1. CSED101 INTRODUCTION TO COMPUTING FUNCTION ( 함수 ) 유환조 Hwanjo Yu

2. Function ( 함수 )  When same expressions are computed multiple times, functions can be used.  E.g., We want to compute x 4 for some integer x like 2*2*2*2 + 3*3*3*3 + 5*5*5*5.  Assume there is a function f(x) that returns x 4 for an integer x.  Then, we can express f(2) + f(3) + f(5), which is much convenient. –2–2

3. Function: basic  Define a function  fun x -> x * x  The x in the left is called argument, and x * x is called the body of function.  Can have multiple arguments like “fun x y -> x*y”  fun x y z -> x*y+z  fun x y z w -> x*y+z*w  fun x y z w v -> (x*y+z*w)*v  Fun … -> –3–3

4. Function: basic  Arguments must have different names  “fun x y x -> x + y” => error, which x?  Can use local variables within a function  “fun x y -> let x = x+y in x+x” => f(x, y) = 2(x+y) –4–4

5. Function: application  Function do nothing until it is “called”.  …  (fun x -> x * x) 1  (fun x y -> x*y) (1+1) (2+2)  (fun x y z -> x*y+z) 1 1 (1+1)  Each expression is an argument of the function –5–5

6. Function: name  A function without name cannot be called later because it doesn’t have a name to call.  A function must have a name to be called later.  Try in OCAML  let f = fun x -> x*x;;  f 1;;  f 2;;  Val f: int -> int = –6–6

7. Function: name scope  Function within an expression  let f = fun x -> x*x in (f 1) + (f 2);;  f;;  f cannot be used outside the expression since it is defined like a local variable. –7–7

8. Function: variable  Variables used in a function body work as constants  let x = 1;;  let f = fun y -> x*y;;  f 0;;  let x = -1;;  f 0;; –8–8

9. Function: variable  Other case  let f = fun a -> let g = fun x -> a*x in (g 1) + (g 2);;  f 1;;  f 2;;  Whenever f is called, g is newly defined. –9–9

10. Function: definition  let = fun.. -> ;;  let.. = ;;  Eg.,  let f x y z = x*y+z;;  let g x y z w = x*y*+z*w;;  let h x y z w v = (x*y+z*w)*v;;  let f x = x + 1 in f 0;;  let f a = let g x = a*x in (g 1) + (g 2);; –10

11. Function: precedence  Function has the highest precedence  f 0 + f 1 = (f 0) + (f 1) –11

12. Function: type  Function arguments and output may have different types.  let f x = x > 0;; val f: int -> bool =  let f x y = x+1 < y-1;; val f: int -> int -> bool =  let f x = x + x;;  f 0.0;; –12

13. Function: type  let f x y z = x > 0 && y > 0.0 && z;;  val f: int -> float -> bool -> bool =  f 1 1.0 true;;  f 1.0 1 false;; –13