A Refinement Algebra for ObjectOriented Programming

1
A Refinement Algebra for Object-Oriented
Programming
Paulo Borba, Augusto Sampaio, Márcio Cornélio

• Informatics Center
• Federal University of Pernambuco
• Recife, Brazil

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Programming laws...

• state properties about programming constructs
• and
• are useful for reasoning about programs, deriving
  refactorings, etc.

But is there a comprehensive set of nice laws
for OOP?
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Change attribute visibility
class C extends D pri a T ads ops end
class C extends D pub a T ads ops end
cds,c
(?) B.a, for all B ? C, does not appear in cds,c
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Relative completeness

• Laws are used to define a normal form
  reduction process for ROOL programs
• an empty class hierarchy except for Object, which
  contains only public attributes
• the types of attributes and variables are
  primitive types or Object
• eliminates methods, type casts, super, pri, pro

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Normal form reduction process
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Reduction process in brief

• Rename methods and attributes
• Move the code to the Object class
• Introduce trivial casts
• Eliminate super
• Eliminate casts
• Change all the declarations of object identifiers
  to type Object
• Eliminate method calls and declarations

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Move attribute to superclass
class B extends A ads ops end class C
extends B pub a T ads ops end
class B extends A pub a T ads
ops end class C extends B ads ops end
cds,c
(?) a is not declared by the subclasses of B in
cds (?) ...
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Moving attributes up
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Introduce trivial cast
If e C then
e
(C) e
cds,A
Useful for avoiding problems when moving up code
such as x self
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Introduce method redefinition
class B extends A ads meth m pc end
ops end class C extends B ads ops end
class B extends A ads meth m pc end
ops end class C extends B ads meth m
super.m end ops end

(?) m is not declared in ops
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Eliminating super
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Move up redefined method
class B extends A ads meth m pds b end
ops end class C extends B ads meth m pds
b end ops end
class B extends A ads meth m pds if
(self is C) ? b self is C ? b end
ops end class C extends B ads ops end

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Move up redefined method, provided
(?) private attributes and super do not
appear in b (?) super.m does not appear in
ops (?) b does not contain uncast occurrences
of self nor expressions in the form
((C)self).a for any private or protected
attribute a in ads (?) ...
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Moving up redefined methods
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Moving up methods
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Change attribute type
class C extends D pub a T ads ops end
class C extends D pub a T ads ops end
cds,c
(?) T ? T and every occurrence of a in
non-assignable expressions of ops, cds and c
is cast with T or any subtype of T declared
in cds (?) ...
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Changing types to Object
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Eliminate non trivial cast
If le B, e B, C ? B and B ? B, then
e is C le e
le (C)e
cds,A
If e B, C ? B and m is declared in B or in any
of its superclasses in cds, then
e is C e.m(e)
((C)e).m(e)
cds,A
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Eliminate method call
Let m be declared as pc. Then
e?null ? e?error pce/self (e)
e.m(e)
cds,A
(?) m is not redefined in cds (?) pc does not
contain references to super (?) all attributes in
pc are public
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Eliminating methods
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Conclusions

• Comprehensive set of laws, but not enough to
  eliminate all OO constructs
• Formal derivation of refactorings from the laws
• Local changes
• Separation of concerns
• Increase or decrease OO qualities
• Soundness of the laws do not rely on copy
  semantics and the renaming step

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A Refinement Algebra for Object-Oriented
Programming
Paulo Borba, Augusto Sampaio, Márcio Cornélio

• Informatics Center
• Federal University of Pernambuco
• Recife, Brazil