Program Slicing

1
Program Slicing

• By
• Mark Weiser

2
Overview

• Introduction
• Slicing Algorithms
• Dataflow Algorithms
• Practical Slicing
• Interprocedural Slicing
• Slicing Based Metrics
• Conclusion

3
Introduction

• Program Slicing New complimentary method of
  program decomposition.
• Starts with observation that only a portion of a
  programs behavior is of interest.
• Slicing Criterion If behavior of interest is
  expressed as the values of some sets of variables
  at some set of statements.
• An executable program, whose behavior must be
  identical to the specified subset of original
  programs behavior is called Slice.

4
Example Of Slice

• The original program
• l BEGIN
• 2 READ(X,Y)
• 3 TOTAL 0.0
• 4 SUM 0.0
• 5 IF Xlt l
• 6 THEN SUM Y
• 7 ELSE BEGIN
• 8 READ(Z)
• 9 TOTAL XY
• lO END
• II WRITE(TOTAL,SUM)
• 12 END.

• on the value of Z at statement 12.
• BEGIN
• READ(X,Y)
• IF X lt l
• THEN
• ELSE READ(Z)
• END.
• Slice on the value of X at statement 9.
• BEGIN
• REAB(X,Y)
• END.

5
Example Of Slice

• Slice on the value of TOTAL at statement 12.
• BEGIN
• READ(X,Y)
• TOTAL 0
• IF X lt-- l
• THEN
• ELSE TOTAL XY
• END
• Slice on the value of X at statement 9.
• BEGIN
• REAB(X,Y)
• END.

• on the value of Z at statement 12.
• BEGIN
• READ(X,Y)
• IF X lt l
• THEN
• ELSE READ(Z)
• END.
• Slice on the value of TOTAL at statement 12.
• BEGIN
• READ(X,Y)
• TOTAL 0
• IF X lt-- l
• THEN
• ELSE TOTAL XY
• END

6
Slicing Algorithms

• Slicing Source code transformation of program .
• Window Specifies as a statement and a set of
  variables.
• Slicing criterion is a pair of lt i,v gt, where
• i- number of statements
• v- set of variable values
• Two desirable properties in a slice
• Slice obtained from original program by statement
  deletion.
• Slice behavior should correspond to original
  program behavior.
• Source code becomes ungrammatical with statement
  deletion.

7
Slicing Algorithm

• Flowgraph is used to represent a program.
• Flowgraph is a structure G ltN,E,n0gt, where
• N set of nodes
• E set of edges in NxN
• n0 initial node
• By deletion of statements (with single successor)
  a new flowgraph is produced.
• Deleted statement have a single successor which
  also becomes for all the predecessors of the new
  flowgraph.
• Window for new graph is lt succ(i),v gt.

8
Group Of Statements With A Single Successor
A
A
B
B
C
F
E
D
H
G
F
G
H
9
Slicing Algorithm

• Identical behavior for slice and original program
  for all inputs which is too strong.
• Finding smallest slice becomes a problem.
• Impossibility of evaluating functional
  equivalence of two different pieces of code.
• Thus, we use dataflow analysis.

• Consider the example
• 1 BEGIN
• 2 READ(X)
• 3 IF X 0
• 4 THEN BEGIN
• Perform infinite loop
• without changing X.
• 5 X 1
• 6 END
• 7 ELSE X 2
• 8 END.

10
Dataflow Algorithms

• Begins with backward tracing similar to reaching
  definitions.
• Finding which var assignments can reach the vars
  observed through window of the criterion.
• For example, consider statement yx followed
  by zy.
• R0,c(n) variables at statement n whose values
  directly effect what is observed through window
  defined by criterion c.
• Consider dataflow information DEF(n) and REF(n)
  to define R0,c.

11
Dataflow Algorithms

• Assumption w and x as variable names, with w in
  DEF(n) and x in REF(n) then value of x can
  influence the value of w.
• Above assumption cannot be applied to multiple
  assignments.
• More precise formulation
• RO,C(n), where C lti,vgt, is defined
  recursively as follows
• RO,C(n) all variables v such that either
• I. ni and v is in V,
• or 2. n is an immediate predecessor of
  a node m, such that either
• a) v is in REF(n) and there is a w in
  both DEF(n) and RO,C(m),
• or b) v is not in DEF(n) and v is inRo,
  c(m).

12
Dataflow Algorithms

• If REF and DEF information not obtained by code
  inspection we use interprocedural dataflow
  method.
• Statements included in slice by R0,c are
  denoted S0,c.
• S0,c all nodes n such that R0,c(n)
  intersect DEF(n) is non-empty.
• Consider following example
• Slicing Criterion C lt5,Zgt
• l READ(X)
• 2 IFXltI
• 3 THEN Z l
• 4 ELSE Z 2
• 5 WRITE(Z)

13
Dataflow Algorithms

• Considering branch statements that may not
  execute some statements we use the inverse
  denominator.
• With this we could exert an indirect influence
  over any variable directly influenced by x.
• Slice properties
• Let C lti,vgt, D lti,wgt, E lti,v union wgt,
• C, D, and E are all slicing criteria .
• Property
• SC union SD SE
• RC union RID RE
• Even this can produce anomalies as shown in next
  example .

14
Dataflow Algorithms

• l A constant
• 2 WHILE P(K)
• DO
• BEGIN
• 3 IF Q(C)
• THEN BEGIN
• 4 BA
• 5 XL
• END
• ELSE BEGIN
• 6 CB
• 7 Y2
• END

• 8 KKI
• END
• 9 ZXY
• l0 WRITE(Z)
• Criterion lt I0,Z gt
• The first level of anlaysis gives
• SO 5,7,g
• BO 2,3
• Because statement 3 uses C, the next level shows
• Sl 1,2,3,4,5,6,7,8,9

15
Practical Slicing

• Preliminary indications that slicing is useful
  were obtained by showing that experienced
  programmers already use slicing during debugging.
• Later Slicing tools are constructed.
• Using these results show that slicing is fairly
  fast and eliminates large number of unnecessary
  statements.
• Practically experiment was conducted in which
  participants were 21 experienced programmers from
  University of Michigan.
• This shows difference between slicing taught or
  not taught as debugging technique.

16
Slicing Real Programs

• First slicer was implemented to DAVE program for
  analyzing FORTRAN source code.
• This could slice only main program.
• Prototype system slicing criteria based on
  variables whose values were printed near the end
  of program.
• Results from
  Prototype Slicer
• PROGRAM Number of Lines
  Average Slice Size
• MMGS 15 15
• PH2B 60 20
• TALLY 67 25
• MAIN 380 lO0

17
Slicing Real Programs

• MMGS is a matrix multiplication subroutine in IBM
  Scientific Subroutine Library.
• Code was difficult to slice. Not possible even by
  trivial slicing criterion as trivial is not
  applicable to all mathematical software.
• Now slicer is implemented(to slice programs in
  SIMPL family) for a language independent
  representation.
• A program is incorporated into the SIMPL compiler
  which writes to a file all the information
  necessary to slice program.
• Programmer is not aware of this file until
  program is sliced.

18
Interprocedural Slicing

• The SIMPL slicer performs full interprocedural
  dataflow analysis.
• Two steps to slice systems of subroutines
• Single slice is made. Summary dataflow
  information about call to other procedures is
  used but no attempt is made to slice those
  procedures.
• To procedure calls that influence variables
  relevant to slice in step one, a new slicing
  criterion is created in the call procedure.
• Steps 1 and 2 are repeated until no new
  criterion is generated.
• Two ways slicing can cross a procedure boundary.
• This is shown in the example presented.

19
Interprocedural Slicing

• Extending slices to called and calling routines
• l READ(A,B)
• 2 CALL Q(A,B)
• 3 ZAB
• procedure Q(var x,y integer)
• 4 XO
• 5 Y X3
• Slicing on criterion Clt3,zgt causes new
  slicing criterion Clt6,x,ygt to be generated.
  The complete on C is 2,3,4,5.
• Now take Dlt4,ygt causes new one Dlt2,Bgt to
  be generated. Complete slice on D is 1.

20
Slicing Based Metrics

• Two investigations in progress
• Use slicing in program debugging and maintenance
  aid.
• Second is slicing based metrics. Number of slices
  their spacial arrangement etc.. hold significant
  information about restructuring a program.
• Some slicing based metrics
• Coverage ratio of mean slice length to program
  length.
• Overlap mean of ratios of non-unique to unique
  statements in each slice.
• Clustering reveals the degree to which slices
  are reflected in the original code layout.
• Parallelism number of slices which have few
  statements in common.
• Tightness measures number of statements which
  are in every slice.
• These metrics are applied in student-written
  load-and-go compilers.

21
Slicing Based Metrics

• Slicing on every output statement lead to many
  similar slices.
• Clustering together slices gives a more
  meaningful set of slices on which to apply
  metrics.
• Fo r instance, the 48 output statements in one
  compiler could be clustered into seven
  categories
• 1)object code interpretation messages and errors
• 2). source code scanning messages and errors.
• 3)miscellaneous fixed messages(e.g "EXECUTION
  BEGINS")
• 4) global error messages (e.g. "NO PROCEDURES")
• 5) symbol table listing
• 6)object code listing
• 7) symbol table error messages.

22
Slicing Based Metrics

• The 48 original slicing criteria generated 217
  additional slicing criteria as a result of called
  and calling procedures.
• Calculating the 217 intraproceduarl slices took
  about 10 minutes of cpu time.

23
Conclusion

• Limited to code already written, it may prove
  useful during debugging, testing, and
  maintenance.
• Many slicing decompositions can be chosen by
  selecting appropriate criteria.
• This paper concentrates on basic methods for
  slicing programs.
• Future work on slicing-based programming aids and
  program metrics is necessary .