什麽是形式集合Formal Sets/PowerFormalSet？

lilianjie

哪位能给理解下：
' U  i! I$ z' ~9 c
- P* R- s! ?1 C/ Q7 @Formal Sets
4 z7 y/ H  R0 b2 E. qA formal set consists of the subset of elements of some carrier set (structure) on which a certain predicate assumes the value `true'.

% I- Q# |0 h/ d+ f: J) S  VThe only set-theoretic operations that can be performed on formal sets are union, intersection, difference and symmetric difference, and element membership testing.



$ {  l3 S5 }1 C" L( w( QS := { 1 .. 5};
$ ]# L$ L+ x& e) M> P := PowerSet(S);
" L: M5 \4 }* J* J  `& @  O8 GP;
PFS:=PowerFormalSet(S);
+ n9 Q- A# B" i: {3 j4 \PFS;
F := { 2, 4 };
. q7 H" j: w9 ]1 u# PFF := { 2/3, 4 };

! |$ f; E/ T/ X3 M2 l F in P;
3 O+ d0 E1 C8 A5 j/ r* GFF in P;
2 y, s+ Q0 R! G! \& }3 n+ _ F in PFS;
FF in PFS;
Set of subsets of { 1 .. 5 }
) V' u7 @5 i2 T8 u2 SSet of formal subsets of { 1 .. 5 }
true
8 [. k% C0 j8 G0 K, W- B7 Cfalse
& K. n* ?/ x9 f+ x
>>  F in PFS;
1 D& Q1 a0 ?1 C6 S. A" p      ^
) ^. O. h: e- s& |2 }Runtime error in 'in': Bad argument types
7 b0 u. q6 X. L) c5 z  h

>> FF in PFS;
      ^
9 P  A( p, ?6 ?" p- P0 SRuntime error in 'in': Bad argument types