feat(ssa refactor): Implement dominator tree (#1278)

* feat(ssa refactor): dominator tree

* reorder functions

* chore(ssa refactor): use true post order

* chore(ssa refactor): externalise PostOrder

* chore(ssa refactor):  use FunctionBuilder in tests

* chore(ssa refactor): add header comments

* chore(ssa refactor): clippy

* chore(ssa refactor): elaborate header comments

* chore(ssa refactor): domtree/post-order cleanup:
- Comment tweaks
- rm unneeded collect iter into vec
- clippy changes
- DominatorTree::with_function helper
- rename DomNode DominatorTreeNode

* chore(ssa refactor): use domtree helper in tests

* fix: update usage of cfg.pred_iter to cfg.predecessors

* chore(saa refactor): tidy up test and naming

crates/noirc_evaluator/src/ssa_refactor/ir.rs

@@ -2,9 +2,11 @@ pub(crate) mod basic_block;
 pub(crate) mod cfg;
 pub(crate) mod constant;
 pub(crate) mod dfg;
+pub(crate) mod dom;
 pub(crate) mod function;
 pub(crate) mod instruction;
 pub(crate) mod map;
+pub(crate) mod post_order;
 pub(crate) mod printer;
 pub(crate) mod types;
 pub(crate) mod value;

crates/noirc_evaluator/src/ssa_refactor/ir/basic_block.rs

@@ -76,7 +76,9 @@ impl BasicBlock {
     /// Iterate over all the successors of the currently block, as determined by
     /// the blocks jumped to in the terminator instruction. If there is no terminator
     /// instruction yet, this will iterate 0 times.
-    pub(crate) fn successors(&self) -> impl ExactSizeIterator<Item = BasicBlockId> {
+    pub(crate) fn successors(
+        &self,
+    ) -> impl ExactSizeIterator<Item = BasicBlockId> + DoubleEndedIterator {
         match &self.terminator {
             Some(TerminatorInstruction::Jmp { destination, .. }) => vec![*destination].into_iter(),
             Some(TerminatorInstruction::JmpIf { then_destination, else_destination, .. }) => {