What is the difference between assign() and <<- in R?

Question

The normal approach to writing functions in R (as I understand) is to avoid side-effects and return a value from a function.

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Answer 1

According to the manual page here,

The operators <<- and ->> cause a search to made through the environment for an existing definition of the variable being assigned.

I've never had to do this in practice, but to my mind, assign wins a lot of points for specifying the environment exactly, without even having to think about R's scoping rules. The <<- performs a search through environments and is therefore a little bit harder to interpret.

EDIT: In deference to @Dirk and @Hadley, it sounds like assign is the appropriate way to actually assign to the global environment (when that's what you know you want), while <<- is the appropriate way to "bump up" to a broader scope.