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<p class="MsoNormal"><span style="mso-fareast-language:EN-US">I don’t think there is a standard definition of strict equality in Agda.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-US">It is possible to have both weak and strict equality in Agda as described in our paper<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"-webkit-standard",serif;color:black"><a href="http://www.cs.nott.ac.uk/~psztxa/publ/csl16.pdf">Extending Homotopy Type Theory with Strict Equality</a></span><span style="font-family:"-webkit-standard",serif;color:black"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-US">At the last Agda meeting Jesper implemented some extension to the universe mechanism which allows us to have a universe of pretypes with strict equality and fibrant types with weak equality.
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-US">The syntax of equality in agda is a bit confusing. In writing I would use = for the usual weak equality type and \equiv for either judgemental or strict equality. However, in agda it is the other
way around, because traditionally = is used in definitions and it has the advantage of being an ASCII character.
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-US">Thorsten<o:p></o:p></span></p>
<p class="MsoNormal"><span style="mso-fareast-language:EN-US"><o:p> </o:p></span></p>
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<p class="MsoNormal" style="margin-left:36.0pt"><b><span style="font-size:12.0pt;color:black">From:
</span></b><span style="font-size:12.0pt;color:black">Agda <agda-bounces@lists.chalmers.se> on behalf of Herminie Pagel <herminie.pagel@gmail.com><br>
<b>Date: </b>Tuesday, 21 April 2020 at 08:04<br>
<b>To: </b>Agda mailing list <agda@lists.chalmers.se><br>
<b>Subject: </b>[Agda] Strict equality _</span><span style="font-size:12.0pt;font-family:"Cambria Math",serif;color:black">≣</span><span style="font-size:12.0pt;color:black">_ in agda<o:p></o:p></span></p>
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<p class="MsoNormal" style="margin-left:36.0pt"><o:p> </o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:0cm;margin-right:0cm;margin-bottom:12.0pt;margin-left:36.0pt">
Hi,<o:p></o:p></p>
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<p class="MsoNormal" style="margin-left:36.0pt">Is there a standard interpretation of the strict equality _<span style="font-family:"Cambria Math",serif">≣</span>_ (latex \===) in agda similar to the standard interpretation of _≡_ as the identity type former?<o:p></o:p></p>
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<p class="MsoNormal" style="margin-left:36.0pt"><o:p> </o:p></p>
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<p class="MsoNormal" style="margin-left:36.0pt">best,<o:p></o:p></p>
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<p class="MsoNormal" style="margin-left:36.0pt"><o:p> </o:p></p>
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<p class="MsoNormal" style="margin-left:36.0pt">-- h<o:p></o:p></p>
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