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Computability of Combinators

Computability of Combinators. Position Statement Yingfei Xiong , Peking University, 2013. Computability of Combinators. Many BX approaches are built on top of combinators Is there a limitation of the combinator model? What is the computability of any possible combinator -based BX?

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Computability of Combinators

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  1. Computability of Combinators Position Statement Yingfei Xiong, Peking University, 2013

  2. Computability of Combinators • Many BX approaches are built on top of combinators • Is there a limitation of the combinator model? • What is the computability of any possible combinator-based BX? • How to characterize the computability? • How to prove the characterization? • Combintor model could be replaced by • Rule-based model? • Bidirectionalization model? • Anything else?

  3. Turing-Computable / Lambda-Computable BX • Could express any two functions, get and put, expressible in a Turing machine/Lambda Calculus that • satisfy GETPUT and PUTGET • are total functions • Problems: • How to encode different data types? • Probably not true because of the totality requirements, but how to formally prove it? • What weaker model could possibly be?

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