equality:<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> data NT a b = MkNT (a ~#R b)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">There are many problems here<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> - It's tiresome for the programmer to remember whether<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> to use rep or wrap<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> - Many levels of newtype would require repeated application<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> of rep (or wrap). But if I say (rep (rep x)) I immediately<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> get ambiguity, unless I also supply a type sig for each
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> intermediate level.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">Good version (this may be what you are doing already)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">~~~~~~~~~~~~<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> class NT a b
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> ntCast :: NT a b => a -> b<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">Notice only one ntCast, which will work both ways.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">Then for each newtype<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> newtype Age = Int<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">we generate<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> axiom axAge :: Age ~ Int<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> instance NT Int b => NT Age b<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> instance NT a Int => NT b Age<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">Notice *two* instances<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">For data types, same as before<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> data (a,b) = (a,b)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">we generate<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> instance (NT a a', NT b b') => NT (a,b) (a',b')<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">And we have instance NT a a.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">Now try this<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> f :: (Age, Bool, Int) -> (Int, Bool, Age)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> f x = ntCast x<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">From the ntCast we get the wanted constraint<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> NT (Age,Bool,Int) (Int,Bool,Age)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">Then we simplify as follows<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> NT (Age,Bool,Int) (Int,Bool,Age)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">---> by instance decl for (,,)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> NT Age Int, NT Bool Bool, NT Int Age<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">---> by instance NT a a, solves NT Bool Bool<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> NT Age Int, NT Int Age<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">---> by instance NT Int a => NT Age a<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> NT Int Int, NT Int Age<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">---> by instance NT a a, solves NT Int Int<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> NT Int Age<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">...and so on...<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">In effect, we normalise both arguments of the NT independently<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">until they match (are equal, or have an outermost list). This<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">will even do a good job of<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> newtype Moo = MkMoo Age<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> f :: Moo -> Age<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> f x = ntCast x<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">Try it.. it'll normalise the (NT Moo Age) to (NT Int Int), so the<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">coercion we ultimately build wil take x down to Int, then back up<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">to Age. But that's fine... the coercion optimiser will remove the<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">intermediate steps.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">This has lots of advantages:<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> - No need to remember directions; ntCast does the job in either<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> direction or both<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> - No need for multiple levels of unwrapping... and hence no<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> ambiguity for the intermediate steps.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">A note about roles<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">~~~~~~~~~~~~~~~~~~<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">We are very keen that if we declare<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> data Map key val = [(key,val)]<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">where the keys are kept ordered, then we do NOT want to allow<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">a cast from (Map Int val) to (Map Age val)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">We were thinking about exercising this control by saying, in<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">a standalone deriving clause<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> deriving NT v1 v2 => NT (Map k v1) (Map k v2)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">But another, and more robust, way to express the fact that we<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">should not allow you to cast (Map Int val) to (Map Age val) is<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">to give Map the rules<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">p Map key@Nominal val@Representational<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">in Richard's new system (about to be committed). This gives<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">Map's first argument a more restrictive role than role inference
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">would give it.
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">And for good reason! If we had<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> class C k where<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> foo :: Map k Int -> Bool<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">then we would NOT want to allow<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> newtype Age = MkAge Int deriving( C )<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">And the thing that now prevents us doing that 'deriving( C )' is
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">precisely the more restrictive role on Map.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">So, our proposal is: for every
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> data T a = ... deriving( NT )
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">we get the lifting instance<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> instance NT a b => NT (T a) (T b)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">whose shape is controlled by T's argument roles.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">We probably want to be able to say -XAutoDeriveNT, like -XAutoDeriveTypeable.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""><o:p> </o:p></span></p>
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