算法3：子程序VarJoinsRefinement(σ, x)

输出：一组已经连接优化完毕的tgds Σ'

1: 初始化σ得到σ'

2: let σ' = φ' → ψ'

3: C_cand ← generate set of possibles candidates from σ'

4: C_v ←∅

5: repeat

6: P ← SelectPartition(C_cand, C_v)

7: σ'' ← UnifyVariables(σ', P)

8: if AskJoinsValidity(σ'') then

9: add P to C_v

10: remove P and its More rough partitions from C_cand

11: else

12: remove P from C_cand

13: end if

14: until C_cand =∅

15: Σ' ←∅

16: for all P∈C_v do

17: σ'' ← UnifyVariables(σ', P)

18: add σ'' to Σ'

19: end for

20: return Σ'