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?• How to characterize the computability?• How to prove the characterization?

• Combintor model could be replaced by• Rule-based model?• Bidirectionalization model?• Anything else?

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?