## A Game Semantics of Linearly Used Continuations (2002)

Venue: | FoSSaCs’03, LNCS 2620, 313–327 |

Citations: | 6 - 0 self |

### BibTeX

@TECHREPORT{Laird02agame,

author = {J. Laird},

title = {A Game Semantics of Linearly Used Continuations},

institution = {FoSSaCs’03, LNCS 2620, 313–327},

year = {2002}

}

### OpenURL

### Abstract

We present an analysis of the \linearly used continuationpassing interpretation" of functional languages, based on game semantics.

### Citations

205 | Full abstraction for PCF
- Abramsky, Jagadeesan, et al.
(Show Context)
Citation Context ...r on a heavy restriction of the types in the target language. We shall achieve a more general result by semantic means. Game semantics has been used to give models of both purely functional languages =-=[4, 10, 16, 3] and -=-non-functional features, including continuations [11], which are free of \junk" and hence fully abstract. Another useful feature of games is that intensional phenomena such as controlsow and line... |

102 | Relational properties of domains
- Pitts
- 1996
(Show Context)
Citation Context ...k ]] [[T 1 ]] : : : [[T m ]] to [[U ]] following e.g. [5]. (We shall write [[S 1 ; : : : ; Sn ; T 1 ; : : : Tm ` U ]] for the set of such natural transformations.) Using approximation relations as in =-=[17, 1-=-6], we prove the following computational adequacy result. Proposition 3. For any program M of A , M + if and only if [[M ]] 6= ?. We also have a universality result forsnite types, and hence a full ab... |

92 |
Dual intuitionistic linear logic
- Barber
- 1996
(Show Context)
Citation Context ...ndependently, the linear -caluli used as target languages for the linear CPS translations in [13] and [6] are very similar; both are presented using dual contexts in a similar style to Barber's DILL [=-=5-=-]. We shall study an ane version as this is simpler to model and retains the key property that the ane CPS translation of v is fully abstract. In the terminology of [6], we shall restrict our attenti... |

69 | Full abstraction for functional languages with control - Laird - 1997 |

64 | Call-by-value games
- Abramsky, McCusker
- 1998
(Show Context)
Citation Context ...r on a heavy restriction of the types in the target language. We shall achieve a more general result by semantic means. Game semantics has been used to give models of both purely functional languages =-=[4, 10, 16, 3] and -=-non-functional features, including continuations [11], which are free of \junk" and hence fully abstract. Another useful feature of games is that intensional phenomena such as controlsow and line... |

51 |
Games and full abstraction for a functional metalanguage with recursive types
- McCusker
- 1996
(Show Context)
Citation Context ...r on a heavy restriction of the types in the target language. We shall achieve a more general result by semantic means. Game semantics has been used to give models of both purely functional languages =-=[4, 10, 16, 3] and -=-non-functional features, including continuations [11], which are free of \junk" and hence fully abstract. Another useful feature of games is that intensional phenomena such as controlsow and line... |

32 | Syntactic considerations on recursive types
- Abadi, Fiore
- 1996
(Show Context)
Citation Context ...bstraction and application is used for the introduction and elmination of both ) and (, so the type which can be assigned to a term-in-context is not unique. As in [6] we take the \equality approach&q=-=uo-=-t; [1] to recursive types | i.e. we let type-equality be the least congruence on types such that X:T = T [X:T=X ] and extend the typing rules in Table 1 with: ; ` M : S ; ` M : T S = T ;x:T ;`x:T ;;... |

32 | A semantic analysis of control
- Laird
- 1999
(Show Context)
Citation Context .... More precisely, relaxing it leads to models of functional languages with non-local control operators such as call=cc [11] which are equivalent to models constructed indirectly by CPS interpretation =-=[12]-=-. A connection between bracketing and linearity is evident in one direction; in a well-bracketed sequence, every question has at most one answer. More surprising is a result proved here | that under a... |

28 | Full abstraction for
- Abramsky, Jagadeesan, et al.
- 2000
(Show Context)
Citation Context |

27 |
A fully abstract game semantics of local exceptions
- Laird
- 2001
(Show Context)
Citation Context ... but have \state-like" features, making them dicult to capture via translation into A on its own. Game semantics has been proposed as the basis for a detailed semantic account of such hybrid eect=-=s [14]-=-, since it allows state and control to be combined seamlessly. However, one apparent diculty in giving a linear continuation passing semantics of state and state-like features is that by storing conti... |

18 | Designs, disputes and strategies, in
- Faggian, Hyland
- 2002
(Show Context)
Citation Context ...cher 's domain equation for the designs of Ludics [18] corresponds to a type of A ; the correspondence between designs and the strategies at this type seems to parallel closely the account given in [8]. There is also a close relationship between A , and proofs in polarized classical linear logic with both lifting and the exponentials, and we can construct a model of the latter along the lines of ... |

16 |
Axioms for full abstraction and full completeness
- Abramsky
- 1997
(Show Context)
Citation Context ...m-in-context ; ` M : F such that = [[M ]]. Proof. (Sketch) We apply an inductive decomposition similar to the decomposition theorem for the simply-typed -calculus, described axiomatically in [2]. Formally, proof is by induction on #(). If this is zero then is the empty strategy, which is denable as a divergent program. We prove the inductive case by a series of lemmas, all of which are i... |

16 |
Polarized games
- Laurent
- 2004
(Show Context)
Citation Context .... There is also a close relationship between A , and proofs in polarized classical linear logic with both lifting and the exponentials, and we can construct a model of the latter along the lines of [1=-=-=-5] which is, moreover, fully complete. As described in [6], several other control features, including exception-handling, GOTO-style jumps and coroutines can be given linear CPS translations in A , an... |

7 |
Uday Reddy, and Hayo Thielecke. Linear continuation passing
- Berdine, O’Hearn
- 2002
(Show Context)
Citation Context ...ns. This paper is a semantic investigation of such a \linear CPS interpretation" 1 with the object of establishing its completeness as a basis for reasoning about program equivalence. Berdine et.=-= al. [-=-6] have given linear CPS translations of the call-by-value - calculus | and other control features such as exceptions, jumps and coroutines | into a linear -calculus. Syntactic mehods have been used t... |

3 |
Linearly Used Eects: Monadic and CPS Transformations into the Linear Lambda Calculus
- Hasegawa
(Show Context)
Citation Context ...utines | into a linear -calculus. Syntactic mehods have been used to show that these translations are complete (in the sense that the target language does not contain any \junk" at translated typ=-=es) [13, 7, 9] but -=-these rely either on the restriction 1 Notwithstanding the fact that, as emphasized in [6], \it is continuation transformers rather than the continuations which are linear" it seems reasonable to... |

1 | Hayo Thielecke. On ane typing and completeness of cps - Berdine, O'Hearn - 2000 |

1 |
Finite models and full completeness
- Laird
- 2000
(Show Context)
Citation Context ...utines | into a linear -calculus. Syntactic mehods have been used to show that these translations are complete (in the sense that the target language does not contain any \junk" at translated typ=-=es) [13, 7, 9] but -=-these rely either on the restriction 1 Notwithstanding the fact that, as emphasized in [6], \it is continuation transformers rather than the continuations which are linear" it seems reasonable to... |

1 |
A domain equation for the designs of Ludics
- Streicher
- 2002
(Show Context)
Citation Context ... so by Proposition 5 M 6' N . 5 Conclusions and Further Directions There are several possibilities for extending this work. On the logical side, Streicher 's domain equation for the designs of Ludics =-=-=-[18] corresponds to a type of A ; the correspondence between designs and the strategies at this type seems to parallel closely the account given in [8]. There is also a close relationship between A , ... |