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18
Inductive datatypes in HOL  lessons learned in FormalLogic Engineering
 Theorem Proving in Higher Order Logics: TPHOLs ’99, LNCS 1690
, 1999
"... Isabelle/HOL has recently acquired new versions of definitional packages for inductive datatypes and primitive recursive functions. In contrast to its predecessors and most other implementations, Isabelle/HOL datatypes may be mutually and indirect recursive, even infinitely branching. We also su ..."
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Cited by 42 (6 self)
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Isabelle/HOL has recently acquired new versions of definitional packages for inductive datatypes and primitive recursive functions. In contrast to its predecessors and most other implementations, Isabelle/HOL datatypes may be mutually and indirect recursive, even infinitely branching. We also support inverted datatype definitions for characterizing existing types as being inductive ones later. All our constructions are fully definitional according to established HOL tradition. Stepping back from the logical details, we also see this work as a typical example of what could be called "FormalLogic Engineering". We observe that building realistic theorem proving environments involves further issues rather than pure logic only. 1
LiftedFL: A Pragmatic Implementation of Combined Model Checking and Theorem Proving
, 1999
"... Abstract. Combining theorem proving and model checking o ers the tantalizing possibility of e ciently reasoning about large circuits at high levels of abstraction. We have constructed a system that seamlessly integrates symbolic trajectory evaluation based model checking with theorem proving in a hi ..."
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Cited by 33 (3 self)
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Abstract. Combining theorem proving and model checking o ers the tantalizing possibility of e ciently reasoning about large circuits at high levels of abstraction. We have constructed a system that seamlessly integrates symbolic trajectory evaluation based model checking with theorem proving in a higherorder classical logic. The approach is made possible by using the same programming language ( ) as both the meta and object language of theorem proving. This is done by \lifting ",essentially deeply embedding in itself. The approach is a pragmatic solution that provides an e cient and extensible veri cation environment. Our approach is generally applicable to any dialect of the ML programming language and any modelchecking algorithm that has practical inference rules for combining results. 1
An industrially effective environment for formal hardware verification
 IEEE Transactions on ComputerAided Design of Integrated Circuits and Systems
, 2005
"... This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author’s copyrig ..."
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Cited by 33 (5 self)
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This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author’s copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.
IsaPlanner: A prototype proof planner in Isabelle
 In Proceedings of CADE’03, LNCS
, 2003
"... Abstract. IsaPlanner is a generic framework for proof planning in the interactive theorem prover Isabelle. It facilitates the encoding of reasoning techniques, which can be used to conjecture and prove theorems automatically. This paper introduces our approach to proof planning, gives and overview o ..."
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Cited by 30 (9 self)
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Abstract. IsaPlanner is a generic framework for proof planning in the interactive theorem prover Isabelle. It facilitates the encoding of reasoning techniques, which can be used to conjecture and prove theorems automatically. This paper introduces our approach to proof planning, gives and overview of IsaPlanner, and presents one simple yet effective reasoning technique. 1
Formalizing the Java Virtual Machine in Isabelle/HOL
, 1998
"... We present a formalization of the central parts of the Java Virtual Machine (JVM) with the theorem prover Isabelle/HOL. We formalize the class file format and give an operational semantics for a nontrivial subset of JVM instructions, covering the central parts of object oriented programming. ..."
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Cited by 18 (0 self)
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We present a formalization of the central parts of the Java Virtual Machine (JVM) with the theorem prover Isabelle/HOL. We formalize the class file format and give an operational semantics for a nontrivial subset of JVM instructions, covering the central parts of object oriented programming.
Complete sequent calculi for induction and infinite descent
 Proceedings of LICS22
, 2007
"... This paper compares two different styles of reasoning with inductively defined predicates, each style being encapsulated by a corresponding sequent calculus proof system. The first system supports traditional proof by induction, with induction rules formulated as sequent rules for introducing induct ..."
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Cited by 18 (6 self)
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This paper compares two different styles of reasoning with inductively defined predicates, each style being encapsulated by a corresponding sequent calculus proof system. The first system supports traditional proof by induction, with induction rules formulated as sequent rules for introducing inductively defined predicates on the left of sequents. We show this system to be cutfree complete with respect to a natural class of Henkin models; the eliminability of cut follows as a corollary. The second system uses infinite (nonwellfounded) proofs to represent arguments by infinite descent. In this system, the left rules for inductively defined predicates are simple casesplit rules, and an infinitary, global condition on proof trees is required to ensure soundness. We show this system to be cutfree complete with respect to standard models, and again infer the eliminability of cut. The second infinitary system is unsuitable for formal reasoning. However, it has a natural restriction to proofs given by regular trees, i.e. to those proofs representable by finite graphs. This restricted “cyclic ” system subsumes the first system for proof by induction. We conjecture that the two systems are in fact equivalent, i.e., that proof by induction is equivalent to regular proof by infinite descent.
Higher order rippling in IsaPlanner
 Theorem Proving in Higher Order Logics 2004 (TPHOLs’04), LNCS 3223
, 2004
"... Abstract. We present an account of rippling with proof critics suitable for use in higher order logic in Isabelle/IsaPlanner. We treat issues not previously examined, in particular regarding the existence of multiple annotations during rippling. This results in an efficient mechanism for rippling th ..."
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Cited by 15 (7 self)
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Abstract. We present an account of rippling with proof critics suitable for use in higher order logic in Isabelle/IsaPlanner. We treat issues not previously examined, in particular regarding the existence of multiple annotations during rippling. This results in an efficient mechanism for rippling that can conjecture and prove needed lemmas automatically as well as present the resulting proof plans as Isar style proof scripts. 1
A Proof Planning Framework for Isabelle
, 2005
"... Proof planning is a paradigm for the automation of proof that focuses on encoding intelligence to guide the proof process. The idea is to capture common patterns of reasoning which can be used to derive abstract descriptions of proofs known as proof plans. These can then be executed to provide fully ..."
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Cited by 13 (9 self)
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Proof planning is a paradigm for the automation of proof that focuses on encoding intelligence to guide the proof process. The idea is to capture common patterns of reasoning which can be used to derive abstract descriptions of proofs known as proof plans. These can then be executed to provide fully formal proofs. This thesis concerns the development and analysis of a novel approach to proof planning that focuses on an explicit representation of choices during search. We embody our approach as a proof planner for the generic proof assistant Isabelle and use the Isar language, which is humanreadable and machinecheckable, to represent proof plans. Within this framework we develop an inductive theorem prover as a case study of our approach to proof planning. Our prover uses the difference reduction heuristic known as rippling to automate the step cases of the inductive proofs. The development of a flexible approach to rippling that supports its various modifications and extensions is the second major focus of this thesis. Here, our inductive theorem prover provides a context in which to evaluate rippling experimentally. This work results in an efficient and powerful inductive theorem prover for Isabelle as well as proposals for further improving the efficiency of rippling. We also draw observations in order
foetus – Termination Checker for Simple Functional Programs
, 1998
"... We introduce a simple functional language foetus (lambda calculus with tuples, constructors and pattern matching) supplied with a termination checker. This checker tries to find a wellfounded structural order on the parameters on the given function to prove termination. The components of the check ..."
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Cited by 12 (1 self)
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We introduce a simple functional language foetus (lambda calculus with tuples, constructors and pattern matching) supplied with a termination checker. This checker tries to find a wellfounded structural order on the parameters on the given function to prove termination. The components of the check algorithm are: function call extraction out of the program text, call graph completion and finding a lexical order for the function parameters. The HTML version of this paper contains many readytorun Webbased examples.
Verifying and reflecting quantifier elimination for Presburger arithmetic
 LOGIC FOR PROGRAMMING, ARTIFICIAL INTELLIGENCE, AND REASONING
, 2005
"... We present an implementation and verification in higherorder logic of Cooper’s quantifier elimination for Presburger arithmetic. Reflection, i.e. the direct execution in ML, yields a speedup of a factor of 200 over an LCFstyle implementation and performs as well as a decision procedure handcode ..."
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Cited by 11 (7 self)
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We present an implementation and verification in higherorder logic of Cooper’s quantifier elimination for Presburger arithmetic. Reflection, i.e. the direct execution in ML, yields a speedup of a factor of 200 over an LCFstyle implementation and performs as well as a decision procedure handcoded in ML.