5
Fixpoints
•
Consider transitive closure, expressed as LFP:
•
tc(u,v) = lfp
R
[E(x,y)
Ç
9
z.(E(x,z)
Æ
R(z,y)](u,v)
•
•
Can “unfold” it:
•
tc
0
(x,y) = E(x,y)
•
tc
n+1
(x,y) =
9
z.(E(x,z)
Æ
9
x.(x=z
Æ
tc
n
(x,y)))
•
•
Hence tc(u,v) =
Ç
n
¸
0
tc
n
(u,v)
2
L
w
1
,
w