What are mapped types?

Question presented to candidate: "What is a mapped type in TypeScript? Show me how you would write Partial or Readonly yourself, and tell me what else mapped types can do."

What a strong answer should cover:

• Syntax { [K in Keys]: Type }: a type-level loop over a union of keys that produces one property per key, usually [K in keyof T]: T[K]
• Changing value types (T[K] | null, functions per property) and the modifiers: adding ? / readonly, removing them with -? / -readonly (the +/- syntax arrived in TypeScript 2.8)
• That Partial, Required, Readonly, Record and Pick are mapped types in the standard library
• Homomorphic mapped types (in keyof T, or K extends keyof T) copy the original modifiers, work element-wise on arrays and tuples, and distribute over unions; mapping over an unrelated key union does not keep modifiers
• Mapped types are compile-time only: building the matching run-time object still needs a loop (and usually one cast); readonly is not enforced at run time
• Key remapping with as exists for renaming or filtering keys (its own topic)

Code / implementation expected: Yes — implement Partial, Readonly or a Mutable helper with a mapped type.