Parent-Task:

• SR-13166 Default derivative implementations for protocol requirements

Issue Description:

Resilient protocol default implementations are encoded in SIL default witness tables: https://github.com/apple/swift/blob/master/docs/SIL.rst#default-witness-tables.

Derivatives registered for protocol requirements should be lowered to entries in SIL default witness tables. SILDeclRef already has support for derivative functions (via SILDeclRef::derivativeFunctionIdentifier).

protocol P {
  static func +(lhs: Self, rhs: Self) -> Self
}

extension P where Self: Differentiable {
  @derivative(of: add)
  static func vjpAdd(lhs: Self, rhs: Self) -> (value: Self, pullback: (TangentVector) -> (TangentVector, TangentVector)) {
    return (lhs + rhs, { v in (v, v) }
  }
}

The default derivative P.vjpAdd should appear in a default witness table for P.

You can start implementing this by:

• Finding existing SILGen logic for generating default witness tables. Add logic that finds derivatives registered for protocol requirements (@derivative) and emits default witness table entries for those derivatives.

• You can test generated default witness tables via swiftc -emit-silgen.