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> what makes SSA so special for compiler construction

It makes doing immutability and loop invariant reasoning a ton easier, along with constant propagation: https://en.wikipedia.org/wiki/Static_single_assignment_form

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More generally, SSA means implicit use/def information. Use/def information and traversal are critical components of many static analyses and transformations: having the IR in SSA form greatly simplifies reasoning about and implementing these analyses and transformations.

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