什麽是形式集合Formal Sets/PowerFormalSet？

lilianjie

哪位能给理解下：
% l( |4 N- q0 S& p
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.


) R0 ~; J  K+ H
S := { 1 .. 5};
* l" k# l3 E7 X$ C> P := PowerSet(S);
7 V  O$ C. N, S; ?5 O/ M2 IP;
PFS:=PowerFormalSet(S);
PFS;
F := { 2, 4 };
FF := { 2/3, 4 };

F in P;
2 m5 T1 s/ p: X. F! d5 ~FF in P;
F in PFS;
" k' h2 R# O! n$ j6 XFF in PFS;
/ U8 E. j; P7 Q7 I2 I# W7 F+ ASet of subsets of { 1 .. 5 }
* A7 _" F; o" V6 o  V+ LSet of formal subsets of { 1 .. 5 }
true
false

: Q; l8 p; D4 p% e" ?>>  F in PFS;
      ^
Runtime error in 'in': Bad argument types

6 [! a8 z# {  f( m
>> FF in PFS;
# v- X6 V/ `0 B+ x: ]3 }9 w. S      ^
; H# v: J% Q% G5 }3 yRuntime error in 'in': Bad argument types