In Common Lisp, how to define a generic data type

Question

I would like to define a type specifier that describes a list of things of the same type. So I would like to have (list-of integer) similar to (array integer) (which is built-in). I am able to create it for a specific type, like this:

(defun elements-are-integer (seq) 
  (every #'(lambda (x) (typep x 'integer)) seq))
(deftype list-of-integer ()
  '(and list (satisfies elements-are-integer)))

However, this means I have to do this for every possible type. How can I change this code so that the type would take another type as an argument, and construct the satisfies predicate on the fly? The problem is that the satisfies requires a global symbol, and I don't know how to define the predicate function in proper context (I guess I need to gensym it somehow, but how?). Also, the solution should work so that the type could be created inside another package.

Answer 1

Try this:

(defun elements-are-of-type (seq type)
  (every #'(lambda (x) (typep x type)) seq))

(deftype list-of-type (type)
  (let ((predicate (gensym)))
    (setf (symbol-function predicate)
      #'(lambda (seq) (elements-are-of-type seq type)) )
    `(and list (satisfies ,predicate)) ))

(typep '(1 2 3) '(list-of-type integer))
; -> T

(typep '(1 2 a) '(list-of-type integer))
; -> NIL

(typep '(a b c) '(list-of-type symbol))
; -> T