<html><head>
<meta http-equiv="Content-Type" content="text/html; charset=Windows-1252"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; color: rgb(0, 0, 0); font-size: 14px; font-family: Calibri, sans-serif;"><div>I am looking for specific examples.</div><div><br></div><div>T.</div><div><br></div><span id="OLK_SRC_BODY_SECTION"><div style="font-family:Calibri; font-size:11pt; text-align:left; color:black; BORDER-BOTTOM: medium none; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 0in; PADDING-RIGHT: 0in; BORDER-TOP: #b5c4df 1pt solid; BORDER-RIGHT: medium none; PADDING-TOP: 3pt"><span style="font-weight:bold">From: </span> Dmytro Starosud <<a href="mailto:d.starosud@gmail.com">d.starosud@gmail.com</a>><br><span style="font-weight:bold">Date: </span> Tuesday, 1 July 2014 17:23<br><span style="font-weight:bold">To: </span> Thorsten Altenkirch <<a href="mailto:psztxa@exmail.nottingham.ac.uk">psztxa@exmail.nottingham.ac.uk</a>><br><span style="font-weight:bold">Cc: </span> Sergei Meshveliani <<a href="mailto:mechvel@botik.ru">mechvel@botik.ru</a>>, Agda mailing list <<a href="mailto:agda@lists.chalmers.se">agda@lists.chalmers.se</a>><br><span style="font-weight:bold">Subject: </span> Re: [Agda] termination by contradiction<br></div><div><br></div><div dir="ltr"><div><div>> What would be a good application of MP in programming?<br></div><div></div>It will extend the set of positively type-checked programs.<br></div>i.e. will decrease amount of first order errors, which in general is very good.<br></div><div class="gmail_extra"><br><br><div class="gmail_quote">2014-07-01 18:19 GMT+03:00 Altenkirch Thorsten <span dir="ltr"><<a href="mailto:psztxa@exmail.nottingham.ac.uk" target="_blank">psztxa@exmail.nottingham.ac.uk</a>></span>:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word;color:rgb(0,0,0);font-size:14px;font-family:Calibri,sans-serif"><div>Yes, this is true.</div><div><br></div><div>However, it is not clear how to do symbolic evaluation with MP. That is if we have a hypothetical classical proof of termination this doesn’t tell us wether we can partially execute our program.</div><div>In the case of a constructive proof this is the case.</div><div><br></div><div>We could say that we can run the program if the proof is closed but this seems a bit weird.</div><div><br></div><div>What would be a good application of MP in programming?</div><div><br></div><div>Cheers,</div><div>Thorsten</div><div><br></div><div><br></div><span><div style="font-family:Calibri;font-size:11pt;text-align:left;color:black;BORDER-BOTTOM:medium none;BORDER-LEFT:medium none;PADDING-BOTTOM:0in;PADDING-LEFT:0in;PADDING-RIGHT:0in;BORDER-TOP:#b5c4df 1pt solid;BORDER-RIGHT:medium none;PADDING-TOP:3pt"><span style="font-weight:bold">From: </span> Dmytro Starosud <<a href="mailto:d.starosud@gmail.com" target="_blank">d.starosud@gmail.com</a>><br><span style="font-weight:bold">Date: </span> Tue, 1 Jul 2014 15:19:34 +0100<br><span style="font-weight:bold">To: </span> Sergei Meshveliani <<a href="mailto:mechvel@botik.ru" target="_blank">mechvel@botik.ru</a>><br><span style="font-weight:bold">Cc: </span> Agda mailing list <<a href="mailto:agda@lists.chalmers.se" target="_blank">agda@lists.chalmers.se</a>><br><span style="font-weight:bold">Subject: </span> Re: [Agda] termination by contradiction<br></div><div><div class="h5"><div><br></div><div dir="ltr"><div><div>Markov axiom (for Nat) doesn't leed to a total excluded third.<br>
Constructive logic together with Markov axiom (for Nat) is still constructive.<br></div>Here is really nice <a href="http://scs.hosted.panopto.com/Panopto/Pages/Sessions/List.aspx#folderID=%2207756bb0-b872-4a4a-95b1-b77ad206dab3%22" target="_blank">course</a> (and <a href="http://homotopytypetheory.org/book/" target="_blank">book</a>) explaining in very deep details all that stuff with constructive vs classic vs whatever.<br><br></div>Dmytro <br></div></div></div></span><br><p>This message and any attachment are intended solely for the addressee and may contain confidential information. If you have received this message in error, please send it back to me, and immediately delete it. Please do not use, copy or disclose the information contained in this message or in any attachment. Any views or opinions expressed by the author of this email do not necessarily reflect the views of the University of Nottingham.</p><p>This message has been checked for viruses but the contents of an attachment may still contain software viruses which could damage your computer system, you are advised to perform your own checks. Email communications with the University of Nottingham may be monitored as permitted by UK legislation.</p><br></div></blockquote></div><br></div></span>
<br><p>This message and any attachment are intended solely for the addressee and may contain confidential information. If you have received this message in error, please send it back to me, and immediately delete it. Please do not use, copy or disclose the information contained in this message or in any attachment. Any views or opinions expressed by the author of this email do not necessarily reflect the views of the University of Nottingham.</p><p>This message has been checked for viruses but the contents of an attachment may still contain software viruses which could damage your computer system, you are advised to perform your own checks. Email communications with the University of Nottingham may be monitored as permitted by UK legislation.</p>
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