Mathematica: Unevaluated vs Defer vs Hold vs HoldForm vs HoldAllComplete vs etc etc

Question

I'm bewildered by all the built-in Mathematica functions that purport to prevent evaluation in some way: Unevaluated, Defer, Hold, and over half a dozen of the form Hold*. The Mathematica documentation just explains each function in isolation without explaining why you would choose one or the other. Can anyone offer a coherent explanation of all these functions? The whole thing seems like a convoluted mess to me. Relating it all to Lisp macros might be a good place to start.

Most of the Mathematica language is amazingly well-designed but it seems like Wolfram really painted himself into a corner on this aspect. Or I could be missing something.

Answer 1

These are pretty tricky constructs, and it's tough to give clear explanations; they aren't as straightforward as Lisp macros (or, for that matter, the relationship between Lisp's QUOTE and EVAL). However, there's a good, lengthy discussion available in the form of notes from a talk on Wolfram's website.

Defer is omitted from that talk, because it's new as of Mathematica 6.0. It's a lot like HoldForm, except that when it's output in a front-end (but not a bare kernel) it's stripped away, leaving an expression that can be used as input. This is very useful if you want to programmatically construct expressions that a user can edit and evaluate, say in a palette.