Into the Immortal Cultivation

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Wang Qi lost his soul and said: "Unexpectedly, unexpectedly ... In ordinary times, I would also have such a severe obstacle to seeing and seeing ... Really, I can't relax for a moment ..."

Wang Qi said so.

how to say……

In the history of mathematics on earth, the war between formalism and intuitionism is indeed a miserable battle.

However, the story after the fight is not so popular.

In the next paragraph, the special book on the history of mathematics is the Bulbaki school, that is, Pope Grothendieck, who has mastered half of the mathematics, is the Langlands program.

As for formalism and intuitionism ... To be precise, it is neo-formalism and constructivism, but some people are doing it.

But after all, it is marginal, and it is not so dazzling in history.

Um, how to describe ...

The history department studies the history of the Qing Dynasty more than the Nanming history, right?

In the Ming dynasty, "how the emperor guarded the country and the king died," Nanming was just a salted fish that lost his ancestors' foundation, and he did not even have the qualification to fight the deer.

Even if history lovers see Chongzhen here, how many people will study Nanming's salted fish?

That's probably it.

To be honest, the students of intuitionism and formalism are not without success in the follow-up.

For example, the recursion theory behind it can be regarded as a typical "offensive achievement".

But whether it is the recursion theory with distinct characteristics of the sect, or the type theory with obvious characteristics of the sect, they all have a common feature-that is part of computer science.

In other words, it simply lives on computer science.

In other words, they are all wage earners under computer science.

This is indeed miserable.

In the early years of Henry Poincaré, the intuition that first appeared was like the Western Zhou Dynasty, but it was the co-owner of the world.

The intuitionism of the David Hilbert era is like the Eastern Zhou Dynasty. There is an "orthodox" name in the sky, but no one cares about it.

——If we consider the scenes of formalism, intuitionism and logicism, it might be more appropriate to use the analogy of “Shu Han” and “East Han”?

Later, intuitionism becomes more vulnerable, almost a younger brother. This is like a descendant of the royal family of Zhou in the Warring States Period. If you say it, it is also an identity.

But the Bulbaki school over there will have to play the "Qin Wang sweeping Liuhe, Hu Shixiong", who still cares about your "descendants of the royal family of the Zhou Dynasty".

By that time, formalism and intuitionism could only be applied.

"Mathematical foundation" This kind of orthodox dispute involving Jiuding, they can not blend.

This is also the reason why Wang Qi withdrew from Geting School. The Geting School has an orderly heritage. Even if He Waier was really willing to give him certain authority, he could not reverse the atmosphere of the Geting School to reproduce the achievements of the Buerbach School.

Even if the master is no longer, He Waier, Ai Ruoche, are quite powerful mathematicians.

He couldn't build his influence at once.

However, in any case, the Bulbaki School, according to the division of the world, is considered a Lizong School.

He categorically did not expect that the typical succession of "type theory" would be born in the hands of a member of the school.

Especially this member is his wife.

"The world view is about to be challenged ..." Wang Qi covered his head: "Maya, Mama ..."

Zhao Qingtan also froze: "How is this possible ..."

"Yes ... how is this possible?"

Zhao Qingtan was shocked, and was surprised: "Can it be said that a book written by Junjun can wash a disciple of Lizong into a disciple of Lianzong? So dangerous?"

"This ... Okay, she actually likes to apply direction when she was a child ... Maybe she is the least of us who don't care about Lizonglianzong." Wang Qi said.

Zhao Qingtan did not dare to read that manuscript. He directly asked Wang Qi: "What did the sister come up with?"

Wang Qi was taken aback.

....................................................................................

Within Tiangong, Ke Lanyin let go of his arm holding Tianjian.

He found that he was all sweating behind him.

"It's really scary ..."

It is difficult for him to describe what kind of change happened to Wang Qi as a whole just now. He felt that Wang Qi's breath suddenly became like a bomb, as if it would collapse at any time.

At that time, he almost thought it was Dragon Emperor's prophecy. Wang Qi is almost done.

And the mana of his celestial demon spirit series will also leave an indelible impact on this big Japanese territory.

Fortunately, this feeling was only momentary.

However, Ke Lanyin still felt a little panic.

"This kind of work can't let me an old man do it ... Really, I have been left behind for many years ..." Yun Zhongjun laughed helplessly.

An application should be made so that they can send one or two more free ...

It ’s better to be a little more powerful, otherwise it ’s really hard to do this junior.

..............................................................................

In the history of the earth, "type theory" was an attempt to break through Gödel's incomplete theorem. In fact, it has succeeded somewhat. Gödel's first incompleteness, second incompleteness and Tarski's indefiniteness were all broken through one after another.

However, this is only "shallow".

Gödel's incomplete theorem has not yet been completely broken through.

Because studying a type of mathematical entity requires a higher level of meta-mathematics than this type.

Therefore, research involving the mathematical entity of infinite super-poor becomes meta-mathematics requiring infinite super-poor.

Intuitionism does not recognize the existence of "infinite entities".

It is as if there is no "infinite entity" in the physical world.

This makes it uncomfortable for formalists and Platonics, but intuitionism has always regarded “mathematics” as a poorly constructed activity of human intelligence.

In the era of increasing computer development, the successor of intuitionism has put forward a brand new slogan, which has also been strictly defined.

"Definition is construction, construction is proof, and proof is a program."

They intend to use the computer machines developed by the formalists to strict their mathematical philosophy.

The most rigorous type of system, there is no circulation and self-referential.

Therefore, this system, even if it involves the "infinite" problem, because it does not cause an infinite logical loopback, so it can still be shut down.

Because strongly normalized type systems are all end-to-end, that is, all functions can be stopped and give unique results.

There are no ghosts on the two shutdown issues of self-referential and infinite loop.

This is a use of the downtime problem at the expense of Turing completeness.

In other words, "type theory" is an achievement in the field of basic mathematics.

And derived from this is a class of absolutely reliable computer languages: strongly normalized type languages.

In theory, there will be no malicious bugs caused by problems in programming language design, but only programmers who understand wrong design intents and analyze benign bugs caused by wrong design requirements.

Seriously, have you heard of a language that can be called "never go wrong"?

Does your Windows have a blue screen? Has your Android ever crashed?

Everything in the world comes at a price. Strongly standardized type languages ​​are really not something that ordinary people can play.

Without Turing Completion, writing something similar to loop execution is not impossible at all, but it must become a human-driven execution branch predictor.

Carefully counted as the cornerstone. One by one, predict and reason about the changes of each logical branch and each iteration.

The strong normalization of the type system itself made the programmers at that time caught in the quagmire of living compilers.

How can a person with this level of intelligence really be willing to work as a human compiler to build wheels for this kind of hard work in a lifetime?

And people with high IQ will prefer languages ​​with greater freedom.

Therefore, this language is used only in places where the national environment is driven by the military environment, and in scenarios such as aerospace for safety at all costs.

It is only in today ’s era when there is a surplus of brain resources that research laborers and even research slaves are not new, that there will be a business that “protects blockchain smart contracts with trusted programming”.

Turing's complete programming structure with loops is more in line with human usage habits, and gave the computer science frontiers the freedom to use their imagination at the time, and most importantly, lowered the threshold for programmers to enter Programming workers leek breeding laid a good foundation.

This is the early industrial programming language. Memorize the types of pointers and parameters you created yourself, and calculate the type conversion and pointer recovery.

On the basis of strong typing, if the programmer deduces the change process of type parameters and type deduction to the compiler of the programming language to do it, it is weak type.

If further garbage collection and pointer collection are thrown to the interpreter or virtual machine, it will change from a static language to a dynamic language.

By mixing these types of unsafe language and type theory again, you get a catch of errors.

The language coupled with strict this mechanism is a type-safe language: in theory, if the program is bugged, it will only kill the program, and will not randomly run some unpredictable, even let the owner ’s efforts be broken. Malicious code.

Of course, it's actually not reliable ... everyone who has used computers for so many years is counted.

The legendary type safety + concurrency safety Rust was only made when the programming migrant workers walked everywhere. They bumped along the way, and no formal verification of related features has been completed so far.

If you look at it from the perspective of type theory, then ... the Wanxiang hexagram before Wang Qi should be regarded as ... a typeless language.

Untyped languages ​​piled from a bunch of unsafe modules through various transformation rules are unsafe and concurrently unsafe.

Typeless language has a high degree of freedom, which can make the reasoning process of advanced mathematics be realized directly on the physical machine, and it is closer to human thinking habits.

Yes, it is very close to the "no type" programming languages ​​on the earth that are piled up from the type through the type conversion rules, but the Vientiane Gua Wen really has "typeless" "type unsafe" "concurrency" "Unsafe" nature.

Freedom is freedom, but relative, this thing is also not easy to use.

If a compilation error really occurs, the computer is likely to output unpredictable results instead of directly shutting down.

This means that the code farmers must know very well what their codes are, and even need to use their mental arithmetic to correct errors for their own code. It is the same as the logic branch of manpower prediction, but it is to predict what is wrong.

This is also a high requirement for the programmer's ability.

It's just that in this world, as long as you have a few cultivation methods like Wandingshujing, you can solve this problem.

In other words, after so many years, you do n’t really mind being a personal error corrector.

This is the general status of typology on earth.

In this world, the situation is a bit strange.

Chen Youjia relied on the Dongfeng of Shenzhou's current Lizong Lianzong debate to deduce this theory from the algorithm of clustering the beasts of the king.

Moreover, he was inspired by formal linguistics.

Formal linguistics can be regarded as a parallel development of computer science.

However, this process ...

Indeed ...

Full of style of this history of cosmic technology.

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