Object Oriented Software Construction - Bertrand Meyer
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Object Oriented Software Construction - Bertrand Meyer


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recorded once again in
eld. Like the Hydra in its famous fight, the mailer kept growing a new head
 thought we had cut the last neck.
 repeating for the modern era the earlier feat of Hercules, we slew the beast
hen we had removed more than twenty code extracts which all accessed, in
other, information about the message sender. 
h the previous sections have only got us barely started on our road to abstract
hould be clear by now that any program written in accordance with even the
ary concepts of data abstraction would treat MAIL_MESSAGE as a carefully
act notion, supporting a query operation, perhaps called sender, which
ation about the message sender. Any portion of the mail program that needs
on would obtain it solely through the sender query. Had the mail program
d according to this seemingly obvious principle, it would have been
 the purpose of my little exercise, to modify the code of the sender query.
e software would also then have provided an associated command operation
 update sender information, making the job even easier. 
 the real moral of that little story (besides lowering the reader\u2019s guard in
r the surprise mathematical offensive of the next section)? After all, the mail
estion is successful, at least judging by its widespread use. But it typifies the
y standard in the industry. Until we move significantly beyond that standard,
ftware engineering\u201d will remain a case of wishful thinking. 
 one more note. Some time after my brief encounter with the mail program,
rtain network hackers had intruded into the computer systems of highly
rnment laboratories, using a security hole of that very mail program \u2014 a hole
miliar, so the press reported, to all those in the know. I was not in the know;
arned the news, I was not surprised. 
ALIZING THE SPECIFICATION 
of data abstraction presented so far is too informal to be of durable use.
in our staple example: a stack, as we now understand it, is defined in terms
ble operations; but then we need to define these operations! 
l descriptions as above (put pushes an element \u201con top of\u201d the stack, remove
ent \u201clast pushed\u201d and so on) do not suffice. We need to know precisely how
ns can be used by clients, and what they will do for them. 
ABSTRACT DATA TYPES §6.4130
An abstract data type specification will provide this information. It consists of four
paragraphs, explained in the next sections: 
\u2022 TYPES. 
\u2022 FUNCT
\u2022 AXIOM
\u2022 PRECO
These p
properties of 
The nota
notation 
style \u2014 
point for
being co
specifica
Specifying 
The TYPES
convenient to
By the w
developed in
functions, ax
objects, in th
possible stack
are not guilty
able to refine
\u201cset\u201d for \u201ctyp
On one 
data type suc
(the set of al
modules of o
on one partic
sense. O-O de
airplanes, all 
An obje
an instance o
STACK abstr
over to objec
explaining th
IONS. 
S. 
NDITIONS. 
aragraphs will rely on a simple mathematical notation for specifying the
an abstract data type (ADT for short).
tion \u2014 a mathematical formalism, not to be confused with the software
of the rest of this book even though for consistency it uses a similar syntactic
has no name and is not a programming language; it could serve as the starting
 a formal specification language, but we shall not pursue this avenue here,
ntent enough to use self-explanatory conventions for the unambiguous
tion of abstract data types.
types 
 paragraph indicates the types being specified. In general, it may be
 specify several ADTs together, although our example has only one, STACK. 
ay, what is a type? The answer to this question will combine all the ideas
 the rest of this chapter; a type is a collection of objects characterized by
ioms and preconditions. If for the moment you just view a type as a set of
e mathematical sense of the word \u201cset\u201d \u2014 type STACK as the set of all
s, type INTEGER as the set of all possible integer values and so on \u2014 you
 of any terrible misunderstanding. As you read this discussion you will be
 this view. In the meantime the discussion will not be too fussy about using
e\u201d and conversely. 
point, however, you should make sure to avoid any confusion: an abstract
h as STACK is not an object (one particular stack) but a collection of objects
l stacks). Remember what our real goal is: finding a good basis for the
ur software systems. As was noted in the previous chapter, basing a module
ular object \u2014 one stack, one airplane, one bank account \u2014 would not make
sign will enable us to build modules covering the properties of all stacks, all
bank accounts \u2014 or at least of some stacks, airplanes or accounts. 
ct belonging to the set of objects described by an ADT specification is called
f the ADT. For example, a specific stack which satisfies the properties of the
act data type will be an instance of STACK. The notion of instance will carry
t-oriented design and programming, where it will play an important role in
e run-time behavior of programs. 
§6.4 FORMALIZING THE SPECIFICATION 131
The TYPES paragraph simply lists the types introduced in the specification. Here:
Our spe
objects of an 
Genericity 
In STACK [G
parameter of
The mechanis
already encou
It is po
unjustified re
accounts\u201d, \u201cs
where they ex
Writing them
Reusability is
we can make 
to represent th
As a res
obtain a dire
ACCOUNT, 
parameter G. 
STACK 
is a fully defi
generic type, 
The not
principle, hav
abstract data 
produce a gen
right to use
STACK
specifying a 
elements are 
As this
qualification.
noted, is a ty
STACK, for e
TYPES 
\u2022 STACK [G] 
See \u201cGenericity\u201d, 
page 96.
cification is about a single abstract data type STACK, describing stacks of
arbitrary type G. 
], G denotes an arbitrary, unspecified type. G is called a formal generic
 the abstract data type STACK, and STACK itself is said to be a generic ADT.
m permitting such parameterized specifications is known as genericity; we
ntered a similar concept in our review of package constructs.
ssible to write ADT specifications without genericity, but at the price of
petition. Why have separate specifications for the types \u201cstack of bank
tack of integers\u201d and so on? These specifications would be identical except
plicitly refer to the type of the stack elements \u2014 bank accounts or integers.
, and then performing the type substitutions manually, would be tedious.
 desirable for specifications too \u2014 not just programs! Thanks to genericity,
the type parameterization explicit by choosing some arbitrary name, here
 G,
e variable type of stack elements. 
ult, an ADT such as STACK is not quite a type, but rather a type pattern; to
ctly usable stack type, you must obtain some element type, for example
and provide it as actual generic parameter corresponding to the formal
So although STACK is by itself just a type pattern, the notation 
[ACCOUNT]
ned type. Such a type, obtained by providing actual generic parameters to a
is said to be generically derived. 
ions just seen are applicable recursively: every type should, at least in
e an ADT specification, so you may view ACCOUNT as being itself an
type; also, a type that you use as actual generic parameter to STACK (to
erically derived type) may itself be generically derived, so it is perfectly all
 
[STACK [ACCOUNT]]
certain abstract data type: the instances of that type are stacks, whose
themselves stacks; the elements of these latter stacks are bank accounts. 
 example shows, the preceding definition of \u201cinstance\u201d needs some
 Strictly speaking, a particular stack is an instance not of STACK (which, as
pe pattern rather than a type) but of some type generically derived from
xample STACK [ACCOUNT]. It is convenient, however, to continue talking
ABSTRACT DATA TYPES §6.4132
about instances of STACK and similar type patterns, with the understanding that this
actually means instances