Lisp II

1
Lisp II
2
How EQUAL could be defined

• (defun equal (x y)
• this is how equal could be defined
• (cond ((numberp x) ( x y))
• ((atom x) (eq x y))
• ((atom y) nil)
• ((equal (car x) (car y))
• (equal (cdr x) (cdr y)))))

3
Some simple list processing examples

• (defun member (x theList)
• (cond ((atom theList) nil)
• ((equal x (car theList)) (cdr
  theList))
• (T (member x (cdr theList))))
• (defun append (l1 l2)
• (if (null l1)
• l2
• (cons (car l1) (append (cdr l1) l2))))

4
Variations on reverse

• either of these does O(n2) cons operations
• (defun reverse (theList)
• (if (null theList) nil
• (append (reverse (cdr theList))
• (list (car theList)))))
  
• (defun reverse (theList)
• (and theList
• (append (reverse (cdr theList)) (list
  (car theList)))))

5
Variations on reverse

• this tail recursive operation does O(n) conses
• (defun reverse (theList) (reverse1 theList nil))
• (defun reverse1 (theList acc)
• (if (null theList)
• acc
• (reverse (cdr theList) (cons (car
  theList) acc))))

6
Flatten I

• (defun flatten (theList)
• (cond
• ((null theList) nil) empty list
  do nothing
• ((atom (car theList)) cons an atom
  onto flattend cdr
• (cons (car theList) (flatten (cdr
  theList))))
• otherwise flatten head tail
  and append results
• (t (append (flatten (car theList))
• (flatten (cdr
  theList))))))

7
Flatten II

• this version avoids append, which is
  expensive.
• (defun flatten (theList) (flatten1 theList nil))
• (defun flatten1 (theList acc)
• (cond ((null theList) acc) all done
• ((atom theList) stick atom
  on the front of acc
• (cons theList acc)) of the
  accumulator
• (t (flatten1 (car theList) (flatten1
  (cdr theList) acc)))

8
Higher order functions

• (defun mapcar (f theList)
• (if (null theList)
• nil
• (cons (apply f (list (car theList)))
• (mapcar f (cdr theList)))))

9
Mapcar II

• (defun mapcar1 (f theList)
• (if (null theList) nil
• (cons (apply f (list (car theList)))
  (mapcar f (cdr theList)))))
• (defun mapcar (f rest args)
• "Apply f to successive cars of all ARGS.
  Return the list of results."
• If no list is exhausted,
• (if (not (memq 'nil args)) apply function
  to CARs.
• (cons (apply f (mapcar1 'car args))
• (mapcar f (mapcar1 'cdr
  args)))))

10
The End