Danila Fedorin 94278a6389 Add computational reaching-definitions analysis ...

Introduce a finite-height lattice instance for Bool, then build the
reaching-definitions analysis on top of the forward framework:

* Spa/Lattice/Bool.lean: FiniteHeightLattice Bool (the two-element
  lattice false ≤ true), making FiniteMap A Bool ks a finite-height
  "power set" lattice for free.
* Spa/Analysis/Reaching.lean: DefSet prog = FiniteMap prog.State Bool
  prog.states as the per-variable lattice of definition sites, with a
  StmtEvaluator whose transfer function performs a strong update
  (assignment to k at node s sets k's def-set to {s}).

The analysis computes a least fixed point and produces correct
reaching-definitions sets. Soundness (relating def-sets to actual
execution provenance) is deferred; not yet exposed in Spa.lean.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

2026-06-25 09:12:11 -05:00

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