tutor answers step by step in plain text, islands finish, and the audit's money and login holes are closed
Tutor (prompt tutor-v3-stepwise-plain): plain text instead of LaTeX/markdown, with rag/services/mathtext.py converting whatever still slips through; full step-by-step solutions with a check before the final answer; three tones by grade; the last 6 messages of the conversation go to the model and follow-ups are no longer served from another user's cache; book solutions the checker disputes are kept out of the context; a questionId gives the tutor the practice question and the student's wrong answer. /api/health reports when the AI credit runs out. rag_model_benchmark compares chat models on verified book problems (run on the server; credit ran out mid-run). Map: only lessons that have questions count toward finishing an island, lessonIds[0] / nextLessonId is always the next lesson to play, and a finished island stays finished. The Seyar characters (sigma/delta/pi) are seeded. Audit fixes, each reproduced before fixing: - the plan is stored on the order, so paying a monthly order after starting a yearly checkout no longer grants a year - opening checkout no longer demotes an active subscription; renewals extend from the current expiry; expired subscriptions are not reported active - one discount code per order and only before the gateway; a 100% code completes the purchase; lost Zarinpal confirmations are re-verified - the unused /api/payment/webhook "mark paid" endpoint is removed - XP counts only answers recorded on the server - 6-digit OTP, each code dies after 5 wrong guesses; POST /api/auth/logout - a guest who signs up keeps their account and progress (test phones excluded) - affiliate commission on the first real payment; guests excluded - parents with several children no longer get a 500 - SQLite runs transactions IMMEDIATE, since it ignores select_for_update - admin login is rate-limited; display names drop phone numbers and links; userQuestion is capped at 2000 characters - server-side heart enforcement exists behind HEARTS_ENFORCED (off until the frontend handles 403 no_hearts) Not done on purpose: rotating the server's secret key and moving to Postgres. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
This commit is contained in:
308
rag/services/mathtext.py
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308
rag/services/mathtext.py
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"""
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تبدیلِ LaTeX و markdown در پاسخِ دستیار به متنِ ساده با نمادهای یونیکد.
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چرا لازم است: صفحه‌ی «از پی بپرس» پاسخ را همان‌طور که هست، به‌صورتِ متنِ خام
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نشان می‌دهد. مدل‌ها برای ریاضی عادت دارند `\\( \\frac{1}{2} \\)` و `### مرحله ۱`
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بنویسند؛ روی گوشی این‌ها عیناً دیده می‌شوند و فرمولِ حسابان به رشته‌ای از
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بک‌اسلش و آکولاد تبدیل می‌شود. پرامپت از مدل می‌خواهد متنِ ساده بنویسد، ولی
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مدل همیشه گوش نمی‌دهد — این ماژول تورِ ایمنیِ قطعی پشتِ آن است.
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قاعده‌ی مهم: آکولادی که جزوِ LaTeX نیست دست نمی‌خورد. مجموعه‌ها در ریاضیِ نهم
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با `{1, 2, 3}` نوشته می‌شوند و نباید پاک شوند.
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"""
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import re
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from contextvars import ContextVar
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# برای دبستان «/» ممیزِ اعشار است (مثلِ کتابشان)، پس کسر «۳ بر ۴» نوشته می‌شود.
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_FRACTION_WORD: ContextVar[bool] = ContextVar('fraction_word', default=False)
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_SUPERSCRIPT = str.maketrans('0123456789+-=()nixyk', '⁰¹²³⁴⁵⁶⁷⁸⁹⁺⁻⁼⁽⁾ⁿⁱˣʸᵏ')
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_SUBSCRIPT = str.maketrans('0123456789+-=()', '₀₁₂₃₄₅₆₇₈₉₊₋₌₍₎')
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_SUP_CHARS = set('0123456789+-=()nixyk')
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_SUB_CHARS = set('0123456789+-=()')
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_SYMBOLS = {
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'times': '×', 'cdot': '·', 'div': '÷', 'pm': '±', 'mp': '∓',
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'leq': '≤', 'le': '≤', 'geq': '≥', 'ge': '≥', 'neq': '≠', 'ne': '≠',
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'approx': '≈', 'simeq': '≃', 'equiv': '≡', 'infty': '∞',
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'pi': 'π', 'alpha': 'α', 'beta': 'β', 'gamma': 'γ', 'theta': 'θ',
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'Delta': 'Δ', 'delta': 'δ', 'lambda': 'λ', 'mu': 'μ', 'sigma': 'σ',
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'Sigma': 'Σ', 'phi': 'φ', 'varphi': 'φ', 'omega': 'ω', 'epsilon': 'ε',
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'varepsilon': 'ε', 'rho': 'ρ', 'tau': 'τ',
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'rightarrow': '→', 'to': '→', 'leftarrow': '←', 'Rightarrow': '⇒',
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'implies': '⇒', 'Leftrightarrow': '⇔', 'iff': '⇔', 'mapsto': '↦',
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'in': '∈', 'notin': '∉', 'subset': '⊂', 'subseteq': '⊆', 'supset': '⊃',
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'cup': '∪', 'cap': '∩', 'emptyset': '∅', 'varnothing': '∅',
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'forall': '∀', 'exists': '∃', 'angle': '∠', 'perp': '⊥', 'parallel': '∥',
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'triangle': '△', 'circ': '∘', 'degree': '°', 'prime': '′',
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'ldots': '…', 'dots': '…', 'cdots': '⋯', 'int': '∫', 'sum': 'Σ',
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'prod': '∏', 'therefore': '∴', 'propto': '∝', 'neg': '¬',
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'quad': ' ', 'qquad': ' ', 'lbrace': '{', 'rbrace': '}',
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'setminus': '−', 'mid': '|', 'vert': '|',
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}
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_PREFIX_SIGNS = {'pm', 'mp', 'neg', 'angle', 'triangle', 'forall', 'exists'}
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_BLACKBOARD = {'R': 'ℝ', 'N': 'ℕ', 'Z': 'ℤ', 'Q': 'ℚ', 'C': 'ℂ'}
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# \sin و \log و ... فقط بک‌اسلششان حذف می‌شود.
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_FUNCTIONS = {
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'sin', 'cos', 'tan', 'cot', 'sec', 'csc', 'log', 'ln', 'exp', 'lim',
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'max', 'min', 'arcsin', 'arccos', 'arctan', 'sinh', 'cosh', 'det', 'gcd',
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}
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# دستورهایی که فقط محتوای آرگومانشان می‌ماند.
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_UNWRAP = {'text', 'textbf', 'textit', 'mathrm', 'mathbf', 'mathit', 'operatorname',
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'boxed', 'displaystyle', 'mbox', 'underline', 'bm', 'textrm'}
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_DROP = {'left', 'right', 'big', 'Big', 'bigg', 'Bigg', 'displaystyle', 'limits',
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'nonumber', 'hline', 'noindent'}
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def _read_group(s: str, i: int) -> tuple[str, int]:
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"""از s[i] یک آرگومانِ LaTeX می‌خواند: {…} با آکولادِ تودرتو، یا یک نویسه."""
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while i < len(s) and s[i] == ' ':
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i += 1
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if i >= len(s):
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return '', i
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if s[i] != '{':
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if s[i] == '\\':
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m = re.match(r'\\[A-Za-z]+', s[i:])
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if m:
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return m.group(0), i + len(m.group(0))
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return s[i], i + 1
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depth, j = 0, i
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while j < len(s):
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if s[j] == '\\' and j + 1 < len(s):
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j += 2
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continue
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if s[j] == '{':
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depth += 1
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elif s[j] == '}':
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depth -= 1
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if depth == 0:
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return s[i + 1:j], j + 1
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j += 1
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return s[i + 1:], len(s)
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_ATOM = re.compile(r'√?[\d.]+|√?\w|\(.*\)')
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def _needs_parens(expr: str) -> bool:
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"""«2h» در مخرج باید (2h) شود، وگرنه 1/2h یعنی h/2."""
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return not _ATOM.fullmatch(expr.strip())
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def _script(body: str, table, allowed: set, marker: str) -> str:
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if body and all(ch in allowed for ch in body):
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return body.translate(table)
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return f'{marker}({body})' if len(body) > 1 else f'{marker}{body}'
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def _convert(s: str) -> str:
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"""یک عبارتِ LaTeX را (بازگشتی) به یونیکد تبدیل می‌کند."""
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out: list[str] = []
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i = 0
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while i < len(s):
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ch = s[i]
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if ch == '\\':
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if i + 1 < len(s) and not s[i + 1].isalpha():
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nxt = s[i + 1]
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if nxt == '\\':
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out.append('\n')
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elif nxt in '{}%$&#_':
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out.append(nxt)
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elif nxt in ',;:! ':
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out.append(' ' if nxt != '!' else '')
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else:
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out.append(nxt)
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i += 2
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continue
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m = re.match(r'\\([A-Za-z]+)', s[i:])
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name = m.group(1)
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i += len(m.group(0))
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if name == 'frac' or name in ('dfrac', 'tfrac'):
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num, i = _read_group(s, i)
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den, i = _read_group(s, i)
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num, den = _convert(num), _convert(den)
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num = f'({num})' if _needs_parens(num) else num
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den = f'({den})' if _needs_parens(den) else den
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out.append(f'{num} بر {den}' if _FRACTION_WORD.get() else f'{num}/{den}')
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elif name == 'sqrt':
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index = ''
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if i < len(s) and s[i] == '[':
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close = s.find(']', i)
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if close != -1:
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index, i = s[i + 1:close], close + 1
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body, i = _read_group(s, i)
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body = _convert(body)
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root = (index.translate(_SUPERSCRIPT) if index else '') + '√'
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out.append(root + (f'({body})' if len(body) > 1 else body))
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elif name == 'mathbb':
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body, i = _read_group(s, i)
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out.append(_BLACKBOARD.get(body, body))
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elif name in ('vec', 'overrightarrow'):
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body, i = _read_group(s, i)
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out.append(_convert(body) + '⃗')
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elif name in ('overline', 'bar', 'widehat', 'hat'):
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body, i = _read_group(s, i)
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out.append(_convert(body))
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elif name in ('begin', 'end'):
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_env, i = _read_group(s, i)
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elif name in _UNWRAP:
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if i < len(s) and s[i] == '{':
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body, i = _read_group(s, i)
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out.append(_convert(body))
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elif name in _DROP:
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# \left( → ( — خودِ پرانتز در دورِ بعدِ حلقه نوشته می‌شود.
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if name in ('left', 'right') and i < len(s) and s[i] == '.':
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i += 1
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elif name in _SYMBOLS:
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out.append(_SYMBOLS[name])
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# «\pm 2» → «±2»: نمادِ یک‌طرفه به عددش می‌چسبد.
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if name in _PREFIX_SIGNS:
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while i < len(s) and s[i] == ' ':
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i += 1
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elif name in _FUNCTIONS:
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out.append(name)
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else:
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out.append(name)
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elif ch in '^_':
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# مدل «x^10» را به معنیِ ده می‌نویسد، نه «x¹0» — رقم‌ها با هم خوانده می‌شوند.
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digits = re.match(r'\d+', s[i + 1:])
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if digits:
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body, i = digits.group(0), i + 1 + len(digits.group(0))
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else:
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body, i = _read_group(s, i + 1)
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if ch == '^' and body in ('\\circ', 'circ', '°'):
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out.append('°')
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continue
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if ch == '^' and body in ('\\prime', "'"):
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out.append('′')
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continue
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body = _convert(body)
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if ch == '_' and ''.join(out).endswith('lim'):
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out.append(f'({body})')
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continue
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if ch == '^':
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out.append(_script(body, _SUPERSCRIPT, _SUP_CHARS, '^'))
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else:
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out.append(_script(body, _SUBSCRIPT, _SUB_CHARS, '_'))
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elif ch == '{':
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# آکولادِ گروه‌بندیِ LaTeX (بعد از پاک شدنِ دستورِ صاحبش)
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body, i = _read_group(s, i)
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out.append(_convert(body))
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elif ch == '&':
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i += 1
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else:
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out.append(ch)
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i += 1
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return ''.join(out)
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# \( … \) و \[ … \] و $$ … $$ و $ … $ — محتوا تبدیل و جداکننده حذف می‌شود.
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_MATH_SPANS = re.compile(
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r'\\\[(.+?)\\\]|\\\((.+?)\\\)|\$\$(.+?)\$\$|(?<![\w$])\$([^$\n]+?)\$(?!\w)',
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re.DOTALL,
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)
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# LaTeXِ بی‌جداکننده که مدل گاهی وسطِ متن می‌نویسد: \frac{..}{..}، x^{2}، \sqrt{..}
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_BARE_LATEX = re.compile(r'\\[A-Za-z{}]|[\^_]\{|(?<=[\w)])\^\d')
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def _math_span(match: re.Match) -> str:
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body = next(g for g in match.groups() if g is not None)
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# بلوکِ نمایشی را مدل خودش در خطِ جدا می‌نویسد؛ خطِ خالیِ اضافه نمی‌سازیم.
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if '\\\\' in body: # چندخطی (\\ یا cases/aligned)
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return '\n'.join(' '.join(line.split()) for line in _convert(body).strip().split('\n'))
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return ' '.join(_convert(body).split())
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def _strip_markdown(text: str) -> str:
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lines = []
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for line in text.split('\n'):
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stripped = line.strip()
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if re.fullmatch(r'\|?\s*:?-{2,}:?\s*(\|\s*:?-{2,}:?\s*)*\|?', stripped):
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continue # خطِ جداکننده‌ی جدولِ markdown
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if stripped.startswith('|') and stripped.endswith('|') and stripped.count('|') >= 2:
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cells = [c.strip() for c in stripped.strip('|').split('|')]
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line = ' | '.join(cells)
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line = re.sub(r'^\s{0,3}#{1,6}\s+', '', line)
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line = re.sub(r'^(\s*)[-*]\s+', r'\1• ', line)
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line = re.sub(r'^\s*(-{3,}|\*{3,}|_{3,})\s*$', '', line)
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line = re.sub(r'\*\*(.+?)\*\*', r'\1', line)
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line = re.sub(r'__(.+?)__', r'\1', line)
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line = line.replace('`', '')
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lines.append(line.strip()) # تورفتگی در حبابِ راست‌به‌چپ معنایی ندارد
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return '\n'.join(lines)
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def to_plain(text: str, *, fraction_word: bool = False) -> str:
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"""
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پاسخِ مدل → متنِ ساده‌ی قابلِ خواندن روی گوشی.
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fraction_word: کسرِ LaTeX به‌صورتِ «a بر b» (برای دبستان) به‌جای a/b.
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"""
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if not text:
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return text
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token = _FRACTION_WORD.set(fraction_word)
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try:
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return _to_plain(text)
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finally:
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_FRACTION_WORD.reset(token)
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def _to_plain(text: str) -> str:
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text = _MATH_SPANS.sub(_math_span, text)
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if _BARE_LATEX.search(text):
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text = '\n'.join(_convert(line) if _BARE_LATEX.search(line) else line
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for line in text.split('\n'))
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text = _strip_markdown(text)
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text = re.sub(r'[ \t]+\n', '\n', text)
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text = re.sub(r'\n{3,}', '\n\n', text)
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return text.strip()
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class StreamSanitizer:
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"""
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همان to_plain برای پاسخِ استریمی. یک دستورِ LaTeX ممکن است بینِ دو تکه‌ی
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استریم نصف شود (`\\fr` + `ac{1}{2}`)، پس متن تا پایانِ هر خط نگه داشته و
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خط‌به‌خط تبدیل می‌شود؛ یک بلوکِ `\\[ … \\]` چندخطی هم تا بسته شدنش نگه
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داشته می‌شود.
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"""
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def __init__(self, *, fraction_word: bool = False):
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self._fraction_word = fraction_word
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self._buffer = ''
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self._emitted_any = False
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self._newlines = 0 # خط‌های خالیِ معلق؛ مثلِ to_plain حداکثر دوتا
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def _ready_cut(self) -> int:
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cut = self._buffer.rfind('\n')
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if cut == -1:
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return -1
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head = self._buffer[:cut + 1]
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# بلوکِ نمایشیِ باز را نصفه نفرست.
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if head.count('\\[') > head.count('\\]') or head.count('$$') % 2:
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return -1
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return cut + 1
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def feed(self, delta: str) -> str:
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self._buffer += delta
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cut = self._ready_cut()
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if cut == -1:
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return ''
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head, self._buffer = self._buffer[:cut], self._buffer[cut:]
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return self._emit(head, final=False)
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def flush(self) -> str:
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head, self._buffer = self._buffer, ''
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return self._emit(head, final=True)
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def _emit(self, chunk: str, *, final: bool) -> str:
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plain = to_plain(chunk, fraction_word=self._fraction_word)
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if not plain:
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# خطِ واقعاً خالی خطِ خالی است؛ خطی که محتوایش حذف شد (جداکننده‌ی
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# جدول) مثلِ to_plain هیچ ردی نمی‌گذارد.
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if not chunk.strip():
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self._newlines += chunk.count('\n')
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return ''
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leading = len(chunk) - len(chunk.lstrip('\n'))
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prefix = '\n' * min(self._newlines + leading, 2) if self._emitted_any else ''
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self._emitted_any = True
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self._newlines = 0 if final else len(chunk) - len(chunk.rstrip('\n'))
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return prefix + plain
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Reference in New Issue
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