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      <p style="margin: 0px 0px 1.2em !important;">Hi Thorsten,</p>
      <p style="margin: 0px 0px 1.2em !important;">This looks bad! Have
        you tried checking the following code (with the second
        definition of <code style="font-size: 0.85em; font-family: Consolas, Inconsolata, Courier, monospace;margin: 0px 0.15em; padding: 0px 0.3em; white-space: pre-wrap; border: 1px solid rgb(234, 234, 234); background-color: rgb(248, 248, 248); border-radius: 3px; display: inline;">_*∞_</code>)?</p>
      <pre style="font-size: 0.85em; font-family: Consolas, Inconsolata, Courier, monospace;font-size: 1em; line-height: 1.2em;margin: 1.2em 0px;"><code style="font-size: 0.85em; font-family: Consolas, Inconsolata, Courier, monospace;margin: 0px 0.15em; padding: 0px 0.3em; white-space: pre-wrap; border: 1px solid rgb(234, 234, 234); background-color: rgb(248, 248, 248); border-radius: 3px; display: inline;white-space: pre; overflow: auto; border-radius: 3px; border: 1px solid rgb(204, 204, 204); padding: 0.5em 0.7em; display: block !important;">inf∞ : ℕ∞
prd∞ inf∞ = just inf∞

test : Is-nothing (prd∞ (inf∞ *∞ zero∞))
test = nothing
</code></pre>
      <p style="margin: 0px 0px 1.2em !important;">The bug is not that
        the first definition is rejected; it’s that the second
        definition is accepted. I can’t really say why it’s accepted,
        though.</p>
      <p style="margin: 0px 0px 1.2em !important;">Conat multiplication
        needs some other trick to make it productive. In the test case,
        <code style="font-size: 0.85em; font-family: Consolas, Inconsolata, Courier, monospace;margin: 0px 0.15em; padding: 0px 0.3em; white-space: pre-wrap; border: 1px solid rgb(234, 234, 234); background-color: rgb(248, 248, 248); border-radius: 3px; display: inline;">n</code>
        is added to itself infinitely many times. If it’s a successor,
        that’s okay because the consumer just gets infinitely many
        successors. But if it’s 0, the consumer has to wait (forever) as
        to whether the result is a zero or a successor.</p>
      <p style="margin: 0px 0px 1.2em !important;">Regards,</p>
      <p style="margin: 0px 0px 1.2em !important;">James</p>
      <p style="margin: 0px 0px 1.2em !important;">On 03/03/2019 12:16,
        Thorsten Altenkirch wrote:</p>
      <p style="margin: 0px 0px 1.2em !important;"></p>
      <div class="markdown-here-exclude">
        <p></p>
        <blockquote type="cite"
          cite="mid:2067A3E1-C1AA-41FD-B00A-7731BA3B4E49@nottingham.ac.uk">
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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>
          </div>
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where permitted by law.



</pre>
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