Implement expression normalisation
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@@ -1,3 +1,9 @@
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pub mod normalise;
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#[derive(Debug)]
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pub enum Error {
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}
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pub trait Evaluator {
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type Expr;
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type Error;
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@@ -0,0 +1,305 @@
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use crate::expression::Expression;
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use crate::eval::{Error, Evaluator};
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pub struct Normaliser;
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impl Normaliser {
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pub fn new() -> Self {
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Normaliser {}
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}
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}
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impl Evaluator for Normaliser {
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type Expr = Expression;
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type Error = Error;
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fn eval(&mut self, input: Expression) -> Result<Expression, Error> {
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Ok(normalise(input))
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}
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}
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fn normalise(expr: Expression) -> Expression {
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match expr {
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Expression::Integer(_) => expr,
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Expression::Symbol(_) => expr,
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Expression::Sum(x, y) =>
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Expression::Sum(normalise_boxed(x), normalise_boxed(y)),
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Expression::Product(x, y) =>
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Expression::Product(normalise_boxed(x), normalise_boxed(y)),
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Expression::Exponent(x, y) =>
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Expression::Exponent(normalise_boxed(x), normalise_boxed(y)),
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Expression::Difference(x, y) =>
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Expression::Sum(
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normalise_boxed(x), negation(normalise_boxed(y))),
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Expression::Quotient(x, y) => {
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if x.integer().is_some() && y.integer().is_some() {
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Expression::Quotient(x, y)
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} else {
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Expression::Product(
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normalise_boxed(x), reciprocal(normalise_boxed(y)))
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}
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},
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}
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}
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fn normalise_boxed(
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mut b: std::boxed::Box<Expression>) -> std::boxed::Box<Expression> {
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*b = normalise(*b);
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b
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}
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fn negation(
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expr: std::boxed::Box<Expression>) -> std::boxed::Box<Expression> {
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let res = Expression::Product(
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std::boxed::Box::new(Expression::Integer(-1)), expr);
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std::boxed::Box::new(res)
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}
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fn reciprocal(
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expr: std::boxed::Box<Expression>) -> std::boxed::Box<Expression> {
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let res = if expr.is_constant() {
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Expression::Quotient(
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std::boxed::Box::new(Expression::Integer(1)), expr)
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} else {
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Expression::Exponent(
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expr, std::boxed::Box::new(Expression::Integer(-1)))
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};
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std::boxed::Box::new(res)
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}
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#[cfg(test)]
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mod tests {
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use super::*;
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#[test]
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fn integer_is_unchanged() {
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let input = Expression::Integer(0);
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let result = Normaliser::new().eval(input).unwrap();
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assert_eq!(result, Expression::Integer(0));
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}
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#[test]
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fn symbol_is_unchanged() {
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let input = Expression::Symbol('x');
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let result = Normaliser::new().eval(input).unwrap();
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assert_eq!(result, Expression::Symbol('x'));
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}
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#[test]
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fn sum_of_integers_is_unchanged() {
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let input = Expression::sum(
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Expression::Symbol('x'),
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Expression::Symbol('x'));
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let result = Normaliser::new().eval(input).unwrap();
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assert_eq!(
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result,
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Expression::sum(
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Expression::Symbol('x'),
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Expression::Symbol('x')));
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}
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#[test]
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fn product_of_integers_is_unchanged() {
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let input = Expression::product(
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Expression::Symbol('x'),
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Expression::Symbol('x'));
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let result = Normaliser::new().eval(input).unwrap();
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assert_eq!(
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result,
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Expression::product(
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Expression::Symbol('x'),
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Expression::Symbol('x')));
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}
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#[test]
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fn exponent_of_integers_is_unchanged() {
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let input = Expression::exponent(
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Expression::Symbol('x'),
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Expression::Symbol('x'));
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let result = Normaliser::new().eval(input).unwrap();
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assert_eq!(
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result,
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Expression::exponent(
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Expression::Symbol('x'),
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Expression::Symbol('x')));
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}
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#[test]
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fn difference_is_transformed_to_sum() {
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let input = Expression::difference(
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Expression::Symbol('x'),
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Expression::Symbol('x'));
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let result = Normaliser::new().eval(input).unwrap();
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assert_eq!(
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result,
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Expression::sum(
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Expression::Symbol('x'),
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Expression::product(
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Expression::Integer(-1),
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Expression::Symbol('x'))));
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}
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#[test]
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fn quotient_of_symbols_is_transformed_to_product() {
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let input = Expression::quotient(
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Expression::Symbol('x'),
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Expression::Symbol('x'));
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let result = Normaliser::new().eval(input).unwrap();
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assert_eq!(
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result,
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Expression::product(
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Expression::Symbol('x'),
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Expression::exponent(
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Expression::Symbol('x'),
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Expression::Integer(-1))));
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}
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#[test]
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fn quotient_of_integer_and_symbol_is_transformed_to_product() {
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let input = Expression::quotient(
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Expression::Integer(2),
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Expression::Symbol('x'));
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let result = Normaliser::new().eval(input).unwrap();
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assert_eq!(
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result,
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Expression::product(
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Expression::Integer(2),
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Expression::exponent(
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Expression::Symbol('x'),
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Expression::Integer(-1))));
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}
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#[test]
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fn quotient_of_symbol_and_integer_is_transformed_to_product() {
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let input = Expression::quotient(
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Expression::Symbol('x'),
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Expression::Integer(2));
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let result = Normaliser::new().eval(input).unwrap();
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assert_eq!(
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result,
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Expression::product(
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Expression::Symbol('x'),
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Expression::quotient(
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Expression::Integer(1),
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Expression::Integer(2))));
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}
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#[test]
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fn differences_inside_sum_are_normalised() {
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let input = Expression::sum(
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Expression::difference(
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Expression::Symbol('x'),
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Expression::Symbol('x')),
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Expression::difference(
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Expression::Symbol('x'),
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Expression::Symbol('x')));
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let result = Normaliser::new().eval(input).unwrap();
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assert_eq!(
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result,
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Expression::sum(
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Expression::sum(
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Expression::Symbol('x'),
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Expression::product(
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Expression::Integer(-1),
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Expression::Symbol('x'))),
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Expression::sum(
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Expression::Symbol('x'),
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Expression::product(
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Expression::Integer(-1),
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Expression::Symbol('x')))));
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}
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#[test]
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fn differences_inside_exponent_are_normalised() {
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let input = Expression::exponent(
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Expression::difference(
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Expression::Symbol('x'),
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Expression::Symbol('x')),
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Expression::difference(
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Expression::Symbol('x'),
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Expression::Symbol('x')));
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let result = Normaliser::new().eval(input).unwrap();
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assert_eq!(
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result,
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Expression::exponent(
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Expression::sum(
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Expression::Symbol('x'),
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Expression::product(
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Expression::Integer(-1),
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Expression::Symbol('x'))),
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Expression::sum(
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Expression::Symbol('x'),
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Expression::product(
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Expression::Integer(-1),
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Expression::Symbol('x')))));
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}
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#[test]
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fn differences_inside_difference_are_normalised() {
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let input = Expression::difference(
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Expression::difference(
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Expression::Symbol('x'),
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Expression::Symbol('x')),
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Expression::difference(
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Expression::Symbol('x'),
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Expression::Symbol('x')));
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let result = Normaliser::new().eval(input).unwrap();
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assert_eq!(
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result,
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Expression::sum(
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Expression::sum(
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Expression::Symbol('x'),
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Expression::product(
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Expression::Integer(-1),
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Expression::Symbol('x'))),
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Expression::product(
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Expression::Integer(-1),
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Expression::sum(
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Expression::Symbol('x'),
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Expression::product(
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Expression::Integer(-1),
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Expression::Symbol('x'))))));
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}
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#[test]
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fn differences_inside_quotient_are_normalised() {
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let input = Expression::quotient(
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Expression::difference(
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Expression::Symbol('x'),
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Expression::Symbol('x')),
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Expression::difference(
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Expression::Symbol('x'),
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Expression::Symbol('x')));
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let result = Normaliser::new().eval(input).unwrap();
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assert_eq!(
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result,
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Expression::product(
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Expression::sum(
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Expression::Symbol('x'),
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Expression::product(
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Expression::Integer(-1),
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Expression::Symbol('x'))),
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Expression::exponent(
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Expression::sum(
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Expression::Symbol('x'),
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Expression::product(
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Expression::Integer(-1),
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Expression::Symbol('x'))),
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Expression::Integer(-1))));
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}
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#[test]
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fn quotient_of_integers_is_unchanged() {
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let input = Expression::quotient(
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Expression::Integer(1),
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Expression::Integer(2));
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let result = Normaliser::new().eval(input).unwrap();
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assert_eq!(
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result,
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Expression::quotient(
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Expression::Integer(1),
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Expression::Integer(2)));
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}
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}
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@@ -35,6 +35,14 @@ impl Expression {
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std::boxed::Box::new(left), std::boxed::Box::new(right))
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}
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pub fn integer(&self) -> Option<i32> {
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if let Expression::Integer(x) = self {
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Some(*x)
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} else {
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None
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}
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}
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pub fn is_constant(&self) -> bool {
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match self {
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Expression::Integer(_) => true,
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