# Type holes in TypeScript Giulio Canti Updated on ・3 min read

Sandy Maguire recently wrote a nice article about type holes (Implement With Types, Not Your Brain!), this blog post is a porting to TypeScript.

## What's a type hole?

The idea is to implement the tiny part of a function that you know how to do, and then ask the compiler for help on the rest of it. It's an iterative process. It's a discussion with the compiler. Each step of the way, you get a little closer to the right answer, and after enough iterations your function has written itself — even if you're not entirely sure how.

TypeScript doesn't support type holes but they can be kind of simulated.

# A first example

Let's see the first example from the article

``````declare function jonk<A, B>(
ab: (a: A) => B,
ann: (an: (a: A) => number) => number
): (bn: (b: B) => number) => number
``````

In order to simulate a type hole I'm going to use the following function declaration

``````declare function _<T>(): T
``````

Let's put it into the `jonk`'s body

``````function jonk<A, B>(
ab: (a: A) => B,
ann: (an: (a: A) => number) => number
): (bn: (b: B) => number) => number {
return _()
}
``````

If you move the mouse over the "type hole" `_` you can see what TypeScript infers for its type parameter `T`

``````(bn: (b: B) => number) => number
``````

So what is the type checker telling us? Two things

• The expression we want to replace `_()` with must have type `(bn: (b: B) => number) => number`.
• We have some local binds (`ab`, `ann`, `jonk`, and their types) that we can use to help with the implementation.

Since our hole has type `(bn: (b: B) => number) => number` we should bind the `bn` in a lambda (I'll just write the function body from now on)

``````return bn => _() // inferred type: number
``````

What's the new inferred type? `number`. How can we produce a `number`? We can use `ab`, `ann` or `bn`. Since both `ann` and `bn` return a `number` let's choose `ann` as a guess

``````return bn => ann(_()) // inferred type: (a: A) => number
``````

Our new hole has a function type, so let's introduce a lambda

``````return bn => ann(a => _()) // inferred type: number
``````

We need to produce a `number` again, let's choose `bn` this time

``````return bn => ann(a => bn(_())) // inferred type: B
``````

Now we need to produce a `B`. We have a function that can do that, `ab: (a: A) => B`

``````return bn => ann(a => bn(ab(_()))) // inferred type: A
``````

Finally, we have a hole whose type is `A`. Since we have an `A` (the `a` parameter) let's just use that

``````function jonk<A, B>(
ab: (a: A) => B,
ann: (an: (a: A) => number) => number
): (bnn: (b: B) => number) => number {
return bn => ann(a => bn(ab(a)))
}
``````

Now we have a complete implementation, almost driven by the type checker.

# The second example

Let's tackle the second example of the blog post: `zoop`

``````declare function zoop<A, B>(abb: (a: A) => (b: B) => B, b: B, as: Array<A>): B
``````

We notice that `as` has type `Array<A>`, let's "pattern match" on that using `foldLeft`

``````import { foldLeft } from 'fp-ts/lib/Array'
import { pipe } from 'fp-ts/lib/pipeable'

function zoop<A, B>(abb: (a: A) => (b: B) => B, b: B, as: Array<A>): B {
return pipe(
as,
foldLeft(
() => _(), // inferred type: B
(head, tail) => _() // inferred type: B
)
)
}
``````

We need to produce a `B` for the "nil" case (i.e. when the array is empty). Since we have a `B` let's just use that (I'll just write the function body from now on)

``````return pipe(
as,
foldLeft(
() => b,
(head, tail) => _() // inferred type: B
)
)
``````

Again we want to produce a `B` for the other case and we want to call `abb`. Since it takes two arguments, let's give it two holes

``````return pipe(
as,
foldLeft(
() => b,
abb(
_() // inferred type: A
)(
_() // inferred type: B
)
)
)
``````

`head` has type `A` so let's use it

``````return pipe(
as,
foldLeft(
() => b,
_() // inferred type: B
)
)
)
``````

Now we must to produce a `B` and we want to use `tail` which has type `Array<A>`. Our only option is using `zoop` itself

``````function zoop<A, B>(abb: (a: A) => (b: B) => B, b: B, as: Array<A>): B {
return pipe(
as,
)
}

// p.s. `zoop` is `reduceRight`
``````

The reason why this works is known as theorems for free, which roughly states that we can infer lots of facts about a type signature (assuming it's correct.)

### Discussion  Darrik Moberg

Would you consider doing an edit/follow up using more user friendly variable names? This is super interesting and I just noticed that it was easy to get lost with the filler variables if you weren't reading closely. This can be a problem to new coders/coders from other backgrounds.

I know that you were using the examples from the article you linked, but having a stand-alone series on this could be useful/interesting, especially with a Typescript focus. As someone with 0 Haskell exposure, I found the original article hard to grok.

Thanks for the article. Giulio Canti

My guess reading the original article is that the naming convention is based on the contraction of the signatures, so

• `(a: A) => B` becomes `ab`
• `(a: A) => number` becomes `an`
• `(an: (a: A) => number) => number` becomes `ann`
• etc...

Actually it looks good to me as the examples are such a general functions but I'm open to alternatives, what naming convention are you proposing?  