feat(control): bridge the program-logic kernel to core's lattice-generic WP stack - #187
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feat(control): bridge the program-logic kernel to core's lattice-generic WP stack#187dtumad wants to merge 1 commit into
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…ric WP stack Give every PolyFun judgment a core `Std.Internal.Do.WPMonad` interpretation (the stack that becomes public `Std.WP` in v4.35 and that `vcgen` drives), so that `vcgen` decomposes `do` programs through PolyFun's own semantics and core's `Spec.*` lemmas apply to them without re-proof: - `Control/Monad/Algebra/WP.lean`: `MAlgOrdered.toWP` / `toWPMonad` turn an ordered monad algebra over a Mathlib complete lattice into a `WPMonad m l EPost.Nil` through the `ToCslib.Order.LeanOrder` bridge; `wp` agrees with `MAlgOrdered.wp` by `rfl`, core's `Triple` is PolyFun's (`toWP_triple_iff`), `wpConjunctiveOf` derives conjunctivity from meet preservation, and `top_eq_top` / `meet_eq_inf` / `join_eq_sup` move between core's and Mathlib's lattice operations on a bridged carrier; - `Control/Monad/Support/WP.lean`: `MonadAttach.toWPMonadDemonic` and `toWPMonadAngelic` interpret exact support as `WPMonad m Prop EPost.Nil` (`wp x post = AllOutputs post x`, resp. `SomeOutput`); the angelic reading is expressible here because the laws are inequalities. The demonic reading is conjunctive and sound: `LawfulWPMonadAttach` mirrors, field for field, the soundness class on Lean master, declared in the `Std.Internal.Do` namespace so the v4.35 rename deletes it; `support_subset_of_wp` / `allOutputs_of_wp` turn any sound triple into a support fact; - `Control/Monad/Hom/WP.lean`: `MonadHom.transportWP` / `transportWPMonad` and the unbundled `transportWPMonadOf` pull an interpretation back along a monad morphism. None of these is a global instance; they are installed `local` or `scoped` at the carrier. The legacy `Std.Do` bridge keeps working under the names `MonadHom.transportSPredWP(Monad)` and `MonadAttach.support_subset_of_wpSPred` / `allOutputs_of_wpSPred`, freeing the canonical names. The bridge modules import the `Std.Internal.Do` root: `vcgen` consults the `@[spec]` database, whose `Spec.bind` lives in `Triple.SpecLemmas`, and importing only the `WP` submodules yields `No spec found` on every `do` block. `PolyFunTest/Do/Algebra.lean` and `PolyFunTest/Do/Support.lean` run `vcgen` through a Mathlib-carrier algebra and through the demonic reading of `SetM`, and convert the result back into an "always" judgment. Docs: the program-logic page now describes the lattice-generic stack as canonical, records the three practical rules (root import, binding a non-instance interpretation with `let` before projecting, keeping transfer lemmas out of the `Lean.Order` namespace) and the v4.35 rename table; the landscape memo, repo map, AGENTS.md, and two new gotchas follow. Validated with `./scripts/validate.sh --lint --test --axioms` (zero sorry/axiom taint). Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01Nb4g3Vxgjhnhsca7BzAsFc
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September 3, 2026 18:32
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Summary
Stacked on #185 (and #184, the draft rc2 base). Gives every PolyFun judgment a core
Std.Internal.Do.WPMonadinterpretation — the stack that becomes publicStd.WPin v4.35 and thatvcgendrives — sovcgendecomposesdoprograms through PolyFun's own semantics and core'sSpec.*lemmas apply without re-proof.Control/Monad/Algebra/WP.lean—MAlgOrdered.toWP/toWPMonad: an ordered monad algebra over a Mathlib complete lattice as aWPMonad m l EPost.Nil(via theToCslib.Order.LeanOrderbridge);wpagreement byrfl,toWP_triple_iff,wpConjunctiveOf, and lattice-operation transfer lemmas.Control/Monad/Support/WP.lean—MonadAttach.toWPMonadDemonic/toWPMonadAngelic(wp x post = AllOutputs post x, resp.SomeOutput): the angelic reading is expressible because the laws are inequalities. Demonic conjunctivity; a field-for-field mirror of master'sLawfulWPMonadAttach(in theStd.Internal.Donamespace so the v4.35 rename deletes it);support_subset_of_wp/allOutputs_of_wp.Control/Monad/Hom/WP.lean—MonadHom.transportWP/transportWPMonad/ unbundledtransportWPMonadOf.Nothing here is a global instance. The legacy
Std.Dobridge is kept (renamedtransportSPredWP(Monad),*_of_wpSPred) until the free-monad layer moves over in the next PR.Findings worth knowing
Std.Internal.Doroot:vcgen's@[spec]database (Spec.bind) lives inTriple.SpecLemmas, and importing onlyWP.BasicgivesNo spec found for program …on everydoblock. Recorded as a gotcha.Triple,WPConjunctive,LawfulWPMonadAttachre-synthesize the instance-implicitWP; proofs about non-instance interpretations bind them withlet inst := …first. Recorded as a gotcha.Validation
./scripts/validate.sh --lint --test --axioms— lint passes forPolyFunandToCslib; 10970 declarations, zero sorry/axiom taintPolyFunTest/Do/Algebra.lean:vcgenthroughMAlgOrdered.toWPMonadat carrierℕ∞;PolyFunTest/Do/Support.lean:vcgenthrough the demonic reading ofSetMand conversion back toAllOutputs🤖 Generated with Claude Code
https://claude.ai/code/session_01Nb4g3Vxgjhnhsca7BzAsFc