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Mizar: the first 30 years
 Mechanized Mathematics and Its Applications
, 2005
"... The papers were selected for presentation at workshop (with two exemptions) and publication in the journal by workshop’s program committee which consists of the following: ..."
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Cited by 24 (0 self)
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The papers were selected for presentation at workshop (with two exemptions) and publication in the journal by workshop’s program committee which consists of the following:
Escape to Mizar from ATPs
, 2012
"... We announce a tool for mapping E derivations to Mizar proofs. Our mapping complements earlier work that generates problems for automated theorem provers from Mizar inference checking problems. We describe the tool, explain the mapping, and show how we solved some of the difficulties that arise in ma ..."
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We announce a tool for mapping E derivations to Mizar proofs. Our mapping complements earlier work that generates problems for automated theorem provers from Mizar inference checking problems. We describe the tool, explain the mapping, and show how we solved some of the difficulties that arise
On Equivalents of Wellfoundedness  An experiment in Mizar
, 1998
"... Four statements equivalent to wellfoundedness (wellfounded induction, existence of recursively defined functions, uniqueness of recursively defined functions, and absence of descending omegachains) have been proved in Mizar and the proofs mechanically checked for correctness. It seems not to be w ..."
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Cited by 13 (3 self)
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not to be widely known that the existence (without the uniqueness assumption) of recursively defined functions implies wellfoundedness. In the proof we used regular cardinals, a fairly advanced notion of set theory. The theory of cardinals in Mizar was developed earlier by G. Bancerek. With the current state
Mizar’s Soft Type System
"... Abstract. In Mizar, unlike in most other proof assistants, the types are not part of the foundations of the system. Mizar is based on untyped set theory, which means that in Mizar expressions are typed but the values of those expressions are not. In this paper we present the Mizar type system as a c ..."
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Cited by 4 (1 self)
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Abstract. In Mizar, unlike in most other proof assistants, the types are not part of the foundations of the system. Mizar is based on untyped set theory, which means that in Mizar expressions are typed but the values of those expressions are not. In this paper we present the Mizar type system as a
Mizar's Soft Type System
"... Abstract. In Mizar, unlike in most other proof assistants, the types are not part of the foundations of the system. Mizar is based on untyped set theory, which means that in Mizar expressions are typed but the values of those expressions are not. In this paper we present the Mizar type system as a c ..."
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Abstract. In Mizar, unlike in most other proof assistants, the types are not part of the foundations of the system. Mizar is based on untyped set theory, which means that in Mizar expressions are typed but the values of those expressions are not. In this paper we present the Mizar type system as a
Combining Mizar and TPTP Semantic Presentation Tools
, 2007
"... This paper describes a combination of several Mizarbased tools (the MPTP translator, XSL style sheets for Mizar), and TPTPbased tools (IDV, AGInT, SystemOnTPTP) used for visualizing and analyzing Mizar proofs. The combination delivers to the readers of the Mizar Mathematical Library (MML) an easy, ..."
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Cited by 2 (1 self)
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This paper describes a combination of several Mizarbased tools (the MPTP translator, XSL style sheets for Mizar), and TPTPbased tools (IDV, AGInT, SystemOnTPTP) used for visualizing and analyzing Mizar proofs. The combination delivers to the readers of the Mizar Mathematical Library (MML) an easy
Combining Mizar and TPTP Semantic Presentation and Verification Tools
"... This paper describes a combination of several Mizarbased tools (the MPTP translator, XSL style sheets for Mizar), and TPTPbased tools (IDV, AGInT, SystemOnTPTP, GDV) used for visualizing, analyzing, and independent verification of Mizar proofs. The combination delivers to the readers of the Mizar M ..."
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Cited by 1 (0 self)
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This paper describes a combination of several Mizarbased tools (the MPTP translator, XSL style sheets for Mizar), and TPTPbased tools (IDV, AGInT, SystemOnTPTP, GDV) used for visualizing, analyzing, and independent verification of Mizar proofs. The combination delivers to the readers of the Mizar
Gröbner Bases — Theory Refinement in the Mizar System
"... Abstract. We argue that for building mathematical knowledge repositories a broad development of theories is of major importance. Organizing mathematical knowledge in theories is an obvious approach to cope with the immense number of topics, definitions, theorems, and proofs in a general repository t ..."
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this flexibility and to provide collections of welldeveloped theories. As an example we describe the Mizar development of the theory of Gröbner bases, a theory which is built upon the theory of polynomials, ring (ideal) theory, and the theory of rewriting systems. Here, polynomials are considered both as ring
Isar  a Generic Interpretative Approach to Readable Formal Proof Documents
, 1999
"... We present a generic approach to readable formal proof documents, called Intelligible semiautomated reasoning (Isar). It addresses the major problem of existing interactive theorem proving systems that there is no appropriate notion of proof available that is suitable for human communication, or ..."
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Cited by 98 (16 self)
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, or even just maintenance. Isar's main aspect is its formal language for natural deduction proofs, which sets out to bridge the semantic gap between internal notions of proof given by stateoftheart interactive theorem proving systems and an appropriate level of abstraction for userlevel work
Theorem Proving with the Real Numbers
, 1996
"... This thesis discusses the use of the real numbers in theorem proving. Typically, theorem provers only support a few `discrete' datatypes such as the natural numbers. However the availability of the real numbers opens up many interesting and important application areas, such as the verification ..."
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Cited by 116 (14 self)
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This thesis discusses the use of the real numbers in theorem proving. Typically, theorem provers only support a few `discrete' datatypes such as the natural numbers. However the availability of the real numbers opens up many interesting and important application areas, such as the verification of floating point hardware and hybrid systems. It also allows the formalization of many more branches of classical mathematics, which is particularly relevant for attempts to inject more rigour into computer algebra systems. Our work is conducted in a version of the HOL theorem prover. We describe the rigorous definitional construction of the real numbers, using a new version of Cantor's method, and the formalization of a significant portion of real analysis. We also describe an advanced derived decision procedure for the `Tarski subset' of real algebra as well as some more modest but practically useful tools for automating explicit calculations and routine linear arithmetic reasoning. Finally,...
Results 1  10
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506