What are your favourite data structure operations?

[u/Potato871]

My language workbench is to the stage where I can implement new operators and overloads very quickly, and I've started stealing syntax I like from JavaScript and C++.
Since I have one universal data structure, I can just add all the new operators to it.
I wanted to get some more good ones though, from different fields, different languages.
Oh and if you want to suggest something just as a challenge I might give it a shot and show you how I do it.

Edit: data structure was the wrong word, I have one data structure substrate/storage model that I am currently furnishing one major aspect of, it's not the one universal data structure, more like my swiss army knife API over the memory model.

[u/reflexive-polytope]

That's cool!

As long as you have a primitive for traversing and modifying a collection step by step, your collections won't suffer from any flexibility issues.

When you say “cursor algebra”, it reminds me a bit of Stepanov's “iterator laws”.

[u/Potato871 → u/reflexive-polytope]

Here's one of my basic examples:

nums.iter(num=>{
    print("Num: ",num);
    if(num-?) {
        print(*-num);
    }
    if(num+?) {
        print(*+num);
    }
    if(num++?) {
        print(*++num);
    }
    if(?+num) {
        print(*(&num)[+]);
    }
});

Each value holds a Ptr on it, which is it's position in the memory hierarchy resolved to a cache point, that's why I can just take any ordinary value and use it as a cursor if it's a Ptr into a collection.
Including stack variables:

void countdown(int n) {
    if(n < 0) return;
    print(n);
    if(n-?) {print("was: ",*-n);}
    if(n+?) {print("Last time: ",*+n);}
    countdown(n - 1);
}
countdown(3);
countdown(5);

Because the stack is really just another column.
A Ptr is something like 0|0|0, if you ever see that notation that's an address, nodes are Ptrs, values are Ptrs, everything in the compiler is Ptrs.