The study of computability has its origin in Hilbert's conference of 1900, where an adjacent question, to the ones he asked, is to give a precise description of the notion of algorithm. In the search for a good definition arose three independent theories: Turing and the Turing machines, G\"odel and the recursive functions, Church and the Lambda Calculus. Later there were established by Kleene that the classic models of computation are equivalent. This fact is widely accepted by many textbooks and the proof is omitted since the proof is tedious and unreadable. We intend to fill this gap presenting the proof in a modern way, without forgetting the mathematical details.

中文翻译：

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三种计算模型及其等价

对可计算性的研究起源于 1900 年的希尔伯特会议，在那里，与他提出的问题相邻的一个问题是对算法概念的精确描述。在寻找一个好的定义的过程中出现了三个独立的理论：图灵和图灵机、G\"模型和递归函数、丘奇和 Lambda 演算。后来 Kleene 建立了经典的计算模型是等价的。这个事实被许多教科书广泛接受，由于证明乏味且不可读，因此省略了证明。我们打算填补这一空白，以现代方式呈现证明，同时又不忘记数学细节。