[Agda] Why the light gray highlighting here?

[Jason -Zhong Sheng- Hu]

to expand, "not hold definitionally" means that Agda does not recognize

x     xor ⟨⟩     =  x

as a definitional equality, as opposed to

⟨⟩    xor y      =  y

namely, Agda knows ⟨⟩ xor y and y are identical.

The reason is, the function is defined by first doing a case split on x​. so the case tree on x​ is expanded. writing

x     xor ⟨⟩     =  x

is the same as writing

⟨⟩     xor ⟨⟩     =  x
(x O) xor ⟨⟩     =  x O
(x I) xor ⟨⟩     =  x I

Thanks,
Jason Hu
https://hustmphrrr.github.io/
________________________________
From: Georgi Lyubenov <godzbanebane at gmail.com>
Sent: September 29, 2020 10:08 AM
To: Jason -Zhong Sheng- Hu <fdhzs2010 at hotmail.com>
Cc: David Banas <capn.freako at gmail.com>; Agda mailing list <agda at lists.chalmers.se>
Subject: Re: [Agda] Why the light gray highlighting here?

Hi!

Related links in the wiki:
https://agda.readthedocs.io/en/v2.6.1.1/tools/emacs-mode.html#highlight
https://agda.readthedocs.io/en/v2.6.1.1/language/function-definitions.html#case-trees

I'm just still not sure what is meant by "hold definitionally" in this context, seeing as how he is currently defining a function, not trying to prove anything based on the case tree of some function. Could someone clarify this?

======
Georgi
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