Crate discrete

Combinatorial phantom types for discrete mathematics.

All discrete spaces has the following functions:

    fn count(dim) -> uint;
    fn to_index(dim, pos) -> uint;
    fn to_pos(dim, index, &mut pos);

This makes it possible to allocate to solve tasks as:

• Allocate enough memory for the space
• Read and write data
• Convert from and to natural numbers
• Iterate through the space
• Pick a random object of the space

Iterating through the space can be done simply by counting from zero up to the size of the space.

Phantom types are used because they represents the general spaces. For example, we can represent a general two-dimensional space, instead of binding the type to the size.

For any constructed space, there is a dimension and position type. The dimension and position types are compositions, given by the type of the constructed space.

Structs

Context	A discrete space that can model spatial operations over arbitrary states, therefore useful for context analysis.
Data	Used by the final subspace.
Dimension	Dimension is natural number, position is the same as index.
DimensionN	Dimension is a list of numbers, position is a list of numbers.
DirectedContext	Same as Context, but for directed edges.
EqPair	Dimension is natural number, position is (min, max).
NeqPair	Dimension is natural number, position is (min, max).
Of	Used to combine the dimensional and position types.
Pair	Dimension is natural number, position is (min, max).
Permutation	Dimension is natural number, position is a list of numbers.
PowerSet	Dimension is natural number, position is a list of numbers.
Subspace	Used to nest a subspace.

Traits

Construct	Constructs a new space.
Count	Implemented by spaces that can count the number of objects.
ToIndex	Implemented by spaces that can convert position to index.
ToPos	Implemented for spaces which can convert an index to position type.