Adding generic parameter to a lambda function removes typing from the function argument

TypeScript Version: 3.2.2

Search Terms: generic removes parameter type

Code

// OKAY
// declare const labmda function with typings, then implement with minimal type annotations.
// "input" has type of "string".
export const foo: (input: string) => string
    = (input) => (input);

// OKAY
// declare const lambda generic function without typings, then implement with full inline type annotations.
// "input" has type of "string".
export const bar
    = <TResult>(input: string) => ({ } as Partial<TResult>);

// ERROR
// declare const labmda generic function with typings, then implement with minimal type annotations.
// "input" has type of "any".
export const baz: <TResult>(input: string) => Partial<TResult>
    = <TResult>(input) => ({ [input]: input } as Partial<TResult>);

Expected behavior:
input is typed as string.

Actual behavior:
input is typed as any.

Playground Link: https://www.typescriptlang.org/play/index.html#src=%2F%2F%20OKAY%0D%0A%2F%2F%20declare%20const%20labmda%20function%20with%20typings%2C%20then%20implement%20with%20minimal%20type%20annotations.%0D%0A%2F%2F%20%22input%22%20has%20type%20of%20%22string%22.%0D%0Aexport%20const%20foo%3A%20(input%3A%20string)%20%3D%3E%20string%0D%0A%20%20%20%20%3D%20(input)%20%3D%3E%20(input)%3B%0D%0A%0D%0A%2F%2F%20OKAY%0D%0A%2F%2F%20declare%20const%20lambda%20generic%20function%20without%20typings%2C%20then%20implement%20with%20full%20inline%20type%20annotations.%0D%0A%2F%2F%20%22input%22%20has%20type%20of%20%22string%22.%0D%0Aexport%20const%20bar%0D%0A%20%20%20%20%3D%20%3CTResult%3E(input%3A%20string)%20%3D%3E%20(%7B%20%7D%20as%20Partial%3CTResult%3E)%3B%0D%0A%0D%0A%2F%2F%20ERROR%0D%0A%2F%2F%20declare%20const%20labmda%20generic%20function%20with%20typings%2C%20then%20implement%20with%20minimal%20type%20annotations.%0D%0A%2F%2F%20%22input%22%20has%20type%20of%20%22any%22.%0D%0Aexport%20const%20baz%3A%20%3CTResult%3E(input%3A%20string)%20%3D%3E%20Partial%3CTResult%3E%0D%0A%20%20%20%20%3D%20%3CTResult%3E(input)%20%3D%3E%20(%7B%20%5Binput%5D%3A%20input%20%7D%20as%20Partial%3CTResult%3E)%3B

(NOTE: options -> noImplicitAny to have the issue highlighted as an error.)

Related Issues:

https://github.com/Microsoft/TypeScript/issues/18606
I think this issue might be related, but I don't understand it enough to judge.
If this is the same issue then the answer is "this is correct, and a limitation of the type system", which is fair enough.

Start by reproducing the example in the linked TypeScript Playground with noImplicitAny enabled, then compare the three lambda declarations and the related issue #18606. Trace how contextual typing is applied to the generic lambda assignment. Done means determining whether the argument should be inferred as string and adding a regression test if the behavior is confirmed as a bug.