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Module Map_Lattice.Make_without_cardinal.M

module M: Hptmap.Make(K)(V)(Comp)(sig


val v : (K.t * V.t) list list
end)(sig


val l : State.t list
end)
type key
type of the keys
type v
type of the values
type 'a shape 
type prefix 
include Datatype.S_with_collections
val id : t -> int
Bijective function. The ids are positive.
val self : State.t
val empty : t
the empty map
val is_empty : t -> bool
is_empty m returns true if and only if the map m defines no bindings at all.
val add : key -> v -> t -> t
add k d m returns a map whose bindings are all bindings in m, plus a binding of the key k to the datum d. If a binding already exists for k, it is overridden.
val find : key -> t -> v
val find_check_missing : key -> t -> v
Both find key m and find_check_missing key m return the value bound to key in m, or raise Not_found is key is unbound. find is optimised for the case where key is bound in m, whereas find_check_missing is more efficient for the cases where m is big and key is missing.
val find_key : key -> t -> key
This function is useful where there are multiple distinct keys that are equal for Key.equal.
val remove : key -> t -> t
remove k m returns the map m deprived from any binding involving k.
val mem : key -> t -> bool
mem k m returns true if k is bound in m, and false otherwise.
val iter : (key -> v -> unit) -> t -> unit
iter f m applies f to all bindings of the map m.
val map : (v -> v) -> t -> t
map f m returns the map obtained by composing the map m with the function f; that is, the map $k\mapsto f(m(k))$.
val map' : (key -> v -> v option) -> t -> t
Same as map, except if f k v returns None. In this case, k is not bound in the resulting map.
val fold : (key -> v -> 'b -> 'b) -> t -> 'b -> 'b
fold f m seed invokes f k d accu, in turn, for each binding from key k to datum d in the map m. Keys are presented to f in increasing order according to the map's ordering. The initial value of accu is seed; then, at each new call, its value is the value returned by the previous invocation of f. The value returned by fold is the final value of accu.
val fold_rev : (key -> v -> 'b -> 'b) -> t -> 'b -> 'b
fold_rev performs exactly the same job as fold, but presents keys to f in the opposite order.
val for_all : (key -> v -> bool) -> t -> bool
for_all p m returns true if all the bindings of the map m satisfy the predicate p.
val exists : (key -> v -> bool) -> t -> bool
for_all p m returns true if at least one binding of the map m satisfies the predicate p.
type empty_action =
| Neutral
| Absorbing
| Traversing of (key -> v -> v option) 
val merge : cache:Hptmap_sig.cache_type ->
       symmetric:bool ->
       idempotent:bool ->
       decide_both:(key ->
                    v -> v -> v option) ->
       decide_left:empty_action ->
       decide_right:empty_action -> t -> t -> t
Merge of two trees, parameterized by a merge function. If symmetric holds, the function must verify merge x y = merge y x. If idempotent holds, the function must verify merge x x = x. For each key k present in both trees, and bound to v1 and v2 in the left and the right tree respectively, decide_both k v1 v2 is called. If the decide function returns None, the key will not be in the resulting map; otherwise, the new value computed will be bound to k. The decide_left action is performed to the left subtree t when a right subtree is empty (and conversely for the decide_right action when a left subtree is empty): 
val generic_join : cache:Hptmap_sig.cache_type ->
       symmetric:bool ->
       idempotent:bool ->
       decide:(key ->
               v option -> v option -> v) ->
       t -> t -> t
Merge of two trees, parameterized by the decide function. If symmetric holds, the function must verify decide key v1 v2 = decide key v2 v1. If idempotent holds, the function must verify decide k (Some x) (Some x) = x.
val join : cache:Hptmap_sig.cache_type ->
       symmetric:bool ->
       idempotent:bool ->
       decide:(key ->
               v -> v -> v) ->
       t -> t -> t
Same as generic_merge, but we assume that decide key None (Some v) = decide key (Some v) None = v holds.
val inter : cache:Hptmap_sig.cache_type ->
       symmetric:bool ->
       idempotent:bool ->
       decide:(key ->
               v -> v -> v option) ->
       t -> t -> t
Intersection of two trees, parameterized by the decide function. If the decide function returns None, the key will not be in the resulting map. Keys present in only one map are similarly unmapped in the result.
val inter_with_shape : 'a shape -> t -> t
inter_with_shape s m keeps only the elements of m that are also bound in the map s. No caching is used, but this function is more efficient than successive calls to Hptmap_sig.S.remove or Hptmap_sig.S.add to build the resulting map.

Binary predicates


type decide_fast =
| Done
| Unknown (*
Shortcut for functions that decide whether a predicate holds on a tree. Done means that the function returns its default value, which is usually unit. Unknown means that the evaluation must continue in the subtrees.
*) 
val generic_predicate : exn ->
       cache:string * 'a ->
       decide_fast:(t -> t -> decide_fast) ->
       decide_fst:(key -> v -> unit) ->
       decide_snd:(key -> v -> unit) ->
       decide_both:(v -> v -> unit) -> t -> t -> unit
generic_is_included e (cache_name, cache_size) ~decide_fast ~decide_fst ~decide_snd ~decide_both t1 t2 decides whether some relation holds between t1 and t2. All decide functions must raise e when the relation does not hold, and do nothing otherwise.

decide_fst (resp. decide_snd) is called when one key is present only in t1 (resp. t2).

decide_both is called when a key is present in both trees.

decide_fast is called on entire keys. As its name implies, it must be fast; in doubt, returning Unknown is always correct. Raising e means that the relation does not hold. Returning Done means that the relation holds.

The computation of this relation cached. cache_name is used to identify the cache when debugging. cache_size is currently unused.

type predicate_type =
| ExistentialPredicate
| UniversalPredicate
Existential (||) or universal (&&) predicates.
type predicate_result =
| PTrue
| PFalse
| PUnknown
Does the given predicate hold or not. PUnknown indicates that the result is uncertain, and that the more aggressive analysis should be used.
val binary_predicate : Hptmap_sig.cache_type ->
       predicate_type ->
       decide_fast:(t -> t -> predicate_result) ->
       decide_fst:(key -> v -> bool) ->
       decide_snd:(key -> v -> bool) ->
       decide_both:(key -> v -> v -> bool) ->
       t -> t -> bool
Same functionality as generic_predicate but with a different signature. All decisin functions return a boolean that are combined differently depending on whether the predicate is existential or universal.
val generic_symmetric_predicate : exn ->
       decide_fast:(t -> t -> decide_fast) ->
       decide_one:(key -> v -> unit) ->
       decide_both:(v -> v -> unit) -> t -> t -> unit
Same as generic_predicate, but for a symmetric relation. decide_fst and decide_snd are thus merged into decide_one.
val symmetric_binary_predicate : Hptmap_sig.cache_type ->
       predicate_type ->
       decide_fast:(t -> t -> predicate_result) ->
       decide_one:(key -> v -> bool) ->
       decide_both:(key -> v -> v -> bool) ->
       t -> t -> bool
Same as binary_predicate, but for a symmetric relation. decide_fst and decide_snd are thus merged into decide_one.
val decide_fast_inclusion : t -> t -> predicate_result
Function suitable for the decide_fast argument of binary_predicate, when testing for inclusion of the first map into the second. If the two arguments are equal, or the first one is empty, the relation holds.
val decide_fast_intersection : t -> t -> predicate_result
Function suitable for the decide_fast argument of symmetric_binary_predicate when testing for a non-empty intersection between two maps. If one map is empty, the intersection is empty. Otherwise, if the two maps are equal, the intersection is non-empty.
val cached_fold : cache_name:string ->
       temporary:bool ->
       f:(key -> v -> 'b) ->
       joiner:('b -> 'b -> 'b) -> empty:'b -> t -> 'b
val cached_map : cache:string * int ->
       temporary:bool ->
       f:(key -> v -> v) -> t -> t
val singleton : key -> v -> t
singleton k d returns a map whose only binding is from k to d.
val is_singleton : t -> (key * v) option
is_singleton m returns Some (k, d) if m is a singleton map that maps k to d. Otherwise, it returns None.
val on_singleton : (key -> v -> bool) -> t -> bool
on_singleton f m returns f k d if m is a singleton map that maps k to d. Otherwise, it returns false.
val cardinal : t -> int
cardinal m returns m's cardinal, that is, the number of keys it binds, or, in other words, its domain's cardinal.
val min_binding : t -> key * v
val max_binding : t -> key * v
val split : key -> t -> t * v option * t
val compositional_bool : t -> bool
Value of the compositional boolean associated to the tree, as computed by the Compositional_bool argument of the functor.
val clear_caches : unit -> unit
Clear all the persistent caches used internally by the functions of this module. Those caches are not project-aware, so this function must be called at least each time a project switch occurs.
val from_shape : (key -> 'a -> v) -> 'a shape -> t
Build an entire map from another map indexed by the same keys. More efficient than just performing successive Hptmap_sig.S.add the elements of the other map
val shape : t -> v shape
Export the map as a value suitable for functions Hptmap_sig.S.inter_with_shape and Hptmap_sig.S.from_shape
val fold2_join_heterogeneous : cache:Hptmap_sig.cache_type ->
       empty_left:('a shape -> 'b) ->
       empty_right:(t -> 'b) ->
       both:(key -> v -> 'a -> 'b) ->
       join:('b -> 'b -> 'b) -> empty:'b -> t -> 'a shape -> 'b
fold2_join_heterogeneous ~cache ~empty_left ~empty_right ~both ~join ~empty m1 m2 iterates simultaneously on m1 and m2. If a subtree t is present in m1 but not in m2 (resp. in m2 but not in m1), empty_right t (resp. empty_left t) is called. If a key k is present in both trees, and bound to v1 and v2 respectively, both k v1 v2 is called. If both trees are empty, empty is returned. The values of type 'b returned by the auxiliary functions are merged using join, which is called in an unspecified order. The results of the function may be cached, depending on cache.