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Abstractions with data

Our reference book “Structure and Interpretetion of Computer Programs”, on the chapter “2 Building Abstractions with Data”.

We concentrated in chapter 1 on computational processes and on the role of procedures in program design. We saw how to use primitive data (numbers) and primitive operations (arithmetic operations), how to combine procedures to form compound procedures through composition, conditionals, and the use of parameters, and how to abstract procedures by using define. We saw that a procedure can be regarded as a pattern for the local evolution of a process, and we classified, reasoned about, and performed simple algorithmic analyses of some common patterns for processes as embodied in procedures. We also saw that higher-order procedures enhance the power of our language by enabling us to manipulate, and thereby to reason in terms of, general methods of computation. This is much of the essence of programming.

In this chapter we are going to look at more complex data. All the procedures in chapter 1 operate on simple numerical data, and simple data are not sufficient for many of the problems we wish to address using computation. Programs are typically designed to model complex phenomena, and more often than not one must construct computational objects that have several parts in order to model real-world phenomena that have several aspects. Thus, whereas our focus in chapter 1 was on building abstractions by combining procedures to form compound procedures, we turn in this chapter to another key aspect of any programming language: the means it provides for building abstractions by combining data objects to form compound data.

Why do we want compound data in a programming language? For the same reasons that we want compound procedures: to elevate the conceptual level at which we can design our programs, to increase the modularity of our designs, and to enhance the expressive power of our language. Just as the ability to define procedures enables us to deal with processes at a higher conceptual level than that of the primitive operations of the language, the ability to construct compound data objects enables us to deal with data at a higher conceptual level than that of the primitive data objects of the language.

Consider the task of designing a system to perform arithmetic with rational numbers. We could imagine an operation add-rat that takes two rational numbers and produces their sum. In terms of simple data, a rational number can be thought of as two integers: a numerator and a denominator. Thus, we could design a program in which each rational number would be represented by two integers (a numerator and a denominator) and where add-rat would be implemented by two procedures (one producing the numerator of the sum and one producing the denominator). But this would be awkward, because we would then need to explicitly keep track of which numerators corresponded to which denominators. In a system intended to perform many operations on many rational numbers, such bookkeeping details would clutter the programs substantially, to say nothing of what they would do to our minds. It would be much better if we could ``glue together`` a numerator and denominator to form a pair – a compound data object – that our programs could manipulate in a way that would be consistent with regarding a rational number as a single conceptual unit.

The use of compound data also enables us to increase the modularity of our programs. If we can manipulate rational numbers directly as objects in their own right, then we can separate the part of our program that deals with rational numbers per se from the details of how rational numbers may be represented as pairs of integers. The general technique of isolating the parts of a program that deal with how data objects are represented from the parts of a program that deal with how data objects are used is a powerful design methodology called data abstraction. We will see how data abstraction makes programs much easier to design, maintain, and modify.

Abstractions with data

Our reference book “Structure and Interpretetion of Computer Programs”, on the chapter “2.1 Introduction to data abstraction” define very well, the elements for the “Abstractions of datas”.

In section 1.1.8, we noted that a procedure used as an element in creating a more complex procedure could be regarded not only as a collection of particular operations but also as a procedural abstraction. That is, the details of how the procedure was implemented could be suppressed, and the particular procedure itself could be replaced by any other procedure with the same overall behavior. In other words, we could make an abstraction that would separate the way the procedure would be used from the details of how the procedure would be implemented in terms of more primitive procedures. The analogous notion for compound data is called data abstraction. Data abstraction is a methodology that enables us to isolate how a compound data object is used from the details of how it is constructed from more primitive data objects.

The basic idea of data abstraction is to structure the programs that are to use compound data objects so that they operate on ``abstract data.'' That is, our programs should use data in such a way as to make no assumptions about the data that are not strictly necessary for performing the task at hand. At the same time, a ``concrete`` data representation is defined independent of the programs that use the data. The interface between these two parts of our system will be a set of procedures, called selectors and constructors, that implement the abstract data in terms of the concrete representation. To illustrate this technique, we will consider how to design a set of procedures for manipulating rational numbers.

But dataflow ?

Dataflow or abstraction with data, solve a lot or problems generated by “Abstraction with procedure”… but produce another problem, it is not really done to manage complex data computation. But very well done to manage streams of data having small interactions.

With Dataflow, if you want complex interactions between datas, you need to transform the data to “agents”. This mean the “data” have some procedures… Then we are back to the Abstractions by Procedure, not exactly in the same conditions or environment, but all the problems of this way will come back as soon as the firsts “Procedures” will be modified or updated.

Vs Evenja

If you want to see the différences between Evenja and Dataflow read Software ?, Principles, Structure and Breakthrough.

Next page of Evenja's theory, Principles.

principles/dataflow.txt · Last modified: 2022/02/21 23:34 (external edit)