Strange use of undefined (et al.) in list comprehension
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.
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#x8-420003.1...) 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@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.
_______________________________________________ Beginners mailing list Beginners@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners
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@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#x8-420003.1...) 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@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.
_______________________________________________ Beginners mailing list Beginners@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners
_______________________________________________ Beginners mailing list Beginners@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners
Glad it helped! You might also be interested in the forums at https://discourse.haskell.org/ - there is a dedicated learning topic, which has a question at a bunch of different levels including very beginning. On Sat, Apr 10, 2021 at 9:49 AM Galaxy Being <borgauf@gmail.com> wrote:
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@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#x8-420003.1...) 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@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.
_______________________________________________ Beginners mailing list Beginners@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners
_______________________________________________ Beginners mailing list Beginners@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners
_______________________________________________ Beginners mailing list Beginners@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners
I missed this question:
But the evaluation is, indeed, left-to-right ... correct? Correct (though note that in the second example, evaluating y <- undefined will throw and exception so (even x) will not be evaluated)
On Sat, Apr 10, 2021 at 1:19 PM Matthew Low <mlow@ualberta.ca> wrote:
Glad it helped! You might also be interested in the forums at https://discourse.haskell.org/ - there is a dedicated learning topic, which has a question at a bunch of different levels including very beginning.
On Sat, Apr 10, 2021 at 9:49 AM Galaxy Being <borgauf@gmail.com> wrote:
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@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#x8-420003.1...) 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@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.
_______________________________________________ Beginners mailing list Beginners@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners
_______________________________________________ Beginners mailing list Beginners@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners
_______________________________________________ Beginners mailing list Beginners@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners
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Galaxy Being -
Matthew Low