Functional Programming 之二三事

Functional Programming Leeheng July 31, 2009

Functional Bet Programming a Leeheng July 31, 2009

Agenda About Myself Why This Topic Programming Paradigm 10min PL Moving On Why FP Matters IP VS DP Function, Lambda Calculus High Order Function, Currying No Side Effect, Referential Transparent Least Surprise, No Update 25min Recursion, Lazy Evaluation Pattern Matching, Tail recursion Memoization, Closure Loop Helper Example Story 25min Reference Question 2

ABOUT MYSELF Leeheng Ma Y! 2009 Search Team Intern NCCU MIS undergraduate Interests : Algorithm, Programming language, Compiler, Web Technology. 3

WHY THIS TOPIC 4

WHY THIS TOPIC .... 4

WHY THIS TOPIC .... Programming Language RD 4

Programming Paradigm Programming paradigm is a Fundamental style of computer programming. 5

Programming Paradigm Programming paradigm is a Fundamental style of computer programming. For solving Software Engineering Problems. 5

Programming Paradigm Programming paradigm is a Fundamental style of computer programming. For solving Software Engineering Problems. Programming Paradigm SHIFT 5

Think Different • A language that doesn't affect the way you think about programming, is not worth knowing. --Alan Perlis 6

HOW MANY YOU KNOW ? • Concurrent • Imperative • Declarative • Functional • Procedural Programming • Prototype-based • Event-driven • Aspect-Oriented • Object-Oriented • Meta-Programming • Generic 7

HOW MANY YOU KNOW ? ... Orz ..... ... 7

WHERE PL MOVING ON ? 8

WHY FP MATTERS 9

WHY FP MATTERS • Python, Ruby, Perl all use ideas form FP • Y! ’s Hadoop and G ‘s MapReduce are large scale FP 9

WHY FP MATTERS • Python, Ruby, Perl all use ideas form FP • Y! ’s Hadoop and G ‘s MapReduce are large scale FP Modularity Interchangeable parts Easy test and debug Easy optimization Function as data • No Side Effect Pattern Matching Concurrent Processing • High Order Function Closure Lazy Evaluation Referential transparency 9

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 10

IP VS FP OO C+ P • Imperative Programming Java + – 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 10

IP VS FP OO C+ P • Imperative Programming Java + – Computation Executing statements to change state. – Program Consists of a sequence of commands. g Lisp Ha E rlan • Functional Programming ske ll – Computation Evaluation of expressions. – Expression Formed by using functions to combine basic values. The focus is on what, not how 10

Create Sandwich Imperative Functional 11

Create Sandwich Imperative 1. Take a bread 2. Spread bread with butter 3. Put cheese on the bread 4. return sandwich Functional 11

Create Sandwich Imperative 1. Take a bread 2. Spread bread with butter 3. Put cheese on the bread 4. return sandwich Functional return put ( cheese, spread(butter, bread) ) 11

Features 12

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. 12

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). 12

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). So we minimize function!! 12

Lambda Calculus The λ-calculus was developed by the logician Alonzo Church in 1930’s as a tool to study functions and computability. 13

λ Calculus Equivalent to Turing Machines Turing 1937 Equivalent to recursive functions Kleene 1936 (λ x. x + 2) 14

λ Calculus Equivalent to Turing Machines Turing 1937 Equivalent to recursive functions Kleene 1936 (λ x. x + 2) = (x) { return x + 2} 14

λ Calculus Equivalent to Turing Machines Turing 1937 Equivalent to recursive functions Kleene 1936 (λ x. x + 2) = (x) { return x + 2} (λ x. x + 2) 3 = 5 14

λ Calculus Equivalent to Turing Machines Turing 1937 Equivalent to recursive functions Kleene 1936 (λ f. f 3)(λ x. x+2) = ? 14

λ Calculus Equivalent to Turing Machines Turing 1937 Equivalent to recursive functions Kleene 1936 (λ f. f 3)(λ x. x+2) = ? = (λ x. x + 2) 3 =3+2 14

High Order Function • Functions take other functions as parameters • Functions return functions as results 15

High Order Function • Functions take other functions as parameters ∑ f(x) x∈L • Functions return functions as results 15

High Order Function • Functions take other functions as parameters ∑ f(x) x∈L • Functions return functions as results d f(x) dx = f’(x) 15

Mathematics 16

Mathematics OK, no more mathematics. 16

Design Pattern 17

Design Pattern Adapter Pattern 17

Design Pattern Adapter Pattern + 17

Design Pattern Adapter Pattern 17

Currying ( ) AJAX callback function 18

No Side Effect Output is solely dependent of input. input output Pure Function 19

No Side Effect Output is solely dependent of input. States input output Impure Function With Assignment 19

No Side Effect Output is solely dependent of input. States input output Impure Function With Assignment Can replace f(x) + f(x) with 2*f(x)? 19

Referential Transparent If the function f is referential transparent. 20

Referential Transparent If the function f is referential transparent. What is this? 20

Referential Transparent What is this? Definition: If Function result depends only on the values of its parameters. 20

Referential Transparent What is this? Definition: If Function result depends only on the values of its parameters. Murmur: This concept occurs in mathematics, but it is broken by imperative programming languages. 20

Side Effect Consider the following C/Java function f: 21

Side Effect Consider the following C/Java function f: f change the state outside the function. 21

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) 22

No Update On Variables Definition: Variables are similar to Variables in mathematics, they hold a value but they can’t be updated. Variables only assigned once. Pure 23

No Update On Variables Definition: Variables are similar to Variables in mathematics, they hold a value but they can’t be updated. Variables only assigned once. So...We don’t need to care call by value, call by reference...etc. Pure 23

Recursion Basics How to Loop? Functional programs are usually H . (with map, fold, filter) Pure 24

Recursion Basics How to Loop? Functional programs are usually Heavily Recursive. (with map, fold, filter) Pure 24

Recursion Basics How to Loop? Functional programs are usually Heavily Recursive. (with map, fold, filter) Iteration.isEqualTo( Recursive); Pure 24

Efficiency Early: It is true... Now: Tail Recursion. Lazy Evaluation. Memoization Common Subexpression Elimination Parallel Computing 25

Efficiency Early: It is true... Now: Tail Recursion. != Lazy Evaluation. Memoization Common Subexpression Elimination Parallel Computing 25

Efficiency Early: It is true... Now: Tail Recursion. Lazy Evaluation. Memoization Common Subexpression Elimination Parallel Computing 25

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 sec 19:09 < 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 ok 19:11 < 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. enjoy 19:14 < malaire> that's quite fast development :) 19:14 < autrijus> :) 26

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); Pure 27

Lazy Evaluation lazy evaluation is the technique of delaying a computation until the result is required. Benefits: In Haskell, we don’t run S1 = EXPR 1(); S1 and S2 before we call Concatenate, we S2 = EXPR 2(); even don’t know which S2 = Concatenate(S1, S2); one evaluate first! Pure 27

Lazy Evaluation lazy evaluation is the technique of delaying a computation until the result is required. Benefits: In Haskell, we don’t run S1 = EXPR 1(); S1 and S2 before we call Concatenate, we S2 = EXPR 2(); even don’t know which S2 = Concatenate(S1, S2); one evaluate first! Benefits: Pure 27

Pattern Matching A Good Picture Can Tell Every Thing! 28

Tail Recursion 29

Tail Recursion Stack fac 5 5 * (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 Time 29

Tail Recursion 29

Tail Recursion Stack fac 5 tailfac 5 1 tailfac 4 5 * 1 tailfac 3 4 * 5 * 1 tailfac 2 3 * 4 * 5 * 1 tailfac 1 2 * 3 * 4 * 5 * 1 tailfac 0 1 * 2 * 3 * 4 * 5 * 1 . . 120 Time 29

Tail Recursion Stack fac 5 tailfac 5 1 tailfac 4 5 * 1 tailfac 3 4 * 20 5 * 1 tailfac 2 3 * 60 4 * 5 * 1 tailfac 1 2 * 120 3 * 4 * 5 * 1 tailfac 0 1 * 120 2 * 3 * 4 * 5 * 1 . . 120 Time 29

Tail Recursion Stack fac 5 tailfac 5 1 tailfac 4 5 * 1 tailfac 3 4 * 20 5 * 1 tailfac 2 3 * 60 4 * 5 * 1 tailfac 1 2 * 120 3 * 4 * 5 * 1 tailfac 0 1 * 120 2 * 3 * 4 * 5 * 1 . . Tail Recursion can be Time 120 optimize to loop!! 29

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. 30

Closure In C 31

Closure In C New or Malloc. 31

Closure In C But Global is 31

Closure In C Another issue: scope static and dynamic. 31

Closure In C Another issue: scope static and dynamic. Global I Am Symbol Table 31

Closure In C Another issue: scope static and dynamic. Global Local I Am I Am Symbol Table Symbol Table 31

Closure In C Another issue: scope static and dynamic. Global I Am Symbol Table 31

Closure In C Another issue: scope static and dynamic. 31

Loop Helper Not only Recursion, but also Loop Helper? Recursion : divided and conquer Loop : don’t do that so complicate 32

Folding Alias : reduce 33

Folding Alias : reduce Operator Initial value List 33

Folding Alias : reduce 33

Mapping 34

Mapping a, b, c, ..., z f(a), f(b), f(c), ..., f(z) Function f() 34

Mapping 34

Filtering Definition: if (p?) w, then send w to output a, b, c, ..., z a’, b’, c’, ..., z’ Function f() 35

Quick Sort 36

Insert Sort 37

Story Paul Graham Develop Y! Store by Lisp. Develop Perl6 by Haskell. “ Lisp ” by Beyond Java MIT CS 6.001 Structure and Interpretation of Computer Programs 38

Reference • Blog – C Functional Language 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 39

Reference • Web – DJWS – 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 40

Question ? 41

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Functional Programming 之二三事

by Leeheng Ma on Jul 31, 2009

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