The list type constructor ([] :: * -> *) is a functor, and if you add the implementations of join/return (or just return and bind) those together make the monad. The value-level list [3,5,8] is just a list :)<br><br><div class="gmail_quote">
On Wed, Jan 27, 2010 at 1:30 PM, Andrew Coppin <span dir="ltr"><<a href="mailto:andrewcoppin@btinternet.com">andrewcoppin@btinternet.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
Here's one for you to ponder.<br>
<br>
7 is a number. 7 is an integer, and integers are numbers.<br>
<br>
7 is not a field. 7 is an element of [at least one] field, but 7 itself is not a field.<br>
<br>
7 is not a group. 7 is a member of the set of integers, but the set of integers is not a group either. The set of integers form a group when taken together with the addition operator. (And, actually, forms another, different, group when taken with the multiplication operator.)<br>
<br>
Now, here's the question: Is is correct to say that [3, 5, 8] is a monad? Is it correct to say that lists are a monad? Or would it be more correct to say that lists "form" a monad?<br>
<br>
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