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* Rename README.MD to README.md

* Rename AbstractAlgebra.MD to AbstractAlgebra.md

* rename *.MD => *.md

* rename links *.MD => *.md

* remove broken links, drop publications section
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lemastero authored Dec 4, 2024
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6 changes: 3 additions & 3 deletions BasicAbstractions.MD → BasicAbstractions.md
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Expand Up @@ -71,7 +71,7 @@ def widen[A, B >: A](fa: F[A]): F[B]

Functor definition does not require any conditions on type constructor `F` or any other operations (unlike Applicative, Monad).
Therefore pretty much everything is a Functor. Notable exceptions are:
1. function input arguments (they are in `negative position`) or any input like type - see [Contravariant](./Contravariant.MD#contravariant-contravariant-functor) We can define Functor only for return type - because type is in `positive position`.
1. function input arguments (they are in `negative position`) or any input like type - see [Contravariant](./Contravariant.md#contravariant-contravariant-functor) We can define Functor only for return type - because type is in `positive position`.
2. abstractions where type can be both input and output, see [Invariant](#invariant-invariant-functor-exponential-functor) and blog post [Rotten Bananas by Edward Kmett](http://comonad.com/reader/2008/rotten-bananas/)
3. abstractions that behave like a Functor but not there are some controversies:

Expand All @@ -82,7 +82,7 @@ Therefore pretty much everything is a Functor. Notable exceptions are:

* Many abstractions have enough structure, so we can define `map` that obeys the laws. Such as `Monad` defined using `pure` and `flatMap`.
Another notable example is `Coyoneda` that wraps any type constructor and allows to use `map` on it. Functor instance is neccessary only when we want to extract the end result.
See [Free constructions](./Free.MD#free-constructions) for `Free functors`.
See [Free constructions](./Free.md#free-constructions) for `Free functors`.

* Resources:
* herding cats - Functor - @eed3si9n [(blog post)](http://eed3si9n.com/herding-cats/Functor.html)
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### State Monad

You can define useful operations on [State](./README.MD#state). This could be abstract over in `StateMonad` typeclass:
You can define useful operations on [State](./README.md#state). This could be abstract over in `StateMonad` typeclass:
```scala
trait StateMonad[F[_],S] extends Monad[F] {
def update: (S => S) => F[S]
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75 changes: 6 additions & 69 deletions ComputationalTrinitarianism.MD → ComputationalTrinitarianism.md

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# [Functional data structures](./FunctionalDataStructures.MD)
# [Functional data structures](./FunctionalDataStructures.md)
* Resources:
* [typelevel/cats-collections](https://github.com/typelevel/cats-collections)
* [What's new in purely functional data structures since Okasaki?](https://cstheory.stackexchange.com/questions/1539/whats-new-in-purely-functional-data-structures-since-okasaki)
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3 changes: 1 addition & 2 deletions Optics.MD → Optics.md
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## Van Laarhoven Optics

* [Monocle Learning Resources](https://julien-truffaut.github.io/Monocle/learning_resources.html)
* [Twan van Laarhoven: CPS based functional references](https://www.twanvl.nl/blog/haskell/cps-functional-references)
* [Functor Optics](http://oleg.fi/gists/posts/2017-12-23-functor-optics.html)

Expand Down Expand Up @@ -90,4 +89,4 @@ trait Grates[S, T, A, B] { // https://r6research.livejournal.com/28050.html
* Jeremy Gibbons - Profunctor Optics Modular Data Accessors [(video)](https://www.youtube.com/watch?v=sfWzUMViP0M)
* Grate: A new kind of Optic: [(blog post)](https://r6research.livejournal.com/28050.html)
* Tambara Modules - Brendan Fong [(video)](https://www.youtube.com/watch?v=67hJW6J4Mic)
* Profunctor optics, a categorical update - Mario Román, Bryce Clarke, Fosco Loregian, Emily Pillmore, Derek Elkins, Bartosz Milewski [(video)](https://www.youtube.com/watch?v=ceCwD7L0t3w), [(slides)](http://events.cs.bham.ac.uk/syco/strings3-syco5/slides/roman.pdf), [(gist)](https://gist.github.com/emilypi/407838d9c321d5b21ebc1828ad2bedcb)
* Profunctor optics, a categorical update - Mario Román, Bryce Clarke, Fosco Loregian, Emily Pillmore, Derek Elkins, Bartosz Milewski [(video)](https://www.youtube.com/watch?v=ceCwD7L0t3w), [(gist)](https://gist.github.com/emilypi/407838d9c321d5b21ebc1828ad2bedcb)
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70 changes: 35 additions & 35 deletions README.MD → README.md

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6 changes: 3 additions & 3 deletions RecursionSchemas.MD → RecursionSchemas.md
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case class Fix[F[_]](unFix: F[Fix[F]])
```

* Implementations: [Scalaz](https://github.com/slamdata/matryoshka/blob/master/core/shared/src/main/scala/matryoshka/data/Fix.scala) [ekmett/recursion-schemes](http://hackage.haskell.org/package/recursion-schemes/docs/Data-Functor-Foldable.html#t:Fix) [andyscott/droste](https://github.com/andyscott/droste/blob/master/modules/core/src/main/scala/qq/droste/data/Fix.scala)
* Implementations: [Scalaz](https://github.com/slamdata/matryoshka/blob/master/core/shared/src/main/scala/matryoshka/data/Fix.scala) [ekmett/recursion-schemes](http://hackage.haskell.org/package/recursion-schemes/docs/Data-Functor-Foldable.html#t:Fix) [andyscott/droste](https://github.com/higherkindness/droste/blob/main/modules/core/src/main/scala-2/higherkindness/droste/data/Fix.scala)

## Mu

* Implementations: [matryoshka](https://github.com/slamdata/matryoshka/blob/master/core/shared/src/main/scala/matryoshka/data/Mu.scala), [andyscott/droste](https://github.com/andyscott/droste/blob/master/modules/core/src/main/scala/qq/droste/data/Mu.scala), [ekmett/recursion-schemes](http://hackage.haskell.org/package/recursion-schemes/docs/Data-Functor-Foldable.html#t:Mu), [purescript-fixed-points](https://pursuit.purescript.org/packages/purescript-fixed-points/docs/Data.Functor.Mu)
* Implementations: [matryoshka](https://github.com/slamdata/matryoshka/blob/master/core/shared/src/main/scala/matryoshka/data/Mu.scala), [andyscott/droste](https://github.com/higherkindness/droste/blob/main/modules/core/src/main/scala/higherkindness/droste/data/Mu.scala), [ekmett/recursion-schemes](http://hackage.haskell.org/package/recursion-schemes/docs/Data-Functor-Foldable.html#t:Mu), [purescript-fixed-points](https://pursuit.purescript.org/packages/purescript-fixed-points/docs/Data.Functor.Mu)

## Nu

* Implementations: [Scala matryoshka](https://github.com/slamdata/matryoshka/blob/master/core/shared/src/main/scala/matryoshka/data/Nu.scala), [andyscott/droste](https://github.com/andyscott/droste/blob/master/modules/core/src/main/scala/qq/droste/data/Nu.scala), [ekmett/recursion-schemes](http://hackage.haskell.org/package/recursion-schemes/docs/Data-Functor-Foldable.html#t:Nu), [purescript-fixed-points](https://pursuit.purescript.org/packages/purescript-fixed-points/docs/Data.Functor.Nu)
* Implementations: [Scala matryoshka](https://github.com/slamdata/matryoshka/blob/master/core/shared/src/main/scala/matryoshka/data/Nu.scala), [andyscott/droste](https://github.com/higherkindness/droste/blob/main/modules/core/src/main/scala/higherkindness/droste/data/Nu.scala), [ekmett/recursion-schemes](http://hackage.haskell.org/package/recursion-schemes/docs/Data-Functor-Foldable.html#t:Nu), [purescript-fixed-points](https://pursuit.purescript.org/packages/purescript-fixed-points/docs/Data.Functor.Nu)

# Recursion schemas - Folds

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Expand Up @@ -23,5 +23,5 @@ Resources:
* Category Theory: Toposes - MathProofsable [(video playlist)](https://www.youtube.com/watch?v=gKYpvyQPhZo&list=PL4FD0wu2mjWM3ZSxXBj4LRNsNKWZYaT7k)
* Computational Quadrinitarianism (Curious Correspondences go Cubical) - Gershom Bazerman [(blog post)](http://comonad.com/reader/2018/computational-quadrinitarianism-curious-correspondences-go-cubical/)
* [fdilke/bewl](https://github.com/fdilke/bewl) (A DSL for the internal language of a topos)
* [resources about topos theory](./ComputationalTrinitarianism.MD#topos-theory)
* [resources about topos theory](./ComputationalTrinitarianism.md#topos-theory)
* nLab [Topos](https://ncatlab.org/nlab/show/topos), [Subobject Classifier](https://ncatlab.org/nlab/show/subobject+classifier), [Lawvere-Tierney topology](https://ncatlab.org/nlab/show/Lawvere-Tierney+topology)
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# References
* Some Definitions Everyone Should Know - John C. Baez [(pdf)](http://math.ucr.edu/home/baez/qg-fall2004/definitions.pdf)
* Monoidal Categories, Higher Categories - Jamie Vicary [(pdf)](http://events.cs.bham.ac.uk/mgs2019/vicary.pdf)
* Notions of Computation as Monoids - Exequiel Rivas, Mauro Jaskelioff [(arxiv.org/abs/1406.4823)](https://arxiv.org/pdf/1406.4823.pdf)
* Discrimination is Wrong: Improving Productivity - Edward Kmett [(video from YOW! Conferences)](https://www.youtube.com/watch?v=eXDJ5Jcbgk8), [(video from ZuriHac 2015)](https://www.youtube.com/watch?v=cB8DapKQz-I), [(slides)](http://yowconference.com.au/slides/yowlambdajam2015/Kmett-DiscriminationIsWrong.pdf)
* Braided Monoidal Categories - Andre Joyal, Ross Street [(pdf)](http://maths.mq.edu.au/~street/JS1.pdf)
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