On Wed, Aug 17, 2011 at 8:12 AM, Sam Tobin-Hochstadt <[email protected]> wrote: > Here's how to see why you need that. To say that (A -> B) is a subtype > of (C -> D), you're saying that you can use (A -> B) anywhere you need > (C -> D). But some program that expects a (C -> D) function might > pass it a C, of course, so your new replacement function must accept > all of the Cs. Therefore, A needs to accept all of the Cs, which > means that A must be a subtype of C.
Contravariance strikes again! A typo concludes a good explanation: C must be a subtype of A. C <: A B <: D ------------------------- A -> B <: C -> D Norman, one resource on this topic with an ML flavor is <http://www.cis.upenn.edu/~bcpierce/sf/Subtyping.html> Writing the natural deduction rule and staring at it every minute you talk about contravariance is de rigueur. Jon Postel summed up contravariance by thinking about HTML: "Be liberal in what you accept, and conservative in what you send." Anthony _________________________________________________ For list-related administrative tasks: http://lists.racket-lang.org/listinfo/users
