There is nothing magic about how &1 is working here. Rather, it’s the Agent.get function that is doing the work. &Map.get(&1, key) is just an anonymous function that takes a map and grabs a key from it. For example:

iex(1)> key = :name            
:name
iex(2)> fun = &Map.get(&1, key)
#Function<7.91303403/1 in :erl_eval.expr/5>
iex(3)> map = %{name: "Ben", country: "USA"}
%{country: "USA", name: "Ben"}
iex(4)> fun.(map) 
"Ben"

In this example, &1 becomes whatever you pass to it, in my case map

When you do:

Agent.get(bucket, &Map.get(&1, key))

This is exactly equivalent to just doing:

fun = &Map.get(&1, key)
Agent.get(bucket, fun)

where fun in that example is 100% identical to the fun in my example.

SO how does it get the process state? Well, that’s the job of Agent.get. It takes that anonymous function sends it to the process, the process calls fun with its state, and sends the result back to you.

Hello and welcome,

& is a shortcut for defining anonymous function, and &1, &2… are the parameters to this function.

&Map.get(&1, key)

# is equal to

fn x -> Map.get(x, key) end

You might find version with two parameters, in particular with reduce…

For example.

iex> Enum.reduce [1, 2, 3], & &1 + &2
6

# is equal to

iex> Enum.reduce [1, 2, 3], fn x, acc -> x + acc end

More on this here

That is the power of function as first class citizen, You can pass the implementation as an argument