Peruse SICP 1 : Building Abstractions with Procedures

We are about to study the idea of a computational process. Computational processes are abstract beings that inhabit computers. As they evolve, processes manipulate other abstract things called data. The evolution of a process is directed by a pattern of rules called a program. People create programs to direct processes. In effect, we conjure the spirits of the computer with our spells.

Rules means program, good rules means good generation which can good world. So rules is everything.

A computational process is indeed much like a sorcerer’s idea of a spirit. It cannot be seen or touched. It is not composed of matter at all. However, it is very real. It can perform intellectual work. It can answer questions. It can affect the world by disbursing money at a bank or by controlling a robot arm in a factory. The programs we use to conjure processes are like a sorcerer’s spells. They are carefully composed from symbolic expressions in arcane and esoteric programming languages that prescribe the tasks we want our processes to perform.

A programmer is a sorcerer.

A computational process, in a correctly working computer, executes programs precisely and accurately. Thus, like the sorcerer’s apprentice, novice programmers must learn to understand and to anticipate the consequences of their conjuring. Even small errors (usually called bugs or glitches) in programs can have complex and unanticipated consequences.

Fortunately, learning to program is considerably less dangerous than learning sorcery, because the spirits we deal with are conveniently contained in a secure way. Real-world programming, however, requires care, expertise, and wisdom. A small bug in a computer-aided design program, for example, can lead to the catastrophic collapse of an airplane or a dam or the self-destruction of an industrial robot.

Master software engineers have the ability to organize programs so that they can be reasonably sure that the resulting processes will perform the tasks intended. They can visualize the behavior of their systems in advance. They know how to structure programs so that unanticipated problems do not lead to catastrophic consequences, and when problems do arise, they can debug their programs. Well-designed computational systems, like well-designed automobiles or nuclear reactors, are designed in a modular manner, so that the parts can be constructed, replaced, and debugged separately.

Programming in Lisp #

We need an appropriate language for describing processes, and we will use for this purpose the programming language Lisp. Just as our everyday thoughts are usually expressed in our natural language (such as English, French, or Japanese), and descriptions of quantitative phenomena are expressed with mathematical notations, our procedural thoughts will be expressed in Lisp. Lisp was invented in the late 1950s as a formalism for reasoning about the use of certain kinds of logical expressions, called recursion equations, as a model for computation. The language was conceived by John McCarthy and is based on his paper “Recursive Functions of Symbolic Expressions and Their Computation by Machine” (McCarthy 1960).

Despite its inception as a mathematical formalism, Lisp is a practical programming language. A Lisp interpreter is a machine that carries out processes described in the Lisp language. The first Lisp interpreter was implemented by McCarthy with the help of colleagues and students in the Artificial Intelligence Group of the MIT Research Laboratory of Electronics and in the MIT Computation Center.1 Lisp, whose name is an acronym for LIST Processing, was designed to provide symbol-manipulating capabilities for attacking programming problems such as the symbolic differentiation and integration of algebraic expressions. It included for this purpose new data objects known as atoms and lists, which most strikingly set it apart from all other languages of the period.

Lisp is a minimum PL as a foundation. And foundation is very important even though it cannot be used in the real business world.

Lisp was not the product of a concerted design effort. Instead, it evolved informally in an experimental manner in response to users’ needs and to pragmatic implementation considerations. Lisp’s informal evolution has continued through the years, and the community of Lisp users has traditionally resisted attempts to promulgate any “official” definition of the language. This evolution, together with the flexibility and elegance of the initial conception, has enabled Lisp, which is the second oldest language in widespread use today (only Fortran is older), to continually adapt to encompass the most modern ideas about program design. Thus, Lisp is by now a family of dialects, which, while sharing most of the original features, may differ from one another in significant ways. The dialect of Lisp used in this book is called Scheme.

Because of its experimental character and its emphasis on symbol manipulation, Lisp was at first very inefficient for numerical computations, at least in comparison with Fortran. Over the years, however, Lisp compilers have been developed that translate programs into machine code that can perform numerical computations reasonably efficiently. And for special applications, Lisp has been used with great effectiveness. Although Lisp has not yet overcome its old reputation as hopelessly inefficient, Lisp is now used in many applications where efficiency is not the central concern. For example, Lisp has become a language of choice for operating-system shell languages and for extension languages for editors and computer-aided design systems.

If Lisp is not a mainstream language, why are we using it as the framework for our discussion of programming? Because the language possesses unique features that make it an excellent medium for studying important programming constructs and data structures and for relating them to the linguistic features that support them. The most significant of these features is the fact that Lisp descriptions of processes, called procedures, can themselves be represented and manipulated as Lisp data. The importance of this is that there are powerful program-design techniques that rely on the ability to blur the traditional distinction between “passive” data and “active” processes. As we shall discover, Lisp’s flexibility in handling procedures as data makes it one of the most convenient languages in existence for exploring these techniques. The ability to represent procedures as data also makes Lisp an excellent language for writing programs that must manipulate other programs as data, such as the interpreters and compilers that support computer languages. Above and beyond these considerations, programming in Lisp is great fun.

1.1 The Elements of Programming #

A powerful programming language is more than just a means for instructing a computer to perform tasks. The language also serves as a framework within which we organize our ideas about processes. Thus, when we describe a language, we should pay particular attention to the means that the language provides for combining simple ideas to form more complex ideas. Every powerful language has three mechanisms for accomplishing this:

A programming language is an idea framework. Thus, it needs ideas combine ability. We call it 3 mechanisms as below:

• primitive expressions, which represent the simplest entities the language is concerned with,

Definition of minimal element (Data and procedures)

• means of combination, by which compound elements are built from simpler ones, and

Definition of element combination.
What is the host of combination?

It should be Expression but Procedure. Procedure is negative but expression is the positive one which is more close to the higher dimension engine which is the interpreter.

Interpreter from surface to deep:
element(data/procedure) ~ expression ~ scheme interpreter ~ physical interpreter ~ relay ~ 光电效应(Interpreter/Rule of nature) ~ electric energy(Energy of nature) ~ meta energy(The One)

What is the essence of interpreter?
The answer is that the information cover the energy.
The information can be host as ether physical or un-physical.
And the information transfer energy to another form which means transform.
Transform also means entropy reduction.

More deeper concepts: Information and energy.
What is the essence of ENERGY?

How is information generated?

• Expression Expression (Data data data) in which the first data also has combination capacity but with an runtime exception : cannot call. So the capacity comes from expression not procedure itself, data could be combined at first unit an runtime exception. Call means evaluate , evaluate means do combine, combine means transformation which follows the wirelines of paraments of procedure.

(3 1 1)
SchemeError: Cannot call 3

Current Eval Stack:
-------------------------
0: (3 1 1)

• means of abstraction, by which compound elements can be named and manipulated as units.

Definition of definition (packaging/index/naming)

In programming, we deal with two kinds of elements: procedures and data. (Later we will discover that they are really not so distinct.) Informally, data is “stuff” that we want to manipulate, and procedures are descriptions of the rules for manipulating the data. Thus, any powerful programming language should be able to describe primitive data and primitive procedures and should have methods for combining and abstracting procedures and data.

Data vs Procedure #

Data and Procedures are element

Data, in which, it is made by procedure.
Procedure, in which, it is made by data.
Infinitely.

In this chapter we will deal only with simple numerical data so that we can focus on the rules for building procedures.4 In later chapters we will see that these same rules allow us to build procedures to manipulate compound data as well.

1.1.1 Expressions #

One easy way to get started at programming is to examine some typical interactions with an interpreter for the Scheme dialect of Lisp. Imagine that you are sitting at a computer terminal. You type an expression, and the interpreter responds by displaying the result of its evaluating that expression.

One kind of primitive expression you might type is a number. (More precisely, the expression that you type consists of the numerals that represent the number in base 10.) If you present Lisp with a number

486
the interpreter will respond by printing5
486

Expressions representing numbers may be combined with an expression representing a primitive procedure (such as + or *) to form a compound expression that represents the application of the procedure to those numbers. For example:

(+ 137 349)
486
(- 1000 334)
666
(* 5 99)
495
(/ 10 5)
2
(+ 2.7 10)
12.7

Expressions such as these, formed by delimiting a list of expressions within parentheses in order to denote procedure application, are called combinations. The leftmost element in the list is called the operator, and the other elements are called operands. The value of a combination is obtained by applying the procedure specified by the operator to the arguments that are the values of the operands.

The convention of placing the operator to the left of the operands is known as prefix notation, and it may be somewhat confusing at first because it departs significantly from the customary mathematical convention. Prefix notation has several advantages, however. One of them is that it can accommodate procedures that may take an arbitrary number of arguments, as in the following examples:

(+ 21 35 12 7)
75
(* 25 4 12)
1200

No ambiguity can arise, because the operator is always the leftmost element and the entire combination is delimited by the parentheses.

A second advantage of prefix notation is that it extends in a straightforward way to allow combinations to be nested, that is, to have combinations whose elements are themselves combinations:

(+ (* 3 5) (- 10 6))
19

There is no limit (in principle) to the depth of such nesting and to the overall complexity of the expressions that the Lisp interpreter can evaluate. It is we humans who get confused by still relatively simple expressions such as

(+ (* 3 (+ (* 2 4) (+ 3 5))) (+ (- 10 7) 6))

which the interpreter would readily evaluate to be 57. We can help ourselves by writing such an expression in the form

(+ (* 3
      (+ (* 2 4)
         (+ 3 5)))
   (+ (- 10 7)
      6))

following a formatting convention known as pretty-printing, in which each long combination is written so that the operands are aligned vertically. The resulting indentations display clearly the structure of the expression.6

Even with complex expressions, the interpreter always operates in the same basic cycle: It reads an expression from the terminal, evaluates the expression, and prints the result. This mode of operation is often expressed by saying that the interpreter runs in a read-eval-print loop. Observe in particular that it is not necessary to explicitly instruct the interpreter to print the value of the expression.7

1.1.2 Naming and the Environment #

A critical aspect of a programming language is the means it provides for using names to refer to computational objects. We say that the name identifies a variable whose value is the object.

In the Scheme dialect of Lisp, we name things with define. Typing

(define size 2)

causes the interpreter to associate the value 2 with the name size.8 Once the name size has been associated with the number 2, we can refer to the value 2 by name:

size
2
(* 5 size)
10

Here are further examples of the use of define:

(define pi 3.14159)
(define radius 10)
(* pi (* radius radius))
314.159
(define circumference (* 2 pi radius))
circumference
62.8318