
638
Mäher
For some properties of the function T
p
we are able to characterize syntac-
tically those sets of clauses Ρ such that the property holds. These results,
when taken with the obvious algorithm for computing the canonical form of a
program, will mean that the presence or absence of such properties can be
determined simply and without the need to deal directly with the functions.
Theorem 2 greatly simplifies the proofs of these results.
T
p
is distributive if T
p
(\J X.) = \JT
p
(X
t
) for every collection {X. : i EI}
of subsets of HB. But, since T
p
is continuous, this condition is equivalent to
VX, Y C HBJ
P
{X UY) = T
P
(X) UT
P
(Y). Distributiv