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Part 2 Summer 2014 Web.pdf
Part_2_Summer_2014_Web.pdf
Showing 36-40 out of 53
Part 2 Summer 2014 Web.pdf-Part II: Functional Pro...
Part_2_Summer_2014_Web.pdf-Part II: Functional Programming with LISP
Part 2 Summer 2014 Web.pdf-Part II:...
Part_2_Summer_2014_Web.pdf-Part II: Functional Programming with LISP
Page 36
36
71
Example 1
;returns absolute difference between
;two numbers
(
defun
absdiff (x y)
(
cond
((> x y) (- x y))
(
t
(- y x))))
72
Example 2: Tutorial
•
Write a function, which takes a list and an element, and
returns the original list with the first occurrence of the
element removed
.
•
(defun my-remove (lst elt)
•
(cond ((null lst) nil)
•
((equal (first lst) elt) (rest lst))
•
(t (cons (first lst)
•
(my-remove (rest lst) elt)))))
Page 37
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73
Executing The Function
(my-remove '(a 1 c 2 c 7) 'c)
= (cons 'a (my-remove '(1 c 2 c 7) 'c))
= (cons 'a (cons '1 (my-remove '(c 2 c 7) 'c)))
= (cons 'a (cons '1 '(2 c 7)))
= (cons 'a '(1 2 c 7))
= '(a 1 2 c 7)
(my-remove '(a (1 q) 2) 'q)
= (cons 'a (my-remove '((1 q) 2) 'q))
= (cons 'a (cons '(1 q) (my-remove '(2) 'q)))
= (cons 'a (cons '(1 q)
(cons 2 (my-remove '() 'q))))
= (cons 'a (cons '(1 q) (cons 2 '())))
= (cons 'a (cons '(1 q) '(2)))
= (cons 'a '((1 q) 2))
= '(a (1 q) 2)
74
Recursive Functions
•
Every recursive function consists of:
–
One or more base cases, and
–
One or more recursive cases.
•
Each recursive case consists of:
–
Splitting the data into smaller pieces (for example, with
car
and
cdr
),
–
Handling the pieces, often with recursive calls, and
–
Combining the results into a single result.
Page 38
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75
Some Guidelines for Writing
Functions
•
Unless the function is extremely simple, begin with a
cond
to break the logic into cases.
•
When handling lists, you would normally adopt a
recursive solution. Make sure you treat the
NULL
list as
a base case.
•
Normally you would operate on the
first
element
(
car
) and recur with the
rest
of the list (
cdr
).
76
•
To delete the first element, just recur on the
rest
.
•
To keep the first element as is, use
cons
to place it at
the head of the returning list (whose tail is determined by
the recursive call).
•
Use
else
(or
t
) to protect your logic from forgotten
cases.
Some Guidelines for Writing
Functions
Page 39
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77
Example: Summing the Numbers in
a List
•
Base case: if (empty list) then sum is 0.
•
Inductive (or recursive) case: add the first element to the
sum of the rest of the elements.
•
(defun sum (lst)
•
(cond
•
((null lst) 0)
•
(t (+ (car lst) (sum (cdr lst))))))
78
We can unfold the definition of sum with an example:
(sum ‘(1 2 3)) is evaluated as
1 + sum(‘(2 3))
= 1 + 2 + sum(‘(3))
= 1 + 2 + 3 + sum(‘())
= 1 + 2 + 3 + 0
= 6
Example: Summing the Numbers in
a List
Page 40
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79
Example: Multiplying the Numbers
in a List
•
This is very similar to the sum function.
•
(defun product (lst)
•
(cond
•
((null lst) 1)
•
(t (* (car lst) (product (cdr lst))))))
80
Example: Reversing a List by
Recursion
•
Base case: if (empty list) then reverse is also the empty
list.
•
Inductive (or recursive) case: concatenate the reversed
list (excluding the first element) to the first element.
•
(defun my-reverse (lst)
•
(cond
•
((null lst) ‘())
•
(t
(append (my-reverse (cdr lst))
(list (car lst))))))
(setf lst (list 'a 'b 'c 'd 'e 'f 'g))
> (my-reverse lst)
(list 'g 'f 'e 'd 'c 'b 'a)
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