Formalizing in Coq Hidden Algebras to Specify Symbolic Computation Systems

This work is an attempt to formalize, using the Coq proof assistant, the algebraic specification of the data structures appearing in two symbolic computation systems for algebraic topology called EAT and Kenzo. The specification of these structures have been obtained through an operation, called impoperation, between different specification frameworks as standard algebraic specifications and hidden specifications. Reusing previous Coq implementations of universal algebra and category theory we have proposed a Coq formalization of the impoperation, extending the representation to the particular hidden algebras which take part in this operation.

[1]  David Aspinall,et al.  Formalising Java's Data Race Free Guarantee , 2007, TPHOLs.

[2]  César Domínguez,et al.  Modeling Inheritance as Coercion in the Kenzo System , 2006, J. Univers. Comput. Sci..

[3]  Christoph Lüth,et al.  A Framework for Interactive Proof , 2007, Calculemus/MKM.

[4]  Julio Rubio,et al.  Constructive algebraic topology , 2002 .

[5]  Hans-Dieter Ehrich,et al.  Specification of abstract data types , 1996 .

[6]  César Domínguez,et al.  Object oriented institutions to specify symbolic computation systems , 2007, RAIRO Theor. Informatics Appl..

[7]  Vico Pascual,et al.  An Object-oriented Interpretation of the EAT System , 2003, Applicable Algebra in Engineering, Communication and Computing.

[8]  Jesús Aransay,et al.  A Mechanized Proof of the Basic Perturbation Lemma , 2008, Journal of Automated Reasoning.

[9]  Julio Rubio.  Locally Effective Objects and Artificial Intelligence , 2000, AISC.

[10]  Julio Rubio,et al.  Executing in Common Lisp, Proving in ACL2 , 2007, Calculemus/MKM.

[11]  Venanzio Capretta,et al.  Universal Algebra in Type Theory , 1999, TPHOLs.

[12]  Joseph A. Goguen,et al.  Institutions: abstract model theory for specification and programming , 1992, JACM.

[13]  Joseph A. Goguen,et al.  A hidden agenda , 2000, Theor. Comput. Sci..

[14]  Thierry Coquand,et al.  Towards Constructive Homological Algebra in Type Theory , 2007, Calculemus/MKM.

[15]  Giovanni Sambin,et al.  Twenty-five years of constructive type theory. , 1998 .

[16]  G. Plotkin,et al.  Proof, language, and interaction: essays in honour of Robin Milner , 2000 .

[17]  Joseph A. Goguen,et al.  A hidden Herbrand theorem: combining the object and logic paradigms , 2002, J. Log. Algebraic Methods Program..

[18]  Gérard P. Huet,et al.  Constructive category theory , 2000, Proof, Language, and Interaction.