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

CSED101 INTRODUCTION TO COMPUTINGFUNCTION ( 함수 )

유환조Hwanjo Yu

Function ( 함수 ) When same expressions are computed

multiple times, functions can be used. E.g., We want to compute x4 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

x4 for an integer x. Then, we can express f(2) + f(3) + f(5),

which is much convenient.

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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 <argument1> <argument2>… -> <body>

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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)

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Function: application Function do nothing until it is “called”. <Function> <Expression1>

<Expression2> … (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

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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 = <fun>

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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.

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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;;

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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.

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Function: definition let <name> = fun <arg1><arg2> .. ->

<body>;; let <name> <arg1> <arg2> .. = <body>;; 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);;

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Function: precedence Function has the highest precedence f 0 + f 1 = (f 0) + (f 1)

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Function: type Function arguments and output may

have different types. let f x = x > 0;;

val f: int -> bool = <fun> let f x y = x+1 < y-1;;

val f: int -> int -> bool = <fun> let f x = x + x;; f 0.0;;

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Function: type let f x y z = x > 0 && y > 0.0 && z;;

val f: int -> float -> bool -> bool = <fun> f 1 1.0 true;; f 1.0 1 false;;

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

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