### 4 releases

0.1.3 | Jan 14, 2023 |
---|---|

0.1.2 | Jan 6, 2023 |

0.1.1 | Jan 5, 2023 |

0.1.0 | Jan 1, 2023 |

#**1557** in Data structures

**MIT/Apache**

365KB

517 lines

# 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:

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

to this:

`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.

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

For working with this

type we'll define a `Expr`*frame* type

.
It's exactly the same as `ExprFrame <A>`

`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.

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

Now all we need is some mechanical boilerplate:

for `MappableFrame`

and `ExprFrame`

and `Expandable`

for `Collapsible`

.
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.`Expr`

## Collapsing an Expr into a value

Here's how to evaluate an

using this idiom, by collapsing it frame by frame via a function `Expr`

:`ExprFrame <i64>`

`->``i64``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``>``
``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

for `try_collapse_frames`

:`valid_expr`

And here's a GIF visualizing the operation of

for `try_collapse_frames`

:`invalid_expr`

## Expanding an Expr from a seed value

Here's an example showing how to expand a simple

from a seed value`Expr`

`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

crate, via `recursion-visualize`

.`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

as `MappableFrame`

and `Functor`

/`Expandable`

as `Collapsible`

/`Corecursive`

. If you're not
familiar with these idioms, there's a great blog post series here that explains the various concepts involved.`Recursive`

License: MIT OR Apache-2.0

#### Dependencies

~3–5MB

~84K SLoC