@callback discrete?() :: boolean()

Is this implementation of an interval considered discrete?

The interval is implicitly continuous if not discrete.

@callback new(new_opts()) :: Interval.t()

Create a new Interval.t/0

@callback point_compare(Interval.point(), Interval.point()) :: :eq | :gt | :lt

Compare two points, returning if a == b, a > b or a < b.

@callback point_step(Interval.point(), n :: integer()) :: Interval.point()

Step a discrete point n steps.

If n is negative, the point is stepped backwards. For integers this is simply addition (point + n)

@callback point_valid?(Interval.point()) :: boolean()

Is the given argument a valid point in this Interval implementation.

@callback size(Interval.t()) :: any()

Return the "size" of the interval. The returned value depends on the interval implementation used.

for-discrete-intervals

For Discrete Intervals

For discrete point types, the size represents the number of elements the interval contains.

I.e. for Date the size is the number of Date structs the interval can be said to "contain" (the number of days)

examples

Examples

iex> size(new(module: Interval.Integer, left: 1, right: 1, bounds: "[]"))
1

iex> size(new(module: Interval.Integer, left: 1, right: 3, bounds: "[)"))
2

# Note that this interval will be normalized to an empty interval
# due to the bounds:
iex> size(new(module: Interval.Integer, left: 1, right: 2, bounds: "()"))
0

for-continuous-intervals

For Continuous Intervals

For continuous intervals, the size is reported as the difference between the left and right points.

examples-1

Examples

# The size of the interval `[1.0, 5.0)` is also 4:
iex> size(new(module: Interval.Float, left: 1.0, right: 5.0, bounds: "[)"))
4.0

# And likewise, so is the size of `[1.0, 5.0]` (note the bound change)
iex> size(new(module: Interval.Float, left: 1.0, right: 5.0, bounds: "[]"))
4.0

# Exactly one point contained in  this continuous interval,
# so technically not empty, but it also has zero  size.
iex> size(new(module: Interval.Float, left: 1.0, right: 1.0, bounds: "[]"))
0.0

# Empty continuous interval
iex> size(new(module: Interval.Float, left: 1.0, right: 1.0, bounds: "()"))
0.0