## Nuprl-Light: An implementation framework for higher-order logics (1997)

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### Download Links

- [www.cs.cornell.edu]
- [www.nuprl.org]
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- [www.cs.cornell.edu]
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### Other Repositories/Bibliography

Venue: | IN 14TH INTERNATIONAL CONFERENCE ON AUTOMATED DEDUCTION |

Citations: | 12 - 7 self |

### BibTeX

@INPROCEEDINGS{Hickey97nuprl-light:an,

author = {Jason J. Hickey},

title = {Nuprl-Light: An implementation framework for higher-order logics},

booktitle = {IN 14TH INTERNATIONAL CONFERENCE ON AUTOMATED DEDUCTION},

year = {1997},

pages = {395--399},

publisher = {Springer}

}

### OpenURL

### Abstract

Recent developments in higher-order logics and theorem prover design have led to an

### Citations

889 | A Theory of Objects
- Abadi, Cardelli
- 1996
(Show Context)
Citation Context ...closely modeled on the interpretation of Hofmann, Pierce, and Turner [14, 27], where objects are abstracted over a \state" type. We also draw on the interpretation of Abadi, Cardelli, and Viswanathan =-=[1, 2]-=-, where objects contain only methods and state update is provided by method override. There has been a great deal of research on logical frameworks. Our work develops the meta-logical framework (in Nu... |

420 | Isabelle: A generic theorem prover
- Paulson
- 1994
(Show Context)
Citation Context ...s, the implementation framework is tied closely to a programming language (in this case Caml-Light) and the formal module system is tied closely to the programming language modules. Like the Isabelle =-=[9]-=- generic theorem prover, Nuprl-Light uses generalized Horn clauses for logical speci cation. Indeed, speci cations in Nuprl-Light appear quite similar to those in Isabelle. However, where Isabelle use... |

342 |
Intuitionistic type theory
- Martin-Löf
- 1984
(Show Context)
Citation Context ...been a great deal of research on logical frameworks. Our work develops the meta-logical framework (in Nuprl) of Constable and Basin [4]. Nuprl itself was developed out of the early work of Martin{Lof =-=[20, 21]-=-, as well as the Automath logical framework [22]. Our framework has much in common with the Isabelle generic theorem prover [23, 25], which is based on hereditary Harrop formulas. Both Nuprl-Light and... |

267 | A type-theoretic approach to higher-order modules with sharing - Harper, Lillibridge - 1994 |

165 |
Logic and Computation: Interactive Proof with Cambridge LCF
- Paulson
- 1987
(Show Context)
Citation Context ...tion. Indeed, speci cations in Nuprl-Light appear quite similar to those in Isabelle. However, where Isabelle uses higher order uni cation and resolution, Nuprl-Light retains a tactic{tree [3] of LCF =-=[8]-=- style reasoning based on tactics and tacticals, and Nuprl-Light also allows theories to contain speci cations of rewrites, using the computational congruence of Howe [7]. Like LF, the Nuprl-Light met... |

158 | Simple type-theoretic foundations for object-oriented programming
- Pierce, Turner
- 1994
(Show Context)
Citation Context ...In this example, we give only the signatures (although implementation can be shown to exist). This example follows an encoding of object similar to the existential interpretation of Pierce and Turner =-=[27]-=-, with the exception that the \state" or \carrier" of the object (car) is not abstract. A deeper encoding would use existential types to hide the value of the car method. More detail of this interpret... |

156 |
An intuitionistic theory of types: Predicative part
- Martin-Löf
- 1975
(Show Context)
Citation Context ...been a great deal of research on logical frameworks. Our work develops the meta-logical framework (in Nuprl) of Constable and Basin [4]. Nuprl itself was developed out of the early work of Martin{Lof =-=[20, 21]-=-, as well as the Automath logical framework [22]. Our framework has much in common with the Isabelle generic theorem prover [23, 25], which is based on hereditary Harrop formulas. Both Nuprl-Light and... |

104 |
Introduction to HOL
- Gordon, Melham
- 1993
(Show Context)
Citation Context ...a general architecture where provers can be combined in a \plug{and{play" manner. As this task proceeds, we need a semantic basis for relating theories, as Howe [16] provides in his semantics for HOL =-=[7]-=- and Nuprl. 6 Conclusion We have described the Nuprl-Light framework, which extends the results of generic theorem provers by adding formal, rst{class theories. First{class theories enable a new style... |

95 | Equality in lazy computation systems
- Howe
- 1989
(Show Context)
Citation Context ...ains a tactic{tree [3] of LCF [8] style reasoning based on tactics and tacticals, and Nuprl-Light also allows theories to contain speci cations of rewrites, using the computational congruence of Howe =-=[7]-=-. Like LF, the Nuprl-Light meta-logic also relies on the judgments{as{ types principle (an extension of propositions{as{type), where proofs are terms that inhabit the clauses. ? Support for this resea... |

51 | An Interpretation of Objects and Object Types
- Abadi, Cardelli, et al.
- 1996
(Show Context)
Citation Context ...closely modeled on the interpretation of Hofmann, Pierce, and Turner [14, 27], where objects are abstracted over a \state" type. We also draw on the interpretation of Abadi, Cardelli, and Viswanathan =-=[1, 2]-=-, where objects contain only methods and state update is provided by method override. There has been a great deal of research on logical frameworks. Our work develops the meta-logical framework (in Nu... |

47 | Reasoning theories – towards an architecture for open mechanized reasoning systems
- Giunchiglia, Pecchiari, et al.
- 1996
(Show Context)
Citation Context ...t{oriented techniques. On this theme, Mart -Oliet and Meseguer [19] propose rewriting logics a solution to the proliferation of logics; they also propose object{oriented theories. Guinchiglia et. al. =-=[6]-=- are also exploring a general architecture where provers can be combined in a \plug{and{play" manner. As this task proceeds, we need a semantic basis for relating theories, as Howe [16] provides in hi... |

44 | Enhancing the Nuprl proof-development system and applying it to computational abstract algebra
- Jackson
- 1995
(Show Context)
Citation Context ...ent function type. Our plans for the future include further development of the tactic collection and improvements to proof search algorithms. 5 Related Work Our framework draws on the work of Jackson =-=[18, 17]-=-, who formulated a great deal of abstract constructive algebra in the Nuprl system. Jackson's system formalized algebraic objects in the type theory using dependent Cartesian products, which su ered f... |

37 | A unifying type-theoretic framework for objects
- Hofmann, Pierce
- 1994
(Show Context)
Citation Context ...d as objects, and the expected subtyping properties are ful lled by object subsumption. Our object interpretation in this paper is closely modeled on the interpretation of Hofmann, Pierce, and Turner =-=[14, 27]-=-, where objects are abstracted over a \state" type. We also draw on the interpretation of Abadi, Cardelli, and Viswanathan [1, 2], where objects contain only methods and state update is provided by me... |

33 |
Elf: A meta-language for deductive systems
- Pfenning
- 1995
(Show Context)
Citation Context ...erpretation of type theory is available in set theory, the interpretation should be formalizable. We can also compare Nuprl-Light to the (Edinburgh) Logical Framework [9] (which is implemented in ELF =-=[26]-=-, for instance). In a sense, our framework has a di erent purpose than LF|where LF provides a framework for logics, our framework is for their implementations. Our basic logic is much weaker, andstype... |

29 | Formal objects in type theory using very dependent types
- Hickey
- 1996
(Show Context)
Citation Context ...heorems, and proofs. { A method for constructing formal types from module signatures, and formal object for module implementations, based on recent theoretical work with very{dependent function types =-=[6]-=-. { An architecture for incrementally implementing algorithms for automated reasoning. { A mechanism for generic shared tactics and derived rules. 2 The Framework The formal system uses a term languag... |

26 |
A framework for de ning logics
- Harper, Honsell, et al.
- 1992
(Show Context)
Citation Context ...ing a modular, object-oriented framework for specifying, relating, and developing type theories and mathematical domains. The framework itself assumes (and provides) no type theory or logic, as in LF =-=[4]-=-, which iswhywe call it an implementation framework. Instead, Nuprl-Light provides a meta-framework where logical frameworks such as LF, Nuprl, set theory, and other theories can be de ned and develop... |

22 |
Exploring abstract algebra in constructive type theory
- Jackson
- 1994
(Show Context)
Citation Context ...ent function type. Our plans for the future include further development of the tactic collection and improvements to proof search algorithms. 5 Related Work Our framework draws on the work of Jackson =-=[18, 17]-=-, who formulated a great deal of abstract constructive algebra in the Nuprl system. Jackson's system formalized algebraic objects in the type theory using dependent Cartesian products, which su ered f... |

20 |
A module system for a programming language based on the LF logical framework
- Harper, Pfenning
- 1992
(Show Context)
Citation Context ...ur framework is for their implementations. Our basic logic is much weaker, andstype theories, including LF, are implemented by asserting their inference rules, much like Isabelle. Harper and Pfenning =-=[11]-=- propose a module system for LF, which is similar to ours in some ways. However, we place an additional emphasis on relations between logics through object{oriented techniques. On this theme, Mart -Ol... |

7 | The Semantics of Re ected Proof - Allen, Constable, et al. - 1990 |

5 |
Semantic Foundations for Embedding HOL
- Howe
- 1996
(Show Context)
Citation Context ...chiglia et. al. [6] are also exploring a general architecture where provers can be combined in a \plug{and{play" manner. As this task proceeds, we need a semantic basis for relating theories, as Howe =-=[16]-=- provides in his semantics for HOL [7] and Nuprl. 6 Conclusion We have described the Nuprl-Light framework, which extends the results of generic theorem provers by adding formal, rst{class theories. F... |

1 |
Gri n. Notational De nition and Top-Down Re nement for Interactive Proof Development Systems
- Timothy
- 1988
(Show Context)
Citation Context ...al speci cation. Indeed, speci cations in Nuprl-Light appear quite similar to those in Isabelle. However, where Isabelle uses higher order uni cation and resolution, Nuprl-Light retains a tactic{tree =-=[3]-=- of LCF [8] style reasoning based on tactics and tacticals, and Nuprl-Light also allows theories to contain speci cations of rewrites, using the computational congruence of Howe [7]. Like LF, the Nupr... |

1 |
Oliet and Jose Meseguer. Rewriting logic as a logical and semantic framework
- Mart
- 1993
(Show Context)
Citation Context ... system for LF, which is similar to ours in some ways. However, we place an additional emphasis on relations between logics through object{oriented techniques. On this theme, Mart -Oliet and Meseguer =-=[19]-=- propose rewriting logics a solution to the proliferation of logics; they also propose object{oriented theories. Guinchiglia et. al. [6] are also exploring a general architecture where provers can be ... |