## Intersection types for explicit substitutions (2003)

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Citations: | 17 - 6 self |

### BibTeX

@MISC{Lengrand03intersectiontypes,

author = {Stéphane Lengrand and Pierre Lescanne and Dan Dougherty and Mariangiola Dezani-Ciancaglini and Steffen van Bakel},

title = {Intersection types for explicit substitutions},

year = {2003}

}

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### Abstract

We present a new system of intersection types for a composition-free calculus of explicit substitutions with a rule for garbage collection, and show that it characterizes those terms which are strongly normalizing. This system extends previous work on the natural generalization of the classical intersection types system, which characterized head normalization and weak normalization, but was not complete for strong normalization. An important role is played by the notion of available variable in a term, which is a generalization of the classical notion of free variable.

### Citations

1115 | The Lambda Calculus: Its Syntax and Semantics - Barendregt - 1981 |

518 | Lambda calculi with types - Barendregt - 1992 |

391 | Explicit substitutions
- Abadi, Cardelli, et al.
- 1991
(Show Context)
Citation Context ...lement, so that making substitutions explicit leads to a more pertinent analysis of the correctness and efficiency of compilers, theorem provers, and proof-checkers. Abadi, Cardelli, Curien, and Lévy =-=[1]-=- and de Bruijn [12] defined the first calculi of explicit substitutions. Intersection type disciplines originated in [14,15] to overcome the limitations of Curry’s type assignment system and to provid... |

329 | Foundations for Programming Languages - Mitchell - 1996 |

213 | Intensional Interpretations of Functionals of Finite Type - Tait - 1967 |

207 | Modal Logics - Feys - 1965 |

198 | Z.: Proving termination with multiset orderings - Dershowitz, Manna - 1979 |

141 | Type systems for programming languages - Mitchell - 1990 |

123 | Lambda-calcul types et modèles - Krivine - 1990 |

103 | Complete restrictions of the Intersection Type Discipline
- Bakel
- 1992
(Show Context)
Citation Context ...terization of the strongly normalizing terms of the λ-calculus [36]. Since then, intersection types disciplines have been used in a series of papers for characterizing evaluation properties of λterms =-=[29,28,3,4,23,2,22,17]-=-. As discussed in [20], one can see an explicit substitution calculus as an improvement on both the system of combinators and LC, since it is a system whose mechanics are first-order and as simple as ... |

98 | λυ, a calculus of explicit substitutions which preserves strong normalisation - Benaissa, Briaud, et al. - 1996 |

65 | Preservation of strong normalisation in named lambda calculi with explicit substitution and garbage collection - Bloo, Rose - 1995 |

61 | Intersection Type Assignment Systems
- Bakel
- 1995
(Show Context)
Citation Context ...terization of the strongly normalizing terms of the λ-calculus [36]. Since then, intersection types disciplines have been used in a series of papers for characterizing evaluation properties of λterms =-=[29,28,3,4,23,2,22,17]-=-. As discussed in [20], one can see an explicit substitution calculus as an improvement on both the system of combinators and LC, since it is a system whose mechanics are first-order and as simple as ... |

56 | Mathematical Intuitionism: Introduction to Proof Theory, volume 67 - Dragalin - 1988 |

46 | Two extensions of Curry's type inference system - Cardone, Coppo - 1990 |

44 | Typed -calculi with explicit substitution may not terminate - Mellies - 1995 |

41 | Preservation of Termination for Explicit Substitution - Bloo - 1997 |

41 | On stepwise explicit substitution - Kamareddine, Nederpelt - 1993 |

39 | An extension of the basic functionality theory for the - calculus - Coppo, Dezani-Ciancaglini - 1980 |

36 | A type assignment for the strongly normalizable terms - Pottinger - 1980 |

35 | Lambda-calculus, types and models - Krivine - 1993 |

35 | Typing and computation properties of lambda expressions - Leivant - 1986 |

30 | Explicit substitution: on the edge of strong normalization - Bloo, Geuvers - 1999 |

27 | Modeling Sharing and Recursion for Weak Reduction Strategies using Explicit Substitution - Benaissa, Lescanne, et al. - 1996 |

25 |
Domains and Lambda Calculi
- Amadio, Curien
(Show Context)
Citation Context ...terization of the strongly normalizing terms of the λ-calculus [36]. Since then, intersection types disciplines have been used in a series of papers for characterizing evaluation properties of λterms =-=[29,28,3,4,23,2,22,17]-=-. As discussed in [20], one can see an explicit substitution calculus as an improvement on both the system of combinators and LC, since it is a system whose mechanics are first-order and as simple as ... |

24 | Operational Reduction Models for Functional Programming Languages - Rose - 1996 |

22 | Strong Normalization of Explicit Substitutions via Cut Elimination in Proof Nets - Cosmo, Kesner - 1997 |

21 | Strong normalization and typability with intersection types - Ghilezan - 1996 |

20 | A New Type Assignment for Lambda-Terms. Archive für Mathematischer Logic und Grundlagenforschung - Coppo, Dezani-Ciancaglini - 1978 |

20 | de Bruijn. A namefree lambda calculus with facilities for internal definition of expressions and segments. TH-Report 78-WSK-03 - G - 1978 |

18 | A namefree lambda calculus with facilities for internal definition of expressions and segments - Bruijn - 1978 |

15 | From ## to ##, a journey through calculi of explicit substitutions - Lescanne - 1994 |

11 | Foundation for Programmimg Languages - Mitchell - 1996 |

7 | Con uence Properties of Weak and Strong Calculi of Explicit Substitutions - Curien, Hardin, et al. - 1991 |

7 | Explicit Substitutions and Reducibility - Herbelin |

7 | Extending a lambda-calculus with explicit substitution which preserves strong normalisation into a confluent calculus on open terms - Kamareddine, Ríos - 1997 |

5 | Perpetuality in a named lambda calculus with explicit substitutions - Bonelli |

5 | Characterizing explicit substitutions which preserve termination - Ritter - 1999 |

4 | Typed -calculi with explicit substitution may not terminate - Mellis - 1995 |

4 | The calculus of explicit substitutions - Lescanne, Rouyer-Degli - 1994 |

3 | Relating the lambda-sigma and lambda-s styles of explicit substitutions - Kamareddine, Ríos - 2000 |

3 | Compositional characterizations of lambda-terms using intersection types (extended abstract - Dezani-Ciancaglini, Honsell, et al. |

3 | Typing untyped lambda terms, or reducibility strikes again - Gallier - 1998 |

3 | An improved system of intersection types for explicit substitutions - Lengrand, Dougherty, et al. - 2001 |

1 | Axiomatic rewriting theory III, a factorisation theorem in rewriting theory - Mellis - 1997 |

1 | logique et machines. École Normale Sup érieure de - Lambda-calcul - 2001 |

1 |
Characterizing strong normalization for explicit substitutions
- Bakel, Dezani-Ciancaglini
(Show Context)
Citation Context ... in explicit substitutions calculi. In fact, we present two different characterizations of strong normalization, in the form of two different type systems. These systems were discovered independently =-=[5,30]-=-. Each system starts with the natural generalization of the classical intersection types system to the explicit substitutions calculus and adds a new typing rule. In one system [5], the new rule essen... |

1 | The Lambda-Calculus, its syntax and semantics. Studies in Logic and the Foun-dation of Mathematics - Domains, Cambridge - 1998 |

1 | An improved system of intersection types forexplicit substitutions - Lengrand, Dougherty, et al. - 2002 |