## Using Theory Morphisms for Implementing Formal Methods Tools (2003)

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Citations: | 6 - 5 self |

### BibTeX

@MISC{Brucker03usingtheory,

author = {Achim D. Brucker and Burkhart Wolff},

title = {Using Theory Morphisms for Implementing Formal Methods Tools},

year = {2003}

}

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### Abstract

Tools for a specification language can be implemented directly (by building a special purpose theorem prover) or by a conservative embedding into a typed meta-logic, which allows their safe and logically consistent implementation and the reuse of existing theorem prover engines.

### Citations

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Citation Context ... functor T ME. Our Framework and Isabelle/HOL. Our chosen meta-logic and implementation platform Isabelle/HOL is the instance of the generic theorem prover Isabelle [10] with higher-order logic (HOL) =-=[25, 26]-=-. Isabelle directly implements order sorted types ([24]; Note, however, that we do not make use of the ordering on sorts throughout this paper), and supports the conservative extension schemes abstrac... |

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Citation Context ...ecently [6]. For the formal analysis of specification languages, their representation, i.e. their embedding, within a logical framework based on typed λ-calculi such as NuPRL [7], Coq [8] or Isabelle =-=[9, 10]-=- is a widely accepted technique that has been applied in many studies in recent years. With respect to tools implementing specification languages, the situation is not so clear-cut: while direct imple... |

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Citation Context ...ative theory morphism” which leads to the key observations and their practical observations for the construction of shallow embeddings. The terminology used here follows the framework of institutions =-=[23]-=-. Throughout this paper, however, it is sufficient to base our notions on simple set-theoretic concepts instead of full-blown category theory. The concept of signature is inspired by [24], but can be ... |

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Citation Context ...ple, for some semantic aspects like exception handling or state propagation, monads have been proposed as a flexible means for describing the semantics of a language “facet by facet” in a modular way =-=[31, 32]-=-. While we will not use monads in this work (which is a result of our chosen standard example, OCL, and thus accidental), and while we do not even suggest a similar fixed semantic framework here, mere... |

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Citation Context ... functor T ME. Our Framework and Isabelle/HOL. Our chosen meta-logic and implementation platform Isabelle/HOL is the instance of the generic theorem prover Isabelle [10] with higher-order logic (HOL) =-=[25, 26]-=-. Isabelle directly implements order sorted types ([24]; Note, however, that we do not make use of the ordering on sorts throughout this paper), and supports the conservative extension schemes abstrac... |

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Citation Context ...e invention of typed λ-calculi (see for the special case of the quantifiers in [25]), it was not before the late seventies that the overall importance of higherorder abstract syntax (a term coined by =-=[28]-=-) for the representation of binding in logical rules and program transformations [29] and for implementations [28] was recognized. The term “shallow embedding” (invented in [30]) extends higherorder a... |

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Citation Context ...nal constructs such as quantifiers or universally quantified variables. Among the plethora of specification languages that has been developed, we will refer here only to examples such as Hoare-Logics =-=[1, 2]-=-, Z [3, 4] or its semantic sister Higher-order Logics (HOL) [5], which has been advertised as “functional language with quantifiers” recently [6]. For the formal analysis of specification languages, t... |

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Citation Context ... it was not before the late seventies that the overall importance of higherorder abstract syntax (a term coined by [28]) for the representation of binding in logical rules and program transformations =-=[29]-=- and for implementations [28] was recognized. The term “shallow embedding” (invented in [30]) extends higherorder abstract syntax (HOAS) to a semantic definition and is contrasted to “deep embeddings”... |

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Citation Context ...bles. Among the plethora of specification languages that has been developed, we will refer here only to examples such as Hoare-Logics [1, 2], Z [3, 4] or its semantic sister Higher-order Logics (HOL) =-=[5]-=-, which has been advertised as “functional language with quantifiers” recently [6]. For the formal analysis of specification languages, their representation, i.e. their embedding, within a logical fra... |

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Citation Context ...nal constructs such as quantifiers or universally quantified variables. Among the plethora of specification languages that has been developed, we will refer here only to examples such as Hoare-Logics =-=[1, 2]-=-, Z [3, 4] or its semantic sister Higher-order Logics (HOL) [5], which has been advertised as “functional language with quantifiers” recently [6]. For the formal analysis of specification languages, t... |

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Citation Context ...ll refer here only to examples such as Hoare-Logics [1, 2], Z [3, 4] or its semantic sister Higher-order Logics (HOL) [5], which has been advertised as “functional language with quantifiers” recently =-=[6]-=-. For the formal analysis of specification languages, their representation, i.e. their embedding, within a logical framework based on typed λ-calculi such as NuPRL [7], Coq [8] or Isabelle [9, 10] is ... |

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Citation Context ...ntax (a term coined by [28]) for the representation of binding in logical rules and program transformations [29] and for implementations [28] was recognized. The term “shallow embedding” (invented in =-=[30]-=-) extends higherorder abstract syntax (HOAS) to a semantic definition and is contrasted to “deep embeddings”. Moreover, throughout this paper, we will distinguish typed64 Achim D. Brucker and Burkhar... |

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Citation Context ...daption layer and — to a lesser extent — the data adaption layer. In principle, the overall construction is also applicable for other higher-order typed theorem proving systems such as Coq [8] or ALF =-=[33]-=-; however, the theories over the semantic combinators and the core of the tactic procedure will have to be adapted to these frameworks. Besides the obvious need for more generic theorems and more powe... |

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Citation Context ...ucts such as quantifiers or universally quantified variables. Among the plethora of specification languages that has been developed, we will refer here only to examples such as Hoare-Logics [1, 2], Z =-=[3, 4]-=- or its semantic sister Higher-order Logics (HOL) [5], which has been advertised as “functional language with quantifiers” recently [6]. For the formal analysis of specification languages, their repre... |

33 | Order-sorted polymorphism in Isabelle
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Citation Context ...institutions [23]. Throughout this paper, however, it is sufficient to base our notions on simple set-theoretic concepts instead of full-blown category theory. The concept of signature is inspired by =-=[24]-=-, but can be expressed in other typed λ-calculi too. First we introduce the notion of sorts, types and terms; we assume a set ρ of sorts and a set χ of type constructors, e.g. bool, _ → _, list, _ set... |

29 |
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Citation Context ...ucts such as quantifiers or universally quantified variables. Among the plethora of specification languages that has been developed, we will refer here only to examples such as Hoare-Logics [1, 2], Z =-=[3, 4]-=- or its semantic sister Higher-order Logics (HOL) [5], which has been advertised as “functional language with quantifiers” recently [6]. For the formal analysis of specification languages, their repre... |

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Citation Context ... the 90 percent that are library functions, our approach may significantly facilitate the embedding approach and lead to more portability. This work was partly motivated by the development of HOL-OCL =-=[17, 18]-=- a conservative embedding of the Object Constraint Language (OCL) [19, 20, 21] into HOL. OCL is a textual extension of the object-oriented Unified Modeling Language (UML) [22] which is widely used wit... |

15 | HOL-OCL: Experiences, Consequences and Design Choices
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Citation Context ... the 90 percent that are library functions, our approach may significantly facilitate the embedding approach and lead to more portability. This work was partly motivated by the development of HOL-OCL =-=[17, 18]-=- a conservative embedding of the Object Constraint Language (OCL) [19, 20, 21] into HOL. OCL is a textual extension of the object-oriented Unified Modeling Language (UML) [22] which is widely used wit... |

9 | B.: Hol-z 2.0: A proof environment for zspecifications
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Citation Context ...mming environment are predominant [11, 12, 13], which result in special logic, special purpose theorem provers sometimes based on ad-hoc deduction technology, only a few tools are based on embeddings =-=[14, 15, 16]-=-. H. Geuvers and F. Wiedĳk (Eds.): TYPES 2002, LNCS 2646, pp. 59–77, 2003. c○ 2003 Springer-Verlag. This is the author’s version of the work. It is posted at http://www.brucker. ch/bibliography/abstra... |

8 |
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Citation Context ... facilitate the embedding approach and lead to more portability. This work was partly motivated by the development of HOL-OCL [17, 18] a conservative embedding of the Object Constraint Language (OCL) =-=[19, 20, 21]-=- into HOL. OCL is a textual extension of the object-oriented Unified Modeling Language (UML) [22] which is widely used within the object oriented software development process. In principle, OCL is a s... |

5 |
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Citation Context ... facilitate the embedding approach and lead to more portability. This work was partly motivated by the development of HOL-OCL [17, 18] a conservative embedding of the Object Constraint Language (OCL) =-=[19, 20, 21]-=- into HOL. OCL is a textual extension of the object-oriented Unified Modeling Language (UML) [22] which is widely used within the object oriented software development process. In principle, OCL is a s... |

1 | 19] OMG: Object Constraint Language Specification. [22] chapter 6 [20 - Warmer, Kleppe, et al. - 1999 |

1 | S.: DOVE: A tool for design modelling and verification in safety critical systems
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Citation Context ...mming environment are predominant [11, 12, 13], which result in special logic, special purpose theorem provers sometimes based on ad-hoc deduction technology, only a few tools are based on embeddings =-=[14, 15, 16]-=-. H. Geuvers and F. Wiedĳk (Eds.): TYPES 2002, LNCS 2646, pp. 59–77, 2003. c○ 2003 Springer-Verlag. This is the author’s version of the work. It is posted at http://www.brucker. ch/bibliography/abstra... |

1 |
P.: Combining monads. In: Glasgow functional programming workshop
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Citation Context ...ple, for some semantic aspects like exception handling or state propagation, monads have been proposed as a flexible means for describing the semantics of a language “facet by facet” in a modular way =-=[31, 32]-=-. While we will not use monads in this work (which is a result of our chosen standard example, OCL, and thus accidental), and while we do not even suggest a similar fixed semantic framework here, mere... |