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<p class="MsoNormal">Exactly. It is not a cost but it means that a certain definitional equality doesn’t hold which makes it harder to check your programs. I would be much more flexible with “judgemental equality” anyway, maybe following the lines of Andromeda.
The user should be able to define her own eqaulity as long as it is sound (ie.e it has to produce a proof of equality).<o:p></o:p></p>
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<p class="MsoNormal"><b><span style="font-size:12.0pt;color:black">From: </span></b><span style="font-size:12.0pt;color:black">Jesper Cockx <Jesper@sikanda.be><br>
<b>Date: </b>Wednesday, 1 May 2019 at 16:22<br>
<b>To: </b>Thorsten Altenkirch <psztxa@exmail.nottingham.ac.uk><br>
<b>Cc: </b>Jon Sterling <jon@jonmsterling.com>, "agda@lists.chalmers.se" <agda@lists.chalmers.se><br>
<b>Subject: </b>Re: [Agda] Pattern matching on irrelevant types with only one constructor?<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-family:"-webkit-standard",serif;color:black">@Thorsten: But we *can* reduce the term when we give it the actual termination proof, the point here is only that the termination proof is not irrelevant for checking conversion.
When compiling the code to Haskell, Agda even detects that Acc does not contain any interesting information and erases the termination proofs, so there's no run-time cost, only a compile-time one.<o:p></o:p></span></p>
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