Re: [Haskell-cafe] Re: Mysterious fact

Jon, you beat me to it. I was going to mention Ponder. But Ponder did have a builtin type, it had the function type built in. :) -- Lennart On Tue, Nov 2, 2010 at 9:47 PM, Jon Fairbairn wrote:

Andrew Coppin writes:

...

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)

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