# Resolved: SWI-Prolog: Looking for some predicate which reduces a set in some generator set for some invariant predicate?

## Question:

I am looking some predicate say `generator1_inv` which is able to convert invariant generator parameter `+Inv` (with `Inv(a) = a`) and some list +ListIn of form `[...ai ... Inv(bi)]` into some list `+ListOut` which has distinct members respect to `+Inv` and if `a` and `Inv(b)=a` are members of `+ListIn`, then `Inv(Inv(...(a))` (not `a`) is a member of `+ListOut`, where `Inv` occurs `+Order` times.
Here some examples what `generator1_inv(+ListIn, -ListOut, +Inv, +Order)` should do:
Example 1)
``````?- generator1_inv([k(a), a, k(k(a)), v, b ], ListOut, k, 1)
ListOut = [k(a), v, b]
``````
Example 2)
``````?- generator1_inv([k(a), r(a), a, k(k(a)), v, b ], ListOut, k, 1)
ListOut = [k(a), r(a), v, b
``````
]
Example 3)
``````?- generator1_inv([r(a), a, r(abc), d(a), k(k(a)), v, b ], ListOut, k, 1)
ListOut = [r(a), k(a), r(abc), d(a) v, b]
``````
Example 4)
``````?- generator1_inv([r(a), a, r(abc), d(a), k(k(a)), v, b ], ListOut, k, 0)
ListOut = [r(a), a, r(abc), d(a) v, b]
``````

Found some solution based on this predicate `calc_power`:
``````generator_inv(ListIn, ListOut, Inv, Order) :-
findall(X, ( member(Y, ListIn),
member(Z, ListIn),
not(Y = Z),
calc_power(Y, X , Inv, _),
calc_power(Z, X , Inv, _),
not(calc_power(X, _, Inv, 1))), Roots),
findall(X, (member(Y, Roots),
member(X, ListIn),
calc_power(X, Y , Inv, _)), ListSub),
findall(X, (member(Y, Roots),
calc_power(X, Y , Inv, Order)), List1),
subtract(ListIn, ListSub, ListBase),
union(ListBase, List1, ListOutD),
sort(ListOutD, ListOut).
``````