If you haven't read the original challenge, go ahead and give it a look, think about how you would solve it, then come back. This post will give spoilers and (one of many) answers.

To recap though, we want to make a classic FizzBuzz *without* using `if`

(or ternaries or anything like that).

Let's give this a first run using that fantastic buzz-word, **Functional Programming**. But first...

# What is Functional Programming?

There's the highlights that most everyone talks about:

- Pure Functions (aka no side-effects, only input and output)
- Function composition
- Higher order functions (functions that take functions as parameters)
- Avoid shared state

But most of those things can be done (or mimicked) in a "non-functional" programming style (and are just downright good ideas IMHO).

So what *really* is the heart of functional?

You may or may not know that functional programming is rooted in the Lambda Calculus. Which is a model where *functions* are the basic building block of computation.

That's it. In functional programming, all we mean is that functions are what *do* the program. The looping, the conditionals, the control flow, the data: all functions.

# How to use it to control logic

It's nice to *say* that functions are all that the program needs. But what does that *mean*. In a practical way; how do we write code that does that?

It all starts with defining the elements we need using the language of `input => output`

. And for changes in behavior we lean on changes in implementation instead of built-in statements like `if`

.

So what are the behaviors of if?

- When
`true`

, evaluate the`then`

code - When
`false`

, evaluate the`else`

code

Two behaviors, so let's make two functions:

```
const functionalTrue = (onTrue, onFalse) => onTrue;
const functionalFalse = (onTrue, onFalse) => onFalse;
```

A little simple, but promising. In our functional solution the booleans *are* the conditionals. To prove that out, let's see what some boolean operations look like; starting with `and`

:

```
const and = (lhs, rhs) => (onTrue, onFalse) => lhs(rhs(onTrue, onFalse), onFalse);
// lhs and rhs for left-hand side and right-hand side
```

Let's work through this right to left:

- If the left-hand side (lhs) is
`false`

, then there isn't a point checking the right-hand side (rhs); just return the`onFalse`

. - If the left-hand side (lhs) is
`true`

, then also check the right-hand side (rhs); simply passing the parameters unchanged.

In a non-functional approach, this is basically what we've done:

```
function and(lhs, rhs) {
if (lhs) {
if (rhs) {
return true;
} else {
return false;
}
} else {
return false;
}
}
```

And we can do a similar thing for `or`

:

```
const or = (lhs, rhs) => (onTrue, onFalse) => lhs(onTrue, rhs(onTrue, onFalse));
```

In fact for any truth table, just directly transcribe it into `lhs(rhs(firstCase, secondCase), rhs(thirdCase, fourthCase))`

(and remove any `rhs`

calls where the two parameters are the same). So for `xor`

(exclusive or), the truth table looks something like this:

lhs | rhs | => | xor |

true | true | => | false |

true | false | => | true |

false | true | => | true |

false | false | => | false |

and the function looks like this:

```
const xor = (lhs, rhs) => (onTrue, onFalse) => lhs(rhs(onFalse, onTrue), rhs(onTrue, onFalse));
```

# Getting our functional boolean out of a comparison

So we *have* booleans; but how do we *get* them from a divisibility check like `42 % 3 == 0`

?

There's multiple tricks to potentially doing this (in fact I think some of the submitted solutions used better ones than I did), but the one I will use is to make an array long enough so it will always be longer than the range produced by a modulo, with the first element being my functional `true`

and the rest filled with `false`

, then simply selecting the element from that array that the modulo result gives.

```
const isDivisible = (dividend, divisor) => [functionalTrue, ...Array(divisor).fill(functionalFalse)][dividend % divisor];
```

So if the `dividend`

is a multiple of `divisor`

(`dividend % divisor == 0`

) then I will select the first element, which is `true`

(otherwise I'll select a `false`

element). Just what I need to check if something is a multiple of 3 or 5!

# Making the Fizz Buzz and the Buzz Fizz

We have all the basic building blocks we need now. First, let's check if it's divisible by three:

```
const divisible_by_three = isDivisible(n, 3);
```

Easy. Next check if it is divisible by five:

```
const divisible_by_five = isDivisible(n, 5);
```

And lastly, let's extend that little truth table trick into our final output:

divisible_by_three | divisible_by_five | => | fizz_buzz |

true | true | => | FizzBuzz |

true | false | => | Fizz |

false | true | => | Buzz |

false | false | => | n |

which can be directly transcribed into our function:

```
divisible_by_three(divisible_by_five("FizzBuzz", "Fizz"), divisible_by_five("Buzz", n));
```

Putting it all together we have our final FizzBuzz solution without using a single conditional!

```
const functionalTrue = (onTrue, onFalse) => onTrue;
const functionalFalse = (onTrue, onFalse) => onFalse;
const isDivisible = (dividend, divisor) => [functionalTrue, ...Array(divisor).fill(functionalFalse)][dividend % divisor];
const functionalFizzBuzz = (n) => {
const divisible_by_three = isDivisible(n, 3);
const divisible_by_five = isDivisible(n, 5);
return divisible_by_three(divisible_by_five("FizzBuzz", "Fizz"), divisible_by_five("Buzz", n));
};
```

Follow me for the next post in this mini-series: the Object-oriented approach! I'm also planning a final article comparing FP and OOP using these two solutions.