Homotopic parts configuration management using the cellular data system

Lacking proper theory and design, big data has continued to grow in a chaotic way and are now beyond human recognition and control. To address this, we have been researching an application of the concept of homotopy preservation in homotopy type theory to remove the bottleneck in big data processing, originating from combinatorial explosion of information, that makes use of the seven layers, from homotopy to presentation, of the incrementally modular abstraction hierarchy (IMAH). We developed the Cellurar Data System (CDS) as an implementation of the IMAH in our previous work. In this paper, we introduce a position information formula, which identifies the relative position of a specified factor in a formula in CDS. This function has an important role for preserving homotopy in actual changes of objects. We show the effectiveness of the formula by taking up a case study of component configuration information management in manufacturing. In the case study, it is demonstrated that design component configuration information and manufacturing component configuration information are consistently managed by preserving homotopy, even when component configuration frequently changes.