## A Type-theoretic Study on Partial Continuations (2000)

Venue: | Theoretical Computer Science: Exploring New Frontiers of Theoretical Informatics, volume 1872 of Lecture Notes in Computer Science |

Citations: | 12 - 4 self |

### BibTeX

@INPROCEEDINGS{Kameyama00atype-theoretic,

author = {Yukiyoshi Kameyama},

title = {A Type-theoretic Study on Partial Continuations},

booktitle = {Theoretical Computer Science: Exploring New Frontiers of Theoretical Informatics, volume 1872 of Lecture Notes in Computer Science},

year = {2000},

pages = {489--504},

publisher = {Springer}

}

### Years of Citing Articles

### OpenURL

### Abstract

. Partial continuations are control operators in functional programming such that a function-like object is abstracted from a part of the rest of computation, rather than the whole rest of computation. Several dierent formulations of partial continuations have been proposed by Felleisen, Danvy&Filinski, Hieb et al, and others, but as far as we know, no one ever studied logic for partial continuations, nor proposed a typed calculus of partial continuations which corresponds to a logical system through the Curry-Howard isomorphism. This paper gives a simple type-theoretic formulation of a form of partial continuations (which we call delimited continuations), and study its properties. Our calculus does reect the intended operational semantics, and enjoys nice properties such as subject reduction and conuence. By restricting the type of delimiters to be atomic, we obtain the normal form property. We also show a few examples. 1 Introduction The mechanism of rst-class cont...

### Citations

340 | Lambda-mu-calculus: An algorithmic interpretation of classical natural deduction - Parigot - 1992 |

150 |
The theory and practice of first-class prompts
- Felleisen
- 1988
(Show Context)
Citation Context ... Partial continuation is a renement ofsrst-class continuation in that a continuation object is abstracted from a part of the rest of computation, rather than the whole rest of computation. Felleisen [=-=6]-=- introduced a pair of operators # and F to represent partial continuations. The former delimits the range of continuations which will be later invoked by the latter operator. The other distinguished f... |

132 | Representing monads - Filinski - 1994 |

96 | Abstracting control
- Danvy, Filinski
- 1990
(Show Context)
Citation Context ... concisely and eciently using partial continuations. After then, several dierent operators for partial continuations have been proposed by Queinnec and Serpette [20], Gunter [11], Danvy and Filinski [=-=2]-=- and others. If we want to give a logical view to partial continuations through the CurryHoward isomorphism, a fundamental problem arises in these approaches. Namely, the scope of Felleisen's # operat... |

83 | Representing control: A study of the CPS transformation
- Danvy, Filinski
- 1991
(Show Context)
Citation Context ...ence between the #-operator and the F-operator cannot be represented by the variable-binding mechanism (which is lexical). Danvy and Filinski proposed another formulation of partial continuations [2] =-=[-=-3]. Their operators reset and shift dier from Felleisen's ones in that the created partial continuation object is again delimited. This change has a better eect for formalizing partial continuations, ... |

80 | A Curry-Howard foundation for functional computation with control - Ong, Stewart - 1997 |

79 |
Price theory
- Friedman
- 2007
(Show Context)
Citation Context ...nism ofsrst-class continuations (the call/cc-mechanism in Scheme [1]) is a quite powerful control facility, and is equipped with many modern programming languages such as Standard ML. Felleisen et al =-=[5-=-] established a theory forsrst-class continuations by which we can reason about properties of programs withsrst-class continuations. Partial continuation is a renement ofsrst-class continuation in tha... |

56 |
Abstract continuations: A mathematical semantics for handling full jumps
- Felleisen, Wand, et al.
- 1988
(Show Context)
Citation Context ...e as follows: # (calldc V ) ! 1 # (V (u:# u)) (4) # (throw V ) ! 1 #V (5) E s [calldc V ] ! 1 calldc (x:E s [V (y:# x(z:E s [y]))]) (6) #s(calldc x:M) ! 1 calldc x:#sM (if 6s) (7) E s [throw V ] ! 1 throwV (8) In these reductions we assume x; y; z are fresh variables. 7 Thesrst two rules express reductions with an empty partial continuation. The third and fourth rules are o... |

32 |
Parallel Reductions in -calculus
- Takahashi
- 1989
(Show Context)
Citation Context ...))]) : C We also have that the set of free variables are the same. Other cases are proved easily. ut We then show that DC and atomic DC are con uent by using Takahashi's parallel reduction method [19] in conjunction with Hardin's interpretation method. Theorem 3. The calculi DC and atomic DC are con uent. Proof. Wesrst dene a d-normal form d(M) of a term M as the term M where the reduction (3... |

30 | A dynamic extent control operator for partial continuations
- Queinnec, Serpette
- 1991
(Show Context)
Citation Context ...sting examples can be implemented more concisely and eciently using partial continuations. After then, several dierent operators for partial continuations have been proposed by Queinnec and Serpette [=-=20]-=-, Gunter [11], Danvy and Filinski [2] and others. If we want to give a logical view to partial continuations through the CurryHoward isomorphism, a fundamental problem arises in these approaches. Name... |

16 |
A formulae-as-types notion of control
- Grin
- 1990
(Show Context)
Citation Context ...tionistic logical systems. As Grin and other researchers showed, the isomorphism can be extended to the relationship between typed lambda calculi with sequential control operators and classical logic [10]. In this section, we show that atomic DC and DC also correspond to classical logic. atomic DC and DC are Classical Logic We assume that ? is included as an atomic type in atomic DC . (If it... |

13 | Typing First-Class Continuations in - Duba, Harper, et al. - 1993 |

11 |
The Revised Report on the Syntactic Theories
- Felleisen, Hieb
- 1992
(Show Context)
Citation Context ...in our calculus. We think that it is a trade-o of theory and practice. 4 ML-like Operational Semantics In this section we give an operational semantics of our calculi in the style of Felleisen et al [=-=8]-=-. Note that this operational semantics may cause run-time type errors, therefore its direct formalization (in a type safe way) is not possible. We nevertheless state the operational semantics here to ... |

10 | Intuitionistic and classical natural deduction systems with the Catch and the Throw rules
- Sato
- 1997
(Show Context)
Citation Context ...antics, and enjoy the above properties (1)-(3). We also show that the subcalculus with the delimiter and the throw operation (without the invoker) corresponds to the classical catch/throw calculus in =-=[18, 14]-=-, while the subcalculus with the delimiter and the invoker (without the throw operation) corresponds to intuitionistic calculus. The rest of this paper is organized as follows. Section 2 gives the bac... |

6 | Strong normalizability of the non-deterministic catch/throw calculi
- Kameyama, Sato
(Show Context)
Citation Context ...antics, and enjoy the above properties (1)-(3). We also show that the subcalculus with the delimiter and the throw operation (without the invoker) corresponds to the classical catch/throw calculus in =-=[18, 14]-=-, while the subcalculus with the delimiter and the invoker (without the throw operation) corresponds to intuitionistic calculus. The rest of this paper is organized as follows. Section 2 gives the bac... |

1 |
P.: A Simple Calculus of Exception Handling, Typed Lambda Calculi and its Applications
- Groote
- 1995
(Show Context)
Citation Context ...limiter is useless. The last one means that, if two delimiters are set in the same place, they can be unied. The second group of reduction rules are as follows: # (calldc V ) ! 1 # (V (u:# u)) (4) # (throw V ) ! 1 #V (5) E s [calldc V ] ! 1 calldc (x:E s [V (y:# x(z:E s [y]))]) (6) #s(calldc x:M) ! 1 calldc x:#sM (if 6s) (7) E s [throw V ] ! 1 throwV (8) In these reduction... |

1 |
Riecke: A Generalization of Exceptions and
- Gunter, Remy, et al.
- 1995
(Show Context)
Citation Context ...s can be implemented more concisely and eciently using partial continuations. After then, several dierent operators for partial continuations have been proposed by Queinnec and Serpette [20], Gunter [=-=11]-=-, Danvy and Filinski [2] and others. If we want to give a logical view to partial continuations through the CurryHoward isomorphism, a fundamental problem arises in these approaches. Namely, the scope... |

1 | A Type System for Delimited Continuations (Preliminary Version - Kameyama - 2000 |