T5.2 Jugs as a Case Study

T5.2.1. Visualisation in Program Design: The Jugs Program revisited

Designing orthodox sequential programs using definitive scripts is a first step towards concurrent systems modelling. Significantly, in generalising single-agent definitive programming, traditional sequential programming is a not particularly natural special case. This is illustrated by the fact that there is no particular reason why we should not redesign the speedometer display in the VCCS whilst the simulation is in use. Conventions by which agents are restricted to exercise privileges according to a specified pattern are inappropriate in the first stage of specification; they only serve to obscure the experimental foundation for behaviour. A similar philosophy lies behind concepts such as Jackson System Development, where the designer is encouraged to model the application domain prior to developing the application. In this section, we illustrate how single-agent definitive programming can be applied to developing a simple program that is eventually to be used in a sequential mode. Simon Yung designed and implemented Scout, and the analysis and commentary that follows is taken from his doctoral thesis: Definitive Programming as a Paradigm for Exploratory Software Development.

Jugs is a simple simulation program originally developed by Townsend (the original version is written by Ruth Townsend for the BBC computers - it is distributed by the Chiltern Advisory Unit), that was first considered from a DST perspective in [BNRSYY89]. There are two jugs, A and B, with different capacities, capA and capB respectively. capA and capB should be relatively prime. One can choose an operation from a set of permissible menus at a time. The whole range of operations is:

  1. fill Jug A,
  2. fill Jug B,
  3. empty Jug A,
  4. empty Jug B, and
  5. pour as much water from Jug A to Jug B or from Jug B to Jug A as the destination jug can hold.

The target of the game is to leave a specified amount of water in either of the jugs.

The program designer's task is to develop a script in which the roles of a user of the jugs program and of the computer simulation of operations on the jugs can be specified. (The distinction between a pupil user, who selects menu options, and a teacher user, who can set up problems for the pupil is also of interest.) The programming principles necessary to implement the selection and activation of menu options using a definitive approach will be described later. The role of the Scout definitions is to present the values of the variables of interest to the user in a comprehensible way.

T5.2.2. Modelling a Screen Layout Using Scout

When the term 'modelling' is used, we mean that we have already at least a mental picture, if not anything more concrete, of what the target looks like. There is a distinction between modelling activity and exploratory design. For example, in the case of screen layout, exploratory design is necessary when the final screen layout is not known. Bits and pieces may be added, deleted or modified from the intermediate implementations until the designer is satisfied. For the Jugs problem, the emphasis is on modelling rather than exploratory design since the screen layout is prescribed rather than designed from scratch. We are basically following the layout of the output from the original Jugs program by Townsend. Therefore, before we do any exploration on the screen layout design, we begin by modelling the original Jugs output using Scout.

In the following sub-sections we will first discuss the process of modelling a screen layout using Scout, then consider some advantages of definitive notation in the light of the modelling technique demonstrated by Scout.

After the screen layout is modelled in Scout, the designer may go on exploring the design. The advantages of Scout, and in general definitive notation, towards exploratory development of software are going to be discussed in section T1.4.

T5.2.2.1. Screen Layout Modelling Process

There are three informal stages for developing a Scout description of a screen layout:

  1. Develop an idea of what the screen display should look like. For example, Figure 5.1 is what the screen should display when the Jugs program is first started. The colour of the menus represents their availability - black on white indicates a valid option.

    Figure 5.1: A Sample Jugs Output

  2. Characterise the screen layout by identifying the common relationships in the screen layout. Figure 5.2 shows the design for the geometrical information of the Jugs output. Other characteristics such as the number of tildes required to fill up to the level contA (which is widthA ? contA) can be identified as well.

    Figure 5.2: Screen Layout Design

  3. The programming task is almost finished although we have not actually written down anything in the Scout notation! To finish off the work, this final step transforms the information obtained from the first two steps into the Scout notation. Listing 5.1 and Listing 5.2 show parts of the Jugs game screen layout in the Scout notation.

    Listing 5.1: Definitions for Locations

    point base = {1.c, n.r} # 1 char-width(.c) right and n char-height(.r) down from origin
    box	menu1box = [base, 1, strlen(pupilmenu1)]
    # a box whose NE corner is at base, 1 char-height and strlen(menu1) char-width
    box	menu2box = [menu1Box.ne + {1.c, 0}, 1, strlen(pupilmenu2)]
    frame	jugAboxes = ([menu1box.ne+(0, -(2+capA).r}, capA, 1],
    	[menu1box.ne+{(widthA+1).c, -(2+capA).r}, capA, 1],
    	[menu1box.ne+{0, -2.r}, 1, widthA+2])
    frame	jugBboxes = ([jugAboxes.2.sw + {2.c, -capB.r-1}, capB, 1], ...
    box	contAbox = [jugAboxes.1.sw+{1.c, -contA.r}, contA, widthA]
    box	messagebox = [jugBboxes.2.ne +{2.c, (capB/2).r}, 1, strlen(status)]

    Listing 5.2: Other Scout Definitions

    string backgroundi = validi ? "black" : "white"
    			#reverse background  if option invalid
    string cA = repeatChar('~', widthA*contA)    #use '~'s to represent water level
    string jugA= repeatChar('|', 2*capA)//"+"//repeatChar('=', widthA)//"+"
    window menu1window = {
    		frame: (menu1box);		string: pupilmenu1;
    		bgcolour: background1;	fgcolour: foreground1
    # form window by putting string pupilmenu1 (what to display) in frame formed
    # by a single box menu1box (where to display) displaying black on white or
    # white on black depending the availability of the menu option (how to display)
    window	capAwindow = { frame: jugAboxes; string: jugA }
    window	contAwindow = { frame: (contAbox); string: cA }
    display	screen = ( menu1window / menu2window / ... 
    				/ contAwindow / capAwindow / ... )
    # screen represents  the physical screen; it displays the windows listed.
    # If windows overlap, menu1window overlays menu2window etc.

This method of developing a screen layout is similar to writing a program in a traditional software development process; the first two steps are analogous to obtaining an (informal) specification whereas the last step is analogous to implementing the specification. Although the theme of this thesis is exploratory software development, the discussion in this section is not unrelated. The simplicity of the modelling method indicates how easily we can relate a definitive script to reality. This certainly helps the exploratory software designer to understand and make changes to the current design.

T5.2.2.2. Special-Purpose Notation for Specific Task

The job of screen layout design is to decide where information should be placed and how it should be presented. The Scout notation restricts the areas allocated for displaying information to be rectangular or a group of rectangles. For this reason, the Scout notation permits only simple layout design. However, the design of the notation has already taken into account some assumptions of the characteristics of the display unit and the usual layout designs. For example:

  1. The Coordinate System. The addressable points on a display unit normally form a grid. Moreover, Scout is only a notation for describing screen layout and is not a general graphics display notation. Therefore, the obvious choice of the Scout coordinate system is the Cartesian Coordinate System.
  2. Area Allocation. A window in Scout means a fixed region in which a piece of information is displayed. The region that can be allocated depends on the type of information to be displayed. Although no 2-D line drawing window appears in the Jugs example, Scout, at its present stage of development, can incorporate DoNaLD graphics, ARCA diagrams and text. If graphics is going to be displayed, the region must be a box. The following fields are significant in the definition of the window:
    type:	DONALD (or ARCA)
    box:	b
    pict:	picture-name

    where b is a box defining where the graphics should be displayed, and picture-name is the name of the DoNaLD or ARCA picture. If text is going to be displayed, the region is a frame rather than a box. A frame is used because it allows for more general display formats such as multi-column display and other irregular shaped regions. A text window should have the following fields defined:

    type:	TEXT
    frame:	f
    string:	s

    The declaration of text type is often omitted in a Scout program (for instance in the Jugs example) because windows are text windows by default. Note that the boxes of f are most conveniently defined by their top-left corners and by their dimensions (dimensions are expressed in terms of the number of characters in a row and a column).

  3. Presentation of Information. Again, what can be controlled depends on the type of information being presented. We can, for examples, shift and scale the image of the DoNaLD pictures and change the background colour of the window and the colour of the lines. For text, we can change its alignment, foreground and background colour.
  4. Combining Windows. In some cases, say a windowing system, windows may overlap. The Scout notation defines a display to be an ordered list of windows such that if there is overlapping, one window overlays another if it precedes the other in the list (cf. Listing 5.2). This presumes that it is never necessary to represent a situation such as Figure 5.3 where windows overlay cyclically.

    Figure 5.3: Cyclic Overlapping Windows

Although the Scout notation looks simple, its design has already involved a lot of assumptions about the nature of the physical displays, the types of application and the ways of denoting and manipulating information. For this reason, expressing the screen layout in Scout (step 3) is straightforward. Other definitive notations are also special-purpose notations. This means that the notations, including the data types and operators, are designed for particular application domains. This helps to give definitive notations high expressive power.

Moreover, using special-purpose notations reduces the learning time and the programming time of the programmer, increases the understandability and hence eases the maintenance of the program.

T5.2.2.3. Flexibility of Model

Modelling involves analysis and representation of a real world system. Persistent relationships between objects and interaction between objects are two kinds of behaviour we may often observe. For instance, consider the following scenario. "A table lamp lights up when the switch is at position ON and it turns off otherwise." - this is an persistent relationship. There is interaction between a man and the light switch so as to change the state of the switch. This interaction does not change the persistent relationship between the brightness of the table lamp and the light switch, but some interactions do. A sudden impact on the table lamp may cause breakage of the filament so that the relationship is changed to "the table lamp will not glow irrespective of the position of the light switch". This shows that a persistent relationship is not necessarily permanent; it is subject to change by interaction.

We have already experienced problems, such as verification and concurrency, with imperative programming which disregards the persistent relationships; we have also the experience of using functional programming which stresses the permanency of persistent relationships - making use of higher-order function to prevent change of relations adds a degree of complexity to the relationships. Definitive programming paradigm enables us to describe persistent relationships without ruling out the possibility of relationship changes by interaction. Hence it is desirable for modelling.

Furthermore, a set of definitions shows not only the design of the model of current state, it also provides hints for change of design. The intelligent use of constants and formulae in defining variables indicates the flexibility of the model. Using the Jugs example as an illustration, the point base is defined in Figure 5.1 to be {1.c, n.r} where n is currently defined as 20. Redefining base as {1.c, 20.r} rather than {1.c, n.r} does not affect the value of the point base and hence the whole picture remains unchanged. But the definition

base = {1.c, n.r} 

gives base a degree of freedom - the point base can be moved vertically without changing its definition but only changing the explicit value of n. Of course there is no rule to guarantee that the definition of base is fixed or that the definition of n is going to be altered, but the use of implicit formulae and explicit values in definitions suggests that the variables defined by explicit values are more liable to change and the variables defined by implicit formulae are more persistent.

Therefore, variables in a definitive notation are more than variables containing pure values; the formulae defining the variables are significant. In fact, they are more significant than the values. This is because the variables must specify a unique set of values if sufficient definitions are given, but if some definitions are missing (i.e. the model is incomplete) the formulae define latent values of the variables. T5.2.2.4. Separation of Control and Presentation Since definitive notations are special purpose notations, a script written in a single definitive notation is generally insufficient for specifying the whole application. On the other hand, the usefulness of definitive notations is not undermined by this; a script can still be used to model a particular aspect, such as the screen layout, of the application.

With reference to the Jugs example, the Scout definitions only describe the screen layout. They do not specify how the variables like contA and valid1 are maintained. In fact the control in the Jugs example is written in EDEN, a general purpose definitive language. A way of integrating definitive notations via EDEN will be discussed in the next chapter. The basic idea is to translate different kinds of definitions into a single definitive language so that variables of different definitive notations can communicate via definitions. This means, for example, that in order to animate the Jugs layout, designed in Scout, it is only necessary to append the EDEN script and a set of actions that defines the Jugs control. Therefore, a definitive paradigm for representation of state provides a neat way of separating control and presentation. The advantages of the separation are:

T5.2.3. Exploratory Screen Layout Development

The screen layout target is not always known at an early stage of screen layout design. A practical way of screen layout design is to obtain a first approximation and then gradually evolve the design through prototyping and experimentation. During an exploration of design, one of the following activities may be performed:

  1. Removing unwanted items. Example: In our early Jugs program, instead of the 5th option - pour water from one jug to the other - we had an option for pouring water from Jug A to Jug B and another option for pouring from Jug B to Jug A. Although in the actual menu-driven simulation the two menu options for pouring are redundant, the full range of menu options is useful for general simulation of pouring. On this basis, it is not clear whether we should have one menu option for pouring or two. But when we decided to accept the single menu option, options 5 and 6 were then removed.
  2. Displaying new items. Example: Following the example above, after the deletion of the two 'pour' menu options, the current option 5 was added.
  3. Relocating the display items. Example: Changing base so that the whole display shifts. Several tests may be necessary because where base should be is subjective.
  4. Modifying relationships between variables. Example: The message box may be relocated so that it lies below the menus. This action will break the geometrical relationship between the location of the message box and the capacity of Jug B (see Figure 5.2) and establish a new relationship between the message box and the menus.
  5. Testing of design - changing the parameters or testing data. Example: Changing contA and contB to see if the menus and the message box behave as intended.

T5.2.3.1. Convenient State Changes

Although redefining a variable may cause changes to the values of many variables and hence the screen display, the only difference the redefinition makes to the definitive state is the definition of that particular variable. Therefore, reversing the changes made by the redefinition only requires restoring the original definition of the variable. Timbleby argues that the user of an interactive system must be able to undo errors. With a good undo available, users will be encouraged to experiment with the system. In our current system, no undo facility has been implemented. It is our intention to leave the system in a raw operational mode so that there is no fancy user interface to distract our attention from developing higher level control for transitions of definitive states. However, the simplicity of undoing the effect of a definition is an advantage of definitive notations for exploratory design.

T5.2.3.2. Flexible Definition Arrangement

Changing the two pour menu options to one pour option in the jugs example involves replacing of the definition:

display screen = ( ... / pourAtoBwindow / pourBtoAwindow / ... );

by the definition:

display	screen = ( ... / pourwindow / ... );

with the addition of the following definitions:

Listing 5.3: The Scout Definitions Relating to the Pour Menu Option

window	pourwindow = {
		frame:(menu5box);		string: pupilmenu5;
		bgcolour:background5;	fgcolour:foreground5
string 	pupilmenu5 = "5:Pour";
string	foreground5 = if valid5 then "black" else "white" endif;
string	background5 = if valid5 then "white" else "black" endif;
box	menu5box= [menu4box.ne+{1.c, 0}, 1, strlen(pupilmenu5)];

Listing 5.3 defines all the necessary information required to display what can be seen on the screen as the "Pour" menu option (i.e. the region, content and attributes of the window are all defined). The only piece of missing information is menu4box, which is part of the display information of another menu option. Listing 5.3 is therefore similar to a window object in object-oriented programming terms, except that in our paradigm no information hiding is assumed. This grouping of definitions here and the grouping of definitions illustrated in Listing 5.1 and 5.2 shows two grouping methods with different emphasis. One groups the definitions relating a visible window whilst the other groups the definitions according to their functionality. Flexibility of definition arrangement is possible because the ordering of definitions in a script is insignificant. The advantages of having this flexibility are:

  1. One can develop a script in whatever way is most convenient to the current stage of development. Perhaps in the beginning the Scout display is developed in phases such as specifying regions, specifying contents and combining them to form a screen. Later, exploratory design is benefited by developing the screen window by window.
  2. Regrouping of definitions will not affect the meaning of the script. It is possible therefore to develop tools to rearrange definitions in ways that can assist our understanding of the script. Particularly useful arrangements might be obtained by sorting the definitions by types or by their dependency hierarchy.


[BY89]		Definitive Interfaces as a Visualisation Mechanism
[BNRSYY89]	Software Construction using Definitions CS RR#147

This document was manually converted from the original Macintosh Word format to this web form by Ashley Ward in June 2001.