Predicate Reduction

A small summary of the reduction algorithm.

AND is FALSE, reduce(FALSE)

is FALSE	a	b	AND	reduce(FALSE)	Note
No	No	No	reduce(a, FALSE) and reduce(b, FALSE)
Yes	No	No	filter(a) + reduce(b, FALSE)	filter true
No	Yes	No	reduce(a, FALSE) + filter(b)
Yes	Yes	Yes	empty

AND is TRUE, reduce(TRUE)

is TRUE	a	b	AND	reduce(TRUE)	Note
No	No	No	empty
Yes	No	No	empty
No	Yes	No	empty
Yes	Yes	Yes	reduce(a, TRUE) and reduce(b, TRUE)

OR is FALSE, reduce(FALSE)

is FALSE	a	b	OR	reduce(FALSE)	Note
No	No	No	reduce(a, FALSE) and reduce(b, FALSE)	reduce false	change operator to and
Yes	No	Yes	empty
No	Yes	Yes	empty
Yes	Yes	Yes	empty

OR is TRUE, reduce(TRUE)

is TRUE	a	b	OR	reduce(TRUE)	Note
No	No	No	empty
Yes	No	Yes	reduce(a, TRUE) + filter(b)	FILTER false
No	Yes	Yes	filter(a) + reduce(b, TRUE)
Yes	Yes	Yes	reduce(a, TRUE) or reduce(b, TRUE)