ABI Layer 3: monotone safety under policy composition#34
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Raises the Phronesiser Idris2 ABI to Layer 2 with a flagship, machine-checked
semantic proof of the repo's headline property ("provably safe ethical
constraints for AI agents").
Model: a deontic policy partitions agent actions into Allow/Deny. The
`ActionPermitted` proposition has NO constructor admitting a `Deny` verdict, so
a forbidden action is structurally uncertifiable.
Proven:
- decActionPermitted: sound + complete `Dec (ActionPermitted a)`.
- certifyPermittedSound: certifier soundness (Ok => ActionPermitted).
- safeInformPermitted: positive control (inhabited permission witness).
- forbiddenNeverPermitted: negative control / core safety theorem
`Not (ActionPermitted forbiddenDeploy)`.
- forbiddenNeverCertifiedOk: corollary that the forbidden action is never Ok.
Non-vacuity confirmed: a deliberately false witness
`PermitAllow Refl : ActionPermitted forbiddenDeploy` is rejected by idris2
(Allow vs Deny mismatch). Build is clean (exit 0, zero warnings).
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01A6PSzJWpRxtzGDjUCEh7Mx
New module Phronesiser.ABI.Invariants, built over the existing Layer-2
Semantics model (Action / Verdict / verdictOf — nothing redefined). It
proves two properties strictly deeper than the Layer-2 single-action
safety theorem, both quantified over all actions and over policies:
1. Monotone safety (downward-closure of permission): if policy p2
tightens p1, every action p1 forbids stays forbidden under p2 —
tightening never re-permits a previously-forbidden action; the
permitted set only shrinks. Tightening is a proven preorder
(reflexive + transitive).
2. Conjunction composition: an action permitted under andPolicy p1 p2
is permitted under each conjunct (iff via bothPermitsAnd), and the
conjunction provably tightens each conjunct.
Includes a sound+complete Dec (Permits p a), sample policies over the
shared model, positive controls (witnesses + a live application of the
monotone-safety theorem) and negative/non-vacuity controls in Not(...)
form. %default total; no believe_me / postulate / assert_total / sorry /
asserted equalities. Builds with zero warnings; an adversarial false
proof (tightened policy permits the forbidden action) is rejected by the
type checker.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01A6PSzJWpRxtzGDjUCEh7Mx
Signed-off-by: Jonathan D.A. Jewell <6759885+hyperpolymath@users.noreply.github.com>
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Summary
Layer 3 (second, deeper invariant): proves monotone safety under policy composition — tightening a policy never re-permits a previously-forbidden action (the permitted set only shrinks; tightening is a proven reflexive+transitive preorder), and an action permitted under
andPolicy p1 p2is permitted under each conjunct (iff). Quantifies over all actions and the whole policy space — distinct from and deeper than the Layer-2 single-actionforbiddenNeverPermitted.New module
Phronesiser.ABI.Invariants(imports the Layer-2Semanticsmodel). Sound+completeDec, positive + non-vacuity controls.Testing
Idris2 0.7.0
--build→ exit 0, zero warnings. Adversarial rejection confirmed.build/removed. Nobelieve_me/postulate/sorry.🤖 Generated with Claude Code
https://claude.ai/code/session_01A6PSzJWpRxtzGDjUCEh7Mx
Generated by Claude Code