Intro to Functional Programming Workshop (code4lib)

var λ; Introduction to Functional Programming with JavaScript (and a little Haskell) Will Kurt Will Kurt, Creative Commons Attribution-ShareAlike 3.0

"A language that doesn't effect how you think about programming is not worth learning" --Alan Perlis

So what is Functional Programming? http://www.flickr.com/photos/foundphotoslj/466713478/

What does this mean? http://www.flickr.com/photos/61417318@N00/4908148942/

No Side Effects! http://www.flickr.com/photos/rka/1733453/

http://www.flickr.com/photos/23912576@N05/3056871500/

Haskell! http://www.flickr.com/photos/micurs/4870514382/

JavaScript!!! http://www.flickr.com/photos/jurvetson/96972777/

Lists!!! first( [1,2,3,4]) -> 1 (aka: car, head) rest( [1,2,3,4] ) -> [2,3,4] (aka: cdr, tail) empty( [1,2,3,4] ) -> false (aka: null?, nil? empty?,[]) empty( [ ] ) -> true build( 1 , [2,3,4]) -> [1,2,3,4] (aka: cons, ':' ) build( [1] , [2,3,4]) -> [[1],2,3,4]

Recursion! "If you already know what recursion is, just remember the answer. Otherwise, find someone who is standing closer to Douglas Hofstadter than you are; then ask him or her what recursion is." -- Andrew Plotkin

problem 1 var fact = function(x) { return( (x===1) ? 1 : x*fact(x-1) ); } function fact (x) { if(x==1){ return 1; } else { return x*fact2(x-1); } }

problem 2 var fib = function(x){ return( (x==0) ? 0 : (x==1) ? 1 : fib(x-1)+fib(x-2) ); }

problem 2 continued... var fib_answers = [] fib_answers[0] = 0; fib_answers[1] = 1; var fibm = function (x) { return fib_mem(x,fib_answer); } var fib_mem = function(x,m){ if(m[x] != undefined){ return m[x]; } else { m[x] = fib_mem(x-1,m)+fib_mem(x-2,m); return m[x]; } }

problem 2 last one I swear (also very functional)... var fib3wrapper = function(c){ return fib3(c,1,0); } var fib3 = function(c,last1,last2){ return( (c==2) ? last1+last2: fib3(c-1,last1+last2,last1) ); }

problem 1 var length = function (xs) { return( empty (xs) ? 0 : 1 + length( rest (xs)) ); };

problem 2 var nth = function(n,xs){ return( empty(xs) ? [] : (n == 0) ? first(xs) : nth(n-1, rest(xs)) ); };

problem 3 var removeAll = function (x, xs) { return( empty(xs) ? [ ] : (x == first(xs)) ? removeAll(x, rest(xs)) : build( first(xs), removeAll(x,rest(xs))) ); };

First class functions http://www.flickr.com/photos/richardmoross/2211308689/

First Class Functions (Haskell) add2 x = 2 + x add3 x = 3 + x > add2 5 7 > add3 5 8

First Class Functions (Haskell) argIs2 func = (func) 2 argIs3 func = (func) 3 > argIs2(add2) 4 > argIs2(add3) 5 > argIs3(add2) 5 > argIs3(add3) 6

Lambda Functions http://www.flickr.com/photos/jeremymates/2362399109/

Lambda Function (Haskell) add4 = (\x -> 4+x) >argIs2( (\x -> 4+x) ) 6

Lambda Function (JavaScript) $.ajax({ url: "test.html", context: document.body, success: function(){ $(this).addClass("done"); } }); $("#exec").click( function(){ $("#results").prepend("<li>Normal Handler</li>"); } );

problem 1 var argIs2 = function(func) { return func(2); }

problem 2 argIs2(function(x){ add(2,x);} );

problem 3 var flip = function (func) { return( function(x,y){ func(y,x); } ); };

Closures http://www.flickr.com/photos/theredproject/3431459572/

Closures (Haskell) add5 = (+5) makeAdder val = (+val) makeAdderWithLambda val = (\x->x+val) add6 = makeAdder 6 add7 = makeAdderWithLambda 7 > add5 5 10 > add6 5 11 > add7 5 12

problem 1 var makeAdder = function (x) { return( function(y) { return add(x,y); } ); };

problem 2 var apiClosure = function(apiKey){ return( function(x){ return apiSearch(apiKey,x); } ); };

problem 3 var compose = function (f1,f2) { return( function(x){ f1(f2(x)); } ); };

Higher Order Functions http://www.flickr.com/photos/73416633@N00/2425022159/

Map http://www.flickr.com/photos/rosenkranz/3052214847/

Map (Haskell) doubleAll xs = map (*2) xs squareAll xs = map (^2) xs squareAndAdd xs = map (\x->x*x+x) xs upperCase s = map toUpper s > doubleAll [1,2,3,4] [2,4,6,8] > squareAll [1,2,3,4] [1,4,9,16] > squareAndAdd [1,2,3,4] [2,6,12,20] > upperCase "doggie" "DOGGIE"

Map (Haskell) doubleAllv2 = map (*2) squareAllv2 = map (^2) squareAndAddv2 = map (\x->x*x+x)

problem 1 var map = function (func, xs) { return( empty(xs) ? [ ] : build( func (first(xs)), map (func, rest (xs)))); ); };

problem 2 map(function(x){ return x*x}, xs);

Filter (Haskell) evenList xs = filter even xs mod17list xs = filter (== (`mod` 17) 0) xs doubleEvens xs = (doubleAll . evenList) xs > evenList [1,2,3,4,5,6] [2,4,6] > mod17list [1..100] [17,34,51,68,85] > doubleEvens [0,3..27] [0,12,24,36,48]

problem 1 var filter = function (test,xs){ return( empty(xs) ? [ ] : test(first(xs)) ? filter(test, rest(xs)) : build(first(xs),filter(test,rest(xs))) ); };

problem 2 var removeAll = function(x,xs){ return( filter( function(y){ return y == x}, xs ) ); };

Foldl (Reduce) http://en.wikipedia.org/wiki/File:Sermon_in_the_Deer_Park_depicted_at_Wat_Chedi_Liem-KayEss-1.jpeg

Foldl (Haskell) mySum xs = foldl (+) 0 xs sumOfSquares xs = foldl (+) 0 (map (^2) xs) sumOfSquaresv2 = (mySum . squareAll) > mySum [1..2000000] 2000001000000 > sumOfSquares [1..10] 385 > sumOfSquaresv2 [1..10] 385

Foldl (Haskell) myReverse xs = foldl (\x y -> y:x) [] xs myReverse [1,2,3] foldl (\x y -> y:x) [] [1,2,3] .. (\[] 1 -> 1:[]) .. => [1] foldl (\x y -> y:x) [1] [2,3] .. (\[1] 2 -> 2:[1]) .. => [2,1]

problem 1 var foldl = function (step, init, xs) { return( empty(xs) ? init : foldl( step , step(init,first(xs)), rest(xs) ); };

problem 2 var sum = function(xs) { return foldl(add,0,xs); };

Map (JavaScript) 'The Spolsky Map' function spolsky_map(fn, a) { for (i = 0; i < a.length; i++) { a[i] = fn(a[i]) ; } } note the side effects

The Spolsky Reduce (foldl) function spolsky_reduce(fn, a, init) { var s = init; for (i = 0; i < a.length; i++) s = fn( s, a[i] ); return s; }

problem 1 var last = compose(first,reverse);

problem 2 var reverse = function (xs) { return foldl(flip(build),[ ],xs); };

Standard Deviation 1. calculate the arithmetic mean of the list 2. subtract the mean from all the numbers in the list 3. square the number in that list 4. calculate the sum of the list 5. divide the sum by length of list by 1 6. get the square root of this number

Standard Deviation 1. calculate the arithmetic mean of the list mean xs = sum xs / fromIntegral(length xs) 2. subtract the mean from all the numbers in the list deviations xs = map (\x -> x - m ) xs where m = mean xs 3. square the numbers in that list squareDeviations xs = map(^2) devs where devs = deviations xs 4. calculate the sum of the list sumSquareDeviations xs = (sum . squareDeviations) xs 5. divide the sum by length of list minus 1 6. get the square root of this number sd xs = sqrt $ sumSqDev / lsub1 where sumSqDev = sumSquareDeviations xs lsub1 = fromIntegral $ ((-1+) . length)xs

Standard Deviation (JavaScript) var mean = function (xs){ return(sum(xs)/flength(xs)); }; var deviations = function (xs) { var m = mean(xs);//we can remove this return map(function(x){return x-m;},xs); }; var squareDeviations = function(xs){ return map(square,deviations(xs)); };

Standard Deviation (JavaScript) var sumSqDeviations = compose(sum,squareDeviations); var sd = function(xs){ return Math.sqrt( (sumSqDeviations(xs)/(length(xs)-1))); };

Standard Deviation Haskell > sd [1,4,5,9,2,10] 3.65604522218567 JavaScript > sd([1,4,5,9,2,10]); 3.65604522218567

Currying (Haskell) myAdd x y = x + y add8 = myAdd 8 add9 = (+9) > myAdd 8 9 17 > add8 9 17 > add9 8 17

Currying (JavaScript) var curry = function (f,a) { return( function(){ var args = Array.prototype.slice.call(arguments); args.unshift(a); return f.apply(this, args); } ); };

Currying (JavaScript) purely functional var curry = function (f,a) { return( function(){ return( ( function( args ){ return f.apply(this, build(a,args)); } ) (Array.prototype.slice.call(arguments)) ); } ); };

Currying (JavaScript) var add_three = function(a,b,c){ return a+b+c; }; >f1 = curry(add_three,1); >f1(2,3) 6 >f2 = curry(curry(add_three,1),2); >f2(3) 6

problem 1 var makeAdder = curry(add,x); var apiClosure = curry(apiSearch,apiKey);

problem 2 var unrealisticFunction = function (a, b){ (function(c){ return((function(d){ if(c<d){ return c+d; }else{ return c*d; } };)(c+a) ); })(a*b) };

Thanks! email: wckurt@gmail.com twitter: willkurt

Types!!! areaOfTrapezoid :: Float -> Float -> Float -> Float areaOfTrapezoid h b1 b2 = 0.5*h*(b1+b2) evenList :: (Integral a) => [a] -> [a] evenList xs = filter even xs

Lazy Evaluation!!! [2,4..] !! 108 > 218

Pattern Matching patternMatch [a,b,c] = b ++ c ++ a patternMatch [a,b] = a ++ b patternMatch [] = "no list" patternMatch as = "a larger list"

Pattern Matching patternMatch ["a","b","c"] >"bca" patternMatch ["a","b"] >"ab" patternMatch [ ] >"no list" patternMatch ["a","b","c","d"] >"a larger list"

Who actually uses this stuff? http://cufp.org/

more @ http://www.scala-lang.org/node/1658

... continued more @ http://haskell.org/haskellwiki/Haskell_in_industry

Intro to Functional Programming Workshop (code4lib)

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