DIRECTORYRope,IO,AlgebraClasses;ASPowerSetStructure: CEDAR DEFINITIONS ~ BEGIN OPEN Rope, AC: AlgebraClasses;Set: TYPE = AC.Object;SetData: TYPE = LIST OF AC.Object;PowerSetStructureData: TYPE = REF PowerSetStructureDataRec;PowerSetStructureDataRec: TYPE = RECORD [universe: AC.Object -- the elements of the Structure are the subsets of universe];MakePowerSetStructure: AC.SequenceStructureConstructor;PrintName: AC.ToRopeOp;ShortPrintName: AC.ToRopeOp;IsPowerSetStructure: AC.UnaryPredicate;Universe: AC.UnaryOp;Recast: AC.BinaryOp;CanRecast: AC.BinaryPredicate;ToExpr: AC.ToExprOp;LegalFirstChar: AC.LegalFirstCharOp;Read: AC.ReadOp;FromRope: AC.FromRopeOp;ToRope: AC.ToRopeOp;Write: AC.WriteOp;MakeSet: AC.ListImbedOp;IsElement: AC.BinaryPredicate;IsSubset: AC.BinaryPredicate;Cardinality: AC.ElementRankOp;Equal: AC.BinaryPredicate;Union: AC.BinaryOp;Intersection: AC.BinaryOp;DeleteElement: AC.BinaryOp;Difference: AC.BinaryOp;MapUnaryElementOp: AC.BinaryMixedOp;END.  L  ASPowerSetStructure.mesaLast Edited by: Arnon, November 19, 1987 8:31:50 am PSTStructure Constructor: Power set of argument Structure.  Currently, only allows creation of, and can only work with, finite subsets (i.e. finite collections of elements of argument Structure).Element RepresentationThe elements of SetData are assumed to be distinct. The empty set is represented by NIL SetData.  Structure Instance DataStructure ConstructorRecord that the resulting Structure is a BooleanAlgebra.Operations on Power Set Structuresselector: universe of a Power Set StructureConversion and IO for Elements of Power Set Structures (i.e. finite sets)Element ConstructorI.e. makes a finite set belonging to a particular PowerSetStructure.Currently no checks for repetitions of elements.Does check that supplied elements actually belong to universe (recasts if necessary).data = NIL => empty set.Predicates for SetsfirstArg is an Object, and secondArg is a Set.  Returns TRUE if firstArg is an element of secondArg.firstArg and secondArg are Sets. Returns TRUE if firstArg is a subset of secondArg.Operations on SetsfirstArg is a Set, secondArg an element of it. result is firstArg - {secondArg}.  Error if secondArg not an element of firstArgfirstArg is a Set, secondArg an element of it. result is A - B.  ok if B has elements not in A.firstArg is a Set, secondArg is REF to UnaryOp on its elementStructure, result is Set of results of applications of UnaryOp to elements of firstArg.Note that, by elimination of duplicates, cardinality of result may be less than cardinality of argument.Êý  ˜ Jšœ™J™7J˜ JšœÀ™ÀJ™ šÏk	˜	Icodešœ˜Kšœ˜Kšœ˜—Ihead2šÏnœœ˜&Jšœœœœ˜'headšž™Jšœœœ˜J˜ Jš	œ	œœœœ˜"J˜ Jšœ4™4Jšœ.™.—šœ™Kšœœœ˜;šœœœ˜)Kšœ
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