Fix dependence checking in differentiation

Author: HarrisonGrodin

src/differentials.jl

@@ -10,8 +10,8 @@ Base.Expr(D::Differential) = :($(Symbol("D_$(D.x.name)_$(D.order)")))
 function Derivative end
 (D::Differential)(x::Operation) = Operation(Derivative,Expression[x,D])
 function (D::Differential)(x::Variable)
-    D.x === x          && return Constant(1)
-    D.x ∉ x.dependents && return Constant(0)  # FIXME
+    D.x === x             && return Constant(1)
+    has_dependent(x, D.x) || return Constant(0)
     return Variable(x,D)
 end
 Base.:(==)(D1::Differential, D2::Differential) = D1.order == D2.order && D1.x == D2.x

src/utils.jl

@@ -18,3 +18,7 @@ function flatten_expr!(x)
 end
 
 toexpr(ex) = MacroTools.postwalk(x->x isa Union{Expression,Operation} ? Expr(x) : x, ex)
+
+has_dependent(t::Variable) = Base.Fix2(has_dependent, t)
+has_dependent(x::Variable, t::Variable) =
+    t ∈ x.dependents || any(has_dependent(t), x.dependents)

test/derivatives.jl

@@ -41,3 +41,7 @@ jac = ModelingToolkit.calculate_jacobian(sys)
 @test jac[3,1] == y
 @test jac[3,2] == x
 @test jac[3,3] == -1*β
+
+# Variable dependence checking in differentiation
+@Var a(t) b(a)
+@test D(b) ≠ Constant(0)