Documentation

Distinguish between dense and sparse ordered types. A dense type is one in which any two values v1 < v2 have a third value v3 such that v1 < v3 < v2.

In theory the floating types are dense, although in practice they can only have finitely many values. This class treats them as dense.

Tuples up to 4 members are declared as instances. Larger tuples may be added if necessary.

Most values of sparse types have an adjacentBelow, such that, for all x:

case adjacentBelow x of
   Just x1 -> adjacent x1 x
   Nothing -> True

The exception is for bounded types when x == lowerBound. For dense types adjacentBelow always returns Nothing.

This approach was suggested by Ben Rudiak-Gould on comp.lang.functional.

Check adjacency for sparse enumerated types (i.e. where there is no value between x and succ x).

Check adjacency, allowing for case where x = maxBound. Use as the definition of "adjacent" for bounded enumerated types such as Int and Char.

The usual implementation of adjacentBelow for bounded enumerated types.

A Boundary is a division of an ordered type into values above and below the boundary. No value can sit on a boundary.

Known bug: for Bounded types

• BoundaryAbove maxBound < BoundaryAboveAll

• BoundaryBelow minBound > BoundaryBelowAll

This is incorrect because there are no possible values in between the left and right sides of these inequalities.

True if the value is above the boundary, false otherwise.

Same as above, but with the arguments reversed for more intuitive infix usage.