Talk:SKI combinator calculus

In fact, it is possible to define a complete system using only one combinator. An example is Chris Barker's iota combinator, defined as follows:

$ix=x\mathbf {SK}$

I find this unconvincing - $i$ is defined in terms of S and K, which means the system needs three combinators. If you could define i in terms of itself only, then I'd be convinced. I doubt this is possible, but I would be pleased if someone could prove me wrong! The iota language in the link uses S and K internally, it's just in the syntax that it is forbidden.

So I think this might mislead readers into thinking that single combinator systems are possible. Can anyone provide a more compelling example or clarify somehow?

Edwin 20:17, 14 May 2006 (UTC)