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<p style="margin: 0px 0px 1.2em !important;">Welcome to the mailing list!</p>
<p style="margin: 0px 0px 1.2em !important;">My tactic, to a first approximation, when proving in Agda, is to avoid error messages, and not really read them when they come up. This seems to be the intended way of working.</p>
<p style="margin: 0px 0px 1.2em !important;">In this case, the solution avoiding errors would be to get to the point
<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;">
-≤-iff-< (≤-trans ? (-≤-iff'-< n<p))</code> and look at the type required for the hole compared to
<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;">
-≤-iff'-< m<n</code>. The goal has type <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;">
suc m ≤ suc n</code>, and the expression has type <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;">
suc m ≤ n</code>. At this point, you either prove/find a new lemma to get from what you have to what you need, or do what you did and start again from the top. In the latter case, you hopefully have a bit more intuition about the problem, allowing you to plan
more effectively. This is no different from writing a paper proof.</p>
<p style="margin: 0px 0px 1.2em !important;">For completeness of this reply, the error is saying that the red highlighted bit was meant to have the type
<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;">
m ≤ X</code> for fixed <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;">
m</code> and unknown <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;">
X</code>. But <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;">
-≤-iff'-<</code> applied to an argument synthesises a type <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;">
suc Y ≤ Z</code>, for unknowns <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;">
Y</code> and <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;">
Z</code>. In general, there is no open term <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;">
Y</code> such that <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;">
m = suc Y</code> (<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;">m</code>
could be <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;">
zero</code>), so unification fails and you get this error.</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 08/09/2019 01:32, mo jia wrote:</p>
<p style="margin: 0px 0px 1.2em !important;"></p>
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<p></p>
<blockquote type="cite" cite="mid:CAJ17HSeU_aFJnU04VP_0imZgmwXncpmST1f99euR62uR5XnXBQ@mail.gmail.com">
<div dir="ltr">Hi:<br>
<br>
I am following the <a href="https://plfa.github.io/" moz-do-not-send="true">https://plfa.github.io/</a> In this exercise.<br>
<br>
<-trans'' : ∀ {m n p : ℕ}<br>
→ m < n<br>
→ n < p<br>
-----<br>
→ m < p<br>
<-trans'' m<n n<p = -≤-iff-< (≤-trans (s≤s (-≤-iff'-< (m<n))) (-≤-iff'-< n<p))<br>
<br>
I got the error<br>
<br>
suc _m_357 != m of type ℕ<br>
when checking that the inferred type of an application<br>
suc _m_357 ≤ _n_358<br>
matches the expected type<br>
m ≤ _n_356<br>
<br>
<div><img src="cid:part2.A87A09A2.86A90A0B@strath.ac.uk" alt="agda_error.png" class="" width="490" height="93"><br>
</div>
<div>The error is is hard for me to figure out the real wrong place.</div>
<div><br>
</div>
<div>At the end. I find the right way:</div>
<div><br>
</div>
<div><-trans' m<n n<p = -≤-iff''-< (-≤-iff-< (≤-trans (s≤s (-≤-iff'-< (m<n))) (-≤-iff'-< n<p)))<br>
</div>
<div><br>
</div>
<div>So the right answer contain my first try </div>
<div>`(-≤-iff-< (≤-trans (s≤s (-≤-iff'-< (m<n))) (-≤-iff'-< n<p))`</div>
<div>When I try to fix the problem. I always want to change `s≤s (-≤-iff'-< (m<n))`</div>
<div>But it don't work.</div>
<div><br>
</div>
<div>So my question is how to understand the error message? Or is there some learning path before following the plfa book? (I suck almost 1 hour to find out the right way which need the -≤-iff''-< helper)</div>
<div><br>
</div>
<div><br>
</div>
<div>------------- The help functions ----------------</div>
<div>-≤-iff'-< : ∀ {m n : ℕ}<br>
→ m < n<br>
-------------<br>
→ suc m ≤ n<br>
-≤-iff'-< {zero} {suc n} s<n = s≤s z≤n -- 0 < suc n whcich suc 0 <= suc n <br>
-≤-iff'-< {suc m} {n} (s<s m<n) = s≤s (-≤-iff'-< m<n)<br>
<br>
-≤-iff''-< : ∀ {m n : ℕ}<br>
→ suc m < n<br>
-------------<br>
→ m < n<br>
-≤-iff''-< {zero} {suc n} m<n = z<s -- 0 < suc n whcich suc 0 <= suc n <br>
-≤-iff''-< {suc m} {n} (s<s m<n) = s<s (-≤-iff''-< m<n)</div>
<div>
<div>------------- The help functions ----------------</div>
</div>
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<pre class="moz-quote-pre" wrap="">_______________________________________________
Agda mailing list
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</pre>
</blockquote>
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