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Compositional Models for Complex Systems 269

processes and configurations. These are powerful enough to support calcula-
tionsinquantummechanicsbutcanbereadaseasilyasaflowchart.Thelogical
sketches mentioned above can be presented through box-and-arrow dia-
grams that are not much different from unified modeling language class dia-
grams (Breiner, Padi, et al., 2017). These graphical representations support
the way that humans think and understand, without sacrificing the formal
mathematical character that is needed for machine interaction.
The speed and independence of contemporary technologies force us to
reconsider traditional approaches in engineering, and also encourage us to
adopt techniques that have been fruitful in the design and analysis of com-
putational systems. CT provides a powerful toolbox of such techniques,
with deep connections to other formal methods, structured representations
for compositional systems, structured mappings relating these representa-
tions, and a graphical approach that supports human-machine interaction.
Although CT is generally regarded as an abstract area of pure mathematics,
in recent years the field of applied CT has begun to grow. This burgeoning
field offers a wealth of potential applications to help tame the complexity of
the modern world.

DISCLAIMER

Commercial products are identified in this chapter to adequately specify the
material. This does not imply recommendation or endorsement by the
National Institute of Standards and Technology, nor does it imply the mate-
rials identified are necessarily the best available for the purpose.

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