[Functional Programming] Write simple Semigroups type

An introduction to concatting items via the formal Semi-group interface. Semi-groups are simply a type with a concat method that are associative. We define three semigroup instances and see them in action.

1. What is Semigroups:

Array type, String type, they are semigroup, because both has ´concat´ method:

"a".concat("b").concat("c"); // abc
[1].concat([2]).concat([3]); //[1,2,3]

Sum:

But Number type is not semigroup, because you cannot concat two number... well, for now...

Not let's define a Semigroup for Number as well, it is called 'Sum':

// Sum :: Sum s => a -> s a
const Sum = x => ({
    x,
    concat: ({x: y}) => Sum(x + y),
    inspect: () => `Sum ${x}`
})

Sum takes a variable 'a' and return Sum(a). Here 'a' should be number type. We export 'x' to outside world from Sum is for easy accessing the value from Another Sum.

const res1 = Sum(11).concat(Sum(12)).concat(Sum(2));
console.log(res1); // Sum 25

All / Any:

Boolean in JS is not a semigroup type, we can make it so by introduces 'All & Any' semigroup type:

// All :: All s => b -> s b
const All = x => ({
    x,
    concat: ({x: y}) => All(y && x),
    inspect: () => `All ${x}`
});
// Any :: Any s => b -> s b
const Any = x => ({
    x,
    concat: ({x: y}) => Any( y || x),
    inspect: () => `Any ${x}`
})
const res2 = All(false).concat(All(true));
const res23 = Any(false).concat(Any(true));
console.log(res2) // All false
console.log(res3) // Any true

First:

Wcan define a semigroup type for any other Object in JS, which only return the First one, ignore the rest:

// First :: First f => a -> f a
const First = x => ({
    x,
    concat: (_) => First(x),
    inspect: () => `First ${x}`
})

const res3 = First('a').concat(First(2)).concat(First(2));
console.log(res3) // 'a'

Map:

Object in JS don't have 'concat' method, of course you can use some libs such as https://github.com/DrBoolean/immutable-ext

But here, we will define a simple version of Map by ourselves. Which loop though each props of the given object, apply concat method for each prop:

// Map :: Map m => a -> m a
const Map = x => ({
    x,
    concat: ({x: y}) => Object.keys(y).map(k => y[k].concat(x[k]))
});

Let take a example to see how those semigroup types can be useful:

For example we have to object, we want to 'concat' them, by concat, I mean, for the name prop, we just want to keep the First one, for the 'isPaid' prop we want to take 'All' operation, for 'points' we want to take 'Sum' operation, for 'friends', you guess so... 'concat' operation.

const _acct1 = {name: 'Nico', isPaid: true, points: 10, friends: ['Franklin']};
const _acct2 = {name: 'Nico', isPaid: false, points: 30, friends: ['Gatsby']};

So the final result should be:

// [ Nico, false, 40, [ 'Gatsby', 'Franklin' ] ]

First, let's apply the Semigroup types we already have to those two objects:

const acct1 = {name: First('Nico'), isPaid: All(true), points: Sum(10), friends: ['Franklin']};
const acct2 = {name: First('Nico'), isPaid: All(false), points: Sum(30), friends: ['Gatsby']};

OK, now we need to concat 'acct1' and 'acct2', but Object doesn't have 'concat' method as we discussed before, therefore we need to wrap our objects into 'Map':

const acct1 = Map({name: First('Nico'), isPaid: All(true), points: Sum(10), friends: ['Franklin']});
const acct2 = Map({name: First('Nico'), isPaid: All(false), points: Sum(30), friends: ['Gatsby']});

Now we can call:

const res4 = acct1.concat(acct2);
console.log(res4); // [ First Nico, All false, Sum 40, [ 'Gatsby', 'Franklin' ] ]

OK, that's it. The end of Semigroup... 

Below I append a better version:

const R = require('ramda');

// Sum :: Sum s => a -> s a
const Sum = x => ({
    x,
    concat: ({x: y}) => Sum(x + y),
    inspect: () => `Sum ${x}`
})
const res1 = Sum(11).concat(Sum(12)).concat(Sum(2));
console.log(res1); // {x: 25}

// All :: All s => b -> s b
const All = x => ({
    x,
    concat: ({x: y}) => All(y && x),
    inspect: () => `All ${x}`
});
// Any :: Any s => b -> s b
const Any = x => ({
    x,
    concat: ({x: y}) => Any( y || x),
    inspect: () => `Any ${x}`
})
const res2 = All(false).concat(All(true));
console.log(res2) // All false

// First :: First f => a -> f a
const First = x => ({
    x,
    concat: (_) => First(x),
    inspect: () => `First ${x}`
})

const res3 = First('a').concat(First(2)).concat(First(2));
console.log(res3) // 'a'


const _acct1 = {name: 'Nico', isPaid: true, points: 10, friends: ['Franklin']};
const _acct2 = {name: 'Nico', isPaid: false, points: 30, friends: ['Gatsby']};

// Map :: Map m => a -> m a
const Map = x => ({
    x,
    concat: ({x: y}) => Object.keys(y).map(k => y[k].concat(x[k]))
});
const transformations = R.evolve({
    name: First,
    isPaid: All,
    points: Sum
});
const semi_transform = R.compose(
    Map,
    transformations
);
const acct1 = semi_transform(_acct1);
const acct2 = semi_transform(_acct2);
const res4 = acct1.concat(acct2);
console.log(res4); // [ First Nico, All false, Sum 40, [ 'Gatsby', 'Franklin' ] ]