Take a look here http://bm380.user.srcf.net/cgi-bin/stepeval.cgi?expr=let+fix+f+%3D+f+%28fix+... . The above webpage uses stepval https://github.com/bmillwood/stepeval, it can evaluate any expression step by step using equational reasoning. On 27 January 2015 at 11:54, Karl Voelker wrote:

On Mon, Jan 26, 2015, at 08:43 PM, Animesh Saxena wrote:

I stumbled across this example as a shiny way of explaining why Lazy eval matters....

fact = fix $ \f n -> if n == 0 then 1 else n * f (n-1) fix f = f (fix f)

With lazy eval, I get

fact 4 = fix $ \f 4 (......)

Not quite. Let's go one step at a time:

fact 4 = (fix $ \f n -> if n == 0 then 1 else n * f (n - 1)) 4

Now we can bring in the definition of fix, substituting the argument to fix for all of the occurrences of f in the definition of fix. Notice that we can't substitute the 4 for n yet.

fact 4 = ((\f n -> if n == 0 then 1 else n * f (n - 1)) (fix $ \f n -> if n == 0 then 1 else n * f (n - 1))) 4

I think if you are very patient and methodical about performing the substitutions (and writing them out fully - no dot-dot-dot), then you'll figure out how it all works.

-Karl

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