(* Pasted from Pottier's PP compiler *)
(* This signature defines a few operations over maps of keys to
nonempty sets of items. Keys and items can have distinct types,
hence the name [Heterogeneous].
These maps can be used to represent directed bipartite graphs whose
source vertices are keys and whose target vertices are items. Each
key is mapped to the set of its successors. *)
module type Heterogeneous = sig
(* These are the types of keys, items, and sets of items. *)
type key
type item
type itemset
(* This is the type of maps of keys to sets of items. *)
type t
(* [find x m] is the item set associated with key [x] in map [m], if
such an association is defined; it is the empty set otherwise. *)
val find: key -> t -> itemset
(* [add x is m] extends [m] with a binding of [x] to the item set
[is], if [is] is nonempty. If [is] is empty, it removes [x] from
[m]. *)
val add: key -> itemset -> t -> t
(* [update x f m] is [add x (f (find x m)) m]. *)
val update: key -> (itemset -> itemset) -> t -> t
(* [mkedge x i m] extends [m] with a binding of [x] to the union of
the set [m x] and the singleton [i], where [m x] is taken to be
empty if undefined. In terms of graphs, [mkedge x i m] extends
the graph [m] with an edge of [x] to [i]. *)
val mkedge: key -> item -> t -> t
(* [rmedge x i m] extends [m] with a binding of [x] to the
difference of the set [m x] and the singleton [i], where the
binding is considered undefined if that difference is empty. In
terms of graphs, [rmedge x i m] removes an edge of [x] to [i]
to the graph [m]. *)
val rmedge: key -> item -> t -> t
(* [iter] and [fold] iterate over all edges in the graph. *)
val iter: (key * item -> unit) -> t -> unit
val fold: (key * item -> 'a -> 'a) -> t -> 'a -> 'a
(* [pick m p] returns an arbitrary edge that satisfies predicate
[p], if the graph contains one. *)
val pick: t -> (key * item -> bool) -> (key * item) option
end
(* This functor offers an implementation of [Heterogeneous] out of
standard implementations of sets and maps. *)
module MakeHetero
(Set : sig
type elt
type t
val empty: t
val is_empty: t -> bool
val add: elt -> t -> t
val remove: elt -> t -> t
val fold: (elt -> 'a -> 'a) -> t -> 'a -> 'a
end)
(Map : sig
type key
type 'a t
val add: key -> 'a -> 'a t -> 'a t
val find: key -> 'a t -> 'a
val remove: key -> 'a t -> 'a t
val fold: (key -> 'a -> 'b -> 'b) -> 'a t -> 'b -> 'b
end)
= struct
type key = Map.key
type item = Set.elt
type itemset = Set.t
type t = Set.t Map.t
let find x m =
try
Map.find x m
with Not_found ->
Set.empty
let add x is m =
if Set.is_empty is then
Map.remove x m
else
Map.add x is m
let update x f m =
add x (f (find x m)) m
let mkedge x i m =
update x (Set.add i) m
let rmedge x i m =
update x (Set.remove i) m
let fold f m accu =
Map.fold (fun source targets accu ->
Set.fold (fun target accu ->
f (source, target) accu
) targets accu
) m accu
let iter f m =
fold (fun edge () -> f edge) m ()
exception Picked of (key * item)
let pick m p =
try
iter (fun edge ->
if p edge then
raise (Picked edge)
) m;
None
with Picked edge ->
Some edge
end
(* This signature defines a few common operations over maps of keys
to sets of keys -- that is, keys and items have the same type,
hence the name [Homogeneous].
These maps can be used to represent general directed graphs. *)
module type Homogeneous = sig
include Heterogeneous (* [key] and [item] intended to be equal *)
(* [mkbiedge x1 x2 m] is [mkedge x1 x2 (mkedge x2 x1 m)]. *)
val mkbiedge: key -> key -> t -> t
(* [rmbiedge x1 x2 m] is [rmedge x1 x2 (rmedge x2 x1 m)]. *)
val rmbiedge: key -> key -> t -> t
(* [reverse m] is the reverse of graph [m]. *)
val reverse: t -> t
(* [restrict m] is the graph obtained by keeping only the vertices
that satisfy predicate [p]. *)
val restrict: (key -> bool) -> t -> t
end
module MakeHomo
(Set : sig
type elt
type t
val empty: t
val is_empty: t -> bool
val add: elt -> t -> t
val remove: elt -> t -> t
val fold: (elt -> 'a -> 'a) -> t -> 'a -> 'a
val filter: (elt -> bool) -> t -> t
end)
(Map : sig
type key = Set.elt
type 'a t
val empty: 'a t
val add: key -> 'a -> 'a t -> 'a t
val find: key -> 'a t -> 'a
val remove: key -> 'a t -> 'a t
val fold: (key -> 'a -> 'b -> 'b) -> 'a t -> 'b -> 'b
end)
= struct
include MakeHetero(Set)(Map)
let symmetric transform x1 x2 m =
transform x1 x2 (transform x2 x1 m)
let mkbiedge =
symmetric mkedge
let rmbiedge =
symmetric rmedge
let reverse m =
Map.fold (fun source targets predecessors ->
Set.fold (fun target predecessors ->
(* We have a direct edge from [source] to [target]. Thus, we
record the existence of a reverse edge from [target] to
[source]. *)
mkedge target source predecessors
) targets predecessors
) m Map.empty
let restrict p m =
Map.fold (fun source targets m ->
if p source then
let targets = Set.filter p targets in
if Set.is_empty targets then
m
else
Map.add source targets m
else
m
) m Map.empty
end