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We need to know not only what are the primitives, but how do we make things meaningful in that language.
我们不仅需要知道什么是基本类型，还要知道我们在那种语言中,怎样使其变得有意义。
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Given a fixed set of primitives, all right, a good programmer can program anything.
对，给出一对混乱的基本类型，对了，一个优秀的编程师可以编出任何程序来。
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But out of the box, you generally just get these so-called "primitives."
但是立即可以用的，我们通常只有这些所谓的“基本数据类型“
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A low-level language, we used to call this assembly programming, you're down at the level of, your primitives are literally moving pieces of data from one location of memory to another, through a very simple operation.
一个低级的语言，我们曾经将其称为假设编程，你们只是处于用基本要素，把一些数据碎片,从记忆存储器的一个地方，通过简单的操作来转到另外一个地方。
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It says, with six primitives, I can rule the world. With six primitives, I can program anything.
它说，用六个基本类型，我可以规定整个世界，用六个数字，我可以编写任何程序。
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And one of the things that was useful here is, that we actually know that the set of primitives that you want to use is very straight-forward.
这儿有一个很有用的东西是，我们实际知道你想用的,一系列基本类型是非常明显的。
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Now, one of things I left hanging is, I said, OK, you build it out of primitives.
现在，我落下的一件事情是，我说过了，好的，你在原始数字之外建造它。
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OK. Now, fortunately we're not going to start with Turing's six primitives, this would be really painful programming, because they're down at the level of, "take this value and write it onto this tape."
好了，现在，幸好我们能开始讲述,图灵的六个基本类型了，这会是非常痛苦的编程，因为它们只在这个阶段上，“拿到这个结果并写在这一卷磁盘上“
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And by that, I mean anything that can be described in one of these process, you can capture in that set of primitives.
对于那个，我的意思是任何东西,都可以用这个流程中的一部分来表达出来，你可以从那堆基本类型中间挑选。
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We're typically going to use as basic steps the built-in primitives that a machine comes with.
我们要用计算机内置的原始体来,定义基本的步骤，换句话说。
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And by that I mean, do the set of primitives support a broad range of applications, or is it really aimed at a very specific set of applications?
也就是说这个基本集合，是不是支持,比较多的程序，或者是不是面向,某一特定种类的程序的？
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To do that, we need to describe: not only, what are the primitives, but how do we capture things legally in that language, and interact with the computer?
为了达到这个目的，我们需要描述：,包括程序基本的东西，以及怎么在这种语言中，做我们想做的事情并和计算机交互？
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A traditional recipe actually is based on a small set of primitives, and a good chef with, or good cook, I should say, with that set of primitives, can create an unbounded number of great dishes.
一个传统的菜谱实际上是,建立在一小堆的原材料，和一个好厨师，或者好厨子之上的，我要说，根据那堆原材料，可以创造出无数的美味佳肴来。
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All right, the question is, as I started to say, is, "What are the right primitives?"
好了，就像我刚开始说的，问题在于，“什么才是正确的基本类型呢？“
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So one of the questions is, well, what are the right primitives to use?
因此问题之一是，好吧，要使用的正确基本类型是什么呢？
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A broader set of primitives, but nonetheless the same fundamental thing holds.
一些广阔的基本类型，但还是同样的基本东西。
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Alan Turing In 1936, that same guy, Alan Turing, showed that with six simple primitives, anything that could be described in a mechanical process, it's actually algorithmically, could be programmed just using those six primitives.
在1936年，还是那个人，展示了六个基本类型，可以在计算过程中,表达出任何含义来，其实这是演算性质的，可以根据六个数字编程。
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With those six primitives, you can do it.
用六个基本类型你能做的。
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Second thing they're going to do is let us suppress detail. And in essence what that does is, the functions, and we're going to look at a bunch of examples in a second, these functions are going to give us a way to, in some or in one way of thinking about it is to create new primitives.
第二件要做的事,是忽略细节,函数的本质到底是什么,我们将在接下来的几分钟，举一些例子，这些函数将给我们提供,一种创建原语的思考方式。
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What we're saying is, in order to do computation, we want to describe recipes, we want to describe this sequence of steps built on some primitives, and we want to describe the flow of control that goes through those sequence of steps as we carry on So the last thing we need before we can start talking about real programming is, we need to describe those recipes.
我们在说，为了做计算，我们想描述一个方法，想描述建立在,相同基本类型上的步骤序列，而且我们想描述经过我们设计的,步骤的序列的，控制流程,因此我们开始谈论真正的编程之前,的最后一件事是，我们需要描述一下那些方法。
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But one of the teaching fellas also passed long to us recently, a little real world example of what happens when you're not mindful of various data types and you're not mindful of the imprecision that's inherent in representing data in a computer, at least using a language like C and low level primitives like floats and even doubles.
最近有个助教告诉我们，一个现实世界中的例子,当你不注意各种各样的数据类型,也不注意在计算机中表示数据时,其内在的不精确性，至少在用像C语言,和float甚至double型数据时，那将会发生什么？
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