notes multiplyfunctionmultiply two complex numbers ib and ib preconditionno precondition post conditiona ia ib ia ib abstract data type (adtis mathematical model with collection of operations defined on that model sets of integerstogether with the operations of unionintersection and set differenceform simple example of an adt the adt encapsulates data type in the sense that the definition of the type and all operations on the type can be localized and are not visible to the users of the adt to the usersjust the declaration of the adt and its operations are important abstract data type (adt framework for an object interface what kind of stuff it' be made of (no details) what kind of messages it would receive and kind of action it'll perform when properly triggereddo_this ( conceptualization phase also_this ( object do_that ( from this we figure out object make-up (in terms of data object interface (what sort of messages it would handle? how and when it should act when triggered from outside (public triggerand by another object friendly to itthese concerns lead to an adt definition for the object an abstract data type (adtis set of data items and the methods that work on them an implementation of an adt is translation into statements of programming languageof the declaration that defines variable to be of that adtplus procedure in that language for each operation of the adt an implementation chooses data structure to represent the adteach data structure is built up from the basic data types of the underlying programming language thusif we wish to change the implementation of an adtonly the procedures implementing the operations would change this change would not affect the users of the adt although the terms 'data type''data structureand 'abstract data typesound alikethey have different meanings in programming languagethe data type of variable is the set of values that the variable may assume for examplea variable of type boolean can assume either the value true or the value falsebut no other value an abstract data type is mathematical modeltogether with various operations defined on the model as we have indicatedwe shall design algorithms in terms of adtsbut to implement an algorithm in given programming language lovely professional university