Return, if possible, the maximum value of the list.

When number of arguments is equal one, then return this argument.

When number of arguments is equal two, then return, if possible, the value from (a, b) that is \(\ge\) the other.

In common case, when the length of list greater than 2, the task is more complicated. Return only the arguments, which are greater than others, if it is possible to determine directional relation.

If is not possible to determine such a relation, return a partially evaluated result.

Assumptions are used to make the decision too.

Also, only comparable arguments are permitted.

It is named Max and not max to avoid conflicts with the built-in function max.

Examples

Algorithm

The task can be considered as searching of supremums in the directed complete partial orders [R303].

The source values are sequentially allocated by the isolated subsets in which supremums are searched and result as Max arguments.

If the resulted supremum is single, then it is returned.

The isolated subsets are the sets of values which are only the comparable with each other in the current set. E.g. natural numbers are comparable with each other, but not comparable with the \(x\) symbol. Another example: the symbol \(x\) with negative assumption is comparable with a natural number.

Also there are “least” elements, which are comparable with all others, and have a zero property (maximum or minimum for all elements). For example, in case of \(\infty\), the allocation operation is terminated and only this value is returned.

if \(A > B > C\) then \(A > C\)

if \(A = B\) then \(B\) can be removed

See also

find minimum values

References

https://en.wikipedia.org/wiki/Directed_complete_partial_order

https://en.wikipedia.org/wiki/Lattice_%28order%29