.TH SETS 2.SH NAMESets \-sets of non-negative integers.SH SYNOPSIS.EXinclude    "sets.m";\fIOR\fP include "sets32.m";sets := load Sets Sets->PATH;A, B: import Sets; Sets: adt {    init:       fn();    set:        fn(): Set;    str2set:    fn(str: string): Set;    bytes2set:  fn(d: array of byte): Set;    Set: adt {        # opaque data         X:          fn(s1: self Set, op: int, s2: Set): Set;        add:        fn(s: self Set, n: int): Set;        addlist:    fn(s: self Set, ns: list of int): Set;        del:        fn(s: self Set, n: int): Set;        invert:     fn(s: self Set): Set;         eq:         fn(s1: self Set, s2: Set): int;        holds:      fn(s: self Set, n: int): int;        isempty:      fn(s: self Set): int;        msb:        fn(s: self Set): int;        limit:      fn(s: self Set): int;         str:        fn(s: self Set): string;        bytes:      fn(s: self Set, n: int): array of byte;    };};.EE.SH DESCRIPTION.PPThe.B Setsmodule provides routines for manipulating setsof small non-negative integers. There are currentlytwo implementations available:the implementation declared in.B sets32.mstores sets of numbers from 0 to 31 inclusive;the implementation in.B sets.mstores arbitrary sets of non-negative integers.The description given is for the more generalimplementation; behaviour of the other is undefinedif an integer higher than 31 is used..PP.B Initmust be called first, to allow.B Setsto initialise its internal state..B Setreturns a new set, containing nothing..B Str2setconverts a string to a new set; the stringshould have been created with.BR Set.str() ..B Bytes2setconverts an array of bytes,.IR d ,as returned by.BR Set.bytes() ,to a new set..PPNote that all set operations are copy operations;none change an existing set..TP 10.IB s1 .X(\fIop\fP,\ \fIs2\fP)Returns a new set, the result of combining.I s1and.I s2according to boolean operator.IR op ..I Opcan be any bitwise boolean combination of thetwo constants.B Aand.BR B ,defined in the module. Notionally, eachset is an infinitely long string of bits, eachbit representing a non-negative integer:zero if the integer is present, and one if absent.For each corresponding bit in.I s1and.IR s2 ,.B Xsets a corresponding bit in the returned setaccording to the calculation.IR "s1 op s2" ..TP.IB s .add(\fIn\fP)Returns the set.I swith.I nadded..TP.IB s .addlist(\fIns\fP).B Addlistis the same as calling.B addon each member of the list.IR ns ,but somewhat more efficient..TP.IB s .del(\fIn\fP)Returns.I swith.I nremoved..TP.IB s .invert().B Invertreturns a set holding all non-negative integersother than those already in.IR s .Hence.B set().invert()holds all non-negative integers..TP.IB s1 .eq(\fIs2\fP)Returns non-zero if.I s1is identical to.IR s2 ..TP.IB s .holds(\fIn\fP)Returns non-zero if.I sholds.I nas a member..TP.IB s .isempty()Returns non-zero if.I sholds no members..TP.IB s .msb()Returns the "most significant bit": the membershipstatus of all members that have not been explicitlyset. For example,.B set().msb()is 0;.B set().invert().msb()is 1..TP.IB s .limit()If.IB s .msb()is zero,.IB s .limit()returns one more than the largest member contained in.IR s ,otherwise it returns one more than the largest member.I notcontained in.IR s .Thus.B set().limit()yields 0,and.B set().invert().del(5).limit()yields 6..TP.IB s .str()Returns a string corresponding to.IR s .The format is.IB hexdigits : msb\fR,\fPwhere.I hexdigitsgive the least significant members of the set,most significant on the left, in hexadecimal format;.I msbgives the padding bit that fills the rest of the set.Note that this format is compatible between thetwo implementations..TP.IB s .bytes(\fIn\fP)Returns a packed byte representaton of.I s .The array is held in little-endian order,with the topmost bit of the top byteholding the msb of the set.The array returned will contain at least.I nbytes..SH EXAMPLESGiven two sets,.I s1and.IR s2 ,.IB s1 ".X(A&B," " s2" )gives their intersection;.IB s1 ".X(A|B," " s2" )their union;.IB s1 ".X(A&~B," " s2" )gives the set of all members of.I s1that aren't in.IR s2 ;.IB s1 ".X(~(A|B), " s2 )gives the set of all integers in neither.I s1nor.IR s2 ..PP.EX	sys->print("%s\en", set().addlist(1::2::5::nil)		.invert().X(A|B, set().add(2)).str());.EEproduces the string.RB `` dd:1 '',corresponding to the set of all non-negativeintegers except 1 and 5.