Category Theory and Decision Tables

Marek will define a business problem that illustrates how category theory is applicable

Category Theory definition

Some Categories of Decision Tables

s->s Example

Applying rules to data elements that are not part of a collection to modify other data elements i.e. singleton inputs, outputs or intermediate variables in the decision.

s->A Example

Applying rules to data elements that are not part of a collection to create one or more instance of a collection.

A->A Example

Applying rules independently to every instance in a collection to modify or delete that instance (effectively looping through the elements of a collection). Necessitates revisiting any element that is modified.

A->B Example

Applying rules to every instance of A to create new instances of B. Not necessary to revisit elements of A if they are not modified.

AxA->A Example

Applying rules to 2 instances of the same collection and merging or eliminating one of them (effectively looping through all possible pairs of instances)

AxA->B Example

Applying rules to 2 instances of the same collection and creating a new collection of the matched pairs

AxB->C Example

Applying rules to 2 instances of the different collections and creating a new collection of the matched pairs