## Normalization and partial evaluation (2002)

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Venue: | Applied Semantics, number 2395 in LNCS |

Citations: | 18 - 0 self |

### BibTeX

@INPROCEEDINGS{Dybjer02normalizationand,

author = {Peter Dybjer and Andrzej Filinski},

title = {Normalization and partial evaluation},

booktitle = {Applied Semantics, number 2395 in LNCS},

year = {2002},

pages = {137--192},

publisher = {Springer-Verlag}

}

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### Abstract

Abstract. We give an introduction to normalization by evaluation and type-directed partial evaluation. We first present normalization by evaluation for a combinatory version of Gödel System T. Then we show normalization by evaluation for typed lambda calculus with β and η conversion. Finally, we introduce the notion of binding time, and explain the method of type-directed partial evaluation for a small PCF-style functional programming language. We give algorithms for both call-by-name and call-by-value versions of this language.

### Citations

552 | Lambda calculi with types - Barendregt - 1992 |

239 | Tutorial notes on partial evaluation - Consel, Danvy - 1993 |

223 | Cayenne—a language with dependent types
- Augustsson
- 1998
(Show Context)
Citation Context ...mits terminating functions. Nevertheless, the dependent type structure would be useful here too, and one might want to use a version of dependent type theory, such as the programming language Cayenne =-=[Aug98]-=-, which allows non-terminating functions. We do not pursue this idea further here either. Notation. NBE-algorithms use the interpretation of an object language in a meta-language. Since our object- an... |

210 | Type-directed partial evaluation
- Danvy
(Show Context)
Citation Context ...tion of reify will instantiate them to exp. Moreover, any (monomorphic) dynamic constants can also be handled using explicit lambda-abstractions. This approach was used in early presentations of TDPE =-=[Dan96]-=-, but gets awkward for larger examples. The functor-based approach described below scales up more gracefully. Example 2. Returning to the possible annotations of the power function from Example 1, we ... |

64 | Program extraction from normalization proofs
- Berger
- 1993
(Show Context)
Citation Context ...alization bysNormalization and Partial Evaluation 141 evaluation provided a simple solution. Berger then noticed that the NBE program could be extracted from a normalization proof using Tait’s method =-=[Ber93]-=-. The method has been refined using categorical methods [AHS95, ČDS98], and also extended to System F [AHS96] and to include strong sums [ADHS01]. Type-Directed Partial Evaluation (TDPE). Type-directe... |

57 |
An inverse of the evaluation functional for typed λ–calculus
- Berger, Schwichtenberg
- 1991
(Show Context)
Citation Context ...ion of terms in combinatory logic, and we shall present this case in Section 2. Normalization by evaluation for typed lambda calculus with β and η conversion was invented by Berger and Schwichtenberg =-=[BS91]-=-. Initially, they needed a normalization algorithm for their proof system MINLOG, and normalization bysNormalization and Partial Evaluation 141 evaluation provided a simple solution. Berger then notic... |

50 | An inverse of the evaluation functional for typed -calculus - Berger, Schwichtenberg - 1991 |

47 | Intuitionistic model constructions and normalization proofs
- Coquand, Dybjer
- 1997
(Show Context)
Citation Context ...ecially for a different basis, such as categorical combinators [AHS95]. The following (obviously incomplete) table summarizes the situation: notion of conversion syntax weak β strong β βη combinators =-=[CD97]-=- [AHS95] lambda-terms [ML75b,CD93b] [Mog92] [BS91] We should also mention that a main advantage with the glueing technique is that it extends smoothly to datatypes. We showed only how to treat natural... |

40 | Normalization by evaluation for typed lambda calculus with coproducts
- Altenkirch, Dybjer, et al.
- 2001
(Show Context)
Citation Context ...xtracted from a normalization proof using Tait’s method [Ber93]. The method has been refined using categorical methods [AHS95, ČDS98], and also extended to System F [AHS96] and to include strong sums =-=[ADHS01]-=-. Type-Directed Partial Evaluation (TDPE). Type-directed partial evaluation stems from the study of “two-level η-expansions”, a technique for making programs specialize better [DMP95]. This technique ... |

27 | Functional Programming and Lambda Calculus - Barendregt |

24 | Normalization and the Yoneda embedding - Čubrić, Dybjer, et al. - 1998 |

23 | Categorical reconstruction of a reduction free normalization proof
- Altenkirch, Hofmann, et al.
- 1995
(Show Context)
Citation Context ...s based on β-conversion only [Mog92]. Likewise, it is also perfectly possible to consider βη-convertibility in a combinatory setting, especially for a different basis, such as categorical combinators =-=[AHS95]-=-. The following (obviously incomplete) table summarizes the situation: notion of conversion syntax weak β strong β βη combinators [CD97] [AHS95] lambda-terms [ML75b,CD93b] [Mog92] [BS91] We should als... |

17 | The type free lambda calculus - Barendregt - 1977 |

13 | Binding-Time Analysis for Both Static and Dynamic Expressions - Asai - 1999 |

2 |
Category Theory and Computer
- Rydeheard
- 1986
(Show Context)
Citation Context ...ced that the NBE program could be extracted from a normalization proof using Tait’s method [Ber93]. The method has been refined using categorical methods [AHS95, ČDS98], and also extended to System F =-=[AHS96]-=- and to include strong sums [ADHS01]. Type-Directed Partial Evaluation (TDPE). Type-directed partial evaluation stems from the study of “two-level η-expansions”, a technique for making programs specia... |

2 | Reductionfree normalization for a polymorphic system - Altenkirch, Hofmann, et al. - 1996 |