Of Monads and Men

Aiden Chow

03:25

. . . . . what is a functor?

ok u know what im just gonna search it up lol

nvm i dont understand it

Unrelated String

a really shitty way to explain it is it's something you can define fmap for

Nitrodon

Not quite, you also need to be able to define pure.

Aiden Chow

@UnrelatedString and what does fmap do?

Unrelated String

isn't pure only for applicative

DLosc

@UnrelatedString Circular definition goes brrrr :P

Unrelated String

03:27

fmap having the signature Functor f => (a -> b) -> f a -> f b

a list is a functor with fmap = map

and an applicative functor with pure x = [x]

Aiden Chow

but like, i still dont get what a functor even is

Nitrodon

The difference between applicative functor and just plain functor is <*>, not pure, right?

Unrelated String

applicative also requires <*> which is uhh

it's both

Aiden Chow

is a functor a function?

Unrelated String

...it's complicated

DLosc

03:31

Is it something that takes a type and returns a new type? Like how [a] is the type "list that contains items of type a"?

Aiden Chow

@DLosc huh, dont functions already do that (take in some value and return another), or am i missing something

Unrelated String

i'm hazy on the precise terminology but all functors do that (have kind * -> *) but not everything that does that is a functor

a trivial and uninteresting example is the hugeass tuples where they just didn't bother to give them Functor instances but totally could have

DLosc

@AidenChow I'm not sure if I'm looking at it the way Haskell does, but at least in my mind I'm distinguishing between doing something with a value of a given type, and doing something with the type itself

Nitrodon

[a] isn't a functor. It's the return of applying the list functor to the type a.

DLosc

@Nitrodon Yeah, that's what I meant

Aiden Chow

03:34

ok so functor = type ?????

so confused here

Unrelated String

no

DLosc

Functor is to type what function is to value

(right?)

Nitrodon

A functor (e.g., list) takes a type (e.g. integer) and returns another type (e.g., list of integers).

Aiden Chow

@DLosc took me a while to realize that that was an analogy lol

couldnt understand what you were saying for a split second :P

Unrelated String

a functor is a type of kind * -> * for which there's a definition of fmap (i.e. a Functor instance)

let me whip up a redefinition of the identity functor rq

DLosc

03:36

@AidenChow I considered using : :: : syntax but thought the English words might be more understandable. Glad you got there eventually. :)

Nitrodon

Does Haskell have the identity functor?

Unrelated String

it's in a module somewhere

99% sure it's called Identity and it's probably in Data.Functor

but reimplementing it is Instructive™

Aiden Chow

so, i kinda get what a functor is, but how would i actually define a functor? similar to a function?

Nitrodon

Anyway, in order for something of kind * -> * to be a functor, it has to have the fmap function.

and this function must satisfy the laws fmap id x = x and (fmap f) (fmap g x) = fmap (f . g) x

DLosc

@Nitrodon Ohhh--is Maybe a functor?

Nitrodon

03:40

It is. It's even a monad.

Aiden Chow

still dont understand what fmap is

Unrelated String

tio.run/…

Aiden Chow

is it kinda like map but for functors and types instead of functions and values?

Nitrodon

and apparently I was mistaken earlier and functors don't require pure. Does this mean that there's an empty functor?

Unrelated String

Either is also a functor

DLosc

03:41

@Nitrodon Okay, that's helpful. Maybe makes sense to me because I've used the equivalent in Scala.

Unrelated String

@Nitrodon i vaguely remember a question on so about this and i thiiiiiink the answer was yes

Nitrodon

Well, list is a functor, and its implementation of fmap is map.

Unrelated String

^

Nitrodon

There's also the Maybe functor that DLosc mentioned. Maybe a is defined as Nothing | Just a.

and then fmap on Maybe is defined by fmap f Nothing = Nothing; fmap f (Just x) = Just (f x)

DLosc

@AidenChow Okay, I think I understand it now, so let's try this explanation. Say I define a functor called Box. I can put any type into a Box: I can have a Box containing an Int, or a Box containing a String, or whatever.

Now say x is a Box containing the Int 42, and I want to add 1 to it. I can't just add 1 to x directly, because x isn't an Int; it's a Box of Int. I need to add 1 to the Int inside the Box, and then return a new Box of Int containing that result.

That's what fmap does. It applies the function ("plus 1," in this case) to whatever's inside the Box, and returns a new Box containing the result.

Unrelated String

03:50

what's critical is you can do that with any function from the type "inside the box" to some other type, whatever the type inside the box is

Nitrodon

You can also fmap a function like show, which converts its input into a string.

DLosc

So if the function was "convert to a string and concatenate !," I could fmap that to the Box of 42 and get a Box of "42!" back

Nitrodon

or the "put it in a box" function, so you'd have a Box of a Box of 42.

(and since Box is actually a monad, you can convert that Box of Box of 42 back into a Box of 42)

DLosc

What does monad mean? I think I might finally be in a position to understand the answer, lol

Bubbler

Looks like we're going down the hard route, and yet we haven't touched some easier and good-for-golf stuff like list comprehension

DLosc

03:56

Is there a Haskell chat room? We could take the deeper stuff there.

Nitrodon

It's a functor with return :: a -> m a and >>= :: m a -> (a -> m b) -> m b.

Bubbler

There used to be Of Monads and Men but it's been frozen for 2 years straight

Nitrodon

Equivalently, you can say it has return and a "flatten" function of type m m a -> m a.

Feeds

Jo King has unfrozen this room.

17

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code-golf tips haskell

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Jo King

oh wow you were holding those in for a while bot

← 6 messages moved from The Nineteenth Byte

DLosc

04:05

@Nitrodon ... Nope, I don't understand that. Can you say that again but with more English? ;P

Nitrodon

For instance, you can flatten a list of lists of integers into just a list of integers.

Jo King

← 63 messages moved from The Nineteenth Byte

Nitrodon

Maybe is also a monad.

>>= :: Maybe a -> (a -> Maybe b) -> Maybe b would be defined as Nothing >>= f = Nothing; Just x >>= f = f x

or at least I think that's what >>= is. All these weird combinations of punctuation can get confusing.

Unrelated String

@Nitrodon also worth noting that this "flatten" function is join (in Control.Monad) and is just (>>=id)

Nitrodon

I'm aware that it's (>>=id), but I'm not familiar enough with Haskell to know that it's called join.

Unrelated String

04:12

np

DLosc

Is List a monad?

Nitrodon

yes

DLosc

B/c I'm having trouble understanding what [1,2,3] >>= id would return

Unrelated String

and you can go back to >>= from join with flip((join.).fmap)

@DLosc it doesn't

since Ints aren't a monad

DLosc

Ah, okay

Nitrodon

04:13

because Int isn't [a] for some a

DLosc

So >>= requires its argument to be a monad containing a monad?

Unrelated String

unless you have some Monad m, Num m a but let's not worry about literals being polymorphic

yep

specifically the same monad

Nitrodon

>>=id does, yes.

Unrelated String

(>>=) :: Monad m => m a -> (a -> m b) -> m b

er yeah >>=id specifically

Nitrodon

[1,2,3] >>= (\x -> [x, 2*x]) is just fine.

Aiden Chow

04:14

whats this chat room

Unrelated String

since the a -> m b is a -> a it has to be m b -> m b

DLosc

Right, okay

Nitrodon

I've been wondering off and on for a bit: is join . join = join . fmap join?

DLosc

@UnrelatedString So let me try to rephrase in words so I can make sure I understand:

Nitrodon

and how would one prove that with the monad laws?

Unrelated String

04:16

@Nitrodon ...probably

DLosc

Suppose m is some kind of Monad. Then >>= is a function that takes an (m containing as), and a function from as to (m containing bs)s, and returns an (m containing bs).

Nitrodon

yes

Unrelated String

there doesn't seem to be a sequencing difference but i am wondering how you'd prove it too now

Aiden Chow

what does >>= do?

DLosc

@Nitrodon Okay, I think I get it

DLosc

04:33

@AidenChow Partial answer: if you give it a List of Somethings and a function that transforms each Something into a List of SomethingElses, it applies the function to each element of the list and then joins the resulting list of lists into one flat list (somewhat like flatMap in JavaScript).

It also works on things that aren't Lists, but for that you'll need to read through the preceding discussion about monads.

Nitrodon

@DLosc Indeed. Notice that a Haskell string is just a list of characters.

DLosc

@Nitrodon Right, which is why I picked that example; I was trying to think of a non-contrived function Int -> [a] and then I realized that show had that signature.

BTW, why is it that specific types use InitialCaps but these abstract types (?) in function signatures use lowercase?

Unrelated String

to make that distinction

Aiden Chow

what does show do?

Unrelated String

since a type variable is very distinctly different from an actual type in that kind of context

there's a reason ScopedTypeVariables is an extension

@AidenChow string representations

DLosc

04:37

@UnrelatedString Makes sense... I kinda wish there were also a distinction between type variables and regular variables, tho

Unrelated String

specifically, for any type implementing Show, you can get a string from showing it

@DLosc it's not really a problem since types and values don't really exist in the same places syntactically

Nitrodon

show is also used internally by print.

Unrelated String

note that you can define algebraic data types where their constructors look the same as the type itself and where they don't

it just doesn't matter since the constructors and the type itself can't occur in the same places

DLosc

@UnrelatedString Well, sure, it's not a problem for the compiler or for fluent Haskellers. But I am neither of those things. ;P

Unrelated String

(and constructors have to be distinguished from normal functions syntactically so you can pattern-match them)

lol

user

16:09

What about infix constructors?

How do you distinguish those from normal infix functions?

Bubbler

23:23

@user I think all infix constructors start with a colon.

user

23:56

Ah, interesting

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