On fuctional programming, high order functions, ML

WhyFunctional Programming

Matters

“Well-structured software is easy to write to and to debug, and provides a collection of modules that can reused to reduce future programming costs.”John Hughes - The university, Glasgow

WhyFunctional Programming

Matters

?

What is a function

The basic, and not very enlightening definition is this: “in a functional language, functions are first-class citizens.”

What is a function

The mean is that the function takes a function as one of its arguments.

let double x = x * 2 inList.map double [ 1; 2; 3 ];;- : int list = [2; 4; 6]

What is a functional program

FP won't make your word processing program faster or better. But there are domains where it is highly useful, and in particular FP looks like the paradigm of choice for unlocking the power of multicore processors.

What is a functional program

A functional program contains no assignment statements, so the variables once defined never change their value.The property to change the variable’s value is called “side effect”...

A functional program has no side effect.

A function call can have no effect other than to compute its result, so the function can be evaluated at any time because the no side-effect.

A function call can have no effect other than to compute its result, so the function can be evaluated at any time because the no side-effect.

A function call can have no effect other than to compute its result, so the function can be evaluated at any time because the no side-effect.

multi core calculus

A function

val double = fn x:int =>

x * 2;

like the math

This function accepts an integer argument and yields its double.

A function

val double = fn x:int =>

x * 2;

like the math

The keyword val binds a value to the variable, in this case the value is a function.

A function

val double = fn x:int =>

x * 2;

like the math

The function get a list of arguments and yields the computed result.

Partial application

fun sum x y = x + y;

sum -> is a function

sum 1 3 -> is an integer value

Partial application

sum 2 = ??? WTF

the partial applicationreturns a function that

takes an int and returns an int

fn : int -> int

Partial application

Haskell Curry

fn (x, y, z, ...)

fn x => fn y => fn z => ...

Datatype [ list ]

listof * := Nil | Cons * (listof *)

This line defines a list of * (whatever is *) that could be either Nil (an empty list)or a Cons of * and another list.Example:[] means Nil[1,2] means Cons 1(Cons 2(Cons Nil))

Datatype [ list ]

* *

*

Cons n ( )

Cons n ( )

Cons n ( Nil )

Pattern Matchingdefining functions by cases:

fun and_operator true true = true | and_operator x y = false;

When both arguments are true the result is true, result is false in the other cases.

Sum the elements of listThe elements of the list could be added by a recursive “sum“ function

fun sum Nil = 0 | sum (Cons n list) = n + sum (list)

Sum the elements of listExamining the definition of sum we see that there are only two specific computation parts

fun sum Nil = 0 | sum (Cons n list) = n + sum (list)

Modularizing the function

fun sum Nil = 0 | sum (Cons n list) = n + sum (list)

Modularizing the function

fun sum Nil = 0 | sum (Cons n list) = n + sum (list)

foldr f x Nil = xfoldr f x (Cons n list) =

f n ((foldr f x) list)

Modularizing the function

fun sum Nil = 0 | sum (Cons n list) = n + sum (list)

foldr f x Nil = xfoldr f x (Cons n list) =

f n ((foldr f x) list)

0 is the base value used for the base case (empty list)

Modularizing the function

fun sum Nil = 0 | sum (Cons n list) = n + sum (list)

foldr f x Nil = xfoldr f x (Cons n list) =

f n ((foldr f x) list)

the + operator is a function

0 is the base value used for the base case (empty list)

Modularizing the function

fun sum Nil = 0 | sum (Cons n list) = n + sum (list)

foldr f x Nil = xfoldr f x (Cons n list) =

f n ((foldr f x) list)

sum == foldr (+) 0

the + operator is a function

0 is the base value used for the base case (empty list)

The “foldr” functionNow we are able to use the “foldr” function

sum = foldr (+) 0

multiply = foldr (*) 1

subtract = foldr (-) 0

The “foldr” functionTest whether any list of boolean is trueanytrue = foldr (or) false

Test all elements are truealltrue = foldr (and) true

These are a functions

Everything is a functionIn a functional world a complete program is a function, so like in the math we could combine programs together.

Combining programs | functionsNow combining the first program with the second one becomes like combining mathematical functions

Math says g • fin Standard MLfun combine f g x = f(g(x));

Functional and the Real World

http://www.leafpetersen.com/leaf/publications/hs2013/hrc-paper.pdf

Thanks

@toretto460