The Dual of Substitution is Redecoration

: 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.

• Type: Conference
• Year: 2001
• Where: SFP
• Authors: Tarmo Uustalu, Varmo Vene
• Keywords: Extension Operation, Incomplete Trees, Programming Languages, SFP 2001, Type Constructors