Module `Bigraph.Fun`

type t: Type of finite functions over integers.

Standard map operations

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
val iter : (int -> int -> unit) -> t -> unit

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 pp : Stdlib.Format.formatter -> t -> unit: Pretty printer.

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 0,...,n-1, false otherwise.

val is_surj : int -> t -> bool: is_surj n f returns true if function f is surjective over codomain 0,...,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 : int -> t -> bool: check_codom n f returns true if the codomain of f is in the range [0, n-1].