by
Roland Backhouse
,
Paul Hoogendijk

Citations: | 4 - 1 self |

@MISC{Backhouse02genericproperties,

author = {Roland Backhouse and Paul Hoogendijk},

title = {Generic Properties of Datatypes},

year = {2002}

}

Generic programming adds a new dimension to the parametrisation of programs by allowing programs to be dependent on the structure of the data that they manipulate.

936 | A theory of type polymorphism in progra.mming - Milner - 1978 |

733 | Notions of Computation and Monads
- Moggi
- 1991
(Show Context)
Citation Context ...ind a \broadcast" is very simple. A broadcast for datatype F is a way of duplicating a given value of type B across every location in an F -structure of A 's. The broadcasting operation is what M=-=oggi [Mog91]-=- calls the \strength" of a datatype. The type of bcst A;B of datatype F is the same as the type of (zip:(B):F) A , namely F:(A B) F:A B . We give a generic specication of a zip such that, if F a... |

156 |
Fundamental concepts in programming languages
- Strachey
- 1967
(Show Context)
Citation Context ...nstance of the function length that maps a list of A 's to a natural number. A polymorphic function is said to be \parametric" if its behaviour does not depend on the type at which it is instanti=-=ated [Str67]-=-. That the length function on lists is parametric can be expressed formally. Suppose a function is applied to each element of a list |the function may, for example, map each character to a number| . C... |

37 | The Standard ML Core Language - Milner - 1985 |

27 | der Woude. Polynomial relators - Backhouse, Bruin, et al. - 1992 |

26 |
Relations Binaires, Fermetures, Correspondances de Galois. Bulletin de la Société deMathématiques de France 76
- Riguet
- 1948
(Show Context)
Citation Context ...ter. 4. Allegories and Relators 16 and is contravariant with respect to composition, (RS)[ = S[ R[ : All three operators of an allegory are connected by the modular law , also known as Dedekind's law =-=[Rig48-=-]: RS \ T (R \ T S[ )S : The standard example of an allegory is Rel , the allegory with sets as objects and relations as arrows. With this allegory in mind, we refer henceforth to the arrows of an al... |

25 |
A Generic Theory of Datatypes
- Hoogendijk
- 1997
(Show Context)
Citation Context ... : AsF:A and for each pair of objects A and B and each R : A B , F:Rsmem B nid B = memA nR : (39) Properties (39) and (37) are equivalent under the assumption of extensionality as shown by Hoogendijk =-=[Hoo97]-=-. Property (39) gives a great deal of insight into the nature of natural transformations. First, the property is easily generalised to: F:Rsmem B nS = memA n(RS) (40) 5. Datatype = Relator + Membershi... |

15 |
de Moor O
- Bird
- 1996
(Show Context)
Citation Context ...ations. There are also two \division" operators, and Rel is \tabulated". In full, Rel is a unitary, tabulated, locally complete, division allegory. For full discussion of these concepts see =-=[Fv90] or [BdM96-=-]. Here we brie y summarise the relevant denitions. We say that an allegory is locally complete if for each set S of relations of type A B , the union [S : A B exists and, furthermore, intersection an... |

15 | R.: When do datatypes commute - Hoogendijk, Backhouse - 1997 |

10 |
and Oege De Moor. Container types categorically
- Hoogendijk
- 2000
(Show Context)
Citation Context ... to the (non-nested) datatypes that one can dene in a functional programming language. They all have an associated membership relation; this leads to the proposal,srst made by De Moor and Hoogendijk [=-=HdM00]-=-, that a datatype is a relator with membership. There are two basic means for forming composite relators, namely induction and pointwise closure. We begin with a brief discussion of pointwise closure,... |

4 |
Commuting relators. Available via World-Wide Web at http://www.cs.nott.ac.uk/~rcb/MPC/papers
- Backhouse, Doornbos, et al.
- 1992
(Show Context)
Citation Context ...atypes. Then, if ^ G is the fan function of G , ( ^ GF):R = (zip:F:G) As(F ^ G):R ; (62) for all R : A B . It is (62) that often uniquely characterises zip:F:G . (In fact, our initial study of zips [B=-=DH92-=-] was where the notion of a fan wassrst introduced, and (62) was proposed as one of the dening properties of a zip.) 7.2 All regular datatypes commute We conclude this discussion by showing that all r... |

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