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Comparing mathematical provers
 In Mathematical Knowledge Management, 2nd Int’l Conf., Proceedings
, 2003
"... Abstract. We compare fifteen systems for the formalizations of mathematics with the computer. We present several tables that list various properties of these programs. The three main dimensions on which we compare these systems are: the size of their library, the strength of their logic and their le ..."
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Abstract. We compare fifteen systems for the formalizations of mathematics with the computer. We present several tables that list various properties of these programs. The three main dimensions on which we compare these systems are: the size of their library, the strength of their logic and their level of automation. 1
A Comparison of PVS and Isabelle/HOL
 Theorem Proving in Higher Order Logics, number 1479 in Lect. Notes Comp. Sci
, 1998
"... . There is an overwhelming number of different proof tools available and it is hard to find the right one for a particular application. Manuals usually concentrate on the strong points of a proof tool, but to make a good choice, one should also know (1) which are the weak points and (2) whether the ..."
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. There is an overwhelming number of different proof tools available and it is hard to find the right one for a particular application. Manuals usually concentrate on the strong points of a proof tool, but to make a good choice, one should also know (1) which are the weak points and (2) whether the proof tool is suited for the application in hand. This paper gives an initial impetus to a consumers' report on proof tools. The powerful higherorder logic proof tools PVS and Isabelle are compared with respect to several aspects: logic, specification language, prover, soundness, proof manager, user interface (and more). The paper concludes with a list of criteria for judging proof tools, it is applied to both PVS and Isabelle. 1 Introduction There is an overwhelming number of different proof tools available (e.g. in the Database of Existing Mechanised Reasoning Systems one can find references to over 60 proof tools [Dat]). All have particular applications that they are especially suited ...
Set Theory, Higher Order Logic or Both?
"... The majority of general purpose mechanised proof assistants support versions of typed higher order logic, even though set theory is the standard foundation for mathematics. For many applications higher order logic works well and provides, for specification, the benefits of typechecking that are ..."
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The majority of general purpose mechanised proof assistants support versions of typed higher order logic, even though set theory is the standard foundation for mathematics. For many applications higher order logic works well and provides, for specification, the benefits of typechecking that are wellknown in programming. However, there are areas where types get in the way or seem unmotivated. Furthermore, most people with a scientific or engineering background already know set theory, but not higher order logic. This paper discusses some approaches to getting the best of both worlds: the expressiveness and standardness of set theory with the efficient treatment of functions provided by typed higher order logic.
Transforming RSL into PVS
, 2002
"... conceptually. In that case these dierences become a challenge and we are obliged to solve theoretical problems before the transformation can be done. We describe in this report some of these problems and how they can be overcome, illustrating the problematic issues using two formal languages: RSL an ..."
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conceptually. In that case these dierences become a challenge and we are obliged to solve theoretical problems before the transformation can be done. We describe in this report some of these problems and how they can be overcome, illustrating the problematic issues using two formal languages: RSL and PVS. Both PVS and RSL are formal languages that can be used to do formal speci cations of complex software systems. And although both languages have some similarities they dier in aspects that are crucial RSL is a much bigger language than PVS and moreover has several constructs that make the languages substantially, and in some cases, conceptually dierent (partial as well as total functions against only total ones, etc.). The description here includes solutions to some of these problems as well as a the details of the design of a tool that automatically translates RSL into PVS. There is an added bene t to this namely the fact that although both methods have a prover tool, PVS's is free, so a translator from RSL to PVS would allow a speci cation written in RSL to be proved in PVS using the freely available PVS prover.
On the Integration of Formal Methods: Events and Scenarios in PVS and VDM
, 1999
"... Tool support is known to be one of the success factors in formal specification based analysis andprogram development. This paper investigates tool support in the context of a case study where a wide range of tool features is required: For an access control, C++ code has to be developed based on t ..."
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Tool support is known to be one of the success factors in formal specification based analysis andprogram development. This paper investigates tool support in the context of a case study where a wide range of tool features is required: For an access control, C++ code has to be developed based on the user's requirements expressed in natural language. The access control has been classified a mixed datacontrol problem. This paper discusses (1) why VDMTools and PVS have been selected and (2) how they can be used together. Another aspect is the use of VDM as a framework for modeling event based systems. In our approach to tool integration, two specifications are considered to share a common part. For the present application this part consists of the scenario of all possible events. 1 Introduction 1.1 An Access Control as a Case Study CSS is a security system which has been developed by ARCS (the Austrian Research Center at Seibersdorf [32]). CSS includes features from digital vi...
Computer Theorem Proving in Math
"... We give an overview of issues surrounding computerverified theorem proving in the standard puremathematical context. ..."
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We give an overview of issues surrounding computerverified theorem proving in the standard puremathematical context.
Partizan Games in Isabelle/HOLZF
"... Abstract. Partizan Games (PGs) were invented by John H. Conway and are described in his book On Numbers and Games. We formalize PGs in Higher Order Logic extended with ZF axioms (HOLZF) using Isabelle, a mechanical proof assistant. We show that PGs can be defined as the unique fixpoint of a function ..."
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Abstract. Partizan Games (PGs) were invented by John H. Conway and are described in his book On Numbers and Games. We formalize PGs in Higher Order Logic extended with ZF axioms (HOLZF) using Isabelle, a mechanical proof assistant. We show that PGs can be defined as the unique fixpoint of a function that arises naturally from Conway’s original definition. While the construction of PGs in HOLZF relies heavily on the ZF axioms, operations on PGs are defined on a game type that hides its set theoretic origins. A polymorphic type of sets that are not bigger than ZF sets facilitates this. We formalize the induction principle that Conway uses throughout his proofs about games, and prove its correctness. For these purposes we examine how the notions of wellfoundedness in HOL and ZF are related in HOLZF. Finally, games (modulo equality) are added to Isabelle’s numeric types by showing that they are an instance of the axiomatic type class of partially ordered abelian groups. 1