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Lean migration: Phase 5 (language, CFGs, traces, Program)

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- Spa.Language.Base: Expr/BasicStmt/Stmt + HasVar relations; StringSet
  lifts to Finset String
- Spa.Language.Semantics: Value/Env/Env.Mem, big-step relations,
  LatticeInterpretation (respects-≈ field drops out with =)
- Spa.Language.Graphs: Graph with nodes : Fin size → List BasicStmt
  (Vec lookup lemmas lift to Fin.append_left/right), comp/link/loop/
  skipto/singleton/wrap/buildCfg, predecessors via List.finRange
- Spa.Language.Traces: Trace + EndToEndTrace (Prop-valued)
- Spa.Language.Properties: trace embeddings, loop lemmas,
  buildCfg_sufficient; the 80-line Fin-disjointness block reduces to
  castAdd_ne_natAdd + mathlib list lemmas
- Spa.Language: Program (vars via Finset.sort — toList is noncomputable)

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
This commit is contained in:
Danila Fedorin
2026-06-09 19:30:42 -07:00
parent 781d7947e0
commit 2cfd0a2fb7
9 changed files with 763 additions and 1 deletions
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LEAN_MIGRATION.md
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@@ -78,6 +78,6 @@ validate phase by phase.
- [x] Phase 2
- [x] Phase 3
- [x] Phase 4
- [ ] Phase 5
- [x] Phase 5
- [ ] Phase 6
- [ ] Phase 7