What's the difference between abstraction and generalization?

Question

I understand that abstraction is about taking something more concrete and making it more abstract. That something may be either a data structure or a procedure. For example:

Answer 1

Abstraction

Abstraction is specifying the framework and hiding the implementation level information. Concreteness will be built on top of the abstraction. It gives you a blueprint to follow to while implementing the details. Abstraction reduces the complexity by hiding low level details.

Example: A wire frame model of a car.

Generalization

Generalization uses a “is-a” relationship from a specialization to the generalization class. Common structure and behaviour are used from the specializtion to the generalized class. At a very broader level you can understand this as inheritance. Why I take the term inheritance is, you can relate this term very well. Generalization is also called a “Is-a” relationship.

Example: Consider there exists a class named Person. A student is a person. A faculty is a person. Therefore here the relationship between student and person, similarly faculty and person is generalization.

Answer 2

I'd like to offer an answer for the greatest possible audience, hence I use the Lingua Franca of the web, Javascript.

Let's start with an ordinary piece of imperative code:

// some data

const xs = [1,2,3];

// ugly global state

const acc = [];

// apply the algorithm to the data

for (let i = 0; i < xs.length; i++) {
  acc[i] = xs[i] * xs[i];
}

console.log(acc); // yields [1, 4, 9]

In the next step I introduce the most important abstraction in programming - functions. Functions abstract over expressions:

// API

const foldr = f => acc => xs => xs.reduceRight((acc, x) => f(x) (acc), acc);
const concat = xs => ys => xs.concat(ys);
const sqr_ = x => [x * x]; // weird square function to keep the example simple

// some data

const xs = [1,2,3];

// applying

console.log(
  foldr(x => acc => concat(sqr_(x)) (acc)) ([]) (xs) // [1, 4, 9]
)

As you can see a lot of implementation details are abstracted away. Abstraction means the suppression of details.

Another abstraction step...

// API

const comp = (f, g) => x => f(g(x));
const foldr = f => acc => xs => xs.reduceRight((acc, x) => f(x) (acc), acc);
const concat = xs => ys => xs.concat(ys);
const sqr_ = x => [x * x];

// some data

const xs = [1,2,3];

// applying

console.log(
  foldr(comp(concat, sqr_)) ([]) (xs) // [1, 4, 9]
);

And another one:

// API

const concatMap = f => foldr(comp(concat, f)) ([]);
const comp = (f, g) => x => f(g(x));
const foldr = f => acc => xs => xs.reduceRight((acc, x) => f(x) (acc), acc);
const concat = xs => ys => xs.concat(ys);
const sqr_ = x => [x * x];

// some data

const xs = [1,2,3];

// applying

console.log(
  concatMap(sqr_) (xs) // [1, 4, 9]
);

The underlying principle should now be clear. I'm still dissatisfied with concatMap though, because it only works with Arrays. I want it to work with every data type that is foldable:

// API

const concatMap = foldr => f => foldr(comp(concat, f)) ([]);
const concat = xs => ys => xs.concat(ys);
const sqr_ = x => [x * x];
const comp = (f, g) => x => f(g(x));

// Array

const xs = [1, 2, 3];

const foldr = f => acc => xs => xs.reduceRight((acc, x) => f(x) (acc), acc);

// Option (another foldable data type)

const None =      r => f => r;
const Some = x => r => f => f(x);

const foldOption = f => acc => tx => tx(acc) (x => f(x) (acc));

// applying

console.log(
  concatMap(foldr) (sqr_) (xs), // [1, 4, 9]
  concatMap(foldOption) (sqr_) (Some(3)), // [9]
  concatMap(foldOption) (sqr_) (None) // []
);

I broadened the application of concatMap to encompass a larger domain of data types, nameley all foldable datatypes. Generalization emphasizes the commonalities between different types, (or rather objects, entities).

I achieved this by means of dictionary passing (concatMap's additional argument in my example). Now it is somewhat annoying to pass these type dicts around throughout your code. Hence the Haskell folks introduced type classes to, ...um, abstract over type dicts:

concatMap :: Foldable t => (a -> [b]) -> t a -> [b]

concatMap (\x -> [x * x]) ([1,2,3]) -- yields [1, 4, 9]
concatMap (\x -> [x * x]) (Just 3) -- yields [9]
concatMap (\x -> [x * x]) (Nothing) -- yields []

So Haskell's generic concatMap benefits from both, abstraction and generalization.