CSE-321 Programming Languages Introduction to Functional Programming

1. CSE-321 Programming LanguagesIntroduction to Functional Programming 박성우 POSTECH

2. Programming Paradigms • Structuredprogramming • C, Pascal, … • Object-oriented programming • C++, Java, … • Logic programming • Prolog, … • Functional programming • SML, Haskell, Objective Caml, Lisp, Scheme, F#, …

3. Outline • Expressions and values • Variables • Functions • Types • Recursion • Datatypes • Pattern matching • Higher-order functions • Exceptions • Modules

4. Imperative Language C • A program consists of commands. • command = “do something” • Nothing wrong: if (x == 1) then x = x + 1; else x = x - 1; • Nothing wrong either: if (x == 1) then x = x + 1;

5. Functional Language OCaml • A program consists of expressions. • expression = “obtain a value” • Nothing wrong: if (x = 1) then x + 1 else x - 1 • But this does not make sense: if (x = 1) then x + 1 • what is the value if x <> 1?

6. Evaluation • An expression “evaluates” to a value. • We “evaluate” an expression to obtain a value. Expression Value

7. Integer Evaluation 1 + 1 2 1 - 1 0 1 * 1 1 …

8. Boolean Evaluation 1 = 1 true 1 <> 1 false 1 <> 0 true …

9. An Integer Expression if1 = -1then 10 else -10 iffalsethen 10 else-10 -10

10. Values as Expressions 1 ???

11. Outline • Expressions and values V • Variables • Functions • Types • Recursion • Datatypes • Pattern matching • Higher-order functions • Exceptions • Modules

12. Variable Declaration - letx = 1 + 1;; val x : int = 2 • A variable x is “bound” to value 2. • From now on, any occurrence of x is replaced by 2. - let y = x + x;; val x : int = 4

13. Local Declaration let x = 1 in let y = x + x in let x = y + y in z + z + x 8

14. Nested Local Declaration let x = 1 in x + x let y = <expression> in y + y let y = let x = 1 in x + xin y + y

15. Why “Local”? • let y = let • x = 1 • in • x + x • in • x + y okay???

16. Variables are NOT variable. • The contents of a variable never change. • immutability of variables • Surprise? • That’s because you are thinking about variables in imperative programming. variables in OCaml <> variables in C

17. Then Why Variables? • Any advantage in using variables at all? let x = 1 in let y = x + x in let z = y + y in z + z ((1 + 1) + (1 + 1)) + ((1 + 1) + (1 + 1)) VS. What if it takes 10 hours to evaluate 1?

18. Outline • Expressions and values V • Variables V • Functions • Types • Recursion • Datatypes • Pattern matching • Higher-order functions • Exceptions • Modules

19. When is the first time you learned the concept of function?

20. 함수의 사전 정의 • 함수(函數): 두 변수 x, y간에 어떤 관계가 있어 x의 변화에 따라 y가 일정한 법칙으로 변화할 때 y를 x의 함수라 함. (function) (동아 마스타 국어사전)

21. 한자 함 • 函 1. 함(함). 2. 편지(함) 3. 갑옷(함) 4. 넣을, 들일(함) 예: (書函) 서함: 책을 넣는 상자

22. Function = 函數 = Box Number!

23. Using a Box Number

24. Using a Box Number - Generalized … …

25. Function in OCaml= Box Number fun x -> x + 1 n =

26. Function Application • We “apply” (fun x -> x + 1) to n. • x is called a formal argument/parameter. • n is called an actual argument/parameter. … (fun x -> x + 1) n

27. … … Evaluating a Function Application (fun x -> x + 1) n n+ 1

28. Functions in OCaml • Nameless function • fun x -> x + 1;; • Storing a nameless function to a variable • let incr = fun x -> x + 1;; • Function declaration • let incr x = x + 1;;

29. Function Applications incr 1 (fun x -> x + 1) 1 1 + 1 2

30. First-Class Stamps

31. First-class Objects • First-class objects = primitive objects • can be stored in a variable. • can be passed as an argument to a function. • can be returned as a return value of a function. • Examples: • integers • booleans • characters • floating-point numbers • …

32. First-class Objects in C • First-class objects • integers • characters • floating-point numbers • pointers • structures • … • Functions? • Function pointers are first-class objects. • But functions are not. • Why? You cannot create new functions on the fly!

33. Functions = First-class Objects in OCaml • Functions: • can be passed as an argument to a function. • can be returned as a return value of a function.

34. … … … … Box Number as Output such that

35. … … Box Number as Output x +x

36. Box Number as Output x y y+x

37. Box Number as Output x y fun y -> y+x y+x

38. Box Number as Output x y fun y -> y+x y+x fun y -> y+x

39. Box Number as Output x y funx -> (fun y -> y+x) fun y -> y+x y+x fun y -> y+x

40. In OCaml • Recall the following declarations are equivalent: • let incr = funx -> x + 1;; • let incr x = x + 1;; • Then: • let add = funx -> (funy -> y + x); • let add x = funy -> y + x; • let add xy = y + x; • add can take a single argument to return a function.

41. Adding Two Integers add 1 2 (funx -> (funy -> y + x)) 1 2 (funy -> y + 1) 2 2 + 1 3

42. Box Number as Input ( true, false)

43. Box Number as Input f funf -> (f true, f false) ( true, false) f f

44. Outline • Expressions and values V • Variables V • Functions V • Types • Recursion • Datatypes • Pattern matching • Higher-order functions • Exceptions • Modules

45. Types • A type specifies what kind of value a given expression evaluates to. • 1 + 1 : int • true && false : bool • ’A’ : char • ”hello” : string • (1, true) : int * bool • (1, -1, true) : int * int * bool • 1.0 : float • () : unit

46. Type Preservation • An evaluation preserves the type of a given expression. Expression : T Value : T

47. Example let x = 1 in let y = x + x in let z = y + y in z + z : int 8 : int

48. Function Types • T -> T’ • type of functions: • taking arguments of type T • returning values of type T’ • Example: # let incr = fun x -> x + 1;; val incr : int -> int = <fun> # let incr x = x + 1;; val incr : int -> int = <fun> • Explicit type annotation # let inc = fun (x:int) -> x + 1;; val inc : int -> int = <fun> # let incr (x:int) = x + 1;; val incr : int -> int = <fun>

49. x funx -> (fun y -> y+x) fun y -> y+x Type of add

50. Type of add int funx -> (fun y -> y+x) fun y -> y+x