# jQuery, but for types

Will Crichton   —   May 14, 2020
Using type-level programming, I show how to use a jQuery-like selector language to perform updates on nested types in Rust.

Part of an ongoing series about type-level programming in Rust. Read part one first!
All code in this note is available on GitHub: willcrichton/tquery

When doing type-level programming, sometimes our types become quite large, which can make them unwieldy to work with. In this note, we’re going to develop a library of type selectors to perform accesses and updates on deeply nested types.

As a real world example, we’re going to look at the state machine underlying Java’s ResultSet API for handling database query outputs. The linked documentation contains the full description, but here’s a brief ASCII diagram summarizing the state.

                                                                  |‾InvalidRow
|                  |_InsertRow-----OR-|‾Inserting
ResultSet---OR-|‾Open----AND-|                                     |_Inserted
|             |                  |_Updatable
|             |_Direction-----OR-|‾Scrollable
|                                |_ForwardOnly
|_Closed


To encode this diagram in Rust with typestate, each branch of an “OR” is a unique struct, and each branch of an “AND” is a type parameter to a struct.

// obligatory PhantomData are omitted
struct ResultSet<SetState>;

struct Open<Position, Concurrency, Direction>;
struct Closed;

struct CurrentRow<CRowState>;
struct InsertRow<InsState>;

struct ValidRow<VRowState>;
struct InvalidRow;

struct Inserting;
struct Inserted;

struct Concurrency<CcState>;
struct Updatable;

struct Direction<DirState>;
struct Scrollable;
struct ForwardOnly;


Here’s an example of a possible state of the result set.

ResultSet<
Open<
ForwardOnly>>


This is a large type! It contains a lot of information. It’s like a struct, but with types instead of values.

To see how large types can be hard to work with, let’s try to implement the next method for the ResultSet. This method requires the ResultSet to be in the CurrentRow state. Then it either returns NotYetRead if successfully moving to the next row, or InvalidRow otherwise. We can write the impl like this:

impl<CRowState, Concurrency, Direction>
ResultSet<Open<CurrentRow<CRowState>, Concurrency, Direction>> {
pub fn next(mut self)
-> Result<
Concurrency, Direction>>,
ResultSet<Open<CurrentRow<InvalidRow>,
Concurrency, Direction>>
> {
...
}
}


Whew, that’s a lot of characters for a return type! Contrast this with the concision of the ResultSet documentation:

Intuitively, the difference is that the documentation only references a change, i.e. the part of the ResultSet state that was modified as a result of next(). By contrast, our Rust code has to spell out the entire type each time, even though e.g. Concurrency and Direction are the same.

Ideally, we’d have some way of describing these kinds of surgical updates to a type in Rust. Think about it like a struct. What if I could write this:

type RS = ResultSet<Open<CurrentRow<CRowState>, Concurrency, Direction>;
RS.SetState.Position.CRowState = InvalidRow;


That kind of nested mutation on a struct works perfectly fine for values, but we don’t have an equivalent notation for types. Another way to think about it is as a language of selectors. In JavaScript, you can use jQuery to access an arbitrary part of the DOM tree:

\$('#result-set .set-state .position .c-row-state').html(
'<div class="InvalidRow" />'
);


Let’s do that, but for types!

## Accessing individual types

First, we need some way of reading and writing to the sub-pieces of a type. For example, Open<P, C, D> is essentially a tuple with three components. I want an API that looks like:

Get<Open<P, C, D>, 0> = P
Get<Open<P, C, D>, 2> = D
Set<Open<P, C, D>, 1, T> = Open<P, T, D>


Using our type operators pattern, we can encode this idea through traits.

pub trait ComputeGetType<Idx> { type Output; }
pub type GetType<T, Idx> = <T as ComputeGetType<Idx>>::Output;

pub trait ComputeSetType<Idx, NewT> { type Output; }
pub type SetType<T, Idx, NewT> = <T as ComputeSetType<Idx, NewT>>::Output;


Using the typenum crate for type-level numbers (e.g. U0, U1, …), we can implement these traits for e.g. the Open type.

impl<P, C, D> ComputeGetType<U0> for Open<P, C, D> { type Output = P; }
impl<P, C, D> ComputeGetType<U1> for Open<P, C, D> { type Output = C; }
impl<P, C, D> ComputeGetType<U2> for Open<P, C, D> { type Output = D; }

impl<P, C, D, T> ComputeSetType<U0, T> for Open<P, C, D> {
type Output = Open<T, C, D>;
}
impl<P, C, D, T> ComputeSetType<U1, T> for Open<P, C, D> {
type Output = Open<P, T, D>;
}
impl<P, C, D,T > ComputeSetType<U2, T> for Open<P, C, D> {
type Output = Open<P, C, T>;
}


This translation is fairly mechanical, so we can implement it with a custom derive. I won’t go into the details, but you can find a proof-of-concept here.

#[derive(TQuery)]
struct Open<Position, Concurrency, Direction>;


Now, we can use our getter/setter type operators. For example:

GetType<Open<P, C, D>, U1> = C


## Traversing nested types

Next, we need the ability to apply multiple getters/setters to a nested type. Ultimately, my goal is to implement a type operator UpdateCurrentRow that traverses the ResultSet three layers down to change CurrentRow. For example:

type UpdateCurrentRow<RS, T> = ???
type RS2 = UpdateCurrentRow<
ResultSet<Open<CurrentRow<S>, C, D>>,
T>;
RS2 == ResultSet<Open<CurrentRow<T>, C, D>>


Think about traversing a nested tuple in Rust. It looks like this:

let t = (((0, 1), 2, 3), 4);
assert!(((t.0).0).1 == 1);
assert!(t.1 == 4);
assert!((t.0).2 == 3);


This code would, of course, be extremely bad style in practice. But when we’re in type-land, we don’t get to live a life of luxury.

Similarly for the ResultSet, I will represent the type traversal as a list of indices.

type UpdateCurrentRow<RS, T> =
Replace<RS, (U0, (U0, (U0, ()))), T>;


Now our challenge is to implement the Replace operator. It should take as input a type, a selector, and a new type to replace at the location of the selector. Before looking at the gory Rust code, consider a simple implementation in OCaml-style:

let rec replace (t1 : type) (sel : int list) (t2 : type) =
match sel with
| [] -> t2
| (n :: sel') ->
let t2' = replace (type_get t1 n) sel' t2 in
type_set t1 n t2'


To replace a type, we recursively iterate over the selector list. In the base case, we return the replacing type. In the inductive case, we get the N-th type from t1, then recurse with the remaining selector sel'. We place this updated type back into its context in t1 using type_set.

To lower this code into a Rust type operator, we first define the trait as usual:

pub trait ComputeReplace<Selector, Replacement> { type Output; }
pub type Replace<T, Selector, Replacement> =
<T as ComputeReplace<Selector, Replacement>>::Output;


The base case is fairly simple:

impl<Replacement, T> ComputeReplace<(), Replacement> for T {
type Output = Replacement;
}


The inductive case is a little crazy though:

impl<Sel, SelList, Replacement, T>
ComputeReplace<(Sel, SelList), Replacement> for T
where
T: ComputeGetType<Sel>,
GetType<T, Sel>: ComputeReplace<SelList, Replacement>,
T: ComputeSetType<Sel, Replace<GetType<T, Sel>, SelList, Replacement>>
{
type Output = SetType<
T, Sel,
Replace<
GetType<T, Sel>, SelList, Replacement>>;
}


Again, this code makes most sense when placed in correspondence with the OCaml program. The type Output section describes the actual computation. The where bound is is necessary to make the computation possible.

With this type operator in place, our UpdateCurrentRow alias now works as planned! Bringing this back to the original problem, we can rewrite the next() type signature:

type UpdateCurrentRow<RS, T> =
Replace<RS, (U0, (U0, (U0, ()))), T>;

impl<S, C, D> ResultSet<Open<CurrentRow<S>, C, D>> {
pub fn next(mut self) ->
Result<
UpdateCurrentRow<Self, InvalidRow>
>
{
panic!()
}
}


Note that the wonderful implicit Self type allows us to avoid repeating the ResultSet definition, making the return type much more readable than before. Now, the change between the typestates is more clearly the focus.

## Named selectors

While the type signature externally looks nice, the selector is still hard to read. To understand what U0 means, you have to go back to the original struct type parameters and do the lookup yourself. One way around this is to create struct-specific named aliases. For example:

#[derive(TQuery)]
struct Open<Position, Concurrency, Direction>;
type TPosition = U0;
type TConcurrency = U1;
type TDirection = U2;

GetType<Open<P, C, D>, TConcurrency> = C


This feature can also be automatically derived. So now we can rewrite our selector as:

type UpdateCurrentRow<RS, T> = Replace<
RS, (TSetState, (TPosition, (TRowState, ()))), T>;


Much clearer than before!

## Is this jQuery?

Wrapping up, we’ve seen how to implement a selector language for replacing nested types. The language is still pretty far from actual jQuery. There’s no way to tag classes of types, or to distinguish between a direct vs. indirect descendent. I would love to hear of any use cases for that style of functionality!