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 '*))
describe shows that the symbol
is a primitive type-specifier that has optional information lower bound and
upper bound. Meanwhile, it is a built-in class. But why?
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>
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 Types
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 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] ...
Compile-time type checking
You may provide type information for variables, function arguments
However, similar to the
introduced in CLOS section, the effects of type declarations are
undefined in Lisp standard and are implementation specific. So there is no
guarantee that the Lisp compiler will perform compile-time type checking.
However, it is possible, and SBCL is an implementation that does thorough type checking.
Let’s recall first that Lisp already warns about simple type warnings. The following function wrongly wants to concatenate a string and a number. When we compile it, we get a type warning.
(defconstant +foo+ 3) (defun bar () (concatenate 'string "+" +foo+)) ; caught WARNING: ; Constant 3 conflicts with its asserted type SEQUENCE. ; See also: ; The SBCL Manual, Node "Handling of Types"
The example is simple, but it already shows a capacity some other languages don’t have, and it is actually useful during development ;) Now, we’ll do better.
Declaring the type of variables
Use the macro
Let’s declare that our global variable
*name* is a string (you can
type the following in any order in the REPL):
(declaim (type (string) *name*)) (defparameter *name* "book")
Now if we try to set it with a bad type, we get a
(setf *name* :me) Value of :ME in (THE STRING :ME) is :ME, not a STRING. [Condition of type SIMPLE-TYPE-ERROR]
We can do the same with our custom types. Let’s quickly declare the type
(defun list-of-strings-p (list) "Return t if LIST is non nil and contains only strings." (and (consp list) (every #'stringp list))) (deftype list-of-strings () `(satisfies list-of-strings-p))
Now let’s declare that our
*all-names* variables is a list of strings:
(declaim (type (list-of-strings) *all-names*)) ;; and with a wrong value: (defparameter *all-names* "") ;; we get an error: Cannot set SYMBOL-VALUE of *ALL-NAMES* to "", not of type (SATISFIES LIST-OF-STRINGS-P). [Condition of type SIMPLE-TYPE-ERROR]
We can compose types:
(declaim (type (or null list-of-strings) *all-names*))
Declaring the input and output types of functions
We use again the
declaim macro, with
ftype (function …) instead of just
(declaim (ftype (function (fixnum) fixnum) add)) ;; ^^input ^^output [optional] (defun add (n) (+ n 1))
With this we get nice type warnings at compile time.
If we change the function to erroneously return a string instead of a fixnum, we get a warning:
(defun add (n) (format nil "~a" (+ n 1))) ; caught WARNING: ; Derived type of ((GET-OUTPUT-STREAM-STRING STREAM)) is ; (VALUES SIMPLE-STRING &OPTIONAL), ; conflicting with the declared function return type ; (VALUES FIXNUM &REST T).
If we use
add inside another function, to a place that expects a
string, we get a warning:
(defun bad-concat (n) (concatenate 'string (add n))) ; caught WARNING: ; Derived type of (ADD N) is ; (VALUES FIXNUM &REST T), ; conflicting with its asserted type ; SEQUENCE.
If we use
add inside another function, and that function declares
its argument types which appear to be incompatible with those of
add, we get a warning:
(declaim (ftype (function (string)) bad-arg)) (defun bad-arg (n) (add n)) ; caught WARNING: ; Derived type of N is ; (VALUES STRING &OPTIONAL), ; conflicting with its asserted type ; FIXNUM.
This all happens indeed at compile time, either in the REPL,
either with a simple
C-c C-c in Slime, or when we
load a file.
Declaring &key parameters
&key (:argument type).
(declaim (ftype (function (string &key (:n integer))) foo)) (defun foo (bar &key n) …)
Declaring class slots types
A class slot accepts a
:type slot option. It is however generally
not used to check the type of the initform. SBCL, starting with
version 1.5.9 released on
november 2019, now gives those warnings, meaning that this:
(defclass foo () ((name :type number :initform "17")))
throws a warning at compile time.
Note: see also sanity-clause, a data
serialization/contract library to check slots’ types during
make-instance (which is not compile time).
Alternative type checking syntax: defstar, serapeum
The Serapeum library provides a shortcut that looks like this:
(-> mod-fixnum+ (fixnum fixnum) fixnum) (defun mod-fixnum+ (x y) ...)
The Defstar library provides
defun* macro that allows to add the type declarations into the
lambda list. It looks like this:
(defun* sum ((a real) (b real)) (+ a b))
It also allows:
- to declare the return type, either in the function definition or in its body
- to quickly declare variables that are ignored, with the
- to add assertions for each arguments
- to do the same with
Complex types involving
satisfies are not checked inside a function
body, only at its boundaries. Even if it does a lot, SBCL doesn’t do
as much as a statically typed language.
Consider this example, where we badly increment an integer with a string:
(declaim (ftype (function () string) bad-adder)) (defun bad-adder () (let ((res 10)) (loop for name in '("alice") do (incf res name)) ;; bad (format nil "finally doing sth with ~a" res)))
Compiling this function doesn’t throw a type warning.
However, if we had the problematic line at the function’s boundary we’d get the warning:
(defun bad-adder () (let ((res 10)) (loop for name in '("alice") return (incf res name)))) ; in: DEFUN BAD-ADDER ; (SB-INT:NAMED-LAMBDA BAD-ADDER ; NIL ; (BLOCK BAD-ADDER ; (LET ((RES 10)) ; (LOOP FOR NAME IN *ALL-NAMES* RETURN (INCF RES NAME))))) ; ; caught WARNING: ; Derived type of ("a hairy form" NIL (SETQ RES (+ NAME RES))) is ; (VALUES (OR NULL NUMBER) &OPTIONAL), ; conflicting with the declared function return type ; (VALUES STRING &REST T).
What can we conclude? This is yet another reason to decompose your code into small functions.
- the article Static type checking in SBCL, by Martin Cracauer
- the article Typed List, a Primer - let’s explore Lisp’s fine-grained type hierarchy! with a shallow comparison to Haskell.
- the Coalton library: an efficient, statically typed functional programming language that supercharges Common Lisp. It is as an embedded DSL in Lisp that resembles Haskell or Standard ML, but lets you seamlessly interoperate with non-statically-typed Lisp code (and vice versa).
The term object here has nothing to do with Object-Oriented or so. It means “any Lisp datum”. ↩
Page source: type.md