User:Duplode/Foldable and Traversable plan

Foldable edit

foldr revisited (deconstructing foldr, the monoidal heart of a fold, folding as querying/summarising, understanding vs. implementation)
The Foldable class (the relation with lists, tons of generalised methods, pick-your-monoid folding. Exercise about mapM_)
- Folding in a list-like way. (Can we say there is a list-likeness to the monoidal structure? Opt.: lists as the free monoid?)
- From "can I get this by going down the list in such-and-such-a-way" to "can I express what I want as a monoidal query?" (cf. the specialised folds in Data.Foldable)
- concat routes to Foldable via msum and asum (does this have to do with the alternative-monoid connection?)
(Possibly talk about Set - foldable but not a functor.)
(Is there a way to talk about monoid homomorphisms here?)

(This is less well organised)

"Special functors" (Identity, Const, Compose)
"But traverse looks like a map. What does it have to do with traversal?"
(Is this right?: Traversal involves a monoidal summary on an applicative context. (And that's what sequenceA does?)(Can the Monoidal presentation help with that?))
Recovering Foldable and Functor
(folding destroys structure, traverse preserves it, and adds an extra layer on top. (But you can destroy it anyway if you ask nicely.)
Traversable laws (how to discuss them?)
(How to explain sequenceA?)
Examples, examples, examples.
(Make sense of mapAccum* somehow? It does look like State in a very disguised form.)
Interpreting stuff in terms of monoids and functors.
GHC deriving extensions.