Proof Assistants: history, ideas and future
نویسنده
چکیده
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.
منابع مشابه
Applied Logic - CS4860
Logic has been an important element of mathematics for over two millennia and of computer science (CS) since its birth. Logic is in fact one of the oldest academic disciplines, going back to Aristotle in 350 BCE and to Euclid in 300 BCE. Logic played a major role in shaping mathematics as can be seen in Euclid’s Elements of Geometry and in the creation of set theory and type theory as languages...
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