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[Docs] [AutoDiff] Fix incorrectly rendered table and dead link. #28721

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Dec 12, 2019
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[Docs] [AutoDiff] Fix incorrectly rendered table and dead link. #28721

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13 changes: 6 additions & 7 deletions docs/DifferentiableProgramming.md
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Expand Up @@ -2016,10 +2016,11 @@ differentiating either one will provide derivatives with respect to parameters
`T` and `U`. Here are some examples of first-order function types and their
corresponding curried function types:

| First-order function type | Curried function type |
| @differentiable (T, U) -> V | @differentiable (T) -> @differentiable (U) -> V |
| @differentiable (T, @noDerivative U) -> V | @differentiable (T) -> (U) -> V |
| @differentiable (@noDerivative T, U) -> V | (T) -> @differentiable (U) -> V |
| First-order function type | Curried function type |
|---------------------------------------------|---------------------------------------------------|
| `@differentiable (T, U) -> V` | `@differentiable (T) -> @differentiable (U) -> V` |
| `@differentiable (T, @noDerivative U) -> V` | `@differentiable (T) -> (U) -> V` |
| `@differentiable (@noDerivative T, U) -> V` | `(T) -> @differentiable (U) -> V` |

A curried differentiable function can be formed like any curried
non-differentiable function in Swift.
Expand Down Expand Up @@ -2540,9 +2541,7 @@ func valueWithDifferential<T: FloatingPoint, U: Differentiable>(

To differentiate `valueWithDifferential`, we need to be able to differentiate
its return value, a tuple of the original value and the differential, with
respect to its `x` argument. Since the return type contains a function,
[differentiation of higher-order functions](#differentiation-of-higher-order-functions)
is required for differentiating this differential operator.
respect to its `x` argument.

A kneejerk solution is to differentiate derivative functions generated by the
differentiation transform at compile-time, but this leads to problems. For
Expand Down