什麽是形式集合Formal Sets/PowerFormalSet？

lilianjie

哪位能给理解下：
& P- B' q2 q8 S7 {9 ~+ {( n, e
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'.

The only set-theoretic operations that can be performed on formal sets are union, intersection, difference and symmetric difference, and element membership testing.



& [+ m9 E2 S* p& F! r8 F1 c9 z3 Z" ZS := { 1 .. 5};
' J; o( x3 M- E4 Z  }6 X! N> P := PowerSet(S);
& U& C# A, n3 h$ s, v, C: G* DP;
# F' y9 T. `+ U8 |PFS:=PowerFormalSet(S);
PFS;
9 v2 I9 o7 w8 y% c2 Q" bF := { 2, 4 };
6 T  q4 ^5 B/ x  N+ n* f+ w8 U3 eFF := { 2/3, 4 };

  I& l( N) b# O* f$ k4 K# [) n; x F in P;
$ N: D6 m. {& G# B" MFF in P;
; [; A  r. ~  y% ~ F in PFS;
: W$ @: s# J& p( X  UFF in PFS;
Set of subsets of { 1 .. 5 }
Set of formal subsets of { 1 .. 5 }
true
false

! D- W& x5 s; b% q( g>>  F in PFS;
! W- V. x& J  i0 l; ^      ^
& A" B, g6 D& _+ t& M* S+ c2 jRuntime error in 'in': Bad argument types


>> FF in PFS;
      ^
Runtime error in 'in': Bad argument types