There are the following constraints on type-of:

• Let x be an object such that (typep x type) is true and type is one of the following:

  array	float	package	sequence
  bit-vector	function	pathname	short-float
  character	hash-table	random-state	single-float
  complex	integer	ratio	stream
  condition	long-float	rational	string
  cons	null	readtable	symbol
  double-float	number	restart	vector

  Then (subtypep (type-of x) type)) must return the values t and t; that is, type-of applied to x must return either type itself or a subtype of type that subtypep can recognize in that implementation.

• For any object x, (subtypep (type-of x) (class-of x)) must produce the values t and t.
• For every object x, (typep x (type-of x)) must be true. (This implies that type-of can never return nil, for no object is of type nil.)
• type-of never returns t and never uses a satisfies, and, or, not, or values type specifier in its result.
• For objects of CLOS metaclass structure-class or of standard-class, type-of returns the proper name of the class returned by class-of if it has a proper name, and otherwise returns the class itself. In particular, for any object created by a defstruct constructor function, where the defstruct had the name name and no :type option, type-of will return name.

As an example, (type-of "acetylcholinesterase") may return string or simple-string or (simple-string  20), but not array or simple-vector. As another example, it is permitted for (type-of 1729) to return integer or fixnum (if it is indeed a fixnum) or (signed-byte 16) or (integer 1729 1729) or (integer 1685 1750) or even (mod 1730), but not rational or number, because

is true, integer is in the list of types mentioned above, and

would be false if type-of were to return rational or number.