Error handling for repeated variable names

[mforets]

From discussion on gitter, consider this PR in place of #155.

[schillic]

I accept but I do not think this is a good solution.

[ueliwechsler]

After thinking everything through more again more carefully, I think you are right.

In order for me to understand what is going on, I like to write everything I know down
(sorry for the long comment)

As far as i know, this PR should give reasonable error messages for cases where
a specified input or noise is added which does collide with another

A = B = D = rand(2,2)
@system(a⁺= Aa + Bw, input:a)
ERROR: ArgumentError: state and input variables have the same name `a`
# instead of the old error message
ERROR: ArgumentError: the entry (:A, :D) does not match a `MathematicalSystems.jl` structure
@system(x⁺= Ax + Bx, input:x)
ERROR: ArgumentError: state and input variables have the same name `x`
@system(x⁺= Ax + Bu + Bw, input:u, noise:u)
ERROR: ArgumentError: input and noise variables have the same name `u`

without throwing exceptions where the input is "overwritten" with the noise variable
(and the noise not defined) or vice versa where the input is overwritten

# we can use 
@system(x⁺= Ax + Bw, input:w) #creates a LinearControlDiscreteSystem system
system(x⁺= Ax + Bu, noise:u) # 
# instead of 
@system(x⁺= Ax + Bw, input:w, noisestr:evry_but_w)

in the @system(x⁺= Ax + Bw, input:w), the input and the noise variable are both :w but
since we do not "use" the noise variable we accept that "inconsistency" for shortness of the
macro.

However, this cases are not covered so far in this PR (but we also should add it)

@system(x⁺= Ax + Bw + Dw, input:w)
@system(x⁺= Ax + Bu + Bu,  noise:u)
@system(x⁺= Ax + Bx)
@system(x⁺= Ax + c + c)
# etc

which gives a non-sensical error messsage. (for which my aforementioned fix
should help).

Hoooowever, going through this logic it should also give the right error for

@system(x⁺= Ax + Bu + Bw,  noise:u)
ERROR: ArgumentError: the entry (:A, :B, :c) does not match a `MathematicalSystems.jl` structure
@system(x⁺= Ax + Bu + Bw,  input:w)
ERROR: ArgumentError: the entry (:A, :c, :B) does not match a `MathematicalSystems.jl` structure

which it does not, and also will not get caught by my solutions.

Sooo, too sum up, I am bit confused. I think we could do it better, you are right,
but I am not sure how. Maybe throwing the error at a later stage, where we no the
exact system types and all the variables.

EDIT: noo, it does not work to make the test later, because we will infer the wrong system types 🙈🤷‍♂️

[mforets]

Maybe throwing the error at a later stage, where we no the
exact system types and all the variables.

Yes, that is what i thought (but i haven't tried it).

👍 i moved your comment to the follow up issue, #181

[ueliwechsler]

Thanks! But we still have to catch the error from @system(x⁺= Ax + Bu + Bw, noise:u) and @system(x⁺= Ax + Bu + Bw, input:w) I think this one could be caught after here after this line

MathematicalSystems.jl/src/macros.jl

Line 807 in a1d94d6

sys_type = _corresponding_type(AT, field_names)

... it is getting quite ugly if we have 3 separate places for tests.