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38
Proving Java Type Soundness
, 1997
"... This technical report describes a machine checked proof of the type soundness of a subset of the Java language called Java S . A formal semantics for this subset has been developed by Drossopoulou and Eisenbach, and they have sketched an outline of the type soundness proof. The formulation developed ..."
Abstract

Cited by 86 (2 self)
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This technical report describes a machine checked proof of the type soundness of a subset of the Java language called Java S . A formal semantics for this subset has been developed by Drossopoulou and Eisenbach, and they have sketched an outline of the type soundness proof. The formulation developed here complements their written semantics and proof by correcting and clarifying significant details; and it demonstrates the utility of formal, machine checking when exploring a large and detailed proof based on operational semantics. The development also serves as a case study in the application of `declarative' proof techniques to a major property of an operational system. Contents 1 Introduction 2 1.1 Java . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 What is Type Soundness for Java? . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 The Tool: DECLARE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 Outl...
Set Theory for Verification: II  Induction and Recursion
 Journal of Automated Reasoning
, 2000
"... A theory of recursive definitions has been mechanized in Isabelle's ZermeloFraenkel (ZF) set theory. The objective is to support the formalization of particular recursive definitions for use in verification, semantics proofs and other computational reasoning. ..."
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Cited by 43 (21 self)
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A theory of recursive definitions has been mechanized in Isabelle's ZermeloFraenkel (ZF) set theory. The objective is to support the formalization of particular recursive definitions for use in verification, semantics proofs and other computational reasoning.
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
Generic Automatic Proof Tools
, 1997
"... This article explores a synthesis between two distinct traditions in automated reasoning: resolution and interaction. In particular it discusses Isabelle, an interactive theorem prover based upon a form of resolution. It aims to demonstrate the value of proof tools that, compared with traditional re ..."
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Cited by 26 (9 self)
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This article explores a synthesis between two distinct traditions in automated reasoning: resolution and interaction. In particular it discusses Isabelle, an interactive theorem prover based upon a form of resolution. It aims to demonstrate the value of proof tools that, compared with traditional resolution systems, seem absurdly limited. Isabelle's classical reasoner searches for proofs using a tableau approach. The reasoner is generic: it accepts rules proved in applied theories, involving defined connectives. The reasoner works in a variety of domains without reducing them to firstorder logic. Resolution systems such as Otter [13], setheo [11] and pttp [34] represent automatic theorem proving at its highest point of refinement. They achieve extremely high inference rates and can run continuously for days without running out of storage. They can crack many of the toughest challenge problems that have been circulated. While they exploit many specialized algorithms, data structures and optimizations, they rely crucially on unification. Interactive systems let the user direct each step of the proof. They can implement complicated formalisms, chosen for maximum expressiveness, and typically based on the typed calculus. hol [7, 8] and pvs [23] are used for verification of hardware and realtime systems, while Coq [4] is used for formalizing mathematics. Large numbers of axioms  say, the description of a cpu design  do not overwhelm them, because finding the proof is the user's job. Partial automation is sometimes provided, but a resolution enthusiast would regret the lack of uniform search procedures based on unification. One procedure provided by most interactive provers is rewriting. Rewrite rules have many advantages. Unlike programmed inference rules, they are ...
Correct and UserFriendly Implementations of Transformation Systems
, 1996
"... . We present an approach to integrate several existing tools and methods to a technical framework for correctly developing and executing program transformations. The resulting systems enable program derivations in a userfriendly way. We illustrate the approach by proving and implementing the transf ..."
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Cited by 18 (9 self)
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. We present an approach to integrate several existing tools and methods to a technical framework for correctly developing and executing program transformations. The resulting systems enable program derivations in a userfriendly way. We illustrate the approach by proving and implementing the transformation Global Search on the basis of the tactical theorem prover Isabelle. A graphical userinterface based on the XWindow toolkit Tk provides user friendly access to the underlying machinery. 1 Introduction Development by transformation is a prominent approach in formal program development (CIP [Bau + 85], PROSPECTRA [HK 93], KIDS [Smi 90]). Many case studies have proven its feasibility and demonstrated how much more abstract and useroriented developments could be achieved than using usual postverification approaches (fundamental for systems like PVS [OSR 93]). One recent case study is [KW 95]; and a prominent one is [SPW 95] where a strategic transportation scheduling algorithm is de...
Isabelle/Isar  a generic framework for humanreadable proof documents
 UNIVERSITY OF BIA̷LYSTOK
, 2007
"... ..."
A Concrete Final Coalgebra Theorem for ZF Set Theory
 Types for Proofs and Programs: International Workshop TYPES ’94, LNCS 996
, 1994
"... . A special final coalgebra theorem, in the style of Aczel's [2], is proved within standard ZermeloFraenkel set theory. Aczel's AntiFoundation Axiom is replaced by a variant definition of function that admits nonwellfounded constructions. Variant ordered pairs and tuples, of possibly infinite len ..."
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Cited by 16 (7 self)
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. A special final coalgebra theorem, in the style of Aczel's [2], is proved within standard ZermeloFraenkel set theory. Aczel's AntiFoundation Axiom is replaced by a variant definition of function that admits nonwellfounded constructions. Variant ordered pairs and tuples, of possibly infinite length, are special cases of variant functions. Analogues of Aczel's Solution and Substitution Lemmas are proved in the style of Rutten and Turi [12]. The approach is less general than Aczel's, but the treatment of nonwellfounded objects is simple and concrete. The final coalgebra of a functor is its greatest fixedpoint. The theory is intended for machine implementation and a simple case of it is already implemented using the theorem prover Isabelle [10]. ? Thomas Forster alerted me to Quine's work. Peter Aczel and Andrew Pitts offered considerable advice and help. Daniele Turi gave advice by electronic mail. I have used Paul Taylor's macros for commuting diagrams. K. Mukai commented on the ...
Mechanizing set theory: Cardinal arithmetic and the axiom of choice
 Journal of Automated Reasoning
, 1996
"... Abstract. Fairly deep results of ZermeloFrænkel (ZF) set theory have been mechanized using the proof assistant Isabelle. The results concern cardinal arithmetic and the Axiom of Choice (AC). A key result about cardinal multiplication is κ ⊗ κ = κ, where κ is any infinite cardinal. Proving this resu ..."
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Cited by 16 (9 self)
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Abstract. Fairly deep results of ZermeloFrænkel (ZF) set theory have been mechanized using the proof assistant Isabelle. The results concern cardinal arithmetic and the Axiom of Choice (AC). A key result about cardinal multiplication is κ ⊗ κ = κ, where κ is any infinite cardinal. Proving this result required developing theories of orders, orderisomorphisms, order types, ordinal arithmetic, cardinals, etc.; this covers most of Kunen, Set Theory, Chapter I. Furthermore, we have proved the equivalence of 7 formulations of the Wellordering Theorem and 20 formulations of AC; this covers the first two chapters of Rubin and Rubin, Equivalents of the Axiom of Choice, and involves highly technical material. The definitions used in the proofs are