The relationship between Turing and lambda calculus

Leibniz once had two dreams:
1. Create a "universal language" (universal language) so that any problem can be expressed in this language;
2. Find a "decision method" to address all the issues that can be expressed in the universal language.
These two problems are the core and essence of mathematical logic, Mathematics Philosophy and Mathematics Foundation in the last hundred years. The answer to the previous question is from the beginning of Frege, Russell, the final result of the axiom set theory movement: set theory, which is formalized by the first order predicate logic as language, has now become the universal language of mathematics, modern logic, especially the mathematical logic which is applied in the field of mathematics, Its most important goal is to provide a rigorous and precise language for the whole of mathematics. This is the direction we should grasp when we learn mathematical logic.
And the second question is one of the most concerned questions about modern philosophy and computer science: Is it possible to solve all the problems that are formalized in this "universal language"? The problem is the so-called "entscheidungsproblem,decision" (problem). The study of this problem eventually led to the birth of theoretical computer science: Alonzo Chuchi and Alan Turing in their respective ways to answer the question in a negative way. In the study of this problem, they first studied the intuitive concept of "decidable" and gave a formal definition and explanation, further putting the problem into a "computable" (computable) problem, and finally defining it as "computable function". (computable function) problem research. For this reason, Church and Turing presented a model of computable function respectively. Turing's model is the famous Turing machine, which has become the theoretical foundation of modern computer science, and Church's model is lambda calculus, which becomes the theoretical basis of the later computer language Lisp and modern functional programming language. Turing then demonstrated that the two models actually defined the same class of computable functions. It can be said that church and Turing's study of mathematical logic has opened up a new field from the traditional problem of solving mathematical foundations: Computational Science.

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The relationship between Turing and lambda calculus