Chapter 98: Type Theory [Third Update]

The foundation of type theory is intuitive logic.

Master Hai Ting has absorbed the "logic" of Li Zong, rewritten the arithmetic axioms, and completed the logic of Lian Zong.

The goal of type theory is to "break through Gödel's incompleteness theorem", and the idea is to "cut off self-reference".

Master Suan proposed a way to bypass "Gödel's incompleteness theorem", including "cutting off self-reference".

Feng Luoyi followed this line of thought to prove the security of the "infinite axiom".

It can be said that everything is ready.

Then, Master Suan contributed... the achievement of type theory results.

That is, the chaotic topological network algorithm of the beast machine cluster.

Master Suan did not propose "type theory" alone, because he was really not interested in the basic arithmetic that everyone was arguing about.

However, he is indeed a genius, and he completed such a rigorous system with his own thinking.

It's like using coq language to write a complete operating system for you, and it can run smoothly, and even the interface is very beautiful, which is incredible and amazing.

Wang Qi even suspected that the method of Suanjun was not to sacrifice "Turing completeness", but... Suanjun didn't care about "Turing completeness" at all.

The beast mechanism cluster is quite safe. From the perspective of type theory, it is absolutely "strongly standardized and strongly typed", and will not input any "unexpected" results. Once there is a slight error, it will shut down directly for you to see.

On a macro level, it can be compatible with the achievements of Feng Luoyi's system.

Even if there is a problem with the macro calculation, it will only cause the cluster at the macro level to temporarily lose cohesion, rather than causing the beast mechanism itself to lose control.

Wang Qi thought about it and realized that this kind of thing that can destroy a star if you are not careful does need such a rigid thing to constrain it.

If he is asked to use the typeless and type-unsafe Wanxiang Guawen to write the bottom layer directly...

Haha...hahahahaha...

It can be said that all the conditions for the birth of type theory are already complete.

It's just that at present, the Lianzong monks in Shenzhou still don't pay enough attention to the calculator.

They are still staring at the basic calculation theory, and want to fight to the death with Lizong and Ge Tingpa in this regard.

I occasionally dabbled in the theory of calculators, but it was just to "refute the other party".

But what almost shattered Wang Qi's three views was...

Such an achievement in the history of the earth came from basic mathematics, but in this world, it was actually deduced from the application...

"Haha...hahahaha..." Wang Qi had to say: "I feel that my knowledge and views are indeed quite serious..."

Although the monks of the modern law have always been proud of "opening the black box", in this universe, there is no way to completely avoid the magic brought by the "black box".

In other words, no one can live without a black box.

Let's take the most direct example. If you have to understand the "central law" to have a baby, then humans don't need to reproduce-but relatively speaking, the virus will not spread.

"Application" comes first and "theory" comes later. It is a common thing in any world.

Zhao Qingtan was surprised and said, "Junior sister, this achievement is quite remarkable..."

"Yes, it is quite remarkable." Wang Qi shook his head: "Shenzhou is afraid that things will change again."

"What do you mean?"

Wang Qi said, "Constructing a new high-level calculator language has become simpler, because someone has directly pointed out the essence of the 'language', so everyone knows how to construct a language that 'even fools can use'."

The challenge of strong specifications and strong types to IQ is that you have to dance with shackles. Because Turing completeness is lost, there is really no fault tolerance.

The challenge of type insecurity and typelessness to IQ is that you never know what bugs will be output.

Then the idea of ​​combining peeing shrimp and beef balls to make peeing beef balls is also there.

There are languages ​​that have both "type theory" and "Turing completeness".

It is indeed not pleasing to both sides.

This kind of language mostly pleases the "lower".

Because of the type, it will not output completely unpredictable results.

Because of Turing completeness, there is a certain fault tolerance.

The popular language at the bottom of the programmers' contempt chain was born.

Wang Qi and Feng Luoyi would not take the initiative to develop this kind of thing, and Suanjun would not even think about it.

However, this undoubtedly pointed out a clear path.

As long as we go in this direction, the language used by programmers will always be born.

"And, this is also meaningful in the basic mathematics part, right?" Wang Qi said so.

Zhao Qingtan smiled.

Li Zong Lian Zong, Ge Ting Shao Li and other names are indeed loud.

But cultivators like him firmly believe that the "structure" of the basic school is the power of the next era.

The next day, Chen Youjia woke up and was stunned after listening to Wang Qi's introduction of these things.

"Am I so powerful?"

The girl blinked blankly.

Wang Qi nodded: "Super powerful."

Chen Youjia narrowed his eyes and smiled.

But immediately, she was a little confused: "This... is considered basic mathematics? I originally wanted to develop applications..."

"This is very useful for analyzing the achievements of the Calculator." Wang Qi said: "Furthermore, you deduced from the Calculator's 'applications', which can also be regarded as a path 'from theory to application'."

Type theory is also closely related to functional programming.

Although on earth, functional programming that can be actually used, such as Lisp, was developed long before type theory, this does not prevent type theory from taking programming as a whole, especially the art of functional programming, to a higher level.

Another obstacle to the application of Bourbaki's theory has been eliminated.

Wang Qi took a deep breath and said seriously: "But, junior sister, this is not finished yet. In your hands, this type theory has only just taken shape."

Chen Youjia was stunned: "What do you call it? Type theory?"

Wang Qi nodded: "Define the language type...what are you dissatisfied with?"

Chen Youjia smiled: "I feel like I will be overshadowed by your theory [K theory]."

Wang Qi was stunned. This is a trouble that did not exist in the context of the previous life.

"Then let's call it 'type theory'."

"It sounds like it's the same as your 'similarity theory'. Isn't that right..."

Wang Qi raised Chen Youjia's chin and asked, "What's wrong with a couple?"

"Don't make trouble, these two theories are completely different in the field of mathematics..."

"The names are just similar!"

Amid the laughter, the name of this theory destined to shock history has finally been finalized.

Chen Youjia suddenly sighed: "This time, it was really a coincidence... If it weren't for the debate between Master Hai Ting and Teacher Feng, I would never have been able to touch even a trace of Suan Jun's 'thoughts'; and if it hadn't been for Suan Jun's manuscript, even if I Even if you can get a glimpse of the door, you may not be able to enter..."

"Be more confident." Wang Qi patted Chen Youjia on the head: "You are strong enough."

After the excitement, Chen Youjia suddenly became worried: "Speaking of which, the fundamental arithmetic is mainly for the foundation of arithmetic. This time I publish my paper, that is... I am joining the current debate as Lian Zong, right? Isn't that right? ...Not good?”

A school of thought must have a consistent philosophy.

Wang Qi thought for a moment: "I don't see anything wrong with it. When I made my ill-advised remarks, I was still considered a non-staff member of the Geting Sect."

"Huh? I always feel like you made an unlucky metaphor..."

Wang Qi waved his hand: "Where are you thinking... In short, poor calculation can be regarded as a point of rise in our Wanfa sect, and it can also be regarded as the origin of the fundamental sect? It can be said that the last debate between Lian Zong and Li Zong, It was ended by me, and now, their final debate is also started by me.”

Now even sects from different sects are trying to challenge the incompleteness theorem. What Wang Qi said is correct.

"It's precisely because of this that I have the capital of the component group."

"This chaos started because of the fundamentalists, so there is nothing wrong with ending it by the members of the fundamentalists."

Chen Youjia's tone paused: "The end..."

Wang Qi nodded: "End. I should say...go and end this old generation."

Chen Youjia couldn't help but laugh: "It sounds like the feud between Ge Ting and Shao Li is about to end."

Wang Qi didn't smile. That's pretty much it.

The mathematical laws of this world are basically the same as those of the non-aura universe. In the foreseeable direction, intuitionism and formalism will inevitably decline.

Even if there is a difference, then at most... As long as you are still alive, intuitionism will not be reduced to working for computer science, but will turn its back on the guest and let intuitionism dominate the field of computer science?

This is just the "worst" possibility.

After all, Teacher Feng and Master Turing didn’t kneel, right?

Wang Qi said: "Senior Brother Su is also paying attention to this aspect. You can communicate with him."

Chen Youjia nodded: "By the way, can you contact Suanjun?"

Wang Qi was stunned: "What are you doing?"

"Please give me advice and thanks."

"You don't want to die?" Wang Qi exclaimed: "Weren't you exhausted just now? And why are you thanking him? Isn't it a natural thing to write a book for other scholars to read? To inspire other scholars or something..."

"You said it yourself, why should you be afraid of Suanjun?" Chen Youjia said calmly: "Not only Suanjun, but also Teacher Feng and Master Hai Ting have to express their gratitude. Of course, I also want to ask for advice."

Wang Qi grinned: "Don't you think... this is a bit too aggressive?"

"If you don't help, I'll go find my father." Chen Youjia stared at Wang Qi.

Although there are communication restrictions between his hometown and China, Chen Jingyun is also a free monk, and his relatives are not restricted from communicating with him.

But it would be difficult for Chen Youjia to find the right person.

Wang Qi raised his hand: "No, no, forwarding from the earth consumes the precious bandwidth of the Immortal Alliance. It's not worth it. It's not worth it. Can I send the letter to the head office for you?"

He is treated as an immortal, and the secret level is high enough. He happens to know that Mr. Suan is in that corner right now, so he can really send a letter to Mr. Suan.