已知，

snippet.txt

A∩(B∪C) = (A∩C)∪(A∪C)
A∪(B∩C) = (A∪C)∩(A∪C)
A∩A = A
(A∩B)∩C = A∩B∩C = A∩C∩B

那么，

snippet.txt

(A∩B)∪(C∩D) = ((A∩B)∪C) ∩ ((A∩B)∪D)
= ((A∪C)∩(B∪C)) ∩ ((A∪D)∩(B∪D))
= (A∪C) ∩ (B∪C) ∩ (A∪D) ∩ (B∪D)
 
=> ((A∩B)∪(C∩D)) ∩ (A∪C) ∩ (B∪D) = (A∪C) ∩ (B∪C) ∩ (A∪D) ∩ (B∪D) ∩ (A∪C) ∩ (B∪D)
=> ((A∩B)∪(C∩D)) ∩ (A∪C) ∩ (B∪D) = (A∪C) ∩ (B∪C) ∩ (A∪D) ∩ (B∪D)

同理，

snippet.txt

((A∩B)∪(C∩D)) ∩ (A∪C) = (A∪C) ∩ (B∪C) ∩ (A∪D) ∩ (B∪D) ∩ (A∪C)
或，
((A∩B)∪(C∩D)) ∩ (B∪D) = (A∪C) ∩ (B∪C) ∩ (A∪D) ∩ (B∪D) ∩ (B∪D)
 
=> ((A∩B)∪(C∩D)) ∩ (A∪C) = (A∪C) ∩ (B∪C) ∩ (A∪D) ∩ (B∪D)
或，
((A∩B)∪(C∩D)) ∩ (B∪D) = (A∪C) ∩ (B∪C) ∩ (A∪D) ∩ (B∪D)

所以，

(A∩B)∪(C∩D) = ((A∩B)∪(C∩D)) ∩ (A∪C) ∩ (B∪D)
= ((A∩B)∪(C∩D)) ∩ (A∪C)
= ((A∩B)∪(C∩D)) ∩ (B∪D)

基于上述布尔等式，Q07，

snippet.sql

……
SELECT
    n1.n_name AS supp_nation,
    n2.n_name AS cust_nation,
    EXTRACT(YEAR FROM l_shipdate) AS l_year,
    l_extendedprice * (1 - l_discount) AS volume
FROM
    supplier, lineitem, orders, customer, nation n1, nation n2
WHERE
    s_suppkey = l_suppkey
    AND o_orderkey = l_orderkey
    AND c_custkey = o_custkey
    AND s_nationkey = n1.n_nationkey
    AND c_nationkey = n2.n_nationkey
    AND (
        (n1.n_name = 'ROMANIA' AND n2.n_name = 'INDONESIA')
        OR (n1.n_name = 'INDONESIA' AND n2.n_name = 'ROMANIA')
    )
    AND l_shipdate BETWEEN DATE '1995-01-01' AND DATE '1996-12-31';
……

等价改写方法为：

snippet.sql

……
SELECT
    n1.n_name AS supp_nation,
    n2.n_name AS cust_nation,
    EXTRACT(YEAR FROM l_shipdate) AS l_year,
    l_extendedprice * (1 - l_discount) AS volume
FROM
    supplier, lineitem, orders, customer, nation n1, nation n2
WHERE
    s_suppkey = l_suppkey
    AND o_orderkey = l_orderkey
    AND c_custkey = o_custkey
    AND s_nationkey = n1.n_nationkey
    AND c_nationkey = n2.n_nationkey
    AND (
        (n1.n_name = 'ROMANIA' AND n2.n_name = 'INDONESIA')
        OR (n1.n_name = 'INDONESIA' AND n2.n_name = 'ROMANIA')
    )
    AND (n1.n_name = 'ROMANIA' OR n1.n_name = 'INDONESIA')
    AND (n2.n_name = 'INDONESIA' OR n2.n_name = 'ROMANIA')
    AND l_shipdate BETWEEN DATE '1995-01-01' AND DATE '1996-12-31';
……

以上如果在执行计划层优化，则，

1. 相当于增加了两组单表条件。
2. (n1.n_name = 'ROMANIA' and n2.n_name = 'INDONESIA')or (n1.n_name = 'INDONESIA' and n2.n_name = 'ROMANIA')可以作为复杂Join条件一次执行，避免or算子拆分条件导致两次Join运算。