Parsing systems defined by ModelingToolkit

[mforets]

We can already define some lazy sets using ModelingToolkit types. The next step would be to allow creating systems and the natural place is to do it in this library. Ideally @system should create an "appropriate" system, eg. below, a linear system without inputs.

For instance,

@parameters t
@variables x(t) y(t)
@derivatives D'~t

f = [D(x) ~ y, D(y) ~ -x]
2-element Array{Equation,1}:
 Equation(derivative(x(t), t), y(t))
 Equation(derivative(y(t), t), -(x(t)))

G = HalfSpace(x >= 1.25, [x, y]) # works
HalfSpace{Float64,Array{Float64,1}}([-1.0, 0.0], -1.25)

@ivp(x' = f(x), x(0) ∈ X0) # to-do
ArgumentError: for a blackbox system, the dimension has to be defined

Stacktrace:
 [1] top-level scope at In[72]: