Group Title: Department of Computer and Information Science and Engineering Technical Reports
Title: A New approach to finding objects in programs
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Title: A New approach to finding objects in programs
Series Title: Department of Computer and Information Science and Engineering Technical Reports
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Language: English
Creator: Livadas, Panos E.
Johnson, Theodore
Publisher: Department of Computer and Information Sciences, University of Florida
Place of Publication: Gainesville, Fla.
Copyright Date: 1992
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A New Approach to Finding Objects in Programs


Panos E. Livadas
Theodore Johnson

Computer and Information Sciences Department
University of Florida, Gainesville, FL 32611


ABSTRACT
Software maintenance is difficult and costly because the maintainer must understand the existing relation-
ships in the maintained code. The maintainer's job can be made considerably easier if the objects in the
code (related groups of types, data, and procedures) are identified. In this paper, we discuss methods for
identifying objects in programs, and present a new approach that relies on these key features. First, our
internal program representation (IPR) lets us make a more precise identification of objects than previous
methods allowed. Second, we introduce the idea of receiver-based object identification. Third, we intro-
duce the idea of two-step object identification, which gives the user greater control in precisely identifying
objects. Our object finding tool can be used with the other tools our IPR provides to create an integrated
software maintenance environment.

1. Introduction
Although conventional programming languages do not directly support object-oriented program-
ming constructs, they do provide several object-like features (such as groupings of related data,
abstract data types, and inheritance). It would be very useful to the maintenance programmer to
understand the data and function relationships and objects the original designer had in mind.
Furthermore, successful maintenance requires a precise knowledge of the data items in the sys-
tem, the ways these items are created and modified, and their relationships. Identifying objects as
well as dependence in procedural code helps to
* understand system design;
* test and debug;
* reengineer the system from a conventional programming language into a object-oriented
language;
* avoid degradation of original designs during maintenance;
* facilitate the reuse of existing methods contained in the system.
An object in a conventional programming language can be defined as a collection of routines
(functions or procedures), types, and/or data items. Routines implement the methods associated
with the object, types structure the data it conceals or processes, and data items represent or point
to actual instances of the object class. What is needed is an identification method, M, to group
objects into a meaningful context of the target program and its real world domain. Let P be a pro-
gram and let F = f, : i =1,2...,1 be the set of its routines. Let T = 4 t, : i= 1,2...,m } be the set
of its types, and let D = d, : i= 1,2...,n } be the set of its data items. We define a candidate
object in P relative to M, Cj, to be a triple
cl= (,,,8)

where pcF, tcT, 6cD, and M is the identification method used in identifying objects.
We use a two-step method of object finding. First, we identify a set of objects via queries to
our internal program representation (IPR). Objects found from the IPR are called primary







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objects. Another set of objects can be found by queries on the primary objects, plus some addi-
tional information. These are the secondary objects. Because object identification methods are
necessarily heuristic, a fixed algorithm for querying the IPR will often provide misleading results.
Thus, we decided on a two-step process that gives the user the ability to refine the primary object
groupings. In addition, the distinction between primary and secondary object identification per-
mits a clearer description of the identification algorithms.
In section 2, we discuss three primary identification methods: global-based (M=g), type-
based (M=t), and receiver-based (M=r); the first two have been proposed in [2]. In section 3,
we discuss secondary object identification methods. In section 4, we discuss our internal program
representation, and algorithms that return precise primary objects. In section 5, we draw some
conclusions.

2. Primary Object Identification Methods
The primary object identification methods that we consider can be grouped into global-based
(M=g), type-based (M=t), and receiver-based (M=r) methods. Global and type-based object
finding has been discussed in [2]; and receiver-based object finding is a novel approach that is
often more accurate than type-based object finding.
We need to make a definition for our discussion of primary object finding. Let x be a vari-
able of type t and letfe F. We say that x is visible inf if and only ifx is either defined or used inf
Ifx is visible then x is either a global variable, a local variable (toj), or a formal parameter (to]).

2.1. Global-based Object Identification
Global-based object identification (GBOI) defines a candidate object to be a triple ((, 0,x) where
(cF and x is a global variable that is visible to each element of (. Objects identified by this
method will be referred to as globally accessible objects.
The method in [2] for identifying global objects overlooked two important cases, so their
"objects" are not precisely identified. First, in languages such as Pascal that permit nested pro-
cedures, non-local variables can be regarded as global variables for the purpose of the object
finder. Hence, the object finder shouldn't distinguish between global and non-local variables for
programs written in these languages. We will use the term global to mean both global and non-
local variables in the remainder of this paper. Second, in [2] the global-based object finder clus-
ters instances of a global variable with a routine. However, if a variable x is global to a routinely,
andf, calls2 with x as the actual parameter, an interpretation should be that x is global tof2. The
algorithm for the object finder described in [2] is unable to find the threads that would be caused
by such bindings. As we discuss, our algorithm uses a graph as an underlying structure where
bindings, as well as the results of flow-sensitive analysis, are explicitly represented. Therefore,
those threads can be identified and traversed.
In the sample program in Table 1, we can distinguish two globally accessible objects.
Namely, global variable gs is clustered with procedures push, pop, empty_GS, empty_s whereas
gq is clustered with procedures insert, delete, empty_GQ. Therefore, the output of the global
based object identification algorithm when executed on the program in Table 1 is:
CP ={
CgP[1] = push, pop, empty_GS, empty_S 0, gsr),
Cg [2] =( insert, delete, empty_GQ \, 0, gq \) \.
As an extension, we note that static variables as in C can be considered as global variables of lim-
ited scope, since a static variable exists between the invocations of the routines that define it. It is
a simple matter to provide the user with the flexibility to treat static variables as global, and we
identify this primary object identification method as the global-static (M=gs) method.
















=array of elem;

record
top : integer;
info : el type;


end;

queue = record



end;

stcque = record


end;


front:
back :
info :


integer;
integer;
eltype;


part : stack;
part2 : stack;


var gs: stack; gq : queue;


proc copy (var Sl:stcque; var S:stack);
{ insert the top element of S into S }

function empty_Q(Q:queue):boolean;
{ return T if Q is empty; otherwise F

proc insert(x:elem)
{ insert x into (global) queue gq


program P;

type elem =

el type

stack


Table 1. Program illustrating the object finder.


2.2. Type-based Object Identification

Type-based object identification (TBOI) clusters a routine with the set of types of all its formal
parameters and the type of its returned value [2]. For example, each routine
n
r:(a ,a2,......... an)->b is clustered with the set T = ju a, yj b , where a,'s represent the
1=]
types of the parameters and b the type of the returned variable (if any). As an example, we
applied the TBOI algorithm to the program in Table 1. All routines whose type set is T are
clustered together, and the result is:

ctP+tr 4

CP+tr[] =( copy \,4 stack, stcque ,(),

CP+tr[2]=(4 push_S, pop_S f,4 stack,elem ,0),

CtP+r[3]=(4 insert_Q, delete_Q f, queue, elem ,(),

Ct+tr[4]=(4 empty_Q \, queue, boolean ,),

CP +tr[5]=(4 empty_S ,4 stack, boolean ,0),

CPp+tr[6]=(4 push, pop, insert, delete K, elem ,),

CPt+t[7]= ( empty_GQ, empty_GS \,4 boolean i,0) .

It might be useful to cluster a routine with the types of the global and static variables that it
accesses as well as the types of its parameters and return value. For example, using the static and
global types reduces the number of objects found in program P from seven to five:


-3-


proc push S(var S:stack; var x:elem);
{ push x into S }

function pop S(var S:stack):elem;
{ pop from S }

function empty_S(S:stack):boolean;
{ return T if S is empty; otherwise F

proc push(x:elem);
{ push x into a (global) stack gs

function pop:elem;
{ pop from global stack gs

function empty_GS:boolean;
empty_GS := empty_S(sg);
{ return T if GS is empty; otherwise F


proc insert Q(var Q:queue;x:elem);
{ insert x into Q }

function delete Q(var Q:queue):elem;
{ insert x into Q }

function empty_GQ:boolean;
{ return T if gq is empty; otherwise F

function delete:elem;
{ delete from (global) queue gq







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Cp +tr+tg ~
Cp+tr+tg(l)= (copy stack, stcque ),
Ctp+tr+tg(2)= ( pushS, pop_S, push, pop f,1 stack,elem ,0),
CPt+tr+tg(3)= ( insert_Q, delete_Q, insert, delete H, queue, elem ,0),
Ctp+tr+tg(4)= ( empty_Q, empty_GQ queue, boolean ,0),
CP+tr+tg(5)= ( empty_S, empty_GS stack, boolean ,0) I.
We observe that perhaps the routine should not be clustered with the type of the return value. For
example, the empty_Q routine is clustered with the boolean type of its return value, but empty_Q is
naturally an operation on stacks, not booleans.
These considerations lead us to provide three primary TBOI methods: parameter type tp,
global type tg, and return value type tr. The examples we present in this section use combinations
of the three primary object identification methods (tp +tr +tg, for example). We discuss methods
for combining object identification methods in section 3.

2.3. Receiver-based Object Identification
We define a receiver parameter type (or simply receiver) of routinefto be the type of a parameter
that is modified in at least one execution path of f The receiver-based object identification
(RBOI) clusters a routine with the types of its receivers. One can intuitively realize that a routine
might be called with several parameters, but the object associated with the routine contains only a
few of these parameters. However, we can often distinguish which of the parameters are the
objects because those parameters will be modified. For example, the push_ routine takes param-
eters of types stack and elem. One typically clusters a push operation with the stack type, and in
fact the push routine only modifies the stack parameter.
As in type-based object identification, we can apply receiver-based object identification to
global and static variables as well. We denote RBOI performed on parameters as the rp
identification method, and RBOI performed on global and statics as the rg identification method.
For an example of the utility of RBOI, we applied a combined rp +rg identification on the pro-
gram in Table 1:
C'rp+rg =
Cpp+rg(1)= copy U, stcque r,0),
CPp+rg(2)=({ pushS, pop_S, push, pop stack f,0),
Crp+rg(3)= ( insert_Q, delete_Q, insert, delete H, queue ,0),
CPp+rg(4)= ( push, pop, insert, delete f,1 stack r,0) .
The stricter requirement of grouping routines with their receiver types returns a finer object set
than TBOI returns. In our example, RBOI returns exactly the objects that one intuitively feels do
exist in program P. As we show in the section 4, we can identify which fields and subfields of a
record a routine modifies, so that we can perform RBOI at the level of primitive types. In prac-
tice, such low-level information might not be useful.

3. Secondary Object Identification Methods
The object finding methods that we propose in this paper are of necessity heuristic. Since
automatic object finding may return spurious or misleading object groupings, the programmer
should be provided with flexible object finding tools. We can view the object groupings returned
by the primary object identification methods as a database we can use to construct secondary
object groupings. Some operations that we can perform are:










* Selection: The selection operation lets us perform object finding on a subset of the routines,
types, and global that exist in the program. It is a simple matter to select explicitly named
types, routines, and global, or types, etc., that have some property (for example, select all
routines that access global x).
* Union: The union operation lets us group routines based on mixed criteria. The RBOI
example used the union of global receiver and parameter receiver object identification to
identify its objects.
* Intersection: Returning to the example presented in the RBOI section, the insert_Q and
delete_Q routines are grouped with the insert and delete routines. We might feel that
insert_o and delete_Q are different objects because they access a global variable that the
insert and delete routines do not. We can specify this distinction by grouping routines
that both have a queue receiver type, but which also access the Q global variable.
* Subtraction: When grouping routines, we might want to rule out routines that access some
particular global or use some particular type. For example, after identifying insert_Q and
delete_Q in an object, we can identify the insert and delete in an object by requiring that
the objects don't access Q.
* Deletion: The program might contain dependencies that the user feels are to be disregarded
during object finding. For example, a simulation program might access a global simulated-
time variable in most of its routines, yet these routines naturally belong to difficult objects.
We can remove this spurious dependency by deleting references to the simulated-time vari-
able.
Many other queries can be added to the secondary object identification repertoire, once the
framework is in place. The secondary object finding methods are similar to relational database
queries, and can be implemented using the same algorithms. In the next section, we discuss
another query that is very useful for refining the object groupings.

3.1. Least Upper Bound Types
The TBOI and RBOI identification methods can cluster objects with a large set of types. Intui-
tively, there are only a few (perhaps one) types in an object. If we are to cluster a routine with a
small subset of its types, then intuitively we should cluster the routine with the most complex
types [5]. If type x is used to define type y, then we say x is apart ofy or that y contains x. Ify
contains x, then is a more complex, or more highly structured, type than x. If T is a set of types,
then we define the relation << on T by
x < The << relation forms a Directed Acyclic Graph (DAG) on the types in T. Figure 1 illustrates this
relation on the set of types T of the program P in Table 1.


oolean


Figure 1. The << relation on the set of types of the program in Table 1.







-6-


A least upper bound of a set T is an element le T with the property that there is no element ee T
such that << e. We will denote the least upper bounds of T by lub (T). As can be seen in Figure
1, the least upper bound of the set of types corresponds to the roots of the DAG. Because << is a
partial order, lub(T) will in general contain more than one element. However, lub(T) is likely to
be much smaller than T, which will greatly clarify the types that should be grouped with the
object. We can further reduce the types that are grouped with the routines by weighting the types
(perhaps by their size) and grouping the routines with only the type(s) with the highest weight.
As an example of the utility of using least upper bound types, consider that the first TBOI
example clustered the pushs and pop_s routines with the stack and elem types. Figure 1 shows
that /ub(stack,elem) = stack \. Intuitively, it is the stack type that forms the object.

4. Algorithms
The first step is to construct the internal program representation, the System Dependence Graph
(SDG). The SDG models a grammar that permits the following: all primitive (scalar) data types,
records, while and for loops, C-like return statements that can be located anywhere in a function,
functions that may or not return values (of structured types), nested procedures (as in Pascal) as
well as recursive procedures, and differentiation between call-by-reference and call-by-value
parameter passing mechanism. We should note that no pointer variables are considered at this
time. Furthermore, we must emphasize that the SDG is not constructed for implementing only
the algorithms discussed here; it is also the basis for a number of other software maintenance
activities -- namely, program slicing, dicing, and ripple analysis [4].
Even though the system dependence graph as well as its construction has been discussed
extensively elsewhere ([1], [3], [4]) for the sake of completness we present its highlights. An
SDG is a directed, labeled multigraph that consists of a program dependence graph and a collec-
tion of procedure dependence graphs. The program dependence graph models the main program
and the procedure dependence graphs model the procedure bodies. There is a one-to-one
correspondence between procedure bodies and procedure dependence graphs1. Each vertex of
these graphs represents a program construct such as a declaration, assignment, or control predi-
cate. A collection of additional vertices represent formal parameters, actual parameters, call sites,
and entry nodes. The edges represent several kinds of dependence among the vertices and are
distinguishable by the labels attached to them. Specifically, we can distinguish three types of
dependence edges: control, data, and declaration dependence edges.
In each call site, we create two set of nodes, the actualin and actualout nodes. The
former nodes are in a one-to-one correspondence with the actual parameters. The latter are in a
one-to-one correspondence with the actual parameters that are passed by reference. By definition,
all these nodes are control dependent on the call-site node. Moreover, when a call to a procedure
is encountered for the first time, two new sets of nodes, the formal_in and formal_out nodes are
created. They are control dependent to the entry node. It must be clear that the sets of actual_in
and formal_in nodes are isomorphic, as are the sets of actual_out and formal_out nodes at the
call-site and entry node, respectively, of a procedure. Formal and actual nodes, as well as call-site
and entry nodes, are "linked" via edges. Specifically, a parameterin edge is incident from an
actual_in node and incident to its corresponding formal_in node; a parameter_out edge is
incident from the formal_out node and incident to its corresponding actual_out node. A call edge
is incident from the call-site node to its corresponding entry node.
When a global or a static variable is encountered in a procedure it is introduced as an additional
pass by reference parameter to its entry node; therefore, an additional formal_in and formal_out


1 As discussed later, each aliasing pattern is assumed to give rise to a new procedure body.







-7-


nodes are created for this procedure. These nodes are tagged to indicate that they correspond to
either global or static variables. Notice that we treat the static variables as global variables of
limited scope. The motivation for introducing global as pass-by-reference parameters is to avoid
having flow edges cross procedure boundaries when using or defining global variables [1]
whereas static variables are persistent in the sense that they are alive between calls. All pro-
cedures that call a procedure directly or those which indirectly use or define global (static)
variable(s) are modified to include the global variable(s) as pass-by-reference parameters. The
call-sites are also internally modified to include the new parameter. For example, when the pro-
cedure example in Table 2 is encountered and the variable g is identified as global2 while s is
identified as static, then both variables are treated as pass-by-reference parameters.

function example(var y;var x;var z;w;var v):a;
static s;

if s = 0
{ g g g;
z 2 s;
s <- g + v;
x.x <- y.y + x.x ;
if y.y x.x
{y.y2 x.x
x.x _- x.x };
x.x <- 0;

Table 2. A function abstraction. x, y, z w, v, a and s represent the types of the vari-
ables whereas g is the identifier of a global variable. Subscripted expressions represent the
types of subfields of records. For example, x is the type of the subfield of a record of type x.


Consequently, the function's example procedure dependence graph is built as though its prototype
had been defined as
example(var y;var x;var z;w;var v;var s; var g):a;
and the call site would be adjusted accordingly. As mentioned earlier, however, these changes are
made on the SDG and not in the source program, which remains unaltered.
To facilitate precise intraprocedural (and therefore interprocedural) data dependence
analysis, when a passed parameter is of a non-scalar type such as a record we "decompose" the
record into the set of its primitive components. At the same time we allocate a set of nodes
whose cardinality is the same as the former set so that they can be properly represented. For
example, referring to the program in Table 2, when the call to procedure example is encountered
we create the new variables x.x1, x.x x.x y.yl, and y.y besides the instances of the records
x and y (Figure 2). Decomposition not only permits precise data dependence calculations but
enables us to identify subrecords as receivers, as we demonstrate shortly.
Functions in both Pascal and C require special attention. For both languages, we introduce
two new types of edges. The first, the affect_param edge, denotes the dependence between an
actual parameter and the return value of the function (i.e., if a parameter influences the return
value of the function, then an affect_param edge is incident from the actual_in node correspond-
ing to the parameter of its call-site). The second, the return_link edge, is an interprocedural
dependence edge which denotes the dependence between the return nodes in the function and the
corresponding call-site.

2 This is accomplished by a simple "look-up" in the scoped declaration table that is maintained during
the construction of the SDG.







-8 -


A transitive dependence edge exists from an actual_in node to an actual_out node if the
formal_out node corresponding to the latter node is intraslice-path-reachable from the formal_in
node (that corresponds to the formal_out node). Notice that this is equivalent to saying that the
intraprocedural slice of the PDG at the formal_out node contains the formal_in node. The collec-
tion of the transitive dependence, affectparam dependence, and return_link dependence edges at
each call site is defined as the procedure's summary information. Figure 2 illustrates the sum-
mary information of the function example.







N S

/ I / \
SA N A S SA
y x 2 Z W v s g z v S 1 1 XI 2 3





Legend: formal in formal out static F global

Figure 2. The portion of the program dependence graph corresponding to the function exam-
ple and its summary information. Bold solid arrows represent control dependence; dashed
arrows the "<<" relation; and solid arrows represent transitive edges. Other edges such as
affectparam are not shown.


During the construction of the SDG we can recognize and therefore classify a formal_out node as
either an N, S, or A node. The first case occurs when the variable is passed to the procedure and is
never modified, the second when it is sometimes modified, and the third when is always modified.
For example, in Figure 2 the formal_out nodes have been classified. Notice that for our purposes
a formal out node corresponding to a record is classified as either an S node or an N node. The
classification is equal to the logical or of its subordinate fields with A and S nodes corresponding
to true and N nodes to false.

4.1. Aliasing
The problem of aliasing (given our grammar) arises when a call to a procedure is made with two
or more parameters that share the same memory3 location. A technique that will identify direct
and indirect aliasing and the dependency analysis of procedures in the presence of aliasing has
been discussed elsewhere ([1], [4]). We have created a separate copy of the procedure for each
unique alias configuration and solve the procedure taking into account the variables that are
bound to the same memory location. If there is a call with an identical alias configuration which
has already been solved, we do not make another copy of the procedure and solve it; we merely
reflect the summary information from the procedure that was previously solved. Since aliased
objects are of the same type, we must examine the entry node of the procedure that corresponds to


3 Global variables are already treated as parameters.







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the most "alias-free" configuration of the procedure. This means that the object finder uses the
entry node that corresponds to the minimum number of aliased parameters.

4.2. Unknown Procedures
One of the advantages of using the SDG is that it can represent a program even if the bodies of
the procedures are unknown, such as library procedures. The only information that is required is
the data dependence between the parameters and the return type of the procedure. A simple way
to capture these procedure dependence is to write a "stub" routine and include it in another file.
The user's source file and this file are then merged; the SDG is then constructed on the merged
file. For example, to model a procedure whose first and second parameters are passed by value
and whose third parameter is passed by reference and is also dependent on both the first two
parameters and on itself, a stub procedure could be written as shown in Table 3.

procedure example(a, b: integer; var c:integer);
{
c <- a + b + c;
}
Table 3. Modeling unknown procedures.

It is not necessary for the code of the "stub" procedure to look anything like the real procedure
we are trying to model. In the case of unknown procedures, we are only interested in the data
dependence, so the the summary information can be derived.

4.3. Identifying M-based Objects
Algorithms that identify global-, type- and receiver-based objects using the system dependence
graph are discussed in the following paragraphs.
We have two cases of determining global-based objects. In the first case, no global variable
is passed as a parameter to another procedure. Therefore, we only examine the summary informa-
tion at each entry node and cluster all tagged, formal-in parameters with their procedure. In the
second case, when global are passed to a procedure as a parameter, some additional work is
required. To visualize the problem more clearly assume a call sequence such as A -B (y)->C(z);
let g be a global variable defined or used in A that is passed as a parameter to B and then in turn
to c. Then g can not be "threaded" based only on its name; a more powerful technique is
required. For this reason we introduce a new edge called global_thread edge which is incident
from the formal_in node to the corresponding actual_in node of the parameter. Our example
demonstrates that there would be a global-thread edge from the formal_in node corresponding to
g (in A) with the actual_in node corresponding to y (in B). Also notice that the latter node must
be tagged to indicate that it corresponds to a global variable, and also linked with its correspond-
ing formal_in node via a globalthread edge. Hence, clustering a global variable with the
procedures) with which it is defined (or used) directly or indirectly is accomplished by a simple
traversal of the path that has as its starting vertex the node representing the global variable in
question and consists of only globalthread edges.
Determination of type-based objects consists of clustering all non-tagged, formal_in param-
eters and the return type of the most alias-free configuration of the procedure. Determining
whether or not a function returns a value is done by examining to see if a retum_link edge is
incident to some call site associated with the procedure in question; in this case, the retum_link
edge is followed "backwards" to determine the type of the returned value. We note that our
method permits one to cluster the type of a global variable to a procedure given our internal pro-
gram representation.







- 10-


Finally, to determine receiver-based objects, the formal_out nodes of the most alias-free
configuration of a procedure are examined. If the formal_out node is sometimes or always
modified, then the variable has been changed in the procedure, and therefore it becomes a
receiver.

5. Conclusions and Future Work
Identifying object-like features in code written in conventional programming languages is a useful
step in applying object-oriented methods to the reengineering and maintenance of old code and in
porting programs written in procedural languages to object-oriented languages. We have shown
the shortcomings of the global-and type-based methods suggested in [2] and [5], proposed a more
precise method based on receiver types, and presented a flexible method for secondary object
finding. We have implemented the object finder and the dependence analysis tool for a large sub-
set of ANSI C and Pascal. We are currently exploring new methods to handle pointer variables in
the context of the internal representation that we employ.

6. References
[1] S. Horwitz, T. Reps and D. Binkley, Interprocedural slicing using dependence graphs, ACM
TOPLAS, January 1990.
[2] S.S. Liu, N. Wilde, "k, iuir,, objects in a conventional procedural language", in Proceed-
ings of the Conference on Software Maintenance, November 1990.
[3] P.E. Livadas, S. Croll and P.K. Roy, "Towards an Integrated Software Maintenance Environ-
ment", in Proceedings of the 1st Symposium on Software Engineering Research Forum, Tampa,
Florida, November 1991.
[4] P.E. Livadas, S. Croll, "Program Slicing", SERC-TR-55F, Software Engineering Research
Center, Computer and Information Sciences Department, University of Florida, October 1992.
[5] R.M. Ogando, "An Approach to Software System Modularization Based on Data and Type
Binding ", PhD thesis, University of Florida, Gainesville, Florida, 1991.




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