# Recursive Enum expression trees in Rust

I mused about an implementation of expression trees in Rust two days ago. This is to build a Genetic Programming library in Rust - an biologically-inspired approach to finding robust solutions to difficult problems.

As discussed elsewhere I’ve become a keen fan of Rust. This language’s limited generics pose interesting problems for expressing and generating equations as described above.

There are two common ways to represent a tree datastructure:

- The most obvious way is similar to a Linked List: allocate a separate portion of memory for each node in the tree and store pointers to the child/parent nodes. This makes it cheap to expand the tree and is a very natural representation.
- The other way is to put the tree into an array. Map the parent-child relationships into indices and you can store a tree as a single block of memory. Adding nodes can require copying all this data into a larger region of memory but this has a variety of benefits such as cache locality.

We can define the semantics of a heap-allocated expression tree at compile time. Here’s a cut-down example - you can get and play with the full code here.

```
#[derive(Clone, Debug, PartialEq, Eq)]
enum Equation {
Add(Node<Equation>, Node<Equation>), // `a + b`
Sub(Node<Equation>, Node<Equation>), // `a - b`
Mul(Node<Equation>, Node<Equation>), // `a * b`
Div(Node<Equation>, Node<Equation>), // `a / b`
Neg(Node<Equation>), // `-a`
Sin(Node<Equation>), // `sin(a)`
Float(f64), // evaluates to a constant 64-bit float
Input, // evaluates to an inputted 64-bit float
}
impl Equation {
fn eval(&self, env: &Self::Environment) -> Self::Action {
match *self {
Add(ref left, ref right) => left.eval(env) + right.eval(env),
Sub(ref left, ref right) => left.eval(env) - right.eval(env),
Mul(ref left, ref right) => left.eval(env) * right.eval(env),
Div(ref left, ref right) => protected_div(left.eval(env), right.eval(env)),
Neg(ref left) => -left.eval(env),
Sin(ref left) => left.eval(env).sin(),
Float(i) => i,
Input => *env,
}
}
}
fn main() {
// represent the equation `x` and evaluate for `x=5`
let tree1 = Equation::Input;
println!("{:?}", tree1.eval(5.0));
// represent the equation `x * sin(4.0)` and evaluate for `x=-7.3`
let tree2 =
Equation::Mul(
node(Equation::Input),
node(Equation::Sin(
node(Equation::Float(4.0))
))
);
println!("{:?}", tree2.eval(-7.3));
// represent the equation `x + sin(x)` and evaluate for `x=99.1` and `x=16.3`
let tree3 =
Equation::Add(
node(Equation::Input),
node(Equation::Sin(
node(Equation::Input)
))
);
println!("{:?}", tree3.eval(99.1), tree3.eval(16.3));
}
```

This works for Genetic Programming and I’ve devised nice ways to randomly generate these trees - see the Symbolic Regression example and (this might not be obvious) `evco::gp::tree`

.

However this does limit flexibility. Using a generic tree datastructure would allow for easily introducing or removing sorts of nodes at compile time. I found that in DEAP this sort of flexibility helped for experimenting but tended not to stick around, so it might well be better.

*That’s all for now, it’s time for bed. Sometime soon I’d like to write about diversity experiences in tech, and how EVCO generates trees.*