## A Type-theoretic Approach to Deadlock-freedom of Asynchronous Systems (1997)

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Venue: | In Proc. TACS |

Citations: | 9 - 1 self |

### BibTeX

@INPROCEEDINGS{Abramsky97atype-theoretic,

author = {Samson Abramsky and Simon Gay and Rajagopal Nagarajan},

title = {A Type-theoretic Approach to Deadlock-freedom of Asynchronous Systems},

booktitle = {In Proc. TACS},

year = {1997},

pages = {295--320},

publisher = {SpringerVerlag}

}

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### Abstract

We present a type-based technique for the verification of deadlock-freedom in asynchronous concurrent systems. Our approach is to start with an interaction category such as ASProc, where objects are types containing safety specifications and morphisms are processes. We then use a specification structure to add information to the types so that they specify stronger properties. The extra information in this case concerns deadlock-freedom, and in the resulting category ASProc D , combining well-typed processes preserves deadlock-freedom. It is also possible to accommodate non-compositional methods within the same framework. The systems we consider are asynchronous, hence issues of divergence become significant; our approach incorporates an elegant treatment of both divergence and successful termination. As an example, we use our methods to verify the deadlock-freedom of an implementation of the alternating-bit protocol. Address for Correspondence Dr S. J. Gay Department of ...

### Citations

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(Show Context)
Citation Context ...l with such cases, we introduce an additional verification rule. After presenting the necessary theory, we illustrate the use of our type system by analysing a version of the alternating-bit protocol =-=[18]-=- and verifying that it is deadlock-free. 2 2 The Interaction Category ASProc In this section we briefly review those parts of the definition of ASProc which are relevant to the present paper. This inc... |

986 |
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Citation Context ... : C 2 ! C , an object I , and natural isomorphisms assoc A;B;C : (A\Omega B)\Omega C = A\Omega (B\Omega C) unitl A : I\Omega A = A unitr A : A\Omega I = A satisfying the standard coherence equations =-=[16]-=-. A specification structure for C must then correspondingly be extended with an action \Omega A;B : P S A \Theta P S B ! P S (A\Omega B) and an element u 2 P S I satisfying, for f : A ! B, f 0 : A 0 !... |

144 | Linearity and the Pi-Calculus
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Citation Context ...e of a class of communication errors; these errors can be viewed as weak forms of deadlock, but do not include the possibility of cyclic dependencies. Based on this work, Kobayashi, Pierce and Turner =-=[15]-=- have developed a linear type system for the -calculus. Recently Kobayashi [14] has proposed 16 a process calculus with a type system which captures information about order of channel usage, and uses ... |

125 | Interaction categories and the foundations of types concurrent programming
- Abramsky, Gay, et al.
- 1996
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Citation Context ...a prolonged, dynamic pattern of communication rather than a simple procedure call, and both parties must agree about the expected nature of the dialogue. Our recent research on interaction categories =-=[1, 2]-=- has led to a framework for the design of sophisticated type systems which are able to specify communication protocols of this form. In this framework, type-checking and verification are seen as diffe... |

117 | An interaction-based language and its typing system
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Citation Context ..., and hence offers the possibility of constructing deadlock-free networks from deadlock-free subcomponents. None of the above-mentioned approaches is based on types. However, Takeuchi, Honda and Kubo =-=[25]-=- have recently developed a typed language for interaction, in which the type system guarantees avoidance of a class of communication errors; these errors can be viewed as weak forms of deadlock, but d... |

105 | Parametricity and local variables
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Citation Context ...is highly suggestive, particularly from a Computer Science point of view. Similar notions have been studied, for a variety of purposes, by Burstall and McKinna [17], Hoofman [13], O'Hearn and Tennent =-=[20] and Pitts-=- [22]. Let C be a category. A specification structure S over C is defined by the following data: ffl for each object A of C , a set P S A of "properties over A". ffl for each pair of objects... |

88 |
autonomous categories and linear logic
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Citation Context ...ck-free. 2 2 The Interaction Category ASProc In this section we briefly review those parts of the definition of ASProc which are relevant to the present paper. This includes the -autonomous structure =-=[5]-=-, corresponding to the multiplicative connectives\Omega , O and (\Gamma) ? of linear logic [12], but not the additive structure (products and coproducts) or the delay operator. Complete definitions ca... |

78 | A partially deadlock-free typed process calculus. To appear as a technical report
- Kobayashi
- 1997
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Citation Context ...of deadlock, but do not include the possibility of cyclic dependencies. Based on this work, Kobayashi, Pierce and Turner [15] have developed a linear type system for the -calculus. Recently Kobayashi =-=[14]-=- has proposed 16 a process calculus with a type system which captures information about order of channel usage, and uses this information to guarantee deadlock-freedom. In this calculus, a distinction... |

56 | A typed calculus of synchronous processes - Gay, Nagarajan - 1995 |

40 | Termination, deadlock, and divergence
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Citation Context .... No further checking is needed in order to establish the correctness of these connections. 6 Related Work The analysis of deadlock-freedom in concurrency has been investigated by a number of authors =-=[4, 6, 7, 9, 21, 23, 24]-=-. The work of Roscoe and Daithi [23] is one of the most recent, and also the most relevant to our own. Their approach is to define a variant function which assigns a value to each state of a process. ... |

35 | Interaction categories and communicating sequentim processes - Abramsky - 1995 |

31 |
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Citation Context ...s can be automated to some extent, perhaps under certain conditions. The use of variants as in Roscoe and Daithi's work [23] may provide some clues. Another possibility is the cycle sum test of Wadge =-=[26]-=-. Future work will include applications of these ideas to more substantial examples, perhaps illustrating the use of successful termination. Although we have focused on deadlock-freedom in this paper,... |

24 | Deliverables: A categorical approach to program development in type theory
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Citation Context ...ve view of these standard notions which is highly suggestive, particularly from a Computer Science point of view. Similar notions have been studied, for a variety of purposes, by Burstall and McKinna =-=[17], Hoo-=-fman [13], O'Hearn and Tennent [20] and Pitts [22]. Let C be a category. A specification structure S over C is defined by the following data: ffl for each object A of C , a set P S A of "properti... |

21 | Specification structures and propositions-as-types for concurrency. In Logics ]or Concurrency: Structure vs
- Abramsky, Gay, et al.
- 1996
(Show Context)
Citation Context ...a prolonged, dynamic pattern of communication rather than a simple procedure call, and both parties must agree about the expected nature of the dialogue. Our recent research on interaction categories =-=[1, 2]-=- has led to a framework for the design of sophisticated type systems which are able to specify communication protocols of this form. In this framework, type-checking and verification are seen as diffe... |

15 | Relational properties of recursively defined domains
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Citation Context ...stive, particularly from a Computer Science point of view. Similar notions have been studied, for a variety of purposes, by Burstall and McKinna [17], Hoofman [13], O'Hearn and Tennent [20] and Pitts =-=[22]. Let C be-=- a category. A specification structure S over C is defined by the following data: ffl for each object A of C , a set P S A of "properties over A". ffl for each pair of objects A, B of C , a ... |

15 |
The Pursuit of Deadlock Freedom
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(Show Context)
Citation Context .... No further checking is needed in order to establish the correctness of these connections. 6 Related Work The analysis of deadlock-freedom in concurrency has been investigated by a number of authors =-=[4, 6, 7, 9, 21, 23, 24]-=-. The work of Roscoe and Daithi [23] is one of the most recent, and also the most relevant to our own. Their approach is to define a variant function which assigns a value to each state of a process. ... |

12 |
Deadlock analysis in networks of communicating processes
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(Show Context)
Citation Context .... No further checking is needed in order to establish the correctness of these connections. 6 Related Work The analysis of deadlock-freedom in concurrency has been investigated by a number of authors =-=[4, 6, 7, 9, 21, 23, 24]-=-. The work of Roscoe and Daithi [23] is one of the most recent, and also the most relevant to our own. Their approach is to define a variant function which assigns a value to each state of a process. ... |

11 |
Linear Types for Communicating Processes
- Gay
- 1995
(Show Context)
Citation Context ...e connectives\Omega , O and (\Gamma) ? of linear logic [12], but not the additive structure (products and coproducts) or the delay operator. Complete definitions can be found in previous publications =-=[1, 2, 3, 10]-=-. Our use of ASProc in the present paper allows us to analyse asynchronous systems, in which different components are able to evolve at their own rate. This is in contrast to much of our previous work... |

9 |
Deadlock absence proofs for networks of communicating processes
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Citation Context |

9 |
de Bakker. Mathematical Theory of Program Correctness
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Citation Context ...C, ' 2 P S A, / 2 P S B and ` 2 P S C: 'fid A g' (1) 'ffg/; /fgg` =) 'ff ; gg` (2) The axioms (1) and (2) are typed versions of the standard Hoare logic axioms for "skip" and "sequentia=-=l composition" [8]-=-. Given C and S as above, we can define a new category C S as follows. The objects are pairs (A; ') with A 2 ob C and ' 2 P S A. A morphism f : (A; ') ! (B; /) is a morphism f : A ! B in C such that '... |

9 |
Non-stable models of linear logic
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(Show Context)
Citation Context ...se standard notions which is highly suggestive, particularly from a Computer Science point of view. Similar notions have been studied, for a variety of purposes, by Burstall and McKinna [17], Hoofman =-=[13], O'Hearn -=-and Tennent [20] and Pitts [22]. Let C be a category. A specification structure S over C is defined by the following data: ffl for each object A of C , a set P S A of "properties over A". ff... |

5 |
Verifying Properties of Parallel Programs
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- 1976
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Citation Context |

4 |
Deadlocks and livelocks in transition systems
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Citation Context |

3 |
A class of simple communication patterns
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3 |
Relational properties of recursively de ned domains
- Pitts
- 1993
(Show Context)
Citation Context ...stive, particularly from a Computer Science point of view. Similar notions have been studied, for a variety of purposes, by Burstall and McKinna [18], Hoofman [14], O'Hearn and Tennent [21] and Pitts =-=[23]-=-. Let C be a category. Aspeci cation structureSover C is de ned by the following data: { for each objectAof C, a setPSA of \properties overA". { for each pair of objectsA,B of C, a relationSA;BPSA C(A... |

2 | Typed Concurrent Programs: Specification & Verification
- Nagarajan
- 1996
(Show Context)
Citation Context ...nterpretations in terms of labelled transition systems [18]. A formal calculus of typed asynchronous processes (with a weaker type system which does not guarantee deadlock-freedom) has been developed =-=[19]-=-, and this calculus will eventually be combined with ideas of the present paper, but for now we will concentrate on the semantic aspects of the type system for deadlock-freedom. A significant differen... |

2 |
Speci cation structures and propositions-as-types for concurrency
- Abramsky, Gay, et al.
- 1996
(Show Context)
Citation Context ...write'ffg forSA;B(';f; ), borrowing the notation of Hoare triples. This relation is required to satisfy the following axioms, forf :A!B,g:B !C,s' 2PSA, 2PSB and 2PSC: 'fidAg' (1) 'ffg ; fgg =)'ff ;gg =-=(2)-=- The axioms (1) and (2) are typed versions of the standard Hoare logic axioms for \skip" and \sequential composition" [9]. Given C andS as above, we can de ne a new category CS as follows. The objects... |

2 |
Typed Concurrent Programs: Speci cation & Veri cation
- Nagarajan
- 1997
(Show Context)
Citation Context ...ry SProc whose types are safety speci cations [12]; the synchronous category SProcD whose types specify deadlock-freedom [6]; and the asynchronous category ASProc whose types are safety speci cations =-=[20]-=-. Future work will combine the ideas of these calculi into a syntax to accompany the semantic type system of the present paper. Much of our previous work has concentrated on deadlock-freedom of synchr... |

2 |
An extensional treatment of data ow deadlock
- Wadge
- 1981
(Show Context)
Citation Context ...s can be automated to some extent, perhaps under certain conditions. The use of variants as in Roscoe and Daithi's work [24] may provide some clues. Another possibility is the cycle sum test of Wadge =-=[27]-=-, which captures the idea that the presence of non-trivial delays in feedback loops is a necessary condition for deadlock-freedom. In any case, extra information about processes would be needed in ord... |

1 |
A typed calculus of deadlock-free processes
- Berger, Gay, et al.
- 1997
(Show Context)
Citation Context ...pond to the structure of various interaction categories: the synchronousscategory SProc whose types are safety speci cations [12]; the synchronous category SProcD whose types specify deadlock-freedom =-=[6]-=-; and the asynchronous category ASProc whose types are safety speci cations [20]. Future work will combine the ideas of these calculi into a syntax to accompany the semantic type system of the present... |