Database Reference
In-Depth Information
q
1
,q
2
,q
3
,
1
r
∅
}
with
M
AB
=
MakeOperads(
M
AB
)
={
where:
1. The operation
q
1
∈
O(
EmpAcme
,
Emp
)
is the expression
(
_
)
1
(x
e
)
⇒
(
_
)(x
e
)
;
2. The operation
q
2
∈
O(
EmpAjax
,
Emp
)
is the expression
(
_
)
1
(x
e
)
⇒
(
_
)(x
e
)
;
3. The operation
q
3
∈
O(
Local
,
Local1
)
is the expression
(
_
)
1
(x
p
)
⇒
(
_
)(x
p
)
;
and
M
BC
=
∃
f
1
∀
x
e
Emp
(x
e
)
∧
Local1
(x
e
)
⇒
Office
x
e
,f
1
(x
e
)
x
e
Emp
(x
e
)
∧
Over65
(x
e
)
⇒
CanRetire
(x
e
)
,
∧∀
q
1
,q
2
,
1
r
∅
}
with
M
BC
=
MakeOperads(
M
BC
)
={
where:
4. The operation
q
1
∈
O(
Emp
,
Local1
,
Office
)
is the expression
((
_
)
1
(x
e
)
∧
(
_
)(x
e
,f
1
(x
e
))
;
5. The operation
q
2
∈
O(
Emp
,
Over65
,
CanRetire
)
is the expression
((
_
)
1
(x
e
)
∧
(
_
)
2
(x
e
))
⇒
(
_
)(x
e
)
.
Then, by applying the new algorithm for composition, we obtain the composed map-
ping
(
_
)
2
(x
e
))
⇒
M
AC
=
Compose(
M
AB
,
M
BC
)
equal to
M
AC
=
∃
f
Over
65
f
1
∃
f
2
∃
x
e
EmpAcme
(x
e
)
∧
Local
(x
e
)
⇒
Office
x
e
,f
1
(x
e
)
∀
∧
Local
(x
e
)
⇒
Office
x
e
,f
2
(x
e
)
∧∀
x
e
EmpAcme
(x
e
)
∧
f
Over
65
(x
e
)
.
x
e
EmpAjax
(x
e
)
∧∀
1
⇒
CanRetire
(x
e
)
=
x
e
EmpAjax
(x
e
)
∧
f
Over
65
(x
e
)
.
1
⇒
CanRetire
(x
e
)
.
∧∀
=
Then, by a transformation into abstract operad's operations, we obtain
M
AC
=
MakeOperads(
M
AC
)
={
q
1
,q
2
,q
3
,q
4
,
1
r
∅
}
where:
6. The operation
q
1
∈
O(
EmpAcme
,
Local
,
Office
)
is the expression
(
_
)
1
(x
e
)
(
_
)
2
(x
e
)
⇒
(
_
)
x
e
,f
1
(x
e
)
;
∧
7. The operation
q
2
∈
O(
EmpAjax
,
Local
,
Office
)
is the expression
(
_
)
1
(x
e
)
(
_
)
2
(x
e
)
⇒
(
_
)
x
e
,f
2
(x
e
)
;
∧
8. The operation
q
3
∈
O(
EmpAcme
,
Over65
,
CanRetire
)
is the expression
(
_
)
1
(x
e
)
(
_
)
2
(x
e
)
⇒
∧
(
_
)(x
e
)
;
9. The operation
q
4
∈
O(
EmpAjax
,
Over65
,
CanRetire
)
is the expression
(
_
)
1
(x
e
)
(
_
)
2
(x
e
)
⇒
∧
(
_
)(x
e
).
