The type of ordering functions returning an order variant.

The legacy int-returning comparisons :

• compare a b < 0 means a < b
• compare a b = 0 means a = b
• compare a b > 0 means a > b

We use compare as member name instead of comp, so that the Comp modules can be used as the legacy OrderedType interface.

Returns a variant ordering from a legacy comparison

Returns an legacy comparison from a variant ordering

Polymorphic comparison functions, based on the Pervasives.compare function from inria's stdlib, have polymorphic types: they claim to be able to compare values of any type. In practice, they work for only some types, may fail on function types and may not terminate on cyclic values.

They work by runtime magic, inspecting the values in an untyped way. While being an useful hack for base types and simple composite types (say (int * float) list, they do not play well with functions, type abstractions, and structures that would need a finer notion of equality/comparison. For example, if one represent sets as balanced binary tree, one may want set with equal elements but different balancings to be equal, which would not be the case using the polymorphic equality function.

When possible, you should therefore avoid relying on these polymorphic comparison functions. You should be especially careful if your data structure may later evolve to allow cyclic data structures or functions.

Reverse a given ordering. If Int.ord sorts integer by increasing order, rev Int.ord will sort them by decreasing order.

The type for equality function.

All ordered types also support equality, as equality can be derived from ordering. However, there are also cases where elements may be compared for equality, but have no natural ordering. It is therefore useful to provide equality as an independent notion.

Derives an equality function from an ordering function.

choice functions, see min and max.

min ord will choose the smallest element, according to ord. For example, min Int.ord 1 2 will return 1.

  (* the minimum element of a list *)
  let list_min ord = List.reduce (min ord)

max ord will choose the biggest element according to ord.

binary lifting of the comparison function, using lexicographic order: bin_ord ord1 v1 v1' ord2 v2 v2' is ord2 v2 v2' if ord1 v1 v1' = Eq, and ord1 v1 v1' otherwise.

These functions extend an existing equality/comparison/ordering to a new domain through a mapping function. For example, to order sets by their cardinality, use map_ord Set.cardinal Int.ord. The input of the mapping function is the type you want to compare, so this is the reverse of List.map.