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

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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.

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