ABI Layer 3: monotonicity of cost accounting + downward-closed budget#33
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Flagship semantic proof: totalCost (xs ++ ys) = totalCost xs + totalCost ys (conservation, by induction), plus a decidable WithinBudget proposition with sound+complete Dec, certifier soundness, and positive + negative controls (an over-budget ledger is provably rejected). Verified with idris2 0.7.0 (build clean, zero warnings) + adversarial rejection. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01A6PSzJWpRxtzGDjUCEh7Mx
Add Eclexiaiser.ABI.Invariants, a second, deeper machine-checked theorem distinct from the Layer-2 conservation (additivity) proof. Reuses the existing Semantics model (Ledger, totalCost, WithinBudget) without redefining datatypes, and proves the ordering structure of cost accounting: - prefixMonotone / costMonotoneAppend: appending work never decreases total cost (an LTE inequality, derived via additivity + lteAddRight) — not the Layer-2 equality. - budgetWeakening: budget compliance is downward-closed in the budget (WithinBudget b l -> LTE b b2 -> WithinBudget b2 l), via hand-proven LTE transitivity. - decBudgetLE: sound+complete decision for the ordering side condition. - Positive controls (concrete monotone step, prefix split, weakened witness) plus non-vacuity controls (Not on a false equality and on a false ordering), all machine-checked. Builds with exit 0 and zero warnings; adversarial false-statement checks are rejected by the type-checker. Registered last in the .ipkg. 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 monotonicity of cost accounting —
prefixMonotone(a prefix never costs more than the whole) — and that budget compliance is downward-closed (within budget B ⇒ within any B′≥B). Distinct from and deeper than the Layer-2 additivity equality.New module
Eclexiaiser.ABI.Invariants(imports the Layer-2Semanticsmodel). 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