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

lmcs:4392 - Logical Methods in Computer Science, March 20, 2018, Volume 14, Issue 1
The sequential functionals of type $(\iota \rightarrow \iota)^n \rightarrow \iota$ form a dcpo for all $n \in \Bbb N$

Authors: Normann, Dag

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,


Source : oai:arXiv.org:1607.02970
DOI : 10.23638/LMCS-14(1:23)2018
Volume: Volume 14, Issue 1
Published on: March 20, 2018
Submitted on: August 18, 2017
Keywords: Computer Science - Logic in Computer Science,Mathematics - Logic


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