#### logtk 2.1 2.0 1.6 1.5.1 0.8.1

Core types and algorithms for logic
IN THIS PACKAGE
Module . .
`type key = int`

The type of the map keys.

`type !+'a t`

The type of maps from type `key` to type `'a`.

`val empty : 'a t`

The empty map.

`val is_empty : 'a t -> bool`

Test whether a map is empty or not.

`val mem : key -> 'a t -> bool`

`mem x m` returns `true` if `m` contains a binding for `x`, and `false` otherwise.

`val add : key -> 'a -> 'a t -> 'a t`

`add key data m` returns a map containing the same bindings as `m`, plus a binding of `key` to `data`. If `key` was already bound in `m` to a value that is physically equal to `data`, `m` is returned unchanged (the result of the function is then physically equal to `m`). Otherwise, the previous binding of `key` in `m` disappears.

• before 4.03

Physical equality was not ensured.

`val update : key -> ( 'a option -> 'a option ) -> 'a t -> 'a t`

`update key f m` returns a map containing the same bindings as `m`, except for the binding of `key`. Depending on the value of `y` where `y` is `f (find_opt key m)`, the binding of `key` is added, removed or updated. If `y` is `None`, the binding is removed if it exists; otherwise, if `y` is `Some z` then `key` is associated to `z` in the resulting map. If `key` was already bound in `m` to a value that is physically equal to `z`, `m` is returned unchanged (the result of the function is then physically equal to `m`).

• since 4.06.0
`val singleton : key -> 'a -> 'a t`

`singleton x y` returns the one-element map that contains a binding `y` for `x`.

• since 3.12.0
`val remove : key -> 'a t -> 'a t`

`remove x m` returns a map containing the same bindings as `m`, except for `x` which is unbound in the returned map. If `x` was not in `m`, `m` is returned unchanged (the result of the function is then physically equal to `m`).

• before 4.03

Physical equality was not ensured.

```val merge : ( key -> 'a option -> 'b option -> 'c option ) -> 'a t -> 'b t -> 'c t```

`merge f m1 m2` computes a map whose keys are a subset of the keys of `m1` and of `m2`. The presence of each such binding, and the corresponding value, is determined with the function `f`. In terms of the `find_opt` operation, we have `find_opt x (merge f m1 m2) = f x (find_opt x m1) (find_opt x m2)` for any key `x`, provided that `f x None None = None`.

• since 3.12.0
`val union : ( key -> 'a -> 'a -> 'a option ) -> 'a t -> 'a t -> 'a t`

`union f m1 m2` computes a map whose keys are a subset of the keys of `m1` and of `m2`. When the same binding is defined in both arguments, the function `f` is used to combine them. This is a special case of `merge`: `union f m1 m2` is equivalent to `merge f' m1 m2`, where

• `f' _key None None = None`
• `f' _key (Some v) None = Some v`
• `f' _key None (Some v) = Some v`
• `f' key (Some v1) (Some v2) = f key v1 v2`
• since 4.03.0
`val compare : ( 'a -> 'a -> int ) -> 'a t -> 'a t -> int`

Total ordering between maps. The first argument is a total ordering used to compare data associated with equal keys in the two maps.

`val equal : ( 'a -> 'a -> bool ) -> 'a t -> 'a t -> bool`

`equal cmp m1 m2` tests whether the maps `m1` and `m2` are equal, that is, contain equal keys and associate them with equal data. `cmp` is the equality predicate used to compare the data associated with the keys.

`val iter : ( key -> 'a -> unit ) -> 'a t -> unit`

`iter f m` applies `f` to all bindings in map `m`. `f` receives the key as first argument, and the associated value as second argument. The bindings are passed to `f` in increasing order with respect to the ordering over the type of the keys.

`val fold : ( key -> 'a -> 'b -> 'b ) -> 'a t -> 'b -> 'b`

`fold f m init` computes `(f kN dN ... (f k1 d1 init)...)`, where `k1 ... kN` are the keys of all bindings in `m` (in increasing order), and `d1 ... dN` are the associated data.

`val for_all : ( key -> 'a -> bool ) -> 'a t -> bool`

`for_all f m` checks if all the bindings of the map satisfy the predicate `f`.

• since 3.12.0
`val exists : ( key -> 'a -> bool ) -> 'a t -> bool`

`exists f m` checks if at least one binding of the map satisfies the predicate `f`.

• since 3.12.0
`val filter : ( key -> 'a -> bool ) -> 'a t -> 'a t`

`filter f m` returns the map with all the bindings in `m` that satisfy predicate `p`. If every binding in `m` satisfies `f`, `m` is returned unchanged (the result of the function is then physically equal to `m`)

• since 3.12.0
• before 4.03

Physical equality was not ensured.

`val filter_map : ( key -> 'a -> 'b option ) -> 'a t -> 'b t`

`filter_map f m` applies the function `f` to every binding of `m`, and builds a map from the results. For each binding `(k, v)` in the input map:

• if `f k v` is `None` then `k` is not in the result,
• if `f k v` is `Some v'` then the binding `(k, v')` is in the output map.

For example, the following function on maps whose values are lists

``````filter_map
(fun _k li -> match li with [] -> None | _::tl -> Some tl)
m``````

drops all bindings of `m` whose value is an empty list, and pops the first element of each value that is non-empty.

• since 4.11.0
`val partition : ( key -> 'a -> bool ) -> 'a t -> 'a t * 'a t`

`partition f m` returns a pair of maps `(m1, m2)`, where `m1` contains all the bindings of `m` that satisfy the predicate `f`, and `m2` is the map with all the bindings of `m` that do not satisfy `f`.

• since 3.12.0
`val cardinal : 'a t -> int`

Return the number of bindings of a map.

• since 3.12.0
`val bindings : 'a t -> (key * 'a) list`

Return the list of all bindings of the given map. The returned list is sorted in increasing order of keys with respect to the ordering `Ord.compare`, where `Ord` is the argument given to `Make`.

• since 3.12.0
`val min_binding : 'a t -> key * 'a`

Return the binding with the smallest key in a given map (with respect to the `Ord.compare` ordering), or raise `Not_found` if the map is empty.

• since 3.12.0
`val min_binding_opt : 'a t -> (key * 'a) option`

Return the binding with the smallest key in the given map (with respect to the `Ord.compare` ordering), or `None` if the map is empty.

• since 4.05
`val max_binding : 'a t -> key * 'a`

Same as `S`.min_binding, but returns the binding with the largest key in the given map.

• since 3.12.0
`val max_binding_opt : 'a t -> (key * 'a) option`

Same as `S`.min_binding_opt, but returns the binding with the largest key in the given map.

• since 4.05
`val choose : 'a t -> key * 'a`

Return one binding of the given map, or raise `Not_found` if the map is empty. Which binding is chosen is unspecified, but equal bindings will be chosen for equal maps.

• since 3.12.0
`val choose_opt : 'a t -> (key * 'a) option`

Return one binding of the given map, or `None` if the map is empty. Which binding is chosen is unspecified, but equal bindings will be chosen for equal maps.

• since 4.05
`val split : key -> 'a t -> 'a t * 'a option * 'a t`

`split x m` returns a triple `(l, data, r)`, where `l` is the map with all the bindings of `m` whose key is strictly less than `x`; `r` is the map with all the bindings of `m` whose key is strictly greater than `x`; `data` is `None` if `m` contains no binding for `x`, or `Some v` if `m` binds `v` to `x`.

• since 3.12.0
`val find : key -> 'a t -> 'a`

`find x m` returns the current value of `x` in `m`, or raises `Not_found` if no binding for `x` exists.

`val find_opt : key -> 'a t -> 'a option`

`find_opt x m` returns `Some v` if the current value of `x` in `m` is `v`, or `None` if no binding for `x` exists.

• since 4.05
`val find_first : ( key -> bool ) -> 'a t -> key * 'a`

`find_first f m`, where `f` is a monotonically increasing function, returns the binding of `m` with the lowest key `k` such that `f k`, or raises `Not_found` if no such key exists.

For example, `find_first (fun k -> Ord.compare k x >= 0) m` will return the first binding `k, v` of `m` where `Ord.compare k x >= 0` (intuitively: `k >= x`), or raise `Not_found` if `x` is greater than any element of `m`.

• since 4.05
`val find_first_opt : ( key -> bool ) -> 'a t -> (key * 'a) option`

`find_first_opt f m`, where `f` is a monotonically increasing function, returns an option containing the binding of `m` with the lowest key `k` such that `f k`, or `None` if no such key exists.

• since 4.05
`val find_last : ( key -> bool ) -> 'a t -> key * 'a`

`find_last f m`, where `f` is a monotonically decreasing function, returns the binding of `m` with the highest key `k` such that `f k`, or raises `Not_found` if no such key exists.

• since 4.05
`val find_last_opt : ( key -> bool ) -> 'a t -> (key * 'a) option`

`find_last_opt f m`, where `f` is a monotonically decreasing function, returns an option containing the binding of `m` with the highest key `k` such that `f k`, or `None` if no such key exists.

• since 4.05
`val map : ( 'a -> 'b ) -> 'a t -> 'b t`

`map f m` returns a map with same domain as `m`, where the associated value `a` of all bindings of `m` has been replaced by the result of the application of `f` to `a`. The bindings are passed to `f` in increasing order with respect to the ordering over the type of the keys.

`val mapi : ( key -> 'a -> 'b ) -> 'a t -> 'b t`

Same as `S`.map, but the function receives as arguments both the key and the associated value for each binding of the map.

## Iterators

`val to_seq : 'a t -> (key * 'a) Seq.t`

Iterate on the whole map, in ascending order of keys

• since 4.07
`val to_rev_seq : 'a t -> (key * 'a) Seq.t`

Iterate on the whole map, in descending order of keys

• since 4.12
`val to_seq_from : key -> 'a t -> (key * 'a) Seq.t`

`to_seq_from k m` iterates on a subset of the bindings of `m`, in ascending order of keys, from key `k` or above.

• since 4.07
`val add_seq : (key * 'a) Seq.t -> 'a t -> 'a t`

Add the given bindings to the map, in order.

• since 4.07
`val of_seq : (key * 'a) Seq.t -> 'a t`

Build a map from the given bindings

• since 4.07