什麽是形式集合Formal Sets/PowerFormalSet？

lilianjie

哪位能给理解下：
4 O" r4 @" k' Q+ B7 {* Y
8 ^( h, C+ j- S( p: o/ B7 b- wFormal 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 w& x9 l# S1 d* J) a( RThe only set-theoretic operations that can be performed on formal sets are union, intersection, difference and symmetric difference, and element membership testing.


; r- q. Z! q/ `6 _
S := { 1 .. 5};
/ B. k5 `: H: r" c+ W> P := PowerSet(S);
1 k# u- e- V7 y6 nP;
PFS:=PowerFormalSet(S);
1 t/ y$ k2 M5 E  ~# l: TPFS;
F := { 2, 4 };
FF := { 2/3, 4 };
: P  q4 T, q" f: _1 d, W$ K! `1 x
F in P;
! q/ d& a3 A9 t- Q8 `FF in P;
4 l5 E6 f7 p) m1 z5 `( h) ]8 o F in PFS;
FF in PFS;
$ B$ k; `' t/ T, D9 l* fSet of subsets of { 1 .. 5 }
Set of formal subsets of { 1 .. 5 }
$ t) o8 y2 X% T; R( _2 [7 strue
false
/ U+ J# Y. s$ ~: b" ~& i9 V
( J0 _0 K: {6 [>>  F in PFS;
      ^
  f1 B" B% F, ?Runtime error in 'in': Bad argument types
  i5 }) n# R. ?! z% r

>> FF in PFS;
/ X6 H6 f& w8 m/ f, v) v* x      ^
Runtime error in 'in': Bad argument types