本文提出了利用循环体转换关系式的程序证明方法。

In this paper a method of proving the correctness of a computer program based on a transformation relation of the loop body is presented.

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刑事诉讼证明中程序证明标准是一个新概念，该概念与实体证明标准并列。

The procedural standard of proof is a new concept in the criminal procedure, and both of the procedural standard of proof and the substantive standard of proof are all important.

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并不是不能为命令式程序进行那种程序证明，而是状态改变发生的次数之多使得那些证明不具意义。

It's not that program proofs cannot be done with imperative programs, but that the number of state changes that occur make them unwieldy.

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This is boring. In fact, you can do some nice things to prove what is the class of functions you can compute with straight-line programs, and what you'd see if you did that is, it's not particularly interesting.

这很无聊，实际上，你可以通过做一些很有趣的事情,来证明你可以通过直线程序,来做很多功能，但是你也看到我们之前讲过的了，这不太有趣。

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Now, some of these things can prove things that are mathematically way over my head.

如今,这些程序都可以证明一些,令我头大的数学题了

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And, in fact, a computer program has come up with a proof that, as far as was known, nobody in the world had ever come up with before.

而实际上,电脑程序的证明方式,据目前所知,是前人们从未曾提出过的

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