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The Evolution of Programming Languages

The Evolution of Programming Languages. Day 2 Lecturer: Xiao Jia xjia@cs.sjtu.edu.cn. The Functional Paradigm. High Order Functions. zeroth order: only variables and constants first order: function invocations, but results and parameters are zeroth order

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The Evolution of Programming Languages

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  1. The Evolution of Programming Languages Day 2 Lecturer: Xiao Jia xjia@cs.sjtu.edu.cn The Evolution of PLs

  2. The FunctionalParadigm The Evolution of PLs

  3. 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 (n-1)-th order • high order: n >= 2 The Evolution of PLs

  4. 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

  5. It’s straightforward to build languages and systems “on top of” LISP • (LISP is often used in this way) The Evolution of PLs

  6. Lambda • f = λx.x2 (lambda (x) (* x x)) • ((lambda (x) (* x x)) 4)  16 The Evolution of PLs

  7. Dynamic Scoping Static Scoping int x = 4; f() { printf(“%d”, x); } main() { int x = 7; f(); } Dynamic Scoping Describe a situation in which dynamic scoping is useful The Evolution of PLs

  8. Interpretation Defining car (cond ((eq (car expr) ’car) (car (cadrexpr)) ) … The Evolution of PLs

  9. 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

  10. 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

  11. Static Scoping (define n 4) (define f (lambda () n)) (define n 7) (f) LISP: 7 Scheme: 4 The Evolution of PLs

  12. Example: Differentiating The Evolution of PLs

  13. Example: Differentiating (define derive (lambda (f dx) (lambda (x) (/ (- (f (+ x dx)) (f x)) dx)))) (define square (lambda (x) (* x x))) (define Dsq (derive sq 0.001)) -> (Dsq 3) 6.001 The Evolution of PLs

  14. SASL • St. Andrew’s Symbolic Language The Evolution of PLs

  15. Lazy Evaluation nums(n) = n::nums(n+1) second (x::y::xs) = y second(nums(0)) = second(0::nums(1)) = second(0::1::nums(2)) = 1 infinite list The Evolution of PLs

  16. Lazy Evaluation if x = 0 then 1 else 1/x In C: X&&Y ifXthenYelsefalse X||Y  ifXthentrueelseY if (p != NULL && p->f > 0) … The Evolution of PLs

  17. Standard ML (SML) • MetaLanguage The Evolution of PLs

  18. Function Composition - infix o; - fun (f o g) x = g (f x); val o = fn : (’a -> ’b) * (’b -> ’c) -> ’a -> ’c - val quad = sqosq; val quad = fn : real -> real - quad 3.0; val it = 81.0 : real The Evolution of PLs

  19. 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

  20. 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

  21. Declaration by cases fun fac n = if n = 0 then 1 else n * fac(n-1); fun fac 0 = 1 | fac n = n * fac(n-1); The Evolution of PLs

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