LatticeInterpretation now extends Interp L (Value → Prop), so each analysis
defines only its LatticeInterpretation instance and gets the ⟦⟧ notation for
free. Drops the standalone per-analysis Interp instances (signInterp and the
anonymous constInterp). The Interp class is kept for other uses.
The interp*_mk_disjoint bootstrap lemmas now state on the raw interp function
since they feed the instance and run before any Interp instance exists; the
trivial sup/inf wrappers are inlined into the instance.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
These eight one-line projections of plus_mono₂/minus_mono₂ were never
referenced; eval_mono uses the bundled Monotone₂ facts directly.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
Per convention, create a new instance for 'interpretable' thing,
with an fundep'ed semantic domain. I feel at peace with this notation
even though it conflicts with Mathlib's quotients.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
The fable-based migration left a two-layer design (a standalone `FixedHeight α h`
struct, height carried as a type index, plus a `FiniteHeightLattice` wrapper).
This collapses it to the single `FiniteHeightLattice` typeclass (height as a
plain field, `⊥`/`⊤` via `extends Bot`/`Top`), and fixes the fallout so the
whole project builds again (`lake build` green).
- Lattice: repair `FixedHeight.bot_le` (compute the `▸` motive via a forward
`rw`, drop the leftover `fh.length_longestChain`) and the `bot_le` alias.
- Isomorphism: transport rewritten directly onto `FiniteHeightLattice`, taking
the source as an instance argument.
- Lattice/Prod, AboveBelow: `FixedHeight`-producing def + wrapper instance
collapsed into one `FiniteHeightLattice` instance. `head`/`last` proofs use
term-mode `congrArg` to bridge the `Bot`/`Top` defeq through the
under-construction instance projection (where `rw`+`rfl` cannot).
- Lattice/IterProd: `fixedHeight` recursion now yields a `FiniteHeightLattice`
(no height index, so the `.cast (by ring)` reassociations vanish);
`bot_fixedHeight` reprojected onto the def's own `.bot`.
- Lattice/FiniteMap: `fixedHeight`/`bot_contains_bots` go through transport with
the IterProd instance resolved by typeclass search; `punitFixedHeight`
replaced by the `PUnit` instance.
- Analysis/Forward/Lattices: `botV` uses `⊥` instead of the deleted
`FiniteHeightLattice.bot` accessor.
- Analysis/Sign: `num` case used unimported `ring`; the goal is a pure ℕ→ℤ
cast identity, closed with `norm_cast`. Also fixes the missing `show` in
`AboveBelow.monotone₂_of_strict` that left un-beta-reduced redexes.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
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>
