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editor : alpha [82.255.25.228] 2013/06/06 06:27:11
_h2 derivee with curryfication 
_ul [[curry-cooking-up-tastier-functions|http://javascriptweblog.wordpress.com/2010/04/05/curry-cooking-up-tastier-functions/]]
_ul [[top_ten|http://javascriptweblog.wordpress.com/2010/04/02/my-top-10-javascript-blogs/]]
_ul [[www.svendtofte.com/code/curried_javascript|http://www.svendtofte.com/code/curried_javascript/]]
_ul [[slid.es/gsklee/functional-programming-in-5-minutes|http://slid.es/gsklee/functional-programming-in-5-minutes#]]

_p Grace to curryfication, the derivee of a function for a given value can be done in two "partial" steps, first creating the function, then applying it at a given value. And so, it is possible to define next derivees {u before} applying them at a given value.

{pre 
Instead of : 
  derivee( func, x), 
we use : 
  derivee(func)(x)
or in 2 steps :
  1) f1 = derivee(func) -> function
  2) f1(x) -> value
}

_h4 first derivees of cubic function
{p Enter a value : {input {@ type="text" value="2" onblur="°°

var derivee = function (f) {
  return function (x) {
    return (f(x+0.01)-f(x-0.01))/(2*0.01)
  }
}

var f0 = function (x) { 
  return x*x*x; }       // f0 = x^3 = 1

var f1 = derivee(f0);   // f1 = 3*x^2 = 3
var f2 = derivee(f1);   // f2 = 6*x = 6
var f3 = derivee(f2);   // f3 = 6
var f4 = derivee(f3);   // f4 = 0

var x = parseFloat( this.value );

getId('console').innerHTML = 
   f0(x)+'\n'+f1(x)+'\n'+f2(x)+'\n'+f3(x)+'\n'+f4(x);

°°"}}, then click outside the field.}

{pre {@ id="console"}}

_h4 code

{pre °°

var derivee = function (f) {
  return function (x) {
    return (f(x+0.01)-f(x-0.01))/(2*0.01)
  }
}

var f0 = function (x) { 
  return x*x*x; }       // f0 = x^3 = 1

var f1 = derivee(f0);   // f1 = 3*x^2 = 3
var f2 = derivee(f1);   // f2 = 6*x = 6
var f3 = derivee(f2);   // f3 = 6
var f4 = derivee(f3);   // f4 = 0

var x = parseFloat( this.value );

getId('console').innerHTML = 
   f0(x)+'\n'+f1(x)+'\n'+f2(x)+'\n'+f3(x)+'\n'+f4(x);

°°}

_h6 The 4th derivee can be rewritten as :
{pre
var f4 = derivee(f3) 
       = derivee(derivee(f2))
       = derivee(derivee(derivee(f1)))
       = derivee(derivee(derivee(derivee(f0))))

var y  = derivee(derivee(derivee(derivee(f0))))(x)
       = (derivee (derivee (derivee (derivee (f0)))) (x))
}
_h6 a javascript code which  looks like pure LISP code (see [[diff_int|../lambdaway_2.0/?view=diff_int]] in lambdaway) 
{pre °°
  function cubic at x=1
{define cubic (:x) (* :x :x :x)} -> cubic 
{cubic 1} -> 1
{{D cubic} 1} -> 3.0000009999997523 (≠ 3)
{{D {D cubic}} 1} -> 5.999999999894978 (≠ -6)
{{D {D {D cubic}}} 1} -> 6.0000000245974405 (≠ 6)
{{D {D {D {D cubic}}}} 1} -> 0.00004163336342344337 (≠ 0)

°°}

_h3 todo
_p Transpose the javascript curryfication in lambdatalk(lite).