This function will return true if expr is a factorial, and false otherwise.  For more information about factorials, see factorial.

An expression of the type n!, where $n$ is an integer, is not of type `!`, since its value is calculated before the call to the type function is executed.

Note that the factorial function is both of type function and type `!`. In the function call, it is important that the exclamation mark, !, be enclosed in quotes.  Missing quotes will cause a syntax error.

$\mathrm{type}\left(n!\,\mathrm{`!`}\right)$

$\mathrm{true}$

$\mathrm{type}\left(n!\,\mathrm{function}\right)$

$\mathrm{true}$

$\mathrm{type}\left(6!\,\mathrm{`!`}\right)$

$\mathrm{false}$

$\mathrm{type}\left(0.5!\,\mathrm{`!`}\right)$

$\mathrm{false}$