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34
Extensible universes for objectoriented data models
 Journal of Automated Reasoning
"... Abstract We present a datatype package that enables the shallow embedding technique to objectoriented specification and programming languages. This datatype package incrementally compiles an objectoriented data model to a theory containing objectuniverses, constructors, accessors functions, coerc ..."
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Abstract We present a datatype package that enables the shallow embedding technique to objectoriented specification and programming languages. This datatype package incrementally compiles an objectoriented data model to a theory containing objectuniverses, constructors, accessors functions, coercions between dynamic and static types, characteristic sets, their relations reflecting inheritance, and the necessary class invariants. The package is conservative, i. e., all properties are derived entirely from axiomatic definitions. As an application, we use the package for an objectoriented corelanguage called IMP++, for which correctness of a HoareLogic with respect to an operational semantics is proven. 1
A FirstOrder Syntax for the piCalculus in Isabelle/HOL using Permutations
"... . A formalized theory of alphaconversion for the #calculus in ..."
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. A formalized theory of alphaconversion for the #calculus in
Verification of the Redecoration Algorithm for Triangular Matrices
, 2007
"... Abstract. Triangular matrices with a dedicated type for the diagonal elements can be profitably represented by a nested datatype, i. e., a heterogeneous family of inductive datatypes. These families are fully supported since the version 8.1 of the Coq theorem proving environment, released in 2007. R ..."
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Abstract. Triangular matrices with a dedicated type for the diagonal elements can be profitably represented by a nested datatype, i. e., a heterogeneous family of inductive datatypes. These families are fully supported since the version 8.1 of the Coq theorem proving environment, released in 2007. Redecoration of triangular matrices has a succinct implementation in this representation, thus giving the challenge of proving it correct. This has been achieved within Coq, using also induction with measures. An axiomatic approach allowed a verification in the Isabelle theorem prover, giving insights about the differences of both systems. 1
Inductive data types with negative occurrences in HOL
, 2002
"... We identify that a useful inductive data type ty with negative occurrences like ty!bool in the arguments of its constructors can have a settheoretic interpretation when the negative occurrence models only fnite sets. Subsequently, we show how such data types can be manually added to higher order lo ..."
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We identify that a useful inductive data type ty with negative occurrences like ty!bool in the arguments of its constructors can have a settheoretic interpretation when the negative occurrence models only fnite sets. Subsequently, we show how such data types can be manually added to higher order logic using equivalence sets.
General Bindings and AlphaEquivalence in Nominal Isabelle
"... Abstract. Nominal Isabelle is a definitional extension of the Isabelle/HOL theorem prover. It provides a proving infrastructure for reasoning about programming language calculi involving named bound variables (as opposed to deBruijn indices). In this paper we present an extension of Nominal Isabell ..."
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Abstract. Nominal Isabelle is a definitional extension of the Isabelle/HOL theorem prover. It provides a proving infrastructure for reasoning about programming language calculi involving named bound variables (as opposed to deBruijn indices). In this paper we present an extension of Nominal Isabelle for dealing with general bindings, that means termconstructors where multiple variables are bound at once. Such general bindings are ubiquitous in programming language research and only very poorly supported with single binders, such as lambdaabstractions. Our extension includes new definitions of αequivalence and establishes automatically the reasoning infrastructure for αequated terms. We also prove strong induction principles that have the usual variable convention already built in. 1
Generating Counterexamples for Structural Inductions by Exploiting Nonstandard Models
"... Abstract. Induction proofs often fail because the stated theorem is noninductive, in which case the user must strengthen the theorem or prove auxiliary properties before performing the induction step. (Counter)model finders are useful for detecting nontheorems, but they will not find any counterexa ..."
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Abstract. Induction proofs often fail because the stated theorem is noninductive, in which case the user must strengthen the theorem or prove auxiliary properties before performing the induction step. (Counter)model finders are useful for detecting nontheorems, but they will not find any counterexamples for noninductive theorems. We explain how to apply a wellknown concept from firstorder logic, nonstandard models, to the detection of noninductive invariants. Our work was done in the context of the proof assistant Isabelle/HOL and the counterexample generator Nitpick. 1
• Arithmetic
, 2005
"... We are still looking at how the different parts of mathematics are encoded in the Isabelle/HOL library. ..."
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We are still looking at how the different parts of mathematics are encoded in the Isabelle/HOL library.
α Isabelle’s Logics: HOL 1
, 2010
"... Logical Frameworks, and 6453: Types) and by the DFG Schwerpunktprogramm ..."