<html><head><style>body{font-family:Helvetica,Arial;font-size:13px}</style></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;"><div id="bloop_customfont" style="font-family:Helvetica,Arial;font-size:13px; color: rgba(0,0,0,1.0); margin: 0px; line-height: auto;"><div id="bloop_customfont" style="margin: 0px;">Yes, my bad, thanks for pointing it out.</div><br><div id="bloop_sign_1465712486385425920" class="bloop_sign"><div style="font-family: helvetica, arial;">-- <br>Csongor</div></div></div> <br><p class="airmail_on">On 12 June 2016 at 07:19:37, Theodore Lief Gannon (<a href="mailto:tanuki@gmail.com">tanuki@gmail.com</a>) wrote:</p> <blockquote type="cite" class="clean_bq"><span><div><div></div><div>
<title></title>
<p dir="ltr">Nitpick: (&) is flipped function application ($),
not composition (.) -- though the signature you gave was
correct.</p>
<div class="gmail_quote">On Jun 11, 2016 11:07 PM, "Csongor Kiss"
<<a href="mailto:kiss.csongor.kiss@gmail.com">kiss.csongor.kiss@gmail.com</a>>
wrote:<br type="attribution">
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div style="word-wrap:break-word">
<div style="font-family:Helvetica,Arial;font-size:13px;color:rgba(0,0,0,1.0);margin:0px;line-height:auto">
Hi,</div>
<div style="font-family:Helvetica,Arial;font-size:13px;color:rgba(0,0,0,1.0);margin:0px;line-height:auto">
<br></div>
<div style="font-family:Helvetica,Arial;font-size:13px;color:rgba(0,0,0,1.0);margin:0px;line-height:auto">
(>>=) :: Monad m => m a -> (a -> m b) -> m b, and
if I understand correctly, what you need is a ‘generic’ version,
that works without the returns?</div>
<div style="font-family:Helvetica,Arial;font-size:13px;color:rgba(0,0,0,1.0);margin:0px;line-height:auto">
<br></div>
<div style="font-family:Helvetica,Arial;font-size:13px;color:rgba(0,0,0,1.0);margin:0px;line-height:auto">
'return :: a -> m a' for some monad m. This m comes from the
monad instance you use, but if we want a generic one, it’s only
possible by fixing a specific m. The obvious choice is to use the
Identity monad and have a specialised (>>=‘) :: Identity a
-> (a -> Identity b) -> Identity b.</div>
<div style="font-family:Helvetica,Arial;font-size:13px;color:rgba(0,0,0,1.0);margin:0px;line-height:auto">
<br></div>
<div style="font-family:Helvetica,Arial;font-size:13px;color:rgba(0,0,0,1.0);margin:0px;line-height:auto">
For all `a`, `Identity a` is isomorphic to `a`, so with a bit of
cheating, you could rewrite the above to (>>=‘’) :: a ->
(a -> b) -> b,</div>
<div style="font-family:Helvetica,Arial;font-size:13px;color:rgba(0,0,0,1.0);margin:0px;line-height:auto">
which starts to look really familiar, in fact, it’s just the
function composition (.) with its arguments flipped, and is
actually defined</div>
<div style="font-family:Helvetica,Arial;font-size:13px;color:rgba(0,0,0,1.0);margin:0px;line-height:auto">
as (&) in Data.Function.</div>
<div style="font-family:Helvetica,Arial;font-size:13px;color:rgba(0,0,0,1.0);margin:0px;line-height:auto">
<br></div>
<div style="font-family:Helvetica,Arial;font-size:13px;color:rgba(0,0,0,1.0);margin:0px;line-height:auto">
<span style="font-family:'helvetica Neue',helvetica">g' = 2 &
\n -> (n + 1) & \n -> (n + 3)</span></div>
<div style="font-family:Helvetica,Arial;font-size:13px;color:rgba(0,0,0,1.0);margin:0px;line-height:auto">
<span style="font-family:'helvetica Neue',helvetica"><br></span></div>
<div style="font-family:Helvetica,Arial;font-size:13px;color:rgba(0,0,0,1.0);margin:0px;line-height:auto">
<span style="font-family:'helvetica Neue',helvetica">This was
obviously a really roundabout way of arriving at the result, but I
think the analogy with function composition is really nice, as we
can think of (a -> b) as a special case of (a -> m b), the
so-called Kleisli arrow. What monads do is they compose these
Kleisli arrows.</span></div>
<br>
<div>
<div style="font-family:helvetica,arial;font-size:13px">
-- <br>
Csongor<br></div>
</div>
<p>On 12 June 2016 at 06:47:13, Christopher Howard (<a href="mailto:ch.howard@zoho.com" target="_blank">ch.howard@zoho.com</a>)
wrote:</p>
<blockquote type="cite">
<div>
<div><span>Hi, I am learning about monads, and this question came
to mind: is there<br>
a way to have a sequence of functions left to right like so:<br>
<br>
g = return 2 >>= \n -> return (n + 1) >>= \n ->
return (n + 3)<br>
<br>
Either: some kind of generic monad that makes this legal, or some
way to<br>
do this without monad (i.e., without the "returns").<br>
<br>
--<br>
<a href="http://justonemoremathproblem.com" target="_blank">http://justonemoremathproblem.com</a><br>
To protect my privacy, please use PGP encryption. It's free and
easy<br>
to use! My public key ID is 0x340EA95A (<a href="http://pgp.mit.edu" target="_blank">pgp.mit.edu</a>).<br>
<br>
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