Way to redefine builtin function inside a lisp package

Question

I'm currently writing small implementation of vector arithmetics, and I want to define my own «-» and «+» (and maybe other) functions that will operate on vectors.

And I also want to place all these functions in a package.

And I want this hypothetical package, let's say it's called «vec», to behave like this:

• While inside the package, I define functions «-» and «+», but when I call + or - (inside the same package), Common Lisp builtins are invoked.
• If previous is not possible, I want to call builtin + and - as cl:+ and cl:-, but without necessity of explicitly importing every single other needed function from :cl.
• When I import vec package, or mention it in :use section of definition of another package, common-lisp package's «-» and «+» are still available, and package vec's functions are called like (vec:+ v1 v2), so there is no name conflict between vec:+ and cl:+.

So, what is considered the best (and proper) way to achieve this behaviour?

Answer 1

It is not possible to define a symbol + and have it refer to + from another package at the same time.

You don't need to import symbols. If they are exported you can use them as foo:+. If they are not exported, they can be used as foo::+.

There is no point of using (in the programmatic sense - sure it makes sense to introduce a package as a namespace for vector operations) a package if you don't want to make symbols accessible in the using package. If you want to write vec:+, then there is no point in using the package VEC. Just export symbols from VEC.

Just for illustration:

CL-USER 6 > (defpackage "VEC"
               (:use "CL")
               (:shadow cl:+ cl:-)
               (:export "+" "-"))
#<The VEC package, 0/16 internal, 2/16 external>

CL-USER 7 > (defun vec:+ (a b) (+ a b))
VEC:+

CL-USER 8 > (defun vec:- (a b) (- a b))
VEC:-

CL-USER 9 > (defpackage "GRAPH" (:use "CL"))
#<The GRAPH package, 0/16 internal, 0/16 external>

CL-USER 10 > (in-package "GRAPH")
#<The GRAPH package, 0/16 internal, 0/16 external>

GRAPH 11 > (defun foo (a b) (+ (vec:+ a b) 42))
FOO

Note, if the current package is VEC, then + refers to VEC:+. For the CL + you would then need to write CL:+.

Always keep in mind:

• packages are resolved at read time.
• the current package determines the default package which is used during read time. changing the current package does not change already read symbols.