# Semantics

To give a semantics for value terms over a signature , we need a category with chosen finite products, and an interpretation for . For example:

- Set (sets and functions).

- Cpo (complete partial orders, not necessarily with bottom).

- Term() (the appropriate term algebra).

- Graph() (single-coloured flow graphs up to bisimulation).

Call such a category a cartesian category over .

Proposition Graph() is the initial strict cartesian category over .

As a corollary, giving a flow graph semantics for a language uniquely defines a semantics in any other strict cartesian category over .