A wrapper around a regular HashMap with a type parameter s identifying the set of keys present in the map.

A key of type k may not be present in the map, but a Key s k is guaranteed to be present (if the s parameters match). Thus the map is isomorphic to a (total) function Key s k -> a, which motivates many of the instances below.

A HashMap always knows its set of keys, so given HashMap s k a we can always derive KnownHashSet s k by pattern matching on the Dict returned by keysSet.

Key s k is a key of type k that has been verified to be an element of the set s, and thus verified to be present in all HashMap s k maps.

Thus, Key s k is a "refinement" type of k, and this library integrates with an implementation of refimenement types in Refined, so the machinery from there can be used to manipulate Keys (however see revealPredicate).

The underlying k value can be obtained with unrefine. A k can be validated into an Key s k with member.

An existential wrapper for a HashMap with an as-yet-unknown set of keys. Pattern maching on it gives you a way to refer to the set (the parameter s), e.g.

case fromHashMap ... of
  SomeHashMap @s m -> doSomethingWith @s

case fromHashMap ... of
  SomeHashMap (m :: HashMap s k a) -> doSomethingWith @s

Apply a map with an unknown set of keys to a continuation that can accept a map with any set of keys. This gives you a way to refer to the set (the parameter s), e.g.:

withHashMap (fromHashMap ...
  $ (m :: HashMap s k a) -> doSomethingWith @s

An existential wrapper for a HashMap with an as-yet-unknown set of keys, together with a proof of some fact p about the set. Pattern matching on it gives you a way to refer to the set (the parameter s). Functions that change the set of keys in a map will return the map in this way, together with a proof that somehow relates the keys set to the function's inputs.

Apply a map with proof for an unknown set of keys to a continuation that can accept a map with any set of keys satisfying the proof. This gives you a way to refer to the set (the parameter s).

An existential wrapper for a pair of maps with as-yet-unknown sets of keys, together with a proof of some fact p relating them.

Apply a pair of maps with proof for unknown sets of keys to a continuation that can accept any pair of maps with any sets of keys satisfying the proof. This gives you a way to refer to the sets (the parameters s and t).

Proof that s is a superset of the set r.

Proof that the set r is empty.

An empty map.

Create a map with a single key-value pair, and return a proof that the key is in the resulting map.

Proof that r contains an element of type a.

Create a map from a set of keys, and a function that for each key computes the corresponding value.

Construct a map from a regular HashMap.

Create a map from an arbitrary traversable of key-value pairs.

Proof that elements of t a are contained in r.

Insert a key-value pair into the map to obtain a potentially larger map, guaranteed to contain the given key. If the key was already present, the associated value is replaced with the supplied value.

Proof that r is s with a inserted.

Overwrite a key-value pair that is known to already be in the map. The set of keys remains the same.

Insert a key-value pair into the map using a combining function, and if the key was already present, the old value is returned along with the proof that the key was present.

Delete a key and its value from the map if present, returning a potentially smaller map.

Update the value at a specific key known the be in the map using the given function. The set of keys remains the same.

If the given key is in the map, update the associated value using the given function with a proof that the key was in the map; otherwise return the map unchanged. In any case the set of keys remains the same.

Update or delete a key known to be in the map using the given function, returning a potentially smaller map.

If the given key is in the map, update or delete it using the given function with a proof that the key was in the map; otherwise the map is unchanged. Alongside return the new value if it was updated, or the old value if it was deleted, and a proof that the key was in the map.

If the key is in the map, return the proof of this, and the associated value; otherwise return Nothing.

Given a key that is proven to be in the map, return the associated value.

Unlike ! from Data.HashMap.Lazy, this function is total, as it is impossible to obtain a Key s k for a key that is not in the map HashMap s k a.

If a key is in the map, return the proof that it is.

If a map is empty, return a proof that it is.

If all keys of the first map are also present in the second map, and the given function returns True for their associated values, return a proof that the keys form a subset.

Proof that s is a subset of the set r.

If two maps are disjoint (i.e. their intersection is empty), return a proof of that.

Proof that s and r are disjoint.

Given two maps proven to have the same keys, for each key apply the function to the associated values, to obtain a new map with the same keys.

bind m f is a map that for each key k :: Key s k, contains the value f (m ! k) ! k, similar to >>= for functions.

Return the union of two maps, with a given combining function for keys that exist in both maps simultaneously.

You can use andLeft and andRight to obtain Key s k and Key t k respectively.

Proof that unioning s and t gives r.

Remove the keys that appear in the second map from the first map.

Proof that if from s you subtract t, then you get r.

For keys that appear in both maps, the given function decides whether the key is removed from the first map.

You can use andLeft and andRight to obtain Key s k and Key t k respectively.

Proof that r is obtained by removing some of t's elements from s.

Return the intersection of two maps with the given combining function.

You can use andLeft and andRight to obtain Key s k and Key t k respectively.

Proof that intersecting s and t gives r.

Apply a function to all values in a map, together with their corresponding keys, that are proven to be in the map. The set of keys remains the same.

Map an Applicative transformation with access to each value's corresponding key and a proof that it is in the map. The set of keys remains unchanged.

Thread an accumularing argument through the map in ascending order of hashes.

Thread an accumularing argument through the map in descending order of hashes.

mapKeysWith c f m applies f to each key of m and collects the results into a new map. For keys that were mapped to the same new key, c acts as the combining function for corresponding values.

Proof that r is the direct image of s under some mapping f :: a -> b.

Apply the inverse image of the given function to the keys of the given map, so that for all k :: Key s2 k2, backpermuteKeys f m ! k = m ! f k.

If maps are identified with functions, this computes the composition.

Map each key-value pair of a map into a monoid (with proof that the key was in the map), and combine the results using <>.

Right associative fold with a lazy accumulator.

Left associative fold with a lazy accumulator.

Right associative fold with a strict accumulator.

Left associative fold with a strict accumulator.

Convert to a regular HashMap, forgetting its set of keys.

Return the set of keys in the map, with the contents of the set still tracked by the s parameter. See Data.HashSet.Refined.

Convert to a list of key-value pairs.

Restrict a map to only those keys that are elements of t.

Remove all keys that are elements of t from the map.

Retain only the key-value pairs that satisfy the predicate, returning a potentially smaller map.

Partition a map into two disjoint submaps: those whose key-value pairs satisfy the predicate, and those whose don't.

Proof that s is the union of disjoint subsets r and q, together with a procedure that decides which of the two an element belongs to.

Apply a function to all values in a map, together with their corresponding keys, and collect only the Just results, returning a potentially smaller map.

Apply a function to all values in a map, together with their corresponding keys, and collect the Left and Right results into separate (disjoint) maps.

If elements of s can be weakened to elements of t and vice versa, then s and t actually stand for the same set and Key s can be safely interconverted with Key t.

The requirement that the weakenings are natural transformations ensures that they don't actually alter the keys. To build these you can compose :->'s from proofs returned by functions in this module, or Refined functions like andLeft or leftOr.

If keys can be interconverted (e.g. as proved by castKey), then the maps can be interconverted too. For example, zipWithKey can be implemented via intersectionWithKey by proving that the set of keys remains unchanged:

zipWithKey
  :: forall s k a b c. Hashable k
  => (Key s k -> a -> b -> c) -> HashMap s k a -> HashMap s k b -> HashMap s k c
zipWithKey f m1 m2
  | SomeHashMapWith @r m proof <- intersectionWithKey (f . andLeft) m1 m2
  , IntersectionProof p1 p2 <- proof
  , ( Coercion :: Coercion (HashMap r k c) (HashMap s k c))
    <- app $ cast $ castKey (andLeft . p1) (p2 id id)
  = coerce m
  where
    app :: Coercion f g -> Coercion (f x) (g x)
    app Coercion = Coercion

This function can be used to freely convert between Element and Key types of various flavors (Regular, Int, Hashed), corresponding to the different implementations of sets and maps.