## The Church-Rosser Theorem in Isabelle: A Proof Porting Experiment (1995)

Citations: | 10 - 0 self |

### BibTeX

@TECHREPORT{Rasmussen95thechurch-rosser,

author = {Ole Rasmussen},

title = {The Church-Rosser Theorem in Isabelle: A Proof Porting Experiment},

institution = {},

year = {1995}

}

### Years of Citing Articles

### OpenURL

### Abstract

This paper describes a proof of the Church-Rosser theorem for the pure -calculus formalised in the Isabelle theorem prover. The initial version of the proof is ported from a similar proof done in the Coq proof assistant by Gérard Huet, but a number of optimisations have been performed. The development involves the introduction of several inductive and recursive definitions and thus gives a good presentation of the inductive package of Isabelle.

### Citations

1119 |
The Lambda Calculus: Its Syntax and Semantics
- BARENDREGT
- 1984
(Show Context)
Citation Context ...es [dB72], although they will also be defined and exemplified in Section 4. A thorough description of the lambda calculus and the Tait -- MartinL of proof of the Church-Rosser theorem can be found in =-=[Bar84]-=-. The Church-Rosser theorem for fi-reduction states that if two terms, m and n, are fi-convertible then there exists a common reduct u: m /! fi n ) 9u \Delta m \Gamma! usn \Gamma! u where \Gamma! is t... |

155 |
de Bruijn. Lambda calculus notation with nameless dummies, a tool for automatic formula manipulation, with application to the Church-Rosser theorem
- G
- 1972
(Show Context)
Citation Context ...her informal but all notions used will be defined formally in Section 4. We expect some familiarity with the -calculus, such as the notion of fi-reduction and representing -terms by de Bruijn indexes =-=[dB72]-=-, although they will also be defined and exemplified in Section 4. A thorough description of the lambda calculus and the Tait -- MartinL of proof of the Church-Rosser theorem can be found in [Bar84]. ... |

136 |
Isabelle: A Generic Theorem
- Paulson
- 1994
(Show Context)
Citation Context ... the Church-Rosser theorem. The proof originates from G'erard Huet [Hue94] using the Coq proof assistant [D + 93]. In this development we construct the same proof but with the Isabelle theorem prover =-=[Pau94b]-=- using the object-logic of Zermelo-Fraenkel set theory (from now on just called ZF). The project illustrates the use of Isabelle's inductive package [Pau94a] on a large proof development, definition o... |

44 |
A fixedpoint approach to implementing (co)inductive definitions
- Paulson
(Show Context)
Citation Context ...proof but with the Isabelle theorem prover [Pau94b] using the object-logic of Zermelo-Fraenkel set theory (from now on just called ZF). The project illustrates the use of Isabelle's inductive package =-=[Pau94a]-=- on a large proof development, definition of recursive functions, and how the automation tools of Isabelle can be employed effectively to solve major proof steps. Formalisation of this proof is not ne... |

42 | Reasoning with inductively defined relations in the HOL theorem prover
- Camilleri, Melham
- 1992
(Show Context)
Citation Context ...ore prover by Shankar [Sha88] and has later been described by Huet as mentioned above and in for example [Pfe92]. The Church-Rosser theorem has also been proved for combinatorial logic in for example =-=[CM92]-=- and by Paulson contained in the Isabelle ZF distribution. The proofs for combinatorial logic are however much simpler. The major goal of this project is not to prove that the Church-Rosser theorem is... |

37 |
A mechanical proof of the Church-Rosser theorem
- Shankar
- 1988
(Show Context)
Citation Context ...utomation tools of Isabelle can be employed effectively to solve major proof steps. Formalisation of this proof is not new and the first mechanical proof was done in the Boyer-Moore prover by Shankar =-=[Sha88]-=- and has later been described by Huet as mentioned above and in for example [Pfe92]. The Church-Rosser theorem has also been proved for combinatorial logic in for example [CM92] and by Paulson contain... |

36 | A proof of the Church-Rosser theorem and its representation in a logical framework
- Pfenning
- 1992
(Show Context)
Citation Context ... Formalisation of this proof is not new and the first mechanical proof was done in the Boyer-Moore prover by Shankar [Sha88] and has later been described by Huet as mentioned above and in for example =-=[Pfe92]-=-. The Church-Rosser theorem has also been proved for combinatorial logic in for example [CM92] and by Paulson contained in the Isabelle ZF distribution. The proofs for combinatorial logic are however ... |

27 |
Residual theory in -calculus: A formal development
- Huet
- 1994
(Show Context)
Citation Context ...le. 1 Introduction In this paper we describe a formal development of the residual theory for the pure -calculus leading to a proof of the Church-Rosser theorem. The proof originates from G'erard Huet =-=[Hue94]-=- using the Coq proof assistant [D + 93]. In this development we construct the same proof but with the Isabelle theorem prover [Pau94b] using the object-logic of Zermelo-Fraenkel set theory (from now o... |

3 |
Constructive Computation Theory, Part I
- Huet
- 1992
(Show Context)
Citation Context ...nitial version to be finished in less than two weeks of normal working hours. Huet used 3 months to construct the proof (or "1 monk month" as he writes) using an existing pre-formal developm=-=ent in ML [Hue92]-=-. 5.2 Remove Superfluous Type Information The observation behind this optimisation is that all inductive predicates are defined as subtypes. For example, the subset relation on redexes, !==, is define... |