They aren't talking about using recursion instead of loops. They are talking about the map method for iterators. For each element yielded by the iterator, map applies a specified function/closure and collects the results in a new iterator (usually a list). This is a functional programming pattern that's common in many languages including Python and Rust.

This pattern has no risk of stack overflow since each invocation of the function is completed before the next invocation. The construct does expand to some sort of loop during execution. The only possible overhead is a single function call within the loop (whereas you could have written it as the loop body). However, that won't be a problem if the compiler can inline the function.

The fact that this is functional programming creates additional avenues to optimize the program. For example, a chain of maps (or other iterator adaptors) can be intelligently combined into a single loop. In practice, this pattern is as fast as hand written loops.

Compiler optimizations like function inlining are your friend.

Especially in functional languages, there are a lot of tricks a compiler can use to output more efficient code due to not needing to worry about possible side effects.

Also, in a lot of cases the performance difference does not matter.

I'm not familiar with any special LLVM instructions for Haskell. Regardless, LLVM is not actually a commonly used backend for Haskell (even though you can) since it's not great for optimizing the kind of code that Haskell produces. Generally, Haskell is compiled down to native code directly.

Haskell has a completely different execution model to imperative languages. In Haskell, almost everything is heap allocated, though there may be some limited use of stack allocation as an optimization where it's safe. GHC has a number of aggressive optimizations it can do (that is, optimizations that are safe in Haskell thanks to purity that are unsafe in other languages) to make this quite efficient in practice. In particular, GHC can aggressively inline a lot more code than compilers for imperative languages can, which very often can eliminate the indirection associated with function calls entirely. https://gitlab.haskell.org/ghc/ghc/-/wikis/commentary/compiler/generated-code goes into a lot more depth about the execution model if you're interested.

As for languages other than Haskell without such an execution model (especially imperative languages), it's true that there can be the overhead you describe, which is why the vast majority of them use iterators to achieve the effect, which avoids the overhead. Rust (which has mapping/filtering, etc. as a pervasive part of its ecosystem) does this, for example, even though it's a systems programming language with a great deal of focus on performance.

As for the advantage, it's really about expressiveness and clarity of code, in addition to eliminating the bugs so often resulting from mutation.

I looked at the post again and they do talk about recursion for looping (my other reply talks about map over an iterator). Languages that use recursion for looping (like scheme) use an optimization trick called 'Tail Call Optimization' (TCO). The idea is that if the last operation in a function is a recursive call (call to itself), you can skip all the complexities of a regular function call - like pushing variables to the stack and creating a new stack frame. This way, recursion becomes as performant as iteration and avoids problems like stack overflow.

Some languages have to optimize it with various tricks. There's a good reason why I call heavily functional "programmer wankery". It took me a while to run into an issue that was caused by a variable modified in a wrong way, which I fixed by saving the value of the variable before a call that seems to alter it. Probably I should have instead properly fix it so I could understand the actual root cause, but I have limited time to spend on things.