package logtk
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doc/logtk.proofs/Logtk_proofs/LLTerm/Set/index.html
Module LLTerm.Set
include Set.S with type elt = t
type elt = t
The type of the set elements.
val empty : t
The empty set.
val is_empty : t -> bool
Test whether a set is empty or not.
add x s
returns a set containing all elements of s
, plus x
. If x
was already in s
, s
is returned unchanged (the result of the function is then physically equal to s
).
remove x s
returns a set containing all elements of s
, except x
. If x
was not in s
, s
is returned unchanged (the result of the function is then physically equal to s
).
Total ordering between sets. Can be used as the ordering function for doing sets of sets.
equal s1 s2
tests whether the sets s1
and s2
are equal, that is, contain equal elements.
iter f s
applies f
in turn to all elements of s
. The elements of s
are presented to f
in increasing order with respect to the ordering over the type of the elements.
map f s
is the set whose elements are f a0
,f a1
... f aN
, where a0
,a1
...aN
are the elements of s
.
The elements are passed to f
in increasing order with respect to the ordering over the type of the elements.
If no element of s
is changed by f
, s
is returned unchanged. (If each output of f
is physically equal to its input, the returned set is physically equal to s
.)
fold f s init
computes (f xN ... (f x2 (f x1 init))...)
, where x1 ... xN
are the elements of s
, in increasing order.
for_all f s
checks if all elements of the set satisfy the predicate f
.
exists f s
checks if at least one element of the set satisfies the predicate f
.
filter f s
returns the set of all elements in s
that satisfy predicate f
. If f
satisfies every element in s
, s
is returned unchanged (the result of the function is then physically equal to s
).
filter_map f s
returns the set of all v
such that f x = Some v
for some element x
of s
.
For example,
filter_map (fun n -> if n mod 2 = 0 then Some (n / 2) else None) s
is the set of halves of the even elements of s
.
If no element of s
is changed or dropped by f
(if f x = Some x
for each element x
), then s
is returned unchanged: the result of the function is then physically equal to s
.
partition f s
returns a pair of sets (s1, s2)
, where s1
is the set of all the elements of s
that satisfy the predicate f
, and s2
is the set of all the elements of s
that do not satisfy f
.
val cardinal : t -> int
Return the number of elements of a set.
Return the list of all elements of the given set. The returned list is sorted in increasing order with respect to the ordering Ord.compare
, where Ord
is the argument given to Make
.
Return the smallest element of the given set (with respect to the Ord.compare
ordering), or raise Not_found
if the set is empty.
Return one element of the given set, or raise Not_found
if the set is empty. Which element is chosen is unspecified, but equal elements will be chosen for equal sets.
split x s
returns a triple (l, present, r)
, where l
is the set of elements of s
that are strictly less than x
; r
is the set of elements of s
that are strictly greater than x
; present
is false
if s
contains no element equal to x
, or true
if s
contains an element equal to x
.
find x s
returns the element of s
equal to x
(according to Ord.compare
), or raise Not_found
if no such element exists.
of_list l
creates a set from a list of elements. This is usually more efficient than folding add
over the list, except perhaps for lists with many duplicated elements.
Iterators
to_seq_from x s
iterates on a subset of the elements of s
in ascending order, from x
or above.
Safe version of find_first
.
find_first_map f s
find the minimum element x
of s
such that f x = Some y
and return Some y
. Otherwise returns None
.
find_last_map f s
find the maximum element x
of s
such that f x = Some y
and return Some y
. Otherwise returns None
.
val of_iter : elt CCSet.iter -> t
Build a set from the given iter
of elements.
val add_iter : t -> elt CCSet.iter -> t
val to_iter : t -> elt CCSet.iter
to_iter t
converts the set t
to a iter
of the elements.
Print the set in a string
val pp :
?pp_start:unit CCSet.printer ->
?pp_stop:unit CCSet.printer ->
?pp_sep:unit CCSet.printer ->
elt CCSet.printer ->
t CCSet.printer
Print the set.