pascal.scm

;;; Calculates all elements of Pascal's Triangle up to a particular width/row.

(define (pascal width)
  (reverse (pascal-helper '((1)) width)))

(define (pascal-helper rows width)
  (if (= (length rows) width)
    rows
    (pascal-helper (cons (next-row (car rows))
                         rows)
                   width)))

(define (next-row previous)
  (let ((body (row-body '() previous)))
    (if (null? body)
      '(1 1)
      (cons 1 (append body '(1))))))

(define (row-body body previous)
  (if (null? (cdr previous))
    body
    (row-body (cons (+ (car previous) (cadr previous))
                    body)
              (cdr previous))))