ahem.

One huge difference in general between C++ templates and Rust's generics (I _believe_ Java/C# are more like Rust here, and I'm not sure about Swift) in that C++ templates generally don't check that their calling code actually supports the type that's passed into the template. In other words, the check happens after the template is expanded. (This is the sort example on page 3). Rust's generics system does the opposite: it requires that if you call a method on some generic parameter, that generic parameter is constrained by a trait that has that method. This happens before expansion. So concepts are, in some ways, an attempt to make the C++ system closer to Rust's system. (This is ignoring the actual chronology here, of course: concepts have been in development a long time).

The way "requires" works here is very different than in Rust, as well. In Rust, you define a trait the same way you'd define regular methods. If those methods have a body, then it's used as a default implementation, if it does not, then you must implement that method. The equivalent of "must have an iterator type" is associated types, you add "type Name;" instead of a method signature.

So the equivalent of the "Sequence" type on page 7 would be

  trait Sequence {
      type Value;
      type Iterator<Item=Value>; // Iterator itself has an associated type, Value
    
      fn begin() -> Self::Iterator;
      fn end() -> Self::Iterator;
  }

That's my impressions after reading this. I have been meaning to read about concepts for a while, but since I only have so much time, have mostly waited to see how they shake out before really digging in. It's slightly slower going since my C++ isn't spectacular. This post mostly represents my understanding of the differences, I'm not trying to make any judgements here, etc.

The name has been used in the C++ community since at last mid 90s as it originated from Alex Stephanov work on the STL. Stephanov himself might have used the name even earlier than that. Formalization of concepts which has been attempted at least since the early 00s was influenced by Haskell and in turn did influence both Rust and Swift.

That is, it is resolved at compilation time and not at run-time as these that you cited except for some cases in Rust where Traits can be both run-time or compile-time depending on how you use them.

For decades C++ has the equivalent of these, it is called virtual pure classes (we may even consider virtual in general).

But those cannot really fulfill the role of concepts in templates.