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Logic Program Synthesis in a Higher-Order Setting [chapter]

David Lacey, Julian Richardson, Alan Smail
2000 Lecture Notes in Computer Science  
The system has been implemented within the proof planning system λClam.  ...  We describe a system for the synthesis of logic programs from specifications based on higher-order logical descriptions of appropriate refinement operations.  ...  The research was supported by EPSRC grant GR/M45030, and EPSRC funding for David Lacey's MSc in Artificial Intelligence.  ... 
doi:10.1007/3-540-44957-4_6 fatcat:24o64zh5abdero5uagownflvka

TPS: A hybrid automatic-interactive system for developing proofs

Peter B. Andrews, Chad E. Brown
2006 Journal of Applied Logic  
Mathematical theorems can be expressed very naturally in TPS using higher-order logic. A number of proof representations are available in TPS, so proofs can be inspected from various perspectives.  ...  The theorem proving system TPS provides support for constructing proofs using a mix of automation and user interaction, and for manipulating and inspecting proofs.  ...  Acknowledgements Over the history of the TPS project the following people (in addition to the authors) have contributed to the development of the TPS system: Dale Miller, Frank Pfenning, Sunil Issar, Carl  ... 
doi:10.1016/j.jal.2005.10.002 fatcat:gtdbq6xwqbar3codoqoedpa35i

Experiments in automating hardware verification using inductive proof planning [chapter]

Francisco J. Cantu, Alan Bundy, Alan Smaill, David Basin
1996 Lecture Notes in Computer Science  
User interaction is limited to specifying circuits and their properties and, in some cases, suggesting lemmas. We have implemented our work in an extension of the Clam proof planning system.  ...  We present a new approach to automating the veri cation of hardware designs based on planning techniques.  ...  We have implemented our approach to planning in an extension of the Clam proof planning system 8].  ... 
doi:10.1007/bfb0031802 fatcat:obhgnszzlfatbgs7mc4hganv7q

Ordinal Arithmetic: A Case Study for Rippling in a Higher Order Domain [chapter]

Louise A. Dennis, Alan Smaill
2001 Lecture Notes in Computer Science  
Accordingly, ordinal arithmetic has been implemented in λClam, a higher order proof planning system for induction, and standard undergraduate text book problems have been successfully planned with a simple  ...  Accordingly, ordinal arithmetic has been implemented in LambdaClam, a higher order proof planning system for induction, and standard undergraduate text book problems have been successfully planned with  ...  Proof Planning in λClam Proof planning in λClam works as follows: A goal is presented to the system.  ... 
doi:10.1007/3-540-44755-5_14 fatcat:bndrfnhgdngg7liu7kusje6w2u

Higher Order Rippling in IsaPlanner [chapter]

Lucas Dixon, Jacques Fleuriot
2004 Lecture Notes in Computer Science  
We present an account of rippling with proof critics suitable for use in higher order logic in Isabelle/IsaPlanner.  ...  Examples of such information include a conjecture database, annotations for rippling, and a high level description of the proof planning process.  ...  Acknowledgments This research was funded by the EPSRC grant A Generic Approach to Proof Planning -GR/N37414/01.  ... 
doi:10.1007/978-3-540-30142-4_7 fatcat:wr7wwhdxbfeedfwsg326sfdxpi

Page 6540 of Mathematical Reviews Vol. , Issue 2000i [page]

2000 Mathematical Reviews  
Ian Green, System description: proof plan- 68 COMPUTER SCIENCE 6540 ning in higher-order logic with AClam (129-133); Konrad Slind, Mike Gordon, Richard Boulton and Alan Bundy, System descrip- tion: an  ...  interface between CLAM and HOL (134-138); Christoph Benzmiiller and Michael Kohlhase, System description: LEO—a higher-order theorem prover (139-143); Uwe Waldmann, Super- position for divisible torsion-free  ... 

Cooperative reasoning for automatic software verification

Andrew Ireland
2007 Proceedings of the second workshop on Automated formal methods - AFM '07  
He supported the group's research activities with the lambda-Clam proof planner and took over development of the IsaPlanner proof-planning system built on top of the Isabelle/HOL theorem prover.  ...  Finally, in [39] the Coq proof environment has been extended with separation logic in order to verify the C source code of the Topsy heap manager.  ... 
doi:10.1145/1345169.1345175 fatcat:2c5i67mz4fguzogyeoflfoe2li

Automation of Higher-Order Logic [chapter]

Christoph Benzmüller, Dale Miller
2014 Handbook of the History of Logic  
We thank Chad Brown for sharing notes that he has written related to the material in this chapter.  ...  Proof certificates from these external systems can be transformed and verified in ΩMEGA. λClam and IsaPlanner. λ-Clam (Richardson et al., 1998 ) is a higher-order variant of the CLAM proof planner (Bundy  ...  The higher-order proof assistant ΩMEGA (Benzmüller et al., 1997) combines tactic based interactive theorem proving with automated proof planning.  ... 
doi:10.1016/b978-0-444-51624-4.50005-8 fatcat:jfcztdvymjfujg3bzb2rq2qyzy

The Automation of Proof by Mathematical Induction [chapter]

Alan Bundy
2001 Handbook of Automated Reasoning  
Mathematical induction is required for reasoning about objects or events containing repetition, e.g. computer programs with recursion or iteration, electronic circuits with feedback loops or parameterized  ...  Thus mathematical induction is a key enabling technology for the use of formal methods in information technology.  ...  This talks presents an extension of the colouring method to higher-order logics.  ... 
doi:10.1016/b978-044450813-3/50015-1 fatcat:y2m3e2cjjfhf5nvs734xddyxqi

SAD as a mathematical assistant—how should we go from here to there?

Alexander Lyaletski, Andrey Paskevich, Konstantin Verchinine
2006 Journal of Applied Logic  
The SAD system works on three levels of reasoning: (a) the level of text presentation where proofs are written in a formal natural-like language for subsequent verification; (b) the level of foreground  ...  We illustrate our approach with a series of examples, in particular, with the classical problem √ 2 / ∈ Q.  ...  We thank everybody who took part in the development of the SAD system.  ... 
doi:10.1016/j.jal.2005.10.009 fatcat:yzxc73hb2fhmjciwukuq6ii4bu

Proof Planning for Feature Interactions: A Preliminary Report [chapter]

Claudio Castellini, Alan Smaill
2002 Lecture Notes in Computer Science  
We have integrated the proof planner lambda-CLAM with an object-level FOLTL theorem prover called FTL, and have so far re-discovered a feature interaction in a basic (but far from trivial) example.  ...  So far, FIs have been solved mainly via approximation plus finite-state methods (model checking being the most popular); in our work we attack the problem via proof planning in First-Order Linear Temporal  ...  Acknowledgements This work is being carried out at the University of Edinburgh and is supported by the EPSRC Grant GR/M46624, "Mechanising First-Order Temporal Logics".  ... 
doi:10.1007/3-540-36078-6_7 fatcat:zhqaurnyjzanjgjti65cn5fphy

A proof-centric approach to mathematical assistants

Lucas Dixon, Jacques Fleuriot
2006 Journal of Applied Logic  
We examine an implementation that combines the Isar language, the Isabelle theorem prover and the IsaPlanner proof planner.  ...  We present an approach to mathematical assistants which uses readable, executable proof scripts as the central language for interaction.  ...  Acknowledgements This research was funded by the EPSRC grant A Generic Approach to Proof Planning-GR/N37414/01.  ... 
doi:10.1016/j.jal.2005.10.007 fatcat:nmzu53bazfhvbfofhtl3muid34

On Process Equivalence = Equation Solving in CCS

Raúl Monroy, Alan Bundy, Ian Green
2009 Journal of automated reasoning  
This planner increases the number of verification problems that can be dealt with fully automatically, thus improving upon the current degree of automation in the field.  ...  We call these kinds of systems VIPSs. VIPSs is the acronym of Value-passing, Infinite-State and Parameterised Systems. Automating the application of UFI in the context of VIPSs has been neglected.  ...  This is achieved by replacing parts of the theorem goal with higher-order meta-variables. These meta-variables are gradually refined as further proof steps take place.  ... 
doi:10.1007/s10817-009-9125-x fatcat:lm32vi7tmjhtxfenvncj25peyq

Hiproofs: A Hierarchical Notion of Proof Tree

Ewen Denney, John Power, Konstantinos Tourlas
2006 Electronical Notes in Theoretical Computer Science  
A hierarchical proof tree, or hiproof for short, is a hierarchical tree with nodes labelled by tactics.  ...  Hierarchy per se is independent of the underlying logic. Moreover, tactics alone support rich structure, and we seek the simplest possible framework in which to study it.  ...  Acknowledgements The first author thanks Alan Bundy for his encouragement and interest in this work.  ... 
doi:10.1016/j.entcs.2005.11.063 fatcat:goqa2l2ravf5hl225cmg6bk6za

Dynamic Rippling, Middle-Out Reasoning and Lemma Discovery [chapter]

Moa Johansson, Lucas Dixon, Alan Bundy
2010 Lecture Notes in Computer Science  
Middle-out reasoning and lemma speculation have been implemented in higher-order logic and evaluated on typical libraries of formalised mathematics.  ...  In comparison, we show that theory formation methods, combined with simpler proof methods, offer an effective alternative.  ...  A positive result for our version of middle-out rippling is that, as well as working in higher-order domains, it supports speculating the same lemmas as the earlier implementation in CLAM 3.  ... 
doi:10.1007/978-3-642-17172-7_6 fatcat:uixnhbgfi5e4jgxapigkes5yci
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