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<p class="MsoNormal"><span style="font-size:11.0pt">Hi,<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">I just set the exercise to define multiplication for conats for my course on type theory. So please don’t blurt put the solution – see the attached code. The following is not a solution because agda doesn’t
see that the definition is productive (even though it is):<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">prd∞ (m *∞ n) with prd∞ m <o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">prd∞ (m *∞ n) | (just pm) = prd∞ (n +∞ (pm *∞ n))<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">prd∞ (m *∞ n) | nothing = nothing<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">but after the following change<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">prd∞ (m *∞ n) with prd∞ m
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">prd∞ (m *∞ n) | (just pm) with (pm *∞ n)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">prd∞ (m *∞ n) | (just pm) | x = prd∞ (n +∞ x)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">prd∞ (m *∞ n) | nothing = nothing<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">agda seems to accept is. Actually even if +∞ is not contractive.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">Is this a known bug? Otherwise can somebody remind e how to report this?<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">Cheers,<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">Thorsten<o:p></o:p></span></p>
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