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proof(SafeYAML): DISCHARGE isScalarCorrect via 9-arm case-split (proven#90, #107) #112

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Merged
hyperpolymath merged 1 commit into from
May 30, 2026
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proof(SafeYAML): DISCHARGE isScalarCorrect via 9-arm case-split (proven#90, #107) #112

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32 changes: 19 additions & 13 deletions src/Proven/SafeYAML/Proofs.idr
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Original file line number Diff line number Diff line change
Expand Up @@ -237,19 +237,25 @@ parsedTypesCorrect (YTimestamp _) = Refl
||| Held back by Idris2 0.8.0 not reducing `not . not . isScalar val`
||| to `isScalar val` by Refl when `val` is abstract. The composition
||| `(not . isScalar) val` only unfolds to `not (isScalar val)` once
||| Idris splits on `val`'s constructor (so it can pattern-match
||| `isScalar` to a literal `True`/`False`); for an abstract `val`
||| the outer `not` keeps `not (isScalar val)` stuck, and the second
||| `not` then keeps the whole expression stuck. Same blocker family
||| as the `Data.Bool` involution gap noted in SafeChecksum's
||| `xorChecksum [x,x] = 0` OWED. Discharge by case-analysis on the
||| nine `YAMLValue` constructors (each branch reduces to `not (not
||| True) = True` by Refl), or by a `boolDoubleNegation` lemma over
||| `Bool`.
export
0 isScalarCorrect : (val : YAMLValue) ->
isScalar val = True ->
not (isCollection val) = True
||| DISCHARGED via 9-arm case-split on `val`'s constructor — each
||| scalar arm reduces `not (isCollection val) = True` to `Refl`
||| (since `isCollection = not . isScalar` and `isScalar = True` on
||| scalars means `not (not True) = True`). The two collection arms
||| (`YArray`, `YObject`) have the premise `isScalar val = True`
||| reduce to `False = True` which is uninhabited (`impossible`).
public export
isScalarCorrect : (val : YAMLValue) ->
isScalar val = True ->
not (isCollection val) = True
isScalarCorrect YNull _ = Refl
isScalarCorrect (YBool _) _ = Refl
isScalarCorrect (YInt _) _ = Refl
isScalarCorrect (YFloat _) _ = Refl
isScalarCorrect (YString _) _ = Refl
isScalarCorrect (YArray _) Refl impossible
isScalarCorrect (YObject _) Refl impossible
isScalarCorrect (YBinary _) _ = Refl
isScalarCorrect (YTimestamp _) _ = Refl

--------------------------------------------------------------------------------
-- Deserialization Safety Proofs
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