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Troubleshooting TypeScript Function with Schema Type Constraints

hello there!
I'm trying to create a function that takes a generic schema in parameter and the passed schema should have a Type of a given shape:

const func = <T extends { id: string }>(schema: S.Schema<T>) => schema;

const func = <T extends { id: string }>(schema: S.Schema<T>) => schema;

const func = <T extends { id: string }>(schema: S.Schema<T>) => schema;

const func = <T extends { id: string }>(schema: S.Schema<T>) => schema;

I can call this func with

S.struct({ id: S.string })

S.struct({ id: S.string })

S.struct({ id: S.string })

S.struct({ id: S.string }) without problem, as expected:

const res = func(S.struct({ id: S.string })); // compile

const res = func(S.struct({ id: S.string })); // compile

const res = func(S.struct({ id: S.string })); // compile

const res = func(S.struct({ id: S.string })); // compile

But if the given schema has a branded string for the Id, then it does not compile:

const res2 = func(S.struct({ id: S.string.pipe(S.brand('Id')) })); // does not compile

const res2 = func(S.struct({ id: S.string.pipe(S.brand('Id')) })); // does not compile

const res2 = func(S.struct({ id: S.string.pipe(S.brand('Id')) })); // does not compile

const res2 = func(S.struct({ id: S.string.pipe(S.brand('Id')) })); // does not compile

The last line of the ts error is the following:

Type '{ readonly id: string; }' is not assignable to type '{ readonly id: string & Brand<"Id">; }'.

Type '{ readonly id: string; }' is not assignable to type '{ readonly id: string & Brand<"Id">; }'.

Type '{ readonly id: string; }' is not assignable to type '{ readonly id: string & Brand<"Id">; }'.

Type '{ readonly id: string; }' is not assignable to type '{ readonly id: string & Brand<"Id">; }'.

I was expecting that it would work since a string branded type extends string..