swaitsandClaude Fable 5.1
055decf7e2
The first edition's five laws (debits equal credits; the accounting equation; the trial balance balances; net income articulates to equity; the cash-flow sections sum to the change in cash) are theorems in bookspec/lean, ported from verify/lean (Basic, Entry, Statements, Closing, Ledger under namespace Bookspec) and restated by name in Laws.lean, each a statement about every reachable state of the books. Audit.lean prints their axioms; the checker's lean.rs test fails on a sorry, a law not audited, or any axiom beyond propext, Quot.sound and Classical.choice. Money is Int, the exact count of the smallest unit: every law is a law of addition, so the model is faithful to exact decimals. Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01HS8WZziDnyxunC23MUxrLp
63 lines
2.8 KiB
Lean4
63 lines
2.8 KiB
Lean4
import Bookspec.Ledger
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/-!
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# bookspec's five laws
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The five laws of the first edition (`bookspec/spec/00-model.md`, "The five
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laws"), each stated once, by name, as a theorem about *every* reachable
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state of the books, ported from `verify/lean` (P13 step 4). Money is `Int`,
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an exact count of the smallest unit; any finite set of exact decimals
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scales to integers without loss, and every law is a law of addition.
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1. Debits equal credits (BS-entry-1).
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2. Assets = Liabilities + Equity + (Revenue - Expenses) (BS-statement-2).
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3. The trial balance balances (BS-statement-1).
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4. Net income articulates to equity: a close credits equity with exactly
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revenue less expenses (BS-period-1).
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5. The cash-flow sections sum to the change in cash (BS-statement-3).
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-/
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namespace Bookspec
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/-- Law 1. In every reachable state the posted lines' debits equal their
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credits (`net` is debits less credits). -/
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theorem law_debits_equal_credits {L : Ledger} (r : Reachable L) :
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net (allLines L.posted) = 0 :=
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r.books_net_zero
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/-- Law 2. The accounting equation, in every reachable state. -/
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theorem law_accounting_equation {L : Ledger} (r : Reachable L) :
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let ls := allLines L.posted
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typeTotal .asset ls L.chart
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= typeTotal .liability ls L.chart + typeTotal .equity ls L.chart
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+ (typeTotal .revenue ls L.chart - typeTotal .expense ls L.chart) :=
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r.accounting_equation
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/-- Law 3. The trial balance balances, in every reachable state. -/
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theorem law_trial_balance {L : Ledger} (r : Reachable L) :
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tbDebits (allLines L.posted) (codes L.chart)
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= tbCredits (allLines L.posted) (codes L.chart) :=
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r.trial_balance
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/-- Law 4. A close credits equity with exactly the period's net income. -/
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theorem law_net_income_articulates (L : Ledger) (p : Period) (ts : List (Nat × Int))
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(hsum : total (ts.map Prod.snd)
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= net (closings (nominalCodes L.chart) (allLines (through p.stop L.posted)))) :
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let ls := allLines (through p.stop L.posted)
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total (ts.map Prod.snd) = typeTotal .revenue ls L.chart - typeTotal .expense ls L.chart :=
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close_credits_net_income L p ts hsum
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/-- Law 5. The three sections of the statement of cash flows sum to the
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change in the cash accounts. -/
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theorem law_cash_flow_is_change_in_cash {L : Ledger} (r : Reachable L) (b c : Nat)
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(hbc : b ≤ c) (F : List Line → Line → Flow) (C : List Line → List Int)
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(hC : ∀ e, sum3 (C e) = 0) (cash : List Nat) (hd : Distinct cash)
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(hF : ∀ e l, F e l = .cash ↔ l.account ∈ cash) :
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let es := (between b c L.posted).map Entry.lines
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sectionTotal F C 0 es + sectionTotal F C 1 es + sectionTotal F C 2 es
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= sumOver (fun a => movement a (allLines (through c L.posted))) cash
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- sumOver (fun a => movement a (allLines (through b L.posted))) cash :=
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r.cashflow_is_change_in_cash b c hbc F C hC cash hd hF
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end Bookspec
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