## An axiomatisation of computationally adequate domain theoretic models of fpc (1994)

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Venue: | In 9 th LICS Conf |

Citations: | 34 - 6 self |

### BibTeX

@INPROCEEDINGS{Fiore94anaxiomatisation,

author = {Marcelo P. Fiore and Gordon D. Plotkin},

title = {An axiomatisation of computationally adequate domain theoretic models of fpc},

booktitle = {In 9 th LICS Conf},

year = {1994},

pages = {92--102},

publisher = {IEEE Computer Society Press}

}

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### Abstract

Categorical models of the metalanguage FPC (a type theory with sums, products, exponentials and recursive types) are defined. Then, domain-theoretic models of FPC are axiomatised and a wide subclass of them —the non-trivial and absolute ones — are proved to be both computationally sound and adequate.

### Citations

379 | Basic Concepts of Enriched Category Theory
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Citation Context ...ion form another possibility. However, a correspondingly general view of behaviour is completely lacking. 2 Order-enriched category theory For a thorough treatment of enriched category theory consult =-=[Kel82]-=-. In the rest of the paper we let V stand for either Poset (the category of small posets and monotone functions) or Cpo (the category of small cpos and continuous functions). But we stress that all ou... |

268 |
Semantics of Programming Languages: Structures and Techniques
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92 |
Algebraically complete categories
- Freyd
- 1990
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Citation Context ...ded by transforming them into covariant type constructors on universal involutory categories (those that are self-dual via an involution). One can then interpret recursive types (Section 5) following =-=[Fre91]-=- and using a notion of parameterised algebraic compactness. Categorical models of FPC are defined to be parameterised algebraically compact partial cartesian closed categories with finite coproducts; ... |

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Remarks on algebraically compact categories
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- 1991
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Full Abstraction for sequential languages: the state of the art
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Cpo-categories of partial maps
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Citation Context ...setting u ⊏ ∼A,B v iff for every x : X → A, u ◦ x ↓ ⇒ (v ◦ x ↓ ∧ u ◦ x ⊑X,B v ◦ x). � 3 Proposition 3.4 For every [m, f], [n, g] : A ⇀ B, [m, f] ⊏ ∼ [n, g] ⇐⇒ m = n ◦ i ∧ f ⊑ g ◦ i for unique i.� See =-=[Fio93]-=- for characterisations of when categories of partial maps induced by arbitrary domain structures or uniform domain structures (in the sense of the definition below) respectively Poset-enrich or Cpoenr... |

1 | Data types in algebraically ωcomplete categories - Adámek - 1993 |