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type Id = <A>(a: A) => A



const id: Id = (a: number) => a;

If I use generics in this way the compiler will return an error saying

Type '(a: number) => number' is not assignable to type 'Id'.

  Types of parameters 'a' and 'a' are incompatible.

    Type 'A' is not assignable to type 'number'.

I know it can be solved with
type Id<A> = (a: A) => A
But what if I can't declare A at every point. Is there a way to just have it flow through, or be inferred?

I think what you're experiencing is the difference between these two type definitions.

type Func1<A> = (a: A) =>  A;



type Func2 = <A>(a: A) =>  A;

Any function of type Func1<A> must specify its type at the time it is defined.

const func1: Func1<number> = (a: number): number => a;



func1(10); // works

func1("x"); // fails - we already decided it is of type `number`

Anything of type Func2 must not specify its type until it is called.

const func2: Func2 = <X>(a: X): X => a;



func2(10); // works

func2("x"); // works

Here is a playground link that illustrates.

The problem you were experiencing happened because you tried to specify the type of the function when you defined it instead of when you called it.