;;;; streams-math.scm
;;;; Kon Lovett, Apr '09

; Copyright (C) 2007 by Philip L. Bewig of Saint Louis, Missouri, USA.  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. 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.


;;;

(module streams-math (;export
  stream-max
  stream-min
  stream-sum
  odd-numbers-stream
  even-numbers-stream
  cardinal-numbers-stream
  natural-numbers-stream
  prime-numbers-stream
  hamming-sequence-stream)

  (import scheme chicken (only data-structures left-section) streams streams-utils)

  (require-library streams streams-utils)

  (include "chicken-primitive-object-inlines")
  (include "streams-inlines")

  #; ;WHAT TO DO ABOUT THE full-numeric-tower!
  (declare
    (not usual-integrations < + * max min) )

;;;

(define (stream-max streem)
  (%check-stream 'stream-max streem 'stream)
  (stream-fold-one max streem) )

(define (stream-min streem)
  (%check-stream 'stream-min streem 'stream)
  (stream-fold-one min streem) )

(define stream-sum (left-section stream-fold + 0))

(define odd-numbers-stream (stream-from 1 2))

(define even-numbers-stream (stream-from 0 2))

(define cardinal-numbers-stream (stream-iterate add1 0))

(define natural-numbers-stream (stream-iterate add1 1))

(define-stream (prime-sieve$ strm)
  (define-stream (sift$ base strm)
    (define-stream (next$ base mult strm)
      (let ((first (stream-car strm))
            (rest (stream-cdr strm)))
        (cond ((< first mult)
                (stream-cons first (next$ base mult rest)) )
              ((< mult first)
                (next$ base (+ base mult) strm) )
              (else
                (next$ base (+ base mult) rest) ) ) ) )
    (next$ base (+ base base) strm) )
  (let ((first (stream-car strm))
        (rest (stream-cdr strm)))
    (stream-cons first (prime-sieve$ (sift$ first rest))) ) )

(define prime-numbers-stream (prime-sieve$ (stream-from 2)))

;; http://www.research.att.com/~njas/sequences/A051037

(define hamming-sequence-stream
  (stream-cons 1
   (stream-unique =
    (stream-merge <
     (stream-map (left-section * 2) hamming-sequence-stream)
     (stream-map (left-section * 3) hamming-sequence-stream)
     (stream-map (left-section * 5) hamming-sequence-stream)))) )

) ;module streams-math