Replication via Invalidating the Applicability of the Fixed Point Theorem

Details Replication via Invalidating the Applicability of the Fixed Point Theorem Replication via Invalidating the Applicability of the Fixed Point Theorem

2008-05-14

arxiv.org/abs/0805.2063v2

Computer Science

Logic in Computer Science

26 pages, 2 figures

Scientific paper

We present a construction of a certain infinite complete partial order (CPO) that differs from the standard construction used in Scott's denotational semantics. In addition, we construct several other infinite CPO's. For some of those, we apply the usual Fixed Point Theorem (FPT) to yield a fixed point for every continuous function $\mu:2\to 2$ (where 2 denotes the set $\{0,1\}$), while for the other CPO's we cannot invoke that theorem to yield such fixed points. Every element of each of these CPO's is a binary string in the monotypic form and we show that invalidation of the applicability of the FPT to the CPO that Scott's constructed yields the concept of replication.

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