"""Parser for agent-emitted equations of motion.

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