## A temporal-logic approach to binding-time analysis (1996)

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Venue: | In Proceedings, 11 th Annual IEEE Symposium on Logic in Computer Science |

Citations: | 82 - 5 self |

### BibTeX

@INPROCEEDINGS{Davies96atemporal-logic,

author = {Rowan Davies},

title = {A temporal-logic approach to binding-time analysis},

booktitle = {In Proceedings, 11 th Annual IEEE Symposium on Logic in Computer Science},

year = {1996},

pages = {184--195},

publisher = {IEEE Computer Society Press}

}

### Years of Citing Articles

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### Abstract

is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent publications in the BRICS Report Series. Copies may be obtained by contacting: BRICS

### Citations

652 |
Partial evaluation and automatic program generation. Englewood Cliffs
- Jones, Gomard, et al.
- 1993
(Show Context)
Citation Context ... author to BRICS (Basic Research in Computer Science, Centre of the Danish National Research Foundation) in the summer of 1995. y WWW: http://www.cs.cmu.edu/~rowan 1 1 Introduction Partial evaluation =-=[8]-=- is a method for specializing a program given part of the program's input. The basic technique is to execute those parts of the program that do not depend on the unknown data, while constructing a res... |

453 |
The formulae-as-type notion of construction
- Howard
- 1980
(Show Context)
Citation Context ...al construction of a binding-time type system based on temporal logic. Temporal logic is an extension of classical logic to include proofs that formulas are valid at particular times. The CurryHoward =-=[7]-=- isomorphism relates constructive proofs to typed -terms and formulas to types. Thus, we expect that extending the Curry-Howard isomorphism to constructive temporal logic should yield a typed -calculu... |

208 | Type-directed partial evaluation
- Danvy
- 1996
(Show Context)
Citation Context ... ! flB) ! fl(A ! B) which allows a form of lift on functions: f : fl A ! flB: next (x:A: prev (f (next x))) For more discussion on lift coercions in partial evaluation, including sum types, see Danvy =-=[4]-=-. As an example of a more realistic program in an extension of Standard ML with temporal operators, we show the regular expression matcher example from [5]. Figure 1 shows a version of the regular exp... |

196 |
Modal and temporal logics
- Stirling
- 1992
(Show Context)
Citation Context ... relationship between binding-time analysis and temporal logic. The structure of this paper is then as follows. In the following section, we start with L fl , an axiomatic formulation due to Stirling =-=[13]-=- for a small classical linear-time temporal logic including fl. We then formulate a natural-deduction system in a similar style to the modal systems of Martini and Masini [9], and prove that it has th... |

194 | A modal analysis of staged computation
- Davies, Pfenning
(Show Context)
Citation Context ...ng, thus showing that these languages are equivalent as type systems. We conclude by discussing some practical concepts from binding-time analysis. This work is similar to work by Davies and Pfenning =-=[3]-=- which shows that a typed language Mini-ML 2 based on modal logic captures a powerful form of staged computation, including run-time code generation. They also show that Mini-ML 2 is a conservative ex... |

182 | Refinement types for ML - Freeman, Pfenning - 1991 |

175 | Logic programming in the LF logical framework
- Pfenning
- 1991
(Show Context)
Citation Context ...luding modal logics, though this is still a speculative direction for future research. We have implemented type checkers for the languagessfl andsm in the logic programming language Elf (see Pfenning =-=[12]-=-). Using logic programming variables, the same programs will also perform type inference. We have also implemented the translations and proof of equivalence between these languages in Elf. 5 Acknowled... |

123 | Inheritance as Implicit Coercion
- Breazu-Tannen, Coquand, et al.
- 1991
(Show Context)
Citation Context ...ercions to all be implicit coercions in the original language, then we have a type system including fl for this language that is reminiscent of sub-typing in the style of work by Breazu-Tannen et.al. =-=[1]. Doing ty-=-pe inference and making these "coercions" explicit is then exactly a binding-time analysis. However, next and prev are not functions, so they are quite different from other implicit coercion... |

118 | Automatic autoprojection of recursive equations with global variables and abstract data types. Science of Computer Programming 16(2):151–195
- Bondorf, Danvy
- 1991
(Show Context)
Citation Context ...es can generally be formulated as binding-time preserving transformations in a language like Mini-ML fl . For example, the generation of specialization points in a partial evaluator like Similix (see =-=[1]-=- or [12]) can be expressed as adding memoizing functions to the binding-time separated program. The semantics of the binding-time analyzed program is then the composition of these binding-time preserv... |

97 |
A Simple Applicative Language: Mini-ML
- Clément, Despeyroux, et al.
- 1986
(Show Context)
Citation Context ...d version of a language like ML. For example, in a language extending Standard ML with Next, Prev and O fromsfl , and a type of natural numbers represented using zero and successor similar to Mini-ML =-=[2]-=-, we have the following lift coercion: (* val liftNat : nat -? O nat *) fun liftNat Z = Next Z --- liftNat (S x) = Next (S (Prev (liftNat x))) With these lift coercions defined appropriately,sm is alm... |

95 | A partial evaluator for the untyped lambda calculus
- Gomard, Jones
- 1991
(Show Context)
Citation Context ...lso partly supported by a Hackett Studentship from the University of Western Australia languages that include binding-time annotations, as for example by Nielson and Nielson [14] and Gomard and Jones =-=[9]-=-. However, the motivation for the particular typing rules that are chosen is often not clear. There has been some work, for example by Palsberg [15], on modular proofs that binding-time analyses gener... |

62 | Efficient multi-level generating extensions for program specialization
- Glück, Jørgensen
- 1995
(Show Context)
Citation Context ...Further, since temporal logics generally allow an unbounded number of "times", they should naturally correspond to a binding-time analysis with many levels, such as that studied by Gluck and=-= Jrgensen [5]-=-. The more traditional two-level binding-time analyzes can then be trivially obtained by restriction. Also, in binding-time analysis we have a simple linear ordering of the binding times, so we consid... |

46 |
and Hanne Riis Nielson. Two-Level Functional Languages, volume 34 of Cambridge Tracts
- Nielson
- 1992
(Show Context)
Citation Context ...regardless of the actual value of the known (static) data. Binding-time analyzes are usually described via typed languages that include binding-time annotations, as for example by Nielson and Nielson =-=[10]-=- and Gomard and Jones [6]. However, the motivation for the particular typing rules that are chosen is often not clear. There has been some work, for example by Palsberg [11], on modular proofs that bi... |

41 |
Two-level functional languages
- Nielson, Nielson
- 1992
(Show Context)
Citation Context ...e summer of 1995. It was also partly supported by a Hackett Studentship from the University of Western Australia languages that include binding-time annotations, as for example by Nielson and Nielson =-=[14]-=- and Gomard and Jones [9]. However, the motivation for the particular typing rules that are chosen is often not clear. There has been some work, for example by Palsberg [15], on modular proofs that bi... |

29 | A.: A computational interpretation of modal proofs
- Martini, Masini
- 1996
(Show Context)
Citation Context ...mulation due to Stirling [13] for a small classical linear-time temporal logic including fl. We then formulate a natural-deduction system in a similar style to the modal systems of Martini and Masini =-=[9]-=-, and prove that it has the same theorems as the axiomatic formulation. This allows us to directly apply the Curry-Howard isomorphism to the natural-deduction system, yielding the typedsfl -calculus w... |

18 | Queiroz. Extending the Curry-Howard interpretation to linear, relevant and other resource logics
- Gabbay, de
- 1990
(Show Context)
Citation Context ...e stages and provide an explicit quantifier over them, rather than using next and prev to move between stages. This is similar to the systems of labelled natural deduction 12 of Gabbay and de Queiroz =-=[4]-=-, which allow many different logics to be formulated including modal logics, though this is still a speculative direction for future research. We have implemented type checkers for the languagessfl an... |

12 | Mechanically verifying the correctness of an offline partial evaluator (extended version
- Hatcliff
- 1995
(Show Context)
Citation Context ...ables have time greater than 0, and we thus depend on the fact that substitution avoids variable capture. The operational semantics forsfl is similar to the specialization logic presented by Hatcliff =-=[10]-=- for a two-level binding-time language, and our binding-time correctness theorem is also somewhat similar to Hatcliff's. Values v 0 ::= x:A: e j hv 0 1 ; v 0 2 i j z j s v 0 j next v 1 v n+1 ::= x j x... |

8 |
Correctness of binding time analysis
- Palsberg
- 1993
(Show Context)
Citation Context ...ple by Nielson and Nielson [10] and Gomard and Jones [6]. However, the motivation for the particular typing rules that are chosen is often not clear. There has been some work, for example by Palsberg =-=[11]-=-, on modular proofs that binding-time analyzes generate annotations that allow large classes of partial evaluators to specialize correctly. However this still does not provide a direct motivation for ... |

3 |
Very efficient conversions
- Welinder
- 1995
(Show Context)
Citation Context ...rom other implicit coercions. fl could also serve as the basis for an extension of a statically typed language like Standard ML to allow hand-written programs that generate specialized code. Welinder =-=[14]-=- has shown this to be a useful technique in some situations, since it gives the programmer direct control over bindingtime decisions, and forces them to think about binding-times when writing code. Th... |

1 |
Partial Evaluation and Automatic Program Generation
- Sestoft
- 1993
(Show Context)
Citation Context ... this operational semantics correctly reflects the bindingtimes in the language, a theorem which is the functional programming analog of time-ordered normalization. 1. Introduction Partial evaluation =-=[12]-=- is a method for specializing a program given part of the program's input. The basic technique is to execute those parts of the program that do not depend on the unknown data, while constructing a res... |