TweetFollow Us on Twitter

Draw Towers
Volume Number:1
Issue Number:7
Column Tag:STRUCTURED PRogramming in Modula-2

Draw the Towers of Hanoi

By John Bogan

This month we will explore three items. First, we will continue to introduce the elements of Software Engineering in a historical perspective. Second, we will discuss why Modula-2 is not a hackers’ language and finally, we will look at a sample program that uses the Mac ROM to draw the starting position for the Towers of Hanoi.

A New Direction

Last month we saw that Software Engineering is capable of being abused as well as being able to provide important insights into the process of building good computer software. By the late 1960’s the Software Engineers had, in effect, dictated that COBOL would be the primary language of the FORTUNE 1000 probably until the end of the century. Most microcomputer programmers faced with the prospect of coding in COBOL would shudder in terror at the thought.

In 1968 Software Engineering took a turn for the better when a famous and well regarded European computer scientist lit a fire under the COBOL and FORTRAN programming community, a fire whose embers still smolder and flare up to this day. The scientist was E.W. Dijkstra and the arson was committed in the Communications of the ACM with a letter entitled “GOTO Statement Considered Harmful”. In this letter Dijkstra observed that after having read a multitude of programs in a variety of languages that the quality of a program was inversely proportional to the number of GOTO statements in that program. The graph below illustrates this discovery.

The idea is simple ... jumping around a program with branching statements leads to unreadable program texts (known in the trade as spaghetti code) which are next to impossible to debug or for a third party to pick up and read. Since ALGOL-60 (the European’s favorite language) has advanced control structures which permits GOTOless programming and FORTRAN doesn’t, the battle lines were drawn. Letter after letter poured into the journals feeding the flames.

Finally in 1972 in an effort to quell the controversy Dijkstra together with Dahl and Hoare published a book on just how to write high quality programs without using the dangerous GOTO statement. This book, Structured Programming, estab- lished once and for all that GOTOs are redundant. Every sequential program- ming task can be accomplished with a combination of three constructs.

• sequence:

BEGIN ... s1 ... s2 ... s3 ... END

• iteration:

WHILE c1 DO ... s1 ... ENDWHILE

• conditional:


If acceptance in the curriculum of the worlds’ Universities’ Computer Science Departments is a valid measure then Structured Programming is an overwhelming success. Only those programmers corrupted by traditional BASIC or Assembler still grasp at the past and argue the merits of the GOTO. Meanwhile the course of Software Engineering was changed forever. An example of this change is Modula-2. This language is rich in structured control statements and does not support the GOTO at all. There are no statement labels in Modula-2 and while it is possible to write poor code in Modula it is impossible to write spaghetti code.

The structured control statements supported by Modula are the statement sequence, the WHILE ... DO, the REPEAT ... UNTIL, the FOR ... TO ... BY ... DO, the LOOP ... EXIT, the IF ... THEN ... ELSIF, the CASE ... OF and the WITH ... DO statements.

What is Structured?

In some ways this is a very difficult question to answer. For adherents of the Structured Techniques the concept of “Structured” is very much like the Bible is to Jerry Falwell. It is the guiding light, the one true path to paradise, the blessed and final word on how to think about solving complex logical problems.

A slightly more dispassionate view might produce the following definition of structured - a philosophy for solving problems which attempts to conserve scarce resources by arriving at the perfect solution in the fewest attempts by following a plan.

Why Plan When You Can Hack?

The idea of a plan is very important in understanding the Structured Techniques, Software Engineering and Modula-2. It also illustrates why Modula-2 is not particularly well suited for hacking. Most hackers I have known use the technique of incremental discovery or trial by error. In other words programs just grow from line 1 until the last bell and whistle is debugged. Assembly language and to a lesser extent C are well suited for this type of programming. Modula-2 most definitely is not. As we will see in future columns the quaility of a Modula-2 program is dependent on the quality of the detailed planning that occurs before the first line of code is written. In many ways this dependence on upfront planning is a distinct disadvantage for learning a new and unique system like the Mac. So many of the techniques peculiar to the Mac (such as the entire user interface or resources or Quickdraw) are best approached and mastered by trial and error hacks. When you combine this reality with the compile-link-execute overhead of Modula-2 it should be obvious why Modula-2 is not particularly suited to casual hacking. A good strategy for making the best use of Modula-2 would be to learn the Mac with Apple’s interpreted Pascal and then to translate these programs into the much faster Modula-2. As we progress in these columns we will see just how close Modula and Pascal are to each other so this suggestion won’t seem so painful. The bottom line is that Modula-2 is not a language for the seat-of-the-pants hacker.

This Month’s Code

The piece of Modula-2 code that follows is primarily useful because it shows how to access the Mac ROM on a 128K machine. The Quickdraw calls used are SetRect, PaintRect and PaintRoundRect. You should be aware that the method of specifying ROM calls is different for a 512K box. Also it should be noted that the data types VHSelect, Point and Rect could have been imported blindly instead of spelled out but then their internal structures would have been hidden and the topic of information hiding in Modula-2 is an advanced and complex issue.

   (* build starting position for Hanoi Towers *)

   FROM Terminal IMPORT ClearScreen;
   FROM InOut IMPORT WriteString, ReadCard, WriteLn;
   (* data structures for Quickdraw calls *)
      VHSelect = (v,h);
      Point = RECORD
                 CASE INTEGER OF
     0: v: INTEGER;
        h: INTEGER;
    |1: vh: ARRAY VHSelect OF INTEGER;
  END; (* CASE *)
       END; (* RECORD *)
      Rect = RECORD
                CASE INTEGER OF
    0: top: INTEGER;
       left: INTEGER;
       bottom: INTEGER;
       right: INTEGER;
   |1: topLeft: Point;
       botRight: Point;
  END; (* CASE *)
              END; (* RECORD *)
     CX = 355B;
     QuickDraw1ModNum = 2; (* absolute module number 
        of QuickDraw1 *)
      r: Rect; NumDisks: CARDINAL;
   PROCEDURE SetRect (VAR r: Rect; left,top,right,bottom: INTEGER);
      CODE CX; QuickDraw1ModNum; 51 END SetRect;
   PROCEDURE PaintRect  (r: Rect);
      CODE CX; QuickDraw1ModNum; 62 END PaintRect;
   PROCEDURE PaintRoundRect(r: Rect; ovWd, ovHt: INTEGER);
      CODE CX; QuickDraw1ModNum; 67 END PaintRoundRect;
   PROCEDURE DrawBase;
  BaseLeft = 36;
  BaseTop = 261;
  BaseRight = 476;
  BaseBottom = 270;
   END DrawBase;
   PROCEDURE DrawPosts;
         PostTop = 144;
  PostBottom = 261;
  PostWidth = 6;
  HalfPostWidth = PostWidth DIV 2;
  PostPosition = 128;
         n, PostLeft, PostRight: INTEGER;
      WHILE n <= 3 DO
  PostLeft := (PostPosition * n) - HalfPostWidth;
  PostRight := PostLeft + PostWidth;
  n:= n + 1;
      END; (* WHILE *)
   END DrawPosts;
   PROCEDURE DrawVarDisks(numberofdisks: CARDINAL);
         bigdiskleft = 128 - 60;
  bigdisktop = 261 - 12;
  bigdiskright = 128 + 60;
  bigdiskbottom = 261;
  deltalength = 5;
  deltadepth = 12;
      VAR leftedge, topedge, rightedge, bottomedge: INTEGER;
          i: CARDINAL;
      IF (numberofdisks > 2) AND (numberofdisks < 10)
     leftedge := bigdiskleft; topedge := bigdisktop;
     rightedge := bigdiskright; bottomedge := bigdiskbottom;
     FOR i := 1 TO numberofdisks - 1 DO
        leftedge := leftedge + deltalength;
        topedge := topedge - deltadepth;
        rightedge := rightedge - deltalength;
        bottomedge := bottomedge - deltadepth;
     END; (* FOR *)
  END; (* IF *)
   END DrawVarDisks;
      WriteString(“Enter number of disks (between 3 to 9)”);
      WriteString(“To quit - enter number out of range”);
   END GetInput;
   PROCEDURE InitGraphics(NumberofDisks: CARDINAL);
   END InitGraphics;
   PROCEDURE ExecuteTowers;
      FOR Delay := 1 TO 30000 DO  END; (* FOR *)
   END ExecuteTowers;
   WHILE (NumDisks >= 3) AND (NumDisks <= 9) DO
   END; (* WHILE *)
END Hanoi.


Community Search:
MacTech Search:

Software Updates via MacUpdate

World of Tanks Generals guide - Tips and...
World of Tanks Generals is a brand new card game by the developer behind the World of Tanks shooter franchise. It plays like a cross between chess and your typical card game. You have to keep in consideration where you place your tanks on the board... | Read more »
TruckSimulation 16 guide: How to succeed...
Remember those strangely enjoyable truck missions in Grand Theft Auto V whereit was a disturbing amount of fun to deliver cargo? TruckSimulation 16 is reminiscent of that, and has you play the role of a truck driver who has to deliver various... | Read more »
The best GIF making apps
Animated GIFs have exploded in popularity recently which is likely thanks to a combination of Tumblr, our shorter attention spans, and the simple fact they’re a lot of fun. [Read more] | Read more »
The best remote desktop apps for iOS
We've been sifting through the App Store to find the best ways to do computer tasks on a tablet. That gave us a thought - what if we could just do computer tasks from our tablets? Here's a list of the best remote desktop apps to help you use your... | Read more »
Warhammer 40,000: Freeblade guide - How...
Warhammer 40,000: Freebladejust launched in the App Store and it lets you live your childhood dream of blowing up and slashing a bunch of enemies as a massive, hulking Space Marine. It's not easy being a Space Marine though - and particularly if... | Read more »
Gopogo guide - How to bounce like the be...
Nitrome just launched a new game and, as to be expected, it's a lot of addictive fun. It's called Gopogo, and it challenges you to hoparound a bunch of platforms, avoiding enemies and picking up shiny stuff. It's not easy though - just like the... | Read more »
Sago Mini Superhero (Education)
Sago Mini Superhero 1.0 Device: iOS Universal Category: Education Price: $2.99, Version: 1.0 (iTunes) Description: KAPOW! Jack the rabbit bursts into the sky as the Sago Mini Superhero! Fly with Jack as he lifts impossible weights,... | Read more »
Star Wars: Galaxy of Heroes guide - How...
Star Wars: Galaxy of Heroes is all about collecting heroes, powering them up, and using them together to defeat your foes. It's pretty straightforward stuff for the most part, but increasing your characters' stats can be a bit confusing because it... | Read more »
The best cooking apps (just in time for...
It’s that time of year again, where you’ll be gathering around the dinner table with your family and a huge feast in front of you. [Read more] | Read more »
Square Rave guide - How to grab those te...
Square Rave is an awesome little music-oriented puzzle game that smacks of games like Lumines, but with its own unique sense of gameplay. To help wrap your head around the game, keep the following tips and tricks in mind. [Read more] | Read more »

Price Scanner via

13-inch 128GB MacBook Air now on sale for $79...
Best Buy has just lowered their price on the 2015 13″ 1.6GHz/128GB MacBook Air to $799.99 on their online store for Cyber Monday. Choose free shipping or free local store pickup (if available). Sale... Read more
Best Buy lowers 13-inch MacBook Pro prices, n...
Best Buy has lowered prices on select 13″ MacBook Pros this afternoon. Now save up to $200 off MSRP for Cyber Monday on the following models. Choose free shipping or free local store pickup (if... Read more
Cyber Monday: Apple MacBooks on sale for up t...
Apple resellers have MacBook Pros, MacBook Airs, and MacBooks on sale for up to $250 off MSRP for Cyber Monday 2015. The following is a roundup of the lowest prices available for new models from any... Read more
Cyber Monday: Apple Watch on sale for up to $...
B&H Photo has the Apple Watch on sale for Cyber Monday for $50-$100 off MSRP. Shipping is free, and B&H charges NY sales tax only: - Apple Watch Sport: $50 off - Apple Watch: $50-$100 off B... Read more
Cyber Monday: 15% off Apple products, and sto...
Use code CYBER15 on Cyber Monday only to take 15% on Apple products at Target, and store-wide. Choose free shipping or free local store pickup (if available). Sale prices for online orders only, in-... Read more
iPad Air 2 And iPad mini Among Top Five Black...
Adobe has released its 2015 online shopping data for Black Friday and Thanksgiving Day. The five best selling electronic products on Black Friday were Samsung 4K TVs, Apple iPad Air 2, Microsoft Xbox... Read more
All-in-one PC Shipments Projected To Drop Ove...
Digitimes’ Aaron Lee and Joseph Tsai report that all-in-one (AIO) PC shipments may drop a double-digit percentage on-year in 2015 due to weaker-than-expected demand, although second-largest AIO make... Read more
Sprint Offers iPad Pro
Sprint now offers Apple’s new iPad Pro with Wi-Fi + Cellular, featuring a 12.9-inch Retina display with 5.6 million pixels. Customers can pick up iPad Pro at select Sprint retail locations. It can... Read more
Cyber Monday: Target offers 15% discount on A...
Target has discounted Apple Watches by 15% for Cyber Monday. Choose free shipping or free local store pickup (if available). Sale prices for online orders only, in-store prices may vary: - Apple... Read more
Sunday roundup of Holiday weekend Mac sales:...
Take up to $500 off MSRP on the price of a new Mac at B&H Photo today as part of their Black Friday/Holiday weekend sale. Shipping is free, and B&H charges NY tax only. These prices are... Read more

Jobs Board

Software Engineer, *Apple* Watch - Apple (U...
# Software Engineer, Apple Watch Job Number: 33362459 Santa Clara Valley, Califo ia, United States Posted: Jul. 28, 2015 Weekly Hours: 40.00 **Job Summary** Join the Read more
SW Engineer - *Apple* Music - Apple (United...
# SW Engineer - Apple Music Job Number: 40899104 San Francisco, Califo ia, United States Posted: Aug. 18, 2015 Weekly Hours: 40.00 **Job Summary** Join the Android Read more
Sr Software Engineer *Apple* Pay - Apple (U...
# Sr Software Engineer Apple Pay Job Number: 44003019 Santa Clara Valley, Califo ia, United States Posted: Nov. 13, 2015 Weekly Hours: 40.00 **Job Summary** Apple Read more
*Apple* Site Security Manager - Apple (Unite...
# Apple Site Security Manager Job Number: 42975010 Culver City, Califo ia, United States Posted: Oct. 2, 2015 Weekly Hours: 40.00 **Job Summary** The Apple Site Read more
iOS Wallet & *Apple* Pay Engineer - App...
# iOS Wallet & Apple Pay Engineer Job Number: 40586801 Santa Clara Valley, Califo ia, United States Posted: Nov. 16, 2015 Weekly Hours: 40.00 **Job Summary** The iOS Read more
All contents are Copyright 1984-2011 by Xplain Corporation. All rights reserved. Theme designed by Icreon.