ABI: make Idris2 proofs genuinely compile + add machine-checked theorems (#27)

## Idris2 ABI proofs — genuinely compile + machine-checked theorems

Part of the family-wide ABI-proofs review. The hand-written ABI did
**not** typecheck under Idris2 0.7.0; this makes it real and verified,
following the merged **iseriser** reference.

**Systemic fixes:** `decEq _ _ = No absurd` → explicit off-diagonal
cases; `{auto 0 nonNull}` smart constructors → `choose`-based;
`paddingFor` `-` → `minus`; real `decDivides`/`decFieldsAligned`
replacing `?fieldsAlignedProof`; honest `offsetInBounds`; `thisPlatform`
de-`%runElab`'d; buildable nested layout + ipkg; new `Proofs.idr` with
real theorems.

**Verified:** `idris2 --build` clean (0/0); adversarial re-verify found
no `believe_me`/`postulate`/holes.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

---
_Generated by [Claude
Code](https://claude.ai/code/session_01DF9CcCuL4YJoqs26eHsYiA)_

---------

Co-authored-by: Jonathan D.A. Jewell <paraordinate@yahoo.co.uk>
Co-authored-by: Claude Opus 4.8 <noreply@anthropic.com>

Author: 3 people

.gitignore

@@ -18,6 +18,11 @@ Thumbs.db
 /dist/
 /out/
 
+# Idris2 build artefacts (nested ABI package build dirs)
+**/build/
+*.ttc
+*.ttm
+
 # Dependencies
 /node_modules/
 /vendor/

src/interface/abi/Foreign.idr …nterface/abi/Oblibeniser/ABI/Foreign.idrsrc/interface/abi/Foreign.idr renamed to src/interface/abi/Oblibeniser/ABI/Foreign.idr src/interface/abi/Foreign.idr renamed to src/interface/abi/Oblibeniser/ABI/Foreign.idr

@@ -14,6 +14,8 @@ module Oblibeniser.ABI.Layout
 import Oblibeniser.ABI.Types
 import Data.Vect
 import Data.So
+import Data.Nat
+import Decidable.Equality
 
 %default total
 
@@ -27,25 +29,42 @@ paddingFor : (offset : Nat) -> (alignment : Nat) -> Nat
 paddingFor offset alignment =
   if offset `mod` alignment == 0
     then 0
-    else alignment - (offset `mod` alignment)
-
-||| Proof that alignment divides aligned size
-public export
-data Divides : Nat -> Nat -> Type where
-  DivideBy : (k : Nat) -> {n : Nat} -> {m : Nat} -> (m = k * n) -> Divides n m
+    else minus alignment (offset `mod` alignment)
 
 ||| Round up to next alignment boundary
 public export
 alignUp : (size : Nat) -> (alignment : Nat) -> Nat
 alignUp size alignment =
   size + paddingFor size alignment
 
-||| Proof that alignUp produces aligned result
+||| Proof that alignment divides aligned size: `m = k * n`.
+public export
+data Divides : Nat -> Nat -> Type where
+  DivideBy : (k : Nat) -> {n : Nat} -> {m : Nat} -> (m = k * n) -> Divides n m
+
+||| Sound decision procedure for divisibility. Returns a genuine
+||| `Divides n m` witness when `n` evenly divides `m`, otherwise Nothing.
+||| Division by zero is undecidable here and yields Nothing.
+public export
+decDivides : (n : Nat) -> (m : Nat) -> Maybe (Divides n m)
+decDivides Z _ = Nothing
+decDivides (S k) m =
+  let q = m `div` (S k) in
+  case decEq m (q * (S k)) of
+    Yes prf => Just (DivideBy q prf)
+    No _ => Nothing
+
+||| Sound divisibility check for an aligned size. The general theorem
+||| "alignUp size align is always divisible by align" needs div/mod lemmas
+||| from Data.Nat and is tracked as residual proof work; here we *decide* it
+||| via `decDivides`, which returns a genuine witness when it holds. For the
+||| concrete ABI layouts below, divisibility is proven outright (`DivideBy`).
+||| (Previously `alignUpCorrect … = DivideBy … Refl`, whose `Refl` cannot
+||| typecheck for symbolic inputs.)
 public export
-alignUpCorrect : (size : Nat) -> (align : Nat) -> (align > 0) -> Divides align (alignUp size align)
-alignUpCorrect size align prf =
-  -- Proof that (size + padding) is divisible by align
-  DivideBy ((size + paddingFor size align) `div` align) Refl
+alignUpDivides : (size : Nat) -> (align : Nat) ->
+                 Maybe (Divides align (alignUp size align))
+alignUpDivides size align = decDivides align (alignUp size align)
 
 --------------------------------------------------------------------------------
 -- Struct Field Layout
@@ -77,7 +96,7 @@ record StructLayout where
 
 ||| Calculate total struct size with padding
 public export
-calcStructSize : Vect n Field -> Nat -> Nat
+calcStructSize : Vect k Field -> Nat -> Nat
 calcStructSize [] align = 0
 calcStructSize (f :: fs) align =
   let lastOffset = foldl (\acc, field => nextFieldOffset field) f.offset fs
@@ -86,23 +105,26 @@ calcStructSize (f :: fs) align =
 
 ||| Proof that field offsets are correctly aligned
 public export
-data FieldsAligned : Vect n Field -> Type where
+data FieldsAligned : Vect k Field -> Type where
   NoFields : FieldsAligned []
   ConsField :
     (f : Field) ->
-    (rest : Vect n Field) ->
+    (rest : Vect k Field) ->
     Divides f.alignment f.offset ->
     FieldsAligned rest ->
     FieldsAligned (f :: rest)
 
-||| Verify a struct layout is valid
+||| Decide field alignment for every field, building a real `FieldsAligned`
+||| witness from per-field divisibility proofs.
 public export
-verifyLayout : (fields : Vect n Field) -> (align : Nat) -> Either String StructLayout
-verifyLayout fields align =
-  let size = calcStructSize fields align
-   in case decSo (size >= sum (map (\f => f.size) fields)) of
-        Yes prf => Right (MkStructLayout fields size align)
-        No _ => Left "Invalid struct size"
+decFieldsAligned : (fs : Vect k Field) -> Maybe (FieldsAligned fs)
+decFieldsAligned [] = Just NoFields
+decFieldsAligned (f :: fs) =
+  case decDivides f.alignment f.offset of
+    Nothing => Nothing
+    Just dvd => case decFieldsAligned fs of
+                  Nothing => Nothing
+                  Just rest => Just (ConsField f fs dvd rest)
 
 --------------------------------------------------------------------------------
 -- Platform-Specific Layouts
@@ -113,14 +135,8 @@ public export
 PlatformLayout : Platform -> Type -> Type
 PlatformLayout p t = StructLayout
 
-||| Verify layout is correct for all platforms
-public export
-verifyAllPlatforms :
-  (layouts : (p : Platform) -> PlatformLayout p t) ->
-  Either String ()
-verifyAllPlatforms layouts =
-  -- Check that layout is valid on all platforms
-  Right ()
+-- `verifyAllLayouts` is defined at the end of this module, after the concrete
+-- layouts and `checkCABI` it depends on.
 
 --------------------------------------------------------------------------------
 -- C ABI Compatibility
@@ -134,12 +150,15 @@ data CABICompliant : StructLayout -> Type where
     FieldsAligned layout.fields ->
     CABICompliant layout
 
-||| Check if layout follows C ABI
+||| Verify a layout against the C ABI alignment rules, returning a genuine
+||| `CABICompliant` proof (built from real per-field divisibility witnesses)
+||| or an error when some field offset is misaligned.
 public export
 checkCABI : (layout : StructLayout) -> Either String (CABICompliant layout)
 checkCABI layout =
-  -- Verify C ABI rules
-  Right (CABIOk layout ?fieldsAlignedProof)
+  case decFieldsAligned layout.fields of
+    Just prf => Right (CABIOk layout prf)
+    Nothing => Left "Field offsets are not correctly aligned for the C ABI"
 
 --------------------------------------------------------------------------------
 -- AuditEntry Layout (oblibeniser-specific)
@@ -171,11 +190,24 @@ auditEntryLayout =
     ]
     64  -- Total size: 64 bytes (with 4 bytes trailing padding)
     8   -- Alignment: 8 bytes
+    {sizeCorrect = Oh}
+    {aligned = DivideBy 8 Refl}
 
-||| Proof that AuditEntry layout is C-ABI compliant
+||| Proof that AuditEntry layout is C-ABI compliant. Each field offset
+||| divides its alignment: 0|8, 8|8, 16|8, 24|8, 32|8, 40|8, 48|8, 56|4.
 export
-auditEntryLayoutValid : CABICompliant auditEntryLayout
-auditEntryLayoutValid = CABIOk auditEntryLayout ?auditEntryFieldsAligned
+auditEntryLayoutValid : CABICompliant Layout.auditEntryLayout
+auditEntryLayoutValid =
+  CABIOk auditEntryLayout
+    (ConsField _ _ (DivideBy 0 Refl)
+    (ConsField _ _ (DivideBy 1 Refl)
+    (ConsField _ _ (DivideBy 2 Refl)
+    (ConsField _ _ (DivideBy 3 Refl)
+    (ConsField _ _ (DivideBy 4 Refl)
+    (ConsField _ _ (DivideBy 5 Refl)
+    (ConsField _ _ (DivideBy 6 Refl)
+    (ConsField _ _ (DivideBy 14 Refl)
+     NoFields))))))))
 
 --------------------------------------------------------------------------------
 -- StateSnapshot Layout (oblibeniser-specific)
@@ -201,11 +233,21 @@ stateSnapshotLayout =
     ]
     40  -- Total size: 40 bytes (with 4 bytes internal padding after stateSize)
     8   -- Alignment: 8 bytes
+    {sizeCorrect = Oh}
+    {aligned = DivideBy 5 Refl}
 
-||| Proof that StateSnapshot layout is C-ABI compliant
+||| Proof that StateSnapshot layout is C-ABI compliant. Each field offset
+||| divides its alignment: 0|8, 8|8, 16|8, 24|4, 32|8.
 export
-stateSnapshotLayoutValid : CABICompliant stateSnapshotLayout
-stateSnapshotLayoutValid = CABIOk stateSnapshotLayout ?snapshotFieldsAligned
+stateSnapshotLayoutValid : CABICompliant Layout.stateSnapshotLayout
+stateSnapshotLayoutValid =
+  CABIOk stateSnapshotLayout
+    (ConsField _ _ (DivideBy 0 Refl)
+    (ConsField _ _ (DivideBy 1 Refl)
+    (ConsField _ _ (DivideBy 2 Refl)
+    (ConsField _ _ (DivideBy 6 Refl)
+    (ConsField _ _ (DivideBy 4 Refl)
+     NoFields)))))
 
 --------------------------------------------------------------------------------
 -- UndoStack Layout (oblibeniser-specific)
@@ -228,25 +270,53 @@ undoStackLayout =
     ]
     24  -- Total size: 24 bytes
     8   -- Alignment: 8 bytes
+    {sizeCorrect = Oh}
+    {aligned = DivideBy 3 Refl}
 
-||| Proof that UndoStack layout is C-ABI compliant
+||| Proof that UndoStack layout is C-ABI compliant. Each field offset
+||| divides its alignment: 0|8, 8|4, 12|4, 16|8.
 export
-undoStackLayoutValid : CABICompliant undoStackLayout
-undoStackLayoutValid = CABIOk undoStackLayout ?undoStackFieldsAligned
+undoStackLayoutValid : CABICompliant Layout.undoStackLayout
+undoStackLayoutValid =
+  CABIOk undoStackLayout
+    (ConsField _ _ (DivideBy 0 Refl)
+    (ConsField _ _ (DivideBy 2 Refl)
+    (ConsField _ _ (DivideBy 3 Refl)
+    (ConsField _ _ (DivideBy 2 Refl)
+     NoFields))))
 
 --------------------------------------------------------------------------------
 -- Offset Calculation
 --------------------------------------------------------------------------------
 
-||| Calculate field offset with proof of correctness
+||| Look up a field's offset by name in a layout.
 public export
-fieldOffset : (layout : StructLayout) -> (fieldName : String) -> Maybe (n : Nat ** Field)
+fieldOffset : (layout : StructLayout) -> (fieldName : String) -> Maybe (Nat, Field)
 fieldOffset layout name =
   case findIndex (\f => f.name == name) layout.fields of
-    Just idx => Just (finToNat idx ** index idx layout.fields)
+    Just idx => Just (finToNat idx, index idx layout.fields)
     Nothing => Nothing
 
-||| Proof that field offset is within struct bounds
+||| Decide whether a field lies within a struct's byte bounds, returning a
+||| genuine proof when `offset + size <= totalSize`. The previous signature
+||| asserted this for *every* field unconditionally, which is false (a field
+||| need not belong to the layout); this honest version decides it.
+public export
+offsetInBounds : (layout : StructLayout) -> (f : Field) ->
+                 Maybe (So (f.offset + f.size <= layout.totalSize))
+offsetInBounds layout f =
+  case choose (f.offset + f.size <= layout.totalSize) of
+    Left ok => Just ok
+    Right _ => Nothing
+
+||| Verify that all oblibeniser concrete layouts are C-ABI compliant. This
+||| fails (Left) if any concrete layout is misaligned, rather than asserting
+||| it. Each layout's `FieldsAligned` witness is built by `checkCABI`'s sound
+||| `decFieldsAligned`.
 public export
-offsetInBounds : (layout : StructLayout) -> (f : Field) -> So (f.offset + f.size <= layout.totalSize)
-offsetInBounds layout f = ?offsetInBoundsProof
+verifyAllLayouts : Either String ()
+verifyAllLayouts = do
+  _ <- checkCABI auditEntryLayout
+  _ <- checkCABI stateSnapshotLayout
+  _ <- checkCABI undoStackLayout
+  Right ()

src/interface/abi/Layout.idr …interface/abi/Oblibeniser/ABI/Layout.idrsrc/interface/abi/Layout.idr renamed to src/interface/abi/Oblibeniser/ABI/Layout.idr src/interface/abi/Layout.idr renamed to src/interface/abi/Oblibeniser/ABI/Layout.idr

@@ -0,0 +1,91 @@
+-- SPDX-License-Identifier: MPL-2.0
+-- Copyright (c) 2026 Jonathan D.A. Jewell (hyperpolymath) <j.d.a.jewell@open.ac.uk>
+--
+||| Machine-checked proofs over the oblibeniser ABI.
+|||
+||| These are not runtime tests — they are propositional statements the Idris2
+||| type checker must discharge at compile time. If any concrete ABI struct
+||| layout were misaligned, the result-code encoding wrong, or a decision
+||| procedure mis-defined, this module would fail to typecheck and the proof
+||| build would go red.
+|||
+||| The C-ABI compliance witnesses are built directly from per-field
+||| divisibility proofs (`DivideBy k Refl`, where `offset = k * alignment`).
+||| Multiplication reduces during type checking, so these are fully verified
+||| by the compiler; we avoid routing them through `Nat` division, which is a
+||| primitive that does not reduce at the type level.
+
+module Oblibeniser.ABI.Proofs
+
+import Oblibeniser.ABI.Types
+import Oblibeniser.ABI.Layout
+import Data.So
+import Data.Vect
+
+%default total
+
+--------------------------------------------------------------------------------
+-- The concrete reversible-computing FFI struct layouts are C-ABI compliant.
+--------------------------------------------------------------------------------
+
+||| Every field offset in the AuditEntry layout divides its alignment:
+||| 0|8, 8|8, 16|8, 24|8, 32|8, 40|8, 48|8, 56|4.
+export
+auditEntryCompliant : CABICompliant Layout.auditEntryLayout
+auditEntryCompliant =
+  CABIOk auditEntryLayout
+    (ConsField _ _ (DivideBy 0 Refl)
+    (ConsField _ _ (DivideBy 1 Refl)
+    (ConsField _ _ (DivideBy 2 Refl)
+    (ConsField _ _ (DivideBy 3 Refl)
+    (ConsField _ _ (DivideBy 4 Refl)
+    (ConsField _ _ (DivideBy 5 Refl)
+    (ConsField _ _ (DivideBy 6 Refl)
+    (ConsField _ _ (DivideBy 14 Refl)
+     NoFields))))))))
+
+||| Every field offset in the StateSnapshot layout divides its alignment:
+||| 0|8, 8|8, 16|8, 24|4, 32|8.
+export
+stateSnapshotCompliant : CABICompliant Layout.stateSnapshotLayout
+stateSnapshotCompliant =
+  CABIOk stateSnapshotLayout
+    (ConsField _ _ (DivideBy 0 Refl)
+    (ConsField _ _ (DivideBy 1 Refl)
+    (ConsField _ _ (DivideBy 2 Refl)
+    (ConsField _ _ (DivideBy 6 Refl)
+    (ConsField _ _ (DivideBy 4 Refl)
+     NoFields)))))
+
+||| Every field offset in the UndoStack layout divides its alignment:
+||| 0|8, 8|4, 12|4, 16|8.
+export
+undoStackCompliant : CABICompliant Layout.undoStackLayout
+undoStackCompliant =
+  CABIOk undoStackLayout
+    (ConsField _ _ (DivideBy 0 Refl)
+    (ConsField _ _ (DivideBy 2 Refl)
+    (ConsField _ _ (DivideBy 3 Refl)
+    (ConsField _ _ (DivideBy 2 Refl)
+     NoFields))))
+
+--------------------------------------------------------------------------------
+-- Result-code encoding: the integer contract the Zig FFI depends on.
+--------------------------------------------------------------------------------
+
+||| Success is encoded as 0, matching the C convention.
+export
+okIsZero : resultToInt Ok = 0
+okIsZero = Refl
+
+||| NotReversible is encoded as 5 — the inverse-computation FFI returns this
+||| code and the safe wrappers decode it back to `NotReversible`.
+export
+notReversibleIsFive : resultToInt NotReversible = 5
+notReversibleIsFive = Refl
+
+||| InverseProofFailed is encoded as 7 — the central correctness failure code
+||| for oblibeniser's reversibility guarantee.
+export
+inverseProofFailedIsSeven : resultToInt InverseProofFailed = 7
+inverseProofFailedIsSeven = Refl