[AutoDiff] Improve @derivative attribute diagnostics.

[dan-zheng]

Previously, @derivative attribute type-checking produced a confusing error
referencing unbound types T and U:

'@derivative(of:)' attribute requires function to return a two-element tuple of
type '(value: T..., pullback: (U.TangentVector) -> T.TangentVector...)' or
'(value: T..., differential: (T.TangentVector...) -> U.TangentVector)'

Now, the error is less confusing:

'@derivative(of:)' attribute requires function to return a two-element tuple;
first element must have label 'value:' and second element must have label
'pullback:' or 'differential:'

---

Attempt to look up original function before checking whether the value: result
conforms to Differentiable.

This improves diagnostics: "original function not found" should be diagnosed as
early as possible.

---

Add utility for checking whether differentiable programming is enabled.

[dan-zheng]

Note: derivative_attr_expected_result_tuple (1) is somewhat duplicated by derivative_attr_invalid_result_tuple_value_label (2) and derivative_attr_invalid_result_tuple_func_label (3).

(1) is produced when the @derivative function type doesn't return a two-element tuple. (2) and (3) are produced when the returned two-element tuple's labels are incorrect.

Unless someone has suggestions, I'm content to leave (2) and (3) as is, since they're more specific than (1).

[rxwei]

Why's "conform to Differentiable" special here in a derivative function? Would it be better to just emit a diagnostic that suggests the expected derivative type?

[dan-zheng]

Would it be better to just emit a diagnostic that suggests the expected derivative type?

That would be ideal. However, for @derivative attribute type-checking, the "expected derivative type" is not known - we start with the type of the @derivative declaration and try to compute the appropriate original function type.

[rxwei]

Okay, but I feel the "must conform to Differentiable" error message is making it worse because it seems to suggest that derivative function's value: result is somehow special with regards to Differentiable conformance, while it's in fact simply the same as the original function's result. Just my two cents. I think a better diagnostic could be:

'value:' element type %0 must be the same as the result of the original function being differentiated

[dan-zheng]

I understand your point. I pushed some further diagnostics improvements along this direction.

Now, original function lookup occurs before the "does first element type conform to Differentiable?" check. In effect, this delays "find Differentiable conformance for value: result" as late as possible, so original function lookup diagnostics trigger first.

---

Example:

import _Differentiation
@derivative(of: nonexistentFunction)
func derivative(_ x: Float) -> (value: Int, pullback: (Float) -> Float) {
  fatalError()
}

Before: unideal diagnostic about value: result.

derivative.swift:2:2: error: '@derivative(of:)' attribute requires function to return a two-element tuple (first element type 'Int' must conform to 'Differentiable')
@derivative(of: nonexistentFunction)
 ^

After: ideal diagnostic about original function not found.

derivative.swift:2:17: error: use of unresolved identifier 'nonexistentFunction'
@derivative(of: nonexistentFunction)
                ^

Example:

import _Differentiation

func original(_ x: Int) -> Int { x }

@derivative(of: original)
func vjpOriginalFunctionNotFound2(_ x: Float) -> (value: Int, pullback: (Float) -> Float) {
  fatalError()
}

Before: unideal diagnostic about value: result.

derivative2.swift:5:2: error: '@derivative(of:)' attribute requires function to return a two-element tuple (first element type 'Int' must conform to 'Differentiable')
@derivative(of: original)
 ^

After: ideal diagnostic about original function not found.

derivative2.swift:5:17: error: could not find function 'original' with expected type '(Float) -> Int'
@derivative(of: original)
                ^

---

Let me know if these changes make sense, and if you'd like further changes! I'd like to defer major diagnostic changes until later to unblock progress.

[rxwei]

This is very nice!

[dan-zheng]

Edit: oops, accidentally triggered CI before seeing feedback above.
@swift-ci Please smoke test

[dan-zheng]

@swift-ci Please smoke test and merge