什麽是形式集合Formal Sets/PowerFormalSet？

lilianjie

哪位能给理解下：

Formal Sets
A formal set consists of the subset of elements of some carrier set (structure) on which a certain predicate assumes the value `true'.

4 |; w2 g& {( S) j9 YThe only set-theoretic operations that can be performed on formal sets are union, intersection, difference and symmetric difference, and element membership testing.



. ]& I/ c! [1 h  n' r6 f* v6 mS := { 1 .. 5};
$ ]1 q2 s! l2 i3 }- m! @) X> P := PowerSet(S);
P;
4 [0 L, N+ |4 R( `6 t  W0 GPFS:=PowerFormalSet(S);
8 y, R+ D* L  E5 ?PFS;
F := { 2, 4 };
FF := { 2/3, 4 };

- H. T2 y* r' ? F in P;
2 ?+ M  R+ O* F* EFF in P;
F in PFS;
- w! A: O- c6 K1 t5 x& cFF in PFS;
Set of subsets of { 1 .. 5 }
Set of formal subsets of { 1 .. 5 }
true
false
7 k# L0 l3 I2 N) |, o7 {
>>  F in PFS;
% _% h+ [* m' q5 w      ^
Runtime error in 'in': Bad argument types
$ R( f/ Y; [* K" |3 X8 D

>> FF in PFS;
/ C7 }7 {  b: O  z7 Q! l      ^
' X  r- m! z4 d! e9 c* A& dRuntime error in 'in': Bad argument types