The R language defines two different types of functions: primitive functions, which are low-level, and closures, which are the regular kind of functions.
Details
Closures are functions written in R, named after the way their arguments are scoped within nested environments (see https://en.wikipedia.org/wiki/Closure_(computer_programming)). The root environment of the closure is called the closure environment. When closures are evaluated, a new environment called the evaluation frame is created with the closure environment as parent. This is where the body of the closure is evaluated. These closure frames appear on the evaluation stack, as opposed to primitive functions which do not necessarily have their own evaluation frame and never appear on the stack.
Primitive functions are more efficient than closures for two
reasons. First, they are written entirely in fast low-level
code. Second, the mechanism by which they are passed arguments is
more efficient because they often do not need the full procedure of
argument matching (dealing with positional versus named arguments,
partial matching, etc). One practical consequence of the special
way in which primitives are passed arguments is that they
technically do not have formal arguments, and formals() will
return NULL if called on a primitive function. Finally, primitive
functions can either take arguments lazily, like R closures do,
or evaluate them eagerly before being passed on to the C code.
The former kind of primitives are called "special" in R terminology,
while the latter is referred to as "builtin". is_primitive_eager()
and is_primitive_lazy() allow you to check whether a primitive
function evaluates arguments eagerly or lazily.
You will also encounter the distinction between primitive and
internal functions in technical documentation. Like primitive
functions, internal functions are defined at a low level and
written in C. However, internal functions have no representation in
the R language. Instead, they are called via a call to
base::.Internal() within a regular closure. This ensures that
they appear as normal R function objects: they obey all the usual
rules of argument passing, and they appear on the evaluation stack
as any other closures. As a result, fn_fmls() does not need to
look in the .ArgsEnv environment to obtain a representation of
their arguments, and there is no way of querying from R whether
they are lazy ('special' in R terminology) or eager ('builtin').
You can call primitive functions with .Primitive() and internal
functions with .Internal(). However, calling internal functions
in a package is forbidden by CRAN's policy because they are
considered part of the private API. They often assume that they
have been called with correctly formed arguments, and may cause R
to crash if you call them with unexpected objects.
Examples
# Primitive functions are not closures:
is_closure(base::c)
#> [1] FALSE
is_primitive(base::c)
#> [1] TRUE
# On the other hand, internal functions are wrapped in a closure
# and appear as such from the R side:
is_closure(base::eval)
#> [1] TRUE
# Both closures and primitives are functions:
is_function(base::c)
#> [1] TRUE
is_function(base::eval)
#> [1] TRUE
# Many primitive functions evaluate arguments eagerly:
is_primitive_eager(base::c)
#> [1] TRUE
is_primitive_eager(base::list)
#> [1] TRUE
is_primitive_eager(base::`+`)
#> [1] TRUE
# However, primitives that operate on expressions, like quote() or
# substitute(), are lazy:
is_primitive_lazy(base::quote)
#> [1] TRUE
is_primitive_lazy(base::substitute)
#> [1] TRUE