Functional Programming 之二三事

Functional

LeehengJuly 31, 2009

的二三事Programming

2009年7月31日星期五

Functional

LeehengJuly 31, 2009

的二三事ProgrammingBeta

Agenda

About MyselfWhy This Topic

Programming ParadigmPL Moving On

Why FP MattersIP VS DP

Function, Lambda CalculusHigh Order Function, Currying

No Side Effect, Referential TransparentLeast Surprise, No UpdateRecursion, Lazy Evaluation

Pattern Matching, Tail recursionMemoization, Closure

Loop Helper

ExampleStory

ReferenceQuestion

開場 10min

過場 25min

下場 25min

Agenda

Loop Helper

ExampleStory

ReferenceQuestion

開場 10min

過場 25min

下場 25min

Agenda

Loop Helper

ExampleStory

ReferenceQuestion

開場 10min

過場 25min

下場 25min

Agenda

Loop Helper

ExampleStory

ReferenceQuestion

開場 10min

過場 25min

下場 25min

ABOUT MYSELF

Y! 2009 Search Team InternLeeheng Ma

NCCU MIS undergraduateInterests : Algorithm, Programming language, Compiler,

Web Technology.

WHY THIS TOPIC

因為我沒有研究可報....

WHY THIS TOPIC

因為我沒有研究可報....

因為 Programming Language 是最貼近我們 RD 的東西

Programming Paradigm

Programming paradigm is a Fundamental style of computer programming.

For solving Software Engineering Problems.

編程典範正在Programming Paradigm SHIFT

Think Different

• A language that doesn't affect the way you think about programming, is not worth knowing.

--Alan Perlis

Think Different

--Alan Perlis

Think Different

--Alan Perlis

這是圖靈獎獎杯

HOW MANY YOU KNOW ?

• Concurrent• Imperative• Declarative• Functional• Procedural• Prototype-based• Event-driven• Aspect-Oriented• Object-Oriented• Meta-Programming• Generic

Programming

HOW MANY YOU KNOW ?

其實還有很多... Orz但.....就不管了...

WHERE PL MOVING ON ?

WHY FP MATTERS

名家背書

抽象思考

WHY FP MATTERS

• Python, Ruby, Perl all use ideas form FP• Y!牌’s Hadoop and G牌‘s MapReduce are large

scale FP

名家背書

抽象思考

WHY FP MATTERS

• Python, Ruby, Perl all use ideas form FP• Y!牌’s Hadoop and G牌‘s MapReduce are large

scale FP

名家背書

抽象思考

ModularityInterchangeable partsEasy test and debugEasy optimizationFunction as dataPattern MatchingConcurrent ProcessingClosureLazy EvaluationReferential transparency

• No Side Effect• High Order Function

IP VS FP

•Imperative Programming– Computation：Executing statements to change state.– Program：Consists of a sequence of commands.

•Functional Programming– Computation：Evaluation of expressions.– Expression：Formed by using functions to combine

basic values.

The focus is on what, not how

IP VS FP

basic values.

C++ JavaOOP

IP VS FP

basic values.

C++ JavaOOP

Lisp HaskellErlang

Create Sandwich

Imperative

Functional

Create Sandwich

1. Take a bread2. Spread bread with butter3. Put cheese on the bread4. return sandwich

Imperative

Functional

Create Sandwich

1. Take a bread2. Spread bread with butter3. Put cheese on the bread4. return sandwich

Imperative

return put ( cheese, spread(butter, bread) )

Functional

Features

Function is ?

In computer science, a subroutine or subprogram (also called procedure, method, function, or routine) is a portion of code within a larger program, which performs a specific task and is relatively independent of the remaining code.

Function is ?

The mathematical concept of a function expresses the intuitive idea that one quantity (the argument of the function, also known as the input) completely determines another quantity (the value, or output).

Function is ?

So we minimize function!!

Lambda Calculus

The λ-calculus was developed by the logician Alonzo Church in 1930’s as a tool to study functions and computability.

λ Calculus

Equivalent to Turing MachinesTuring 1937

Equivalent to recursive functionsKleene 1936

(λ x. x + 2)

λ Calculus

(λ x. x + 2) = (x) { return x + 2}

λ Calculus

(λ x. x + 2)

(λ x. x + 2) 3 = 5

= (x) { return x + 2}

λ Calculus

(λ f. f 3)(λ x. x+2) = ?

λ Calculus

(λ f. f 3)(λ x. x+2) = ?

= (λ x. x + 2) 3= 3 + 2

High Order Function

• Functions take other functions as parameters

• Functions return functions as results

High Order Function

• Functions return functions as results

∑ f(x) x∈L

High Order Function

• Functions return functions as results d f(x)

dx = f’(x)

∑ f(x) x∈L

Mathematics

OK, no more mathematics.

Design Pattern

Adapter Pattern

Design Pattern

Adapter Pattern

Design Pattern

Adapter Pattern

Design Pattern

Adapter Pattern

Design Pattern

Adapter Pattern

Currying

把接受多個參數的函數變換成接受一個單一參數(最初函數的第一個參數)的函數，並且返回接受餘下的參數而且返回結果的新函數的技術。

AJAX 的 callback function

No Side Effect

Output is solely dependent of input.

input outputPure Function

No Side Effect

input output

States

With Assignment

Impure Function

No Side Effect

input output

States

With Assignment

Impure Function

Can replace f(x) + f(x) with 2*f(x)?

Referential Transparent

If the function f is referential transparent.

What is this?

If Function result depends only on the values of its parameters.

Definition:

What is this?

If Function result depends only on the values of its parameters.

Definition:

This concept occurs in mathematics, but it is broken by imperative programming languages.

Murmur:

Side Effect

Consider the following C/Java function f:

Side Effect

Consider the following C/Java function f:

f change the state outside the function.

Principle Of Least Surprise

All possible inputs are listed in the parameter list, noworries about global state.Single assignment means that you never have to find where a variable updated, cause it is only defined one place in the entire function.Small function, easy to testing.(suit with TDD)

No Update On Variables

Variables are similar to Variables in mathematics, they hold a value but they can’t be updated.

Definition:

Variables only assigned once.

Definition:

So...We don’t need to care call by value, call by reference...etc.

Definition:

So...We don’t need to care call by value, call by reference...etc.

Recursion Basics

How to Loop?Functional programs are usually H .

(with map, fold, filter)

Recursion Basics

(with map, fold, filter)eavily Recursive

Recursion Basics

(with map, fold, filter)eavily Recursive

Iteration.isEqualTo( Recursive); Pure

Efficiency

It is true...Early:

Tail Recursion.Lazy Evaluation.MemoizationCommon Subexpression EliminationParallel Computing

Efficiency

It is true...Early:

Efficiency

It is true...Early:

Now:!=

Efficiency

It is true...Early:

Efficiency

It is true...Early:

Chat in Pugs Project

From freenode, #perl6, 2005/3/2 http://xrl.us/e98m

19:08 < malaire> Does pugs yet have system() or backticks or qx// or any way to use system commands?19:08 < autrijus> malaire: no, but I can do one for you now. a sec19:09 < malaire> ok, I'm still reading YAHT, so I won't try to patch pugs just yet...19:09 < autrijus> you want unary system or list system?19:09 < autrijus> system("ls -l") vs system("ls", "-l")19:10 < malaire> perhaps list, but either is ok19:11 < autrijus> \\n Bool pre system (Str)\19:11 < autrijus> \\n Bool pre system (Str: List)\19:11 < autrijus> I'll do both :)19:11 < autrijus> done. testing.19:14 < autrijus> test passed. r386. enjoy19:14 < malaire> that's quite fast development :)19:14 < autrijus> :)

Lazy Evaluation

lazy evaluation is the technique of delaying a computation until the result is required.Benefits:S1 = EXPR 1();S2 = EXPR 2();S2 = Concatenate(S1, S2);

Lazy Evaluation

In Haskell, we don’t run S1 and S2 before we call Concatenate, we even don’t know which one evaluate first!

Lazy Evaluation

In Haskell, we don’t run S1 and S2 before we call Concatenate, we even don’t know which one evaluate first!

Benefits:

Pattern Matching

A Good Picture Can Tell Every Thing!

Tail Recursion

fac 55 * (fac 4) 5 * 4 * (fac 3)5 * 4 * 3 * (fac 2) 5 * 4 * 3 * 2 * (fac 1) 5 * 4 * 3 * 2 * 1 * (fac 0) 5 * 4 * 3 * 2 * 1 * 1..120

Tail Recursion

fac 5tailfac 5 1tailfac 4 5 * 1tailfac 3 4 * 5 * 1tailfac 2 3 * 4 * 5 * 1tailfac 1 2 * 3 * 4 * 5 * 1tailfac 0 1 * 2 * 3 * 4 * 5 * 1..120

Tail Recursion

5 14 53 202 601 1200 120

Tail Recursion

5 14 53 202 601 1200 120

Tail Recursion can be optimize to loop!!

Memoization

Definition:Memoization is an optimization technique used primarily to speed up computer programs by having function calls avoid repeating the calculation of results for previously-processed inputs.

Memoization

Definition:Memoization is an optimization technique used primarily to speed up computer programs by having function calls avoid repeating the calculation of results for previously-processed inputs.

Closure

New or Malloc.

Closure

But Global is

Closure

static and dynamic.Another issue: scope

Closure

I AmSymbol Table

GlobalI Am

Symbol Table

Closure

I AmSymbol Table

GlobalI Am

Symbol Table

Closure

I AmSymbol Table

Global

Closure

Loop Helper

Not only Recursion, but also Loop Helper?

Recursion : divided and conquer

Loop : don’t do that so complicate

Folding

Alias : reduce

Folding

Alias : reduce

OperatorInitial valueList

Folding

Alias : reduce

Folding

Alias : reduce

Folding

Alias : reduce

Mapping

Function f()a, b, c, ..., z f(a), f(b), f(c), ..., f(z)

Mapping

Filtering

Definition:

Function f()a, b, c, ..., z a’, b’, c’, ..., z’

if (p?) w, then send w to output

Filtering

Definition:

Function f()a, b, c, ..., z a’, b’, c’, ..., z’

if (p?) w, then send w to output

Quick Sort

Insert Sort

Paul GrahamDevelop Y! Store by Lisp.唐鳳Develop Perl6 by Haskell.蔡學鏞“學會 Lisp 會讓你生產力大增” by Beyond JavaMIT CS6.001 Structure and Interpretation of Computer Programs

Reference

• Blog– 以 C 語言實做 Functional Language 的 Currying– JavaScript Memoization– Functional Programming For The Rest of Us– Functional Programming in JavaScript and Ruby

• Book– Practical Common Lisp– Haskell: The Craft of Functional Programming– The Haskell School of Expression: Learning Functional

Programming through Multimedia• Web

– Wikipedia– Understanding Haskell Monads

Reference

• Web– DJWS的網路日誌– Why Functional Programming Matters• Slide– Introduction To Functional Programming– Functional Programming With Python (EuroPython 2008)– Functional Programming In Java– Understanding Functional Programming– Functional Programming– Functional Concepts for OOP Developers– Special thanks the slides form NCCU CS Chen Kung professor

Question ?

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