## Nominal System T (2010)

Citations: | 6 - 1 self |

### BibTeX

@MISC{Pitts10nominalsystem,

author = {Andrew M. Pitts},

title = {Nominal System T},

year = {2010}

}

### OpenURL

### Abstract

This paper introduces a new recursion principle for inductive data modulo

### Citations

335 |
Functions as Processes
- Milner
- 1992
(Show Context)
Citation Context ...nd (6) correspond to basic “structural” properties of a notion of name restriction. Structural congruence for name-restriction first arose in connection with the reduction semantics of the ... |

311 |
Higher-order abstract syntax
- Pfenning, Elliott
(Show Context)
Citation Context ...g so has the consequence that the object-level capture-avoidance property of sub is delegated to the properties of meta-level ... |

226 | A new approach to abstract syntax with variable binding - Gabbay, Pitts |

225 |
Intentional Interpretations of Functionals of Finite Type I
- Tait
- 1967
(Show Context)
Citation Context .... We call the calculus presented in this paper Nominal System T since it takes Gödel’s System T for primitive recursive functions of higher type [13] (formulated as a typed ... |

222 | The practice of logical frameworks
- Pfenning
- 1996
(Show Context)
Citation Context ... bijection with ... |

176 | Nominal logic, a first order theory of names and binding - Pitts |

166 |
Lambda Calculus: its Syntax and Semantics (North-Holland
- Barendregt
- 1984
(Show Context)
Citation Context ...equivalence of bound names. To bring out the ideas underlying our approach without too much syntactic clutter, we use the familiar and simple example of such data, the terms of the untyped ... |

150 |
Abstract syntax and variable binding
- Fiore, Plotkin, et al.
- 1999
(Show Context)
Citation Context ...esting feature of [16, 17, 29]. Nominal versus presheaf representations. The nominal sets model of names and binding has close connections with the use of certain presheaf categories to model binding =-=[9]-=-. Indeed the category ... |

121 | On the observable properties of higher order functions that dynamically create local names (preliminary report - Pitts, Stark - 1993 |

115 | Operational reasoning for functions with local state - Pitts, Stark - 1998 |

101 | Programming in MartinLof’s Type Theory
- Nordstrom, Petersson, et al.
- 1990
(Show Context)
Citation Context ... try to extend Nominal System T with dependent types. Historically speaking, Gödel’s System T was a stepping-stone on the way to Martin Löf’s much more expressive treatment of recursion and induction =-=[19]-=-. Gödel’s System T is the simply typed kernel of Martin Löf’s constructive type theory. It would be interesting to investigate whether the approach introduced here extends to a “nominal Martin-Löf typ... |

81 | Freshml: Programming with binders made simple
- Shinwell, Pitts, et al.
- 2003
(Show Context)
Citation Context ..., of “recursive functions modulo ... |

58 | Nominal unification - Urban, Pitts, et al. |

54 | Five axioms of alpha conversion - Gordon, Melham - 1996 |

50 |
A type-theoretic foundation for programming with higher-order abstract syntax and first-class substitutions
- Pientka
- 2008
(Show Context)
Citation Context ...t previous uses of typed ... |

48 | Alpha-structural recursion and induction
- Pitts
(Show Context)
Citation Context ...ition should we impose on ... |

36 | An extension to ML to handle bound variables in data structures: Preliminary report
- Miller
- 1990
(Show Context)
Citation Context ...lyses of Poswolsky and Schürmann [29] and Licata et al. [16] are pertinent: most previous uses of typed ... |

31 | A functional theory of local names
- Odersky
- 1994
(Show Context)
Citation Context ...mple 1.2]. Instead of trying to tame dynamic allocation in this context [30], here we propose to avoid it altogether by using (a typed version of) the pure functional theory of local names of Odersky =-=[21]-=-. We give this a denotational semantics using nominal sets, which in turn suggests adding an explicit name-swapping operation to Odersky’s calculus. Odersky’s theory of local names may seem too simple... |

28 | Practical programming with higher-order encodings and dependent types
- Poswolsky, Schürmann
- 2008
(Show Context)
Citation Context ...onstructive), or representation plus computation (functional or logical), or both? Here the primary focus is on functional computation with representations and the analyses of Poswolsky and Schürmann =-=[29]-=- and Licata et al. [16] are pertinent: most previous uses of typed ... |

26 | On a monadic semantics for freshness
- Shinwell, Pitts
(Show Context)
Citation Context ... example, it does not disturb function extensionality) and is in a sense more general than dynamic allocation, because the latter can be encoded in it via a continuation monad; cf. Shinwell and Pitts =-=[32]-=-. The conversions in Fig. 3 for (... |

24 | Static name control for FreshML - Pottier - 2007 |

22 | Focusing on binding and computation
- Licata, Zeilberger, et al.
- 2008
(Show Context)
Citation Context ...entation plus computation (functional or logical), or both? Here the primary focus is on functional computation with representations and the analyses of Poswolsky and Schürmann [29] and Licata et al. =-=[16]-=- are pertinent: most previous uses of typed ... |

21 | A Recursion Combinator for Nominal Datatypes Implemented in Isabelle/HOL
- Urban, Berghofer
- 2006
(Show Context)
Citation Context ...ample of capture-avoiding substitution mentioned above, (FCB) holds because ... |

18 | Normalization and partial evaluation
- Dybjer, Filinski
(Show Context)
Citation Context ...evaluation” (NbE). Since its introduction by Berger and Schwichtenberg [4], NbE has been applied to a number of applied ... |

17 | A universe of binding and computation
- Licata, Harper
- 2009
(Show Context)
Citation Context ...ties [24] when trying to develop recursion and induction for higher-order abstract syntax. These authors advocate separating the two notions of function, leading to forms of locally scoped symbols in =-=[15, 16, 29, 37]-=- similar to the notion of atom-abstraction (... |

16 | Combining generic judgments with recursive definitions - Gacek, Miller, et al. - 2008 |

14 | Recursive function definition for types with binders - Norrish - 2004 |

13 |
Über eine bisher noch nicht benütze erweiterung des finiten standpunktes
- Gödel
- 1958
(Show Context)
Citation Context ...assed to functions as arguments and returned as results. We call the calculus presented in this paper Nominal System T since it takes Gödel’s System T for primitive recursive functions of higher type =-=[13]-=- (formulated as a typed ... |

12 | Term rewriting for normalization by evaluation
- Berger, Eberl, et al.
(Show Context)
Citation Context ...evaluation” (NbE). Since its introduction by Berger and Schwichtenberg [4], NbE has been applied to a number of applied ... |

10 | Fresh objective caml user manual
- Shinwell, Pitts
- 2005
(Show Context)
Citation Context ..., of “recursive functions modulo ... |

8 | A dependent nominal type theory
- Cheney
(Show Context)
Citation Context ...constructive type theory extended with atom-abstraction/concretion, locally scoped atoms, atom-equality tests and explicit swapping. 8. Context SNTT. The “simple nominal type theory” (SNTT) of Cheney =-=[6]-=- is the work most closely related to the results presented in this paper. The motivation behind both works is the same: to produce a calculus combining simple type theory 3 with some of the distinctiv... |

7 | M.: A modular type-checking algorithm for type theory with singleton types and proof irrelevance - Abel, Coquand, et al. - 2011 |

7 |
Nominal logic and abstract syntax
- Cheney
(Show Context)
Citation Context ...very common to use typed ... |

3 |
R.: Higher-order abstract syntax: setting the record straight
- Crary, Harper
- 2006
(Show Context)
Citation Context ...very common to use typed ... |

2 |
The calculus of nominal inductive constructions: an intensional approach to encoding name-bindings
- Westbrook, Stump, et al.
- 2009
(Show Context)
Citation Context ...ation of its bunched contexts might provide useful conditions in a conditional-equational calculus more expressive than the simple equational notion of conversion we have given here. Westbrook et al. =-=[37]-=- use some of the ideas behind SNTT to design an extension of the calculus of inductive constructions, the type theory underlying Coq. This is certainly the right direction in which to go. However, we ... |

1 |
An inverse of the evaluation functional for typed
- Berger, Schwichtenberg
- 1991
(Show Context)
Citation Context ...ollows that conversion is decidable too. 5. Normalization by Evaluation We prove Theorem 10 using a version of “normalization by evaluation” (NbE). Since its introduction by Berger and Schwichtenberg =-=[4]-=-, NbE has been applied to a number of applied ... |

1 | A Theory of Inductive Definitions with - Gabbay - 2000 |