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proof(SafeNetwork): annotate 5 bodyless decls as OWED (Refs standards#158) #49

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hyperpolymath merged 4 commits into from
May 20, 2026
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proof(SafeNetwork): annotate 5 bodyless decls as OWED (Refs standards#158) #49

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proof(SafeNetwork): annotate 5 bodyless decls as OWED-with-justification
hyperpolymath May 20, 2026
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Merge branch 'main' into proof/owed-SafeNetwork-158
hyperpolymath May 20, 2026
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Merge branch 'main' into proof/owed-SafeNetwork-158
hyperpolymath May 20, 2026
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Merge branch 'main' into proof/owed-SafeNetwork-158
hyperpolymath May 20, 2026
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84 changes: 48 additions & 36 deletions src/Proven/SafeNetwork/Proofs.idr
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Original file line number Diff line number Diff line change
Expand Up @@ -28,28 +28,35 @@ public export
portAlwaysValid : (p : Port) -> ValidPort p
portAlwaysValid p = MkValidPort p

-- | mkPort succeeds for values <= 65535.
-- | Postulated: mkPort uses a runtime Bool check (`n <= 65535`), and the
-- | connection between the runtime `<=` and the type-level `LTE` requires
-- | showing that `(n <= 65535) = True` implies `checkPort n = Just ItIsPort`,
-- | which involves the opaque primitive Nat comparison.
-- TODO: Update for Idris2 0.8.0 -- prove via decidability of Nat comparison.
export
mkPortSucceeds : (n : Nat) -> LTE n 65535 -> IsJust (mkPort n)
||| OWED: `mkPort n` returns `Just _` whenever `n <= 65535`. Held back
||| by Idris2 0.8.0 not bridging the runtime `Bool` test
||| `n <= 65535 = True` (used by `checkPort`) to the type-level `LTE n
||| 65535` witness: `mkPort` branches on `checkPort n`, which evaluates
||| the opaque primitive Nat `<=`, so `IsJust (mkPort n)` does not
||| reduce by Refl from an `LTE` premise. Discharge once a Nat
||| decidability bridge (`lteReflectsLTE : (n <= m) = True -> LTE n m`)
||| is exposed by `Data.Nat`, or `mkPort` is refactored to take the
||| `LTE` proof directly.
public export
0 mkPortSucceeds : (n : Nat) -> LTE n 65535 -> IsJust (mkPort n)

-- | Network address is always contained in its own CIDR.
-- | Postulated: `contains` does not reduce on abstract `CIDRBlock` in
-- | Idris 2 0.8.0 because it involves runtime Nat comparisons
-- | (`ipToNat ... >= ipToNat ...`) that are opaque at the type level.
-- TODO: Update for Idris2 0.8.0 -- prove via ipToNat monotonicity lemmas.
export
networkInOwnCIDR : (cidr : CIDRBlock) -> contains cidr (networkAddress cidr) = True
||| OWED: every CIDR block contains its own network address. Held back
||| by Idris2 0.8.0 not reducing `contains` on an abstract `CIDRBlock`:
||| `contains` is defined via `ipToNat ... >= ipToNat ...`, and those
||| primitive Nat `>=` comparisons stay opaque at the type level when
||| the `CIDRBlock` is a free variable rather than a concrete literal.
||| Discharge once `ipToNat` monotonicity lemmas are proven and a
||| reflective bridge from primitive `>=` to `GTE` is available.
public export
0 networkInOwnCIDR : (cidr : CIDRBlock) -> contains cidr (networkAddress cidr) = True

-- | Broadcast address is always contained in its own CIDR.
-- | Postulated for same reason as networkInOwnCIDR.
-- TODO: Update for Idris2 0.8.0 -- prove via ipToNat monotonicity lemmas.
export
broadcastInOwnCIDR : (cidr : CIDRBlock) -> contains cidr (broadcastAddress cidr) = True
||| OWED: every CIDR block contains its own broadcast address. Same
||| blocker family as `networkInOwnCIDR` — `contains` does not reduce
||| on an abstract `CIDRBlock` argument because of opaque primitive
||| Nat `>=`. Discharge once `ipToNat` monotonicity + a `>=`-to-`GTE`
||| reflective bridge are in place.
public export
0 broadcastInOwnCIDR : (cidr : CIDRBlock) -> contains cidr (broadcastAddress cidr) = True

||| CIDR subset transitivity: if A is a subset of B and B is a subset of C then A is a subset of C
||| This follows from the transitivity of the containment relation
Expand All @@ -59,23 +66,28 @@ data SubsetTransitive : CIDRBlock -> CIDRBlock -> CIDRBlock -> Type where
isSubsetOf b c = True ->
SubsetTransitive a b c

-- | System ports are always < 1024.
-- | Postulated: requires connecting the runtime Bool classification
-- | (`isSystemPort`) with the type-level `LTE` relation, which involves
-- | the opaque Nat comparison primitives.
-- TODO: Update for Idris2 0.8.0 -- prove via decidability of Nat comparison.
export
systemPortBound : (p : Port) -> isSystemPort p = True -> LTE (portValue p) 1023
||| OWED: a port classified as a system port has value `<= 1023`.
||| Held back by Idris2 0.8.0's Bool-to-LTE bridge: `isSystemPort` is a
||| runtime classification that pattern-matches on the result of
||| `classify`, and the `True` outcome does not type-level reduce to a
||| `LTE` witness without an opaque primitive Nat comparison.
||| Discharge once `classify` is reformulated to return a dependent
||| witness (e.g. `(c : Class ** ClassifiedAs p c)`) carrying the
||| `LTE` proof, or once a primitive-Nat reflective bridge lands.
public export
0 systemPortBound : (p : Port) -> isSystemPort p = True -> LTE (portValue p) 1023

-- | Every port value is <= 65535.
-- | Postulated: Port construction now uses a runtime bounds check via
-- | `checkPort` with an erased `IsPort` witness, rather than a
-- | constructive `LTE n 65535` proof. The bound holds by the runtime
-- | check in mkPort/unsafeMkPort.
-- TODO: Update for Idris2 0.8.0 -- either restore LTE proof with
-- efficient representation, or prove from IsPort witness semantics.
export
portBounded : (p : Port) -> LTE (portValue p) 65535
||| OWED: every well-typed `Port` has `portValue p <= 65535`. Held
||| back by the move to runtime bounds checking: `mkPort` / `unsafeMkPort`
||| now carry an erased `IsPort` witness (`data IsPort : Nat -> Type
||| where ItIsPort : IsPort n`) rather than a constructive `LTE n
||| 65535` proof, so the bound is enforced dynamically by `checkPort`
||| but not recoverable at the type level by Refl. Discharge once
||| `IsPort` is refined to a non-trivial witness carrying the `LTE`
||| (i.e. `IsPort n := LTE n 65535`), or `Port` is rebuilt to store
||| the `LTE` proof directly.
public export
0 portBounded : (p : Port) -> LTE (portValue p) 65535

||| Proof that host count is positive for prefix < 32
public export
Expand Down