Sequentiality in Bounded Biorders


We study a notion of bounded stable biorder, showing that the monotone and stable functions on such biorders are sequential. We construct bounded biorder models of a range of sequential, higher-order functional calculi, including unary PCF, (typed and untyped) call-by-value and lazy λ-calculi, and non-deterministic SPCF. We prove universality and full abstraction results for these models by reduction to the case of unary PCF, for which we give a simple new argument to show that any order-extensional and sequential model is universal.

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@article{Laird2005SequentialityIB, title={Sequentiality in Bounded Biorders}, author={James Laird}, journal={Fundam. Inform.}, year={2005}, volume={65}, pages={173-191} }