NLP parser assumes `::Model` and violates MethodError principle

[odow]

_process_NL_expr gets called from the @NL macros, and doesn't have any type requirements:

JuMP.jl/src/parse_nlp.jl

Line 233 in 1e6b5d8

function _process_NL_expr(model, ex)

but it eventually calls a _process_NL_expr_runtime which are restricted to ::Model.

JuMP.jl/src/parse_nlp.jl

Line 181 in 1e6b5d8

function _parse_NL_expr_runtime(m::Model, x::Real, tape, parent, values)

Thus, someone (e.g., BilevelJuMP, x-ref: joaquimg/BilevelJuMP.jl#57) using this machinery with an <:AbstractModel encounters a MethodError:
https://discourse.julialang.org/t/methoderror-no-method-matching-parse-nl-expr-runtime-bilevel-problem/51681

We could either add a type-restriction to _process_NL_expr and have a fallback with an informative error message, or we could probably relax the type-restrictions, and see what happens. It probably means relaxing this as well to AbstractVariableRef:

JuMP.jl/src/parse_nlp.jl

Lines 187 to 188 in 1e6b5d8

	function _parse_NL_expr_runtime(m::Model, x::VariableRef, tape, parent, values)
	if owner_model(x) !== m

cc @pulsipher who might be messing with this stuff

[pulsipher]

This has indeed come up with InfiniteOpt.jl as I've looked into how to enable NLP expressions (see infiniteopt/InfiniteOpt.jl#16). At one point, I did make a version of _parse_NL_expr_runtime that could work with InfiniteModels and my variable types, however I ran into a number of other problems further down the NLP pipeline.

Thus, I came to the conclusion that the JuMP NLP interface in its current form is essentially non-extendable for use with AbstractModels and AbstractVariableRefs without a significant rewrite such as what is proposed in jump-dev/MathOptInterface.jl#846. Since this is a long way out, I am actually looking into developing a native NLP expression tree abstraction to InfiniteOpt.jl to enable NLP expressions/constraints.

For what it is worth, my recommendation here would be to add a meaningful fallback method and reserve any additional effort for use toward jump-dev/MathOptInterface.jl#846 once the time comes to work on it.