The document presents a general framework for slicing programs and models. It defines a slicing framework with syntax, semantics, projections, and slicing criteria. It applies the framework to program slicing examples and proposes adapting it for model slicing. The framework is then demonstrated on a class model case study, showing how slicing can reduce models for comprehension and debugging.

1. Program Slicing
Model Slicing
A General Slicing Framework
Case Study
Conclusion
A General Model Based Slicing Framework
Tony Clark
School of Engineering and Information Sciences, Middlesex University
September 30, 2011
Tony Clark A General Model Based Slicing Framework

2. Program Slicing
Model Slicing
A General Slicing Framework
Case Study
Conclusion
Contents
1 Program Slicing
2 Model Slicing
3 A General Slicing Framework
GSF for Programs
GSF for Models
4 Case Study
5 Conclusion
Tony Clark A General Model Based Slicing Framework

3. Program Slicing
Model Slicing
A General Slicing Framework
Case Study
Conclusion
Definition and Use Cases
What? Slicing is used to reduce the size of programs by
removing those statements that do not contribute to
the values of specified variables at a given program
location.
Why? Debugging; comprehension; verification.
How? Static (backwards,forwards); dynamic; conditioned;
union.
Tony Clark A General Model Based Slicing Framework

4. Program Slicing
Model Slicing
A General Slicing Framework
Case Study
Conclusion
Backward Slicing: Example1
Original Criterion Slice
x = 42
d = 23 d d = 23
Tony Clark A General Model Based Slicing Framework

5. Program Slicing
Model Slicing
A General Slicing Framework
Case Study
Conclusion
Backward Slicing: Example2
Original Criterion Slice
sum=0
prod=1 prod = 1
read(i) read(i)
while(i<11) { while (i<11) {
sum=sum+i
prod=prod*i prod=prod*i
i=i+1 i=i+1
} prod }
Tony Clark A General Model Based Slicing Framework

6. Program Slicing
Model Slicing
A General Slicing Framework
Case Study
Conclusion
Dynamic Slicing
Original Criterion Slice
sum=0
prod=1
prod = 1
read(i)
read(i)
while(i<11) {
sum=sum+i
prod=prod*i
i=i+1
} prod, pos(next(input))=11
Tony Clark A General Model Based Slicing Framework

7. Program Slicing
Model Slicing
A General Slicing Framework
Case Study
Conclusion
Conditioned Slicing
Original Criterion Slice
read(a) read(a)
if(a<0)
a=-a
x=1/a x, +ve(next(input)) x=1/a
Tony Clark A General Model Based Slicing Framework

8. Program Slicing
Model Slicing
A General Slicing Framework
Case Study
Conclusion
Unions
Original Criterion Slice
a = 42 a = 42
x = 2
b = 23 + a b = 23 + a
y = 3
c = b + 2 c c = b + 2
a = 42
x = 2
b = 23 + a
y = 3 y = 3
c = b + 2 y
a = 42 a = 42
x = 2
b = 23 + a b = 23 + a
y = 3 y = 3
c = b + 2 y and c c = b + 2
Tony Clark A General Model Based Slicing Framework

9. Program Slicing
Model Slicing
A General Slicing Framework
Case Study
Conclusion
Contents
1 Program Slicing
2 Model Slicing
3 A General Slicing Framework
GSF for Programs
GSF for Models
4 Case Study
5 Conclusion
Tony Clark A General Model Based Slicing Framework

10. Program Slicing
Model Slicing
A General Slicing Framework
Case Study
Conclusion
Definition and Use Cases
What? erm - drop some bits?
Why? Model management and comprehension; debugging
transformations; debugging executable models; model
verification.
How? State machines; class diagrams (syntax); specific
technologies.
Problem No general definition for model slicing.
Tony Clark A General Model Based Slicing Framework

11. Program Slicing
Model Slicing
A General Slicing Framework
Case Study
Conclusion
Differences to Programs
No starting point for execution.
Static and dynamic slices.
Multiple languages.
DSLs, profiles, meta-models.
Highly structured.
Weak semantics.
Links to model transformations; transformation combinations.
Tony Clark A General Model Based Slicing Framework

12. Program Slicing
Model Slicing
GSF for Programs
A General Slicing Framework
GSF for Models
Case Study
Conclusion
Contents
1 Program Slicing
2 Model Slicing
3 A General Slicing Framework
GSF for Programs
GSF for Models
4 Case Study
5 Conclusion
Tony Clark A General Model Based Slicing Framework

13. Program Slicing
Model Slicing
GSF for Programs
A General Slicing Framework
GSF for Models
Case Study
Conclusion
A General Slicing Framework
φ - σ:Σ
γ:Γ
p
x
q
-
-
φ z-
p γ :Γ - σ :Σ - q ω:Σ
-
q
p
y
? ?
-
γ :Γ - σ :Σ
φ
Γ Syntax domain.
Σ Semantic domain.
p, q Projections.
φ Semantics.
(x, ω) Slicing criterion.
Tony Clark A General Model Based Slicing Framework

14. Program Slicing
Model Slicing
GSF for Programs
A General Slicing Framework
GSF for Models
Case Study
Conclusion
Key Features
To set up the framework for a particular domain you will need:
syntax (Γ) The things you want to slice.
semantics (Σ, φ) The meaning of the syntax defined as a semantic
domain and a semantic mapping.
projections (p, q) Relationships that hold between syntactic and
semantic elements and that remove items that are
not of interest.
criterion (x, ω) The things that remain invariant, defined in terms
of the semantic domain.
products If the syntax and semantic domain also define
products for elements and projections then there is
scope for slicing composition.
Tony Clark A General Model Based Slicing Framework

15. Program Slicing
Model Slicing
GSF for Programs
A General Slicing Framework
GSF for Models
Case Study
Conclusion
Semantic Domain for Programs
Tony Clark A General Model Based Slicing Framework

16. Program Slicing
Model Slicing
GSF for Programs
A General Slicing Framework
GSF for Models
Case Study
Conclusion
GSF: Program Example1
Original Criterion Slice
x = 42
d = 23 d d = 23
Semantics is σ = {[{x → 41; d → 23}]} The slice criterion requires
that any trace in σ when projected onto the second step has a
value for d, so ω = {{d → v } | v ∈ V } Therefore the smallest set
of traces for which there exists a structural projection is
σ = {[{d → v } | v ∈ V }]}.
Tony Clark A General Model Based Slicing Framework

17. Program Slicing
Model Slicing
GSF for Programs
A General Slicing Framework
GSF for Models
Case Study
Conclusion
GSF: Program Example2
Original Criterion Slice
sum=0
prod=1 prod = 1
read(i) read(i)
while(i11) { while (i11) {
sum=sum+i
prod=prod*i prod=prod*i
i=i+1 i=i+1
} prod }
Semantics is σ = {[{sum → 0}, {sum → 0; prod → 1}, {sum → 0; prod →
1; i → v }] + trace(v ) | v ∈ 0 . . . 10} ] where trace(0) = []
trace(v ) = trace(v − 1) + [{sum → i; prod →!v ; i → v }]
i∈0...v
Criterion requires that ω = {prod → v | v ∈ V } and x maps each trace onto
the last maplet for prod.
Tony Clark A General Model Based Slicing Framework

18. Program Slicing
Model Slicing
GSF for Programs
A General Slicing Framework
GSF for Models
Case Study
Conclusion
Modelling Language: Syntax
Tony Clark A General Model Based Slicing Framework

19. Program Slicing
Model Slicing
GSF for Programs
A General Slicing Framework
GSF for Models
Case Study
Conclusion
Modelling Language: Semantic Domain
Tony Clark A General Model Based Slicing Framework

20. Program Slicing
Model Slicing
A General Slicing Framework
Case Study
Conclusion
Contents
1 Program Slicing
2 Model Slicing
3 A General Slicing Framework
GSF for Programs
GSF for Models
4 Case Study
5 Conclusion
Tony Clark A General Model Based Slicing Framework

21. Program Slicing
Model Slicing
A General Slicing Framework
Case Study
Conclusion
Case Study: Use Cases
Tony Clark A General Model Based Slicing Framework

22. Program Slicing
Model Slicing
A General Slicing Framework
Case Study
Conclusion
Case Study: Class Model
Tony Clark A General Model Based Slicing Framework

23. Program Slicing
Model Slicing
A General Slicing Framework
Case Study
Conclusion
OCL
c o n t e x t Library :: borrow ( reader , book )
p r e not hasFine ( reader ) and
p o s t borrows - includes ( b |
b . reader = getReader ( reader ) and
b . book = getBook ( book ) and
b . date = date ())
Tony Clark A General Model Based Slicing Framework

24. Program Slicing
Model Slicing
A General Slicing Framework
Case Study
Conclusion
Case Study: State Machine
Tony Clark A General Model Based Slicing Framework

25. Program Slicing
Model Slicing
A General Slicing Framework
Case Study
Conclusion
Case Study: Sequence Model
Tony Clark A General Model Based Slicing Framework

26. Program Slicing
Model Slicing
A General Slicing Framework
Case Study
Conclusion
A Borrowing Step
( s1 , ok = 0 - borrow ( fred , b ) ,f , s6 )
where
s1 = ({(0 ,* , Library )[ limit = l ] ,(1 ,* , Book )[ name =n , id =1] ,
(2 , initialized , Reader )[ name = fred , id =2]} ,{})
f = [( s1 , false = 0 - hasFine ( fred ) ,... , s1 ) ,
( s1 ,2 = 0 - getReader ( fred ) ,... , s1 ) ,
( s1 ,1 = 0 - getBook ( n ) ,... , s1 ) ,
( s1 , d = 0 - getDate () ,... , s1 ) ,
( s1 ,3 = 0 - new ( Borrows ) ,[] , s2 ) ,
( s2 , ok = 3 - setReader (2) ,... , s4 ) ,
....]
s2 = ({(0 ,* , Library )[ limit = l ] ,(1 ,* , Book )[ name =n , id =1] ,
(2 , initialized , Reader )[ name = fred , id =2] ,
(3 ,* , Borrows )[]} ,{})
Tony Clark A General Model Based Slicing Framework

27. Program Slicing
Model Slicing
A General Slicing Framework
Case Study
Conclusion
Slicing Criterion
B ={( s1 , v = l - borrow (r , b ) ,F , s2 ) |
F - Filmstrip ,
s1 - Snapshot ,
s2 - Snapshot ,
v - Value ,
l - Id ,
r - Str ,
b - Str }
Use ω = B ∗ as basis for slicing criterion.
x1 projects a filmstrip to the sequence of borrow steps it contains.
Tony Clark A General Model Based Slicing Framework

28. Program Slicing
Model Slicing
A General Slicing Framework
Case Study
Conclusion
Sliced Model
Tony Clark A General Model Based Slicing Framework

29. Program Slicing
Model Slicing
A General Slicing Framework
Case Study
Conclusion
Refining the Slice
{[( s1 , v = l - borrow (r , b ) ,[] , s2 )] |
s1 - Snapshot ,
s2 - Snapshot ,
v - Value ,
l - Id ,
r - Str ,
b - Str }
The mapping part x2 is a refinement of x1 that maps all nested
filmstrips to [].
Tony Clark A General Model Based Slicing Framework

30. Program Slicing
Model Slicing
A General Slicing Framework
Case Study
Conclusion
Refined Slice
Tony Clark A General Model Based Slicing Framework

31. Program Slicing
Model Slicing
A General Slicing Framework
Case Study
Conclusion
Contents
1 Program Slicing
2 Model Slicing
3 A General Slicing Framework
GSF for Programs
GSF for Models
4 Case Study
5 Conclusion
Tony Clark A General Model Based Slicing Framework

32. Program Slicing
Model Slicing
A General Slicing Framework
Case Study
Conclusion
Issues and Problems
Constructing slicing transformations: use of existing model
transformation languages? New languages?
Projection definition for OCL - requires theorem proving?
Combination of slices? Consistency of slices?
Slicing theories?
Restricted forms of slicing: static, dynamic, conditioned?
Tony Clark A General Model Based Slicing Framework