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Hi all,</div>
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I am hitting a case where termination checker is unhappy with two mutual functions on my induction-recursion definitions. I am still trying to nail down a smaller reproduction but at least I would like to have an understanding of how things work.</div>
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Essentially I have a PER model for dependently typed languages, where I define a PER U and another PER on U:</div>
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U A B : means A and B are two values related by U. That is A and B are two types.</div>
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Given (AB : U A B), El AB a b: means a and b are two values related by El AB, where El AB computes the PER generated by the type A (or equivalently B).</div>
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Now I shall move on to prove symmetry. I have</div>
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<span style="font-family: "Courier New", monospace;">​mutual</span></div>
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<span style="font-family: "Courier New", monospace;"> U-sym : U A B -> U B A</span></div>
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<span style="font-family: "Courier New", monospace;"> U-sym AB = ...</span></div>
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<span style="font-family: "Courier New", monospace;"> El-sym : (AB : U A B) <span>(BA : U B A)</span> -> El AB a b -> El BA b a</span></div>
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<span style="font-family: "Courier New", monospace;"> El-sym AB BA = ...</span></div>
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Now, U-sym proceeds by pattern matching on AB and El-sym proceeds by pattern matching on AB
<b>and</b> BA. In U-sym, I can call U-sym and El-sym on smaller structure. However, for some reason, in El-sym, I can only El-sym on smaller structure. Any call of U-sym on smaller structure in El-sym will (almost) cause a termination checking error*.<br>
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I cannot possibly figure out why calling U-sym in El-sym is forbidden. How exactly termination checking with induction-recursion definitions work in Agda? Could anyone give some insights about what could go wrong if U-sym can be called in El-sym, if Agda is
doing the right thing?<br>
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* almost means I have counterexample but I cannot summarize the pattern<br>
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<font size="3"><b>Thanks,</b></font></div>
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<font size="3"><b>Jason Hu</b></font></div>
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<font size="3"><b><a href="https://hustmphrrr.github.io/">https://hustmphrrr.github.io/</a></b></font><br>
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