Best formalism to define the interface

When we define the new API, there will be abstract types with some methods that must be implemented. In base Julia, I see two main ways of specifying this (as in, defining the function name, possibly with a generic docstring):

julia> function myfunc1 end
myfunc1 (generic function with 0 methods)

julia> myfunc2(args...) = error("Not implemented")
myfunc2 (generic function with 1 method)

julia> myfunc1(1)
ERROR: MethodError: no method matching myfunc1(::Int64)
Stacktrace:
 [1] top-level scope
   @ REPL[4]:1

julia> myfunc2(1)
ERROR: Not implemented
Stacktrace:
 [1] error(s::String)
   @ Base ./error.jl:35
 [2] myfunc2(args::Int64)
   @ Main ./REPL[2]:1
 [3] top-level scope
   @ REPL[5]:1

I believe a methodless function is better than a single method throwing an error by default. The end result is nearly the same in terms of user experience, but I find the first error clearer because it directly tells you what to implement. @simonschoelly what do you think?

Of course we could also consider more advanced options like Interfaces.jl or InterfaceSpecs.jl but maybe it's a bit overkill?

See also: https://github.com/JuliaGraphs/Graphs.jl/pull/262

Start by reviewing the proposed interface choices in this issue and the referenced Graphs.jl pull request #262. Compare the methodless-function and default-error approaches, along with the linked Interfaces.jl and InterfaceSpecs.jl options. Done means the maintainers agree on and document the formalism for the new API.