Values Have Types, Not Variables
Being different from some languages such as C/C++, variables in Lisp are just
placeholders for objects1. When you
setf a variable, an object
is “placed” in it. You can place another value to the same variable later, as
This implies a fact that in Common Lisp objects have types, while variables do not. This might be surprising at first if you come from a C/C++ background.
* (defvar *var* 1234) *VAR* * (type-of *var*) (INTEGER 0 4611686018427387903)
type-of returns the type of the given object. The
returned result is a type-specifier. In this case the first
element is the type and the remaining part is extra information (lower and
upper bound) of that type. You can safely ignore it for now. Also remember
that integers in Lisp have no limit!
Now let’s try to
setf the variable:
* (setf *var* "hello") "hello" * (type-of *var*) (SIMPLE-ARRAY CHARACTER (5))
type-of returns a different result:
of length 5 with contents of type
character. This is because
*var* is evaluated to string
"hello" and the function
returns the type of object
"hello" instead of variable
The inheritance relationship of Lisp types consists a type graph and the root
of all types is
T. For example:
* (describe 'integer) COMMON-LISP:INTEGER [symbol] INTEGER names the built-in-class #<BUILT-IN-CLASS COMMON-LISP:INTEGER>: Class precedence-list: INTEGER, RATIONAL, REAL, NUMBER, T Direct superclasses: RATIONAL Direct subclasses: FIXNUM, BIGNUM No direct slots. INTEGER names a primitive type-specifier: Lambda-list: (&OPTIONAL (SB-KERNEL::LOW '*) (SB-KERNEL::HIGH '*))
Most common Lisp types are implemented as CLOS classes. Some types are simply
“wrappers” of other types. Each CLOS class maps to a corresponding type. In
Lisp types are referred to indirectly by the use of
There are some differences between the function
class-of. The function
type-of returns the type of a given
object in type specifier format while
class-of returns the implementation
* (type-of 1234) (INTEGER 0 4611686018427387903) * (class-of 1234) #<BUILT-IN-CLASS COMMON-LISP:FIXNUM>
Working with Types
typep can be used to check if the first argument is of
the given type specified by the second argument.
* (typep 1234 'integer) T
subtypep can be used to inspect if a type inherits
from the another one. It returns 2 values:
T, Tmeans first argument is sub-type of the second one.
NIL, Tmeans first argument is not sub-type of the second one.
NIL, NILmeans “not determined”.
* (subtypep 'integer 'number) T T * (subtypep 'string 'number) NIL T
Sometimes you may want to perform different actions according to the type of
an argument. The macro
typecase is your friend:
* (defun plus1 (arg) (typecase arg (integer (+ arg 1)) (string (concatenate 'string arg "1")) (t 'error))) PLUS1 * (plus1 100) 101 (7 bits, #x65, #o145, #b1100101) * (plus1 "hello") "hello1" * (plus1 'hello) ERROR
A type specifier is a form specifying a type. As mentioned above, returning
value of the function
type-of and the second argument of
typep are both
As shown above,
(type-of 1234) returns
4611686018427387903). This kind of type specifiers are called compound type
specifier. It is a list whose head is a symbol indicating the type. The rest
part of it is complementary information.
* (typep '#(1 2 3) '(vector number 3)) T
Here the complementary information of the type
vector is its elements type
and size respectively.
The rest part of a compound type specifier can be a
*, which means
“anything”. For example, the type specifier
(vector number *) denotes a
vector consisting of any number of numbers.
* (typep '#(1 2 3) '(vector number *)) T
The trailing parts can be omitted, the omitted elements are treated as
* (typep '#(1 2 3) '(vector number)) T * (typep '#(1 2 3) '(vector)) T
As you may have guessed, the type specifier above can be shortened as following:
* (typep '#(1 2 3) 'vector) T
You may refer to the CLHS page for more information.
Defining New Type
You can use the macro
deftype to define a new type-specifier.
Its argument list can be understood as a direct mapping to elements of rest part of a compound type specifier. They are be defined as optional to allow symbol type specifier.
Its body should be a macro checking whether given argument is of this type
Now let us define a new data type. The data type should be a array with at most 10 elements. Also each element should be a number smaller than 10. See following code for an example:
* (defun small-number-array-p (thing) (and (arrayp thing) (<= (length thing) 10) (every #'numberp thing) (every (lambda (x) (< x 10)) thing))) * (deftype small-number-array (&optional type) `(and (array ,type 1) (satisfies small-number-array-p))) * (typep '#(1 2 3 4) '(small-number-array number)) T * (typep '#(1 2 3 4) 'small-number-array) T * (typep '#(1 2 3 4 100) 'small-number-array) NIL * (small-number-array-p '#(1 2 3 4 5 6 7 8 9 0 1)) NIL
Common Lisp supports run-time type checking via the macro
check-type. It accepts a
place and a type specifier
as arguments and signals an
type-error if the contents of
place are not of the given type.
* (defun plus1 (arg) (check-type arg number) (1+ arg)) PLUS1 * (plus1 1) 2 (2 bits, #x2, #o2, #b10) * (plus1 "hello") ; Debugger entered on #<SIMPLE-TYPE-ERROR expected-type: NUMBER datum: "Hello"> The value of ARG is "Hello", which is not of type NUMBER. [Condition of type SIMPLE-TYPE-ERROR] ...
What about compile-time type checking?
Well, you may provide type information for variables, function arguments etc
etc via the macro
declare. However, similar to
introduced in CLOS section, the effects of type declarations are
undefined in Lisp standard and are implementation specific. So there is no
guarantee that Lisp compiler will perform compile-time type checking.
The term object here has nothing to do with Object-Oriented or so. It means “any Lisp datum”. ↩
Page source: type.md