EiffelBase, Iteration

The classes of the Iteration cluster encapsulate control structures representing common traversal operations.

Iterators and Agents

Eiffel's agent mechanism offers an attractive alternative to the Iterator cluster of EiffelBase.

The Notion of iterator

Let us first explore the role of iterators in the architecture of a system.

Iterating over data structures

Client software that uses data structures of a certain type, for example lists or trees, often needs to traverse a data structure of that type in a predetermined order so as to apply a certain action to all the items of the structure, or to all items that satisfy a certain criterion. Such a systematic traversal is called an iteration.
Cases of iteration can be found in almost any system. Here are a few typical examples:

• A text processing system may maintain a list of paragraphs. In response to a user command, such as a request to resize the column width, the system will iterate over the entire list so as to update all paragraphs.
• A business system may maintain a list of customers. If the company decides that a special promotion will target all customers satisfying a certain criterion (for example all customers that have bought at least one product over the past six months), the system will iterate over the list, generating a mailing for every list item that satisfies the criterion.
• An interactive development environment for a programming language may maintain a syntax tree. In response to a program change, the system will traverse the tree to determine what nodes are affected by the change and update them.

These examples illustrate the general properties of iteration. An iteration involves a data structure of a known general type and a particular ordering of the structure's items. For some structures, more than one ordering will be available; for example a tree iteration may use preorder, postorder or breadth-first (as defined below). The iteration involves an operation, say item_action, to be applied to the selected items. It may also involve a boolean-valued query, say item_test, applicable to candidate items. Finally, it involves a certain policy, usually based on item_test, as to which items should be subjected to item_action. Typical example policies are:

• Apply item_action to all the items in the structure. (In this case item_test is not relevant).
• Apply item_action to all items that satisfy item_test.
• Apply item_action to all items up to the first one that satisfies item_test.

The Iteration library provides many more, covering in particular all the standard control structures.

Iterations and control structures

You can perform iterations without any special iteration classes. For example if customers is declared ascustomers: LIST [CUSTOMER]

then a class SPECIAL_PROMOTION of a text processing system may include in one of its routines a loop of the form from customers.start until customers.exhausted loop if recent_purchases.has (customers.item) then target_list.put (customers.item) end customers.forth end

Such schemes are quite common. But it is precisely because they occur frequently that it is useful to rely on library classes to handle them. One of the principal tasks of object-oriented software development is to identify recurring patterns and build reusable classes that encapsulate them, so that future developers will be able to rely on ready-made solutions.
The classes of the Iteration library address this need. Using them offers two benefits:

• You avoid writing loops, in which the definition of sub-components such as exit conditions, variants and invariants is often delicate or error-prone.
• You can more easily adapt the resulting features in descendant classes. The rest of this chapter shows how to obtain these benefits.

Simple Examples

To get a first grasp of how one can work with the Iteration library, let us look at a typical iteration class and a typical iteration client.

An example iterator routine

Here, given with its full implementation, is a typical Iteration library routine: the procedure until_do from LINEAR_ITERATOR , the class defining iteration mechanisms on linear (sequential) structures. until_do (action: PROCEDURE [G]; test: FUNCTION [G, BOOLEAN]) -- Apply `action' to every item of `target' up to -- but excluding first one satisfying `test'. -- (Apply to full list if no item satisfies `test'.) do start until_continue (action, test) ensure then achieved: not exhausted implies test.item ([target.item]) end until_continue (action: PROCEDURE [G]; test: FUNCTION [G, BOOLEAN]) -- Apply `action' to every item of `target' from current -- position, up to but excluding first one satisfying `test'. require invariant_satisfied: invariant_value do from invariant invariant_value until exhausted or else test.item ([target.item]) loop action.call ([item]) forth end ensure achieved: exhausted or else test.item ([target.item]) invariant_satisfied: invariant_value end

The precise form of the procedure in the class relies on a call to another procedure, until_continue, and on inherited assertions. Here the routines are shown as they are found in the current implementation of the class LINEAR_ITERATOR.
This procedure will traverse the linear structure identified by target and apply the procedure called action on every item up to but excluding the first one satisfying test.
The class similarly offers do_all, do_while, do_for, do_if and other procedures representing the common control structures. It also includes functions such as exists and forall, corresponding to the usual quantifiers.
These iteration schemes depend on the procedure action, defining the action to be applied to successive elements, and on the function test, defining the boolean query to be applied to these elements. Both routines are used trough the Eiffel's agent mechanism; here is an example of a test function intended to be used with iteration over a data structure whose elements are STRINGs. test (a_item: STRING): BOOLEAN -- Test to be applied to a_item do Result := a_item.count > 0 end

This indicates that the value of the boolean function test will be obtained by verifying that a_item is an empty string or not.

An example use of iteration

Here now is an example illustrating the use of these mechanisms. The result will enable us to resize all the paragraphs of a text up to the first one that has been modified - as we might need to do, in a text processing system, to process an interactive user request. Assume a class TEXT that describes lists of paragraphs with certain additional features. The example will also assume a class PARAGRAPH with a procedure resize, and a boolean-valued attribute modified which indicates whether a paragraph has been modified. Class TEXT inherits from LINKED_LIST and so is a descendant of LINEAR : class TEXT inherit LINKED_LIST [PARAGRAPH] ... feature ... end

In a class TEXT_PROCESSOR, you can use an iteration procedure to write a very simple procedure resize_ paragraphs that will resize all paragraphs up to but excluding the first one that has been modified: class TEXT_PROCESSOR inherit LINEAR_ITERATOR [PARAGRAPH] feature resize_paragraphs (t: TEXT) -- Resize all the paragraphs of t up to but excluding -- the first one that has been modified. do set (t) until_do (agent item_action, agent item_test) end feature {NONE} item_test (p: PARAGRAPH): BOOLEAN -- Has p been modified? do Result := p.modified end item_action (p: PARAGRAPH) -- Resize p. do p.resize end ... end

Thanks to the iteration mechanism, the procedure resize_paragraphs simply needs two procedure calls:

• To set its argument t as the iteration target, it uses procedure set. (This procedure is from class ITERATOR which passes it on to all iterator classes.)
• Then it simply calls until_do as defined above.

Procedure item_action is defined to describe the operation to be performed on each successive element. Function item_test is defined to describe the exit test.
As presented so far, the mechanism seems to limit every descendant of an iteration class to just one form of iteration. As shown later in this chapter, it is in fact easy to generalize the technique to allow a class to use an arbitrary number of iteration schemes.
What is interesting here is that the definitions of item_test and item_action take care of all the details. There is no need to write any loop or other control structure. We are at the very heart of the object-oriented method, enjoying the ability to encapsulate useful and common software schemes so that client developers will only need to fill in what is specific to their application.

Using the Iteration Library

Let us now explore the classes of the Iteration library and the different ways of using them.

Overview of the classes

There are only four Iteration classes, whose simple inheritance structure appeared at the beginning of this chapter.

• ITERATOR , a deferred class which describes the most general notion.
• LINEAR_ITERATOR , for iterating over linear structures and chains.
• TWO_WAY_CHAIN_ITERATOR , a repeated heir of LINEAR_ITERATOR , for iterating in either direction over a bilinear structure.
• CURSOR_TREE_ITERATOR , for iterating over trees.

As you will remember from the presentation of the abstract overall taxonomy, the traversal hierarchy describes how data structures can be traversed; its most general class is TRAVERSABLE .
Each one of the iterator classes is paired with a traversal class (or two in one case):

ITERATOR	TRAVERSABLE
LINEAR_ITERATOR	LINEAR
TWO_WAY_CHAIN_ITERATOR	TWO_WAY_LIST
TWO_WAY_CHAIN_ITERATOR	TWO_WAY_LIST , TWO_WAY_CIRCULAR
CURSOR_TREE_ITERATOR	CURSOR_TREE

Each iterator class relies on the corresponding traversal class to provide the features for traversing the corresponding data structures, such as start, forth, and exhausted for linear structures.
Of course the data structure class used in connection with a given iterator class does not need to be the iterator's exact correspondent as given by the above table; it may be any one of its descendants. For example you may use LINEAR_ITERATOR to iterate over data structures described not just by LINEAR but also by such descendants as LIST , LINKED_LIST , ARRAYED_LIST , or even TWO_WAY_LIST if you do not need the backward iteration features (for which you will have to use TWO_WAY_CHAIN_ITERATOR ).

General iteration facilities

Class ITERATOR defines the features that apply to all forms of iterator.
An iterator will always apply to a certain target structure. The target is introduced in ITERATOR by the feature target: TRAVERSABLE [G]
Both the iterator classes and the traversal classes are generic, with a formal generic parameter G. The actual generic parameters will be matched through the choice of iteration target: for a generic derivation of the form SOME_ITERATOR [ ACTUAL_TYPE] the target can only be of type SOME_TRAVERSABLE [ACTUAL_TYPE] for the same ACTUAL_TYPE, where SOME_TRAVERSABLE is the traversal class matching SOME_ITERATOR according to the preceding table (LINEAR for LINEAR_ITERATOR and so on), or one of its proper descendants.
Each of the proper descendants of ITERATOR redefines the type of target to the matching proper descendant of TRAVERSABLE , to cover more specific variants of the iteration target. For example in LINEAR_ITERATOR the feature is redefined to be of type LINEAR. ITERATOR also introduces the procedure for selecting a target: set (s: like target) -- Make s the new target of iterations. require s /= Void do target := s ensure target = s target /= Void end

Another feature introduced in ITERATOR is the query invariant_value, describing invariant properties that must be ensured at the beginning of any iteration and preserved by every iteration step. As declared in ITERATOR this query always returns true, but proper descendants can redefine it to describe more interesting invariant properties.
Finally, ITERATOR introduces in deferred form the general iteration routines applicable to all iteration variants. They include two queries corresponding to the quantifiers of first-order predicate calculus:

• for_all will return true if all items of the target structure satisfy test.
• there_exists will return true if at least one item satisfies test.

The other routines are commands which will traverse the target structure and apply action to items selected through test:

• do_all applies action to all items.
• do_if, to those items which satisfy test.
• until_do, to all items up to but excluding the first one that satisfies test.
• do_until, to all items up to and including the first one that satisfies test.
• while_do and do_while, to all items up to the first one that does not satisfy test. (This can also be achieved with until_do or do_until by choosing the opposite test.)

Some of these features and most of the other iteration features introduced in proper descendants of ITERATOR and described next, have either an action argument that must be of type PROCEDURE [G] or an argument test of type FUNCTION [G, BOOLEAN]. Some have both. Information about the target of the iterations comes from feature target, set by procedure set; information about what needs to be done for each item of the target structure comes from the argument action passed to the routines referenced above.

Linear and chain iteration

LINEAR_ITERATOR , an effective class, refines the iteration mechanisms for cases in which the target is a linear structure, such as a list in any implementation or a circular chain.
The class effects all the deferred features inherited from ITERATOR , taking advantage of the linear traversal mechanisms present in the corresponding traversal class, LINEAR . Here for example is the effecting of until_do.
This routine text relies on features start, forth and exhausted which, together with off, have for convenience been carried over to LINEAR_ITERATOR from their counterparts in LINEAR , with feature declarations such as off: BOOLEAN -- Is position of target off? require traversable_exists: target /= Void do Result := target.off end

and similarly for the others.
In addition to effecting the general iteration features from ITERATOR , class LINEAR_ITERATOR introduces iteration features that apply to the specific case of linear structures:

• search (test: FUNCTION [G, BOOLEAN]; b: BOOLEAN) moves the iteration to the first position satisfying test if both test and b have the same value (both True or both False).
• With a linear structure we can implement an iteration corresponding to the 'for' loop of traditional programming languages, defined by three integers: the starting position, the number of items to be traversed, and the step between consecutive items. This is provided by procedure do_for (action: PROCEDURE [G]; starting , number , step: INTEGER).
• Since with a linear target the iterator can advance the cursor step by step, the basic iteration operations are complemented by variants which pick up from the position reached by the last call: continue_until, until_continue, continue_while, while_continue, continue_search, continue_for.

Two-way iteration

Class TWO_WAY_CHAIN_ITERATOR has all the features of LINEAR_ITERATOR , to which it adds features for iterating backward as well as forward.
The class introduces commands finish and back, applying the corresponding operations to the two-way target. It also has a backward variant for every iteration feature. The name of each such variant is the name of the forward feature followed by _back: do_all_back, until_do_back and so on.
An alternative design would have kept just one set of features and added two features: a command reverse to reverse the direction of future iteration operations, and a query backward to find out the direction currently in force.
Contrary to what one might at first imagine, class TWO_WAY_CHAIN_ITERATOR is extremely short and simple; its Feature clause only contains the declarations of two features, finish and back.
The trick is to use repeated inheritance. TWO_WAY_CHAIN_ITERATOR inherits twice from LINEAR_ITERATOR ; the first inheritance branch yields the forward iteration features, the second yields those for backward iteration. There is no need for any explicit declaration or redeclaration of iteration features. Here is the entire class text that yields this result: class TWO_WAY_CHAIN_ITERATOR [G] inherit LINEAR_ITERATOR [G] redefine target select start, forth, do_all, until_do, do_until, while_do, do_while, do_if, do_for, search, for_all, there_exists, until_continue, continue_until, while_continue, continue_while, continue_for, continue_search end LINEAR_ITERATOR [G] rename start as finish, forth as back, do_all as do_all_back, until_do as until_do_back, do_until as do_until_back, do_while as do_while_back, while_do as while_do_back, do_if as do_if_back, do_for as do_for_back, search as search_back, for_all as for_all_back, there_exists as there_exists_back, until_continue as until_continue_back, continue_until as continue_until_back, while_continue as while_continue_back, continue_while as continue_while_back, continue_for as continue_for_back, continue_search as continue_search_back redefine back, finish, target end create set feature -- Access target: CHAIN [G] feature -- Cursor movement finish -- Move cursor of `target' to last position. do target.finish end back -- Move cursor of `target' backward one position. do target.back end end

This class provides a good example of the economy of expression that the full inheritance mechanism affords through the combination of renaming, redefinition, repeated inheritance rules and selection, without sacrificing clarity and maintainability.

Tree iteration

Tree iterations, provided by class CURSOR_TREE_ITERATOR , work on trees of the cursor tree form; only with this form of tree are traversal operations possible. Three forms of iteration are provided: preorder, postorder and breadth-first. They correspond to the three traversal policies described in the discussion of trees. Here too it would seem that a rather lengthy class is needed, but repeated inheritance works wonders.
CURSOR_TREE_ITERATOR simply inherits three times from LINEAR_ITERATOR , renaming the features appropriately in each case:

• pre_do_all, pre_until, and so on.
• post_do_all, post_until, and so on.
• breadth_do_all, breadth_until, and so on.

All it needs to do then is to redefine the type of target to be CURSOR_TREE [G] , and to redefine six features: the three renamed start (pre_start, etc.) and the three forth ( pre_ forth, and so on). These seven redefinitions give us a full-fledged battery of tree iteration mechanisms.

Building and Using Iterators

To conclude this discussion, let us now put together the various mechanisms studied so far, to see how authors of client software can use the Iteration library to perform possibly complex iterations on various data structures without ever writing a single loop or test. The basic ideas were sketched above but now we have all the elements for the full view.
An application class may use one of the iteration classes in either of two ways: as a descendant (single or repeated) or as a client. The descendant technique is extremely simple but less versatile.

The single descendant technique

Assume an application class PROCESSOR that is a proper descendant of one of the effective iteration classes studied in this chapter. Then a routine of PROCESSOR, say iterate, may iterate a certain action over a data structure, subject to a certain test. First, class PROCESSOR must specify the action by redefining item_action and item_test (or, in the most general case, action and test). Then routine iterate must specify the target data structure through a call of the form set (t) where t represents the selected target data structure. The type of t must correspond to the iteration class selected as ancestor of PROCESSOR: for LINEAR_ITERATOR it must be a descendant of LINEAR (such as LINKED_LIST , ARRAYED_LIST , LINKED_CIRCULAR or any other list or circular chain classes); for TWO_WAY_CHAIN_ITERATOR it must be a descendant of BILINEAR such as TWO_WAY_LIST or TWO_WAY_CIRCULAR ; for CURSOR_TREE_ITERATOR it must be a descendant of CURSOR_TREE . In all cases the actual generic parameters of the iterator class and ofthe data structure class must be compatible. Then the iteration proper is obtained simply by calling the appropriate procedure, without any qualification or arguments, for example: do_ if
It is hard to imagine a simpler scheme: no loops, no initialization, no arguments. Feature item_action may need to rely on some variable values. Because it does not take any argument, such values will have to be treated as attributes, with the corresponding set_... procedures to set and change their values. This also applies to the two schemes set next.
The single descendant technique has one drawback: it provides the iterating class, PROCESSOR, with only one set of iteration particulars. This limitation does not affect the number of targets: you may use as many targets as you wish, as long as they are of compatible types, by calling a routine such as iterate several times, or calling several such routines, each call being preceded by a call to set to define a new target. The limitation also does not affect the iterating scheme: one iteration could use do_if, the next do_all and so on. But it does require the action and test to be the same in all cases.
The next two techniques will remove this limitation.

Using repeated inheritance

One way to obtain several iteration schemes is a simple extension to the single descendant technique. You can use repeated inheritance to provide two or more variants. We have in fact already encountered the technique when studying how to derive TWO_WAY_CHAIN_ITERATOR and CURSOR_TREE_ITERATOR from LINEAR_ITERATOR . The general pattern, applied here to just two iteration schemes but easily generalized to more, is straightforward:class DUAL_PROCESSOR inherit LINEAR_ITERATOR [SOME_TYPE] rename item_action as action1, item_test as test1, do_if as do_if1, redefine action1, test1 select action1, test1 end LINEAR_ITERATOR [SOME_TYPE] rename item_action as action2, item_test as test2, do_if as do_if2, redefine action2, test2 end feature action1 -- Action for the first scheme do ... end test1: BOOLEAN -- Test for the first scheme do ... end action2 -- Action for the second scheme do ... end test2: BOOLEAN -- Test for the second scheme do ... end iterate1 -- Execute iteration of first kind. do set (...) do_if1 end iterate2 -- Execute iteration of second kind. do set (...) do_if2 end ... end

The repeated inheritance machinery takes care of the rest.

Using explicit iterator objects

To obtain maximum flexibility, classes that need iteration facilities should be clients rather than descendants of the iteration classes. The resulting scheme is completely dynamic: to perform iterations you use iterator objects as discussed earlier.
The following example illustrates the technique. Consider a deferred class FIGURE describing the notion of graphical figure, with many effective descendants ( POLYGON, CIRCLE and so on). It is useful to define COMPLEX_FIGURE, describing figures that are recursively composed of sub-figures. This is a remarkable example of multiple inheritance: class COMPLEX_FIGURE inherit FIGURE, LINKED_LIST [FIGURE] feature ... end

In the feature clause we want to provide the appropriate effectings for the deferred features of class FIGURE: display, hide, translate and all other basic figure operations.
We can use loops for that purpose, for example display -- Recursively display all components of the complex -- figure do from start until exhausted loop item.display forth end end

Although acceptable and even elegant, this scheme will cause significant duplication: all the FIGURE features - not just display but also hide, rotate, move and others - will have the same structure, with a loop. We can use iterators to avoid this duplication. The repeated inheritance technique would work, but given the large number of FIGURE features the amount of repeated inheritance that would be needed seems unwieldy. It is also not very desirable to have to change the inheritance structure of the system just to add a new feature to FIGURE. The more dynamic approach using iterator objects seems preferable.
To implement this approach, define a class for iterating on complex figures: class COMPLEX_FIGURE_ITERATOR inherit LINEAR_ITERATOR redefine target end create set feature target: COMPLEX_FIGURE end

Then for each operation to be iterated define a small class. For example:class FIGURE_DISPLAYER inherit COMPLEX_FIGURE_ITERATOR redefine item_action end create set feature item_action (f: FIGURE) -- Action to be applied to each figure: display -- it. do f.display end end

Similarly, you may define FIGURE_HIDER, FIGURE_MOVER and others. Then the features of COMPLEX_FIGURE are written almost trivially, without any explicit loops; for example: display -- Recursively display all components of the complex -- figure local disp: FIGURE_DISPLAYER do create disp.set (Current) disp.do_all end

and similarly for all the others.
Note the use of set as creation procedure, which is more convenient than requiring the clients first to create an iterator object and then to call set. This is also safer, since with set as a creation procedure the client cannot forget to initialize the target. (If a class C has a creation clause, the creation instruction create C.)