fix(ehoare): reject negative probability bound in byehoare deno - #1095
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The ehoare-deno rule (`t_ehoare_deno_r`) coerces the real bound `bd` into a non-negative extended real via `f_r2xr`, which clamps any `bd < 0` to `0`. The non-negativity side-condition on `bd` was therefore never enforced, so `byehoare` accepted an absurd negative bound and could "prove" `Pr[M.f() @ &m : false] <= -1%r` (hence `false`). Emit the real side-goal `0%r <= bd`. When `bd` is a concrete non-negative literal it is discharged in the rule (`f_real_le_simpl`) so common uses stay effort-free; for a symbolic bound the goal is surfaced (and is unprovable for a genuinely negative bound). `examples/ehoare/adversary.ec` (the only ehoare-deno user) discharges the new goal from `eps_ge0`, `Q_nneg`, `0 < p`. Regression: tests/byehoare-neg-bound.ec (asserts the buggy proof no longer closes, via the `fail` idiom). Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
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Summary
byehoare/ the ehoare-deno path accepts a negative probability bound, which isunsound: it lets one derive
Pr[M.f() @ &m : false] <= -1%r, and hencefalse.Root cause
The real bound supplied to the deno rule is coerced into a non-negative extended real
(
xreal) and negative values are silently clamped to0. The side-condition that thebound is non-negative (
0%r <= bd) is never emitted, so a user-supplied negative literalis accepted as if it were
0.Fix (
src/phl/ecPhlDeno.ml)Emit the real side-goal
0%r <= bdfor concrete/literal bounds instead of relying on theclamping coercion. A genuinely non-negative bound discharges trivially (
f_real_le_simpl);a negative one now produces an open, unprovable obligation.
Test
tests/ko/byehoare-neg-bound.ec(must-fail): the previously-accepted negative-boundjudgment is now rejected.