Module `Logtk.Comparison`

Partial Ordering values

type t = | Lt | Eq | Gt | Incomparable partial order
type comparison = t

include Interfaces.PRINT with type t := t

type t

val pp : t CCFormat.printer
val to_string : t -> string

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 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