Add more morphisms #146

stevemao · 2017-04-10T10:40:32Z

I was watching @DrBoolean's A Million Ways to Fold in JS but I couldn't understand most of the morphism jargons. I presume the video is for experienced devs who are from a FP language background. The moment when I tried to search for "Catamorphism javascript" on google I couldn't get anything. I really hope there would be more in depth FP resources written in JavaScript. Luckily @i-am-tom kindly wrote up something that could be understood by JS devs like me. I have fixed a minor mistake in @i-am-tom's original write up and tweaked a few wording.

Also cc @joneshf @getify @shineli1984

Thanks!

@DrBoolean

I was watching @DrBoolean's [A Million Ways to Fold in JS](https://www.youtube.com/watch?v=JZSoPZUoR58) but I couldn't understand most of the morphism jargons. I presume the video is for experienced devs who are from a FP language background. The moment when I tried to search for "Catamorphism javascript" on google I couldn't get anything. I really hope there would be more in depth FP resources written in JavaScript. Luckily @i-am-tom kindly wrote up something that could be understood by JS devs like me. I have fixed a minor mistake in @i-am-tom's [original write up](DrBoolean/RecursionTalk#2 (comment)) and tweaked a few wording. Also cc @joneshf @getify @shineli1984 Thanks!

i-am-tom · 2017-04-10T10:45:56Z

Oh no :O what was my mistake?

stevemao · 2017-04-10T10:50:26Z

readme.md

+  list
+)
+
+suffixes([1, 2, 3, 4, 5]) // [[2, 3, 4, 5], [3, 4, 5], [4, 5], [5], []]


@i-am-tom There should be an empty array as the last element 😺

Oh yeah 😳 Good catch!

i-am-tom

Yaaay :D

i-am-tom · 2017-04-10T10:47:44Z

readme.md

+
+### Paramorphism
+
+Enhancement of catamorphism. It's like `reduceRight`. However, there's a difference:


I'd be cautious around the word "enhancement"; for most cases, para wouldn't be an enhancement - just unnecessary bloat. Kinda similar to how Monad, in a lot of cases, definitely isn't an enhancement to Functor.

Sorry, "enhancement" is not the right word. More like "extension". Looking at Monad in the docs it doesn't mention the relationship with Functor so I'll follow the same way.

i-am-tom · 2017-04-10T10:48:11Z

readme.md

+An `unfold` function. An `unfold` is the opposite of `fold` (`reduce`). It generates a list from a single value.
+
+```js
+const unfold = (f, seed) => {


I stole this code from @DrBoolean, so I'd probably give him a shout-out.

i-am-tom · 2017-04-10T10:52:57Z

readme.md

+// Obviously not safe for lists containing `undefined`,
+// but good enough to make the point.
+const para = (reducer, accumulator, [x, ... xs]) =>
+  x !== undefined


Probably best to update this to match the better example I posted. undefined is kinda confusing :(

shineli1984 · 2017-04-10T10:54:44Z

readme.md


+A `reduceRight` function. Take a bunch of things, and combine them into another. The morphism is from "bunch of things" to "another".


@stevemao By just looking at this line, I don't have the context as in how 'generalised' we want to be in this repo, but Catamorphism can be for other ADTs and not just list. List certainly provides good intuition, but should we mention bunch of things could be just one thing here?

Quite right. In the most general case, it applies to any Foldable structure. bunch of things could indeed be thing or even no things!

…f `reduce` doesn't seem to be right either. Changed both to mdn's definition.

shineli1984 · 2017-04-10T11:37:31Z

readme.md


+A `reduceRight` function that applies a function against an accumulator and each value of the array (from right-to-left) to reduce it to a single value.


each value of the array

What I meant here was that it doesn't need to be an array and

against an accumulator

it doesn't need to be an accumulator

It can be a Maybe Int. The catamorphism can help to "break" it down into just Int, so that the Maybe structure is not preserved.

reduce it to a single value

It may not be a single value. You can re-implement map using reduce for list:

const map = reduce((acc, cur) => concat(acc, [cur]))

So I think maybe another example not using list will be better here? just to illustrate that Catamorphism is more general than a fold for a list.

@hemanth thoughts?

dmitriz · 2017-04-20T03:13:40Z

readme.md

@@ -727,7 +811,7 @@ An object that has a `concat` function that combines it with another object of t

 ## Foldable

-An object that has a `reduce` function that can transform that object into some other type.
+An object that has a `reduce` function that applies a function against an accumulator and each element in the array (from left to right) to reduce it to a single value.


Perhaps the detail about left to right can be omitted as there is also right to left reduce?

In maths, the right to left is actually more common as it is how the functions compose.

dmitriz · 2017-04-20T03:21:12Z

readme.md

+A homomorphism is just a structure preserving map. In fact, a functor is just a homomorphism between categories as it preserves the original category's structure under the mapping.
+
+```js
+A.of(f).ap(A.of(x)) == A.of(f(x))


Perhaps also give simpler examples such as x => x*2 preserving the addition structure?

char0n · 2017-05-10T21:13:40Z

readme.md

+
+### Catamorphism
+
+A `reduceRight` function that applies a function against an accumulator and each value of the array (from right-to-left) to reduce it to a single value.


Hi,

Maybe more simpler and polymorphic explanation presented by Tom Harding.

catamorphism: a way of folding a type up into a value

anamorphism: a way of unfolding a type from a single value

@char0n A link?

@dmitriz http://www.tomharding.me/2017/02/24/reductio-and-abstract-em/

I like this idea. Catamorphisms are more general than just a reduce and don't always require an accumulator

@jethrolarson exactly; catamorphism can be seen on multiple monadic types with or without Foldable spec

Identity.of(1).get(); //=> catamorphism Identity.of(1).fold((acc, val) => acc + val, 1); //=> catamorphism Maybe.fromNull(value).cata(identity, identity); //=> catamorphism

jethrolarson · 2017-05-20T19:08:50Z

Trailing spaces are meaningful in markdown so you shouldn't be stripping them automatically

stevemao · 2017-05-21T02:22:22Z

@jethrolarson not with one space. Two spaces would create a \n but there are two newlines after it so it creates a seperate node already.

mrtnbroder · 2017-09-28T20:41:10Z

Whats up with this whole project? so many PRs and issues, can we get this merged in?

hemanth · 2017-09-28T23:16:28Z

@mrtnbroder This is pretty much active, there are many reasons for open PRs and issues if you go through them.

@stevemao it needs a rebase.

stevemao · 2019-03-07T00:00:39Z

@hemanth Sorry for the delay. Conflicts should be resolved

hemanth · 2019-03-07T07:09:53Z

NP!

Awesomeness after ~2years this PR is going!

stevemao commented Apr 10, 2017

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i-am-tom reviewed Apr 10, 2017

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shineli1984 reviewed Apr 10, 2017

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stevemao added 2 commits April 10, 2017 21:08

Address @i-am-tom and @shineli1984's review

c39c733

Since the definition of reduceRight wan't correct, the definition o…

72fe695

…f `reduce` doesn't seem to be right either. Changed both to mdn's definition.

shineli1984 reviewed Apr 10, 2017

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add Homomorphism

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dmitriz reviewed Apr 20, 2017

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char0n reviewed May 10, 2017

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Merge branch 'master' into morphisms

05d7e94

hemanth merged commit 77f9117 into hemanth:master Mar 7, 2019

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Add more morphisms #146

Add more morphisms #146

stevemao commented Apr 10, 2017

i-am-tom commented Apr 10, 2017

stevemao Apr 10, 2017

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jethrolarson commented May 20, 2017

stevemao commented May 21, 2017

mrtnbroder commented Sep 28, 2017

hemanth commented Sep 28, 2017

stevemao commented Mar 7, 2019

hemanth commented Mar 7, 2019


		### Paramorphism

		Enhancement of catamorphism. It's like `reduceRight`. However, there's a difference:


		A `reduceRight` function. Take a bunch of things, and combine them into another. The morphism is from "bunch of things" to "another".


		A `reduceRight` function that applies a function against an accumulator and each value of the array (from right-to-left) to reduce it to a single value.


		### Catamorphism

		A `reduceRight` function that applies a function against an accumulator and each value of the array (from right-to-left) to reduce it to a single value.

Add more morphisms #146

Add more morphisms #146

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stevemao commented Apr 10, 2017

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stevemao Apr 15, 2017 • edited Loading

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char0n May 20, 2017 • edited Loading

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hemanth commented Sep 28, 2017

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