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Topic: Isabelle theorem prover

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	Isabelle theorem prover - Wikipedia, the free encyclopedia
		The Isabelle theorem prover is an interactive theorem proving framework, a successor of the HOL theorem prover.
		Isabelle is generic: it provides a meta-logic (a weak type theory), which is used to encode object logics like FOL, HOL or ZFC.
		Isabelle has been used to formalize numerous theorems from mathematics and computer science, like Gödel's completeness theorem, Gödel's theorem about the consistency of the axiom of choice, correctness of security protocols, and properties of programming language semantics.
	en.wikipedia.org /wiki/Isabelle_theorem_prover (262 words)

	HOL theorem prover - Wikipedia, the free encyclopedia
		This library implements an abstract data type of proven theorems; it is impossible to create a new object of this type without using the functions in the library.
		HOL is a successor of the LCF theorem prover.
		Among the successors of HOL is the Isabelle theorem prover.
	en.wikipedia.org /wiki/HOL_theorem_prover (333 words)

	Automated theorem proving - Encyclopedia.WorldSearch (Site not responding. Last check: 2007-10-08)
		Automated theorem proving (currently the most important subfield of automated reasoning) is the proving of mathematical theorems by a computer program.
		Interactive provers are used for a variety of tasks, but even fully automatic systems have by now proven a number of interesting and hard theorems, including some that have eluded human mathematicians for a long time.
		A good example of this was the machine-aided proof of the four color theorem, which was very controversial as the first claimed mathematical proof which was essentially impossible to verify by humans due to the enourmous size of the program's calculation (such proofs are called non-surveyable proofs).
	encyclopedia.worldsearch.com /automated_theorem_proving.htm (729 words)

	LCF theorem prover - Wikipedia, the free encyclopedia
		An interactive theorem prover developed at the universities of Edinburgh and Stanford by Robin Milner and others.
		Theorems in the system are propositions of a special "theorem" abstract datatype.
		The ML type system ensures that theorems are derived using only the inference rules given by the operations of the abstract type.
	en.wikipedia.org /wiki/LCF_theorem_prover (113 words)

	LCF theorem prover
		A theorem prover was developed at University of Edinburgh by Robin Milner.
		Theorems are proposition of special "theorem" type, the ML type system ensures that theorems are derived using only sound inference rules.
		Successors include: HOL theorem prover, Isabelle theorem prover.
	www.ebroadcast.com.au /lookup/encyclopedia/lc/LCF_theorem_prover.html (77 words)

	README with abstracts
		A semantics for a subset of ELLA is described, and an outline of a proof of the equivalence of parallel and recursive implementations of an n-bit adder is given as an illustration of the semantics.
		Isabelle is a generic theorem prover, supporting formal proof in a variety of logics.
		The theorem prover Isabelle is used to formalise and reproduce some of the styles of reasoning used by Newton in his Principia.
	www.ftp.cl.cam.ac.uk /ftp/papers/reports/abstract.html (14873 words)

	Mechanized Reasoning Systems (Site not responding. Last check: 2007-10-08)
		E is a theorem prover for clausal logic with equality.
		LeanTAP -- a micro prolog prover for FOL
		Nqthm is a prover for quantifier free logic for recursive functions over the integers and other finitely generated structures, combining rewriting, heuristics for induction, and other techniques.
	www-formal.stanford.edu /clt/ARS/systems.html (1545 words)

	Isabelle available by FTP
		This means you do not need to sign a license to obtain a copy of Isabelle, and you are free to redistribute Isabelle as long as you retain the copyright notices and permission notice.
		Isabelle resides on the same directory as Standard ML of New Jersey.
		Although Isabelle has been tested under SML of New Jersey, the compilers are not completely compatible.
	www.seas.upenn.edu /~sweirich/types/archive/1990/msg00028.html (442 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		The only difference between the definitions and the theorems is the types they deal with: int's and intlist's on the one hand, and bool's and boollist's on the other.
		This is because Isabelle is a 'generic' theorem prover which can support multiple different logics, each with its own syntax.
		Isabelle also has a flag for displaing sorts, which say what "class" of types a particular type variable belongs to.
	www.cse.ogi.edu /~johnm/courses/CSE58X/intro.thy (1881 words)

	Isabelle - A Generic Theorem Prover (Site not responding. Last check: 2007-10-08)
		Isabelle is a logic independent theorem prover developed by Larry Paulson.
		It is similar to a compiler-compiler in that it takes a formal description of the syntax and inference rules of the desired object-logic, generating an LCF-like theorem prover from it.
		Using the idea of tactical theorem proving, complex proof procedures in the form of ML functions can be added to the system without endangering its soundness.
	www.cl.cam.ac.uk /Research/HVG/ARG_Talks/abstracts/abstract_910425.html (174 words)

	Encyclopedia: LCF theorem prover
		The University of Edinburgh, founded in 1583, is a renowned centre for teaching and research in Edinburgh, Scotland.
		Historically, ML stands for metalanguage as it was conceived to develop proof tactics in the LCF theorem prover (the language of which ML...
		On computer science, a datatype (often simply type) is a name or label for a set of values and some operations which can be performed on that set of values.
	www.nationmaster.com /encyclopedia/LCF-theorem-prover (311 words)

	Proving Zariski Space Theorems in Isabelle: A Case Study in the Application of Automated Theorem Proving ... (Site not responding. Last check: 2007-10-08)
		Fortunately, there has been a steady increase of the usability, capability and efficiency of automated theorem proving, and the time may now be ripe to re-evaluate the applicability of theorem proving technology to mathematical research.
		Isabelle is one of the most popular and successful tactic-based, interactive theorem proving systems.
		The excitement of this project will be the chance to apply Isabelle to cutting edge, but accessible, mathematics, and to work with one of the leading experts in the field.
	www.inf.ed.ac.uk /teaching/courses/diss/props/031_bundy16.html (473 words)

	Citations: Isabelle: A Generic Theorem Prover - Paulson (ResearchIndex) (Site not responding. Last check: 2007-10-08)
		According to its original author the early history of Isabelle is a tale of errors, not grand designs [Paulson, 1990] Apart from the generic....
		Isabelle HOL is an instance of Isabelle with Church s higher order logic (HOL) 11] a classical logic with equality enriched by total polymorphic higher order functions.
		The computer theorem proving framework is mechanized by a wide range of di erent kinds of computer theorem provers.
	citeseer.lcs.mit.edu /context/2888/0 (3518 words)

	Isabelle (Site not responding. Last check: 2007-10-08)
		Abstract Using the theorem prover Isabelle as a tool for executing DATR programs is a spin-off from our work on developing a formal semantics in logic for the programming language DATR.
		Isabelle is a meta reasoner in which object logics can be implemented.
		Therefore our system consists of four components: a) the prover Isabelle, b) a file defining the semantics of DATR as a set of axioms, c) a file defining the search strategies for proving a theorem, d) a translator.
	www.rvs.uni-bielefeld.de /~thorsten/isabelle.html (483 words)

	HOL theorem prover: Definition and Links by Encyclopedian.com - All about HOL theorem prover
		HOL theorem prover: Definition and Links by Encyclopedian.com - All about HOL theorem prover
		HOL (which stands for Higher Order Logic) is a family of automated theorem proving systems.
		HOL is a succesor of LCF theorem prover.
	www.encyclopedian.com /ho/HOL-theorem-prover.html (292 words)

	Theorem-proving distributed algorithms with dynamic analysis (Site not responding. Last check: 2007-10-08)
		Theorem provers are notoriously hard to use because of the amount of human interaction they require, but they are important tools that can verify infinite state distributed systems.
		The human work in using a theorem prover is reduced because our technique provides two forms of assistance: lemmas generated by the dynamic invariant detection for use in the prover; and prover scripts, or tactics, generated from our experience with the I/O automaton model and the knowledge embedded in the test suite used for execution.
		We describe a new model for specifying I/O automata in the Isabelle theorem prover's logic, and prove the soundness of a technique for verifying invariants in this model in the Isabelle prover.
	pag.csail.mit.edu /pubs/thmprove-newin-mengthesis-abstract.html (351 words)

	Can a Higher-Order and a First-Order Theorem Prover Cooperate?
		Rather than modelling each theorem prover as a separate inference rule (and hence needing to translate the communication via the language of the central proof object), we model the cooperation between a higher-order (concretely, Leo) and a first-order theorem prover (in our case study Bliksem) in Oants as a single inference rule.
		Concretely, the single inference rule modelling the cooperation between Leo and a first-order theorem prover needs four arguments to be applicable: (1) an open proof goal, (2) a partial Leo proof, (3) a set of FO-like clauses in the partial proof, (4) a first-order refutation proof for the set of FO-like clauses.
		Namely, to prove a theorem it is sufficient to show that a subset of clauses generated in the proof is inconsistent.
	www.cs.bham.ac.uk /~mmk/papers/05-LPAR.html (6017 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		Using Isabelle to define a logic, or better, extending the generic theorem prover Isabelle to reason on a particular logic, means to give syntax to write the formulae of the logic, and to give rules to be applied when trying to perform proofs in this logic.
		After building this structure, Isabelle looks for and read, if present, the file T.ML which is contains all the proofs perfomed using theory T built as explained in the next section.
		Theory PC extends theory FOL, which is the Isabelle implementation of First Order Logic, by providing some interesting predicate calculus theorems: contraposition, introduction and elimination of double implication, and de morgan.
	www.di.unipi.it /~semprini/isabelle.htm (1919 words)

	µJava: Embedding a Programming Language in a Theorem Prover (Site not responding. Last check: 2007-10-08)
		The type system and semantics of this language (and a corresponding abstract Machine µJVM) are formalized in the theorem prover Isabelle/HOL.
		Type safety both of µJava and the µJVM are mechanically verified.
		The type system and semantics of this language (and a corresponding abstract Machine $\mu$JVM) are formalized in the theorem prover Isabelle/HOL.
	isabelle.in.tum.de /Bali/papers/MOD99.html (171 words)

	Isabelle theorem prover - Encyclopedia, History, Geography and Biography
		Isabelle theorem prover - Encyclopedia, History, Geography and Biography
		This encyclopedia, history, geography and biography article about Isabelle theorem prover contains research on
		Isabelle theorem prover, Example taken from a theory file and External link.
	www.arikah.net /encyclopedia/Isabelle_theorem_prover (173 words)

	An Isabelle-based Theorem Prover for VDM-SL - Agerholm, Frost (ResearchIndex)
		This paper describes the theorem proving component of a larger software development environment for the ISO standardized specification language VDM-SL.
		This component is constructed as an instantiation of the generic theorem prover Isabelle with a VDM-SL variant of the Logic of Partial Functions (LPF).
		We describe the development of this instantiation, focusing on both the embedding of syntax and the automation of proof support, which is a challenge due to the three-valued nature of LPF.
	citeseer.ist.psu.edu /agerholm97isabellebased.html (653 words)

	Professor Alan Bundy - School of Informatics, University of Edinburgh - teaching project proposals
		Proving Zariski Space Theorems in Isabelle: A Case Study in the Application of Automated Theorem Proving to Mathematical Research.
		To build a theorem prover which can prove theorems in which lists are represented using ellipsis.
		To augment a model elimination theorem prover with heuristics for selecting literals and choosing clauses to resolve with them.
	homepages.inf.ed.ac.uk /bundy/teaching_projectProposals.html (1575 words)

	Isabelle theorem prover -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-08)
		The Isabelle theorem prover an interactive (Click link for more info and facts about theorem proving) theorem proving framework, a successor of the
		(Click link for more info and facts about HOL theorem prover) HOL theorem prover.
		See also: (Click link for more info and facts about theorem prover) theorem prover.
	www.absoluteastronomy.com /encyclopedia/i/is/isabelle_theorem_prover.htm (69 words)

	ISABELLE USERS EMAIL FORUM (Site not responding. Last check: 2007-10-08)
		To: logic@theory.lcs.mit.edu, types@theory.lcs.mit.edu, proof-sci@cs.chalmers.se Date: Thu, 23 Aug 90 12:05:54 +0100 ISABELLE USERS EMAIL FORUM isabelle-users@cl.cam.ac.uk A new electronic mailing list is available for users of the theorem prover Isabelle.
		The list is open to everybody who is interested in Isabelle.
		If you would like to be placed on the mailing list, please send a message to isabelle-users-request@cl.cam.ac.uk This address should also be used for administrative requests such as "please remove me from this list".
	www.cis.upenn.edu /~bcpierce/types/archives/1990/msg00050.html (108 words)

	Inferencing for the Semantic Web (Site not responding. Last check: 2007-10-08)
		This is reflected in the test-bed used by the automated theorem proving community ("Thousends of Problems for Theorem Pover (TPTP)").
		Many small, tricky problems are inside the problem library, and theorem provers try to solve these problems and often fail (cf.
		A different approach is taken by CYC, consisting of roughly 1MB of axioms and using the first-order framework, CYC is organizing its axioms in contexts, maintaining consistency just for one context, and limiting deductions only to a few steps.
	www.semanticweb.org /inference.html (952 words)

	Converting Student ML Programs into input for the Isabelle Theorem Prover (Site not responding. Last check: 2007-10-08)
		Isabelle is a general purpose theorem prover adaptable to a wide range of tasks.
		Isabelle is, itself written in ML and their are many similarities between the syntax it uses for theorems and that used by ML to express programs however there are differences and translating ML programs into Isabelle syntax is a tedious, though not especially difficult task.
		A strong student might wish to extend the project so that the system also performed a few simple automatic proofs about the ML Programs once they were translated into Isabelle syntax, or they might want to examine correctness issues involved in the assumption made by the translation.
	www.cs.nott.ac.uk /~lad/projects/mlisabelle.html (278 words)

	Theorem Prover Support for the Refinement of Stream Processing Functions - Sandner, Mller (ResearchIndex)
		Abstract: In this paper, we show how to use the theorem prover Isabelle to provide tool support for Focus, a specification and verification framework for the stepwise development of distributed systems.
		Focus is embedded into Isabelle by modeling the basic notion of stream processing functions and by formalizing an appropriate set of assumption/ commitment refinement rules.
		Theorem Prover Support for the Refinement of Stream Processing Functions.
	citeseer.ist.psu.edu /sandner97theorem.html (486 words)

	Abstracts
		Its formal representation within higher order logic in the theorem prover Isabelle/HOL [Pau 94] revealed an error in the basic definition of CSP concerning the treatment of the termination symbol tick.
		The corner stone of this theory is a confluence proof for orthogonal transformations (partly implemented in the proof assistant Isabelle).
		We present a family of prototypical user interfaces (built on the theorem prover Isabelle) implemented solely in Standard ML, avoiding the disadvantages of other approaches based on mixed code (with Tcl).
	www.informatik.uni-freiburg.de /~wolff/papers/abstracts.html (668 words)

	HOL theorem prover (Site not responding. Last check: 2007-10-08)
		All of these systems follow the LCF theorem prover approach.
		This language was originally developed along with LCF theorem prover to serve the purpose of a meta-language for theorem proving systems, in fact, the name stands for Meta-Language.
		There should be information on the HOL logic here.
	read-and-go.hopto.org /Theorem-provers/HOL-theorem-prover.html (307 words)

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