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Andrej Bauer - Formalizing invisible mathematics - IPAM at UCLA ΡΠΊΠ°Ρ‡Π°Ρ‚ΡŒ Π² Ρ…ΠΎΡ€ΠΎΡˆΠ΅ΠΌ качСствС

Andrej Bauer - Formalizing invisible mathematics - IPAM at UCLA 2 Π³ΠΎΠ΄Π° Π½Π°Π·Π°Π΄

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Ρ‚Π΅Π»Π΅Ρ„ΠΎΠ½ с ΠΊΠ°ΠΌΠ΅Ρ€ΠΎΠΉ

Ρ‚Π΅Π»Π΅Ρ„ΠΎΠ½ с Π²ΠΈΠ΄Π΅ΠΎ

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Andrej Bauer - Formalizing invisible mathematics - IPAM at UCLA
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Π‘ΠΊΠ°Ρ‡Π°Ρ‚ΡŒ Π²ΠΈΠ΄Π΅ΠΎ с ΡŽΡ‚ΡƒΠ± ΠΏΠΎ ссылкС ΠΈΠ»ΠΈ ΡΠΌΠΎΡ‚Ρ€Π΅Ρ‚ΡŒ Π±Π΅Π· Π±Π»ΠΎΠΊΠΈΡ€ΠΎΠ²ΠΎΠΊ Π½Π° сайтС: Andrej Bauer - Formalizing invisible mathematics - IPAM at UCLA Π² качСствС 4k

Π£ нас Π²Ρ‹ ΠΌΠΎΠΆΠ΅Ρ‚Π΅ ΠΏΠΎΡΠΌΠΎΡ‚Ρ€Π΅Ρ‚ΡŒ бСсплатно Andrej Bauer - Formalizing invisible mathematics - IPAM at UCLA ΠΈΠ»ΠΈ ΡΠΊΠ°Ρ‡Π°Ρ‚ΡŒ Π² максимальном доступном качСствС, Π²ΠΈΠ΄Π΅ΠΎ ΠΊΠΎΡ‚ΠΎΡ€ΠΎΠ΅ Π±Ρ‹Π»ΠΎ Π·Π°Π³Ρ€ΡƒΠΆΠ΅Π½ΠΎ Π½Π° ΡŽΡ‚ΡƒΠ±. Для Π·Π°Π³Ρ€ΡƒΠ·ΠΊΠΈ Π²Ρ‹Π±Π΅Ρ€ΠΈΡ‚Π΅ Π²Π°Ρ€ΠΈΠ°Π½Ρ‚ ΠΈΠ· Ρ„ΠΎΡ€ΠΌΡ‹ Π½ΠΈΠΆΠ΅:

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Andrej Bauer - Formalizing invisible mathematics - IPAM at UCLA

Recorded 13 February 2023. Andrej Bauer of the University of Ljubljana presents "Formalizing invisible mathematics" at IPAM's Machine Assisted Proofs Workshop. Abstract: It has often been said that all of mathematics can in principle be formalized in a suitably chosen foundation, such as first-order logic with set theory, higher-order logic, or type theory. When one attempts to actually do so on a large scale, the true meaning of the qualifier β€œin principle” is revealed: mathematical practice consists not only text written on paper, however detailed they might be, but also of unspoken conventions and techniques that enable efficient communication and understanding of mathematical texts. While students may be able to learn these through observation and imitation, the same cannot be expected of computers, yet. In this talk we will first review some of the informal mathematical practices and relate them to corresponding techniques in proof assistants, such as implicit arguments, type classes, and tactics. We shall then ask more generally whether these need be just a bag of tricks, or can they be organized into a proper mathematical theory. Inspired by the theory of programming languages we construe processing of formalized mathematics as a computation whose side effects embody the techniques found in proof assistants, including user interaction, and the computed value a mathematical assertion. These idea provide a basis for the design of a flexible proof assistant that can be extended by the user. Learn more online at: http://www.ipam.ucla.edu/programs/wor...

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