[Agda] Checking termination is not sufficiently exploratory.

[Jason -Zhong Sheng- Hu]

I am wondering if there is any implementation of dependent type theory performs normalization before termination checking?


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.


I am wondering if there is an example makes normalization here looks non-trivial?


Sincerely Yours,

Jason Hu
________________________________
From: Agda <agda-bounces at lists.chalmers.se> on behalf of Serge Leblanc <33dbqnxpy7if at gmail.com>
Sent: July 30, 2018 9:02:29 PM
To: agda at lists.chalmers.se
Subject: Re: [Agda] Checking termination is not sufficiently exploratory.

In my opinion, a normal form verification phase could be added without changing the termination checking algorithm.
Laŭ mi, normala kontrola fazo povus esti aldonita sen ŝangi la finiĝan kontrolan algoritmon.

Sincere

On 2018-07-30 20:06, a.j.rouvoet wrote:

I believe that you are right that the two snippets are equivalent, but it requires some computation to show that this is the case.
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 ;-)


On 07/30/2018 06:04 PM, Serge Leblanc wrote:
Yes, but you translat the code (toCostring ">>") ++ coSplit "(♭ xs) to its normal form, it equals to '>' ∷ ♯ ('>' ∷ ♯ coSplit '(♭ xs)). Right?
So, the recursive call is well protected by a constructor.

Jes, sed vi plenumas la kodon (toCostring ">>") ++ coSplit″ (♭ xs) ĝis sia normala formo, ĝi egalas al  '>' ∷ ♯ ('>' ∷ ♯ coSplit′ (♭ xs)). Ĉu ne ?
Do, la memsinkceva alvoko estas bone ŝirmi per konstruisto.

On 2018-07-30 16:59, a.j.rouvoet wrote:

For coSplit to pass the checker, the recursive invocation must appear guarded by a constructor.
This is clearly the case in coSplit', but not necessarily in coSplit'' (e.g. when toString ">>" returns the empty costring).

On 07/30/2018 04:55 PM, Serge Leblanc wrote:
Dear all,
Why the checking termination rejects the coSplit" function although the coSplit' function is accepted ?
Why the checking termination so suspicious?
Sincerely

Estimataj ĉiuj,
Kial la finiĝa kontrolo malakceptas la funkcion coSplit″ kvankam la funkcio coSplit′ trafas ?
Kial la finiĝa kontrolo estas tiel malakceptanda ?
Sincere

  coSplit′ : Costring → Costring
  coSplit′ [] = []
  coSplit′ (x ∷ xs) with x ≐ '!'
  ... | false = x ∷ ♯ coSplit′ (♭ xs)
  ... | true = '>' ∷ ♯ ('>' ∷ ♯ coSplit′ (♭ xs))

  coSplit″ : Costring → Costring
  coSplit″ [] = []
  coSplit″ (x ∷ xs) with x ≐ '!'
  ... | false = x ∷ ♯ coSplit″ (♭ xs)
  ... | true = (toCostring ">>") ++ coSplit″ (♭ xs)

  main = run $ ♯ getContents >>= λ s → ♯ (putStrLn∞ ∘ coSplit′) s

--
Serge Leblanc
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--
Serge Leblanc
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