Instance

Instance

An instance is a way to populate a schema with data. For each entity, it describes which are its possible values.

Syntax

An instance is described providing some generators and some equations, like in the following example

instance MyInstance = literal : MySchema {
	generators
		a b c : Employee
		m s : Department
	equations
		first(a) = Al
		first(b) = Bob  last(b) = Bo
		first(c) = Carl
		name(m)  = Math name(s) = CS
		age(a) = age(c)
		manager(a) = a manager(b) = c manager(c) = c
		worksIn(a) = m worksIn(b) = s worksIn(c) = s
		secretary(s) = c secretary(m) = a
		secretary(worksIn(a)) = manager(a)
		worksIn(a) = worksIn(manager(a))
		age(a) = "1"
		age(b) = "5"

where each generator correspond to a "row" of its entity "table" and the equations define the attributes and the forreign keys of the entities, in such a way that the path_equations of the schema are satisfied.

Categorical interpretation

An instance is a functor from the category presented by the schema to the category Set. This means that for every entity we need to associate a set of elements, which can be tought as the rows of the table. Moreover, for every foreign_key of the schema, which is nothing else than a morphism in our starting category, we need to associate a function in the Set category. Specifically, if we have a foreign key worksIn : Employee -> Department, we need to define a function from the set of Employees to the set of Department. In other terms, we need to say, for every employee, to which department he belongs to.