Stream: beginners

Topic: wildcard type

Prajwal S N (Oct 07 2022 at 19:23):

I'm not quite understanding the difference between these two:

Num a -> Bool
Num * -> Bool

What exactly does the * indicate here? I'm also slightly confused about why numbers are of the type Num * instead of Num by default

jan kili (Oct 07 2022 at 19:25):

In a vacuum, those two lines are equivalent

jan kili (Oct 07 2022 at 19:27):

The second half of that type (whether it's * or a or apples or Integer) describes what kind of number (Num) it is - it's like a type adjective

jan kili (Oct 07 2022 at 19:28):

If it's lowercase or *, it's a placeholder for a specific adjective like Integer

jan kili (Oct 07 2022 at 19:29):

The lowercase letters/words are for referencing it and keeping track of matches, like this:

Num a, Num *, Num b -> { foo: Num b, bar: Num a }

jan kili (Oct 07 2022 at 19:30):

The asterisk means it doesn't have to match any others in the signature

Prajwal S N (Oct 07 2022 at 19:31):

Got it :thumbs_up: thank you!

jan kili (Oct 07 2022 at 19:32):

TLDR, the way to write "any kind of number" is Num x, where x is * or any identifier that starts with a lowercase letter

jan kili (Oct 07 2022 at 19:34):

I think Int * is a shorthand/alias for Num (Integer *), because there are subtypes of integers, too (I think size & signedness, like U8 vs. I128)

Alexander McLin (Feb 02 2023 at 21:17):

Adding new question about wildcard type to this stream, the tutorial says List * is the type for the empty list [] so it make me think that a function with the type List * -> List * would only accept and return an empty list. But the tutorial seem to imply that if List * is the type of a function argument than it means a list of any type but if it is used for a return value then it means only the empty list. I find this confusing, why would List * in one context mean an arbitrary list but the empty list in another context?

Additionally, when testing out in the repl, it says List.isEmpty's type is List a -> Bool instead of List * -> Bool in the tutorial. Is the difference significant?

Folkert de Vries (Feb 02 2023 at 21:19):

naming the type variable (so using a instead of *) can be helpful when there are multiple type variables at play

Folkert de Vries (Feb 02 2023 at 21:19):

if I said to you: make me a list of an arbitrary type, how would you go about it?

Folkert de Vries (Feb 02 2023 at 21:20):

the problem is: you don't know what the element type will be, so you cannot actually create any elements

Folkert de Vries (Feb 02 2023 at 21:20):

hence the only list you can make, from scratch, that has an arbitrary element type, is the empty list

Folkert de Vries (Feb 02 2023 at 21:21):

so in this way, the element list and "a list with elements of an arbitrary type" are related

Folkert de Vries (Feb 02 2023 at 21:22):

but as you notice, they are not the same: in the input of a function, we can say we make no assumptions about the element type. This is what isEmpty does: it does not matter what the element type is if all we want to do is see whether the list is empty

Alexander McLin (Feb 02 2023 at 21:45):

Folkert de Vries said:

naming the type variable (so using a instead of *) can be helpful when there are multiple type variables at play

I see, that sort of make sense to me, my take away from your comment is that it's about describing what a type can be versus being able to construct a value satisfying the type which are two different things.

Last updated: Jul 26 2025 at 12:14 UTC