# Yet Another Haskell Tutorial/Language basics/Solutions

## Arithmetic edit

It binds more tightly; actually, function application binds more tightly than anything else. To see this, we can do something like:

**Example:**

Prelude> sqrt 3 * 3 5.19615

If multiplication bound more tightly, the result would have been 3.

## Pairs, Triples and More edit

Solution: `snd (fst ((1,'a'),"foo"))`

. This is because first we
want to take the first half the tuple: `(1,'a')`

and then out
of this we want to take the second half, yielding just `'a'`

.

If you tried `fst (snd ((1,'a'),"foo"))`

you will have gotten a
type error. This is because the application of `snd`

will leave
you with `fst "foo"`

. However, the string "foo" isn't a tuple,
so you cannot apply `fst`

to it.

## Lists edit

### Strings edit

### Simple List Functions edit

Solution: `map Data.Char.isLower "aBCde"`

Solution: `length (filter Data.Char.isLower "aBCde")`

Solution: `foldr max 0 [5,10,2,8,1]`

.

You could also use `foldl`

. The foldr case is easier to explain: we replace each
cons with an application of `max`

and the empty list with 0.
Thus, the inner-most application will take the maximum of 0 and the
last element of the list (if it exists). Then, the next-most inner
application will return the maximum of whatever was the maximum
before and the second-to-last element. This will continue on,
carrying to current maximum all the way back to the beginning of the
list.

In the foldl case, we can think of this as looking at each element in the list in order. We start off our "state" with 0. We pull off the first element and check to see if it's bigger than our current state. If it is, we replace our current state with that number and the continue. This happens for each element and thus eventually returns the maximal element.

Solution: `fst (head (tail [(5,'b'),(1,'c'),(6,'a')]))`

## Source Code Files edit

## Functions edit

### Let Bindings edit

### Infix edit

## Comments edit

## Recursion edit

We can define a fibonacci function as:

fib 1 = 1 fib 2 = 1 fib n = fib (n-1) + fib (n-2)

We could also write it using explicit ` if` statements, like:

fib n = if n == 1 || n == 2 then 1 else fib (n-1) + fib (n-2)

Either is acceptable, but the first is perhaps more natural in Haskell.

We can define:

And then type out code:

mult a 0 = 0 mult a 1 = a mult a b = if b < 0 then 0 - mult a (-b) else a + mult a (b-1)

Note that it doesn't matter that of and we do the recursion on. We could just as well have defined it as:

mult 0 b = 0 mult 1 b = b mult a b = if a < 0 then 0 - mult (-a) b else b + mult (a-1) b

We can define `my_map`

as:

my_map f [] = [] my_map f (x:xs) = f x : my_map f xs

Recall that the `my_map`

function is supposed to apply a function
`f`

to every element in the list. In the case that the list is
empty, there are no elements to apply the function to, so we just
return the empty list.

In the case that the list is non-empty, it is an element `x`

followed by a list `xs`

. Assuming we've already properly applied
`my_map`

to `xs`

, then all we're left to do is apply `f`

to
`x`

and then stick the results together. This is exactly what the
second line does.

## Interactivity edit

The code below appears in `Numbers.hs`

. The only tricky parts are
the recursive calls in `getNums`

and `showFactorials`

.

module Main where import System.IO main = do nums <- getNums putStrLn ("The sum is " ++ show (sum nums)) putStrLn ("The product is " ++ show (product nums)) showFactorials nums getNums = do putStrLn "Give me a number (or 0 to stop):" num <- getLine if read num == 0 then return [] else do rest <- getNums return ((read num :: Int):rest) showFactorials [] = return () showFactorials (x:xs) = do putStrLn (show x ++ " factorial is " ++ show (factorial x)) showFactorials xs factorial 1 = 1 factorial n = n * factorial (n-1)

The idea for `getNums`

is just as spelled out in the hint. For
`showFactorials`

, we consider first the recursive call. Suppose we
have a list of numbers, the first of which is `x`

. First we print
out the string showing the factorial. Then we print out the rest,
hence the recursive call. But what should we do in the case of the
empty list? Clearly we are done, so we don't need to do anything at
all, so we simply `return ()`

.

Note that this must be `return ()`

instead of just `()`

because
if we simply wrote `showFactorials [] = ()`

then this wouldn't be
an IO action, as it needs to be. For more clarification on this, you
should probably just keep reading the tutorial.