[profquail]

In F#, yield emits a new element in the sequence (just as in C#), while yield! emits all of the elements from another sequence you provide. This effectively allows you to "splice" sequences together, or create a new sequence by prepending/appending some elements to an existing sequence.

As another commenter mentioned below, yield! has nothing to do with repeating the function name -- the name is repeated because it's a recursive function (i.e., a function which calls itself). So the sqrtGuesses function produces a sequence which emits (yields) the value it's given (x), computes the next value of x, stores it in the variable next_x, then emits all of the values in the sequence produced by calling sqrtGuesses for the next value of x (next_x).

The |> is called the "forward pipeline operator" in F#, and it's very simple -- whereas you normally call a function f with a value x by writing f x, you can swap the order of the arguments with |> to write x |> f. This effectively allows you to write nested function applications without all of the parentheses: f(g(h(x)) can instead be written x |> h |> g |> f or h x |> g |> f or whatever.