## Syntactic Type Soundness Results for the Region Calculus (2001)

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Venue: | INFORMATION AND COMPUTATION |

Citations: | 15 - 5 self |

### BibTeX

@ARTICLE{Calcagno01syntactictype,

author = {Cristiano Calcagno and Simon Helsen and Peter Thiemann},

title = {Syntactic Type Soundness Results for the Region Calculus},

journal = {INFORMATION AND COMPUTATION},

year = {2001},

volume = {173},

pages = {173--2}

}

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### Abstract

The region calculus of Tofte and Talpin is a polymorphically typed lambda calculus with annotations that make memory allocation and deallocation explicit. It is intended as an intermediate language for implementing ML without garbage collection. Static region and eect inference can be used to generate annotations from a given ML program. Soundness of the calculus with respect to the region and eect system is crucial to guarantee safe deallocation of regions, i.e., deallocation should only take place for objects which are provably dead. The original soundness proof by Tofte and Talpin requires a complex co-inductive safety relation. In this paper, we present two small-step operational semantics for the region calculus and prove their soundness. Following the syntactic approach of Wright, Felleisen, and Harper, we obtain simple inductive proofs. The rst semantics is store-less. It is simple and elegant and gives rise to perspicuous proofs. The second semantics provides a store-based model for the region calculus. It is slightly more complicated, but includes operations on references with destructive update. We prove (the pure fragment of) both semantics equivalent to the original evaluation-style formulation by Tofte and Talpin.

### Citations

1286 | A structural approach to operational semantics
- Plotkin
- 1981
(Show Context)
Citation Context ...ndness, using the syntactic approach due to Wright and Felleisen [16] in a variation pioneered by Harper [8]. The reduction semantics in this paper follows Plotkin’s approach to operational semantics =-=[12]-=-. Section 5 contains another novel contribution of the present work. It relates the three calculi by proving the equivalence of TTRC and IRC, as well as the equivalence of IRC and SRC. These technical... |

605 | The Definition of Standard ML (Revised - Milner, Tofte, et al. - 1997 |

539 | A Syntactic Approach to Type Soundness
- Wright, Felleisen
- 1994
(Show Context)
Citation Context ...f Section 2.3 using the additional rules from Section 3.1. The proof is structured as usual: first we formulate some standard lemmas. Then, we prove type preservation, also known as subject reduction =-=[7, 16]-=-, which states that a well-typed term remains well-typed under the small-step transition relation →s. The second result is the progress property, which states that a well-typed closed term is either a... |

280 | Region-based memory management
- Tofte, Talpin
- 1997
(Show Context)
Citation Context ...e execution of programs. Finally, inter-operability between garbage collected languages, like ML, and non-garbage collected languages, such as C, is difficult. The region calculus of Tofte and Talpin =-=[14, 15]-=- (TTRC) provides an alternative method of memory management for the functional language ML [11]. It is used as an intermediate language in an ML compiler, the ML-kit [3,4,13–15]. The basic idea of the... |

194 | Typed Memory Management in a Calculus of Capabilities
- Crary, Walker, et al.
- 1999
(Show Context)
Citation Context ...egion from the store in their particular formulation of the big-step semantics. Recently, alternative type-soundness proofs for the region calculus have been proposed. 1. Crary, Walker, and Morrisett =-=[6]-=- provide an indirect soundness proof by translating the region calculus into their capability calculus. The capability calculus has a sophisticated type-and-effect system that supports safe 2allocati... |

89 | From region inference to von Neumann machines via region representation inference
- Birkedal, Tofte, et al.
- 1996
(Show Context)
Citation Context ...less formulation is extremely simple and elegant, the store-based formulation is more complicated but supplies a soundness proof for the calculus with references, as it is actually used in the ML-kit =-=[4]-=-. The proofs themselves use routine inductive techniques and are therefore considerably easier than the co-inductive proofs of Tofte and Talpin. The second technical result is the statement and proof ... |

70 | A region inference algorithm - Tofte, Birkedal - 1998 |

57 | A simplified account of polymorphic references
- Harper
- 1994
(Show Context)
Citation Context ...de a small-step operational semantics for IRC based on an explicit store and prove its type soundness, using the syntactic approach due to Wright and Felleisen [16] in a variation pioneered by Harper =-=[8]-=-. The reduction semantics in this paper follows Plotkin’s approach to operational semantics [12]. Section 5 contains another novel contribution of the present work. It relates the three calculi by pro... |

57 | Implementation of the typed call-byvalue λ-calculus using a stack of regions
- Tofte, Talpin
- 1994
(Show Context)
Citation Context ...e execution of programs. Finally, inter-operability between garbage collected languages, like ML, and non-garbage collected languages, such as C, is difficult. The region calculus of Tofte and Talpin =-=[14, 15]-=- (TTRC) provides an alternative method of memory management for the functional language ML [11]. It is used as an intermediate language in an ML compiler, the ML-kit [3,4,13–15]. The basic idea of the... |

51 | Implementation of the typed call-by-value -calculus using a stack of regions - Tofte, Talpin - 1994 |

28 | Region analysis and the polymorphic lambda calculus
- Banerjee, Heintze, et al.
- 1999
(Show Context)
Citation Context ...e, since there are cases where a region may be de-allocated earlier than in the region calculus. They provide a syntactic soundness proof for the capability calculus. 2. Banerjee, Heintze, and Riecke =-=[2]-=- translate the region calculus into F#, an extension of the polymorphic lambda calculus with a special type constructor for encapsulation. They construct an original denotational model for their calcu... |

22 | Stratified operational semantics for safety and correctness of the region calculus
- Calcagno
- 2001
(Show Context)
Citation Context ...Helsen and Thiemann [10] define a store-less small-step operational semantics for the region calculus and prove type soundness using the syntactic method of Wright, Felleisen, and Harper. 5. Calcagno =-=[5]-=- defines a high-level big-step operational semantics and proves type soundness for it. Calcagno formally relates the high-level semantics to the original low-level semantics of the TTRC. 1.2 Contribut... |

18 | Syntactic type soundness for the region calculus
- Helsen, Thiemann
- 2000
(Show Context)
Citation Context ...onsequence of a more general result for a typed πcalculus with name groups. This is shown using a translation from the region calculus to the typed π-calculus with name groups. 4. Helsen and Thiemann =-=[10]-=- define a store-less small-step operational semantics for the region calculus and prove type soundness using the syntactic method of Wright, Felleisen, and Harper. 5. Calcagno [5] defines a high-level... |

11 | Region analysis and a pi-calculus with groups
- Dal-Zilio, Gordon
- 2000
(Show Context)
Citation Context ...lus with a special type constructor for encapsulation. They construct an original denotational model for their calculus and give a semantic soundness proof based on the model. 3. Dal Zilio and Gordon =-=[17]-=- modify the operational semantics of Tofte and Talpin so that it also keeps track of deallocated regions. Albeit artificial, this extra information allows an inductive definition of the consistency re... |

9 | A constraint-based region inference algorithm - Birkedal, Tofte - 1999 |

1 |
Program Analysis, and Computing Environments for Memory Management (SPACE’01
- Semantics
- 2001
(Show Context)
Citation Context ...cagno formally relates the high-level semantics to the original low-level semantics of the TTRC. 1.2 Contribution and Overview The present paper is based on the work of Calcagno, Helsen, and Thiemann =-=[1, 5, 10]-=-. After recalling the syntax and the semantics of TTRC in Section 2, Section 3 gives a simplified account of the store-less region calculus (SRC) [10], without the standard treatment of polymorphism. ... |