A few days ago one of my friends from Recurse Center, David Shaked, asked me to review references—i.e. pointers—in Go with him. Primarily a Clojure developer, he had a bit of trouble to get a feeling when to use references and when to use values. After talking about that for about an hour he seemed to have a much better intuition about what to use when. This, however, is not what I want to talk about today.

What I want to talk about is an intuition about the operators involved in working with pointers and what they mean on a type-level. They happen to be very simple in Go, and even in C/C++, where we have such interesting—some might use other words to describe this, e.g. “unsavory”—constructs as pointer arithmetic.

Let's define some type signatures!

*Fair Warning*: This blog post uses Haskell notation, but you should be able to follow without knowing the language.

## Dramatis Personae

We only need three operators to describe pointers in Go: `*`

and `&`

. I am aware that those are only two operators, but one of them has two distinct purposes—`*`

is both a type-level and a value-level operator. What this means is that we can use `*`

in a type signature and in the normal flow of a program. Let me give you an intuition of that, in Haskell notation:

```
-- * on a type level
type * t = Address t
-- The operators * and &
& :: v -> Address v
-- or:
& :: v -> * v
* :: Address v -> v
-- or, unreadably:
* :: * v -> v
```

`*`

and `&`

.
Let me explain what this means in prose: There is a type `*`

that has as parameter any type `t`

and means it is an address of `t`

. In Go, the address type is opaque and stands on its own, so we won't explain it further yet. When we later move on to C/C++, we will have to be more concrete about this.

After that we define the unary—i.e. single-argument—operators `&`

and `*`

, which convert between the values `v`

and the addresses of these values. If we want to throw in some monads just for kicks, we could talk about `&`

in terms of the `return`

operator, but as we have no unified operator for getting values out of a monad, this isn't a particularly useful abstraction^{1}.

These definitions are enough to talk about pointers in Go! Go thankfully has a very simplistic pointer system that gives us the ability to pass around things as pointers without making us suffer from pointer arithmetic—or enjoy it, depending on what type of person you are. How would we achieve that, using our little intuition?

## Addresses as values

If we want to think about pointer arithmetic, we need to go back to our earlier point of pointers being opaque types and changing that notion. After all, this is a deliberate restriction introduced by Go, whose primary developers considered pointer arithmetic a thing of the past. I largely agree, but there are languages where it is perfectly normal to do calculations on pointers. If we want to extend this system to include them, we only need to roll back the restriction, think about pointers as the thing they truly are—things that point to the location of other things in memory—, and construct a useful notion of memory. Memory can be thought of as a big blob of bytes that supports indexing—in this context called addressing. A big blob of bytes that supports indexing can be thought of as an array, if that helps your mental model^{2}.

If we think of memory as an array that supports indexing, all we need to know is the size of the array to determine our pointer size—these days commonly 32 or 64 bit. This is because we do not want to waste any space, but we also want to be able to index everything. In Haskell notation, this leaves us with:

```
type Address t = Int
-- where Int is either 32 or 64 bits long
```

And that's it! We cheated by relying on the integer type for pedagogical purposes and because I don't know any better, but it enables us to do pointer arithmetic.

I also learned that it is valid to do have an unused type parameter in Haskell, although this is arguably most senseless.

## A useful abstraction

When I first thought of the operators involved in reasoning about pointers, my intuition was that they *must* be hard to think about. But, as it turns out, the type signatures of the functions are rather simple, even if the underlying mechanics are still Operating System Magic to us.

I hope my little abstraction was helpful to you. Have a beautiful day and see you soon!

##### Footnotes

1. I left it in there anyway, because I understand people who use monads are very insistent to talk about everything in terms of this occasionally useful structure.

2. Please note that we're making things simpler than they truly are, which is okay in this context.