test return types for frule and rrule

[CarloLucibello]

See JuliaDiff/ChainRules.jl#233 and reference therein for possible issues when unexpected casts happen

[nickrobinson251]

it'd be good to add a little more detail here :) For example, does this in anyway require JuliaDiff/FiniteDifferences.jl#97, @willtebbutt ?

[willtebbutt]

For example, does this in anyway require JuliaDiff/FiniteDifferences.jl#97

Hmm this seems like a separate issue from checking the numerical correctness of the gradients. Rather, this would require some functionality to say whether a particular "differential" is valid for a particular primal.

I don't think we'll be able to do this with 100% accuracy, but we should be able to catch it in a lot of cases. So you could imagine this taking the form of a passing default implementation, with methods implemented to catch specific cases that we know / care about - e.g. to check for the casting behaviour that @CarloLucibello pointed out / not representing the differential of a Float64 with a ComplexF64 or whatever.

This relates to conversations like:

• RFC: Rules for real-to-complex and complex-to-real functions ChainRulesCore.jl#176
• Type Constraints ChainRules.jl#232

(232 probably being the main conversation around this now)

[nickrobinson251]

also JuliaDiff/ChainRulesCore.jl#106