Pure/Total Functions

In this blog, I am going to explain about pure/total function.

Let's discuss what is a function?

A function is a process which takes some input, called arguments, and produces some output called a return value

A pure function is a function which:
1. Given the same input, will always return the same output, called Determinism.
2. Produces no side effects.

It described how inputs relate to outputs, without spelling out the steps to get from A to B. Every function call must produce results in isolation. Pure functions are required to construct pure expressions.

The function result value cannot depend on any hidden information or state that may change while program execution proceeds or between different executions of the program, nor can it depend on any external input from I/O devices.

They are easy to parallelize. The pure functions are referentially transparent, we only need to compute their output once for given inputs. Caching and reusing the result of a computation is called memoization, and can only be done safely with pure functions.

Pure functions are also extremely independent — easy to move around, refactor, and reorganize in your code, making your programs more flexible and adaptable to future changes.

In general,

Pure function = Output depends on input + No side effects

> f:X->Y, The f is a function which takes X as input and returns Y as output.  
> There is an expression like (f(3),f(3)), here we are calling function f two times for the same input.  
> so f is a pure function, you can modify an expression.I have lifted out common expression f(3) into a variable because I know every time f(3) will give me the same result.  
> cont x = f(3)  
> result = (x,x)

For example, Pure functions

• sin(x), returning the sine of a number x
• length(s), returning the size of a string s

Pure functions in Scala,

scala>def square(a: Int) = a * a
square: (a: Int)Int

scala> def pureFunc(x : Int, y : Int) = x + y
pureFunc: (x: Int, y: Int)Int

scala> pureFunc(1,2)
res0: Int = 3
scala> (pureFunc(1,2), pureFunc(1,2))
res1:(Int,Int) =(3,3)
scala> val fr = pureFunc(1,2)
scala>(fr,fr) //fr would not evaluate again and 
res2:(Int,Int) =(3,3)

scala> def impureFunc(x: Int,y: Int) = println(x+y)
impureFunc: (x: Int, y: Int)Unit

scala> impureFunc(1,2)
3

scala> def anotherImpureFunc(x: Int) = if(x > 0) x
anotherImpureFunc: (x: Int)AnyVal

scala> anotherImpureFunc(2)
res2: AnyVal = 2

scala> anotherImpureFunc(-1)
res3: AnyVal = ()