Generic function
In certain systems for object-oriented programming such as the Common Lisp Object System[1] and Dylan, a generic function is an entity made up of all methods having the same name. Typically generic function is a class that inherits both from function and standard-object. Thus generic functions are both functions (that can be called with and applied to arguments) and ordinary objects. The book The Art of the Metaobject Protocol explains the implementation and usage of CLOS generic functions in detail.
Flavors is one of the early object-oriented extensions to Lisp. It used the usual message sending paradigm influenced by Smalltalk. The syntax for sending a message in Flavors is:
(send object :message)
With New Flavors it was decided the message should be a real function and the usual function calling syntax should be used:
(message object)
message now is a generic function, an object and function in its own right. Individual implementations of the message are called methods.
The same idea was implemented in CommonLoops[2]. New Flavors and CommonLoops were the main influence for the Common Lisp Object System.
Example
Common Lisp
Define a generic function with two parameters object-1 and object-2. The name of the generic function is collide.
(defgeneric collide (object-1 object-2))
Methods belonging to the generic function are defined outside of classes. Here we define a method for the generic function collide which is specialized for the classes asteroid (first parameter object-1) and spaceship (second parameter object-2). The parameters are used as normal variables inside the method body. There is no special namespace that has access to class slots.
(defmethod collide ((object-1 asteroid) (object-2 spaceship))
(format t "asteroid ~a collides with spaceship ~a" object-1 object-2))
Calling the generic function:
? (collide (make-instance 'asteroid) (make-instance 'spaceship))
asteroid #<ASTEROID 4020003FD3> collides with spaceship #<SPACESHIP 40200048CB>
Common Lisp can also retrieve individual methods from the generic function. FIND-METHOD finds the method from the generic function collide specialized for the classes asteroid and spaceship.
? (find-method #'collide nil (list (find-class 'asteroid) (find-class 'spaceship)))
#<STANDARD-METHOD COLLIDE NIL (ASTEROID SPACESHIP) 4150015E43>
Comparison to other languages
Generic functions correspond roughly to what Smalltalk calls methods. In a programming language with multiple dispatch when a generic function is called, method dispatch occurs on the basis of all arguments, not just a single privileged one. New Flavors also provided generic functions, but only single dispatch.
Another, completely separate definition of generic function is a function that uses parametric polymorphism. This is the definition used when working with a language like OCaml. An example of a generic function is
id: a->a
let id a = a
which takes an argument of any type and returns something of that same type.