Part 2 Summer 2014 Web.pdf-Part II: Func...
Part_2_Summer_2014_Web.pdf-Part II: Functional Programming with LISP
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Part 2 Summer 2014 Web.pdf-Part II:...
Part_2_Summer_2014_Web.pdf-Part II: Functional Programming with LISP
##### Page 47
47
93
Example: list-append
(defun list-append (L1 L2)
(if (null L1)
L2
(cons (car L1) (list-append (cdr L1) L2))))
94
Set Operations
Set theory: a set is different from a list
Operations:
Membership
Union
Intersection
Difference
Symmetric Difference

##### Page 48
48
95
Some Set Operations: Membership
(defun is-member? (element lst)
(cond
((null lst)
'())
((equal element (car lst))
t)
(t
(is-member? element (cdr lst)))))
> (is-member? 'a '())
nil
> (is-member? 'a '(a b c d))
true
> (is-member? '(a b) '(a (a b) b))
true
96
Some Set Operations: Intersection
(defun my-intersection (lst1 lst2)
(cond
((null lst1) '())
;((null lst2) '())
((member (car lst1) lst2)
(cons (car lst1)
(my-intersection (cdr lst1) lst2)))
(t (my-intersection (cdr lst1) lst2))))
> (my-intersection '(a b) '(a b c))
(list 'a 'b)
> (my-intersection '(a b c) ‘())
nil

##### Page 49
49
97
Some Set Operations: Difference
(defun setdiff (lst1 lst2)
(cond
((null lst1) '())
((null lst2) lst1)
((member (car lst1) lst2)
(setdiff (cdr lst1) lst2))
(t (cons (car lst1)
(setdiff (cdr lst1) lst2)))))
> (setdiff '(a b c) '(c d e))
(list 'a 'b)
> (setdiff '() '(a b c))
nil
> (setdiff '(a b c d e f g) '(a b c d e f))
(list 'g)
98
(defun my-union (lst1 lst2)
(cond
((null lst1) lst2)
((null lst2) lst1)
((member (car lst1) lst2)
(cons (car lst1)
(my-union (cdr lst1)
(setdiff lst2
(cons (car lst1) '())))))
(t (cons (car lst1) (my-union (cdr lst1)
lst2)))))
> (my-union '(a b c) '(d e f))
(list 'a 'b 'c 'd 'e 'f)
> (my-union '(a b c) '(b c))
(list 'a 'b 'c)
Some Set Operations: Union

##### Page 50
50
99
(my-merge '(1 2 6 8 1) '(3 4 7 9))
(1 2 3 4 6 7 8 1 9)
(my-merge '(1 2 3 6) '(3 4 5 7))
(1 2 3 3 4 5 6 7)
(my-merge '(1 3 4) '())
(1 3 4)
Execute Merging Two Lists
100
Merging Two Lists
(defun my-merge (los1 los2)
(if (null los1)
los2
(if (null los2)
los1
(if (< (car los1) (car los2))
(cons (car los1)
(my-merge (cdr los1) los2))
(cons (car los2)
(my-merge los1 (cdr los2)))))))

##### Page 51
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101
Higher-Order Functions
Higher-order functions or functionals are functions which
do at least one of the following:
Take one or more functions as an input.
Produce as output a function.
The derivative in calculus is a common example, since it
maps a function to another function.
102
Higher-Order Functions
The functions
f: X
Y
and
g: Y
Z
can be composed by
first applying
f
to an argument
x
and then applying
g
to
the result.
Thus one obtains a function
g o f: X
Z
defined by
(g o f)(x) = g(f(x))
for all
x
in
X
.
The notation
g o f
is read as “g circle f” or “g composed
with f”.

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