Proof-Pattern Recognition and Lemma Discovery in ACL2

Jonathan Heras; Ekaterina Komendantskaya; Moa Johansson; Ewen Maclean

doi:10.1007/978-3-642-45221-5_27

Proof-Pattern Recognition and Lemma Discovery in ACL2

Jonathan Heras, Ekaterina Komendantskaya, Moa Johansson, Ewen Maclean

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

25 Citations (Scopus)

Abstract

We present a novel technique for combining statistical machine learning for proof-pattern recognition with symbolic methods for lemma discovery. The resulting tool, ACL2(ml), gathers proof statistics and uses statistical pattern-recognition to pre-processes data from libraries, and then suggests auxiliary lemmas in new proofs by analogy with already seen examples. This paper presents the implementation of ACL2(ml) alongside theoretical descriptions of the proof-pattern recognition and lemma discovery methods involved in it.

Original language	English
Title of host publication	Logic for Programming, Artificial Intelligence, and Reasoning
Subtitle of host publication	19th International Conference, LPAR-19, Stellenbosch, South Africa, December 14-19, 2013. Proceedings
Editors	Ken McMillan, Aart Middeldorp, Andrei Voronkov
Publisher	Springer
Pages	389-406
Number of pages	18
ISBN (Electronic)	9783642452215
ISBN (Print)	9783642452208
DOIs	https://doi.org/10.1007/978-3-642-45221-5_27
Publication status	Published - 2013
Event	19th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning - Stellenbosch, United Kingdom Duration: 14 Dec 2013 → 19 Dec 2013

Publication series

Name	Lecture Notes in Computer Science
Publisher	Springer Berlin Heidelberg
Volume	8312
ISSN (Print)	0302-9743

Conference

Conference	19th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Abbreviated title	LPAR 2013
Country/Territory	United Kingdom
City	Stellenbosch
Period	14/12/13 → 19/12/13

Keywords

Theorem Proving
Statistical Machine-Learning
Pattern Recognition
Lemma Discovery
Analogy

Access to Document

10.1007/978-3-642-45221-5_27

Cite this

Heras, J., Komendantskaya, E., Johansson, M., & Maclean, E. (2013). Proof-Pattern Recognition and Lemma Discovery in ACL2. In K. McMillan, A. Middeldorp, & A. Voronkov (Eds.), Logic for Programming, Artificial Intelligence, and Reasoning: 19th International Conference, LPAR-19, Stellenbosch, South Africa, December 14-19, 2013. Proceedings (pp. 389-406). (Lecture Notes in Computer Science; Vol. 8312). Springer. https://doi.org/10.1007/978-3-642-45221-5_27

Heras, Jonathan ; Komendantskaya, Ekaterina ; Johansson, Moa et al. / Proof-Pattern Recognition and Lemma Discovery in ACL2. Logic for Programming, Artificial Intelligence, and Reasoning: 19th International Conference, LPAR-19, Stellenbosch, South Africa, December 14-19, 2013. Proceedings. editor / Ken McMillan ; Aart Middeldorp ; Andrei Voronkov. Springer, 2013. pp. 389-406 (Lecture Notes in Computer Science).

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abstract = "We present a novel technique for combining statistical machine learning for proof-pattern recognition with symbolic methods for lemma discovery. The resulting tool, ACL2(ml), gathers proof statistics and uses statistical pattern-recognition to pre-processes data from libraries, and then suggests auxiliary lemmas in new proofs by analogy with already seen examples. This paper presents the implementation of ACL2(ml) alongside theoretical descriptions of the proof-pattern recognition and lemma discovery methods involved in it.",

keywords = "Theorem Proving, Statistical Machine-Learning, Pattern Recognition, Lemma Discovery, Analogy",

author = "Jonathan Heras and Ekaterina Komendantskaya and Moa Johansson and Ewen Maclean",

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language = "English",

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series = "Lecture Notes in Computer Science",

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pages = "389--406",

editor = "Ken McMillan and Aart Middeldorp and Andrei Voronkov",

booktitle = "Logic for Programming, Artificial Intelligence, and Reasoning",

note = "19th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning, LPAR 2013 ; Conference date: 14-12-2013 Through 19-12-2013",

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Heras, J, Komendantskaya, E, Johansson, M & Maclean, E 2013, Proof-Pattern Recognition and Lemma Discovery in ACL2. in K McMillan, A Middeldorp & A Voronkov (eds), Logic for Programming, Artificial Intelligence, and Reasoning: 19th International Conference, LPAR-19, Stellenbosch, South Africa, December 14-19, 2013. Proceedings. Lecture Notes in Computer Science, vol. 8312, Springer, pp. 389-406, 19th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning, Stellenbosch, United Kingdom, 14/12/13. https://doi.org/10.1007/978-3-642-45221-5_27

Proof-Pattern Recognition and Lemma Discovery in ACL2. / Heras, Jonathan; Komendantskaya, Ekaterina; Johansson, Moa et al.
Logic for Programming, Artificial Intelligence, and Reasoning: 19th International Conference, LPAR-19, Stellenbosch, South Africa, December 14-19, 2013. Proceedings. ed. / Ken McMillan; Aart Middeldorp; Andrei Voronkov. Springer, 2013. p. 389-406 (Lecture Notes in Computer Science; Vol. 8312).

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

TY - CHAP

T1 - Proof-Pattern Recognition and Lemma Discovery in ACL2

AU - Heras, Jonathan

AU - Komendantskaya, Ekaterina

AU - Johansson, Moa

AU - Maclean, Ewen

PY - 2013

Y1 - 2013

N2 - We present a novel technique for combining statistical machine learning for proof-pattern recognition with symbolic methods for lemma discovery. The resulting tool, ACL2(ml), gathers proof statistics and uses statistical pattern-recognition to pre-processes data from libraries, and then suggests auxiliary lemmas in new proofs by analogy with already seen examples. This paper presents the implementation of ACL2(ml) alongside theoretical descriptions of the proof-pattern recognition and lemma discovery methods involved in it.

AB - We present a novel technique for combining statistical machine learning for proof-pattern recognition with symbolic methods for lemma discovery. The resulting tool, ACL2(ml), gathers proof statistics and uses statistical pattern-recognition to pre-processes data from libraries, and then suggests auxiliary lemmas in new proofs by analogy with already seen examples. This paper presents the implementation of ACL2(ml) alongside theoretical descriptions of the proof-pattern recognition and lemma discovery methods involved in it.

KW - Theorem Proving

KW - Statistical Machine-Learning

KW - Pattern Recognition

KW - Lemma Discovery

KW - Analogy

U2 - 10.1007/978-3-642-45221-5_27

DO - 10.1007/978-3-642-45221-5_27

M3 - Chapter

SN - 9783642452208

T3 - Lecture Notes in Computer Science

SP - 389

EP - 406

BT - Logic for Programming, Artificial Intelligence, and Reasoning

A2 - McMillan, Ken

A2 - Middeldorp, Aart

A2 - Voronkov, Andrei

PB - Springer

T2 - 19th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning

Y2 - 14 December 2013 through 19 December 2013

ER -

Heras J, Komendantskaya E, Johansson M, Maclean E. Proof-Pattern Recognition and Lemma Discovery in ACL2. In McMillan K, Middeldorp A, Voronkov A, editors, Logic for Programming, Artificial Intelligence, and Reasoning: 19th International Conference, LPAR-19, Stellenbosch, South Africa, December 14-19, 2013. Proceedings. Springer. 2013. p. 389-406. (Lecture Notes in Computer Science). doi: 10.1007/978-3-642-45221-5_27

Proof-Pattern Recognition and Lemma Discovery in ACL2

Abstract

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Keywords

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