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proof(SafePassword): DISCHARGE withMinLengthCorrect via nested constructor case-split #143

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Merged
hyperpolymath merged 1 commit into from
May 31, 2026
Merged

proof(SafePassword): DISCHARGE withMinLengthCorrect via nested constructor case-split #143

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23 changes: 12 additions & 11 deletions src/Proven/SafePassword/Proofs.idr
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Original file line number Diff line number Diff line change
Expand Up @@ -402,18 +402,19 @@ public export
public export
0 builderProducesPolicy : build Policy.policyBuilder = Policy.defaultPolicy

||| OWED: `withMinLength n` followed by `build` yields a policy whose
||| `minLength` field equals `n`. The implementation is
||| `withMinLength n (MkPolicyBuilder p) = MkPolicyBuilder ({minLength
||| := n} p)`, so the equation is true by record-update normalisation
||| — but Idris2 0.8.0 does not reduce the record-update through the
||| `MkPolicyBuilder` wrapper for an abstract starting builder
||| `b : PolicyBuilder`. Discharge by case-splitting on
||| `b = MkPolicyBuilder _` plus `Refl`, or by marking `build` and
||| `withMinLength` `%inline`.
||| DISCHARGED: `withMinLength n` followed by `build` yields a policy
||| whose `minLength` field equals `n`. The OWED comment suggested the
||| pattern: case-split on `b = MkPolicyBuilder _` to expose the
||| constructor. Verified empirically that a DOUBLE case-split
||| (`MkPolicyBuilder (MkPolicy _ _ _ _ _ _ _ _ _ _)`) is needed —
||| the inner `PasswordPolicy` constructor also has to be exposed for
||| the record-update projection `({ minLength := n } p).minLength`
||| to reduce. Once both are exposed, the chain collapses to `Refl`.
||| Test at `/tmp/charrefl/src/TestPolicyBuilder.idr`.
public export
0 withMinLengthCorrect : (n : Nat) -> (b : PolicyBuilder) ->
minLength (build (withMinLength n b)) = n
withMinLengthCorrect : (n : Nat) -> (b : PolicyBuilder) ->
minLength (build (withMinLength n b)) = n
withMinLengthCorrect n (MkPolicyBuilder (MkPolicy _ _ _ _ _ _ _ _ _ _)) = Refl

||| OWED: chained builder calls compose correctly — `withMinLength n
||| (withUppercase policyBuilder)` then `build`'s `minLength` is `n`.
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