Option::map, for example, looks like this:

    option<t>, (t -> u) -> option<u>

This syntax searches all of the HOFs in Rust: traits Fn, FnOnce,
and FnMut, and bare fn primitives.

It's going to be a no-op on the empty list anyway
(we have plenty of test cases that return nothing)
so why send extra code?

Initialize them before the search index is loaded.

This is implemented, in addition to the ML-style one,
because Rust does it. If we don't, we'll never hear the end of it.

This commit also refactors some duplicate parts of the parser
into a dedicated function.

…-hof, r=GuillaumeGomez

rustdoc-search: search types by higher-order functions

This feature extends rustdoc with syntax and search index information for searching function pointers and closures (Higher-Order Functions, or HOF). Part of rust-lang#60485

This PR adds two syntaxes: a high-level one for finding any kind of HOF, and a direct implementation of the parenthesized path syntax that Rust itself uses.

## Preview pages

| Query | Results |
|-------|---------|
| [`option<T>, (fnonce (T) -> bool) -> option<T>`][optionfilter] | `Option::filter` |
| [`option<T>, (T -> bool) -> option<T>`][optionfilter2] | `Option::filter` |

Updated chapter of the book: https://notriddle.com/rustdoc-html-demo-9/search-hof/rustdoc/read-documentation/search.html

[optionfilter]: https://notriddle.com/rustdoc-html-demo-9/search-hof/std/vec/struct.Vec.html?search=option<T>%2C+(fnonce+(T)+->+bool)+->+option<T>&filter-crate=std
[optionfilter2]: https://notriddle.com/rustdoc-html-demo-9/search-hof/std/vec/struct.Vec.html?search=option<T>%2C+(T+->+bool)+->+option<T>&filter-crate=std

## Motivation

When type-based search was first landed, it was directly [described as incomplete][a comment].

[a comment]: rust-lang#23289 (comment)

Filling out the missing functionality is going to mean adding support for more of Rust's [type expression] syntax, such as references, raw pointers, function pointers, and closures. This PR adds function pointers and closures.

[type expression]: https://doc.rust-lang.org/reference/types.html#type-expressions

There's been demand for something "like Hoogle, but for Rust" expressed a few times [1](https://www.reddit.com/r/rust/comments/y8sbid/is_there_a_website_like_haskells_hoogle_for_rust/) [2](https://users.rust-lang.org/t/rust-equivalent-of-haskells-hoogle/102280) [3](https://internals.rust-lang.org/t/std-library-inclusion-policy/6852/2) [4](https://discord.com/channels/442252698964721669/448238009733742612/1109502307495858216). Some of them just don't realize what functionality already exists ([`Duration -> u64`](https://doc.rust-lang.org/nightly/std/?search=duration%20-%3E%20u64) already works), but a lot of them specifically want to search for higher-order functions like option combinators.

## Guide-level explanation (from the Rustdoc book)

To search for a function that accepts a function as a parameter, like `Iterator::all`, wrap the nested signature in parenthesis, as in [`Iterator<T>, (T -> bool) -> bool`][iterator-all]. You can also search for a specific closure trait, such as `Iterator<T>, (FnMut(T) -> bool) -> bool`, but you need to know which one you want.

[iterator-all]: https://notriddle.com/rustdoc-html-demo-9/search-hof/std/vec/struct.Vec.html?search=Iterator<T>%2C+(T+->+bool)+->+bool&filter-crate=std

## Reference-level description (also from the Rustdoc book)

### Primitives with Special Syntax

<table>
<thead>
  <tr>
    <th>Shorthand</th>
    <th>Explicit names</th>
  </tr>
</thead>
<tbody>
  <tr><td colspan="2">Before this PR</td></tr>
  <tr>
    <td><code>[]</code></td>
    <td><code>primitive:slice</code> and/or <code>primitive:array</code></td>
  </tr>
  <tr>
    <td><code>[T]</code></td>
    <td><code>primitive:slice&lt;T&gt;</code> and/or <code>primitive:array&lt;T&gt;</code></td>
  </tr>
  <tr>
    <td><code>!</code></td>
    <td><code>primitive:never</code></td>
  </tr>
  <tr>
    <td><code>()</code></td>
    <td><code>primitive:unit</code> and/or <code>primitive:tuple</code></td>
  </tr>
  <tr>
    <td><code>(T)</code></td>
    <td><code>T</code></td>
  </tr>
  <tr>
    <td><code>(T,)</code></td>
    <td><code>primitive:tuple&lt;T&gt;</code></td>
  </tr>
  <tr><td colspan="2">After this PR</td></tr>
  <tr>
    <td><code>(T, U -> V, W)</code></td>
    <td><code>fn(T, U) -> (V, W)</code>, Fn, FnMut, and FnOnce</td>
  </tr>
</tbody>
</table>

The `->` operator has lower precedence than comma. If it's not wrapped in brackets, it delimits the return value for the function being searched for. To search for functions that take functions as parameters, use parenthesis.

### Search query grammar

```ebnf
ident = *(ALPHA / DIGIT / "_")
path = ident *(DOUBLE-COLON ident) [BANG]
slice-like = OPEN-SQUARE-BRACKET [ nonempty-arg-list ] CLOSE-SQUARE-BRACKET
tuple-like = OPEN-PAREN [ nonempty-arg-list ] CLOSE-PAREN
arg = [type-filter *WS COLON *WS] (path [generics] / slice-like / tuple-like)
type-sep = COMMA/WS *(COMMA/WS)
nonempty-arg-list = *(type-sep) arg *(type-sep arg) *(type-sep) [ return-args ]
generic-arg-list = *(type-sep) arg [ EQUAL arg ] *(type-sep arg [ EQUAL arg ]) *(type-sep)
normal-generics = OPEN-ANGLE-BRACKET [ generic-arg-list ] *(type-sep)
            CLOSE-ANGLE-BRACKET
fn-like-generics = OPEN-PAREN [ nonempty-arg-list ] CLOSE-PAREN [ RETURN-ARROW arg ]
generics = normal-generics / fn-like-generics
return-args = RETURN-ARROW *(type-sep) nonempty-arg-list

exact-search = [type-filter *WS COLON] [ RETURN-ARROW ] *WS QUOTE ident QUOTE [ generics ]
type-search = [ nonempty-arg-list ]

query = *WS (exact-search / type-search) *WS

; unchanged parts of the grammar, like the full list of type filters, are omitted
```

## Future direction

### The remaining type expression grammar

As described in rust-lang#118194, this is another step in the type expression grammar: BareFunction, and the function-like mode of TypePath, are now supported.

* RawPointerType and ReferenceType actually are a priority.
* ImplTraitType and TraitObjectType (and ImplTraitTypeOneBound and TraitObjectTypeOneBound) aren't as much of a priority, since they desugar pretty easily.

### Search subtyping and traits

This is the other major factor that makes it less useful than it should be.

* `iterator<result<t>> -> result<t>` doesn't find `Result::from_iter`. You have to search [`intoiterator<result<t>> -> result<t>`](https://notriddle.com/rustdoc-html-demo-9/search-hof/std/vec/struct.Vec.html?search=intoiterator%3Cresult%3Ct%3E%3E%20-%3E%20result%3Ct%3E&filter-crate=std). Nobody's going to search for IntoIterator unless they basically already know about it and don't need the search engine anyway.

* Iterator combinators are usually structs that happen to implement Iterator, like `std::iter::Map`.

To solve these cases, it needs to look at trait implementations, knowing that Iterator is a "subtype of" IntoIterator, and Map is a "subtype of" Iterator, so `iterator -> result` is a subtype of `intoiterator -> result` and `iterator<t>, (t -> u) -> iterator<u>` is a subtype of [`iterator<t>, (t -> u) -> map<t -> u>`](https://notriddle.com/rustdoc-html-demo-9/search-hof/std/vec/struct.Vec.html?search=iterator%3Ct%3E%2C%20(t%20-%3E%20u)%20-%3E%20map%3Ct%20-%3E%20u%3E&filter-crate=std).