[Haskell-cafe] List Monads and non-determinism

[Rogan Creswick]

On Fri, Jul 19, 2013 at 3:58 PM, Matt Ford <matt at dancingfrog.co.uk> wrote:

> Hi,
>
> Thanks for the help.
>
> I thought >>= was left associative?  It seems to be in the examples from
> Learn You A Haskell.
>
> I tried to use the associative law to bracket from the right but it didn't
> like that either...
>
> [1,2] >>= (\x -> (\n -> [3,4])) x  >>= \m -> return (n,m))
>

I think the issue is that you need to first take into account the lambdas
*then* use what you know about the properties of (>>=).

I found this stackoverflow answer helpful (
http://stackoverflow.com/a/11237469)

"The rule for lambdas is pretty simple: the body of the lambda extends as
far to the right as possible without hitting an unbalanced parenthesis."

 So, the first lambda runs to the end of the expression:

[1,2] >>= (\n -> [3,4] >>= \m -> return (n,m))

Now, there is still a lambda nested inside the first lambda: \m -> return
(n,m)

[1,2] >>= (\n -> [3,4] >>= (\m -> return (n,m)))

You violated the implied grouping that these new parentheses make explicit
when you tried to apply the associative law above.

Timon's post continues from this point to show the full deconstruction.

--Rogan


> Any thoughts?
>
> Matt
>
> On 19 Jul 2013, at 23:35, Rogan Creswick <creswick at gmail.com> wrote:
>
> On Fri, Jul 19, 2013 at 3:23 PM, Matt Ford <matt at dancingfrog.co.uk> wrote:
>
>> I started by putting brackets in
>>
>> ([1,2] >>= \n -> [3,4]) >>= \m -> return (n,m)
>>
>> This immediately fails when evaluated: I expect it's something to do
>> with the n value now not being seen by the final return.
>>
>
> You're bracketing from the wrong end, which your intuition about n's
> visibility hints at.  Try this as your first set of parens:
>
>  [1,2] >>= (\n -> [3,4] >>= \m -> return (n,m))
>
> --Rogan
>
>
>>
>> It seems to me that the return function is doing something more than
>> it's definition (return x = [x]).
>>
>> If ignore the error introduced by the brackets I have and continue to
>> simplify I get.
>>
>> [3,4,3,4] >>= \m -> return (n,m)
>>
>> Now this obviously won't work as there is no 'n' value.  So what's
>> happening here? Return seems to be doing way more work than lifting the
>> result to a list, how does Haskell know to do this?  Why's it not in the
>> function definition?  Are lists somehow a special case?
>>
>> Any pointers appreciated.
>>
>> Cheers,
>>
>> --
>> Matt
>>
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>>
>>
>
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