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RHS is parsed via Python's ``ast`` module, then walked by a whitelist visitor
that only permits Constant / Name / UnaryOp (+/-) / BinOp (+ - * / **) /
Call (bare allowed-function name, no kwargs). Anything else — Attribute,
Subscript, Lambda, IfExp, keyword args, etc. — raises ParseError by
construction. We never call sympify on raw text, so there is no eval stage
that can crash the trainer with an AttributeError.
Pre-transforms before AST parse:
- ``^`` → ``**`` (physics power notation)
- ``dx/dt`` / bare ``dx`` → ``vx`` when the system pairs x with vx
"""
from __future__ import annotations
import ast
import re
import sympy as sp
from pydantic import BaseModel, ConfigDict
class ParseError(ValueError):
"""Raised when the agent's text payload violates the equation grammar."""
ALLOWED_FUNCTIONS: dict[str, sp.Function] = {
"sin": sp.sin,
"cos": sp.cos,
"tan": sp.tan,
"exp": sp.exp,
"log": sp.log,
"sqrt": sp.sqrt,
"abs": sp.Abs,
"Abs": sp.Abs,
}
def _build_grammar_hint() -> str:
funcs = sorted({name.lower() for name in ALLOWED_FUNCTIONS})
return (
"The 'equation' field is an infix ODE in plain ASCII. "
"LHS form: 'dN<var>/dtN' where N is 1 or 2 (omit N for first "
"order, e.g. 'dy/dt' or 'd2y/dt2'). "
"RHS uses operators + - * / ** (or ^ for power), parentheses, "
"the state variables listed under STATE_VARIABLES, and any "
"names you declare in 'params'. "
f"Allowed functions: {' '.join(funcs)}. "
"Velocity convention: when STATE_VARIABLES lists both 'x' and 'vx' "
"(or 'y'/'vy', etc.), use the 'vx' name on the RHS to refer to the "
"first time-derivative of x. The aliases 'dx/dt' and bare 'dx' are "
"also accepted for that case. The system is autonomous: time 't' is "
"not a valid RHS symbol. "
"No LaTeX, no \\frac, no array indexing, no library prefixes "
"(write 'sqrt(x)', not 'np.sqrt(x)'), no keyword arguments. "
"Working examples appear in the HISTORY block of each subsequent turn."
)
GRAMMAR_HINT: str = _build_grammar_hint()
_LHS_PATTERN = re.compile(
r"""
^\s*
d(?P<order>\d*)
(?P<var>[A-Za-z_][A-Za-z0-9_]*)
/
d t
(?P<order2>\d*)
\s*$
""",
re.VERBOSE,
)
_BIN_OP_TO_SYMPY: dict[type, "callable"] = {
ast.Add: lambda a, b: a + b,
ast.Sub: lambda a, b: a - b,
ast.Mult: lambda a, b: a * b,
ast.Div: lambda a, b: a / b,
ast.Pow: lambda a, b: a**b,
}
class Equation(BaseModel):
model_config = ConfigDict(frozen=True, arbitrary_types_allowed=True)
var: str
order: int
rhs: sp.Expr
class ParsedEquation(BaseModel):
model_config = ConfigDict(frozen=True, arbitrary_types_allowed=True)
equations: tuple[Equation, ...]
free_symbols: frozenset[str]
operator_count: int
def parse_equation(
text: str,
state_variables: tuple[str, ...],
parameter_names: frozenset[str],
) -> ParsedEquation:
"""Parse and validate the agent's equation payload.
Only ParseError ever escapes — callers convert it to r_format=0.
"""
if not text or not text.strip():
raise ParseError("Empty equation payload.")
raw_equations = _split_equations(text)
if not raw_equations:
raise ParseError("No equations found in payload.")
allowed_symbols = frozenset(state_variables) | parameter_names
parsed: list[Equation] = []
free_symbol_names: set[str] = set()
operator_count = 0
for raw in raw_equations:
eq = _parse_one(raw, allowed_symbols, state_variables)
parsed.append(eq)
free_symbol_names.update(s.name for s in eq.rhs.free_symbols)
operator_count += _count_operators(eq.rhs)
return ParsedEquation(
equations=tuple(parsed),
free_symbols=frozenset(free_symbol_names),
operator_count=operator_count,
)
def _split_equations(text: str) -> list[str]:
parts = re.split(r"[;\n]+", text)
return [p.strip() for p in parts if p.strip()]
def _parse_one(
raw: str,
allowed_symbols: frozenset[str],
state_variables: tuple[str, ...],
) -> Equation:
if "=" not in raw:
raise ParseError(f"Equation has no '=' sign: {raw!r}")
lhs_text, rhs_text = raw.split("=", 1)
var, order = _parse_lhs(lhs_text)
rhs_expr = _parse_rhs(rhs_text, allowed_symbols, state_variables)
return Equation(var=var, order=order, rhs=rhs_expr)
def _parse_lhs(lhs: str) -> tuple[str, int]:
match = _LHS_PATTERN.match(lhs)
if not match:
raise ParseError(
f"Cannot parse LHS {lhs!r}. Expected 'dN<var>/dtN' where N is "
"1 or 2 (or empty for first order)."
)
order_top = match.group("order")
order_bot = match.group("order2")
var = match.group("var")
if order_top != order_bot:
raise ParseError(
f"LHS order mismatch in {lhs!r}: top order {order_top!r} vs "
f"bottom order {order_bot!r}."
)
if order_top == "":
order = 1
elif order_top in {"1", "2"}:
order = int(order_top)
else:
raise ParseError(f"Only orders 1 and 2 are supported. Got {order_top!r}.")
return var, order
def _parse_rhs(
rhs: str,
allowed_symbols: frozenset[str],
state_variables: tuple[str, ...],
) -> sp.Expr:
rhs = rhs.strip()
if not rhs:
raise ParseError("Empty RHS.")
rhs = rhs.replace("^", "**")
rhs = _apply_velocity_alias(rhs, state_variables)
try:
tree = ast.parse(rhs, mode="eval")
except SyntaxError as exc:
raise ParseError(
f"Syntax error in RHS {rhs!r}: {exc.msg}. "
"Expected an infix expression like '-k*x + c*vx'."
) from exc
return _ast_to_sympy(tree.body, allowed_symbols, state_variables)
def _ast_to_sympy(
node: ast.AST,
allowed_symbols: frozenset[str],
state_variables: tuple[str, ...],
) -> sp.Expr:
if isinstance(node, ast.Constant):
if isinstance(node.value, bool) or not isinstance(node.value, (int, float)):
raise ParseError(
f"Only numeric literals allowed on RHS; got "
f"{node.value!r} ({type(node.value).__name__})."
)
return sp.Number(node.value)
if isinstance(node, ast.Name):
return _name_to_sympy(node.id, allowed_symbols, state_variables)
if isinstance(node, ast.UnaryOp):
operand = _ast_to_sympy(node.operand, allowed_symbols, state_variables)
if isinstance(node.op, ast.UAdd):
return +operand
if isinstance(node.op, ast.USub):
return -operand
raise ParseError(
f"Unsupported unary operator {type(node.op).__name__}. "
"Allowed: + (positive), - (negation)."
)
if isinstance(node, ast.BinOp):
op_fn = _BIN_OP_TO_SYMPY.get(type(node.op))
if op_fn is None:
raise ParseError(
f"Unsupported binary operator {type(node.op).__name__}. "
"Allowed: + - * / ** (also '^' as a power synonym)."
)
left = _ast_to_sympy(node.left, allowed_symbols, state_variables)
right = _ast_to_sympy(node.right, allowed_symbols, state_variables)
return op_fn(left, right)
if isinstance(node, ast.Call):
return _call_to_sympy(node, allowed_symbols, state_variables)
if isinstance(node, ast.Attribute):
raise ParseError(
"Attribute access is not allowed in equation RHS "
f"(saw '.{node.attr}'). Use bare function names like "
"'sqrt(x)' or 'sin(theta)', not 'np.sqrt(x)'."
)
if isinstance(node, ast.Subscript):
raise ParseError(
"Array indexing is not allowed in equation RHS. "
"Use named scalars declared in 'params'."
)
if isinstance(node, ast.Compare):
raise ParseError(
"Comparisons (==, <, >, etc.) are not allowed in equation RHS."
)
if isinstance(node, ast.BoolOp):
raise ParseError(
"Boolean operators ('and', 'or') are not allowed in equation RHS."
)
if isinstance(node, ast.IfExp):
raise ParseError(
"Conditional expressions ('a if cond else b') are not allowed in "
"equation RHS."
)
if isinstance(node, ast.Lambda):
raise ParseError("Lambda expressions are not allowed in equation RHS.")
if isinstance(node, (ast.Tuple, ast.List, ast.Set, ast.Dict)):
raise ParseError(
f"Collection literal ({type(node).__name__}) is not allowed in "
"equation RHS."
)
raise ParseError(
f"Unsupported expression construct {type(node).__name__}. "
"The grammar accepts: numeric literals, allowed identifiers, "
f"+ - * / **, parentheses, and {sorted(ALLOWED_FUNCTIONS)}."
)
def _name_to_sympy(
name: str,
allowed_symbols: frozenset[str],
state_variables: tuple[str, ...],
) -> sp.Symbol:
if name in ALLOWED_FUNCTIONS:
raise ParseError(
f"{name!r} is a function and must be called with parentheses, "
f"e.g. {name}(x)."
)
if name not in allowed_symbols:
hint = _explain_unknown_symbol(name, state_variables)
suffix = f" {hint}" if hint else ""
raise ParseError(
f"Unknown symbol {name!r}; allowed {sorted(allowed_symbols)!r}."
f"{suffix}"
)
return sp.Symbol(name)
def _call_to_sympy(
node: ast.Call,
allowed_symbols: frozenset[str],
state_variables: tuple[str, ...],
) -> sp.Expr:
if node.keywords:
raise ParseError(
"Keyword arguments are not allowed in function calls "
"(e.g. 'sin(theta=0.1)'). Pass positional arguments only."
)
for arg in node.args:
if isinstance(arg, ast.Starred):
raise ParseError("Star-arg / unpacking ('*args') is not allowed.")
if isinstance(node.func, ast.Attribute):
raise ParseError(
"Attribute access is not allowed in equation RHS "
f"(saw '.{node.func.attr}'). Use bare function names like "
"'sqrt(x)' or 'sin(theta)', not 'np.sqrt(x)'."
)
if not isinstance(node.func, ast.Name):
raise ParseError(
"Only direct calls to named functions are allowed. "
f"Use one of {sorted(ALLOWED_FUNCTIONS)}, not a computed-name call."
)
func_name = node.func.id
if func_name not in ALLOWED_FUNCTIONS:
raise ParseError(
f"Unknown function {func_name!r}; "
f"allowed: {sorted(ALLOWED_FUNCTIONS)}."
)
args = [_ast_to_sympy(a, allowed_symbols, state_variables) for a in node.args]
return ALLOWED_FUNCTIONS[func_name](*args)
def _apply_velocity_alias(rhs: str, state_variables: tuple[str, ...]) -> str:
aliases = _velocity_aliases(state_variables)
if not aliases:
return rhs
out = rhs
for var, velocity in aliases:
slash_pattern = rf"\bd{re.escape(var)}\s*/\s*dt\b"
out = re.sub(slash_pattern, velocity, out)
bare_pattern = rf"\bd{re.escape(var)}\b"
out = re.sub(bare_pattern, velocity, out)
return out
def _velocity_aliases(state_variables: tuple[str, ...]) -> list[tuple[str, str]]:
state_set = set(state_variables)
out: list[tuple[str, str]] = []
for var in state_variables:
if not var or var.startswith(("d", "v")):
continue
velocity = f"v{var}"
if velocity in state_set:
out.append((var, velocity))
return out
def _explain_unknown_symbol(name: str, state_variables: tuple[str, ...]) -> str:
state_set = set(state_variables)
if name == "t":
return (
"'t' is not allowed — the equation must be autonomous "
"(express forces via state variables only, no explicit time)."
)
if name.startswith("d") and len(name) > 1:
base = name[1:]
velocity = f"v{base}"
if velocity in state_set:
return (
f"Did you mean '{velocity}'? "
f"Use '{velocity}' for the velocity of '{base}'."
)
if base in state_set:
return (
f"'{name}' looks like a derivative; this system has no "
f"separate velocity name, write '{base}' on the RHS."
)
return ""
def _count_operators(expr: sp.Expr) -> int:
count = 0
for node in sp.preorder_traversal(expr):
if not isinstance(node, (sp.Symbol, sp.Number)):
count += 1
return count
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