The Dual of Substitution is Redecoration (2002) [7 citations — 3 self]
by
Tarmo Uustalu
,
Varmo Vene
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@MISC{Uustalu02thedual,
author = {Tarmo Uustalu and Varmo Vene},
title = {The Dual of Substitution is Redecoration},
year = {2002}
}
author = {Tarmo Uustalu and Varmo Vene},
title = {The Dual of Substitution is Redecoration},
year = {2002}
}
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Abstract:
It is well known that type constructors of incomplete trees (trees with variables) carry the structure of a monad with substitution as the extension operation. Less known are the facts that the same is true of type constructors of incomplete cotrees (=non-wellfounded trees) and that the corresponding monads exhibit a special structure. We wish to draw attention to the dual facts which are as meaningful for functional programming: type constructors of decorated cotrees carry the structure of a comonad with redecoration as the coextension operation, and so do---even more interestingly---type constructors of decorated trees.
Citations
| 89 | and Order in Algorithmics – Law - 1992 |
| 23 | Upwards and downwards accumulations on trees – Gibbons - 1992 |
| 21 | Computational comonads and intensional semantics – Brookes, Geva - 1992 |
| 12 | A coalgebraic view of infinite trees and iteration – Aczel, Adámek, et al. - 2001 |
| 12 | Generalised coinduction – Bartels - 2000 |
| 1 | Toposes, Triples and Theories, vol. 278 of Grundlehren der mathematischen Wissenschaften – Barr, Wells - 1984 |
| 1 | Generic Programming with Types and Relations – Bird, Moor, et al. - 1996 |
