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Proof Assistants: history, ideas and future
"... In this paper we will discuss the fundamental ideas behind proof assistants: What are they and what is a proof anyway? We give a short history of the main ideas, emphasizing the way they ensure the correctness of the mathematics formalized. We will also briefly discuss the places where proof assista ..."
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In this paper we will discuss the fundamental ideas behind proof assistants: What are they and what is a proof anyway? We give a short history of the main ideas, emphasizing the way they ensure the correctness of the mathematics formalized. We will also briefly discuss the places where proof assistants are used and how we envision their extended use in the future. While being an introduction into the world of proof assistants and the main issues behind them, this paper is also a position paper that pushes the further use of proof assistants. We believe that these systems will become the future of mathematics, where definitions, statements, computations and proofs are all available in a computerized form. An important application is and will be in computer supported modelling and verification of systems. But their is still along road ahead and we will indicate what we believe is needed for the further proliferation of proof assistants.
N.G. de Bruijnās Contribution to the Formalization of Mathematics
"... N.G. de Bruijn was one of the pioneers to explore the idea of using a computer to formally check mathematical proofs. The Automath project, that started in 1967 and ran until 1980, was the first in developing computer programs to actually check mathematical proofs. But Automath is more than that: it ..."
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N.G. de Bruijn was one of the pioneers to explore the idea of using a computer to formally check mathematical proofs. The Automath project, that started in 1967 and ran until 1980, was the first in developing computer programs to actually check mathematical proofs. But Automath is more than that: it is a language for doing mathematics and it has philosophical implications for the way we look at logic and the