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739fbb503cf169c2fb8405156f46d328f0a80fa6
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Author SHA1 Message Date
Danila Fedorin
739fbb503c Lean migration: Phase 6 (forward analysis framework) 
- Spa.Analysis.Forward.Lattices: VariableValues/StateVariables (FiniteMap
  instantiations), fixed heights, variablesAt, joinForKey/joinAll, interpV
  and its sup/foldr lemmas
- Spa.Analysis.Forward.Evaluation: StmtEvaluator/ExprEvaluator + validity
  (the Agda Valid* instance records become plain Props)
- Spa.Analysis.Forward.Adapters: expr-to-stmt evaluator adapter + validity
- Spa.Analysis.Forward: updateAll, analyze, result (least fixpoint via the
  gas-based Fixedpoint), walkTrace, analyze_correct — the framework's main
  soundness theorem

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
 2026-06-09 20:14:53 -07:00
Danila Fedorin
2cfd0a2fb7 Lean migration: Phase 5 (language, CFGs, traces, Program) 
- 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>
 2026-06-09 19:30:42 -07:00
Danila Fedorin
781d7947e0 Lean migration: Phase 4 (IterProd + FiniteMap lattices) 
- Spa.Lattice.IterProd: k-fold product, recursive Lattice instance,
  fixed height k*hA + hB, bot = build of bottoms
- Spa.Lattice.FiniteMap: spine-pinned assoc lists ({l // l.map fst = ks});
  with = the 1100-line Map.agda collapses into positional 'combine'.
  Same lemma inventory (membership, locate, updating, GeneralizedUpdate,
  valuesAt, Provenance-union, le_of_mem_mem) — Nodup is now an explicit
  hypothesis where the Agda Map carried it intrinsically. Fixed height
  |ks|*hB still via transport along the IterProd isomorphism, which no
  longer needs Unique ks (representation is canonical).

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
 2026-06-09 19:12:39 -07:00
Danila Fedorin
4c337afa9c Lean migration: Phase 3 (Unit, Prod, AboveBelow lattices) 
- Spa.Lattice.Unit: PUnit fixed height 0 (lattice lifted from mathlib)
- Spa.Lattice.Prod: chain unzip + FixedHeight (h1+h2) on products
  (componentwise lattice lifted from mathlib's Prod.instLattice)
- Spa.Lattice.AboveBelow: flat lattice via Lattice.mk' (mirrors the Agda
  semilattices+absorption construction), boundedness via rank into Nat,
  Plain x ↦ plainFixedHeight x, height 2

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
 2026-06-09 18:48:02 -07:00
Danila Fedorin
ae030386b4 Lean migration: Phases 0-2 (core lattice/chain, fixpoint, transport) 
- lean/ lake project pinned to Lean v4.17.0 + mathlib v4.17.0
- Spa.Lattice: fold monotonicity, FixedHeight/BoundedChains (LTSeries-based),
  FiniteHeightLattice, chain-bottom-is-least; the rest of Lattice.agda,
  Chain.agda and Equivalence.agda lift into mathlib (see LEAN_MIGRATION.md)
- Spa.Fixedpoint: gas-based least-fixpoint computation (doStep/fix/aFix)
- Spa.Isomorphism: FixedHeight transport along monotone inverse pairs

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
 2026-06-09 18:36:43 -07:00