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OOSC - Lecture 4
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Chair of Software Engineering
Object-Oriented Software Construction
Bertrand Meyer
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Chair of Software Engineering
Reading assignment
OOSC2 Chapter 10: Genericity
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Lecture 4:
Abstract Data Types
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Abstract Data Types (ADT)
Why use the objects? The need for data abstraction Moving away from the physical representation Abstract data type specifications Applications to software design
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The first step
A system performs certain actions on certain data. Basic duality:
Functions [or: Operations, Actions] Objects [or: Data]
Action Object
Processor
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Finding the structure
The structure of the system may be deducedfrom an analysis of the functions (1) or theobjects (2).
Resulting analysis and design method: Process-based decomposition: classical
(routines) Object-oriented decomposition
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Arguments for using objects
Reusability: Need to reuse whole data structures,not just operations
Extendibility, Continuity: Objects remain morestable over time.
Employeeinformation
Hoursworked
ProducePaychecks
Paychecks
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Object technology: A first definition
Object-oriented software construction is theapproach to system structuring that bases thearchitecture of software systems on the types ofobjects they manipulate — not on “the” functionthey achieve.
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The O-O designer’s motto
Ask NOT first WHAT the system does:
Ask WHAT it does it TO!
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Issues of object-oriented design
How to find the object types. How to describe the object types. How to describe the relations and commonalities
between object types. How to use object types to structure programs.
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Description of objects
Consider not a single object but a type of objectswith similar properties.
Define each type of objects not by the objects’physical representation but by their behavior: theservices (FEATURES) they offer to the rest of theworld.
External, not internal view: ABSTRACT DATA TYPES
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The theoretical basis
The main issue: How to describe program objects(data structures):
Completely
Unambiguously
Without overspecifying? (Remember information hiding)
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A stack, concrete object
count
representation
(array_up)
capacity
representation [count] := x
free
(array_down)
1representation
nnew
(linked)
item
item
previous
item
previousprevious
“Push” operation:count := count + 1
representation [free] := x“Push” operation:
free := free - 1
new (n)n.item := x
“Push” operation:
n.previous := lasthead := n
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Chair of Software Engineering
A stack, concrete object
count
representation
(array_up)
capacity
representation [count] := x
free
(array_down)
1representation
nnew
(linked)
item
item
previous
item
previousprevious
“Push” operation:count := count + 1
representation [free] := x“Push” operation:
free := free - 1
new (n)n.item := x
“Push” operation:
n.previous := lasthead := n
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Stack: An abstract data type
Types: STACK [G]
-- G: Formal generic parameter
Functions (Operations): put: STACK [G] × G → STACK [G] remove: STACK [G] → STACK [G] item: STACK [G] → G empty: STACK [G] → BOOLEAN
new: STACK [G]
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Using functions to model operations
put , =( )
s x s’
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Reminder: Partial functions
A partial function, identified here by →, is afunction that may not be defined for all possiblearguments.
Example from elementary mathematics:
inverse: ℜ → ℜ, such that
inverse (x) = 1 / x
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The STACK ADT (cont’d)
Preconditions: remove (s: STACK [G]) require not empty (s) item (s: STACK [G]) require not empty (s)
Axioms: For all x: G, s: STACK [G] item (put (s, x)) = x remove (put (s, x)) = s empty (new)
(or: empty (new) = True)
not empty (put (s, x))(or: empty (put (s, x)) = False)
put ( , ) =
s x s’
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Exercises
Adapt the preceding specification of stacks (LIFO,Last-In First-Out) to describe queues instead(FIFO).
Adapt the preceding specification of stacks toaccount for bounded stacks, of maximum sizecapacity. Hint: put becomes a partial function.
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Formal stack expressions
value = item (remove (put (remove (put (put(remove (put (put (put (new, x8), x7), x6)), item(remove (put (put (new, x5), x4)))), x2)), x1)))
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Expressed differently
s1 = new
s2 = put (put (put (s1, x8), x7), x6)
s3 = remove (s2)
s4 = new
s5 = put (put (s4, x5), x4)
s6 = remove (s5)
y1 = item (s6)
s7 = put (s3, y1)
s8 = put (s7, x2)
s9 = remove (s8)
s10 = put (s9, x1)
s11 = remove (s10)
value = item (s11)
value = item (remove (put (remove (put (put (remove (put (put (put (new, x8),x7), x6)), item (remove (put (put (new, x5), x4)))), x2)), x1)))
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Expression reduction (1/10)
value = item ( remove (
put ( remove (
put ( put ( remove (
put (put (put (new, x8), x7), x6) )
, item ( remove ( put (put (new, x5), x4)
) )
) , x2)
) , x1) )
)
x7
x8
x6
x5
x4
Stack 1 Stack 2
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Chair of Software Engineering
Expression reduction (2/10)
x7
put remove
x8
x7
x8
x7
x8
x6
value = item ( remove (
put ( remove (
put ( put ( remove (
put (put (put (new, x8), x7), x6) )
, item ( remove ( put (put (new, x5), x4)
) )
) , x2)
) , x1) )
)
x5
x4
Stack 1 Stack 2
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Chair of Software Engineering
Expression reduction (3/10)
value = item ( remove (
put ( remove (
put ( put ( remove (
put (put (put (new, x8), x7), x6) )
, item ( remove ( put (put (new, x5), x4)
) )
) , x2)
) , x1) )
)
x7
put remove
x8
x7
x8
x7
x8
x2
x7
put remove
x8
x7
x8
x7
x8
x2
Stack 1
x5
x4
Stack 2
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Expression reduction (4/10)
value = item ( remove (
put ( remove (
put ( put ( remove (
put (put (put (new, x8), x7), x6) )
, item ( remove ( put (put (new, x5), x4)
) )
) , x2)
) , x1) )
)
x5
put remove
x5 x5
x4x7
x8
x7
x8
Stack 1 Stack 2
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Chair of Software Engineering
Expression reduction (5/10)
value = item ( remove (
put ( remove (
put ( put ( remove (
put (put (put (new, x8), x7), x6) )
, item ( remove ( put (put (new, x5), x4)
) )
) , x2)
) , x1) )
)
item
x5
Stack 2
x7
x8
x7
x8
Stack 1
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value = item ( remove (
put ( remove (
put ( put ( remove (
put (put (put (new, x8), x7), x6) )
, item ( remove ( put (put (new, x5), x4)
) )
) , x2)
) , x1) )
)
Expression reduction (6/10)
x5
Stack 2
x7
x8
x7
x8
Stack 1
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Chair of Software Engineering
value = item ( remove (
put ( remove (
put ( put ( remove (
put (put (put (new, x8), x7), x6) )
, item ( remove ( put (put (new, x5), x4)
) )
) , x2)
) , x1) )
)
Expression reduction (7/10)
x5
x7
x8
x7
x8
Stack 3
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Chair of Software Engineering
Expression reduction (8/10)
value = item ( remove (
put ( remove (
put ( put ( remove (
put (put (put (new, x8), x7), x6) )
, item ( remove ( put (put (new, x5), x4)
) )
) , x2)
) , x1) )
)
x5
x7
x8
x7
x8
Stack 3
put removex1
x5
x7
x8
x7
x8
x5
x7
x8
x7
x8
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Chair of Software Engineering
Expression reduction (9/10)item
x5
x7
x8
x7
x8
Stack 3
value = item ( remove (
put ( remove (
put ( put ( remove (
put (put (put (new, x8), x7), x6) )
, item ( remove ( put (put (new, x5), x4)
) )
) , x2)
) , x1) )
)
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Chair of Software Engineering
Expression reduction (10/10)
value = item ( remove (
put ( remove (
put ( put ( remove (
put (put (put (new, x8), x7), x6) )
, item ( remove ( put (put (new, x5), x4)
) )
) , x2)
) , x1) )
)
value = x5
x5
x7
x8
x7
x8
Stack 3
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Chair of Software Engineering
Expressed differently
s1 = new
s2 = put (put (put (s1, x8), x7), x6)
s3 = remove (s2)
s4 = new
s5 = put (put (s4, x5), x4)
s6 = remove (s5)
y1 = item (s6)
s7 = put (s3, y1)
s8 = put (s7, x2)
s9 = remove (s8)
s10 = put (s9, x1)
s11 = remove (s10)
value = item (s11)
value = item (remove (put (remove (put (put (remove (put (put (put (new, x8),x7), x6)), item (remove (put (put (new, x5), x4)))), x2)), x1)))
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Chair of Software Engineering
An operational view of the expression
value = item (remove (put (remove (put (put (remove (put (put (put (new,x8), x7), x6)), item (remove (put (put (new, x5), x4)))), x2)), x1)))
x8
x7
x6
x8
x7
s2 s3(empty)
s1x5
x4
s5(empty)
s4x5
s6
y1
x8
x7
x5
s7 (s9, s11)x8
x7
x5
s8
x2
x8
x7
x5
s10
x1
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Sufficient completeness
Three forms of functions in the specification of anADT T: Creators:
OTHER → T e.g. new Queries:
T ×... → OTHER e.g. item, empty Commands:
T ×... → T e.g. put, remove
Sufficiently complete specification: a “QueryExpression” of the form:
f (...)
where f is a query, may be reduced throughapplication of the axioms to a form not involving T
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Chair of Software Engineering
Stack: An abstract data type
Types: STACK [G]
-- G: Formal generic parameter
Functions (Operations): put: STACK [G] × G → STACK [G] remove: STACK [G] → STACK [G] item: STACK [G] → G empty: STACK [G] → BOOLEAN
new: STACK [G]
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ADT and software architecture
Abstract data types provide an ideal basis formodularizing software.
Identify every module with an implementation ofan abstract data type, i.e. the description of a setof objects with a common interface.
The interface is defined by a set of operations(implementing the functions of the ADT)constrained by abstract properties (the axiomsand preconditions).
The module consists of a representation for theabstract data type and an implementation foreach of the operations. Auxiliary operations mayalso be included.
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Chair of Software Engineering
Implementing an ADT
Three components:(E1) The ADT’s specification: functions,
axioms, preconditions.(Example: stacks.)
(E2) Some representation choice.(Example: <representation, count>.)
(E3) A set of subprograms (routines) and attributes, each implementing one of thefunctions of the ADT specification (E1) in
terms of the chosen representation (E2).(Example: routines put, remove, item, empty, new.)
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A choice of stack representation
count
representation
(array_up)
capacity “Push” operation:count := count + 1
representation [count] := x
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Application to information hiding
Secret part:
•Choice of representation (E2)
•Implementation of functionsby features (E3)
ADT specification (E1)Public part:
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Chair of Software Engineering
Object technology: A first definition
Object-oriented software construction is theapproach to system structuring that bases thearchitecture of software systems on the types ofobjects they manipulate — not on “the” functionthey achieve.
OOSC - Lecture 4
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Chair of Software Engineering
Object technology: More precise definition
Object-oriented software construction is theconstruction of software systems as structuredcollections of (possibly partial) abstract data typeimplementations.
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Classes: The fundamental structure
Merging of the notions of module and type: Module = Unit of decomposition: set of services Type = Description of a set of run-time objects
(“instances” of the type)
The connection: The services offered by the class, viewed as a
module, are the operations available on theinstances of the class, viewed as a type.
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Class relations
Two relations: Client Heir
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Overall system structure
CHUNK
word_countjustified?
add_wordremove_word
justifyunjustify
lengthfontFIGURE
PARAGRAPH WORD
space_before
space_afteradd_space_before
add_space_after
set_fonthyphenate_onhyphenate_off
QUERIES COMMANDS
FEATURES
Inheritance
Client
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A very deferred class
deferred class COUNTER
feature
item: INTEGER is deferred end-- Counter value
up is-- Increase item by 1.
deferredensure
item = old item + 1end
down is-- Decrease item by 1.
deferredensure
item = old item – 1end
invariant
item >= 0
end
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Chair of Software Engineering
End of lecture 4
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