/*
 * "Canonical" Expressions
 *
 * AKA, simplified, normalized algebraic expressions.
 */

use crate::sexpr::SExpr;
use std::fmt;

#[derive(Debug, Clone, PartialEq, PartialOrd)]
pub enum NumericConstant {
    Pi,
    E,
    GoldenRatio,
}

impl NumericConstant {
    /*
        pub fn as_number(&self) -> CNumber {
            use CNumber::*;
            use NumericConstant::*;
            match self {
                Pi => Float(3.14159265358979323846f64),
                E => Float(2.71828182845904523536f64),
                GoldenRatio => Float(1.61803398874989484820f64),
            }
        }
    */

    pub fn as_string(&self) -> String {
        use NumericConstant::*;
        match self {
            Pi => "pi".to_string(),
            E => "e".to_string(),
            GoldenRatio => "golden-ratio".to_string(),
        }
    }
}

#[derive(Clone, PartialEq, PartialOrd, Debug)]
pub enum CNumber {
    // order here is important for sorting, etc
    Integer(i64),
    Rational(i64, i64),
    Float(f64),
}

impl CNumber {
    pub fn to_sexpr(&self) -> Result<SExpr, String> {
        match self {
            CNumber::Integer(v) => Ok(SExpr::SInteger(*v)),
            CNumber::Rational(a, b) => Ok(SExpr::SList(vec![
                SExpr::SIdentifier("/".to_string()),
                SExpr::SInteger(*a),
                SExpr::SInteger(*b),
            ])),
            CNumber::Float(v) => Ok(SExpr::SFloat(*v)),
        }
    }

    pub fn sum(&self, other: &CNumber) -> CNumber {
        use CNumber::*;
        match (self, other) {
            (Integer(a), Integer(b)) => Integer(a + b),
            (Integer(i), Rational(n, d)) | (Rational(n, d), Integer(i)) => Rational(n + d * i, *d),
            (Rational(a, b), Rational(c, d)) if b == d => Rational(a + c, *d),
            (Rational(a, b), Rational(c, d)) => Rational(a * d + c * b, b * d),
            (Float(a), Float(b)) => Float(a + b),
            (Integer(i), Float(f)) | (Float(f), Integer(i)) => Float((*i as f64) + f),
            (Rational(n, d), Float(f)) | (Float(f), Rational(n, d)) => {
                Float(f + (*n as f64) / (*d as f64))
            }
        }
    }

    pub fn product(&self, other: &CNumber) -> CNumber {
        use CNumber::*;
        match (self, other) {
            (Integer(0), _) | (_, Integer(0)) => Integer(0),
            (Integer(a), Integer(b)) => Integer(a * b),
            (Integer(i), Rational(n, d)) | (Rational(n, d), Integer(i)) => Rational(i * n, *d),
            (Rational(a, b), Rational(c, d)) if a == d && b == c => Integer(1),
            (Rational(a, b), Rational(c, d)) => Rational(a * c, b * d),
            (Float(a), Float(b)) => Float(a * b),
            (Integer(i), Float(f)) | (Float(f), Integer(i)) => Float((*i as f64) * f),
            (Rational(n, d), Float(f)) | (Float(f), Rational(n, d)) => {
                Float(f * (*n as f64) / (*d as f64))
            }
        }
    }

    pub fn is_negative(&self) -> bool {
        use CNumber::*;
        match self {
            Integer(i) => *i < 0,
            Rational(n, _) => *n < 0,
            Float(f) => *f < 0.0f64,
        }
    }
}

#[derive(Clone, PartialEq, PartialOrd, Debug)]
pub enum CExpr {
    // order here is important for sorting, etc
    Number(CNumber),
    Constant(NumericConstant),
    Symbol(String),
    Sum(Option<CNumber>, Vec<CExpr>),
    Product(Option<CNumber>, Vec<CExpr>),
    Exponent(Box<CExpr>, Box<CExpr>),
    Factorial(Box<CExpr>),
    UnaryFunction(String, Box<CExpr>),
}

fn compute_factorial(n: i64) -> i64 {
    if n < 0 {
        panic!("tried to compute negative factorial");
    } else if n == 0 {
        return 1;
    } else {
        return n * compute_factorial(n - 1);
    }
}

impl CExpr {
    pub fn from_sexpr(sexpr: &SExpr) -> Result<CExpr, String> {
        // not all cases are handled; some atoms are covered trivialy
        match sexpr {
            SExpr::SNull => Err("null not handled".to_string()),
            SExpr::SBoolean(_) => Err("booleans not handled".to_string()),
            SExpr::SInteger(v) => Ok(CExpr::Number(CNumber::Integer(*v))),
            SExpr::SFloat(v) => Ok(CExpr::Number(CNumber::Float(*v))),
            SExpr::SString(_) => Err("strings not handled".to_string()),
            SExpr::SIdentifier(v) => match v.as_str() {
                "pi" => Ok(CExpr::Constant(NumericConstant::Pi)),
                "e" => Ok(CExpr::Constant(NumericConstant::E)),
                "golden-ratio" => Ok(CExpr::Constant(NumericConstant::GoldenRatio)),
                _ => Ok(CExpr::Symbol(v.to_string())),
            },
            SExpr::SList(l) => CExpr::from_sexpr_list(l),
        }
    }

    pub fn from_sexpr_list(list: &Vec<SExpr>) -> Result<CExpr, String> {
        use CExpr::*;
        use CNumber::*;
        use SExpr::*;
        // https://adventures.michaelfbryan.com/posts/daily/slice-patterns/
        if let [SExpr::SIdentifier(ident), rest @ ..] = list.as_slice() {
            match (ident.as_str(), rest.len()) {
                ("factorial", 1) => match CExpr::from_sexpr(&rest[0])? {
                    Number(n) if n.is_negative() => {
                        Err("negative factorial is not defined".to_string())
                    }
                    Number(Integer(i)) if i <= 18 => Ok(Number(Integer(compute_factorial(i)))),
                    other => Ok(Factorial(Box::new(other))),
                },
                ("cos" | "sin" | "tan", 1) => Ok(CExpr::UnaryFunction(
                    ident.to_string(),
                    Box::new(CExpr::from_sexpr(&rest[0])?),
                )),
                ("^", 2) => {
                    let base = CExpr::from_sexpr(&rest[0])?;
                    let power = CExpr::from_sexpr(&rest[1])?;
                    match (base, power) {
                        (Number(Integer(0)), _) => Ok(Number(Integer(0))),
                        (Number(Integer(1)), _) => Ok(Number(Integer(1))),
                        (_, Number(Integer(0))) => Ok(Number(Integer(1))),
                        (base, Number(Integer(1))) => Ok(base),
                        (Number(Rational(1, d)), Number(Integer(-1))) => Ok(Number(Integer(d))),
                        (Number(Rational(n, d)), Number(Integer(-1))) => Ok(Number(Rational(d, n))),
                        (Exponent(base, p1), p2) => match (*p1, p2) {
                            (Number(n1), Number(n2)) => {
                                Ok(Exponent(base, Box::new(Number(n1.product(&n2)))))
                            }
                            (p1, p2) => {
                                Ok(Exponent(base, Box::new(CExpr::new_product(vec![p1, p2])?)))
                            }
                        },
                        (base, power) => Ok(Exponent(Box::new(base), Box::new(power))),
                    }
                }
                ("/", 2) => match (&rest[0], &rest[1]) {
                    (_, SInteger(0)) => Err("division by zero".to_string()),
                    (SInteger(0), _) => Ok(Number(Integer(0))),
                    (se, SInteger(1)) => CExpr::from_sexpr(se),
                    (SInteger(a), SInteger(b)) if a == b => Ok(Number(Integer(1))),
                    (SInteger(a), SInteger(b)) if a % b == 0 => Ok(Number(Integer(a / b))),
                    (SInteger(a), SInteger(b)) => Ok(Number(Rational(*a, *b))),
                    (SInteger(1), b) => {
                        let denom = CExpr::from_sexpr(b)?;
                        Ok(Exponent(Box::new(denom), Box::new(Number(Integer(-1)))))
                    }
                    (a, b) => {
                        let (numer, denom) = (CExpr::from_sexpr(a)?, CExpr::from_sexpr(b)?);
                        CExpr::new_product(vec![
                            numer,
                            Exponent(Box::new(denom), Box::new(Number(Integer(-1)))),
                        ])
                    }
                },
                // TODO: how to make range unbounded? or less bounded?
                ("+", 2..=5000) => {
                    CExpr::new_sum(rest.iter().map(|v| CExpr::from_sexpr(v)).collect::<Result<
                        Vec<CExpr>,
                        String,
                    >>(
                    )?)
                }
                ("*", 2..=5000) => {
                    CExpr::new_product(rest.iter().map(|v| CExpr::from_sexpr(v)).collect::<Result<
                        Vec<CExpr>,
                        String,
                    >>(
                    )?)
                }
                ("-", 2) => {
                    let a = CExpr::from_sexpr(&rest[0])?;
                    let b = CExpr::from_sexpr(&rest[1])?;
                    match (a, b) {
                        (expr, Number(Integer(0))) => Ok(expr),
                        (Number(Integer(a)), Number(Integer(b))) => Ok(Number(Integer(a - b))),
                        (a, b) => CExpr::new_sum(vec![
                            a,
                            CExpr::new_product(vec![Number(Integer(-1)), b])?,
                        ]),
                    }
                }
                ("factorial" | "^" | "cos" | "sin" | "tan", count) => {
                    Err(format!("wrong number of arguments to {}: {}", ident, count))
                }
                _ => Err(format!("procedure not handled: {}", ident)),
            }
        } else {
            Err(format!("S-Expr pattern not handled: {:?}", list))
        }
    }

    pub fn new_sum(list: Vec<CExpr>) -> Result<CExpr, String> {
        use CExpr::*;
        use CNumber::*;
        let (numeric, mut rest): (Vec<CExpr>, Vec<CExpr>) = list
            .into_iter()
            .flat_map(|e| match e {
                Sum(None, l) => l,
                Sum(Some(num), mut l) => {
                    l.push(Number(num));
                    l
                }
                e => vec![e],
            })
            .partition(|v| {
                if let Number(Integer(_) | Rational(_, _)) = v {
                    true
                } else {
                    false
                }
            });

        let num: Option<CNumber> = numeric
            .into_iter()
            .map(|v| if let Number(n) = v { n } else { unreachable!() })
            .reduce(|a, b| a.sum(&b));

        rest.sort_by(|a, b| a.partial_cmp(b).unwrap());

        match (num, rest) {
            (None, mut rest) if rest.len() == 1 => Ok(rest.remove(0)),
            (None, rest) if rest.is_empty() => unreachable!("empty list passed to new_product()"),
            (Some(n), rest) if rest.is_empty() => Ok(Number(n)),
            (Some(Integer(0)), rest) => Ok(Sum(None, rest)),
            (n, r) => Ok(Sum(n, r)),
        }
    }

    pub fn new_product(list: Vec<CExpr>) -> Result<CExpr, String> {
        use CExpr::*;
        use CNumber::*;
        let (numeric, mut rest): (Vec<CExpr>, Vec<CExpr>) = list
            .into_iter()
            .flat_map(|e| match e {
                Product(None, l) => l,
                Product(Some(num), mut l) => {
                    l.push(Number(num));
                    l
                }
                e => vec![e],
            })
            .partition(|v| {
                if let Number(Integer(_) | Rational(_, _)) = v {
                    true
                } else {
                    false
                }
            });

        let num: Option<CNumber> = numeric
            .into_iter()
            .map(|v| if let Number(n) = v { n } else { unreachable!() })
            .reduce(|a, b| a.product(&b));

        rest.sort_by(|a, b| a.partial_cmp(b).unwrap());

        match (num, rest) {
            (None, mut rest) if rest.len() == 1 => Ok(rest.remove(0)),
            (None, rest) if rest.is_empty() => unreachable!("empty list passed to new_product()"),
            (Some(n), rest) if rest.is_empty() => Ok(Number(n)),
            (Some(Integer(1)), rest) => Ok(Product(None, rest)),
            (n, r) => Ok(Product(n, r)),
        }
    }

    pub fn to_sexpr(&self) -> Result<SExpr, String> {
        match self {
            CExpr::Symbol(s) => Ok(SExpr::SIdentifier(s.to_string())),
            CExpr::Number(n) => n.to_sexpr(),
            CExpr::Constant(n) => Ok(SExpr::SIdentifier(n.as_string())),
            CExpr::Sum(n, l) => {
                let mut list = l
                    .iter()
                    .map(|v| v.to_sexpr())
                    .collect::<Result<Vec<SExpr>, String>>()?;
                list.insert(0, SExpr::SIdentifier("+".to_string()));
                if let Some(num) = n {
                    list.insert(1, num.to_sexpr()?);
                }
                Ok(SExpr::SList(list))
            }
            CExpr::Product(n, l) => {
                let mut list = l
                    .iter()
                    .map(|v| v.to_sexpr())
                    .collect::<Result<Vec<SExpr>, String>>()?;
                list.insert(0, SExpr::SIdentifier("*".to_string()));
                if let Some(num) = n {
                    list.insert(1, num.to_sexpr()?);
                }
                Ok(SExpr::SList(list))
            }
            CExpr::Exponent(a, b) => Ok(SExpr::SList(vec![
                SExpr::SIdentifier("^".to_string()),
                a.to_sexpr()?,
                b.to_sexpr()?,
            ])),
            CExpr::Factorial(v) => Ok(SExpr::SList(vec![
                SExpr::SIdentifier("factorial".to_string()),
                v.to_sexpr()?,
            ])),
            CExpr::UnaryFunction(s, v) => Ok(SExpr::SList(vec![
                SExpr::SIdentifier(s.to_string()),
                v.to_sexpr()?,
            ])),
        }
    }

    pub fn from_str(raw: &str) -> Result<CExpr, String> {
        let ast = SExpr::from_str(raw)?;
        CExpr::from_sexpr(&ast)
    }
}

impl fmt::Display for CExpr {
    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
        match self.to_sexpr() {
            Ok(ast) => ast.fmt(f),
            Err(_) => Err(std::fmt::Error),
        }
    }
}