CSE-321 Programming Languages Introduction to Functional Programming 박성우 POSTECH March 5, 2009

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

Functional Language SML Standard ML ML = Meta-Language An example of programming language whose design is based on the programming language theory type theory Programming language for your assignments

Designer of SML

Familiar?

WTH?

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

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:

Functional Language SML 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: what is the value if x <> 1?

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

Integer Evaluation 1 + 1 2 1 - 1 1 * 1 1 …

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

An Integer Expression if 1 = ~1 then 10 else ~10 if false then 10 else ~10 ~10

Values as Expressions 1 ???

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

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

Local Declaration let val x = 1 val y = x + x val z = y + y in z + z end 8

Nested Local Declaration let val x = 1 in x + x end let val y = <expression> in y + y end let val y = let val x = 1 in x + x end in y + y end

Why “Local”? let val y = let val x = 1 in x + x end x + y okay???

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 SML <> variables in C

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

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

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

즐거운 낱말 공부 시간 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)

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

Function = 函數 = Box Number!

Using a Box Number

Using a Box Number - Generalized … …

Function in SML = Box Number (fn x => x + 1) n =

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

Evaluating a Function Application … (fn x => x + 1) n n + 1

Functions in SML Nameless function fn x => x + 1; Storing a nameless function to a variable val incr = fn x => x + 1; Function declaration fun incr x = x + 1;

Function Applications incr 1 (fn x => x + 1) 1 1 + 1 2

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 …

First-class Objects in C 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!

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

Box Number as Output … … such that

Box Number as Output x … +x …

Box Number as Output x y y+x

Box Number as Output x y fn y => y+x y+x

Box Number as Output x y fn y => y+x y+x fn y => y+x

Box Number as Output x y y+x fn x => (fn y => y+x)

In SML Recall the following declarations are equivalent: val incr = fn x => x + 1; fun incr x = x + 1; Then: val add = fn x => (fn y => y + x); fun add x = fn y => y + x; fun add x y = y + x; add takes only one argument, not two! In fact, every function in SML takes only one argument.

(fn x => (fn y => y + x)) 1 2 Adding Two Integers add 1 2 (fn x => (fn y => y + x)) 1 2 (fn y => y + 1) 2 2 + 1 3

Box Number as Input ( true, false)

Box Number as Input f fn f => (f true, f false) ( f true, f false)

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

Types A type specifies what kind of value a given expression evaluates to. 1 + 1 : int true andalso false : bool #”A” : char ”hello” : string (1, true) : int * bool (1, ~1, true) : int * int * bool 1.0 : real () : unit

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

Example let val x = 1 val y = x + x val z = y + y in z + z end : int

Function Types T -> T’ type of functions: taking arguments of type T returning values of type T’ Example: val incr = fn x => x + 1; val incr = fn : int -> int fun incr x = x + 1; val incr = fn : int -> int Explicit type annotation val incr = fn (x:int) => x + 1; val incr = fn (x:int) : int => x + 1; fun incr (x:int) = x + 1; fun incr (x:int) : int = x + 1;

Type of add x fn y => y+x fn x => (fn y => y+x)

Type of add int fn x => (fn y => y+x) fn y => y+x

Type of add int fn x => (fn y => y+x) int -> int

Type of add int int -> (int -> int) int -> int

What is the Type? f fn f => (f true, f false) ( f true, f false)

f : bool -> int ? ( true, false) f : (bool -> int) -> int * int fn f => (f true, f false) ( f true, f false)

But why is it f : bool -> int ?

Why not f : bool -> char ? char * char fn f => (f true, f false) ( f true, f false)

f : bool -> int * string ? f : bool -> unit ? Then why not f : bool -> string ? f : bool -> int * string ? f : bool -> unit ? f : bool -> (int -> int) ? f : bool -> <crazy type> ? …

So we need Polymorphism.

Announcement Assignment 1 will be out tonight. Due at 11:59pm, March 12 (next Thursday) Details of the instruction are all in the handout. If you don't find your handin directory, email me. Makeup lecture 정통연 143호, 9:30am, tomorrow