Maybe https://en.m.wikipedia.org/wiki/Use-define_chain https://en.m.wikipedia.org/wiki/Use-define_chain SSA form might be a clearer expression of this idea, s

Maybe https://en.m.wikipedia.org/wiki/Use-define_chain https://en.m.wikipedia.org/wiki/Use-define_chain SSA form might be a clearer expression of this idea, since there variable assignments more tightly conform to the idea of nodes in a graph, since they are assigned to once, and so produce a clear graph of the whole program If we just looked at registers (rather than SSA variables), then register reuse for different values would be more complex, since then the nodes of the graph would mean different things as the register is reassigned (assuming we were going for that representation) Another way to think about it would be as relations. For instance assembly ops like MULT ADD can be seen as ternary relations, and as you join relations togother into an expression, such as a+b*c, you are forming a graph This graph like correspondence is used to good effect in BDDs and ZDDs, which use that correspondance to compress the representation of expressions Part of the reason behind this is because nodes of a graph are restricted in the same way registers are -- they are only refered to by name, never by an offset. Whereas for stacks, they are refered to by offset, never by name We could remove this separation by naming the top 16 (say) offsets of a stack. Then registers could be referenced by name and by an offset index This would allow lots of fun things. If at the software level, it could mean having normal named variables, aswell as #n offset variables. Which might be a great addressing mode for assembly too. It is done for main memory with Base+Offset addressing, but not for registers The graph equivalent might be Register Direct. Or others, but at this point we're expanding to think beyond registers to memory itself Another path you might like to explore could be the G Machine, or Spineless Tagless G Machine which (along with many other compilers) represents data as a graph, to ultimately convert it into registers