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Add `PFunctor.FreeM.possibleOutputs responses x`, the results `x` can return when each operation answers within `responses op`, as the fold of `x` into `SetM`. Allowing all responses gives a lawful `MonadAttach` instance, and interpreting a program by a handler can only remove possible results. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
With the program first, `x.possibleOutputs responses` fixes the polynomial
before elaborating the response sets, so literals such as `fun _ => {true}`
need no annotation.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
dtumad
requested review from
SamuelSchlesinger,
arademaker,
chenson2018,
crei,
fmontesi and
sorrachai
as code owners
October 5, 2026 23:04
Add `x.attachWith responses interp`, which interprets `x` in an arbitrary monad by a handler whose responses carry membership proofs, and labels the result with a proof that it lies in `x.possibleOutputs responses`. Erasing the proofs recovers `x.liftM` of the underlying handler. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
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Adds
PFunctor.FreeM.possibleOutputs:x.possibleOutputs responsesis the set of resultsxcan return when each operation answers withinresponses op, defined as the fold ofxintoSetM. Allowing every response gives a lawfulMonadAttachinstance whoseattachkeeps every branch of the program, and interpreting a program by a handler can only remove possible results (canReturn_of_liftM).attachWithattaches the same proofs while interpreting into any monad, given a handler whose responses carry membership proofs. Ported from PolyFun.AI agents were used to adapt VCVio definitions/proofs to Cslib definitions and conventions.