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
.