*Everything described in the article is relevant for the 4.2.3 version of TypeScript.*

Hi there!

The TypeScript now supports Variadic Tuple Types. It's mean that we can use spread operator and generic parameters to create types that contvert on array-like type to another. For example, let's create a type that appends an element to an array.

```
type Append<T extends unknown[], R> = [R, ...T];
let a1: Append<[1, 2, 3], 0>;
// ^ = let a1: [0, 1, 2, 3]
let a2: Append<[], "some">;
// ^ = let a2: ["some"]
let a3: Append<[1, "q", false], {a: number}>;
// ^ = let a3: [{a: number}, 1, "q", false]
```

OK, but what if we want to create a type that will remove the first element of the array. This type isn't that simple because an empty array `[]`

extends `unknown[]`

and we have to check that there are elements in the original array. We can do this using conditional type and type inference

```
type Slice<T extends unknown[]> = T extends [infer _, ...infer Tail]
? Tail
: [];
let b1: Slice<[1, 2, 3]>;
// ^ = let b1: [2, 3]
let b2: Slice<[1]>;
// ^ = let b2: [];
let b3: Slice<[]>;
// ^ = let b3: [];
```

Let's complicate the task. How to create a type that will reverse an array? In typical situation we would use loops or recursion to iterate the array. In Typescript types we can use recursive type alias.

```
type Reverse<T extends unknown[]> =
T extends [infer Item, ...infer Tail]
? [...Reverse<Tail>, Item]
: [];
let c1: Reverse<[1, 2, 3]>;
// ^ = let c1: [3, 2, 1]
let c2: Reverse<[1]>;
// ^ = let c2: [1]
let c3: Reverse<[]>;
// ^ = let c3: []
```

There is one unpleasant moment with this approach - typescript doesn't use generics' constraints to define the inference types. If we have `type Some<T extends number> = T`

we can't use infer defined type as T parameter.

```
type Some<A extends number> = A;
type Some2<A extends number[]> = A extends Array<infer B>
? Some<B>
// ^ Error: Type 'B' does not satisfy the constraint 'number'
: number;
```

But if we change `Some`

type to `type Some<T> = T extends number ? T : number`

, we can use infered type. These two vertion of `Some`

type are not equal, but sometimes this approach can be used.

## Type-based binary adder

Ok, now we know everything to create a binary adder. If we don't know what a binary adder is, you can learn it yourself. Firstly, we create several logical operations.

```
type Xor<A, B> = A extends B ? 0 : 1;
/*
A B Xor<A, B>
0 0 0
1 0 1
0 1 1
1 1 0
*/
type And<A, B> = A extends 1 ? B extends 1 ? 1 : 0 : 0;
/*
A B And<A, B>
0 0 0
1 0 0
0 1 0
1 1 1
*/
type Or<A, B> = A extends 1 ? 1 : B extends 1 ? 1 : 0;
/*
A B Or<A, B>
0 0 0
1 0 1
0 1 0
1 1 1
*/
```

Secondly, consider the adder circuit.

As you can see we have to use 2 bits of 2 numbers and *carry-in* and return result bit and *carry-out*.

```
type Sum<A, B, CIn> = Xor<Xor<A, B>, CIn>;
type COut<A, B, CIn> = Or<And<A, B>, And<Xor<A, B>, CIn>>;
```

Finally, we create the adder type.

```
type Add<A, B, CIn = 0> =
A extends [...infer AN, infer AC]
? B extends [...infer BN, infer BC]
? [...Add<AN, BN, COut<AC, BC, CIn>>, Sum<AC, BC, CIn>]
: []
: [];
let d1: Add<[0], [1]>
// ^ = let d1: [1]
let d2: Add<[0, 1], [0, 1]>
// ^ = let d2: [1, 0]
let d3: Add<[0, 1, 1, 1], [0, 0, 0, 1]>
// ^ = let d3: [1, 0, 0, 0]
let d4: Add<[1, 1, 1, 1], [0, 0, 0, 1]>
// ^ = let d4: [0, 0, 0, 0]
```

Other binary operations can be implemented using these principles. Will such types be needed in real projects? I don’t think so. But I think these principles will help you create really useful types. Subscribe to me and I will try to tell you more about interesting types of TypeScript.

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