[Haskell-beginners] Strange use of undefined (et al.) in list comprehension

[Galaxy Being]

So the Bool predicates and the generators are not purposefully grouped
separately -- it just appears that way from the simplistic beginner book
examples. But the evaluation is, indeed, left-to-right in that the first
example above has even x evaluated directly after x <- [1,3], whereas in
the second example the y <- undefined is evaluated directly after x <-
[1,3], then
the even x, correct? Again, the beginner book examples give the impression
that any and all predicates are A) always pushed to the far right, closest
to the right bracket, and B) follow no order of application such as being
bound to the form closest to the left. So yes, it's visually obvious that
there is an outer-inner looping happening when you see the output of two
generators doing combinations, but, again, the beginner treatments I've
seen make no explicit mention of order in an LC. This is all news to me,
but thanks! That's what these forums are for!



On Sat, Apr 10, 2021 at 12:18 AM Matthew Low <mlow at ualberta.ca> wrote:

> First, I'm confused about what is the input and what is the predicate
>
> The haskell 2010 report (
> https://www.haskell.org/onlinereport/haskell2010/haskellch3.html#x8-420003.11)
> says that after the | we can have any type of qualifier, which can be 1. a
> generator (I think you called this the input) 2. a local binding (we don't
> care about these in your example, there are none) or 3. boolean guards,
> which are any expression that evaluate to Bool (your predicates). So there
> isn't really a `predicate postion`, predicates can occur anywhere after the
> `|`.
>
> As for the behaviour, its easiest to see what happens with a regular list
> of inputs:
>
> λ> [(x,y) | x <- [1,2], y <- ['A', 'B']]
> [(1,'A'),(1,'B'),(2,'A'),(2,'B')]
>
> so `y` acts as an inner loop and `x` the outer.
>
> > [1 | x <- [1,3], even x, y <- undefined]
>>
> Here we start the outer loop over x, and only if x is even, then we loop
> over y. But x is never even, so we never loop over y, so we never evaluate
> `undefined` (Haskell is lazy). So essentially filter out all elements of x
> and are left with []
>
> > [1 | x <- [1,3], y <- undefined, even x]
>>
> Now we've moved the guard into the inner loop, after we try to evaluate y.
> So we blow up trying to do that and GHCi catches the exception
>
> [1 | x <- [1,3], y <- [1..], even x]
>>
> Similar to the above, the (even x) isn't guarding the evaluation of y, so
> we're stuck generating all the infinite pairings of x = 1, y = 1...
>
> On Fri, Apr 9, 2021 at 9:59 PM Galaxy Being <borgauf at gmail.com> wrote:
>
>> I'm looking at Bird's *Thinking Functionally with Haskell *and he gives
>> two list comprehensions, asking under what conditions they deliver the same
>> results
>>
>> [e | x <- xs, p x, y <- ys]
>> [e | x <- xs, y <- ys, p x]
>>
>> First, I'm confused about what is the input and what is the predicate.
>> The y <- ys in the first LC seems to be in a predicate position, and in
>> the second it's a second input after x <- xs with p x in the predicate
>> position . . . confusing me.
>>
>> The answer examples Bird gives are beyond me:
>>
>> They deliver the same result only if ys is a finite list:
>>
>> > [1 | x <- [1,3], even x, y <- undefined]
>> []
>> > [1 | x <- [1,3], y <- undefined, even x]
>> Exception: Prelude.undefined
>> > [1 | x <- [1,3], y <- [1..], even x]
>> {Interruped}
>>
>> I'm not sure what's being said here, or what points are being made.
>>
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