Mapped types with type parameter are not assignable to `{ [key: string]: any}`

[wonderful-panda]

TypeScript Version: 2.1.4 and nightly(2.2.0-dev.20161213)

Code

interface Base {
   foo: { [key: string]: any };
   bar: any;
   baz: any;
}

interface E1<T> extends Base {
  foo: T;
}

interface Something { name: string, value: string };
interface E2 extends Base {
  foo: Partial<Something>;  // or other mapped type
}

interface E3<T> extends Base {
  foo: Partial<T>; // or other mapped type
}

Expected behavior:
Successfully compiled.

Actual behavior:
E1 and E2 are OK, but E3 causes compile error.

error TS2430: Interface 'E3<T>' incorrectly extends interface 'Base'.
Types of property 'foo' are incompatible.
Type 'Partial<T>' is not assignable to type '{ [key: string]: any; }'.

[DanielRosenwasser]

In some sense, I feel like all three should cause a compiler error since none none of the subtypes redefines a foo with an index signature.

[RyanCavanaugh]

An index signature returning any is special, though. Assignability to { [k: string]: any } is supposed to be guaranteed, I believe.