## Relational Reasoning about Functions and Nondeterminism (1998)

Citations: | 33 - 4 self |

### BibTeX

@TECHREPORT{Lassen98relationalreasoning,

author = {Søren Bøgh Lassen and Søren Bøgh Lassen},

title = {Relational Reasoning about Functions and Nondeterminism},

institution = {},

year = {1998}

}

### Years of Citing Articles

### OpenURL

### Abstract

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Citation Context ...in from University of Cambridge, I have been applying the relational techniques from this dissertation in investigations of operational equivalence for Abadi and Cardelli’s imperative object calculi (=-=Abadi and Cardelli 1996-=-). Results for the simple untyped version of the calculus are reported in Gordon, Hankin and Lassen (1997a, 1997b). After the dissertation was originally submitted in February 1998, I have further dev... |

435 | Testing equivalences for processes
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Citation Context ...t proofs by co-induction, but in the presence of nondeterminism it can be argued that they are finer-grained than is warranted by reasonable notions of observation. In contrast, testing equivalences (=-=DeNicola and Hennessy 1984-=-) are defined in terms of observations, more in the style of contextual equivalence. In operationally-based theories for nondeterministic higher-order languages, the choice between bisimulation and te... |

243 | The lazy lambda calculus
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Citation Context ...rators (Talcott 1998; Bierman 1998), and nondeterminism (Lassen 1997). Another approach is the operational theory of applicative bisimulation, first developed to model lazy and call-by-value calculi (=-=Abramsky 1990-=-; Howe 1989; Egidi et al. 1992; Perez 1991; Ong 1992) and later adapted to call-by-name theories (Gordon 1995a) and to state-less object calculi (Gordon and Rees 1996; Gordon 1998). For deterministic ... |

235 | A foundation for actor computation - Agha, Mason, et al. - 1997 |

203 |
The Lambda Calculus: its Syntax and Semantics (revised ed
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Citation Context ...losure is monotone and idempotent, (R C ) C = R C . By definition, R C is the least compatible relation that contains R, so context closure could more accurately be called ‘compatible closure’ (as in =-=Barendregt 1984-=-). An open relation R is compatible if and only if R = R C . Closure under substitutions is preserved by context closure but substitutivity is not, in general. In several cases, we will encounter rela... |

200 | Standard ML of New Jersey
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Citation Context ...xtensions of the language. The first extension is a parallel combinator, proposed by Boudol (1994) for λ-calculus. The other is references and control operators as found in Standard ML of New Jersey (=-=Appel and MacQueen 1991-=-). The encodings are included as a curiosity and are presented without proofs. For readers who are familiar with Boudol’s parallel operator or with control operators, the encodings may clarify the com... |

138 | On the Expressive Power of Programming Languages - Felleisen - 1991 |

108 |
Functional Programming and Input/Output
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Citation Context ...,S,S ′ ∈REL, (1) (S ≫ R)(S ′ ≫ R ′ ) ⊆ (SS ′ ) ≫(RR ′ ) (2) S ≫ R ⊆ S ≫ R ∪ S (3) R = R ≫ R,ifRis substitutive 3.5 Compatible refinement For every open relation R, itscompatible refinement � R ∈ REL (=-=Gordon 1994-=-) relates expressions with identical outermost syntactic constructor and immediate subterms pairwise related by R. Table 3.2 makes this definition precise for our language; it is obtained quite mechan... |

78 |
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Citation Context ...h we shall generally avoid working with explicit representations of contexts, we now give a formal definition of contexts. 2.4.1 Evaluation contexts A simple form of contexts are evaluation contexts (=-=Felleisen and Friedman 1987-=-). An evaluation context, E, is a closed expression with a hole, •, at redex position. (EvCtx) E ::= • | let x = E in b, b ∈ Expx We write E[a ] for the expression obtained by filling in a closed expr... |

77 | Countable nondeterminism and random assignment - APT, PLO'rKIN - 1986 |

61 |
Towards a lambda calculus for concurrent and communicating systems
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Citation Context ...tensions of contextual approximation and equivalence to nondeterministic languages. Similar definitions appear elsewhere, e.g., in the work of Jagadeesan and Panangaden (1990) on Boudol’s γ-calculus (=-=Boudol 1989-=-) and in Moran (1994). The may and must modalities appear in work on testing theories for processes (DeNicola and Hennessy 1984; Hennessy 1988). We may regard may and must contextual approximation as ... |

43 |
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Citation Context ...efactthattheseareexpressibleasλ-terms (Church and Kleene 1937) to encode the transfinite fixed point expressions in various other extensions of the language, e.g., using Boudol’s parallel combinator (=-=Boudol 1994-=-), or by means of control operators and a global queue of continuations—the details of these two encodings can be found ins6.7. TRANSFINITE UNWINDING AND SYNTACTIC ω CK 1 -CONTINUITY 81 Appendix A. Un... |

40 | A theory of weak bisimulation for core CML
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Citation Context ...d precise proof, both technically and notationally. Moreover, the proof applies to many different typed and untyped higher-order languages and operational orderings; see, e.g., (Sands 1991; Ong 1992; =-=Ferreira et al. 1996-=-; Lassen 1997; Gordon 1998; Lassen 1996). Pitts (1995) extended Howe’s congruence proof for applicative bisimilarity to also establish an “up to context” proof rule (Sangiorgi 1994) for applicative bi... |

35 | Relational interpretations of recursive types in an operational setting (summary
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Citation Context ... is mainly concerned with relations between program inputs and outputs, an issue which is largely orthogonal to our study of relations between programs.) Recent work by Pitts and others (Pitts 1997b; =-=Birkedal and Harper 1997-=-; Pitts 1998) employs the versatile notion of logical relations (surveyed in Mitchell 1990, 1996) to reason about operational semantics and operationally-based equivalence relations. The central notio... |

29 | Domains and denotational semantics: history, accomplishments, and open problems - Jung - 1996 |

27 | Uncountable limits and the lambda calculus - Gianantonio, Honsell, et al. - 1995 |

26 | On Semantic Foundations for Applicative Multiprogramming - Abramsky - 1983 |

26 | An axiomatic approach to adequacy
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Citation Context ... Suppose y :(t⇀t)⇀t⊢a:t ′ and t is a function type. Then a[Y/y] terminates if and only if a[Y (n) /y] terminates for some n<ω. There is an equational variant of the theorem, called rational openness (=-=Braüner 1996-=-), Γ ⊢ a[Y/y] ∼ = Ω : t ′ iff ∀n <ω.Γ⊢a[Y (n) /y] ∼ =Ω:t ′ It is equivalent to the Unwinding Theorem because, by (4.9), a closed expression terminates if and only if it is not contextually equivalent ... |

25 | A theory for nondeterminism, parallelism, communication, and concurrency - Broy - 1986 |

24 |
Formal definitions in the theory of ordinal numbers
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Citation Context ...exes range over recursive ordinals rather than, e.g., countable ordinals. However, one consequence of the restriction to recursive ordinals is thatwecanexploitthefactthattheseareexpressibleasλ-terms (=-=Church and Kleene 1937-=-) to encode the transfinite fixed point expressions in various other extensions of the language, e.g., using Boudol’s parallel combinator (Boudol 1994), or by means of control operators and a global q... |

18 |
Categories for Types. Cambridge Mathematical Textbooks
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Citation Context ...t ′ ⎛ Γ⊢⎝ case u of inj 1 x1.a1 [] ... [] inj n xn.an ⎞ ⎛ ⎠R� ⎝ Table 3.2: Compatible refinement case u ′ of inj 1 x1.a ′ 1 [] ... [] inj n xn.a ′ n ⎞ ⎠:t ′ if t = µχ. t1 + ...+tn and n ≥ 1 (see e.g. =-=Crole 1994-=-). By easy calculations, using the adjunction (3.8), the following properties follows from the corresponding properties of relation substitution in Lemma 3.4.1. Lemma 3.4.2 For all R, R ′ ,S,S ′ ∈REL,... |

12 |
Adding Fair Choice to Dijkstra's Calculus
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Citation Context ...mains with different notions of approximation. These ideas have also been applied to derive fixed-point principles for a version of Dijkstra’s guarded command language extended with ambiguous choice (=-=Broy and Nelson 1994-=-). Moran (1994) investigates contextual equivalences and applicative similarity for a call-by-name λ-calculus with ambiguous choice. He highlights the difficulties of reasoning about must contextual e... |

11 |
Non-Determinism and Fully Abstract Models
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Citation Context ...sults are extended to countable nondeterminism. This work is also reported in Lassen (1997) and Lassen and Pitcher (1998). Contextual equivalences have been considered in (Hennessy and Ashcroft 1980; =-=Astesiano and Costa 1980-=-; Astesiano and Costa 1984; Sieber 1993; Dezani-Ciancaglini, de’Liguoro, and Piperno 1996; de’Liguoro and Piperno 1995) but mainly as a reference for judging full abstraction properties of domain-theo... |

10 | A computational interpretation of the lambda-mu calculus
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Citation Context ...lid and useful for reasoning about higher-order functions, even in the presence of mutable state (Mason and Talcott 1991), objects (Gordon, Hankin, and Lassen 1997a), control operators (Talcott 1998; =-=Bierman 1998-=-), and nondeterminism (Lassen 1997). Another approach is the operational theory of applicative bisimulation, first developed to model lazy and call-by-value calculi (Abramsky 1990; Howe 1989; Egidi et... |

8 | Nondeterministic extensions of untyped λcalculus - de’Liguoro, Piperno - 1995 |

3 |
Distributive Semantics for Nondeterministic Typed - calculi
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Citation Context ...table nondeterminism. This work is also reported in Lassen (1997) and Lassen and Pitcher (1998). Contextual equivalences have been considered in (Hennessy and Ashcroft 1980; Astesiano and Costa 1980; =-=Astesiano and Costa 1984-=-; Sieber 1993; Dezani-Ciancaglini, de’Liguoro, and Piperno 1996; de’Liguoro and Piperno 1995) but mainly as a reference for judging full abstraction properties of domain-theoretic models. Sieber (1993... |

3 |
LCF be topped? Flat lattice models of typed λ-calculus
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Citation Context ...(Gordon and Rees 1996; Gordon 1998). For deterministic languages without side-effects, applicative bisimulation generally matches contextual equivalence, a property called operational extensionality (=-=Bloom 1990-=-), yielding a slightly stronger characterisation than the CIU Theorem. Forms of applicative bisimulation have also been used to model state (Ritter and Pitts 1995) and nondeterminism (Ong 1993; Lassen... |

3 | Semantique Operationelle et Algebrique des Programmes Recursifs Non-Deterministes", These d'Etat, Universite deParis VII - Boudol - 1980 |

3 |
della Rocca
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(Show Context)
Citation Context ...man 1998), and nondeterminism (Lassen 1997). Another approach is the operational theory of applicative bisimulation, first developed to model lazy and call-by-value calculi (Abramsky 1990; Howe 1989; =-=Egidi et al. 1992-=-; Perez 1991; Ong 1992) and later adapted to call-by-name theories (Gordon 1995a) and to state-less object calculi (Gordon and Rees 1996; Gordon 1998). For deterministic languages without side-effects... |

2 | Finite models for conjunctive-disjunctive λ-calculi - Dezani-Ciancaglini, de’Liguoro, et al. - 1996 |