Module Comparison

module Comparison: sig .. end

Partial Ordering values

type t =

`\|`	`Lt`
`\|`	`Eq`
`\|`	`Gt`
`\|`	`Incomparable`	`(*`	partial order	`*)`

type comparison = t

include Interfaces.PRINT

val combine : t -> t -> t

combine two partial comparisons, that are assumed to be compatible, ie they do not order differently if Incomparable is not one of the values.
Raises Invalid_argument if the comparisons are inconsistent.

val opp : t -> t

Opposite of the relation: a R b becomes b R a

val to_total : t -> int

Conversion to a total ordering. Incomparable is translated to 0 (equal).

val of_total : int -> t

Conversion from a total order

val lexico : t -> t -> t

Lexicographic combination (the second is used only if the first is Incomparable

val (++) : t -> t -> t

Infix version of Comparison.lexico

type 'a comparator = 'a -> 'a -> t

val (@>>) : 'a comparator ->
       'a comparator -> 'a comparator

Combination of comparators that work on the same values. Its behavior is the following: (f1 @>> f2) x y is the same as f1 x y if f1 x y is not Eq; otherwise it is the same as f2 x y

type ('a, 'b) combination

Lexicographic combination of comparators. It is, roughly, equivalent to 'a -> 'a -> 'b

val (>>>) : 'a comparator ->
       ('b, 'c) combination ->
       ('a, 'b -> 'b -> 'c) combination

Lexicographic combination starting with the given function

val last : 'a comparator -> ('a, t) combination

Last comparator

val call : ('a, 'b) combination -> 'a -> 'a -> 'b

Call a lexicographic combination on arguments

val dominates : ('a -> 'b -> t) -> 'a list -> 'b list -> bool

dominates f l1 l2 returns true iff for all element y of l2, there is some x in l1 with f x y = Gt

module type PARTIAL_ORD = sig .. end