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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