4 ms·

For those, like me, who might not be familiar with those terms, this StackOverflow question strives to answer it: https://stackoverflow.com/questions/36851766/

For those, like me, who might not be familiar with those terms, this StackOverflow question strives to answer it: https://stackoverflow.com/questions/36851766/histomorphisms-zygomorphisms-and-futumorphisms-specialised-to-lists https://stackoverflow.com/questions/36851766/histomorphisms-... Oh, and what is a zipper as a data structure?

lmm 8y ago
It's usually some kind of "cursor into" a datastructure, that gives you both the "focus" / point you're operating at and also the rest of the surrounding datastructure. They tend to be comonadic and a nice way to express transformations where an element depends on its neighbours (but I'm wondering whether folding down the structure with history would achieve the same thing, hence the morphism suggestion). https://wiki.haskell.org/Zipper https://wiki.haskell.org/Zipper
cstrahan 8y ago
I'll preface: this is more of an interesting connection, rather than a direct answer to your question. Zippers can be seen as (or at least isomorphic to) the derivative of a type with respect to one of its type parameters. This is described in Conor McBride's paper "The Derivative of a Regular Type is its Type of One-Hole Contexts." http://strictlypositive.org/diff.pdf http://strictlypositive.org/diff.pdf If a video is more your speed, Kenneth Foner gave a great talk titled "`choose` your own derivative" that takes the concept of derivatives of types and takes it a step further. You can skip to the 11 minute mark to watch his explanation of zippers as derivatives here: https://www.youtube.com/watch?v=79zzgL75K8Q&t=11m https://www.youtube.com/watch?v=79zzgL75K8Q&t=11m With that said, the standard go-to paper for Zippers would probably be "The Zipper" by Gerard Huet: http://gallium.inria.fr/~huet/PUBLIC/zip.pdf http://gallium.inria.fr/~huet/PUBLIC/zip.pdf

4 ms·

For those, like me, who might not be familiar with those terms, this StackOverflow question strives to answer it: https://stackoverflow.com/questions/36851766/

by whitten 8y ago

lmm 8y ago
It's usually some kind of "cursor into" a datastructure, that gives you both the "focus" / point you're operating at and also the rest of the surrounding datastructure. They tend to be comonadic and a nice way to express transformations where an element depends on its neighbours (but I'm wondering whether folding down the structure with history would achieve the same thing, hence the morphism suggestion). https://wiki.haskell.org/Zipper https://wiki.haskell.org/Zipper
cstrahan 8y ago
I'll preface: this is more of an interesting connection, rather than a direct answer to your question. Zippers can be seen as (or at least isomorphic to) the derivative of a type with respect to one of its type parameters. This is described in Conor McBride's paper "The Derivative of a Regular Type is its Type of One-Hole Contexts." http://strictlypositive.org/diff.pdf http://strictlypositive.org/diff.pdf If a video is more your speed, Kenneth Foner gave a great talk titled "`choose` your own derivative" that takes the concept of derivatives of types and takes it a step further. You can skip to the 11 minute mark to watch his explanation of zippers as derivatives here: https://www.youtube.com/watch?v=79zzgL75K8Q&t=11m https://www.youtube.com/watch?v=79zzgL75K8Q&t=11m With that said, the standard go-to paper for Zippers would probably be "The Zipper" by Gerard Huet: http://gallium.inria.fr/~huet/PUBLIC/zip.pdf http://gallium.inria.fr/~huet/PUBLIC/zip.pdf