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I'm working through MMA Cookbook by Mangano, page 54. He shows Map is a compact form of Fold function. Is using Fold function important?

myMap3[f_, l_] := Fold[Prepend[#1, f[#2]]&, {}, l]
myMap3[Sqrt, {1, 2, 3}]
(* Out: {Sqrt[3], Sqrt[2], 1} *)

I value writing better MMA code. Mastering Functional forms, then moving into Rewrite-rules. Thanks in advance.

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    $\begingroup$ Sure. Fold solves problems that Map does not (at least not without uncomfortable contortions). Map is perhaps more intuitive to me and certainly very convenient. It also has a nice infix form (/@), which is handy. You would certainly want to be aware of both to write idiomatic MMA code. $\endgroup$
    – MarcoB
    May 15, 2020 at 21:36
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    $\begingroup$ As @MarcoB notes, Fold can solve problems that Map cannot. I have not read Mangano's book, but to me, the more interesting comparison is between Fold and recursive functions. Understanding why recursion is more powerful than Fold is valuable exercise. $\endgroup$ May 15, 2020 at 22:17
  • $\begingroup$ Thank you, now I get it. @Shredderroy $\endgroup$
    – prog9910
    May 15, 2020 at 23:35
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    $\begingroup$ Magnano's point was, "so you can understand" what is happening inside of the Map[ command, by a drawn out equivalent. I'm really enjoying trying to get inside MMA head. Just everything is so abstract & full of symbols. $\endgroup$
    – prog9910
    May 16, 2020 at 3:06

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