The sequential functionals of type $(\iota \rightarrow \iota)^n \rightarrow \iota$ form a dcpo for all $n \in \Bbb N$
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,
- Publication:
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arXiv e-prints
- Pub Date:
- July 2016
- DOI:
- 10.48550/arXiv.1607.02970
- arXiv:
- arXiv:1607.02970
- Bibcode:
- 2016arXiv160702970N
- Keywords:
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- Computer Science - Logic in Computer Science;
- Mathematics - Logic
- E-Print:
- 10 pages