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Isabelle/Isar  a generic framework for humanreadable proof documents
 UNIVERSITY OF BIA̷LYSTOK
, 2007
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A Comparison of Mizar and Isar
 J. Automated Reasoning
, 2002
"... Abstract. The mathematical proof checker Mizar by Andrzej Trybulec uses a proof input language that is much more readable than the input languages of most other proof assistants. This system also differs in many other respects from most current systems. John Harrison has shown that one can have a Mi ..."
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Abstract. The mathematical proof checker Mizar by Andrzej Trybulec uses a proof input language that is much more readable than the input languages of most other proof assistants. This system also differs in many other respects from most current systems. John Harrison has shown that one can have a Mizar mode on top of a tactical prover, allowing one to combine a mathematical proof language with other styles of proof checking. Currently the only fully developed Mizar mode in this style is the Isar proof language for the Isabelle theorem prover. In fact the Isar language has become the official input language to the Isabelle system, even though many users still use its lowlevel tactical part only. In this paper we compare Mizar and Isar. A small example, Euclid’s proof of the existence of infinitely many primes, is shown in both systems. We also include slightly higherlevel views of formal proof sketches. Moreover a list of differences between Mizar and Isar is presented, highlighting the strengths of both systems from the perspective of endusers. Finally, we point out some key differences of the
An Idealistic Formalization of Stokes’ Theorem: Pedagogical Math in Isabelle/ISAR
"... In this thesis, we describe the trials and tribulations of an attempt to formalize the ndimensional version of Stokes ’ theorem, aka the fundamental theorem of multivariate calculus, in Isabelle/HOL. A fundamental goal of this development was to obtain textbookstyle readable proofs that would be ..."
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In this thesis, we describe the trials and tribulations of an attempt to formalize the ndimensional version of Stokes ’ theorem, aka the fundamental theorem of multivariate calculus, in Isabelle/HOL. A fundamental goal of this development was to obtain textbookstyle readable proofs that would be reusable by future proof developers. We analyze the nature of modularity in mathematics and compare it to Isabelle’s programmatic support for modularism. We also present an extension to Isabelle that manages predicate subtype information transparently. Finally, we let the proofs themselves tell their mathematical story, with commentary on their design process. iii Acknowledgements Many thanks to all of the dreamers of Edinburgh, who put up with me for an entire summer. Extra special thanks to Lucas Dixon, for being an Isabelle superstar, Robbert Brak, for adding some inconsistency to my academic life, and Jacques Fleuriot, without whose enthusiastic oversight, none of this would have been possible.
A SYNTHESIS OF THE PROCEDURAL AND DECLARATIVE STYLES OF INTERACTIVE THEOREM PROVING
"... Abstract. We propose a synthesis of the two proof styles of interactive theorem proving: the procedural style (where proofs are scripts of commands, like in Coq) and the declarative style (where proofs are texts in a controlled natural language, like in Isabelle/Isar). Our approach combines the adva ..."
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Abstract. We propose a synthesis of the two proof styles of interactive theorem proving: the procedural style (where proofs are scripts of commands, like in Coq) and the declarative style (where proofs are texts in a controlled natural language, like in Isabelle/Isar). Our approach combines the advantages of the declarative style – the possibility to write formal proofs like normal mathematical text – and the procedural style – strong automation and help with shaping the proofs, including determining the statements of intermediate steps. Our approach is new, and differs significantly from the ways in which the procedural and declarative proof styles have been combined before in the Isabelle, Ssreflect and Matita systems. Our approach is generic and can be implemented on top of any procedural interactive theorem prover, regardless of its architecture and logical foundations. To show the viability of our proposed approach, we fully implemented it as a proof interface called miz3, on top of the HOL Light interactive theorem prover. The declarative language that this interface uses is a slight variant of the language of the Mizar system, and can be used for any interactive theorem prover regardless of its logical foundations. The miz3 interface allows easy access to the full set of tactics and formal libraries of HOL Light, and as such has ‘industrial strength’. Our approach gives a way to automatically convert any procedural proof to a declarative counterpart, where the converted proof is similar in size to the original. As all declarative systems have essentially the same proof language, this gives a straightforward way to port proofs between interactive theorem provers. 1.