A presentation I did for work on functional programming. It's meant as an introduction to functional programming, and I implemented the fundamentals of functional programming (Church Numerals, Y-Combinator, etc.) in JavaScript.

1. Functional Programming Tommy “is awesome” Montgomery 2009-03-06

13. Higher order function example //f is a function function derivative ( f ) { return function ( x ) { //approximation of derivative return ( f ( x + 0.00001 ) – f ( x )) / 0.00001 ; } }

14. Higher order function example //evaluate derivative of x 2 : var deriv_x_squared = derivative ( function ( x ) { return x * x ; } ); alert ( deriv_x_squared ( 3 )); //alerts 6ish

23. Church numerals in JavaScript //identity function // λ x . x function identity ( x ) { return x ; } //Church numeral zero // λ f . λ x . x function zero ( f ) { return identity ; }

24. Church numerals in JavaScript //successor function (succ(n) = n + 1) // λ n . λ f . f (n f x) function succ ( n ) { return function ( f ) { return function ( x ) { return f ( n ( f )( x )); } } }

25. Church numerals in JavaScript //gets a function representing //the nth church number function getChurchNumber ( n ) { var ret = zero ; for ( var i = 0 ; i < n ; i ++) { ret = succ ( ret ); } return ret ; }

26. Church numerals in JavaScript //gets the nth church number function getNaturalNumber ( n ) { var value = 0 ; for ( var i = 0 ; i < n ; i ++) { value += getChurchNumber ( i )( function ( x ) { return x + 1 ; } )( 0 ); } return value ; }

33. Recursion To properly define recursion, a recursive function g must take as an argument a function f , which expands to g which takes an argument f .

44. Questions…