#!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 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)

(library (srfi :101)
  (export quote
          pair?
          cons
          car
          cdr
          caar
          cadr
          cddr
          cdar
          caaar
          caadr
          caddr
          cadar
          cdaar
          cdadr
          cdddr
          cddar
          caaaar
          caaadr
          caaddr
          caadar
          cadaar
          cadadr
          cadddr
          caddar
          cdaaar
          cdaadr
          cdaddr
          cdadar
          cddaar
          cddadr
          cddddr
          cdddar
          null?
          list?
          list
          make-list
          length
          append
          reverse
          list-tail
          list-ref
          list-set
          list-ref/update
          map
          for-each
          random-access-list->linear-access-list
          linear-access-list->random-access-list
          )
  
  (import (srfi :101 random-access-lists))
      
  ) ; (srfi :101)
