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/*
* Canonical Expressions
*
* AKA, simplified, normalized algebraic expressions.
*
*/
use std::fmt;
use crate::sexpr::SExpr;
/*
pub enum NumericConstant {
Pi, // 3.141592...
E, // 2.718281...
}
*/
#[derive(Clone, PartialEq, PartialOrd)]
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)),
}
}
}
#[derive(Clone, PartialEq, PartialOrd)]
pub enum CExpr {
// order here is important for sorting, etc
Number(CNumber),
Symbol(String),
Sum(Option<CNumber>, Vec<CExpr>),
Product(Option<CNumber>, Vec<CExpr>),
Exponent(Box<CExpr>, Box<CExpr>),
Factorial(Box<CExpr>),
UnaryFunction(String, Box<CExpr>),
}
impl CExpr {
/*
fn sort_type_val(&self) -> u8 {
use CExpr::*;
match self {
Number(Integer(_)) => 1,
Number(Rational(_)) => 2,
Number(Float(_)) => 3,
Symbol(_) => 3,
Sum(Some(_), _) => 4,
Sum(None, _) => 4,
Product(Some(_), _) => 4,
Product(None, _) => 4,
Exponent(_, _) => 4,
Factorial(_) => 4,
UnaryFunction(_, _) => 4,
}
}
*/
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("null not handled".to_string()),
SExpr::SIdentifier(v) => 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> {
// 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) =>
Ok(CExpr::Factorial(Box::new(CExpr::from_sexpr(&rest[0])?))),
("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])?;
use CExpr::*;
use CNumber::*;
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),
(base, power) => Ok(Exponent(Box::new(base), Box::new(power))),
}
},
("/", 2) => {
if let (SExpr::SInteger(numer), SExpr::SInteger(denom)) = (&rest[0], &rest[1]) {
match (numer, denom) {
(_, 0) => Err("division by zero".to_string()),
(0, _) => Ok(CExpr::Number(CNumber::Integer(0))),
(a, 1) => Ok(CExpr::Number(CNumber::Integer(*a))),
(a, b) if a == b => Ok(CExpr::Number(CNumber::Integer(1))),
(a, b) if a % b == 0 => Ok(CExpr::Number(CNumber::Integer(a/b))),
_ => Ok(CExpr::Number(CNumber::Rational(*numer, *denom))),
}
} else {
Err("only integers in fractions supported".to_string())
}
},
// 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>>()?),
// TODO: subtraction, division
("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(mut list: Vec<CExpr>) -> Result<CExpr, String> {
use CExpr::*;
use CNumber::*;
list.sort_by(|a, b| a.partial_cmp(b).unwrap());
match list.as_slice() {
[Number(Integer(0)), e] => Ok(e.clone()), // XXX: remove clone()
[Number(Integer(a)), Number(Integer(b))] => Ok(Number(Integer(a+b))),
[Number(Integer(a)), Number(Rational(n, d))] => Ok(Number(Rational(n+a*d, *d))),
_ => Ok(Sum(None, list))
}
}
pub fn new_product(mut list: Vec<CExpr>) -> Result<CExpr, String> {
use CExpr::*;
use CNumber::*;
list.sort_by(|a, b| a.partial_cmp(b).unwrap());
match list.as_slice() {
[Number(Integer(1)), e] => Ok(e.clone()), // XXX: remove clone()
[Number(Integer(a)), Number(Integer(b))] => Ok(Number(Integer(a*b))),
[Number(Integer(a)), Number(Rational(n, d))] => Ok(Number(Rational(a*n, *d))),
_ => Ok(Product(None, list))
}
}
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::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),
}
}
}
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