Download Day2-func

The Evolution of
Programming Languages
Day 2
Lecturer: Xiao Jia
[email protected]
The Evolution of PLs
1
The Functional Paradigm
The Evolution of PLs
2
High Order Functions
• zeroth order: only variables and constants
• first order: function invocations, but results
and parameters are zeroth order
• n-th order: results and parameters are (n1)-th order
• high order: n >= 2
The Evolution of PLs
3
LISP
• f(x, y)  (f x y)
• a + b  (+ a b)
• a – b – c  (- a b c)
• (cons head tail)
• (car (cons head tail))  head
• (cdr (cons head tail))  tail
The Evolution of PLs
4
• It’s straightforward to build languages and
systems “on top of” LISP
• (LISP is often used in this way)
The Evolution of PLs
5
Lambda
• f = λx.x2  (lambda (x) (* x x))
• ((lambda (x) (* x x)) 4)  16
The Evolution of PLs
6
Dynamic Scoping
int x = 4;
Static Scoping
f()
{
printf(“%d”, x);
}
main()
{
int x = 7;
Dynamic Scoping
f();
}
Describe a situation in which dynamic scoping is useful
The Evolution of PLs
7
Interpretation
Defining car
(cond
((eq (car expr) ’car)
(car (cadr expr)) )
…
The Evolution of PLs
8
Scheme
• corrects some errors of LISP
• both simpler and more consistent
(define factorial
(lambda (n) (if (= n 0)
1
(* n (factorial (- n 1))))))
The Evolution of PLs
9
Factorial with actors
(define actorial
(alpha (n c)
(if (= n 0)
(c 1)
(actorial (- n 1)
(alpha (f) (c (* f n)))))))
The Evolution of PLs
10
Static Scoping
(define n 4)
(define f (lambda () n))
(define n 7)
(f)
LISP:
7
Scheme: 4
The Evolution of PLs
11
Example: Differentiating
The Evolution of PLs
12
Example: Differentiating
(define derive (lambda
(lambda (x)
(/ (- (f (+ x dx))
(define square (lambda
(define Dsq (derive sq
(f dx)
(f x)) dx))))
(x) (* x x)))
0.001))
-> (Dsq 3)
6.001
The Evolution of PLs
13
SASL
• St. Andrew’s Symbolic Language
The Evolution of PLs
14
Lazy Evaluation
nums(n) = n::nums(n+1)
infinite list
second (x::y::xs) = y
second(nums(0))
= second(0::nums(1))
= second(0::1::nums(2))
= 1
The Evolution of PLs
15
Lazy Evaluation
if x = 0 then 1 else 1/x
In C:
X && Y  if X then Y
else false
X || Y  if X then true else Y
if (p != NULL && p->f > 0) …
The Evolution of PLs
16
Standard ML (SML)
• MetaLanguage
The Evolution of PLs
17
Function Composition
- infix o;
- fun (f o g) x = g (f x);
val o = fn : (’a -> ’b) * (’b -> ’c) -> ’a -> ’c
- val quad = sq o sq;
val quad = fn :
real -> real
- quad 3.0;
val it = 81.0 :
real
The Evolution of PLs
18
List Generator
infix --;
fun (m -- n) =
if m < n
then m :: (m+1 -- n)
else [];
1 -- 5  [1,2,3,4,5] : int list
The Evolution of PLs
19
Sum & Products
fun sum [] = 0
| sum (x::xs) = x + sum xs;
fun prod [] = 1
| prod (x::xs) = x * prod xs;
sum (1 -- 5);  15 : int
prod (1 -- 5);  120 : int
The Evolution of PLs
20
Declaration by cases
fun fac n =
if n = 0 then 1 else n * fac(n1);
fun fac 0 = 1
| fac n = n * fac(n-1);
The Evolution of PLs
21