+Note [Case of cast]
+~~~~~~~~~~~~~~~~~~~
+Consider case (v `cast` co) of x { I# ->
+ ... (case (v `cast` co) of {...}) ...
+We'd like to eliminate the inner case. We can get this neatly by
+arranging that inside the outer case we add the unfolding
+ v |-> x `cast` (sym co)
+to v. Then we should inline v at the inner case, cancel the casts, and away we go
+
+Note [Improving seq]
+~~~~~~~~~~~~~~~~~~~
+Consider
+ type family F :: * -> *
+ type instance F Int = Int
+
+ ... case e of x { DEFAULT -> rhs } ...
+
+where x::F Int. Then we'd like to rewrite (F Int) to Int, getting
+
+ case e `cast` co of x'::Int
+ I# x# -> let x = x' `cast` sym co
+ in rhs
+
+so that 'rhs' can take advantage of the form of x'. Notice that Note
+[Case of cast] may then apply to the result.
+
+This showed up in Roman's experiments. Example:
+ foo :: F Int -> Int -> Int
+ foo t n = t `seq` bar n
+ where
+ bar 0 = 0
+ bar n = bar (n - case t of TI i -> i)
+Here we'd like to avoid repeated evaluating t inside the loop, by
+taking advantage of the `seq`.
+
+At one point I did transformation in LiberateCase, but it's more robust here.
+(Otherwise, there's a danger that we'll simply drop the 'seq' altogether, before
+LiberateCase gets to see it.)
+
+Note [Case elimination]
+~~~~~~~~~~~~~~~~~~~~~~~
+The case-elimination transformation discards redundant case expressions.
+Start with a simple situation:
+
+ case x# of ===> e[x#/y#]
+ y# -> e
+
+(when x#, y# are of primitive type, of course). We can't (in general)
+do this for algebraic cases, because we might turn bottom into
+non-bottom!
+
+The code in SimplUtils.prepareAlts has the effect of generalise this
+idea to look for a case where we're scrutinising a variable, and we
+know that only the default case can match. For example:
+
+ case x of
+ 0# -> ...
+ DEFAULT -> ...(case x of
+ 0# -> ...
+ DEFAULT -> ...) ...
+
+Here the inner case is first trimmed to have only one alternative, the
+DEFAULT, after which it's an instance of the previous case. This
+really only shows up in eliminating error-checking code.
+
+We also make sure that we deal with this very common case:
+
+ case e of
+ x -> ...x...
+
+Here we are using the case as a strict let; if x is used only once
+then we want to inline it. We have to be careful that this doesn't
+make the program terminate when it would have diverged before, so we
+check that
+ - e is already evaluated (it may so if e is a variable)
+ - x is used strictly, or
+
+Lastly, the code in SimplUtils.mkCase combines identical RHSs. So
+
+ case e of ===> case e of DEFAULT -> r
+ True -> r
+ False -> r
+
+Now again the case may be elminated by the CaseElim transformation.
+
+
+Further notes about case elimination
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+Consider: test :: Integer -> IO ()
+ test = print
+
+Turns out that this compiles to:
+ Print.test
+ = \ eta :: Integer
+ eta1 :: State# RealWorld ->
+ case PrelNum.< eta PrelNum.zeroInteger of wild { __DEFAULT ->
+ case hPutStr stdout
+ (PrelNum.jtos eta ($w[] @ Char))
+ eta1
+ of wild1 { (# new_s, a4 #) -> PrelIO.lvl23 new_s }}
+
+Notice the strange '<' which has no effect at all. This is a funny one.
+It started like this:
+
+f x y = if x < 0 then jtos x
+ else if y==0 then "" else jtos x
+
+At a particular call site we have (f v 1). So we inline to get
+
+ if v < 0 then jtos x
+ else if 1==0 then "" else jtos x
+
+Now simplify the 1==0 conditional:
+
+ if v<0 then jtos v else jtos v
+
+Now common-up the two branches of the case:
+
+ case (v<0) of DEFAULT -> jtos v
+
+Why don't we drop the case? Because it's strict in v. It's technically
+wrong to drop even unnecessary evaluations, and in practice they
+may be a result of 'seq' so we *definitely* don't want to drop those.
+I don't really know how to improve this situation.
+
+
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