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|
## Copyright (c) Eduardo Julian. All rights reserved.
## This Source Code Form is subject to the terms of the Mozilla Public License, v. 2.0.
## If a copy of the MPL was not distributed with this file,
## You can obtain one at http://mozilla.org/MPL/2.0/.
(;module:
lux
(lux (control hash
eq)
(data maybe
(struct [list "List/" Fold<List> Functor<List> Monoid<List>]
[array #+ Array "Array/" Functor<Array> Fold<Array>])
[bit]
[product]
text/format
[number])
))
## This implementation of Hash Array Mapped Trie (HAMT) is based on
## Clojure's PersistentHashMap implementation.
## That one is further based on Phil Bagwell's Hash Array Mapped Trie.
## [Utils]
## Bitmaps are used to figure out which branches on a #Base node are
## populated. The number of bits that are 1s in a bitmap signal the
## size of the #Base node.
(type: BitMap Nat)
## Represents the position of a node in a BitMap.
## It's meant to be a single bit set on a 32-bit word.
## The position of the bit reflects whether an entry in an analogous
## position exists within a #Base, as reflected in it's BitMap.
(type: BitPosition Nat)
## An index into an array.
(type: Index Nat)
## A hash-code derived from a key during tree-traversal.
(type: Hash-Code Nat)
## Represents the nesting level of a leaf or node, when looking-it-up
## while exploring the tree.
## Changes in levels are done by right-shifting the hashes of keys by
## the appropriate multiple of the branching-exponent.
## A shift of 0 means root level.
## A shift of (* branching-exponent 1) means level 2.
## A shift of (* branching-exponent N) means level N+1.
(type: Level Nat)
## Nodes for the tree data-structure that organizes the data inside
## Dicts.
(type: (Node k v)
(#Hierarchy Nat (Array (Node k v)))
(#Base BitMap
(Array (Either (Node k v)
[k v])))
(#Collisions Hash-Code (Array [k v])))
## #Hierarchy nodes are meant to point down only to lower-level nodes.
(type: (Hierarchy k v)
[Nat (Array (Node k v))])
## #Base nodes may point down to other nodes, but also to leaves,
## which are KV pairs.
(type: (Base k v)
(Array (Either (Node k v)
[k v])))
## #Collisions are collections of KV-pairs for which the key is
## different on each case, but their hashes are all the same (thus
## causing a collision).
(type: (Collisions k v)
(Array [k v]))
## That bitmap for an empty #Base is 0.
## Which is the same as 0000 0000 0000 0000 0000 0000 0000 0000.
## Or 0x00000000.
## Which is 32 zeroes, since the branching factor is 32.
(def: clean-bitmap
BitMap
+0)
## Bitmap position (while looking inside #Base nodes) is determined by
## getting 5 bits from a hash of the key being looked up and using
## them as an index into the array inside #Base.
## Since the data-structure can have multiple levels (and the hash has
## more than 5 bits), the binary-representation of the hash is shifted
## by 5 positions on each step (2^5 = 32, which is the branching
## factor).
## The initial shifting level, though, is 0 (which corresponds to the
## shift in the shallowest node on the tree, which is the root node).
(def: root-level
Level
+0)
## The exponent to which 2 must be elevated, to reach the branching
## factor of the data-structure.
(def: branching-exponent
Nat
+5)
## The threshold on which #Hierarchy nodes are demoted to #Base nodes,
## which is 1/4 of the branching factor (or a left-shift 2).
(def: demotion-threshold
Nat
(bit;<< (n.- +2 branching-exponent) +1))
## The threshold on which #Base nodes are promoted to #Hierarchy nodes,
## which is 1/2 of the branching factor (or a left-shift 1).
(def: promotion-threshold
Nat
(bit;<< (n.- +1 branching-exponent) +1))
## The size of hierarchy-nodes, which is 2^(branching-exponent).
(def: hierarchy-nodes-size
Nat
(bit;<< branching-exponent +1))
## The cannonical empty node, which is just an empty #Base node.
(def: empty
Node
(#Base clean-bitmap (array;new +0)))
## Expands a copy of the array, to have 1 extra slot, which is used
## for storing the value.
(def: (insert! idx value old-array)
(All [a] (-> Index a (Array a) (Array a)))
(let [old-size (array;size old-array)]
(|> (: (Array ($ +0))
(array;new (n.inc old-size)))
(array;copy idx +0 old-array +0)
(array;put idx value)
(array;copy (n.- idx old-size) idx old-array (n.inc idx)))))
## Creates a copy of an array with an index set to a particular value.
(def: (update! idx value array)
(All [a] (-> Index a (Array a) (Array a)))
(|> array array;clone (array;put idx value)))
## Creates a clone of the array, with an empty position at index.
(def: (vacant! idx array)
(All [a] (-> Index (Array a) (Array a)))
(|> array array;clone (array;remove idx)))
## Shrinks a copy of the array by removing the space at index.
(def: (remove! idx array)
(All [a] (-> Index (Array a) (Array a)))
(let [new-size (n.dec (array;size array))]
(|> (array;new new-size)
(array;copy idx +0 array +0)
(array;copy (n.- idx new-size) (n.inc idx) array idx))))
## Given a top-limit for indices, produces all indices in [0, R).
(def: indices-for
(-> Nat (List Index))
(|>. n.dec (list;n.range +0)))
## Increases the level-shift by the branching-exponent, to explore
## levels further down the tree.
(def: level-up
(-> Level Level)
(n.+ branching-exponent))
(def: hierarchy-mask BitMap (n.dec hierarchy-nodes-size))
## Gets the branching-factor sized section of the hash corresponding
## to a particular level, and uses that as an index into the array.
(def: (level-index level hash)
(-> Level Hash-Code Index)
(bit;& hierarchy-mask
(bit;>>> level hash)))
## A mechanism to go from indices to bit-positions.
(def: (->bit-position index)
(-> Index BitPosition)
(bit;<< index +1))
## The bit-position within a base that a given hash-code would have.
(def: (bit-position level hash)
(-> Level Hash-Code BitPosition)
(->bit-position (level-index level hash)))
(def: (bit-position-is-set? bit bitmap)
(-> BitPosition BitMap Bool)
(not (n.= clean-bitmap (bit;& bit bitmap))))
## Figures out whether a bitmap only contains a single bit-position.
(def: only-bit-position?
(-> BitPosition BitMap Bool)
n.=)
(def: (set-bit-position bit bitmap)
(-> BitPosition BitMap BitMap)
(bit;| bit bitmap))
(def: unset-bit-position
(-> BitPosition BitMap BitMap)
bit;^)
## Figures out the size of a bitmap-indexed array by counting all the
## 1s within the bitmap.
(def: bitmap-size
(-> BitMap Nat)
bit;count)
## A mask that, for a given bit position, only allows all the 1s prior
## to it, which would indicate the bitmap-size (and, thus, index)
## associated with it.
(def: bit-position-mask
(-> BitPosition BitMap)
n.dec)
## The index on the base array, based on it's bit-position.
(def: (base-index bit-position bitmap)
(-> BitPosition BitMap Index)
(bitmap-size (bit;& (bit-position-mask bit-position)
bitmap)))
## Produces the index of a KV-pair within a #Collisions node.
(def: (collision-index Hash<K> key colls)
(All [K V] (-> (Hash K) K (Collisions K V) (Maybe Index)))
(:: Monad<Maybe> map product;left
(array;find+ (lambda [idx [key' val']]
(:: Hash<K> = key key'))
colls)))
## When #Hierarchy nodes grow too small, they're demoted to #Base
## nodes to save space.
(def: (demote-hierarchy except-idx [h-size h-array])
(All [k v] (-> Index (Hierarchy k v) [BitMap (Base k v)]))
(List/fold (lambda [idx (^@ node [bitmap base])]
(case (array;get idx h-array)
#;None node
(#;Some sub-node) (if (n.= except-idx idx)
node
[(set-bit-position (->bit-position idx) bitmap)
(array;put idx (#;Left sub-node) base)])
))
[clean-bitmap
(: (Base ($ +0) ($ +1))
(array;new (n.dec h-size)))]
(list;indices (array;size h-array))))
## When #Base nodes grow too large, they're promoted to #Hierarchy to
## add some depth to the tree and help keep it's balance.
(def: (promote-base put' Hash<K> level bitmap base)
(All [K V]
(-> (-> Level Hash-Code K V (Hash K) (Node K V) (Node K V))
(Hash K) Level
BitMap (Base K V)
(Array (Node K V))))
(product;right (List/fold (lambda [hierarchy-idx (^@ default [base-idx h-array])]
(if (bit-position-is-set? (->bit-position hierarchy-idx)
bitmap)
[(n.inc base-idx)
(case (array;get base-idx base)
(#;Some (#;Left sub-node))
(array;put hierarchy-idx sub-node h-array)
(#;Some (#;Right [key' val']))
(array;put hierarchy-idx
(put' (level-up level) (:: Hash<K> hash key') key' val' Hash<K> empty)
h-array)
#;None
(undefined))]
default))
[+0
(: (Array (Node ($ +0) ($ +1)))
(array;new hierarchy-nodes-size))]
(indices-for hierarchy-nodes-size))))
## All empty nodes look the same (a #Base node with clean bitmap is
## used).
## So, this test is introduced to detect them.
(def: (empty?' node)
(All [K V] (-> (Node K V) Bool))
(case node
(^~ (#Base ;;clean-bitmap _))
true
_
false))
(def: (put' level hash key val Hash<K> node)
(All [K V] (-> Level Hash-Code K V (Hash K) (Node K V) (Node K V)))
(case node
## For #Hierarchy nodes, I check whether I can add the element to
## a sub-node. If impossible, I introduced a new singleton sub-node.
(#Hierarchy _size hierarchy)
(let [idx (level-index level hash)
[_size' sub-node] (: [Nat (Node ($ +0) ($ +1))]
(case (array;get idx hierarchy)
(#;Some sub-node)
[_size sub-node]
_
[(n.inc _size) empty]))]
(#Hierarchy _size'
(update! idx (put' (level-up level) hash key val Hash<K> sub-node)
hierarchy)))
## For #Base nodes, I check if the corresponding BitPosition has
## already been used.
(#Base bitmap base)
(let [bit (bit-position level hash)]
(if (bit-position-is-set? bit bitmap)
## If so...
(let [idx (base-index bit bitmap)]
(case (array;get idx base)
#;None
(undefined)
## If it's being used by a node, I add the KV to it.
(#;Some (#;Left sub-node))
(let [sub-node' (put' (level-up level) hash key val Hash<K> sub-node)]
(#Base bitmap (update! idx (#;Left sub-node') base)))
## Otherwise, if it's being used by a KV, I compare the keys.
(#;Some (#;Right key' val'))
(if (:: Hash<K> = key key')
## If the same key is found, I replace the value.
(#Base bitmap (update! idx (#;Right key val) base))
## Otherwise, I compare the hashes of the keys.
(#Base bitmap (update! idx
(#;Left (let [hash' (:: Hash<K> hash key')]
(if (n.= hash hash')
## If the hashes are
## the same, a new
## #Collisions node
## is added.
(#Collisions hash (|> (: (Array [($ +0) ($ +1)])
(array;new +2))
(array;put +0 [key' val'])
(array;put +1 [key val])))
## Otherwise, I can
## just keep using
## #Base nodes, so I
## add both KV pairs
## to the empty one.
(let [next-level (level-up level)]
(|> empty
(put' next-level hash' key' val' Hash<K>)
(put' next-level hash key val Hash<K>))))))
base)))))
## However, if the BitPosition has not been used yet, I check
## whether this #Base node is ready for a promotion.
(let [base-count (bitmap-size bitmap)]
(if (n.>= promotion-threshold base-count)
## If so, I promote it to a #Hierarchy node, and add the new
## KV-pair as a singleton node to it.
(#Hierarchy (n.inc base-count)
(|> (promote-base put' Hash<K> level bitmap base)
(array;put (level-index level hash)
(put' (level-up level) hash key val Hash<K> empty))))
## Otherwise, I just resize the #Base node to accommodate the
## new KV-pair.
(#Base (set-bit-position bit bitmap)
(insert! (base-index bit bitmap) (#;Right [key val]) base))))))
## For #Collisions nodes, I compare the hashes.
(#Collisions _hash _colls)
(if (n.= hash _hash)
## If they're equal, that means the new KV contributes to the
## collisions.
(case (collision-index Hash<K> key _colls)
## If the key was already present in the collisions-list, it's
## value gets updated.
(#;Some coll-idx)
(#Collisions _hash (update! coll-idx [key val] _colls))
## Otherwise, the KV-pair is added to the collisions-list.
#;None
(#Collisions _hash (insert! (array;size _colls) [key val] _colls)))
## If the hashes are not equal, I create a new #Base node that
## contains the old #Collisions node, plus the new KV-pair.
(|> (#Base (bit-position level _hash)
(|> (: (Base ($ +0) ($ +1))
(array;new +1))
(array;put +0 (#;Left node))))
(put' level hash key val Hash<K>)))
))
(def: (remove' level hash key Hash<K> node)
(All [K V] (-> Level Hash-Code K (Hash K) (Node K V) (Node K V)))
(case node
## For #Hierarchy nodes, find out if there's a valid sub-node for
## the Hash-Code.
(#Hierarchy h-size h-array)
(let [idx (level-index level hash)]
(case (array;get idx h-array)
## If not, there's nothing to remove.
#;None
node
## But if there is, try to remove the key from the sub-node.
(#;Some sub-node)
(let [sub-node' (remove' (level-up level) hash key Hash<K> sub-node)]
## Then check if a removal was actually done.
(if (is sub-node sub-node')
## If not, then there's nothing to change here either.
node
## But if the sub-removal yielded an empty sub-node...
(if (empty?' sub-node')
## Check if it's due time for a demotion.
(if (n.<= demotion-threshold h-size)
## If so, perform it.
(#Base (demote-hierarchy idx [h-size h-array]))
## Otherwise, just clear the space.
(#Hierarchy (n.dec h-size) (vacant! idx h-array)))
## But if the sub-removal yielded a non-empty node, then
## just update the hiearchy branch.
(#Hierarchy h-size (update! idx sub-node' h-array)))))))
## For #Base nodes, check whether the BitPosition is set.
(#Base bitmap base)
(let [bit (bit-position level hash)]
(if (bit-position-is-set? bit bitmap)
(let [idx (base-index bit bitmap)]
(case (array;get idx base)
#;None
(undefined)
## If set, check if it's a sub-node, and remove the KV
## from it.
(#;Some (#;Left sub-node))
(let [sub-node' (remove' (level-up level) hash key Hash<K> sub-node)]
## Verify that it was removed.
(if (is sub-node sub-node')
## If not, there's also nothing to change here.
node
## But if it came out empty...
(if (empty?' sub-node')
### ... figure out whether that's the only position left.
(if (only-bit-position? bit bitmap)
## If so, removing it leaves this node empty too.
empty
## But if not, then just unset the position and
## remove the node.
(#Base (unset-bit-position bit bitmap)
(remove! idx base)))
## But, if it didn't come out empty, then the
## position is kept, and the node gets updated.
(#Base bitmap
(update! idx (#;Left sub-node') base)))))
## If, however, there was a KV pair instead of a sub-node.
(#;Some (#;Right [key' val']))
## Check if the keys match.
(if (:: Hash<K> = key key')
## If so, remove the KV pair and unset the BitPosition.
(#Base (unset-bit-position bit bitmap)
(remove! idx base))
## Otherwise, there's nothing to remove.
node)))
## If the BitPosition is not set, there's nothing to remove.
node))
## For #Collisions nodes, It need to find out if the key already existst.
(#Collisions _hash _colls)
(case (collision-index Hash<K> key _colls)
## If not, then there's nothing to remove.
#;None
node
## But if so, then check the size of the collisions list.
(#;Some idx)
(if (n.= +1 (array;size _colls))
## If there's only one left, then removing it leaves us with
## an empty node.
empty
## Otherwise, just shrink the array by removing the KV pair.
(#Collisions _hash (remove! idx _colls))))
))
(def: (get' level hash key Hash<K> node)
(All [K V] (-> Level Hash-Code K (Hash K) (Node K V) (Maybe V)))
(case node
## For #Hierarchy nodes, just look-up the key on its children.
(#Hierarchy _size hierarchy)
(case (array;get (level-index level hash) hierarchy)
#;None #;None
(#;Some sub-node) (get' (level-up level) hash key Hash<K> sub-node))
## For #Base nodes, check the leaves, and recursively check the branches.
(#Base bitmap base)
(let [bit (bit-position level hash)]
(if (bit-position-is-set? bit bitmap)
(case (array;get (base-index bit bitmap) base)
#;None
(undefined)
(#;Some (#;Left sub-node))
(get' (level-up level) hash key Hash<K> sub-node)
(#;Some (#;Right [key' val']))
(if (:: Hash<K> = key key')
(#;Some val')
#;None))
#;None))
## For #Collisions nodes, do a linear scan of all the known KV-pairs.
(#Collisions _hash _colls)
(:: Monad<Maybe> map product;right
(array;find (|>. product;left (:: Hash<K> = key))
_colls))
))
(def: (size' node)
(All [K V] (-> (Node K V) Nat))
(case node
(#Hierarchy _size hierarchy)
(Array/fold n.+ +0 (Array/map size' hierarchy))
(#Base _ base)
(Array/fold n.+ +0 (Array/map (lambda [sub-node']
(case sub-node'
(#;Left sub-node) (size' sub-node)
(#;Right _) +1))
base))
(#Collisions hash colls)
(array;size colls)
))
(def: (entries' node)
(All [K V] (-> (Node K V) (List [K V])))
(case node
(#Hierarchy _size hierarchy)
(Array/fold (lambda [sub-node tail] (List/append (entries' sub-node) tail))
#;Nil
hierarchy)
(#Base bitmap base)
(Array/fold (lambda [branch tail]
(case branch
(#;Left sub-node)
(List/append (entries' sub-node) tail)
(#;Right [key' val'])
(#;Cons [key' val'] tail)))
#;Nil
base)
(#Collisions hash colls)
(Array/fold (lambda [[key' val'] tail] (#;Cons [key' val'] tail))
#;Nil
colls)))
## [Exports]
(type: #export (Dict k v)
{#;doc "A dictionary implemented as a Hash-Array Mapped Trie (HAMT)."}
{#hash (Hash k)
#root (Node k v)})
(def: #export (new Hash<K>)
(All [K V] (-> (Hash K) (Dict K V)))
{#hash Hash<K>
#root empty})
(def: #export (put key val [Hash<K> node])
(All [K V] (-> K V (Dict K V) (Dict K V)))
[Hash<K> (put' root-level (:: Hash<K> hash key) key val Hash<K> node)])
(def: #export (remove key [Hash<K> node])
(All [K V] (-> K (Dict K V) (Dict K V)))
[Hash<K> (remove' root-level (:: Hash<K> hash key) key Hash<K> node)])
(def: #export (get key [Hash<K> node])
(All [K V] (-> K (Dict K V) (Maybe V)))
(get' root-level (:: Hash<K> hash key) key Hash<K> node))
(def: #export (contains? key table)
(All [K V] (-> K (Dict K V) Bool))
(case (get key table)
#;None false
(#;Some _) true))
(def: #export (put~ key val table)
{#;doc "Only puts the KV-pair if the key is not already present."}
(All [K V] (-> K V (Dict K V) (Dict K V)))
(if (contains? key table)
table
(put key val table)))
(def: #export (update key f table)
{#;doc "Transforms the value located at key (if available), using the given function."}
(All [K V] (-> K (-> V V) (Dict K V) (Dict K V)))
(case (get key table)
#;None
table
(#;Some val)
(put key (f val) table)))
(def: #export size
(All [K V] (-> (Dict K V) Nat))
(|>. product;right size'))
(def: #export empty?
(All [K V] (-> (Dict K V) Bool))
(|>. size (n.= +0)))
(def: #export (entries dict)
(All [K V] (-> (Dict K V) (List [K V])))
(entries' (product;right dict)))
(def: #export (from-list Hash<K> kvs)
(All [K V] (-> (Hash K) (List [K V]) (Dict K V)))
(List/fold (lambda [[k v] dict]
(put k v dict))
(new Hash<K>)
kvs))
(do-template [<name> <elem-type> <side>]
[(def: #export <name>
(All [K V] (-> (Dict K V) (List <elem-type>)))
(|>. entries (List/map <side>)))]
[keys K product;left]
[values V product;right]
)
(def: #export (merge dict2 dict1)
(All [K V] (-> (Dict K V) (Dict K V) (Dict K V)))
(List/fold (lambda [[key val] dict] (put key val dict))
dict1
(entries dict2)))
(def: #export (merge-with f dict1 dict2)
(All [K V] (-> (-> V V V) (Dict K V) (Dict K V) (Dict K V)))
(List/fold (lambda [[key val] dict]
(case (get key dict)
#;None
(put key val dict)
(#;Some val')
(put key (f val' val) dict)))
dict1
(entries dict2)))
(def: #export (re-bind from-key to-key dict)
(All [K V] (-> K K (Dict K V) (Dict K V)))
(case (get from-key dict)
#;None
dict
(#;Some val)
(|> dict
(remove from-key)
(put to-key val))))
(def: #export (select keys (^@ old-dict [Hash<K> _]))
{#;doc "Creates a sub-set of the given dict, with only the specified keys."}
(All [K V] (-> (List K) (Dict K V) (Dict K V)))
(List/fold (lambda [key new-dict]
(case (get key old-dict)
#;None new-dict
(#;Some val) (put key val new-dict)))
(new Hash<K>)
keys))
## [Structures]
(struct: #export (Eq<Dict> Eq<v>) (All [k v] (-> (Eq v) (Eq (Dict k v))))
(def: (= test subject)
(and (n.= (size test)
(size subject))
(list;every? (lambda [k]
(case [(get k test) (get k subject)]
[(#;Some tk) (#;Some sk)]
(:: Eq<v> = tk sk)
_
false))
(keys test)))))
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