Automating Change of Representation for Proofs in Discrete Mathematics

Daniel Raggi; Alan Bundy; Gudmund Grov; Alison Pease

doi:10.1007/978-3-319-20615-8_15

Automating Change of Representation for Proofs in Discrete Mathematics

Daniel Raggi^*, Alan Bundy, Gudmund Grov, Alison Pease

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

Representation determines how we can reason about a specific problem. Sometimes one representation helps us find a proof more easily than others. Most current automated reasoning tools focus on reasoning within one representation. There is, therefore, a need for the development of better tools to mechanise and automate formal and logically sound changes of representation.

In this paper we look at examples of representational transformations in discrete mathematics, and show how we have used Isabelle's Transfer tool to automate the use of these transformations in proofs. We give a brief overview of a general theory of transformations that we consider appropriate for thinking about the matter, and we explain how it relates to the Transfer package. We show our progress towards developing a general tactic that incorporates the automatic search for representation within the proving process.

Original language	English
Title of host publication	Intelligent Computer Mathematics
Subtitle of host publication	International Conference, CICM 2015, Washington, DC, USA, July 13-17, 2015, Proceedings.
Editors	Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, Volker Sorge
Publisher	Springer
Pages	227-242
Number of pages	16
ISBN (Electronic)	978-3-319-20615-8
ISBN (Print)	978-3-319-20614-1
DOIs	https://doi.org/10.1007/978-3-319-20615-8_15
Publication status	Published - 2015
Event	International Conference on Intelligent Computer Mathematics 2015 - Washington, United States Duration: 13 Jul 2015 → 17 Jul 2015

Publication series

Name	Lecture Notes in Computer Science
Volume	9150
ISSN (Print)	0302-9743

Conference

Conference	International Conference on Intelligent Computer Mathematics 2015
Abbreviated title	CICM 2015
Country/Territory	United States
City	Washington
Period	13/07/15 → 17/07/15

Keywords

Change of representation
Transformation
Automated reasoning
Isabelle proof assistant

Access to Document

10.1007/978-3-319-20615-8_15

Cite this

Raggi, D., Bundy, A., Grov, G., & Pease, A. (2015). Automating Change of Representation for Proofs in Discrete Mathematics. In M. Kerber, J. Carette, C. Kaliszyk, F. Rabe, & V. Sorge (Eds.), Intelligent Computer Mathematics: International Conference, CICM 2015, Washington, DC, USA, July 13-17, 2015, Proceedings. (pp. 227-242). (Lecture Notes in Computer Science; Vol. 9150). Springer. https://doi.org/10.1007/978-3-319-20615-8_15

Raggi, Daniel ; Bundy, Alan ; Grov, Gudmund et al. / Automating Change of Representation for Proofs in Discrete Mathematics. Intelligent Computer Mathematics: International Conference, CICM 2015, Washington, DC, USA, July 13-17, 2015, Proceedings.. editor / Manfred Kerber ; Jacques Carette ; Cezary Kaliszyk ; Florian Rabe ; Volker Sorge. Springer, 2015. pp. 227-242 (Lecture Notes in Computer Science).

@inproceedings{34e82b590ad8483cb5afee5a44f1c3f3,

title = "Automating Change of Representation for Proofs in Discrete Mathematics",

abstract = "Representation determines how we can reason about a specific problem. Sometimes one representation helps us find a proof more easily than others. Most current automated reasoning tools focus on reasoning within one representation. There is, therefore, a need for the development of better tools to mechanise and automate formal and logically sound changes of representation.In this paper we look at examples of representational transformations in discrete mathematics, and show how we have used Isabelle's Transfer tool to automate the use of these transformations in proofs. We give a brief overview of a general theory of transformations that we consider appropriate for thinking about the matter, and we explain how it relates to the Transfer package. We show our progress towards developing a general tactic that incorporates the automatic search for representation within the proving process.",

keywords = "Change of representation, Transformation, Automated reasoning, Isabelle proof assistant",

author = "Daniel Raggi and Alan Bundy and Gudmund Grov and Alison Pease",

year = "2015",

doi = "10.1007/978-3-319-20615-8_15",

language = "English",

isbn = "978-3-319-20614-1",

series = "Lecture Notes in Computer Science",

publisher = "Springer",

pages = "227--242",

editor = "Manfred Kerber and Jacques Carette and Cezary Kaliszyk and Florian Rabe and Volker Sorge",

booktitle = "Intelligent Computer Mathematics",

note = "International Conference on Intelligent Computer Mathematics 2015, CICM 2015 ; Conference date: 13-07-2015 Through 17-07-2015",

}

Raggi, D, Bundy, A, Grov, G & Pease, A 2015, Automating Change of Representation for Proofs in Discrete Mathematics. in M Kerber, J Carette, C Kaliszyk, F Rabe & V Sorge (eds), Intelligent Computer Mathematics: International Conference, CICM 2015, Washington, DC, USA, July 13-17, 2015, Proceedings.. Lecture Notes in Computer Science, vol. 9150, Springer, pp. 227-242, International Conference on Intelligent Computer Mathematics 2015, Washington, United States, 13/07/15. https://doi.org/10.1007/978-3-319-20615-8_15

Automating Change of Representation for Proofs in Discrete Mathematics. / Raggi, Daniel; Bundy, Alan; Grov, Gudmund et al.

Intelligent Computer Mathematics: International Conference, CICM 2015, Washington, DC, USA, July 13-17, 2015, Proceedings.. ed. / Manfred Kerber; Jacques Carette; Cezary Kaliszyk; Florian Rabe; Volker Sorge. Springer, 2015. p. 227-242 (Lecture Notes in Computer Science; Vol. 9150).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Automating Change of Representation for Proofs in Discrete Mathematics

AU - Raggi, Daniel

AU - Bundy, Alan

AU - Grov, Gudmund

AU - Pease, Alison

PY - 2015

Y1 - 2015

N2 - Representation determines how we can reason about a specific problem. Sometimes one representation helps us find a proof more easily than others. Most current automated reasoning tools focus on reasoning within one representation. There is, therefore, a need for the development of better tools to mechanise and automate formal and logically sound changes of representation.In this paper we look at examples of representational transformations in discrete mathematics, and show how we have used Isabelle's Transfer tool to automate the use of these transformations in proofs. We give a brief overview of a general theory of transformations that we consider appropriate for thinking about the matter, and we explain how it relates to the Transfer package. We show our progress towards developing a general tactic that incorporates the automatic search for representation within the proving process.

AB - Representation determines how we can reason about a specific problem. Sometimes one representation helps us find a proof more easily than others. Most current automated reasoning tools focus on reasoning within one representation. There is, therefore, a need for the development of better tools to mechanise and automate formal and logically sound changes of representation.In this paper we look at examples of representational transformations in discrete mathematics, and show how we have used Isabelle's Transfer tool to automate the use of these transformations in proofs. We give a brief overview of a general theory of transformations that we consider appropriate for thinking about the matter, and we explain how it relates to the Transfer package. We show our progress towards developing a general tactic that incorporates the automatic search for representation within the proving process.

KW - Change of representation

KW - Transformation

KW - Automated reasoning

KW - Isabelle proof assistant

U2 - 10.1007/978-3-319-20615-8_15

DO - 10.1007/978-3-319-20615-8_15

M3 - Conference contribution

SN - 978-3-319-20614-1

T3 - Lecture Notes in Computer Science

SP - 227

EP - 242

BT - Intelligent Computer Mathematics

A2 - Kerber, Manfred

A2 - Carette, Jacques

A2 - Kaliszyk, Cezary

A2 - Rabe, Florian

A2 - Sorge, Volker

PB - Springer

T2 - International Conference on Intelligent Computer Mathematics 2015

Y2 - 13 July 2015 through 17 July 2015

ER -

Raggi D, Bundy A, Grov G, Pease A. Automating Change of Representation for Proofs in Discrete Mathematics. In Kerber M, Carette J, Kaliszyk C, Rabe F, Sorge V, editors, Intelligent Computer Mathematics: International Conference, CICM 2015, Washington, DC, USA, July 13-17, 2015, Proceedings.. Springer. 2015. p. 227-242. (Lecture Notes in Computer Science). doi: 10.1007/978-3-319-20615-8_15

Automating Change of Representation for Proofs in Discrete Mathematics

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