[Haskell-cafe] Calculating with list comprehension

[R J]

I can calculate non-nested list comprehensions without a problem, but am unable to calculate nested comprehensions involving, for example, the generation of a list of pairs where the first and separate elements are drawn from two separate lists, as in:

   [(a, b) | a <- [1..3], b <- [1..2]]


How does one calculate the expansion of this list?  The two rules for expanding list comprehensions are:

1.  Generator rule:  [e | x <- xs, Q]  =  concat (map f xs)
                                          where
                                              f x = [e | Q]

2.  Guard rule:      [e | p, Q]        =  if p then [e | Q] else []


There is a third rule that I've seen on the Internet, not in an authoritative text:



   [e | Q1 , Q2]     =  concat [ [e | Q 2] | Q1 ]



I don't understand what this third rule means, or whether it's relevant.


Concat and map are defined as:

concat           :: [[a]] -> [a]
concat []        =  []
concat (xs:xss)  =  xs ++ concat xss

map              :: (a -> b) -> [a] -> [b]
map f []         =  []
map f (x:xs)     =  f x : (map f xs)

Any help is appreciated.





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