From aad169c24f2d4d1a9401dbc1f6737de5e876c6fb Mon Sep 17 00:00:00 2001
From: Camden Dixie O'Brien <cdo@wip.sh>
Date: Sat, 26 Sep 2026 09:41:44 +0100
Subject: [PATCH] Create binding power algebra handling associativity

---
 src/binding.rs | 187 +++++++++++++++++++++++++++++++++++++++++++++++++
 src/lib.rs     |   1 +
 2 files changed, 188 insertions(+)
 create mode 100644 src/binding.rs

diff --git a/src/binding.rs b/src/binding.rs
new file mode 100644
index 0000000..fc00e4a
--- /dev/null
+++ b/src/binding.rs
@@ -0,0 +1,187 @@
+use crate::token::Token;
+use crate::expression::Expression;
+
+#[derive(Copy, Clone, Debug, PartialEq)]
+pub enum Associativity {
+	Left,
+	Right,
+	Full,
+}
+
+#[derive(Copy, Clone, Debug, PartialEq, PartialOrd)]
+pub enum Power {
+	Minimum,
+	Addition,
+	Multiplication,
+	Exponentiation,
+	Maximum,
+}
+
+#[derive(Copy, Clone, Debug)]
+pub struct Binding {
+	power: Power,
+	associativity: Associativity,
+}
+
+impl Binding {
+	pub fn left(power: Power) -> Self {
+		Self { power, associativity: Associativity::Left }
+	}
+
+	pub fn right(power: Power) -> Self {
+		Self { power, associativity: Associativity::Right }
+	}
+
+	pub fn full(power: Power) -> Self {
+		Self { power, associativity: Associativity::Full }
+	}
+
+	pub fn of_operator(token: &Token) -> Self {
+		if token.starts_expression() {
+			Binding::full(Power::Multiplication)
+		} else {
+			match token {
+				Token::Plus => Binding::full(Power::Addition),
+				Token::Minus => Binding::left(Power::Addition),
+				Token::Times => Binding::full(Power::Multiplication),
+				Token::Divide => Binding::left(Power::Multiplication),
+				Token::Caret => Binding::right(Power::Exponentiation),
+				Token::CloseParen => Binding::left(Power::Minimum),
+				_ => unreachable!(),
+			}
+		}
+	}
+
+
+	pub fn of_expression(expr: &Expression) -> Self {
+		match expr {
+			Expression::Sum(_, _) => Self::full(Power::Addition),
+			Expression::Difference(_, _) => Self::left(Power::Addition),
+			Expression::Product(_, _) => Self::full(Power::Multiplication),
+			Expression::Quotient(_, _) => Self::left(Power::Multiplication),
+			Expression::Exponent(_, _) => Self::right(Power::Exponentiation),
+			Expression::Integer(_) => Self::left(Power::Maximum),
+			Expression::Symbol(_) => Self::left(Power::Maximum),
+		}
+	}
+}
+
+impl std::cmp::PartialEq for Binding {
+	fn eq(&self, other: &Self) -> bool
+	{
+		self.associativity == Associativity::Full
+			&& self.power == other.power
+	}
+}
+
+impl std::cmp::PartialOrd for Binding {
+	fn partial_cmp(&self, rhs: &Self) -> Option<std::cmp::Ordering>
+	{
+		Some(if self.power < rhs.power {
+			std::cmp::Ordering::Less
+		} else if self.power > rhs.power {
+			std::cmp::Ordering::Greater
+		} else {
+			match self.associativity {
+				Associativity::Left => std::cmp::Ordering::Less,
+				Associativity::Right => std::cmp::Ordering::Greater,
+				Associativity::Full => std::cmp::Ordering::Equal,
+			}
+		})
+	}
+}
+
+#[cfg(test)]
+mod tests {
+	use super::*;
+
+	#[test]
+	fn left_assoc_min_is_less_than_left_assoc_add() {
+		assert_eq!(
+			Binding::left(Power::Minimum).partial_cmp(
+				&Binding::left(Power::Addition)),
+			Some(std::cmp::Ordering::Less));
+	}
+
+	#[test]
+	fn left_assoc_add_is_less_than_left_assoc_add() {
+		assert_eq!(
+			Binding::left(Power::Addition).partial_cmp(
+				&Binding::left(Power::Addition)),
+			Some(std::cmp::Ordering::Less));
+	}
+
+	#[test]
+	fn left_assoc_mult_is_greater_than_left_assoc_add() {
+		assert_eq!(
+			Binding::left(Power::Multiplication).partial_cmp(
+				&Binding::left(Power::Addition)),
+			Some(std::cmp::Ordering::Greater));
+	}
+
+	#[test]
+	fn right_assoc_min_is_less_than_right_assoc_add() {
+		assert_eq!(
+			Binding::right(Power::Minimum).partial_cmp(
+				&Binding::right(Power::Addition)),
+			Some(std::cmp::Ordering::Less));
+	}
+
+	#[test]
+	fn right_assoc_add_is_greater_than_right_assoc_add() {
+		assert_eq!(
+			Binding::right(Power::Addition).partial_cmp(
+				&Binding::right(Power::Addition)),
+			Some(std::cmp::Ordering::Greater));
+	}
+
+	#[test]
+	fn right_assoc_mul_is_greater_than_right_assoc_add() {
+		assert_eq!(
+			Binding::right(Power::Multiplication).partial_cmp(
+				&Binding::right(Power::Addition)),
+			Some(std::cmp::Ordering::Greater));
+	}
+
+	#[test]
+	fn full_assoc_min_is_less_than_full_assoc_add() {
+		assert_eq!(
+			Binding::full(Power::Minimum).partial_cmp(
+				&Binding::full(Power::Addition)),
+			Some(std::cmp::Ordering::Less));
+	}
+
+	#[test]
+	fn full_assoc_add_is_equal_to_full_assoc_add() {
+		assert_eq!(
+			Binding::full(Power::Addition).partial_cmp(
+				&Binding::full(Power::Addition)),
+			Some(std::cmp::Ordering::Equal));
+	}
+
+	#[test]
+	fn full_assoc_mul_is_greater_than_full_assoc_add() {
+		assert_eq!(
+			Binding::full(Power::Multiplication).partial_cmp(
+				&Binding::full(Power::Addition)),
+			Some(std::cmp::Ordering::Greater));
+	}
+
+	#[test]
+	fn left_assoc_min_is_not_equal_to_left_assoc_min() {
+		assert_ne!(
+			Binding::left(Power::Minimum), Binding::left(Power::Minimum));
+	}
+
+	#[test]
+	fn right_assoc_min_is_not_equal_to_right_assoc_min() {
+		assert_ne!(
+			Binding::right(Power::Minimum), Binding::right(Power::Minimum));
+	}
+
+	#[test]
+	fn full_assoc_min_is_equal_to_full_assoc_min() {
+		assert_eq!(
+			Binding::full(Power::Minimum), Binding::left(Power::Minimum));
+	}
+}
diff --git a/src/lib.rs b/src/lib.rs
index 6769acd..4139ad5 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -1,4 +1,5 @@
 pub mod token;
 pub mod expression;
+pub mod binding;
 
 pub mod lex;