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srfi-101.sls.txt
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srfi-101.sls.txt
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#!r6rs
;; SRFI 101: Purely Functional Random-Access Pairs and Lists
;; Copyright (c) David Van Horn 2009. All Rights Reserved.
;; Permission is hereby granted, free of charge, to any person obtaining
;; a copy of this software and associated documentation
;; files (the "Software"), to deal in the Software without restriction,
;; including without limitation the rights to use, copy, modify, merge,
;; publish, distribute, sublicense, and/or sell copies of the Software,
;; and to permit persons to whom the Software is furnished to do so,
;; subject to the following conditions:
;; The above copyright notice and this permission notice shall be
;; included in all copies or substantial portions of the Software.
;; THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
;; EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
;; MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
;; NONINFRINGEMENT. REMEMBER, THERE IS NO SCHEME UNDERGROUND. IN NO EVENT
;; SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM,
;; DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR
;; OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR
;; THE USE OR OTHER DEALINGS IN THE SOFTWARE.
(library (srfi :101)
(export (rename (ra:quote quote)
(ra:pair? pair?)
(ra:cons cons)
(ra:car car)
(ra:cdr cdr)
(ra:caar caar)
(ra:cadr cadr)
(ra:cddr cddr)
(ra:cdar cdar)
(ra:caaar caaar)
(ra:caadr caadr)
(ra:caddr caddr)
(ra:cadar cadar)
(ra:cdaar cdaar)
(ra:cdadr cdadr)
(ra:cdddr cdddr)
(ra:cddar cddar)
(ra:caaaar caaaar)
(ra:caaadr caaadr)
(ra:caaddr caaddr)
(ra:caadar caadar)
(ra:cadaar cadaar)
(ra:cadadr cadadr)
(ra:cadddr cadddr)
(ra:caddar caddar)
(ra:cdaaar cdaaar)
(ra:cdaadr cdaadr)
(ra:cdaddr cdaddr)
(ra:cdadar cdadar)
(ra:cddaar cddaar)
(ra:cddadr cddadr)
(ra:cddddr cddddr)
(ra:cdddar cdddar)
(ra:null? null?)
(ra:list? list?)
(ra:list list)
(ra:make-list make-list)
(ra:length length)
(ra:append append)
(ra:reverse reverse)
(ra:list-tail list-tail)
(ra:list-ref list-ref)
(ra:list-set list-set)
(ra:list-ref/update list-ref/update)
(ra:map map)
(ra:for-each for-each)
(ra:random-access-list->linear-access-list
random-access-list->linear-access-list)
(ra:linear-access-list->random-access-list
linear-access-list->random-access-list)))
(import (rnrs base)
(rnrs lists)
(rnrs control)
(rnrs hashtables)
(rnrs records syntactic)
(rnrs arithmetic bitwise))
(define-record-type kons (fields size tree rest))
(define-record-type node (fields val left right))
;; Nat -> Nat
(define (sub1 n) (- n 1))
(define (add1 n) (+ n 1))
;; [Tree X] -> X
(define (tree-val t)
(if (node? t)
(node-val t)
t))
;; [X -> Y] [Tree X] -> [Tree Y]
(define (tree-map f t)
(if (node? t)
(make-node (f (node-val t))
(tree-map f (node-left t))
(tree-map f (node-right t)))
(f t)))
;; [X -> Y] [Tree X] -> unspecified
(define (tree-for-each f t)
(if (node? t)
(begin (f (node-val t))
(tree-for-each f (node-left t))
(tree-for-each f (node-right t)))
(f t)))
;; [X Y Z ... -> R] [List [Tree X] [Tree Y] [Tree Z] ...] -> [Tree R]
(define (tree-map/n f ts)
(let recr ((ts ts))
(if (and (pair? ts)
(node? (car ts)))
(make-node (apply f (map node-val ts))
(recr (map node-left ts))
(recr (map node-right ts)))
(apply f ts))))
;; [X Y Z ... -> R] [List [Tree X] [Tree Y] [Tree Z] ...] -> unspecified
(define (tree-for-each/n f ts)
(let recr ((ts ts))
(if (and (pair? ts)
(node? (car ts)))
(begin (apply f (map node-val ts))
(recr (map node-left ts))
(recr (map node-right ts)))
(apply f ts))))
;; Nat [Nat -> X] -> [Tree X]
;; like build-list, but for complete binary trees
(define (build-tree i f) ;; i = 2^j-1
(let rec ((i i) (o 0))
(if (= 1 i)
(f o)
(let ((i/2 (half i)))
(make-node (f o)
(rec i/2 (add1 o))
(rec i/2 (+ 1 o i/2)))))))
;; Consumes n = 2^i-1 and produces 2^(i-1)-1.
;; Nat -> Nat
(define (half n)
(bitwise-arithmetic-shift n -1))
;; Nat X -> [Tree X]
(define (tr:make-tree i x) ;; i = 2^j-1
(let recr ((i i))
(if (= 1 i)
x
(let ((n (recr (half i))))
(make-node x n n)))))
;; Nat [Tree X] Nat [X -> X] -> X [Tree X]
(define (tree-ref/update mid t i f)
(cond ((zero? i)
(if (node? t)
(values (node-val t)
(make-node (f (node-val t))
(node-left t)
(node-right t)))
(values t (f t))))
((<= i mid)
(let-values (((v* t*) (tree-ref/update (half (sub1 mid))
(node-left t)
(sub1 i)
f)))
(values v* (make-node (node-val t) t* (node-right t)))))
(else
(let-values (((v* t*) (tree-ref/update (half (sub1 mid))
(node-right t)
(sub1 (- i mid))
f)))
(values v* (make-node (node-val t) (node-left t) t*))))))
;; Special-cased above to avoid logarathmic amount of cons'ing
;; and any multi-values overhead. Operates in constant space.
;; [Tree X] Nat Nat -> X
;; invariant: (= mid (half (sub1 (tree-count t))))
(define (tree-ref/a t i mid)
(cond ((zero? i) (tree-val t))
((<= i mid)
(tree-ref/a (node-left t)
(sub1 i)
(half (sub1 mid))))
(else
(tree-ref/a (node-right t)
(sub1 (- i mid))
(half (sub1 mid))))))
;; Nat [Tree X] Nat -> X
;; invariant: (= size (tree-count t))
(define (tree-ref size t i)
(if (zero? i)
(tree-val t)
(tree-ref/a t i (half (sub1 size)))))
;; Nat [Tree X] Nat [X -> X] -> [Tree X]
(define (tree-update size t i f)
(let recr ((mid (half (sub1 size))) (t t) (i i))
(cond ((zero? i)
(if (node? t)
(make-node (f (node-val t))
(node-left t)
(node-right t))
(f t)))
((<= i mid)
(make-node (node-val t)
(recr (half (sub1 mid))
(node-left t)
(sub1 i))
(node-right t)))
(else
(make-node (node-val t)
(node-left t)
(recr (half (sub1 mid))
(node-right t)
(sub1 (- i mid))))))))
;; ------------------------
;; Random access lists
;; [RaListof X]
(define ra:null (quote ()))
;; [Any -> Boolean]
(define ra:pair? kons?)
;; [Any -> Boolean]
(define ra:null? null?)
;; X [RaListof X] -> [RaListof X] /\
;; X Y -> [RaPair X Y]
(define (ra:cons x ls)
(if (kons? ls)
(let ((s (kons-size ls)))
(if (and (kons? (kons-rest ls))
(= (kons-size (kons-rest ls))
s))
(make-kons (+ 1 s s)
(make-node x
(kons-tree ls)
(kons-tree (kons-rest ls)))
(kons-rest (kons-rest ls)))
(make-kons 1 x ls)))
(make-kons 1 x ls)))
;; [RaPair X Y] -> X Y
(define ra:car+cdr
(lambda (p)
(assert (kons? p))
(if (node? (kons-tree p))
(let ((s* (half (kons-size p))))
(values (tree-val (kons-tree p))
(make-kons s*
(node-left (kons-tree p))
(make-kons s*
(node-right (kons-tree p))
(kons-rest p)))))
(values (kons-tree p) (kons-rest p)))))
;; [RaPair X Y] -> X
(define (ra:car p)
(call-with-values (lambda () (ra:car+cdr p))
(lambda (car cdr) car)))
;; [RaPair X Y] -> Y
(define (ra:cdr p)
(call-with-values (lambda () (ra:car+cdr p))
(lambda (car cdr) cdr)))
;; [RaListof X] Nat [X -> X] -> X [RaListof X]
(define (ra:list-ref/update ls i f)
;(assert (< i (ra:length ls)))
(let recr ((xs ls) (j i))
(if (< j (kons-size xs))
(let-values (((v* t*)
(tree-ref/update (half (sub1 (kons-size xs)))
(kons-tree xs) j f)))
(values v* (make-kons (kons-size xs)
t*
(kons-rest xs))))
(let-values (((v* r*)
(recr (kons-rest xs)
(- j (kons-size xs)))))
(values v* (make-kons (kons-size xs)
(kons-tree xs)
r*))))))
;; [RaListof X] Nat [X -> X] -> [RaListof X]
(define (ra:list-update ls i f)
;(assert (< i (ra:length ls)))
(let recr ((xs ls) (j i))
(let ((s (kons-size xs)))
(if (< j s)
(make-kons s (tree-update s (kons-tree xs) j f) (kons-rest xs))
(make-kons s (kons-tree xs) (recr (kons-rest xs) (- j s)))))))
;; [RaListof X] Nat X -> (values X [RaListof X])
(define (ra:list-ref/set ls i v)
(ra:list-ref/update ls i (lambda (_) v)))
;; X ... -> [RaListof X]
(define (ra:list . xs)
(fold-right ra:cons ra:null xs))
;; Nat X -> [RaListof X]
(define ra:make-list
(case-lambda
((k) (ra:make-list k 0))
((k obj)
(let loop ((n k) (a ra:null))
(cond ((zero? n) a)
(else
(let ((t (largest-skew-binary n)))
(loop (- n t)
(make-kons t (tr:make-tree t obj) a)))))))))
;; A Skew is a Nat 2^k-1 with k > 0.
;; Skew -> Skew
(define (skew-succ t) (add1 (bitwise-arithmetic-shift t 1)))
;; Computes the largest skew binary term t <= n.
;; Nat -> Skew
(define (largest-skew-binary n)
(if (= 1 n)
1
(let* ((t (largest-skew-binary (half n)))
(s (skew-succ t)))
(if (> s n) t s))))
;; [Any -> Boolean]
;; Is x a PROPER list?
(define (ra:list? x)
(or (ra:null? x)
(and (kons? x)
(ra:list? (kons-rest x)))))
(define ra:caar (lambda (ls) (ra:car (ra:car ls))))
(define ra:cadr (lambda (ls) (ra:car (ra:cdr ls))))
(define ra:cddr (lambda (ls) (ra:cdr (ra:cdr ls))))
(define ra:cdar (lambda (ls) (ra:cdr (ra:car ls))))
(define ra:caaar (lambda (ls) (ra:car (ra:car (ra:car ls)))))
(define ra:caadr (lambda (ls) (ra:car (ra:car (ra:cdr ls)))))
(define ra:caddr (lambda (ls) (ra:car (ra:cdr (ra:cdr ls)))))
(define ra:cadar (lambda (ls) (ra:car (ra:cdr (ra:car ls)))))
(define ra:cdaar (lambda (ls) (ra:cdr (ra:car (ra:car ls)))))
(define ra:cdadr (lambda (ls) (ra:cdr (ra:car (ra:cdr ls)))))
(define ra:cdddr (lambda (ls) (ra:cdr (ra:cdr (ra:cdr ls)))))
(define ra:cddar (lambda (ls) (ra:cdr (ra:cdr (ra:car ls)))))
(define ra:caaaar (lambda (ls) (ra:car (ra:car (ra:car (ra:car ls))))))
(define ra:caaadr (lambda (ls) (ra:car (ra:car (ra:car (ra:cdr ls))))))
(define ra:caaddr (lambda (ls) (ra:car (ra:car (ra:cdr (ra:cdr ls))))))
(define ra:caadar (lambda (ls) (ra:car (ra:car (ra:cdr (ra:car ls))))))
(define ra:cadaar (lambda (ls) (ra:car (ra:cdr (ra:car (ra:car ls))))))
(define ra:cadadr (lambda (ls) (ra:car (ra:cdr (ra:car (ra:cdr ls))))))
(define ra:cadddr (lambda (ls) (ra:car (ra:cdr (ra:cdr (ra:cdr ls))))))
(define ra:caddar (lambda (ls) (ra:car (ra:cdr (ra:cdr (ra:car ls))))))
(define ra:cdaaar (lambda (ls) (ra:cdr (ra:car (ra:car (ra:car ls))))))
(define ra:cdaadr (lambda (ls) (ra:cdr (ra:car (ra:car (ra:cdr ls))))))
(define ra:cdaddr (lambda (ls) (ra:cdr (ra:car (ra:cdr (ra:cdr ls))))))
(define ra:cdadar (lambda (ls) (ra:cdr (ra:car (ra:cdr (ra:car ls))))))
(define ra:cddaar (lambda (ls) (ra:cdr (ra:cdr (ra:car (ra:car ls))))))
(define ra:cddadr (lambda (ls) (ra:cdr (ra:cdr (ra:car (ra:cdr ls))))))
(define ra:cddddr (lambda (ls) (ra:cdr (ra:cdr (ra:cdr (ra:cdr ls))))))
(define ra:cdddar (lambda (ls) (ra:cdr (ra:cdr (ra:cdr (ra:car ls))))))
;; [RaList X] -> Nat
(define (ra:length ls)
(assert (ra:list? ls))
(let recr ((ls ls))
(if (kons? ls)
(+ (kons-size ls) (recr (kons-rest ls)))
0)))
(define (make-foldl empty? first rest)
(letrec ((f (lambda (cons empty ls)
(if (empty? ls)
empty
(f cons
(cons (first ls) empty)
(rest ls))))))
f))
(define (make-foldr empty? first rest)
(letrec ((f (lambda (cons empty ls)
(if (empty? ls)
empty
(cons (first ls)
(f cons empty (rest ls)))))))
f))
;; [X Y -> Y] Y [RaListof X] -> Y
(define ra:foldl/1 (make-foldl ra:null? ra:car ra:cdr))
(define ra:foldr/1 (make-foldr ra:null? ra:car ra:cdr))
;; [RaListof X] ... -> [RaListof X]
(define (ra:append . lss)
(cond ((null? lss) ra:null)
(else (let recr ((lss lss))
(cond ((null? (cdr lss)) (car lss))
(else (ra:foldr/1 ra:cons
(recr (cdr lss))
(car lss))))))))
;; [RaListof X] -> [RaListof X]
(define (ra:reverse ls)
(ra:foldl/1 ra:cons ra:null ls))
;; [RaListof X] Nat -> [RaListof X]
(define (ra:list-tail ls i)
(let loop ((xs ls) (j i))
(cond ((zero? j) xs)
(else (loop (ra:cdr xs) (sub1 j))))))
;; [RaListof X] Nat -> X
;; Special-cased above to avoid logarathmic amount of cons'ing
;; and any multi-values overhead. Operates in constant space.
(define (ra:list-ref ls i)
;(assert (< i (ra:length ls)))
(let loop ((xs ls) (j i))
(if (< j (kons-size xs))
(tree-ref (kons-size xs) (kons-tree xs) j)
(loop (kons-rest xs) (- j (kons-size xs))))))
;; [RaListof X] Nat X -> [RaListof X]
(define (ra:list-set ls i v)
(let-values (((_ l*) (ra:list-ref/set ls i v))) l*))
;; [X ... -> y] [RaListof X] ... -> [RaListof Y]
;; Takes advantage of the fact that map produces a list of equal size.
(define ra:map
(case-lambda
((f ls)
(let recr ((ls ls))
(if (kons? ls)
(make-kons (kons-size ls)
(tree-map f (kons-tree ls))
(recr (kons-rest ls)))
ra:null)))
((f . lss)
;(check-nary-loop-args 'ra:map (lambda (x) x) f lss)
(let recr ((lss lss))
(cond ((ra:null? (car lss)) ra:null)
(else
;; IMPROVE ME: make one pass over lss.
(make-kons (kons-size (car lss))
(tree-map/n f (map kons-tree lss))
(recr (map kons-rest lss)))))))))
;; [X ... -> Y] [RaListof X] ... -> unspecified
(define ra:for-each
(case-lambda
((f ls)
(when (kons? ls)
(tree-for-each f (kons-tree ls))
(ra:for-each f (kons-rest ls))))
((f . lss)
;(check-nary-loop-args 'ra:map (lambda (x) x) f lss)
(let recr ((lss lss))
(when (ra:pair? (car lss))
(tree-map/n f (map kons-tree lss))
(recr (map kons-rest lss)))))))
;; [RaListof X] -> [Listof X]
(define (ra:random-access-list->linear-access-list x)
(ra:foldr/1 cons '() x))
;; [Listof X] -> [RaListof X]
(define (ra:linear-access-list->random-access-list x)
(fold-right ra:cons '() x))
;; This code based on code written by Abdulaziz Ghuloum
;; http://ikarus-scheme.org/pipermail/ikarus-users/2009-September/000595.html
(define get-cached
(let ((h (make-eq-hashtable)))
(lambda (x)
(define (f x)
(cond
((pair? x) (ra:cons (f (car x)) (f (cdr x))))
((vector? x) (vector-map f x))
(else x)))
(cond
((not (or (pair? x) (vector? x))) x)
((hashtable-ref h x #f))
(else
(let ((v (f x)))
(hashtable-set! h x v)
v))))))
(define-syntax ra:quote
(syntax-rules ()
((ra:quote datum) (get-cached 'datum))))
) ; (srfi :101 random-access-lists)