A type system for counting instances of software components

We identify an abstract language for component software based on process algebra. Besides the usual operators for sequential, alternative and parallel composition, it has primitives for instantiating components and for deleting instances of components. We define an operational semantics for our language and give a type system in which types express quantitative information on the components involved in the execution of the expressions of the language. Included in this information is for each component the maximum number of instances that are simultaneously active during the execution of the expression. The type system is compositional by the novel use of 'deficit types'. The type inference algorithm runs in time quadratic in the size of the input. We consider extensions of the language with loops and tail recursion, and with a scope mechanism. We illustrate the approach with some examples, one on UML diagram refinement and one on counting objects on the free store in C++.