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## A Flexible Framework for Visualisation of Computational Properties of General Explicit Substitutions Calculi (2010)

### Citations

1696 | The Definition of Standard ML
- MILNER, TOFTE, et al.
- 1991
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Citation Context ...25,3,17,10,15,14,2,13,21]. These developments have illustrated the usefulness of explicit substitutions calculi for practical notions like the implementation of typed functional programming languages =-=[24,29,16]-=- and higher-order proof assistants [9,27,8,6]. SUBSEXPL concentrates on the simulation of the application of the rewriting rules citeBaNi98 of different calculi. Some of these calculi were developed u... |

1193 |
Term Rewriting and All That
- Baader, Nipkow
- 1998
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Citation Context ...http://pauillac.inria.fr/∼ddr/camlp5/). It permits the definition of new calculi and its rewriting rules in an easy way because it implements a generic notion of term based on a first-order signature =-=[5]-=- given by: type expression = [ T of string and array expression | V of string ]; In addition, a notion of a (meta-) capture avoiding substitution, denoted by {x := N}, and of an explicit unary substit... |

1041 |
Isabelle/HOL — A Proof Assistant for Higher-Order Logic, LNCS 2283
- Nipkow, Paulson, et al.
- 2002
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Citation Context ... have illustrated the usefulness of explicit substitutions calculi for practical notions like the implementation of typed functional programming languages [24,29,16] and higher-order proof assistants =-=[9,27,8,6]-=-. SUBSEXPL concentrates on the simulation of the application of the rewriting rules citeBaNi98 of different calculi. Some of these calculi were developed using de Bruijn indexes that are very adequate... |

432 | Explicit Substitutions
- Abadi, Cardelli, et al.
- 1991
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Citation Context ...al system, because now it is possible to insert new calculi by giving as input their grammatical descriptions. In the last twenty years, much work has been done in the field of explicit substitutions =-=[22,1,7,19,25,3,17,10,15,14,2,13,21]-=-. These developments have illustrated the usefulness of explicit substitutions calculi for practical notions like the implementation of typed functional programming languages [24,29,16] and higher-ord... |

364 | Lambda calculus notation with nameless dummies, a tool for automatic formula manipulation, with application to the Church-Rosser theorem
- Bruijn
- 1972
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Citation Context ...eduction then all this information must be typed in a file with extension .se (cf. Figure 2). Fig. 3. The λσ-calculus 72.2 Calculi in de Bruijn notation Moura et.al. The so called de Bruijn notation =-=[11]-=- uses indexes to represent bound and free variables. In this notation, free variables are stored in a list that represents the context of the term, and its reference corresponds to its position in thi... |

116 |
et al., Implementing Mathematics with the Nuprl Proof Development System
- Constable
- 1986
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Citation Context ... have illustrated the usefulness of explicit substitutions calculi for practical notions like the implementation of typed functional programming languages [24,29,16] and higher-order proof assistants =-=[9,27,8,6]-=-. SUBSEXPL concentrates on the simulation of the application of the rewriting rules citeBaNi98 of different calculi. Some of these calculi were developed using de Bruijn indexes that are very adequate... |

113 | Engineering formal metatheory
- Aydemir, Charguéraud, et al.
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Citation Context ...n several styles of explicit substitutions. Several real specifications and implementations of calculi of explicit substitutions in modern systems use a new hybrid approach known as locally nameless] =-=[4]-=- in which bound variables are represented by de Bruijn indexes, and free variables by names. This approach benefits the unitary representation of classes of α-equivalent terms without the need of cont... |

82 | A -calculus a la de Bruijn with Explicit Substitutions
- Kamareddine, Ros
- 1995
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Citation Context ...al system, because now it is possible to insert new calculi by giving as input their grammatical descriptions. In the last twenty years, much work has been done in the field of explicit substitutions =-=[22,1,7,19,25,3,17,10,15,14,2,13,21]-=-. These developments have illustrated the usefulness of explicit substitutions calculi for practical notions like the implementation of typed functional programming languages [24,29,16] and higher-ord... |

71 | Preservation of strong normalisation in named lambda calculi with explicit substitution and garbage collection
- Bloo, Rose
- 1995
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Citation Context ...al system, because now it is possible to insert new calculi by giving as input their grammatical descriptions. In the last twenty years, much work has been done in the field of explicit substitutions =-=[22,1,7,19,25,3,17,10,15,14,2,13,21]-=-. These developments have illustrated the usefulness of explicit substitutions calculi for practical notions like the implementation of typed functional programming languages [24,29,16] and higher-ord... |

63 | On stepwise explicit substitution
- Kamareddine, Nederpelt
- 1993
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43 |
A confluent calculus of substitutions
- Hardin, L'evy
- 1989
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29 |
A lambda-calculus with explicit weakening and explicit substitution
- David, Guillaume
- 2001
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25 |
Typed λ-calculi with explicit substitutions may not terminate
- Melliès
- 1995
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Citation Context ...teraction allow us to give a much more readable presentation of Melliès’s counter8Moura et.al. example than the one presented in previous version of the system [12]. 2.2.1 Melliès counter-example In =-=[23]-=-, Melliès proved that the λσ-calculus does not preserve strong normalisation. This proof consists in building, by an adequate combination of the rules, an infinite derivation from the well-typed λ-ter... |

25 | Fine-Grained Notation for Lambda Terms and Its Use in Intensional Operations
- NADATHUR, “A
- 1999
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25 |
de Vrijer. Selected papers on Automath
- Nederpelt, Geuvers, et al.
- 1994
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Citation Context ...ndexes: (i) The λσ-style [1] which introduces two different sets of entities: one for terms and one for substitutions. (ii) The λs-style [19] which makes use of the philosophy of de Bruijn’s Automath =-=[26]-=- elaborated in the new item notation [18]. The philosophy states that terms are built by applications (a function applied to an argument), abstraction (a function), substitution or updating. The advan... |

25 | Explicit cyclic substitutions
- Rose
- 1993
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Citation Context ...tution in the SUBSEXPL system. 2.1 The λex calculus The λex calculus [21] is a calculus with explicit substitutions that uses named notation. The λex calculus is obtained by extending the λx calculus =-=[22,28,7]-=- 4Moura et.al. Fig. 1. The SUBSEXPL menu with one rewriting rule to specify the composition of dependent substitutions and one equation to specify the commutation of independent substitutions, as fol... |

13 |
A useful λ-notation
- Kamareddine, Nederpelt
- 1996
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Citation Context ...uces two different sets of entities: one for terms and one for substitutions. (ii) The λs-style [19] which makes use of the philosophy of de Bruijn’s Automath [26] elaborated in the new item notation =-=[18]-=-. The philosophy states that terms are built by applications (a function applied to an argument), abstraction (a function), substitution or updating. The advantages of this philosophy include remainin... |

12 |
Verification of Combinational Logic in Nuprl
- Basin, Vecchio
(Show Context)
Citation Context ... have illustrated the usefulness of explicit substitutions calculi for practical notions like the implementation of typed functional programming languages [24,29,16] and higher-order proof assistants =-=[9,27,8,6]-=-. SUBSEXPL concentrates on the simulation of the application of the rewriting rules citeBaNi98 of different calculi. Some of these calculi were developed using de Bruijn indexes that are very adequate... |

8 | Comparing and Implementing Calculi of Explicit Substitutions with Eta-Reduction
- Ayala-Rincón, Moura, et al.
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8 | Relating the λσ- and λs-Styles of Explicit Substitutions
- Kamareddine, Ríos
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Citation Context ... and Future Work We presented an extension of the SUBSEXPL system which is an OCaml implementation for comparing, simulating and 12Moura et.al. studying λ-calculus and explicit substitutions calculi =-=[20]-=-. The source code is freely available at the SUBSEXPL web page: http://www.cic.unb.br/∼flavio/subsexpl/index.html. We showed how SUBSEXPL has been used for both educational and research purposes with ... |

7 |
A new formula for the execution of a categorical combinators
- Lins
- 1986
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6 | A theory of explicit substitutions with safe and full composition
- Kesner
- 2009
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4 |
Order Matching via Explicit Substitutions
- MOURA, KAMAREDDINE, et al.
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3 | Explicit Substitutions and All That
- Ayala-Rincón, Muñoz
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3 |
The Objective Caml system, release 3.11
- Leroy, Doligez, et al.
- 2008
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Citation Context ...25,3,17,10,15,14,2,13,21]. These developments have illustrated the usefulness of explicit substitutions calculi for practical notions like the implementation of typed functional programming languages =-=[24,29,16]-=- and higher-order proof assistants [9,27,8,6]. SUBSEXPL concentrates on the simulation of the application of the rewriting rules citeBaNi98 of different calculi. Some of these calculi were developed u... |

1 | SUBSEXPL: A Framework for Simulating and Comparing Explicit Substitutions Calculi
- Moura, Ayala-Rincón, et al.
- 2006
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Citation Context ...ail: fairouz@macs.hw.ac.uk This paper is electronically published in Electronic Notes in Theoretical Computer Science URL: www.elsevier.nl/locate/entcsMoura et.al. 1 Introduction The system SUBSEXPL =-=[12]-=- was developed in OCaml as a system to simulate and compare calculi of explicit substitutions in de Bruijn notation (variables as indices). In this work we present an extension of this system that has... |

1 | Higher-Order Unification: A structural relation between Huet’s method and the one based on explicit substitutions
- Moura, Ayala-Rincón, et al.
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