by
Norbert Völker

Citations: | 1 - 1 self |

@TECHREPORT{Völker01adeep,

author = {Norbert Völker},

title = {A Deep Embedding of Z_C in Isabelle/HOL},

institution = {},

year = {2001}

}

This report describes a deep embedding of the logic ZC [HR00] in Isabelle /HOL. The development is based on a general theory of de Bruijn terms. Wellformed terms, propositions and judgements are represented as inductive sets. The embedding is used to prove elementary properties of ZC such as uniqueness of types, type inhabitation and that elements of judgements are wellformed propositions 1 De Bruijn Terms The representation of logical syntax in Isabelle/HOL will be based on a polymorphic datatype dbterm of de Bruijn terms. This development follows the example of A. Gordon [Gor94] who constructed a similar theory for the HOL system. The datatype dbterm is independent of ZC and can be used as a foundation for deep embeddings in general. For other HOL representations of terms see [Owe95] and [Von95].

44 |
A fixedpoint approach to implementing (co)inductive definitions
- Paulson
(Show Context)
Citation Context ...erived ZC constants such as SUBSET can be derived by unfolding the definition of such constants. Inductive sets are defined in Isabelle/HOL to be least fixed points of a monotonic set valued function =-=[Pau94]. This-=- made it necessary to prove monotonicity of the function zip rcd before the definition of the sets tterm and prop could be processed by the inductive set package: A ⊆ B =⇒ zip rcd A ⊆ zip rcd B ... |

31 |
A mechanisation of name-carrying syntax up to alpha-conversion
- Gordon
- 1994
(Show Context)
Citation Context ...ropositions 1 De Bruijn Terms The representation of logical syntax in Isabelle/HOL will be based on a polymorphic datatype dbterm of de Bruijn terms. This development follows the example of A. Gordon =-=[Gor94]-=- who constructed a similar theory for the HOL system. The datatype dbterm is independent of ZC and can be used as a foundation for deep embeddings in general. For other HOL representations of terms se... |

13 |
Representing higher-order logic proofs in HOL
- Wright
- 1995
(Show Context)
Citation Context ...ed a similar theory for the HOL system. The datatype dbterm is independent of ZC and can be used as a foundation for deep embeddings in general. For other HOL representations of terms see [Owe95] and =-=[Von95]. The definition o-=-f the datatype (α, β, γ) dbterm of de Bruijn terms is: (α, β, γ) dbterm = Const α | Free β | Bound N | dAbs ((α, β, γ) dbterm) γ | ((α, β, γ) dbterm) $ ((α, β, γ) dbterm) The five ty... |

11 | Investigating Z
- Henson, Reeves
- 2000
(Show Context)
Citation Context ...puter Science University of Essex, England Technical Report CSM-343 A Deep Embedding of ZC in Isabelle/HOL Norbert Völker July 25, 2001 Abstract This report describes a deep embedding of the logic ZC=-= [HR00]-=- in Isabelle/HOL. The development is based on a general theory of de Bruijn terms. Wellformed terms, propositions and judgements are represented as inductive sets. The embedding is used to prove eleme... |

4 | Revising Z: Part I - logic and semantics - Henson, Rees - 1999 |

3 | Revising Z: Part II - logical development - Henson, Reeves - 1999 |

3 | Coding binding and substitution explicitly in Isabelle
- Owens
- 1995
(Show Context)
Citation Context ...ho constructed a similar theory for the HOL system. The datatype dbterm is independent of ZC and can be used as a foundation for deep embeddings in general. For other HOL representations of terms see =-=[Owe95] and [Von95]. The -=-definition of the datatype (α, β, γ) dbterm of de Bruijn terms is: (α, β, γ) dbterm = Const α | Free β | Bound N | dAbs ((α, β, γ) dbterm) γ | ((α, β, γ) dbterm) $ ((α, β, γ) dbterm)... |

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