Higher Order Functions

• Definition

  • when a function accepts another function as its argument, or it yields another function as its return value

  • or both

• Examples

  • map, filter

Function composition

• To compose two functions means to arrange them so that the result of one function is applied directly as the input of the other function.

• it is useful to consider two composed functions as a third function in its own right.

• It is a form of chaining

• Say you have a function f that takes a value x as its argument and returns a value y :

  • f ( x ) = y

  • and you have another function g that takes y as its argument and returns z

  • g ( y ) = z

  • clearly, then, you can apply g to the output of f like this :

  • g ( f ( x )) = z

  • This implies, therefore, that there is a third function h that maps x directly to z :

  • h ( x ) = z

• Examples

  • unix pipes ie ls -al | grep blah

  • map(x -> ...).filter(x -> ...)

  • builder pattern