Andrew Coppin
The other day, I accidentally came up with this:
|{-# LANGUAGE RankNTypes #-}
type Either x y= forall r. (x -> r) -> (y -> r) -> r
left :: x -> Either x y left x f g= f x
right :: y -> Either x y right y f g= g y
|
This is one example; it seems that just about any algebraic type can be encoded this way. I presume that somebody else has thought of this before. Does it have a name?
You could try reading my PhD thesis! http://www.cl.cam.ac.uk/techreports/UCAM-CL-TR-75.html contains a link to the full text scanned to a pdf. (That -- 1985 -- was a long time ago. One thing I really regret about it is that there should have been a comma between "simple" and "typed" in the title. I suspect people think "simply typed" when they see it). It isn't hard to read (one of my examiners said it made good bed-time reading). Anyway, the relevant part is that Ponder was a programming language (Stuart Wray even wrote a GUI programme in it) that had (in principle) no built-in types, relying on the type system being powerful enough to express anything and the optimiser being good enough to convert them to something more sensible. In practice neither was /quite/ true, but it got quite close. -- Jón Fairbairn Jon.Fairbairn@cl.cam.ac.uk http://www.chaos.org.uk/~jf/Stuff-I-dont-want.html (updated 2010-09-14)