Functions and functional programming

Reading

Programming paradigms

  • Conceptual frameworks for software engineering
  • Ways of understanding how a piece of software works
  • Ways of writing a piece of software
Procedural or imperative
Software is a series of instructions (“procedures”), which the computer carries out in order. Special instructions (if-then, loops) are used to change the order based on inputs or other conditions.
- Examples: FORTRAN, BASIC, C, a calculator
Object-oriented
Software is made up of objects, which have properties (“attributes,” including other objects) and do things (“methods”).
- Examples: Python, Java
Functional
Software is made up of functions, which are run sequentially on the inputs.
- Examples: Lisp, Haskell

R is both object-oriented and functional

  • But the object-oriented side is … idiosyncratic (Chambers 2014)

Functional programming

“Software is made up of functions, which are run sequentially on the inputs.”

flowchart LR
  pre1[" "] -- data --> extract[extract\nDV & IV]
  pre2[" "] -- specification --> extract
  extract -- X --> QR[QR\ndecomposition] -- "Q, R" --> combine
  extract -- Y --> combine
  combine -- "Rβ = Q<sup>T</sup>Y" --> backsolve
  backsolve -- β --> post[" "]
  style pre1 height:0px;
  style pre2 height:0px;
  style post height:0px;

A regression model as a series of functions

Writing functions in R

## Standard syntax
normalize <- function(x) {
    z = (x - mean(x)) / sd(x)
    return(z)
}

## Lambda syntax (R >= 4.1.0)
normalize <- \(x){(x - mean(x)) / sd(x)}


normalize(mtcars$mpg)
 [1]  0.15088482  0.15088482  0.44954345  0.21725341 -0.23073453 -0.33028740
 [7] -0.96078893  0.71501778  0.44954345 -0.14777380 -0.38006384 -0.61235388
[13] -0.46302456 -0.81145962 -1.60788262 -1.60788262 -0.89442035  2.04238943
[19]  1.71054652  2.29127162  0.23384555 -0.76168319 -0.81145962 -1.12671039
[25] -0.14777380  1.19619000  0.98049211  1.71054652 -0.71190675 -0.06481307
[31] -0.84464392  0.21725341

Some terminology

arguments
The inputs to the function, the things inside the parentheses
calling a function
normalize is the function itself, as an object. normalize(mtcars$mpg) calls or applies the function to the argument mtcars$mpg
passing
The relationship between arguments in the call and the function’s internal variables. In normalize(mtcars$mpg), mtcars$mpg is passed to x.
return
The output of the function. Either (a) the argument passed to return or (b) the value of the last line of the function.

Features of functional programming

first-class functions
Functions can be used like any other data type, including as inputs to and outputs from other functions (functionals; function factories)
determinism
Given the same input values, the function always returns the same output value
no side effects
The function doesn’t have any effects other than returning its output
immutability
Once a variable is assigned a value, that value cannot be changed


  • Functional programming implements software as strict input-output flow
  • R doesn’t enforce determinism, no side effects, or immutability
  • But writing your own code around them makes it easier to reason about how your code works

References