The port had flattened Agda's instance arguments ({{flA}}, {{evaluator}},
{{latticeInterpretation}}, {{validEvaluator}}) into explicitly threaded
values (fhL, E, I, hE). Restore them as typeclasses:
- Spa.FiniteHeightLattice: now actually used — Fixedpoint takes the
instance instead of a FixedHeight value; FiniteMap gets the missing
instance (height = ks.length * height B), so varsFixedHeight /
statesFixedHeight / signFixedHeight / constFixedHeight plumbing
disappears (instance bottoms are defeq to the old ones)
- Spa.Analysis.Forward.Evaluation: StmtEvaluator/ExprEvaluator become
classes; the Valid* Props become Prop-classes, as in Agda
- Spa.Analysis.Forward.Adapters: the expr→stmt adapter and its validity
are instances (Agda: the ExprToStmtAdapter instances)
- LatticeInterpretation is a class; sign/const interpretations,
evaluators and validity proofs are instances; use sites read like the
Agda module applications: result SignLattice prog
Proof simplifications (same theorems, proofs factored):
- Spa.Lattice.AboveBelow.monotone₂_of_strict: any ⊥-strict/⊤-dominated
operation on a flat lattice is monotone — replaces the four near-
identical case bashes per analysis (postulates in Agda)
- Spa.Lattice.AboveBelow.interp_sup_of/interp_inf_of: the shared flat-
lattice interpretation case analysis, making interpSign_sup/inf and
interpConst_sup/inf one-liners
lake build green with zero warnings; lake exe spa output verified
byte-identical (diff) to the previous, Agda-verified output.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
- Spa.Showable: port of Showable.agda (quoted strings, map format) for
output parity
- Spa.Analysis.Utils: eval_combine₂
- Spa.Lattice.AboveBelow.le_cases: order of the flat lattice by cases
- Spa.Analysis.Sign / Spa.Analysis.Constant: the four monotonicity
POSTULATES from the Agda files are now proved theorems (via le_cases);
interpretations, evaluator validity, analyze_correct per analysis
- Main + lake exe spa: runs both analyses on the Agda test program;
constant analysis folds unknown=0, sign analysis gives unknown=⊤
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
- 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>
- 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>
- 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>
