<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;">Hi,</div><div id="bloop_customfont" style="font-family:Helvetica,Arial;font-size:13px; color: rgba(0,0,0,1.0); margin: 0px; line-height: auto;"><br></div><div id="bloop_customfont" 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 id="bloop_customfont" style="font-family:Helvetica,Arial;font-size:13px; color: rgba(0,0,0,1.0); margin: 0px; line-height: auto;"><br></div><div id="bloop_customfont" 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 id="bloop_customfont" style="font-family:Helvetica,Arial;font-size:13px; color: rgba(0,0,0,1.0); margin: 0px; line-height: auto;"><br></div><div id="bloop_customfont" 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 id="bloop_customfont" 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 id="bloop_customfont" 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 id="bloop_customfont" style="font-family:Helvetica,Arial;font-size:13px; color: rgba(0,0,0,1.0); margin: 0px; line-height: auto;"><br></div><div id="bloop_customfont" 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 id="bloop_customfont" 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 id="bloop_customfont" 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 id="bloop_sign_1465710578162078976" class="bloop_sign"><div style="font-family:helvetica,arial;font-size:13px">-- <br>Csongor<br></div></div><p class="airmail_on">On 12 June 2016 at 06:47:13, Christopher Howard (<a href="mailto:ch.howard@zoho.com">ch.howard@zoho.com</a>) wrote:</p> <blockquote type="cite" class="clean_bq"><span><div><div></div><div>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>
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