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| 1 | +-- SPDX-License-Identifier: MPL-2.0 |
| 2 | +-- Copyright (c) 2026 Jonathan D.A. Jewell (hyperpolymath) <j.d.a.jewell@open.ac.uk> |
| 3 | +-- |
| 4 | +||| Semantic octad-model invariants for VeriSimiser. |
| 5 | +||| |
| 6 | +||| `Proofs.idr` checks the octad only shallowly (`length allDimensions = 8`, |
| 7 | +||| a couple of tag values). This module proves the *defining* invariants of the |
| 8 | +||| VeriSimDB octad model as genuine theorems: |
| 9 | +||| |
| 10 | +||| 1. Octad ≅ Fin 8 — the eight dimensions are exactly eight, all distinct and |
| 11 | +||| with no gaps: a full bijection (both round-trips), not just a count. |
| 12 | +||| 2. DriftCategory ≅ OctadDimension — the asserted "drift categories biject |
| 13 | +||| onto octad dimensions" proven as a real bijection. |
| 14 | +||| 3. Sidecar isolation — the per-dimension write model agrees with the tier |
| 15 | +||| classification: every Tier-1 (piggyback) dimension provably never writes |
| 16 | +||| to the target database, and every Tier-2 (overlay) dimension does. |
| 17 | + |
| 18 | +module Verisimiser.ABI.Octad |
| 19 | + |
| 20 | +import Verisimiser.ABI.Types |
| 21 | +import Data.Fin |
| 22 | +import Data.Vect |
| 23 | + |
| 24 | +%default total |
| 25 | + |
| 26 | +-------------------------------------------------------------------------------- |
| 27 | +-- 1. Octad ≅ Fin 8 (exactly eight distinct dimensions, no gaps) |
| 28 | +-------------------------------------------------------------------------------- |
| 29 | + |
| 30 | +||| Ordinal position of each octad dimension (matches `octadToInt`). |
| 31 | +public export |
| 32 | +octadToFin : OctadDimension -> Fin 8 |
| 33 | +octadToFin Data = 0 |
| 34 | +octadToFin Metadata = 1 |
| 35 | +octadToFin Provenance = 2 |
| 36 | +octadToFin Lineage = 3 |
| 37 | +octadToFin Constraints = 4 |
| 38 | +octadToFin AccessControl = 5 |
| 39 | +octadToFin Temporal = 6 |
| 40 | +octadToFin Simulation = 7 |
| 41 | + |
| 42 | +||| Inverse: recover the dimension from its ordinal. |
| 43 | +public export |
| 44 | +octadFromFin : Fin 8 -> OctadDimension |
| 45 | +octadFromFin FZ = Data |
| 46 | +octadFromFin (FS FZ) = Metadata |
| 47 | +octadFromFin (FS (FS FZ)) = Provenance |
| 48 | +octadFromFin (FS (FS (FS FZ))) = Lineage |
| 49 | +octadFromFin (FS (FS (FS (FS FZ)))) = Constraints |
| 50 | +octadFromFin (FS (FS (FS (FS (FS FZ))))) = AccessControl |
| 51 | +octadFromFin (FS (FS (FS (FS (FS (FS FZ)))))) = Temporal |
| 52 | +octadFromFin (FS (FS (FS (FS (FS (FS (FS FZ))))))) = Simulation |
| 53 | + |
| 54 | +||| Round-trip 1: every dimension survives ordinal encode/decode (injective). |
| 55 | +export |
| 56 | +octadFinInverseL : (d : OctadDimension) -> octadFromFin (octadToFin d) = d |
| 57 | +octadFinInverseL Data = Refl |
| 58 | +octadFinInverseL Metadata = Refl |
| 59 | +octadFinInverseL Provenance = Refl |
| 60 | +octadFinInverseL Lineage = Refl |
| 61 | +octadFinInverseL Constraints = Refl |
| 62 | +octadFinInverseL AccessControl = Refl |
| 63 | +octadFinInverseL Temporal = Refl |
| 64 | +octadFinInverseL Simulation = Refl |
| 65 | + |
| 66 | +||| Round-trip 2: every ordinal in [0,8) names a dimension (surjective, no gaps). |
| 67 | +export |
| 68 | +octadFinInverseR : (i : Fin 8) -> octadToFin (octadFromFin i) = i |
| 69 | +octadFinInverseR FZ = Refl |
| 70 | +octadFinInverseR (FS FZ) = Refl |
| 71 | +octadFinInverseR (FS (FS FZ)) = Refl |
| 72 | +octadFinInverseR (FS (FS (FS FZ))) = Refl |
| 73 | +octadFinInverseR (FS (FS (FS (FS FZ)))) = Refl |
| 74 | +octadFinInverseR (FS (FS (FS (FS (FS FZ))))) = Refl |
| 75 | +octadFinInverseR (FS (FS (FS (FS (FS (FS FZ)))))) = Refl |
| 76 | +octadFinInverseR (FS (FS (FS (FS (FS (FS (FS FZ))))))) = Refl |
| 77 | + |
| 78 | +-------------------------------------------------------------------------------- |
| 79 | +-- 2. DriftCategory ≅ OctadDimension (the asserted bijection, made real) |
| 80 | +-------------------------------------------------------------------------------- |
| 81 | + |
| 82 | +||| Each drift category detects inconsistency in exactly one octad dimension, |
| 83 | +||| paired by ordinal. |
| 84 | +public export |
| 85 | +driftToDim : DriftCategory -> OctadDimension |
| 86 | +driftToDim Structural = Data |
| 87 | +driftToDim SemanticDrift = Metadata |
| 88 | +driftToDim TemporalDrift = Provenance |
| 89 | +driftToDim Statistical = Lineage |
| 90 | +driftToDim Referential = Constraints |
| 91 | +driftToDim ProvenanceDrift = AccessControl |
| 92 | +driftToDim SpatialDrift = Temporal |
| 93 | +driftToDim EmbeddingDrift = Simulation |
| 94 | + |
| 95 | +||| Inverse pairing. |
| 96 | +public export |
| 97 | +dimToDrift : OctadDimension -> DriftCategory |
| 98 | +dimToDrift Data = Structural |
| 99 | +dimToDrift Metadata = SemanticDrift |
| 100 | +dimToDrift Provenance = TemporalDrift |
| 101 | +dimToDrift Lineage = Statistical |
| 102 | +dimToDrift Constraints = Referential |
| 103 | +dimToDrift AccessControl = ProvenanceDrift |
| 104 | +dimToDrift Temporal = SpatialDrift |
| 105 | +dimToDrift Simulation = EmbeddingDrift |
| 106 | + |
| 107 | +||| The drift↔octad correspondence is a genuine bijection (round-trip 1). |
| 108 | +export |
| 109 | +driftDimInverseL : (c : DriftCategory) -> dimToDrift (driftToDim c) = c |
| 110 | +driftDimInverseL Structural = Refl |
| 111 | +driftDimInverseL SemanticDrift = Refl |
| 112 | +driftDimInverseL TemporalDrift = Refl |
| 113 | +driftDimInverseL Statistical = Refl |
| 114 | +driftDimInverseL Referential = Refl |
| 115 | +driftDimInverseL ProvenanceDrift = Refl |
| 116 | +driftDimInverseL SpatialDrift = Refl |
| 117 | +driftDimInverseL EmbeddingDrift = Refl |
| 118 | + |
| 119 | +||| …and round-trip 2. |
| 120 | +export |
| 121 | +driftDimInverseR : (d : OctadDimension) -> driftToDim (dimToDrift d) = d |
| 122 | +driftDimInverseR Data = Refl |
| 123 | +driftDimInverseR Metadata = Refl |
| 124 | +driftDimInverseR Provenance = Refl |
| 125 | +driftDimInverseR Lineage = Refl |
| 126 | +driftDimInverseR Constraints = Refl |
| 127 | +driftDimInverseR AccessControl = Refl |
| 128 | +driftDimInverseR Temporal = Refl |
| 129 | +driftDimInverseR Simulation = Refl |
| 130 | + |
| 131 | +-------------------------------------------------------------------------------- |
| 132 | +-- 3. Sidecar isolation: the write model agrees with the tier classification |
| 133 | +-------------------------------------------------------------------------------- |
| 134 | + |
| 135 | +||| Whether augmenting a given octad dimension writes to the *target* database. |
| 136 | +||| Defined per-dimension (independently of `dimensionTier`): the three |
| 137 | +||| read-path/sidecar dimensions never touch the target; the overlay dimensions |
| 138 | +||| add storage alongside it. |
| 139 | +public export |
| 140 | +writesTarget : OctadDimension -> Bool |
| 141 | +writesTarget Provenance = False -- piggyback: append-only provenance sidecar |
| 142 | +writesTarget Temporal = False -- piggyback: read-path temporal snapshots |
| 143 | +writesTarget Constraints = False -- piggyback: read-path drift observation |
| 144 | +writesTarget Data = True |
| 145 | +writesTarget Metadata = True |
| 146 | +writesTarget Lineage = True |
| 147 | +writesTarget AccessControl = True |
| 148 | +writesTarget Simulation = True |
| 149 | + |
| 150 | +||| SIDECAR ISOLATION (the core safety guarantee): every Tier-1 (piggyback) |
| 151 | +||| dimension provably never writes to the target database. This proves the |
| 152 | +||| independently-defined write model is *consistent* with the tier model — a |
| 153 | +||| real cross-check, not a tautology. |
| 154 | +export |
| 155 | +tier1NeverWritesTarget : (d : OctadDimension) -> |
| 156 | + dimensionTier d = Tier1 -> writesTarget d = False |
| 157 | +tier1NeverWritesTarget Provenance _ = Refl |
| 158 | +tier1NeverWritesTarget Temporal _ = Refl |
| 159 | +tier1NeverWritesTarget Constraints _ = Refl |
| 160 | +tier1NeverWritesTarget Data Refl impossible |
| 161 | +tier1NeverWritesTarget Metadata Refl impossible |
| 162 | +tier1NeverWritesTarget Lineage Refl impossible |
| 163 | +tier1NeverWritesTarget AccessControl Refl impossible |
| 164 | +tier1NeverWritesTarget Simulation Refl impossible |
| 165 | + |
| 166 | +||| Dual: every Tier-2 (overlay) dimension does write to the target — so the |
| 167 | +||| isolation above is not vacuous (the two tiers genuinely partition by write |
| 168 | +||| behaviour). |
| 169 | +export |
| 170 | +tier2WritesTarget : (d : OctadDimension) -> |
| 171 | + dimensionTier d = Tier2 -> writesTarget d = True |
| 172 | +tier2WritesTarget Data _ = Refl |
| 173 | +tier2WritesTarget Metadata _ = Refl |
| 174 | +tier2WritesTarget Lineage _ = Refl |
| 175 | +tier2WritesTarget AccessControl _ = Refl |
| 176 | +tier2WritesTarget Simulation _ = Refl |
| 177 | +tier2WritesTarget Provenance Refl impossible |
| 178 | +tier2WritesTarget Temporal Refl impossible |
| 179 | +tier2WritesTarget Constraints Refl impossible |
| 180 | + |
| 181 | +-------------------------------------------------------------------------------- |
| 182 | +-- Negative controls (the invariants are non-vacuous) |
| 183 | +-------------------------------------------------------------------------------- |
| 184 | + |
| 185 | +||| Distinct dimensions are genuinely distinct — the ordinal tagging cannot |
| 186 | +||| collide two dimensions onto one slot. |
| 187 | +export |
| 188 | +dataNotMetadata : Not (Data = Metadata) |
| 189 | +dataNotMetadata Refl impossible |
| 190 | + |
| 191 | +||| Sidecar isolation has real content: at least one dimension *does* write to |
| 192 | +||| the target, so `writesTarget` is not constantly `False`. |
| 193 | +export |
| 194 | +dataDoesWrite : writesTarget Data = True |
| 195 | +dataDoesWrite = Refl |
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