Module Fun

module Fun: sig .. end
This module provides an implementation of finite functions over integers.
Author(s): Michele Sevegnani

type t 
Type of finite functions over integers.

Standard map operations



These functions are described in the standard library.
val add : int -> int -> t -> t
val compare : t -> t -> int
val empty : t
val equal : t -> t -> bool
val fold : (int -> int -> 'b -> 'b) -> t -> 'b -> 'b

Additional functions


val dom : t -> IntSet.t
Return the domain of a function.
val codom : t -> IntSet.t
Return the codomain of a function.
val inverse : t -> Rel.t
Return the inverse of a function. Note that the inverse of a function is, in the general case, a binary relation.
val to_list : t -> (int * int) list
Return the list of pairs defined by a function.
val of_list : (int * int) list -> t
Inverse of Fun.to_list. Note that in case of clashing pairs only the right-most is used.
val parse : int list -> t
parse l returns a function in which the numbers from 0 to n - 1 (with n the length of l) are mapped to the elements of l, in the given order. Example:

parse [0;0;3;1;2] = [(0,0);(1,0);(2,3);(3,1);(4,2)].

val to_string : t -> string
Return the string representation of a function. Example:

"{(1, 2), (2, 3), (3, 3)}".

val apply : t -> int -> int option
apply f x returns f(x).
val transform : iso_dom:Iso.t -> iso_codom:Iso.t -> t -> t
transform ~iso_dom ~iso_codom f returns the function obtained by applying iso_dom and iso_codom to the domain and codomain of f, respectively.
val is_total : int -> t -> bool
is_total n f returns true if function f is total over domain 1,...,n-1, false otherwise.
val is_id : t -> bool
is_id f returns true if f(i) = i for each i, false otherwise.
val check_codom : min:int -> max:int -> t -> bool
check_codom ~min ~max f returns true if the codomain of f is in the range [min, max].