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 .