The sequential functionals of type $(\iota \rightarrow \iota)^n \rightarrow \iota$ form a dcpo for all $n \in \Bbb N$

Dag Normann

doi:10.23638/lmcs-14(1:23)2018

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arXiv · 1607.02970

The sequential functionals of type $(\iota \rightarrow \iota)^n \rightarrow \iota$ form a dcpo for all $n \in \Bbb N$

Dag Normann

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Abstract

We prove that the sequential functionals of some fixed types at type level 2, taking finite sequences of unary functions as arguments, do form a directed complete partial ordering. This gives a full characterisation of for which types the partially ordered set of sequential functionals has this property. As a tool, we prove a normal form theorem for the finite sequential functionals of the types in question,

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Dag Normann. 2016-07-11. The sequential functionals of type $(\iota \rightarrow \iota)^n \rightarrow \iota$ form a dcpo for all $n \in \Bbb N$. https://doi.org/10.23638/lmcs-14(1%3A23)2018

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