Semantics
Premonoidal structure (together with an interpretation of base types
and constructors) is exactly what is required to give a semantics
of process terms. For example:
- V
C
StateZ(C),
where StateZ(C)[X,Y] is
C[X
Z,Y
Z].
- V
VT
VU,
where T is any commutative monad satisfying the monic condition,
U is any monad satisfying the monic condition, and there
is an appropriate natural transform from T to U.
- Term(
)
Term(
,
)
Term(
,
,
).
- Graph(
)
Graph(
,
)
Graph(
,
,
).
Proposition
Graph(
,
,
) is the
initial strict symmetric premonoidal category over
over
with Graph(
,
) as its centre.