Control.IndexT.Tuple

Type family and class definitions for dealing with tuples.

See the Control.IndexT module description for an overview.

Documentation

type family TupleN (n :: Nat) a

TupleN seems a bit weird, but it's an important part of defining constraints that allow one to say "t is a pair" in TupleConstraint.

Instances

type TupleN 0 a

type TupleN 0 a = ()

type TupleN 1 a

type TupleN 1 a = Identity a

type TupleN 2 a

type TupleN 2 a = (IndexT 0 a, IndexT 1 a)

type TupleN 3 a

type TupleN 3 a = (IndexT 0 a, IndexT 1 a, IndexT 2 a)

type TupleN 4 a

type TupleN 4 a = (IndexT 0 a, IndexT 1 a, IndexT 2 a, IndexT 3 a)

type TupleN 5 a

type TupleN 5 a = (IndexT 0 a, IndexT 1 a, IndexT 2 a, IndexT 3 a, IndexT 4 a)

type TupleN 6 a

type TupleN 6 a = (IndexT 0 a, IndexT 1 a, IndexT 2 a, IndexT 3 a, IndexT 4 a, IndexT 5 a)

type TupleN 7 a

type TupleN 7 a = (IndexT 0 a, IndexT 1 a, IndexT 2 a, IndexT 3 a, IndexT 4 a, IndexT 5 a, IndexT 6 a)

type TupleN 8 a

type TupleN 8 a = (IndexT 0 a, IndexT 1 a, IndexT 2 a, IndexT 3 a, IndexT 4 a, IndexT 5 a, IndexT 6 a, IndexT 7 a)

type TupleN 9 a

type TupleN 9 a = (IndexT 0 a, IndexT 1 a, IndexT 2 a, IndexT 3 a, IndexT 4 a, IndexT 5 a, IndexT 6 a, IndexT 7 a, IndexT 8 a)

type TupleN 10 a

type TupleN 10 a = (IndexT 0 a, IndexT 1 a, IndexT 2 a, IndexT 3 a, IndexT 4 a, IndexT 5 a, IndexT 6 a, IndexT 7 a, IndexT 8 a, IndexT 9 a)

type TupleN 11 a

type TupleN 11 a = (IndexT 0 a, IndexT 1 a, IndexT 2 a, IndexT 3 a, IndexT 4 a, IndexT 5 a, IndexT 6 a, IndexT 7 a, IndexT 8 a, IndexT 9 a, IndexT 10 a)

type TupleN 12 a

type TupleN 12 a = (IndexT 0 a, IndexT 1 a, IndexT 2 a, IndexT 3 a, IndexT 4 a, IndexT 5 a, IndexT 6 a, IndexT 7 a, IndexT 8 a, IndexT 9 a, IndexT 10 a, IndexT 11 a)

type TupleN 13 a

type TupleN 13 a = (IndexT 0 a, IndexT 1 a, IndexT 2 a, IndexT 3 a, IndexT 4 a, IndexT 5 a, IndexT 6 a, IndexT 7 a, IndexT 8 a, IndexT 9 a, IndexT 10 a, IndexT 11 a, IndexT 12 a)

type TupleN 14 a

type TupleN 14 a = (IndexT 0 a, IndexT 1 a, IndexT 2 a, IndexT 3 a, IndexT 4 a, IndexT 5 a, IndexT 6 a, IndexT 7 a, IndexT 8 a, IndexT 9 a, IndexT 10 a, IndexT 11 a, IndexT 12 a, IndexT 13 a)

type TupleN 15 a

type TupleN 15 a = (IndexT 0 a, IndexT 1 a, IndexT 2 a, IndexT 3 a, IndexT 4 a, IndexT 5 a, IndexT 6 a, IndexT 7 a, IndexT 8 a, IndexT 9 a, IndexT 10 a, IndexT 11 a, IndexT 12 a, IndexT 13 a, IndexT 14 a)

type TupleConstraint n a = a ~ TupleN n a

To best explain this, lets consider the particular example TupleConstraint 2.

As TupleN 2 t = (IndexT 0 t, IndexT 1 t) we get:

TupleConstraint 2 t = t ~ (IndexT 0 t, IndexT 1 t)

What does this say? Well, firstly, as t ~ (IndexT 0 t, IndexT 1 t), it must be a pair at least.

What are the elements of the pair? Well, the first element of t is IndexT 0 t.

And what's IndexT 0 t defined as? The first element of t.

So we know that the first element of t is well, the first element of t.

Which tells us nothing at all.

We can go through the same argument with the second element of t.

So all we know after this is that t is a pair. TupleConstraint 2 t is the same as saying t is a pair.

So TupleConstraint n t basically says t is a n-tuple.

type family HomoTupleConstraint (n :: Nat) a :: Constraint

HomoTupleConstraint simply further constrains TupleConstraint so that all the elements are the same.

So HomoTupleConstraint 3 t basically says t ~ (u,u,u) for some u,

("Homo" is short for "Homogeneous". As in, all the same. Or like milk.)

Instances

type HomoTupleConstraint 0 a

type HomoTupleConstraint 0 a = TupleConstraint 0 a

type HomoTupleConstraint 1 a

type HomoTupleConstraint 1 a = TupleConstraint 1 a

type HomoTupleConstraint 2 a

type HomoTupleConstraint 2 a = (TupleConstraint 2 a, (~) * (IndexT 0 a) (IndexT 1 a))

type HomoTupleConstraint 3 a

type HomoTupleConstraint 3 a = (TupleConstraint 3 a, (~) * (IndexT 0 a) (IndexT 1 a), (~) * (IndexT 1 a) (IndexT 2 a))

type HomoTupleConstraint 4 a

type HomoTupleConstraint 4 a = (TupleConstraint 4 a, (~) * (IndexT 0 a) (IndexT 1 a), (~) * (IndexT 1 a) (IndexT 2 a), (~) * (IndexT 2 a) (IndexT 3 a))

type HomoTupleConstraint 5 a

type HomoTupleConstraint 5 a = (TupleConstraint 5 a, (~) * (IndexT 0 a) (IndexT 1 a), (~) * (IndexT 1 a) (IndexT 2 a), (~) * (IndexT 2 a) (IndexT 3 a), (~) * (IndexT 3 a) (IndexT 4 a))

type HomoTupleConstraint 6 a

type HomoTupleConstraint 6 a = (TupleConstraint 6 a, (~) * (IndexT 0 a) (IndexT 1 a), (~) * (IndexT 1 a) (IndexT 2 a), (~) * (IndexT 2 a) (IndexT 3 a), (~) * (IndexT 3 a) (IndexT 4 a), (~) * (IndexT 4 a) (IndexT 5 a))

type HomoTupleConstraint 7 a

type HomoTupleConstraint 7 a = (TupleConstraint 7 a, (~) * (IndexT 0 a) (IndexT 1 a), (~) * (IndexT 1 a) (IndexT 2 a), (~) * (IndexT 2 a) (IndexT 3 a), (~) * (IndexT 3 a) (IndexT 4 a), (~) * (IndexT 4 a) (IndexT 5 a), (~) * (IndexT 5 a) (IndexT 6 a))

type HomoTupleConstraint 8 a

type HomoTupleConstraint 8 a = (TupleConstraint 8 a, (~) * (IndexT 0 a) (IndexT 1 a), (~) * (IndexT 1 a) (IndexT 2 a), (~) * (IndexT 2 a) (IndexT 3 a), (~) * (IndexT 3 a) (IndexT 4 a), (~) * (IndexT 4 a) (IndexT 5 a), (~) * (IndexT 5 a) (IndexT 6 a), (~) * (IndexT 6 a) (IndexT 7 a))

type HomoTupleConstraint 9 a

type HomoTupleConstraint 9 a = (TupleConstraint 9 a, (~) * (IndexT 0 a) (IndexT 1 a), (~) * (IndexT 1 a) (IndexT 2 a), (~) * (IndexT 2 a) (IndexT 3 a), (~) * (IndexT 3 a) (IndexT 4 a), (~) * (IndexT 4 a) (IndexT 5 a), (~) * (IndexT 5 a) (IndexT 6 a), (~) * (IndexT 6 a) (IndexT 7 a), (~) * (IndexT 7 a) (IndexT 8 a))

type HomoTupleConstraint 10 a

type HomoTupleConstraint 10 a = (TupleConstraint 10 a, (~) * (IndexT 0 a) (IndexT 1 a), (~) * (IndexT 1 a) (IndexT 2 a), (~) * (IndexT 2 a) (IndexT 3 a), (~) * (IndexT 3 a) (IndexT 4 a), (~) * (IndexT 4 a) (IndexT 5 a), (~) * (IndexT 5 a) (IndexT 6 a), (~) * (IndexT 6 a) (IndexT 7 a), (~) * (IndexT 7 a) (IndexT 8 a), (~) * (IndexT 8 a) (IndexT 9 a))

type HomoTupleConstraint 11 a

type HomoTupleConstraint 11 a = (TupleConstraint 11 a, (~) * (IndexT 0 a) (IndexT 1 a), (~) * (IndexT 1 a) (IndexT 2 a), (~) * (IndexT 2 a) (IndexT 3 a), (~) * (IndexT 3 a) (IndexT 4 a), (~) * (IndexT 4 a) (IndexT 5 a), (~) * (IndexT 5 a) (IndexT 6 a), (~) * (IndexT 6 a) (IndexT 7 a), (~) * (IndexT 7 a) (IndexT 8 a), (~) * (IndexT 8 a) (IndexT 9 a), (~) * (IndexT 9 a) (IndexT 10 a))

type HomoTupleConstraint 12 a

type HomoTupleConstraint 12 a = (TupleConstraint 12 a, (~) * (IndexT 0 a) (IndexT 1 a), (~) * (IndexT 1 a) (IndexT 2 a), (~) * (IndexT 2 a) (IndexT 3 a), (~) * (IndexT 3 a) (IndexT 4 a), (~) * (IndexT 4 a) (IndexT 5 a), (~) * (IndexT 5 a) (IndexT 6 a), (~) * (IndexT 6 a) (IndexT 7 a), (~) * (IndexT 7 a) (IndexT 8 a), (~) * (IndexT 8 a) (IndexT 9 a), (~) * (IndexT 9 a) (IndexT 10 a), (~) * (IndexT 10 a) (IndexT 11 a))

type HomoTupleConstraint 13 a

type HomoTupleConstraint 13 a = (TupleConstraint 13 a, (~) * (IndexT 0 a) (IndexT 1 a), (~) * (IndexT 1 a) (IndexT 2 a), (~) * (IndexT 2 a) (IndexT 3 a), (~) * (IndexT 3 a) (IndexT 4 a), (~) * (IndexT 4 a) (IndexT 5 a), (~) * (IndexT 5 a) (IndexT 6 a), (~) * (IndexT 6 a) (IndexT 7 a), (~) * (IndexT 7 a) (IndexT 8 a), (~) * (IndexT 8 a) (IndexT 9 a), (~) * (IndexT 9 a) (IndexT 10 a), (~) * (IndexT 10 a) (IndexT 11 a), (~) * (IndexT 11 a) (IndexT 12 a))

type HomoTupleConstraint 14 a

type HomoTupleConstraint 14 a = (TupleConstraint 14 a, (~) * (IndexT 0 a) (IndexT 1 a), (~) * (IndexT 1 a) (IndexT 2 a), (~) * (IndexT 2 a) (IndexT 3 a), (~) * (IndexT 3 a) (IndexT 4 a), (~) * (IndexT 4 a) (IndexT 5 a), (~) * (IndexT 5 a) (IndexT 6 a), (~) * (IndexT 6 a) (IndexT 7 a), (~) * (IndexT 7 a) (IndexT 8 a), (~) * (IndexT 8 a) (IndexT 9 a), (~) * (IndexT 9 a) (IndexT 10 a), (~) * (IndexT 10 a) (IndexT 11 a), (~) * (IndexT 11 a) (IndexT 12 a), (~) * (IndexT 12 a) (IndexT 13 a))

type HomoTupleConstraint 15 a

type HomoTupleConstraint 15 a = (TupleConstraint 15 a, (~) * (IndexT 0 a) (IndexT 1 a), (~) * (IndexT 1 a) (IndexT 2 a), (~) * (IndexT 2 a) (IndexT 3 a), (~) * (IndexT 3 a) (IndexT 4 a), (~) * (IndexT 4 a) (IndexT 5 a), (~) * (IndexT 5 a) (IndexT 6 a), (~) * (IndexT 6 a) (IndexT 7 a), (~) * (IndexT 7 a) (IndexT 8 a), (~) * (IndexT 8 a) (IndexT 9 a), (~) * (IndexT 9 a) (IndexT 10 a), (~) * (IndexT 10 a) (IndexT 11 a), (~) * (IndexT 11 a) (IndexT 12 a), (~) * (IndexT 12 a) (IndexT 13 a), (~) * (IndexT 13 a) (IndexT 14 a))

class TupleConstraint n a => IsTuple n a

GHC does not allow you to partially apply type families (or any type declaration for that matter). So if you have a type of * -> Constraint you can't pass TupleConstraint 2, because TupleConstraint is partially applied and this is not allowed.

But you can partially apply classes.

So IsTuple is basically the same as TupleConstraint except that it's a class, not a type family.

Instances

TupleConstraint n a => IsTuple n a

class HomoTupleConstraint n a => IsHomoTuple n a

The version of IsTuple for homogenous tuples (i.e. all the same type).

Instances

HomoTupleConstraint n a => IsHomoTuple n a