How to show all the functions and classes that are defined in a library?

library(some_library_name)

Suppose I load a library.

You mean "package" right ? A library is a set of packages

I'm wondering what command I should use to
list all the functions, classes and variables defined in the library.

Check ?ls :

 > ls( "package:some_package_name" )
 > ls( "package:some_package_name", all = TRUE )

Sometimes you want to see even those that are not exported from the 
namespace:

 > ls( asNamespace( "some_package_name" ) )
 > ls( asNamespace( "some_package_name" ), all = TRUE )

Romain

Romain Francois
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