MonadPlus

[Andrew Coppin]

OK, so I feel I understand monads fine. I regularly use Maybe, [] and
IO, and I've even constructed a few monads of my own. But here's a
question: what is the purpose of the MonadPlus class?

Clearly it defines a binary operation over monadic values and an
identity element for that operation. But... what is this supposed to
*do*? (For example, (>>) has an almost identical signature to mplus. But
presumably they don't both do the same thing...) What functionallity is
this supposed to give you?

[In a somewhat unrelated question... I saw some code the other day that
used Either as if it were a monad. And yet, I don't see an instance
given in the standard libraries - even though there should be one. I can
see Functor (Either a), but not Monad (Either a) or even Monad (Either
String)...]

_______________________________________________
Haskell-Cafe mailing list
Haskell-Cafe@...
http://www.haskell.org/mailman/listinfo/haskell-cafe

[David Roundy-2]

On Fri, May 09, 2008 at 08:39:38PM +0100, Andrew Coppin wrote:
> OK, so I feel I understand monads fine. I regularly use Maybe, [] and
> IO, and I've even constructed a few monads of my own. But here's a
> question: what is the purpose of the MonadPlus class?
>
> Clearly it defines a binary operation over monadic values and an
> identity element for that operation. But... what is this supposed to
> *do*? (For example, (>>) has an almost identical signature to mplus. But
> presumably they don't both do the same thing...) What functionallity is
> this supposed to give you?

MonadPlus is a crude way of achieving the catching of exceptional cases,
and you should think of mplus as being equivalent to (catch . const).  The
trouble is that MonadPlus doesn't provide any mechanism for finding out
what went wrong, so I've only ever found it useful when using the Maybe
monad (which itself has no way of identifying what went wrong).

> [In a somewhat unrelated question... I saw some code the other day that
> used Either as if it were a monad. And yet, I don't see an instance
> given in the standard libraries - even though there should be one. I can
> see Functor (Either a), but not Monad (Either a) or even Monad (Either
> String)...]

I am pretty certain that there is a monad instance for Either, but also
don't know where it's defined.
--
David Roundy
Department of Physics
Oregon State University
_______________________________________________
Haskell-Cafe mailing list
Haskell-Cafe@...
http://www.haskell.org/mailman/listinfo/haskell-cafe

[Rich Neswold-2]

On Fri, May 9, 2008 at 2:39 PM, Andrew Coppin <andrewcoppin@...> wrote:

[In a somewhat unrelated question... I saw some code the other day that used Either as if it were a monad. And yet, I don't see an instance given in the standard libraries - even though there should be one. I can see Functor (Either a), but not Monad (Either a) or even Monad (Either String)...]

It's used in the Error Monad.
 

--
Rich

JID: rich@...
LOI: https://www.google.com/reader/shared/00900594587109808626
_______________________________________________
Haskell-Cafe mailing list
Haskell-Cafe@...
http://www.haskell.org/mailman/listinfo/haskell-cafe

[Bryan O'Sullivan]

Andrew Coppin wrote:
> But here's a
> question: what is the purpose of the MonadPlus class?

It gives you a way of working with monads as monoids.  Consider a Parsec
example:

metasyntactic = text "foo" `mplus` text "bar" `mplus` text "baz"

You'll get back whichever one matched, in left-to-right-order, or mzero
(a parse failure) if all of them fail.

        <b
_______________________________________________
Haskell-Cafe mailing list
Haskell-Cafe@...
http://www.haskell.org/mailman/listinfo/haskell-cafe

[Andrew Coppin]

Bryan O'Sullivan wrote:

> Andrew Coppin wrote:
>  
>> But here's a
>> question: what is the purpose of the MonadPlus class?
>>    
>
> It gives you a way of working with monads as monoids.  Consider a Parsec
> example:
>
> metasyntactic = text "foo" `mplus` text "bar" `mplus` text "baz"
>
> You'll get back whichever one matched, in left-to-right-order, or mzero
> (a parse failure) if all of them fail.
>  

...so it's a kind of choice operator? Run all actions until you get to
one that succeeds and return the result from that?

_______________________________________________
Haskell-Cafe mailing list
Haskell-Cafe@...
http://www.haskell.org/mailman/listinfo/haskell-cafe

[Derek Elkins]

On Fri, 2008-05-09 at 12:47 -0700, David Roundy wrote:

> On Fri, May 09, 2008 at 08:39:38PM +0100, Andrew Coppin wrote:
> > OK, so I feel I understand monads fine. I regularly use Maybe, [] and
> > IO, and I've even constructed a few monads of my own. But here's a
> > question: what is the purpose of the MonadPlus class?
> >
> > Clearly it defines a binary operation over monadic values and an
> > identity element for that operation. But... what is this supposed to
> > *do*? (For example, (>>) has an almost identical signature to mplus. But
> > presumably they don't both do the same thing...) What functionallity is
> > this supposed to give you?
>
> MonadPlus is a crude way of achieving the catching of exceptional cases,
> and you should think of mplus as being equivalent to (catch . const).  The
> trouble is that MonadPlus doesn't provide any mechanism for finding out
> what went wrong, so I've only ever found it useful when using the Maybe
> monad (which itself has no way of identifying what went wrong).

MonadPlus is a crude way of doing that, but that isn't the motivating
example of MonadPlus, indeed, that arguably shouldn't be a MonadPlus
instance.  Cale Gibbard suggests (perhaps not originally) splitting
MonadPlus into MonadPlus (and MonadZero) and MonadOrElse.  They'd have
essentially the same operations, but would be intended to satisfy
different laws.  Maybe, Either e, IO are better instances of MonadOrElse
while [], Parser, LogicT, other non-determinism, parser, or concurrency
monads would more appropriately be MonadPlus.

_______________________________________________
Haskell-Cafe mailing list
Haskell-Cafe@...
http://www.haskell.org/mailman/listinfo/haskell-cafe

[Brandon S. Allbery KF8NH]

On May 9, 2008, at 15:56 , Andrew Coppin wrote:

> Bryan O'Sullivan wrote:
>> Andrew Coppin wrote:
>>
>>> But here's a
>>> question: what is the purpose of the MonadPlus class?
>>>
>>
>> It gives you a way of working with monads as monoids.  Consider a  
>> Parsec
>> example:
>>
>> metasyntactic = text "foo" `mplus` text "bar" `mplus` text "baz"
>>
>> You'll get back whichever one matched, in left-to-right-order, or  
>> mzero
>> (a parse failure) if all of them fail.
>>
>
> ...so it's a kind of choice operator? Run all actions until you get  
> to one that succeeds and return the result from that?

In monadic guise that's how it's usually used, yes (since monoids  
like (+) are not generally all that useful as monads; (++) (list  
monad) and (.) (Monad ((-) r)) might be, though).

--
brandon s. allbery [solaris,freebsd,perl,pugs,haskell] allbery@...
system administrator [openafs,heimdal,too many hats] allbery@...
electrical and computer engineering, carnegie mellon university    KF8NH


_______________________________________________
Haskell-Cafe mailing list
Haskell-Cafe@...
http://www.haskell.org/mailman/listinfo/haskell-cafe

[Bryan O'Sullivan]

Andrew Coppin wrote:

> ...so it's a kind of choice operator? Run all actions until you get to
> one that succeeds and return the result from that?

In the context of Parsec, yes.  In the grander scheme of things, the
behaviour depends on whatever is appropriate for the particular monad
you're working in.

So, for example, mplus for lists is (++) and mzero is [], which is quite
a different set of behaviours from the Parsec case.  Usually, you can
rely on MonadPlus behaving like a monoid.  There are occasional
exceptions, which is a mite upsetting.

http://www.haskell.org/haskellwiki/MonadPlus

        <b
_______________________________________________
Haskell-Cafe mailing list
Haskell-Cafe@...
http://www.haskell.org/mailman/listinfo/haskell-cafe

[Derek Elkins]

On Fri, 2008-05-09 at 12:48 -0700, Bryan O'Sullivan wrote:
> Andrew Coppin wrote:
> > But here's a
> > question: what is the purpose of the MonadPlus class?
>
> It gives you a way of working with monads as monoids.

I find this description mostly useless.  Monads form monoids without
being MonadPlus.

instance Monad m => Monoid (m ()) where
    mempty = return ()
    mappend = (<<)

You can form monoids out of Kleisli arrows,

instance Monad m => Monoid (a -> m a) where
    mempty = return
    mappend = (<=<)

You could form monads into a monoid in another way,

instance (Monad m, Monoid a) => Monoid (m a)
    mempty = return mempty
    mappend = liftM2 mappend

So "It gives you a way of working with monads as monoids." is
significantly underspecified and doesn't actually say what MonadPlus
means, let alone what it is intended for.

A more interesting statement in that vein is:
It gives you a way of working with monads as (distributive) near-rigs.

This statement does actually encode some (all?) of the intended meaning
of MonadPlus, e.g. mzero is intended to be a zero of (>>) beyond simply
being a unit for mplus.

_______________________________________________
Haskell-Cafe mailing list
Haskell-Cafe@...
http://www.haskell.org/mailman/listinfo/haskell-cafe

[Nicolas Frisby]

It sounds like the semantics of the MonadPlus methods are
under-specified. I recall once writing a newtype wrapper to treat the
same non-determinism monad with different mplus semantics, akin to cut
versus backtracking.

I think of MonadPlus as a less expressive version of msplit, from

  Backtracking, Interleaving, and Terminating Monad Transformers
  The Functional Pearl paper by Oleg Kiselyov, Chung-chieh Shan,
Daniel P. Friedman and Amr Sabry. ICFP 2005.

Is that an over-simplification?

On Fri, May 9, 2008 at 3:12 PM, Bryan O'Sullivan <bos@...> wrote:

> Andrew Coppin wrote:
>
>> ...so it's a kind of choice operator? Run all actions until you get to
>> one that succeeds and return the result from that?
>
> In the context of Parsec, yes.  In the grander scheme of things, the
> behaviour depends on whatever is appropriate for the particular monad
> you're working in.
>
> So, for example, mplus for lists is (++) and mzero is [], which is quite
> a different set of behaviours from the Parsec case.  Usually, you can
> rely on MonadPlus behaving like a monoid.  There are occasional
> exceptions, which is a mite upsetting.
>
> http://www.haskell.org/haskellwiki/MonadPlus
>
>        <b
> _______________________________________________
> Haskell-Cafe mailing list
> Haskell-Cafe@...
> http://www.haskell.org/mailman/listinfo/haskell-cafe
>

_______________________________________________
Haskell-Cafe mailing list
Haskell-Cafe@...
http://www.haskell.org/mailman/listinfo/haskell-cafe

[Dan Piponi-2]

Andrew asked,

> ...so it's a kind of choice operator? Run all actions until you get to one
> that succeeds and return the result from that?

The eternal bit of trickiness for Haskell is that type classes group
often together things that people don't immediately see as similar -
monads probably being the best example. So it's probably best not to
immediately try to find an all-encompassing summary of MonadPlus like
"a kind of choice operator" but instead concentrate on the definition.
The key thing is the line

> mplus :: m a -> m a -> m a

You can combine two m a's together with a binary operation to get
another m a. Absolutely any binary operation (with an identity) that
fits the rather lax laws that come with MonadPlus will do. Depending
on context mplus might mean "either/or", or "and", or "this first, or
else that" or something entirely different that nobody here has
anticipated yet. For each monad m, just try to think about how you
might combine a pair of m a's and what might serve as an identity.
--
Dan
_______________________________________________
Haskell-Cafe mailing list
Haskell-Cafe@...
http://www.haskell.org/mailman/listinfo/haskell-cafe

[Miguel Mitrofanov]

On 10 May 2008, at 00:43, Dan Piponi wrote:

> Andrew asked,
>
>> ...so it's a kind of choice operator? Run all actions until you get  
>> to one
>> that succeeds and return the result from that?
>
> The eternal bit of trickiness for Haskell is that type classes group
> often together things that people don't immediately see as similar -
> monads probably being the best example.

Well, that's the whole point of mathematics, isn't it? Mathematics is  
just a way to name different things with one word (opposed to  
philosophy, which is a way to name the same thing with different words).
_______________________________________________
Haskell-Cafe mailing list
Haskell-Cafe@...
http://www.haskell.org/mailman/listinfo/haskell-cafe

[Dan Piponi-2]

Miguel said:

> Well, that's the whole point of mathematics, isn't it?

Abstraction is common to mathematics and computing. But in computing
the abstraction often follows lines that seem obvious. For example a
GUI library might have a Widget class and people can immediately
identify various regions of the screen with Widgets and know that when
they want a new kind of device in their GUI it's time to define a
widget. Although the Widget class may be technically defined by the
interface it exposes, in practice people just think "a gadget that can
appear on the screen". Even someone who has never programmed can
probably quickly guess what kinds of things correspond to instances of
the Widget class.

But mathematics is full of abstractions that aren't like this. Times
modulo 24 hours and the way a closed loop can travel around a knot
both form a group. The thing they have in common is that there's a
binary operation with identity and inverses. Sometimes it can be more
confusing to try to find a snappy English phrase that sums them up
without restating the definition. Many common Haskell type classes
lean towards the latter kind of abstraction.
--
Dan
_______________________________________________
Haskell-Cafe mailing list
Haskell-Cafe@...
http://www.haskell.org/mailman/listinfo/haskell-cafe