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Category: Logic and Foundations

  • Logic and Foundations
  • Maths
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Why is Lambda Calculus?

Alonzo Church’s Lambda Calculus is what makes type-free functional programming work. A powerful model of computation, at its heart is a very simple abstract rewrite system. This short article touches upon why Lambda-calculus might be a natural thing to think about, and presents an elegant proof of the Church-Rosser theorem.

Parth
October 5, 2020October 5, 2020
18 Min Read
0
  • Logic and Foundations
  • Maths
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Consistency and Cut

This study of meta-mathematics, of proofs and propositions as objects in themselves,  was started off by David Hilbert, and revolves around the question of “what can be proven?” This is the notion of consistency- we explore Gentzen’s neat trick of cut-elimination and provide a formal proof of the consistency of Peano arithmetic.

Parth
August 28, 2020August 28, 2020
30 Min Read
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  • Logic and Foundations
  • Maths
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Winning Strategies (and Sylver Coinage)

Sylver Coinage is a two-player game of perfect information proposed by Conway. Discussing whether this has a winning strategy, we build the rich theory of more general Gale-Stewart games and when the outcomes of these infinite games are determined.

Parth
August 6, 2020August 7, 2020
19 Min Read
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Consistency and Cut

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