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https://github.com/lindig/colibri-ml

Formal Concept Analysis in OCaml
https://github.com/lindig/colibri-ml

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Formal Concept Analysis in OCaml

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README 

        

# Colibri



This is Colibri, a library and a demo application for formal concept

analysis implemented in Objective Caml.



## Concept Analysis



Formal Concept Analysis is an algebraic theory for binary relations.

Every binary relation induces a complete lattice of so-called concepts.

Concept lattices is also known as Galois Lattices. The definite text

book for concept analysis is:



    Formal Concept Analysis : Mathematical Foundations

    by  Bernhard Ganter, Rudolf Wille, C. Franzke

    Springer, 1998.



    http://www.amazon.com/gp/product/3540627715/104-1061763-0179914



## Example



What are concepts and what is a concept lattice? A binary relation

over objects and associated attributes may be represented

as a context table:



    objects		attributes

    -------------------------------------------------------------

    chmod:		change file mode permission ;

    chown:		change file group owner;

    fstat:		get file status ;

    fork:		create new process ;

    chdir:		change directory ;

    mkdir:		create directory new ;

    open:		create file open read write;

    read:		file input read ;

    rmdir:		directory file remove ;

    write:		file output write ;

    creat:		create file new ;

    access:		access check file ;



Here objects are Unix system calls and attributes are associated terms

describing a system call. Any set of objects shares a (possibly empty)

set of common attributes: the set {chdir,mkdir} shares {directory} for

example. The same is true for attribute sets which share common

objects. So every set of objects determines a set of common attributes

and every set of attributes determines a set of common objects,

forming a pair of object and attribute set. A pair (O,A) of such two

sets is called a concept, if the following holds: the set of

attributes common to the objects in O is A and the set of objects

commonly shared by the attributes in A is O. Every binary relation

induces such concepts and the program calculates them.



All concepts from a binary relation are (partially) ordered and even

more, form a lattice. Concepts are ordered by (O1,A1) <= (O2,A2) if and

only if A1 <= A2 holds. Concepts computes for every concept its super-

and subconcepts and permits to output the lattice structure. The

complete set of concepts from the example above is shown below. Each

concept contains a unique number, the set of objects and the set of

attributes.



    {0 {access creat write rmdir read open mkdir chdir fork fstat chown chmod} {}}

    {1 {access creat write rmdir read open fstat chown chmod} {file}}

    {2 {access} {file check access}}

    {3 {creat open mkdir fork} {create}}

    {4 {creat open} {file create}}

    {5 {creat mkdir fork} {new create}}

    {6 {creat} {file new create}}

    {7 {write open} {file write}}

    {8 {write} {file write output}}

    {9 {rmdir mkdir chdir} {directory}}

    {10 {rmdir} {file remove directory}}

    {11 {read open} {file read}}

    {12 {read} {file read input}}

    {13 {open} {file create write read open}}

    {14 {mkdir} {new create directory}}

    {15 {chdir chown chmod} {change}}

    {16 {chdir} {directory change}}

    {17 {fork} {new create process}}

    {18 {fstat} {file status get}}

    {19 {chown chmod} {file change}}

    {20 {chown} {file change owner group}}

    {21 {chmod} {file change permission mode}}

    {22 {} {file check access new create write output remove directory

            read input open change process status get owner group permission mode}}



## Compilation



Take a look at the `Makefile`. You might want to change `PREFIX` but for a

first try there is no need to change anything. The build process assumes a

Unix system and an OCaml installation. It does not depend on libraries

outside of the OCaml standard libraries

    

    make

    make install



## User Manual



There is a Unix man page in doc/ (after compilation). You can format it

using nroff:



    nroff -man doc/colibri.1 | less



## Development Documentation



This software is implemented as a literate program - the source code are

the `*.nw` (NoWeb) files that contain LaTeX documentation and OCaml source

code. For compilation source code is automatically extracted.



## Applications



Directory `doc/` contains a [paper](doc/mining-patterns.pdf) that uses

formal concept analysis to find anomalies in software that may indicate

bugs. The idea is to find frequent patterns and few deviations from these

patterns could indicate a problem.  Pattern and deviations from patterns

are formalized in a framework of formal concepts. This was later used in

this paper:



    @inproceedings{wasylkowski2007FSE,

        title={Detecting object usage anomalies},

        author={Wasylkowski, Andrzej 

            and Zeller, Andreas 

            and Lindig, Christian},

        booktitle={Proceedings of the the 6th joint meeting of the European

            software engineering conference and the 

            ACM SIGSOFT symposium on The foundations of 

            software engineering},

        pages={35--44},

        year={2007},

        organization={ACM}

    }



You can find some more papers using formal concept analysis here:



    http://scholar.google.de/citations?user=M8QezN0AAAAJ



##  Download



Source code is available from GitHub



    https://github.com/lindig/colibri-ml.git



## Author 



Christian Lindig

[email protected]