## Operational Theories of Improvement in Functional Languages (Extended Abstract) (1991)

Venue: | In Proceedings of the Fourth Glasgow Workshop on Functional Programming |

Citations: | 21 - 9 self |

### BibTeX

@INPROCEEDINGS{Sands91operationaltheories,

author = {David Sands},

title = {Operational Theories of Improvement in Functional Languages (Extended Abstract)},

booktitle = {In Proceedings of the Fourth Glasgow Workshop on Functional Programming},

year = {1991},

pages = {298--311},

publisher = {Springer-Verlag}

}

### Years of Citing Articles

### OpenURL

### Abstract

) David Sands y Department of Computing, Imperial College 180 Queens Gate, London SW7 2BZ email: ds@uk.ac.ic.doc Abstract In this paper we address the technical foundations essential to the aim of providing a semantic basis for the formal treatment of relative efficiency in functional languages. For a general class of "functional" computation systems, we define a family of improvement preorderings which express, in a variety of ways, when one expression is more efficient than another. The main results of this paper build on Howe's study of equality in lazy computation systems, and are concerned with the question of when a given improvement relation is subject to the usual forms of (in)equational reasoning (so that, for example, we can improve an expression by improving any sub-expression). For a general class of computation systems we establish conditions on the operators of the language which guarantee that an improvement relation is a precongruence. In addition, for...

### Citations

672 |
Concurrency and automata on infinite sequences
- Park
- 1981
(Show Context)
Citation Context ...ion. The importance of this maximal fixed point definition is that it comes with a useful proof technique, sometimes referred to in the context of process algebra as "Park Induction" (in ref=-=erence to [Par80]), or in a-=- more general setting as "co-induction" ([MT90]): To show that R `s, for some binary relation R on T (L) ffi , it is sufficient to show that R is an improvement simulation. So, in order to s... |

450 | Computational Lambda-Calculus and Monads
- Moggi
- 1989
(Show Context)
Citation Context ... a refinement of weak bisimulation. They prove that it is preserved by all ccs contexts except summation, and develop a proof system for finite processes. Moggi's categorical semantics of computation =-=[Mog89]-=- is intended to be suitable for capturing broader descriptions of computation than just input-output behaviour. Gurr [Gur91] has studied extensions of denotational semantics to take account of resourc... |

321 |
Calculi for synchrony and asynchrony
- Milner
- 1983
(Show Context)
Citation Context ...in any context; as a generalisation of "applicative bisimulation " [Abr90] we define the desired improvement relation, improvement simulation, by analogy with strong (bi)simulation in proces=-=s algebra [Mil83]-=-. The remaining problem is to verify, for a given language and a particular notion of improvement, that improvement simulation is a precongruence. This problem is the primary focus of this paper. In t... |

239 | The lazy lambda calculus
- Abramsky
- 1990
(Show Context)
Citation Context ...relation. However, the basic evaluation relation for a lazy language is too "shallow", in itself, to capture the behaviour of a term in any context; as a generalisation of "applicative =-=bisimulation " [Abr90]-=- we define the desired improvement relation, improvement simulation, by analogy with strong (bi)simulation in process algebra [Mil83]. The remaining problem is to verify, for a given language and a pa... |

116 |
Calculi for Higher Order Communicating Systems
- Thomsen
- 1990
(Show Context)
Citation Context ...th more complex forms of abstraction (the paradigmatic example being lambda abstraction), a more elaborate relation seems necessary, such as the transitive closure of this substitution-closure (as in =-=[Tho90]-=-). In this general setting, the form of Howe's intermediate relation can be shown somewhere between these definitions (using proposition 2.11), although in the cases where simulation is closed under s... |

97 | Equality in lazy computation systems
- Howe
- 1989
(Show Context)
Citation Context ...improvement extensionality condition holds for each of the operators of the language. This result is based on, and generalises, the main result of Howe's study of equality in lazy computation systems =-=[How89]-=-; as in [How89], the significance of the condition is that in practice it seems relatively simple to check. In the second part of the paper we study a particular lazy computation system, a variant of ... |

78 |
Co-induction in relational semantics
- Milner, Tofte
- 1990
(Show Context)
Citation Context ... is that it comes with a useful proof technique, sometimes referred to in the context of process algebra as "Park Induction" (in reference to [Par80]), or in a more general setting as "=-=co-induction" ([MT90]-=-): To show that R `s, for some binary relation R on T (L) ffi , it is sufficient to show that R is an improvement simulation. So, in order to show that two closed terms are related bysit is sufficient... |

72 | An EÆciency Preorder for Processes
- Arun-Kumar, Hennessy
- 1992
(Show Context)
Citation Context ...sen's extended bisimulation in ccs induced by a preorder on actions [Tho87], particularly if we consider a notion of improvement bisimulation assI "sI \Gamma1 . More recently, Arun-Kumar and Henn=-=essy [AKH91]-=- have considered a specific efficiency preorder for ccs processes based on the number of internal (silent) actions performed by a process, and expressed as a refinement of weak bisimulation. They prov... |

47 | Complexity analysis for a lazy higher-order language
- Sands
- 1990
(Show Context)
Citation Context ...ction) that we can safely (w.r.t. call-by-need improvement) close-up this subset under substitution into any context, not just the linear ones. It is likely that notions such as strictness may, as in =-=[San90b]-=-, have an important role to play in such an approach. Acknowledgements Thanks to numerous members of the Semantique project for constructive feedback on the material presented here, and to the referee... |

41 | The Lazy Lambda Calculus: An Investigation into the Foundations of Functional Programming - ONG - 1988 |

33 | Calculi for time analysis of functional programs - Sands - 1990 |

22 |
Combinatory Reduction Systems, volume 127
- Klop
- 1980
(Show Context)
Citation Context ...lso be handled in this framework), together with an evaluation relation. We begin with the language. A lazy computation language is reminiscent of the syntax of terms in combinatory reduction systems =-=[Klo80]-=- and Martin-Lof's type theory, although unlike these, application is not a predefined construct (c.f. Aczel's syntax, [Klo80], remark 1.5). Definition 2.1 A lazy computation language L is specified by... |

17 | On computational open-endedness in Martin-Löf’s type theory - Howe - 1991 |

15 |
Generalized bisimulation in relational specifications
- Astesiano, Giovini, et al.
- 1988
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Citation Context ...y, and is a generalisation 6 of [How89], although by contrast the motivation in Howe's case is in connection with the study of open-endedness and type-free reasoning in type theories. Astesiano et al =-=[AGR88]-=- consider a highly parameterised definition of bisimulation which also could have been adapted for our purpose, although as far as we know there is no general study of congruence for such relations. T... |

13 |
Semantic Frameworks for Complexity
- Gurr
- 1991
(Show Context)
Citation Context ...f system for finite processes. Moggi's categorical semantics of computation [Mog89] is intended to be suitable for capturing broader descriptions of computation than just input-output behaviour. Gurr =-=[Gur91]-=- has studied extensions of denotational semantics to take account of resource-use, and has shown how Moggi's approach can be used to model a notion 6 If we takesto be the whole of W \Theta W then the ... |

9 |
The Essence of Rum: A Theory of the Intensional and Extensional Aspects of Lisp-type Computation
- Talcott
- 1985
(Show Context)
Citation Context ...nt of cost equivalence a program refinement relation arose naturally. This is a simple instance of the improvement simulation in a language which can easily be shown to be improvement extensional. In =-=[Tal85]-=- a class preorderings called comparison relations are considered for a side-effect free lisp derivative. The class of comparison relations is sufficiently general to express relations analogous to the... |

7 |
Time analysis, cost equivalence and program refinement
- Sands
- 1991
(Show Context)
Citation Context ...les the exact choice of such an intermediate relation seems crucial to such a direct proof of congruence. One possibility is to take the minimal substitution-closure of the simulation relation (as in =-=[San91]-=- for a specific improvement simulation); for languages with more complex forms of abstraction (the paradigmatic example being lambda abstraction), a more elaborate relation seems necessary, such as th... |

1 |
An extended bisimulation induced by a prorder on actions
- Thomsen
- 1987
(Show Context)
Citation Context ...as far as we know there is no general study of congruence for such relations. The form of simulation we introduce is related to Thomsen's extended bisimulation in ccs induced by a preorder on actions =-=[Tho87], par-=-ticularly if we consider a notion of improvement bisimulation assI "sI \Gamma1 . More recently, Arun-Kumar and Hennessy [AKH91] have considered a specific efficiency preorder for ccs processes ba... |