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<p style="margin-top:0;margin-bottom:0">I am wondering if there is any implementation of dependent type theory performs normalization before termination checking?</p>
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<p style="margin-top:0;margin-bottom:0">It sounds theoretical doable, but somehow termination checking is commonly syntactical, like agda and coq. However, those who care about compilation performance might not be too happy about it.<br>
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<p style="margin-top:0;margin-bottom:0">I am wondering if there is an example makes normalization here looks non-trivial?<br>
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<div><font style="font-size:12pt" size="3"><span style="color:rgb(69,129,142)"><span style="font-family:trebuchet ms,sans-serif"><b>Sincerely Yours,<br>
</b></span></span></font></div>
<font style="font-size:12pt" size="3"><span style="color:rgb(69,129,142)"><span style="font-family:trebuchet ms,sans-serif"><b><br>
Jason Hu<a target="_blank" id="LPNoLP"></a></b></span></span></font> </div>
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<div id="divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" style="font-size:11pt" color="#000000"><b>From:</b> Agda <agda-bounces@lists.chalmers.se> on behalf of Serge Leblanc <33dbqnxpy7if@gmail.com><br>
<b>Sent:</b> July 30, 2018 9:02:29 PM<br>
<b>To:</b> agda@lists.chalmers.se<br>
<b>Subject:</b> Re: [Agda] Checking termination is not sufficiently exploratory.</font>
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<div style="background-color:#FFFFFF"><span id="x_result_box" class="" lang="en"><span class="">In my opinion, a normal form verification phase could be added without changing the termination checking algorithm.</span></span><span id="x_result_box" class="" lang="en"><span class=""></span></span><br>
<span id="x_result_box" class="" lang="en"><span class=""></span></span><span id="x_result_box" class="" lang="en"><span class="">Laŭ mi, normala kontrola fazo povus esti aldonita sen ŝangi la finiĝan kontrolan algoritmon.
</span></span><br>
<span id="x_result_box" class="" lang="en"><span class=""></span></span>
<p><span id="x_result_box" class="" lang="en"><span class="">Sincere<br>
</span></span></p>
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<div class="x_moz-cite-prefix">On 2018-07-30 20:06, a.j.rouvoet wrote:<br>
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<p>I believe that you are right that the two snippets are equivalent, but it requires some computation to show that this is the case.<br>
The check that Agda runs on the other hand is very syntactic. This is indeed a limitation, but at least it ensures that checking for termination terminates ;-)<br>
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<div class="x_moz-cite-prefix">On 07/30/2018 06:04 PM, Serge Leblanc wrote:<br>
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<blockquote type="cite">Yes, but you translat the code <font color="#3333ff">(toCostring ">>") ++ coSplit "(♭ xs)</font> to its normal form, it equals to
<font color="#3333ff">'>' ∷ ♯ ('>' ∷ ♯ coSplit '(♭ xs))</font>. Right?<br>
So, the recursive call is well protected by a constructor.<br>
<br>
Jes, sed vi plenumas la kodon (toCostring ">>") ++ coSplit″ (♭ xs) ĝis sia normala formo, ĝi egalas al '>' ∷ ♯ ('>' ∷ ♯ coSplit′ (♭ xs)). Ĉu ne ?<br>
Do, la memsinkceva alvoko estas bone ŝirmi per konstruisto.<br>
<br>
<div class="x_moz-cite-prefix">On 2018-07-30 16:59, a.j.rouvoet wrote:<br>
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<p>For coSplit to pass the checker, the recursive invocation must appear guarded by a constructor.<br>
This is clearly the case in coSplit', but not necessarily in coSplit'' (e.g. when toString ">>" returns the empty costring).<br>
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<div class="x_moz-cite-prefix">On 07/30/2018 04:55 PM, Serge Leblanc wrote:<br>
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<blockquote type="cite"><span id="x_result_box" class="" lang="en"><span class="">Dear all,<br>
Why the checking termination rejects the coSplit" function although the coSplit' function is accepted ?</span></span><br>
<span id="x_result_box" class="" lang="en"><span class=""><span id="x_result_box" class="x_short_text" lang="en"><span class=""><span id="x_result_box" class="" lang="en"><span class="">Why the checking termination so suspicious?</span></span><br>
</span></span>Sincerely<br>
</span></span><br>
Estimataj ĉiuj,<br>
Kial la finiĝa kontrolo malakceptas la funkcion coSplit″ kvankam la funkcio coSplit′ trafas ?<br>
Kial la finiĝa kontrolo estas tiel malakceptanda ?<br>
Sincere<br>
<br>
<font color="#3333ff"> coSplit′ : Costring → Costring<br>
coSplit′ [] = []<br>
coSplit′ (x ∷ xs) with x ≐ '!'<br>
... | false = x ∷ ♯ coSplit′ (♭ xs)<br>
... | true = '>' ∷ ♯ ('>' ∷ ♯ coSplit′ (♭ xs))<br>
<br>
coSplit″ : Costring → Costring<br>
coSplit″ [] = []<br>
coSplit″ (x ∷ xs) with x ≐ '!'<br>
... | false = x ∷ ♯ coSplit″ (♭ xs)<br>
... | true = (toCostring ">>") ++ coSplit″ (♭ xs)<br>
<br>
main = run $ ♯ getContents >>= λ s → ♯ (putStrLn∞ ∘ coSplit′) s<br>
<span id="x_result_box" class="" lang="en"><span class=""></span></span></font>
<div class="x_moz-signature"><font color="#3333ff"><br>
</font>-- <br>
Serge Leblanc
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gpg --search-keys 0x67B17A3F <br>
Fingerprint = 2B2D AC93 8620 43D3 D2C2 C2D3 B67C F631 67B1 7A3F</div>
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