# recursion


Tools for working with recursive data structures in a concise, stack safe, and performant manner.


This crate provides abstractions for separating the _machinery_ of recursion from the _logic_ of recursion.
This is similar to how iterators separate the _machinery_ of iteration from the _logic_ of iteration, allowing us to go from this:

```rust
let mut n = 0;
while n < prices.len() {
    print!("{}", prices[n]);
    n += 1;
}
```

to this:

```rust
for n in prices.iter() {
    print!("{}", n)
}
```

This second example is less verbose, has less boilerplate, and is generally nicer to work with. This crate
aims to provide similar tools for working with recursive data structures.

## Here's how it works: Expr

For these examples, we will be using a simple recursive data structure - an expression language
that supports a few mathematical operations.

```rust
pub enum Expr {
    Add(Box<Expr>, Box<Expr>),
    Sub(Box<Expr>, Box<Expr>),
    Mul(Box<Expr>, Box<Expr>),
    LiteralInt(i64),
}
```

For working with this `Expr` type we'll define a _frame_ type `ExprFrame<A>`.
It's exactly the same as `Expr`, except the recursive self-reference `Box<Self>` is replaced with `A`.
This may be a bit confusing at first, but this idiom unlocks a lot of potential (expressiveness, stack safety, etc).
You can think of `ExprFrame<A>` as representing a single _stack frame_ in a recursive algorithm.

```rust
pub enum ExprFrame<A> {
    Add(A, A),
    Sub(A, A),
    Mul(A, A),
    LiteralInt(i64),
}
```

Now all we need is some mechanical boilerplate: [`MappableFrame`] for `ExprFrame` and [`Expandable`] and [`Collapsible`] for `Expr`.
I'll elide that for now, but you can read the documentation for the above traits to learn what they do and how to implement them.

## Collapsing an Expr into a value

Here's how to evaluate an `Expr` using this idiom, by collapsing it frame by frame via a function `ExprFrame<i64> -> i64`:

```rust
fn eval(e: &Expr) -> i64 {
    e.collapse_frames(|frame| match frame {
        ExprFrame::Add(a, b) => a + b,
        ExprFrame::Sub(a, b) => a - b,
        ExprFrame::Mul(a, b) => a * b,
        ExprFrame::LiteralInt(x) => x,
    })
}

let expr = multiply(subtract(literal(1), literal(2)), literal(3));
assert_eq!(eval(&expr), -3);
```

Here's a GIF visualizing the operation of `collapse_frames`:

## Fallible functions

At this point, you may have noticed that We've ommited division, which is a fallible operation
because division by 0 is undefined. Many real world algorithms also have to handle failible operations,
such as this. That's why this crate also provides tools for collapsing and expanding recursive data
structures using fallible functions, like (in this case) `ExprFrame<i64> -> Result<i64, Err>`.


```rust

fn try_eval(e: &Expr) -> Result<i64, &str> {
    e.try_collapse_frames(|frame| match frame {
                ExprFrame::Add(a, b) => Ok(a + b),
                ExprFrame::Sub(a, b) => Ok(a - b),
                ExprFrame::Mul(a, b) => Ok(a * b),
                ExprFrame::Div(a, b) =>
                    if b == 0 { Err("cannot divide by zero")} else {Ok(a / b)},
                ExprFrame::LiteralInt(x) => Ok(x),
    })
}

let valid_expr = multiply(subtract(literal(1), literal(2)), literal(3));
let invalid_expr = divide(literal(2), literal(0));

assert_eq!(try_eval(&valid_expr), Ok(-3));
assert_eq!(try_eval(&invalid_expr), Err("cannot divide by zero"));
```

Here's a GIF visualizing the operation of `try_collapse_frames` for `valid_expr`:

And here's a GIF visualizing the operation of `try_collapse_frames` for `invalid_expr`:

## Expanding an Expr from a seed value

Here's an example showing how to expand a simple `Expr` from a seed value

```rust
fn build_expr(depth: usize) -> Expr {
    Expr::expand_frames(depth, |depth| {
        if depth > 0 {
            ExprFrame::Add(depth - 1, depth - 1)
        } else {
            ExprFrame::LiteralInt(1)
        }
    })
}

let expected = add(add(literal(1), literal(1)), add(literal(1), literal(1)));

assert_eq!(expected, build_expr(2));

```

Here's a GIF visualizing the operation of `expand_frames``:

## Miscellaneous errata

All GIFs in this documentation were generated via tooling in my `recursion-visualize` crate, via `examples/expr.rs`.

If you're familiar with Haskell, you may have noticed that this crate makes heavy use of recursion schemes idioms.
I've named the traits used with an eye towards readability for users unfamiliar with those idioms, but feel free to
read [`MappableFrame`] as `Functor` and [`Expandable`]/[`Collapsible`] as `Corecursive`/`Recursive`. If you're not
familiar with these idioms, there's a great blog post series [here](https://blog.sumtypeofway.com/posts/introduction-to-recursion-schemes.html) that explains the various concepts involved.


License: MIT OR Apache-2.0
