poissonBracket : Expression(Float) ->  Expression(Float) ->
Expression(Float)
poissonBracket f g == D(f,q) * D(g,p) - D(f,p) * D(g,q)

Just a warning. In SPAD this means

poissonBracket f g is the same as poissonBracket(f(g)).

In this example q and p have type SYMBOL. Does it mean I need
something like a constructor for SYMBOL that would take INT as an
argument? Some kind of function INT ->  SYMBOL.

(1) -> )display op subscript

There is one exposed function called subscript :
   [1] (Symbol,List(OutputForm)) -> Symbol from Symbol

You can easily turn an integer into a proper second argument for that function.

(1) -> subscript(x,[1::OutputForm])

   (1)  x
         1
                                            Type: Symbol

Ralf

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