Fwd: Give alternate default definition for (<=)

Dannyu NDos

8 May 2020 8 May '20

6:18 p.m.

---------- Forwarded message --------- 보낸사람: Dannyu NDos Date: 2020년 5월 8일 (금) 16:35 Subject: Re: Give alternate default definition for (<=) To: Sven Panne 2020년 5월 8일 (금) 15:33, Sven Panne 님이 작성:

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Eq is a superclass of Ord, so how do you define that for Computable?

instance Eq Computable where x == y = x <= y && y <= x

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Carter Schonwald

8 May 8 May

11:35 p.m.

New subject: Give alternate default definition for (<=)

That seems undecidable in general. On Fri, May 8, 2020 at 6:18 PM Dannyu NDos wrote:

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---------- Forwarded message --------- 보낸사람: Dannyu NDos Date: 2020년 5월 8일 (금) 16:35 Subject: Re: Give alternate default definition for (<=) To: Sven Panne

2020년 5월 8일 (금) 15:33, Sven Panne 님이 작성:

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Eq is a superclass of Ord, so how do you define that for Computable?

instance Eq Computable where x == y = x <= y && y <= x

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Dannyu NDos

9 May 9 May

12:14 a.m.

New subject: Give alternate default definition for (<=)

2020년 5월 9일 (토) 12:35, Carter Schonwald 님이 작성:

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That seems undecidable in general.

True. It is proven that there is no algorithm that compares arbitrary computable numbers. In other words, min and max are algorithms, but (==) and (<=) are not.

Dannyu NDos

27 May 27 May

1:37 a.m.

New subject: Give alternate default definition for (<=)

Sorry for the mix-up. It really turns out that I can't really define (==) with only min and max. However, it turns out that the suggested default definition is effective when (==) is properly given. I've come up with another type where it is effective, so stay tuned.

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Carter Schonwald
Dannyu NDos