## Extracting constructive content from classical logic via control-like reductions (1993)

Venue: | In Bezem and Groote [12 |

Citations: | 34 - 1 self |

### BibTeX

@INPROCEEDINGS{Barbanera93extractingconstructive,

author = {Franco Barbanera and Stefano Berardi},

title = {Extracting constructive content from classical logic via control-like reductions},

booktitle = {In Bezem and Groote [12},

year = {1993},

pages = {45--59},

publisher = {Springer-Verlag}

}

### Years of Citing Articles

### OpenURL

### Abstract

### Citations

340 |
Lambda-mu-calculus: An algorithmic interpretation of classical natural deduction
- Parigot
- 1992
(Show Context)
Citation Context ...s. In the direction of finding new logical systems in which it could be better understood and extracted the constructive content of classical proofs we can mention the works of Girard [7] and Parigot =-=[11]-=-. Game theory has been instead investigated as an environment in which it is possible to interpret the constructive content of classical connectives and proofs (see, among others, Coquand [3]). In thi... |

269 | The revised report on the syntactic theories of sequential control and state
- Felleisen, Hieb
- 1989
(Show Context)
Citation Context ...rol operators in functional languages people like Felleisen investigated pure calculi like the pure control language consisting in the pure lambda calculus enriched with a particular operator C ( C ) =-=[4]-=-,[5]. C can be rightly considered as an abstraction of the actual control operators. For this language it is possible to give a machine-like operational semantics or to define a calculus extending the... |

252 | A formulae-as-types notion of control
- Griffin
- 1990
(Show Context)
Citation Context ...ors in [1]. However, one of the most appealing directions for the computer scientist, not only the theoretical one, is that which has begun being developed with works by Griffin ? To Roberta Gottardi =-=[8]-=- and Murthy [10] (indeed it was these works that made raise the interest for the topic we are speaking about). In these works a strong relation has been established between classical logic and the con... |

83 |
Classical and intuitionistically provably recursive functions
- Friedman
- 1978
(Show Context)
Citation Context ...urpose of extending to classical logic the well known proofs-as-programs paradigm of constructive logic. The basis of all the presents investigations are quite old results by Kreisel [9] and Friedman =-=[6]-=-, showing that classical and intuitionistic provability coincide for \Sigma 0 1 formulas. Now, since from the programming point of view constructivity is needed just for this class of formulas, the pr... |

64 |
Extracting Constructive Content from Classical Proofs
- Murthy
- 1990
(Show Context)
Citation Context ...ever, one of the most appealing directions for the computer scientist, not only the theoretical one, is that which has begun being developed with works by Griffin ? To Roberta Gottardi [8] and Murthy =-=[10]-=- (indeed it was these works that made raise the interest for the topic we are speaking about). In these works a strong relation has been established between classical logic and the control operators u... |

59 |
Programming with continuations
- Friedman, Haynes, et al.
- 1985
(Show Context)
Citation Context ...operators in functional languages people like Felleisen investigated pure calculi like the pure control language consisting in the pure lambda calculus enriched with a particular operator C ( C ) [4],=-=[5]-=-. C can be rightly considered as an abstraction of the actual control operators. For this language it is possible to give a machine-like operational semantics or to define a calculus extending the not... |

18 |
1958b, ‘Mathematical Significance of Consistency Proofs
- Kreisel
(Show Context)
Citation Context ...y the ambitious purpose of extending to classical logic the well known proofs-as-programs paradigm of constructive logic. The basis of all the presents investigations are quite old results by Kreisel =-=[9]-=- and Friedman [6], showing that classical and intuitionistic provability coincide for \Sigma 0 1 formulas. Now, since from the programming point of view constructivity is needed just for this class of... |

10 |
Continuations and simple types: A strong normalization result
- Barbanera, Berardi
- 1992
(Show Context)
Citation Context ... and call-by-value, leaving open the problem of arbitrary reduction strategies. To face such a problem the authors studied the problem of strong normalization for the calculussC , a study that led in =-=[2] to -=-a proof of strong normalization for a system ( C�� \Gamma ) similar tosC , where the reduction rules present insC are somewhat restricted and where other reduction rules are added. In the present ... |

4 |
Validity and normalizability of proofs in 1-st and 2-nd order classical and intuitionistic logic
- Prawitz
- 1981
(Show Context)
Citation Context ...Prawitz-style reductions comes out of the fact that the rules of the group we dubbed with such a name are quite similar to the reductions defined by Prawitz to show the consistency of classical logic =-=[12]-=-. Rule C 00 R is an instance of the general rule E[CM ] ! 1 M(x:E[x]) for continuations and has been introduced in order to deal with the case of the elimination of negation. It is easy to see that th... |

3 |
A constructive valuation interpretation for classical logic and its use in witness extraction
- Barbanera, Berardi
- 1992
(Show Context)
Citation Context ...ent of classical connectives and proofs (see, among others, Coquand [3]). In this last direction an interpretation of classical logic in terms of a valuation semantic has been given by the authors in =-=[1]-=-. However, one of the most appealing directions for the computer scientist, not only the theoretical one, is that which has begun being developed with works by Griffin ? To Roberta Gottardi [8] and Mu... |

2 |
A new Constructive Logic
- Girard
- 1991
(Show Context)
Citation Context ...cal constructions. In the direction of finding new logical systems in which it could be better understood and extracted the constructive content of classical proofs we can mention the works of Girard =-=[7]-=- and Parigot [11]. Game theory has been instead investigated as an environment in which it is possible to interpret the constructive content of classical connectives and proofs (see, among others, Coq... |

1 |
A Game-theoric semantic of Classical Logic
- Coquand
- 1992
(Show Context)
Citation Context ...Parigot [11]. Game theory has been instead investigated as an environment in which it is possible to interpret the constructive content of classical connectives and proofs (see, among others, Coquand =-=[3]-=-). In this last direction an interpretation of classical logic in terms of a valuation semantic has been given by the authors in [1]. However, one of the most appealing directions for the computer sci... |