f# Ex 5

// Exercise 5.1
// Write an F# function countNumOfVowels to count the number of vowels in a given string. The type is:


open System

let  countNumOfVowels (s:string)=

    let isVowel (c:char) =
        if (c = 'a' || c = 'A') then true
        else if (c = 'e' || c = 'E') then true
        else if (c = 'i' || c = 'I') then true
        else if (c = 'o' || c = 'O') then true
        else if (c = 'u' || c = 'U') then true
        else false

    let mutable count = 0
    for x in s do
        if (isVowel(x)) then count <- count + 1
    count

printfn "%i" (countNumOfVowels("Higher-order functions can take and return functions of any order"))

Console.ReadKey() |> ignore



// Exercise 5.2
// Define a function primesUpTo n to create a list of prime numbers up to a given
// number. For instance: primesUpTo 10 results in [2; 3; 5; 7]


open System

let  primesUpTo (n:int)=

    let isPrime (k:int) =
        let mutable prime = true
        for i in [2..k-1] do
            if k % i = 0 then prime <- false
        prime

    let list = [for i in [2..n] do if isPrime(i) = true then yield i]
    list

printfn "%A" (primesUpTo(10))

Console.ReadKey() |> ignore



// Exercise 5.3
// Define an F# function pclFib n that, when given a number, returns the nth Fibonacci number.

open System

let rec fib (n:int) =
    if n = 1  then 0
    else if n = 2 || n = 3 then 1
    else fib (n - 1) + fib (n - 2)


printfn "%i" (fib(10))

Console.ReadKey() |> ignore



// Exercise 5.4
// a. Define two F# functions doubleNum x that multiplies x by 2 and sqrNum x that multiplies x by itself.

open System

let doubleNum (x) = x * 2
let sqrNum (x) = x*x

printfn "Result for double num for %i is %i" 10 (doubleNum(10))
printfn "Result for sqrare num for %i is %i" 10 (sqrNum(10))

Console.ReadKey() |> ignore



// b. Define another F# function pclQuad x that applies the doubleNum function defined above twice.

open System

let doubleNum (x) = x * 2
let pclQuad (x) = (doubleNum(doubleNum(x)))

printfn "Result for pclQuad for %i is %i" 10 (pclQuad(10))

Console.ReadKey() |> ignore

// c. Define another F# function pclFourth x that applies the sqrNum function defined (in a.) above twice.

open System

let sqrNum (x) = x*x
let pclFourth (x) = (sqrNum(sqrNum(x)))

printfn "Result for pclFourth for %i is %i" 10 (pclFourth(10))

Console.ReadKey() |> ignore