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

On Mon, May 3, 2010 at 10:13 PM, 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)?

No they're just integers. fac is a beta expansion of fix prefac. Obseve the magic: (\x -> x x) (\x -> prefac (x x)) 2 (\x -> prefac (x x)) (\x -> prefac (x x)) 2 prefac ((\x -> prefac (x x)) (\x -> prefac (x x))) 2 2 * ((\x -> prefac (x x)) (\x -> prefac (x x)) (2-1) 2 * prefac ((\x -> prefac (x x)) (\x -> prefac (x x))) (2-1) 2 * prefac ((\x -> prefac (x x)) (\x -> prefac (x x))) 1 2 * (1 * ((\x -> prefac (x x)) (\x -> prefac (x x))) (1-1)) 2 * (1 * prefac ((\x -> prefac (x x)) (\x -> prefac (x x))) (1-1)) 2 * (1 * prefac ((\x -> prefac (x x)) (\x -> prefac (x x))) 0) 2 * (1 * 1) 2 Luke