Decompiler, Expression Propagation, Intermediate Representation problems

Hi guys,


          I'm an confused newbie to compilers and have to find some
answers:


(1) Expression Propagation Problem


I'm implementing a decompiler with some data-flow optimizations
therefore I build complex expression from simple assignments e.g.


c = a + b
e = c + d


they will be the following after expression propagation


c = a + b
e = a + b + d


in a situation it's not safe:


c = a + b
e = c + d
a = 1
some_use(e) ; we must forbid the propagation of e = c+d since a = 1
kills c = a + b so does e = c + d


Now is the question: How to efficently/correctly implement this
propagation? What's the analysis' name in theory?


(2) Intermediate Representation


      SSA form seems awesome but in reversing engineering, memory, stack,
register alias everywhere. as far as I know, SSA represention for
memory/array is not good because of the complexity of point alias or
deep down halting problem


      How to representation of the following memory derference code in
SSA form?


      [sp] = a
      [sp] = b


      or


      eax = 123
      bx = ax


      Also, PUSH/POP is hard to analyze too. e.g.


      push 1
      b = [sp]
      pop a


Discussion: What a good IR for decompilation should be?


(3) Lattice Theory


What the hell it is? Many lecture mentions the lattice. I'm completely
baffled by the mathamatics symbols.


Regards,

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