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'.
5 G9 T5 O- |' S* f: S
The only set-theoretic operations that can be performed on formal sets are union, intersection, difference and symmetric difference, and element membership testing.
* |  H/ i; }8 a
- y# m2 k, ?0 q( O7 @0 X& E* B/ Z; i

& c. z& \% y4 t' ~5 }0 @: iS := { 1 .. 5};
; A- @+ q7 u; R( I> P := PowerSet(S);
( J6 }* O( e* x  W6 HP;
  b" |+ ]* `$ jPFS:=PowerFormalSet(S);
PFS;
' v  Z6 ^0 w- v& {7 j' `1 _: ?F := { 2, 4 };
& e8 f9 F, B9 Y7 H6 V) mFF := { 2/3, 4 };

F in P;
" A1 \! k5 I' c3 t/ x; U- @+ RFF in P;
2 `4 O) j/ p" @$ c) k' x1 a F in PFS;
* `4 ?. y" |2 u9 ~0 OFF in PFS;
, v$ N, s& Y; T' y% ^. WSet of subsets of { 1 .. 5 }
Set of formal subsets of { 1 .. 5 }
true
false

- X! J) a+ L3 u! M, m0 N# s! x>>  F in PFS;
8 V( F+ W4 X+ }/ }/ N9 w1 q1 V      ^
* o6 _8 d$ {; u( o% K' I  ORuntime error in 'in': Bad argument types


>> FF in PFS;
8 h2 R' e* a7 i$ [      ^
$ s9 E# D% g2 X/ S3 S& pRuntime error in 'in': Bad argument types