Exercise: Expression Evaluation

Let’s write a simple recursive evaluator for arithmetic expressions.

An example of a small arithmetic expression could be 10 + 20, which evaluates to 30. We can represent the expression as a tree:

A bigger and more complex expression would be (10 * 9) + ((3 - 4) * 5), which evaluates to 85. We represent this as a much bigger tree:

In code, we will represent the tree with two types:

// Copyright 2023 Google LLC
// SPDX-License-Identifier: Apache-2.0

/// An operation to perform on two subexpressions.
#[derive(Debug)]
enum Operation {
    Add,
    Sub,
    Mul,
    Div,
}

/// An expression, in tree form.
#[derive(Debug)]
enum Expression {
    /// An operation on two subexpressions.
    Op { op: Operation, left: Box<Expression>, right: Box<Expression> },

    /// A literal value
    Value(i64),
}

The Box type here is a smart pointer, and will be covered in detail later in the course. An expression can be “boxed” with Box::new as seen in the tests. To evaluate a boxed expression, use the deref operator (*) to “unbox” it: eval(*boxed_expr).

Create a new Cargo library project with

cargo new --lib evaluator

Copy and paste the code below into a the src/lib.rs file.

Then begin implementing eval. Use cargo test to ensure that the final library passes the tests. It may be helpful to use todo!() and get the tests to pass one-by-one. You can also skip a test temporarily with #[ignore]:

#[test]
#[ignore]
fn test_value() { .. }

// Copyright 2023 Google LLC
// SPDX-License-Identifier: Apache-2.0

/// An operation to perform on two subexpressions.
#[derive(Debug)]
enum Operation {
    Add,
    Sub,
    Mul,
    Div,
}

/// An expression, in tree form.
#[derive(Debug)]
enum Expression {
    /// An operation on two subexpressions.
    Op { op: Operation, left: Box<Expression>, right: Box<Expression> },

    /// A literal value
    Value(i64),
}

fn eval(e: Expression) -> i64 {
    todo!()
}

#[test]
fn test_value() {
    assert_eq!(eval(Expression::Value(19)), 19);
}

#[test]
fn test_sum() {
    assert_eq!(
        eval(Expression::Op {
            op: Operation::Add,
            left: Box::new(Expression::Value(10)),
            right: Box::new(Expression::Value(20)),
        }),
        30
    );
}

#[test]
fn test_recursion() {
    let term1 = Expression::Op {
        op: Operation::Mul,
        left: Box::new(Expression::Value(10)),
        right: Box::new(Expression::Value(9)),
    };
    let term2 = Expression::Op {
        op: Operation::Mul,
        left: Box::new(Expression::Op {
            op: Operation::Sub,
            left: Box::new(Expression::Value(3)),
            right: Box::new(Expression::Value(4)),
        }),
        right: Box::new(Expression::Value(5)),
    };
    assert_eq!(
        eval(Expression::Op {
            op: Operation::Add,
            left: Box::new(term1),
            right: Box::new(term2),
        }),
        85
    );
}

#[test]
fn test_zeros() {
    assert_eq!(
        eval(Expression::Op {
            op: Operation::Add,
            left: Box::new(Expression::Value(0)),
            right: Box::new(Expression::Value(0))
        }),
        0
    );
    assert_eq!(
        eval(Expression::Op {
            op: Operation::Mul,
            left: Box::new(Expression::Value(0)),
            right: Box::new(Expression::Value(0))
        }),
        0
    );
    assert_eq!(
        eval(Expression::Op {
            op: Operation::Sub,
            left: Box::new(Expression::Value(0)),
            right: Box::new(Expression::Value(0))
        }),
        0
    );
}

#[test]
fn test_div() {
    assert_eq!(
        eval(Expression::Op {
            op: Operation::Div,
            left: Box::new(Expression::Value(10)),
            right: Box::new(Expression::Value(2)),
        }),
        5
    )
}