markandrus / aljebra Goto Github PK

Toy implementations of the algebraic structures defined in the Fantasy Land specification, mostly borrowed from Haskell libraries.

JavaScript 96.79% Makefile 3.21%

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joneshf tzkmx

aljebra's Issues

Semigroup & Monoid Hierarchy

The Haskell library Data.Semigroup defines a few semigroups that are not monoids, two of which are

The rest of the library re-exports instances from the Haskell library Data.Monoid.

I'm going to look at refactoring the instances to model Data.Semigroup's re-export of Data.Monoid, as well as writing test/Monoid/laws.js in a way that "extends" the associativity law defined in test/Semigroup/laws.js. Benefits are

Less duplicate code
Fewer unique names, e.g. Semigroup can refer to Sum rather than Add, Product rather than Mult, etc.

@joneshf

Dual Monoid

How is the Dual monoid supposed to work? As it is right now, I'm not sure how to test it. The way I understand it, this should work.

var instances = {
  Dual: {
    constructor: Monoid.instances.Dual(Monoid.instances.Array),
    domain: [[1,2], [3,4]],
    check: complex
  }
}

However, both of the identites fail. The Left identity fails but the test suite keeps running, while the right identity has an error:

/home/joneshf/programming/javascript/aljebra/Monoid.js:59
    return b.concat(a);
             ^
TypeError: Object function () {
  return new Array();
} has no method 'concat'
    at /home/joneshf/programming/javascript/aljebra/Monoid.js:59:14
    at MonoidInstance.Monoid.MonoidInstance.concat (/home/joneshf/programming/javascript/aljebra/Monoid.js:18:18)
    at laws.Right Identity (/home/joneshf/programming/javascript/aljebra/MonoidTests.js:32:16)
    at /home/joneshf/programming/javascript/aljebra/MonoidTests.js:157:18
    at Array.reduce (native)
    at /home/joneshf/programming/javascript/aljebra/MonoidTests.js:156:17
    at Array.map (native)
    at TestLaw (/home/joneshf/programming/javascript/aljebra/MonoidTests.js:155:16)
    at TestLaws (/home/joneshf/programming/javascript/aljebra/MonoidTests.js:176:5)
    at TestInstances (/home/joneshf/programming/javascript/aljebra/MonoidTests.js:184:5)

Throwing in a couple of console.log's into the complex check function, we can see what is causing the issue:

aljebra [master●] % node MonoidTests.js
All
  Associativity
    Pass

  Left Identity
    Pass

  Right Identity
    Pass

Any
  Associativity
    Pass

  Left Identity
    Pass

  Right Identity
    Pass

Array
  Associativity
a:  [[1,2],[1,2],[1,2]] b:  [[1,2],[1,2],[1,2]]
a:  [[3,4],[1,2],[1,2]] b:  [[3,4],[1,2],[1,2]]
a:  [[1,2],[3,4],[1,2]] b:  [[1,2],[3,4],[1,2]]
a:  [[3,4],[3,4],[1,2]] b:  [[3,4],[3,4],[1,2]]
a:  [[1,2],[1,2],[3,4]] b:  [[1,2],[1,2],[3,4]]
a:  [[3,4],[1,2],[3,4]] b:  [[3,4],[1,2],[3,4]]
a:  [[1,2],[3,4],[3,4]] b:  [[1,2],[3,4],[3,4]]
a:  [[3,4],[3,4],[3,4]] b:  [[3,4],[3,4],[3,4]]
    Pass

  Left Identity
a:  [[1,2]] b:  [[1,2]]
a:  [[3,4]] b:  [[3,4]]
    Pass

  Right Identity
a:  [[1,2]] b:  [[1,2]]
a:  [[3,4]] b:  [[3,4]]
    Pass

Dual
  Associativity
a:  {"value":[1,2,1,2,1,2,1,2,1,2]} b:  {"value":[1,2,1,2,1,2,1,2,1,2]}
a:  {"value":[1,2,1,2,1,2,1,2,3,4]} b:  {"value":[1,2,1,2,1,2,1,2,3,4]}
a:  {"value":[1,2,3,4,1,2,3,4,1,2]} b:  {"value":[1,2,3,4,1,2,3,4,1,2]}
a:  {"value":[1,2,3,4,1,2,3,4,3,4]} b:  {"value":[1,2,3,4,1,2,3,4,3,4]}
a:  {"value":[3,4,1,2,3,4,1,2,1,2]} b:  {"value":[3,4,1,2,3,4,1,2,1,2]}
a:  {"value":[3,4,1,2,3,4,1,2,3,4]} b:  {"value":[3,4,1,2,3,4,1,2,3,4]}
a:  {"value":[3,4,3,4,3,4,3,4,1,2]} b:  {"value":[3,4,3,4,3,4,3,4,1,2]}
a:  {"value":[3,4,3,4,3,4,3,4,3,4]} b:  {"value":[3,4,3,4,3,4,3,4,3,4]}
    Pass

  Left Identity
a:  {"value":[1,2,null]} b:  {"value":[1,2]}
a:  {"value":[3,4,null]} b:  {"value":[3,4]}
    Fail

  Right Identity

The first issue is that it's adding more elements than it should. The next issue is that it's modifying the domain. The final thing to note is that the only reason Associativity, and Left Identity even ran was because Array's have a concat method. Any other monoid would fail with a TypeError of not having concat.

I haven't actually tried to figure out how to fix anything, just some things I found after looking around.

As an aside. I think this is a pretty good example of the whole point of this. With a little analysis we can clearly see that the current implementation of Dual is not actually a monoid. However, it does almost look like a Flattener or something.

Expose Mocha's `done` callback to Cont instances

I think the equality check for Cont will need to synchronize results and use Mocha's done function. See error branch.

Extending Instances

Currently, ./lib/Applicative.js mutates the Monad instances in ./lib/Monad.js if it is ever required (in order to derive ap). This is hard to reason about.

There are also instances like EIther whose constructor is defined in ./lib/Semigroup.js. Other files—such as ./lib/Functor.js—mutate the original instance before re-exporting it.

Goals:

Determine a canonical location for such constructors. Perhaps in the most "powerful" algebraic structure (i.e. move Either to ./lib/Monad.js), or in a separate ./lib/constructors.js?
Determine best way to extend these instances without mutating them. There is a pure Object.prototype.extend in ./index.js. I don't think it can copy constructors; however, going with the latter option above would allow extending in ./lib/constructors.js.

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