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|
(.module:
[lux #*
[control
[functor (#+ Functor)]
[apply (#+ Apply)]
[monad (#+ do Monad)]
[equivalence (#+ Equivalence)]
monoid
fold
["p" parser]
[predicate (#+ Predicate)]]
[data
["." maybe]
["." product]
[number
["." i64]]
[collection
["." list ("list/." fold functor monoid)]
["." array (#+ Array) ("array/." functor fold)]]]
[macro (#+ with-gensyms)
["." code]
["s" syntax (#+ syntax: Syntax)]]])
## [Utils]
(type: (Node a)
(#Base (Array a))
(#Hierarchy (Array (Node a))))
(type: (Base a) (Array a))
(type: (Hierarchy a) (Array (Node a)))
(type: Level Nat)
(type: Index Nat)
(def: branching-exponent
Nat
5)
(def: root-level
Level
0)
(do-template [<name> <op>]
[(def: <name>
(-> Level Level)
(<op> branching-exponent))]
[level-up n/+]
[level-down n/-]
)
(def: full-node-size
Nat
(i64.left-shift branching-exponent 1))
(def: branch-idx-mask
Nat
(dec full-node-size))
(def: branch-idx
(-> Index Index)
(i64.and branch-idx-mask))
(def: (new-hierarchy _)
(All [a] (-> Any (Hierarchy a)))
(array.new full-node-size))
(def: (tail-off vec-size)
(-> Nat Nat)
(if (n/< full-node-size vec-size)
0
(|> (dec vec-size)
(i64.logical-right-shift branching-exponent)
(i64.left-shift branching-exponent))))
(def: (new-path level tail)
(All [a] (-> Level (Base a) (Node a)))
(if (n/= 0 level)
(#Base tail)
(|> (new-hierarchy [])
(array.write 0 (new-path (level-down level) tail))
#Hierarchy)))
(def: (new-tail singleton)
(All [a] (-> a (Base a)))
(|> (array.new 1)
(array.write 0 singleton)))
(def: (push-tail size level tail parent)
(All [a] (-> Nat Level (Base a) (Hierarchy a) (Hierarchy a)))
(let [sub-idx (branch-idx (i64.logical-right-shift level (dec size)))
## If we're currently on a bottom node
sub-node (if (n/= branching-exponent level)
## Just add the tail to it
(#Base tail)
## Otherwise, check whether there's a vacant spot
(case (array.read sub-idx parent)
## If so, set the path to the tail
#.None
(new-path (level-down level) tail)
## If not, push the tail onto the sub-node.
(#.Some (#Hierarchy sub-node))
(#Hierarchy (push-tail size (level-down level) tail sub-node))
_
(undefined))
)]
(|> (array.clone parent)
(array.write sub-idx sub-node))))
(def: (expand-tail val tail)
(All [a] (-> a (Base a) (Base a)))
(let [tail-size (array.size tail)]
(|> (array.new (inc tail-size))
(array.copy tail-size 0 tail 0)
(array.write tail-size val))))
(def: (put' level idx val hierarchy)
(All [a] (-> Level Index a (Hierarchy a) (Hierarchy a)))
(let [sub-idx (branch-idx (i64.logical-right-shift level idx))]
(case (array.read sub-idx hierarchy)
(#.Some (#Hierarchy sub-node))
(|> (array.clone hierarchy)
(array.write sub-idx (#Hierarchy (put' (level-down level) idx val sub-node))))
(^multi (#.Some (#Base base))
(n/= 0 (level-down level)))
(|> (array.clone hierarchy)
(array.write sub-idx (|> (array.clone base)
(array.write (branch-idx idx) val)
#Base)))
_
(undefined))))
(def: (pop-tail size level hierarchy)
(All [a] (-> Nat Level (Hierarchy a) (Maybe (Hierarchy a))))
(let [sub-idx (branch-idx (i64.logical-right-shift level (n/- 2 size)))]
(cond (n/= 0 sub-idx)
#.None
(n/> branching-exponent level)
(do maybe.monad
[base|hierarchy (array.read sub-idx hierarchy)
sub (case base|hierarchy
(#Hierarchy sub)
(pop-tail size (level-down level) sub)
(#Base _)
(undefined))]
(|> (array.clone hierarchy)
(array.write sub-idx (#Hierarchy sub))
#.Some))
## Else...
(|> (array.clone hierarchy)
(array.delete sub-idx)
#.Some)
)))
(def: (to-list' node)
(All [a] (-> (Node a) (List a)))
(case node
(#Base base)
(array.to-list base)
(#Hierarchy hierarchy)
(|> hierarchy
array.to-list
list.reverse
(list/fold (function (_ sub acc) (list/compose (to-list' sub) acc))
#.Nil))))
## [Types]
(type: #export (Row a)
{#level Level
#size Nat
#root (Hierarchy a)
#tail (Base a)})
## [Exports]
(def: #export empty
Row
{#level (level-up root-level)
#size 0
#root (array.new full-node-size)
#tail (array.new 0)})
(def: #export (size row)
(All [a] (-> (Row a) Nat))
(get@ #size row))
(def: #export (add val vec)
(All [a] (-> a (Row a) (Row a)))
## Check if there is room in the tail.
(let [vec-size (get@ #size vec)]
(if (|> vec-size (n/- (tail-off vec-size)) (n/< full-node-size))
## If so, append to it.
(|> vec
(update@ #size inc)
(update@ #tail (expand-tail val)))
## Otherwise, push tail into the tree
## --------------------------------------------------------
## Will the root experience an overflow with this addition?
(|> (if (n/> (i64.left-shift (get@ #level vec) 1)
(i64.logical-right-shift branching-exponent vec-size))
## If so, a brand-new root must be established, that is
## 1-level taller.
(|> vec
(set@ #root (|> (: (Hierarchy ($ 0))
(new-hierarchy []))
## TODO: Remove version above once new-luxc becomes the standard compiler.
## (new-hierarchy [])
(array.write 0 (#Hierarchy (get@ #root vec)))
(array.write 1 (new-path (get@ #level vec) (get@ #tail vec)))))
(update@ #level level-up))
## Otherwise, just push the current tail onto the root.
(|> vec
(update@ #root (push-tail vec-size (get@ #level vec) (get@ #tail vec)))))
## Finally, update the size of the row and grow a new
## tail with the new element as it's sole member.
(update@ #size inc)
(set@ #tail (new-tail val)))
)))
(def: (base-for idx vec)
(All [a] (-> Index (Row a) (Maybe (Base a))))
(let [vec-size (get@ #size vec)]
(if (and (n/>= 0 idx)
(n/< vec-size idx))
(if (n/>= (tail-off vec-size) idx)
(#.Some (get@ #tail vec))
(loop [level (get@ #level vec)
hierarchy (get@ #root vec)]
(case [(n/> branching-exponent level)
(array.read (branch-idx (i64.logical-right-shift level idx)) hierarchy)]
[#1 (#.Some (#Hierarchy sub))]
(recur (level-down level) sub)
[#0 (#.Some (#Base base))]
(#.Some base)
[_ #.None]
#.None
_
(error! "Incorrect row structure."))))
#.None)))
(def: #export (nth idx vec)
(All [a] (-> Nat (Row a) (Maybe a)))
(do maybe.monad
[base (base-for idx vec)]
(array.read (branch-idx idx) base)))
(def: #export (put idx val vec)
(All [a] (-> Nat a (Row a) (Row a)))
(let [vec-size (get@ #size vec)]
(if (and (n/>= 0 idx)
(n/< vec-size idx))
(if (n/>= (tail-off vec-size) idx)
(|> vec
## (update@ #tail (|>> array.clone (array.write (branch-idx idx) val)))
## TODO: Remove once new-luxc becomes the standard compiler.
(update@ #tail (: (-> (Base ($ 0)) (Base ($ 0)))
(|>> array.clone (array.write (branch-idx idx) val))))
)
(|> vec
(update@ #root (put' (get@ #level vec) idx val))))
vec)))
(def: #export (update idx f vec)
(All [a] (-> Nat (-> a a) (Row a) (Row a)))
(case (nth idx vec)
(#.Some val)
(put idx (f val) vec)
#.None
vec))
(def: #export (pop vec)
(All [a] (-> (Row a) (Row a)))
(case (get@ #size vec)
0
empty
1
empty
vec-size
(if (|> vec-size (n/- (tail-off vec-size)) (n/> 1))
(let [old-tail (get@ #tail vec)
new-tail-size (dec (array.size old-tail))]
(|> vec
(update@ #size dec)
(set@ #tail (|> (array.new new-tail-size)
(array.copy new-tail-size 0 old-tail 0)))))
(maybe.assume
(do maybe.monad
[new-tail (base-for (n/- 2 vec-size) vec)
#let [[level' root'] (let [init-level (get@ #level vec)]
(loop [level init-level
root (maybe.default (new-hierarchy [])
(pop-tail vec-size init-level (get@ #root vec)))]
(if (n/> branching-exponent level)
(case [(array.read 1 root) (array.read 0 root)]
[#.None (#.Some (#Hierarchy sub-node))]
(recur (level-down level) sub-node)
## [#.None (#.Some (#Base _))]
## (undefined)
_
[level root])
[level root])))]]
(wrap (|> vec
(update@ #size dec)
(set@ #level level')
(set@ #root root')
(set@ #tail new-tail))))))
))
(def: #export (to-list vec)
(All [a] (-> (Row a) (List a)))
(list/compose (to-list' (#Hierarchy (get@ #root vec)))
(to-list' (#Base (get@ #tail vec)))))
(def: #export from-list
(All [a] (-> (List a) (Row a)))
(list/fold ..add ..empty))
(def: #export (member? a/Equivalence vec val)
(All [a] (-> (Equivalence a) (Row a) a Bit))
(list.member? a/Equivalence (to-list vec) val))
(def: #export empty?
(All [a] (-> (Row a) Bit))
(|>> (get@ #size) (n/= 0)))
## [Syntax]
(syntax: #export (row {elems (p.some s.any)})
{#.doc (doc "Row literals."
(row +10 +20 +30 +40))}
(wrap (list (` (from-list (list (~+ elems)))))))
## [Structures]
(structure: #export (node-equivalence Equivalence<a>) (All [a] (-> (Equivalence a) (Equivalence (Node a))))
(def: (= v1 v2)
(case [v1 v2]
[(#Base b1) (#Base b2)]
(:: (array.equivalence Equivalence<a>) = b1 b2)
[(#Hierarchy h1) (#Hierarchy h2)]
(:: (array.equivalence (node-equivalence Equivalence<a>)) = h1 h2)
_
#0)))
(structure: #export (equivalence Equivalence<a>) (All [a] (-> (Equivalence a) (Equivalence (Row a))))
(def: (= v1 v2)
(and (n/= (get@ #size v1) (get@ #size v2))
(let [(^open "Node/.") (node-equivalence Equivalence<a>)]
(and (Node/= (#Base (get@ #tail v1))
(#Base (get@ #tail v2)))
(Node/= (#Hierarchy (get@ #root v1))
(#Hierarchy (get@ #root v2))))))))
(structure: node-fold (Fold Node)
(def: (fold f init xs)
(case xs
(#Base base)
(array/fold f init base)
(#Hierarchy hierarchy)
(array/fold (function (_ node init') (fold f init' node))
init
hierarchy))))
(structure: #export fold (Fold Row)
(def: (fold f init xs)
(let [(^open ".") node-fold]
(fold f
(fold f
init
(#Hierarchy (get@ #root xs)))
(#Base (get@ #tail xs))))))
(structure: #export monoid (All [a] (Monoid (Row a)))
(def: identity ..empty)
(def: (compose xs ys)
(list/fold add xs (..to-list ys))))
(structure: node-functor (Functor Node)
(def: (map f xs)
(case xs
(#Base base)
(#Base (array/map f base))
(#Hierarchy hierarchy)
(#Hierarchy (array/map (map f) hierarchy)))))
(structure: #export functor (Functor Row)
(def: (map f xs)
{#level (get@ #level xs)
#size (get@ #size xs)
#root (|> xs (get@ #root) (array/map (:: node-functor map f)))
#tail (|> xs (get@ #tail) (array/map f))}))
(structure: #export apply (Apply Row)
(def: &functor ..functor)
(def: (apply ff fa)
(let [(^open ".") ..functor
(^open ".") ..fold
(^open ".") ..monoid
results (map (function (_ f) (map f fa))
ff)]
(fold compose identity results))))
(structure: #export monad (Monad Row)
(def: &functor ..functor)
(def: wrap (|>> row))
(def: join
(let [(^open ".") ..fold
(^open ".") ..monoid]
(fold (function (_ post pre) (compose pre post)) identity))))
## TODO: This definition of 'reverse' shouldn't work correctly.
## Investigate if/why it does.
(def: #export reverse
(All [a] (-> (Row a) (Row a)))
(let [(^open ".") ..fold
(^open ".") ..monoid]
(fold add identity)))
(do-template [<name> <array> <init> <op>]
[(def: #export <name>
(All [a]
(-> (Predicate a) (Row a) Bit))
(let [help (: (All [a]
(-> (Predicate a) (Node a) Bit))
(function (help predicate node)
(case node
(#Base base)
(<array> predicate base)
(#Hierarchy hierarchy)
(<array> (help predicate) hierarchy))))]
(function (<name> predicate row)
(let [(^slots [#root #tail]) row]
(<op> (help predicate (#Hierarchy root))
(help predicate (#Base tail)))))))]
[every? array.every? #1 and]
[any? array.any? #0 or]
)
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