20091128 func prog

A Glance at FuncProgramming

Hu Zi Ming

[email protected]

Nov 28, 2009

1 / 20A Glance at FuncProgramming

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mailto://[email protected]

Outline

1 What is FPSome StoriesFeaturesCompare with imperative Programming

2 Why Functional Programming

3 Demos and Applications


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Two models of computation

Ideal from Leibniz

Create a universal language in which all possible problems can bestatedFind a decision method to solve all the problems stated in theuniversal language

How to solve a computable problem

Turing machine by Alan TuringLambda calculus by Alonzo Church


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Feature of Functional Programming

Lazy evaluation

No assignment, no side effect

Closures and high-order functions


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Lazy Evaluation

Delaying computation until the result is required

Avoiding unnecessary calculations

Be able to construct infinite data structures

Minimal computation


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Snippets of Lazy

Lazy in c/c++/java/. . .

if a then b else c

Lazy in python

def lazy_fib(foo_list = [1, 1]):

while True:

yield foo_list

foo_list.append(foo_list [-2] + foo_list [-1])

Lazy in haskell

fibs = 0 : 1 : zipWith (+) fibs (tail fibs)


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No Assignment, No Side Effects

No destructive update (x = x + 1)

Referential Transparent: output ONLY depends on input

State change: assign only ONCE make no state change

Good for debuging/referactoring/parallel. . .


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List of Side Effects in Functions

Variable assignment (static, global, . . . )

Change arguments passed in

Raise exceptions

Write data to display or file

Call other side-effecting functions (malloc, fwrite, . . . )


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Closures and Higher-order Functions

First-order functions and bounded variables make closure

Can be used for lambda function

Can be used to construct higher-order functions

Good for modularization


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Snippets for Closures and High-orderFunctions

filter/map/reduce in python

filter(lambda x: x % 2 == 0, range (30)) # even numbers

map(lambda x: x ** 2, range (30)) # power

reduce(lambda x, y: x * y, range (30)) # factorial


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Compare with Imperative Programming

Function is a first-class type in FP

Solving problems: IP concern on how while FP on what

Most functions in FP are state-less

The position of invoking may effect the result of functions in IP

IP use loop/condition for flow control while recursion in FP

IP is instruction-oriented while FP is function/data-oriented


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Outline

1 What is FP


3 Demos and Applications


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Why Functional Programming

No unit test

Easier for glueing

Faster for some building blocks

Easier for some algorithm


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Outline

1 What is FP


3 Demos and ApplicationsSome DemosApplications in Real World


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Some Demons

Quick sort

Sum of prime list

Point 24


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Quick Sort

Quick Sort

qsort [] = []

qsort (x:xs) = (qsort (filter (<x) xs)) ++ [x] ++ (qsort (filter (>=x) xs))


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Sum of Prime List

Sieve of Eratosthenes

sieve (x:xs) = x : sieve [n | n<-xs, n ‘\mod ‘ x /=0]

prime_list_sieve n = sieve [2..n]

main = sum (prime_list_sieve 2000)

Another Method

is_prime x = x > 1 && (all (\n -> x ‘mod ‘ n /= 0 )

$ takeWhile (\n -> n*n <= x) [2..])

prime_list_is n = filter is_prime [2..n]

main = sum (prime_list_is 2000)


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Point 24

24 Points

ops1 = [(+), (-), (*), (/)]

ops2 = [(-), (/)]

listall [a, b] = [op a b | op <- ops1] ++ [op b a | op <- ops2]

listall (x:xs) = [op x y | op <- ops1 , y <- nub (listall xs)]

++ [op x y | op <- ops2 , y <- nub (listall xs)]

p24 x = elem 24 (listall x)

main = p24 [1,2,3,4]


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Applications in Real World

elisp in emacs

mathmatics

Erlang in web server

list in AI related area

ML in compiler related area


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Q AND A


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20091128 func prog

Technology

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