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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#,
…
2
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
3
Designer of SML
4
Familiar?
5
WTH?
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Outline
•
•
•
•
•
•
•
•
•
•
Expressions and values
Variables
Functions
Types
Recursion
Datatypes
Pattern matching
Higher-order functions
Exceptions
Modules
7
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;
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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:
if (x = 1) then
x + 1
– what is the value if x <> 1?
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Evaluation
Expression
Value
• An expression “evaluates” to a value.
• We “evaluate” an expression to obtain a value.
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Integer Evaluation
1 + 1
2
1 - 1
0
1 * 1
1
…
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Boolean Evaluation
1 = 1
true
1 <> 1
false
1 <> 0
true
…
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An Integer Expression
if 1 = ~1 then 10
else ~10
if false then 10
else ~10
~10
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Values as Expressions
1
???
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Outline
•
•
•
•
•
•
•
•
•
•
Expressions and values V
Variables
Functions
Types
Recursion
Datatypes
Pattern matching
Higher-order functions
Exceptions
Modules
17
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
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Local Declaration
let
val x = 1
val y = x + x
val z = y + y
in
z + z
end
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Nested Local Declaration
let
let
val x = 1
in
val y = <expression>
in
x + x
y + y
end
end
let
val y = let val x = 1 in x + x end
in
y + y
end
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Why “Local”?
let
val y = let
val x = 1
in
x + x
end
in
x + y
end
okay???
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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
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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
VS.
((1 + 1) + (1 + 1)) +
((1 + 1) + (1 + 1))
What if it takes 10 hours to evaluate 1?
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Outline
•
•
•
•
•
•
•
•
•
•
Expressions and values V
Variables V
Functions
Types
Recursion
Datatypes
Pattern matching
Higher-order functions
Exceptions
Modules
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When is the first time you learned the concept of
function?
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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)
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즐거운 한자 공부 시간
•函
1. 함(함).
2. 편지(함)
3. 갑옷(함)
4. 넣을, 들일(함)
예:
(書函) 서함: 책을 넣는 상자
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Function = 函數 = Box Number!
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Using a Box Number
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Using a Box Number - Generalized
…
…
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Function in SML = Box Number
(fn x => x + 1) n
=
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Function Application
…
(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.
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Evaluating a Function Application
…
(fn x => x + 1) n
n+ 1
…
33
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;
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Function Applications
incr 1
(fn x => x + 1) 1
1 + 1
2
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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
–…
36
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!
37
Functions = First-class Objects in SML
• Functions:
– can be passed as an argument to a function.
– can be returned as a return value of a function.
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Box Number as Output
…
…
such that
…
…
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Box Number as Output
x
…
…
+x
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Box Number as Output
x
y
y+x
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Box Number as Output
x
y
fn y => y+x
y+x
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Box Number as Output
x
y
fn y => y+x
y+x
fn y => y+x
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Box Number as Output
x
y
fn x => (fn y => y+x)
fn y => y+x
y+x
fn y => y+x
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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.
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Adding Two Integers
add 1 2
(fn x => (fn y => y + x)) 1 2
(fn y => y + 1) 2
2 + 1
3
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Box Number as Input
(
true,
false)
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Box Number as Input
f
fn f => (f true, f false)
( f
true,
f
false)
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Outline
•
•
•
•
•
•
•
•
•
•
Expressions and values V
Variables V
Functions V
Types
Recursion
Datatypes
Pattern matching
Higher-order functions
Exceptions
Modules
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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
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Type Preservation
Expression : T
Value : T
• An evaluation preserves the type of a given
expression.
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Example
let
val x = 1
val y = x + x
val z = y + y
in
z + z
end
: int
8 : int
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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;
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Type of add
x
fn x => (fn y => y+x)
fn y => y+x
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Type of add
int
fn x => (fn y => y+x)
fn y => y+x
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Type of add
int
fn x => (fn y => y+x)
int -> int
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Type of add
int
int -> (int -> int)
int -> int
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What is the Type?
f
fn f => (f true, f false)
( f
true,
f
false)
58
f : bool -> int ?
f
: (bool -> int) ->
fn f => (f true, f false)
int * int
( f
true,
f
false)
59
But why is it
f : bool ->
int ?
60
Why not f : bool -> char ?
f
: (bool -> char) ->
fn f => (f true, f false)
char * char
( f
true,
f
false)
61
Then why not
f :
f :
f :
f :
f :
…
bool
bool
bool
bool
bool
->
->
->
->
->
string ?
int * string ?
unit ?
(int -> int) ?
<crazy type> ?
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So we need
Polymorphism.
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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
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