Keep in mind this is a *lexical* rewrite. In the generator rule x and e are not independent: x is a pattern (which introduces a bind variable) and e is an expression (with free variables, one of which may be bound by x) After one application of the generator rule, we get (using a lambda expression instead of introducing a fresh function name f): concatMap (\a -> [(a,b) | b <- [1..2]]) [1..3] After another: concatMap (\a -> concatMap (\b -> [(a,b)]) [1..2]) [1..3] Note that the "a <-" and "b <-" map into \a -> and \b -> and bind the free variables a and b in the expression (a,b). Dan R J wrote:

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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