#!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 s101 random-access-lists)
  (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)
