Primitive combination

An additional operation on PRFs is a combination of functions, denoted f ⨯ g.

Both f and g take the same k-tuple of args, but each can return a different m-tuple where 0 <= m <= k. The returned tuples are concatenated together, forming a single m+n-tuple, provided f returns an m-tuple and g returns a n-tuple.

That is, in the returned m+n-tuple, the first m elements come form the f's applications to the arg-list, and the following n elements come from the g's applications to the (same input) arg-list.

f :: (ℕ ⨯ ℕ ⨯ ℕ) -> (ℕ ⨯ ℕ) f : ℕ³ -> ℕ¹ g :: (ℕ ⨯ ℕ ⨯ ℕ) -> (ℕ ⨯ ℕ ⨯ ℕ) g : ℕ³ -> ℕ³

f ⨯ g (x, y, z) = (f x, f y, g x, g y, g z)

fᵏ ⨯ gᵏ (x₁ … xₖ)

Combination operation is similar to composition, if was somehow defined without the rightmost f function.