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Proof-Pattern Recognition and Lemma Discovery in ACL2 [article]

Jónathan Heras, Ekaterina Komendantskaya, Moa Johansson, Ewen Maclean
2013 arXiv   pre-print
We present a novel technique for combining statistical machine learning for proof-pattern recognition with symbolic methods for lemma discovery.  ...  This paper presents the implementation of ACL2(ml) alongside theoretical descriptions of the proof-pattern recognition and lemma discovery methods involved in it.  ...  We compare our tool with QuickSpec [5] -a state of the art system for generating equational conjectures about Haskell programs.  ... 
arXiv:1308.1780v2 fatcat:e2vvq2y3a5e6jglfkqxdgtrji4

Proof-Pattern Recognition and Lemma Discovery in ACL2 [chapter]

Jónathan Heras, Ekaterina Komendantskaya, Moa Johansson, Ewen Maclean
2013 Lecture Notes in Computer Science  
We present a novel technique for combining statistical machine learning for proof-pattern recognition with symbolic methods for lemma discovery.  ...  This paper presents the implementation of ACL2(ml) alongside theoretical descriptions of the proof-pattern recognition and lemma discovery methods involved in it.  ...  We compare our tool with QuickSpec [5] -a state of the art system for generating equational conjectures about Haskell programs.  ... 
doi:10.1007/978-3-642-45221-5_27 fatcat:fzqriuvmi5afterecszjwzjcdi

Model-Guided Synthesis of Inductive Lemmas for FOL with Least Fixpoints [article]

Adithya Murali, Lucas Peña, Eion Blanchard, Christof Löding, P. Madhusudan
2022 arXiv   pre-print
In this paper, we undertake a novel approach for synthesizing inductive hypotheses in order to prove validity in this logic.  ...  Recursively defined linked data structures embedded in a pointer-based heap and their properties are naturally expressed in pure first-order logic with least fixpoint definitions (FO+lfp) with background  ...  The main proposal of this paper is to build automated reasoning for FO+lfp with background theories using a combination of (a) complete procedures for FO reasoning to prove theorems and PFPs of lemmas,  ... 
arXiv:2009.10207v3 fatcat:hn6nmx3ttzhldmzkm67rj2vwrq

Special issue on symbolic computation in software science

Adel Bouhoula, Bruno Buchberger, Laura Kovács, Temur Kutsia
2015 Journal of symbolic computation  
Automation of algorithm synthesis and theory exploration are the problems considered in the paper by Isabela Drȃmnesc and Tudor Jebelean.  ...  It is intended for debugging and optimizing Rewriting Logic-based tools that manipulate computations in conditional rewrite theories modulo equations.  ...  Harald Zankl, Sarah Winkler, and Aart Middeldorp present an automated termination proof for a rewrite system whose derivational complexity cannot be bounded by a multiple recursive function.  ... 
doi:10.1016/j.jsc.2014.09.027 fatcat:ty5l4i7zgzedpkijxtxpisojfe

Hipster: Integrating Theory Exploration in a Proof Assistant [chapter]

Moa Johansson, Dan Rosén, Nicholas Smallbone, Koen Claessen
2014 Lecture Notes in Computer Science  
The first is exploratory mode, used for automatically generating basic lemmas about a given set of datatypes and functions in a new theory development.  ...  Theory exploration is a technique for automatically discovering new interesting lemmas in a given theory development. Hipster can be used in two main modes.  ...  The final version of this publication is available at http://link.springer.com.  ... 
doi:10.1007/978-3-319-08434-3_9 fatcat:n4opckzg2jgk5e3zjafthjy3yy

Hipster: Integrating Theory Exploration in a Proof Assistant [article]

Moa Johansson and Dan Rosen and Nicholas Smallbone and Koen Claessen
2014 arXiv   pre-print
The first is exploratory mode, used for automatically generating basic lemmas about a given set of datatypes and functions in a new theory development.  ...  Theory exploration is a technique for automatically discovering new interesting lemmas in a given theory development. Hipster can be used in two main modes.  ...  The final version of this publication is available at http://link.springer.com.  ... 
arXiv:1405.3426v1 fatcat:zbsrlil6uvaafcolhjjqr5dopi

Recursive Program Optimization Through Inductive Synthesis Proof Transformation

Peter Madden, Alan Bundy, Alan Smaill
1999 Journal of automated reasoning  
We describe a working proof transformation system which, by exploiting the duality between mathematical induction and recursion, employs the novel strategy of optimizing recursive programs by transforming  ...  The research described in this paper involved developing transformation techniques which increase the efficiency of the noriginal program, the source, by transforming its synthesis proof into one, the  ...  The OYSTER System The OYSTER system is an implementation of a constructive type theory which is based on Martin-Löf type theory, [?] .  ... 
doi:10.1023/a:1005969312327 dblp:journals/jar/MaddenBS99 fatcat:bfa4t4khaje2donwrokh4u7yc4

The Matrix Reproved (Verification Pearl) [chapter]

Martin Clochard, Léon Gondelman, Mário Pereira
2016 Lecture Notes in Computer Science  
In this paper we describe a complete solution for the first challenge of the VerifyThis 2016 competition held at the 18th ETAPS Forum.  ...  The proofs are conducted using the Why3 platform for deductive program verification, and automated theorem provers to discharge proof obligations.  ...  Acknowledgements We thank Arthur Charguéraud, Jean-Christophe Filliâtre, and Claude Marché for their comments and remarks.  ... 
doi:10.1007/978-3-319-48869-1_8 fatcat:jg5x2z2oj5h6tcgaqf3ge6yat4

Verifying a logic synthesis tool in Nuprl: A case study in software verification [chapter]

Mark Aagaard, Miriam Leeser
1993 Lecture Notes in Computer Science  
We have proved a logic synthesis tool with the Nuprl proof development system.  ...  Our goal was to develop a proven and usable implementation of a hardware synthesis tool. Pbs consists of approximately 1000 lines of code implemented in a functional subset of Standard ML.  ...  In addition we would like to thank Chet Murthy and Doug Howe, who were always willing to help and gave us a number of useful suggestions.  ... 
doi:10.1007/3-540-56496-9_7 fatcat:7sr6qhxu6vf37ejjvcr7tzq4te

The Automation of Proof by Mathematical Induction [chapter]

Alan Bundy
2001 Handbook of Automated Reasoning  
Thus mathematical induction is a key enabling technology for the use of formal methods in information technology.  ...  Failure to automate inductive reasoning is one of the major obstacles to the widespread use of formal methods in industrial hardware and software development.  ...  Our proofs are semantic and do not require lemmas or induction as would be needed when employing a conventional theory of strings as a recursive data type. [Bas95] David A. Basin and Nils Klarlund.  ... 
doi:10.1016/b978-044450813-3/50015-1 fatcat:y2m3e2cjjfhf5nvs734xddyxqi

Page 2136 of Mathematical Reviews Vol. , Issue 85e [page]

1985 Mathematical Reviews  
A constructive description of the automatic program synthesis method used in the PRIZ programming system is presented.  ...  A. V. Anisimov (Kiev) 85e:68060 COMPUTER SCIENCE 2136 Nepeivoda, N. N.; Sviridenko, D. I. 85e:68061 On the theory of program synthesis.  ... 

Translating Scala Programs to Isabelle/HOL [chapter]

Lars Hupel, Viktor Kuncak
2016 Lecture Notes in Computer Science  
We present a trustworthy connection between the Leon verification system and the Isabelle proof assistant. Leon is a system for verifying functional Scala programs.  ...  It uses a variety of automated theorem provers (ATPs) to check verification conditions (VCs) stemming from the input program.  ...  Leon system (http://leon.epfl.ch) is a verification and synthesis system for a subset of Scala [2, 10] .  ... 
doi:10.1007/978-3-319-40229-1_38 fatcat:wryklognxfgfvmrccw7ske2vxa

Theory Exploration Powered By Deductive Synthesis [article]

Eytan Singher, Shachar Itzhaky
2020 arXiv   pre-print
In this work, we introduce a new symbolic technique for bottom-up lemma discovery, that is, the generation of a library of lemmas from a base set of inductive data types and recursive definitions.  ...  Recent years have seen tremendous growth in the amount of verified software. Proofs for complex properties can now be achieved using higher-order theories and calculi.  ...  knowledge base. is provides a conceptual framework for theory exploration through use of formal methods. • A system for theory synthesis on top of canonical equational reasoning via congruence closure  ... 
arXiv:2009.04826v1 fatcat:q2avwtxx3vcprofivqttinzjc4

Formal methods for automated program improvement [chapter]

Peter Madden
1994 Lecture Notes in Computer Science  
synthesis of efficient programs from standard equational definitions.  ...  For example, we are able to automate the identification of efficient recursive data-types which usua11y correspond to eureka steps in "pure" transformational techniques such as unfoldjfold.  ...  The synthesis of efficient programs from standard equational definitions is achieved through the use of (meta-level) proof-planning techniques.  ... 
doi:10.1007/3-540-58467-6_32 fatcat:jckmgdfumngshiffwn7ibcsc5q

Theory Exploration Powered by Deductive Synthesis [chapter]

Eytan Singher, Shachar Itzhaky
2021 Lecture Notes in Computer Science  
generation of a library of lemmas from a base set of inductive data types and recursive definitions.  ...  This limits the applicability of these theory exploration techniques to complex programs and properties.In this work, we introduce a new symbolic technique for theory exploration, capable of (offline)  ...  These lemmas can be used for SMT solving, automated and interactive theorem proving, and as a basis for equivalence reduction in enumerative synthesis.  ... 
doi:10.1007/978-3-030-81688-9_6 fatcat:6nzwbykqofftlciqg453veclia
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