Re: [Haskell-cafe] Strict type system allows for a maximum number of programming errors to be caught at compile time.

On Tue, May 4, 2010 at 12:13 AM, Ivan Miljenovic wrote:

On 4 May 2010 13:30, Luke Palmer wrote:

...

Here is a contrived example of what I am referring to:

prefac f 0 = 1 prefac f n = n * f (n-1)

fac = (\x -> x x) (\x -> prefac (x x))

I can't work out how this works (or should work rather); is it meant to be using church numerals or something (assuming that they have been made an instance of Num so that - and * work)?

Looks like a variation on H. Curry's fixed-point combinator to me, e.g.: y f = (\x -> f (x x)) (\x -> f (x x)) Which of course is perfectly useful, but not valid in any type system that excludes absurdities. The otherwise-infinite type signature for Y is circumvented by built-in recursion in Haskell (making halting undecidable in the process, unfortunately). - C.