By Manoochehr Azmoodeh (auth.)
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Additional resources for Abstract Data Types and Algorithms
Thus a lot of time and effort is saved when developing a large program. This mechanism also hides details of the implementation of each module, and only makes accessible the operations which can be performed on an ADT. Unfortunately, the Pascal language does not, in general, encompass the concept of a module. Other languages, such as Modula-2 and Ada, have facilities for defining modules. However, certain implementations of Pascal do provide some limited but useful mechanisms for defining modules.
As an example, let us consider the 'push' operation. push and a. push respectively. push(f(s),a). We assume that each data type on its own is consistent - that is, the pre-condition and post-condition of each operation do not contradict the invariances of that data type. push(s,a)) is also true. push(f(s),a)) must also be true. Formally, two things must be proved. (a) V s E a_stack: pre-condition(s. push(s, a)) (b) V s E a_stack: pre-condition( s. push( f( s), a) and post-condition( a. push(s,a)) =last< n Therefore (a) is proved.
In the context of a large program, all we need to know about this operation is that it adds a number at the end of a list. Information regarding its representation in the memory etc. is totally irrelevant from this perspective. Of course, these issues must be considered at some stage in order to optimise the way memory, registers, the ALU and the CU are used. But these factors need not get into the design stage. So, if we can reduce the amount of information needed at any point in time by discarding many irrelevant details, the task of developing a program becomes much easier.
Abstract Data Types and Algorithms by Manoochehr Azmoodeh (auth.)