Variable with two different type-annotations in a function

[jishnub]

julia> using ApproxFunOrthogonalPolynomials

julia> f = Fun((x,y)->x*y, Ultraspherical(1) ⊗ Chebyshev());

julia> @descend_code_warntype ApproxFunBase.standardLowRankFun(f, NormalizedUltraspherical(1), Ultraspherical(1))
standardLowRankFun(f::Function, dx::Space, dy::Space; tolerance, gridx, gridy, maxrank) @ ApproxFunBase ~/Dropbox/JuliaPackages/ApproxFunBase/src/Multivariate/LowRankFun.jl:113
[ Info: This method only fills in default arguments; descend into the body method to see the full source.
113 function standardLowRankFun(f::Fun{TensorSpace{Tuple{Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64}, Chebyshev{ChebyshevInterval{Float64}, Float64}}, DomainSets.FixedIntervalProduct{2, Float64, ChebyshevInterval{Float64}}, Float64}, Float64, Vector{Float64}}::Function, dx::NormalizedUltraspherical{Int64, ChebyshevInterval{Float64}, Float64}::Space, dy::Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64}::Space;
114         tolerance::Union{Symbol,Tuple{Symbol,Number}}=:relative,
115         gridx::Integer=64,
116         gridy::Integer=64,
117         maxrank::Integer=100
118         )::Tuple{Any, Float64}
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 • %1 = #standardLowRankFun#92(::Symbol,::Int64,::Int64,::Int64,::#standardLowRankFun,::Fun{…},::NormalizedPolynomialSpace{…},::Ultraspherical{…})::Tuple{Any, Float64}
   ↩
var"#standardLowRankFun#92"(tolerance::Union{Symbol, Tuple{Symbol, Number}}, gridx::Integer, gridy::Integer, maxrank::Integer, ::typeof(ApproxFunBase.standardLowRankFun), f::Function, dx::Space, dy::Space) @ ApproxFunBase ~/Dropbox/JuliaPackages/ApproxFunBase/src/Multivariate/LowRankFun.jl:113
113 function standardLowRankFun(f::Fun{TensorSpace{Tuple{Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64}, Chebyshev{ChebyshevInterval{Float64}, Float64}}, DomainSets.FixedIntervalProduct{2, Float64, ChebyshevInterval{Float64}}, Float64}, Float64, Vector{Float64}}::Function, dx::NormalizedUltraspherical{Int64, ChebyshevInterval{Float64}, Float64}::Space, dy::Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64}::Space;
114         tolerance::Symbol::Union{Symbol,Tuple{Symbol,Number}}=:relative,
115         gridx::Int64::Integer=64,
116         gridy::Int64::Integer=64,
117         maxrank::Int64::Integer=100
118         )::Tuple{Any, Float64}
119 
120     xy::Vector{StaticArraysCore.SVector{2, Float64}} = checkpoints((dx::NormalizedUltraspherical{Int64, ChebyshevInterval{Float64}, Float64}⊗dy::Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64})::TensorSpace{Tuple{NormalizedUltraspherical{Int64, ChebyshevInterval{Float64}, Float64}, Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64}}, DomainSets.FixedIntervalProduct{2, Float64, ChebyshevInterval{Float64}}, Float64})::Vector{StaticArraysCore.SVector{2, Float64}}
121     T::Core.Const(Float64) = promote_type(eltype(f::Fun{TensorSpace{Tuple{Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64}, Chebyshev{ChebyshevInterval{Float64}, Float64}}, DomainSets.FixedIntervalProduct{2, Float64, ChebyshevInterval{Float64}}, Float64}, Float64, Vector{Float64}}(first(xy::Vector{StaticArraysCore.SVector{2, Float64}})::StaticArraysCore.SVector{2, Float64}...)::Float64)::Type{Float64},prectype(dx::NormalizedUltraspherical{Int64, ChebyshevInterval{Float64}, Float64})::Type{Float64},prectype(dy::Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64})::Type{Float64})::Type{Float64}
122 
123     # We start by sampling on the given grid, find the approximate maximum and create the first rank-one approximation.
124     ptsx::FastTransforms.ChebyshevGrid{1, Float64},ptsy::FastTransforms.ChebyshevGrid{1, Float64}=points(dx::NormalizedUltraspherical{Int64, ChebyshevInterval{Float64}, Float64},gridx::Int64)::FastTransforms.ChebyshevGrid{1, Float64},points(dy::Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64},gridy::Int64)::FastTransforms.ChebyshevGrid{1, Float64}
125     X::Matrix{Float64} = zeros(T::Type{Float64},gridx::Int64,gridy::Int64)::Matrix{Float64}
126     maxabsf::Float64,r::Vector{Float64}=findapproxmax!(f::Fun{TensorSpace{Tuple{Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64}, Chebyshev{ChebyshevInterval{Float64}, Float64}}, DomainSets.FixedIntervalProduct{2, Float64, ChebyshevInterval{Float64}}, Float64}, Float64, Vector{Float64}},X::Matrix{Float64},ptsx::FastTransforms.ChebyshevGrid{1, Float64},ptsy::FastTransforms.ChebyshevGrid{1, Float64},gridx::Int64,gridy::Int64)::Tuple{Vector{Float64}, Int64}::Vector{Float64}
127     if (maxabsf::Float64 < (eps(zero(T::Type{Float64})::Float64)::Float64/eps(T::Type{Float64})::Float64)::Float64)::Bool
128         return LowRankFun::Type{LowRankFun}([Fun::Type{Fun}(dx::NormalizedUltraspherical{Int64, ChebyshevInterval{Float64}, Float64},[zero(T)])::Fun{NormalizedUltraspherical{Int64, ChebyshevInterval{Float64}, Float64}, Float64, Vector{Float64}}]::Vector{Fun{NormalizedUltraspherical{Int64, ChebyshevInterval{Float64}, Float64}, Float64, Vector{Float64}}},[Fun::Type{Fun}(dy::Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64},[zero(T)])::Fun{Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64}, Float64, Vector{Float64}}]::Vector{Fun{Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64}, Float64, Vector{Float64}}})::LowRankFun{NormalizedUltraspherical{Int64, ChebyshevInterval{Float64}, Float64}, Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64}, TensorSpace{Tuple{NormalizedUltraspherical{Int64, ChebyshevInterval{Float64}, Float64}, Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64}}, DomainSets.FixedIntervalProduct{2, Float64, ChebyshevInterval{Float64}}, Float64}, Float64}, maxabsf::Float64::Tuple{LowRankFun{NormalizedUltraspherical{Int64, ChebyshevInterval{Float64}, Float64}, Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64}, TensorSpace{Tuple{NormalizedUltraspherical{Int64, ChebyshevInterval{Float64}, Float64}, Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64}}, DomainSets.FixedIntervalProduct{2, Float64, ChebyshevInterval{Float64}}, Float64}, Float64}, Float64}
129     end
130 
131     a::Fun{NormalizedUltraspherical{Int64, ChebyshevInterval{Float64}, Float64}, Float64, Vector{Float64}},b::Fun{Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64}, Float64, Vector{Float64}}=let r1::Float64=r::Vector{Float64}[1]::Float64, r2::Float64=r::Vector{Float64}[2]::Float64 # avoid boxing r
132         Fun::Type{Fun}(x->f(x,r2),dx::NormalizedUltraspherical{Int64, ChebyshevInterval{Float64}, Float64})::Fun{NormalizedUltraspherical{Int64, ChebyshevInterval{Float64}, Float64}, Float64, Vector{Float64}},Fun::Type{Fun}(y->f(r1,y),dy::Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64})::Fun{Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64}, Float64, Vector{Float64}}::Tuple{Fun{Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64}, Float64, Vector{Float64}}, Int64}
133     ::Fun{Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64}, Float64, Vector{Float64}}end
134 
135     # If necessary, we resize the grid to be at least as large as the
136     # lengths of the first row and column Funs and we recompute the values of X.
137     if (gridx::Int64 < ncoefficients(a::Any)::Int64)::Bool || (gridy::Int64 < ncoefficients(b::Any)::Int64)::Bool
138         gridx::Int64,gridy::Int64 = max(gridx,ncoefficients(a::Any)::Int64)::Int64,max(gridy,ncoefficients(b::Any)::Int64)::Int64
139         ptsx::FastTransforms.ChebyshevGrid{1, Float64},ptsy::FastTransforms.ChebyshevGrid{1, Float64}=points(dx::NormalizedUltraspherical{Int64, ChebyshevInterval{Float64}, Float64},gridx::Int64)::FastTransforms.ChebyshevGrid{1, Float64},points(dy::Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64},gridy::Int64)::FastTransforms.ChebyshevGrid{1, Float64}
140         X::Matrix{Float64} = zeros(T::Type{Float64},gridx::Int64,gridy::Int64)::Matrix{Float64}
141         maxabsf::Float64,r::Vector{Float64}=findapproxmax!(f::Fun{TensorSpace{Tuple{Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64}, Chebyshev{ChebyshevInterval{Float64}, Float64}}, DomainSets.FixedIntervalProduct{2, Float64, ChebyshevInterval{Float64}}, Float64}, Float64, Vector{Float64}},X::Matrix{Float64},ptsx::FastTransforms.ChebyshevGrid{1, Float64},ptsy::FastTransforms.ChebyshevGrid{1, Float64},gridx::Int64,gridy::Int64)::Tuple{Vector{Float64}, Int64}::Vector{Float64}
142         a::Fun{NormalizedUltraspherical{Int64, ChebyshevInterval{Float64}, Float64}, Float64, Vector{Float64}},b::Fun{Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64}, Float64, Vector{Float64}}=let r1::Float64=r::Vector{Float64}[1]::Float64, r2::Float64=r::Vector{Float64}[2]::Float64
143             Fun::Type{Fun}(x->f(x,r2),dx::NormalizedUltraspherical{Int64, ChebyshevInterval{Float64}, Float64})::Fun{NormalizedUltraspherical{Int64, ChebyshevInterval{Float64}, Float64}, Float64, Vector{Float64}},Fun::Type{Fun}(y->f(r1,y),dy::Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64})::Fun{Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64}, Float64, Vector{Float64}}::Tuple{Fun{Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64}, Float64, Vector{Float64}}, Int64}
144         ::Fun{Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64}, Float64, Vector{Float64}}end
145     end
146 
147     A::Vector{Fun{NormalizedUltraspherical{Int64, ChebyshevInterval{Float64}, Float64}, Float64, Vector{Float64}}},B::Vector{Fun{Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64}, Float64, Vector{Float64}}}=typeof(a::Any)::Type{Fun{NormalizedUltraspherical{Int64, ChebyshevInterval{Float64}, Float64}, Float64, Vector{Float64}}}[]::Vector{Fun{NormalizedUltraspherical{Int64, ChebyshevInterval{Float64}, Float64}, Float64, Vector{Float64}}},typeof(b::Any)::Type{Fun{Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64}, Float64, Vector{Float64}}}[]::Vector{Fun{Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64}, Float64, Vector{Float64}}}
148     if (tolerance::Symbol == :relative)::Bool
149         tol::Float64 = (100maxabsf::Float64::Float64*eps(T::Type{Float64})::Float64)::Float64
150     elseif tolerance::Symbol[1] == :absolute
151         tol = 100*tolerance[2]*eps(T)
152     end
153     tol10::Float64 = (tol::Float64/10)::Float64
154     Avals::Vector{Float64},Bvals::Vector{Float64} = zeros(T::Type{Float64},gridx::Int64)::Vector{Float64},zeros(T::Type{Float64},gridy::Int64)::Vector{Float64}
155     p₁::ApproxFunBase.CanonicalTransformPlan{Float64, NormalizedUltraspherical{Int64, ChebyshevInterval{Float64}, Float64}, ApproxFunBase.CanonicalTransformPlan{Float64, Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64}, FastTransforms.ChebyshevTransformPlan{Float64, 1, Vector{Int32}, false, 1, Tuple{Int64}}, Chebyshev{ChebyshevInterval{Float64}, Float64}, false}, Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64}, false},p₂::ApproxFunBase.CanonicalTransformPlan{Float64, Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64}, FastTransforms.ChebyshevTransformPlan{Float64, 1, Vector{Int32}, false, 1, Tuple{Int64}}, Chebyshev{ChebyshevInterval{Float64}, Float64}, false} = plan_transform(dx::NormalizedUltraspherical{Int64, ChebyshevInterval{Float64}, Float64},Avals::Vector{Float64})::ApproxFunBase.CanonicalTransformPlan{Float64, NormalizedUltraspherical{Int64, ChebyshevInterval{Float64}, Float64}, ApproxFunBase.CanonicalTransformPlan{Float64, Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64}, FastTransforms.ChebyshevTransformPlan{Float64, 1, Vector{Int32}, false, 1, Tuple{Int64}}, Chebyshev{ChebyshevInterval{Float64}, Float64}, false}, Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64}, false},plan_transform(dy::Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64},Bvals::Vector{Float64})::ApproxFunBase.CanonicalTransformPlan{Float64, Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64}, FastTransforms.ChebyshevTransformPlan{Float64, 1, Vector{Int32}, false, 1, Tuple{Int64}}, Chebyshev{ChebyshevInterval{Float64}, Float64}, false}
156 
157     # Eat, drink, subtract rank-one, repeat.
158     for k::Int64=(1:maxrank::Int64)::Int64::Union{Nothing, Tuple{Int64, Int64}}
159         if ((norm(a::Any.coefficients::Any,Inf::Float64)::Any < tol::Float64)::Any || (norm(b::Any.coefficients::Any,Inf::Float64)::Any < tol::Float64)::Any)
160             return LowRankFun::Type{LowRankFun}(A::Any,B::Any)::Any,maxabsf::Float64::Tuple{Any, Float64}
161         end
162         A::Any,B::Any =[A;(a/sqrt(abs(a::Any(r::Vector{Float64}[1]::Float64)::Any)::Any)::Any)::Any]::Any,[B;(b/((sqrt(abs(b(r[2]))::Any)::Any*sign(b(r[2]))::Any)::Any))::Any]::Any
163         r::Vector{Float64}=findapproxmax!(A::Any[k::Int64]::Any,B::Any[k::Int64]::Any,X::Matrix{Float64},ptsx::FastTransforms.ChebyshevGrid{1, Float64},ptsy::FastTransforms.ChebyshevGrid{1, Float64},gridx::Int64,gridy::Int64)::Vector{Float64}
164         Ar::Any,Br::Any=evaluate(A::Any,r::Vector{Float64}[1]::Float64)::Any,evaluate(B::Any,r::Vector{Float64}[2]::Float64)::Any
165         for i::Int64=(1:gridx::Int64)::Int64::Union{Nothing, Tuple{Int64, Int64}}
166             @inbounds Avals[i] = f::Fun{TensorSpace{Tuple{Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64}, Chebyshev{ChebyshevInterval{Float64}, Float64}}, DomainSets.FixedIntervalProduct{2, Float64, ChebyshevInterval{Float64}}, Float64}, Float64, Vector{Float64}}(ptsx::FastTransforms.ChebyshevGrid{1, Float64}[i::Int64]::Float64,r::Vector{Float64}[2]::Float64)::Float64
167         end
168         for j::Int64=(1:gridy::Int64)::Int64::Union{Nothing, Tuple{Int64, Int64}}
169             @inbounds Bvals[j] = f::Fun{TensorSpace{Tuple{Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64}, Chebyshev{ChebyshevInterval{Float64}, Float64}}, DomainSets.FixedIntervalProduct{2, Float64, ChebyshevInterval{Float64}}, Float64}, Float64, Vector{Float64}}(r::Vector{Float64}[1]::Float64,ptsy::FastTransforms.ChebyshevGrid{1, Float64}[j::Int64]::Float64)::Float64
170         end
171         a::Any,b::Any = (Fun::Type{Fun}(dx::NormalizedUltraspherical{Int64, ChebyshevInterval{Float64}, Float64},(p₁::ApproxFunBase.CanonicalTransformPlan{Float64, NormalizedUltraspherical{Int64, ChebyshevInterval{Float64}, Float64}, ApproxFunBase.CanonicalTransformPlan{Float64, Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64}, FastTransforms.ChebyshevTransformPlan{Float64, 1, Vector{Int32}, false, 1, Tuple{Int64}}, Chebyshev{ChebyshevInterval{Float64}, Float64}, false}, Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64}, false}*Avals::Vector{Float64})::Vector{Float64})::Fun{NormalizedUltraspherical{Int64, ChebyshevInterval{Float64}, Float64}, Float64, Vector{Float64}} - dotu(Br::Any,A::Any)::Any)::Any,(Fun::Type{Fun}(dy::Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64},(p₂::ApproxFunBase.CanonicalTransformPlan{Float64, Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64}, FastTransforms.ChebyshevTransformPlan{Float64, 1, Vector{Int32}, false, 1, Tuple{Int64}}, Chebyshev{ChebyshevInterval{Float64}, Float64}, false}*Bvals::Vector{Float64})::Vector{Float64})::Fun{Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64}, Float64, Vector{Float64}} - dotu(Ar::Any,B::Any)::Any)::Any
172         chop!(a::Any,tol10::Float64)::Any,chop!(b::Any,tol10::Float64)::Any
173     end
174     @warn "Maximum rank of " * string(maxrank::Int64)::String * " reached"
175     return LowRankFun::Type{LowRankFun}(A::Any,B::Any)::Any,maxabsf::Float64::Tuple{Any, Float64}
176 end
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 • dx::NormalizedUltraspherical{Int64, ChebyshevInterval{Float64}, Float64}⊗dy::Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64}
   checkpoints((dx::NormalizedUltraspherical{Int64, ChebyshevInterval{Float64}, Float64}⊗dy::Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64})::TensorSpace{Tuple{NormalizedUlt…
   first(xy::Vector{StaticArraysCore.SVector{2, Float64}})
   f::Fun{TensorSpace{Tuple{Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64}, Chebyshev{ChebyshevInterval{Float64}, Float64}}, DomainSets.FixedIntervalProduct{2, Float64, Cheb…
   eltype(f::Fun{TensorSpace{Tuple{Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64}, Chebyshev{ChebyshevInterval{Float64}, Float64}}, DomainSets.FixedIntervalProduct{2, Float6…
   prectype(dx::NormalizedUltraspherical{Int64, ChebyshevInterval{Float64}, Float64})
   prectype(dy::Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64})
   promote_type(eltype(f::Fun{TensorSpace{Tuple{Ultraspherical{Int64, ChebyshevInterval{Float64}, Float64}, Chebyshev{ChebyshevInterval{Float64}, Float64}}, DomainSets.FixedIntervalProd…
   points(dx,gridx)
v  points(dy,gridy)

On line 131, the variables a and b are annotated with concrete types, but from line 137 onwards, a and b are annotated with Any. It's unclear which one represents the actual inferred type. However, the function call ncoefficients(a::Any) on line 137 is annotated with Int64, so perhaps the type of a isn't inferred to be Any?

Looking into the typed code, I find

│    %74  = Base.indexed_iterate(%73, 1)::Core.PartialStruct(Tuple{Fun{NormalizedUltraspherical{Int64, ChebyshevInterval{Float64}, Float64}, Float64, Vector{Float64}}, Int64}, Any[Fun{NormalizedUltraspherical{Int64, ChebyshevInterval{Float64}, Float64}, Float64, Vector{Float64}}, Core.Const(2)])
│           (a = Core.getfield(%74, 1))

and this call seems to be inferred concretely, but overall the variable is inferred to be of type Any. I guess the concrete type arises from the call, and is not the inferred type of the variable being assigned to?

This is using ApproxFunBase v0.9.7 and ApproxFunOrthogonalPolynomials v0.6.44.