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proof(SafeHTTP): annotate 3 bodyless decls as OWED (Refs standards#158) #43

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hyperpolymath merged 2 commits into from
May 20, 2026
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proof(SafeHTTP): annotate 3 bodyless decls as OWED (Refs standards#158) #43

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proof(SafeHTTP): annotate 3 bodyless decls as OWED-with-justification
hyperpolymath May 20, 2026
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Merge branch 'main' into proof/owed-SafeHTTP-158
hyperpolymath May 20, 2026
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45 changes: 34 additions & 11 deletions src/Proven/SafeHTTP/Proofs.idr
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Expand Up @@ -90,20 +90,43 @@ parseEmptyMethodFails = Refl
-- HTTP Status Code Properties
--------------------------------------------------------------------------------

||| Success status codes are not errors.
||| If isSuccess returns True, isError must return False.
||| Proved by contradiction: if code >= 200 && code < 300, then code < 400.
||| OWED: success status codes are not errors. If `isSuccess sc = True`
||| (i.e. `sc.code >= 200 && sc.code < 300`), then `isError sc = False`
||| (i.e. `sc.code >= 400` is false). Held back by Idris2 0.8.0 not
||| reducing the comparison-chain `>=`/`<` on the abstract `Nat`
||| `sc.code` to literal `True`/`False` by `Refl` alone — `sc.code` is
||| existentially bound by `MkStatusCode` and only carries the range
||| witness `So (code >= 100 && code <= 599)`, not a concrete value.
||| Same blocker family as SafeChecksum's `Nat`-mod reductions.
||| Discharge once a `Data.Nat` linear-arithmetic reflective tactic
||| is available, or by deriving via `boolAnd`/`boolNot` case-split on
||| the `So` witness plus `lteTransitive` (200 <= sc.code < 300 < 400).
export
successNotError : (sc : StatusCode) -> isSuccess sc = True -> isError sc = False

||| Error status codes are not successes.
0 successNotError : (sc : StatusCode) -> isSuccess sc = True -> isError sc = False

||| OWED: error status codes are not successes. If `isError sc = True`
||| (i.e. `sc.code >= 400`), then `isSuccess sc = False` (i.e.
||| `sc.code >= 200 && sc.code < 300` is false because `sc.code < 300`
||| contradicts `sc.code >= 400`). Held back by Idris2 0.8.0 not
||| reducing `Nat` order comparisons on the abstract record-projected
||| `sc.code` by `Refl`. Same blocker family as `successNotError`.
||| Discharge once a `Data.Nat` linear-arithmetic reflective tactic
||| is available, or by case-split on `>=`/`<` with `lteTransitive`.
export
errorNotSuccess : (sc : StatusCode) -> isError sc = True -> isSuccess sc = False

||| Retryable status codes are errors.
||| 429, 502, 503, 504 are all >= 400.
0 errorNotSuccess : (sc : StatusCode) -> isError sc = True -> isSuccess sc = False

||| OWED: retryable status codes are errors. 429, 502, 503, 504 are
||| each `>= 400`, so `isRetryable sc = True` implies `isError sc =
||| True`. Held back by Idris2 0.8.0 not reducing the four-way `||`
||| equality-disjunction (`sc.code == 429 || ... || sc.code == 504`)
||| into a definite value of `sc.code >= 400` by `Refl` — the `Nat`
||| equality primitives on the abstract record field do not unfold.
||| Same blocker family as `successNotError`. Discharge once a
||| `Data.Nat` reflective tactic is available, or by four-arm case
||| analysis on the `||` chain with literal `lteSucc`-derived proofs
||| `429 >= 400`, `502 >= 400`, `503 >= 400`, `504 >= 400`.
export
retryableIsError : (sc : StatusCode) -> isRetryable sc = True -> isError sc = True
0 retryableIsError : (sc : StatusCode) -> isRetryable sc = True -> isError sc = True

--------------------------------------------------------------------------------
-- Header Injection Prevention Properties
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