<div dir="ltr">We have a discussion on pattern matching without K in the book:<br><div><div><br><a href="http://books.google.nl/books?id=LkDUKMv3yp0C&pg=PA163">http://books.google.nl/books?id=LkDUKMv3yp0C&pg=PA163</a><br>
</div></div></div><div class="gmail_extra"><br><br><div class="gmail_quote">On Sun, Dec 1, 2013 at 9:58 PM, Martin Escardo <span dir="ltr"><<a href="mailto:m.escardo@cs.bham.ac.uk" target="_blank">m.escardo@cs.bham.ac.uk</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><br>
<br>
On 29/11/13 19:01, Altenkirch Thorsten wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
Shouldn't the semantics simply be that you can only prove things you can<br>
prove using only J but not K?<br>
</blockquote>
<br>
I like this specification. But is it complete?<br>
<br>
Let me propose a possible elaboration of this specification.<br>
<br>
In MLTT, you don't have pattern matching: everything has to be defined<br>
in terms of predefined combinators, which include J but not K.<br>
<br>
We can imagine pattern matching as syntax sugar for definitions with<br>
combinators.<br>
<br>
So an ideal Agda compiler would translate Agda into MLTT combinators<br>
(perhaps for MLTT with various extensions for inductive definitions).<br>
<br>
In this case, the correctness criterion is simply that Streicher's<br>
combinator K is not needed for this (ideal) translation.<br>
<br>
Actually, it would be very good if Agda did work like the idealized<br>
Agda discussed above, by compilation to combinators. This would allow<br>
for proof terms that can be exported to other proof assistants, for<br>
instance, e.g. for checking that an Agda proof is a proof, without<br>
having to rely on Agda to be sure.<br>
<br>
Best,<br>
Martin<br>
<br>
<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<br>
Thorsten<br>
<br>
On 29/11/2013 17:36, "Andreas Abel" <<a href="mailto:andreas.abel@ifi.lmu.de" target="_blank">andreas.abel@ifi.lmu.de</a>> wrote:<br>
<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
On 29.11.2013 18:11, Harley D. Eades III wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
On Nov 29, 2013, at 5:00 AM, Nils Anders Danielsson <<a href="mailto:nad@cse.gu.se" target="_blank">nad@cse.gu.se</a>><br>
wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
On 2013-11-28 23:34, Andreas Abel wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
Yes, some of the fail test cases seem only to be there to document<br>
what *is* rejected. I do not know what purpose this serves, since I<br>
would expect only stuff there that *must be* rejected.<br>
</blockquote>
<br>
The point is that the semantics of --without-K should not be changed by<br>
accident. These examples "must" be rejected until we make a conscious<br>
decision to change the semantics.<br>
</blockquote>
<br>
Where is the semantics of --without-K formally written down?<br>
</blockquote>
<br>
There is not much written. The documentation of the --without-K<br>
variants is in the respective release notes.<br>
<br>
Cheers,<br>
Andreas<br>
<br>
<br>
--<br>
Andreas Abel <>< Du bist der geliebte Mensch.<br>
<br>
Theoretical Computer Science, University of Munich<br>
Oettingenstr. 67, D-80538 Munich, GERMANY<br>
<br>
<a href="mailto:andreas.abel@ifi.lmu.de" target="_blank">andreas.abel@ifi.lmu.de</a><br>
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