On Sat, Jan 30, 2010 at 1:24 AM, Conal Elliott <span dir="ltr"><<a href="mailto:conal@conal.net">conal@conal.net</a>></span> wrote:<br><div class="gmail_quote"><blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;">
I call it "an m" or (more specifically) "an Int m" or "a list of Int". For instance, "a list" or "an Int list" or "a list of Int". - Conal<div><div></div><div class="h5">
<br><br><div class="gmail_quote">
On Wed, Jan 27, 2010 at 12:14 PM, Luke Palmer <span dir="ltr"><<a href="mailto:lrpalmer@gmail.com" target="_blank">lrpalmer@gmail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;">
<div>On Wed, Jan 27, 2010 at 11:39 AM, Jochem Berndsen <<a href="mailto:jochem@functor.nl" target="_blank">jochem@functor.nl</a>> wrote:<br>
>> Now, here's the question: Is is correct to say that [3, 5, 8] is a<br>
>> monad?<br>
><br>
> In what sense would this be a monad? I don't quite get your question.<br>
<br>
</div>I think the question is this: if m is a monad, then what do you call<br>
a thing of type m Int, or m Whatever.<br>
<font color="#888888"><br>
Luke<br>
</font><div><div></div><div></div></div></blockquote></div></div></div></blockquote><div><br></div></div>Conal's is the most sensible approach - "what do you call it" amounts to "what sort of a thing is it", and the best we can say in that respect is "er, its a thing of type m Whatever". (My preference, if maximal explicitness is needed, is to say "it's a token of its type"; some say "term of type m Whatever".) Trying to classify such a thing as "value", "object", "computation", "reduction" etc. inevitably (and necessarily) leads to tail-chasing since those notions are all essentially equivalent. Plus they miss the essential point, which is the typing.<br>
<br>Original poster would probably find Martin-Lof's philosophically-tinged writings very good on this - clear, reasonably simple, and revelatory, if you've never closely looked at intuitionistic logic before. <a href="http://www.jstor.org/pss/20116466">Truth of a proposition, evidence of a judgment, validity of a proof</a> is especially readable, as is <a href="http://www.hf.uio.no/ifikk/filosofi/njpl/vol1no1/meaning/meaning.html">On the meanings of the Logical Constants and the Justifications of the Logical Laws</a>. Presents a completely new (to me) way of thinking about "what is it, really?" questions about computation, monads, etc., i.e. ask not "what is it?" but "how do you know?" or even "how do you make it?" The Stanford article on <a href="http://plato.stanford.edu/entries/types-tokens/">types and tokens</a> is also very enlightening in this respect.<br>
<br>-g<br>