mathhook_core/formatter/

wolfram.rs

use super::{FormattingContext, FormattingError};
use crate::core::expression::smart_display::SmartDisplayFormatter;
use crate::core::expression::{CalculusData, RelationType};
use crate::core::{Expression, Number};
use crate::functions::intelligence::get_universal_registry;

const MAX_RECURSION_DEPTH: usize = 1000;
const MAX_TERMS_PER_OPERATION: usize = 10000;

/// Wolfram formatting context
#[derive(Debug, Default, Clone)]
pub struct WolframContext {
    pub needs_parentheses: bool,
}

impl FormattingContext for WolframContext {}

/// Format the expression to Wolfram Language
pub trait WolframFormatter {
    /// Format an Expression as Wolfram Language notation
    ///
    /// Converts mathematical expressions into Wolfram Language format suitable for
    /// use in Mathematica and other Wolfram products.
    ///
    /// # Arguments
    /// * `context` - Wolfram formatting configuration
    ///
    /// # Context Options
    /// * `needs_parentheses` - Whether to wrap the entire expression in parentheses
    ///
    /// # Examples
    /// ```
    /// use mathhook_core::{Expression, expr};
    /// use mathhook_core::formatter::wolfram::{WolframFormatter, WolframContext};
    ///
    /// let expression = expr!(x ^ 2);
    /// let context = WolframContext::default();
    /// let result = expression.to_wolfram(&context).unwrap();
    /// assert!(result.contains("Power"));
    /// assert!(result.contains("x"));
    /// ```
    ///
    /// # Error Handling
    /// Returns error messages for expressions that exceed safety limits:
    /// - Maximum recursion depth (1000 levels)
    /// - Maximum terms per operation (10000 terms)
    fn to_wolfram(&self, context: &WolframContext) -> Result<String, FormattingError> {
        self.to_wolfram_with_depth(context, 0)
    }

    /// Format with explicit recursion depth tracking
    ///
    /// Internal method that provides stack overflow protection by tracking
    /// recursion depth. This method returns a Result to allow proper error
    /// propagation during recursive formatting.
    ///
    /// # Arguments
    /// * `context` - Wolfram formatting configuration
    /// * `depth` - Current recursion depth (starts at 0)
    ///
    /// # Returns
    /// * `Ok(String)` - Successfully formatted Wolfram expression
    /// * `Err(String)` - Error message if limits exceeded
    ///
    /// # Safety Limits
    /// * Maximum recursion depth: 1000 levels
    /// * Maximum terms per operation: 10000 terms/factors/arguments
    fn to_wolfram_with_depth(
        &self,
        context: &WolframContext,
        depth: usize,
    ) -> Result<String, FormattingError>;

    /// Convert function to Wolfram Language with depth tracking
    fn format_function_with_depth(
        &self,
        name: &str,
        args: &[Expression],
        context: &WolframContext,
        depth: usize,
    ) -> Result<String, FormattingError>;
}

impl WolframFormatter for Expression {
    fn to_wolfram_with_depth(
        &self,
        context: &WolframContext,
        depth: usize,
    ) -> Result<String, FormattingError> {
        if depth > MAX_RECURSION_DEPTH {
            return Err(FormattingError::RecursionLimitExceeded {
                depth,
                limit: MAX_RECURSION_DEPTH,
            });
        }

        match self {
            Expression::Number(Number::Integer(n)) => Ok(n.to_string()),
            Expression::Number(Number::BigInteger(n)) => Ok(n.to_string()),
            Expression::Number(Number::Rational(r)) => {
                if r.denom() == &num_bigint::BigInt::from(1) {
                    Ok(r.numer().to_string())
                } else {
                    // Use Power[denominator, -1] for proper Wolfram syntax
                    Ok(format!("Times[{}, Power[{}, -1]]", r.numer(), r.denom()))
                }
            }
            Expression::Number(Number::Float(f)) => Ok(f.to_string()),
            Expression::Symbol(s) => Ok(s.name().to_owned()),
            Expression::Add(terms) => {
                if terms.len() > MAX_TERMS_PER_OPERATION {
                    return Err(FormattingError::TooManyTerms {
                        count: terms.len(),
                        limit: MAX_TERMS_PER_OPERATION,
                    });
                }

                if terms.len() == 1 {
                    terms[0].to_wolfram_with_depth(context, depth + 1)
                } else if terms.len() == 2
                    && SmartDisplayFormatter::is_negated_expression(&terms[1])
                {
                    // Smart subtraction detection: x + (-1 * y) → Subtract[x, y]
                    if let Some(positive_part) =
                        SmartDisplayFormatter::extract_negated_expression(&terms[1])
                    {
                        Ok(format!(
                            "Subtract[{}, {}]",
                            terms[0].to_wolfram_with_depth(context, depth + 1)?,
                            positive_part.to_wolfram_with_depth(context, depth + 1)?
                        ))
                    } else {
                        let mut term_strs = Vec::with_capacity(terms.len());
                        for term in terms.iter() {
                            term_strs.push(term.to_wolfram_with_depth(context, depth + 1)?);
                        }
                        Ok(format!("Plus[{}]", term_strs.join(", ")))
                    }
                } else {
                    let mut term_strs = Vec::with_capacity(terms.len());
                    for term in terms.iter() {
                        term_strs.push(term.to_wolfram_with_depth(context, depth + 1)?);
                    }
                    Ok(format!("Plus[{}]", term_strs.join(", ")))
                }
            }
            Expression::Mul(factors) => {
                if factors.len() > MAX_TERMS_PER_OPERATION {
                    return Err(FormattingError::TooManyTerms {
                        count: factors.len(),
                        limit: MAX_TERMS_PER_OPERATION,
                    });
                }

                if factors.len() == 1 {
                    factors[0].to_wolfram_with_depth(context, depth + 1)
                } else if let Some((dividend, divisor)) =
                    SmartDisplayFormatter::extract_division_parts(factors)
                {
                    // Smart division detection: x * y^(-1) → Divide[x, y]
                    Ok(format!(
                        "Divide[{}, {}]",
                        dividend.to_wolfram_with_depth(context, depth + 1)?,
                        divisor.to_wolfram_with_depth(context, depth + 1)?
                    ))
                } else {
                    let mut factor_strs = Vec::with_capacity(factors.len());
                    for factor in factors.iter() {
                        factor_strs.push(factor.to_wolfram_with_depth(context, depth + 1)?);
                    }
                    Ok(format!("Times[{}]", factor_strs.join(", ")))
                }
            }
            Expression::Pow(base, exp) => Ok(format!(
                "Power[{}, {}]",
                base.to_wolfram_with_depth(context, depth + 1)?,
                exp.to_wolfram_with_depth(context, depth + 1)?
            )),
            Expression::Function { name, args } => {
                self.format_function_with_depth(name, args, context, depth + 1)
            }
            Expression::Complex(complex_data) => Ok(format!(
                "Complex[{}, {}]",
                complex_data
                    .real
                    .to_wolfram_with_depth(context, depth + 1)?,
                complex_data
                    .imag
                    .to_wolfram_with_depth(context, depth + 1)?
            )),
            Expression::Matrix(_) => Ok("matrix".to_owned()),
            Expression::Constant(c) => Ok(format!("{:?}", c)),
            Expression::Relation(relation_data) => {
                let left_wolfram = relation_data
                    .left
                    .to_wolfram_with_depth(context, depth + 1)?;
                let right_wolfram = relation_data
                    .right
                    .to_wolfram_with_depth(context, depth + 1)?;
                let operator = match relation_data.relation_type {
                    RelationType::Equal => "Equal",
                    RelationType::NotEqual => "Unequal",
                    RelationType::Less => "Less",
                    RelationType::LessEqual => "LessEqual",
                    RelationType::Greater => "Greater",
                    RelationType::GreaterEqual => "GreaterEqual",
                    RelationType::Approximate => "TildeEqual",
                    RelationType::Similar => "Tilde",
                    RelationType::Proportional => "Proportional",
                    RelationType::Congruent => "Congruent",
                };
                Ok(format!("{}[{}, {}]", operator, left_wolfram, right_wolfram))
            }
            Expression::Piecewise(piecewise_data) => {
                let mut conditions = Vec::new();
                let mut values = Vec::new();

                for (condition, value) in &piecewise_data.pieces {
                    conditions.push(condition.to_wolfram_with_depth(context, depth + 1)?);
                    values.push(value.to_wolfram_with_depth(context, depth + 1)?);
                }

                if let Some(default_value) = &piecewise_data.default {
                    conditions.push("True".to_owned());
                    values.push(default_value.to_wolfram_with_depth(context, depth + 1)?);
                }

                let conditions_list = format!("{{{}}}", conditions.join(", "));
                let values_list = format!("{{{}}}", values.join(", "));
                Ok(format!("Piecewise[{}, {}]", values_list, conditions_list))
            }
            Expression::Set(elements) => {
                if elements.len() > MAX_TERMS_PER_OPERATION {
                    return Err(FormattingError::TooManyTerms {
                        count: elements.len(),
                        limit: MAX_TERMS_PER_OPERATION,
                    });
                }

                if elements.is_empty() {
                    Ok("{}".to_owned())
                } else {
                    let mut element_strs = Vec::with_capacity(elements.len());
                    for elem in elements.iter() {
                        element_strs.push(elem.to_wolfram_with_depth(context, depth + 1)?);
                    }
                    Ok(format!("{{{}}}", element_strs.join(", ")))
                }
            }
            Expression::Interval(_) => Ok("interval".to_owned()),
            Expression::Calculus(calculus_data) => {
                Ok(match calculus_data.as_ref() {
                    CalculusData::Derivative {
                        expression,
                        variable,
                        order,
                    } => {
                        if *order == 1 {
                            format!(
                                "D[{}, {}]",
                                expression.to_wolfram_with_depth(context, depth + 1)?,
                                variable.name()
                            )
                        } else {
                            format!(
                                "D[{}, {{{}, {}}}]",
                                expression.to_wolfram_with_depth(context, depth + 1)?,
                                variable.name(),
                                order
                            )
                        }
                    }
                    CalculusData::Integral {
                        integrand,
                        variable,
                        bounds,
                    } => match bounds {
                        None => format!(
                            "Integrate[{}, {}]",
                            integrand.to_wolfram_with_depth(context, depth + 1)?,
                            variable.name()
                        ),
                        Some((start, end)) => format!(
                            "Integrate[{}, {{{}, {}, {}}}]",
                            integrand.to_wolfram_with_depth(context, depth + 1)?,
                            variable.name(),
                            start.to_wolfram_with_depth(context, depth + 1)?,
                            end.to_wolfram_with_depth(context, depth + 1)?
                        ),
                    },
                    CalculusData::Limit {
                        expression,
                        variable,
                        point,
                        direction: _,
                    } => {
                        // Simplified Wolfram limit format for roundtrip consistency
                        format!(
                            "Limit[{}, {} -> {}]",
                            expression.to_wolfram_with_depth(context, depth + 1)?,
                            variable.name(),
                            point.to_wolfram_with_depth(context, depth + 1)?
                        )
                    }
                    CalculusData::Sum {
                        expression,
                        variable,
                        start,
                        end,
                    } => {
                        format!(
                            "Sum[{}, {{{}, {}, {}}}]",
                            expression.to_wolfram_with_depth(context, depth + 1)?,
                            variable.name(),
                            start.to_wolfram_with_depth(context, depth + 1)?,
                            end.to_wolfram_with_depth(context, depth + 1)?
                        )
                    }
                    CalculusData::Product {
                        expression,
                        variable,
                        start,
                        end,
                    } => {
                        format!(
                            "Product[{}, {{{}, {}, {}}}]",
                            expression.to_wolfram_with_depth(context, depth + 1)?,
                            variable.name(),
                            start.to_wolfram_with_depth(context, depth + 1)?,
                            end.to_wolfram_with_depth(context, depth + 1)?
                        )
                    }
                })
            }
            Expression::MethodCall(method_data) => {
                let object_str = method_data
                    .object
                    .to_wolfram_with_depth(context, depth + 1)?;
                let args_str = method_data
                    .args
                    .iter()
                    .map(|arg| arg.to_wolfram_with_depth(context, depth + 1))
                    .collect::<Result<Vec<_>, _>>()?
                    .join(", ");
                Ok(format!(
                    "{}.{}[{}]",
                    object_str, method_data.method_name, args_str
                ))
            }
        }
    }

    /// Convert function to Wolfram Language with depth tracking
    fn format_function_with_depth(
        &self,
        name: &str,
        args: &[Expression],
        context: &WolframContext,
        depth: usize,
    ) -> Result<String, FormattingError> {
        if args.len() > MAX_TERMS_PER_OPERATION {
            return Err(FormattingError::TooManyTerms {
                count: args.len(),
                limit: MAX_TERMS_PER_OPERATION,
            });
        }

        let registry = get_universal_registry();
        let wolfram_name = registry
            .get_properties(name)
            .and_then(|props| match props {
                crate::functions::properties::FunctionProperties::Elementary(elem_props) => {
                    elem_props.wolfram_name
                }
                crate::functions::properties::FunctionProperties::Special(spec_props) => {
                    spec_props.wolfram_name
                }
                _ => None,
            })
            .unwrap_or(name);

        if args.is_empty() {
            Ok(wolfram_name.to_owned())
        } else {
            let mut arg_strs = Vec::with_capacity(args.len());
            for arg in args.iter() {
                arg_strs.push(arg.to_wolfram_with_depth(context, depth + 1)?);
            }
            Ok(format!("{}[{}]", wolfram_name, arg_strs.join(", ")))
        }
    }
}