jmatsushita/Comonadic notes

## Comonadic notes
Comonadic explorations

- Is day convolution as comonadic composition really free? What's the difference with Kenneth's Distribute based composition?
    - How do specific comonads compose?
- cursors -> apart
    - The cursor like intuition, extended to a range, starts feeing exactly like a lens !?
- If the data space has this comonadic structure, how does it compose with the ui components?
- If we can model time also as a comonadic cofree module/pattern, how do we sync with an event loop? Seems like the shape of the time dimension(s?) define a clock type!!! Actions are a time dimension :O ?!? I think that's also the coeffect/effect dimension (tricky with cursors on data, does it depends on whether a query is sent or should we abstract that out?).

- Chris's Zippers feel like Pairing
- What about Paul Chiusano's admonition against zippers in favor of paths? https://pchiusano.github.io/2014-08-12/zippers-not-useful.html Is it just about providing a comonadic (zipper like) interface to otherwise simple mappy things under the hood? He also makes a case for Path algebras which sounds like Kmett's relocatable stuff (semi direct product).
- Cfix in purescript
    - What about this conway with a 3rd time dimension, how does this relate to time in LVS? Seems like PVS goves you access to any past and future whereas cfix only to the next tick. http://blog.sigfpe.com/2007/02/comonads-and-reading-from-future.html?showComment=1171056660000&m=1#c2284986681058924897 Can we express timed rules (adaptive scripts) with that? Does PHOAS applies for declarative cycles in time (or in data paths/bounds).
    - mra as a comonad?
- Apart graph -> with rose tree pulled out of it?
    -  Can I make it for labelled edges in graphs (and labelled branches in rose trees).
- Apart graph -> can you have the stored structure as n-path indices with distance (to have a fast cursor with streaming loading from disk?).
    - What's that in the browser if we have some disk based storage (how to persist indexeddb in the browser? Do we need to if there's data in a hypercore), something like IndexedDB


Coeffects and effect handlers https://youtu.be/GEDMSZVkv3M is basically about Zap/Pair and comonadic UIs, a coeffect feels like a driver in cycle.js,  mutation and queries for data stores.

  Observables https://iokasimov.github.io/posts/2018/12/observable seem to go into LTL or modal logic without naming it.
	Comonadic explorations

	- Is day convolution as comonadic composition really free? What's the difference with Kenneth's Distribute based composition?
	- How do specific comonads compose?
	- cursors -> apart
	- The cursor like intuition, extended to a range, starts feeing exactly like a lens !?
	- If the data space has this comonadic structure, how does it compose with the ui components?
	- If we can model time also as a comonadic cofree module/pattern, how do we sync with an event loop? Seems like the shape of the time dimension(s?) define a clock type!!! Actions are a time dimension :O ?!? I think that's also the coeffect/effect dimension (tricky with cursors on data, does it depends on whether a query is sent or should we abstract that out?).

	- Chris's Zippers feel like Pairing
	- What about Paul Chiusano's admonition against zippers in favor of paths? https://pchiusano.github.io/2014-08-12/zippers-not-useful.html Is it just about providing a comonadic (zipper like) interface to otherwise simple mappy things under the hood? He also makes a case for Path algebras which sounds like Kmett's relocatable stuff (semi direct product).
	- Cfix in purescript
	- What about this conway with a 3rd time dimension, how does this relate to time in LVS? Seems like PVS goves you access to any past and future whereas cfix only to the next tick. http://blog.sigfpe.com/2007/02/comonads-and-reading-from-future.html?showComment=1171056660000&m=1#c2284986681058924897 Can we express timed rules (adaptive scripts) with that? Does PHOAS applies for declarative cycles in time (or in data paths/bounds).
	- mra as a comonad?
	- Apart graph -> with rose tree pulled out of it?
	- Can I make it for labelled edges in graphs (and labelled branches in rose trees).
	- Apart graph -> can you have the stored structure as n-path indices with distance (to have a fast cursor with streaming loading from disk?).
	- What's that in the browser if we have some disk based storage (how to persist indexeddb in the browser? Do we need to if there's data in a hypercore), something like IndexedDB


	Coeffects and effect handlers https://youtu.be/GEDMSZVkv3M is basically about Zap/Pair and comonadic UIs, a coeffect feels like a driver in cycle.js, mutation and queries for data stores.

	Observables https://iokasimov.github.io/posts/2018/12/observable seem to go into LTL or modal logic without naming it.