[Haskell-cafe] Converting list comprehensions to combinatory style

[R J]

Can anyone help with this problem from Bird:

a. Convert the following list comprehensions to combinatory style:

   i.   [(x, y) | x <- [1..n], odd x, y <- [1..n]]
   ii.  [(x, y) | x <- [1..n], y <- [1..n], odd x]

b. Are they equal?

c. Compare the costs of evaluating the two expressions.

I gather that by combinatory style, he means the use of concat, map, and filter.  While Bird provides the following conversion rules, he doesn't prove them, justify them, or even provide an example using them:

   R1.  [ f x | x <- xs      ]  =  map f xs
   R2.  [   x | x <- xs, p x ]  =  filter p xs
   R3.  [ e   | Q, P         ]  =  concat [[e | P] | Q]
   R4.  [ e   | x <- [d | P] ]  =  [e [x := d] | Q, P]

Thanks.


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