Add structural zero tangent code for higher order

Author: oxinabox

src/tangent_types/abstract_zero.jl

@@ -113,8 +113,15 @@ zero_tangent(x::Number) = zero(x)
 
 zero_tangent(::Type) = NoTangent()
 
-zero_tangent(x::Tangent) = ZeroTangent()
-# TODO: zero_tangent(x::MutableTangent)
+function zero_tangent(x::MutableTangent{P}) where P
+    zb = backing(zero_tangent(backing(x)))
+    return MutableTangent{P}(zb)
+end
+
+function zero_tangent(x::Tangent{P}) where P
+    zb = backing(zero_tangent(backing(x)))
+    return Tangent{P, typeof(zb)}(zb)
+end
 
 @generated function zero_tangent(primal)
     fieldcount(primal) == 0 && return NoTangent()  # no tangent space at all, no need for structural zero.

test/tangent_types/abstract_zero.jl

@@ -182,6 +182,14 @@ end
         @test zero_tangent([[1.0, 2.0], [3.0]]) == [[0.0, 0.0], [0.0]]
 
         @test zero_tangent((1.0, 2.0)) == Tangent{Tuple{Float64,Float64}}(0.0, 0.0)
+
+        # Higher order
+        # StructuralTangents are valid tangents for themselves (just like Numbers)
+        # and indeed we prefer that, otherwise higher order structural tangents are kinda
+        # nightmarishly complex types.
+        @test zero_tangent(zero_tangent(Demo(1.5))) == zero_tangent(Demo(1.5))
+        @test zero_tangent(zero_tangent((1.5, 2.5))) == Tangent{Tuple{Float64, Float64}}(0.0, 0.0)
+        @test zero_tangent(zero_tangent(MutDemo(1.5))) == zero_tangent(MutDemo(1.5))
     end
 
     @testset "Weird types" begin