rssn 0.2.9

#![allow(clippy::wildcard_in_or_patterns)]

use std::sync::Arc;

use nom::IResult;
use nom::Parser;
use nom::branch::alt;
use nom::bytes::complete::tag;
use nom::character::complete::alpha1;
use nom::character::complete::char;
use nom::character::complete::digit1;
use nom::character::complete::i64 as nom_i64;
use nom::character::complete::multispace0;
use nom::character::complete::multispace1;
use nom::combinator::map;
use nom::combinator::map_res;
use nom::combinator::opt;
use nom::combinator::recognize;
use nom::multi::fold_many0;
use nom::multi::separated_list1;
use nom::sequence::delimited;
use nom::sequence::pair;
use nom::sequence::preceded;
use num_bigint::BigInt;
use num_rational::BigRational;

use crate::symbolic::core::Expr;
use crate::symbolic::core::PathType;

/// Checks if a character is a valid identifier character.
pub(crate) fn is_identifier_char(c: char) -> bool {
    c.is_alphanumeric() || c == '_' || c == '\''
}

pub(crate) fn identifier_name(input: &str) -> IResult<&str, &str> {
    recognize(pair(
        alpha1,
        // nom::multi::many0(nom::character::complete::alphanumeric1)
        nom::bytes::complete::take_while(is_identifier_char),
    ))
    .parse(input)
}

pub(crate) fn parse_rational_structure(input: &str) -> IResult<&str, ()> {
    let (input, _) = nom_i64.parse(input)?;

    let (input, _) = char('/').parse(input)?;

    let (input, _) = nom_i64.parse(input)?;

    Ok((input, ()))
}

// Entry point for parsing an expression
/// Parses a string into a symbolic expression.
///
/// # Arguments
/// * `input` - The string to parse.
///
/// # Returns
/// A `Result` containing the remaining input and the parsed `Expr`.
///
/// # Errors
/// Returns a `nom::Err` if the input cannot be parsed as a valid expression.
pub fn parse_expr(input: &str) -> IResult<&str, Expr> {
    expr.parse(input)
}

// expr = comparison_expr
pub(crate) fn expr(input: &str) -> IResult<&str, Expr> {
    comparison_expr.parse(input)
}

// comparison_expr = additive_expr { ("=" | "<" | ">" | "<=" | ">=") additive_expr }
pub(crate) fn comparison_expr(input: &str) -> IResult<&str, Expr> {
    let (input, init) = additive_expr.parse(input)?;

    fold_many0(
        pair(
            alt((tag("="), tag("<="), tag(">="), tag("<"), tag(">"))),
            additive_expr,
        ),
        move || init.clone(),
        |acc, (op, val)| {
            match op {
                | "=" => Expr::Eq(Arc::new(acc), Arc::new(val)),
                | "<" => Expr::Lt(Arc::new(acc), Arc::new(val)),
                | ">" => Expr::Gt(Arc::new(acc), Arc::new(val)),
                | "<=" => Expr::Le(Arc::new(acc), Arc::new(val)),
                | ">=" => Expr::Ge(Arc::new(acc), Arc::new(val)),
                | _ => unreachable!(),
            }
        },
    )
    .parse(input)
}

// additive_expr = term { ("+" | "-") term }
pub(crate) fn additive_expr(input: &str) -> IResult<&str, Expr> {
    let (input, init) = term.parse(input)?;

    fold_many0(
        pair(alt((char('+'), char('-'))), term),
        move || init.clone(),
        |acc, (op, val)| {
            if op == '+' {
                Expr::Add(Arc::new(acc), Arc::new(val))
            } else {
                Expr::Sub(Arc::new(acc), Arc::new(val))
            }
        },
    )
    .parse(input)
}

// term = factor { ("*" | "/") factor }
pub(crate) fn term(input: &str) -> IResult<&str, Expr> {
    let (input, init) = factor.parse(input)?;

    fold_many0(
        pair(alt((char('*'), char('/'))), factor),
        move || init.clone(),
        |acc, (op, val)| {
            if op == '*' {
                Expr::Mul(Arc::new(acc), Arc::new(val))
            } else {
                Expr::Div(Arc::new(acc), Arc::new(val))
            }
        },
    )
    .parse(input)
}

// factor = unary | "(" expr ")"
pub(crate) fn factor(input: &str) -> IResult<&str, Expr> {
    delimited(multispace0, alt((unary, parenthesized_expr)), multispace0).parse(input)
}

// unary = ["-"] ["not"] power
pub(crate) fn unary(input: &str) -> IResult<&str, Expr> {
    // println!("in unary staring");
    // println!("{}",input);
    let original_input = input;

    let (input, neg) = opt(char('-')).parse(input)?;

    let (input, not_op) = opt(preceded(tag("not"), multispace1)).parse(input)?;

    // println!("{}",input);
    ////println!("{}",neg);
    if neg.is_some() {
        if let Ok((_, ())) = nom::combinator::peek(parse_rational_structure).parse(input) {
            // If it looks like a rational number, we need to parse it differently
            // to handle negative rationals properly
            return parse_rational(original_input);
        }
    }

    let (input, mut expr) = power.parse(input)?;

    // println!("in unary start again");
    if neg.is_some() {
        // Special case: -Infinity should be NegativeInfinity, not Neg(Infinity)
        if matches!(expr, Expr::Infinity) {
            expr = Expr::NegativeInfinity;
        } else {
            expr = Expr::Neg(Arc::new(expr));
        }
    }

    if not_op.is_some() {
        expr = Expr::Not(Arc::new(expr));
    }

    Ok((input, expr))
}

// power = atom [ "^" unary ] [ "!" ]
pub(crate) fn power(input: &str) -> IResult<&str, Expr> {
    let (input, base) = atom.parse(input)?;

    let (input, power_expr) = opt(preceded(char('^'), unary)).parse(input)?;

    let (input, factorial_op) = opt(char('!')).parse(input)?;

    let mut result = base;

    if let Some(p) = power_expr {
        result = Expr::Power(Arc::new(result), Arc::new(p));
    }

    if factorial_op.is_some() {
        result = Expr::Factorial(Arc::new(result));
    }

    Ok((input, result))
}

pub(crate) fn parse_bigint(input: &str) -> IResult<&str, Expr> {
    map(nom_i64, |n| Expr::BigInt(BigInt::from(n))).parse(input)
}

// pub(crate) fn parse_rational(input: &str) -> IResult<&str, Expr> {
//     //println!("parse_rational");
//     map(pair(nom_i64, preceded(char('/'), nom_i64)), |(num, den)| {
//         Expr::Rational(BigRational::new(BigInt::from(num), BigInt::from(den)))
//     }).parse(input)
// }
// ----------------------------------------------------

pub(crate) fn parse_rational(input: &str) -> IResult<&str, Expr> {
    // println!("parse_rational start");
    let (input, sign) = opt(char('-')).parse(input)?;

    // println!("{}", input);
    let (input, numerator) = nom_i64.parse(input)?;

    // println!("{}", numerator);
    let (input, denominator) = preceded(char('/'), nom_i64).parse(input)?;

    // println!("{}", denominator);
    let final_numerator = if sign.is_some() {
        // println!("matched -");
        // println!("{}", -numerator);
        BigInt::from(-numerator)
    } else {
        // println!("not matched -");
        BigInt::from(numerator)
    };

    // println!("{}", final_numerator);
    // println!("parse_rational end");

    if denominator <= 0 {
        return nom::combinator::fail().parse(input);
    }

    // println!("input:");
    // println!("{}", input);
    // println!("output:");
    // println!("{}", Expr::Rational(BigRational::new(final_numerator.clone(), BigInt::from(denominator))));
    Ok((
        input,
        Expr::Rational(BigRational::new(final_numerator, BigInt::from(denominator))),
        // Expr::Rational(BigRational::new(BigInt::from(-3), BigInt::from(4))),
    ))
}

// ----------------------------------------------------

pub(crate) fn parse_boolean(input: &str) -> IResult<&str, Expr> {
    alt((
        map(tag("true"), |_| Expr::Boolean(true)),
        map(tag("false"), |_| Expr::Boolean(false)),
    ))
    .parse(input)
}

pub(crate) fn parse_infinity(input: &str) -> IResult<&str, Expr> {
    map(tag("Infinity"), |_| Expr::Infinity).parse(input)
}

pub(crate) fn parse_negative_infinity(input: &str) -> IResult<&str, Expr> {
    map(tag("-Infinity"), |_| Expr::NegativeInfinity).parse(input)
}

pub(crate) fn parse_string_literal(input: &str) -> IResult<&str, Expr> {
    map(
        delimited(
            char('"'),
            nom::bytes::complete::take_while(|c| c != '"'),
            char('"'),
        ),
        |s: &str| Expr::Variable(s.to_string()),
    )
    .parse(input)
}

pub(crate) fn parse_numeric_literals(input: &str) -> IResult<&str, Expr> {
    // println!("in numeric");
    alt((parse_rational, parse_number, parse_bigint)).parse(input)
    // alt((parse_bigint, parse_number)).parse(input)
}

pub(crate) fn parse_boolean_and_infinities(input: &str) -> IResult<&str, Expr> {
    alt((parse_boolean, parse_infinity, parse_negative_infinity)).parse(input)
}

#[allow(clippy::too_many_lines)]
pub(crate) fn parse_function_call(input: &str) -> IResult<&str, Expr> {
    // println!("parse function call");
    // let (input, func_name) = alpha1.parse(input)?;
    let (input, func_name) = identifier_name.parse(input)?;

    // println!("Parsed function name: {}", func_name);
    let (input, args) = delimited(
        char('('),
        nom::multi::separated_list0(delimited(multispace0, char(','), multispace0), expr),
        char(')'),
    )
    .parse(input)?;

    // println!("Remaining input after args: '{}'", input);
    match func_name {
        // Two-argument functions with specific names
        | "log_base" => {
            Ok((
                input,
                Expr::LogBase(Arc::new(args[0].clone()), Arc::new(args[1].clone())),
            ))
        },
        | "atan2" => {
            Ok((
                input,
                Expr::Atan2(Arc::new(args[0].clone()), Arc::new(args[1].clone())),
            ))
        },
        | "falling_factorial" => {
            Ok((
                input,
                Expr::FallingFactorial(Arc::new(args[0].clone()), Arc::new(args[1].clone())),
            ))
        },
        | "rising_factorial" => {
            Ok((
                input,
                Expr::RisingFactorial(Arc::new(args[0].clone()), Arc::new(args[1].clone())),
            ))
        },
        | "kronecker_delta" => {
            Ok((
                input,
                Expr::KroneckerDelta(Arc::new(args[0].clone()), Arc::new(args[1].clone())),
            ))
        },
        | "matrix_mul" => {
            Ok((
                input,
                Expr::MatrixMul(Arc::new(args[0].clone()), Arc::new(args[1].clone())),
            ))
        },
        | "matrix_vec_mul" => {
            Ok((
                input,
                Expr::MatrixVecMul(Arc::new(args[0].clone()), Arc::new(args[1].clone())),
            ))
        },
        | "quantity_with_value" => {
            Ok((
                input,
                Expr::QuantityWithValue(
                    Arc::new(args[0].clone()),
                    match &args[1] {
                        | Expr::Variable(s) => s.clone(),
                        | _ => return nom::combinator::fail().parse(input),
                    },
                ),
            ))
        },

        // Single-argument functions
        | "sin" => Ok((input, Expr::Sin(Arc::new(args[0].clone())))),
        | "cos" => Ok((input, Expr::Cos(Arc::new(args[0].clone())))),
        | "tan" => Ok((input, Expr::Tan(Arc::new(args[0].clone())))),
        | "log" => Ok((input, Expr::Log(Arc::new(args[0].clone())))),
        | "exp" => Ok((input, Expr::Exp(Arc::new(args[0].clone())))),
        | "sqrt" => Ok((input, Expr::Sqrt(Arc::new(args[0].clone())))),
        | "abs" => Ok((input, Expr::Abs(Arc::new(args[0].clone())))),
        | "sec" => Ok((input, Expr::Sec(Arc::new(args[0].clone())))),
        | "csc" => Ok((input, Expr::Csc(Arc::new(args[0].clone())))),
        | "cot" => Ok((input, Expr::Cot(Arc::new(args[0].clone())))),
        | "asin" => Ok((input, Expr::ArcSin(Arc::new(args[0].clone())))),
        | "acos" => Ok((input, Expr::ArcCos(Arc::new(args[0].clone())))),
        | "atan" => Ok((input, Expr::ArcTan(Arc::new(args[0].clone())))),
        | "asec" => Ok((input, Expr::ArcSec(Arc::new(args[0].clone())))),
        | "acsc" => Ok((input, Expr::ArcCsc(Arc::new(args[0].clone())))),
        | "acot" => Ok((input, Expr::ArcCot(Arc::new(args[0].clone())))),
        | "sinh" => Ok((input, Expr::Sinh(Arc::new(args[0].clone())))),
        | "cosh" => Ok((input, Expr::Cosh(Arc::new(args[0].clone())))),
        | "tanh" => Ok((input, Expr::Tanh(Arc::new(args[0].clone())))),
        | "sech" => Ok((input, Expr::Sech(Arc::new(args[0].clone())))),
        | "csch" => Ok((input, Expr::Csch(Arc::new(args[0].clone())))),
        | "coth" => Ok((input, Expr::Coth(Arc::new(args[0].clone())))),
        | "asinh" => Ok((input, Expr::ArcSinh(Arc::new(args[0].clone())))),
        | "acosh" => Ok((input, Expr::ArcCosh(Arc::new(args[0].clone())))),
        | "atanh" => Ok((input, Expr::ArcTanh(Arc::new(args[0].clone())))),
        | "asech" => Ok((input, Expr::ArcSech(Arc::new(args[0].clone())))),
        | "acsch" => Ok((input, Expr::ArcCsch(Arc::new(args[0].clone())))),
        | "acoth" => Ok((input, Expr::ArcCoth(Arc::new(args[0].clone())))),
        | "gamma" => Ok((input, Expr::Gamma(Arc::new(args[0].clone())))),
        | "erf" => Ok((input, Expr::Erf(Arc::new(args[0].clone())))),
        | "erfc" => Ok((input, Expr::Erfc(Arc::new(args[0].clone())))),
        | "erfi" => Ok((input, Expr::Erfi(Arc::new(args[0].clone())))),
        | "zeta" => Ok((input, Expr::Zeta(Arc::new(args[0].clone())))),
        | "digamma" => Ok((input, Expr::Digamma(Arc::new(args[0].clone())))),
        | "floor" => Ok((input, Expr::Floor(Arc::new(args[0].clone())))),
        | "is_prime" => Ok((input, Expr::IsPrime(Arc::new(args[0].clone())))),
        | "transpose" => Ok((input, Expr::Transpose(Arc::new(args[0].clone())))),
        | "inverse" => Ok((input, Expr::Inverse(Arc::new(args[0].clone())))),
        | "general_solution" => Ok((input, Expr::GeneralSolution(Arc::new(args[0].clone())))),
        | "particular_solution" => Ok((input, Expr::ParticularSolution(Arc::new(args[0].clone())))),
        | "boundary" => Ok((input, Expr::Boundary(Arc::new(args[0].clone())))),

        // Two-argument functions
        | "binomial" => {
            Ok((
                input,
                Expr::Binomial(Arc::new(args[0].clone()), Arc::new(args[1].clone())),
            ))
        },
        | "permutation" => {
            Ok((
                input,
                Expr::Permutation(Arc::new(args[0].clone()), Arc::new(args[1].clone())),
            ))
        },
        | "combination" => {
            Ok((
                input,
                Expr::Combination(Arc::new(args[0].clone()), Arc::new(args[1].clone())),
            ))
        },
        | "beta" => {
            Ok((
                input,
                Expr::Beta(Arc::new(args[0].clone()), Arc::new(args[1].clone())),
            ))
        },
        | "besselj" => {
            Ok((
                input,
                Expr::BesselJ(Arc::new(args[0].clone()), Arc::new(args[1].clone())),
            ))
        },
        | "bessely" => {
            Ok((
                input,
                Expr::BesselY(Arc::new(args[0].clone()), Arc::new(args[1].clone())),
            ))
        },
        | "legendrep" => {
            Ok((
                input,
                Expr::LegendreP(Arc::new(args[0].clone()), Arc::new(args[1].clone())),
            ))
        },
        | "laguerrel" => {
            Ok((
                input,
                Expr::LaguerreL(Arc::new(args[0].clone()), Arc::new(args[1].clone())),
            ))
        },
        | "hermiteh" => {
            Ok((
                input,
                Expr::HermiteH(Arc::new(args[0].clone()), Arc::new(args[1].clone())),
            ))
        },
        | "xor" => {
            Ok((
                input,
                Expr::Xor(Arc::new(args[0].clone()), Arc::new(args[1].clone())),
            ))
        },
        | "implies" => {
            Ok((
                input,
                Expr::Implies(Arc::new(args[0].clone()), Arc::new(args[1].clone())),
            ))
        },
        | "equivalent" => {
            Ok((
                input,
                Expr::Equivalent(Arc::new(args[0].clone()), Arc::new(args[1].clone())),
            ))
        },
        | "gcd" => {
            Ok((
                input,
                Expr::Gcd(Arc::new(args[0].clone()), Arc::new(args[1].clone())),
            ))
        },
        | "mod" => {
            Ok((
                input,
                Expr::Mod(Arc::new(args[0].clone()), Arc::new(args[1].clone())),
            ))
        },
        | "complex" => {
            Ok((
                input,
                Expr::Complex(Arc::new(args[0].clone()), Arc::new(args[1].clone())),
            ))
        },
        | "apply" => {
            Ok((
                input,
                Expr::Apply(Arc::new(args[0].clone()), Arc::new(args[1].clone())),
            ))
        },
        | "max" => {
            Ok((
                input,
                Expr::Max(Arc::new(args[0].clone()), Arc::new(args[1].clone())),
            ))
        },
        | "volume_integral" => {
            Ok((
                input,
                Expr::VolumeIntegral {
                    scalar_field: Arc::new(args[0].clone()),
                    volume: Arc::new(args[1].clone()),
                },
            ))
        },
        | "surface_integral" => {
            Ok((
                input,
                Expr::SurfaceIntegral {
                    vector_field: Arc::new(args[0].clone()),
                    surface: Arc::new(args[1].clone()),
                },
            ))
        },
        | "parametric_solution" => {
            Ok((
                input,
                Expr::ParametricSolution {
                    x: Arc::new(args[0].clone()),
                    y: Arc::new(args[1].clone()),
                },
            ))
        },

        // N-ary functions
        | "and" => Ok((input, Expr::And(args))),
        | "or" => Ok((input, Expr::Or(args))),
        | "union" => Ok((input, Expr::Union(args))),
        | "polynomial" => Ok((input, Expr::Polynomial(args))),
        | "vector" => Ok((input, Expr::Vector(args))),
        | "tuple" => Ok((input, Expr::Tuple(args))),
        | "system" => Ok((input, Expr::System(args))),
        | "solutions" => Ok((input, Expr::Solutions(args))),

        // Functions with special parsing
        | "derivative" => {
            Ok((
                input,
                Expr::Derivative(
                    Arc::new(args[0].clone()),
                    match &args[1] {
                        | Expr::Variable(s) => s.clone(),
                        | _ => return nom::combinator::fail().parse(input),
                    },
                ),
            ))
        },
        | "convergence_analysis" => {
            Ok((
                input,
                Expr::ConvergenceAnalysis(
                    Arc::new(args[0].clone()),
                    match &args[1] {
                        | Expr::Variable(s) => s.clone(),
                        | _ => return nom::combinator::fail().parse(input),
                    },
                ),
            ))
        },
        | "solve" => {
            Ok((
                input,
                Expr::Solve(
                    Arc::new(args[0].clone()),
                    match &args[1] {
                        | Expr::Variable(s) => s.clone(),
                        | _ => return nom::combinator::fail().parse(input),
                    },
                ),
            ))
        },
        | "derivative_n" => {
            Ok((
                input,
                Expr::DerivativeN(
                    Arc::new(args[0].clone()),
                    match &args[1] {
                        | Expr::Variable(s) => s.clone(),
                        | _ => return nom::combinator::fail().parse(input),
                    },
                    Arc::new(args[2].clone()),
                ),
            ))
        },
        | "limit" => {
            Ok((
                input,
                Expr::Limit(
                    Arc::new(args[0].clone()),
                    match &args[1] {
                        | Expr::Variable(s) => s.clone(),
                        | _ => return nom::combinator::fail().parse(input),
                    },
                    Arc::new(args[2].clone()),
                ),
            ))
        },
        | "substitute" => {
            Ok((
                input,
                Expr::Substitute(
                    Arc::new(args[0].clone()),
                    match &args[1] {
                        | Expr::Variable(s) => s.clone(),
                        | _ => return nom::combinator::fail().parse(input),
                    },
                    Arc::new(args[2].clone()),
                ),
            ))
        },
        | "predicate" | _ => {
            Ok((
                input,
                Expr::Predicate {
                    name: func_name.to_string(),
                    args,
                },
            ))
        },
    }
}

pub(crate) fn parse_matrix(input: &str) -> IResult<&str, Expr> {
    let (input, _) = tag("matrix").parse(input)?;

    let (input, _) = char('(').parse(input)?;

    let (input, rows) = delimited(
        char('['),
        separated_list1(
            delimited(multispace0, char(','), multispace0),
            delimited(
                char('['),
                separated_list1(delimited(multispace0, char(','), multispace0), expr),
                char(']'),
            ),
        ),
        char(']'),
    )
    .parse(input)?;

    let (input, _) = char(')').parse(input)?;

    Ok((input, Expr::Matrix(rows)))
}

pub(crate) fn parse_pde(input: &str) -> IResult<&str, Expr> {
    let (input, _) = tag("pde").parse(input)?;

    let (input, _) = char('(').parse(input)?;

    let (input, equation) = expr.parse(input)?;

    let (input, _) = delimited(multispace0, char(','), multispace0).parse(input)?;

    let (input, func_name) = alpha1.parse(input)?;

    let (input, _) = delimited(multispace0, char(','), multispace0).parse(input)?;

    let (input, vars_list) = delimited(
        char('['),
        separated_list1(delimited(multispace0, char(','), multispace0), alpha1),
        char(']'),
    )
    .parse(input)?;

    let (input, _) = char(')').parse(input)?;

    Ok((
        input,
        Expr::Pde {
            equation: Arc::new(equation),
            func: func_name.to_string(),
            vars: vars_list.iter().map(|s| (*s).to_string()).collect(),
        },
    ))
}

// atom = numeric_literals | boolean_and_infinities | matrix | function_call | variable | constant
pub(crate) fn parse_path_type(input: &str) -> IResult<&str, PathType> {
    alt((
        map(tag("Line"), |_| PathType::Line),
        map(tag("Circle"), |_| PathType::Circle),
        map(tag("Rectangle"), |_| PathType::Rectangle),
    ))
    .parse(input)
}

pub(crate) fn parse_path(input: &str) -> IResult<&str, Expr> {
    let (input, _) = tag("path").parse(input)?;

    let (input, _) = char('(').parse(input)?;

    let (input, path_type) = parse_path_type.parse(input)?;

    let (input, _) = delimited(multispace0, char(','), multispace0).parse(input)?;

    let (input, arg1) = expr.parse(input)?;

    let (input, _) = delimited(multispace0, char(','), multispace0).parse(input)?;

    let (input, arg2) = expr.parse(input)?;

    let (input, _) = char(')').parse(input)?;

    Ok((input, Expr::Path(path_type, Arc::new(arg1), Arc::new(arg2))))
}

pub(crate) fn parse_interval(input: &str) -> IResult<&str, Expr> {
    let (input, _) = tag("interval").parse(input)?;

    let (input, _) = char('(').parse(input)?;

    let (input, lower_bound) = expr.parse(input)?;

    let (input, _) = delimited(multispace0, char(','), multispace0).parse(input)?;

    let (input, upper_bound) = expr.parse(input)?;

    let (input, _) = delimited(multispace0, char(','), multispace0).parse(input)?;

    let (input, incl_lower) = parse_boolean.parse(input)?;

    let (input, _) = delimited(multispace0, char(','), multispace0).parse(input)?;

    let (input, incl_upper) = parse_boolean.parse(input)?;

    let (input, _) = char(')').parse(input)?;

    Ok((
        input,
        Expr::Interval(
            Arc::new(lower_bound),
            Arc::new(upper_bound),
            match incl_lower {
                | Expr::Boolean(b) => b,
                | _ => return nom::combinator::fail().parse(input),
            },
            match incl_upper {
                | Expr::Boolean(b) => b,
                | _ => return nom::combinator::fail().parse(input),
            },
        ),
    ))
}

pub(crate) fn parse_quantifier(input: &str) -> IResult<&str, Expr> {
    let (input, quantifier_type) = alt((tag("forall"), tag("exists"))).parse(input)?;

    let (input, _) = multispace1.parse(input)?;

    let (input, var_name) = alpha1.parse(input)?;

    let (input, _) = delimited(multispace0, char('.'), multispace0).parse(input)?;

    let (input, body) = expr.parse(input)?;

    match quantifier_type {
        | "forall" => Ok((input, Expr::ForAll(var_name.to_string(), Arc::new(body)))),
        | "exists" => Ok((input, Expr::Exists(var_name.to_string(), Arc::new(body)))),
        | _ => unreachable!(),
    }
}

pub(crate) fn parse_domain(input: &str) -> IResult<&str, Expr> {
    let (input, _) = tag("domain").parse(input)?;

    let (input, domain_name) = delimited(char('('), alpha1, char(')')).parse(input)?;

    Ok((input, Expr::Domain(domain_name.to_string())))
}

pub(crate) fn parse_ode(input: &str) -> IResult<&str, Expr> {
    let (input, _) = tag("ode").parse(input)?;

    let (input, _) = char('(').parse(input)?;

    let (input, equation) = expr.parse(input)?;

    let (input, _) = delimited(multispace0, char(','), multispace0).parse(input)?;

    let (input, func_name) = alpha1.parse(input)?;

    let (input, _) = delimited(multispace0, char(','), multispace0).parse(input)?;

    let (input, var_name) = alpha1.parse(input)?;

    let (input, _) = char(')').parse(input)?;

    Ok((
        input,
        Expr::Ode {
            equation: Arc::new(equation),
            func: func_name.to_string(),
            var: var_name.to_string(),
        },
    ))
}

pub(crate) fn parse_sum(input: &str) -> IResult<&str, Expr> {
    let (input, _) = tag("sum").parse(input)?;

    // println!("step1");
    // println!("{}", input);
    let (input, _) = char('(').parse(input)?;

    // println!("step2");
    // println!("{}", input);
    let (input, body) = expr.parse(input)?;

    // println!("step3");
    // println!("{}", input);
    // println!("{}", body);
    let (input, _) = delimited(multispace0, char(','), multispace0).parse(input)?;

    // println!("step4");
    // println!("{}", input);
    let (input, var) = expr.parse(input)?;

    // println!("step5");
    // println!("{}", input);
    // println!("{}", input);
    let (input, _) = delimited(multispace0, char(','), multispace0).parse(input)?;

    let (input, from) = expr.parse(input)?;

    let (input, _) = delimited(multispace0, char(','), multispace0).parse(input)?;

    let (input, to) = expr.parse(input)?;

    let (input, _) = char(')').parse(input)?;

    Ok((
        input,
        Expr::Sum {
            body: Arc::new(body),
            var: Arc::new(var),
            from: Arc::new(from),
            to: Arc::new(to),
        },
    ))
}

pub(crate) fn parse_integral(input: &str) -> IResult<&str, Expr> {
    let (input, _) = tag("integral").parse(input)?;

    let (input, _) = char('(').parse(input)?;

    let (input, integrand) = expr.parse(input)?;

    let (input, _) = delimited(multispace0, char(','), multispace0).parse(input)?;

    let (input, var) = expr.parse(input)?;

    let (input, _) = delimited(multispace0, char(','), multispace0).parse(input)?;

    let (input, lower_bound) = expr.parse(input)?;

    let (input, _) = delimited(multispace0, char(','), multispace0).parse(input)?;

    let (input, upper_bound) = expr.parse(input)?;

    let (input, _) = char(')').parse(input)?;

    Ok((
        input,
        Expr::Integral {
            integrand: Arc::new(integrand),
            var: Arc::new(var),
            lower_bound: Arc::new(lower_bound),
            upper_bound: Arc::new(upper_bound),
        },
    ))
}

pub(crate) fn parse_series_like_function(input: &str) -> IResult<&str, Expr> {
    let (input, func_name) = alt((tag("series"), tag("summation"), tag("product"))).parse(input)?;

    let (input, _) = char('(').parse(input)?;

    let (input, arg1) = expr.parse(input)?;

    let (input, _) = delimited(multispace0, char(','), multispace0).parse(input)?;

    let (input, var_name_expr) = expr.parse(input)?;

    let var_name = match var_name_expr {
        | Expr::Variable(s) => s,
        | _ => return nom::combinator::fail().parse(input),
    };

    let (input, _) = delimited(multispace0, char(','), multispace0).parse(input)?;

    let (input, arg3) = expr.parse(input)?;

    let (input, _) = delimited(multispace0, char(','), multispace0).parse(input)?;

    let (input, arg4) = expr.parse(input)?;

    let (input, _) = char(')').parse(input)?;

    match func_name {
        | "series" => {
            Ok((
                input,
                Expr::Series(Arc::new(arg1), var_name, Arc::new(arg3), Arc::new(arg4)),
            ))
        },
        | "summation" => {
            Ok((
                input,
                Expr::Summation(Arc::new(arg1), var_name, Arc::new(arg3), Arc::new(arg4)),
            ))
        },
        | "product" => {
            Ok((
                input,
                Expr::Product(Arc::new(arg1), var_name, Arc::new(arg3), Arc::new(arg4)),
            ))
        },
        | _ => unreachable!(),
    }
}

pub(crate) fn parse_asymptotic_expansion(input: &str) -> IResult<&str, Expr> {
    // println!("asymptotic_expansion started");
    let (input, _) = tag("asymptotic_expansion").parse(input)?;

    // println!("step2");
    // println!("{}", input);
    let (input, _) = char('(').parse(input)?;

    // println!("step3");
    // println!("{}", input);
    let (input, arg1) = expr.parse(input)?;

    // println!("step4");
    // println!("{}", arg1);
    // println!("{}", input);
    let (input, _) = delimited(multispace0, char(','), multispace0).parse(input)?;

    // println!("step5");
    let (input, var_name_expr) = expr.parse(input)?;

    // println!("Nom started");
    let var_name = match var_name_expr {
        | Expr::Variable(s) => s,
        | _ => return nom::combinator::fail().parse(input),
    };

    // println!("Nom end");
    let (input, _) = delimited(multispace0, char(','), multispace0).parse(input)?;

    let (input, arg3) = expr.parse(input)?;

    let (input, _) = delimited(multispace0, char(','), multispace0).parse(input)?;

    let (input, arg4) = expr.parse(input)?;

    let (input, _) = char(')').parse(input)?;

    // println!("{}", input);
    // println!("{}", arg1);
    // println!("{}", arg3);
    // println!("{}", arg4);
    Ok((
        input,
        Expr::AsymptoticExpansion(Arc::new(arg1), var_name, Arc::new(arg3), Arc::new(arg4)),
    ))
}

pub(crate) fn parse_fredholm(input: &str) -> IResult<&str, Expr> {
    let (input, _) = tag("fredholm").parse(input)?;

    let (input, _) = char('(').parse(input)?;

    let (input, arg1) = expr.parse(input)?;

    let (input, _) = delimited(multispace0, char(','), multispace0).parse(input)?;

    let (input, arg2) = expr.parse(input)?;

    let (input, _) = delimited(multispace0, char(','), multispace0).parse(input)?;

    let (input, arg3) = expr.parse(input)?;

    let (input, _) = delimited(multispace0, char(','), multispace0).parse(input)?;

    let (input, arg4) = expr.parse(input)?;

    let (input, _) = char(')').parse(input)?;

    Ok((
        input,
        Expr::Fredholm(
            Arc::new(arg1),
            Arc::new(arg2),
            Arc::new(arg3),
            Arc::new(arg4),
        ),
    ))
}

pub(crate) fn parse_volterra(input: &str) -> IResult<&str, Expr> {
    let (input, _) = tag("volterra").parse(input)?;

    let (input, _) = char('(').parse(input)?;

    let (input, arg1) = expr.parse(input)?;

    let (input, _) = delimited(multispace0, char(','), multispace0).parse(input)?;

    let (input, arg2) = expr.parse(input)?;

    let (input, _) = delimited(multispace0, char(','), multispace0).parse(input)?;

    let (input, arg3) = expr.parse(input)?;

    let (input, _) = delimited(multispace0, char(','), multispace0).parse(input)?;

    let (input, arg4) = expr.parse(input)?;

    let (input, _) = char(')').parse(input)?;

    Ok((
        input,
        Expr::Volterra(
            Arc::new(arg1),
            Arc::new(arg2),
            Arc::new(arg3),
            Arc::new(arg4),
        ),
    ))
}

pub(crate) fn parse_parametric_solution(input: &str) -> IResult<&str, Expr> {
    let (input, _) = tag("parametric_solution").parse(input)?;

    let (input, _) = char('(').parse(input)?;

    let (input, x_expr) = expr.parse(input)?;

    let (input, _) = delimited(multispace0, char(','), multispace0).parse(input)?;

    let (input, y_expr) = expr.parse(input)?;

    let (input, _) = char(')').parse(input)?;

    Ok((
        input,
        Expr::ParametricSolution {
            x: Arc::new(x_expr),
            y: Arc::new(y_expr),
        },
    ))
}

pub(crate) fn parse_root_of(input: &str) -> IResult<&str, Expr> {
    let (input, _) = tag("root_of").parse(input)?;

    let (input, _) = char('(').parse(input)?;

    let (input, poly) = expr.parse(input)?;

    let (input, _) = delimited(multispace0, char(','), multispace0).parse(input)?;

    let (input, index_expr) = expr.parse(input)?;

    let index = match index_expr {
        | Expr::Constant(c) => (c as i64).try_into().unwrap_or(0),
        | _ => return nom::combinator::fail().parse(input),
    };

    let (input, _) = char(')').parse(input)?;

    Ok((
        input,
        Expr::RootOf {
            poly: Arc::new(poly),
            index,
        },
    ))
}

pub(crate) fn atom(input: &str) -> IResult<&str, Expr> {
    alt((
        parse_numeric_literals,
        parse_series_like_function,
        parse_asymptotic_expansion,
        parse_matrix,
        parse_pde,
        parse_path,
        parse_interval,
        parse_quantifier,
        parse_domain,
        parse_ode,
        parse_sum,
        parse_integral,
        parse_fredholm,
        parse_volterra,
        parse_parametric_solution,
        parse_root_of,
        parse_function_call, // New unified function parser
        parse_boolean_and_infinities,
        parse_constant,
        alt((parenthesized_expr, parse_string_literal, parse_variable)),
    ))
    .parse(input)
}

pub(crate) fn parse_float(input: &str) -> IResult<&str, f64> {
    map_res(
        recognize(pair(
            opt(char('-')),
            alt((
                // Leading decimal point (e.g., ".45")
                recognize(pair(char('.'), digit1)),
                // Digits with decimal point and more digits (e.g., "123.45")
                recognize(pair(digit1, pair(char('.'), digit1))),
                // Just digits (e.g., "123")
                digit1,
            )),
        )),
        |s: &str| s.parse::<f64>(),
    )
    .parse(input)
}

// Parses a floating-point number
pub(crate) fn parse_number(input: &str) -> IResult<&str, Expr> {
    map(parse_float, Expr::Constant).parse(input)
}

// Parses a mathematical constant
pub(crate) fn parse_constant(input: &str) -> IResult<&str, Expr> {
    alt((
        map(tag("Pi"), |_| Expr::Pi),
        map(tag("E"), |_| Expr::E),
        map(tag("InfiniteSolutions"), |_| Expr::InfiniteSolutions),
        map(tag("NoSolution"), |_| Expr::NoSolution),
    ))
    .parse(input)
}

// Parses a variable (a sequence of alphabetic characters)
pub(crate) fn parse_variable(input: &str) -> IResult<&str, Expr> {
    map(identifier_name, |s: &str| {
        // If the identifier contains a quote or underscore, treat it as a Predicate (e.g., y', u_xx)
        if s.contains('\'') || s.contains('_') {
            Expr::Predicate {
                name: s.to_string(),
                args: vec![],
            }
        } else {
            Expr::Variable(s.to_string())
        }
    })
    .parse(input)
}

// Parses an expression enclosed in parentheses
pub(crate) fn parenthesized_expr(input: &str) -> IResult<&str, Expr> {
    delimited(char('('), expr, char(')')).parse(input)
}

#[cfg(test)]
mod tests {

    use std::sync::Arc;

    use super::*;
    use crate::symbolic::core::Expr;

    #[test]
    fn test_parse_number() {
        assert_eq!(parse_expr("123.45"), Ok(("", Expr::Constant(123.45))));
    }

    #[test]
    fn test_parse_variable() {
        assert_eq!(parse_expr("x"), Ok(("", Expr::Variable("x".to_string()))));
    }

    #[test]
    fn test_parse_addition() {
        assert_eq!(
            parse_expr("x + 2"),
            Ok((
                "",
                Expr::Add(
                    Arc::new(Expr::Variable("x".to_string())),
                    Arc::new(Expr::Constant(2.0))
                )
            ))
        );
    }

    #[test]
    fn test_parse_subtraction() {
        assert_eq!(
            parse_expr("y - 3.14"),
            Ok((
                "",
                Expr::Sub(
                    Arc::new(Expr::Variable("y".to_string())),
                    Arc::new(Expr::Constant(3.14))
                )
            ))
        );
    }

    #[test]
    fn test_parse_multiplication() {
        assert_eq!(
            parse_expr("a * b"),
            Ok((
                "",
                Expr::Mul(
                    Arc::new(Expr::Variable("a".to_string())),
                    Arc::new(Expr::Variable("b".to_string()))
                )
            ))
        );
    }

    #[test]
    fn test_parse_division() {
        assert_eq!(
            parse_expr("z / 2.5"),
            Ok((
                "",
                Expr::Div(
                    Arc::new(Expr::Variable("z".to_string())),
                    Arc::new(Expr::Constant(2.5))
                )
            ))
        );
    }

    #[test]
    fn test_parse_parentheses() {
        assert_eq!(
            parse_expr("(a + b) * c"),
            Ok((
                "",
                Expr::Mul(
                    Arc::new(Expr::Add(
                        Arc::new(Expr::Variable("a".to_string())),
                        Arc::new(Expr::Variable("b".to_string()))
                    )),
                    Arc::new(Expr::Variable("c".to_string()))
                )
            ))
        );
    }

    #[test]
    fn test_parse_complex_expression() {
        assert_eq!(
            parse_expr("x + y * (z - 1)"),
            Ok((
                "",
                Expr::Add(
                    Arc::new(Expr::Variable("x".to_string())),
                    Arc::new(Expr::Mul(
                        Arc::new(Expr::Variable("y".to_string())),
                        Arc::new(Expr::Sub(
                            Arc::new(Expr::Variable("z".to_string())),
                            Arc::new(Expr::Constant(1.0))
                        ))
                    ))
                )
            ))
        );
    }

    #[test]
    fn test_parse_unary_negation() {
        assert_eq!(
            parse_expr("-x"),
            Ok(("", Expr::Neg(Arc::new(Expr::Variable("x".to_string())))))
        );
    }

    #[test]
    fn test_parse_pi() {
        assert_eq!(parse_expr("Pi"), Ok(("", Expr::Pi)));
    }

    #[test]
    fn test_parse_e() {
        assert_eq!(parse_expr("E"), Ok(("", Expr::E)));
    }

    #[test]
    fn test_parse_bigint() {
        fn print_type_of<T>(_: &T) {
            println!("{}", std::any::type_name::<T>());
        }

        let expected = Expr::Neg(Arc::new(Expr::BigInt(BigInt::from(456))));

        let aa = parse_expr("123");

        print_type_of(&aa);

        print_type_of(&aa.unwrap().1);

        let bb = Expr::BigInt(BigInt::from(123));

        print_type_of(&bb);

        print_type_of(&Expr::BigInt(BigInt::from(123)));

        assert_eq!(
            parse_expr("123")
                .expect(
                    "Parse Expr \
                     failed."
                )
                .1,
            Expr::BigInt(BigInt::from(123))
        );

        assert_eq!(
            parse_expr("-456")
                .expect(
                    "Parse Expr \
                     failed."
                )
                .1,
            expected
        );
    }

    #[test]
    fn test_parse_rational() {
        let expected = Expr::Neg(Arc::new(Expr::Div(
            Arc::new(Expr::BigInt(BigInt::from(3))),
            Arc::new(Expr::BigInt(BigInt::from(4))),
        )));

        assert_eq!(
            parse_expr("1/2"),
            Ok((
                "",
                Expr::Rational(BigRational::new(BigInt::from(1), BigInt::from(2)))
            ))
        );
        // assert_eq!(
        //     parse_expr("-3/4"),
        //     Ok((
        //         "",
        //         Expr::Rational(BigRational::new(BigInt::from(-3), BigInt::from(4)))
        //         //expected
        //     ))
        // );
    }

    #[test]
    fn test_parse_boolean() {
        assert_eq!(parse_expr("true"), Ok(("", Expr::Boolean(true))));

        assert_eq!(parse_expr("false"), Ok(("", Expr::Boolean(false))));
    }

    #[test]
    fn test_parse_infinity() {
        assert_eq!(parse_expr("Infinity"), Ok(("", Expr::Infinity)));
    }

    #[test]
    fn test_parse_negative_infinity() {
        assert_eq!(parse_expr("-Infinity"), Ok(("", Expr::NegativeInfinity)));
    }

    #[test]
    fn test_parse_eq() {
        assert_eq!(
            parse_expr("x = 5"),
            Ok((
                "",
                Expr::Eq(
                    Arc::new(Expr::Variable("x".to_string())),
                    Arc::new(Expr::Constant(5.0))
                )
            ))
        );
    }

    #[test]
    fn test_parse_lt() {
        assert_eq!(
            parse_expr("x < 5"),
            Ok((
                "",
                Expr::Lt(
                    Arc::new(Expr::Variable("x".to_string())),
                    Arc::new(Expr::Constant(5.0))
                )
            ))
        );
    }

    #[test]
    fn test_parse_gt() {
        assert_eq!(
            parse_expr("x > 5"),
            Ok((
                "",
                Expr::Gt(
                    Arc::new(Expr::Variable("x".to_string())),
                    Arc::new(Expr::Constant(5.0))
                )
            ))
        );
    }

    #[test]
    fn test_parse_le() {
        assert_eq!(
            parse_expr("x <= 5"),
            Ok((
                "",
                Expr::Le(
                    Arc::new(Expr::Variable("x".to_string())),
                    Arc::new(Expr::Constant(5.0))
                )
            ))
        );
    }

    #[test]
    fn test_parse_ge() {
        assert_eq!(
            parse_expr("x >= 5"),
            Ok((
                "",
                Expr::Ge(
                    Arc::new(Expr::Variable("x".to_string())),
                    Arc::new(Expr::Constant(5.0))
                )
            ))
        );
    }

    #[test]
    fn test_parse_sin() {
        assert_eq!(
            parse_expr("sin(x)"),
            Ok(("", Expr::Sin(Arc::new(Expr::Variable("x".to_string())))))
        );
    }

    #[test]
    fn test_parse_cos() {
        assert_eq!(
            parse_expr("cos(y+1)"),
            Ok((
                "",
                Expr::Cos(Arc::new(Expr::Add(
                    Arc::new(Expr::Variable("y".to_string())),
                    Arc::new(Expr::Constant(1.0))
                )))
            ))
        );
    }

    #[test]
    fn test_parse_power() {
        assert_eq!(
            parse_expr("x^2"),
            Ok((
                "",
                Expr::Power(
                    Arc::new(Expr::Variable("x".to_string())),
                    Arc::new(Expr::Constant(2.0))
                )
            ))
        );
    }

    #[test]
    fn test_parse_sec() {
        assert_eq!(
            parse_expr("sec(x)"),
            Ok(("", Expr::Sec(Arc::new(Expr::Variable("x".to_string())))))
        );
    }

    #[test]
    fn test_parse_csc() {
        assert_eq!(
            parse_expr("csc(x)"),
            Ok(("", Expr::Csc(Arc::new(Expr::Variable("x".to_string())))))
        );
    }

    #[test]
    fn test_parse_cot() {
        assert_eq!(
            parse_expr("cot(x)"),
            Ok(("", Expr::Cot(Arc::new(Expr::Variable("x".to_string())))))
        );
    }

    #[test]
    fn test_parse_arcsin() {
        assert_eq!(
            parse_expr("asin(x)"),
            Ok(("", Expr::ArcSin(Arc::new(Expr::Variable("x".to_string())))))
        );
    }

    #[test]
    fn test_parse_arccos() {
        assert_eq!(
            parse_expr("acos(x)"),
            Ok(("", Expr::ArcCos(Arc::new(Expr::Variable("x".to_string())))))
        );
    }

    #[test]
    fn test_parse_arctan() {
        assert_eq!(
            parse_expr("atan(x)"),
            Ok(("", Expr::ArcTan(Arc::new(Expr::Variable("x".to_string())))))
        );
    }

    #[test]
    fn test_parse_arcsec() {
        assert_eq!(
            parse_expr("asec(x)"),
            Ok(("", Expr::ArcSec(Arc::new(Expr::Variable("x".to_string())))))
        );
    }

    #[test]
    fn test_parse_arccsc() {
        assert_eq!(
            parse_expr("acsc(x)"),
            Ok(("", Expr::ArcCsc(Arc::new(Expr::Variable("x".to_string())))))
        );
    }

    #[test]
    fn test_parse_arccot() {
        assert_eq!(
            parse_expr("acot(x)"),
            Ok(("", Expr::ArcCot(Arc::new(Expr::Variable("x".to_string())))))
        );
    }

    #[test]
    fn test_parse_sinh() {
        assert_eq!(
            parse_expr("sinh(x)"),
            Ok(("", Expr::Sinh(Arc::new(Expr::Variable("x".to_string())))))
        );
    }

    #[test]
    fn test_parse_cosh() {
        assert_eq!(
            parse_expr("cosh(x)"),
            Ok(("", Expr::Cosh(Arc::new(Expr::Variable("x".to_string())))))
        );
    }

    #[test]
    fn test_parse_tanh() {
        assert_eq!(
            parse_expr("tanh(x)"),
            Ok(("", Expr::Tanh(Arc::new(Expr::Variable("x".to_string())))))
        );
    }

    #[test]
    fn test_parse_sech() {
        assert_eq!(
            parse_expr("sech(x)"),
            Ok(("", Expr::Sech(Arc::new(Expr::Variable("x".to_string())))))
        );
    }

    #[test]
    fn test_parse_csch() {
        assert_eq!(
            parse_expr("csch(x)"),
            Ok(("", Expr::Csch(Arc::new(Expr::Variable("x".to_string())))))
        );
    }

    #[test]
    fn test_parse_coth() {
        assert_eq!(
            parse_expr("coth(x)"),
            Ok(("", Expr::Coth(Arc::new(Expr::Variable("x".to_string())))))
        );
    }

    #[test]
    fn test_parse_arcsinh() {
        assert_eq!(
            parse_expr("asinh(x)"),
            Ok(("", Expr::ArcSinh(Arc::new(Expr::Variable("x".to_string())))))
        );
    }

    #[test]
    fn test_parse_arccosh() {
        assert_eq!(
            parse_expr("acosh(x)"),
            Ok(("", Expr::ArcCosh(Arc::new(Expr::Variable("x".to_string())))))
        );
    }

    #[test]
    fn test_parse_arctanh() {
        assert_eq!(
            parse_expr("atanh(x)"),
            Ok(("", Expr::ArcTanh(Arc::new(Expr::Variable("x".to_string())))))
        );
    }

    #[test]
    fn test_parse_arcsech() {
        assert_eq!(
            parse_expr("asech(x)"),
            Ok(("", Expr::ArcSech(Arc::new(Expr::Variable("x".to_string())))))
        );
    }

    #[test]
    fn test_parse_arccsch() {
        assert_eq!(
            parse_expr("acsch(x)"),
            Ok(("", Expr::ArcCsch(Arc::new(Expr::Variable("x".to_string())))))
        );
    }

    #[test]
    fn test_parse_arccoth() {
        assert_eq!(
            parse_expr("acoth(x)"),
            Ok(("", Expr::ArcCoth(Arc::new(Expr::Variable("x".to_string())))))
        );
    }

    #[test]
    fn test_parse_gamma() {
        assert_eq!(
            parse_expr("gamma(x)"),
            Ok(("", Expr::Gamma(Arc::new(Expr::Variable("x".to_string())))))
        );
    }

    #[test]
    fn test_parse_beta() {
        assert_eq!(
            parse_expr("beta(a, b)"),
            Ok((
                "",
                Expr::Beta(
                    Arc::new(Expr::Variable("a".to_string())),
                    Arc::new(Expr::Variable("b".to_string()))
                )
            ))
        );
    }

    #[test]
    fn test_parse_erf() {
        assert_eq!(
            parse_expr("erf(x)"),
            Ok(("", Expr::Erf(Arc::new(Expr::Variable("x".to_string())))))
        );
    }

    #[test]
    fn test_parse_erfc() {
        assert_eq!(
            parse_expr("erfc(x)"),
            Ok(("", Expr::Erfc(Arc::new(Expr::Variable("x".to_string())))))
        );
    }

    #[test]
    fn test_parse_erfi() {
        assert_eq!(
            parse_expr("erfi(x)"),
            Ok(("", Expr::Erfi(Arc::new(Expr::Variable("x".to_string())))))
        );
    }

    #[test]
    fn test_parse_zeta() {
        assert_eq!(
            parse_expr("zeta(s)"),
            Ok(("", Expr::Zeta(Arc::new(Expr::Variable("s".to_string())))))
        );
    }

    #[test]
    fn test_parse_digamma() {
        assert_eq!(
            parse_expr("digamma(x)"),
            Ok(("", Expr::Digamma(Arc::new(Expr::Variable("x".to_string())))))
        );
    }

    #[test]
    fn test_parse_besselj() {
        assert_eq!(
            parse_expr("besselj(n, x)"),
            Ok((
                "",
                Expr::BesselJ(
                    Arc::new(Expr::Variable("n".to_string())),
                    Arc::new(Expr::Variable("x".to_string()))
                )
            ))
        );
    }

    #[test]
    fn test_parse_bessely() {
        assert_eq!(
            parse_expr("bessely(n, x)"),
            Ok((
                "",
                Expr::BesselY(
                    Arc::new(Expr::Variable("n".to_string())),
                    Arc::new(Expr::Variable("x".to_string()))
                )
            ))
        );
    }

    #[test]
    fn test_parse_legendrep() {
        assert_eq!(
            parse_expr("legendrep(n, x)"),
            Ok((
                "",
                Expr::LegendreP(
                    Arc::new(Expr::Variable("n".to_string())),
                    Arc::new(Expr::Variable("x".to_string()))
                )
            ))
        );
    }

    #[test]
    fn test_parse_laguerrel() {
        assert_eq!(
            parse_expr("laguerrel(n, x)"),
            Ok((
                "",
                Expr::LaguerreL(
                    Arc::new(Expr::Variable("n".to_string())),
                    Arc::new(Expr::Variable("x".to_string()))
                )
            ))
        );
    }

    #[test]
    fn test_parse_hermiteh() {
        assert_eq!(
            parse_expr("hermiteh(n, x)"),
            Ok((
                "",
                Expr::HermiteH(
                    Arc::new(Expr::Variable("n".to_string())),
                    Arc::new(Expr::Variable("x".to_string()))
                )
            ))
        );
    }

    #[test]
    fn test_parse_xor() {
        assert_eq!(
            parse_expr("xor(a, b)"),
            Ok((
                "",
                Expr::Xor(
                    Arc::new(Expr::Variable("a".to_string())),
                    Arc::new(Expr::Variable("b".to_string()))
                )
            ))
        );
    }

    #[test]
    fn test_parse_implies() {
        assert_eq!(
            parse_expr("implies(a, b)"),
            Ok((
                "",
                Expr::Implies(
                    Arc::new(Expr::Variable("a".to_string())),
                    Arc::new(Expr::Variable("b".to_string()))
                )
            ))
        );
    }

    #[test]
    fn test_parse_and() {
        assert_eq!(
            parse_expr("and(a, b, c)"),
            Ok((
                "",
                Expr::And(vec![
                    Expr::Variable("a".to_string()),
                    Expr::Variable("b".to_string()),
                    Expr::Variable("c".to_string()),
                ])
            ))
        );
    }

    #[test]
    fn test_parse_forall() {
        assert_eq!(
            parse_expr("forall x. P(x)"),
            Ok((
                "",
                Expr::ForAll(
                    "x".to_string(),
                    Arc::new(Expr::Predicate {
                        name: "P".to_string(),
                        args: vec![Expr::Variable("x".to_string())],
                    })
                )
            ))
        );
    }

    #[test]
    fn test_parse_floor() {
        assert_eq!(
            parse_expr("floor(3.14)"),
            Ok(("", Expr::Floor(Arc::new(Expr::Constant(3.14)))))
        );
    }

    #[test]
    fn test_parse_is_prime() {
        assert_eq!(
            parse_expr("is_prime(7)"),
            Ok(("", Expr::IsPrime(Arc::new(Expr::Constant(7.0)))))
        );
    }

    #[test]
    fn test_parse_gcd() {
        assert_eq!(
            parse_expr("gcd(12, 18)"),
            Ok((
                "",
                Expr::Gcd(
                    Arc::new(Expr::Constant(12.0)),
                    Arc::new(Expr::Constant(18.0))
                )
            ))
        );
    }

    #[test]
    fn test_parse_mod() {
        assert_eq!(
            parse_expr("mod(10, 3)"),
            Ok((
                "",
                Expr::Mod(
                    Arc::new(Expr::Constant(10.0)),
                    Arc::new(Expr::Constant(3.0))
                )
            ))
        );
    }

    #[test]
    fn test_parse_vector() {
        assert_eq!(
            parse_expr("vector(1, 2, 3)"),
            Ok((
                "",
                Expr::Vector(vec![
                    Expr::Constant(1.0),
                    Expr::Constant(2.0),
                    Expr::Constant(3.0),
                ])
            ))
        );
    }

    #[test]
    fn test_parse_complex() {
        assert_eq!(
            parse_expr("complex(1, 2)"),
            Ok((
                "",
                Expr::Complex(Arc::new(Expr::Constant(1.0)), Arc::new(Expr::Constant(2.0)))
            ))
        );
    }

    #[test]
    fn test_parse_transpose() {
        assert_eq!(
            parse_expr("transpose(A)"),
            Ok((
                "",
                Expr::Transpose(Arc::new(Expr::Variable("A".to_string())))
            ))
        );
    }

    #[test]
    fn test_parse_inverse() {
        assert_eq!(
            parse_expr("inverse(A)"),
            Ok(("", Expr::Inverse(Arc::new(Expr::Variable("A".to_string())))))
        );
    }

    #[test]
    fn test_parse_matrix_mul() {
        assert_eq!(
            parse_expr("matrix_mul(A, B)"),
            Ok((
                "",
                Expr::MatrixMul(
                    Arc::new(Expr::Variable("A".to_string())),
                    Arc::new(Expr::Variable("B".to_string()))
                )
            ))
        );
    }

    #[test]
    fn test_parse_derivative_n() {
        assert_eq!(
            parse_expr("derivative_n(f(x), x, 2)"),
            Ok((
                "",
                Expr::DerivativeN(
                    Arc::new(Expr::Predicate {
                        name: "f".to_string(),
                        args: vec![Expr::Variable("x".to_string())],
                    }),
                    "x".to_string(),
                    Arc::new(Expr::Constant(2.0))
                )
            ))
        );
    }

    #[test]
    fn test_parse_volume_integral() {
        assert_eq!(
            parse_expr("volume_integral(f(x,y,z), V)"),
            Ok((
                "",
                Expr::VolumeIntegral {
                    scalar_field: Arc::new(Expr::Predicate {
                        name: "f".to_string(),
                        args: vec![
                            Expr::Variable("x".to_string()),
                            Expr::Variable("y".to_string()),
                            Expr::Variable("z".to_string()),
                        ],
                    }),
                    volume: Arc::new(Expr::Variable("V".to_string())),
                }
            ))
        );
    }

    #[test]
    fn test_parse_series() {
        assert_eq!(
            parse_expr("series(f(x), x, 0, 3)"),
            Ok((
                "",
                Expr::Series(
                    Arc::new(Expr::Predicate {
                        name: "f".to_string(),
                        args: vec![Expr::Variable("x".to_string())],
                    }),
                    "x".to_string(),
                    Arc::new(Expr::Constant(0.0)),
                    Arc::new(Expr::Constant(3.0)),
                )
            ))
        );
    }

    #[test]
    fn test_parse_summation() {
        assert_eq!(
            parse_expr("summation(i, i, 1, N)"),
            Ok((
                "",
                Expr::Summation(
                    Arc::new(Expr::Variable("i".to_string())),
                    "i".to_string(),
                    Arc::new(Expr::Constant(1.0)),
                    Arc::new(Expr::Variable("N".to_string())),
                )
            ))
        );
    }

    #[test]
    fn test_parse_convergence_analysis() {
        assert_eq!(
            parse_expr("convergence_analysis(sum(1/n, n, 1, inf), n)"),
            Ok((
                "",
                Expr::ConvergenceAnalysis(
                    Arc::new(Expr::Sum {
                        body: Arc::new(Expr::Div(
                            Arc::new(Expr::Constant(1.0)),
                            Arc::new(Expr::Variable("n".to_string())),
                        )),
                        var: Arc::new(Expr::Variable("n".to_string())),
                        from: Arc::new(Expr::Constant(1.0)),
                        to: Arc::new(Expr::Variable("inf".to_string())),
                    }),
                    "n".to_string(),
                )
            ))
        );
    }

    #[test]
    fn test_parse_general_solution() {
        assert_eq!(
            parse_expr("general_solution(C1*cos(x) + C2*sin(x))"),
            Ok((
                "",
                Expr::GeneralSolution(Arc::new(Expr::Add(
                    Arc::new(Expr::Mul(
                        Arc::new(Expr::Variable("C1".to_string())),
                        Arc::new(Expr::Cos(Arc::new(Expr::Variable("x".to_string())))),
                    )),
                    Arc::new(Expr::Mul(
                        Arc::new(Expr::Variable("C2".to_string())),
                        Arc::new(Expr::Sin(Arc::new(Expr::Variable("x".to_string())))),
                    )),
                )))
            ))
        );
    }

    #[test]
    fn test_parse_particular_solution() {
        assert_eq!(
            parse_expr("particular_solution(sin(x))"),
            Ok((
                "",
                Expr::ParticularSolution(Arc::new(Expr::Sin(Arc::new(Expr::Variable(
                    "x".to_string()
                )))))
            ))
        );
    }

    #[test]
    fn test_parse_fredholm() {
        assert_eq!(
            parse_expr("fredholm(K(x,t), f(t), a, b)"),
            Ok((
                "",
                Expr::Fredholm(
                    Arc::new(Expr::Predicate {
                        name: "K".to_string(),
                        args: vec![
                            Expr::Variable("x".to_string()),
                            Expr::Variable("t".to_string())
                        ],
                    }),
                    Arc::new(Expr::Predicate {
                        name: "f".to_string(),
                        args: vec![Expr::Variable("t".to_string())],
                    }),
                    Arc::new(Expr::Variable("a".to_string())),
                    Arc::new(Expr::Variable("b".to_string())),
                )
            ))
        );
    }

    #[test]
    fn test_parse_apply() {
        assert_eq!(
            parse_expr("apply(f, x)"),
            Ok((
                "",
                Expr::Apply(
                    Arc::new(Expr::Variable("f".to_string())),
                    Arc::new(Expr::Variable("x".to_string()))
                )
            ))
        );
    }

    #[test]
    fn test_parse_max() {
        assert_eq!(
            parse_expr("max(x, y)"),
            Ok((
                "",
                Expr::Max(
                    Arc::new(Expr::Variable("x".to_string())),
                    Arc::new(Expr::Variable("y".to_string()))
                )
            ))
        );
    }

    #[test]
    fn test_parse_quantity_with_value() {
        assert_eq!(
            parse_expr("quantity_with_value(10, \"m\")"),
            Ok((
                "",
                Expr::QuantityWithValue(Arc::new(Expr::Constant(10.0)), "m".to_string())
            ))
        );
    }

    #[test]
    fn test_parse_tuple() {
        assert_eq!(
            parse_expr("tuple(1, x, true)"),
            Ok((
                "",
                Expr::Tuple(vec![
                    Expr::Constant(1.0),
                    Expr::Variable("x".to_string()),
                    Expr::Boolean(true),
                ])
            ))
        );
    }

    #[test]
    fn test_parse_system() {
        assert_eq!(
            parse_expr("system(eq1, eq2)"),
            Ok((
                "",
                Expr::System(vec![
                    Expr::Variable("eq1".to_string()),
                    Expr::Variable("eq2".to_string()),
                ])
            ))
        );
    }

    #[test]
    fn test_parse_solutions() {
        assert_eq!(
            parse_expr("solutions(sol1, sol2)"),
            Ok((
                "",
                Expr::Solutions(vec![
                    Expr::Variable("sol1".to_string()),
                    Expr::Variable("sol2".to_string()),
                ])
            ))
        );
    }

    #[test]
    fn test_parse_boundary() {
        assert_eq!(
            parse_expr("boundary(D)"),
            Ok((
                "",
                Expr::Boundary(Arc::new(Expr::Variable("D".to_string())))
            ))
        );
    }

    #[test]
    fn test_parse_domain() {
        assert_eq!(
            parse_expr("domain(R)"),
            Ok(("", Expr::Domain("R".to_string())))
        );
    }

    #[test]
    fn test_parse_solve() {
        assert_eq!(
            parse_expr("solve(x^2 - 4 = 0, x)"),
            Ok((
                "",
                Expr::Solve(
                    Arc::new(Expr::Eq(
                        Arc::new(Expr::Sub(
                            Arc::new(Expr::Power(
                                Arc::new(Expr::Variable("x".to_string())),
                                Arc::new(Expr::Constant(2.0)),
                            )),
                            Arc::new(Expr::Constant(4.0)),
                        )),
                        Arc::new(Expr::Constant(0.0)),
                    )),
                    "x".to_string(),
                )
            ))
        );
    }

    #[test]
    fn test_parse_parametric_solution() {
        assert_eq!(
            parse_expr("parametric_solution(t^2, t)"),
            Ok((
                "",
                Expr::ParametricSolution {
                    x: Arc::new(Expr::Power(
                        Arc::new(Expr::Variable("t".to_string())),
                        Arc::new(Expr::Constant(2.0)),
                    )),
                    y: Arc::new(Expr::Variable("t".to_string())),
                }
            ))
        );
    }

    #[test]
    fn test_parse_infinite_solutions() {
        assert_eq!(
            parse_expr("InfiniteSolutions"),
            Ok(("", Expr::InfiniteSolutions))
        );
    }

    #[test]
    fn test_parse_no_solution() {
        assert_eq!(parse_expr("NoSolution"), Ok(("", Expr::NoSolution)));
    }

    #[test]
    fn test_parse_root_of() {
        assert_eq!(
            parse_expr("root_of(x^2 - 1, 1)"),
            Ok((
                "",
                Expr::RootOf {
                    poly: Arc::new(Expr::Sub(
                        Arc::new(Expr::Power(
                            Arc::new(Expr::Variable("x".to_string())),
                            Arc::new(Expr::Constant(2.0)),
                        )),
                        Arc::new(Expr::Constant(1.0)),
                    )),
                    index: 1,
                }
            ))
        );
    }

    #[test]
    fn test_parse_substitute() {
        assert_eq!(
            parse_expr("substitute(x^2, x, 2)"),
            Ok((
                "",
                Expr::Substitute(
                    Arc::new(Expr::Power(
                        Arc::new(Expr::Variable("x".to_string())),
                        Arc::new(Expr::Constant(2.0)),
                    )),
                    "x".to_string(),
                    Arc::new(Expr::Constant(2.0)),
                )
            ))
        );
    }

    #[test]
    fn test_parse_path() {
        assert_eq!(
            parse_expr("path(Line, 0, 1)"),
            Ok((
                "",
                Expr::Path(
                    PathType::Line,
                    Arc::new(Expr::Constant(0.0)),
                    Arc::new(Expr::Constant(1.0))
                )
            ))
        );
    }

    #[test]
    fn test_parse_volterra() {
        assert_eq!(
            parse_expr("volterra(K(x,t), f(t), a, x)"),
            Ok((
                "",
                Expr::Volterra(
                    Arc::new(Expr::Predicate {
                        name: "K".to_string(),
                        args: vec![
                            Expr::Variable("x".to_string()),
                            Expr::Variable("t".to_string())
                        ],
                    }),
                    Arc::new(Expr::Predicate {
                        name: "f".to_string(),
                        args: vec![Expr::Variable("t".to_string())],
                    }),
                    Arc::new(Expr::Variable("a".to_string())),
                    Arc::new(Expr::Variable("x".to_string())),
                )
            ))
        );
    }

    #[test]
    fn test_parse_pde() {
        assert_eq!(
            parse_expr("pde(u_xx + u_yy = 0, u, [x, y])"),
            Ok((
                "",
                Expr::Pde {
                    equation: Arc::new(Expr::Eq(
                        Arc::new(Expr::Add(
                            Arc::new(Expr::Predicate {
                                name: "u_xx".to_string(),
                                args: vec![],
                            }),
                            Arc::new(Expr::Predicate {
                                name: "u_yy".to_string(),
                                args: vec![],
                            }),
                        )),
                        Arc::new(Expr::Constant(0.0)),
                    )),
                    func: "u".to_string(),
                    vars: vec!["x".to_string(), "y".to_string()],
                }
            ))
        );
    }

    #[test]
    fn test_parse_ode() {
        assert_eq!(
            parse_expr("ode(y'' + y = 0, y, x)"),
            Ok((
                "",
                Expr::Ode {
                    equation: Arc::new(Expr::Eq(
                        Arc::new(Expr::Add(
                            Arc::new(Expr::Predicate {
                                name: "y''".to_string(),
                                args: vec![],
                            }),
                            Arc::new(Expr::Variable("y".to_string())),
                        )),
                        Arc::new(Expr::Constant(0.0)),
                    )),
                    func: "y".to_string(),
                    var: "x".to_string(),
                }
            ))
        );
    }

    #[test]
    fn test_parse_asymptotic_expansion() {
        assert_eq!(
            parse_expr("asymptotic_expansion(f(x), x, 0, 3)"),
            Ok((
                "",
                Expr::AsymptoticExpansion(
                    Arc::new(Expr::Predicate {
                        name: "f".to_string(),
                        args: vec![Expr::Variable("x".to_string())],
                    }),
                    "x".to_string(),
                    Arc::new(Expr::Constant(0.0)),
                    Arc::new(Expr::Constant(3.0)),
                )
            ))
        );
    }

    #[test]
    fn test_parse_product() {
        assert_eq!(
            parse_expr("product(i, i, 1, N)"),
            Ok((
                "",
                Expr::Product(
                    Arc::new(Expr::Variable("i".to_string())),
                    "i".to_string(),
                    Arc::new(Expr::Constant(1.0)),
                    Arc::new(Expr::Variable("N".to_string())),
                )
            ))
        );
    }

    #[test]
    fn test_parse_sum() {
        assert_eq!(
            parse_expr("sum(i^2, i, 1, 10)"),
            Ok((
                "",
                Expr::Sum {
                    body: Arc::new(Expr::Power(
                        Arc::new(Expr::Variable("i".to_string())),
                        Arc::new(Expr::Constant(2.0)),
                    )),
                    var: Arc::new(Expr::Variable("i".to_string())),
                    from: Arc::new(Expr::Constant(1.0)),
                    to: Arc::new(Expr::Constant(10.0)),
                }
            ))
        );
    }

    #[test]
    fn test_parse_surface_integral() {
        assert_eq!(
            parse_expr("surface_integral(F(x,y,z), S)"),
            Ok((
                "",
                Expr::SurfaceIntegral {
                    vector_field: Arc::new(Expr::Predicate {
                        name: "F".to_string(),
                        args: vec![
                            Expr::Variable("x".to_string()),
                            Expr::Variable("y".to_string()),
                            Expr::Variable("z".to_string()),
                        ],
                    }),
                    surface: Arc::new(Expr::Variable("S".to_string())),
                }
            ))
        );
    }

    #[test]
    fn test_parse_integral() {
        assert_eq!(
            parse_expr("integral(x^2, x, 0, 1)"),
            Ok((
                "",
                Expr::Integral {
                    integrand: Arc::new(Expr::Power(
                        Arc::new(Expr::Variable("x".to_string())),
                        Arc::new(Expr::Constant(2.0)),
                    )),
                    var: Arc::new(Expr::Variable("x".to_string())),
                    lower_bound: Arc::new(Expr::Constant(0.0)),
                    upper_bound: Arc::new(Expr::Constant(1.0)),
                }
            ))
        );
    }

    #[test]
    fn test_parse_limit() {
        assert_eq!(
            parse_expr("limit(f(x), x, 0)"),
            Ok((
                "",
                Expr::Limit(
                    Arc::new(Expr::Predicate {
                        name: "f".to_string(),
                        args: vec![Expr::Variable("x".to_string())],
                    }),
                    "x".to_string(),
                    Arc::new(Expr::Constant(0.0))
                )
            ))
        );
    }

    #[test]
    fn test_parse_derivative() {
        assert_eq!(
            parse_expr("derivative(x^2, x)"),
            Ok((
                "",
                Expr::Derivative(
                    Arc::new(Expr::Power(
                        Arc::new(Expr::Variable("x".to_string())),
                        Arc::new(Expr::Constant(2.0))
                    )),
                    "x".to_string()
                )
            ))
        );
    }

    #[test]
    fn test_parse_matrix() {
        assert_eq!(
            parse_expr(
                "matrix([[1, 2], [3, \
                 4]])"
            ),
            Ok((
                "",
                Expr::Matrix(vec![
                    vec![Expr::Constant(1.0), Expr::Constant(2.0)],
                    vec![Expr::Constant(3.0), Expr::Constant(4.0)],
                ])
            ))
        );
    }

    #[test]
    fn test_parse_matrix_vec_mul() {
        assert_eq!(
            parse_expr("matrix_vec_mul(A, v)"),
            Ok((
                "",
                Expr::MatrixVecMul(
                    Arc::new(Expr::Variable("A".to_string())),
                    Arc::new(Expr::Variable("v".to_string()))
                )
            ))
        );
    }

    #[test]
    fn test_parse_polynomial() {
        print_type_of(&parse_expr("polynomial(1, 2, 3)"));

        let aatest: Result<(&str, Expr), ()> = Ok((
            "",
            Expr::Polynomial(vec![
                Expr::Constant(1.0),
                Expr::Constant(2.0),
                Expr::Constant(3.0),
            ]),
        ));

        print_type_of(&aatest);

        assert_eq!(
            parse_expr("polynomial(1, 2, 3)"),
            Ok((
                "",
                Expr::Polynomial(vec![
                    Expr::Constant(1.0),
                    Expr::Constant(2.0),
                    Expr::Constant(3.0),
                ])
            ))
        );
    }

    #[test]
    fn test_parse_polynomial_unwrapped() {
        let expected_tuple = (
            "",
            Expr::Polynomial(vec![
                Expr::Constant(1.0),
                Expr::Constant(2.0),
                Expr::Constant(3.0),
            ]),
        );

        let orgvalue = parse_expr("polynomial(1, 2, 3)").unwrap();

        print_type_of(&orgvalue);

        print_type_of(&expected_tuple);

        // println!("first test started");
        assert_eq!(orgvalue, expected_tuple);

        // println!("second test passed");
        assert_eq!(parse_expr("polynomial(1, 2, 3)").unwrap(), expected_tuple);
    }

    #[test]
    fn dag_test() {
        let a = Expr::new_variable("a");

        let b = Expr::new_variable("b");

        assert_eq!(Expr::new_add(&a, &b), Expr::new_add(&a, &b));
    }

    #[test]
    fn prove_type02() {
        let static_string: &'static str = "hello";

        let local_string: &str = "hello";

        let different_string: &str = "world";

        assert_eq!(static_string, local_string);

        assert_ne!(static_string, different_string);
    }

    #[test]
    fn prove_type() {
        let u: i32 = 3;

        let i: i32 = 3;

        assert_eq!(Ok::<i32, ()>(u), Ok(i))
    }

    use std::any::type_name;

    fn print_type_of<T>(_: &T) {
        // println!("Type: {}", type_name::<T>());
    }

    #[test]
    fn test_parse_polynomial02() {
        print_type_of(&parse_expr("polynomial(1, 2, 3)"));

        assert_eq!(
            parse_expr("polynomial(1, 2, 3)"),
            parse_expr("polynomial(1, 2, 3)")
        );
    }

    #[test]
    fn test_parse_interval() {
        print_type_of(&parse_expr("polynomial(1, 2, 3)"));

        assert_eq!(
            parse_expr(
                "interval(0, 1, true, \
                 false)"
            ),
            Ok((
                "",
                Expr::Interval(
                    Arc::new(Expr::Constant(0.0)),
                    Arc::new(Expr::Constant(1.0)),
                    true,
                    false
                )
            ))
        );
    }

    #[test]
    fn test_parse_union() {
        assert_eq!(
            parse_expr("union(A, B, C)"),
            Ok((
                "",
                Expr::Union(vec![
                    Expr::Variable("A".to_string()),
                    Expr::Variable("B".to_string()),
                    Expr::Variable("C".to_string()),
                ])
            ))
        );
    }

    #[test]
    fn test_parse_exists() {
        assert_eq!(
            parse_expr("exists y. Q(y)"),
            Ok((
                "",
                Expr::Exists(
                    "y".to_string(),
                    Arc::new(Expr::Predicate {
                        name: "Q".to_string(),
                        args: vec![Expr::Variable("y".to_string())],
                    })
                )
            ))
        );
    }

    #[test]
    fn test_parse_predicate() {
        assert_eq!(
            parse_expr("is_prime(x)"),
            Ok((
                "",
                Expr::Predicate {
                    name: "is_prime".to_string(),
                    args: vec![Expr::Variable("x".to_string())],
                }
            ))
        );

        assert_eq!(
            parse_expr("has_property(y, z)"),
            Ok((
                "",
                Expr::Predicate {
                    name: "has_property".to_string(),
                    args: vec![
                        Expr::Variable("y".to_string()),
                        Expr::Variable("z".to_string()),
                    ],
                }
            ))
        );
    }

    #[test]
    fn test_parse_or() {
        assert_eq!(
            parse_expr("or(x, y)"),
            Ok((
                "",
                Expr::Or(vec![
                    Expr::Variable("x".to_string()),
                    Expr::Variable("y".to_string()),
                ])
            ))
        );
    }

    #[test]
    fn test_parse_equivalent() {
        assert_eq!(
            parse_expr("equivalent(a, b)"),
            Ok((
                "",
                Expr::Equivalent(
                    Arc::new(Expr::Variable("a".to_string())),
                    Arc::new(Expr::Variable("b".to_string()))
                )
            ))
        );
    }

    #[test]
    fn test_parse_not() {
        assert_eq!(
            parse_expr("not x"),
            Ok(("", Expr::Not(Arc::new(Expr::Variable("x".to_string())))))
        );

        assert_eq!(
            parse_expr("not (x = y)"),
            Ok((
                "",
                Expr::Not(Arc::new(Expr::Eq(
                    Arc::new(Expr::Variable("x".to_string())),
                    Arc::new(Expr::Variable("y".to_string()))
                )))
            ))
        );
    }

    #[test]
    fn test_parse_kronecker_delta() {
        assert_eq!(
            parse_expr("kronecker_delta(i, j)"),
            Ok((
                "",
                Expr::KroneckerDelta(
                    Arc::new(Expr::Variable("i".to_string())),
                    Arc::new(Expr::Variable("j".to_string()))
                )
            ))
        );
    }

    #[test]
    fn test_parse_factorial() {
        assert_eq!(
            parse_expr("x!"),
            Ok((
                "",
                Expr::Factorial(Arc::new(Expr::Variable("x".to_string())))
            ))
        );

        assert_eq!(
            parse_expr("(x+1)!"),
            Ok((
                "",
                Expr::Factorial(Arc::new(Expr::Add(
                    Arc::new(Expr::Variable("x".to_string())),
                    Arc::new(Expr::Constant(1.0))
                )))
            ))
        );
    }

    #[test]
    fn test_parse_binomial() {
        assert_eq!(
            parse_expr("binomial(n, k)"),
            Ok((
                "",
                Expr::Binomial(
                    Arc::new(Expr::Variable("n".to_string())),
                    Arc::new(Expr::Variable("k".to_string()))
                )
            ))
        );
    }

    #[test]
    fn test_parse_permutation() {
        assert_eq!(
            parse_expr("permutation(n, k)"),
            Ok((
                "",
                Expr::Permutation(
                    Arc::new(Expr::Variable("n".to_string())),
                    Arc::new(Expr::Variable("k".to_string()))
                )
            ))
        );
    }

    #[test]
    fn test_parse_combination() {
        assert_eq!(
            parse_expr("combination(n, k)"),
            Ok((
                "",
                Expr::Combination(
                    Arc::new(Expr::Variable("n".to_string())),
                    Arc::new(Expr::Variable("k".to_string()))
                )
            ))
        );
    }

    #[test]
    fn test_parse_falling_factorial() {
        assert_eq!(
            parse_expr("falling_factorial(x, n)"),
            Ok((
                "",
                Expr::FallingFactorial(
                    Arc::new(Expr::Variable("x".to_string())),
                    Arc::new(Expr::Variable("n".to_string()))
                )
            ))
        );
    }

    #[test]
    fn test_parse_rising_factorial() {
        assert_eq!(
            parse_expr("rising_factorial(x, n)"),
            Ok((
                "",
                Expr::RisingFactorial(
                    Arc::new(Expr::Variable("x".to_string())),
                    Arc::new(Expr::Variable("n".to_string()))
                )
            ))
        );
    }

    #[test]
    fn test_parse_log_base() {
        assert_eq!(
            parse_expr("log_base(2, 8)"),
            Ok((
                "",
                Expr::LogBase(Arc::new(Expr::Constant(2.0)), Arc::new(Expr::Constant(8.0)))
            ))
        );
    }

    #[test]
    fn test_parse_atan2() {
        assert_eq!(
            parse_expr("atan2(y, x)"),
            Ok((
                "",
                Expr::Atan2(
                    Arc::new(Expr::Variable("y".to_string())),
                    Arc::new(Expr::Variable("x".to_string()))
                )
            ))
        );
    }

    #[test]
    fn test_parse_power_and_negation() {
        assert_eq!(
            parse_expr("-x^2"),
            Ok((
                "",
                Expr::Neg(Arc::new(Expr::Power(
                    Arc::new(Expr::Variable("x".to_string())),
                    Arc::new(Expr::Constant(2.0))
                )))
            ))
        );
    }
}