Use Spec Prover with your AI.

Prove spec function

You must execute a mathematical proof with concrete inputs: (1) CHOOSE a representative input. not a trivial case (0, 1) but a realistic value that exercises the main code path. Show EVERY intermediate step with arithmetic, (2) VERIFY output. does the final value in your trace match your expected output? If not: your formula has an error. The trace proves where the discrepancy starts, (3) CHECK constants. does EVERY declared constant appear in at least one step? If not: the constant is orphaned (spec is incomplete or noisy), (4) CHOOSE an edge case. boundary inputs that stress the formula: zero, negative, maximum, midnight wrap, empty array, single element. The edge case MUST differ from the representative input, (5) VERIFY edge case. does your spec explicitly handle the condition revealed? Does it define behavior for zero division? Negative results? Overflow? Wrap-around? If not: the spec is incomplete. the developer will guess, and guess wrong. If the capability rejects, re-examine your trace. your reasoning has a gap. Structured proof capability. forces the PM agent to TRACE every formula with concrete inputs and verify edge cases BEFORE the spec reaches the developer. Based on ARTEMIS (2026), process reward models, and the mathematical proof methodology where every step must be independently verifiable. The capability validates logical consistency. if your verdict contradicts your own trace, it rejects. Catches Off-by-One Boundary (the most common arithmetic error in specifications. spec says: "Display the last 5 entries." Implementation: entries.slice(entries.length - 5). Input: 3 entries. entries.length - 5 = -2. slice(-2) returns last 2 entries. not an error, but unexpected. Input: 0 entries. entries.length - 5 = -5. slice(-5) on empty array = []. Correct by accident. Input: 5 entries. slice(0) = all 5. Correct. Input: 6 entries. slice(1) = last 5. Correct. But the spec never defined: what happens when entries < 5? Show all? Show empty? Show error? The developer guesses. The PM assumed. The QA tests with 10 entries. Production user has 2 entries and sees unexpected behavior. Fix: spec MUST define behavior for boundary inputs: 0 entries, 1 entry, exactly N, N+1), Floating-Point Precision Loss (arithmetic that loses precision in real computation. spec says: "Calculate 15% discount on $19.99." Trace: $19.99 × 0.15 = $2.9985. Rounded to cents: $3.00. Discounted price: $16.99. Implementation: 19.99 0.15 = 2.9984999999999995 (IEEE 754). Math.round(2.9984999999999995 100) / 100 = 3.00. OK. works here. But: $0.10 + $0.20 = 0.30000000000000004 in JavaScript. If the spec compares prices: if (total === expectedTotal). fails. Fix: spec must define precision strategy: integer cents (1999 not 19.99), Decimal.js for arbitrary precision, or epsilon comparison (Math.abs(a-b) < 0.005). The trace must use ACTUAL floating-point arithmetic, not idealized math), Modular Arithmetic Wrap (time/circular calculations that wrap around boundaries. spec says: "Calculate bedtime: subtract sleep duration from wake time." wakeTime = 08:00 (480 minutes). sleepDuration = 9 hours (540 minutes). Trace: 480 - 540 = -60 minutes. What is -60 minutes? The spec does not say. Correct: (-60 + 1440) % 1440 = 1380 minutes = 23:00. But: what if the result is exactly 0? 0 = 00:00 or 24:00? Are they the same? What if sleepDuration > 24 hours? (480 - 1500 = -1020) → (-1020 + 1440) = 420 → 07:00. Is that correct? The spec MUST define the modular arithmetic explicitly and handle the wrap-around at midnight/boundaries), Undefined Division (division operations where the divisor can be zero. spec says: "Calculate average rating: sum of ratings / number of ratings." Normal case: ratings = [4, 5, 3, 4]. Sum = 16. Count = 4. Average = 4.0. Edge case: ratings = []. Sum = 0. Count = 0. Average = 0/0 = NaN. The spec NEVER addressed empty input. The developer implements sum/count. User with 0 reviews sees "NaN stars" displayed in the UI. Or worse: the NaN propagates through calculations: price × NaN = NaN. Fix: spec must define: "If no ratings exist, display 'No ratings yet' instead of average. Function returns null, not NaN. Caller handles null explicitly"), and Orphan Constants (declared constants that never appear in any formula. spec declares: CYCLE_DURATION_MIN = 90, FALL_ASLEEP_MIN = 15, REM_PHASE_MIN = 20. Formulas use: CYCLE_DURATION_MIN and FALL_ASLEEP_MIN. REM_PHASE_MIN is declared but never used in any step. This means either: (1) the spec forgot to include REM_PHASE_MIN in a formula (spec is incomplete), or (2) REM_PHASE_MIN is unnecessary (spec has dead constants. misleading). Both are errors. Every declared constant MUST appear in at least one formula step. If it does not: the spec has a gap or noise). Call once per engine function in the specification