2.2 Hierarchical Data and the Closure Property

Printer-friendly versionPrinter-friendly version

As we have seen, pairs provide a primitive “glue” that we can use to construct compound data objects. Figure 2.2 shows a standard way to visualize a pair — in this case, the pair formed by (cons 1 2). In this representation, which is called box-and-pointer notation, each object is shown as a pointer to a box. The box for a primitive object contains a representation of the object. For example, the box for a number contains a numeral. The box for a pair is actually a double box, the left part containing (a pointer to) the car of the pair and the right part containing the cdr.

We have already seen that cons can be used to combine not only numbers but pairs as well. (You made use of this fact, or should have, in doing exercises 2.2 and 2.3.) As a consequence, pairs provide a universal building block from which we can construct all sorts of data structures. Figure 2.3 shows two ways to use pairs to combine the numbers 1, 2, 3, and 4.

The ability to create pairs whose elements are pairs is the essence of list structure’s importance as a representational tool. We refer to this ability as the closure property of cons. In general, an operation for combining data objects satisfies the closure property if the results of combining things with that operation can themselves be combined using the same operation.[6] Closure is the key to power in any means of combination because it permits us to create hierarchical structures — structures made up of parts, which themselves are made up of parts, and so on.

From the outset of chapter 1, we’ve made essential use of closure in dealing with procedures, because all but the very simplest programs rely on the fact that the elements of a combination can themselves be combinations. In this section, we take up the consequences of closure for compound data. We describe some conventional techniques for using pairs to represent sequences and trees, and we exhibit a graphics language that illustrates closure in a vivid way.[7]

[6] The use of the word “closure” here comes from abstract algebra, where a set of elements is said to be closed under an operation if applying the operation to elements in the set produces an element that is again an element of the set. The Lisp community also (unfortunately) uses the word “closure” to describe a totally unrelated concept: A closure is an implementation technique for representing procedures with free variables. We do not use the word “closure” in this second sense in this book. [back]
[7] The notion that a means of combination should satisfy closure is a straightforward idea. Unfortunately, the data combiners provided in many popular programming languages do not satisfy closure, or make closure cumbersome to exploit. In Fortran or Basic, one typically combines data elements by assembling them into arrays — but one cannot form arrays whose elements are themselves arrays. Pascal and C admit structures whose elements are structures. However, this requires that the programmer manipulate pointers explicitly, and adhere to the restriction that each field of a structure can contain only elements of a prespecified form. Unlike Lisp with its pairs, these languages have no built-in general-purpose glue that makes it easy to manipulate compound data in a uniform way. This limitation lies behind Alan Perlis’s comment in his foreword to this book: “In Pascal the plethora of declarable data structures induces a specialization within functions that inhibits and penalizes casual cooperation. It is better to have 100 functions operate on one data structure than to have 10 functions operate on 10 data structures.” [back]

Comments

Beats By Dre Monster

SYNC by 50 If you’re like most of us, you woke up one morning this week and realized it’s almost December,SYNC by 50 and the holidays are swiftly approaching. STREET by 50 And, of course, you still don’t know what to get a few people on your list.We all know that headphones are a dime a dozen. STREET by 50 But a headphone that receives equal points for style and functionality, however, is a rare find. sms by 50 Some of our friends in the press know SMS Audio headphones fit the bill, sms by 50 and recommend you put them on your holiday shopping list this year: Beats By Dre Monster Rolling Stone included the limited edition Yellow STREET by 50 over-ear headphones in its 2012 holiday gift guide featured in the December issue.Beats By Dre MonsterWhat did Rolling Stone have to say about SMS Audio?
http://www.smsby50-beatsbydre.com/

三便宝

痩身1号:http://www.china-seiryokuzai.com/view/ssyhmtx.html
ED改善:http://www.china-seiryokuzai.com/class/ED-Improvement.html
三体牛鞭:http://www.china-seiryokuzai.com/view/santiniubian.html
三體牛鞭:http://www.china-seiryokuzai.com/view/santiniubian.html
花痴:http://www.china-seiryokuzai.com/view/huachi.html
蟻力神:http://www.china-seiryokuzai.com/view/yilishen.html
紅蜘蛛:http://www.china-seiryokuzai.com/view/nyhcpj.html
三便宝:http://www.china-seiryokuzai.com/view/sanbianbao.html
巨人倍増:http://www.china-seiryokuzai.com/view/jurenbeizenggouqi(4).html
威哥王:http://www.china-seiryokuzai.com/view/weigwang.html
勃起促進:http://www.china-seiryokuzai.com/class/Penis-Erectile.html
精力剤:http://www.china-seiryokuzai.com/class/energy.html
日本秀身堂:http://www.china-seiryokuzai.com/view/ribenxiushentang.html
法国性奴:http://www.china-seiryokuzai.com/view/SexSlave.html
西班牙蒼蝿水:http://www.china-seiryokuzai.com/view/xbycys.html
三便宝:http://www.china-seiryokuzai.com/view/sanbianbao.html
 媚薬:http://www.china-seiryokuzai.com/class/Aphrodisiac.html

巨人倍増

巨人倍増:http://www.china-seiryokuzai.com/view/jurenbeizenggouqi(4).html
威哥王:http://www.china-seiryokuzai.com/view/weigwang.html
キョジンバイゾウ:http://www.china-seiryokuzai.com/view/jurenbeizenggouqi.html
狼一号:http://www.china-seiryokuzai.com/view/langyihao.html
花痴:http://www.china-seiryokuzai.com/view/huachi.html
紅蜘蛛:http://www.china-seiryokuzai.com/view/nyhcpj.html
新曲美痩身:http://www.china-seiryokuzai.com/view/xqm.html
ウェイカワン:http://www.china-seiryokuzai.com/view/weigwang.html
イカオウ:http://www.china-seiryokuzai.com/view/sbl.html
精力剤:http://www.china-seiryokuzai.com/class/energy.html
韓国痩身一号:http://www.china-seiryokuzai.com/view/ssyhmtx.html
 蟻力神:http://www.china-seiryokuzai.com/view/yilishen.html

2.2 Hierarchical Data and the Closure Property | SICP in Clojure

Spot on with this write-up, I truly believe that this web
site needs far more attention. I’ll probably be back again to read through more,
thanks for the advice!

s attention to itself and away in the topic; the process of writing needs to be transparent on the reader.
A seasoned and professional writer is surely an assigned being investigating extensively around the subject at hand.

best shampoo for dry damaged hair clarifying This gives you additional exposure and possibly more
traffic too. It is not just the words, but also the formatting,
spelling and grammatical errors that always plague the normal student

Post new comment

  • Web page addresses and e-mail addresses turn into links automatically.
  • Allowed HTML tags: <a> <em> <strong> <cite> <code> <pre> <hr> <ul> <ol> <li> <dl> <dt> <dd> <img>
  • Lines and paragraphs break automatically.
  • Adds typographic refinements.

More information about formatting options