## The Coverage of Operational Semantics (1998)

Venue: | Higher Order Operational Techniques in Semantics, Publications of the Newton Institute |

Citations: | 4 - 0 self |

### BibTeX

@INPROCEEDINGS{Smith98thecoverage,

author = {Scott F. Smith},

title = {The Coverage of Operational Semantics},

booktitle = {Higher Order Operational Techniques in Semantics, Publications of the Newton Institute},

year = {1998},

pages = {307--346},

publisher = {Cambridge University Press}

}

### OpenURL

### Abstract

Techniques of operational semantics do not apply universally to all language varieties: techniques that work for simple functional languages may not apply to more realistic languages with features such as objects and memory effects. We focus mainly on the characterization of the so-called finite elements. The presence of finite elements in a semantics allows for an additional powerful induction mechanism. We show that in some languages a reasonable notion of finite element may be defined, but for other languages this is problematic, and we analyse the reasons for these difficulties. We develop a formal theory of language embeddings and establish a number of properties of embeddings. More complex languages are given semantics by embedding them into simpler languages. Embeddings may be used to establish more general results and avoid reproving some results. It also gives us a formal metric to describe the gap between different languages. Dimensions of the untyped programming language design space addressed here include functions, injections, pairs, objects, and memories. 1

### Citations

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Citation Context ...e call-by-value� -calculus, so the above defines projection operations on the pure� -calculus. This approachsThe Coverage of Operational Semantics 15 to finite expressions is not found in Barendregt (=-=Barendregt 1984-=-). Barendregt Chapter 14 does review another similar approach which is worth contrasting: Hyland and Wadsworth’s labelled� -calculus. Rather than defining a syntactic ���(�), the expression� is labell... |

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Citation Context ...expressions; although this may seem restrictive, it is possible to define evaluation relations for languages with control primitives and effects in a purely syntactic fashion (Mason and Talcott 1991; =-=Felleisen and Hieb 1992-=-). We impose some informal regularity on the notation used for languages.� is implicitly���������� ,������� taken to be���������������������������������� ,�� taken to be��������������, etc. We let����... |

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Citation Context ...ther function) before evaluating it. However, proofs are possible. A number of alternate characterizations of ¡ have been developed to make proofs of equivalence much simpler, including bisimulation (=-=Abramsky 1990-=-), applicative orderings (Bloom 1990), and ciu equivalence (Mason and Talcott 1991). These alternate characterizations may be shown to be the same as ¡ (a so-called fully abstract alternate equivalenc... |

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Citation Context ...g it for all �� �� by induction on the finite rank of �� . This is very important because it gives a new, and often powerful, induction principle. A closely related property is fixed point induction (=-=Scott 1976-=-). The greatest utility of the finite elements lies in the proof principle of rank induction, as just mentioned. For special cases of � it is possible to consider special forms of�ordered chain. One s... |

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Citation Context ...n operational evaluation relation, and for embeddings between languages. It is general enough to encompass all languages studied herein, but is not intended as a general framework along the lines of (=-=Mosses 1992-=-). In particular it will not fully capture nondeterministic or concurrent languages. It will allow for a general notion of language embedding to be defined. We will give definitions and properties tha... |

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Citation Context ...the purpose of embedding one programming language in another, a general theory of language embeddings is now defined. Other closely related notions of language embedding have been previously defined (=-=Felleisen 1991-=-; Mitchell 1993; Riecke 1993). Our definitions combine ideas from these approaches. The embeddings will be used to give semantics to a number of languages in Section 4, and will enable a number of pro... |

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Citation Context ...��¦� ¢� ��� THEOREM (CIU)¢� ���£ iff¢� ��� 3.7 . ���£ For a proof, see (Mason, Smith, and Talcott 1996). For this simple language it is even possible characterize� ��� to via a bisimulation ordering (=-=Howe 1996-=-). We now list a collection basic ¡����� ��� of properties, all easily provable from Theorem 3.7. LEMMA 3.8 (BASIC� ���� ¡��� PROPERTIES) (i) If¢� ���£ , then for������� , ¢������ ���£����� . . (ii)��... |

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Citation Context .../Plotkin notion of operational/observational equivalence between program expressions, ¡ . Operational equivalence has also been shown to yield good notions of equivalence for languages with memories (=-=Mason and Talcott 1991-=-), explicit control operators (Talcott 1989), types and objects (Gordon and Rees 1996), and distributed objects (Agha, Mason, Smith, and Talcott 1992). It is important to characterize what “full and f... |

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Citation Context ...mations up to operational equivalence at any level � . The finite decomposition of expressions is critical to constructions that define self-referential structures (MacQueen, Plotkin, and Sethi 1984; =-=Pitts 1996-=-), for it gives an inductive structure by which self-referentiality may be avoided. We construct finite expressions “top-down”, by syntactically projecting arbitrary expressions to produce finite expr... |

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Citation Context ...se there were no global effects. The addition of global effects thus represents a significant change. We first present an embedding into��������� . Strachey’s memory-threading transformation is used (=-=Milne and Strachey 1976-=-). After establishing some results about this embedding, we define an equivalent direct operational semantics: proving facts via the embedding is cumbersome. We then develop a series of results which ... |

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Citation Context ... . Operational equivalence has also been shown to yield good notions of equivalence for languages with memories (Mason and Talcott 1991), explicit control operators (Talcott 1989), types and objects (=-=Gordon and Rees 1996-=-), and distributed objects (Agha, Mason, Smith, and Talcott 1992). It is important to characterize what “full and faithful” means: it is full in the sense that as many programs are equivalent as is po... |

45 |
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Citation Context ...ations: given the type of expression� ,�� an (�) can be partially evaluated to remove all cases on the sort, as the type itself reveals the sort This is one way to characterize Milner’s construction (=-=Milner 1977-=-). The following lemma establishes elementary properties of the syntactic projections. For brevity henceforward we drop subscript��� the from the �� projections . LEMMA 3.13 (ELEMENTARY����� PROPERTIE... |

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Citation Context ...��� ���¦¦¡������� (�������� ) ¥¥����� ¥¥�¦¦� ���¦¦¡���������� ����������� ¥¥�¦¦�� homomorphic for all other� ¥¥�¦¦¡ This encoding does not expose the (�� ,��� ,�� self ) since a fixed point is taken (=-=Kamin and Reddy 1994-=-). We conjecture this encoding is fully abstract. CONJECTURE 4.19¥¥�¦¦������������������ is set fully abstract. If the encoding were not fully abstract, there would be two������� expression sets �� ��... |

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(Show Context)
Citation Context ...ogramming language in another, a general theory of language embeddings is now defined. Other closely related notions of language embedding have been previously defined (Felleisen 1991; Mitchell 1993; =-=Riecke 1993-=-). Our definitions combine ideas from these approaches. The embeddings will be used to give semantics to a number of languages in Section 4, and will enable a number of properties to be proved concern... |

20 | An interpretation of typed OOP in a language with state - Eifrig, Smith, et al. - 1995 |

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(Show Context)
Citation Context ...e to construct structures isomorphic to domains directly on expressions. It is however possible to make progress by using �s-directed sets of expressions as a space over which an ordering is defined (=-=Smith 1992-=-). A simple pre-ordering on directed sets of expressions,�� � � �� � , is defined for this purpose. This pre-ordering has the property that¢� £ iff�¢�� �£� , meaning that it fully and faithfully gener... |

16 | Faithful ideal models for recursive polymorphic types - Abadi, Pierce, et al. - 1991 |

15 |
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Citation Context ... and Talcott 1995). The theorem also follows from set ordering ciu, proved below as Theorem 5.10, by Lemma 2.6 (iii). Applicative bisimulation equivalences may be defined for languages with memories (=-=Ritter and Pitts 1995-=-) and may be effectively used to directly establish equivalences. They (to lesser degree) suffer the same problem of lack of locality does¥¥¢¦¦ ¡��������¥¥£¦¦ as , and so are not fully abstract. An im... |

9 |
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Citation Context ...wever, proofs are possible. A number of alternate characterizations of ¡ have been developed to make proofs of equivalence much simpler, including bisimulation (Abramsky 1990), applicative orderings (=-=Bloom 1990-=-), and ciu equivalence (Mason and Talcott 1991). These alternate characterizations may be shown to be the same as ¡ (a so-called fully abstract alternate equivalence). Bisimulation equivalences give r... |

5 |
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Citation Context ...nce between program expressions, ¡ . Operational equivalence has also been shown to yield good notions of equivalence for languages with memories (Mason and Talcott 1991), explicit control operators (=-=Talcott 1989-=-), types and objects (Gordon and Rees 1996), and distributed objects (Agha, Mason, Smith, and Talcott 1992). It is important to characterize what “full and faithful” means: it is full in the sense tha... |

2 | An ideal model of types - MacQueen, Plotkin, et al. - 1984 |

1 | The Coverage of Operational Semantics 39 - Egidi, Honsell, et al. - 1992 |