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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
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
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.
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
Witnessing (Co)datatypes
"... Abstract. Datatypes and codatatypes are very useful for specifying and reasoning about (possibly infinite) computational processes. The interactive theorem prover Isabelle/HOL has been extended with a definitional package that supports both. Here we describe a complete procedure for deriving nonempt ..."
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Abstract. Datatypes and codatatypes are very useful for specifying and reasoning about (possibly infinite) computational processes. The interactive theorem prover Isabelle/HOL has been extended with a definitional package that supports both. Here we describe a complete procedure for deriving nonemptiness witnesses in the general mutually recursive, nested case—nonemptiness being a proviso for introducing new types in higherorder logic. The nonemptiness problem also provides an illuminating case study that shows the package in action, tracing its journey from abstract category theory to handson functionality. 1
BOOTSTRAPPING INDUCTIVE AND COINDUCTIVE TYPES IN HASCASL
, 812
"... Abstract. We discuss the treatment of initial datatypes and final process types in the widespectrum language HasCASL. In particular, we present specifications that illustrate how datatypes and process types arise as bootstrapped concepts using HasCASL’s type class mechanism, and we describe constru ..."
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Abstract. We discuss the treatment of initial datatypes and final process types in the widespectrum language HasCASL. In particular, we present specifications that illustrate how datatypes and process types arise as bootstrapped concepts using HasCASL’s type class mechanism, and we describe constructions of types of finite and infinite trees that establish the conservativity of datatype and process type declarations adhering to certain reasonable formats. The latter amounts to modifying known constructions from HOL to avoid unique choice; in categorical terminology, this means that we establish that quasitoposes with an internal natural numbers object support initial algebras and final coalgebras for a range of polynomial functors, thereby partially generalising corresponding results from topos theory. Moreover, we present similar constructions in categories of internal complete partial orders in quasitoposes.
BOOTSTRAPPING INDUCTIVE AND COINDUCTIVE TYPES IN HASCASL
, 2007
"... Vol. 4 (4:17) 2008, pp. 1–27 ..."