mathematical unary operator: map notation

Input is unary: a function f; the output is an ordered tuple: (the domain set of f, the codomain set of f, the image of f, the mapping rule of f (defined with a dummy variable which is taken to belong to the the domain set of f), the graph/plot (set of input-output pairs) of f). Might be useful for lambda calculus, etc. Equip the output with ma'o in order to use as a/the function. Extract a term in the tuple in order to use it directly.