Analysis of Software Variants

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1 Analysis of Software Variants Christian Lindig CAROL Software Technology Group Technical University of Braunschweig Germany -BRA

2 Outline Computer platform diversity causes software diversity software exists in variants. Most common strategy: separation at the module level and source code preprocessing for individual platforms. variant HP-UX Unix CPP Solaris Linux Aim: A better understanding of all the variants a specific source can generate. æ How many variants exist? æ How are variants related? æ How to generate a specific variant? æ Is there an easier way to create the same set of variants?

3 Example getopt.c /* This tells Alpha OSF/ not to define a getopt prototype in <stdio.h>. Ditto for AIX. and <stdlib.h>. */ #ifndef _NO_PROTO #define _NO_PROTO #ifdef HAVE_CONFIG_H #if defined (emacs) defined (CONFIG_BROKETS) /* We use <config.h> instead of "config.h" so that a compilation using -I. -I\$srcdir will use./config.h rather than \$srcdir/config.h (which it would do because it found this file in \$srcdir). */ #include <config.h> #else #include "config.h" #ifndef STDC /* This is a separate conditional since some stdc systems reject defined (const). */ #ifndef const #define const

4 Result Result of an analysis: the variant lattice for a source file. 7,5 8 5 expressions segments It shows: æ all variants and their relations, æ how to create them, æ and redundant expressions. Analysis technique: formal concept analysis.

5 Concept Analysis Unix-System-Calls access chdir chmod chown creat fork fstat mkdir rmdir access change check create directory file get group input mode new output owner permission process status remove Keywords A (formal) context is a triple (O, A, R) where O and A are sets of objects and attributes respectively and R O Ais a relation among them. AsetO(A) of objects (attributes) shares a set of common attributes (objects): O A def = {a A o O:(o, a) R} def = {o O a A:(o, a) R} [Krone, Snelting ICSE 9] defined O as ω(o) and A as α(a)

6 access change check create directory file get group input mode new output owner permission process remove status Context Table access chdir chmod chown creat fork fstat mkdir rmdir Keywords Unix-System-Calls

7 Concept Unix-System-Calls access chdir chmod chown creat fork fstat mkdir rmdir access change check create directory file get group input mode new output owner permission process status remove Keywords A concept c = (O, A) of a context (O, A, R) is a pair where O = A and A = O and also O O,A A. Concepts are (partially) ordered: (O,A ) (O,A ) O O ( A A ) The set of all concepts of (O, A, R) is denoted by B(O, A, R).

8 Concept Lattice Keywords attribute object file change create Unix-System-Calls access chdir chmod chown creat fork fstat mkdir rmdir access change check create directory file get group input mode new output owner permission process remove status directory new attribute permission group remove output input status access mode owner process get check rmdir chdir fstat access mkdir chmod chown creat fork object Basic theorem of context analysis by Wille: Let (O, A, R) be a context. Then B(O, A, R) is a complete lattice, the concept lattice of (O, A, R). (O,A ) (O,A ) = (O O,(O O ) ) (O,A ) (O,A ) = ((A A ),A A ) The maximal number of concepts is n where n = max( O, A ). Ganter s algorithm computes all concepts of (O, A, R) with time complexity O( B(O,A,R) ).

9 Concept Lattice Keywords access change check create directory file get group input mode new output owner permission process remove status attribute object file change create Unix-System-Calls access chdir chmod chown creat fork fstat mkdir rmdir directory new attribute permission group remove output input status access mode owner process get check rmdir chdir fstat access mkdir chmod chown creat fork object

10 The Idea #if defined(e ) && defined(e ) && defined(e 8 ) S #if defined (E ) && defined(e 5 ) && defined(e 7 ) S S #if defined(e ) && defined(e 5 ) && defined(e 7 ) S #ifdef E #if defined(e ) && defined(e ) S #ifdef E 8 S 5 Expression Segment E E E E E 5 E E 7 E 8 S S S S S 5 S Encode the meaning of CPP-expressions into a binary relation (i.e. formal context) and analyze it using concept analysis [cf. Krone, Snelting, ICSE 9].

11 A Model of CPP æ A configuration function f evaluates expressions e E: f :E {0,}. æ Avariant is a set of segments, selected by a configuration function f from a configuration table (S, E, T ): f(s,e,t)={s S f(e)= for all (s, e) T}. æ Configuration functions f and f are called equivalent (with respect to (S, E, T )), if they have the same effect: f f f (S, E, T ) = f (S, E, T ) [f ] denotes configuration functions equivalent to f. Expression f f Segment E E E E E 5 E E 7 E 8 S S S S S 5 S

12 Variants T E E f Segment E E E E E 5 E E 7 E 8 S S S S S 5 (S, E) S We find: [f ] is an equivalence class where f(s,e,t)=s iff (S, E) B(S,E,T ). This means: every concept of the inverted configuration table describes an equivalence class. Proof sketch: there is no variant not described by a concept in (S, E, T ). E T E E T E E T E S S S

13 Variant Lattice The example s variant lattice (i.e. the concept lattice of (S, E, T )). 7,5 8 5 expressions segments Each concept describes a variant and the canonical way to create it. T f Segment E E E E E 5 E E 7 E 8 S S S S S 5 S

14 Variant Lattice vs. Configuration Lattice The variant lattice for the example: 7,5 8 5 expressions segments And its configuration lattice [cf. Krone, Snelting, ICSE 9]. 8 7,5 5 expression segment

15 Redundancies Are there expressions in my source file that can be safely eliminated? T Segment E E E E E 5 E E 7 E 8 S S S S S 5 S An expression is called redundant if it can be removed from a configuration table without effect on any configuration function. Formally, e is redundant iff the following holds for any f : f(s,e,t)=f(s,e,t ) where E =E\{e}and T =T (S E )

16 Detecting Redundancies Redundant expressions show up in the concept lattice of the inverted configuration table as -reducible concepts: (redundant) 5 7,5 8 5 expressions segments Formally: e Eis redundant in (S, E, T ) if X E,e X exists in (S, E, T ) such that {e} = X. X e e X e e e e e e e '= X' e '= X' e super concept super concept

17 Problems #if defined(a) defined (b) C #if (defined(a) defined(b)) && defined (c) C #if!defined(a) &&!defined(b) C Expression Segment a b c a b C C C C,C C,C,C C C,C Consider f with f {a b, a, b} then theory says: S ={C,C } is a variant. Problem: Theory does not take interdependencies into account (yet). Future work: use background implications to express dependencies.

18 Future Work æ Extend theory with background implications to overcome limitations. æ Implementation Concept analysis tool written in C available (send !) Re of a concept analysis library in progress Implementation will be based on new library æ Evaluation

19 Conclusions æ Concept analysis is a promising theory for software re-engineering æ Variants generated from a source have a rich structure which can be effectively analyzed using concept analysis æ Variant description may contain redundant expressions which can be detected and removed æ This is work in progress still much room for improvement and research.

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