Fix callable interpolation builder symtype

Register CachedInterpolation's symbolic result as a callable Real-to-Real value, derived through public SymbolicUtils APIs. Add a regression that calls the bound interpolator before building and solving the ODEProblem.

Co-Authored-By: Chris Rackauckas <accounts@chrisrackauckas.com>

Author: ChrisRackauckas

src/Blocks/Blocks.jl

@@ -5,6 +5,7 @@ module Blocks
 using ModelingToolkitBase: ModelingToolkitBase, @component, @connector, @named,
     @parameters, @unpack, System, compose, connect, extend,
     getdefault, t_nounits as t, D_nounits as D
+using SymbolicUtils: @syms, symtype
 using Symbolics: Symbolics, @register_symbolic, @variables, Differential, Equation
 import Base: ifelse
 import ..@symcheck

src/Blocks/sources.jl

@@ -864,7 +864,15 @@ end
 
 Base.nameof(::CachedInterpolation) = :CachedInterpolation
 
-@register_symbolic (f::CachedInterpolation)(u::AbstractArray, x::AbstractArray, args::Tuple)
+const _INTERPOLATOR_SYMTYPE = let
+    @syms interpolator(::Real)::Real
+    symtype(interpolator)
+end
+
+# Calling the builder returns the interpolation function, not an interpolated scalar.
+@register_symbolic (f::CachedInterpolation)(
+    u::AbstractArray, x::AbstractArray, args::Tuple
+)::_INTERPOLATOR_SYMTYPE
 
 """
     ParametrizedInterpolation(interp_type, u, x, args...; name, t = ModelingToolkitBase.t_nounits)

test/sources.jl

@@ -14,6 +14,7 @@ using SymbolicIndexingInterface
 using SciMLStructures: SciMLStructures, Tunable
 using ForwardDiff
 using ADTypes
+using SymbolicUtils: symtype
 
 @testset "Constant" begin
     @named src = Constant(k = 2)
@@ -650,6 +651,9 @@ end
 
     @testset "LinearInterpolation" begin
         @named i = ParametrizedInterpolation(LinearInterpolation, u, x)
+        interpolator = only(values(bindings(i)))
+        @test symtype(interpolator(0.0)) === Real
+
         eqs = [i.input.u ~ t, D(y) ~ i.output.u]
 
         @named model = System(eqs, t, systems = [i])