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 Robby Villegas's 1999 talk "Unevaluated Expressions" 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.