ISet

Alias for member

Alias for Foldable[ISet].index

The Functor composition law only holds for functions that preserve equivalence, i.e. for functions f such that

• ∀ a1, a2 ∈ A
• Order[A].equal(a1, a2) ⇒ Order[B].equal(f(a1), f(a2))

In the case when the equivalence implied by Order[A] is in fact equality, i.e. the finest equivalence, i.e. satisfying the substitution property (which is the above property quantified over all f, see Wikipedia page on Equality), the requirement holds for all f by definition.

When Order instances are viewed as "mere" equivalences (as opposed to equalities), we can loosely say that ISet is an (endo-)functor in the category Equiv of sets with an equivalence relation (where the morphishms are equivalence-preserving functions, i.e. exactly the functions satisfying the above requirement). By contrast, Functor instances are functors in the Scala category, whose morphisms are arbitrary functions, including the ones that don't preserve equivalence.

'''Note:''' this is not able to implement Functor due to the Order constraint on the destination type, however it still is a functor in the mathematical sense.

Documentation as copied from the Haskell source:

    -- | /O(n*log n)/.
    -- @'map' f s@ is the set obtained by applying @f@ to each element of @s@.
    --
    -- It's worth noting that the size of the result may be smaller if,
    -- for some @(x,y)@, @x \/= y && f x == f y@