name for monad-like structure?

Michael Vanier

28 Apr 2009 28 Apr '09

6:54 p.m.

I've stumbled upon a structure that is like a weaker version of a monad, one that supports return and >> but not >>=. Has anyone seen this before, and if so, does it have a standard name? Mike

Show replies by date

Tony Morris

28 Apr 28 Apr

6:58 p.m.

Michael Vanier wrote:

...

I've stumbled upon a structure that is like a weaker version of a monad, one that supports return and >> but not >>=. Has anyone seen this before, and if so, does it have a standard name?

Mike

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

Are you sure it supports (>>) :: m a -> m b -> m b and not mplus :: m a -> m a -> m a ? -- Tony Morris http://tmorris.net/

Michael Vanier

7:33 p.m.

Tony Morris wrote:

...

Michael Vanier wrote:

...
I've stumbled upon a structure that is like a weaker version of a monad, one that supports return and >> but not >>=. Has anyone seen this before, and if so, does it have a standard name?

Mike

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

Are you sure it supports (>>) :: m a -> m b -> m b

and not mplus :: m a -> m a -> m a ?

Yeah, you're right. It's basically a monad where the type a is fixed to be (), so you just have (>>) :: m () -> m () -> m () Mike

Luke Palmer

7:42 p.m.

On Tue, Apr 28, 2009 at 5:33 PM, Michael Vanier wrote:

...

Tony Morris wrote:

Michael Vanier wrote:

I've stumbled upon a structure that is like a weaker version of a monad, one that supports return and >> but not >>=. Has anyone seen this before, and if so, does it have a standard name?

Mike

_______________________________________________ Haskell-Cafe mailing listHaskell-Cafe@haskell.orghttp://www.haskell.org/mailman/listinfo/haskell-cafe

Are you sure it supports (>>) :: m a -> m b -> m b

and not mplus :: m a -> m a -> m a ?

Yeah, you're right. It's basically a monad where the type a is fixed to be (), so you just have

(>>) :: m () -> m () -> m ()

That's a monoid. Luke

Michael Vanier

7:56 p.m.

Luke Palmer wrote:

...

On Tue, Apr 28, 2009 at 5:33 PM, Michael Vanier mailto:mvanier42@gmail.com> wrote:

Tony Morris wrote:

...
Michael Vanier wrote:

...
I've stumbled upon a structure that is like a weaker version of a monad, one that supports return and >> but not >>=. Has anyone seen this before, and if so, does it have a standard name?

Mike

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

Are you sure it supports (>>) :: m a -> m b -> m b

and not mplus :: m a -> m a -> m a ?

Yeah, you're right. It's basically a monad where the type a is fixed to be (), so you just have

(>>) :: m () -> m () -> m ()

That's a monoid.

Luke

Got it. Thanks. Mike

wren ng thornton

8:08 p.m.

Michael Vanier wrote:

...

Luke Palmer wrote:

...
Michael Vanier wrote:

...
Are you sure it supports (>>) :: m a -> m b -> m b

and not mplus :: m a -> m a -> m a ?

Yeah, you're right. It's basically a monad where the type a is fixed to be (), so you just have

(>>) :: m () -> m () -> m ()

That's a monoid.

Got it. Thanks.

If the return is important ---and the structure can be parameterized by non-() types, and the binop is actually mplus not (>>)--- then it may also be a monoid generated from a semigroup. This is the case when there's an (M a) which can't be generated by return and which serves as the identity for the binop. Prime examples are monoids similar to Maybe which are generated by Nothing, return, and any semigroup on the underlying set. -- Live well, ~wren

Dan Weston

7:34 p.m.

I suspect your structure doesn't exist. A Kleisli algebra (a -> m b) has a full subalgebra (() -> m ()), but (() -> m b) is not an algebra (it is not closed). I'm guessing that the largest proper subset of (a -> m b) is just (() -> m ()). Dan Tony Morris wrote:

...

Michael Vanier wrote:

...
I've stumbled upon a structure that is like a weaker version of a monad, one that supports return and >> but not >>=. Has anyone seen this before, and if so, does it have a standard name?

Mike

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

Are you sure it supports (>>) :: m a -> m b -> m b

and not mplus :: m a -> m a -> m a ?

Bryan O'Sullivan

7:11 p.m.

On Tue, Apr 28, 2009 at 3:54 PM, Michael Vanier wrote:

...

I've stumbled upon a structure that is like a weaker version of a monad, one that supports return and >> but not >>=. Has anyone seen this before, and if so, does it have a standard name?

That's similar to Applicative, which supports fmap (via Functor), return (named pure) and ap (named <*>), and hence >> (named *>).

Luke Palmer

7:19 p.m.

On Tue, Apr 28, 2009 at 4:54 PM, Michael Vanier wrote:

...

I've stumbled upon a structure that is like a weaker version of a monad, one that supports return and >> but not >>=. Has anyone seen this before, and if so, does it have a standard name?

That is a strange structure. The type parameter is hardly doing anything: whenever you compose two of them together, you have no choice but to ignore the left one. Let's call your structure S. It's likely that S a is isomorphic to a pair (m, a), where m is some monoid. I would see if you can restate your problem in terms of a monoid. Luke

5867

Age (days ago)

5868

Last active (days ago)

List overview

Download

8 comments

6 participants

participants (6)

Bryan O'Sullivan
Dan Weston
Luke Palmer
Michael Vanier
Tony Morris
wren ng thornton