## Pre-logical Relations (1999)

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Citations: | 26 - 5 self |

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@MISC{Honsell99pre-logicalrelations,

author = {Furio Honsell and Donald Sannella},

title = {Pre-logical Relations},

year = {1999}

}

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### Abstract

this paper but which have some intriguing connections to some of our results and techniques, are [32] and [20]. We believe that the concept of prelogical relation would have a beneficial impact on the presentation and understanding of their results

### Citations

342 |
Foundations for programming languages
- Mitchell
- 1996
(Show Context)
Citation Context ...the study of typed lambda calculus and have applications outside lambda calculus, for example to abstract interpretation [Abr90] and data refinement [Ten94]. A good reference for logical relations is =-=[Mit96]-=-. An important but more difficult reference is [Sta85]. The Basic Lemma is the key to many of the applications of logical relations. It says that any logical relation over A and B relates the interpre... |

209 | An algebraic definition of simulation between programs - Milner - 1971 |

145 | Toward formal development of programs from algebraic specifications: Implementations revisited
- Sannella, Tarlecki
- 1988
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Citation Context ...cal relations is again a pre-logical relation (Prop. 5.5) explains why stepwise refinement is sound. This opens the way to further development of the foundations of data refinement along the lines of =-=[ST88]-=-, but we leave this to a separate future paper, see Sect. 10. 8 Other Applications There are many other applications of logical relations. Take for instance the proof of strong normalization of λ → in... |

68 | On observational equivalence and algebraic specification - Sannella, Tarlecki - 1985 |

61 |
Lambda-de in the full type hierarchy
- Plotkin
- 1980
(Show Context)
Citation Context ...the Basic Lemma is part of the construction, but the family of relations defined is not logical. Examples can be found in Plotkin’s and Jung and Tiuryn’s lambda-definability results using I-relations =-=[Plo80]-=- and Kripke logical relations with varying arity [JT93] respectively, and Gandy’s proof of strong normalization using hereditarily strict monotonic functionals [Gan80]. In each of these cases, the fam... |

54 |
Abstract interpretation, logical relations and Kan extensions
- Abramsky
- 1990
(Show Context)
Citation Context ...ily of relations defined is not logical. Examples can be found in Plotkin’s and Jung and Tiuryn’s lambda-definability results using I-relations [Plo80] and Kripke logical relations with varying arity =-=[JT93]-=- respectively, and Gandy’s proof of strong normalization using hereditarily strict monotonic functionals [Gan80]. In each of these cases, the family of relations involved turns out to be a prelogical ... |

54 | Types, abstraction, and parametric polymorphism, part 2 - Ma, Reynolds - 1992 |

52 | Algebraic theory of automata - Ginzburg - 1968 |

46 |
Data abstraction and the correctness of modular programming
- Schoett
- 1987
(Show Context)
Citation Context ...n be compared. Here we begin by studying and comparing their closure properties (Prop. 5.6) with special attention to closure under composition. The definition of pre-logical relations is not new. In =-=[Sch87]-=-, Schoett uses a first-order version of algebraic relations which he calls correspondences, and he conjectures (p. 281) that for Henkin models, what we have called pre-logical relations (formulated as... |

45 | Kripke-style models for typed lambda calculus
- Mitchell, Moggi
- 1991
(Show Context)
Citation Context ...yield improved results as it has above, but this is just speculation. 15A different dimension of generalization is to consider models having additional structure — e.g. Kripke applicative structures =-=[MM91]-=-, pre-sheaf models or cartesian closed categories — for which logical relations have been studied. We have not yet examined the details of this generalization but it appears that a corresponding weake... |

45 |
Logical relations and the typed lambda calculus
- Statman
- 1985
(Show Context)
Citation Context ...ns outside lambda calculus, for example to abstract interpretation [Abr90] and data refinement [Ten94]. A good reference for logical relations is [Mit96]. An important but more difficult reference is =-=[Sta85]-=-. The Basic Lemma is the key to many of the applications of logical relations. It says that any logical relation over A and B relates the interpretation of each lambda term in A to its interpretation ... |

32 | Behavioural correctness of data representations - Schoett - 1990 |

31 | Kripke logical relations and PCF - O’Hearn, Riecke - 1995 |

30 | Proofs of strong normalization - Gandy - 1980 |

26 | Tiuryn, A New Characterization of Lambda Definability - Jung, A - 1993 |

19 | Logical relations and inductive/coinductive types - Altenkirch - 1999 |

19 | An axiomatic approach to binary logical relations with applications to data re - Kinoshita, O'Hearn, et al. - 1997 |

17 | Matching typed and untyped realizability - Longley - 1999 |

16 | Second-order logical relations - Mitchell, Meyer - 1985 |

13 | A relational account of call-by-value sequentiality - Riecke, Sandholm - 1997 |

13 |
Correctness of data representations in Algol-like languages. In: A Classical Mind: Essays
- Tennent
- 1994
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Citation Context ... σ in Σ. Logical relations are used extensively in the study of typed lambda calculus and have applications outside lambda calculus, for example to abstract interpretation [Abr90] and data refinement =-=[Ten94]-=-. A good reference for logical relations is [Mit96]. An important but more difficult reference is [Sta85]. The Basic Lemma is the key to many of the applications of logical relations. It says that any... |

12 | Constructive data refinement in typed lambda calculus - Honsell, Longley, et al. - 2000 |

11 | A characterization of lambda definability in categorical models of implicit polymorphism - Alimohamed - 1995 |

11 | An abstract notion of application - Gianantonio, Honsell - 1993 |

6 | Lambda-definability in the full type hierarchy, in `To H.B. Curry: essays on combinatory logic, lambda calculus and formalism - Plotkin - 1980 |

4 |
Type Systems for Programming Languages. Chapter 8
- Mitchell
- 1990
(Show Context)
Citation Context ...espondences, and he conjectures (p. 281) that for Henkin models, what we have called pre-logical relations (formulated as in Prop. 3.3) would be closed under composition and yield the Basic Lemma. In =-=[Mit90]-=-, Mitchell makes the same suggestion, referring to Schoett and also crediting Abramsky and Plotkin, but as an assertion rather than a conjecture. The idea is not developed any further. An independent ... |

4 | Logical relations and data abstraction - Robinson - 1996 |

3 | definable functionals and ## conversion - Statman - 1983 |

2 | Proofs of strong normalization. In: To H.B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism, 457--477 - Gandy - 1980 |

1 | The undecidability of #-definability. In: Logic, Meaning and Computation: Essays in Memory of Alonzo Church - Loader - 2001 |

1 | The undecidability of λ-definability. Church Memorial volume - Loader |

1 |
A compositional generalisation of logical relations. Draft report, http://www.dcs.ed.ac.uk/home/dts/pub/ laxlogrel.ps
- Plotkin, Power, et al.
- 1998
(Show Context)
Citation Context ...an assertion rather than a conjecture. The idea is not developed any further. An independent but apparently equivalent definition of pre-logical relations over cartesian closed categories is given in =-=[PPS98]-=- where they are called lax logical relations. It is shown that these compose and that the Basic Lemma holds, and an axiomatic account is provided. Earlier, a closely related notion called L-relations ... |

1 | KOPTT97 - LNCS - 1993 |

1 | The undecidability of -definability. Church Memorial volume - TACS'97 - 1997 |