Rename variablewise functions

[mlubin]

The name "variablewise function" is a holdover from variablewise constraint, which made a bit more sense.
To replace ScalarVariablewiseFunction and VectorVariablewiseFunction, what about ScalarComponentProjection and VectorComponentProjection?

Let the bikeshedding begin. @blegat @joehuchette @chriscoey @odow @joaquimg @IssamT

Thanks to @edljk for pointing this out.

[IssamT]

or ScalarIdentityFunction and VectorIdentityFunction ?

[mlubin]

The issue is that these are not identity functions by any usual definition of identity, except when all variables appear in the map. They are coordinate-wise projections by any usual definition.

[blegat]

Maybe ScalarProjectionFunction and VectorProjectionFunction to keep the Function suffix ?

[mlubin]

A projection is a function, so projection function is a bit redundant. Not all sets end with Set.

[mlubin]

We could say ScalarProjection and VectorProjection to keep it shorter.

[mlubin]

Although in the future I can imagine someone wanting to add other kinds of projections.

[odow]

What's wrong with Variablewise?

I'd almost prefer

ScalarFunction(Variable, args... )
ScalarFunction(Affine, args... )
ScalarFunction(Quadratic, args... )

addconstraint!(m, ScalarFunction(Affine, x, [1.0,1.0], 0.0), LessThan(5.0))

or

VectorFunction{Variable}(args... )
VectorFunction{Affine}(args... )
VectorFunction{Quadratic}(args... )

or just ScalarFunction and VectorFunction and the type is inferred from the number of arguments.

[mlubin]

What's wrong with Variablewise?

Affine and quadratic functions are well-defined and widely used concepts. Variablewise is not. Why not just use the mathematically correct and clear name for the function?

It could be useful to formalize the scalar/vector concept (as @blegat attempted to do in #44) since it seems like we've converged to definitions of sets that are exclusively scalar or vector sets. What are the Variable, Affine, and Quadratic objects though? Wouldn't it be confusing to have a type called Variable which is just a placeholder for dispatch and not an actual variable?

or just ScalarFunction and VectorFunction and the type is inferred from the number of arguments.

That's not extensible, so I'd downvote that.

[mlubin]

Another idea: SingleVariable and VectorOfVariables.
These seem more self-explanatory than ScalarVariablewiseFunction and VectorVariablewiseFunction. The description "single" is meant to evoke the idea that you're extracting one variable out of all of the variables in the model:

addconstraint!(m, SingleVariable(x[1]), LessThan(10.0))
addconstraint!(m, VectorOfVariables(x[1:5]), AllDifferent(5)) # thinking ahead...

It wouldn't be too crazy to have a fallback like:

addconstraint!(m, v::VariableReference, s) = addconstraint!(m, SingleVariable(v), s)
addconstraint!(m, v::Vector{VariableReference}, s) = addconstraint!(m, VectorOfVariables(v), s)

but that's a mostly separate discussion.

[joaquimg]

This is my favorite among all the other suggestions.
And I liked the fallback

[blegat]

I am ok with either ScalarProjection/VectorProjection or SingleVariable/VectorOfVariable and I upvote the callback :)