+ and similar friends.
+
+
+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!
+
+Actually, we 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:
+\begin{verbatim}
+ case x of
+ 0# -> ...
+ other -> ...(case x of
+ 0# -> ...
+ other -> ...) ...
+\end{code}
+Here the inner case can be eliminated. 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
+ - x is used strictly, or
+ - e is already evaluated (it may so if e is a variable)
+
+Lastly, we generalise the transformation to handle this:
+
+ case e of ===> r
+ True -> r
+ False -> r
+
+We only do this for very cheaply compared r's (constructors, literals
+and variables). If pedantic bottoms is on, we only do it when the
+scrutinee is a PrimOp which can't fail.
+
+We do it *here*, looking at un-simplified alternatives, because we
+have to check that r doesn't mention the variables bound by the
+pattern in each alternative, so the binder-info is rather useful.
+
+So the case-elimination algorithm is:
+
+ 1. Eliminate alternatives which can't match
+
+ 2. Check whether all the remaining alternatives
+ (a) do not mention in their rhs any of the variables bound in their pattern
+ and (b) have equal rhss
+
+ 3. Check we can safely ditch the case:
+ * PedanticBottoms is off,
+ or * the scrutinee is an already-evaluated variable
+ or * the scrutinee is a primop which is ok for speculation
+ -- ie we want to preserve divide-by-zero errors, and
+ -- calls to error itself!
+
+ or * [Prim cases] the scrutinee is a primitive variable
+
+ or * [Alg cases] the scrutinee is a variable and
+ either * the rhs is the same variable
+ (eg case x of C a b -> x ===> x)
+ or * there is only one alternative, the default alternative,
+ and the binder is used strictly in its scope.
+ [NB this is helped by the "use default binder where
+ possible" transformation; see below.]
+
+
+If so, then we can replace the case with one of the rhss.
+
+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.
+