Remove the register writes no path reads

[hhugo]

A backward liveness pass over the DFA that removes the register writes no path reads, run at the end of compile_ir.

The pass

remove_dead ~roots takes as roots the cells the bindings read. A register is live on entering a state if some path from it reads it before writing it: as the source of a transition Copy whose destination is live, or as the source of a final operation writing a root. Liveness is a fixpoint over that equation; then

1. transition writes to dead registers are dropped,
2. final operations writing a cell no binding names are dropped,
3. the cells left are renumbered densely and the bindings remapped.

About a hundred self-contained lines. The liveness it computes is the input #210 needs, so that draft can adopt it when it is rebased.

Where dead writes come from

Rules that a higher-priority rule beats on some or all of their matches: the tag was written on a transition shared with the winning rule's path, and is never read there. Anything that later prunes the automaton also produces them: shortest match (#180), or unused boundary tags if the rest of #193 is revisited.

Verified effect

Each test pattern was generated with and without the pass before being pinned.

• Partially shadowed capture: Plus 'a', Plus 'b' beats (Plus 'a' as x), (Plus 'b' | Plus 'c') on every 'b' tail. The write of x's end on the 'b' transition goes, the one on 'c' stays, and cells drop from 3 to 2. A runtime test checks x on both tails and the cell count.
• Fully shadowed rule: no write survives. Its canonical cell stays, since the unreachable action still names it (init_mem 1). Dropping it too would need the PPX to skip the bindings of rules that never accept; left as is for now.

No pre-existing expect block changes: master's automata have no dead writes outside these shapes.

🤖 Generated with Claude Code