## Regular bohm trees (1996)

Citations: | 1 - 1 self |

### BibTeX

@MISC{Huet96regularbohm,

author = {Gérard Huet},

title = {Regular bohm trees},

year = {1996}

}

### OpenURL

### Abstract

We give a decision procedure for the extensional equality of total Böhm trees presented by regular systems of recursion equations. 1. Böhm trees presentations Böhm trees are the natural infinite generalisations of normal forms in pure λ-calculus.

### Citations

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Lambda Calculus: its Syntax and Semantics
- Barendregt
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(Show Context)
Citation Context ...infinite generalisations of normal forms in pure λ-calculus. They arose from the work of Böhm on separability (Böhm 1968), and were first identified by Barendregt, who devotes chapter 10 of his book (=-=Barendregt 1980-=-) to their study, and relates denotational models such as D∞ to appropriate quotients over Böhm trees. There is however no generally agreed presentation of Böhm trees, and the various partial ordering... |

75 |
Codifying guarded definitions with recursion schemes
- Giménez
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(Show Context)
Citation Context ... other hand, ≡E is an inductively defined equivalence relation. ∼E and ≡E are mutually defined in the same recursion. Such mixtures of inductively and co-inductively defined objects are explained in (=-=Giménez 1995-=-); a corresponding proof package, allowing such definitions and the mechanical checking of formal proofs about such objects, is available in the Coq proof assistant (Giménez 1996). From the semantics ... |

42 | A co-induction principle for recursively defined domains
- Pitts
- 1994
(Show Context)
Citation Context ... N are similar. Inversely, M ∼E N =⇒ F alse for any two dissimilar simple expressions. Remarks. Note that ∼E is not defined inductively. It is rather a co-inductive definition, in the sense of Pitts (=-=Pitts 1994-=-). It has the flavor of defining truth as consistency, in the spirit of inductionless induction (Huet and Hullot 1982). For instance, with EY = {Y f := f(Y (f)); Z f := f(Z ′ (f)); Z ′ f := f(Z(f))} w... |

34 |
Séquents qu’on calcule : de l’interprétation du calcul des séquents comme calcul de λ-termes et comme calcul de stratégies gagnantes. Thèse d’université, Université Paris 7
- Herbelin
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(Show Context)
Citation Context ...ve useful in this context. Finally, application of this formalism to typed systems, in particular to proof assistants where Böhm trees may represent sequent calculus partial proofs, in the manner of (=-=Herbelin 1995-=-), remains to be investigated. In particular, the Extensionality rule needs to be constrained (for instance with a notion of η-long normal form). Acknowlegment. We thank Martin Abadi and Gilles Dowek ... |

24 |
Alcune Proprietà delle Forme β-η-Normali nel λ-K-Calcolo
- Böhm
- 1968
(Show Context)
Citation Context ...r systems of recursion equations. 1. Böhm trees presentations Böhm trees are the natural infinite generalisations of normal forms in pure λ-calculus. They arose from the work of Böhm on separability (=-=Böhm 1968-=-), and were first identified by Barendregt, who devotes chapter 10 of his book (Barendregt 1980) to their study, and relates denotational models such as D∞ to appropriate quotients over Böhm trees. Th... |

6 | A Functional Extension to Lustre
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- 1995
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Citation Context ...a particularly good candidate. Recently, Caspi and Pouzet have shown that a functional extension to Lustre could be implemented in a kernel of recursively defined primitives for stream manipulations (=-=Caspi and Pouzet 1995-=-). This kernel can be represented in a rather direct way as a set of regular combinators. Many further investigations are needed to make practical such an application. For instance, there are several ... |

5 | Ronchi Della Rocca S., “A Discrimination Algorithm inside λ-calculus - Böhm, Dezani-Ciancaglini, et al. |

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4 | The axioms of constructive geometry. Annals of Pure and Applied - Plato - 1995 |

2 | Solving equations in Lambda-Calculus - Böhm, Piperno, et al. - 1989 |

1 | Algorithmes d’équivalence et de réduction à des expressions minimales dans une classe d’équations récursives simples - Série, p - 1996 |

1 |
Proofs by Induction
- Huet, Hullot
- 1982
(Show Context)
Citation Context ...E is not defined inductively. It is rather a co-inductive definition, in the sense of Pitts (Pitts 1994). It has the flavor of defining truth as consistency, in the spirit of inductionless induction (=-=Huet and Hullot 1982-=-). For instance, with EY = {Y f := f(Y (f)); Z f := f(Z ′ (f)); Z ′ f := f(Z(f))} we may prove by co-induction that Y ∼EY Z. On the other hand, ≡E is an inductively defined equivalence relation. ∼E an... |

1 | Finite-state Transducers as Regular Böhm Trees
- Huet, Laulhère
- 1997
(Show Context)
Citation Context ... are needed to make practical such an application. For instance, there are several alternative ways to represent data structures or more complexsG. Huet 10 control structures. An exemple is given in (=-=Huet and Laulhère 1997-=-) which considers the encoding of finite-state transducers as regular Böhm trees. The algorithmic aspects of the decision procedure remain to be investigated. If no constraint is put on the way combin... |

1 |
Böhm trees and Extensionality. Private communication
- Lévy
- 1993
(Show Context)
Citation Context ... as D∞ to appropriate quotients over Böhm trees. There is however no generally agreed presentation of Böhm trees, and the various partial orderings considered on them make this topic a difficult one (=-=Lévy 1993-=-). We shall adopt here the point of view that Böhm trees are potentially infinite computational objets similar to the streams studied in the theory of communicating processes, and treat them according... |